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

## TL;DR

This paper applies a novel matrix completion method with propensity score weighting to estimate the causal effects of homestead policies on American frontier states' development, showing significant reductions in government expenditure and revenue.

## Contribution

It introduces an extended matrix completion approach with propensity score weighting for causal inference in panel data with staggered treatments, improving policy impact estimation.

## Key findings

- Homestead policies significantly reduced state government expenditure.
- Homestead policies significantly reduced state revenue.
- The method outperforms traditional estimators in bias and variance in simulations.

## 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.