Takashi Yamano

In this case, we can not identify either curve, because z is included in the both equations.Thus, z does not satisfy the exclusion restrictions. This is illustrated in Panel 2. Weobserve changes in price and quantity from A to C. But, because both curves can shiftfrom A to C, we can not trace curves. Both curves in Panel 2 could be steeper or flatter.Reduced Form Equations in General CasesIn general, we can have more than two simultaneous equations (more than twoendogenous variables) at once. Suppose there are 3-endogenous variables:y 1 = f 1 (y 2 , y 3 , z 1 ,z 2 , z 3 , z 4 )y 2 = f 2 (y 1 , y 3 , z 1 , z 2 , z 5 , z 6 , z 7 )y 3 = f 3 (y 1 , y 2 , z 1 , z 2 , z 8 , z 9 , z 10 )The reduced form equation for each endogenous variable will contain all of theexogenous variables:y 1 = f 1 (z 1 ,z 2 , z 3 , z 4 , z 5 , z 6 , z 7 , z 8 , z 9 , z 10 )y 2 = f 2 (z 1 ,z 2 , z 3 , z 4 , z 5 , z 6 , z 7 , z 8 , z 9 , z 10 )y 3 = f 3 (z 1 ,z 2 , z 3 , z 4 , z 5 , z 6 , z 7 , z 8 , z 9 , z 10 )From these reduced form equations, we can identify endogenous variables in thestructural from equations.Example 13-1: Inflation and Openness by using Openness.dtaSee Example 16.4 and 16.6 in Wooldridge:The Reduced Form Equation for “Open”. reg open lpcinc llandSource | SS df MS Number of obs = 114-------------+------------------------------ F( 2, 111) = 45.17Model | 28606.1936 2 14303.0968 Prob > F = 0.0000Residual | 35151.7966 111 316.682852 R-squared = 0.4487-------------+------------------------------ Adj R-squared = 0.4387Total | 63757.9902 113 564.230002 Root MSE = 17.796------------------------------------------------------------------------------open | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+----------------------------------------------------------------lpcinc | .5464812 1.49324 0.37 0.715 -2.412473 3.505435lland | -7.567103 .8142162 -9.29 0.000 -9.180527 -5.953679_cons | 117.0845 15.8483 7.39 0.000 85.68006 148.489------------------------------------------------------------------------------The OLS for inflation. reg inf open lpcincSource | SS df MS Number of obs = 114-------------+------------------------------ F( 2, 111) = 2.63Model | 2945.92812 2 1472.96406 Prob > F = 0.07643