empir_ex09[1] - Chapter 9 Assessing Studies Based on...

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Chapter 9 Assessing Studies Based on Multiple Regression ± Solutions to Empirical Exercises 1. Data from 2004 (1) (2) (3) (4) (5) (6) (7) (8) Dependent Variable AHE ln( AHE ) ln( AHE ) ln( AHE ) ln( AHE ) ln( AHE ) ln( AHE ) ln( AHE ) Age 0.439** (0.030) 0.024** (0.002) 0.147** (0.042) 0.146** (0.042) 0.190** (0.056) 0.117* (0.056) 0.160 (0.064) Age 2 0.0021** (0.0007) 0.0021** (0.0007) 0.0027** (0.0009) 0.0017 (0.0009) 0.0023 (0.0011) ln( Age ) 0.725** (0.052) Female × Age 0.097 (0.084) 0.123 (0.084) Female × Age 2 0.0015 (0.0014) 0.0019 (0.0014) Bachelor × Age 0.064 (0.083) 0.091 (0.084) Bachelor × Age 2 0.0009 (0.0014) 0.0013 (0.0014) Female 3.158** (0.176) 0.180** (0.010) 0.180** (0.010) 0.180** (0.010) 0.210** (0.014) 1.358* (1.230) 0.210** (0.014) 1.764 (1.239) Bachelor 6.865** (0.185) 0.405** (0.010) 0.405** (0.010) 0.405** (0.010) 0.378** (0.014) 0.378** (0.014) 0.769 (1.228) 1.186 (1.239) Female × Bachelor 0.064** (0.021) 0.063** (0.021) 0.066** (0.021) 0.066** (0.021) Intercept 1.884 (0.897) 1.856** (0.053) 0.128 (0.177) 0.059 (0.613) 0.078 (0.612) 0.633 (0.819) 0.604 (0.819) 0.095 (0.945) F- statistic and p -values on joint hypotheses (a) F -statistic on terms involving Age 98.54 (0.00) 100.30 (0.00) 51.42 (0.00) 53.04 (0.00) 36.72 (0.00) (b) Interaction terms with Age and Age 2 4.12 (0.02) 7.15 (0.00) 6.43 (0.00) SER 7.884 0.457 0.457 0.457 0.457 0.456 0.456 0.456 2 R 0.1897 0.1921 0.1924 0.1929 0.1937 0.1943 0.1950 0.1959 Significant at the *5% and **1% significance level.
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Solutions to Empirical Exercises in Chapter 9 133 Data from 1992 (1) (2) (3) (4) (5) (6) (7) (8) Dependent Variable AHE ln( AHE ) ln( AHE ) ln( AHE ) ln( AHE ) ln( AHE ) ln( AHE ) ln( AHE ) Age 0.461** (0.028) 0.027** (0.002) 0.157** (0.041) 0.156** (0.041) 0.120* (0.057) 0.138* (0.054) 0.104 (0.065) Age 2 0.0022** (0.0006) 0.0022** (0.0007) 0.0015 (0.0010) 0.0020* (0.0009) 0.0013* (0.0011) ln( Age ) 0.786** (0.052) Female × Age 0.088 (0.083) 0.077 (0.083) Female × Age 2 0.0017 (0.0013) 0.0016 (0.0014) Bachelor × Age 0.037 (0.084) 0.046 (0.083) Bachelor × Age 2 0.0004 (0.0014) 0.0006 (0.0014) Female 2.698** (0.152) 0.167** (0.010) 0.167** (0.010) 0.167** (0.010) 0.200** (0.013) 1.273** (1.212) 0.200** (0.013) 1.102 (1.213) Bachelor 5.903** (0.169) 0.377** (0.010) 0.377** (0.010) 0.377** (0.010) 0.340** (0.014) 0.340** (0.014) 0.365** (1.227) 0.504 (1.226) Female × Bachelor 0.085** (0.020) 0.079** (0.020) 0.086** (0.020) 0.080** (0.02) Intercept 0.815 (0.815) 1.776** (0.054) 0.099 (0.178) 0.136 (0.608) 0.119 (0.608) 0.306 (0.828) 0.209 (0.780) 0.617 (0.959) F- statistic and p -values on joint hypotheses (a) F -statistic on terms involving Age 115.93 (0.00) 118.89 (0.00) 62.51 (0.00) 65.17 (0.00) 45.71 (0.00) (b) Interaction terms with Age and Age 2 9.04 (0.00) 4.80 (0.01) 7.26 (0.00) SER 6.716 0.437 0.437 0.437 0.437 0.436 0.436 0.436 2 R 0.1946 0.1832 0.1836 0.1841 0.1858 0.1875 0.1866 0.1883 Significant at the *5% and **1% significance level. (a) (1) Omitted variables: There is the potential for omitted variable bias when a variable is excluded from the regression that (i) has an effect on ln( AHE ) and (ii) is correlated with a variable that is included in the regression. There are several candidates. The most important is a worker’s Ability . Higher ability workers will, on average, have higher earnings and are more likely to go to college. Leaving Ability out of the regression may lead to omitted variable bias, particularly for the estimated effect of education on earnings. Also omitted from the regression is Occupation . Two workers with the same education (a BA for example) may have different occupations (accountant versus 3 rd grade teacher) and have different earnings. To the extent that occupation choice is correlated with gender, this will lead to omitted variable bias. Occupation choice could also be correlated with Age . Because the data are a cross section, older workers entered the labor force before younger workers (35 year- olds in the sample were born in 1969, while 25 year-olds were born in 1979), and their occupation reflects, in part, the state of the labor market when they entered the labor force.
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134 Stock/Watson - Introduction to Econometrics - Second Edition (2) Misspecification of the functional form: This was investigated carefully in exercise 8.1.
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empir_ex09[1] - Chapter 9 Assessing Studies Based on...

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