economic question

HOMEWORK 3 Econ 4400, Elementary Econometrics

Directions: Please follow the instructions closely. Due: All problem sets have to be turned in at the beginning of the class. Due Dates: February 14

1. (10 pts) What are the properties necessary for OLS to be the Best Linear Unbiased Estimator? (List and describe)

2. (15 pts) Table 1 shows summary statistics for a subsample of the 2014 CPS. Use to answer the following questions:

(a) What percent of the sample is Female?

(b) What percent of the sample lists race as American Indian?

(c) How many people in the sample list race as other? (You may need to round it off. )

3. (40 pts)Table 2 shows regression results from an equation where wagei is the dependent variable. Each column has slightly different independent variables. Use the table to answer the following questions:

(a) Interpret the coefficient on years of schooling in column 4.

(b) Interpret the coefficient on female in column 4.

(c) Why is the coefficient on female different in each column?

(d) Write out the estimated equation in column 2. (Write the numbers in for the β’s.)

(e) Use the estimated equation in column 2 to predict the wages for a man with 12 years education and a woman with 12 years education.

(f) What racial group is the reference (or omitted group) in columns 3 and 4?

(g) Interpret the coefficient on race == White in column 3.

4. (35 pts)Use the data set nlsy97 small.dta to complete the following tasks:

(a) Write down an equation for estimating income as a function of age, high- est grade completed, gender, race, and parent’s income during adolescents (income gross yr 1997).

(b) Which coefficient describes the difference in wages by gender? What sign do you expect to find?

(c) Estimate the equation and report the results in a table similar to table 2. (Include the R2 in your table. The STATA help section shows how to make the table.)

(d) Interpret the coefficient on highest grade completed.

(e) What is the R2 and what does it tell us about the regression?

(f) Give a prediction of wage for a 30 year old Hispanic woman with 14 grades completed whose household income was $40,000 when she was an adolescent.

1 Stata Help

The command to run an OLS regression in stata is ”regress” or ”reg” for short. Fol- lowing the command should be a list of variables starting with the dependent variable. So if I want to estimate y = β0 + β1x, I type ”reg y x”. Stata will return something like figure 2. In that example, β̂0 = 2.541224 and β̂1 = 1.947394. We will learn what the other numbers mean at a later point.

1.1 Making a Regression Table

1. Make sure the estout package is installed. (see hw 1)

2. Run regressions: ”reg y x1 x2 x3”

3. store results: eststo r1

4. Make table: esttab r1 using t1.rtf, replace label star(* 0.10 ** 0.05 *** 0.01) se r2 ar2

Table 1: Summary Stats 2014 CPS Data

(1)

Earnings per hour 22.65 (13.90)

Number of own children < 18 0.749 (1.140)

Female 0.503 (0.500)

Male 0.497 (0.500)

Years of Schooling 13.83 (2.828)

Enrolled in School 0.0578 (0.234)

Age 41.60 (10.76)

race==White 0.811 (0.392)

race==Black 0.107 (0.309)

race==American Indian 0.0100 (0.0996)

race==Asian/Pacific Islands 0.0584 (0.235)

race==Other 0.0142 (0.118)

Observations 1199

mean coefficients; sd in parentheses

Table 2: Wage Regressions on 2014 CPS Data

(1) (2) (3) (4) Wage Wage Wage Wage

Female -1.691∗ -2.745∗∗∗ -2.328∗∗∗ -2.238∗∗∗

(0.976) (0.882) (0.862) (0.863)

Years of Schooling 2.197∗∗∗ 2.222∗∗∗ 2.198∗∗∗

(0.160) (0.157) (0.157)

Age 0.249∗∗∗ 0.229∗∗∗

(0.0405) (0.0420)

race==White -6.560∗ -6.857∗∗

(3.417) (3.417)

race==Black -10.45∗∗∗ -10.51∗∗∗

(3.645) (3.640)

race==American Indian -14.41∗∗ -14.16∗∗

(6.017) (6.010)

race==Asian/Pacific Islands -7.099∗ -7.636∗∗

(3.768) (3.775)

race==Other 0 0 (.) (.)

married 1.604∗

(0.906)

Constant 23.45∗∗∗ -6.923∗∗∗ -10.77∗∗ -10.26∗∗

(0.671) (2.294) (4.309) (4.313) Observations 812 812 812 812

Standard errors in parentheses ∗ p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

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