Causal effects on employment after first birth - A ... - University of York

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3.2 Inverse Probability Weighting (IPW)To control the selection of treated women, we estimate a sequence of quarterly propensityscores. 11 The probability of having the first child within the next year is modeled asa function of human capital and employment history, which is particularly important ifdecisions on having a child and decisions on the labor market career are taken jointly.As sequential labor market decisions are correlated (Troske and Voicu, 2010), controllingfor past labor market career is crucial for successful matching. Moreover, we control forstatus of the relationship with the partner and for the self reported importance of havinga family. 12 We include covariates of the partner, such as income and education, tries toproxy the partner’s role in the joint decision process.Under the unconfoundedness of the treatment and perfect overlap in the propensityscore, Busso et al. (2009) conclude that in small samples with unknown propensity score,a modified inverse probability weighting estimator (IPW) performs best in comparison tovarious matching estimators. This result stands in contrast to the conclusions obtained bythe Monte Carlo study in Frölich (2004). The crucial modification of the IPW estimatorinvolves the normalization of weights for the nontreated women. According to the resultsof Busso et al. (2009), the poor performance of IPW reported by Frölich’s (2004) MonteCarlo study is due to the fact that Frölich does not normalize the IPW weights. Doing sostrongly improves the performance of the estimator as found by Busso et al. (2009), whosuggest to estimate the ATT as follows (Busso et al., 2009, eq. (7)):(1)ˆθ BDM =∑ ni=1T i Y i∑ ni=1T i−∑ nj=1(1 − T j )ŴjY j∑ nj=1(1 − T j )Ŵjwith weights Ŵ j = ˆp(X j )/(1 − ˆp(X j )) .Furthermore, T i , T jdenote the treatment dummy variables for individuals i, j (treatedand non-treated), respectively, and ˆp(X j ) denotes the estimated propensity score as afunction of covariates X j . The application of the weights W j leads to a reweighting ofthe nontreated women according to the odds–ratio of having a child within the next year.Note that the denominator corresponds to the sum of the weights in the numerator.For our application, we have to account for the fact that for the estimation of treatmentversus waiting the group of eligible comparison women changes by month of age.11 The size of the treatment sample is not sufficient to go down to a monthly frequency when estimatingthe propensity scores. Furthermore, we think that the selection into childbirth does not change stronglyfrom month to month.12 In fact, in contrast to matching, the reweighting estimator we will use later requires the propensityscore to be a conditional probability (Busso et al., 2009), which is evident in our application. As there issufficient overlap, we do not require any trimming.11
Correspondingly, the alignment between treated and nontreated observations changes aswell by month of age. The higher the age, the smaller the ’eligible’ control group for firstbirth. Thus, we modify the estimator in equation (1) to{ ∑∑ n }ni=1 j=1T i Y i −(1−T j)Ŵi,jY j,age(i)∑nj=1 ˆθ =(1−T j)Ŵi,j(2)∑ ni=1T iwith weights Ŵ i,j = E i,j ˆp(X j )/(1 − ˆp(X j )) .E i,j is a dummy variable which take the value of one if woman j can be used as a controlobservation for treated woman i, i.e. if j remains childless for at least three months afterthe respective age at first birth for the treated woman i. E i,j is set to zero if woman jhas a child earlier than the three months after birth for woman i. Y j,age(i) is the outcomeof control woman j aligned to the age at first birth for treated woman i.This IPW or reweighting estimator has the advantage of not relying on a tuning parametersuch as a bandwidth in kernel matching or the number of nearest neighbors innearest neighbor matching. Moreover, it is easy to implement and standard errors arereadily obtained by bootstrapping. Busso et al. (2009) show that this estimator is preferredin terms of bias and variance in finite sample settings with unknown propensityscore. However, they stress that this only holds with good overlap and when misspecificationof the propensity score is not a concern.3.3 Outcome regression based on IPWIn order to account for time trends and to assess effect heterogeneity by observable characteristics(e.g. by age, education) including the effect of the 2001 reform, we follow Abadieand Imbens (2011) who suggest to estimate ex post outcome regressions after matching.We estimate weighted linear regressions of the individual outcomes on an intercept, atreatment dummy as well as further covariates and the interactions of their demeanedvalues with the treatment dummy (Wooldridge, 2002, p. 612). In addition, we use yeardummies as main <strong>effects</strong> to account for a time trend in female employment rates. Becauseof sample size issues, we do not align treated and controls by calendar year. Thus, allestimated treatment <strong>effects</strong> reported in the following - including the baseline estimateswithout further controls - are based on outcome regressions controlling for year dummies.We adjust the approach by Abadie and Imbens to the IPW case employing a constantweight of 1/ ∑ nj=1 (T j ) for a treated woman i and a weight of (1−T j )Ŵi,j/ ∑ nj=1 (1−T j )Ŵi,jfor a nontreated woman j with outcome Y j,age(i) aligned in age for E i,j = 1 to treatedwoman i.12
Page 3 and 4: This reform increases the income su
Page 5 and 6: a similar propensity to have a firs
Page 7 and 8: our empirical analysis, we will onl
Page 9 and 10: 3.1 Dynamic Treatment ApproachThe t
Page 11: an average counterfactual outcome f
Page 15 and 16: pose a problem if the selection of
Page 17 and 18: drops to zero due to mandatory mate
Page 19 and 20: for university graduates (17 months
Page 21 and 22: of the interaction variables, where
Page 23 and 24: 6 ConclusionsIn a critical phase of
Page 25 and 26: Fortin, N. (2009). Gender role atti
Page 27 and 28: Troske, K. R. and Voicu, A. (2010).
Page 29 and 30: Table 3: Propensity to have first c
Page 31 and 32: Figure 3: Partnership one yearbefor
Page 33 and 34: Figure 9: ATTs for different educat
Page 35 and 36: Treatment groupFigure 11: Childbirt

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