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断点回归设计中的局部多项式阶数选择AI 解读

Treatment effect estimates in regression discontinuity (RD) designs are often sensitive to the choice of bandwidth and polynomial order, the two important ingredients of widely used local regression methods. While Imbens and Kalyanaraman and Calonico, Cattaneo, and Titiunik provided guidance on bandwidth, the sensitivity to polynomial order still poses a conundrum to RD practitioners. It is understood in the econometric literature that applying the argument of bias reduction…

测量不准的混杂因素放在回归左侧更有用AI 解读

Researchers frequently test identifying assumptions in regression-based research designs (which include instrumental variables or difference-in-differences models) by adding additional control variables on the right-hand side of the regression. If such additions do not affect the coefficient of interest (much), a study is presumed to be reliable. We caution that such invariance may result from the fact that the observed variables used in such robustness checks are often poor…

广义回归折点设计中的因果效应推断AI 解读

A.1. Proofs of Propositions 1 and 2IN ORDER TO PROVE PROPOSITION 1, we first present and prove the following lemmas.LEMMA 1: Let ϕ(x t) : I × [c d] → R, where I is a compact subset of R m .Suppose ϕ(x t) and its partial derivative, ϕ 2 (x t), are continuous and that ϕ is integrable with respect to the probability measure α for each t.Then f (t) = ϕ(x t) dα(x) is continuously differentiable on [c d].PROOF: By Theorem 5 (p.97) of Roussas (2004), f (t) = ϕ 2 (x t) dα(x) for all…