3.3  Adding Conditioning Variables[19]

To check whether within-cell heterogeneity can explain the marked pattern of cohort effects, the regression models are augmented with various conditioning variables, controlling for demographics, education, employment, family structure and dwelling tenure. For example, one possible cause of the cohort effects in Table 4 is that there are differences in family structure across birth-year cohorts due, say, to the impact of changing social conditions and welfare policies on the prevalence of sole parenthood. By checking to see if the pattern of cohort effects changes when these conditioning variables are introduced, we test if the shifts in lifecycle saving profiles can be explained by these demographic, education and family structure effects, rather than by pure cohort effects.

Some of the conditioning variables, such as employment status, are likely to change over the lifecycle, whereas others, such as ethnicity and gender obviously remain fixed. In both cases, the conditioning variables are allowed to shift the intercept of the estimated age profile of saving but because of the small sample sizes we do not consider interaction effects where the shape of the age profile can differ between, say, education groups[20]. Therefore, the specification of the regression models is:

(2)     

where:

= the saving rate for household h, observed in year t and belonging to (five-year) birth-cohort c;

= a vector of conditioning variables; and

= the residual term.

When the gender and ethnicity[21] of the household head are included, there is a strong effect of gender, with male-headed households having saving rates approximately nine percentage points higher; but there is no apparent effect of ethnicity on savings. The addition of these demographic controls did not change the basic pattern of cohort intercepts. As in the previous results (Table 4), households whose head was born ca. 1925-1939 show lower than average saving rates, while the rise in savings rates for the more recently born cohorts is even more apparent than when the demographic controls were absent.

The next model included variables for whether the household head is either employed or unemployed, and another variable for whether the head receives self-employment income. In comparison with the reference category, which is households whose head is out of the labour force, average saving rates are seven percent lower if the head is unemployed and 17 percent higher if the head is working. The saving rate appears about 13 percent higher when the household head receives self-employment income. The difference in income levels between the self-employed and other households may be too small to explain this large jump in saving rates,[22] so it may be evidence for theoretical arguments that uninsurable income risk, which is likely to be greater for the self-employed, raises the level of wealth accumulation (Caballero, 1991).

The addition of these three employment variables reinforces the basic cohort pattern in saving rates that was reported in Table 4, with higher saving rates amongst the later born cohorts and lower saving rates amongst the households whose head was born ca. 1920-1939. Adding the employment variables also affects the results for the other demographic controls, halving the coefficient on gender and producing a significantly positive coefficient on ethnicity. Hence, the lower saving rates of female-headed households are partly because of their lower employment rates, while households headed by Maori and Pacific Islanders would have higher than average saving rates if their household heads had employment probabilities that were the same as the rest of the population.[23]

Figure 2 plots the cohort intercepts estimated at the mean, median, 25^th and 75^th percentiles of the distribution of saving rates, along with the intercepts from the models that include conditioning variables. It is evident that the introduction of controls for within-cell heterogeneity does not greatly modify the relative magnitude of the cohort dummies, tending to cause variation only for the most recently born cohorts. There is rather more variation in the patterns of cohort effects estimated at different points in the distribution, so we return to that point below, in considering whether the results are robust to increasingly severe trimming of outliers from the estimation sample.

The other notable feature of Figure 2 is its similarity to results reported by Attanasio (1998, Figure 9). For the U.S., Attanasio finds that the household saving rate falls for the first four five-year birth-cohorts from 1910-14 to 1925-29, and then rises for each of the younger cohorts. With the exception of the later dating of the turning point in New Zealand (the 1930-34 cohort) and the inclusion of cohorts born post-1959, the patterns in the two countries are strikingly similar.