Econometrica: Mar 2013, Volume 81, Issue 2

Inference Based on Conditional Moment Inequalities

https://doi.org/10.3982/ECTA9370
p. 609-666

Donald W. K. Andrews, Xiaoxia Shi

In this paper, we propose an instrumental variable approach to constructing confidence sets (CS's) for the true parameter in models defined by conditional moment inequalities/equalities. We show that by properly choosing instrument functions, one can transform conditional moment inequalities/equalities into unconditional ones without losing identification power. Based on the unconditional moment inequalities/equalities, we construct CS's by inverting Cramér–von Mises‐type or Kolmogorov–Smirnov‐type tests. Critical values are obtained using generalized moment selection (GMS) procedures.

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