250 AMERICAN SOCIOLOGICAL REVIEW and household income flows during the pre- ables that affect household economic status, vious calendar year.Our sample includes so that observations on men between the ages of 18 and 65 who identified themselves as either In yit =xiB+Ei (1) white or black (we excluded others because If we difference this model at two points sample sizes are too small)and who were in time,and if we collect all changes related partners in couple-headed households.Mar- to union dissolution and repartnering into ried men were included if they lived with dummy variables D and R,we obtain their spouse at time t.Men who were cohab- iting with a female partner were included if In(y+)-ln(y-)=△lny the same partner was in the household at =DYD+RYR+△xB+V, (2) time t-1 and time t.2 The analysis sample excludes unions that were dissolved through where yi-is a measure of economic status death or institutionalization between times t at time t-1,Ax;is the subset of control vari- and t+1. ables that change in value between t-1 and To be included in the sample,men who t+1,D is an indicator for union disruption were observed in unions at time t had to be between t-1 and t+1,and R is an indica- followed for the next two interviews,at time tor for a new partner between t-1 and t +1. t+1,by which time a disruption may or (To achieve greater clarity,we have sup- may not have occurred,and at time t+2 pressed explicit subscripts for calendar time when income data is collected retrospec- on the right side of equation 2.)Equation 2 tively for the previous calendar year.Sepa- assumes that change in economic status does ration is associated with a high risk of not depend on the level of economic status sample attrition among men in panel data at time t-1.Because this assumption may (D.Hill 1997;M.Hill 1992;Fitzgerald, not be correct,we estimated a slightly more Gottschalk,and Moffitt 1998),and this risk complex specification that relaxes this as- is particularly high for men with unstable sumption: work histories (Fitzgerald et al.1998).Our sample is therefore likely to underrepresent ln(+i)-ln(-i)=△lny men with the worst economic outcomes fol- lowing separation,and to overrepresent men =In(yi-Iy +DiYD+RYR who pay child support.However,a recent +△xB+V 3) study of attrition bias in the PSID found that the appropriate use of sample weights in re- Because pre-disruption income might be gression analyses produces consistent esti- correlated with other factors affecting in- mates despite the high levels of attrition come change,we estimated this equation (Fitzgerald et al.1998).To adjust for these using standard instrumental variables tech- unequal probabilities of sample selection niques (Greene 2000).One set of valid in- and attrition,we assigned each respondent a struments for equation 3 includes the con- single longitudinal weight equal to the cross- trol variables in equation 1,whose values sectional weight attached to that respondent were constant over time and thus do not ap- in the final year in which the respondent pear in the difference equation because they contributed to the data. cancel out of the right-hand side (e.g.,ques- Our regression model for the average im- tions about men's education are generally pact of union dissolution can be derived as asked only at the initial interview in the follows.Let yi:equal household economic PSID,so Ax =0 for schooling).An alterna- status at time t,and let xi be a vector of vari- tive strategy is to find instruments that do not appear at all in equation 1,such as in- 2 We include only cohabitants in long-term come at time t-2.We applied these two unions because the PSID prorates the income of strategies in turn to estimate instrumental the cohabiting partner to reflect the actual num- variables models,using education and ber of months spent in the same household,but twice-lagged income as the respective in- does not prorate the income of new marital part struments.The results from these two esti- ners. mation strategies were similar,and we re- This content downloaded from 129.96.252.188 on Mon,15 Feb 2016 15:26:54 UTC All use subject to JSTOR Terms and Conditions250 AMERICAN SOCIOLOGICAL REVIEW and household income flows during the pre￾vious calendar year. Our sample includes observations on men between the ages of 18 and 65 who identified themselves as either white or black (we excluded others because sample sizes are too small) and who were partners in couple-headed households. Mar￾ried men were included if they lived with their spouse at time t. Men who were cohab￾iting with a female partner were included if the same partner was in the household at time t - 1 and time t.2 The analysis sample excludes unions that were dissolved through death or institutionalization between times t and t + 1. To be included in the sample, men who were observed in unions at time t had to be followed for the next two interviews, at time t + 1, by which time a disruption may or may not have occurred, and at time t + 2 when income data is collected retrospec￾tively for the previous calendar year. Sepa￾ration is associated with a high risk of sample attrition among men in panel data (D. Hill 1997; M. Hill 1992; Fitzgerald, Gottschalk, and Moffitt 1998), and this risk is particularly high for men with unstable work histories (Fitzgerald et al. 1998). Our sample is therefore likely to underrepresent men with the worst economic outcomes fol￾lowing separation, and to overrepresent men who pay child support. However, a recent study of attrition bias in the PSID found that the appropriate use of sample weights in re￾gression analyses produces consistent esti￾mates despite the high levels of attrition (Fitzgerald et al. 1998). To adjust for these unequal probabilities of sample selection and attrition, we assigned each respondent a single longitudinal weight equal to the cross￾sectional weight attached to that respondent in the final year in which the respondent contributed to the data. Our regression model for the average im￾pact of union dissolution can be derived as follows. Let Yit equal household economic status at time t, and let xit be a vector of vari- 2 We include only cohabitants in long-term unions because the PSID prorates the income of the cohabiting partner to reflect the actual num￾ber of months spent in the same household, but does not prorate the income of new marital part￾ners. ables that affect household economic status, so that lnyit x+it- 1 If we difference this model at two points in time, and if we collect all changes related to union dissolution and repartnering into dummy variables D and R, we obtain ln(Yit+i) - ln(Yi,t-i) = A In yi Di7D =D~yD+R~y+ + Ri7R Axf + vi, (2) +AiD i where yit-l is a measure of economic status at time t - 1, Axi is the subset of control vari￾ables that change in value between t - 1 and t + 1, D is an indicator for union disruption between t - 1 and t + 1, and R is an indica￾tor for a new partner between t - 1 and t + 1. (To achieve greater clarity, we have sup￾pressed explicit subscripts for calendar time on the right side of equation 2.) Equation 2 assumes that change in economic status does not depend on the level of economic status at time t - 1. Because this assumption may not be correct, we estimated a slightly more complex specification that relaxes this as￾sumption: ln(Yit+i) - ln(Yi,t-1) = A In yj = ln(Yit-j ry + DiYD + RiYR + Axf'+vi. (3) Because pre-disruption income might be correlated with other factors affecting in￾come change, we estimated this equation using standard instrumental variables tech￾niques (Greene 2000). One set of valid in￾struments for equation 3 includes the con￾trol variables in equation 1, whose values were constant over time and thus do not ap￾pear in the difference equation because they cancel out of the right-hand side (e.g., ques￾tions about men's education are generally asked only at the initial interview in the PSID, so Ax = 0 for schooling). An alterna￾tive strategy is to find instruments that do not appear at all in equation 1, such as in￾come at time t - 2. We applied these two strategies in turn to estimate instrumental variables models, using education and twice-lagged income as the respective in￾struments. The results from these two esti￾mation strategies were similar, and we re￾This content downloaded from 129.96.252.188 on Mon, 15 Feb 2016 15:26:54 UTC All use subject to JSTOR Terms and Conditions