  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.
