发表机构
University of Warwick（华威大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文发展了大型面板中颗粒工具变量（GIV）的强度渐近理论，区分了强、近弱和弱三种工具强度状态，并提供了相应的推断方法。
AI 中文摘要
我发展了大型面板中颗粒工具变量（GIV）的强度渐近理论，其中$N$和$T$均增长。GIV的强度取决于主导单位的存在。我形式化了主导的含义，并刻画了工具强度的三种状态。当少数单位主导总体时，工具是强的。GIV估计量是一致的，并以标准的$\sqrt{T}$速率渐近正态。当大型单位突出但不主导时，工具变弱。但我表明感兴趣参数仍然可恢复。GIV估计量仍一致且渐近正态，但速率慢于$\sqrt{T}$。当单位大小相当且无突出者时，工具在标准意义上是弱的。GIV估计量不一致且具有非标准分布。Wald推断仅在弱状态之外可靠。当工具弱时，我推荐Anderson-Rubin置信集。在实践中，工具必须在第一阶段构建。我表明可行估计量达到相同速率，但其渐近方差包含来自第一阶段估计的额外项。有效推断必须使用考虑该项的标准误。我应用GIV估计量及正确标准误来恢复三种商品（精炼铜、原油和天然气）的短期需求弹性。
英文摘要
I develop asymptotic theory for Granular Instrumental Variables (GIV) in large panels with both $N$ and $T$ growing. The granular instrument is constructed from individual shocks that must be estimated from the panel. I show that this estimation has a first-order effect on the asymptotic variance of the GIV estimator. Existing methods do not account for this effect, leading to incorrect standard errors and invalid inference. I derive corrected standard errors that deliver valid inference. I also characterize how instrument strength changes as $N$ grows. This yields strong, nearly-weak, and weak regimes for GIV. In particular, I identify a previously uncharacterised nearly-weak regime in which the instrument vanishes asymptotically, but GIV remains valid. If $T$ grows sufficiently fast relative to $N$, the estimator remains consistent and asymptotically normal at a rate slower than $\sqrt{T}$. When $N$ and $T$ grow proportionally, the estimator instead exhibits standard weak-instrument behavior. I apply the theory to estimate short-run demand and supply elasticities for copper, natural gas, and crude oil. Across the six elasticities, accounting for instrument estimation changes standard errors by up to a fifth.
CommentsJob market paper. 165 pages, 2 figures. JEL: C33, C36, C55, C38, C12, Q41
