Parental earnings and children's well-being: an analysis of the survey of income and program participation matched to social security administration earnings data.

Mazumder, Bhashkar ; Davis, Jonathan M.V.

I. INTRODUCTION

In the aftermath of the Great Recession, approximately one in five children in the United States lives in poverty, making children the poorest age group in the United States (Children's Defense Fund 2010; Land 2010). Comprehensive measures of child well-being have also begun to decline after showing steady improvement for most of the past 20 years. Given this backdrop, efforts to improve the material conditions of children are likely to remain a salient issue for policymakers for many years.

An obvious target for policymakers is to improve the economic situation of parents. Indeed, a vast literature in the social sciences has studied the association between parental income and children's outcomes to establish the importance of parental economic resources on children's well-being. One limitation of many of these studies is the lack of availability of parental income or earnings histories over long periods of time. It is well established that the bias in using single year measures of parental income to proxy for long-run income can be sizable and can vary by parental age (Solon 1992; Mazumder 2005; Haider and Solon 2006). Indeed a number of studies have shown that the estimated associations between parental income and child well-being grow larger as parent income is measured over progressively longer time periods (Miller and Korenman 1994; Blau 1999). We further extend these findings using a unique dataset that includes a rich set of measures of child well-being that is also linked to administrative data containing long-term parental earnings histories for much larger samples of families than has typically been available.

Specifically, our dataset pools families from the 1984, 1990-1993, 1996, 2001, and 2004 panels of the Survey of Income and Program Participation (SIPP). Each of these SIPP samples were matched to earnings histories contained in Social Security Administration (SSA) records. We use the administrative data to construct long-term time averages of parents' earnings. We use these time averages of parent earnings to estimate the association between parent earnings and childhood well-being. We use SIPP topical modules on Children's Well-Being, Functional Limitations and Disability, Health Status and Utilization of Health Care, and Extended Measures of Well-Being to obtain a broad set of measures related to childhood health and well-being.

We find that across virtually all of our indicators of childhood well-being, longer time averages lead to substantially larger estimates. In some cases, the associations more than double compared to using a single year of earnings. In certain instances, the estimates are only statistically significant when using the longer time averages. Among our substantive findings we show that a doubling of a 7-year average of earnings is associated with a 48% drop in the mean probability of a teenager reporting poor health, a 39% drop in the mean probability of repeating a grade, an 18% drop in the mean probability of being suspended, a 75 percentage point drop in the mean probability of having insufficient food, and a 6 percentage point increase in the mean number of times a child saw a doctor. Notably, these estimates are 25%-120% larger than those based on using a single year of earnings. Relative to the earlier studies that have shown similar patterns, we use much larger samples and do not rely on self-reported earnings.

We also exploit the very long earnings histories available in the SSA data to examine how the timing of parent earnings received during particular periods of the child's life is associated with adolescent health status, the likelihood of enrolling in college, and adult earnings. We find suggestive evidence that for college enrollment and adult earnings, parental earnings received during the school-going years have a stronger association than earnings received earlier or later in the child's life. We think that this is an important area for future research to further explore.

Another important open question is the extent to which the statistical associations between parental earnings and children's well-being that we document reflect causal processes. Developing research designs that convincingly address this question is a difficult endeavor and is not our aim in this paper. Instead like most of the preceding literature linking parental economic resources to children's well-being, we hope to provide descriptive estimates that may provide important insight for policy discussions and help inform future research on child well-being. To the extent that our results reflect the causal effects of parental economic resources on outcomes, they could have important implications for income support policies, such as the Earned Income Tax Credit, TANF and Food Stamps. (1)

II. BACKGROUND

There is an enormous literature that discusses the many potential determinants of childhood well-being. This paper focuses on the role of just one of these factors, parental labor market earnings. (2) It has been well established that parent income is an important determinant of child well-being (Blau 1999, Brooks-Gunn and Duncan 1997). Therefore, it is critical that parent income be well measured and its association estimated as accurately as possible. The literature on intergenerational income mobility has demonstrated that transitory fluctuations in income and measurement error can lead to substantial bias in the estimated intergenerational income elasticity when using a single year of parent income as a proxy for permanent income (Solon 1992; Mazumder 2005).

In contrast to the literature on intergenerational economic mobility where researchers have generally been interested in measures of lifetime income, our focus is on parental income received during the childhood period and how it affects measures of child well-being. (3) Therefore, for our purposes, it may be optimal to use a short-time average (e.g., 5 to 10 years) of parent income both because we are interested in income during this period and because of the desirable properties of time averages in reducing bias. At a minimum, it may be useful to explore how estimates of socioeconomic gaps or income gradients are altered when using multi-year averages of parental income. For example, Rothstein and Wozny (2011) show that a much greater portion of the black-white test score gap can be explained by parent income when using long-term averages of parent income rather than using just 1 year. For policy analysis, using longer averages is clearly appropriate when evaluating the effects of policies that potentially affect individuals in more than 1 year (e.g., EITC) or that may have a permanent effect on a worker's earnings potential, like a job training program.

Several studies have examined the effect of including additional years of parent income on the measured association between income and different measures of child well-being. Blau (1999) summarizes the results of these studies as follows: "the effect of current income on child outcomes is small; the effect of permanent income is much larger than the effect of current income, but decreases as more covariates are included." One limitation of these studies, however, is that they rely on the relatively small samples available in longitudinal surveys like the National Longitudinal Survey of Youth (NLSY) and the Panel Study of Income Dynamics (PSID). As we describe below these studies typically include fewer than 5,000 individuals. In contrast, our SIPP-SSA samples in some cases exceed 40,000 observations. Furthermore, sample attrition in these longitudinal studies can potentially lead to unrepresentative samples and selection bias when one tries to measure income over longer time periods.

We highlight a few of the notable studies that have used multiple years of parent income to study childhood outcomes. For example, Miller and Korenman (1994) show that the association between poverty status and stunting and wasting is larger when an 11-year poverty measure is used instead of a 1-year measure. Their analysis relies on a sample of just under 5,000 individuals from the NLSY. Korenman, Miller, and Sjaastad (1995) use NLSY data to demonstrate that the associations between poverty and various measures of cognitive and emotional development are twice as large when poverty is defined using 13 years of poverty status instead of 1 year. The sample sizes for these outcomes are even smaller and in some cases are below 2,000 observations. Lubotsky and Wittenberg (2006) use the NLSY and show that the effect of family income on children's reading comprehension test scores rise substantially when using an optimally weighted combination of multiple years of family income. Their samples include fewer than 5,000 children-year observations. Samples using the PSID are often even smaller. For example Case, Lubtosky, and Paxson (2002) use the PSID to examine whether the association between permanent income and children's health outcomes depends on the timing on when during the lifecycle of the child, parent income is received. Their sample size ranges from 809 to 1,078.

III. DATA AND METHODOLOGY

The analysis uses the 1984, 1990, 1991, 1992, 1993, 1996, 2001, and 2004 panels of the SIPP matched to SSA's Summary Earnings Records (SER) and Detailed Earnings Records (DER). (4) The SER covers annual earnings over the period from 1951 to 2007, while the DER is available from 1978 onward. There are two aspects to using SER records that raise potential issues. The first is that some individuals who are working are not covered by the social security system and their earnings will be recorded as zero. Second, earnings in the SER data are censored at the maximum level of earnings subject to the social security tax. On the other hand the DER used in our analysis does not include self-employment earnings. As a result, there are higher rates of non-coverage in the DER than in the SER. For the first part of our analysis, we take the maximum of earnings in a year between the SER and DER to minimize the bias due to the different forms of non-coverage in each dataset. For the second part of our analysis, where we investigate whether the association between income and several outcomes varies over the life course of the child, we use the SER data from 1961 onwards since this exercise requires a longer panel of earnings and we want to use consistently measured earnings over the entire lifecycle. To deal with the top-coding problem in the SER we impute earnings among the topcoded for each year starting in 1961 by using the March CPS and calculating the mean earnings among those above the topcode by cells defined by race, sex, and education.

The sample consists of children who were 0 to 20 years old and who were co-resident with at least one parent at the time of their first interview. (5) The sample was also restricted to children whose parents were between 15 and 45 years old when the child was born. For the first part of our analysis, we progressively average parent earnings over 1,3, 5, and 7 years. The earnings of the father are used if his earnings were positive for all 7 of the years. If not, we use the mother's earnings if her earnings were positive in all 7 years. If neither parent had positive earnings in all 7 years, the family was dropped from the sample. (6) By requiring positive earnings in all 7 years we maintain a balanced panel of families which ensures that any differences across our estimates based on the length of the time average are not due to compositional changes. However, a cost of using a balanced panel approach is that we can only include families with continuous earnings coverage for the entire period. We chose 7 years as a way of balancing our desire for having a long time average with our concern that too long a time average might reduce our sample size and weaken the representativeness of our sample.

The time period covered by the averages ends in the year prior to the interview in which the observation is used. For example, if an outcome was taken from an interview that occurred in October 1992, the l-year average would use 1991 earnings, the 3-year average would use 1989 through 1991 earnings, the 5-year average would use 1987 through 1991 earnings, and the 7-year average would use 1985 through 1991 earnings. (7) Consequently, time averages were generated for each specific outcome depending on the SIPP panel used and the year of the interview.

When we investigate the association between earnings received at different points in a child's life, we restrict our analysis to male children. We use father's earnings if his earnings were positive for 14 of the 21 years beginning 3 years prior to the child's birth and ending when the child is 17. If not, we use the mother's earnings if her earnings were positive in 14 of the 21 years. If neither had positive earnings in 14 years, the family was dropped from the sample.

We organize the outcomes into five distinct groups. Summary statistics are shown in Table 1. The first group is a set of general health outcomes. This includes: (1) an indicator for a physical, learning, or mental condition that limits schoolwork which is asked of children 5 or older; (2) an indicator for a physical, learning or mental condition that limits child behavior asked of children younger than 5; (3) an indicator for fair or poor health among children 15 and older that uses health status (based on health status rated on a 1 to 5 scale where 1 is excellent and 5 is poor) reported in the Functional Limitations and Disability Topical Module (child response); (4) an indicator for fair or poor health that uses health status reported in the Children's Well-Being Topical Module (parent response); (5) an indicator for fair or poor health that combines health status reported in the Children's Well-Being Topical Module and health status reported in the Functional Limitations and Disability Topical module; (6) an indicator for spending the night in a hospital in the last year; (7) the number of nights spent in the hospital in the last year; and (8) the number of days in the last 4 months that illness or injury kept the individual in bed for at least half the day.

The second set of outcomes deals with health care utilization and include: (1) the number of times the child talked to a doctor in the last year; (2) the number of dentist visits in the last year; and (3) an indicator for using prescription drugs daily. The association between parental earnings and these outcomes could reflect a combination of factors since greater parental resources could, for example, make doctor visits more affordable but simultaneously provide a protective effect which could act to decrease such visits. Previous studies have shown that an income gradient exists in health care utilization in the United States despite the potential protective effects of greater income (e.g., Fox and Richards 2010; Blackwell et al. 2009). Below we also show the association between earnings and whether a family member skipped a doctor visit when he or she needed to go.

The third group of outcomes is also health related and includes three anthropomorphic measures of children below the age of 5. These include: (1) a weight-for-height z-score; (2) a weight-for-age z-score; and (3) a height-for-age z-score. All three measures are calculated using 2-or 3-month age bins separately for males and females.

The fourth group of outcomes examines a range of childhood educational measures. These include: (1) the number of times the child changed schools; (2) an indicator for having repeated a grade; (3) an indicator for having been suspended or expelled; (4) an indicator for having received special education services; and (5) an indicator for having a learning disability.

The fifth and final set of outcomes examines a range of measures related to home environment and family resources. These include: (1) the number of times a child was read stories in the last week; (2) a count of the number of days without enough food or money to buy food in the last month; (3) an indicator for whether the child had ever been in day care; (4) an indicator for not being able to meet basic needs (food, rent, utilities, etc.) at some point in the last year; (5) an indicator for the family not having enough food in the last 4 months; and finally (6) an indicator for a family member skipping a doctor visit when he or she needed to go. The associations for the number of days without enough food or money to buy food and the last three outcomes are estimated using one observation per family.

All of the outcomes (denoted by [y.sub.i]) are multiplied by 100 for convenience in displaying and interpreting results. This is mostly useful for the indicator variables so that the coefficients can be interpreted as percentage point effects. For each regression, we include a basic set of covariates, [X.sub.1i], ("Basic Controls") which consist of indicators for survey year, child age when the outcome was measured, race, ethnicity, gender, state of residence, having a one-parent household headed by the mother, having a one-parent household headed by the father, and an indicator for using father's earnings. A more extensive set of controls, [X.sub.2i], ("Added Controls") includes all of the basic controls and adds parent education, parent health status, parent age, and parent age squared. For the regressions dealing with health we also added a third set of controls, [X.sub.3i], which includes separate indicators for the father, mother, and child having private health insurance. Even though health insurance coverage and earnings are likely to be jointly determined, we think it is interesting to document how the income estimates are affected by the inclusion of health insurance control variables since we are primarily interested in descriptive associations rather than true causal effects. The results are weighted using the child's person weight in the fourth month of the wave in which the outcome was observed.

The main object of interest is [gamma] in the equation below:

(1) [y.sub.i] = [gamma] ln([Earn.sub.i]) + [[beta].sub.1] [X.sub.1i] + [[beta].sub.2] [X.sub.2i] + [[beta].sub.3] [X.sub.3i] + [[epsilon].sub.i].

For the second part of the analysis where we examine timing effects we use the following baseline specification:

(2) [y.sub.i] = [5.summation over (j=1)][[delta].sub.j]ln([Earn.sub.ij])+[[beta].sub.1] [X.sub.1i]+[[beta].sub.2][X.sub.2i]+[[epsilon].sub.i]

where i indexes children and j denotes the following five stages in the child's lifecycle when parent earnings are received: (1) 3 years before the child is born to 1 year before the child is born; (2) when the child is between the ages of 0 and 5; (3) when the child is between the ages of 6 and 11; (4) when the child is between the ages of 12 and 17; and (5) when the child is an adult between the ages of 23 and 28. We are interested in whether the [[delta].sub.j]s vary across these periods. For our analysis of children's future earnings as adults, we also include some additional terms to address lifecycle bias as described by Haider and Solon (2006) that arises due to heterogeneous age-earnings profiles. First, we include an interaction of log earnings in each lifecycle stage j, with a quartic in the parent's age (at the time of the child's birth) less 40. This addresses the bias due to the age at which parent's earnings are measured. Second, we also interact earnings in each lifecycle stage with a quadratic in the child's age in 2005 minus 35. With these modifications, the [[delta].sub.j]S can be interpreted as capturing the association between earnings in that stage for children who were 35 in 2005 and whose parents were 40 when the children were born. Summary statistics for the timing results are shown in Table 2. (8)

IV. RESULTS

A. Associations Between Parent Earnings and Child Well-Being Using Longer Time Averages

We start by presenting the results concerning children's health outcomes in Table 3. The first entry in the table, -0.979, shows the coefficient on using log parental earnings from a single year where the outcome is an indicator for having a health condition that prevents school work. The standard error is 0.15 and the association is significant at the 1% level. The point estimate suggests that a doubling of parental earnings would be associated with a reduction in the probability of such a health condition by approximately 0.7 percentage points. (9) Since the mean rate of such health conditions is about 5%, this would be about a 14% "effect size" evaluated at the mean. This would essentially be what the typical researcher would estimate when using only the current income available in the survey. Moving across the row the next three columns shows how the estimate changes as the length of the time average is increased. In column (4), when we use the log of a 7-year time average, the coefficient rises (in absolute value) to -1.37. Moving from a single year of parent earnings to a 7-year average raises the coefficient by 40%. The estimate based on a 7-year average implies that a doubling of earnings reduces the probability of a schoolwork limiting health condition by about 0.95 percentage points, an 18% effect size at the mean.

Columns (5) through (8) use the same lengths of time averages but now include the added set of covariates on parental characteristics. This sharply reduces the point estimates. For example, when using a 7-year average (column 8), a doubling of parental earnings now reduces the probability of a health condition by 0.77 percentage points, a 15% effect size. The difference between using a single year and a 7-year average, however, remains substantial. In fact, the coefficient on using a 7-year average is now almost 50% higher than the coefficient on a single year of earnings. Finally, in column (9) we continue to use a 7-year average but now include a set of covariates for health insurance coverage in the year the outcome was measured in the SIPP. This further reduces the effect of doubling parent earnings to -0.61 percentage points, a 12% effect size.

The second row shows the analogous associations on the probability of a health condition that affects the behaviors of children at or below the age of 5. Here the incidence rates are much lower and so we might expect to find point estimates that are smaller in absolute value than the limitations on school work. For this outcome, however, we see no gradient in the time average of parent earnings and the reverse pattern of smaller estimates corresponding to longer time averages when we include controls. This turns out to be the only outcome in Table 3 where we find a reversal of the pattern.

We next turn to the outcome of fair or poor self-reported health status among teenagers. The results in column (4) using a 7-year time average (-1.74) imply that a doubling of parent earnings would reduce the probability of fair or poor health among children by 1.2 percentage points or 49% of the mean, an effect that is significant at the 1% level. The coefficient from using only a single year of earnings is less than half the size. When additional controls are added, the results using the 7-year average drop by about 25% but remain highly statistically significant. In contrast, the estimate from using a single year of earnings is no longer significant when additional controls are included.

When the outcome is fair or poor health status (parent reported) for a child younger than 15 (row 4) the coefficients are substantially smaller in absolute value and much less robust to the inclusion of additional controls. As one would expect, when the two health status outcomes are combined to form one outcome (row 5), the effects are generally close to a weighted average of the individual results.

For the probability of staying overnight in a hospital, the estimates decrease monotonically as we increase the number of years included in the earnings averages, whether or not we control for additional parental characteristics. All of the coefficients on the time averages of parent earnings are negative and significant, at a minimum, at the 10% level. The results are similar even when controlling for covariates (columns 5 to 8) and even when we include health insurance status (column 9). A doubling of parent earnings reduces the probability that a child will stay overnight in a hospital by about 0.3 percentage points and implies an effect size of about 10% evaluated at the mean. If we focus on column (8), we also find negative coefficients that are significant at the 10% and 5% level, respectively, for the number of days spent in a hospital and the number of days that illness kept the child in bed at least half the day. The effect sizes for these outcomes are 17% (0.024 days) and 9% (0.058 days), respectively.

In Table 4, we turn to health care utilization outcomes. We find that for all three outcomes using a 7-year average instead of a single year generally leads to substantially higher point estimates of the association between parental earnings and the outcome of interest. When only the basic controls are included, the coefficients increase from between 37% to 42%. Notably for the number of dentist visits and daily prescription drug use, controlling for parent characteristics or health insurance coverage reduces, but does not eliminate, the effects which are all generally highly statistically significant. This suggests that the gradient in health care utilization is not due solely to access to health care insurance. Using the column (8) results, the effect sizes for these outcomes, evaluated at the mean, range from 2% to 10%.

In Table 5, we examine the association between parental earnings and the height and weight of children under the age of 5. The first outcome examined is the z-score of weight for height which is sometimes used to classify "wasting" or malnutrition for low levels. Of course, high levels can also be indicative of potential problems such as Type II diabetes. Regardless of whether the basic or added controls are included, we find a small negative association of between 0.02 and 0.04 standard deviations from a unit increase in log parental earnings that is statistically insignificant. Similarly no consistent, let alone statistically significant association is found for weight for age or height for age. Interestingly, the effect of earnings on height for age becomes smaller as more years of earnings are included. This could be evidence that transitory income in the first year or two of life is important for height but that permanent income is not. It is worth noting that these results are not consistent with Miller and Korenman's (1994) estimates of the relationship between poverty status and stunting and wasting. Our specification differs from theirs in several important ways. First, they allow for a nonlinear relationship between poverty status and both outcomes. Most of their results are driven by families whose income is less than half of their needs. It is possible differences in the effect across the earnings distribution are being washed out by imposing a linear relationship across the income distribution. Moreover, the lower bound of their 95% confidence intervals are much closer to one, even for very low income families, when they include additional covariates, as we do in all of our specifications.

The fourth set of measures of child well-being deals with educational outcomes and the results are presented in Table 6. We find a negative association with the number of school changes that rises with the length of the parental earnings time average. Using a 7-year average with the baseline and additional controls yields a marginally significant effect. The imprecisely estimated coefficients are suggestive of an effect size of about 7% or 8% evaluated at the mean (3.25 and 3.56 percentage points). The measured associations for ever repeating a grade or receiving special education services decrease monotonically whether or not additional covariates are included. The specification in column (8) suggests that doubling parent earnings reduces the likelihood of repeating a grade by 1.9 percentage points (25% effect size), reduces suspensions by 0.8 percentage points (9% effect size), and reduces placement in special education classes by 1 percentage point (11% effect size). Further, these results are a powerful example of how lengthening the time averages of parent earnings can dramatically alter the size of the estimated associations. We find that the estimated coefficients are between 30% and 230% larger when using a 7-year average than when using current year earnings. For learning disability, we find that some statistically insignificant earnings effects appear when using only the baseline controls but that these are completely removed when controls for parental characteristics are added.

The estimates for the final group of measures on home environment and family resources are shown in Table 7. The results are mixed. We find that for two of the outcomes, number of times read stories and days without food, there are highly significant effects when we use the baseline controls that are dramatically reduced and no longer significant once we further control for parental characteristics. However, for the other outcomes, ever been in day care, inability to meet basic needs, food inadequacy, and skipped doctor visits, the magnitude of the associations increases monotonically with the length of the average. The implied effect sizes for these outcomes are 4% (1.51 percentage points), 36% (6.22 percentage points), 45% (0.87 percentage points), and 50% (4.14 percentage points), respectively.

While it may seem obvious that parental earnings will be strongly associated with two of the outcomes (inability to meet basic needs and food inadequacy) since these outcomes essentially reflect the availability of parental resources, it is important to point out that once again, the 7-year time averages yield significantly higher coefficients than current earnings. For example for food inadequacy, the effect size is nearly 10% to 25% higher when using a 7-year average than when using current earnings. So even for these most basic indicators of well-being it is clear that the longer time averages matter.

B. Does the Timing of Earnings Matter?

Table 8 shows the estimated association between parent earnings at different stages in the child's lifecycle on three outcome measures: (1) an indicator variable for having fair or poor self-reported health status after age 14, (2) an indicator for enrolling in college within 2 years after starting the 12th grade, and (3) log average earnings between 2003 and 2007. The first entry in the table, -0.007 (0.004), shows the coefficient on log average earnings in the period beginning 3 years before the child was born and ending in the year before the child's birth on health status. This point estimate suggests that a doubling of parent earnings during this stage of a child's life is associated with a reduction in the probability that the child will have fair or poor health in later adolescence by a half percentage point, or 25% of the mean. This is the only coefficient in the column that is statistically significantly different from zero, albeit only at the 10% level. This is consistent with Case, Lubotsky, and Paxson (2002) who found that family income prior to a child's birth was significantly correlated with a child's current health status.

Moving down column (1), we see that parent earnings received when the child was between ages 0 to 5 and 6 to 11 actually have positive coefficients although they are not statistically significantly different from zero. The point estimate for earnings when the child was between the ages of 12 to 17 is -0.009 (0.008) and is of a similar magnitude to the point estimate for earnings between 1 and 3 years before the child's birth, but with a larger standard error. In contrast, Case, Lubotsky, and Paxson (2002) using an ordered probit model, found that income received after the child's birth was correlated with the child's current health regardless of when the income was received. However, they found no statistically significant differences in the magnitudes of the coefficients related to the timing of when income was received.

Column (2)shows estimates from an analogous specification as column (1)that also includes earnings between ages 23 to 28. The association between later life earnings and the child's health in late adolescence is not significantly different from zero, and including these earnings has almost no discernible effect on the estimates in column (1).

Columns (3)and (4)show the estimated associations when the outcome is an indicator for enrolling in college within 2 years after entering the 12th grade. In this case, the coefficient on parent earnings between ages 12 and 17, 0.058 (0.026), is the only coefficient that is statistically significantly different from zero. To the extent that these estimates reflect a causal relationship, this could provide suggestive evidence that credit constraints are a barrier to entering college. On the other hand, the magnitude of the coefficient for earnings between ages 6 to 11 is only a little smaller and the coefficient on earnings in the years prior to birth is also not statistically different than the coefficient on earnings when the child was 12 to 17 years old. Finally, parent earnings when the child is an adult is not significantly related to the child's college attendance and including this as an additional regressor barely affects the other estimates.

Columns (5) and (6) show the associations when the outcome is log average earnings between 2003 and 2007 for sons born between 1964 and 1980. (10) All of the coefficients are positive and significantly different from zero except for earning between ages 0 and 5. Looking at column 5, the coefficients increase as the child becomes older. Now, when the parent's earnings between ages 23 to 28 are included, the coefficients on earnings between ages 6 to 11 and 12 to 17 are reduced, and the coefficient on earnings when the child is between 23 and 28 is significant at the 1% level. These results provide some suggestive evidence that parent earnings during the school-going years may be more strongly associated with children's future earnings than income received at other periods of the child's life. However, given the relatively large standard errors and the broad age bins that we use, we hesitate to make overly strong claims on the basis of these results. We also note that there is also clear evidence that the permanent income of parents is also strongly associated with children's future earnings.

V. CONCLUSION

We construct a unique dataset linking a wide range of child well-being measures for a large sample of families to administrative data containing earnings histories of parents. This data enables us to estimate how the association between parental earnings and childhood outcomes changes as we progressively average earnings over longer time spans. This allows us to sharply reduce the attenuation bias that arises from using only current year income as an explanatory variable. For several key outcomes we show that 7-year averages of parent earnings lead to estimates of effect sizes that are substantially higher than are obtained using only a single year of earnings data. We further show that some (but not all) of these outcomes are also robust to including a rich set of covariates including parental characteristics that are often absent in many cross-sectional datasets.

Our results are consistent with several previous studies which have also found that the associations between parent income and child outcomes are much larger when using longer time averages. Our main contributions relative to the previous literature are that we use much larger samples, use data that are less subject to concerns about sample attrition, and use earnings data from administrative data that are not self-reported. Our study lends further support to the idea that the use of only current earnings or income to document socioeconomic gradients can sharply understate the true associations between parental economic resources and child well-being. If some portions of the statistical associations we document reflect the causal effects of parental economic resources then our results may help identify areas of child well-being that might be particularly responsive to policies that improve the economic situation of families.

We also attempt to identify whether the timing of when parent earnings are received in the lifecycle of the child matters. We find suggestive evidence that for college enrollment and children's future earnings the associations are stronger for parent earnings received when the child is of school-going age (6 to 17) than for parent earnings received earlier or later in the child's life.

ABBREVIATIONS

DER: Detailed Earnings Records

NLSY: National Longitudinal Survey of Youth

PSID: Panel Study of Income Dynamics

SER: Summary Earnings Records

SIPP: Survey of Income and Program Participation

SSA: Social Security Administration

doi: 10.1111/ecin.490

APPENDIX TABLE A1 Effects of the Timing of Parental Earnings over the Lifecycle of the Child on the Child's Adult Earnings (1) (2) Log(mean earnings 3 years to 0.021 0.035 1 year before birth) (0.015) (0.019) * Log(mean earnings ages 0 to 5) 0.025 0.01 (0.022) (0.028) Log(mean earnings ages 6 to 11) 0.029 0.058 (0.025) (0.030) * Log(mean earnings ages 12 to 17) 0.116 0.126 (0.021) *** (0.023) *** Log(mean earnings ages 23 to 28) Observations 11758 11758 Child lifecycle adjustment No No Parent lifecycle adjustment No Yes (3) (4) Log(mean earnings 3 years to 0.022 0.035 1 year before birth) (0.016) (0.021) * Log(mean earnings ages 0 to 5) -0.003 -0.017 (0.026) (0.032) Log(mean earnings ages 6 to 11) 0.077 0.107 (0.033) ** (0.037) *** Log(mean earnings ages 12 to 17) 0.118 0.129 (0.026) *** (0.027) *** Log(mean earnings ages 23 to 28) Observations 11758 11758 Child lifecycle adjustment Yes Yes Parent lifecycle adjustment No Yes (5) (6) Log(mean earnings 3 years to 0.021 0.036 1 year before birth) (0.015) (0.019) * Log(mean earnings ages 0 to 5) 0.023 0.008 (0.022) (0.028) Log(mean earnings ages 6 to 11) 0.025 0.052 (0.025) (0.030) * Log(mean earnings ages 12 to 17) 0.089 0.094 (0.022) *** (0.024) *** Log(mean earnings ages 23 to 28) 0.057 0.053 (0.012) *** (0.014) *** Observations 11758 11758 Child lifecycle adjustment No No Parent lifecycle adjustment No Yes (7) (8) Log(mean earnings 3 years to 0.022 0.034 1 year before birth) (0.016) (0.021) * Log(mean earnings ages 0 to 5) -0.007 -0.019 (0.026) (0.032) Log(mean earnings ages 6 to 11) 0.07 0.098 (0.033) ** (0.037) *** Log(mean earnings ages 12 to 17) 0.08 0.085 (0.027) *** (0.029) *** Log(mean earnings ages 23 to 28) 0.062 0.058 (0.013) *** (0.015) *** Observations 11758 11758 Child lifecycle adjustment Yes Yes Parent lifecycle adjustment No Yes Notes: The specifications include the Basic and Added Controls discussed in the text, except a quartic in parent's age is used instead of a quadratic. In addition to these covariates, the specifications also include the child and adult lifecycle adjustments as noted. Standard errors clustered by family are in parentheses. *** p<.01, ** p<.05, * p<.1.

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(1.) An important caveat is that our analysis pertains to labor market earnings and it is possible that behavioral responses to income obtained through government transfer programs may have different effects and could affect labor market earnings. Hoynes and Whitmore Schanzenbach (2009) show that many households respond similarly to a dollar in food stamps as they do to a dollar in income.

(2.) Although we use income and earnings interchangeably in this section for ease of exposition, all of the empirical estimates concern labor market earnings.

(3.) We abstract from theoretical issues such as the presence of capital markets and the possibility of borrowing constraints in this discussion.

(4.) The match rates in most years are quite high (around 80% to 90%) and an analysis of the match probability by demographic characteristics suggests that selection is not a major concern (Davis and Mazumder 2011).

(5.) Many of our outcomes include only younger children. For outcomes that used 18 to 20 year olds we found that our results were very similar if we dropped this age group thereby minimizing concerns related to endogenous co-residence amongst this older group.

(6.) We use only one parent's earnings because we are not able to identify whether a parent's earnings are zero because they were not working or because they were working in a non-covered job. Although using only one parent's earnings may not be ideal, it allows us to be explicit about what our estimates are measuring. If we used the sum of both parents' earnings, we would be measuring total family earnings for some families and not for others.

(7.) It is worth noting that as we move from shorter to longer averages, the measure includes earnings from earlier in the child's life. Consequently, the coefficient could be capturing heterogeneous earnings effects over the child's lifecycle. Case, Lubotsky, and Paxson (2002) found no evidence of heterogeneous effects with respect to health outcomes. We directly test whether the timing of income matters for a few outcomes in the second part of our analysis and find some suggestive evidence that income received during the school-going years (ages 6 to 17) matters more for some outcomes.

(8.) The outcomes tot this analysis are not multiplied by 100.

(9.) Since our right-hand-side variable is in logs in order to calculate the effect of a 100% increase we multiply our coefficient by ln(2) which is approximately 0.69. We have done this throughout our exposition of the results. Alternatively, to estimate the effect of say, a 10% increase in income we would multiply our coefficient by ln(1.1) or 0.09.

(10.) Columns (5) and (6) were estimated using a specification that included the adult and child lifecycle adjustments that are discussed in the text. Appendix Table AI shows the estimates with and without each of the lifecycle adjustments. Adding the parent lifecycle adjustment to the baseline specification used in columns (1) through (4) increases the coefficient on earnings between ages 6 to l 1 from 0.029 (0.025) to 0.058 (0.030). When the child lifecycle adjustment is also included the coefficient increases further to 0.107 (0.037). Adding the child lifecycle adjustment, but not the parent lifecycle adjustment, increases the coefficient on earnings in the pre-natal stage from 0.021 (0.015) to 0.035 (0.019) but reduces the coefficient on earnings between ages 0 and 5 from 0.025 (0.022) to 0.01 (0.028).

BHASHKAR MAZUMDER and JONATHAN M. V. DAVIS *

* This project was supported by a small grants award from the National Poverty Center and The Census Bureau and was prepared for the NPC Census/SIPP Research Conference. We thank Peter Gottschalk and conference participants for their comments. Two anonymous referees and the editor made useful suggestions.

DISCLAIMER: Any opinions and conclusions expressed herein are those of the author(s) and do not necessarily represent the views of the U.S. Census Bureau. All results have been reviewed to ensure that no confidential information is disclosed.

Mazumder: Senior Economist, Federal Reserve Bank of Chicago, 230 S. La Salle Street, Chicago, IL 60641. Phone 312-322-8166, Fax 312-322-2357, E-mail [email protected]

Davis: Graduate Student, Irving B. Harris Graduate School of Public Policy, 1155 East 60th Street, Chicago, IL 60637. E-mail [email protected] TABLE 1 Summary Statistics of Measures of Child Well-Being Outcome N M SD Health outcomes Condition limits school work 48,131 0.05 0.23 Condition limits child behavior 6,071 0.01 0.12 Fair or poor health (functional limitations) 6,877 0.02 0.15 Fair or poor health (child well-being) 9,569 0.02 0.14 Fair or poor health (combined) 15,318 0.02 0.15 Night in hospital 27,280 0.03 0.16 Number of nights in hospital 27,280 0.14 1.88 Number of sick days last 4 months 27,280 0.65 4.67 Healthcare use Number of times talked to doctor in last year 27,280 2.65 6.07 Number of trips to the dentist 25,061 1.62 2.47 Daily prescription drug use last year 21,856 0.11 0.31 Physical characteristics Weight-for-height z-score 2,058 -0.06 0.93 Weight-for-age z-score 2,058 -0.02 0.96 Height-for-age z-score 2,058 -0.03 0.99 Educational outcomes Number of times changed schools 9,732 0.43 0.98 Ever repeated a grade 9,732 0.07 0.26 Ever been suspended 4,655 0.09 0.29 Special education 41,592 0.09 0.28 Learning disability 40,641 0.02 0.14 Home environment and family resources Number of times read stories 5,862 5.31 6.17 Days without food or food money 3,897 0.16 2.04 Ever been in daycare 10,606 0.38 0.49 Was unable to meet needs in last year 3,897 0.17 0.37 Not enough food in last 4 months 3,897 0.02 0.14 Someone in family skipped doctor 3,897 0.08 0.27 TABLE 2 Summary Statistics for Timing Results Outcome N M SD Health sample Son's age in 2005 5,998 32.13 3.80 Parent's age at birth 5,998 23.72 11.08 Fair or poor health status 5,998 0.02 0.15 Log(parent's income: -3 to -l) 5,998 9.58 2.38 Log(parent's income: 0 to 5) 5,998 10.35 0.96 Log(parent's income: 6 to 11) 5,998 10.48 0.84 Log(parent's income: 12 to 17) 5,998 10.47 1.17 Log(parent's income: 23 to 28) 5,998 9.50 3.18 Dad's earnings indicator 5,998 0.83 0.38 College enrollment sample Son's age in 2005 1,313 31.21 3.41 Parent's age at birth 1,313 23.75 10.55 Enrolled in college after HS 1,313 0.42 0.50 Log(parent's income: -3 to -1) 1,313 9.65 2.32 Log(parent's income: 0 to 5) 1,313 10.36 0.94 Log(parent's income: 6 to 11) 1,313 10.46 0.89 Log(parent's income: 12 to 17) 1,313 10.54 0.97 Log(parent's income: 23 to 28) 1,313 9.52 3.46 Dad's earnings indicator 1,313 0.83 0.38 1964-1980 sample Son's age in 2005 11,758 30.33 4.13 Parent's age at birth 11,758 24.37 10.06 Son's income: 2003-2007 11,758 10.21 1.01 Log(parent's income: -3 to -1) 11,758 9.60 2.35 Log(parent's income: 0 to 5) 11,758 10.32 1.00 Log(parent's income: 6 to 11) 11,758 10.48 0.84 Log(parent's income: 12 to 17) 11,758 10.45 1.18 Log(parent's income: 23 to 28) 11,758 8.49 4.35 Dad's earnings indicator 11,758 0.82 0.39 TABLE 3 Effects of Parental Earnings on Children's Health (1) (2) (3) (4) Basic Controls Parent Earnings Averaged Over ... Outcome x 100 1 year 3 years 5 years 7 years Condition that -0.979 -1.259 -1.331 -1.374 limits school (0.150) *** (0.182) *** (0.195) *** (0.198) *** work 48.131 48,131 48.131 48,131 Condition that -0.429 -0.441 -0.439 -0.39 limits child (0.216) ** (0.233) * (0.258) * (0.266) behavior 6,071 6,071 6,071 6,071 Poor health -0.801 -1.354 -1.566 -1.741 status (Fune. (0.300) *** (0.363) *** (0.401) *** (0.404) *** Lim. Module) 6877 6877 6877 6877 Poor health -0.583 -0.674 -0.695 -0.745 status (Child (0.277) ** (0.289) ** (0.302) ** (0.304) ** WB Module) 9569 9569 9569 9569 Poor health -0.605 -0.917 -1.015 -1.127 status (0.201) *** (0.238) *** (0.255) *** (0.255) *** (Pooled) 15318 15318 15318 15318 Stayed in -0.23 -0.347 -0.405 -0.418 hospital (0.120) * (0.148) ** (0.158) ** (0.159) *** 27280 27280 27280 27280 # Nights in -1.731 -2.05 -2.02 -2.162 Hospital (1.061) (1.393) (1.505) (1.729) 27280 27280 27280 27280 # of Sick Days -2.275 -5.228 -6.215 -7.632 (2.391) (3.051) * (3.451) * (3.874) ** 27280 27280 27280 27280 (5) (6) (7) (8) Added Controls Parent Earnings Averaged Over ... Outcome x 100 1 year 3 years 5 years 7 years Condition that -0.757 -1.01 -1.068 -1.114 limits school (0.160) *** (0.199) *** (0.216) *** (0.220) *** work 48,131 48,131 48,131 48,131 Condition that -0.319 -0.251 -0.215 -0.155 limits child (0.232) (0.263) (0.298) (0.326) behavior 6,071 6,071 6,071 6,071 Poor health -0.376 -0.883 -1.075 -1.271 status (Fune. (0.340) (0.403) ** (0.446) ** (0.432) *** Lim. Module) 6877 6877 6877 6877 Poor health -0.35 -0.368 -0.357 -0.409 status (Child (0.300) (0.326) (0.351) (0.363) WB Module) 9569 9569 9569 9569 Poor health -0.251 -0.509 -0.582 -0.707 status (0.227) (0.269) * (0.291) ** (0.287) ** (Pooled) 15318 15318 15318 15318 Stayed in -0.188 -0.327 -0.399 -0.417 hospital (0.129) (0.165) ** (0.180) ** (0.184) ** 27280 27280 27280 27280 # Nights in -2.204 -2.933 -3.07 -3.431 Hospital (1.007) ** (1.316) ** (1.517) ** (1.841) * 27280 27280 27280 27280 # of Sick Days -0.837 -4.762 -6.285 -8.378 (2.437) (3.043) (3.578) * (4.203) ** 27280 27280 27280 27280 (9) With Hlth Insur. Outcome x 100 7 years Condition that -0.892 limits school (0.221) *** work 48,131 Condition that -0.152 limits child (0.350) behavior 6,071 Poor health -0.985 status (Fune. (0.422) ** Lim. Module) 6877 Poor health -0.062 status (Child (0.372) WB Module) 9569 Poor health -0.488 status (0.289) * (Pooled) 15318 Stayed in -0.344 hospital (0.189) * 27280 # Nights in -2.367 Hospital (1.626) 27280 # of Sick Days -8.827 (4.561) * 27280 Notes: Refer to the text for a discussion of the Basic and Added Controls. Standard errors clustered by family are in parentheses. *** p<.01, ** p<.05, * p<.1. TABLE 4 Effects of Parental Earnings on Health Care Use (1) (2) (3) (4) Basic Controls Parent Earnings Averaged Over ... Outcome x 100 1 year 3 years 5 years 7 years Frequency 16.495 20.162 21.29 22.571 talked to (4.652) *** (5.582) *** (5.983) *** (6.206) *** doctor 27280 27280 27280 27280 Number of 23.627 30.445 32.587 33.565 dentist (1.965) *** (2.492) *** (2.668) *** (2.728) *** visits 25061 25061 25061 25061 Daily 0.839 1.152 1.21 1.195 prescription (0.279) *** (0.342) *** (0.363) *** (0.370) *** drug use 21856 21856 21856 21856 (5) (6) (7) (8) Added Controls Parent Earnings Averaged Over ... Outcome x 100 1 year 3 years 5 years 7 years Frequency 8.581 7.913 7.544 8.394 talked to (5.133) * (6.740) (7.473) (7.827) doctor 27280 27280 27280 27280 Number of 17.489 22.731 24.368 25.224 dentist (2.108) *** (2.810) *** (3.095) *** (3.218) *** visits 25061 25061 25061 25061 Daily 0.59 0.793 0.811 0.756 prescription (0.302) * (0.387) ** (0.419) * (0.432) * drug use 21856 21856 21856 21856 (9) With Hlth Insur. Outcome x 100 7 years Frequency 2.615 talked to (8.393) doctor 27280 Number of 16.213 dentist (3.484) *** visits 25061 Daily 0.644 prescription (0.456) drug use 21856 Notes: Refer to the text for a discussion of the Basic and Added Controls. Standard errors clustered by family are in parentheses. *** p<.01, ** p<.05, * p<.l. TABLE 5 Effects of Parental Earnings on Physical Characteristics (1) (2) (3) (4) Basic Controls Parent Earnings Averaged Over ... Outcome x 100 1 year 3 years 5 years 7 years Weight-for- -2.649 -4.636 -4.122 -3.495 height z-score (2.573) (3.093) (3.196) (3.215) 2058 2058 2058 2058 Weight-for- -0.788 -3.687 -3.705 -3.85 age z-score (2.238) (3.080) (3.175) (3.254) 2058 2058 2058 2058 Height-for- 4.814 3.789 2.893 1.986 age z-score (2.942) (3.295) (3.517) (3.611) 2058 2058 2058 2058 (5) (6) (7) (8) Added Controls Parent Earnings Averaged Over ... Outcome x 100 1 year 3 years 5 years 7 years Weight-for- -2.128 -3.656 -2.785 -1.966 height z-score (2.699) (3.476) (3.725) (3.836) 2058 2058 2058 2058 Weight-for- -1.221 -3.32 -2.955 -3.098 age z-score (2.540) (3.580) (3.854) (4.066) 2058 2058 2058 2058 Height-for- 2.867 2.276 1.26 0.179 age z-score (3.122) (3.989) (4.451) (4.779) 2058 2058 2058 2058 Notes: Refer to the text for a discussion of the Basic and Added Controls. Standard errors clustered by family are in parentheses. *** p<.01, ** p<.05, * p<.1. TABLE 6 Effects of Parental Earnings on Children's Educational Outcomes (1) (2) (3) (4) Basic Controls Parent Earnings Averaged Over ... Outcome x 100 1 year 3 years 5 years 7 years Number of times -2.38 -3.294 -3.446 -4.684 changed school (1.849) (2.178) (2.265) (2.391) * 9732 9732 9732 9732 Ever repeated a -2.259 -3.384 -3.697 -3.953 grade (0.360) *** (0.431) *** (0.457) *** (0.470) *** 9732 9732 9732 9732 Ever suspended -1.173 -2.051 -2.267 -2.391 or expelled (0.498) ** (0.613) *** (0.663) *** (0.680) *** 4655 4655 4655 4655 Special -1.223 -1.573 -1.593 -1.576 education (0.219) *** (0.251) *** (0.265) *** (0.272) *** 41592 41592 41592 41592 Learning -0.138 -0.191 -0.229 -0.266 disability (0.107) (0.134) (0.144) (0.147) * 40641 40641 40641 40641 (5) (6) (7) (8) Added Controls Parent Earnings Averaged Over ... Outcome x 100 1 year 3 years 5 years 7 years Number of times -2.791 -3.919 -3.947 -5.136 changed school (1.981) (2.402) (2.511) (2.699) * 9732 9732 9732 9732 Ever repeated a -1.375 -2.264 -2.483 -2.719 grade (0.383) *** (0.459) *** (0.494) *** (0.514) *** 9732 9732 9732 9732 Ever suspended -0.348 -0.989 -1.113 -1.161 or expelled (0.551) (0.701) (0.771) (0.791) 4655 4655 4655 4655 Special -1.055 -1.455 -1.486 -1.474 education (0.241) *** (0.278) *** (0.296) *** (0.305) *** 41592 41592 41592 41592 Learning -0.056 -0.103 -0.143 -0.186 disability (0.110) (0.143) (0.155) (0.157) 40641 40641 40641 40641 (9) With Hlth Insur. Outcome x 100 7 years Number of times changed school Ever repeated a grade Ever suspended or expelled Special -1.34 education (0.314) *** 41592 Learning -0.145 disability (0.159) 40641 Notes: Refer to the text for a discussion of the Basic and Added Controls. Standard errors clustered by family are in parentheses. *** p<.01, ** p<.05, * p<.1. TABLE 7 Effects of Parental Earnings on Home Environment and Family Resources (1) (2) (3) (4) Basic Controls Parent Earnings Averaged Over ... Outcome x 100 1 year 3 years 5 years 7 years # of times 27.986 45.14 48.19 48.316 read (11.259) ** (12.630) *** (14.500) *** (15.294) *** stories, 5862 5862 5862 5862 past week Days -11.354 -12.786 -12.631 -13.67 without (4.111) *** (3.803) *** (3.800) *** (3.793) *** food (or 3897 3897 3897 3897 money for food) Ever been 3.081 2.965 3.37 3.368 in day care (0.623) *** (0.833) *** (0.895) *** (0.924) *** 10606 10606 10606 10606 Unable to -8.874 -10.727 -11.159 -11.567 meet needs (0.809) *** (0.918) *** (0.975) *** (0.999) *** in past 3897 3897 3897 3897 year Did not -1.658 -2.006 -2.013 -2.084 have enough (0.379) *** (0.434) *** (0.416) *** (0.419) *** food 3897 3897 3897 3897 Family -5.401 -6.313 -6.498 -6.547 member (0.651) *** (0.744) *** (0.759) *** (0.770) *** skipped 3897 3897 3897 3897 doctor visit (5) (6) (7) (8) Added Controls Parent Earnings Averaged Over ... Outcome x 100 1 year 3 years 5 years 7 years # of times 11.308 23256 24.525 24.827 read (12.489) (14.967) (18.280) (20.108) stories, 5862 5862 5862 5862 past week Days -5.597 -5.776 -4.821 -6.06 without (4.950) (4.210) (3.992) (3.596) * food (or 3897 3897 3897 3897 money for food) Ever been 2.233 1.62 2.07 2.185 in day care (0.690) *** (0.922) * (1.012) ** (1.067) ** 10606 10606 10606 10606 Unable to -7.015 -8.315 -8.531 -8.971 meet needs (0.857) *** (1.010) *** (1.088) *** (1.132) *** in past 3897 3897 3897 3897 year Did not -1.141 -1.319 -1.223 -1.252 have enough (0.413) *** (0.469) *** (0.442) *** (0.429) *** food 3897 3897 3897 3897 Family -4.717 -5.583 -5.799 -5.968 member (0.707) *** (0.842) *** (0.878) *** (0.903) *** skipped 3897 3897 3897 3897 doctor visit Notes: Refer to the text for a discussion of the Basic and Added Controls. For the first two outcomes standard errors clustered by family are in parentheses. For the last four outcomes robust standard errors are in parentheses. *** p<.01, ** p<.05, * p<.1. TABLE 8 Effects of the Timing of Parental Earnings over the Lifecycle of the Child (1) (2) (3) (4) Fair or Poor Health Enroll in College after Age 14 After HS Log(mean earnings -0.007 -0.007 0.033 0.033 3 years to 1 year (0.004) * (0.004) * (0.020) (0.021) before birth) Log(mean earnings 0.007 0.007 -0.047 -0.047 ages 0 to 5) (0.006) (0.006) (0.032) (0.032) Log(mean earnings 0.002 0.001 0.053 0.052 ages 6 to 11) (0.008) (0.008) (0.034) (0.034) Log(mean earnings -0.009 -0.009 0.058 0.06 ages 12 to 17) (0.008) (0.008) (0.026) ** (0.027) ** Log(mean earnings 0.002 0.000 ages 23 to 28) (0.003) (0.014) Observations 5,998 5,998 1,313 1,313 (5) (6) Log (Mean Earnings Ages 2003 to 2007) Log(mean earnings 0.035 0.034 3 years to 1 year (0.021) * (0.021) * before birth) Log(mean earnings -0.017 -0.019 ages 0 to 5) (0.032) (0.032) Log(mean earnings 0.107 0.098 ages 6 to 11) (0.037) *** (0.037) *** Log(mean earnings 0.129 0.085 ages 12 to 17) (0.027) *** (0.029) *** Log(mean earnings 0.058 ages 23 to 28) (0.015) *** Observations 11.758 11,758 Notes: The specifications used in columns (1) through (4) included the Basic and Added Controls discussed in the text, except a quartic in parent's age is used instead of a quadratic. In addition to these covariates, columns (5) and (6) also include a parent and child lifecycle adjustment. Standard errors clustered by family are in parentheses. *** p<.01, ** p<.05, * p<.1.