Solutions to Empirical Assignment 1

Solutions for the empirical assignment 1 Q1 (a) The estimated regression is =  512.7 + 707.7× Height (3379.9) (50.4) The 95% confidential interval for the slope coefficient is 707.7 ± 1.96×50.4, or 608.9 ≤  1 ≤ 806.5. This interval does not include  1 = 0, so the estimated slope is significantly different than 0 at the 5% level. Alternatively, the t -statistic is 707.7/50.4 ≈ 14.0, which is greater in absolute value than the 5% critical value of 1.96. And finally, the p -value for the t -statistic is p -value ≈ 0.000, which is smaller than 0.05. (b) For women the estimated regression is = 12650 + 511.2× Height (6299) (97.6) The 95% confidential interval for the slope coefficient is 511.2 ± 1.96×97.6, or 319.9 ≤  1,Female ≤ 702.5. This interval does not include  1,Female = 0, so the estimated slope is significantly different than 0 at the 5% level. (c) For men the estimated regression is = -43130 + 1306.9× Height (6925) (98.9) The 95% confidential interval for the slope coefficient is 1306.9 ± 1.96×98.9, or 1113.1 ≤  1,Male ≤ 1500.6. This interval does not include  1,Male = 0, so the estimated slope is significantly different than 0 at the 5% level. (d) The estimate of  1,Male   1,Female is ˆ  1,Male  ˆ  1,Female and the standard error is SE ˆ  1,Male  ˆ  1,Female ( ) = var( ˆ  1,Male ) + var( ˆ  1,Female ) = SE ( ˆ  1,Male ) 2 + SE ( ˆ  1,Female ) 2 . Using the estimated regressions in (b) and (c): ˆ  1,Male  ˆ  1,Female = 1306.9  511.2 = 795.7, and . SE ˆ  1,Male  ˆ  1,Female ( ) = 98.9 2 + 97.6 2 = 138.9 . 1

The 95% confidence interval for  1,Male   1,Female is 795.7 ± 1.96 × 138.9 or 523.5 ≤  1,Male   1 ≤ 1,067.8. This interval does not include  1,Male   1 = 0, so the estimated difference in the slopes is significantly different than 0 at the 5% level. (e) The table below shows the estimated slope, its standard error, and number of observations for various occupation groups. Occupation ˆ  1 SE ( ˆ  1 ) t  stat n Exec/Manager 469.5 153.0 3.1 1,906 Professionals 622.8 116.2 5.4 3,158 Technicians 649.7 213.0 3.1 875 Sales 1372.4 146.4 9.4 1,957 Administration 201.2 131.5 1.5 3,124 Household service  172.9 637.9  0.3 113 Protective service 1503.0 391.1 3.84 364 Other Service 62.9 132.1 0.48 1,980 Farming 1049.2 297.3 3.53 361 Mechanics 571.2 354.9 1.61 534 Construction/Mining 967.0 308.7 3.13 616 Precision production 1080.3 284.3 3.80 439 Machine Operator 972.9 151.9 6.5 1268 Transport 1138.4 274.0 4.16 684 Laborer 549.1 237.0 2.3 491 Exec/Manager, Professionals, Technicians, Sales, Administration 829.8 65.1 12.7 11020 Protective service, Farming, Mechanics, Construction/Mining, Precision production, Machine Operator, Transport, Laborer 1151.0 88.4 13.0 4,757 The predicted effect of height on earnings (  1 ) is larger for occupations that require more strength (see the last row in the table) than others (see the penultimate row in table). That said, the estimated effect of height on earning is both large and statistically significant in several occupations in which strength would not seem to have a large effect on productivity (again, see the penultimate row in table). Q2 (a) The estimated regression is  0.96  1.68  Tradeshare (0.54) (0.87) The t -statistic for the slope coefficient is t = 1.68/0.87 = 1.94. The t -statistic is larger in absolute value that the 10% critical value (1.64), but less than the 5% and 1% critical values (1.96 and 2.58). Therefore the null hypothesis is rejected at the 10% significance level, but not at the 5% or 1% levels. (b) The p -value is 0.057. (c) The 90% confidence interval is 1.68 ± 1.64×0.87 or 0.25 ≤  1 ≤ 3.11. 2