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20 1 THE^ DEMAND^ SIDE
We can also apply the same logic to modelling consumption deci5ions We can acc0unt
for the fact that the future will affect consumption decmons by calculating the present value
of the stream of expected income over a person's lifetime. If we assume that individuals live forever, we can use the formula for calculating present value to calculate the expected present value of lifetime wealth (WE, pronounced ‘sigh’), which is defined at time t asfollows.
w5=1+rA_+t ( ) t1 ;(1+r),)’t+——-E,.
(expected present value of lifetime wealth)
where 2:0 (ll—rl’y’il is the present value of expected post-tax lifetime labour income and
(1 + r)At_1 are the resources available in period t from the assets the individual held at the
end of the previous period.
1.2.5 Consumption
People’s income fluctuates over their life cycle; it also fluctuates when they lose theirjob,
move to a different job or get a promotion. Given that people prefer to smooth out the
fluctuations in their income in their spending behaviour, they must take account of the future and they must be able to save and borrow. The modelling of consumption should include how households form expectations about the future and how they borrow and save. The desire to smooth consumption in the face of fluctuations in income is captured by the assumption ofdiminishing marginal utility ofconsumption. A simple way of visualizing this is
to consider the choice ofconsumption in a world ofjust two periods. lfwe know income will
be higher next period, how does that affect consumption now? Consider the choice between either low consumption equal to income in the first period and high consumption equal to income in the second period, or having the average of the two consumption levels in each period. If there is diminishing marginal utility of consumption, more consumption always increases utility, but successive increases in consumption deliver smaller and smaller benefits. Therefore, households will make the second choice, because consuming the average in both periods offers higher utility than the first choice.
The permanent income hypothesis (Pl H)
The permanent income hypothesis (PlH) states that individuals optimally choose how much to consume by allocating their resources across their lifetimes.6 Their resources include their
5 The assumption that individuals 'live forever' can be thought of as assuming that households have children or heirs and that they incorporate the utility oftheir children or heirs into their consumption function. In other words, households behave 'as if’ they last forever. The assumption is clearly unrealistic, but it greatly simplifies the mathematical derivation of the permanent income hypothesis (PlH). From this point onward, however, we will refer to lifetime income and earnings in the text, as it is more intuitive to think about forward-looking behaviour in terms ofa household maximising utility over their lifetime. 6 This view of the consumption function was first developed by Modigliani and Brumberg (1954). See also Friedman (1957). For a review of Friedman's theory, its influence on modern economics and the relevant empirical literature, see Meghir (2004).
MODELLING
ails of inmme , 3 Path of consumptior;
yrc
Accumuiating
savings and repaying: debt“ - Running clown 1 , _ _ _ savings ' Eerrowzngr -
l l g. l ‘ Time Start Promotion Retirement work Figure 1.7 The permanent income hypothesis over the life cycle.
assetsandtheircurrentandfutureincome.ThisisafonNardlookingdecisionandwilldepend oninterestrates,asset values,expectationsof futureincome andexpectationsof futuretaxes. ThePIHpredicts thatoptimalconsumptionissmoothascomparedtoincome.Forexample, whenindividualsstartwork,theirincomeislow andtheywillborrowtoconsumemore; whenincomeincreases,theykeep consumptionconstantanduse theexcessincometo payoffdebtsandsaveforretirement;thenatretirement,theirincomefallsandtheydraw downtheir savings.Figure1.7showshowconsumption and income changeoverthelife cycleinthissimplifiedexample.TheimportantpointisthatthePIHpredicts thathouseholds willborrow andsaveinordertosmoothconsumptionovertheirlifetimes.Likewise,over the businesscycle,ifanindividualbecomesunemployed,themodelpredicts thattheywill borrowinorderto sustainconsumptionduring thespellofunemployment.Asweshall seeinChapter 14 onfiscalpolicy,thegovernmentplaysanimportantroleinsmoothing consumption throughtheprovision ofunemploymentbenefits. ThePIHmodelofconsumptionprovidesastarkcontrastwith theKeynesianconsumption functionwherethereisnoexplicitconsideration of thefuture.Aggregateconsumptionof householdsismodelledthereastheconsumptionofafixedamount,coandafixedprOportion ofthe currentperiod'sdisposable income. ThePIHmodelisderivedinmoredetailinSection1.4.2of theAppendix, butitisuse— fultosetout theintuitionand predictions ofthemodel here, as itprovides a frame— workforthinkingaboutfon/vard-lookingconsumptiondecisions.Giventhatincomewill fluctuateovera person’slifetime,thestartingpoint of the PIHistheir desire tosmooth outfluctuationsinconsumption andtheirabilitytosaveand borrowinordertoachieve this. Thenext question that arisesiswhether anindividual prefers theirsmooth consumption path tobe oneof constant consumptionineach period or ofrisingorfallingconsumption. Thiswilldepend onthe relationshipbetween the interest rateonsaving and borrowing and the rate atwhich the individual trades offconsumptioninthe future forconsumptionin
MODELLING
Predictions and empirical evidence on the PIH
The predictions of the PIH can be tested. How does consumption react when a change in income occurs? The answer depends on the nature of the change in income.
- Anticipated or foreseen changes in income should have no effect on consumption when they occur. The reason is that anticipated changes will already have been incorporated into consumption through the recalculation of permanent income. Hence, when the change in current income is recorded, the marginal propensity to consume is predicted to be zero (the multiplier is equal to one). A finding of ’excess sensitivity’ to anticipated income changes would contradict the full smoothing behaviour predicted by the PlH.
- News or unanticipated changes in income should affect consumption because they re- quire the recalculation of future lifetime wealth, \IJf.
(a) News ofa temporary increase in income. If current income yt increases unexpectedly by one unit, consumption increases by the extent to which this raises permanent income. Since the increase in one unit will be spread over the entire future, the PIH consumption function tells us that permanent income and hence consumption rise very little,just by 1’? times the increase in lifetime wealth. The marginal propensity to consume out of temporary income is if. (For example, if the real interest rate is 4%, the MPC is 3.8%, which implies a multiplier barely above one.) (b) News of a permanent increase in income. If there is news that income yt is higher from now and for every future period by one unit, then permanent income and hence consumption rise by the full one unit. This means the marginal propensity to consume out of post-tax permanent income is one. A finding of ’excess smoothness’ of consumption in response to news of permanent income changes would contradict the simple PlH.
Excess sensitivity to anticipated changes in income The first testable hypothesis suggests that there should be no change in consumption at the time income changes, if the change in income was known in advance. This is because consumption should already have adjusted as soon as the news arrived of the change in future income. An influential study by Campbell and Mankiw (1989) tested this hypothesis econometrically using aggregate data on consumption and income from the G7 countries. The study rejected a model in which all consumers were following the PlH but could not reject a model in which half of all consumers were simply following the 'rule of thumb' of spending their current income. In other words, they found that current consumption was overly sensitive to expected changes in income across the G7. A recent study used the 2001 federal income tax rebates in the US as a testing ground: according to the PlH, the one—off (temporary) tax rebate should have very little effect on spending and if there is any effect, it should occur when the announcement was made and not when the cheques arrived. johnson, Parker and Souleles (2006) were able to identify the causal effect of the tax rebate by using household data and the fact that the timing of the sending of cheques was based on the taxpayer’s social security num- ber, which is random. They found that the average household spent 20—40% of the (pre- dictable) tax rebate in the three month period when the cheque was received rather
