Assignment: Elementary Econometrics
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
4. Use the SSR version of the F-test to test the joint significance of the regional variables. (You can ignore the e + 12)
5. Use the R2 version of the F-test to test the joint significance of the regional variables.
6. Why does the coefficient on education change in each regression? Why would it be so much different in columns 1 and 3?
7. Column 4 includes favorite ice cream flavor. Use an F-test to show that they should not be included.
8. 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?
9. Interpret β2 in column 1.
10. 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?
11. 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:
• 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
|
|
(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
|
-1568.1
(23.94)
98311
0.211
|
0.255
|
Standard errors in parentheses
∗ p <0.10, ∗∗ p <0.05, ∗∗∗ p <0.01