Simultaneous Equations Models The Scope of Simultaneous Equations Models The emphasis in this chapter is on situations where two or more variables are jointly determined by a system of equations. Nevertheless, the population model, the identification analysis, and the estimation methods apply to a much broader | Simultaneous Equations Models The Scope of Simultaneous Equations Models The emphasis in this chapter is on situations where two or more variables are jointly determined by a system of equations. Nevertheless the population model the identification analysis and the estimation methods apply to a much broader range of problems. In Chapter 8 we saw that the omitted variables problem described in Example has the same statistical structure as the true simultaneous equations model in Example . In fact any or all of simultaneity omitted variables and measurement error can be present in a system of equations. Because the omitted variable and measurement error problems are conceptually easier and it was for this reason that we discussed them in single-equation contexts in Chapters 4 and 5 our examples and discussion in this chapter are geared mostly toward true simultaneous equations models SEMs . For effective application of true SEMs we must understand the kinds of situations suitable for SEM analysis. The labor supply and wage offer example Example is a legitimate SEM application. The labor supply function describes individual behavior and it is derivable from basic economic principles of individual utility maximization. Holding other factors fixed the labor supply function gives the hours of labor supply at any potential wage facing the individual. The wage offer function describes firm behavior and like the labor supply function the wage offer function is self-contained. When an equation in an SEM has economic meaning in isolation from the other equations in the system we say that the equation is autonomous. One way to think about autonomy is in terms of counterfactual reasoning as in Example . If we know the parameters of the labor supply function then for any individual we can find labor hours given any value of the potential wage and values of the other observed and unobserved factors affecting labor supply . In other words we could in principle .
