Consistent specification testing for conditional moment restrictions

Abstract This paper introduces specification tests for conditional moment restrictions. The proposed tests are generalizations of the Kolmogorov–Smirnov and Cramer–von Mises tests and they are consistent against all alternatives to the null hypothesis, powerful against 1/ n local alternatives and not dependent on any smoothing parameter. A nonparametric bootstrap procedure based on recentered criterion function is suggested to obtain critical values for the tests and is justified asymptotically.

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