Macroeconomics of finance - Teoria ed Esercizi, Dispense di Macroeconomia

Scarica Macroeconomics of finance - Teoria ed Esercizi e più Dispense in PDF di Macroeconomia solo su Docsity! Introduction to Macroeconomics of Finance The most important economic variables There are some economic variables that must be taken into consideration for understanding the wealth of a country, as: o Gross domestic product in % change on year ago (GDP). The GDP takes into account inflation; instead, the real GDP doesn’t take into account it. GDP is equal to the added valued, that represents the production in a given moment in a given country; in the same way, it can be measured by the income of the population. o Consumer prices in % change on year ago. In the United States is 5.4, in the Euro area 3.0 and in Italy 2.1. For the Central Bank it is important the inflation rate, and it has the inflation target of 2.0. Italy is respecting this target, while the United States has got a very high inflation rate compared to the target; this has given some problems to United States, in particular because it is increasing a lot from year to year (3.6 vs 5.4). o Unemployment rate. in %. It is very high in Italy (9.3%), but of course it is an average between sectors, ages, and genders. o Current-account balance in % of GDP. For United State it is -3.0, while in Euro area it is 3.3. It is the account that registers the exchange of goods and services with the rest of the world, and it is computed as the difference between export and import. If this difference is positive, the country has got a positive current- account; otherwise, there is a deficit of current-account. The United States has a negative value, meaning that they import more than what they export (at least before Trump, US imports a lot from China, that has a positive current account of 2.8); for the Euro area, the opposite is true. Germany has a really high current- account, equal to 7.1. o Budget balance of the country (so of the government) in % of GDP. It is the difference between revenues and expenditures. The revenues for the Government are taxes; the expenses are related to the costs sustained, as the construction of infrastructure and facilities. If it is positive, the government has a surplus; otherwise, there is a deficit. In all the whole world, the situation is characterized by a deficit. This because, to face the pandemic and the regression created by it, the government has begun to increase a lot of public expenditures. These policies undertaken are called fiscal policies (they are different from the monetary policies undertaken by central banks, that are not the government!). To have expansion rate fiscal policies, the Governments have started to increase public expenditures and transfers (e.g., pensions, unemployment benefits and so on); this, of course, leads to a decrease of the public budget balance. o Interest rates of 10-years government bonds. The interest rates move as the Central banks move the cost of money. When the Central bank increases the cost of money, usually all the interest rates go up; when the Central bank decreases the cost of money, the interest rates of all the bonds usually go down. o Currency units per $. It is the exchange rate, and it is the currency that should be given to have 1 dollar. Of course, for United States there is not a figure. For Italy, to have 1 dollar, it is necessary to give 0.85€. The business cycle: output gap and recession The horizontal axis of the figure shows the time, the vertical one the GDP. So, the graph shows the representation of the GDP; in a wealth country, in the long run, the real GDP grows following a positive trend (as the bold line shows). This can be explained by technology, because if a country improves the technology, it is going to produce more; by productivity, that is linked with technology, meaning that the country is able to produce more in a given time (maybe, it can be achieved also with better knowledge and with great investments); by population growth, indeed each new birth has to work and so to produce. However, by looking at the figure, there is also a line that goes up and down with respect to the positive trend. That line is the actual GDP of actual income and represents the business cycle. Each point represents the GDP today in a certain country, instead the bold line is the GDP in the long run. The difference between these two lines, so between the actual income and the potential income is called output gap (it is effective – potential). During a recession, the output gap is expected to be negative, because the GDP is low and so the country is under the potential; instead, during a boom, the output gap is expected to be positive, because firms produce a lot and employment is high. According to INSTAT, an economic recession is defined as two consecutive quarters of decline in real GDP. However, there is another definition of recession given by NBER (National Bureau of Economic Research, that is a US institution), according to which a recession is a significant decline in economic activity spread across the economy, lasting more than a few months, normally visible in real GDP, real income, employment, industrial production, and wholesale-retail sales. Hence, there is not a regression in the exact moment in which the output gap is negative, but it is necessary to wait at least two consecutive quarters. It is necessary to give a definition of potential GDP; at first, So, it can be defined as the GDP a country could have if there is no unemployment (i.e., the maximum a country can produce). However, this doesn’t allow to have moments in which the actual GPD is higher than the potential one. This because, the exact definition of potential GDP is slightly different, due to the fact there is not a moment in which a country has all the workers employed. There is the so-called structural unemployment. The Federal Reserve shows that, even in good times, a healthy and dynamic economy will have at least some unemployment as workers switch jobs, and as new workers enter the labor market and other workers leave it. They expected for US that this unemployment rate is in a range between 3.5% and 4.5%. In this way, when the unemployment of the country is lower than the structural one, the actual GDP can be higher than the potential one. To sum up, the bold line doesn’t correspond to unemployment rate equal to zero, but to an unemployment rate equal to the structural one, that can change over time in a country and are different from one place to another (e.g., due to different labor markets – in Italy, the labor market is rigid, meaning that firing is rigid. This leads to have a higher structural unemployment rate, near to 7%). The measurement of the potential GDP is difficult because it is a value that must be forecasted since it has to do with the future. In this case, econometrics is important because allows to do forecasts. Looking at the United States, from 1990 there were 4 recessions (1991 – 2001 – 2008 – 2021); during them, the output gap is negative, because the actual GDP (red line) was lower than the potential GDP (blue line). The figure shows also that the potential GDP is upward sloping over time. Moreover, during the Covid recession there was the largest, even compared to the great recession (2008-2009), and this is shown by the negative pick, in which the effective GDP went down compared to the potential one. This article from Financial Times about the output gap. Looking at the figure, there is a comparison between GFC (Great Financial Crisis – recession of 2008-2009) and covid-19 recession. With covid-19 lockdown of 2020, there was an enormous negative output gap for US, Euro area and Japan (even worse than the one of 2009), instead China and India where not able to grow as much as happened with the GFC. To replicate this graph for Italy, it is necessary to know which are its recessions. To do so, an indicator can be used: it is called OECD indicator. When the indicator is 1, it means there was a recession. Introduction to Macroeconomics of Finance There are 2 main theories in macroeconomics: i. General economic equilibrium theory, also called neo-classical theory. ii. Keynesian theory, 1936, that was born with the book The general theory of employment, interest, and money. NEO-CLASSICAL THEORY - General Economic Equilibrium Theory The Neo-classical theory is based on the idea of a general economic equilibrium, according to which in a capitalistic system, markets are always in equilibrium, so the demand is always equal to the supply. This happens thanks to market forces that coordinate agents’ decisions (i.e., demand and supply) through a change in prices, wages, or interest rates, that are always flexible. This system of forces that allow to reach the equilibrium was even called, by Adam Smith, the invisible hand. Moreover, according to this theory, the role of institutions is just to remove any obstacle or friction to the functioning of this mechanism. LABOR MARKET The most important result of this theory is that, in the labor market, there is not unemployment. Let’s represents a graph with x axis the quantity of labor (N) and with y axis the price of labor, so the real wage (W)1. To find the equilibrium, it is necessary to find where the demand for labor crosses the supply. The demand for labor is asked by firms to produce, and it is downward sloped; the supply of labor is given by individuals, and it is upward sloped in relation to the wage. In correspondence of W* there is the equilibrium of the labor market, meaning that there is not unvoluntary unemployment (i.e., who wants to work succeeds in finding a job). Note that, there could be however voluntary unemployment. If, for any reason, the equilibrium is not reached, according to the Neo-classical theory there are market forces that adjust wages to reach it. Of course, in real world, it is not true that wages are always flexible, due to the existence of Trade Unions that can decide not to decrease the wage under a given level. Consequently, this model assumes that the institutions should not allow Trade Unions because they represent an obstacle to the working of price flexibility. To describe the economy, it is possible to take a representative firm and then assume that all the firms are equal; in this way, the general behavior of the economy is done by the aggregation of the behaviors of each single firm. Let’s assume that this firm has got a production function y = f(N), where y is the output of the firm, N is the input (labor), and f is the function that expresses how the company employees the labor to produce (in general, it represents the technology). Of course, there is the assumption the firm is using only one input to produce, that is the employment. The first derivative of the production function in respect to labor is positive (f’>0), because by increasing the employment, the company is able to produce more. Hence, the production function is increasing. Instead, the second derivative is lower than zero (f’’<=0); this because there is a decreasing marginal productivity of labor, meaning that when the company employees the first unit of labor, the output obtained is high; instead, by increasing a lot the employment, at the end of the day the output obtained is increased much less compared to the first unit. Hence, the production function is concave. By 1 A real variable considers inflation, so the level of prices. Hence, the real wage is defined as nominal wage over prices. In this case, real wage is considered because agents want to know which is the purchasing power of their wage (i.e., how many goods they can buy with those wages). taking the neo-classical equilibrium, in the market there is no unemployment, and the wage is fixed. At the equilibrium, the labor in the market is N* (this is fixed if there are not any shocks); by putting this value into the productive function of the firm, a fixed value of output is obtained (Y̅). This represents the quantity produced if the labor market is in equilibrium, so when there is full employment; it is even called potential output, since it is the maximum output that can be reached. GOODS and BOND MARKETS The production function defined above represents the supply of goods, YS = YS(N), and so it depends on the labor (that is the input for the production). However, in this general economic equilibrium model, the labor is fixed at N*, and this leads always to a fixed value of production Y̅. By representing this function in a graph with x axis the output, and y axis the real interest rate2, it is a vertical line that corresponds Y̅, since there is not a relation with the real interest rate. To describe the goods market, it is necessary to describe even the demand for goods. The assumption of a closed economy (no imports and exports) without government (no public expenditure, G) is done; it means that the demand for goods depends only on consumption from households (C) and investments by firms (I). Both C and I depend on the interest rate: if the interest rate goes up, it is more expensive to issue a bond, and so firms invest less (so, the derivative of the investments in respect to the interest rate is negative). Of course, it is true even the opposite; so, if the interest rate goes down, investments go up. Instead, for understanding the relationship between households’ consumptions and interest rate, it is essential to know that people can either consume their income or can save it. If the interest rate goes up, households will save more, for instance by buying bonds, and they will consume less. Hence, the demand for goods is downward sloping, because if the interest rate increases, the consumption will definitely decrease. The equilibrium is obtained only when the supply meets the demand, so when YS = YD. { YS = YS(N) YD = C(r-) + I(r-) The interest rate that leads to the equilibrium in the goods market is called natural interest rate. Due to the strict relationship between consumptions/investment and bonds, the equilibrium in the bond market must be defined. To find this equilibrium, the demand for bonds should be crossed with the supply for them. Let’s suppose a firm that wants to finance its investments by issuing bonds: this is the supply for bonds, and it is downward sloping. This because, if the interest rate goes up, the company has to pay higher interests to the ones who have bought its bonds, so it will issue a lower quantity of bonds. This BS corresponds to the investments done by the firm: this because, the company issues bonds for doing investments. Note that, for the sake of simplicity, in this model there is no governments, however, even the government can issue bonds. The demand for bonds (done by households) has got an upward slope; this because, the higher is the interest rate, the more the households will ask for bonds. This BD corresponds with the savings done by the households. The equilibrium is at the intersection between these two curves. The interest rate obtained is exactly the natural interest rate obtained in the goods market. This can be explained because savings are income (that is the production of the economy) net consumption; instead, the demand for goods is equal to consumptions plus investments. {S = Y S - C → YS = S + C D = YD = C + I 2 The real interest rate is defined as the difference between the nominal interest rate and the inflation. By crossing YS and YD (that is the point of intersection of the goods market), it is possible to obtain S + C = C + I, from which savings must be equal to investments, that is the point of intersection of the bonds market. Hence, the two interest rates that lead to the equilibrium are the same. If the interest rate is higher than the natural one, there is an excess of savings; this because the interest rate is so high that everyone wants to buy bonds. This means that in the economy the investments are too low. The investments are present also in the goods market; if they are low, it means that the demand is too low compared to the potential, and so there is an excess of supply. According to the neo-classic theory, it is not possible to stay forever in this point: at a certain point, there will be a reduction in r because prices (i.e., price, wage, and interest rate) are flexible. NOTE. This will be very important for the IS curve (I.e., Investment-Saving curve), that is the locus where the good market is in equilibrium, and in which consequently investments are equal to savings (bond market is in equilibrium as well). Money in the neo-classical model In the neo-classical model, it is used the so-called quantitative theory of money, also called Fisher’s equation: Mv̅ = PY̅ M is the nominal quantity of money demanded in the country (while instead money supply is given by the Central Bank) – assumption of the helicopter that passes and throw money); p is the price level in that country; Y̅ is the quantity of goods supplied in that country (it corresponds to the vertical line, so it is a constant), and it is the maximum output because at the equilibrium there is no unemployment; v is called velocity of money and tells how fast the money passes from one holder to the next (it means how many times a coin is used in a given time). The velocity of the money can be assumed as a constant because it depends on the behaviors of the agents. The equilibrium between money demand and money supply is shown in the graph. If the Central bank does a monetary policy expansion and increases the supply of money, the equilibrium goes from A to B. This can happen just through an increase in prices, since the output Y̅ and the velocity of money v̅ are constant. Hence, an increase/decrease of money supply doesn’t have an effect on the output (that is a constant), but it has an effect on prices that is exactly proportional to the change in money. So, there is an effect on inflation: ∆M+→∆P+ Hence, according to the neo-classical theory, money is a veil, meaning that money doesn’t have real effects: it is not possible to move money and make someone find the job (so, Central Bank cannot use monetary policies to go out from a recession). Another way to tell this is to say that money is neutral, so it doesn’t affect GDP. Of course, it is not true; in particular it is true only in the long-run, while in the short-run not. Indeed, in the long run, it is not enough to do monetary and fiscal policies to increase GDP, but structural changes are needed. Instead, in the short run, money affect the real output. According to the Keynesian model, it may happen that the equilibrium income YE is lower than the potential income, called YP, as happened during the 1929 great depression, when Keynes wrote this theory (that was against the full employment of the neo-classical theory). If YE < YP, there is unemployment and according to Keynes, to reach the potential income, it is necessary to go from E to F. Of course, for going to this point, it is necessary to shift upward the aggregate demand. There are several alternatives, as: i. Increase consumption. However, this is not easy, because it is a private decision of households. It is not possible to impose households to consume more. ii. Increase investments. It is the same reasoning because they are private decisions by firms. iii. Increase public expenditures. If the governments increase G, the income will increase more than proportionally. For instance, if ∆G = 30, ∆Y = 50; this is the Keynesian multiplier effect. The economic intuition is related to the Circular Flow of Income: if there is an increase in public expenditure (e.g., ∆G = 10), the aggregate demand will increase as well (∆AD = 10 – from point A to point B) and supply adjusts in the same way as aggregate demand (∆Y = 10 – indeed, to satisfy the higher level of demand, firms increase production). This increase in production implies that income increases as well because income = production, so the economy moves to point C. This increase in income leads to a further increase in demand, reaching point D: for instance, if c = 0,8, the consumption will increase by 8 (∆C = 10 ∙ 0,8 = 8). This increase in consumption leads to an increase in aggregate demand of 8 (∆AD = 8), so to an increase in production and so in income, reaching point E (output will increase by 8, income will increase by 8). Even this point is not of equilibrium. In the future, this increase in income leads to an increase in consumption by ∆C = 8 ∙ 0,8 = 6,4. This cycle is replicated again and again until reaching A’. Of course, if the marginal propensity to consume was 0, a ∆G = 10 leads to an increase in output of 10, so there is not the circular flow of income. To understand how a change in public expenditures will affect ouput, it is necessary to compute the first derivative: dY dG = 1 1 - c1 This is the public expenditure multiplier, that is equal to the Keynesian multiplier. However, the same reasoning of the Keynesian multiplier holds even for increase consumption and increase investments, since both are exogenous variables that have got the same multiplier. iv. Cut taxes. In this model, taxes do not depend on income (lamp-taxes), and so the multiplier will be: dY dT = - c1 1 - c1 It is negative because an increase in tax will lead to a reduction in output. If taxes depend on income (taxes on income), T = t ∙ Y, and YD = Y - t ∙ Y + TR. From this: Y = 1 1 - c1(1 - t) (C0 + I ̅+ G̅ + c1 ∙ TR) So, the multiplier becomes: dY dT = 1 1 - c1(1 - t) Note that, in such a case, there is a change in the slope of the aggregate demand. v. Increase public transfers. In this case, the public transfer multiplier is: dY dTR = c1 1 - c1 NOTE. The higher c1, the higher the multiplier in absolute value. The last 3 policies that can be undertaken by governments are called fiscal policies. Of course, by looking at ∆G and ∆TR, the more effective is the increase in public expenditure, because 1 1 - c1 > c1 1 - c1 . The economic intuition behind it is that, with the public expenditure, the money is putted directly into the economy, while with transfers people can decide not to spend them and save them. So, there is a percentage of transfer that is not putted directly into the economy; this part is related to the marginal propensity to save s1 = 1 - c1. During a recession, savings are expected to increase because the marginal propensity to save increases, so transfers are not very effective in these cases (analytically it happens because the numerator of the multiplier goes down). However, for instance during the covid-19 recession, the governments gave a lot of transfers. This because they have an advantage compared to public expenditures: they can be directed to a given class of agents (e.g., give money just to the owner of restaurants), instead public expenditures go to everyone. The sticky price IS-LM MODEL The IS-LM model, introduced in 1937 by John Hicks, is a sticky price model, meaning that prices are fixed (as in the income-expenditure model). This assumption comes from the fact that this model analyzes the short run, in which firms cannot change prices. This model is done by two curves: the IS-curve, that describes the equilibrium in the goods market, and the LM-curve that describes the equilibrium in the money market (and so in the bond market). The IS-curve is built on the income-expenditure model, but there is an assumption that is no more present: before investments where exogenous, I = I,̅ while now there is the following function: I = I ̅- b ∙ i Where b is a coefficient greater than zero (b>0), and i is the real interest rate. NOTE. The real interest rate is given by the nominal interest rate minus inflation; since in this model prices are fixed; it is indifferent to talk about real or nominal interest rate. However, in the reality, firms look at the real interest rate. This equation tells that the investment demand is down sloping in respect to the interest rate (indeed, the first derivative is -b, that is negative). This negative relation is that, as the interest rate goes up, it becomes more expensive to borrow and so the demand for investment will decreases. However, investments depend negatively on interest rate even if firms have got money and don’t need to borrow, because in such a case the interest rate represents the opportunity cost of the investment. It is what the entrepreneur loses by making the investment instead of buying bonds at that interest rate. When a firm has to decide if invest or not, it looks at the net present value of the investment. The intersection between NPV=0 and interest rate is the IRR (internal rate of return); according to the investment theory, the firm will undertake its investment when the market interest rate is lower than the internal rate of return. This because, in those cases, NPV > 0. However, the interest rate is just one of the two parameters looked by firms, since the net present value schedule changes with expectations about future level of sales: • If firms expect lower demand in the future (pessimistic), it will expect lower profits (lower revenues or higher costs) and so the NPV schedule will shift to the left and the IRR decreases. • If firms expect higher demand in the future (optimistic), it will expect higher profits (higher revenues or lower costs) and so the NPV schedule will shift to the right and the IRR increases. However, this is related to the decision of a single firm; instead, macroeconomic deals with the decisions of investments of the whole economy. Let’s consider the whole economy with different investment projects, and let’s order them from the one with the highest IRR to the one with the lowest IRR. If the market interest rate is i1, the only project that will be undertaken is A, because it is the only with IRR > i1. The Central Bank, looking at this situation, understand that is not quite good because a lot of firms are not investing. To spur investments, the Central Bank (that controls the cost of money and so the market interest rate) can reduce the interest rate from i1 to i2. In this case, A, B, C are the projects that will be undertaken. In this way, investments increase and maybe the country can go out, for instance, from a recession. However, usually during a recession the expectations of the entrepreneurs get worse, so they become more pessimistic of the future and the NPV of the investments will shift to the left, and so every IRR will be lower. If NPV decreases very much, it can happen that, rate: an increase in the interest rate decreases the demand for money, as people put more of their wealth into bonds. Since wealth is fixed, whenever an agent increases the demand for money, he should decrease the demand for bonds, and vice versa. So, in the equilibrium, money and bonds demand (L + Bd) should be equal to the supply of money and bonds ( M p̅ + Bs): L + Bd = M p̅ + Bs → (L - M p̅ ) + (Bd-Bs) = 0 If L - M p̅ > 0, it means there is an excess of money demand and it leads to have even an excess of bonds supply Bd-Bs < 0, because the sum of the two parentheses should be zero. It means that, if money demand goes up, bonds demand should go down (this because wealth is fixed). Of course, if there is an excess of money supply, there should be even an excess of bonds demand. If L - M p̅ = 0, it means there is equilibrium in the money market, and it ensures there is even equilibrium in the bonds market. This comes from the so-called Walras’ law: according to him, if there are N markets, and N-1 are in equilibrium, even the final one (Nth) is in equilibrium. • There is an inverse relationship between price of a bond and its return. Let’s imagine having a bond that at the end of its life gives f. The return can be computed as the difference between f and the price paid, over the price paid (it is the final return, pt is the price paid, f is the value of the bond at the end of its life): it = f - pt pt → (1+it) = f pt The second relationship shows the negative relation between price of a bond and its return. If there is a decrease in demand for bonds, the price of bonds (as happened for goods) goes down as well (it is possible to see it by drawing the graph with supply and demand) and the interest rate on bonds goes up. Even the vice versa is true. Price of bonds can move, even if the model has got sticky prices, because they are prices of financial assets and not prices of goods. Let’s have the equilibrium in the money market. The money supply doesn’t depend on the interest rate, since it is exogenous, so it is a vertical line. The money demand depends positively on Y and negatively on interest rate L (Y+; i-), so it is a downward sloping curve: when interest rate goes up, demand for bonds goes up and demand for money goes down. Of course, the curve drawn is for a given level of production (Y). The intersection between these two curves is an equilibrium in the money market, so it is a point of the LM curve. If nominal income Y increases, from Y0 > Y1, the money demand increases (more money is needed because people will consume more, and they do more transactions). The new equilibrium B is another point of the LM curve. So, it is possible to draw the LM curve, that is upward sloping: it means that, if Y increases, the interest rate increases. The chain of event is the following: if Y increases, the demand for money increases (Ld) but since the wealth is fixed, an excess of money demand leads to a reduction in bond demand (Bd). This leads to a reduction in price of bonds; since there is an inverse relationship between price of bonds and their return, the interest rate is going to increase. Y↑→MD↑→BD↓ →PB↓ → i↑ This process is an adjustment of the portfolio of the agents, while the wealth is the same. This process is characterized by two stages: from A to A’, and then from A’ to B. When Y increases, money demand goes up, so the new curve L(Y1) is drawn. If the interest rate doesn’t move, the equilibrium moves from A to A’, where there is an excess of money demand. This implies a reduction in bond demand and, consequently, a decrease in bonds’ price. Since a negative relation between bond price and interest rate is given, the reduction in bonds’ price causes an upward pressure on the interest rate, moving the equilibrium from A’ to B. This happens because when interest rate goes up, money demand decreases and the gap between money supply and money demand shrinks until it goes to 0 in B, where supply is equal to demand. By moving the income Y or the interest rate i, a movement along the LM-curve is performed. Instead, the LM-curve shifts when there is a change in money supply. An easing monetary policy (more money supplied) by the Central Bank will shift to the right the supply of money; so, the LM curve is shifted to the right. A tightening monetary policy, instead, moves the LM curve to the left. Any point above the LM curve is a point where there is excess of money supply, because to go back to the equilibrium interest rate should decrease, and this means that money demand increases. On the contrary, any point below the LM curve is a point where there is excess of money demand because to go back to the equilibrium, interest rate should increase, and this means that money demand increases. The equilibrium in the IS-LM model. By putting together IS and LM curve, it is possible to find the equilibrium point of the economy at the intersection. This point (E) leads 3 markets in the equilibrium: • Goods market because E is on the IS curve. • Money market because E is on the LM curve. • Bond market. This can be said thanks through the Walras’ law. If no shocks are present in the economy, point E is a stable equilibrium. Let’s now study which can be these shocks. Macroeconomic Policies Macroeconomic policies have the aim to change the business cycle. These policies can be divided into fiscal policies and monetary policies. FISCAL POLICY. Let’s take a graph with IS and LM curve; at the intersection there is the equilibrium. If no shocks are given, the equilibrium will be maintained overtime, because it is a stable equilibrium. By giving a fiscal shock (e.g., government decides to increase the public expenditure), the IS curve will shift and there will be a new equilibrium (from A to B). In particular, it is possible to divide fiscal policies into: o Expansionary: increase in government purchases, increase in transfers, decrease in taxes, for the purpose of increasing aggregated demand and expanding output. However, it leads to an increase in interest rate. o Contractionary: decrease in government purchases, decrease in transfers, and increase in taxes for decreasing aggregate demand and thus controlling inflation. Let’s assume to have an expansionary fiscal policy but keeping stable the interest rate. The point C is not an equilibrium, because it is outside the LM curve. What will happen is that Y is increased, and as a consequence the money demand increases (Ld increases), but money supply is fixed: so, there is an excess of money demand. In this situation, bond demand will go down so price of bonds will go down and interest rate will go up. Hence, agents will adjust their portfolio until reaching point B, that is the equilibrium point (the rebalancing of the portfolio will bring back from point C to B). Going from C to B, there is an increase in the interest rate that crowds out private investments: it is called crowding out effect, meaning that when the IS shift to the right (due to an increase in G), there is an increase in the interest rate that leads to a reduction in private investments. For this reason, some people say that it is not good when the government intervenes in the economy, because it crowds out private investments. The best situation is to being able to keep the equilibrium in the point C, because YC is quite larger than YB. For having equilibrium in point C, it is necessary that the Central Bank adopts an easing monetary policy, so if the central bank puts money into the economy (due to the increase in money supply the LM shifts to the right until point C). After the pandemic, it is very important that Governments and Central Bank work together for avoiding the crowding out effect; so, fiscal policies and monetary policies have an amplified effect on the economy if they act together. This interaction, called policy mix, must be studied carefully, because generally Central Banks are independent from government. The goal of ECB is to control inflation and to reach an inflation rate of 2%. So, the Central Bank should dislike inflation and it should be independent otherwise the government can ask it to increase money supply with the aim of financing government’s public expenditures: if G increases without an increase in the interest rate, Y increases a lot. People have got higher income, so demand for goods increase, and if good supply is fixed, prices and inflation will go up. The reason why an expansionary fiscal policy leads to an increase in the interest rate is the following one: let’s take a graph with x axis bonds and y axis interest rate. If the government increases public expanses (G) without increasing taxes, to do so it must increase debts, so it issues bonds (increases of bonds supply). The equilibrium goes from A to B, and the interest rate increases. Hence, the increase in the interest rate can be explained by the increase in bonds supply. As said before, when interest rate goes up, private investments go down: to avoid this reduction, it is necessary to avoid the increase in the interest rate. This means increase bonds demand, moving Bd to the right. This was exactly what the Central Bank did during the pandemic crisis: it started to buy bonds to reduce interest rate and avoid the crowding out effect. It did so through the so-called quantitative easing (QE). There is another case to avoid the crowding out effect: it is the case in which LM curve is horizontal, and it is called liquidity trap. The LM curve is horizontal when the interest rates are very low, near to zero; this because, if interest rates are so low, people are going to demand money and not bonds (that do not give interests and cannot be used to do transactions). So, people want only liquidity (for this reason it is called liquidity trap). Furthermore, since interest rates are so low and agents know that generally they don’t go under zero (otherwise it means that banks give interest rates to borrowers – this is called zero lower bound), they expect that in the following days interest rates will go up: if interest rate goes up, price of bonds will go down too. Hence, everyone is going to wait ‘tomorrow’ for buying bonds that have a lower price and a higher return. This means that today, every liquidity the Central Bank puts into the economy goes under the pillow of the agents. It also means that agents do not lend their money to entrepreneurs, because they keep money to buy bonds in the future. Hence, in the case of liquidity trap, monetary policies don’t work (because interest rates are close to zero, and the LM-curve is going to shift on itself without changing the equilibrium). Instead, during a period of liquidity trap, fiscal policies work very well: indeed, they lead to a great increase in Y because the interest rate remains the same as the beginning and crowding out effect is avoided. In such a case, the effect on the movement in G on Y is exactly equal to the one of the Keynesian model: ∆Y = 1 1 - c(1 - t) ∆G Note that the multiplier can be used because interest rate doesn’t change (indeed, in the Keynesian model there is no interest rate). NOTE. If taxes are lamp-sum taxes, that do not depend on income, they will shift the aggregate demand, but the slope remains the same; instead, if taxes depend on income (Y), there will be a change in the slope, because the t goes in the Keynesian multiplier (that affects the slope of the IS curve and so of the AD). Aggregate supply. Until now, in all the models seen the supply was given (income-expenditure model and IS-LM model, where supply always adjusts the demand), instead in this case the supply has got its own function. Of course, the expectation is that this curve will be upward sloping because the aggregate supply is given by firms, and the higher the price, the higher the production because companies want to sell as much as possible. To introduce the aggregate supply model, something about the inputs firms employ to produce must be said. Let’s imagine a production function Y = f(N), where N is labor and represents the only input used. Hence, to talk about AS curve, the labor market should be introduced. It is absolutely important to remember that the labor demand is done by firms, while labor supply is by households (they supply their labor force); so, the demand for labor is downward sloping, while the supply is upward sloping. Let’s give some definitions: Labor force (L̅) = Employed (N) + Unemployed + People looking for first employment This sum is called unvoluntary unemployed and it is done by those people that would like to work but do not manage to find a job Unactive population = People that neither work nor look for a job This s called voluntary unemployed, and can be computed as the difference between the total population and the labor force Unemployment rate (u) = Unvoluntary unemployment Labor force ∙100 = L̅ - N L̅ ∙ 100 It is important to remember that there is also another kind of unemployment, called structural unemployment (or frictional unemployment) and represents that unemployment rate that coexists even with the labor market that is in equilibrium (in the sense that it is not possible to have a country with unemployment rate equal to zero, because perhaps some people are changing their job or are waiting to be hire). According to some studies of FED, it is about 3-4%. To introduce the labor market, it is necessary to discuss about the wage determination and price determination, so it is important to understand how the firms set the wages (together with workers), and secondarily, once the wages are set, how firms set the price. WAGE DETERMINATION. There are some characteristics of wages that can be defined: ▪ The wage fixed by a firm is higher than the reservation wage of the individual, that is the minimum wage that an individual accept to go at work. So, if the wage is lower that his threshold, the individual is going to stay at home. ▪ Wages depend on labor market conditions, where a proxy of these labor market conditions is the unemployment rate. For instance, if the unemployment rate increases, wages are expected to decrease. This because, if there is a high unemployment, it is difficult to find a job, and so a person is happy even with a low wage. If unemployment is low, wages are high, because for firms is difficult to find workers and so they have to pay higher wages. A tight labor market means that the number of jobs in that country is higher than the number of workers. So, usually, when there is a tight labor market, the country has low unemployment rate. The opposite is a slake labor market; it denotes a country where the number of jobs is lower than the number of workers, so the unemployment rate is high. Another reason is that, if the unemployment rate increases, the bargaining power of the workers decreases and so they cannot ask for high wages. Instead, if the unemployment rate is low, workers have got high bargaining power, because if they leave their position, the company can have difficulties in finding a replacement. In such a situation, wages usually go up. ▪ According to the theory of the efficiency wages, leaving aside any bargaining power by the workers, companies usually want to set high wages because they have an incentive effect, meaning that the workers are likely to stay in the company for more time and put more effort. Having said that, it is possible to write the wage equation: W = Pe f(u-, z+) - W is the aggregate nominal wage (it is aggregate because the focus is on the whole country; it is nominal, because this wage doesn’t depend on price). - Pe is the expected prices level, so the prices that are expected to be in that country in the future. They are not known, so an expectation must be done. It is interesting to see their value in the future, because the wage is not fixed for a short time, but for a long period (e.g., 10 years). Since the wage is fixed today, it is important to include the price level expected in the future. This because workers are interested in their real wage, not in the nominal one, so they are interested in their purchasing power with their nominal wage (so, how many things they can buy, and this is the real wage). Agents do not suffer from monetary illusion: they perfectly know that what is important is the nominal wage with respect to the price level. So, expectations on prices enter in the calculation of wages, and so on the AD-AS equilibrium; if actual prices differ from expected prices, something will happen and the equilibrium shifts. - f is a function of u, that is the unemployment rate, and z, that are other variables of the labor market, as unemployment insurance (money given when the people do not work) and firing regulations. The sign of the derivative of wages with respect to the unemployment rate is negative: indeed, when u goes up, the bargaining power of agents goes down, and wages go down as well. The sign of the derivative of wages with respect to the other variables in the labor market (z) is positive: indeed, the unemployment insurance protects the workers from the loss of income. If unemployment insurance increases, the wage should increase, otherwise the worker is going to stay at home. Even in the case of firing regulations, if firing a worker becomes more expensive, the bargaining power of the worker increases, and wages go up. PRICE DETERMINATION. To fix its price, firms look at the market in which they operate (e.g., perfect competition, oligopoly, monopoly). Let’s assume that the production function of the firm is y = f(N), meaning that the company employs just one input, that is labor (N), so they do not use other things, as capital or technology. Of course, y is the output and f is the production function. The production function has the first derivative that is positive (f’>0), and the second derivative that is negative (f’’<0). Let’s go from the implicit firm to the explicit form of the production function: y = A ∙ N, where A can be defined as dY dN that is called marginal productivity of labor and tells how many objects can be produce if the company hires one more worker, or as Y N that is called average productivity of labor. For the sake of simplicity, let’s assume that A = 1, and so the production function becomes y = N. The return to scale of this production function is constant (C.R.S. – constant return to scale), because by doubling the input, the output doubles as well. So, for producing one more unit of output, the firm must hire one more worker. Of course, this is quite atypical, because in general the return to scale of a production function is decreasing. Let’s imagine to be in perfect competition: the firm is going to fix the price equal to the marginal cost (and the marginal revenue is equal to the price), since this is the condition of maximization of profits. In this case, having the production function y = N, for producing a unit more of output, a unit more of work is needed (e.g., one extra worker); hence, the marginal cost is the wage of the worker. So, p = w. Instead, in all the other situations (e.g., monopoly and oligopoly), the price is not just equal to the marginal cost, so the wage, but there is even a markup (μ), so p = w ∙ (1 + μ). The markup shows the fact that the company has market power. Indeed, if the firm fixes a markup in perfect competition, where all the firms are the same, no one is going to buy from it; instead, in other cases, the markup can be fixed over the marginal cost. Now, it is necessary to see when wage determination is consistent with price determination, and for doing that the natural rate of unemployment (un) should be looked. It is exactly equal to the structural unemployment (frictional unemployment). To find it, the assumption that expectations are realized is needed, so p = pe, meaning that the effective prices are equal to the expected prices. This is a strong assumption, because in general expectations are not always realized. By doing this assumption, the equation W = Pe f(u, z) becomes W = P f(u, z), and it is possible to find the so-called wage setting relationship (it links effective wages to unemployment rate and other variables): W P = F(u,z) According to this relationship, if unemployment rate increases, the bargaining power of workers will decrease and real wages ( W P ) will decrease. Instead, taking p = w ∙ (1 + μ), it doesn’t contain the expected price, so no changes are done. The price setting relationship can be derived: W P = 1 1 + μ Let’s draw these two relations in a graph with u in the x axis and W/p in the y axis. The price setting doesn’t depend on the unemployment rate, so it is a horizontal line. The wage setting has a negative relationship between the unemployment rate and the real wage, so it is a downward sloping curve. Let’s observe that in this figure, the wage setting is drawn for a given value of z; however, if z changes, the curve changes. The two decisions (price setting and wage setting) are consistent when the two curves meet. In that point, in which price setting = wage setting (so, 1 1 + μ = F(u,z)), there is an unemployment rate called natural rate of unemployment (un). This equilibrium in the labor market (in which wages asked by workers are in line with prices set by firms) can be found only if expectations are realized. It is clear that, at the equilibrium, the unemployment is not zero, indeed it is equal to the structural unemployment. It is important to note that the natural rate of unemployment (un) is not fixed, by chance as wage setting or price setting changes: ▪ If z increases (more protection to workers), the wage setting shifts upward and the natural rate of unemployment increases. ▪ If μ decreases (for instance due to a more stringent antitrust regulation), the price setting shifts upward (because μ is at the denominator) and the natural rate of unemployment decreases. So, un is going to differ among countries, since it depends on the characteristics of the labor market. If u = un, it is possible to define even the natural level of employment by using the following relation: u = L̅ - N L̅ = 1 - N L̅ → N = L̅ (1 - u) Let’s imagine that at year t, the equilibrium is E: in that point, Yt > YN and Pt > Pe t = Pt-1. Agents have fixed their wages according to the expected prices (Pe t = Pt-1) while now the prices are Pt > Pe t. So, for the coming year, wages are going not to be enough, because prices have increased, and wages are too low. Since Pt > Pe t, agents will recalculate their expectations; so, next time, when they will have to fix wages, they will upward their expectations (because they expect that tomorrow prices are going to increase again). So, they will increase Pe (this leads the aggregate supply to shift up) and they will ask for higher wages; firms have higher costs, and to face them they will set higher prices for their goods. So, at year t+1, the new AS leads to a new equilibrium (E’) at the intersection with the AD. This new curve AS’ is going to pass to A’, and according to the adaptive expectations, Pe t+1 = Pt. At the new equilibrium E’, Yt+1 > YN and Pt+1 > Pe t+1. Due to this fact, this is not a long run equilibrium: for the next year agents are going to reevaluate their expectations upward again, so they increase the expected prices, the AS will shift again up exactly as before. The long run equilibrium is reach only when Y = YN; so, the AS shifts up until reaching that point. In that point, there will be no more adjustments because Y = Yn and so P = Pe (there is no more price pressure). This means that in the long run expectations are realized and agents do not have incentives to reset wages. In the long run, Y is always equal to Yn, and this means that the aggregate supply curve is a vertical line. Obviously, the long run is made by a lot of short run periods, and each of them as a slope. Even the last period of the long run has a slope, the vertical line is a generalization of what the economy produces in that period. To sum up, it is possible to say that: SHORT RUN Y ⋚ Yn The output can be higher, lower, or equal to the natural level of output. If it happens that Y = Yn, the economy is even in the long-run equilibrium LONG RUN Y = Yn The output is always equal to the natural level of output DEMAND SHOCKS Let’s assume that there is a positive shock to the aggregate demand: everyone is going to increase the demand for goods, the AD shifts upward, and prices increase. It means that, in the long run the output is fixed and the adjustment occurs just in the price level. Effect of a monetary expansion (increase in money supply M). Let’s imagine that A is a long run equilibrium, with Y = Yn and Pn = Pe t = Pt-1 (for adaptive expectations). If there is any shock, the point A is going to be the equilibrium in all the long run. This monetary policy easing has a positive shock in the aggregate demand, that moves to the right (from AD to AD’). ▪ In the short run, this leads to a shift from point A to point B (new short run equilibrium). It increases output because everyone is going to increase the demand for goods and increases prices. Note that according to the neoclassical model, money is a veil and doesn’t have any effect on the economy; instead, in this case, a variation in M (∆M+) has a real effect on output (∆Y+). So, in the short run, monetary policies are effective. ▪ In the long run, B is not an equilibrium, because in B the output (Yt+1) is higher than Yn. and the prices Pt+1 are higher than the expected prices (Pe t+1 = Pt). Agents are not happy with this, and they will change their expectations upward because they expected a lower price level (instead, the effective price level is higher). This leads to a shift of AS, that goes to the left, by passing to the point A’ that has Y = Yn, and Pe t+2 = Pt+1. There is another equilibrium in point C, where Y = Yt+2 > Yn, so it is not an equilibrium in the long run. The adjustments go on until reaching Y = Yn (let’s call it point Z) and consequently P = Pe, that are higher compared to the initial point. In Z, Y = Yn, as in A. It means that, in the long run, the output is fixed, and the adjustment occurs just in the price level: there is just an increase in price. This is exactly what the neoclassic theory claimed (∆M → ∆P, while ∆Y = 0, so there is just inflation). So, in the long run, monetary policies are not effective (money is neutral, it just changes prices). Let’s take the function of the aggregate demand: Y = Y ( M p ; G; T) M p , G with a positive relation, and T with a negative one. Comparing points A and Z, Y is the same, G is the same, T is the same and M increases. If just M changes and Y is equal, it means that P has increased proportionally as the growth of money (∆M% = ∆P%). So, in the long run, the neoclassic view was right (while in the short run that theory is not true). Effect of a fiscal policy (decrease in the budget deficit G + TR - T, meaning that there is a decrease in expenditures and/or transfer, or an increase in taxes). Let’s imagine that A is a long run equilibrium, with Y = Yn and Pn = Pe t = Pt-1 (for adaptive expectations). The effect of this tithing fiscal policy is the shift to the left of the aggregate demand. ▪ In the short run, this leads to a shift from point A to point B (new short run equilibrium), because the AD shifts to the left. It decreases output and prices. ▪ In the long run, B is not an equilibrium, because Y < YN and P < Pe. So, the expectations are not realized, and agents will change them downward. So, they will ask for low wages and firms will decrease prices. So, the AS will shift down until reaching the point Z in which Y = YN. This is the long run equilibrium (of course, even in this case, the AS is a vertical line in the long run). The effect of the fiscal policy tightening in the long run is just a reduction in prices. Even fiscal policies are not effective in the long run. SUPPLY SHOCKS In the Seventies there were the so-called oil price shocks (1973-1975, 1979-1981 – in 1986 there was the opposite, called counter shock, in which the price decreases): the price increases very much because the cartel of oil producers (OPEC – Organization of Petroleum Exporting Countries) decided to decrease the supply of oil. By decreasing the supply of that good, the price goes up. The problem for introducing the supply restriction, and so the increase in price, is that the production function of the model uses only labor as input (Y= N). An increase in oil price (input) means that the firm has more costs and so it will increase prices. Looking at the price setting relationship, p = w ∙ (1 + μ), the increase in the oil price can be seen as an increase in the mark-up μ that the firm fixes on marginal costs. This leads to a structural change in the economy: if μ increases, 1 1 + μ goes down, and the intersection between the new price setting and the wage setting gives a new natural rate of unemployment, that is higher than before. Let’s take the AD-AS model and assume that A is the long run equilibrium in which Y = YN and Pe t = Pt+1. If μ increases, the aggregate supply moves up (prices increase for every y). However, the natural rate of unemployment has increased (if Yn ’<Yn, then un ’<un), and so the natural level of output must change. Since the unemployment is higher, the employment is lower, and the output will be lower (Yn new < Yn). ▪ In the short run, the equilibrium goes from point A to point B. Output decreases and prices increases. This situation is called stagflation: this is the union of two words i) inflation, so increase in prices ii) stagnation, meaning that output is stable or goes down. Usually, this situation happens when there is a negative supply shock, so an increase in cost of inputs. ▪ In the long run, B is not an equilibrium. The new long run equilibrium should be found in the Yn new. In B, Y > Yn new and P > Pe. So, agents will change their expectations upward, and this means that the AS will shift up until reaching an output equal to Yn new (point Z is the long run equilibrium – there is no more pressure on prices, because the effective prices are equal to the expected ones). So, the effect is that prices increase and output decreases; however, not only the effective output has decreased, but also the structural output (the natural level of output). There is a structural change in the economy. where ϑ is a parameter between 0 and 1 that increases the more the inflation process is persistent. Assuming adaptive static expectation (ϑ = 1), the curve becomes: πt = πt-1 + (μ + z) – αu πt - πt-1 = (μ + z) – αut This formulation can be written as ∆πt = (μ + z) – αut where ∆πt is the change in inflation. The formulation that considers the expected inflation in the Philips curve was introduced by Freedman and Phelps and is called expectation augmented Phillips’s curve or modified Philips’s curve or accelerationist Philips’s curve (if ∆πt > 0 it means that the inflation is becoming higher and higher, so where inflation rates accelerate). The role of natural rate of unemployment In these formulations of Philips ‘curve it is not present the natural rate of unemployment (un): ut= unonly under the assumption of (if and only if) Pt = P e, so the expected inflation is equal to the effective inflation (price expectations are realized). To find where ut = un is in the Philips curve, that is a framework with u on the x axis and π on the y axis, it is necessary to modify the relation Pt = P e in terms of inflation, so πt = πt e. By putting this relation into the Philips curve πt = πt e + (μ + z) - αut, it becomes: 0 = (μ + z) - αun→ αun = μ + z 4 This definition of μ + z can be used to write again the Philips curve: πt = πt e + αun − αut Let’s imagine having adaptive expectations (πt e = πt-1). This relation becomes: πt - πt-1 = - α (ut - un ) In this relation: ▪ α is called sacrifice ratio and tells how inflation responds to the unemployment rate (the derivative of πt with respect to ut is equal to – α): it has got this name because it tells that, for having an inflation rate that is lower than 1%, how much unemployment rate the country must accept (this because there is a negative relation between them). ▪ ut - un is the difference between the effective unemployment rate and the natural rate of unemployment. It is very similar to Yt - Yn , that was called output gap (gap compared to the full employment). So, ut - un is another way to look at that gap. ▪ πt - πt-1 = ∆πt is the change in inflation and it depends on ut - un : o If ut > u n , very low inflation is expected: analytically, the right-hand side is negative, and so the left-hand side is negative too, ∆πt < 0 → πt < πt-1. Hence, inflation is decelerating (it is not just low, but there is a reduction). This happens because there are a lot of unemployed people (unemployment is really high), so wages are low, and inflation will be low. o If ut < u n , very high inflation is expected: analytically, the right-hand side is positive, and so the left-hand side is positive too, ∆πt > 0 → πt > πt-1 Hence, inflation is accelerating. So, if a country wants to get an unemployment rate that is lower than the natural one, it must accept an increasing in inflation rate as time goes by (not just a high one). 4 From this un = μ + z α , where α is the sacrifice ratio, μ is the mark-up (found in the AS curve), z is other variables that affect the labor market, as firing regulations or the minimum wage. So, the natural rate of unemployment cannot be equal in different countries because they may have μ and z different (and maybe even α). Of course, this un changes overtime, according to the value of the variables. Nowadays in US the situation is of ut < u n , but inflation doesn’t increase. This means that the Phillips curve has become horizontal: any change in unemployment does not have any change in inflation. o If ut = u n , effective inflation is equal to expected inflation (as when Yt = Y n happens that Pt = P e), so inflation doesn’t move, and it is constant. In this case, un is called NAIRU (Not Accelerating Inflation Rate of Unemployment), meaning that un keeps inflation constant. It is the level of unemployment that doesn’t produce any acceleration in inflation. Wage indexation – how inflation process affects the Phillips curve As shown by the graph above, the process of inflation changes as time goes by (before the Seventies was on average zero, after becomes high and persistent), so even the relation between inflation and unemployment (i.e., Philips’s curve) can change as time goes by. Let’s imagine a situation in which inflation becomes high and very volatile (prices will change often in the future), the wage setting will be characterized by a high frequency of adjustment (more often workers will ask for a higher wage) with the aim of including in the wage a sufficient purchasing power. In the Seventies, when inflation was very high, there was the phenomenon called wage indexation: it is a rule that changes wages automatically according to inflation. The higher the inflation rate, the higher are wages. Usually, wages are fixed according to the expected inflation; instead, with wage indexation, wages are automatically adjusted with the inflation. COLA (Costs of Living Adjustments) were the contracts that were prevalent in the Seventies, and they had inside the wage indexation (in 1976, 69% have this wage indexation; in 1995, only 22%). The possibility of wage indexation leads to a change in the Philips curve: in particular, if wages are indexed, whenever inflation increases wages immediately increase (while without indexation, wages are just linked to expected inflation, and not to actual inflation); however, this increase in wages leads to an increase in prices, so to an increase in inflation and consequently an increase in wages. So, a given reduction in unemployment rate will cause a higher inflation compared to the case without wage indexation. Let’s suppose to have two types of labor contracts: contract 1, that represents a fraction λ, is indexed (i.e., wages change according to effective inflation), while contract 2, that represents a fraction 1 – λ (the complement), is not indexed (i.e., wages depend on expected inflation). Let’s take the Philips curve: πt - πt e = - α (ut - un ) This can be written using, instead of πt e, for a proportion λ the effective inflation, and for a proportion 1 - λ to expected inflation: πt = [λ πt+ (1 - λ) πt e ] - α (ut - un ) Assuming to use the adaptive expectations: πt = [λ πt+ (1 - λ) πt-1] - α (ut - un ) Hence, if λ = 0, the usual Philips curve is obtained (there is no wage indexation); if λ > 0 (there are some wage indexation contracts), it is possible to write the formulation as: πt = λ (πt- πt-1) + πt-1- α (ut - un ) πt - πt-1 = λ (πt- πt-1) - α (ut - un ) (1 - λ)(πt - πt-1) = - α (ut - un ) πt - πt-1= - α 1 - λ (ut - un ) Let’s compare this new Philips curve with the initial one πt - πt-1= - α (ut - un ). It is easy to see a change in the slope, from - α to - α 1 - λ . If λ = 1, the slope goes to infinite: so, the higher the proportion of indexed wages, the higher (in absolute value) the slope of the Philips curve, meaning that it becomes more and more vertical (steeper Phillips’s curve). Hence, wage indexation leads to a stronger response of inflation to unemployment! (if unemployment rate changes, inflation changes much more). So, when there is high inflation, some indexed wages can be present in the economy, and the Philips curve becomes steeper. Rational expectations Until now, there was always the assumption of adaptive expectations, so agents look at the past for forming their expectations, without looking at the future (they do not search for information). The opposite case of adaptive expectations, that is a stronger assumption, is the rational expectations. Let’s imagine that agents are rational and that the price level is uncertain, so they do not know how the price level will be in the future. Let’s even assume that the price level is a random variable, called p̃. At time t = 1, this random variable can have the following values with the following probability distribution. To know the random variable distribution, agents employ some common information. To forecast how much will be the value of this random variable, agents will take the expected price level: EV(p̃) = 5 ∙ 0,1 + 10 ∙ 0,2 + 15 ∙ 0,4 + 20 ∙ 0,2 + 25 ∙ 0,1 = 15 If the actual price level happens to be 15, then the agents are right. Otherwise, they make a forecast error (fe), that is computed as the difference between the effective price level and the expected price level: fe = p̃ - EV(p̃) Since the price level is a random variable, even the corresponding forecast error will be a random variable, that will be distributed as before. The expected forecast error is computed as: E(fe) = -10 ∙ 0,1 – 5 ∙ 0,2 + 0 ∙ 0,4 + 5 ∙ 0,2 + 10 ∙ 0,1 = 0 If expectations are rational, the expected forecast error of agents will be zero: this means that, on average, agents are right on the value of the price level (sometimes they can overestimate and sometimes underestimate, but on average they get the price). This is called property of non-distortion of rational expectations, meaning that agents cannot be fooled systematically (this fact will be very important for the Central Bank). So, adaptive expectations and rational expectations are two different assumptions: in the first case, agents are myopic since they do not look for additional information before deciding, but they look just at the past (and so, a lot of mistakes can be done), while in the latter case all the information available are used to take a decision (and so the forecast error is on average 0). THE MODEL Let’s draw the Philips curve πt - πt e = - α (ut - un ) and let’s call it PSs, meaning that it is the Philips curve in the short- term. Let’s take the intersection A of this curve with the x axis: if this point on the x axis is u = un, it means that, in corresponding to this point, effective inflation is equal to expected inflation. Since it is the x axis, the effective inflation is zero, and so even the expected one. So, this is the Philips curve when expected inflation is zero. Let’s p̃ 5 10 15 20 25 Probability 0,1 0,2 0,4 0,2 0,1 fe 5-15 10-15 15-15 20-15 25-15 Probability 0,1 0,2 0,4 0,2 0,1 Different strategies to decrease inflation Let’s take as a reference the Seventies, in which the inflation rate was high, and the Central Bank wants to reduce it, for instance from 10% to 2%. The CB controls the MM curve, and to reduce inflation it must do a monetary policy tightening. It is possible to follow two different ways: gradualism and cold shower approach. GRADUALISM. With gradualism, the CB firstly decreases a bit the rate of money growth (little reduction), going from MM to MM’. The new equilibrium point is E’ and, as time goes by, agents will review their expectations until reaching, with a new Philips curve, the equilibrium in the long run (point F). However, this was just a little step for reducing inflation; so, CB must reduce again the rate of money growth with a little tightening monetary policy. This process goes on, until reaching the target interest rate. Of course, this approach requires a lot of time to be acted, and so the unemployment rate is larger than the natural level for a long period. However, the unemployment rate doesn’t increase so much during the process, because there are a lot of small steps. COLD SHOWER APPROACH. In this case, the CB acts immediately by decreasing a lot the rate of money growth. The economy goes from point E to point A, but by passing from point C the unemployment rate increases a lot and a big recession can be generated. However, the advantage is that the adjustment is fast. According to the literature if the Central Bank wants to be credible (i.e., a credible policy is a policy that agents think that will be successfully completed), it must use the faster way, so the cold shower approach. Instead, in the gradualism, it seems that the CB is changing is idea. If the CB announces a monetary policy cold shower that moves inflation rate from 10% to 0%, and this is credible for the rational agents, they do not adapt their expectations, but they move immediately the PC, and the system goes directly from E to A. However, once agents fix their wages with an inflation rate equal to 0%, the CB would prefer a point like B, where there is a bit more of inflation but a lower unemployment rate. In this case, the CB is fooling the agents: this because agents believe to the announcement of the CB, so they fix their wages with an inflation rate equal to 0%, and once it is done the CB shifts the monetary policy for reaching the point B. This behavior of the CB is called dynamic inconsistency or time inconsistency. A dynamic (or time) inconsistency policy is a policy choice that was optimal in period t and was no more optimal in t+1. In this case, if agents react and adapt their expectations, they will reach point H, where both inflation rate and unemployment rate is higher; so, in the long run, a dynamic inconsistency policy is not effective. The CB, to be credible and convince the agents that it will not undertake a dynamic inconsistency, has different ways: a. To be an independent Central Bank from the government. In this way, the CB is not incentivized to reduce the unemployment rate in a way that is lower than the natural one, because it matters just about inflation target. In some way, ECB is more independent from government than Fed (USA Central Bank); this because, ECB goal is just to keep inflation at 2% (price stability), while the Fed has got both price stability and keep unemployment low (the third is financial markets’ stability). This difference is given by the fact that the ECB was born in 1999, so it doesn’t have still a high credibility as the Fed. b. The Central Bank Governor has to have long mandates. In this way, during such a long time, the Governor can build his credibility (if he does something wrong, he can be fired). For instance, Draghi was appointed for 8 years. c. A conservative Governor, that dislike inflation very much. It is even called a hawk, while the opposite is a dove (it cares a lot about unemployment). These are names of birds: the hawk has large wings; the dove has small wings. The dimension of the wings tells how much the CB can increase the interest rate (so, a hawk Governor is a Governor that increases very much the interest rates). If inflation rate is very high, the demand is very high (usually), so the CB is going to set high interest rate to reduce it (the investments are lower, the output is reduced, and the price decreases): this is the case of a hawk. Instead, a dove cares a lot about unemployment, and it will keep interest rates low to spur the economy. d. Employ a simple and accountable rule that is understandable by all the agents (e.g., the CB is going to set the rate of growth of money equal to zero). Flattering process of Phillips curve Nowadays, the Phillips curve is getting flatter and flatter, almost horizontal. It means that, if the Government/CB wants to reduce the unemployment rate it doesn’t lead to a so much increase in the inflation rate. Another way to see it is to use the impulse response, that shows what happens to inflation rate if there is a reduction of 1% to unemployment. This reaction function shows the response of inflation during different years: as time goes by, the response is becoming lower and lower. This means that the Phillips curve is becoming flatter and flatter. The reasons for this flattering of the Philipps curve are: a. The Central Bank has become more able to anchor inflation expectations, so agents do not expect higher inflation in the future and do not ask for higher wages. So, the inflation rate stays low. b. Since inflation is low, there is a lower proportion of indexations contracts (the proportion is high when inflation is high), wages become lower and there is a lower frequency of wage adjustments, and consequently inflation is lower. c. The bargaining power of workers is decreased. It may happen because firms can ask for workers abroad, so if it doesn’t find workers in the country it can go abroad (even shifting the production abroad). This means that, if unemployment decreases, wages do not increase, since firms can delocalize production in other countries. d. The most credible reason is globalization: prices do not increase so much (inflation) because of the competition with the other countries (hence, prices should be kept low). Hence, even if unemployment decreases, prices do not increase. Monetary policy operating procedures The European Central Bank (ECB) decides monetary policies for the Euro Area (before the introduction of ECB in 1999, monetary policies were decided by the National Central Banks NCBs of all the countries). The Governing Council is the main decision-making body of ECB, done by 6 members of the Executive Board and the Governors of the NCBs of the 19 Euro Area countries. The mandate of the presidents of the ECB is 8 years. The Euro Area consists of all the EU countries that have adopted the euro: Austria, Belgium, Cyprus, Estonia, Finland, France, Germany, Greece, Ireland, Italy, Latvia, Lithuania, Luxemburg, Malta, Netherlands, Portugal, Slovakia, Slovenia, and Spain. It is important to do a distinction between: ▪ European System of Central Banks (ESCB) comprises the ECB and the national central banks (NCBs) of all EU Member States even if they have not adopted the euro (but they are part of the European Union). ▪ Euro system comprises the ECB and the NCBs of those countries that have adopted the euro. The Euro system and the ESCB will co-exist as long as there are EU Member States outside the Euro Area. Consolidated Balance Sheet of the Euro system It is called consolidated because it is the Balance Sheet of a lot of NCBs, those that are included in the Euro System (that have adopted the euro). The schema is represented in figure: ASSETS ▪ Gold. ▪ Foreign currencies. These are the foreign reserves kept by the Central Banks (e.g., Dollars, Yelm, and so on) used to operate in the exchange market. ▪ Government bonds. This is the most important element: Central Banks buy some government bonds, so they are lending money to the Government. However, they cannot buy government bonds on the primary market (market of first emission, in which buying a bond from A means to directly finance A), but only in the secondary one (in this case, there is not a direct financing – in general, CBs buy bonds from commercial banks). In this way, the CBs are independent to the Governments. The fact that the CBs cannot buy Government bonds on the primary market is due to Germany, that says that to enter into a European Monetary Union, it wanted the ECB to have the Statute equal to the one of the Bundesbank (i.e., central bank of the Federal Republic of Germany). This because Germany experienced a bad hyperinflation in the Twenties (1920-1929), and so the Governor of Germany dislike inflation very much; so, when he had to decide to enter into the European Monetary Union with other countries, like Italy5, that didn’t dislike inflation very much, it asks that the new ECB has to be very hawkish, so it has to 5 Before the born of the ECB, the National Bank of Italy, as for all the other counties, had the power to decide the monetary policies for its country: it happened that, until 1981, the NB of Italy had to buy all the Governments bonds that were unsold on the primary market (this increases inflation very much). So, before 1981, the Bank of Italy was not independent from the Government; instead, in 1981, there was the so-called divorce between the Bank of Italy and the Government (called Tesoro). From this point on, the Bank of Italy cannot buy anymore the Government bonds on the primary market. needs money, it asks money to the other banks (i.e., interbank market); instead, during the great recession, banks didn’t trust each other anymore (because they were not sure that a bank had in its portfolio some subprime bonds), and they prefer to keep the money. If r increases (this is a tightening monetary policy), mm decreases (to see it mathematically, the first derivate of mm with respect to r must be computed, and it is negative): this because commercial banks must keep a higher proportion of deposits at the CB, and so banks can lend less, and the effect of the money multiplier decreases. Indeed, in such a case, if banks lend less, the deposits’ level goes down, and money supply goes down as well. Someone puts this monetary policy tool (of reducing r) in the non-standard tools: the standards tools are the one used before the great recession; the non-standard tools are the tools used from the great recession on. However, some others disagree, because it was used for instance during the great recession (it was reduced from 2% to 1%). If cu increases, mm decreases: this means that people deposit less money at the bank. It has the same effect of a monetary policy tightening because there is less money at the commercial banks (deposits go down), that so can lend less. If banks lend less, agents do not get loans, and deposits go down even more. Of course, this is not a monetary policy because it depends on the private agents’ behavior. Central Banks’ ultimate goals The main goals of Central Banks are: a. Price stability (ECB and FED). b. Maximum employment (FED). c. Financial markets’ stability (FED), that means to promote moderate long-term interest rates. So, ECB has a single mandate, that is the price stability (only one to acquire credibility – the ECB is born recently - and to show that the ECB dislikes inflation very much – so, there is not a prefer in output compared to inflation, otherwise there can be the dynamic inconsistency), while FED (Federal Reserve System) has got a triple mandate. According to the FED, if they can reach the first two goals, even the third is reached. So, for the ECB, there is an explicit inflation goal: before 2003, the aim was to keep the inflation below 2%, while in 2003 the aim was changed in keeping the inflation rate below, but close to 2% over the medium term. This means to say that the ECB dislikes even the deflation (and not only the inflation); this because, in those years, the ECB was worried to go in the same direction of Japan, in which there was a high deflation during a recession (prices go down, people do not ask for goods because they wait until the prices go even more down, since they know that there is deflation, demand doesn’t increase and it is not possible to go out from a recession; moreover, if prices go down, wages go down as well). To avoid this liquidity trap of Japan, the ECB stressed not to have a deflation. ECB’s strategy review Some months ago, the ECB decided to change its strategy (this is a point of the ECB’s strategy review), saying that the best solution is to have 2% inflation over the medium term. This target is symmetric, meaning that the Governing Council considers negative and positive deviations from this target as equally undesirable (ECB dislikes deflation as well as inflation). This target is simple, clear, and easy to communicate; this contributes to affect and anchor longer-term inflation expectations (the wage setting is anchored considering an inflation target of 2%). Fed’s Strategy review Even Fed’s strategy changes, in September 2020, when it announced to tolerate higher inflation in policy shift, because they appreciate that it is possible to have a robust job market (low unemployment rate), without causing an increase in inflation: with the previous Phillips curve, for reducing unemployment, inflation should increase; instead, this statement reflects that the Phillips curve is becoming flat, and so to reduce unemployment rate, inflation doesn’t have to increase so much. The aim is to enhance the transparency, accountability, and effectiveness of monetary policy. The changes done are: I. Before the FED would have acted if it saw a deviation from the maximum level of employment (output), so both when unemployment was too high or too low (output too high or too low. This because, if output is too high - let’s assume that the aggregate supply is vertical -, if the aggregate demand increases, there is just an effect on prices, so there could be a high inflation). Now, instead, the FED is going to act only when output is too low (unemployment is too low); this because the Phillips curve is becoming flat, and so if the output is too high, there are not so many problems in inflation (inflation has become very low and stable). II. Fed introduces the procedure called average inflation targeting. So, the target of inflation is on average 2% over time. So, if inflation is 1% today, the Fed seeks to achieve an inflation rate of 3% tomorrow, such that the average is 2%. So, low inflation is compensated with high inflation. This is different from the target of the ECB, that wants to have 2% inflation over the medium term. III. Now, interest rates are very low (near zero), and it is difficult to decrease them more because it means to put the cost of money lower than zero. Monetary policy procedures The ECB has got some instruments for monetary policy: the most important one is the interest rates, because for having a monetary policy tightening it can increase interest rates (the cost of money increases and becomes more expensive to borrow), instead for having an easing monetary policy, it is possible to decrease interest rates. Through these instruments, the ECB wants to reach some ultimate goals: the first one is price stability (i.e., control inflation rate), but there are even others as growth, employment, competitiveness and so on. Let’s assume that the inflation is high, so a lot of people demand goods and there is a lot of money. ECB should act through a monetary policy tightening, so it should increase interest rates (i.e., increase cost of money). Once the ECB touches this instrument (or in general, all the instruments), there is an immediate change of the operating targets, that are, for instance, the quantity of money (if the cost of money increases, usually the quantity of money decreases), other interest rates (e.g., interest rates on loans offered by the banks), the exchange rate. The problem is to understand how it is possible to reach the final goal. The ECB has got two ways to do it: a. One-stage procedure. The ECB changes the instruments; as a consequence, the operating targets change, and the objective is to reach immediately the final goals. b. Two-stages procedure. The ECB changes the instruments; as a consequence, the operating targets change, and the objective is to reach the final goals, by reaching firstly the so-called intermediate goals. In the case of the one-stage procedure, the intermediate goals are not target, but just indicators. So, the ECB looks at these indicators to understand how the economy is evolving (indeed, when ECB uses the instruments, it cannot be sure to reach the final goals, because monetary policy operates with long and unpredictable lags – moreover, a lot of time passes between when the ECB acts and when the final goal is reached). An example of these indicators is the quantity of money, as M1, M2, or M3 (if the ECB increases interest rates, it expects that credits should decrease). If these indicators move according to the expectations, it means the ECB is in the right direction; if not, it has to act again. This framework, that wants directly to affect inflation, is called inflation targeting. In the case of the two-stages procedures, since the ECB is aware that a lot of time passes between when it acts and when the inflation rate will be affected, it decided to fix some intermediate targets that comes before the final goal: an example can be to have as a goal a change in the monetary aggregate (e.g., M3, or even M1 or M2). In particular, if the ECB increases interest rates (monetary policy tightening), it expects the monetary aggregate to go down. So, the first aim is to reach this explicit intermediate goal; when it is reached, the ECB tries to reach the final goal. The framework with the two-steps procedures and the monetary aggregate (M) as an intermediate goal is called monetary targeting: indeed, even if the final goal is inflation, before reaching it, the ECB puts a first goal about the monetary aggregate. Since monetary policy affects output and inflation with long and unpredictable lags (so, the ECB cannot be sure about the results and a lot of time passes between the use of instruments and the ultimate goal), Friedman claims that monetary policy should adopt an intermediate target, as for example the rate of money growth or the monetary aggregate. However, the problem with a two-stage procedure is that it requires a stable relation between intermediate and final targets (stable means that, when M3 decreases, inflation decreases – so, they must be linked with a stable relation) and a tight relation between (instruments) operating and intermediate targets (tight means that the ECB must be sure that by increasing interest rates, it will decrease M3). ECB’s Monetary policy strategy Nowadays, the most important CBs are all using an inflation targeting approach (one-step approach), of course with different degrees of flexibility. In particular, the ECB’s monetary policy strategy was this one; however, it was slightly changed with the Monetary Strategy Revision. The strategy before June 2021 followed a so-called two-pillar approach: 1. Monetary analysis. The ECB looks at some monetary indicators, among which the most important one is M3 (but it is not a target), to understand how inflation is changing. This exploits the long-run link between money and prices. It may lead to think that it is a two-stages procedure; however, it is not, but it can be defined as a mixed strategy, since there is even the second pillar, that is the economic analysis and it is more similar to a one-stage procedure, since the ECB looks at same indicators. 2. Economic analysis. The ECB looks at some indicators that are short-medium term determinants of price development, to get how prices are evolving. To do so, the ECB regularly reviews: a. Real activity and financial conditions, so developments in output, demand, and labor market conditions; a broad range of price and cost indicators, fiscal policy, and the balance of payments for the euro area; it also includes a thorough analysis of shocks hitting the euro area economy. b. Asset prices and financial yields, to derive information about the expectations of the financial markets, including expected future price developments. c. Macroeconomic projections. The ECB does these projections to forecast future inflation. According to the new strategy, there is no more a huge difference between the two pillars (monetary analysis and economic analysis), but they will be linked somehow to describe the whole situation. These 3 interest rates give rise to the so-called ECB interest rates corridor, show in the figure: the blue line is the cost of money; the yellow line is the marginal lending facility rate; the red one is the deposit facility rate. Looking at the figure, after the Great Recession (2008-2009), the ECB decreases a lot the cost of money (and all the other interest rates), until reaching the so-called zero-lower bond (0%). The idea was to spur economic activities (monetary policy easing), but they couldn’t go under 0%, otherwise it is a mess. However, when the 0% was reached, the economy was still in recession. To overcome this, the ECB started undertaking some non-standard tools. At the moment, the cost of money (on OMOs) is equal to 0%; the marginal lending facility rate is 0,25%; the deposit facility rate is -0,5%. The fact that the ECB fixes a negative deposit facility rate is a non-standard tool: it is done to incentive bank to lend to the market and firms, and not to deposit the excess reserves at the ECB. In turn, this negative deposit facility rate has a huge effect on the interest rates paid by agents for deposit money at the commercial banks. The Taylor rule The idea is to understand how the Central Bank chooses the policy rate (so, how it should decrease or increase the nominal interest rate). Let’s consider United States, that have a double goal: i) price stability ii) full employment. John Taylor wrote in 1993 the following rule, called Taylor rule, that links the interest rate to deviations of inflation from the target and deviations of output from the potential one. For this reason, it is even called the reaction function, since it tells how the ECB reacts when inflation and output change. 𝑖𝑡 = 𝑖𝑡 ∗ + 𝛼(𝜋𝑡 − 𝜋 ∗) + 𝛽(𝑦𝑡 − 𝑦 ∗) + 𝜀𝑡 In the formula: ▪ 𝑖𝑡 is the nominal interest rate decided by the ECB, so it is the dependent variable. ▪ 𝑖𝑡 ∗ is the target interest rate, called nominal natural rate of interest or nominal neutral rate of interest. In the Neoclassical model, the natural interest rate was the interest rate that takes in equilibrium the goods market and the bond market. In the Taylor rule, 𝑖𝑡 = 𝑖𝑡 ∗ if both the goals are reached, so when 𝜋𝑡 − 𝜋 ∗ and the output gap is zero; so, 𝑖𝑡 ∗ is the desired interest rate, because it leads to reach the goals. ▪ 𝛼, 𝛽 > 0 are positive parameters that shows how much the interest rate changes according to a change in inflation gap or output gap. ▪ 𝜋𝑡 is the effective inflation rate. ▪ 𝜋∗ is the desired inflation rate, that is 2% (let’s see the goals of Fed and ECB). ▪ 𝑦𝑡 is the effective GDP. ▪ 𝑦∗ is the potential GDP. So (𝑦𝑡 − 𝑦 ∗) is the output gap, even called 𝑥𝑡. ▪ 𝜀𝑡 is an error term, so a residual that contains everything different from inflation and output that affects interest rates. Whenever 𝜋𝑡 > 𝜋 ∗, the inflation is high (people are spending too much), ECB should do a tightening monetary policy, so it has to increase interest rate. In fact: 𝑑𝑖𝑡 𝑑(𝜋𝑡 − 𝜋∗) = 𝛼 > 0 It means that, if the inflation rate increases, and becomes higher than the desired one, the interest rate should go up (since the derivative is positive, when the denominator increases, the numerator increases). The more the CB dislikes inflation, the higher 𝛼. Whenever 𝑦𝑡 < 𝑦 ∗, so there is a negative output gap, the effective output is lower than the potential, so there is a lot of unemployment. Hence, ECB should do an easing monetary policy, by decreasing interest rates, in fact: 𝑑𝑖𝑡 𝑑(𝑦𝑡 − 𝑦∗) = 𝑑𝑖𝑡 𝑑𝑥𝑡 = 𝛽 > 0 If 𝑦𝑡 − 𝑦 ∗ increases, the interest rate should increase. The more the CB dislikes output gap, the higher 𝛽. Hence, the Taylor’s rule tells how the ECB should respond to its goals, that are inflation and output. Of course, if the formula is written with unemployment gap instead of output gap, it becomes: 𝑖𝑡 = 𝑖𝑡 ∗ + 𝛼(𝜋𝑡 − 𝜋 ∗) − 𝛽(𝑢𝑡 − 𝑢 ∗) + 𝜀𝑡 If 𝑢𝑡 > 𝑢 ∗, the ECB should decrease interest rates. Usually: ▪ A governor that dislikes unemployment very much, fixes very low interest rates. It is called dovish governor. ▪ A governor that dislikes inflation very much, fixes very high interest rates. It is called hawkish governor. This Taylor’s rule is usually estimated. In fact, 𝛼 and 𝛽 can be estimated through an ordinary least squares regression: the idea is to take the values of the interest rates 𝑖𝑡 fixed by the ECB during the years, as well as the inflation rates 𝜋𝑡 (while 𝜋∗ is fixed to 2%) and the output gap (the effective GDP can be taken by the data, while the 𝑦∗ is the potential GDP, so it is more difficult to find data about it). By doing a regression, it is possible to find out the values of 𝛼 and 𝛽. Of course, it is really interesting to know the values of these parameters, because it allows to understand how much the interest rates react when the inflation rate deviates from the target and how much the interest rates react when the output gap is not zero. Usually, 𝛼 should be higher than 1 (this is called the Taylor principle): 𝛼 > 1. This because, real decisions (e.g., investment decisions) depend on the interest rates (if interest rates go up, investments go down), but they do not depend on the nominal interest rate, but on the real interest rate (𝑟), that is the nominal interest rate (𝑖) net of expected inflation: 𝑟 = 𝑖 − 𝜋𝑒 If inflation increases by 1% compared to the target (so, from 2% to 3%), the ECB should react by increasing the interest rates. If 𝛼 = 0,5, it means that the nominal interest rate should increase by 0,5% (from the Taylor rule). As a consequence, the real interest rate decreases, because the inflation rate increases more than the increasing in the nominal interest rate. It is not a good policy tightening, because when the real interest rate decreases, private investments will increase, aggregate demand will go up, and inflation goes up as well (so, the effect is of an easing policy because the real interest rate goes down). This is a destabilizing monetary policy. For having a good monetary policy, if inflation rate increase by 1%, the nominal interest rate should increase by more than 1%, so that the real interest rate goes up, and this is a good policy tightening. For having such an effect, 𝛼 must be larger than 1, otherwise there is a destabilization of the economy. To sum up, the ECB doesn’t have the control on the real interest rate but can control the nominal one and have an effect in the first one: indeed, the ECB must increase the nominal interest rate more than the increase in inflation. Initially, in 1993, Taylor assumed for US the following values (for the years 1987-1992): 𝛼 = 1,5, 𝛽 = 0,5, 𝜋∗ = 2%. Fixing 𝜋∗ = 2% was a hard assumption because the Federal Reserve fixed 𝜋∗ at 2% only in 2012 (while Taylor did this assumption in 1993). Usually, the ECB moves the nominal interest rates very slowly and the rule used is the following one: 𝑖𝑡 = 𝜃 𝑖𝑡−1 + (1 − 𝜃) 𝑖?̅? Where 𝑖?̅? = 𝑖𝑡 ∗ + 𝛼(𝜋𝑡 − 𝜋 ∗) − 𝛽(𝑢𝑡 − 𝑢 ∗) + 𝜀𝑡, and 𝜃 is a parameter 0 < 𝜃 < 1 called interest rate smoothing term. So, this is a more complete formulation of the Taylor’s rule. Through this formulation, it is clear that the nominal interest rate that the ECB fixes is an average of two terms: one is the interest rate suggested by the Taylor’s rule, the other is the nominal interest rate the ECB fixed in the previous period. So, the ECB smooths its interest rates and doesn’t directly fix the interest rate suggested by the Taylor’s rule. This because, if it fixes directly that value, it may shock the financial markets (i.e., generate a collapse in the financial markets). To avoid this shock (in the bonds return, stocks return, and so on), the ECB looks even at what it did before. Usually, the smoothing term is very high, meaning that 𝜃 is fixed at 0,8 or 0,9. The figure shows the inflation rate in the US economy until 2005, so it doesn’t take into consideration the Great Recession and the covid crisis. It is possible to make a distinction between 3 periods: 1. 1950s-1960s. Inflation was low and not very variable. Inflation is on average 0 and so 𝜋𝑒 = 0. 2. 1970s, that is the great inflation period (during which there was the oil price shock and the stagflation). Inflation was high and variable. 3. Since 1980s until the Great Recession, the inflation rate was low and stable. This period is called Great Moderation: the output was high (unemployment was low), and inflation was low and stable. There are a lot of papers and theories that tried to understand if this period was so good thanks to good policies or only thanks to good luck. One article is attached here, and it analyzes the monetary policy reaction function (the Taylor rule) before and after the appointment of Volcker (it was appointed in 1979, before him there was a high inflation rate, after him it started go down and the Great Moderation began). In particular, the authors found out very different estimation of 𝛼 and 𝛽 pre and post 1979. In particular, after the 1979, 𝛼 increases, so increase the sensitivity of the interest rate to inflation (interest rate policy appears to have been much more sensitive to changes in expected inflation). The formulation (1) is exactly the Taylor’s rule, where 𝑟𝑡 ∗ is the nominal interest rate, 𝑟∗ is the nominal natural interest rate, 𝛽 is the coefficient of the expected inflation (so it is the previous 𝛼, even if before it wasn’t related to the expected inflation because it wasn’t a forward-looking formula), 𝛾 is the coefficient of the output gap, 𝐸{𝜋𝑡,𝑘|Ω𝑡} is the expected inflation from period t to period t+k computed by using the information set Ω, 𝐸{𝑥𝑡,𝑞|Ω𝑡} is the expectation of the output gap from period t to period t+q. The higher is k and q, the higher the expectations are done in the future. Due to the presence of these expected values, it is called forward-looking reaction function, while the formulation defined above is called contemporary-looking reaction function. A backward-looking Taylor rule uses inflation and GDP of the previous period, and so it is defined as: 𝑖𝑡 = 𝑖𝑡 ∗ + 𝛼(𝜋𝑡−𝑖 − 𝜋 ∗) − 𝛽(𝑢𝑡−𝑖 − 𝑢 ∗) + 𝜀𝑡 A question that arises is why before 𝛽 wasn’t putted higher than 1. Some answers are provided by different economists: a. The Fed saw the natural rate of unemployment to be much lower than it really was (or equivalently, that the output gap was much smaller). To understand this sentence, let’s take a graph with a Phillips curve and a MM curve: the intersection is point A, in which the unemployment rate is supposed to be equal to 1 (this is the effective unemployment rate). Let’s assume that the natural level of unemployment expected by the Fed is very low (so, on the left). If the ECB wants to reach that rate of unemployment, it has to move the MM curve on the left, by increasing the rate of money growth until reaching point B. Of course, inflation is increased very much. So, according to the explanation, the Fed though that the natural rate of unemployment was there; however, the real one was higher than what expected. This means that the ECB could have increased the growth of money less than what it did (it did a too large monetary policy easing), and so even the inflation could have been lower. b. Another explanation is that, at that time (1970), neither the Fed nor the economics profession understood the dynamics of inflation very well, because no one was emphasizing the importance of inflation expectations. To explain it, it is necessary to come back to the Phillips curve: before the Seventies, the inflation rate was on average zero and the original Philips curve could be used (because it was possible to expect an inflation rate equal to zero), while after the Seventies it becomes high and persistent, for this reason the Phillips curve with augmented inflation expectations must be used (because it was necessary to consider a positive expected inflation). So, since at that time the expected inflation was not taken into consideration, the ECB didn’t react to it, and didn’t increase the nominal interest rate very much. Definition. A central bank that leans against the wind is a central bank that decreases the interest rate when inflation is low, and unemployment is high. Indeed, if inflation is low, the Taylor rule tells to decrease the interest rate; if unemployment is high, it means that the output gap is negative, so the interest rate should decrease. Hence, a CB that leans against the wind is a central bank that has got both 𝛼 and 𝛽 higher than zero. CONSTRAINTS TO CONVENTIONAL MONETARY POLICY: THE ZERO LOWER BOUND Following the GFC (Great Financial Crisis) in 2007 (the figure in the left shows a huge decrease in the real output growth during that years), all the CBs in the world started to decrease the interest rate. Indeed, the figure in the right shows that, after the Great Recessions, all the banks tried to spur the economy by using the standard tool of decreasing the nominal interest rates (monetary policy easing), until reaching the ZLB (zero-lower bound, that is 0%). However, the economy needed further easing because the economy didn’t go out from the recession. The solution was to use non-standard (unconventional) monetary tools. To describe the monetary transmission mechanism (or interest-rate channel), one way is to use the IS-LM curve. If the ECB wants to go out from a recession, it increases the quantity of money, and the LM shifts to the right and this leads to a decrease in the interest rates: then, the chain of event is that the cost of money decreases, investments will go up, the AD will go up, and so output increases (this brings, if possible, the economy out of the recession). However, real decisions: a) Do not depend on the nominal interest rates (the IS-LM model doesn’t make a distinction between nominal and real interest rates, because prices are fixed and inflation is zero, and so real = nominal), but on the real interest rates computed as 𝑟 = 𝑖 − 𝜋. b) Depend on long-term interest rates, and not just on short-term interest rates. For the expectation theory, long-term interest rates are an average of the future short-term rates (and this is an expectation). So, for having firms to invest, it is necessary to decrease real long-term interest rates. Once the interest rates reach the ZLB, the economy can find itself in the so- called liquidity trap (note that this doesn’t always happen, but can be), that is obtained in the IS-LM curve when the LM curve is horizontal: indeed, if interest rates are close to zero, agents expect that interest rates in the future can only go up and so they wait tomorrow to buy bonds (because the price will go down, since there is a negative relationship between bonds’ price and return) while today they want liquidity; so, they keep money today for buying the bonds tomorrow (all the money putted by the ECB in the system, are kept under the pillow). In this situation, fiscal policies are very effective (people expect interest rates to go up, but they do not go up and so there is not crowding out effect of public investments – this is why Obama package of fiscal expansion worked in 2009), while monetary policies are not effective at all (the money given to the economy is not used to lend and buy bonds but will be kept under the pillow). When nominal interest rate is at zero, to affect real interest rate it is not possible to decrease the nominal one even more, because if the nominal becomes negative it will be very difficult to manage liquidity on the market. For decreasing the real interest rate (𝑟 = 𝑖 − 𝜋) and spur the investments on the market, the only way is that expected inflation should increase. If expected inflation goes up, it means that the economy was spurred. So, the ECB must try to increase the expectation of inflation on the agents: if they expect that tomorrow inflation goes up, they will spend today. However, in those years, inflation was actually going down, and so real interest rate went up (this was a tightening, no one invested): this was a huge problem, because the recession was worsened (to go out of a recession, real interest rate must go down). The figure shows the inflation in those years and how it went down during those years: deflation is a problem in particular during a recession, because people wait to buy goods since they expected they will cost less. Moreover, if prices go down, even wages go down and agents cannot afford to buy goods. Hence, it is not possible to go out from a recession. This problem is called deflation spiral. The situation now is different because after the pandemic the economy has got a problem of inflation; however, economists don’t know if this inflation is transitory or persistent (there are a lot of articles about it). If the inflation is permanent, the Federal Reserve should act; otherwise, if the inflation is transitory, the Federal Reserve can go on putting liquidity in the market with the aim of reducing unemployment. The same holds for the other Central Banks. The Yield Curve As said above, investments are affected by long-term real interest rates. So, to spur the economy, the CB should affect them. These long-term real interest rates are defined by the expectation theory as an average of the short- term interest rates. So, long-term rate is a function of today’s short-term rate (they can be seen on the market by looking at what the Federal Reserve fixes in a given period) and expected future short-term rates (for the future short-term rates, some expectations must be done). In other words, according to the expectations theory, there is not a liquidity premium since long-term interest rates are just an average of short-term ones. Hence, since decisions of investment by firms depend on long-term interest rates, for increasing these investments (and so reducing long- term interest rates), Governors should affect agents’ expectations on future short-term interest rates (so, if the Governor fixes a low interest rate today, it should even convince that the interest rates will remain low even in the future, otherwise he cannot affect long-term interest rates). The Yield curve shows the relationship between the yield of a bond and its maturity. Information on expected future short-term rates can be implied from the Yield Curve. Usually, the Yield Curve is upward sloping, meaning that the longer the maturity, the higher the yield: this means that the market expects the inflation to go up, because it expects that in the long run the interest rates go up (the other reason can be that investors ask a large liquidity premium to hold long term bonds – however, this is not contemplated by the expectation theory), and usually the Central Bank increases inflation when interest rates are high (Taylor rule). So, to increase investments today, the CB should convince agents that the future short-term rates will be low as well, and so that the yield curve doesn’t go up. Another way to do this is that the CB buy long-term bonds (on the secondary market) to have an increase in demand, so an increase in price, and finally a decrease in the return. This was done through the quantitative easing (it is like an open market operation characterized by a definitive purchase). As shown in the following figures, the Yield curve can assume different values: it can be flat, downward sloping, U shape, and so on. Usually, the Yield Curve can predict recessions and so business cycle. Indeed, by putting together: 1. The term spread, that is the difference between the Yields on 10-year bonds and 90-day Treasury securities. In the graph, the term spread is the dotted line, and represents the slope of the Yield curve. 2. The recession dates. It is possible to see that the spread decreases before the recessions, as shown in the following figure. It other words, an inverted Yield Curve signals a recession. This happens because, usually, before a The ECB started buying assets from commercial banks in March 2015 as part of its non-standard monetary policy measures. These asset purchases support economic growth across the euro area and help us return to inflation levels below, but close to, 2%. The differences between quantitative easing and a standard open market operation are that: I. During open market operation, bonds are usually short-term bonds, while in the quantitative easing are long-term bonds. II. During open market operation, bonds are just collaterals taken by the CB when the commercial bank gives back the money, while in the quantitative easing the CB buys bonds (it becomes the owner and so these bonds will be in the asset side of the Balance Sheet of the Central Bank). The figure shows how many bonds the ECB bought after the Great Recession in Eurozone, US, UK, and Japan. Before the Great Recession, the size of the Central Bank Balance Sheet was very low, while then it started to buy a lot of bonds to give liquidity to the market. A particular thing of the QE is that the purchases are based on the equity share of member countries in the ECB (so, the NCB’s shares in the ECB’s capital is looked): it means that the ECB will buy more bonds from countries that have a bigger share of ECB’s equity. The equity shares of each country (and the amount of bonds the ECB can buy from them) are reported in the table: Germany is at the first place. Due to the pandemic, this rule was partially overcome because every country needed a lot of money. The figure shows the declaration of quantitative easing in 2015 when the Governor was Draghi. The sentence they are intended to be carried out until end-September 2016 is a forward guidance, and the CB is going to buy both private and public securities. The sentence achieving inflation rates below, but close to, 2% cannot be said anymore today by Lagarde, because now the goal is at 2%. The concept of continuing the quantitative easing until reaching the objective of inflation is done to affect expectations: indeed, the CB is going to be liquidity not just now, but even in the future, so agents should believe that inflation will go up. Nowadays, there is a quantitative tightening era because there is inflation, and if it is permanent, it is not possible to go on by putting liquidity into the system otherwise inflation will go up even more. Hence, some CBs (Bank of Canada and Bank of Australia) are beginning to taper, so to slow down the purchase of bonds. So, a tapering is not a monetary policy tightening, because the CB is not putting away money from the system: it is just buying less bonds (e.g., from 10 to 8), but it is continuing to buy them. Instead, a true monetary policy tightening happens when there is an increase in the interest rates. So, according to the article, there is not a new regime since the FED, ECB, and the Bank of Japan will not do monetary policy tightening: instead, it will continue to be a quantitative easing era, even with a lot of tapering. UNCONVENTIONALS MONETARY POLICIES post Pandemic On 30 September 2020, Christine Lagarde said: “What should be the standardized toolkit for a world where unconventional policy is “normal”. The implicit assumption since 2008 has been that policy “normalization” will mean returning mainly to interest rate policy and winding down unconventional policies. But if “normal” is closer to what we saw before the outbreak of the pandemic and, I am afraid, what we are seeing even more vividly now, we need to be prepared.” So, after the Pandemic (Great Recession), the idea was that it could be possible to go back to standard monetary policies, so to interest rate policies, and to end quantitative easing; indeed, after the Pandemic, there were no more interest rate policies, since the Zero-Lower Bound was reached. Lagarde said that it is better not to have the illusion to go back to the standard monetary policies: according to her, even due to the pandemic, it is necessary to go on with quantitative easing and keep, for some time, the interest rates at zero (there cannot be monetary policies easing changing the interest rate). The Governing Council meetings in March, April, and June 2020 have left the key interest rates unchanged: a. The main refinancing operations (MRO) is at 0.00% since March 2016. b. The marginal lending facility is at 0.25% since March 2016. c. The deposit facility is at -0.50% since September 2019. What instead change was the asset-purchase program that was called Pandemic emergency purchase program (PEPP). This was announced on 18 March, and it is a new, temporary program for public and private sector asset purchases for a total of €1,850 billion (this amount was updated several times, because there was the decision to increase it). As shown in the figure, it can be seen that the PEPP is much larger than all the APPs that were before. It is interesting to see that not just monetary policies, but even fiscal policies intervene to face the pandemic. There were two mechanisms: 1. The European Stability Mechanism, that was decided in 2012 by Member States of the Euro area with the aim of helping the countries that were in financial distress. This mechanism provides emergency loans to countries, but they must undertake reform programmes, that were: a. Fiscal consolidation (spending cuts, tax increases, privatizations, …). b. Structural reforms to stimulate growth and increase competitiveness. c. Reform of the financial sector. For this reason, countries were not sure about accepting or not these loans. 2. The Recovery Fund was composed by grants and loans (that must be repaid). Italy is the biggest recipient, that takes €209bn of liquidity, made up by €81bn grants and €127bn in repayable loans. Even in this case, there are some conditions to be fulfilled: the countries must invest the money in: a. Green and digital transitions (from 5G to Artificial Intelligence). b. Clean hydrogen to offshore renewable energy. c. Health. Then, each country must prepare a national recovery plan to be approved by the Commission and the Council, in which there is the explanation of how the country intends to use the funds. So, countries must be accountable for the investments. Of course, if one country realizes that another country is not fluffing the recovery plan, it can intervene. It is important to stress another huge problem, that is larger than covid-19 and recession, that is the climate change. The monetary strategy of ECB changes to consider climate change factors. MONETARY-FISCAL INTERACTIONS To face the pandemic, both monetary and fiscal policies were used, and there are very important interactions among them. Let’s have a graph with x axis the bonds and y axis the interest rate, and let’s draw the equilibrium for bonds: so, there is the bond supply curve (downward sloping – delivered by firms or Governments, so from the ones that want to invest: for this reason, it coincides with investments) and the bond demand curve (upward sloping – coming from households, for this reason it coincides with savings). The equilibrium E is at the intersection between investments and savings. If the Government sees a bad situation due to the pandemic, it can decide, for instance, to give transfers (benefits to households that are suffering the recession), and so to increase the public expenditure, without increasing taxes (otherwise the recession worse, because output decreases with an increase in taxes). This fiscal policy leads to an increase in debt: so, the Government issues bonds (collection of money from the market) to increase these transfers and consequently the bond supply goes to the right (red line). The new equilibrium point F is characterized by a higher interest rate on bonds. So, the fiscal policy leads to an increase in the interest rate, and so there is the crowding out effect, meaning that private investments decrease. The fiscal policy can be more effective if there is no crowding out effect: to avoid a crowding out, interest rates must remain the same, and for having that there must be someone that buy bonds and shifts the bond demand to the right (green line) until reaching the new equilibrium G. In this scenario, the fiscal policy doesn’t lead to a decrease in private investments. The agent that bought bonds during the pandemic was the Central Bank through the quantitative easing. Usually, the Governor of the Central Bank doesn’t talk so much about fiscal policies because he is interested in monetary policies. Instead, on 11 November 2020, Christine Lagarde said: For having a sustainable debt/GDP as time goes by, it is necessary to have ∆𝑏𝑡 ≤ 0, so the debt should not increase (or equal to zero, or lower than zero): (𝑖 − 𝑔)𝑏𝑡−1 + 𝑑𝑡 𝑝 ≤ 0 → 𝑑𝑡 𝑝 ≤ (𝑔 − 𝑖)𝑏𝑡−1 The more 𝑔 − 𝑖 > 0, so 𝑔 ≫ 𝑖 (rate of growth of GDP larger than the interest rate on debt), the higher the probability that the previous condition is verified. Nowadays the cost of money is zero, while the rate of growth of GDP is very high because last year it was very low: hence, now there are no problems on debt sustainability. The problem will arrive when the interest rates begin to increase. If the inflation that can be seen today ends up being permanent, CB would increase interest rates: if they became higher than the rate of growth of GDP, this would give huge problems in terms of debt sustainability. This is obvious because the higher the interest rate, the higher the money that Government should give to households as a return for its bonds. The formulation 𝑑𝑡 𝑝 ≤ (𝑔 − 𝑖)𝑏𝑡−1 allows to understand where the 3% and 60% of the Stability ang Growth Pact comes from. The deficit is defined as primary deficit plus interests on bonds: 𝑑𝑡 𝑝 = (𝑔 − 𝑖)𝑏𝑡−1 → 𝑑𝑡 = 𝑑𝑡 𝑝 + 𝑏𝑡−1𝑖 = 𝑔𝑏 − 𝑖𝑏 + 𝑖𝑏 = 𝑔𝑏𝑡−1 When the Stability ang Growth Pact was done, the average of 𝑏 = 𝑑𝑒𝑏𝑡 𝐺𝐷𝑃 in the European Union (in the 90s) was 60%; moreover, they assumed a 𝑔 for the future equal to 5%. Hence, 𝑑 is equal to 3%: this value comes from assumptions of 𝑏 (that is an average of debt/GDP in the 90s) and of 𝑔 (this assumption is very strange, because the European Union has never had in normal time a so high rate of growth of GDP). For this reason, the value of 𝑑 is very criticize. MONETARY-FISCAL INTERACTIONS: a step ahead This is related to the most recent monetary-fiscal interactions. The starting point is the DSGE model (dynamic, stochastic, and general equilibrium) in which there are: ▪ A kind of IS equation, called Euler equation. ▪ A Philips curve, called forward-looking Philips’s curve. ▪ A reaction function, that is a monetary policy rule, as the Taylor’s rule (it tells how the CB should react when inflation gap and output gap change). This DSGE model done with these 3 equations is the easiest one in the literature, for this reason it is called the Mickey-Mouse model. However, among these 3 equations, there is no one that tells explicitly something about fiscal policies: they are hidden somewhere behind this DSGE model. In this model, the assumption behind fiscal policy is that the Government always respects its intertemporal budget constraint, so it always adjusts its budget constraint. The budget constraint of the Government is built in the following way; let’s assume that at time t-1 the Government decides to issue new bonds; then, not to have a deficit on the budget balance 𝑆𝑡, it must increase taxes (since the budget balance is 𝑆𝑡 = 𝑇 − 𝐺 − 𝑇𝑅, if the Government increases G, for having 𝑆𝑡 = 0 it must increase taxes in the same amount), so there is an increase in the surplus from time t to infinite. It is necessary to put a E behind the surplus because it is known just for period t, while for the others it is expected (expectations of future surplus). The following one is the intertemporal budget constrain of the Government: 𝐵𝑡−1 𝑃𝑡 =∑𝜌𝑗𝐸[𝑠𝑡+𝑗] ∞ 𝑗=0 𝐵𝑡−1 is the nominal bond; 𝐵𝑡−1 𝑃𝑡 is the real bond, that consider the price level at time t; 𝜌𝑗 is a discount factor, because what happens tomorrow is discounted differently compared to what happens in twenty years from now. According to DSGE model, whenever there is a change in the left-hand side, the Government is prepared to have a change in the right-hand side. If this intertemporal budget constraint is always in equilibrium (the equation above is always verified), it is possible to avoid putting this equation into the model (it can be disregarded). The important thing to understand is that, if the Government issues new bonds, it doesn’t have to increase taxes immediately, it can even promise agents that it will increase taxes in the future (because in the formula there is the sum of expectations). This framework is called regime M, or regime of monetary dominance: indeed, monetary policy can be seen through the reaction function, instead fiscal policy, even if present, is passive, meaning that it is ready to keep its intertemporal budget constraint balanced. In this regime, monetary policy has an active role (AM – active monetary policy), meaning that the CB acts to stabilize inflation. So, it decides inflation target and: o If inflation increases, CB will increase interest rates (for the Taylor rule – it is a monetary policy tightening). o If inflation decreases, CB will decrease interest rates. Instead, fiscal policy has a passive role (PF – passive fiscal policy): the role of the Government is just to stabilize debt, meaning that whenever it increases debt, it must increase taxes. Let’s assume that inflation is high and so CB acts by increasing interest rates: if CB manages to do so and decrease inflation, prices will go down. In the model, 𝑃𝑡 goes down, and so the left-hand side of the intertemporal budget constraint goes up. This leads to a disequilibrium: to avoid it, the Government should increase the right-hand side, hence it must increase the surplus, for example by increasing taxes or reducing public expenditures now and in the future. Instead, if the Government doesn’t act, the real debt 𝐵𝑡−1 𝑃𝑡 goes up (because 𝑃𝑡 goes down): it means that the agents who have those bonds are now richer, because those bonds have a higher value (this is called wealth effect). Due to this wealth effect, households can spend more: consumption increases, aggregate demand increases (supply is supposed to be fixed), and this brings to an increase in prices. Hence, this goes against the job of the CB, that increased interest rates to decrease prices. To avoid this wealth effect, the Government should increase taxes because in this way people are not going to increase their consumptions. Hence, in the regime M there are no wealth effects (because Government is passive and if there is an unbalance in the intertemporal budget constraints it acts to fix it) and the Ricardian equivalence holds: according to the Ricardian equivalence theory, if the Government increases public expenditures and finances it through new bonds (agents became richer), and agents know that it is going to increase taxes in the future (to finance the increase in G), the agents’ consumption decisions are not affected by this policy: this because the higher richness of today is saved to pay taxes in the future. Hence, according to the Ricardian equivalence, there are no wealth effects and agents do not spend the higher wealth they have got because they know that in the future taxes will be higher. So, in this case, debt stability is due to an active monetary policy and a passive fiscal policy (the Government is ready to answer to every CB’s action to respect the intertemporal budget constraint). However, in the literature, there is another regime, called fiscal regime, but it is not so frequent. In this case, the opposite holds, meaning that there is active fiscal policy and passive monetary policy. Hence, the Government does what he wants, without caring about the intertemporal budget constraint: so, if it wants to increase public expenditure, it can do it; if it wants to increase bonds, it can, without having the duty to increase taxes. Instead, the Central Bank has got the commitment to stabilize debt. Of course, this is strange, because generally CB controls just monetary policies. Let’s assume that the Government increases public expenses (or transfer), as done during the pandemic, so it issues new bonds, so the right-hand side of the intertemporal budget constraint goes down (the surplus decreases). This leads to wealth effects because there are more bonds available that arrives to more agents who becomes richer and can afford a higher consumption; this leads to an increase in aggregate demand, and so an increase in the price (increase in inflation). The denominator of the left-hand side of the intertemporal budget constraint increases. If the CB does its job, when it sees an increase in inflation, it must increase its interest rates. Instead, in this case, monetary policy is passive, meaning that it must do just what is necessary to stabilize debt. To do so, the CB should not react to the increase in prices: indeed, the right-hand side of the intertemporal budget constraint goes down, and the same for the left-hand side, because there is an increase in price and so there is a reduction in real debt. This is a way to say that it is possible to avoid problems with debts by deflating the debt: if inflation increases, the value of the debt decreases, and this is a way to make debt sustainable. By looking at these two regimes, the final consequence on inflation and on debt depends on agents’ expectations about what Government will do. Agents’ expectations are important in monetary policy because of the forward guidance: the Government should be ready to anchor expectations of the agents: if agents do not expect a future increase in taxes, the mechanism doesn’t hold (and this is a problem for the Government). This aspect is crucial nowadays with Biden that had increased a lot the public expenditures and the transfers to face the pandemic: this will be effective only if agents do not think that taxes will increase in the future. Indeed, if the Government gives a transfer and people do not expect an increase in taxes, they will spend the transfer and the GDP increases. If instead they expect an increase in taxes, they will keep the transfer to pay taxes in the future. For this reason, even fiscal forward guidance should be applied (tell people what the Government wants to do with taxes). The same for buying bonds or not. the market fells insured against big losses and so they can get more risk. Agents knows that there is a safety net, represented by the CB. During the period of Greenspan, this safety net was called Greenspan put (it was like an option). The Taylor rule: a benchmark for monetary policy? This figure shows the actual interest rates of the FED and the interest rates suggested by the Taylor rule: it is possible to observe that the CB, during the boom (2003-2005), takes the interest rates too low compared to the one prescribed by the Taylor rule. It means that the Central Bank gave a lot of liquidity (easing monetary policy for a lot of time), and this helped the boom in the asset prices. This deviation was a major source of the housing bubble and other financial excesses. Empirical evidence (1987-2003) In the Taylor rule there are inflation gap, output gap, and an error term (residual term), in which there are all the variables that are different from inflation gap and output gap that affect interest rates. In the analysis in figure, the authors decide to pick out from the residual even the Standard & Pool index (that is an index on asset prices), so they assumed that the Central Bank explicitly reacts even to a gap in this index: 𝑖𝑡 = 𝑖𝑡 ∗ + 𝛼(𝜋𝑡 − 𝜋 ∗) + 𝛽(𝑦𝑡 − 𝑦 ∗) + 𝛾(𝑆𝑃𝑡 − 𝑆𝑃 ∗) + 𝜀𝑡 The sign behind 𝛾(𝑆𝑃𝑡 − 𝑆𝑃 ∗) is a plus because if 𝑆𝑃𝑡 > 𝑆𝑃 ∗ it means that asset prices are very high, and so the Central Bank should increase the interest rates. The figure on the left shows the actual and fitted values obtained through the standard Taylor rule (without S&P); in the right side, the reaction function considers even S&P. Among them, the figure on the right better describes the actual interest rates: it means that, at least in these years, the FED reacted to the stock market (so to the S&P index). ‘Bubbles and crises’ by Allen & Gale (2000) According to Allen & Gale, very often, after an asset price bubble there is a financial crisis that leads to a very big recession. Hence, usually there are 3 different phases of the bubble: 1. Financial liberalization or CB decision to increase in credit that makes asset prices increase (agents have more credits, they increase the demand for assets and so asset prices have a boom). This process lasts a long time and forms a bubble. 2. Bubble bursts and asset prices crash. It happens in a few months or days. 3. Firms’ failures and even failure of agents who borrowed to buy asset at high prices. Asymmetric information and Credit market imperfections The idea is to see how asymmetric information and credit market impefections can lead to some links between the monetary-financial part and the real economic part. FINANCIAL INTERMEDIATION The existence of financial intermediation (i.e., banks) has important consequences for: I. Economic system growth. According to Gurley and Shaw the financial system has evolved during the years following these steps: i. At the beginning, it was a self-financed investments system, meaning that people needed to have money for undertaking an investment. ii. Then it became a system characterized by investments financed by direct bilateral credit relationships in which, if an agent wants to do an investment but doesn’t have money, it had to search for someone that lends him money. iii. Then, it evolved in a system characterized by investments financed by intermediated credit relationships. Hence, there is a banking system in which agents who have got funds deposit them in the bank, and then the bank lend money to agents that need it: these systems are even called a bank-oriented systems. iv. Again, it evolved into a system in which investments are financed by more sophisticated financial instruments. These systems are called market-oriented systems, because done by a lot of market instruments7. According to Mayer, these market-oriented systems suffer from shortermism, meaning that private agents usually want to maximize the immediate return of investments, so they don’t want to wait the future for having a return to their investments. Instead, according to his critique, banks allow a more efficient resource allocation and a higher rate of growth because banks finance investments whose return will show up in the future and moreover, they can, during a recession, go on with their credit lines (it means that, during recessions, even if there is a temporary difficulty, banks don’t cut their credit lines with customers, but they go on giving some credits – obviously not for a lot of time, but for some months they continue). This critique can be seen as a reason for with banks are special agents. II. Business cycle, that is the cycle that goes around the trends (there are some booms and some recessions). Friedman and Schwartz, in their publication, looked at the movement of money during the recessions (business cycles), and they found out that monetary movements are tightly linked to recessions. In particular, they discovered that every recession between 1867 and the Second World War in U.S. goes together with a reduction in money supply (so, before every recession there was a reduction in money supply). More in detail: i. Recessions pre-WWII were mainly linked to bank panics (i.e., depositors run to the bank to withdraw their money). ii. Recessions after-WWII were mainly linked to credit crunch and disintermediation (resources that leave the banking system – there is an increase in the ratio bonds over deposits). Another important theory about the business cycle is the one of Reinhart and Rogoff that built a database of 100 financial crises of the past 200 years and found out that recoveries after financial crises were weaker and more protracted than those after other recessions. So, if there is a financial crisis, this has a larger impact on the economy and so there is a big recession. 7 Thanks to these systems, there was the development of cartolarization: it means that a bank pulls all the credits (loans) that has got toward customers into some bonds that can be sold to third parties. The importance of banks Banks are special agents for different reasons: a. They reduce transaction costs by exploiting their increasing return to scale. Usually, banks trade high sums and face transaction costs, legal costs, and cost of finding the counterparts that are lower than those faced by private agents, hence they can exploit increasing return to scale. This reduction in transaction costs give them an advantage. b. They can reduce portfolio risk by exploiting diversification. The high dimensions of a bank, that trade high sums and deal with a lot of customers, allow a reduction of portfolio risk. This because, by having such a dimension, they invest in different projects and assets whose returns are negatively correlated: if an asset is not a success, there will be another that will perform good, so on average they do not have a loss. These two points (a + b) are putted together in the Diamond model, even called delegated monitoring. c. They act a maturity transformation. To understand it, it is necessary to look at the Balance Sheet of a bank: on the liabilities side there are deposits, while on the assets side there are loans: usually, deposits are short- term because agents can decide immediately to go to the bank and take their money back, while loans are long-term. So, maturity transformation means that banks own relatively illiquid assets, that are the loans to firms and agents, and very liquid liabilities, that are the deposits, and they manage to put together these different needs (of having very liquid deposits and long-term credit lines). The maturity transformation is studied through the Diamond and Dybvig, that shows even the bank panics. d. They acquire information and produce new information to face asymmetric information on the credit market. This happens because banks, before giving credits to agents, undertake screening (before the contract), monitoring (during the contract), and auditing (after the contract) processes that allow to get a lot of information about borrowers. Furthermore, banks know the deposit situation of their customers. The asymmetric information problem in the credit market is shown in the Stiglitz and Weiss model, that is even called credit rationing. ASYMMETRIC INFORMATION Asymmetric information can be divided, if seen in relation to a contract, into 3 parts. So, there is a situation in which an entrepreneur has got an investment, but he need money and so he asks to the bank: when the bank gives the money to the investor, the contract starts; the contract ends when the borrower should back the money to the bank. Having defined this process, there may be 3 kinds of asymmetric information: 1. Ex-ante asymmetric information, that happens before the start of the contract. 2. During asymmetric information, that happens during the life of the contract. 3. Ex-post asymmetric information, that happens after the end of the contract. EX-ANTE asymmetric information The ex-ante asymmetric information is related to an incomplete information on the good’s quality: the problem is that the bank doesn’t know which is the investment that the agent wants to finance, so it doesn’t know if it is a good or a bad investment. The reference model of ex-ante asymmetric information is the market for lemons of Akerlof. The consequence of this asymmetric information is the adverse selection, meaning that only bad investments are financed. The market for lemons model starts with a market characterized by 100 agents that want to sell their car, and 100 agents that want to buy a car. The agents who want to buy a car know only that 50% of the cars are good cars and Let’s suppose to have F entrepreneurs, and each of them has got an investment project that lasts 2 periods (t = 1 and t = 2): in period t =1, the entrepreneurs invest 1$, while in period 2 they receive a return on the investment equal to x̃ (random variable), where x̃ ∈ [xm; xM]. Only the entrepreneurs can observe the value of x̃. Moreover, the expected return of the investments is E(x̃) > 1 + r, where r is the market interest rate (risk-free rate); otherwise, if this condition doesn’t hold, the entrepreneurs are not going to undertake the investment, since it would be better for them to buy a bond that grants 1 + r as a return. However, entrepreneurs don’t have the funds to finance the investments (they do not have 1$), so they should borrow 1$. They have got two possibilities: POSSIBILITY 1. Let’s imagine that there are N potential lenders (agents that have money – both F and N are risk neutral, meaning that their decisions are not affected by the degree of uncertainty): each of them has available a sum that is much lower than 1$, so the entrepreneur that needs 1$ cannot go just to one lender but must ask to a lot of them, suppose exactly N lenders. In this case, the borrower can ask to each lender an amount of money equal to 1 N , with the aim of reaching 1$. In their turn, lenders can decide not to monitor borrower, but in this case, there will be an expected loss (called δ) due to information asymmetry. Instead, if the lenders decide to monitor, each of them should pay γ to monitor how the entrepreneur behaves (how he employees the funds he received), because there is a problem of information asymmetry during the life of the contract (and the solution, as seen before, is to monitor). So, it is necessary to point out that γ is not an auditing cost! Of course, in such a situation, there is a duplication of monitoring costs, because each lender should monitor the borrower: the total monitoring cost is Nγ. POSSIBILITY 2. The borrower can ask the money to a bank, that in turn takes this amount of money from the potential lenders. In this case, the bank should monitor the borrower, and so it pays γ. Between the bank and the borrower there is a standard debt contract (SDC) according to which, if the investment undertaken by the investor is successful, it must give to the bank 1 + r; instead, if the investment is not successful, it must give to the bank the whole return of the investment (the SDC is the optimal contract if there are problem of asymmetric information). Of course, γ < Nγ, hence financial intermediation can avoid duplication costs in monitoring. However, between the bank and the lenders there is the same problem of during information asymmetry that there was in the previous case between the borrower and the lenders: indeed, the potential lenders (in this context they are the depositors for the banks) do not know how the bank is going to employee their money. Diamond shows that potential lenders can incentive the bank to act in their interests by stipulating a standard debt contract: so, there should be a SDC even between the bank and the lenders. This because a SDC tells that the bank should give back to lenders a fixed sum, equal to the deposit plus an interest rate (nowadays, it is zero) if the investments done by the bank are successful: this is a good incentive for the bank to control its asset side and make possible that this asset side give a higher return because, according to the SDC, the bank should give back to the depositors a fixed sum and the whole surplus generated by the asset side is of the bank. So, the return of the bank depends directly on the performance of its asset side and so it is spurred to do good investments (and so the bank is incentive to gain a lot from the lending activity). Moreover, when there is a bank, depositors should pay the so-called delegation cost D for two reasons: I. They want to incentive the bank to undertake a good monitoring on its asset side (so, on the borrower). II. They want to incentive the bank to tell the truth to depositors about the return that the bank has on its assets. To sum up, in this model, borrowers and lenders have got three alternatives: a. Debt contract without monitoring. In this case, the borrower takes the money from the lenders, but they don’t pay any monetary cost (that is the first part of the possibility 1). This is a problem because the lender can have a loss due to the behaviors of the borrower. Let’s call this expected loss δ. b. Debt contract with direct monitoring. In this case, every potential lender monitors the borrower (that is the second part of the possibility 1) and pays γ. As shown above, there is duplication of monitoring costs, for a total amount of Nγ. c. Delegated monitoring meaning that lenders delegate monitoring to the bank (possibility 2), that pays just γ (thanks to bank’s increasing return to scale). So, the bank avoids the duplication of monitoring costs. Let’s remember that there is even the delegation cost D paid by depositors. According to Diamond, delegated monitoring is convenient if and only if the following condition holds: γ + D ≤ min [Nγ; δ] In which γ + D is the total cost associated to the delegated monitoring alternative; Nγ is the cost associated to debt contract with direct monitoring; γ is the expected loss associated to debt contract without monitoring. Let’s imagine that D goes to zero: in such a case, there are two possibilities: 1. Nγ < δ. In this case, the disequation became γ ≤ Nγ, and this is always true. 2. Nγ > δ. In this case, the disequation became γ ≤ δ, and it is reasonable that this condition holds because the cost of monitoring should be lower compared to the expected loss in case of no monitoring (otherwise, no one monitors). Hence, when D goes to zero, the delegated monitoring is the best alternative. Diamond says that the probability of intermediation (delegated monitoring) increases when D decreases. The value of D can be reduced if there is less uncertainty on the bank’s asset side: indeed, if the asset side is certain, the depositors do not pay delegation cost because they know that there are no problems. The bank’s asset side can be certain if the bank can diversify its portfolio (that is one of the reasons for which banks are special), so if number of potential borrowers F goes to infinite: so, if there are a lot of potential borrowers, it means the bank is giving loans to a lot of people and it is highly probable that these people have got returns that are negatively correlated. Hence, diversification makes the return of assets certain. So, delegated monitoring is justified because a bank can: I. Reduce monitoring costs, because it lends to a huge number of lenders (F goes to infinite) and because it has increasing return to scale. Note that, if F goes to infinite in the case of debt contract with direct monitoring, there is not a reduction in monitoring costs. II. Reduce delegation costs since it diversifies the projects it financed. DIAMOND and DYBVIG MODEL – Bank runs, deposit insurance and liquidity This model stresses the importance of banks because they operate the so-called maturity transformation, meaning that banks are able to coordinate different liquidity preferences of the agents: on one side, depositors need to have a very liquid deposits (short-run liability side), on the other, borrowers need to have very long credit lines (long-run asset side). Let’s imagine having: ▪ 3 periods (t=0, t=1, t=2). ▪ N risk averse agents, so agents that don’t like risk. ▪ One technology, that represents the way through which money can be invested. The yield of the investment depends on how long the investment takes, so on the duration of the investment. There are two cases: 1. If the agent invests 1$ in period t=0 and he liquidate the investment at period t=1 (so he wants immediately his money back), he gets 1$. This is called a short-term investment. 2. If the agent invests 1$ in period t=0 and he liquidate the investment at period t=2, he gets R that is larger than 1$. This is called a long-term investment. The assumption at the basis is that, at t=0, every agent has 1$ and he doesn’t want to consume at time t=0 but he uses it to invest. However, agents, at t=0, are uncertain about when they want to consume. So, they do not know if they are impatient agents that want to consume at t=1, and so that will do a short-term investment, or if they are patient agents that want to consume at t=2, and so that will do a long-term investment. If at time t=1 an agent discovers to be impatient, he finds himself in an unlucky situation, because he will liquidate the investment and he will receive just the sum he invested at t=0 (no other returns); instead, if at time t=1 an agent discovers to be patient, he finds himself in a lucky situation, because he will wait time 2 for liquidating the investment and receiving a return. So, the uncertainty at time t=0 of when the agents want to consume allows to understand why the long-term investment doesn’t always dominate the short-term one (R > 1): indeed, just by looking at the return, every agent should prefer the long-term one; however, exactly for the fact that agents do not know if they are impatient or patient, the short-term investment (more liquid investment) can be a better solution. The utility function of the agent is defined as: U = U[ϕC1 + (1 - ϕ)C2] So, it depends on C1 that is the consumption at time 1, C2 that is the consumption at time 2. Of course, C0 is not present because of the assumption of no consumption at time 0. Instead, ϕ is a random variable whose value will be known at time 1. This variable is an IID variable, so it is independently and identically distributed, and each agent has got his own ϕ. The first derivative U’ is larger than zero (U’>0), meaning that the higher the consumption, the higher the utility; however, the second derivative U’’ is lower than zero (U’’<0), and this means that the marginal utility decreases as consumption increases (e.g., if a person is hungry, when he eats the first sandwich his utility increases a lot, instead when he eats the 200° sandwich his utility doesn’t increase so much). For the sake of simplicity, let’s consider this model as a discrete model, so that the random variable ϕ can assume just two values: ▪ ϕ = 0 with probability (1-p). In this case the agent is a patient agent because it will consume just at time 2 (his utility depends just on the consumption in period 2). ▪ ϕ = 1 with probability p. In this case the agent is an impatient agent because it wants to consume at time 1 (his utility will depend just on the consumption in period 1). At period 0, agents do not know the value of their own ϕ; they will discover it at time 1. The expected utility of an agent is defined as the sum between: o Probability of being impatient (ϕ = 1), called p, times the utility obtained in such a case: U = U[ϕC1 + (1 - ϕ)C2] = U(C1) o Probability of being patient (ϕ = 0), called 1 - p, times the utility obtained in such a case: U = U[ϕC1 + (1 - ϕ)C2] = U(C2) So, the general formula of the expected utility of an agent is: p ∙ U(C1) + (1 – p) ∙ U(C2) NOTE. Of course, the continue version in which ϕ can assume all the values between 0 and 1 would be much more reasonable, as well as more complicated. Let’s now analyze what happens in case of autarchy (no banks), so when every agent doesn’t exchange with the others (absence of trades between agents), but every agent behaves as if he was alone. In such a situation, if he realizes to be impatient (ϕ = 1), he will disinvest in period 1 and he can consume a sum equal to 1$; if he realizes to be patient (ϕ = 0), he will consume a sum equal to R in period 2. The expected utility under autarchy is: p ∙ U(1) + (1 - p) ∙ U(R) From this, it can be possible to state that U’(r1) > U’(r2), because U’(r1), U’(r2) are higher than 0 because they are marginal contribution, and R > 1. As said above, the marginal utility is a decreasing function with respect to the consumption r (the second derivative of the utility is negative): hence, if U’(r1) > U’(r2), it must be r1 < r2. So, this is the demonstration that, in the mutual insurance contract offered by the bank to have an optimum it must hold r1 < r2. Demonstrations about r1>1 and R>r2 should be necessary. In this model there are 2 equilibria: 1. The good equilibrium, when the impatient withdraw in period 1 and the patient wait until period 2. 2. The bad equilibrium, when every impatient and patient withdraw in period 1. There is a bank run when all the depositors, at time 1, go to a bank for withdraw their money: so, this situation is restricted to a single bank. Instead, there is a bank panic when the whole banking system is involved, so there is a run to withdraw to all the banks. In such cases (both bank run and bank panic), all the depositors at time 1 withdraw, and banks should give back an amount of money equal to Nr1, that however is larger than N ∙ 1 (the technology gives 1 when the asset is liquidated at time 1). Banks fail because cannot give Nr1: this happens because, in a normal situation, the bank employees the money of the patient agents (that will receive r2 < R, so the bank has a gain) to pay r1 > 1 to the impatient (the bank has a loss), while if even some patient agents decide to withdraw at time 1, the bank doesn’t have the money to pay because he has to liquidate more than expected. However, if r1 < r2 it seems that there is no reason for having a bad equilibrium; however, it may happen. Let’s suppose to have a patient agent that believe that everyone (both patient and impatient) is going to withdraw their deposits at time 1. Of course, as seen above, the bank doesn’t have (N – 1)r1 money and so, following the sequential service constraint just the firsts to come will have the money back. Hence, even this agent will go to withdraw with the aim of arriving in time for having the money back. By applying this reasoning to all the other patient agents, a bank run happens. The solutions for this bad equilibrium are: a. Suspension of convertibility (of giving back money), in which the bank could announce that he will not serve more than pN withdraws (First in First out rule), and so if arrives more than pN people to withdraw, the bank will close (at time t=1) to avoid bankruptcy. So, in this way, the bank is going to liquidate at maximum the expected fraction of investment and will be able to pay r2 to the patient agents in period 2. Just the threat of this suspension of convertibility can be enough to avoid a bank run because agents know they will find their money in the future if they are patient (it is not necessary to realize it, just the threat is enough). b. Deposit insurance, in which the Government ensures the patient agents that they will have their money back in period 2. In the US there is the so-called deposit insurance system. Usually, just the presence of this deposit insurance system can be enough to avoid a bank run. c. Central bank acts as a lender of last resort, meaning that, if the bank is going to fail, the CB (that is the bank of the bank) will intervene giving back the deposits to the agents. So, agents are ensured that, in any case, they will have back their money, so the patient agents will avoid withdrawing at time 1. It is the assumption of too big to fail, meaning that a bank is too big to fail because the CB goes into the economy and gives money. However, this creases a lot of problems in terms of moral hazard: the bank can take more risks because it knows that there is the CB that can give money. Indeed, by looking at the statute of the CB, there is not written explicitly that it acts as a lender of last resort, exactly for avoiding moral hazard problems. In the paper, Diamond and Dybvig write that their model determines three important points: i. Banks issuing demand deposits can improve on a competitive market by providing better risk sharing among people who need to consume at different random times (patients and inpatients). They wrote that: “so, if there is a bank, these people are better off. We showed it with the budget constraint which shifts on the right, and you can see it in the fact that r1 < r2 comes after an optimization problem”. ii. The demand deposit contract providing this improvement has an undesirable equilibrium (bank run) in which all depositors panic and withdraw immediately, including even those who would prefer to leave their deposits in if they were not concerned about the bank failure. This happens when agents lose their confidence about the banking system. iii. Bank runs cause real economic problems because even healthy and solvent banks can fail, causing the recall of loans and the termination of productive investments. Application of Diamond and Dybvig model through Game Theory Since this model has got Nash equilibrium, it is possible to study this model through game theory. Let’s imagine there are 2 investors that want to invest 1$ in a given technology, and both of them are patient. The bank proposes them a contract, according to which r1 is given to the impatient, r2 to the patient, with r1 > 1 and r2 < R. There may be three situations: ▪ If both the agents wait, they will get at time 2, r2. From the 2$ of deposits, the bank will get 2R > 2r2, because in such a case it doesn’t divest anything before time 2. Hence, the bank is in a good financial position. ▪ If both the agents withdraw at time 1, the bank should repay 2r1 > 2 and so it fails. Of course, in such a case, each agent can have back just 1$, because the bank is not able to give them r1. ▪ If only one agent withdraws at time 1 while the other wait, the bank disinvests r1 dollars from the investment 2$ (and will get exactly r1 dollars, because the investment gives 1 if the sum is divested at time 1). So, the agent that withdraws will get r1. The bank will keep invested 2 - r1 dollars: then, at time 2, the bank gets δ = (2 – r1)R and, for the sake of simplicity, let’s assume that everything is given to the patient agent. The equilibria in this situation change according to the value of δ. Let’s have two cases: 1. CASE 1: δ < 1. Let’s suppose to have the following data: r1 = 0.5, r2 = 1.5, R = 1.8, δ = 0.9. A game theory matrix can be drawn. Each agent has got 2 strategies: the first one is to withdraw, the second one is to wait. There are not equilibria in dominant strategy (i.e., a strategy that is always better than the others). For agent 1, withdraw is better when agent 2 withdraw (1 > 0.9), wait is better when agent 2 wait (1.5 > 0.5). The same for agent 2 since the situation is symmetric. However, (withdraw, withdraw) and (wait, wait) are Nash Equilibria: the first one is the bad equilibrium while the second one is the good equilibrium (the definition of the good and the bad depends on the types of agents considered – since in this case they are patient, for them the best is to wait – so, the good equilibrium is an equilibrium in which agents behave as expected). 2. CASE 2: δ > 1. Let’s suppose to have the following data: r1 = 1.5, r2 = 1.6, R = 2.5, δ = 1.25. In this case, there is just one Nash equilibrium that is (wait, wait) and it is even a dominant strategy equilibrium. Hence, having δ > 1 is an incentive for patient agents to behave as expected: in this case, the good equilibrium is reached. Ag. 2 Withdraw Wait Ag. 1 Withdraw 1,1 r1 ; δ Wait δ ; r1 r2 ; r2 Ag. 2 Withdraw Wait Ag1 Withdraw 1;1 0.5; 0.9 Wait 0.9; 0.5 1.5; 1.5 Ag. 2 Withdraw Wait Ag. 1 Withdraw 1,1 r1 ; δ Wait δ ; r1 r2 ; r2 Ag. 2 Withdraw Wait Ag1 Withdraw 1; 1 1.5; 1.25 Wait 1.25; 1.5 1.6; 1.6 STIGLITZ and WEISS MODEL – Credit rationing in markets with imperfect information Credit rationing happens when the demand for credit excesses the supply of credit at the prevailing interest rate: hence, there are some potential borrowers that want to borrow at the current interest rate but that do not get credit (demand > supply), since they do not find a lender. There are 3 kinds of credit rationing: I. Dynamic rationing (it is not the one discussed in the Stiglitz and Weiss model). Let’s take a graph in which the x axis is represented by the quantity of credit (L), and on the y axis the cost of credit (interest rate on loans – iL): in this way, the demand for loans and the supply for loans can be drawn. The equilibrium (L*; IL *) is at the intersection of demand and supply. Let’s imagine, however, that the interest rate is iL,0: in such a case, the demand is not equal to the supply, but demand > supply (excess of demand). This can be due a temporary disequilibrium due to a lack of adjustment of the interest rates. In this case, the amount of credit in the economy is L0 < L*. The difference between these two values represents the quantity of credit that is rationed: all these people would have like to have credits, but they wouldn’t find them. As time goes by, however, the interest rate will adjust and become higher, so that the equilibrium is restored. II. Persistent rationing (it is not the one discussed in the Stiglitz and Weiss model). In this case, the figure is identical at the previous one; however, the reason for which the interest rate is lower compared to the equilibrium one is temporary, but persistent. This can be due, for instance, usury law (that is the law against usuries), according to which it is not possible to fix an interest rate on loans that is higher than a certain threshold (it is exogenously imposed by a legal act). In this case, the excess of demand cannot be satisfied by a movement in the interest rate, since it cannot go up due to these exogenous obstacles in the market to the adjustment of the interest rates. For this reason, the disequilibrium is persistent. III. Equilibrium rationing, that is the one studied by Stiglitz and Weiss. In this case there is not equilibrium between demand and supply due to lenders’ behavior that don’t want to give credit to agents. This happens because there is asymmetric information: the lenders (banks) know that, for reaching the equilibrium, they should increase the interest rates; however, they don’t do so due to 2 phenomena related to asymmetric information: 1. Adverse selection phenomenon. By increasing the interest rate, the bank makes the loan more expensive, and the risk is that the better borrowers go out from the market. 2. Adverse incentive phenomenon (moral hazard). By increasing the interest rate, the bank can give an adverse incentive to borrowers to behave in the wrong way (investors think not to be able to pay the loan, so they undertake riskier investments, and this leads to a reduction in the expected return for the bank). The model. In this model there are a lot of assumptions, some of them on the borrowers and some on the lender. The starting point is that, in the credit market considered, there are some entrepreneurs who want to take investment projects, but they do not have funds, so they should ask for funds to a bank. Assumptions on the borrowers: ▪ There is a big number of firms. ▪ Each firm wants to do an indivisible project that needs 1$ to be undertaken. ▪ These firms have not internal funds, hence if they want to undertake the investment, they should ask for a loan of 1$. ▪ There is not a stock market, meaning that the firms should borrow the money from a bank. Indeed, they cannot issue bonds. ▪ E(π)r = p̅ x̅- p̅ ϑr (1+i). If (1+i) = 0, the intersection is p̅ x̅; if E(π)r = 0, the intersection is x̅ϑr. By connecting these two points, the expected profits for the firm that has got the risky project are obtained. Of course, x̅ϑr > x̅ϑs, since θr > θs. For drawing the second figure, the following assumption must be done. Let’s suppose that the firm population is split as follow: a share γ has a safe project (with 0 ≤ γ ≤ 1), a share 1 - γ has a risky project. Let’s say that this happens for divine will, meaning that the firms are born with these projects, so they have not chosen them. Hence, these projects do not say anything about the behavior of the firms. The value of γ is known to the bank, but as said above, the bank cannot distinguish among safe and risky projects (they know just the fraction). Moreover, this value γ is independent from the interest rate charged by the bank. CASE 1. If both the groups of investors (safe and risky) ask for a loan, the expected return of the bank is: E(ϕ) = γ p̅ ϑs (1+i) + (1 - γ) p̅ ϑr (1+i) = (1+i) [γ p̅ ϑs +(1 - γ) p̅ ϑr ] = p̂ (1+i), where p̂ is the weighted average of the probability of the loan’s refund by each kind of borrower (indeed, it is the sum between the probability that the firm has got a safe project times the probability that this project is successful and the probability that the firm has got a risky project times the probability that this project is successful – so, it is the sum between the probability of loan’s refund by safe investors and the one of risk investors). Note that p̂ can be written as p̂ = p̅ ϑr + γ ( p̅ ϑs - p̅ ϑr ), that is of course larger than p̅ ϑr because γ ( p̅ ϑs - p̅ ϑr ) > 0. CASE 2. If just the risky group asks for a loan, the expected revenues of the bank are E(ϕ) = p̅ ϑr (1+i), where p̅ ϑr < p̂. Let’s now suppose that the bank fixes the interest rate: ▪ Lower or equal to x̅ ϑs. In such a case, the expected profits (that can be seen in the previous graph) of both safe and risky investments are positive, so they will be undertaken, and so the CASE 1 is verified. Hence, the expected revenues for the bank are E(ϕ) = p̂ (1+i): this is a straight line that starts from the origin of the axes and that has got a slope of p̂. Let’s call A the intersection between this line and the line of (1+i) = x̅ ϑs. ▪ Betweenx̅ ϑs and x̅ ϑr. In such a case, only the risky investments are undertaken (CASE 2). The expected revenues for the bank are E(ϕ) = p̅ ϑr (1+i): this is a straight line that starts from the origin of the axes and that has got a slope of p̅ ϑr , that as demonstrated above is lower than p̂. Let’s call A’ the intersection between this line and the line of (1+i) = x̅ ϑs. ▪ Higher than x̅ ϑr, no investors will ask for a loan because the projects are going to give negative profits. The expected profits of the bank have got a discontinuity because it passes from A to A’: to the left of (1+i) = x̅ ϑs, both the investors ask for loan, to the right of (1+i) = x̅ ϑs just the riskier and so profits fall down. The discontinuity happens because of adverse selection: if the bank increases the interest rate above x̅ ϑs it loses the best borrowers, so the firms with the safe investments and this create a fall in the profits of the bank. Of course, in this model, just two projects are considered (risky vs. safe) and so just a discontinuity is created. However, in a more general case, there may be a lot of different projects, each one with different ϑ and the return of the bank can be approximated by a non-monotonic function in respect to (1+i). It is non-monotonic because, by fixing a value of E(ϕ) there are two interest rates. This curve of expected return of the bank has got a maximum when i = iĉ, that in this case is x̅ϑs. CASE OF MORAL HAZARD on the investment projects In this model firms can choose among risky and safe projects. This is very different from the assumption of divine will done before, because in this case firms have the power of choosing the investment to undertake. Of course, this assumption must be done in the case of moral hazard, that is about the behaviors of the agents. Let’s note that in this case, if the assumption of mean preserving spread (MPS) is kept, the two types of projects have the same expected revenue, and just the risky one is selected, because it has got a higher return than the safe one. Hence, this assumption must be relaxed; instead, let’s assume that the expected return of a safe project is higher than the expected return of a risky project, so psxs > prxr. In this formula, ps > pr (so, the probability of success of the safe projects is higher than the one of the risky projects) and xs < xr (so, the return of the safe projects is lower than the one of the risky projects – this because the risky project gives higher probability to lose something, but if it gives results, it gives very big results). The expected profits for the investors are: E(π)s = ps ∙ [xs - (1+i)] = ps xs - ps (1+i) E(π)r = pr ∙ [xr - (1+i)] = pr xr – pr (1+i) The expected returns of the bank are: E(ϕ)s = ps ∙ (1+i) E(ϕ)r = pr ∙ (1+i) Let’s draw the same figure as before. In the first one, related to the expected profits for the firms in case of safe and risky investment, an intersection can be found: iĉ = psxs - prxr ps - pr This is called critical interest rate. If the bank fixes an interest rate: ▪ Lower than the critical, firms will choose the safe projects because the expected revenues are higher. So, the expected return for the bank is E(ϕ)s = ps ∙ (1+i), that is a straight-line with slope ps. Let’s call A the intersection between this line and the critical interest rate. ▪ Higher than the critical, firms will choose the risky projects because the expected revenues are higher. So, the expected return for the bank is E(ϕ)r = pr ∙ (1+i), that is a straight-line with slope pr. However, let’s remember that pr < ps, so this line is flatter than the one of before. Let’s call A’ the intersection between this line and the critical interest rate. The expected profits of the bank have got a discontinuity because it passes from A to A’ that happens because of moral hazard: if the bank increases the interest rate above the critical one, this is seen by firms as an adverse incentive, and all the firms will choose the risky investment. Obviously, this incentive is adverse for the bank because it has a fall in its revenues (so, putting the interest rate higher than the critical one means that the bank is incentivizing investors to behave against it). Even in this case, in a more general model, there may be a lot of different projects, each one with different ϑ and the return of the bank can be approximated by a non-monotonic function in respect to (1+i). It is non-monotonic because, by fixing a value of E(ϕ) there are two interest rates. ADVERSE SELECITON + MORAL HAZARD As shown in the non-monotonic graph of the expected revenues of the bank, the return of the bank has a maximum in correspondence to the critical interest rate. If the bank increases the interest rate over this threshold, two phenomena created by asymmetric information will happen: I. Adverse selection, that leads the best borrowers (with the safe projects given by divine will) to go out from the market because they cannot afford a such high interest rate. II. Adverse incentive (moral hazard), that leads the firms to have an incentive to choose the risky projects. For these two reasons, the expected return of the bank falls. CREDIT SUPPLY vs. CREDIT DEMAND: credit rationing Let’s now do another assumption of the model, according to which the credit supply by the bank is an increasing function of its expected return. To find out how the credit supply is shaped let’s draw the following 4 figures: I. Figure 1 (that has got on the x axis (1+i) and on the y axis E(ϕ)) is the standard expected revenues of the bank. II. Figure 2 (that has got on the x axis L and on the y axis E(ϕ)) uses the assumption according to which the credit supply L is an increasing function of the expected revenues of the bank E(ϕ). This means to draw a positive slop line. III. Figure 3 (that has got on the x axis L and on the y axis L) is a transfer graph useful to go from figure 2 to figure 4. It is a 45° line since x axis is equal to y axis. IV. To draw Figure 4 (that has got (1+i) on the x axis L and on the y axis L), let’s take point A from graph 1 and bring it to the other figures (2 and 3) until reaching Figure 4, in which the point A is defined. By repeating this process for all the points of Figure 1, Figure 4 is obtained. The graph is very similar to the one of Figure 1 (so, it is a non-monotonic function), however it changes depending on how Figure 2 is drawn (so, on the form given to the relation between L and the expected revenue. Indeed, it is said just that this curve is positive sloped, but there is not an explicit function). Figure 4 is the credit supply by the bank, that is a non-monotonic function of the interest rate (as the expected revenues of the bank). According to this graph: dL dî > 0 ∀ i < î The credit supply by the bank has got a maximum in (1+i) = î, in which even the expected revenues of the bank are maximized. Let’s now introduce a further assumption, called representative agent: by imagine that in the economy all the banks are the same, if the graph shown is the credit supply of one bank, by aggregating the graph of the single banks it is possible to find out the aggregate behavior, that is described as Figure 4 (and as Figure 1 for the expected revenues); so, the aggregate credit supply is a non-monotonic function of the interest rate. The last assumption is that the credit demand is downward sloping (as usual). The Credit View By studing the IS-LM model, the money view was defined. If the Central Bank reduces the money supply, the LM curve shifts to the left (from LM to LM’). Note that the IS- LM model has got the following assumption: the Central Bank goes on the economy with a helicopter and throws money, so it doesn’t control the interest rate (as in the reality). Going from A to B, the interest rate goes up; investments go down; aggregate demand goes down; output goes down. This was called the monetary transmission mechanism, or the interest rate channel, because the interest rate acts as a channel between the monetary (money supply goes down) and the real part (output goes down). Another name is the money view: this because, in the IS-LM model, there wasn’t the credit market, but just money or bonds, that are not perfect substitutes (for buying goods, money are needed; for having an interest rate, bonds are needed). In the category of bonds were included, without a clear distinction, all the possible assets, as bonds, equity, bank loans, commercial papers, and so on. However, after a monetary policy stance, empirically it can be possible to see (from the data) that the interest rate increases not so much, while output goes down a lot. Hence, economists start asking themselves how it was possible that such a low increase of interest rate justifies such a huge decrease in output. The explanation was found in the existence of financial frictions that can help in amplifing the effects of monetary policies on aggregate demand. Of course, this is another point against the Modigliani & Miller theorem, because there is a link between financial decisions and real decisions. For this reason, a new view, in addition to the money view, is introduced, since there is not just the working of the interest rate, but there is even the working of financial factors. It is called credit view, and it focuses the attention on 2 sub-views: ▪ The lending view, even called bank credit channel, that is about bank loans. It is studied through the model of Bernanke and Blinder (1988). ▪ The broad credit view, even called balance sheet channel. It is studied by Greenwald and Stiglitz (1993). Both of the views have got, at the basis, asymmetric information problems. LENDING VIEW (BANK CREDIT CHANNEL) – Bernanke and Blinder, 1988 According to the lending view, a reduction in money supply makes deposit at the commercial banks decreases; then, banks can give lower loans (there is a credit crunch) and so investments go down, aggregate demand goes down, and output goes down. MS↓ → D↓ → LS↓ → I↓ → AD↓ → Y↓ This lending view shows the interdependence between financial structure and investment decisions. However, in this lending view there is nothing about the cost of credit, and so about the interest rate (that instead was present in the money view), but just something about the quantity of banks’ loans. Hence, bank loans are picked up from the bond class of the IS-LM model. For having an effective and operating lending view, 3 things must be true: i. Whenever money supply goes down (goes up), reserves decreases (increases) and overnight deposit decreases (increases). The relation between reserves and deposits is shown later with the money multiplier. However, commercial banks, after a decrease in money supply, can decide to offset the decrease of overnight deposits by increasing, for instance, long-term deposits (time deposits), so another kind of liability. In such a case, the bank is performing the so-called liability management. To have an effective lending view, it should be difficult for banks to get funds from sources different from overnight deposits. ii. Whenever deposits decrease (increase), bank’s loans go down (go up). However, commercial banks, after the decrease in deposits (liabilities go down), can decide to decrease something different from loans, as securities or bonds (reserves are more difficult because linked with the Central Bank). Indeed, in any case, it is offsetting the decrease in liabilities with a decrease in assets. In such a case, the bank is performing the so-called asset management; so, the bank is managing its asset-side to decrease not bank loans but securities or bonds. To have an effective lending view, there should be an imperfect substitution between bank loans and securities in banks’ portfolios. iii. Whenever bank’s loans go down (go up), investments decrease (increase). However, it is true just for those companies that cannot issue equity or bonds, so for the firms that depend on bank’s loans. Usually, these firms are the ones with smaller net worth. Note that, here the problem of asymmetric information is important, because those firms cannot issue bonds or equity because the market doesn’t know them, and so no one is going to buy their bonds or invest in their shares. Instead, in case of perfect information, everyone can get funds at the market interest rate, and no firms depend on bank’s loans. Hence, if banks act a liability management or an asset management, or if firms do not rely just on bank loans, the lending view doesn’t hold. Before entering the model of Bernanke and Blinder, let’s have the following example. As shown: Money supply (Currency + Deposits) = mm ∙ Monetary base (Currency + Reserves) The money multiplier mm is defined as: mm = 1 + cu cu + r Let’s suppose to have Currency = 0, ru = Reserves Deposits = 10%. Consequently, the supply of money becomes: C + D = 1 + cu cu + r (C + R) → D = 1 r ∙ R By having a change in the reserves of ∆R, deposits will change of ∆D = 1 r ∙ ∆R = 10 ∙ ∆R. Let’s assume a monetary policy tightening by the Central Bank, in which it sells bonds to commercial banks (for having back money – there is a fewer monetary base – it is an open market operation) and receives money from commercial banks, that decrease reserves of the same amount. If the bonds are sold for an amount of 1 $, securities in the asset side go up of 1$, while reserves go down of 1$, and deposits go down of ∆D = 10 ∙ ∆R = 10$. Let’s now assume that a commercial bank has got the following Balance Sheet before the monetary policy tightening. Remember that time deposits do not have reserve requirements, while overnight deposits have; this means that a part of the overnight deposits should be deposited as reserves at the Central Bank. After the monetary policy tightening, reserves go from 10 to 9, overnight deposits go from 100 to 90, bonds go from 30 to 31. So, the following situation is created. Now, assets and liabilities side are no more equilibrated. Commercial banks, to equilibrate them, can: ▪ If the lending view is operating, after a monetary policy tightening, deposits go down (and it happened) and loans go down. Hence, in this case, banks should decrease loans by 10. Balance Sheet of a commercial bank Assets Reserves 10 Loans 70 Securities 30 TOT. 110 Liabilities Time deposits 10 Overnight deposits 100 TOT. 110 Balance Sheet of a commercial bank Assets Reserves 9 Loans 70 Securities 31 TOT. 110 Liabilities Time deposits 10 Overnight deposits 90 TOT. 100 ▪ Act an assets-side management, by changing securities. So, in this situation, it can sell bonds for an amount of 10 and go on by giving 70 of loans. In this case the lending view is not operating anymore. ▪ Act a liability-side management by increasing time deposits by 10. Even in this case, no lending view is present. The figure shows the empirical evidence done by Bernanke and Blinder in 1992 that studied the United States in years 1959-1978. They used econometrics for doing a VAR analysis (vector autoregressive analysis) to understand how commercial banks react to a monetary policy tightening (i.e., increase in interest rate) in terms of loans, bonds, deposits, and unemployment rate (so, they studied the impulse response function). They found out that: ▪ Deposits decrease immediately. It means that there is not any kind of liability management. ▪ Bonds (securities) decrease until 9 months and then start to increase. Hence, when deposits go down, banks act an asset side management by selling bonds, and so the lending view is not operating; indeed, in this period, bank loans go up. Then, when the banks start to re-build their portfolio of securities (bonds), loans go down: here the lending view starts to operate. Hence, the lending view operates, but not immediately. ▪ Bank loans increase for a short period, and then they decrease a lot (month 6). This happens because banks do not suffer from shortermism since they do not want to maximize immediately their return; hence, even if there is a recession or a monetary policy tightening, they go on to give credit for a given time to their customers. They can go on to give loans even if deposits go down because of the asset-side management, indeed banks sell bonds to have liquidity. ▪ Unemployment rate has got a specular behavior compared to bank loans, and so it decreases at the beginning and then increases. This relation between loans and unemployment rate is very important: indeed, they move together, and so whenever loans are high, unemployment rate is low; whenever loans are low, unemployment rate goes up. This is consistent with the view according to which banks’ loans are an Balance Sheet of a commercial bank Assets Reserves 9 Loans 60 Securities 31 TOT. 100 Liabilities Time deposits 10 Overnight deposits 90 TOT. 100 Balance Sheet of a commercial bank Assets Reserves 9 Loans 70 Securities 21 TOT. 100 Liabilities Time deposits 10 Overnight deposits 90 TOT. 100 Balance Sheet of a commercial bank Assets Reserves 9 Loans 70 Securities 31 TOT. 110 Liabilities Time deposits 20 Overnight deposits 90 TOT. 110 This money supply corresponds to the supply of deposits since there are no currencies. The money demand is a function defined as: MD = D(i-, Y+) As in the IS-LM model, this function is negatively correlated with the interest rate on bonds, and positively correlated with the income. This money demand corresponds to the demand for deposits since there are no currencies. The equilibrium, called deposits market clearing condition, is supply of deposits equal to demand for deposits, so when: mm(i+) ∙ R = D(i-, Y+) Goods market. It is described by a modified IS curve. The goods market clearing condition is: Y = Y(i-, ρ-, G+) It is a negative function of the interest rate on bonds, because if interest rate goes up, investments go down, aggregate demand goes down, and output goes down. However, in this case, since even bank loans are important, the demand for goods will depend on the interest rate on loans ρ; even in this case there is a negative relationship, because if borrowing becomes more expensive, firms will invest less, they will produce less, and Y goes down. Let’s add even G (public expenditure) because the IS curve depends positively on it. Building the CC curve Once the 3 markets (plus the bond one, that as usual, is hidden) are defined, the CC curve was derived by the authors putting together the goods market and the loan market. For building the CC curve, they substituted the D of the loan supply LS = χ(ρ+,i-) ∙ D ∙ (1 - τ) with MS = mm(i+) ∙ R, that is the supply of deposits. The equilibrium of the loan market becomes: LD = LS L(ρ-; i+; Y+) = χ(ρ+,i-) ∙ D ∙ (1 - τ) L(ρ-; i+; Y+) = χ(ρ+,i-) ∙ mm(i+) ∙ R+ ∙ (1 - τ) By solving this equation to respect of ρ, that is the interest rate on bank loans, the solution is: ρ = λ(i+, Y+,R-) So, ρ is a function λ of the variables i, Y, R: o To understand how the first derivative of ρ is in respect to i, let’s take the graph of the loan market, that has got on the x axis L (quantity of loans), and on the y axis ρ (price of loans). Loan demand is defined as L(ρ-; i+; Y+); if the interest rate on bond (i) increases, loan demand goes up as well (dotter one). Loan supply is defined as χ(ρ+,i-) ∙ D ∙ (1 - τ); if the interest rate on bond (i) increases, loan supply decreases (dotter one). The equilibrium goes from A to B, and so if i goes up, ρ goes up as well, and so the first derivate is positive. Note that nothing can be said about the relationship between i and L, because the effect on L depends on how much the curves shift. o To understand how the first derivate of ρ is in respect to Y, let’s take again the same figure of the loan market. The loan demand depends on Y, indeed it is L(ρ-; i+; Y+). When Y goes up, loan demand goes up as well (dotter curve). The equilibrium goes from A to B, and so if Y increases, ρ goes up as well, and so the first derivate is positive. o To understand how the first derivate of ρ is in respect to R, let’s take again the same figure of the loan market. The loan supply depends on R, indeed it is χ(ρ+,i-) ∙ mm(i+) ∙ R+ ∙ (1 - τ). When R goes up, loan supply goes up as well. The equilibrium goes from A to B, and so if R increases, ρ goes down, and so the first derivate is negative. By putting ρ = λ(i+, Y+,R-) into the IS curve (Y = Y(i-, ρ-, G+)), the result is: Y = Y(i+, (λ(i+, Y+,R-))-, G+) This formula can be written again as: Y = ϑ(i-, R+, G+) It is the CC curve, and it is possible to show that it is negatively sloped. Let’s find the first derivative of Y in respect to R: it is positive, because for every interest rate, if reserves increase, ρ decreases (banks can have more loans and so the cost of loans decrease); but if ρ decreases, investments go up (it is less expensive to ask for loans to bank), and output goes up. R ↑ → ρ ↓ → I ↑ → AD ↑ → Y ↑ Let’s have a graph, with x axis Y and y axis i, as in the IS-LM model: whenever reserves increase, the position of the CC curve moves to the right. This didn’t happen in the IS curve because it didn’t contain any reserve. Building the LM curve The LM curve is the usual one, obtained by equating demand for deposits and supply of deposits: mm(i+) ∙ R = D(i-, Y+) From this, the LM curve is: i = i(Y+, R+) The Model By putting together CC and LM curve, the so-called structural form of the model is obtained: { Y = ϑ(i-,R+,G+) i = i(Y+,R+) This model has got 2 equations and 2 unknows (Y and i), while R and G are exogenous. This model has got an economic meaning, since it says that Y decreases if i increases, that i Y increases if G increases, and so on. By solving this model, the reduced form is obtained: { Y* = Y*(R, G) i* = i*(R, G) In this reduced form model, the endogenous variables Y and I are just a function of the exogenous R and G. Hence, this reduced model doesn’t tell anything about the behaviors of the endogenous variables. So, there is not economic theory behind the reduced from model (nothing can be claimed by looking at the reduced model). This didn’t happen in the structural form, in which endogenous variables depend even on other endogenous variables. The equilibrium E0 in this reduced model is shown in the following figure. The LM curve shifts when R shifts; the CC curve shifts when R and/or G changes. The difference with the IS-LM model is that: ▪ In the IS-LM model fiscal policies change the IS curve and monetary policies change the LM curve. ▪ In the CC-LM model, fiscal policies change the CC curve and monetary policies change the LM curve; however, the CC changes even for changes in reserves (because in the CC there is the credit market). Let’s imagine having a shock in reserves, and so R increases (from R0 to R1). Two effects are present: I. The LM will shift to the right because there is an increase in the monetary base (from LM(R0) to LM’(R1)). Hence, the equilibrium goes from E0 to E0’; in such a point, Y increases while i decreases. The movement from E0 to E0’ is called liquidity effect. This is the effect found even in the IS-LM model, and tells that if the quantity of money increases, the interest rate decreases and so money is cheaper. This would be the only effect in the money view (IS-LM curve). II. However, there is another effect, related to the CC curve that shift so the right (from CC (R0, G) to CC’ (R1, G)). This because, if there are more reserves, it means that there are more deposits and there are more bank loans, so firms invest more, and output goes up. The new equilibrium goes from E0’ to E1, and it has got a higher interest rate (the movement depends on how much the curve changes) and a higher output. The movement from E0’ to E1 is called credit availability effect and tells that there are more banks loans, and so Y increases. This effect amplifies the liquidity one. Hence, money is not neutral and acts through a double channel: a. The liquidity channel, that is the money view, according to which firms can invest because the interest rate decreases. b. The credit availability channel, that is the lending view, according to which firms can afford higher investments because there is credit availability. It is needed because, empirically, the economists shows that there was a larger increase in output with a low decrease in the interest rate compared to the one predicted by the IS-LM model. The only way to explain it was something related to the financial side of the situation. The CC-LM curve shows this huge increase in output, with a low decrease in interest rate (that can be even doesn’t move) and explains it with the credit availability channel. These two channels operate together: firms invest more both because money is cheaper and because there is more money availability. This model collapses with the IS-LM model (so, they are the same) when the IS curve doesn’t depend on ρ, and so it is just Y (i, G). This means that if firms do not depend on bank loans (i.e., bank loans are not special), the CC curve becomes the IS curve, and the two models become the same. So, it happens in two situations: o Bank loans and securities are not imperfect substitutes anymore, so when it is the same for a company to employ bank loans or to issue bonds. o The demand for goods does not depend on ρ. THE BALANCE SHEET CHANNEL (THE BROAD CREDIT VIEW) – Greenwald and Stiglitz, 1993 According to the balance sheet channel, a reduction in money supply makes interest rate goes up (like the money view); if interest rate goes up, the net worth of firms goes down (because the present value of the future cash flows decreases) and so the collaterals decrease. Consequently, adverse selection and moral hazard problems worsen, so the problems related to them increase; the external finance premium (EFP) goes up (firms pay more for the external funds), investments go down, and output goes down (this is called small shocks, large cycle puzzle). Of course, the balance sheet channel has got a broader view compared to the lending view, in which a special role was given to banks’ loans; in the balance sheet channel it is states that the problem of asymmetric information can have an amplifying effect on the cost of money (interest rate increases, and external finance premium increases to). So, in this model, there is asymmetric information for all the lenders, not just banks. above dϕ dq > 0) e whenever it increases (it is the employment), wages decrease (in other words, whenever wages increase, firms ask for less workers). This demand for labor is defined when there is a bankruptcy probability, for this reason it is indicated as ND B. Indeed, the previous formula of the labor demand curve has got at the numerator ψ(a), that is the probability that the firm goes bankrupt. In such a case, the equilibrium is in point B, and the firm ask for NB labor. Instead, by considering a firm that has got perfect information and without cost of bankrupt (g=0), the labor demand curve is going to be: w = 1 (1 + r) ∙ ϕ'(q) Hence, the curve shifts up because, for every N, the value of w is higher. The demand for labor under perfect information, and so without bankrupt, can be drawn (ND C). So, if there are no financial frictions, firms ask for a higher quantity of labor (NC > NB); instead, the presence of a positive probability to go bankrupt affects the real investment decisions of the firm (that in this case is the number of workers to employ). This is another proof of the fact that Modigliani & Miller’s theory doesn’t hold. This was the description of just one firm. By using the assumption according to which this firm was a representative agent firm, all the other firms can be described in the same way (all the firms are equal to the representative one). Hence, an aggregation of the demand for labor can be done: W = 1 - g ∙ ψ(A) (1 + r) ∙ ϕ'(Q) In this formulation, A is the net worth of all the firms, Q is the quantity produced by all the firms, and W is the demand for labor of all the firms. So, the demand for labor depends on the interest rate r and on the aggregate net worth of the firms in the economy. If A increases, the bankruptcy probability ψ(A) goes down (because firms have got more collaterals) and the demand labor curve goes up. Let’s have a figure with x axis N and y axis W, and under it another figure with x axis Q and y axis A: when the net worth is A0, firms ask for N0 workers and at this correspond the quantity produced Q0. If goes from A1 > A0, ψ(A) goes down, and the demand for labor goes up; the new intersection with the supply of labor, called E1, has got N1, and Q1. By linking all the points, the green function is obtained. Let’s now invert the axes of the second figure, by putting A on the x axis and Q on the y axis. This represents the relationship between the net worth and the quantity produced. Let’s take two firms, one with a low level of net worth and another with a high level of net worth. If there is a shock in the economy that decreases the net worth for a given quantity (the same shock for the two companies): the consequence is that the company with the highest net worth has got a small reduction in the quantity produced, while the company with the lowest net worth has got a huge reduction in the quantity produced. Hence, the firm that suffers most the shock in the net worth is the one with the lower net worth, that is compelled to reduce a lot its production. The explanation behind is called the phenomena of flight to quality: after a negative shock in the net worth (i.e., during a recession or after a monetary policy tightening), banks want to give finance to the larger firms, that are the ones that provide more collaterals. So, credit goes from smaller firms to larger ones. This is quite important because it is connected with asymmetric information: there is heterogeneity among firms, that are not all equal. EXERCISES EXERCISE IS-LM MODEL C0 = 200, c = 0,75, I = 50 -100i, G = 500, P = 10, T = 0,3Y, TR = 150, M = 3000, L = 0,85Y – 200i. Find the equilibrium. SOLUTION IS curve Supply of goods equal to the demand of goods, so: Y = C0 + c1 ∙ YD + I ̅- bi + G̅ = C0 + c1 ∙ (Y – T + TR) + I ̅- bi + G̅ = 200 + 0,75 (Y – 0,3Y + 150) + 50 – 100i + 500 LM curve Money demand should be equated to the money supplied. The money demand is given, L = 0,85Y – 200i, while the money supply is fixed at M p̅ : 0,85Y – 200i = 3000 10 The equilibrium value of the economy is the intersection between IS and LM, that is Y = 1125,28, i = 3,28.