Economics 310

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Economics 310

• Lecture 21
• Simultaneous Equations

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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.

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Supply and Demand Model
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Supply in matrix form
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Demand in Matrix form
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Demand Supply as SUR model
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Write model as SUR model
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Model Development Continued
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Model Development Continued
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Model Development Continued
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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 Zi the matrix of endogenous and exogenous
  variables in each equation.

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Summary 3sls continued

• Use the 2SLS estimator to estimate each of the
  equations individually and estimate for each
  equation the errors ei.
• 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.

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Menges Example
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Shazam Command
sample 1 52 read Date C P Y I R Q data sample 2
52 genr ylaglag(Y) genr claglag(c) genr
Qlaglag(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
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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 0.9996 ...
CHI-SQUARE 402.81 WITH 9 D.F.
VARIABLE COEFFICIENT ST.ERROR
T-RATIO YLAG 0.99625 0.10830E-01
91.991 I 0.15257E-01 0.45927E-02
3.3219 Y 4.4596 1.9157
2.3279 Q -15.871 10.841
-1.4639 Y 0.24589
0.76694E-01 3.2061 CLAG 0.68184
0.11657 5.8492 P -1.7094
0.86478 -1.9766 QLAG 0.90590
0.67685E-01 13.384 R 1.9816
1.4026 1.4128