Eco311, Final Exam, Fall 2017

Prof. Bill Even

Your Name (Please print) ________________________________________

Directions

Each question is worth 4 points unless indicated otherwise.

Place all answers in the space provided below or within each question. Round all numerical answers to the nearest

100th (e.g. 1.23) unless told otherwise.

Eco311, Final Exam, Fall 2017

Prof. Bill Even

Using a sample of people aged 66 and above drawn from the Current Population Survey, I estimated a regression of annual social

security income measured in 1000s of $ (SSINC) on a person’s age, years of education, and a dummy variable indicating whether the

person is female and followed this regression with several supplemental regressions.

Prob > F = 0.0000

F( 3, 17474) = 1.2e+06

( 3) female = 0

( 2) female - school = 0

( 1) female - age = 0

. test female=age=school=0

_cons 138.9225 .366929 378.61 0.000 138.2032 139.6417

school 21.37386 .0205686 1039.15 0.000 21.33354 21.41417

age .27867 .0046919 59.39 0.000 .2694733 .2878666

female -85.07383 .0559569 -1520.35 0.000 -85.18351 -84.96415

y2 Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 48864118.9 17,477 2795.90999 Root MSE = 3.6436

Adj R-squared = 0.9953

Residual 231976.883 17,474 13.2755455 R-squared = 0.9953

Model 48632142 3 16210714 Prob > F = 0.0000

F(3, 17474) > 99999.00

Source SS df MS Number of obs = 17,478

. reg y2 female age school

Prob > F = 0.0228

F( 2, 17475) = 3.78

( 2) y = 0

( 1) y - y2 = 0

. test y=y2=0

_cons -50.89931 64.17269 -0.79 0.428 -176.6842 74.88556

y2 -.4066632 .3462225 -1.17 0.240 -1.085294 .2719675

y 12.76254 9.500862 1.34 0.179 -5.860093 31.38518

u2 Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 486857193 17,477 27857.0231 Root MSE = 166.88

Adj R-squared = 0.0003

Residual 486646440 17,475 27848.151 R-squared = 0.0004

Model 210753.086 2 105376.543 Prob > F = 0.0228

F(2, 17475) = 3.78

Source SS df MS Number of obs = 17,478

. reg u2 y y2

Prob > F = 0.0124

F( 3, 17474) = 3.63

( 3) female = 0

( 2) female - school = 0

( 1) female - age = 0

. test female=age=school=0

_cons 50.36331 16.80449 3.00 0.003 17.42484 83.30178

school 2.742589 .9419935 2.91 0.004 .896188 4.588991

age -.17304 .2148801 -0.81 0.421 -.5942264 .2481465

female -1.903972 2.562695 -0.74 0.458 -6.927109 3.119165

u2 Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 486857193 17,477 27857.0231 Root MSE = 166.87

Adj R-squared = 0.0005

Residual 486554144 17,474 27844.4629 R-squared = 0.0006

Model 303048.234 3 101016.078 Prob > F = 0.0124

F(3, 17474) = 3.63

Source SS df MS Number of obs = 17,478

. reg u2 female age school

. gen y2=y^2

. gen u2=u^2

. predict y, xb

. predict u, residual

_cons 11.84683 .6801095 17.42 0.000 10.51375 13.17991

school .7802276 .0381243 20.47 0.000 .7055002 .854955

age .0093096 .0086966 1.07 0.284 -.0077366 .0263559

female -3.107464 .1037171 -29.96 0.000 -3.31076 -2.904168

ssinc Coef. Std. Err. t P>|t| [95% Conf. Interval]

Total 861852.969 17,477 49.3135532 Root MSE = 6.7534

Adj R-squared = 0.0751

Residual 796963.424 17,474 45.6085283 R-squared = 0.0753

Model 64889.5451 3 21629.8484 Prob > F = 0.0000

F(3, 17474) = 474.25

Source SS df MS Number of obs = 17,478

. reg ssinc female age school

Eco311, Final Exam, Fall 2017

Prof. Bill Even

Use the regressions from the prior page to answer the following questions.

1. Holding education and age constant, women’s average social security benefits are $3107 lower than men’s.

2. The f-statistic for the Breusch-Pagan test of heteroscedasticity is 3.63_____ and implies that the null hypothesis

of homoscedasticity (should, should not) be rejected at the .01 level of significance.

3. The LM statistic for the Breusch-Pagan test for heteroscedasticity is _10.49______ and has _3_ degrees of

freedom.

4. The f-statistic for the simple version of the White test for heteroscedasticity is __3.78____ and implies that that

null hypothesis of homoscedasticity (should, should not) be rejected at the .05 level of significance.

5. Based on the regressions presented, indicate whether each of the following is true (T) or false (F). The variance

of the residual from the social security regression is

a. Greater for women than men. __F___

b. Greater for older than younger people. _F____

c. Greater for more educated people. __T__

6. If the null hypothesis of homoscedasticity is rejected, indicate whether each of the following is true (T) or false

(F)

a. The standard OLS estimates of the coefficients remain unbiased _T___

b. The standard OLS estimates of the standard errors for the coefficients are incorrect __T___

c. The standard OLS estimates of the coefficients remain efficient __F__

7. Suppose you have data on expenditures per pupil by school district and you estimate the following regression

=0+1+2+

Where the subscript i indexes the school district, expendpp is expenditures per pupil, income is average family

income, and married is the percent of households with married couples. The residuals from this regression (u)

are likely to be

a. Heteroskedastic and their variance will be greater in districts with larger populations

b. Homoskedastic and their variance will be greater districts with larger populations

c. Heteroskedastic and their variance will be greater in districts with smaller populations.

d. Homoskedastic and their variance will be greater districts with smaller populations