Systems of Regression Equations

A sample of 100 observations produces the following sample data  

The weight simplifies a bit as the determinant appears in both the denominator and the numerator. Thus, 

Consider estimation of the following two equation model n. A sample of 50 observations 

To obtain the explicit fonn, note, first, that all tenns a J are of the form Gj/(ai i(j22 - o2 2) But, the denominator in these ratios will be cancelled as it appears in both the inverse matrix and in the vector. Therefore, in terms of the original parameters, (after cancelling n), we obtain 

Finally, to test the hypothesis that 02 = 1 we use the z-statistic (asymptotically distributed as standard normal), z = (1.011 - 1)/ (.007945)2 =. 123. The hypothesis cannot be rejected. 

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