3  The Model and Results

According to the lifecycle model, a person saves at one stage of his or her life to consume in another period. Therefore, saving behaviour should differ for different individuals at different stages of their lifecycles. The results shown in Figure 1 are consistent with the usual pattern of saving with respect to age. However, saving behaviour may also evolve over time and vary across birth-year cohorts as economies grow and as certain fluctuations affect individuals contemporaneously. In this section we first present the basic model (Section 3.1), which when estimated with the aid of some identifying structure, makes it possible to distinguish the separate effects of age, cohort and time when using data observed over different age intervals for different birth cohorts. The basic results are in Section 3.2 while additional variations follow in Sections 3.3 and 3.4.

3.1  The Basic Model

The results in the previous section show that there is considerable noise in both the estimated age profiles of saving rates and the birth-year cohort effects. Hence, to see the underlying patterns more clearly, more structure may be needed. One common technique in the literature is to replace individual age effects with a fifth-order polynomial in the age of the household head. This will tend to smooth out much of the noise while still being sufficiently flexible to capture the shape of the underlying age profile. This approach can also be extended to the cohort effects, replacing them with a fifth-order polynomial in year-of-birth.[13] An alternative approach to smoothing out the noise in the cohort effects is to use broader cohorts, such as five-year intervals of birth-year.[14]

In this section we follow the approach of Attanasio (1998) and model the age profile with a fifth-order polynomial and the cohort effects with a set of five-year intervals of birth-year, which were defined in Table 1. The basic model is:

(1)    

where:

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

f = a function representing the fifth-order polynomial in age (a);

γ = the coefficient vector capturing the effects of the cohort intercept dummies;

δ = a function representing the time effects, d_t; and

= the residual term.

The separate effects of a, c, and a+c which equals t, cannot be identified in equation (3.1) and any trends in the data can be arbitrarily attributed to year effects, or a combination of age and cohort effects (Deaton, 1997).

On the other hand, if the year effects are dropped from the model it rules out any uncertainty, such as due to macroeconomic shocks that surprise all members of a cohort. A less extreme assumption than dropping the year effects is to include them but in a normalised form so that they sum to zero and are orthogonal to a time trend.[15] This is equivalent to assuming that all trends in the data can be interpreted as a combination of age and cohort effects and are therefore, by definition, predictable. The time effects then reflect additive macroeconomic shocks or the residual influence of non-systematic measurement error (Jappelli, 1999).

3.2  The Initial Results

The basic results of estimating equation (1) are presented in this section. In keeping with our previous search for robust patterns in the data, this equation is estimated for mean saving rates and for three quantiles: the 25^th, 50^th, and 75^th percentiles of the distribution of saving-to-expenditure ratios.

Table 4 reports the estimates from four regressions on the individual household saving rates. The separate intercepts for each five-year birth cohort are reported, along with the coefficients on the fifth-order polynomial in the age of the household head.[16]. In all cases we reject the hypotheses that either the year effects, the age effects, or the cohort effects are jointly zero.[17]

Note: Coefficients weighted by population sampling weights. Absolute value of robust t-statistics in parentheses; + significant at 10% level; * significant at 5% level; ** significant at 1% level. The sample has N=46269 observations. Each regression also includes 13 time dummies, whose coefficients are constrained to sum up to zero and to be orthogonal to a linear trend.

The cohort effects in the mean saving rate are reported in the first column of Table 4 and follow a somewhat ‘V’ shaped pattern. Relative to the reference group, which is households headed by someone born in 1910-14, saving rates fall across later born cohorts, reaching their lowest point for households headed by someone from the 1930-34 birth cohort, where the saving rate is 14 percentage points below the reference group. Thereafter, the mean saving rate increases monotonically across the more recent cohorts, until it peaks amongst those households headed by someone from the 1970-74 birth cohort, where it is 28 percentage points above the reference group. This result carries the possible implication that downward trends in aggregate saving rates might be temporary, as middle-aged cohorts with low saving rates will eventually be replaced by younger cohorts with higher saving rates.

However, there are fewer grounds for such optimism when considering median saving rates, which exhibit the same ‘dip’ for cohorts born ca. 1925-39 but do not show any statistically significant rise in saving rates across the more recently born cohorts. It appears that the results for mean saving rates are being caused mainly by the behaviour of households in the upper end of the distribution; at the 25^th percentile there are no significant cohort effects, whereas at the 75^th percentile the ‘V’ shape is accentuated. Amongst these households with high saving rates, the results in the final column of Table 4 show that the saving rate for the 1930-34 birth cohort is 28 percent lower than for the 1910-14 cohort. While the cohort effect appears to be largely restricted to the upper end of the distribution, it must be stressed that these are the households who contribute the bulk of aggregate saving.[18] It is therefore, important to describe and understand these cohort effects if one is to make any inferences about the future path of aggregate savings.