Evaluating the Geographically Weighted Regression for Modeling Fertility Rates in South Korea

Abstract

South Korea’s total fertility rate (TFR) has steadily declined to unprecedented levels, reaching 0.72 in 2023, which is well below the replacement level of 2.1. As this decline continues, the trend poses severe economic and demographic challenges, including rapid population aging, labor force contraction, and increasing strain on welfare systems. This thesis evaluates the effectiveness of using the Geographically Weighted Regression (GWR) to model South Korea’s TFR at the local level. In particular, we revisit the work done by Jung et al. (2019), which fitted the model on data from 2019. One aspect of the model not addressed in their paper is its use of “pseudo-t statistics,” which is a result of the model’s violation of classical OLS assumptions. To address this gap, we re-estimate both an Ordinary Least Squares (OLS) model and a GWR model using updated 2023 data across 190 administrative regions. The model’s fit is assessed using test statistics including AICc, Moran’s I, and Koenker (BP). We then implement a 5,000-iteration nonparametric bootstrap procedure to evaluate the stability of the GWR coefficient estimates, computing empirical confidence intervals and percent-opposite-sign metrics for each coefficient. The results suggest that GWR improves model fit relative to OLS, capturing meaningful spatial heterogeneity in the data which OLS does not take into account. However, the bootstrap analysis reveals instability in the coefficient estimates, casting doubt on the reliability of inference drawn from the GWR pseudo-t statistics. These findings ultimately support the use of GWR as an exploratory rather than an immediately inferential tool and underscore the spatial and statistical complexity of TFR modeling in Korea.