Better Measurement or Larger Samples? Data Collection for Policy Learning with Unobserved Heterogeneity
更精确的测量还是更大的样本?存在未观测异质性时的政策学习数据采集AI 解读 ↓
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Empirical research shows that individuals' responses to treatments vary along latent characteristics, such as innate ability or motivation. Therefore, a policymaker seeking to maximize welfare may consider designing policies based on observed characteristics and estimated latent traits. I characterize how the estimates' precision affects the worst-case performance of policies deriving rate-sharp regret bounds for assignment rules that include or exclude them, highlighting new trade-offs with the policy space complexity. I then study how a policymaker can solve such trade-offs by designing tailored data collections and derive a sufficient condition for a collection plan to be minimax optimal. In an empirical application in development economics, I show that including a proxy for entrepreneurs' business skills in targeting cash transfers increases welfare by 5%, and halves the probability of generating welfare losses. Moreover, I estimate the optimal allocation of resources between improving the precision of the proxy via repeated measurements, and increasing sample size.