Weak Identification in Fuzzy Regression Discontinuity Designs

Abstract

This supplement contains: i) the description of the procedure for selection and evaluation of the influential empirical RD papers; ii) the proofs of Theorem 1, 3, and 4; iii) the Monte Carlo results for standard and weak-identification-robust confidence sets; and iv) the additional tables from the empirical application. Influential applied papers sample procedureWe start with thirty applied papers that were cited by Lee and Lemieux (2010). Of the thirty papers, sixteen did not report enough information to perform the F -test. Of the remaining papers, more than half had specifications which would be suspect according to the test. We reach similar conclusions when only focusing on the ten most cited paper in the list (

Robust uniform inference for quantile treatment effects in regression discontinuity designs

“…Notice that the size becomes smaller and deviates away from the nominal size as the jump becomes weak (i.e., as Σ 33 increases). This observation of size distortions under weak jumps is consistent with prior study, e.g., Feir, Lemieux, and Marmer (2016). Motivated by these results, we present an extended theory of inference with robustness against the possibility of no or weak jumps in Section 7.2.…”

“…Condition (ii) requires the existence of a jump or a kink, which is assumed in most of the prior work as the key identification condition. Exceptions are Otsu, Xu, and Matsushita (2015) and Feir, Lemieux, and Marmer (2016), which provide weak-identification-robust methods of inference. We later use this idea to relax condition (ii) of this assumption in Section 7.2.…”

The Effect of Discretion on Procurement Performance

“…Tables A.21 and A.22 report estimates obtained estimating our baseline model. We (1) do not find evidence of significant effects in the large majority of the two simulated thresholds; and (2) report evidence of very weak instruments in the Fuzzy-RDD estimates (see Marmer et al, 2015). This evidence reassures us about the robustness of our results, as it indicates that they are not driven by random chance or by other thresholds.…”

Short- and Long-Run Estimates of The Local Effects of Retirement on Health

“…As in Feir et al . () we base inference about τ on the ratio of to its standard deviation. To compute p ‐values we implement the restricted efficient wild bootstrap algorithm in Davidson and MacKinnon () duly adapted to handle correlations at cluster (age) level.…”

“…a strong instrumental variable). If not, estimates of the causal effect will be biased and inference will be unreliable (Bound et al, 1995;Staiger and Stock, 1997;Kleibergen, 2002;Davidson and MacKinnon, 2010;Feir et al, 2015). The relationship between age and retirement in the UK presents a way of preventing a potential weak instrument problem.…”