The relationship between workers' wages, age, gender, education and firm size Worker-level wages are potentially affected by a number of factors including the age of the worker, his/her gender, his/her education and the size of the employing firm. The objective of this project is to establish whether and to what extent workers' age, education, gender and size of the employing firm are determinants of worker-level wages in a cross-sectional dataset of workers. The data below contain information, covering a sample of 60 workers, on workers' wages (Wage), age (Age), education (Edu), a commonly used measure of firm size and in particular the number of workers in the employing firm (Size) and a dummy variable indicating whether the worker is male (Gender) or female (Gender-1). Wages are measured in pounds per hour worked while Age and Edu are measured in years. 1. Describe the data, using summary statistics and graphs, as appropriate. 2. Calculate the pair-wise correlation coefficients between Wage and each of the other variables. Test the statistical significance of each correlation coefficient. 3. Consider the two variables Gender and and Size. Compute the pairwise correlation of the two variables and test the significance of the correlation coefficient. Now consider the two values of Gender while grouping the Size variable into 3 intervals (3 intervals of 20 observations each) and construct a contingency Table. Using the contingency Table perform a test for the presence of association between the two variables. Compare and discuss results from the contingency Table analysis with results from the correlation analysis. 4. Consider the two variables Age and Edu and test the null hypothesis that the two variables have equal variance. 5. Estimate a regression model of the form: Wage *a+B Age + B:Edu; + B;Gender +B_Size +u where the i subscript corresponds to worker i. Interpret the coefficients that you obtain, and comment on their economic and statistical significance. 6. Interpret the R statistic from the regression and test whether it is statistically significant 7. Re-estimate the model adding the variable Age to the power two (Age 2) and comment on any changes to the results and goodness of fit: Wage =a + B Age + BAge? + B Edu; + B.Gender + BSize + 8. Estimate a (partial) log-version of the regression model of the form: 1 Log(Wage) =a + B1Age; + B2Age? + B2Edu; + B.Gender; + BLog(Size)+u; Note that this version of the model is the one typically used in applied Labor economics analyses. Interpret the coefficients that you obtain, and comment on their economic and statistical significance. Compare this model with the one estimated in point 7 9. What conclusions do you draw from your analysis? Copy and paste the data into Excel and conduct all the analysis in Excel Worker id Wage Age Edu Gender Size 1 23 53 11 0 2 18 49 7 0 3 30 49 14 0 4 23 40 11 0 46 5 19 32 10 0 8 6 34 47 14 0 24 7 33 61 19 1 4 8 21 15 0 23 9 11 0 3 10 14 0 31 11 0 38 12 42 13 11 0 11 14 16 0 36 15 19 1 13 16 18 0 6 17 16 12 0 9 18 25 11 0 9 19 1 43 20 0 21 22 OOOOO 27 29 29 30 31 32 33 34 41 45 48 55 0 0 0 0 1 34 35 8 16 37 2 1 39 42 43 14 45 40 41 42 43 45 127 12 15 14 15 13 11 15 14 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 17 27 31 34 25 22 34 30 28 33 13 29 36 26 31 38 27 29 35 28 28 33 45 45 53 42 57 51 23 43 57 46 63 52 44 44 62 32 44 58 15 12 11 14 10 12 15 11 17 13 15 16 13 16 OOOOOOOOOOOOOOOOO 16 56 115 91 17 73 5 80 6 57 13 91 40 14 76 19 27 22 1 where: Worker_id Worker identifier Wage - Wage of the worker in pounds per hour worked Age = Age of the worker Edu = Number of years of education of the worker Gender Dummy variable indicating whether the worker is male (Gender-0) of female (Gender-1) Size - Number of workers in the firm employing the worker The relationship between workers' wages, age, gender, education and firm size Worker-level wages are potentially affected by a number of factors including the age of the worker, his/her gender, his/her education and the size of the employing firm. The objective of this project is to establish whether and to what extent workers' age, education, gender and size of the employing firm are determinants of worker-level wages in a cross-sectional dataset of workers. The data below contain information, covering a sample of 60 workers, on workers' wages (Wage), age (Age), education (Edu), a commonly used measure of firm size and in particular the number of workers in the employing firm (Size) and a dummy variable indicating whether the worker is male (Gender) or female (Gender-1). Wages are measured in pounds per hour worked while Age and Edu are measured in years. 1. Describe the data, using summary statistics and graphs, as appropriate. 2. Calculate the pair-wise correlation coefficients between Wage and each of the other variables. Test the statistical significance of each correlation coefficient. 3. Consider the two variables Gender and and Size. Compute the pairwise correlation of the two variables and test the significance of the correlation coefficient. Now consider the two values of Gender while grouping the Size variable into 3 intervals (3 intervals of 20 observations each) and construct a contingency Table. Using the contingency Table perform a test for the presence of association between the two variables. Compare and discuss results from the contingency Table analysis with results from the correlation analysis. 4. Consider the two variables Age and Edu and test the null hypothesis that the two variables have equal variance. 5. Estimate a regression model of the form: Wage *a+B Age + B:Edu; + B;Gender +B_Size +u where the i subscript corresponds to worker i. Interpret the coefficients that you obtain, and comment on their economic and statistical significance. 6. Interpret the R statistic from the regression and test whether it is statistically significant 7. Re-estimate the model adding the variable Age to the power two (Age 2) and comment on any changes to the results and goodness of fit: Wage =a + B Age + BAge? + B Edu; + B.Gender + BSize + 8. Estimate a (partial) log-version of the regression model of the form: 1 Log(Wage) =a + B1Age; + B2Age? + B2Edu; + B.Gender; + BLog(Size)+u; Note that this version of the model is the one typically used in applied Labor economics analyses. Interpret the coefficients that you obtain, and comment on their economic and statistical significance. Compare this model with the one estimated in point 7 9. What conclusions do you draw from your analysis? Copy and paste the data into Excel and conduct all the analysis in Excel Worker id Wage Age Edu Gender Size 1 23 53 11 0 2 18 49 7 0 3 30 49 14 0 4 23 40 11 0 46 5 19 32 10 0 8 6 34 47 14 0 24 7 33 61 19 1 4 8 21 15 0 23 9 11 0 3 10 14 0 31 11 0 38 12 42 13 11 0 11 14 16 0 36 15 19 1 13 16 18 0 6 17 16 12 0 9 18 25 11 0 9 19 1 43 20 0 21 22 OOOOO 27 29 29 30 31 32 33 34 41 45 48 55 0 0 0 0 1 34 35 8 16 37 2 1 39 42 43 14 45 40 41 42 43 45 127 12 15 14 15 13 11 15 14 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 17 27 31 34 25 22 34 30 28 33 13 29 36 26 31 38 27 29 35 28 28 33 45 45 53 42 57 51 23 43 57 46 63 52 44 44 62 32 44 58 15 12 11 14 10 12 15 11 17 13 15 16 13 16 OOOOOOOOOOOOOOOOO 16 56 115 91 17 73 5 80 6 57 13 91 40 14 76 19 27 22 1 where: Worker_id Worker identifier Wage - Wage of the worker in pounds per hour worked Age = Age of the worker Edu = Number of years of education of the worker Gender Dummy variable indicating whether the worker is male (Gender-0) of female (Gender-1) Size - Number of workers in the firm employing the worker