E560095BwTF - Fortin Econ 560 V Social Mobility and Social...

Unformatted text preview: Fortin – Econ 560 V. Social Mobility and Social Interactions Plan B. Measurement of Intergenerational Mobility and Comparative Evidence 1. Early Studies 2. Use of Administrative Data 3. Strategies to Identify Causal Effects a. Adoptive Children b. Exogenous Variation 4. Cross-country Studies Lecture 5B Fortin – Econ 560 Lecture 5B 1. Early Studies • The deceptively simple equation of the intergenerational transmission of income, ˆ y1 = βy 0 + ε , (1) where y 0 denotes the long-run income of the father and y1 the long run income of the son, hides many estimation pitfalls. • Many early studies had not recognized the potential problems and some were still exploring the choice of functional forms, which quickly converge to the log-linear form. ˆ • With the log-linear form, β represents the intergenerational income elasticity (IGE). • For fathers, a key challenge is to derive an accurate measure of long-run earnings. Because of both response error and genuine transitory fluctuations in earnings ν 0 t , single-year measures y 0t are error-ridden proxies for longer-run earnings: y 0t = y 0 + ν 0t (2) Source: Becker and Tomes (1986) Table 1 Regressions of Son's Income or Earnings o n Father's Income or Earnings in Linear, Semilog, and Log-linear Form Variables Location and Son's Year 1966 (older white) 1969 (young black) 1966 (older black) York, England: 1975-78 1975-78 Malmo, Sweden, 1963 Geneva, Switzerland, 1980 Sarpsborg, Norway, 1960 Dependent Independent Other 1957-60 1974 United States, 1981-82 United States: 1969 (young white) Father's Year E IP None 2069 Coefficient t RZ N E Author 1957-60 1957-60 Log E Log E IP Log I P None None N.A. 2493 Hauser, Sewell, and Lutterman (1975) Hauser (in press)? Tsai (1983)t 1981-82 Log E§ Log E§ None 722 Behrman and Taubman (1983) Log I 3 II 1607 Freeman (1981) Log H Log I3 I1 2131 Freeman (1981) Log H Log I 3 I1 634 Freeman (1981) Log H Log I 3 I 1 947 Freeman (1981) 1950 1950 Log H Log W Log W Log W None None 198 307 Atkinson (1981) Atkinson (1981) 1938 Log I ICD None 545 545 545 de \X'olff and van Slijpe (1973) IHH None 801 Girod (1984) 115 Soltow (1965) Log H \!'hen son was 14 When son was 14 When son was 14 When son was 14 IHH 1950 Log I 1960 LORI None NOTE.-& = elasticity of son's income or earnings with respect to father's income o r earnings; E = earnings; H = hourly earnings; I = income; I 3 = income in three-digit occupation; I C D = income-class dummy; I H H = household income; I P = parents' income; W = weekly earnings. * First 5 years in the labor force. t Also ~ o b e r M. Hauser (personal communication, October 2, 1984). t $Adjusted for response variability. Adjusted for work experience. Sons with work experience of 4 years o r less were excluded. The regression was weighted so that each father had equal weight. f\Vork experience, three dummies for re..ion of residence at age 14, five dummies for type of place of residence at age 14, and a dummy for living in one parent/female home at age 14. "The elasticities are values between pairs of income classes ' Fortin – Econ 560 Lecture 5B • This sort of errors-in-variables problem in a regression equation’s explanatory variable tends to dilute the estimated coefficient of that variable and produce a downward bias in the coefficient, 2 ⎡ σy ⎤ ˆ plim β = β ⎢ 2 ⎥ = θβ < β σ y + σ υ20 ⎥ ⎢ ⎣ ⎦ • When the father’s income is not available, it has been typical to used predicted earnings. This two-stage procedure that uses education, occupation or social class to predict father’s earnings is likely to lead to an upward bias. o In the second-stage regression, when father’s education, occupation or social class is used only to predict father’s earnings, but not as a separate explanatory variable in its own right, the resulting omitted-variables bias may lead to overestimation of the intergenerational earnings elasticity. • A different problem has surfaced in measuring son’s earnings. • There may be some measurement error in the sons’ earnings: y1t = y1 + ν 1t (3) Fortin – Econ 560 Lecture 5B • Or, as argued by Haider and Solon (2003), the slope of the linear projection of y1t on y1 may not equal to 1, but varies over the life-cycle: y1t = λt y1 + ν 1t (3’) by contrast with the textbook case where λ t = 1 . • This latter type of measurement error generates the following type of bias ⎡ Cov( y1, y0t ) ⎤ ˆ plim β = ⎢ ⎥ = λβ 2 σ y1 ⎢ ⎥ ⎣ ⎦ • Numerous researchers have indeed reported that they estimate relatively small intergenerational elasticities if they measure son’s earnings near the very beginning of his career, but that their estimates get larger as son’s earnings are measured further along in the lifecycle. • This generates a problem of mean-reversion (the tendency for a stochastic process to remain near, or to return over time to its long-run average value). As explained by Bound et al. (1994), mean-reverting measurement error in a regression’s dependent variable compresses its variation and consequently leads to a tendency to underestimate the magnitude of the regression’s slope coefficient. Fortin – Econ 560 Lecture 5B • A first solution to the estimation of long-run earnings was to average earnings over multiple years. Given that there are a few panel data sets in the U.S., this strategy was used in a number of studies. • Several studies have also used IV as a second way to address the measurement error problem, using education, sex, occupation, industry dummies (e.g. Mulligan, 1997) and the index Duncan index of socioeconomic status (Zimmerman, 1992) as instruments. This strategy has its own problems (Kim and Solon, 2005). • The summary of the U.S. literature is that studies that have used multi-year measures of father’s earnings and have measured son’s earnings after his first few years in the labor market ˆ have estimated β about 0.4 or higher. • There are some problems with the use of these panel data. The intergenerational samples that can be constructed from the PSID and NLS are relatively small, and there is also considerable attrition in these data sets. Moreover, there are some cohort issues with the NLS. Source: Solon (1999) Source: Solon (1999) Fortin – Econ 560 Lecture 5B 2. Use of Administrative Data • Another source of longitudinal data is provided by administrative data, such as income tax data or social security data. • These data have the advantage of large sample size and potentially long observation window to estimate lifetime earnings that allow the relationship between current earnings and lifetime earnings to be evaluated (e.g. Haider and Solon, 2003). • Corak and Heisz (1999) is such an early study using Canadian income tax data on about 400,000 father-son pairs, and they find intergenerational earnings elasticities to be about 0.2. substantially lower than for the U.S, when estimating the relationship: 2 ln y1 = β 0 + β1 ln y0 + β 2 age1 + β 3 age12 + β 4 age0 + β 5 age0 + ε • They use nonparametric techniques to uncover significant nonlinearities and show that I intergenerational earnings mobility is greater at the lower end of the income distribution than at the upper end, and displays an inverted V-shape elsewhere. • A common drawback of using administrative data is that human capital and labour supply variables are typically unavailable, which can introduce considerable measurement error in the earnings measures. Source: Corak and Heisz (1999) Corak and Heisz Table 3 Intergenerational Elasticities for Various Samples and Specifications: Father and Son Earnings and Market Income Earnings Elasticity Standard Error Total Market Income Elasticity Standard Error A. Sample selection rules 1. Average income over five years 2 $1 2. Income in each of five years 2 $1 3. Income in each of five years 2 $100 4. Income in each of five years 3 $1,000 5. Income in each of five years 2 $3,000 B. Life cycle adjustments 1. Quadratic in age of fathers and sons 2. No controls for age 3. Dummy variables for age of sons 4. Quartic in age of fathers and sons 5. Oldest sons born in 1963 6. Oldest sons born in 1966 7. All siblings 8. Controls for marital status C. Choice of regressor 1. Eatnings 2. Total market income D. Estimation method Average income over five years 2 $1 1. Least squares 2. Median regression Income in each of five years 2 $1 3. Least squares 4. Median regression horizon would appear to be long enough to reduce the bias due to transitory income fluctuations. The robustness of these findings to the sample selection rules employed, the way in which adjustments for life cycle differences is made, and the choice of the father's income variable are assessed in Table 3. All of the results in this table are based upon five year averages of the father's income measure. The four rows labeled 1 in each of the panels of Table 3 repeat the results in the last column of Table 2. There are three major findings. First, the selection rules used to define the sample seem to have an important influence on the estimates of the elasticities. This influence seems to be restricted to whether individuals with zero (or negative) earningslincome are included in the sample before the average is calculated. If fathers must have at least $1 of earnings in each of the five years over which the average is calculated (as opposed to the average being at least $1) the earnings-earnings elasticity increases from 0.131 to 0.228 (see Rows 1 and 2 in Panel A). The elasticity does not change much beyond this as the cutoff is raised further, reaching 0.242 at a cutoff of $3,000. 513 Fortin – Econ 560 Lecture 5B • Mazumder (2005) tries to overcome this problem by using the 1984 Survey of Income and Program Participation (SIPP) matched to the Social Security Administration’s Summary Earnings Records (SER) but ends with small sample sizes. • He argues that transitory fluctuations in parental incomes that can have effects lasting more then 5 years so that using even 5-year averages of fathers’ earnings yields estimates that are biased down by approximately 30% and thus the IGE should actually be closer to 0.6. • Using detailed information on wealth from the SIPP, he finds an higher IGE for families with low net worth, offering some empirical support for theoretical models that predict differences in IGE due to borrowing constraints, but again small sample sizes are involved. 246 THE REVIEW OF ECONOMICS AND STATISTICS TABLE 4.—INTERGENERATIONAL ELASTICITIES USING SER FOR FATHERS’ EARNINGS Elasticity (Standard Error) N Fathers Log Avg. Earn. Sons 84–85 82–85 79–85 Daughters 76–85 70–85 84–85 82–85 79–85 Pooled 76–85 70–85 84–85 82–85 79–85 76–85 70–85 Father Earnings Must Be Positive Each Year Drop noncovered fathers 0.253 0.349 0.445 0.553 0.613 0.363 0.425 0.489 0.557 0.570 0.308 0.388 0.470 0.559 0.600 (0.043) (0.059) (0.079) (0.099) (0.096) (0.065) (0.087) (0.110) (0.140) (0.159) (0.039) (0.052) (0.067) (0.084) (0.093) 1262 1218 1160 1111 1063 1178 1124 1070 1031 982 2440 2342 2230 2142 2045 Impute noncovered fathers 0.289 0.313 0.376 (0.050) (0.052) (0.062) 1485 1462 1433 Drop government & self-employed 0.273 0.419 0.474 0.533 0.652 0.526 0.563 0.635 0.750 0.754 0.393 0.487 0.553 0.643 0.707 (0.060) (0.082) (0.096) (0.111) (0.135) (0.089) (0.137) (0.150) (0.173) (0.192) (0.057) (0.077) (0.086) (0.100) (0.118) 844 825 801 779 746 782 758 736 719 690 1626 1583 1537 1498 1436 Drop noncovered fathers 0.234 0.334 0.434 (0.043) (0.057) (0.069) 1295 1268 1227 — — 0.312 0.423 0.506 (0.060) (0.065) (0.091) 1201 1168 1127 — — 0.269 0.377 0.472 (0.034) (0.043) (0.056) 2496 2436 2354 — — Impute noncovered fathers 0.238 0.342 0.403 (0.042) (0.057) (0.059) 1534 1550 1571 — — 0.295 0.384 0.474 (0.055) (0.061) (0.080) 1394 1406 1424 — — 0.266 0.365 0.441 (0.033) (0.042) (0.049) 2928 2956 2995 — — Drop government & self-employed 0.242 0.355 0.441 0.523 0.575 0.400 0.504 0.600 0.731 0.847 0.304 0.422 0.570 0.622 0.703 (0.059) (0.080) (0.084) (0.101) (0.109) (0.084) (0.083) (0.113) (0.130) (0.145) (0.046) (0.061) (0.073) (0.081) (0.087) 874 869 862 895 917 803 794 785 825 831 1677 1663 1647 1720 1748 — — 0.350 0.395 0.422 (0.062) (0.081) (0.096) 1360 1339 1310 — — 0.322 0.358 0.404 (0.039) (0.048) (0.056) 2845 2801 2743 — — Allow Some Years of Zero Father Earnings* Dependent variable is children’s log average earnings, 1995–1998. All results use tobit specification. Note: For the dependent variable, probit models based on the 1996 SIPP matched to SER were used to determine if zero earnings reflected noncoverage or nonworker status and were imputed accordingly. For fathers, earnings for those identified as noncovered are either dropped or imputed for the years 1979–1985 as indicated. For the years before 1979, no adjustment is attempted. Earnings for topcoded fathers are imputed using March CPS data for 1970 to 1980 and using 1984 SIPP for 1981 to 1985. Standard errors are adjusted for within family correlation when more than one sibling is present. *Required years of positive earnings are: 1 for 2-year averages; 2 for 4-year averages; 3 for 7-year averages; 7 for 10-year averages; and 11 for 16-year averages. this analysis. In the top panel of the table, fathers’ earnings must be positive in each year. In the lower panel, some years of zero earnings are allowed. Within each panel, there are three additional selection rules: noncovered fathers are dropped; noncovered fathers’ earnings are imputed; and government and self-employed fathers and noncovered fathers are dropped. In the first set of results in the top panel (row 1 of table 4), it is not necessary to actually identify covered status, because all fathers with years of zero earnings are dropped. Therefore, it is possible to construct averages that include years prior to 1979. Under the second rule (estimates in row 2), in contrast, averages can only be constructed going back to 1979, because it is difficult to identify covered status in prior years. Under the third rule (row 3), those identified as government or self-employed workers at any time during the 1984 SIPP survey period are dropped. The results from using the two-year average with SER data are clearly lower than what was found using the SIPP. The highest coefficient is 0.289 when noncovered fathers are dropped from the analysis. The fact that many fathers have noncovered earnings (in addition to covered earnings) that are not captured in the SER data is the obvious explanation for the greater attenuation using the SER data. In fact, when noncovered fathers are dropped and earnings are required to be at least $3,000 in each year, thereby eliminating many of those whose covered earnings severely misrepresent their true earnings, the estimated coefficient rises to 0.334 (not shown), which is comparable to the SIPP results from table 3. This suggests that the results based on the SER may, in fact, be biased down by even more than would be the case with comparable survey data. It also suggests that the possibility of upward bias from correlated measurement error between fathers and children when using SER data is more than offset by the overall attenuation bias. Otherwise the estimates using the SER would have been higher than those found when using the SIPP. It is also apparent from table 4 that on the whole, the IGE is only slightly lower when the imputed noncovered fathers are added to the sample. The most striking finding is that the IGE rises dramatically as the fathers’ earnings are increasingly averaged over more years. Indeed, the estimated father-son elasticity is 0.613 when the fathers’ earnings are averaged over 16 years. The father-daughter elasticity is a bit lower at 0.570. When the sample of fathers is restricted to private-sector, non-selfemployed workers, however, the father-daughter elasticity is estimated at 0.754. Such a high degree of transmission is rather surprising and may be due to the possible positive correlation between fathers’ earnings and daughters’ labor force participation among this group, as discussed earlier. C. Does Excluding Years of Nonemployment Matter? Couch and Lillard (1998) argue that the results of Solon (1992) and Zimmerman (1992) are sensitive to the inclusion 252 THE REVIEW OF ECONOMICS AND STATISTICS intergenerational mobility.”43 One problem with this approach is that it does not directly measure parents’ ability to finance schooling for their children at the time that such an investment is made. Mulligan’s measure also does not capture inter vivos transfers. Finally, the model focuses solely on an intergenerational budget constraint and does not analyze parents’ potential inability to borrow from their own future income, which may be an important issue in its own right. Gaviria (2002) addresses some of these problems. He also uses the PSID, but categorizes the nonconstrained as those who have actually reported receiving large financial transfers or whose parents have a high net worth. Gaviria also uses a split-sample estimation approach and finds some evidence that intergenerational mobility is in fact lower among borrowing-constrained families. However, the differences are not large, and the samples are too small to find differences in the IGE at the 5% significance level. The SIPP-SER data can bring several clear advantages to this question. First, with a larger sample than the PSID it is easier to detect differences among subgroups when using a sample-splitting strategy. Second, the highly detailed wealth data available in the SIPP make it possible to measure borrowing constraints more directly through net worth. Net worth measures the ability of parents to borrow against their current wealth or to draw down assets in order to finance human capital acquisition for their children. Third, the data on wealth are available for 1984, when the children are between the ages of 16 and 21, and at a time when critical decisions regarding college attendance or continuation are being made. Table 10 shows the results of this exercise. First, on using the SIPP sample, pooling both sons and daughters together, and splitting the sample by the median level of net worth (approximately $65,000 in 1984 dollars) the results point to a sharp difference between those below the median and those above. The IGE is 0.458 for those with lower than median net worth, but only 0.274 for those above the median level. Though the difference looks large, one could not reject the null hypothesis of equality at the 5% significance level. The second set of results compares those at or below the first quartile of net worth with those at the top quartile. In this case the difference is even more dramatic and is statistically significant at the 5% level. In fact, for the top quartile the IGE appears to be close to 0. Indeed, the permanent income model would predict this result if income is uncorrelated with ability. Similar attempts were slightly less conclusive using SER data for fathers’ earnings, as the bottom half of table 10 shows. Whereas estimates for the low end of the net-worth distribution were similar to that found using the SIPP, the estimates for those with high net worth were significantly 43 See Mulligan (1997, p. 247). Source: Mazumder (2005) TABLE 10.—INTERGENERATIONAL ELASTICITY BY LEVEL OF NET WORTH Elasticity (Standard Error) N Overall High Net Low Net Worth Worth Diff. t-Stat. SIPP Results Father earnings Log avg. 84–85 Low is Յmedian High is Ͼmedian Father earnings Log avg. 84–85 Low is Յ25th percentile High is Ն75th percentile 0.369 (0.069) 1514 0.274 (0.184) 757 0.458 (0.112) 757 0.184 0.855 (0.215) Ϫ0.044 (0.135) 380 0.465 (0.122) 379 0.508 2.795 (0.182) SER Results Father earnings Log Avg. 79–85 Low is Յmedian High is Նmedian Father earnings Log Avg. 79–85 Low is Յ25th percentile High is Ն75th percentile 0.480 (0.068) 2,186 0.304 (0.110) 1,093 0.465 (0.090) 1,093 0.160 1.130 (0.142) 0.205 (0.113) 547 0.515 (0.130) 547 0.310 1.799 (0.172) Dependent variable is log average earnings, 1995–1998. All results use tobit specification. Sons...
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