empir_ex08[1]

# empir_ex08[1] - Chapter 8 Nonlinear Regression Functions...

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Chapter 8 Nonlinear Regression Functions ± Solutions to Empirical Exercises 1. This table contains the results from seven regressions that are referenced in these answers. 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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122 Stock/Watson - Introduction to Econometrics - Second Edition (a) The regression results for this question are shown in column (1) of the table. If Age increases from 25 to 26, earnings are predicted to increase by \$0.439 per hour. If Age increases from 33 to 34, earnings are predicted to increase by \$0.439 per hour. These values are the same because the regression is a linear function relating AHE and Age . (b) The regression results for this question are shown in column (2) of the table. If Age increases from 25 to 26, ln( AHE ) is predicted to increase by 0.024. This means that earnings are predicted to increase by 2.4%. If Age increases from 34 to 35, ln( AHE ) is predicted to increase by 0.024. This means that earnings are predicted to increase by 2.4%. These values, in percentage terms, are the same because the regression is a linear function relating ln( AHE ) and Age . (c) The regression results for this question are shown in column (3) of the table. If Age increases from 25 to 26, then ln( Age ) has increased by ln(26) ln(25) = 0.0392 (or 3.92%). The predicted increase in ln( AHE ) is 0.725 × (.0392) = 0.0284. This means that earnings are predicted to increase by 2.8%. If Age increases from 34 to 35, then ln( Age ) has increased by ln(35) ln(34) = .0290 (or 2.90%). The predicted increase in ln( AHE ) is 0.725 × (0.0290) = 0.0210. This means that earnings are predicted to increase by 2.10%. (d) When Age increases from 25 to 26, the predicted change in ln( AHE ) is (0.147 × 26 0.0021 × 26 2 ) (0.147 × 25 0.0021 × 25 2 ) = 0.0399. This means that earnings are predicted to increase by 3.99%. When Age increases from 34 to 35, the predicted change in ln( AHE ) is (0. 147 × 35 0.0021 × 35 2 ) (0. 147 × 34 0.0021 × 34 2 ) = 0.0063. This means that earnings are predicted to increase by 0.63%. (e) The regressions differ in their choice of one of the regressors. They can be compared on the basis of the 2 . R The regression in (3) has a (marginally) higher 2 , R so it is preferred. (f) The regression in (4) adds the variable Age 2 to regression (2). The coefficient on Age 2 is statistically significant ( t = 2.91), and this suggests that the addition of Age 2 is important. Thus, (4) is preferred to (2).
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## This note was uploaded on 11/06/2009 for the course ECON ECON111 taught by Professor Smith during the Spring '09 term at Punjab Engineering College.

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empir_ex08[1] - Chapter 8 Nonlinear Regression Functions...

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