Economics 310 Lecture 21 Simultaneous Equations

Three Stage Least Squares A system estimator. More efficient that two-stage least squares. Uses all information in the system. Estimates all equations simultaneously. Sensitive to specification error.

Supply and Demand Model

Supply in matrix form

Demand in Matrix form

Demand & Supply as SUR model

Write model as SUR model

Model Development Continued

Summary 3sls Transform the system by multiplying each equation by the matrix of all exogenous variables X and count to determine that the column dimension of X is equal to or greater than the column dimension of Z i the matrix of endogenous and exogenous variables in each equation.

Summary 3sls continued Use the 2SLS estimator to estimate each of the equations individually and estimate for each equation the errors e i. Use the estimated errors to compute, for the system of equations, the estimated error covariance matrix and then use the SUR (GLS) procedure to estimate the unknown parameters.

Menges’ Example

Shazam Command sample 1 52 read Date C P Y I R Q data sample 2 52 genr ylag=lag(Y) genr clag=lag(c) genr Qlag=lag(Q) system 4 ylag clag qlag r p ols y ylag i ols i y q ols c y clag p ols q qlag r end stop

Shazam Output THREE STAGE LEAST SQUARES-- 4 EQUATIONS 5 EXOGENOUS VARIABLES 4 POSSIBLE ENDOGENOUS VARIABLES 9 RIGHT-HAND SIDE VARIABLES IN SYSTEM SYSTEM R-SQUARE = CHI-SQUARE = WITH 9 D.F. VARIABLE COEFFICIENT ST.ERROR T-RATIO YLAG E I E E Y Q Y E CLAG P QLAG E R