Introduction to econometric and input-output models^
^ adapted from Dave Clark, Centre for Local and Regional Economic Analysis, University of Portsmouth (2010)
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Introduction to econometric and input-output models^
^ adapted from Dave Clark, Centre for Local and Regional Economic Analysis, University of Portsmouth (20 1 0)
Regional Econometric models
Whilst regional multiplier models can give estimates of changes in total regional employment and income they are not capable of providing more detailed predictions, which estimate the effect of alternative policy strategies. Typically the planner wishes to know the effect of a given policy change on a wider range of economic, demographic and social variables. Regional econometric models should possess several characteristics if they are to be effective: The model must be sufficiently detailed so that the major planning authorities can be provided with the sort of data they need to carry out their functions. –
- Forecasts of output and employment to inform industrial development plans.
- Demographic breakdown and forecasts, for the provision of public services.
- Occupational breakdown and forecasts, for the development of effective training packages. Regional models need to be constructed for differing spatial areas usually corresponding with administrative areas.
- For example education authorities will require demographic information at district levels for the provision of schools and staffing,
- Training and business organisations may require information at the local labour market level (Travel to Work Area).
- Where a number of spatial disaggregations are required this means modelling at the lowest level of disaggregation and aggregating up into larger spatial units – this can be problematic as it is generally accepted that a degree of accuracy is sacrificed at lower levels of disaggregation. Models must be internally consistent. This means that the region must be treated as a set of interdependent elements, (for example the Northern Ireland Economic Research Centre (NIERC) model is comprised of about 3 00 separate but inter-linked equations). If one part of the system is affected by an exogenous shock (change in interest rates, influx of migrants) then the reverberations will be felt throughout the regional economy and the model must be capable of predicting "full system effects". Regional econometric models vary in size and content of for a number of reasons. 1. They are constructed for different purposes. I.e. estimating the differing impact of alternative fiscal policies in different sectors of the regional economy or providing forecasts of economic and demographic variables based on pre-determined scenarios. 2. The availability of data. The researcher may have to compromise on the optimum construct of the model simply because data is not available or alternatively may have to use surrogate data as a second-best option. This problem becomes more acute with finer spatial disaggregation, for instance, annual GDP is not available from CSO below the NUTs 3 level in the UK. 3. Researchers are often reduced to ad-hoc devises to make their models work. Armstrong & Taylor use the example of discarding the well-established theoretical link between private investment and interest rates from the model’s investment function if the researcher finds that the determinant does not in practice help to explain the variations in investment. Therefore, it can be expected that equations in models may not always correspond with a priori theorising. Econometric models are interdependent sets of equations. Each equation determines the numerical value of one of the regions economic variables. The right-hand side may include exogenous variables such as the national wage rate, taxation and birth and death rates within the region or endogenous variables (determined within the model). Such models attempt to measure economic linkages that exist within the region and between the region and the outside world. These links are estimated by econometric methods and represented as equations for the purpose of predictions Armstrong & Taylor use a simplified model based broadly on one developed by Adams, Brooking and Glickman ( 197 5) to demonstrate the effect of an exogenous shock. See page 32 of Armstrong and Taylor
that the modellers may be attempting to model the impossible, particularly because of the lack of differentiated data on marginal propensities to consume locally produce goods and import levels. Gloomily, they see little prospect of significant improvements in the shorter-term. In a follow-up study two of the authors, Hunt and Snell (1997) examine local econometric modelsii. This time they concentrated on the structure of the models rather than attempting simulations. The two models’ under the microscope are the Liverpool – Cardiff suit of models (L-C) and Cambridge Econometrics’ Local Economy Forecasting Model (LEFM). The former consists of three separate models for Merseyside, Wales and a combined model for Gwynedd, Clwyd and Cheshire the latter is a commercial bespoke package customised to the client’s requirements. There are a number of other differences, a selection of which, are set out below: - The L-C model has been subjected to considerable academic scrutiny the LEFM has not (because of its commercial status). The LFEM is much more disaggregated than the L-C model The L-C model is supply-side driven i.e. the region’s growth depends on upon supply of factors (mainly labour) the LEFM is demand driven. The L-C is based on a system of inter-linked equations whereas the LEFM has an input-output approach as its’ underlying philosophy. Hunt and Snell conclude that the two models present contrasting extremes in local economy modelling. Whilst the LFEM is described as “bold” and “ambitious” it is suggested that the level of sector disaggregation may be too great and that there is a need for a more “detail” about the assumptions used within the model. On the other hand, the L-C model is described as a “neat” approach but contains very restrictive assumptions and depends on faith in supply-side economics. They conclude that the potential user has to make a decision based on which model to use based on four criteria: Theoretical viewpoint Belief that changes in demand will work through and directly effect the local economy or that such an effect can only be temporary until a new equilibrium is attained. Methodology Whether to use the econometric approach including dynamics at the local level, or the input-output approach backed by econometric forecasts at national or regional level. Level of aggregation The LEFM forecasts for 49 industry sectors whereas the L-C only provides a manufacturing/non-manufacturing split. Expertise required The LEFM is an off the shelf package (with support) and is effectively a black box, in contrast L-C is comprised of a set of transparent equations requiring standard econometric software and relevant data ideal for the DIY economic enthusiast!!!! For a more up-to-date review of Regional economic impact models (yes these can be used for forecasting) see Loveridge S, A Typology and Assessment of Multi-sector Regional Economic Models, Regional Studies Vol. 38. 3 pp 305 - 317. This is well written and gives an insight to the Economic Base Model, I-O Social Accounting Matrices, Integrated econometric and I-O models and Computable General Equilibrium Models. (A copy of this paper is available on the L Drive).
The input-output method:
Regional econometric models require a large amount of time-series data ideally stretching back over 20 years or more. There are therefore two major problems with econometric models, first the availability of the data over such a long time-span and secondly the consistency of the data set (governments habitually change the way variables are calculated and the range of data that are collect – probably for good reasons). The alternative is to construct a detailed snapshot of the input-output linkages that occur in the regional/local economy. This can then be used to predict the consequences of a change in regional/local output. The technique was developed by the Nobel prise winner Leontief in the 1930 s and has been used for a wide range of applications since then, including regional and local impact analysis.
Inputs purchased by Final demand sectors Agriculture Manufacturing Services Households Government Exports Investment Gross output Output produced by Agriculture 20 ( 0. 2 ) 40 ( 0. 2 ) 0 (0) 20 0 20 0 100 Manufacturing 20 ( 0. 2 ) 20 ( 0. 1 ) 10 ( 0. 1 ) 75 10 55 10 200 Services 0 (0) 40 ( 0. 2 ) 10 ( 0. 1 ) 25 20 5 0 100 Payments for Household services 40 ( 0. 4 ) 45 ( 0. 225 ) 70 ( 0. 7 ) 5 0 0 0 160 Government Services 10 ( 0. 1 ) 15 ( 0. 075 ) 5 ( 0. 05 ) 0 0 0 0 30 Imports into region 10 ( 0. 1 ) 40 ( 0. 2 ) 5 ( 0. 05 ) 0 0 0 5 60 Gross inputs 100 200 100 125 30 80 15 650 () = technical coefficients The approach is based on the simple but fundamental notion that the production of output requires inputs. These may take the form of raw materials, semi-manufactured goods or services (e.g. households supply labour). Having purchased inputs from other industry sectors, households and government, firms sell their products (output) to other producing sectors or final demanders such as, households, government, or households and firms in other regions. The input-output linkages in an economy are formalised by constructing a transaction table (known as a flow or transaction matrix) this records all the payments to and from a sector in any given year. It works on the principle of double-entry book keeping whereby there is equality between the gross inputs and gross outputs of a sector. The total output of a sector must be accounted for by the inputs used in production, any excess of the value of gross output over payment made for inputs is profit (or loss) and is shown in the payments sector. Navigating the transaction matrix. The disaggregation of models varies considerably, the main UK input-output model uses 123 sectors, Armstrong and Taylor cite the 17 sector model used by McNicoll to model the economy of the Shetlands, most including CLREA’s 30 sector model fall somewhere in between. For an example see Armstrong and Taylor Regional Economics and Policy ( 200 0) Table 2 .1. However, for explanation purposes their simplified version with three productive sectors will suffice (see below). Table 4. 1 - The transaction table with technical coefficients Source: Armstrong & Taylor ( 200 0) In simple terms the cells in the columns represent the purchases that a sector makes and the cells in the rows represent the sales of product from the same sector. Thus Agriculture purchases £2 0 from itself, £2 0 from manufacturing, £4 0 from households (labour services), £ 10 worth of services from Government and £1 0 worth of inputs from other regions. Making a total of £ 100. It sells £ 20 to itself, £ 40 to manufacturing, £ 20 to households (as consumption) and exports £ 20 worth of produce to other regions. Making a total of £1 00. Thus, the transaction table records exactly where inputs of an industry come from and where its output goes. The transaction table (Table 5 .1) also contains other information about the underlying structure of the economy. Examining the bottom right-hand portion of the table we can see the relationship between the final demand and the payments sectors. In the example government expenditure equates to payments (i.e. the government’s current account is balanced), there is an external balance of payments surplus (exports = £ 80 imports = £ 60 ) and value added by residents (GDP) is £ 160. This is the difference between payments to government and imports from total final demand (see Armstrong and Taylor, 2000 page 40 ). There are two methods of constructing the transaction table the one above is the domestic-flow approach (inter- industry flows are measured exclusive of their import content), which only records inputs originating in the region itself. The alternative is the total-flows approach (inter-industry flows are measured inclusive of their import content), which records all inputs. In the total-flows approach the import content is shown as a negative entry in the final demand sector. For an example see Armstrong and Taylor, Regional Economics and Policy (1 993 ) Table 2. 3. There are a number of assumptions underlying the input-output technique that should be noted:
- It is assumed that production technology is one of fixed proportions. Thus inputs would have to double if output doubled. This relationship is assumed to be constant over the period for which forecasts are to be made.
- There are assumed to be no constraints on productive capacity, in other words the supply of factor inputs is perfectly elastic. Estimating the effect of a change in final demand on the entire system. The technical coefficients (in parenthesis in table 4 .1) allow us to calculate the effect of an increase in final demand on the entire sector. Technical coefficients are calculated by dividing the flow of output from industry (i the row) to
Table 4. 2 Effect of £ 10 increase in agricultural output (households exogenous) Gross output Gross output Output produced by Output produced by Agriculture 13. 26 Household services 6. 45 Manufacturing 3. 02 Government Services 1. 59 Services 0. 67 Imports into region 1. 96
- 95 10. 00 Total effect 26. 95 Source: Armstrong and Taylor Regional economics and policy ( 2000 ) Type 1 multipliers Although input-output models are able to show the full effect of changes in output across the whole economy industry by industry, what is often required is a summary of these effects. The most usual of these are sectoral output multipliers and household income multipliers. The Type 1 multiplier is the ratio of direct + indirect effects to the direct effect:
Direct Indirect
Direct
In the three-sector economy model example we used we found the affect of a £1 0 increase in agricultural demand, thus the effect of a £ 1 increase (in agricultural demand) on each sector will be: Agriculture 1. 32 6; Manufacturing 0. 302 and Services 0. 06 7. Summed these equate to the direct and indirect effects on gross output ( 1. 695 ) dividing this by the direct effect on output (£1) gives the sectoral output multiplier for agriculture of 1 .6 95. A similar exercise would have to be carried out for each of the other sectors. There is however another way. These can also be obtained by calculating the inverse matrix this shows how the output of each sector will be affected when final demand for a region’s output is increased by £ 1. (You will need a computer to invert anything other than a small matrix ). The inverse matrix is known as the matrix of multipliers. The steps to calculate the inverse matrix are as follows: Take the A matrix which is the input-output matrix of technical coefficients in Table 5. 1 A matrix I-O technical coefficients matrix Agriculture Manufacturing Services Agriculture 0. 200 0. 200 0. 000 Manufacturing 0. 200 0. 100 0. 100 Services 0. 000 0. 200 0. 100 Other input coefficients ( see later ) Households 0. 400 0. 225 0. 700 Government 0. 100 0. 075 0. 050 Imports 0. 100 0.2 0. 050 Calculate I-A matrix ( the I matrix is the identity matrix- the diagonal cells going from top left to bottom right contain the figure 1 all other cells contain 0 s ) Agriculture Manufacturing Services Agriculture 1 0 0 Manufacturing 0 1 0 Services 0 0 1 Thus the I-A matrix becomes Agriculture Agriculture 0. 80 Manufacturing - 0. 20 Services 0. 00 Manufacturing
- 20
- 90
- 20 Services
- 00
- 20 Services
- 10
- 90
Type 2 household income multiplier = Direct +Indirect + Induced effects Direct effect
The type 2 (I-A)-^1 becomes Agriculture Manufacturing Services Households Agriculture Manufacturing Services Households
Giving a Type 2 household income multiplier for agriculture of £1. 332 /£ 0. 4 = 3. 33 (the Type 1 multiplier was 1. 61 ). To obtain the sectoral output multipliers we sum the first three rows in each column thus Agriculture Sectoral output multipliers Type 2 3. 36 (1.7 0 ) ( ) = sectoral output multipliers where households are exogenous Manufacturing
- 28 (1.7 8 ) Services
- 48 (1.3 0 ) A comparison between type 1 and 2 household income multipliers is shown below notice that when households are treated as endogenous the effect is considerably greater. Household income multipliers Agriculture Manufacturing Type 1 1 .6 1 2. 58 Type 2 (1.3 319 /0.4) 3. 33 (1. 1 985/ 0 .225) 5. 33 Services
- 20 (1. 738 9/ 0 .7) 2. 48