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Use the data in INJURY for this exercise.(i) Using the data for Kentucky, reestimate equation $(13.12),$ adding as explanatory variables male,married, and a full set of industry and injury type dummy variables. How does the estimate on afchnge highearn change when these other factors are controlled for? Is the estimate still statistically significant?(ii) What do you make of the small $R$ -squared from part (i)? Does this mean the equation is useless?Estimate equation $(13.12)$ using the data for Michigan. Compare the estimates on the interactionterm for Michigan and Kentucky. Is the Michigan estimate statistically significant? What do you make of this?(iii) Estimate equation $(13.12)$ using the data for Michigan. Compare the estimates on the interaction term for Michigan and Kentucky. Is the Michigan estimate statistically significant? What do you make of this?

(i) stronger effect (ii) $R^2=.041$ (iii) No

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Chapter 13

Pooling Cross Sections Across Time: Simple Panel Data Methods

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but one. The coefficient on the interaction term is point 231 with a standard error of 2310.70 So the estimated effect and T statistic are now larger than when we admitted the control variables. The estimate 0.231 implies a substantial response off direct to the change in the cap for high earnings. Worker, aren't you? The art square is about 0.0 for one, meaning we are explaining only a 4.1% of the variation in lock of direct. This means there are some very important factors that affect our dependent variable. And we are not controlling for them. This doesn't mean the equation is useless. Data. One head could still be unbiased. It could still be an unbiased estimator of the causal effect of changing the earnings cap for workers compensation. And this estimator is unbiased as long as they admitted variables do not correlate with the explanatory variables. In this case, it is the after change and high earnings are three. This is Theis, estimated equation. Using the Michigan data. The estimate of Delta one is 10.193 It is very close. Do what we get when we use Kentucky data, and when we use Kentucky data, we obtain Delta one head of 10.191 However, the Senate Errol for the Michigan Estimate is much higher. It is 0.154 compared with 0.69 in the case of Kentucky. The estimate for Michigan is not statistically significant at the usual confidence level. It seems that even though we have over 1000 and 500 observations, we cannot get a very precise estimate for Kentucky. We have over 5600 observations.

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