Inferring Treatment Effects After Testing Instrument Strength in Linear Models Using Selective Inference
A common practice in IV studies is to check for instrument strength, i.e. the instruments’ association to the treatment, with an F-test from regression. If the F- statistic is above some threshold, usually 10, the instrument is deemed to satisfy one of the three core IV assumptions and used to test for the treatment effect. However, in many cases, the inference on the treatment effect does not take into account the strength test done a priori. In this paper, we show that not accounting for this pretest can severely distort the distribution of the test statistic and propose a method to correct this distortion by using methods in selective inference. We prove that our method provides conditional and marginal Type I error control. We also extend our method to weak instrument settings. We conclude with a reanalysis of studies concerning the effect of education on earning where we show that not accounting for pre-testing can dramatically alter the original conclusion about education’s effects.

Link to paper: arxiv.org/abs/2003.06723

Please sign up for meetings here: docs.google.com/spreadsheets/d/1GRwPBmtpUwstC4fdLZrnxfnARNYHedHykoRZG4Xq2Bo/edit#gid=0
Date: 12 March 2021, 14:15 (Friday, 8th week, Hilary 2021)
Venue: Held on Zoom
Speaker: Hyunseung Khan (University of Wisconsin)
Organising department: Department of Economics
Part of: Nuffield Econometrics Seminar
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Audience: Members of the University only
Editor: Melis Clark