Abstract
We used UK Family Expenditure Surveys to analyse the relationship between savings and age structure. We address two key problems: the sample selection bias when data refer to households and not individuals, and the treatment of pension income when drawing inferences from individuals' savings–age profiles about the relationship between an economy's savings and age structure. Our principal findings are that household data exaggerate savings rates of young adults and the elderly whilst underestimating those of 45- to 60-year-olds, and individual saving rates follow more closely the ‘hump shape’ of the life-cycle model, although the savings rates of the elderly remain positive for some ages.
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Notes
This is a common finding which appears to conflict with the simple life-cycle model. Poterba (1994) found that in virtually all the countries he studied, the median savings rate was positive beyond retirement. In the case of the UK, Attanasio and Banks (1998) found that the savings rates of households tend to rise with the age of the household head. However, for working-age households, Blundell et al. (1994) and Attanasio and Weber (1993) have shown that, after controlling for demographics in preferences and non-separabilities with labour supply in a life-cycle model, it is possible to explain observed consumption age profiles.
In Eq. 5 we make the explicit assumption that cohort membership does not affect the income/age profile. However, there is nothing in theory to prevent the patterns of labour income over the life cycle varying by cohort, and this will mean that \(\overline{{\ln h{\left( a \right)}}}\) and θ(a) will also vary by cohort.
Notable recent examples are Banks et al. (1998); Paxson (1996) and Deaton and Paxson (1997). The FES has been extensively researched because it is considered sufficiently accurate for the analysis of consumption and savings. Atkinson and Micklewright (1983) suggest that there is little evidence of underreporting in the income series, with the exception of investment income. Attanasio and Weber (1993) have more recently suggested that for consumption, ‘under-reporting is noticeable only on alcohol, a relatively small item. Expenditure on other items is thought to be accurately recorded, thanks to the careful sampling design’ (p. 633).
Such income is a minor component of total household income.
In all our results we defined the final age group as those aged 80 and over because the number of household heads/individuals in each yearly age group above 80 becomes very small. Our choice of the lowest age group was similarly determined by our desire to have a minimum cell size of 60.
Estimation of Eq. 7 using household-level data was by weighted least squares. The weights are inversely proportional to the standard deviation of the cohort means of each variable. Weighted and unweighted regressions produced very similar results.
The F value of the null hypothesis that the cohort effects were zero was 2.531, which is distributed as F(79, 1,540). We discuss possible reasons for the significance of cohort effects in Section 4. Banks and Rohwedder (2001), using the same data source, also found little evidence for a hump shape in the savings rate over the life cycle, and they also found evidence of positive savings amongst pensioners—a feature that they suggest is especially pronounced in the UK.
In our data, the average age of the head of house of individuals aged 70 years and over is below the age of the individual, although the difference is markedly smaller than that reported by Deaton and Paxson (2000) for the cases of Taiwan and Thailand. This is to be expected, given the importance of the extended family in those countries.
Note that this procedure differs from that adopted in Section 3, where we took means across households of log income and consumption. Here, we take logs of mean income and consumption.
Deaton and Paxson, in their analysis of Taiwanese and Thai households, also obtained negative income (and consumption) estimates for children, and this forced them to use procedures that avoided the need to take logarithms of negative numbers (see Deaton and Paxson 2000, p. 220).
That is restricting \(\overline{\beta } _{{at}} = 0\) for a=1, 2, ..., 15.
For example, if the income estimates of the elderly are biased because poorer households are more likely to have elderly parent members, we would expect the estimated consumption of the elderly to be similarly biased. If there were economies of scale within households, the magnitude of the bias would increase further. However, there may be mechanisms at work in household formation that apply to income but not consumption.
The consumption estimates we derive for each age and year (i.e. the coefficient estimates in Eq. 9, with consumption as the dependent variable) are estimates of the arithmetic means, whereas in Eq. 4 the dependent variable is strictly the average log of consumption. To ensure consistency, we measure savings below as the difference between the log of mean income and the log of mean consumption.
We exclude the earlier age group because their age effects are erratic and would dominate the graph. The age profiles estimated from regressions without cohort and year dummies were similar to those in Fig. 3; most notably, the rise in the savings rate amongst the elderly was still pronounced. The year and cohort dummies were statistically significant: in the case of corrected consumption, the F values are 2.685 and 2.339 for the cohort and year dummies, respectively, distributed as F(93, 1,764) and F(28, 1,764). We therefore report results derived from regressions, including all dummies.
Miles (1999) also suggests that part of the measured high savings rates amongst the elderly is due to the treatment of pension benefits.
Some annuities are ‘backloaded’, so the nominal payments, although not strictly indexed, are tilted to give a greater share of payments in later years.
We treat state pensions as transfers among generations and do not apply the adjustment factor.
In an alternative approach, we subtracted from the nominal interest rate an estimated expected inflation series to derive a time-varying real interest rate, which we then assumed to be constant over the individual's planning horizon. Our results were largely unaffected by this alternative procedure.
See Finkelstein and Poterba (2002) for a detailed discussion of adverse selection in the UK annuity market.
A similar pattern emerges for women. Attanasio and Rohwedder (2003), in a related calculation, used survivorship rates from the English Life Tables which, for reasons of adverse selection, will exaggerate mortality risk amongst pensioners and annuitants.
We are grateful to Edmund Cannon for providing the annuitants mortality tables. See Cannon and Tonks (2004) for further details.
In fact, there are a small number of people in each year who receive annuity income who are below the age of 50.
Indexation is compulsory for occupational pension schemes but is rare elsewhere.
For the adjusted income and corrected consumption case, the 1953 cohort has a savings profile that is slightly above average. The mean savings rate of 66-year-olds over cohorts born between 1918 and 1953 (i.e. over those cohorts that appear in every survey) is −8.3% compared with −7.8% for the 1953 cohort.
Recall that the omission of employer pension contributions and imputed interest earned by the pension fund mean that we are likely to be underestimating the savings rate of those in employment.
The finding of Banks et al. (1998) that consumption growth is negative over retirement could offer some support for this explanation.
Cohorts born between 1918 and 1953 appear in every year covered in our data set: those born in 1918 were 80 in the last year covered (1998), and those born in 1953 were 16 years old in 1969.
For example, estimating the model using corrected consumption and pension-adjusted income over the period 1969–1980, we derive an F test for the null hypothesis of zero coefficients on the cohort dummies of 1.266, which is distributed as F(75,630) and with a p value of 0.073. The same test statistic using data over the period 1981–1998 was 2.388, which is distributed as F(81, 1,008) with an associated p value of 0.000.
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Acknowledgements
The research reported in this paper is part of the project “The Macroeconomy and Demographic Change” undertaken as part of the Economic and Social Research Council (ESRC) programme Understanding the Evolving Macroeconomy (ESRC award L138251001). Financial support from the ESRC is gratefully acknowledged. Material from the Family Expenditure Surveys used in this paper is Crown Copyright; it has been made available by the Office for National Statistics through The Data Archive, and has been used with permission. Neither the ONS nor The Data Achive bear any responsibility for the analysis or interpretation of the data reported here. The authors are grateful for helpful comments from Cliff Attfield, David Winter, Edmund Cannon, Olwen Renowden, Elisabeth Dedman, Ian Tonks, Caroline Joll and two anonymous referees. We accept full responsibility for all remaining errors.
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Demery, D., Duck, N.W. Savings–age profiles in the UK. J Popul Econ 19, 521–541 (2006). https://doi.org/10.1007/s00148-005-0039-6
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DOI: https://doi.org/10.1007/s00148-005-0039-6