How would states on the American frontier have developed in the absence of homestead policies? This paper explores the role of homestead policies, which opened for settlement hundreds of millions of acres of frontier land, in shaping the size of state governments. Using a matrix completion method, I predict the counterfactual time-series of frontier state size had there been no homesteading. I extend the method to allow for propensity-weighting of the loss function to control for selection bias. Causal estimates signify that homestead policies had significant and long-lasting negative impacts on state government expenditure and revenue. The estimates are in the same direction as those of a continuous difference-in-differences estimator that exploit variation in the timing and intensity of homestead entries, aggregated from 1.46 million individual land patent records.

翻译：在没有农业定居政策的情况下，美国前沿州如何发展？本文探讨了农业定居政策在塑造国家政府规模方面的作用，农业定居政策开放了数亿英亩的前沿土地进行定居。利用矩阵完成方法，预测了在没有农业定居的情况下前沿州规模的反事实时间序列。我将该方法扩展到允许倾向权重化损失函数，以控制选择偏差。因果估计表明，农业定居政策对州政府支出和收入产生了重大而持久的负面影响。这些估计与连续差异差异估计器的方向相同，该估计器利用从146万个土地专利记录汇总的农田入口的时间和强度的变化。