Experiments # 3

Sub-section 2.

In this section, we present the results of the same procedure described in Section 4.1, now incorporating a set of covariates as control variables. Overall, the ATT estimates with control variables for both the total fertility rate and the number of births remain largyly consistent with the previous results in Section 4.1 and are statistically significant. Minor variations are observed depending on the combination of control variables used. Table 5 summarizes the control variables along with the dependent variables. 

 

 

To condition on exogenous time-varying covariates X_it, we follow the approach proposed by Arkhangelsky et al. (2021), which involves covariate adjustment by removing the influence of changes in covariates from the outcome variable Y_it prior to applying the synthetic control method. Specifically, we apply the SDID algorithm to the residuals calculated as:

 

Regading implementation, we first standardize all covariates as Z-scores to ensure that no high-variance variables disproportionately influence the results, while preserving the underlying variation in the covariates. For efficient computation, we adopt the alternative method introduced by Kranz (2022).

Total Fertility Rate

Table 6 presents the estimated effects of the "1 Billion+ i-Dream" on the fertility rate, with control variables introduced incrementally. The results are nearly identical to those reported in the previous section and are statistically significant at the 10% level. In some combinations of covariates, a slight decrease in the ATT is observed; however, these differences are not statistically significant.

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Number of Births

Table 7 displays the estimated effects of the "1 Billion+ i-Dream" on the number of births, again with control variables introduced gradually. The results are consistent with those from the previous section and are statistically significant at the 1%, 5%, or 10% level, depending on the specific combination of covariates.

 

 

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