Search results

We provide a new characterization of the equality of two positive-definite matrices A and B, and we use this to propose several new computationally convenient statistical tests for the equality of two unknown positive-definite matrices. Our primary focus is on testing the information matrix equality (e.g. White, 1982, 1994). We characterize the asymptotic behavior of our new trace-determinant information matrix test statistics under the null and the alternative and investigate their finite-sample performance for a variety of models: linear regression, exponential duration, probit, and Tobit. The parametric bootstrap suggested by Horowitz (1994) delivers critical values that provide admirable level behavior, even in samples as small as n = 50. Our new tests often have better power than the parametric-bootstrap version of the traditional IMT; when they do not, they nevertheless perform respectably.

Since its introduction by Chari, Kehoe, and McGrattan (2007), Business Cycle Accounting (BCA) exercises have become widespread. Much attention has been devoted to the results of such exercises and to methodological departures from the baseline methodology. Little attention has been paid to identification issues within these classes of models. In this chapter, the authors investigate whether such issues are of concern in the original methodology and in an extension proposed by Šustek (2011) called Monetary Business Cycle Accounting. The authors resort to two types of identification tests in population. One concerns strict identification as theorized by Komunjer and Ng (2011) while the other deals both with strict and weak identification as in Iskrev (2010). Most importantly, the authors explore the extent to which these weak identification problems affect the main economic takeaways and find that the identification deficiencies are not relevant for the standard BCA model. Finally, the authors compute some statistics of interest to practitioners of the BCA methodology.