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CHAPTER 6. SIMULTANEOUS EQUATIONS

1 Economics 240B Daniel McFadden 1999 CHAPTER 6. SIMULTANEOUS EQUATIONS1. INTRODUCTIONE conomic systems are usually described in terms of the behavior of various economic agents,and the equilibrium that results when these behaviors are reconciled. For example, the operation ofthe market for economists might be described in terms of demand behavior, supply behavior,and equilibrium levels of employment and wages. The market clearing process feeds back wagesinto the behavioral EQUATIONS for demand and supply, creating SIMULTANEOUS or joint determinationof the equilibrium quantities. This causes econometric problems of correlation between explanatoryvariables and disturbances in estimation of behavioral 1. In the market for economists, let q = number employed, w = wage rate,s = college enrollment, and m = the median income of lawyers. Assume that all these variables arein logs.

same in each equation, so that Eνitνjs = σijρts, or Eνν = R Σ, then GLS using this covariance structure collapses to GLS applied separately to each equation. When there is no correlation across t, GLS collapses to OLS. Suppose you are interested in estimating the pa rameters of the beha vioral demand equation (1).

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