Application of Simultaneous Equation in Finance Research

Abstract

This chapter introduces the concept of simultaneous equation system and the application of such a system to finance research. We first discuss the order and rank condition of identification problem. We then intro-duce the two-stage least squares (2SLS) and three-stage least squares (3SLS) estimation method. The pro and cons of these estimations methods are summarized. Finally, the results of a study in executive compensation structure and risk-taking are used to illustrate the difference between single equation and simultaneous equation method. Keywords Simultaneous equation r Two-stage least squares r Three-stage least squares r Model identification 86.1 Introduction Rarely a single equation arises in economic theory. In a multi-equation system, OLS fails to yield unbiased and consistent estimators for the structural equations. Therefore, appropriate estimation methods must be applied to the es-timation of structural equation parameters. This paper first discusses situations where a simultaneous equation system may arise. We then explain why OLS estimation is not ap-propriate. Section 86.2 introduces two most frequently used methods to estimate structural parameters in a system of equations. Before 2SLS and 3SLS methods are synthesized, we explain the order condition and the rank condition of model identification. 2SLS and 3SLS are then introduced, and the differences between these two methods are discussed. Section 86.3 gives examples from the literature where ap-plications of the simultaneous equation models in finance are shown. In the finance application, Chen et al. (2006)