UNIVERSITY OF ESSEX DEPARTMENT OF ECONOMICS 2016-17 Dr. Abhimanyu Gupta EC252 INTRODUCTION TO ECONOMETRIC METHODS Econometrics Exercise 2017 NOTE: The deadline for handing in this econometric exercise is Wednesday, 22 March 2017, 12:00 mid-day (room 5B.211). The page limit is 10 printed sides, all inclusive, and the minimum font size is 12 in Times New Roman. It is acceptable to copy/paste output from Stata but to get full marks you are required to comment appropriately on the output. Important: You must submit BOTH one paper copy of your answers to Chrissy Brown and also one copy online via FASER. You were provided with an individualized data set. If you have not obtained the data set, please contact Chrissy Brown or Abhimanyu Gupta as a matter of urgency. Your data set is unique to you. You must not use the data set of any other student for your econometrics exercise. Use your data set and Stata to answer the following questions. In this exercise your task is to examine determinants of the (weekly) number of hours worked for a sample of employed married women. The variables in your data set are: hours = weekly hours worked, hrwage = hourly wage (in U.S. dollar), age = individual's age in years, educ = years of education, nwifeinc = non-wife income in the household (in 1,000$), kidlt6 = indicator which takes the value 1 if there are children aged less than 6 in the household, and 0 otherwise. 1. (a) What is, for each variable in your data set, the average, the standard deviation, the minimum value, the maximum value, and the number of observations in your data set? (b) What are their labels? 2. (a) Generate a new variable lwage as the natural logarithm of hrwage. Label this variable. (b) Label the indicator variable for presence of small children in the household. (c) Label each value of the variable kidlt6 appropriately. (d) What percentage of individuals has small children in the household? What is the average number of hours worked for individuals who are older than 28 years of age and do not have small children in the household? 1(e) Create a new variable, agegroup, which takes value 1 if the woman is younger than 25 years, value 2 for age group 25-29, 3 for age group 30-34, 4 for age group 35-39, 5 for age group 40-44, 6 for age group 45-49, and 7 for ages 50 and above. Tabulate the new variable. How many women are there in the age group 30-34? 3. Examine graphically the relationship between age and the presence of small children in the household, using a bar graph (for this question, restrict attention to individuals younger than 45 years of age). 4. Calculate the correlation coefficient between hours worked and years of schooling. Is there a strong relationship between these two variables? 5. (a) Run a regression of hours worked on education and age. (b) If education changes from 10 to 11 years, what is the predicted effect on hours worked? (c) If education changes from 8 to 9 years, what is the predicted effect on hours worked? (d) Explain the conclusion from (b) and (c) above. 6. (a) Run a regression of the natural logarithm of hours, log(hours), on years of schooling and age. (b) If education changes from 12 to 13 years, what is the predicted effect on hours worked? (c) If education changes from 8 to 9 years, what is the predicted effect on hours worked? 7. (a) Run a regression of hours on age, age2, age3 and educ. (b) Plot how predicted hours change with age, holding education constant at 12 years. (c) Making any assumptions you need, test whether the three coefficients on the age variables are jointly significant (at a significance level of 5%). 8. Do you prefer the regression in question 7 (a) to the regression in question 5 (a)? Explain. 9. A simple model of labor supply predicts that the wife's hours worked should go down when non-wife income increases. (a) Run a regression of hours on non-wife income, age, age2, age3 and educ. Interpret the result. 2(b) Test if non-wife income has a statistically significant effect on hours worked (at 1% significance). (c) How much does the R2-measure increase from including non-wife income? Can this measure decrease when an extra explanatory variable is added? Explain. 10. You are interested in the effect of presence of small children on the number of hours worked. (a) Run a regression of hours on kidlt6, non-wife income, age, age2, age3 and educ. (b) Test if the presence of small children has a statistically significant effect on hours worked (at 10% significance). (c) Compare the magnitudes of the coefficients on kidlt6 and non-wife income. 11. We are now interested in an interaction term between nwifeinc and kidlt6: (a) Run a regression of hours on kidlt6, non-wife income, age, age2, age3, educ, and an interaction term between kidlt6 and non-wife income (kidlt6 × nwifeinc). What does the coefficient on the interaction term measure? (b) Does the responsiveness of hours worked to non-wife income differ with the presence of small children? Perform a statistical test for this question. (c) What is the predicted number of hours for a 34 year old individual without children, 15 years of education, and no non-wife income? (d) What is the predicted number of hours for a 24 year old individual with two small children (aged 2 and 3), 9 years of education, and $ 8,000 non-wife income? 12. Investigate how the number of hours worked responds to differences in wage opportunities: (a) Extend the model in question 9 (a) by additionally accounting for lwage. Write down the resulting model and estimate its coefficients. (b) What is the predicted effect on hours worked of a 5% increase in the hourly wage? 13. (a) To assess the extent to which hours worked responds to non-wife income and wage opportunities, test the hypothesis that both coefficients on these economic variables are jointly equal to zero (in the specification from question 12 (a), at a significance level of 5%). 14. After running all these regressions (and any other that you want to run), summarize the main findings you have obtained. Are there any further variables or models you would like to include in the analysis? If yes, explain and state the models. 3***** 4