This paper investigates the implications of aggregation in empirical analyses of Euler equations for consumption. We compare the results obtained after estimating the same model using total and non-durable microeconomic consumption data, from the maximum aggregation level (Spanish National Accounts) to household data from the Spanish Expenditure Survey (Encuesta Continua de Presupuestos Familiares). We use this survey to build cohort and aggregate data to test the model using different aggregate measures for consumption. The results we obtain confirm the theoretical predictions summarised in Blundell and Stoker (J Econ Lit 43:347–391, 2005. https://doi.org/10.1257/0022051054661486) as well as in previous empirical evidence, i.e. aggregation turns out to be crucial to empirically study Euler equations for consumption (Attanasio and Weber in Rev Econ Stud 60:631–649, 1993. https://doi.org/10.2307/229812) or when simulating real business cycle models (Guvenen in J Monet Econ 53:1451–1472, 2006. https://doi.org/10.1016/j.jmoneco.2005.06.001). The estimated elasticity of intertemporal substitution (EIS) with aggregated data is biased as compared with the corresponding estimate using microeconomic data. Further, we find that the size of the bias increases with the level of aggregation. Finally, our estimates confirm Hall (J Polit Econ 96:339–357, 1988. http://dx.doi.org/10.2139/ssrn.2704067) result that the EIS is not statistically different from zero, unless panel data are used.
In this framework, Lucas (1976) critique can be considered as the last strike over the empirical aggregate Keynesian consumption functions, and the most relevant impulse to the empirical analyses of consumption with individual data to estimate Euler equations. This is reflected in Hall (1978). Additionally, Geweke (1985) points out that the Lucas critique is equally valid for the parameters of the aggregator function used, an aspect usually not considered in the empirical analysis.
Indeed, diversity (age, race, education, place of residence…) is very important, so that, it is hard to justify models that do not allow for the presence of both observable and unobservable individual effects, which are usually correlated with income and consumption variables (Deaton 1992). The effects of heterogeneity on consumption constitute an issue, which even with the availability of individual data, is far from being solved (see, for instance, Alan et al. 2018).
As noted by Deaton (1992), no one who has looked at the year-to-year variation in reported consumption and income in a microeconomic data set comes away without being convinced that much of the variation is measurement error.
For some purposes, and with large subsamples, sample averages may be precise enough to be analysed as if they were panel data. Otherwise, the sampling errors can be explicitly considered using an appropriate error in variables estimator (Deaton 1992).
There remain some differences between these two sets of aggregated variables (see Table 1) due to several reasons. First, the period available for each series is different for the three statistical reports: private consumption is available from 1970.1 to 1998.4, while expenditure on food and beverages is available only for the period 1980.1–1998.4. All data from the ECPF are available for the period 1985.1–1997.1. Second, the two first components of expenditures considered correspond to national aggregates, while the information from the ECPF is individual data. Therefore, we have to average individual information from the ECPF by quarters to get the corresponding and comparable national aggregates. For doing this, we use the grossing-up factors provided in the ECPF (there is a detailed explanation on the construction of these factors in the methodological guide of the survey).
There is an aggregate variable for food expenditure in the Regional Accounts data, but it is only trustworthy and available from 1985 onwards. For comparative purposes, we report statistics for this aggregate in Table 1.
We should point out that the results we get using this variable are in line with those obtained both for total and non-durable expenditure, at different levels of aggregation, for the Spanish economy (see, for example, Cutanda and Labeaga 2001).
This exercise follows Campbell and Mankiw (1989) second approach, that is appropriate for micro-data (and can also be performed with aggregate data). However, it is different from their first approach which can only be applied with fully aggregated data.
As before, we have tested the validity of the instrument sets using the three tests mentioned before. We get that the tests perform properly for the cohort and panel data estimates, but not for the aggregate estimates.
In the cross section grouping we include all the individuals; the intermediate (young and old) age cohort includes all households where the age of the head of the household is between 30 and 45 (20 and 30, 40 and 50) years old in 1985.
We have assumed that the interest rate is endogenous but we have not explicitly assumed if the correlation comes from correlated effects or from simultaneity. Now, we assume that the correlation comes from correlated effects as the proper interest rate should be an after-tax interest rate, but we cannot calculate this variable, as we do not have information on household marginal tax rates.