The response of consumption to income: A cross-country investigation

The response of consumption to income: A cross-country investigation

764 J.H. Cochrone, Comments So what should we do instead? Work on equilibrium models can be split up into independent pieces, but by agents rather ...

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J.H. Cochrone,


So what should we do instead? Work on equilibrium models can be split up into independent pieces, but by agents rather than by aggregates: One researcher can study households’ consumption and labor supply (simultaneously) and infer their preferences. Another can study firms’ output supply, investment and labor demand and infer their technology. Euler equation methods - essentially measures of marginal rates of substitution - are particularly convenient to these studies, as they do not require a complete specification of each agent’s budget constraint, or explicit solution for his decision rule. These investigations could go on independently of each other, and contribute information that survives when placed in an equilibrium model, even one with frictions, and is therefore useful to the refinement of such models. If we had never seen ISLM models, we probably would have divided empirical work this way rather than continuing and trying to adapt work on ISLM equations. In fact, equilibrium model-builders, tired of having to reestimate taste and technology in each paper to match equilibrium dynamics with data, are already adopting the preferences from the latest Euler equation tests. Thus, I suspect that this pattern of work will emerge spontaneously, though later than one might have predicted. References Akerlof, George A. and Janet L. Yellen, 1985, A near rational model of the business cycle with wage and price inertia, The Quarterly Journal of Economics 100, 824-838. Cochrane, John H., 1989, The sensitivity of tests of the intertemporal allocation of consumption to near rational alternatives, American Economic Review 79 (June) 319-337. Eichenbaum, Martin S., Lawrence Christian0 and David Marshall, 1990, The permanent income hypothesis revisited, Econometrica, forthcoming. Hansen, Lars Peter, William Roberds and Thomas J. Sargent, 1990, Time series implicauons of present value budget balance and of martingale models of consumption and taxes, Manuscript. Sargent, 1987, Macroeconomic theory, 2nd ed. (Academic Press, New York).


‘The response of consumption A cross-country investigation’ by John Y. Campbell

and N. Gregory

to income: Mankiw

David F. Hendry Nufjeld The

College, Oxford, OXI INF. UK



John Campbell

and Gregory


is an interesting





attempt to test their theoretical paradigm against the data for a number of countries. Given the many results in their paper, I will only consider a subset of their findings, illustrating the analysis with empirical evidence from the data they kindly supplied. In particular, the similarity of the results for their formulation across countries is impressive and cannot be greatly impugned by the findings reported below for the U.K. (using quarterly, not seasonally adjusted, data). Conversely, the error-correction modei proposed in Davidson et al. (1978) (denoted DHSY) also performs well in the U.K., France [see Hendry (1988)] and Holland [see Hendry (1989b)J. The basic argument that a subgroup of consumers may behave in terms of their ‘current income’ rather than their ‘permanent income’ is a wellestablished one in the U.K. literature [see e.g. Flemming (1973)], and was one of the background ideas suggesting the fo~ulation in DHSY, and its extension in Hendry and Ungern-Sternberg (1981)J. The most recent evidence suggests that the last mode1 is continuing to perform well [see Carruth and Henley (1990); also see Hendry, Muellbauer and Murphy (1990) for annual evidence]. The major difference between the DHSY and Campbell-Mankiw approaches concerns the choice of instrumental variables. The former argue for the legitimacy of all the regressors, interpreting their model as a contingent plan which is congruent with the data evidence, whereas the latter employ instrumental variables lagged at least five quarters on the grounds that their ‘annua1 change’ model involves overlapping periods, and so common measurement errors. Since the DHSY equation is actually in ~eue~s, but restricted to be homogeneous in income, it is unclear what the relevance of overlapping measurement errors is, especially as DHSY offer evidence on the minor impact measurement errors must have had on their estimates. From the notes to their table 1, the issue of lag length of instruments is initially unclear for unadjusted data, but ex~rimentation yielded [T= 1957(2) to 1988(2)]? day,=0.041 Qi,+0.006Q21+0.007Q~,-0.043+0.521 d4y,-i (0.010) (0.005) (0.005) (0.024) (0.098) +0.448dg~r_1+0.384d(~-y)~_4-0.011Z;~(c-y),_,, (0.153) (0.088) (0.008) iP=0.590,





This equation results in an R2 value far in excess of any they report. It is important to note that for a government agency, for example, all of the ‘All of the estimates quoted below were calculated using PC-GIVE [see Hendry (1989a)J.


J.H. Cochrane.


regressors are known at the start of period t, so that (1) could be used for forecasting. Apparently the form entailed in table 1 is given by an equation like: d,y,=0.051-0.257d,y,_~+0.190(c-y),-~+0.605d~c,_~ (0.011) (0.135) (0.059) (0.218) -O.l02d(c-y),_,, (0.062) R2=0.152,


(2) F(4,120)=5.38,


Since the most recent allowed information is from live periods earlier, it is not too surprising that the annual growth rate of real disposable income is poorly predicted. Nevertheless, it is possible that data errors have increased as a proportion of the levels of the variables over the last decade, and a comparison of least squares (OLS) with instrumental variables (IV) estimates of their basic equation is not inconsistent with such a proposition, since the coefftcient of income rises from 0.495 (OLS) to 0.685 (IV) using the instruments in (2) above, although there is not much change in 6 (1.25% to 1.38%). However, the specification x2 test [see Sargaran (1964)] yields x2(4)/4= 4.55, strongly rejecting the validity of the instruments (and that of several similar sets). This problem appears to be due to a structural break after 1985, which Hendry et al. (1990) attribute to financial deregulation, which loosened credit constraints on a significant proportion of households. Consistent with such a view. we find: d,c,=O.660 d,y,+O.O21 D85,+0.004, (0.086) (0.003) (0.002) &=0.0118,


DW= 1.822,

Specification x2(4)/4= 1,82, Normality F ARK--5C5,1171=1.98,


x2(2) =2.50,



Eq. (3) entails that given the income stream, annual consumption was 2.1% higher than would have been anticipated. Although (3) fails a number of diagnostic checks, the departure from the pre-1985 relationship is very large on any metric, and inconsistent with the constancy of their basic model over time in the U.K. (see their table 7). If A is not in fact a parameter, then the

J.H. Cochrane. Comments


formulation is open to question. Certainly, Campbell and Mankiw test for the potential presence of an error correction term, and report negative results. This finding also holds for the U.K., and is due in large measure to the inefficiency of the instruments, when the latter are restricted to enter no earlier than 5 quarters previously. The feedback coefficient point estimate, however, is close to that found in other studies (around -0.1). provided some allowance is made for the post-1985 break (see their table 4). Thus, their evidence is not inconsistent with the DHSY model estimates, which have the virtue of ensuring cointegration of consumption and income. An encompassing test does not seem feasible between models where there is such a large disagreement about the legitimacy of the rival sets of instruments. From DHSY’s perspective, the Campbell-Mankiw instruments are valid, but highly inefftcient and their overidentifying instruments are in practice orthogonal to the DHSY residuals. From the perspective of Campbell and Mankiw, this is an unfair test, since illegitimate information (i.e. contemporaneous or one-log depending on the formulation) used. Hopefully, forecast encompassing tests might offer some discriminating power, using the same information minimally acceprable to both parties, and the coefficient estimates based on the two rival views, for ex post data. References Carruth, A. and A. Henley, 1990, Can existing consumption functions forecast consumer spending in the late 198Ck?,Oxford Bulletin of Economics and Statistics 52, 21 l-222. Flemming, J., 1973, The consumption function when capital markets are imperfect, Oxford Economic Papers 25, 160-172. Davidson, J.E.H., D.F. Hendry, F. Srba and S. Yeo, 1978, Econometric modelling of the aggregate time-series relationship between consumers’ expenditure and income in the United Kingdom, Economic Journal 88.661-692. Hendry, D.F. and T. von Ungern-Sternberg, 1981, Liquidity and inflation eNects on consumers’ expenditure, Ch. 9, in: A.S. Deaton, ed.. Essays in the theory and measurement of consumer behaviour (Cambridge University Press, Cambridge). Hendry, D.F., 1988, Some foreign observations on macro-economic model evaluation at INSEEDP, in: Groupes d’etudes macroeconometrique concertees (Institute National de la Statistique et des Etudes Economiques). Hendrv. D.F.. 1989a. PC-GIVE: An interactive econometric modelline- svstem (Institute of Economics and Statistics, Oxford). Hendry, D.F., 1989b. Comment on ‘intertemporal consumer behaviour under structural changes in income’, Econometric Reviews 8, 11l-121. Hendry, D.F.. J.N.J. Muellbauer and A. Murphy, 1990, The econometrics of DHSY, p. 298-334, in: D. Winch and J. Hey, eds., A century of economics (Basil Blackwell, Oxford). Sargan, J.D., 1964, Wages and prices in the United Kingdom: A study in econometric methodology, in: P.E. Hart, G. Mills and J.K. Whitaker, eds., Econometric analysis for national economic planning (Butterworths, London).