مقاله کار از آوریل 1985: آنچه که آن را کشش تقاضا می دانیم و آنچه که ما نیاز به تجزیه و تحلیل سیاست می دانیم؟

This paper presents some results on the theory and estimation of intertemporal allocation mechanisms. The results rely heavily on the distinction between anticipated changes and unanticipated changes.

The efficacy of a wide range of policies depend on the reaction of consumers to changes in prices. As an illustrative example, consider a proposal to reduce capital taxes and increase taxes on some goods that have the avowed intention of increasing the savings rate. If we include leisure amongst our goods then it will be clear that we are looking at possible changes in earned income, capital and commodity taxes. The proposed decrease in capital taxes lowers the discounted price of all goods in the period after the implementation of the change relative to the price of goods before. The increase in tax on some goods off-sets this to a certain extent and also increases the relative price of these goods in any period after the implementation of the policy. The effects of these price changes on demands will determine the success or failure of the proposal but they are not easy to predict. The central theme of this paper is that the analysis of inter-temporal decisions is much facilitated if we make a distinction between anticipated (or evolutionary or dynamic equilibrium) changes and unanticipated (or parametric or dynamic disequilibrium) changes. The reason for this is that anticipated changes have only substitution effects which can often be unambiguously signed. Unanticipated changes, however, have both income and substitution effects which invariably have ambiguous outcomes. The motivation for using the anticipated/unanticipated dichotomy for analysing tax changes is that major changes tend to be few and far between so that in the periods between announcements the effects are anticipated. To illustrate: the announcement of a cut in capital taxes has a once and for all positive income effect for those who, before the announcement, were planning to save (see Tintner, 1938). As well as this, the cut makes consumption in any period cheaper relative to consumption in the period before. For any pair of periods after the announcement these effects are ‘anticipated’. In a world of perfect certainty all changes are anticipated. In such a world rational agents facing perfect capital markets will keep the marginal utility of discounted expenditure constant from period to period. In Section 2 we discuss demand functions that, under the assumption of inter-temporally additive preferences, depend only on prices within the period and the (constant) marginal utility of expenditure that is Frisch demand functions. It is the elasticities associated with these functions that give us responses to anticipated changes. We discuss when Marshallian (constant expenditure) or Hicksian (content utility) elasticities are close to these. Our conclusion is that for the sorts of changes in prices induced by tax changes the use of the inappropriate demand elasticities may give misleading results. As is well known, we may move from Marshallian elasticities to Hicksian elasticities (and back again) by using the Slutsky equation. We can also move from Frisch elasticities to Marshallian elasticities. However, to move from Marshallian elasticities, which are essentially static, to Frisch elasticities, which are dynamic, we need one extra parameter. This parameter is the inter-temporal substitution elasticity. This parameter indicates how (discounted) expenditure changes following an equi-proportional change in all (discounted) prices. A value of ϕ for the intertemporal substitution elasticity implies that a one percent fall in all (discounted) prices (that is a one percent own real interest rate for all goods) leads to a fall of (1+ϕ) percent in (discounted) expenditure. We can either estimate Frisch responses directly or derive them from independent estimates of Marshallian responses and the inter-temporal substitution elasticity. If we choose the former route then we can use the implied estimates of Marshallian elasticities to check our system. The latter course leads to the joint estimation of demand systems and consumptions functions. Much of the rest of the paper is devoted to the estimation of Frisch responses. One other topic dealt with in Section 2 is the interpretation of the specific own-price substitution effect in an inter-temporal context. It is well known that we can decompose the Hicksian (fixed utility) substitution effect into a specific and a general substitution effect (see Houthakker, 1960). The specific substitution effect is the fixed marginal utility of expenditure or Frisch effect. We propose a further decomposition of the own-price specific substitution effect in a temporal context into an inter-temporal effect and an intra-temporal effect. These take account of the fact that a price change for any single good from one period to another constituted a change in the price between periods and a change in intra-period relative prices. This decomposition is intuitively appealing and allows us to talk of the (specific) substitutability or complementarity between any particular good and all other goods taken as a composite commodity. Section 3 takes up the discussion of the analysis of inter-temporal decisions in an uncertain world. We propose realisations of future random variables that are ‘anticipated’ or, at least, that give the same decisions in the first period as would be taken if there were no uncertainty and the ‘anticipated’ realisations were genuinely anticipated. Such ‘action certainty equivalent’ realisations allow us to take over much of the apparatus for dealing with the certainty case. We also discuss the relationship between action certainty equivalent values and mathematically expected values. Since the former depend on beliefs and preferences and the latter only on beliefs, it is not surprising that the relationship between the two should depend on preferences. This has implications for our later econometric work where expected values are used as proxies for action certainty equivalent values. Section 4 takes up the problems of estimating Frisch consumption functions. These are equations that relate the total expenditure (real, nominal or discounted) in any period to prices and the marginal utility of expenditure. The major problem to be overcome is that the latter is, of course, unobservable. The principal parameter to be estimated in such equations is the inter-temporal substitution elasticity. We show the form that preferences over time must take (including the normalisation on the within-period utility function) if this elasticity is to be constant. As a sub-case we look at the implications of assuming that the inter-temporal substitution elasticity is minus one. These assumptions imply particular forms for intra-temporal preferences (that is for the demand system) as well as for inter-temporal responses. Finally we show that using expected values as proxies for action certainty equivalent values lead to a bias in the estimate of the constant in a change-in-expenditure equation. We show that one interpretation of a positive value for this constant is that ‘caution overcomes impatience’. In Section 5 we apply one of the functions derived in Section 4 to UK aggregate time-series data on seven goods for the period 1900–1955. The consumption function estimated does not have income as a regressand; in fact a series for personal disposable income is only available for a sub-period of our data period. Thus our consumption function does not have income as a regressor. Nevertheless it ‘fits’ the data relatively well and gives an estimate of the inter-temporal substitution elasticity that is significantly different from minus one. Section 6 deals with the estimation of Frisch demand systems. These determine individual demands or expenditures as functions of prices and the marginal utility of expenditure. Once again the main focus in on dealing with the unobservability of the latter. Attfield and Browning (1985) used the homogeneity and symmetry constraints in these demand systems to identify the relevant parameters. Here we adopt a more direct, instrumental variable approach that has much in common with the technique suggested by Hansen and Singleton (1982). The final substantive section gives some estimates of a Frisch demand system using UK post war aggregate time-series data. The results here are, on the face of it, encouraging. We can estimate all of the Frisch elasticities and from these derive the implied Marshallian and Hicksian elasticities. All of these are ‘acceptable’, in the sense that all own-price elasticities are negative and the expenditure elasticities are ‘sensible’. We note, however, that there may be problems with the dynamic structure as well as some need to take account of durables and labour supply. Section 8 draws together some of the discussion and makes some suggestions for future investigations

This paper has presented some discussions and estimates of the parameters required for the analysis of the effects of anticipated changes. We argued than many of the important consequences of tax changes will be predictable from such analysis. We also showed that analysis based on static (Marshallian or Hicksian) estimates is likely to be misleading but that we can move to dynamic (Frisch) analysis if we know a single parameter, the intertemporal substitution elasticity. We examined the consequences of assuming that this elasticity is constant and showed that this implies a particular form of intra-temporal preferences (in fact, PIGL preferences). Given the crucial role that the inter-temporal substitution plays, we paid a good deal of attention discussing how we might measure it. Based on this, we presented two independent estimates of the elasticity (=−.16 and −.22 from 5 and 7, respectively). Both are negative, as the theory requires, and both are significantly greater than −1. The estimate from the Frisch demand system is also significantly less than zero. These point estimates are in line with other well-based estimates, see Summers (1982), Muellbauer (1983), Wickens and Molana (1984) and Browning (1984). All in all, the empirical results published here encourage us to investigate further ‘consumption functions without income as a regressor’ and ‘demand systems without expenditure as a regressor’. On the other hand, the link between static and dynamic analysis can be made through more conventional territory or even by assumption. The point still stands that the analysis of anticipated changes is both possible and useful