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Use the data in CONSUMP for this exercise.(i) In Example 16.7, use the method from Section $15-5$ to test the single overidentifying restriction in estimating $(16.35) .$ What do you conclude?(ii) Campbell and Mankiw $(1990)$ use second lags of all variables as IVs because of potential data measurement problems and informational lags. Reestimate $(16.35),$ using only $g c_{t-2}, g y_{t-2},$ and $r 3_{t-2}$ as IVs. How do the estimates compare with those in $(16.36) ?$(iii) Regress $g y_{t}$ on the IVs from part (ii) and test whether $g y_{t}$ is sufficiently correlated with them. Why is this important?

(i) IV pass overidentification restriction test (ii) see video (iii) no correlation between gy and proposed IVs

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Chapter 16

Simultaneous Equations Models

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that's one. The test assumes that there's no serial correlation and also her most good elasticity. So after we estimate equation 16.35 we get the two stage least square residual use of T. And we regress that on variables G. c cept E -1. She was sub teat minus one and our three Sub T -1. The n. R square statistic is calculated as 35 observation times point 0613. That's our square and we get 2.15 with one degree of freedom. The p value for this statistic following a child square Distribution with one degree of freedom is .143. So the instruments past the over identification test At the 10 level part two. When we estimate equation 16.35 with instruments GC, 17 -2 GY 17 -2. and our 3 17 -2. We will get The intercept is -1054. The coefficient on GYT is 1.2 And the coefficient on our three is .0004. We have 34 observations compare with Equation 16.35. The coefficient on g y t has double doubled in size but it is not statistically significant. The coefficient on our three sub t. It's still small and insignificant. Part three When we regress G y sub T On GC 17 -2, GY 17 -2 And our 3 17 -2. This is what we get. The F test for joint significance of all. Explanatory variables has a p value Of .94. That means there is no correlation between the left hand, sir, variable G y T and the proposed instrumental variables, meaning that we should not Yeah, run the I. V. Estimation in part two.

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