Note. At December, 31st 1993: 1 US Dollar = 2110.60 Indonesian Rupiah Table 1 Descriptive statistics of total net equivalized household consumption expenditures in 2000 (in 1993 Rupiah) by treatment status “The standardized difference is the mean difference as a percentage of the average standard deviation: 100(*%7 —Xc)/ (st + se) /2, where for each covariate ¥7 and X¥c are the samples means in the treated and control groups and se. and sp are the corresponding sample variance >The variance ratio is st / Se Table2 Means (standard deviations), standardized differences in percent, and variance ratio for continuous covariates in both treatment groups before matching Table 3 Table of observed proportions and percent differences for categorical covariate (1) All these propensity score methods rely on the unconfoundedness assumption (Assumption |). This assumption may be controversial. It requires that all variables (included missingness) that affect both the outcome and the likelihood of receiving the treatment are observed or that all the others are perfectly collinear with the observed ones. Although this assumption is not testable, it is a very strong assumption, and one that need not generally to be applicable. Table 4 Table of observed proportions and percent differences for categorical covariate (2) Table 4 continued * Covariate suffers from some missing data * The standardized difference in % is the mean difference as a percentage of the average standard deviation: 100%7 —xXc)/ ca + se) /2, where for each covariate x7 and Xc¢ are the samples means in the treated and control groups and se and se are the corresponding sample variance > The percent bias reduction is defined as 100(1 — B/B7), where B is the standardized difference and B, is the initial standardized difference Table6 Standardized differences (in %) and percent reduction in bias for propensity scores, before and after matching using each approaches to the missing covariates problem in combination with nearest neighbor, Kernel, and stratification propensity score matching Table7 Average causal effect of childbearing on consumption expenditures (in 1993 Rupiah) in Indonesia using different approaches to the missing covariates problem in combination with nearest neighbor, Kernel, and stratification propensity score matching 4 Analytical standard errors are reported. If they are not calculable, bootstrapped standard errors are reported Table8 Heterogeneity of the treatment effect with respect to real total equivalised household consumption expenditure in 1993 (Rupiah) and response covariate behavior Results from multiple imputation (with Y) and propensity score matching. Analytical standard errors are reported. If they are not calculable, bootstrapped standard errors are reported women in six categories on the basis of the real net equivalised consumption expen- diture observed at the time of first wave (1993). As cutoffs we consider the percentile corresponding to the percentages 10, 25, 50, 75, and 90 of the sample distribution of this pre-treatment variable. For each subclass k (k = 1, ..., 6), we calculate the aver- age treatment effect on the treated, say ATT;, and the relative ATT effect in percent defined as 1OOATT;/ ¥; (C), where Fi (C) is the mean “counterfactual” consumption level in the case of non-treatment for women belonging to the stratum k. This heterogeneity analysis confirms non-significant results for most of the sub- Results from multiple imputation (with Y) and propensity score matching. Analytical standard errors are reported. If they are not calculable, bootstrapped standard errors are reported Table 9 Effect of a childbearing assignment on consumption expenditure (in 1993 Rupiah) in Indonesia using different equivalence scale study, these methods are complicated by the presence of missing background data. Several approaches for estimating propensity scores with incomplete data exist; here we compare missing completely at random based estimates of propensity scores and the causal effect of interest with estimators based on alternative models for the miss- ing data process, including one developed by Rosenbaum and Rubin (1984) and a combination of propensity score matching with MI. We judge the nlausibilitv of these alternative annroaches bv the halance that the
