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.

This paper examines the intraday 5-minute volatility dynamics of crude oil futures using Market-by-Order (MBO) data from the front-month contract. Within the context of crude oil futures, we report the following key findings: (1) Realized Volatility (RV) serves as a reliable proxy for latent volatility; (2) 5-minute RV displays pronounced intraday seasonality and long-memory characteristics; (3) Deseasonalized 5-minute RV is still long-memory but simultaneously highly stationary, a surprising observation. (4) Fractional differencing tends to eliminate both high- and low-frequency components of the 5-minute deseasonalized RV, making the commonly used AutoRegressive Fractionally Integrated Moving Average (ARFIMA) model less effective. This has profound implications on how we understand volatility. (5) Eventually, we adopt a simpler AutoRegressive Integrated Moving Average (ARIMA) approach and present the results.

I study “three toed pete,” a high-variance, sequential wagering game in which players decide—over multiple rounds—whether to commit to a common pot based on private signals. I develop and compare a suite of computational methods for characterizing equilibrium behavior: (i) simulation-based grid search to identify candidate cutoff strategies; (ii) gradient- based and simulated-annealing optimizers to navigate the noisy, multi-dimensional payoff landscape; (iii) state-dependent cutoff maps that adjust to current “toe” counts and alternating move order; and (iv) backward-induction algorithms that bootstrap the t = 1 solution to solve for general t recursively. My numerical experiments confirm theoretical predictions in the two-player, one toe case, reveal how cutoff thresholds rise with increasing target toes, and demonstrate scalability to more complex, n-player settings. I also prove structural lemmas—such as the weak dominance of non-contiguous strategies—that under- pin our computational approach. Beyond game theory, my methods have direct applications to multi-round auctions, sequential bidding for large-scale contracts (e.g. Olympic host selection, pension-liability transfers, 401(k) administration), and other contexts where agents face uncertainty, risk, and dynamic strategic interaction.