Estimating the Impact of the Increased Earnings Capacity from a Secondary Education on the Future Welfare Recipiency of Female Dropouts

Data from the National Longitudinal Survey of Youth are used to empirically isolate the impact of a secondary education on the long-term welfare participation of young female dropouts. A high school diploma or General Educational Development (GED) degree is assumed to influence welfare recipiency by increasing earnings capacity. Yet, causality may run in both directions. Although an exogenous increase in earnings capacity may reduce subsequent welfare recipiency, higher expectations of welfare recipiency may reduce educational attainment. To control for possible sample selection bias, the determinants of postschooling welfare experience are estimated conditional on these educational outcomes. Although an increase in earnings capacity is found to significantly reduce welfare recipiency, these effects would be overstated by at least 20 percent if the endogenous treatment effects were ignored. For the average dropout, her probability of receiving welfare in any future period is estimated to decline by 14.9 percent with a high school diploma and 8.7 percent with a GED degree. Yet, this secondary education would eliminate less than one-quarter of the substantial gap in welfare participation that currently exists between women who graduated from high school and those who dropped out. ESTIMATING THE IMPACT OF THE INCREASED EARNINGS CAPACITY FROM A SECONDARY EDUCATION ON THE FUTURE WELFARE RECIPIENCY OF FEMALE DROPOUTS. The 1988 Family, Support Act revised the national Aid to Families with Dependent Children (AFDC) program. Its stated purpose was to reduce the long-term welfare dependency of needy families with children. Each state must now establish a Job Opportunities and Basic Skills (JOBS) program to provide AFDC recipients with an array of services including basic and remedial education, specific job training, job placement, and supportive services such as child care and transportation. Some states have emphasized the importance of increasing the general educational attainment of welfare recipients. For example, a recent proposal in Missouri would require AFDC recipients who have not completed their high school education and who are not exempt because of home responsibilities to work toward their high school equivalency or General Educational Development (GED) degree (Ashcroft, 1987). Maloney (1991) used a sample of young women taken from the National Longitudinal Survey 4 of Youth (NLSY) to estimate the impact a secondary education would have on the potential market wage rates or earnings capacities of female dropouts. The estimated rates of return were 10.2 to 10.6 percent for a regular high school diploma and 6.2 to 6.5 percent for a GED degree. This was true even after allowance was made for the lower innate abilities among dropouts, their lower rates of human capital accumulation in school, and possible self-selection in the decision of whether or not to complete a secondary education. One issue not explored in this previous paper was the potential impact of this increased earnings capacity on the future AFDC recipiency among female dropouts. There are a variety of ways in which an exogenous increase in earnings capacity might reduce long-term welfare dependency. It might affect subsequent fertility decisions, household formation or dissolution, attachment to the labor market, job search, occupational mobility, and layoff and recall, as well as potential wage rates. No attempt will be made in this study to disentangle these many effects. Yet 2 for general policy purposes, it is the overall causal link between earnings capacity and AFDC recipiency that may be important. The preferred approach in addressing such a question would be to observe potential market wage rates and AFDC recipiency before and after the completion of a secondary education among female dropouts in a controlled experiment. Since such data are currently unavailable, the next best approach is to econometrically model the determinants of educational attainment and subsequent AFDC recipiency using the same cross-section of women from the NLSY as the earlier paper.' The key is that expectations of future welfare recipiency may have affected observed schooling outcomes. Thus, we must allow for self-selection in educational attainment. In other words, we cannot assume that dropouts who attain a secondary education would face the same long-term AFDC recipiency rates as an observationally equivalent high school graduate or GED recipient. Section I highlights the theoretical and empirical issues raised in this paper by presenting a model of the demand for education under a generic income maintenance program. Section I1 develops an econometric procedure for estimating the determinants of long-term welfare recipiency. Section I11 describes the NLSY data used to estimate these equations, and Section IV presents these empirical findings. Section V draws some general conclusions from this analysis. I. OPTIMAL SCHOOLING CHOICE IN THE PRESENCE OF A SIMPLE INCOME TRANSFER PROGRAM We begin with a theoretical framework that will simplify the relationship between educational attainment and subsequent welfare recipiency, and motivate the empirical model developed in the next section. A model of optimal schooling choice is presented in which individuals can choose between market work with a stochastic wage and welfare recipiency with a guaranteed level of income after the completion of that schooling. 3 The wage rate facing a woman in the labor market in year t is written as a log-linear function of her years of schooling, her innate ability (A), and an error term (4.' The error term summarizes all of the stochastic elements of future wage rates. In each period, the wage is revealed when the person draws E , from a normal distribution with a zero mean and constant variance. Investments in education shift the entire wage distribution for an individual. However, unlike most models of optimal schooling behavior, the precise wage that will be available in any future period is unknown a priori. It is assumed that a woman maximizes the discounted value of her lifetime wealth by choosing the optimal level of schooling (S). She does this with the understanding that in each period after the completion of her education, she can either work for the wage revealed in that period or forgo market work and receive a "guaranteed" level of income G through a government transfer p r ~ g r a m . ~ We consider the possibility that the woman will not evaluate a dollar of labor market earnings and transfer payments equally. The "effective" transfer payment is written as 6,G-6,, where in general 0C-6,<1 and 6 2 0 . This assumption can be motivated in a number of ways. First, there may be some "stigma" attached to welfare recipiency. This could be related to the act of participating in the transfer program (i.e., 6,=l and 6,>O), the level of benefits received (i.e., O<6,< 1 and 6,=O), or both (Moffitt, 1983). Second, it could be said that individuals must pay a "price" to become and remain categorically eligible for this transfer program. Under the AFDC program, for example, this might include living in a single-headed household with children. No wage is received while attending school. This forgone wage is the only "cost" of education. No source of postschooling human capital investment is allowed. For expository 4 convenience, we assume that the individual lives forever. The discounted value of expected lifetime wealth can be written as where future income is discounted by some interest rate (r). The first integral indexes the period of this infinite life. The second integral captures the uncertainty within each period over the market wage. Once the market wage is revealed in a given period, the individual chooses the maximum of the two effective income amounts: the market wage or welfare income. We can rewrite this wealth expression. in the following way: where the expected value of income in any period is the sum of two components within the integral. The first is the probability that the wage draw will exceed the effective income guarantee and the woman will choose market work, multiplied by the expected wage conditional on this decision to work. The second is the probability that the wage draw will be less than or equal to this effective income guarantee and the woman will choose welfare recipiency, multiplied by the effective guarantee. The essence of this simple welfare program is that it provides insurance against bad wage draws. There is clearly a potential moral hazard problem associated with educational attainment in the presence of this simple income transfer program. This can be shown by deriving a general expression 5 for this optimal schooling decision. Since the wage distribution is lognormal, we can simplify this wealth expression: where a(.) is the cumulative distribution function of the standard normal, u, is the standard deviation of E,, Z=[ln(61G-6J-/31S-/32A]/uE, and W = ~ X ~ @ , S + / ~ ~ A ) (i.e., the unconditional mean wage).4 Let this expected income in each period equal Y. As Rosen (1974) shows, the general stopping rule for schooling can be written as where Y, is the partial derivative of expected annual income with respect to schooling. The woman will maximize her expected lifetime wealth by discontinuing her schooling when this marginal benefit is equal to the opportunity cost of this investment. With some algebraic manipulation, we can reduce this partial derivative to the following: where 4(Z) is the probability density function of the standard normal. This expression can be interpreted with some simplifying assumptions. Suppose a woman expects to work in all postschooling periods (i.e., a(Z)=O). This might occur because of high draws on innate ability, because she lives in a state with a relatively low guarantee, or because she heavily discounts the value of these welfare benefits. Under these circumstances, this partial derivative would reduce to /3,W. Substituting this expression into the optimal stopping rule and recognizing that annual income is 6 simply w in this case, the first-order condition for wealth maximization is fll = r. Thus, Rosen's conclusion that the coefficient on years of schooling in the log wage equation is the rate of return to education is a special case of this more general expression. At the other extreme, suppose the woman expects to receive welfare in all postschooling periods (i.e., @(Z)= 1). This might occur because of low draws on innate ability, because she lives in a state with a relatively high guarantee, or because she does not heavily discount the value of these welfare benefits. Under these circumstances, this partial derivative would reduce to zero. The woman has no incentive to invest in education because it has no impact on her expected lifetime wealth.' This theoretical model raises a number of issues that will be incorporated into the empirical model of welfare recipiency developed in the next section. First, educational attainment, and to that extent future earnings capacity, is a choice variable for the individual. Second, any exogenous increase in the expectation of future welfare recipiency will reduce the demand for education. Third, lower levels of schooling will reduce earnings capacity and raise the probability of future welfare recipiency. Our goal is to isolate the impact of an exogenous increase in earnings capacity, associated with additional educational attainment, on the future welfare recipiency of female dropouts. To accomplish this task, we must recognize the possible sample selection bias in the completion of a secondary education. 11. AN EMPIRICAL MODEL OF WELFARE RECIPIENCY Using the theoretical framework of the previous section, we now develop an empirical model for estimating the determinants of welfare recipiency. It was assumed earlier that a woman receives welfare benefits in a given period if the revealed wage is less than the effective income guarantee. If we had retrospective information on the fraction of time in which the woman actually received 7 welfare over her lifetime (P?, we could write this welfare propensity as an exact linear probability function of this effective income guarantee and the mean of her log wage distribution on*). An error term will be added to this expression, because proxy measures will have to be substituted for these dependent and independent variables. First, we only observe the welfare history of a woman over a finite period. Suppose that we observe T months after the completion of her education. In K months she receives welfare. The observed probability of welfare recipiency is P=K/T, and it approximates P* with some error u (i.e., u=P*-P). As the number of months observed increase for all women in the sample, E(u) goes to zero and the Var(u) can be approximated by P(l-P)/T. The minimum chi-squared method or weighted least-squares could then be used to estimate this expression, where the appropriate weights are (T/P(1-P))1'2. Second, we do not observe the effective income guarantee for the individual. A vector of exogenous variables (X) will be used as a proxy for this factor. It will include the mean of the actual guarantee facing the woman over the relevant period and personal and family background characteristics that might be related to any stigma attached to welfare recipiency. Finally, an estimate of the earnings capacity of the woman at the end of her schooling ( l n ~ ) will be included in this expression as a proxy for the mean of her log wage distribution. The next section describes the way in which this estimated earnings capacity is obtained. To simplify the empirical relationship among these variables, we write the observed rate of welfare recipiency as a linear function of X, l n ~ , and a disturbance term p. 8 This raises the question of why the dependent and time-varying independent variables in equation (8) are not subscripted for the period of observation. Changes in the likelihood of welfare recipiency could be regressed on changes in both the structure of welfare programs and earnings capacity over time. For example, a fixed-effect probit model might be used to estimate such an equation, where all measured and unmeasured time-invariant factors are relegated to the individualspecific constant term. A number of problems prevent the implementation of this approach. First, because we would need some variation in the dependent variable for each observation, the large proportion of women who do not change welfare status over the observed period (i.e., those continuously on or off welfare) would have to be dropped from the estimation. Second, we may be interested in how the measured time-invariant factors (i.e., personal and family background characteristics) would affect welfare recipiency. Third, and most important, our estimate of the impact of changing earnings capacity on changing welfare recipiency would be biased, unless we explicitly recognize the simultaneity between these variables. Changes in potential market wage rates over the work life largely depend on accumulated work experience. For example, if no work occurred in the previous period because of welfare recipiency, earnings capacity would not increase. It would be difficult to know whether current welfare recipiency is indirectly or directly related to this past welfare participation (i.e., no change in earnings capacity vs. state dependence). If equation (8) were estimated using weighted ordinary least-squares (OLS), the hypothesized negative impact of earnings capacity on welfare recipiency could be overstated. The problem is that the causality might run in both directions. Although an exogenous decrease in earnings capacity should increase future welfare recipiency, any expectation of higher future welfare recipiency would reduce educational attainment, thereby lowering acquired earnings capacity at the completion of 9 schooling. The solution to this problem is to allow for the endogeneity of educational attainment and the potential sample selection bias associated with actual welfare recipiency. We begin by assuming that educational attainment is the only way in which individuals can choose to increase their earnings capacity. Instead of considering the number of years of schooling as the relevant choice variable, we allow individuals to choose among three alternative educational states: "High school graduates" terminate their formal schooling after receiving their regular high school diploma; "GED recipients" discontinue their formal schooling before receiving their high school diplomas, but receive their high school equivalency degrees; and "Dropouts" receive neither their high school diplomas nor GED degrees. A reduced-form equation is used to represent the high school completion decision: (9) HS* = ?r,Q, + e, where HS* is the latent propensity to receive a regular high school diploma. The vector Q, contains personal and family background characteristics, the quality of the school attended, the condition of the local labor market, and the income guarantee available during formal schooling. These regressors serve as proxies for the benefits and costs that underlie this educational investment decision. The observed outcome is dichotomous. Either the woman completes her high school education (HS = l), or she does not (HS=O). 0 iff HS*O For women who do not finish high school, there is a second opportunity to complete their secondary ed~cat ion.~ A reduced-form equation is used to represent this GED recipiency decision: