# INTERTEMPORAL CHOICE AND THE CROSS-SECTIONAL VARIANCE OF MARGINAL UTILITY: Regression results 2

In Table 4 we compute marginal utility using the specification blue-collar workers, heads out of employment, full-time working spouse, and more than two income recipients. This specification of the instantaneous utility function has been estimated by Attanasio and Weber (1993, 1995) on the same FES and CEX cohort data. Thus, we can readily use their estimates of в to compute marginal utility.19 The actual values of the estimates and the details about the construction of marginal utility are described in the appendix. We do not attempt to fit a flexible Euler equation to Italian data. Due to the few surveys and the fact that we work with annual data, the number of observations is much lower than in the other two countries. The point estimate of к for the UK and the US in Table 4 are again very close to unity, regardless of the instrument set. Given also the small standard errors of the estimate, in no case we reject the hypothesis that я = \. The point estimates obtained by dropping the retired do not show again appreciable differences.

Table 4

Dependent variable: variance of marginal utility

Country | Coefficient | Standard error | P-value | Instrument set | Number of observations |

United Kingdom | 0.924 | 0.068 | 0.26 | !ag2 variance | 766 |

1.001 | 0.073 | 0.93 | age, age^{2} |
776 | |

0.966 | 0.066 | 0.57 | age, age^{2}, lag2 variance |
766 | |

United States | 0.952 | 0.193 | 0.81 | lag2 variance | 500 |

0.925 | 0.217 | 0.73 | age, age^{2} |
510 | |

0.948 | 0.163 | 0.75 | age, age^{2}, tag2 variance |
500 |

The life-cycle hypothesis predicts that the cross-sectional variance of the marginal utility of consumption is equal to its own lag plus a constant and a random component. Using fairly general preference specifications and auxiliary assumptions about the nature of the random component, we provide an explicit test of this hypothesis. Our approach circumvents the necessity to identify a pure age profile of the cross sectional variance of consumption and yields a well specified statistical test. On the other hand, the test we propose is only valid under specific assumptions about the shocks of the Euler equation for consumption.

Cohort data for the UK, the US and Italy provide strong support for the hypothesis that the coefficient of the lagged cross-sectional variance of marginal utility is equal to one, i.e., the joint hypothesis that the theoretical restrictions on the evolution of the cross-sectional variance and the auxiliary identification assumptions we use are consistent with the data.