Applied Econometrics Using the SAS® System

9

SIMULTANEOUS EQUATIONS

9.1 INTRODUCTION

The previous chapters focused on single equations and on systems of single equation models that were characterized by dependent variables (endogenous) on the left-hand side and the explanatory variables (exogenous or endogenous) on the right-hand side of the equations. For example, Chapter 4 dealt with instrumental variables, where the endogenous variables were on the right-hand side. This chapter extends the concept of systems of linear equations where endogenous variables were determined one at a time (sequentially) to the case when they are determined simultaneously.

We begin our discussion of simultaneous equation models by considering the following wage–price equations

where p_t is the price inflation at time t, w_t is wage inflation at time t, m_t is the money supply at time t, u₁ is unemployment rate time t, ε_1t and ε_2t are the error terms with means 0 and constant variances respectively, and γ = (β₁, β₂, α₁, α₂) are the model parameters that need to be estimated. We also assume that the disturbance terms are uncorrelated. These equations are referred to as structural equations. In the wage–price inflation equation, we have two structural equations and four unknown parameters.

The first equation describes the relation of price inflation ...