Econ 2123. Introduction to Econometrics Sections 80/83. Prof. Williams Homework 4 due Thursday February 12 Answer each of the following three problems. You can work together with other students in the class but you must write your assignments up separately. 1. Suppose that a random sample of 200 40-year old men is selected from a population and that these men's annual income is recorded. Suppose I am also able to obtain the annual income of each man's father when the father was 40. A regression of the former on the latter yields Wic = 25 + 0.5 Wif where Wic and Wif are the annual income in thousands of dollars of man i and his father, respectively. i. Explain what the coecient values 25 and 0.5 mean intuitively. ii. What is the predicted annual income for someone whose father earned $100, 000? iii. If I take a job which will pay me $50, 000 more when I am 40 years old, what is the regression's prediction for the increase in my (hypothetical) son's income when he is 40 relative to if I did not take this job? iv. The sample average income across the 200 men is $45, 000. What is the sample average of income across the 200 fathers? v. Suppose the data I used above already converted all income values to be in 2013 dollars using the CPI. Suppose I converted the sons' incomes to 2008 dollars and the fathers' incomes to 1980 dollars and performed the regression again. (The conversion is to divide by 1.08 for 2013 dollars to 2008 dollars and divide by 2.83 for 2013 dollars to 1980 dollars.) What would the new values for the slope and intercept estimators be? 2. Statistical signicance In the 1980s, Tennessee conducted an experiment in which kindergarten students were randomly assigned to \"regular\" and \"small\" classes, and given standardized tests at the end of the year. (Regular classes contained approximately 24 students and small classes contained approximately 15 students.) Suppose that, in the population, the standardized tests have a mean score of 925 points and a standard deviation of 75 points. Let SC denote a binary variable equal to 1 if the student is assigned to a small class and equal to 0 otherwise. A regression of the test score, T S, on SC yields: Constant/Estimated Intercept (robust SE) Estimated Coecient on SC (robust SE) R-squared Standard error of the regression 918.0 (1.6) 13.9 (2.5) 0.01 74.6 i. Do small classes improve test scores? By how much? Is the eect large? Explain. ii. Is the estimated eect of class size on test scores statistically signicant? Carry out a test at the 5% level. iii. Construct a 99% condence interval for the eect of SC on T S. 3. Dahl and Lochner, 2012 In the paper, \"The Impact of Family Income on Child Achievement: Evidence from the Earned Income Tax Credit\