Wooldridge IE AISE SSM ch04 - CHAPTER 4 SOLUTIONS TO...

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This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher. 17 CHAPTER 4 SOLUTIONS TO PROBLEMS 4.2 (i) and (iii) generally cause the t statistics not to have a t distribution under H 0 . Homoskedasticity is one of the CLM assumptions. An important omitted variable violates Assumption MLR.3. The CLM assumptions contain no mention of the sample correlations among independent variables, except to rule out the case where the correlation is one. 4.3 (i) While the standard error on hrsemp has not changed, the magnitude of the coefficient has increased by half. The t statistic on hrsemp has gone from about –1.47 to –2.21, so now the coefficient is statistically less than zero at the 5% level. (From Table G.2 the 5% critical value with 40 df is –1.684. The 1% critical value is –2.423, so the p -value is between .01 and .05.) (ii) If we add and subtract 2 β log( employ ) from the right-hand-side and collect terms, we have log( scrap ) = 0 + 1 hrsemp + [ 2 log(sales) – 2 log( employ )] + [ 2 log( employ ) + 3 log( employ )] + u = 0 + 1 hrsemp + 2 log( sales / employ ) + ( 2 + 3 )log( employ ) + u , where the second equality follows from the fact that log( sales / employ ) = log( sales ) – log( employ ). Defining 3 θ 2 + 3 gives the result. (iii) No. We are interested in the coefficient on log( employ ), which has a t statistic of .2, which is very small. Therefore, we conclude that the size of the firm, as measured by employees, does not matter, once we control for training and sales per employee (in a logarithmic functional form). (iv) The null hypothesis in the model from part (ii) is H 0 : 2 = –1. The t statistic is [–.951 – (–1)]/.37 = (1 – .951)/.37 .132; this is very small, and we fail to reject whether we specify a one- or two-sided alternative. 4.4 (i) In columns (2) and (3), the coefficient on profmarg is actually negative, although its t statistic is only about –1. It appears that, once firm sales and market value have been controlled for, profit margin has no effect on CEO salary. (ii) We use column (3), which controls for the most factors affecting salary. The t statistic on log( mktval ) is about 2.05, which is just significant at the 5% level against a two-sided alternative.
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This edition is intended for use outside of the U.S. only, with content that may be different from the U.S. Edition. This may not be resold, copied, or distributed without the prior consent of the publisher. 18 (We can use the standard normal critical value, 1.96.) So log( mktval ) is statistically significant. Because the coefficient is an elasticity, a ceteris paribus 10% increase in market value is predicted to increase salary by 1%. This is not a huge effect, but it is not negligible, either. (iii) These variables are individually significant at low significance levels, with t ceoten 3.11 and t comten –2.79. Other factors fixed, another year as CEO with the company increases salary by about 1.71%. On the other hand, another year with the company, but not as CEO, lowers salary by about .92%.
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Wooldridge IE AISE SSM ch04 - CHAPTER 4 SOLUTIONS TO...

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