Abstract
This paper examines the role of household formation in providing consumption insurance to the elderly. Using data from the Consumer Expenditure Surveys, raw tabulations of per adult equivalent consumption indicate that the elderly who live alone have higher levels of well-being relative to those who live with others. This is misleading, however, because the decision to live alone is clearly endogenous. The empirical estimation accounts for this endogeneity using data from the Panel Study of Income Dynamics. The results provide evidence that household formation plays a significant role in maintaining consumption levels. Without the opportunity to live with others, the welfare gap measured by the difference between per adult equivalent consumption levels of dependent and independent livers would be even larger. These findings suggest that co-residing with others effectively supplements social security, pensions, and private savings and helps the elderly to smooth consumption in old age.
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Notes
Defining a measure of the standards of living that captures all aspects of well-being is a difficult task. Most of the previous work on the economic status of the elderly simply uses (adjusted) household income as the measure of well-being. Recent literature has shown, however, that consumption (that is also adjusted for differences in household composition) is a superior indicator than income in inferring the standards of living. Therefore, I emphasize here that my goal in the present paper is not to present the best measure of welfare in a multidimensional framework. Rather, given the available data, I focus on “economic” well-being and use (adjusted) household consumption as an indicator to explore the role of household formation in providing insurance to the elderly.
The CEX are available on an annual basis starting from 1980. However, in 1982 and 1983, the data were collected for the urban population only. As I want to keep my analysis representative of the overall US population, I do not use data from these 2 years of the CEX.
In estimating consumption levels, I modify the total expenditure variable recorded in the CEX in a number of ways. Expenditures on gifts and cash contributions are deleted as are retirement contributions and Social Security payments. Outlays on owner-occupied housing, such as mortgage interest payments, insurance, and property taxes are replaced with households’ estimates of the rental equivalents of their homes. Purchases of durable goods are replaced with estimates of the services received from households’ stocks of these goods [for more on the reasoning of these adjustments and on the details of the methods used to compute the rental equivalent of owner occupied housing and the service flows from consumer durables, see Slesnick (2001)]. After these adjustments, my estimate of total expenditure includes spending on nondurables and services (a frequently used measure of consumption) in addition to the service flows from consumer durables and owner-occupied housing. Subsequently, the price levels calculated by Slesnick (2002) are used to deflate total expenditure to obtain a real estimate of consumption.
I define the number of adult equivalent members for household i as \( N_{i} = {\left( {K_{i} + \beta \,L_{i} } \right)}^{\varepsilon } \) where K i is the number of adults in the household and L i is the number of children. For the parameters β and ɛ (which denote the cost of children and the economies of scale), I use the values 0.5 and 0.75, respectively. These values are generally consistent with what has been suggested by previous empirical findings. When I continually increase the parameter values of β and ɛ toward 1, estimation results that will be presented later in the paper change slightly, but the main implications remain robust. In the literature, this form of equivalence scale is referred as the Banks and Johnson’s (1994) specification. Alternative, more rigorous approaches to measuring equivalence scales are surveyed by Browning (1992) and Slesnick (1998).
For a detailed discussion of this imputation, see Skinner (1987).
The PSID collects information on older individuals’ transitions to living in nursing homes or other institutions. However, no consumption data is available for those institutionalized households. Therefore, in the present study I only consider the non-institutionalized households.
In 1990, to make the Hispanic households more representative, 2,000 Latino households, including families originally from Mexico, Puerto Rico, and Cuba are added to the original 1968 core sample of the PSID. However, the wealth data are not collected for the Latino households in 1994, and they are dropped from the sample after 1995. Therefore, rather than including the Latino sample in my study, I use only the 1968 core sample of the PSID, in which the Hispanic households are under-represented considering their 7.5% population share in 1993 CPS.
In the regressions, rather than using all of the ADL and IADL indicators separately and causing multicollinearity, I combine these indicators and define qualitative ADL and IADL health indicators as described in Table 4. Nominal wealth is measured in the amounts of dollar equivalents.
I have also described the health dummies in several different ways, and in all of the cases, the health effects on the living arrangements of the elderly were statistically insignificant. Rather than combining married and single groups all together, my robustness check of this finding using only the single elderly sample provides slightly stronger relationship between health and living arrangements. However, the statistical insignificance of this relationship still holds. Estimation results are available from the author upon request.
Unfortunately, in most of the surveys, wealth is not measured at the individual level except for some components. Individual level wealth here refers to per adult equivalent wealth of the elderly. For the group of the elderly who live independently, it is set equal to the logarithm of their observed per adult equivalent wealth. For the group of the elderly who live with others, I impute it as follows. I first run a regression of per adult equivalent wealth for the elderly who live independently, using some exogenous demographic characteristics such as education, race, and age, observed individual level wealth components, and also the detailed information on income sources such as income from assets, transfers, and labor. The PSID provides the information on income sources at the individual level. Then, using the estimated parameters of this regression and the same explanatory variables for the group of the elderly who live with others, I fit the regression. The logarithm of fitted values is assumed to be the log of their individual level wealth. Rather than using these imputed values, proxying wealth by individual level income and education also yield very similar conclusions regarding the substantive results of the paper.
Indeed, using a Durbin–Wu–Hausman, test I fail to reject the endogeneity of the household structure dummy in Eq. 2.
I would like to emphasize here that the reason I denote “observed” per adult equivalent wealth levels in Table 7 by household types relates to my measurement of consumption by per adult equivalent levels. The purpose of the raw wealth statistics is only to show that in overall terms if those households that have higher per adult equivalent wealth have also higher per adult equivalent consumption. Thus, I do not aim to define individual wealth as household wealth per capita, as it was explained in subnote 10 as well. If I did, it would make little sense if the old individuals are poor and the young kids are wealthy. Furthermore, it would clearly mix the influence of household structure through wealth pooling of poor elderly (which would be the demand effects) and the wealthy kids (supply effects) with the influence of individual level wealth.
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Acknowledgment
I would like to thank two anonymous referees for their helpful comments. All remaining errors, if any, are solely mine.
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Ulker, A. Household structure and consumption insurance of the elderly. J Popul Econ 21, 373–394 (2008). https://doi.org/10.1007/s00148-007-0150-y
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DOI: https://doi.org/10.1007/s00148-007-0150-y