State-Building through Public Land Disposal? An Application of Matrix Completion for Counterfactual Prediction

Abstract: This paper examines how homestead policies, which opened vast frontier lands for settlement, influenced the development of American frontier states. It uses a treatment propensity-weighted matrix completion model to estimate the counterfactual size of these states without homesteading. In simulation studies, the method shows lower bias and variance than other estimators, particularly in higher complexity scenarios. The empirical analysis reveals that homestead policies significantly and persistently reduced state government expenditure and revenue. These findings align with continuous difference-in-differences estimates using 1.46 million land patent records. This study's extension of the matrix completion method to include propensity score weighting for causal effect estimation in panel data, especially in staggered treatment contexts, enhances policy evaluation by improving the precision of long-term policy impact assessments.