INFERRING THE RANK OF A MATRIX

This paper considers methods of inference concerning the rank of a mat rix Pi - Theta based on an asymptotically normal estimate of Pi and so me identifiable specification for Theta. One such specification is The ta = 0, in which case one is interested in the rank of Pi. We first pr opose, and examine the properties of, a test of the hypothesis that th e rank is of a given size against the alternative that the rank is lar ger. We then look at the problem of estimating the rank of this matrix using model selection procedures and sequential hypothesis testing. C onditions for consistency of such procedures are obtained. Some econom ic applications are discussed and the various methods are compared in a Monte Carlo experiment.