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This paper examines how homestead policies, which opened vast frontier landsfor settlement, influenced the development of American frontier states. It usesa treatment propensity-weighted matrix completion model to estimate thecounterfactual size of these states without homesteading. In simulationstudies, the method shows lower bias and variance than other estimators,particularly in higher complexity scenarios. The empirical analysis revealsthat homestead policies significantly and persistently reduced state governmentexpenditure and revenue. These findings align with continuousdifference-in-differences estimates using 1.46 million land patent records.This study's extension of the matrix completion method to include propensityscore weighting for causal effect estimation in panel data, especially instaggered treatment contexts, enhances policy evaluation by improving theprecision of long-term policy impact assessments.

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