hw6 - University of Illinois at Urbana-Champaign Professor...

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University of Illinois at Urbana-Champaign Professor Ron Laschever, ECON 440, Spring 2011 1 Some comments Problem set #6 Below are the results for the first two regressions. On their own, they mean little if you don’t Interpret them. In any empirical work there are two things to focus on. The first is statistical significance. For example, in the second regression we cannot reject the null that the coefficient on being 43 is different than zero. We can never accept a null, but we can reject one. Here we fail to reject, meaning that it’s possible that age has no statistically significant effect (at conventional levels, such as 5%). Second, there is the question of economic significance. Something may be statistically significant, but have very little impact. Social scientists (should) care about this as well. For example, in the first regression, the effect of being over 43 increases your likelihood of being fired by 30.5 percentage points (why? The outcome is between 0 and 1, so 0.30 is like 30%). This is a fairly large effect. If on the other hand the effect was 0.000000003 it’s not clear any court would care much. The last regression adds additional controls, and the result doesn’t seem to change much, adding more confidence to our conclusion that layoffs were not age-based but rather performance related. Is this an air-tight conclusion? Of course not! We would ideally examine additional specifications as well as look more carefully at how these ratings were determined (perhaps they are based on age?) Finally, R-squared is a measure of goodness of fit, but it does not directly tell us about the statistical significance of any particular measure (such as age). It is therefore an additional piece of information, but it really can only tell us how the overall specification (including all the variables we did include) does in explaining the variance. An R-squared of 1 implying that our model fully explains all variance which is not likely to ever happen in a true social science setting. The R-squared might help us decide which specification to use (the one with age- squared, or maybe one with age-cube?) but it doesn’t tell us within a specification which variables have a large or small effect or which variables are statistically significant.
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University of Illinois at Urbana-Champaign Professor Ron Laschever, ECON 440, Spring 2011 2 . reg layoff over43 Source | SS df MS Numberof obs= 35 ‐‐‐‐‐‐‐‐‐‐‐‐‐ + ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ F( 1, 33) = 5.01 Model | .81287594 1 .81287594 Prob> F = 0.0321 Residual | 5.35855263 33 .162380383 R squared = 0.1317 ‐‐‐‐‐‐‐‐‐‐‐‐‐ + ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ Adj R squared= 0.1054 Total | 6.17142857 34 .181512605 RootMSE = .40296 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ layoff | Coef. Std.Err. t P>|t| [95% Conf. Interval]
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