Testing Many Parameter Restrictions Under Mixed Identification Strength (with Appendix)

I propose an inference procedure for a test of many zero restrictions in models for which parameter identification failure may be present. Existing tests cannot simultaneously accommodate identification failure and a parameter vector with large dimension. The test is based upon estimating a sequence of smaller dimension models and examining the maximum of the resulting estimators, and the maximum estimator reduces size distortion when the dimension of the parameter vector is large. The procedure is based on the bootstrap and does not require that we analytically calculate the limiting distribution of the maximum statistic. Several empirical examples are discussed and an empirical exercise examines a test of omitted nonlinearity in exchange rate dynamics.

slides.   MATLAB code coming soon.  


Testing White Noise When Some Parameters may be Weakly Identified (with Appendix)

Testing the white noise hypothesis on the residuals from estimated models can lead to size distortion if some parameters are weakly identified. This paper develops a bootstrapped white noise test for serial correlation that is robust to weak identification in the parameters. We show that existing white noise tests can be extended to allow for bootstrapping models with known sources of identification failure via a modification of the first order expansion utilized by the bootstrap. The test is appropriate for residuals and requires only uncorrelatedness under the null hypothesis, rather than independence of the time series. Basing our test on the most relevant sample serial correlation by use of the maximum statistic improves power, particularly against distant and weak serial dependence.

Previously circulated as Bootstrapping an Identification Robust Max Correlation White Noise Test

slides.   MATLAB code.   Python Code – In Progess.

Testing Many Zero Restrictions Where a Subset May Lie On the Boundary with J.B. Hill.

MATLAB code.