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INTERTEMPORAL CHOICE AND THE CROSS-SECTIONAL VARIANCE OF MARGINAL UTILITY: Appendix

Seasonal adjustment

In the FES and in the CEX consumption is observed at a frequency higher than annual. In the FES consumption refers to the two-week period over which the household is interviewed; in the CEX it measures the flow of expenditure in each of the 3 months preceding the interview. This feature of the data makes seasonal adjustment indispensable: we must avoid mixing seasonal variations with the cross sectional variability of consumption.


Since in the FES each household is interviewed only once, seasonal adjustment is easier. This is performed using a simple log-linear model of monthly seasonality. In the CEX, each household provides up to 12 observations. There are two pitfalls. On the one hand, we do not want to mix seasonal with genuine cross sectional variability; on the other, we want to avoid having the same household providing more than one observation within each period cell.20 If the interviews were synchronized, it would be easy to construct annual (or quarterly) consumption figures and use those in computing means and variances by year. Given the overlapping nature of the sample, we rely on an alternative procedure. Among several alternatives, we report results for the simplest one: for each household we consider only the first monthly observation. We use the first rather than the last observation to minimize the influence of non-random attrition. The data are then adjusted for seasonality using the same model as in the case of the FES data.

Parameters of the Euler equations used to compute the marginal utility
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Further assuming that г includes demographic as well as labor supply variables, and using quarterly cohort data from the FES (1970-1987), Attanasio and Weber (1993) estimate
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where oow is a dummy for the household head out of work, та a dummy indicating more than two adults, wch a dummy for white collar workers, and ww a dummy for working spouse; young children are those of pre-school age (0-5). For details and standard errors, see Attanasio and Weber (1993, column 2 of Table 1 of the Appendix).

For the US, Attanasio and Weber (1995) use quarterly cohort data derived from the CEX from 1981:3 to 1990:4 and estimate
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where children is the household members between the ages of 0 and 15, w>w is a dummy for the wife working full-time and wl is the wife’s annual hours of leisure (see Attanasio and Weber 1995, Table 3, column 3).

We ignore the real interest rate term, which is only a factor of proportionality and does not affect the regression results. We also ignore the seasonal dummies because they do not affect the computation of the cross sectional variance. The parameters above allow straightforward computation of [ln(c(V) + aO z( f ].

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