Intergenerational earnings mobility: A new decomposition of investment and endowment effects☆
Introduction
A number of studies focus on measuring the intergenerational elasticity in earnings by specifying a linear regression equation between log earnings of children and log earnings of parents (Solon, 1992, Zimmerman, 1992, Dearden et al., 1997, Mazumder, 2005). Important extensions of this framework include a comparison of the level of mobility across countries (Corak, 2004, Jäntti et al., 2006, Bratsberg et al., 2007), across time (Blanden et al., 2007), and across parental income (Bratsberg et al., 2007, Grawe, 2004, Corak and Heisz, 1999). For reviews, see Solon (1999) and Black and Devereux (2011).
More recently, the focus is on identifying the underlying factors that determine the overall size of the earnings elasticity. Lefgren et al. (2012) specify a linear model which is estimated using a range of instrumental variables to provide bounds on the relative contributions of financial investments and human capital. Blanden et al. (2007) also adopt a linear model but decompose the mobility elasticity by specifying a broader set of factors covering cognitive and non-cognitive variables, as functions of parents' earnings. An alternative approach is adopted by Sacerdote (2002), Björklund et al. (2006) and Liu and Zeng (2009) who use data on adoptions, and Amin et al. (2011) who use data on twins, to isolate the effect of financial investments from the effects of unobserved endowments. In related work, Brown et al. (2011), Farré et al. (2012), Plug and Vijverberg, 2003, Plug and Vijverberg, 2005 and Plug (2004) focus on the intergenerational transmission of schooling, while Ekhaugen (2009) focuses on the intergenerational transmission of unemployment.
An important feature of the existing literature is the use of specialized data to decompose the intergenerational earnings elasticity. This is especially true for decompositions based on twins and adoption data. The work of Blanden et al. (2007) also requires specialized data, including information on childhood test scores, behavioral problems, attitudes and personality. Even the instrumental variable approach of Lefgren et al. (2012) requires suitable instruments which can distinguish accurately between human and non-human capital factors. Without a set of reliable instruments to identify both factors the usefulness of this approach is limited, as the size of the bounds on the relative contributions of the factors may potentially be wide. There is also the additional problem that if the instruments are weak in the sense of Stock et al. (2002), the sampling distributions of the instrumental variable estimator cannot be expected to have a standard asymptotic form.
The aim of this paper is to provide an alternative decomposition strategy which makes direct use of economic theory and the statistical properties of the stochastic processes underlying the theory, while circumventing the need for specialized data. The approach consists of specifying a heterogeneous model of intergenerational earnings based on the work of Becker and Tomes (1979) and Solon (2004), where log-earnings of children are determined by the log-earnings of parents and two sources of randomness based on labor market and endowment shocks. A key feature of the model is that parental income is shown to impact upon child income via two pathways: (i) through its effect on human capital investments (investment effect), and (ii) through its effect on child endowment (endowment effect). The combination of these two channels results in a nonlinear relationship between log child earnings and log parent earnings, thereby providing theoretical support for the nonlinear polynomial specifications adopted by Bratsberg et al. (2007), Solon (1992) and Behrman and Taubman (1990).
Using PSID data on father–son pairs in the US over the period 1968 to 2005, the results show that at the average father's earnings the intergenerational earnings elasticity estimate is 0.535, with approximately one-third of this elasticity explained by the investment factor (higher human capital investments during childhood), with the remaining two-thirds arising from the endowment factor (higher endowments). This finding is similar to the 37–63 investment–endowment split reported by Lefgren et al. (2012) using Swedish father and son income data. Similar decomposition results are also found by Amin et al. (2011) using Swedish twin data and Björklund et al. (2006) using Swedish adoption data; though, definitions of investments and endowments differ between studies. In addition, as a result of the nonlinear structure of the model the empirical results also show that the relative decomposition varies with log-earnings of fathers, with the investment effect dominating the endowment effect at low incomes and the reverse occurring at high incomes.
The rest of the paper proceeds as follows. A preliminary analysis of the data and structure of the relationship between log-earnings of children and parents is presented in Section 2. A two factor model of intergenerational earnings transmission is presented in Section 3 which is used in Section 4 to decompose the intergenerational mobility elasticity into investment and endowment factors and to construct the likelihood function. The empirical results are presented in Section 5, which are compared to existing findings in the literature in Section 6. Concluding comments are provided in Section 7.
Section snippets
A first look at the data
The data consist of annual earnings of sons (yc) and fathers (yp) in the US, taken from the Panel Study of Income Dynamics (PSID) over the period 1968 to 2005, including data from both the representative sample from the Survey Research Center (SRC) and the sample from the Survey of Economic Opportunity (SEO). The sample is restricted to earnings observations between the ages of 35 and 45, as Haider and Solon (2006) show that it is important to measure father and son earnings at similar ages,
A model of intergenerational earnings mobility
In this section a model of intergenerational earnings mobility with heterogeneous endowments is presented following the approach of Solon (2004), which is an adaptation of the model in Becker and Tomes (1979). The model consists of a continuum of households each comprising one parent (p) with parental income (yp), and one child (c) with heterogeneous endowment (ec). The solution of the model yields an equation which nests intergenerational mobility specifications commonly implemented in the
Methodology
From the model specification in Eq. (9) the intergenerational earnings elasticity is decomposed aswhere β1 represents the investment component and λdec(yp,z)/d ln yp the endowment component. To identify these two components it is necessary to be able to decompose the disturbance term λec(yp,z) + ξc in Eq. (9) into its separate components. To achieve this end the theoretical properties of the model presented in Section 3 and the empirical evidence identified in Section 2,
Point estimates
The maximum likelihood parameter estimates of the heterogeneous-endowment model, based on the log likelihood in Eq. (21), are given in Table 1. With the exception of the parameters β1 and γ3, all of these parameter estimates are statistically significant at the 5% level or better, while the p-value for the estimate of β1 is 0.135 and for γ3 is 0.343.
The economic importance of the latent endowment term ec is evaluated by estimating the proportion of the total variance (σu2) that is attributable
Nonlinear regressions
An alternative approach used to capture potential nonlinear intergenerational relationships is to include higher order polynomial terms of ln yp in Eq. (1) (see, for example Behrman and Taubman (1990) and Solon (1992), and more recently Bratsberg et al. (2007)). This class of statistical models can be viewed as a polynomial approximation of the conditional mean function arising from the heterogeneous-endowment model presented in Eq. (15).
Extending Eq. (1) to allow for a quadratic term in ln yp
Conclusions
Understanding the roles and relative importance of the factors underlying intergenerational mobility can help guide policy aimed at improving economic opportunity and alleviating the persistence of poverty. This paper provides a new approach to identifying these factors. The approach involves estimating a two factor economic model based on the work of Becker and Tomes (1979) and Solon (2004) where earnings of children are a function of the earnings of parents and two sources of randomness
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Cardak and Martin both acknowledge support from a research grant provided by the Australian Research Council (DP0662909).
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