coefficients. We provide a statistical framework for conducting tests for attrition bias that draws a sharp distinction between selection on unobservables and on observables and that shows that weighted least squares can generate consistent parameter estimates when selection is based on observables, even when they are endogenous. Our empirical analysis shows that attrition is highly selective and is concentrated among lower socioeconomic status individuals. We also show that attrition is concentrated among those with more unstable earnings, marriage, and migration histories. Nevertheless, we find that these variables explain very little of the attrition in the sample, and that the selection that occurs is moderated by regression-to-the-mean effects from selection on transitory components that fade over time.Consequently, despite the large amount of attrition, we find no strong evidence that attrition has seriously distorted the representativeness of the PSID through 1989, and considerable evidence that its crosssectional representativeness has remained roughly intact.The increased availability of panel data from household surveys has been one of the most important developments in applied social science research in the last thirty years. Panel data have permitted social scientists to examine a wide range of issues that could not be addressed with cross-sectional data or even repeated cross sections.Nevertheless, the most potentially damaging and frequently-mentioned threat to the value of panel data is the presence of biasing attrition--that is, attrition that is selectively related to outcome variables of interest.In this paper we present the results of a study of attrition and its potential bias in one of the most well-known panel data sets, the Michigan Panel Study of Income Dynamics (PSID). The PSID has suffered a large volume of attrition since it began in 1968--almost 50 percent of initial sample members had attrited by 1989. We study the effect of attrition in the PSID on the means and variances of several important socioeconomic variables --such as individual earnings, educational level, marital status, and welfare participation--and on the coefficients of variables in regressions for these variables. We also examine whether the likelihood of attrition is related to past instability of such behaviors--earnings instability, propensities to migrate or to change marital status, and so on. A companion paper studies the effect of attrition on estimates of intergenerational relationships (Fitzgerald et al., 199733).An understanding of the statistical issues is important to understanding our approach. We provide a statistical framework for the analysis of attrition bias which shows that the common distinction between selection on unobservables and observables is critical to the development of tests for attrition bias and adjustments to eliminate it.However, we show that selection on observables is not the same as exogenous selection, for selection can be based on endogenous observables such as lagged dependent...

coefficients. We provide a statistical framework for conducting tests for attrition bias that draws a sharp distinction between selection on unobservables and on observables and that shows that weighted least squares can generate consistent parameter estimates when selection is based on observables, even when they are endogenous. Our empirical analysis shows that attrition is highly selective and is concentrated among lower socioeconomic status individuals. We also show that attrition is concentrated among those with more unstable earnings, marriage, and migration histories. Nevertheless, we find that these variables explain very little of the attrition in the sample, and that the selection that occurs is moderated by regression-to-the-mean effects from selection on transitory components that fade over time.Consequently, despite the large amount of attrition, we find no strong evidence that attrition has seriously distorted the representativeness of the PSID through 1989, and considerable evidence that its crosssectional representativeness has remained roughly intact.The increased availability of panel data from household surveys has been one of the most important developments in applied social science research in the last thirty years. Panel data have permitted social scientists to examine a wide range of issues that could not be addressed with cross-sectional data or even repeated cross sections.Nevertheless, the most potentially damaging and frequently-mentioned threat to the value of panel data is the presence of biasing attrition--that is, attrition that is selectively related to outcome variables of interest.In this paper we present the results of a study of attrition and its potential bias in one of the most well-known panel data sets, the Michigan Panel Study of Income Dynamics (PSID). The PSID has suffered a large volume of attrition since it began in 1968--almost 50 percent of initial sample members had attrited by 1989. We study the effect of attrition in the PSID on the means and variances of several important socioeconomic variables --such as individual earnings, educational level, marital status, and welfare participation--and on the coefficients of variables in regressions for these variables. We also examine whether the likelihood of attrition is related to past instability of such behaviors--earnings instability, propensities to migrate or to change marital status, and so on. A companion paper studies the effect of attrition on estimates of intergenerational relationships (Fitzgerald et al., 199733).An understanding of the statistical issues is important to understanding our approach. We provide a statistical framework for the analysis of attrition bias which shows that the common distinction between selection on unobservables and observables is critical to the development of tests for attrition bias and adjustments to eliminate it.However, we show that selection on observables is not the same as exogenous selection, for selection can be based on endogenous observables such as lagged dependent...

No abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. University of Wisconsin Press andThe Board of Regents of the University of Wisconsin System are collaborating with JSTOR to digitize, preserve and extend access to The Journal of Human Resources. All use subject to JSTOR Terms and Conditions 302 The Journal of Human Resources vector of parental characteristics at some prior time T < t, and et is a vector of unobservables.4 At is an indicator variable equal to 1 if the child attrites by time t and zero if not, and A is its latent index.5 Zt is a vector of observable characteristics(including Xct and Xp,) that are not necessarily independent of et.6 As in our companion paper, we make the important distinction between selection on observables and unobservables. Selection bias in the estimation of (1) on the nonattriting (At = 0) subsample occurs if Zt and ct are independent but ?t and vt are not (selection on unobservables) t, and vt are independent but Et and Zt are not (selection on observables)7The case of selection on unobservables is well known in the econometrics literature. Identification rests either on nonlinearities in E(?tX IX,, Xp, At = 0) or on an exclusionary restriction (requiring that at least one element of Z, not appear in Xct or Xp, and that its 8 be nonzero.)The case of selection on observables is discussed less frequently in the econometrics literature.8 A selection problem occurs in this case because observables that affect attrition are not independent of et. Thus, though Zt is not structurally related to Y,t (conditional on Xct and Xp), they do covary as a result of the selection mechanism. In our companion paper we show that one solution to this selection on observables problem is to first estimate (2), use the resulting estimated coefficients to form weights given by9 (5) W (Pr(At = OlXct, Xp,, Zt) (5) W = Pr(At = OXct, Xp) and then estimate (1) by WLS.10 In that paper we show that while selection on Zt, and hence on c?, alters the distribution of et, a consistent estimate of the original density can be obtained by reweighting on the basis of the observable Zt's.The critical variable in the case of selection on observables is, therefore, Zt. The advantage of panel data is that variables observed in the initial wave of the survey are potential elements of Zt. As long as these lagged variables are not in the structural 4. To focus attention on attrition we assume Xp, is exogenous. See Gottschalk (1995) and Antel (1992) for discussions of intergenerational correlation in unobservables which would make X,p endogenous. 5. When we say the "child"has attrited, we include the case where the entire parental family attrites before the child has left the household. 6. The additional assumption that Z, is mean independ...

No abstract