CE Set 8 Spring 2007

CE Set 8 Spring 2007 - ECONOMETRICS Spring 2007 CE SET...

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ECONOMETRICS // Spring 2007 CE SET 8 (project assignment) It is generally viewed that older workers have more job experience, leading to higher productivity and earnings. Do earnings really tend to increase with age? If so, by how much more? Will the additional earnings, if any, depend on gender? Will the additional earnings, if any, depend on education? In this exercise, your task is to analyze hourly earnings of full-time workers as it relates to several factors: age, gender, and education level. The variables are defined as follows. WAGE = Hourly wage ($ dollars) AGE = Age of worker (years) SEX = 1 if female; 0 if male BACH = 1 if worker has a bachelor’s degree; 0 if worker has a high school degree Based on these variables, you plan to consider some of the following Population Regression Functions (PRFs): Model 1: E(Wage) = β 0 + β 1 AGE Model 2: E(Wage) = β 0 + β 1 BACH Model 3 : E(Wage) = β 0 + β 1 SEX Model 4: E(Wage) = β 0 + β 1 AGE + β 2 BACH Model 5: E(Wage) = β 0 + β 1 AGE + β 2 SEX Model 6: E(Wage) = β 0 + β 1 SEX + β 2 BACH Model 7: E(Wage) = β 0 + β 1 AGE + β 2 BACH + β 3 SEX Model 8: E(Wage) = β 0 + β 1 AGE + β 2 SEX + β 3 AGE*SEX Model 9: E(Wage) = β 0 + β 1 AGE + β 2 BACH + β 3 AGE*BACH The data set is large with a sample size of n = 7986 observations. Below is a table of some summary statistics of the variables. Note the mean hourly wage of ALL observations in the sample is about $16.77. Of the total sample, 3313 observations are females; their mean hourly wage is about $15.36. There are 4346 observations with bachelor’s degrees in the sample; their mean hourly wage is about $20.31. Data Summary Table AGE AGE Sample Mean 16.771 29.754 15.359 29.665 17.773 29.818 20.307 29.751 13.810 29.757 Maximum 61.058 34.000 57.692 34.000 61.058 34.000 61.058 34.000 60.096 34.000 Minimum 2.098 25.000 2.098 25.000 2.137 25.000 2.308 25.000 2.098 25.000 Sample Std. Dev. 8.759 2.891 7.710 2.926 9.304 2.865 9.554 2.886 6.729 2.896 Observations 7986 7986 3313 3313 4673 4673 3640 3640 4346 4346 1
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(1) Consider Model 1. E(Wage) = β 0 + β 1 AGE a) Write down the ERF ( note: round beta estimates to 2 decimal places). Interpret the slope estimate. b) Provide a 95% CI estimate for the slope coefficient and interpret this interval. c) Based on this interval, is the slope estimate statistically significant at 5% alpha? Explain. Is this finding surprising? Comment. d) About how much of the variation in age helps to explain variation in hourly earnings? e) John is one year older than Jane. According to this regression, is John’s hourly wage expected to be more or less than Jane’s? What is the expected difference between John and Jane’s hourly wage?
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