Inference in Moment Inequality Models That Is Robust to Spurious Precision under Model Misspecification

Abstract

Standard tests and con…dence sets in the moment inequality literature are not robust to model misspeci…cation in the sense that they exhibit spurious precision when the identi…ed set is empty.This paper introduces tests and con…dence sets that provide correct asymptotic inference for a pseudo-true parameter in such scenarios, and hence, do not su¤er from spurious precision.

Simple misspecification adaptive inference for interval identified parameters

“…The construction heavily relies on the structure of the specific case. For a more general but also more complicated (including in relatively simple instances) treatment, I refer to Andrews and Kwon (2019). For reasons alluded to in section 2, their treatment is delicate and involves numerous tuning parameters.…”

“…Molinari (2020) explains the issue in detail and highlights it as important area for further investigation. The most thorough treatment is by Andrews and Kwon (2019), who emphasize the issue's importance and provide a general inference method that avoids spurious precision and ensures coverage of a pseudotrue parameter.…”

“…The present paper is in the spirit of Andrews and Kwon (2019). I focus on the simple but empirically salient case of a scalar parameter with upper and lower bounds whose estimators are jointly asymptotically normal.…”

“…I refer to Andrews and Soares (2010) for details.4 That was the sales pitch inStoye (2009), but not all referees were sold on it. The embedded specification test is analyzed in more detail byAndrews and Soares (2010).5 This equivalence does not generalize, butAndrews and Kwon (2019) show that in "slightly misspecified" parameter regimes, spuriously precise inference generally coexists with low power of specification tests.…”

Advances in Using Vector Autoregressions to Estimate Structural Magnitudes

“…The first is the question we discussed in Section 3.4, which is whether restrictions such as the claim that the supply elasticity must be less than 0.025 are completely credible. Andrews and Kwon (2019) and Kédagni, Li, and Mourifié (2021) noted the possibility that the true values of the reduced-form VAR-that is, the plim of the unrestricted VAR estimates-may not satisfy all the restrictions that researchers are attempting to impose. In such a case, the model is fundamentally misspecified and a narrow range of accepted draws could be a spurious indicator of estimation precision.…”