Chapter 8 Exact small sample theory in the simultaneous equations model

This chapter provides a general framework for the distribution problem and details formulae that are frequently useful in the derivation of sampling distributions and moments. It also provides an account of the genesis of the Edgeworth, Nagar, and saddlepoint approximations. The chapter discusses the Wishart distribution and some related issues that are central to modem multivariate analysis and on which much of the present development of exact small-sample theory depends. The chapter discusses the exact theory of single-equation estimators, commencing with a general discussion on the standardizing transformations that provide research economy in the derivation of exact distribution theory in this context and simplify the presentation of final results without loss of generality. The current information on the exact small-sample behavior of structural variance estimators, test statistics, systems methods, reduced-form coefficient estimators, and estimation under misspecification are also discussed in the chapter.