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：本文探讨了美国边疆地区在没有宅地政策的情况下各州可能的发展轨迹。宅地政策开放了数亿英亩边疆土地用于定居，本研究旨在分析该政策对州政府规模的影响。通过采用矩阵补全方法，我预测了未实施宅地政策时边疆各州规模的反事实时间序列。我进一步扩展该方法，在损失函数中加入倾向性权重以控制选择偏差。因果估计表明，宅地政策对州政府支出和收入产生了显著且持久的负面影响。这些估计结果与连续双重差分估计器的结论方向一致——后者利用从146万份个人土地专利记录中汇总的宅地进入时间和强度差异进行估算。