# Homework help-Econ 4400, Elementary Econometrics

HOMEWORK4

Econ 4400, Elementary Econometrics

Directions: Please follow the instructions closely. Questions 1-10 are worth 9 points each. Question 11 is worth 10 points.

Due: All problem sets have to be turned in at the beginning of the class. Due Dates: March 2

Table 1 includes regression results using the NLSY 97 data set. The omitted racial group is ”non-black/ non-Hispanic”. The omitted census region is ”West”. The omitted favorite ice cream flavor is Chocolate.

Using the regression results in Table 1 perform each of the following tests. Use 0.05 significance level for every problem unless otherwise noted. You should write both the null and alternative hypotheses, calculate the necessary statistics, find correct critical values, and make the correct conclusion

1. Use a t-test to test if education has a statistically significant(2-sided) effect on income in column 1.
2. Use a t-test to test the null hypothesis that black workers make more than nonblack/non-Hispanic, all else equal.
3. Find confidence intervals for the coefficient on education in column 1 and column

1. Use the SSR version of the F-test to test the joint significance of the regional variables. (You can ignore the e + 12)
2. Use the R2 version of the F-test to test the joint significance of the regional variables.
3. Why does the coefficient on education change in each regression? Why would it be so much different in columns 1 and 3?
4. Column 4 includes favorite ice cream flavor. Use an F-test to show that they should not be included.
5. Typically there are stars to denote p-values on regression results. If 1,2, or 3 stars were added for p-values< 0.10, < 0.05, and < 0.01 respectively. How many stars would go on the coefficient for Northeast in column 2?
6. Interpret β2 in column 1.
7. What additional information is needed to test if black workers and Hispanic workers earn different incomes in column 1? What regression could you run to simplify the test?
8. This must be typed. Use the project data set to estimate the equation with all of the variables from columns 1,2,3. of the regression results table and one other regression that you may find of interest for your project. (Your data set is a subsample of this set.) ”grade” is the education variable, the census variable has the regional categories.

To create dummy variables for race type ”tab race, gen(rdum)”. This will create rdum1. rdum2, rdum3, rdum4, and rdum5, each will have the associated race in the variable label. Use the same technique for census group.

(a) Create a table similar to Table 1 with regression results. The table does not need to be identical, but all of the following must be met to receive credit:[1]

• Include all of the listed variables.
• Use variable labels that make sense to someone that has never used the data (ie Years of Education instead of ihigrdc).
• Put standard errors in parentheses.
• Denote coefficients that are statistically significant at 0.01 ***, 0.05 **, and 0.10 * significance levels.

Table 1: Regression Results For Homework 4

 (1) (2) (3) (4) Adult Income Adult Income Adult Income Adult Income Education 3914.8 3934.4 2626.2 3885.8 (226.7) (227.0) (275.9) (227.1) Black -6886.0 -7583.6 -790.1 -7192.8 (1597.8) (1668.6) (1716.4) (1635.8) Hispanic -2270.6 -2144.4 2318.2 -2424.3 (1727.4) (1809.5) (1764.7) (1731.5) Mixed race (non-Hispanic) -1836.1 -1683.2 -2405.2 -1979.6 (6978.8) (6982.2) (6842.2) (6979.6) Female -15382.8 -15434.5 -14758.5 -15478.4 (1291.0) (1291.2) (1266.8) (1294.4) Age 1445.7 1472.3 1378.0 1478.4 (461.1) (461.0) (452.4) (461.2) Northeast 3267.4 (2184.2) North central -195.0 (1955.8) South 2500.6 (1864.7) Armed Services Aptitude Battery 0.149 (0.0291) HH Income as Adolescent 0.112 (0.0164) Vanilla 2217.6 (1692.8) Strawberry -791.6 (1742.8) Butter pecan 1304.7 (2439.6) None of these 3718.6 (2397.3) Constant -57155.2 -59457.3 -52242.0 -58456.2 (14572.0) (14636.8) (14289.6) (14606.5) Observations 1995 1995 1995 1995 ESS 3.79899e+11 3.83837e+11 4.46293e+11 3.84050e+11 RSS 1.62137e+12 1.61743e+12 1.55497e+12 1.61721e+12 R2 0.190 0.192 0.223 0.192

Standard errors in parentheses

Table 2: Project Sample

 (1) (2) Earnings per hour Log(Earnings Per Hour) Highest grade completed 113.5∗∗∗ 0.0574∗∗∗ (1.044) (0.000538) Age 80.32∗∗∗ 0.0545∗∗∗ (1.044) (0.000538) Age2 -0.765∗∗∗ -0.000529∗∗∗ (0.0122) (0.00000628) Female -276.2 -0.168∗∗∗ (5.429) (0.00280) [1em] Black -180.4 -0.0963∗∗∗ (8.843) (0.00455) American Indian -106.1∗∗∗ -0.0495∗∗∗ (25.20) (0.0130) Asian -11.76 -0.0206∗∗∗ (13.22) (0.00681) Other Race -34.41∗ -0.0182∗ (18.27) (0.00941) Adjusted R2 0.211 0.255

Standard errors in parentheses

p < 0.10, ∗∗ p < 0.05, ∗∗∗ p < 0.01

[1] All of these can be done with the esttab command. See the sample estout.do file and previous homework’s on carmen for help.

# Econometrics Paper

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Econometrics Paper

Minimize  = ….we’ll come back to this later

For now, however, we can manually compute the residuals by hand.  Fill in the table.

 i 70 95 65 100 90 120 85 140 110 160 115 194 120 265 148 220 155 236 150 260 verify this sum = 0

The symbolshould have a subscript i to indicate it is not a constant, however, the equation editor does not depict this in a visually appealing manner.

Problem Set A (Fall 2016) You may work with anyone (fellow classmates, not an outside professional) but hand in your own paper. Hand in one, single document (please use the abbreviated answer sheet provided) that is stapled or bounded together in a very, professional manner. _____________________________________________________________ 1. Presented below are hypothetical data on weekly family consumption expenditure Y and weekly family income X. A. Obtain the sample regression function (with computed values) for this data using SAS (write the program in the SAS editor using a cards statement as we did in class). Provide the following: Using symbols, what does the population regression function (PRF) look like (refer to the text if needed)? _____________________________________________________________ Using symbols, what does the sample regression function (SRF) look like? _____________________________________________________________ Based on your SAS output, what is the SRF with the estimated values? ____________________________________________________________ B.

Obtain a correlation matrix for this data. What is the coefficient of correlation indicating about the direction and strength of the 2 variables? C. Now we will produce the sample regression estimates by hand. Compute the sample intercept b1 and sample slope b2 manually. Remind me to give you the formulas in lecture. To help, use the columns set up below to start: yi xi 70 95 65 100 90 120 85 140 110 160 115 194 120 265 148 220 155 236 150 260 D.

We discussed in class the nature of the residuals, ei . When we do Ordinary Least Squares regression (OLS), we choose b1 and b2 in such a way that the residuals are as small as possible1 . The way we do this is to make the residual sum of squares (RSS), ei 2 , as small as possible. In other words, we have a minimization problem!