4. Results
We investigate the impact of the "100 Million+ i-Dream" program, implemented in Incheon, on the total fertility rate and the number of births. The results indicate that Incheon's policy positively influenced both the total fertility rate and the number of births. Specifically, we find evidence that, following the implementation of the "100 Million+ i-Dream" program, Incheon's total fertility rate increased by 5% and the number of births increased by 8% in 2024.
Our analysis specifically examines whether the total fertility rate and the number of births in Incheon significantly differ from those in the other 15 cities, based on observations from 2000 to 2024. Since our synthetic difference-in-differences (SDID) approach accounts for any time-invariant differences across cities through city fixed effects, and for common trends through time fixed effects—while controlling for time-varying, city-specific characteristics—the remaining variation in outcomes can reasonably be interpreted as the causal effect of Incheon's policy.
We present the SDID results without control variables in Section 4.1 and with control variables in Section 4.2. For details on the placebo variance estimation, see Appendix B.
4.1 SDID results without control variables
4.1.1 Total Fertility Rate
Before presenting our SDID estimates from equation (3), we first report the DID results from equation (1) and the SC results from equation (2). This step helps clarify our identification strategy and supports the interpretation of our subsequent findings by comparing them with traditional frameworks. Figure 8 illustrates how the DID method constructs counterfactuals and subsequently calculates the average treatment effect on the treated (ATT), while Table 3 presents the corresponding DID results. According to the DID estimate, the policy effect is a 0.033 increase in the fertility rate. However, the parallel trends assumption underlying the DID approach may not hold if the pre-treatment trends across the 16 cities are not parallel. In that case, the DID estimate could be biased.
On the other hand, Figure 9 illustrates how the SC method estimates an ATT value of 0.027. We calculate the standard error of the SC estimate using a placebo test, which yields a standard error of 0.066 and a corresponding 90% confidence interval of (–0.082, 0.136).
Finally, Figure 10 presents the results of our SDID analysis. We also visualize how the SDID method constructs a synthetic control that closely parallels the treated group during the pre-treatment period. Then, the method estimates the difference-in-differences by weighting pre-treatment periods that are similar to the post-treatment level, and subsequently calculates the ATT by subtracting this counterfactual from the observed outcome.
In Table 4, the SDID estimate indicates that Incheon's policy increased the fertility rate by 0.044, with the effect being statistically significant at the 0.1% level. However, since the regression does not account for the variance arising from the estimation of weights, we compute the standard error using a placebo test. This yields a standard error of 0.025 and a corresponding 90% confidence interval of (0.003, 0.085).
In addition, Figure 11 compares the SDID estimate with that of the traditional SC method. By incorporating both unit and time weights, as well as a regularization term, the SDID approach achieves lower variance than the traditional SC method.
4.1.2 Number of Births
In contrast to the Total Fertility Rate (TFR)—an estimate based on age-specific fertility rates that indicates the average number of children a woman is expected to have over her lifetime—the number of births represents the actual count of babies born in a given year. To complement our analysis and assess the robustness of the findings, we additionally report results using the number of births as the outcome variable, following the same empirical procedure. We employ the logarithm of the number of births as the dependent variable to account for substantial disparities across cities(주석). Using the log-transformed outcome allows us to interpret the estimated policy effect as the percentage change in the number of births relative to a counterfactual scenario in which the policy was not implemented.
(주석 - Seoul and Gyeonggi Province exhibit significantly higher birth counts than other metropolitan areas due to their larger populations and concentration of reproductive-age women, leading to scale imbalances in raw comparisons.)
Figure 12 and Table 5 present the DID estimates of the policy effect. The results suggest that the implementation of the "100 Million+ i-Dream" program may have led to an approximate 17.9% increase in the number of births. However, as noted in the previous section, this estimate may be biased due to a potential violation of the parallel trends assumption.
Figure 13 reports the results from the SC method, which yields an ATT of 0.0999—indicating an approximate 10% increase in the number of births. A placebo test is used to calculate the standard error and 90% confidence interval, which are 0.190 and (-0.215, 0.415), respectively.
Finally, our analysis using the SDID approach estimates the policy effect as an approximate 8.6% increase in the number of births. The standard error and corresponding 90% confidence interval, based on the placebo test, are 0.034 and (0.030, 0.141), respectively. As in the previous section, we also provide a visualization of the SDID mechanism in Figure 14, along with a comparison to the traditional SC method in Figure 15.
4.2 SDID results with control variables
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 largely 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 7 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).
4.2.1 Total Fertility Rate
Table 8 presents the estimated effects of the "100 Million+ 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.
4.2.2 Number of Births
Table 9 displays the estimated effects of the "100 Million+ 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.
Overall, our study provides evidence supporting the positive impact of the "100 Million+ i-dream" program on both fertility rates and the number of births. However, given the potential time lag before the full effects of the policy become evident, it is difficult to rule out the possibility that the observed outcomes may be partially driven by regional migration or temporal shifts in the timing of childbirth (주석). Accordingly, further investigation is warranted. We also intend to continue monitoring and analyzing how the policy's effects evolve over time.
The primary contribution of our study lies not in the specific magnitude of the estimated effects, but in the development of a methodological framework that enables the ongoing assessment of both annual heterogeneous impacts and the long-term effects of Incheon's "100 Million+ i-Dream" program. This framework facilitates empirical validation—using Incheon as a case study—of prior research suggesting that a substantial financial commitment is necessary to generate a measurable increase in fertility(주석). Ultimately, our findings aim to inform the design of more effective, evidence-based fertility support policies.