# INTERTEMPORAL CHOICE AND THE CROSS-SECTIONAL VARIANCE OF MARGINAL UTILITY: Cohort definition and descriptive analysis

In each survey we restrict the sample to households headed by individuals born between 1910 and 1959 and define 10 groups: cohort 1 includes those born in 1915-19, cohort 2 those bom in 1920-24, and so on, up to cohort 10, 1955-59. We define the “age” of the cohort as the median age of each cohort in a given sample period (for instance, the age of cohort 1, born in 1910-14, is 68 in 1980, 69 in 1981, and so on).

Table 1

Average and minimum cell size in the FES, the CEX and the SHIW

Cohort | Year of birth | Age in 1985 | United Kingdom (FES) | United States (CEX) | Italy(SHIW) | |||

Mean | Minimum | Mean | Minimum | Mean | Minimum | |||

] | 1910-14 | 71-75 | 133 | 55 | 65 | 29 | 696 | 582 |

2 | 1915-19 | 66-70 | 127 | 81 | 78 | 47 | 764 | 739 |

3 | 1920-24 | 61-65 | 160 | 125 | 90 | 60 | 937 | 874 |

4 | 1925-29 | 56-60 | 142 | 102 | 88 | 53 | 859 | 838 |

5 | 1930-34 | 51-55 | 134 | 106 | 86 | 55 | 918 | 856 |

6 | 1935-39 | 46-50 | 141 | 114 | 92 | 66 | 836 | 807 |

7 | 1940-44 | 41-45 | 151 | 118 | 114 | 76 | 799 | 766 |

8 | 1945-49 | 36-40 | 183 | 134 | 151 | 96 | 714 | 661 |

9 | 1950-54 | 31-35 | 156 | 58 | 174 | 128 | 390 | 298 |

10 | 1955-59 | 26-30 | 121 | 1 | 201 | 148 | 355 | 284 |

Table 1 reports the cohort definition and, for each survey, mean and minimum cell size by cohort. The assumption behind our procedure is that the cross sectional variance refers to the same group of individuals at different points in time. Even though we do not need to observe the same individuals over time, the test requires that the sample composition be constant. The positive correlation between survival probabilities and wealth implies that rich households are over-represented in the older cohorts. The correlation between wealth and young headship (young working adults living independently are likely to be wealthier than average) suggests that rich households may also be over-represented in the youngest cohorts. Accordingly, we exclude households where the head is older than 80 years or younger than 20.

The construction of cohort data involves taking means of the marginal utility within each of the cells over successive time periods. Aggregation, however, is not an issue in this context. Each of the methods of measuring the marginal utility of consumption first defines an index of marginal utility at the household level; the cross-sectional variance of this index can then be readily computed within each cell.

Before presenting the regression results, we provide a graphical exposition of the data. In Figures 1, 2 and 3 we plot the cross-sectional variance of the logarithm of consumption for the UK, the US, and Italy, respectively. Each connected segment refers to a different cohort, observed over time at different ages. The cohort numbers, let us recall, run from 1 (the oldest) to 10 (the youngest). To facilitate the comparison across countries, the graphs are plotted on the same scale. These graphs are similar to the raw variances produced by Deaton and Paxson (see their Figures 2 and 3 for the US and the UK, respectively).