Wooldridge Solution chapter 3

(1)

C3.1

(i)

Positive

(ii)

Yes.

Positive: High income, can buy more goods

Negative: base on fatheduc, most family have high education and know the danger of smoking, so high

income family with high education tend not to smoke

CIGS FAMINC

CIGS 1.000000 -0.173045

FAMINC -0.173045 1.000000

(iii)

cigs

Dependent Variable: BWGHT Method: Least Squares Date: 12/20/14 Time: 16:35 Sample: 1 1388

Included observations: 1388

Variable Coefficient Std. Error t-Statistic Prob.

C 119.7719 0.572341 209.2668 0.0000

CIGS -0.513772 0.090491 -5.677609 0.0000

R-squared 0.022729 Mean dependent var 118.6996

Adjusted R-squared 0.022024 S.D. dependent var 20.35396 S.E. of regression 20.12858 Akaike info criterion 8.843598 Sum squared resid 561551.3 Schwarz criterion 8.851142 Log likelihood -6135.457 Hannan-Quinn criter. 8.846420

F-statistic 32.23524 Durbin-Watson stat 1.924390

Prob(F-statistic) 0.000000

faminc

Dependent Variable: BWGHT Method: Least Squares Date: 12/20/14 Time: 16:37 Sample: 1 1388

C 116.9741 1.048984 111.5118 0.0000

CIGS -0.463408 0.091577 -5.060315 0.0000

FAMINC 0.092765 0.029188 3.178195 0.0015

(2)

(i) result: price = -19,315 + 0,128 sqrft + 15,198 bdrms Dependent Variable: PRICE

Method: Least Squares Date: 12/20/14 Time: 16:50 Sample: 1 88

C -19.31500 31.04662 -0.622129 0.5355

SQRFT 0.128436 0.013824 9.290506 0.0000

BDRMS 15.19819 9.483517 1.602590 0.1127

(ii) $15.198,19

(iii)

$ 33,17923

(iv) R2_{= 63%}

(v) 354.600

(vi) Estimate price = 354.600 Since actual =300.000

(3)

(i) Log (salary) = B0 + B1 log (sales) + B3 log (mktval)

Log (salary) = 4,621 + 0,162 log (sales) + 0,107 log (mktval) Dependent Variable: LSALARY

C 4.620918 0.254408 18.16339 0.0000

LSALES 0.162128 0.039670 4.086899 0.0001

LMKTVAL 0.106708 0.050124 2.128880 0.0347

(ii) Log (salary) = B0 + B1 log (sales) + B3 log (mktval) + B3 profits

Log (salary) = 4,687 + 0,161 log (sales) + 0,097 log (mktval) + 3,57*10-5_profits

Dependent Variable: LSALARY Method: Least Squares Date: 12/20/14 Time: 19:42 Sample: 1 177

C 4.686924 0.379729 12.34280 0.0000

LSALES 0.161368 0.039910 4.043299 0.0001

LMKTVAL 0.097529 0.063689 1.531333 0.1275

PROFITS 3.57E-05 0.000152 0.234668 0.8147

The R2 _{is almost the same, including variable profits only gives small influence to the model.}

70% of variation in log salary is unexplained.

(iii) Log (salary) = B0 + B1 log (sales) + B3 log (mktval) + B3 profits + B4 ceoten

Log (salary) = 4,558 + 0,162 log (sales) + 0,102 log (mktval) + 2,91*10-5_{profits + 0,012 ceoten}

Dependent Variable: LSALARY Method: Least Squares Date: 12/20/14 Time: 19:49 Sample: 1 177

(4)

C3.4

(i) Descriptive stat

ATNDRTE PRIGPA ACT

Mean 81.70956 2.586775 22.51029 Median 87.50000 2.560000 22.00000 Maximum 100.0000 3.930000 32.00000 Minimum 6.250000 0.857000 13.00000 Std. Dev. 17.04699 0.544714 3.490768 Skewness -1.578799 0.161246 0.075404 Kurtosis 5.693665 2.760582 2.645701 Jarque-Bera 488.0774 4.570791 4.200994 Probability 0.000000 0.101734 0.122396 Sum 55562.50 1759.007 15307.00 Sum Sq. Dev. 197317.3 201.4684 8273.928 Observations 680 680 680

(ii) Estimate the model

Atndrte = 75,70 + 17,261 prigpa – 1,717 act

The intercept of 75.70 is the predicted percent of classes attended for a student with 0 cumulative GPA prior to the current term and an ACT score of 0. I would not call this particular meaning “useful.” The intercept is useful, but its interpretation is not.

Dependent Variable: ATNDRTE Method: Least Squares Date: 12/20/14 Time: 20:09 Sample: 1 680

C 75.70041 3.884108 19.48978 0.0000

PRIGPA 17.26059 1.083103 15.93624 0.0000

ACT -1.716553 0.169012 -10.15640 0.0000

(iii) Additional point for GPA will increase the class attendance. However, additional score for ACT test will decrease the class attendance. Unexpected result. Perhaps gaining high score means that student thinks they do not have the necessity to attend the class

(iv)

104,36

would seem to be a very good student. But no student attends more than 100% of classes!

(observation number 569). The model provides residual

(v)

The difference in predicted attendance between Student A and Student B is 93.09 - 67.23=

25.86%

(5)

log(wage) =0.284+ 0.092 educ + 0.0041 exper + 0.022 tenure. Dependent Variable: LWAGE

C 0.284360 0.104190 2.729230 0.0066

EDUC 0.092029 0.007330 12.55525 0.0000

EXPER 0.004121 0.001723 2.391437 0.0171

TENURE 0.022067 0.003094 7.133071 0.0000

Adjusted R-squared 0.312082 S.D. dependent var 0.531538 S.E. of regression 0.440862 Akaike info criterion 1.207406

Sum squared resid 101.4556 Schwarz criterion 1.239842

Log likelihood -313.5478 Hannan-Quinn criter. 1.220106

Partialling out on educ coefficient

What we are doing is trying to find the effect of educ on log(wage), controlling for exper and tenure This effect is equal to the effect on log(wage) of the portion of educ that is NOT explained by exper and tenure. First we need to construct a variable that is equal to the portion of educ that is not explained by exper and tenure. The easiest way to do that is to take the residual from the regression:

Educ = g0 + g1 exper + g2 tenure + u Educ = 13,574 – 0,074 exper + 0,048 tenure

Dependent Variable: EDUC Method: Least Squares Date: 12/20/14 Time: 20:41 Sample: 1 526

C 13.57496 0.184324 73.64710 0.0000

EXPER -0.073785 0.009761 -7.559282 0.0000

TENURE 0.047680 0.018337 2.600162 0.0096

To find the residuals in this regression I subtract educ from educ:

(6)

C3.6

(i) EDUC 3.533829 0.192210 18.38530 0.0000 (ii) EDUC 0.059839 0.005963 10.03492 0.0000 (iii) EDUC 0.039120 0.006838 5.720784 0.0000 IQ 0.005863 0.000998 5.875413 0.0000 (iv)

C3.7

(7)

(i)

Dependent Variable: MATH10 Method: Least Squares Date: 12/20/14 Time: 21:16 Sample: 1 408

C -20.36076 25.07287 -0.812063 0.4172

LEXPEND 6.229691 2.972634 2.095680 0.0367

LNCHPRG -0.304585 0.035357 -8.614468 0.0000

math10 = -20,36 + 6,23 lexpend – 0,305 lnchprg

The sign of the coefficients are as expected: the percentage of students passing a math exam is increasing in expenditure per student and decreasing in the percentage of students who are in a school lunch program (presumably a subsidized lunch program)

(ii) No. for lexpend cannot set to 0 because log 0 = undefined. At least $1 for lexpend. For lnchprg we can set it to 0

(iii) Math10 with lexpend Dependent Variable: MATH10 Method: Least Squares Date: 12/20/14 Time: 21:27 Sample: 1 408

C -69.34108 26.53013 -2.613673 0.0093

LEXPEND 11.16439 3.169011 3.522990 0.0005

The magnitude of the slope coefficient has gotten larger. It was previously 6.23 and is now 11.16. This speaks to a negative correlation between log(expend) and lnchprg.

(8)

LEXPEND LNCHPRG

LEXPEND 1.000000 -0.192704

LNCHPRG -0.192704 1.000000

student spends more for lexpend than lnchprg. Negative correlation (v) the inclusion of lnchprg suppressed the coefficient on log(expend)

(1) when lnchprg increases, math10 decreases; (2) when lexpend increases, lnchprg decreases. Therefore, when lexpend increases, what happens, in total? When lexpend increases, lnchprg decreases, which causes math10 to go . . . up.

(9)

(i) descriptive stat PRPBLCK INCOME Mean 0.113486 47053.78 Median 0.041444 46272.00 Maximum 0.981658 136529.0 Minimum 0.000000 15919.00 Std. Dev. 0.182416 13179.29 Skewness 2.700012 0.962831 Kurtosis 10.56841 7.551386 Jarque-Bera 1473.100 416.2135 Probability 0.000000 0.000000 Sum 46.41594 19244998

Sum Sq. Dev. 13.57651 7.09E+10

Observations 409 409

prpblck = percentage income = dollar (ii)

Psoda = 0,956 + 0,115 prpblck + 1,6*10-6

Dependent Variable: PSODA Method: Least Squares Date: 12/20/14 Time: 21:39 Sample: 1 410

C 0.956320 0.018992 50.35379 0.0000

PRPBLCK 0.114988 0.026001 4.422515 0.0000

INCOME 1.60E-06 3.62E-07 4.430130 0.0000

Adjusted R-squared 0.059518 S.D. dependent var 0.088798 S.E. of regression 0.086115 Akaike info criterion -2.058820 Sum squared resid 2.951465 Schwarz criterion -2.028940 Log likelihood 415.7934 Hannan-Quinn criter. -2.046988

The coefficient on prpblck is 0.1149882. The literal interpretation would be: when prpblck increases by 1, the price of a medium soda increases by 11 cents. The only problem is, the notion of increasing prpblck by 1 is not very meaningful. prpblck is the proportion of individuals in a zip code who are black cannot increase by 1 unless the proportion of individuals in a zip code starts out as 0. That is, the only zip code that can increase by 1 is a zip code that starts out with no individuals who are black, and then becomes a zip code that is made up only of individuals who are black. This is not a very useful marginal effect. In order to interpret the marginal effect more usefully, look at smaller (more realistically-sized) changes. For instance, an increase of 0.01 (an increase of 1 in the percentage of individuals who are black in a zip code) is predicted to increase the price of a medium soda by 0.1149882 × 0.01 = 0.00114988,

(10)

(11)

C4.1

(i) As expenditure of candidate A increases for 1%, percentage of vote for candidate A will increase for B1/100

(ii) H0: B1=-B2 or H0: B1+B2=0

1% increases expendA and 1% increases expendB leaves voteA unchanged (iii) Estimate model

voteA = 45,079 + 6,083 lexpendA – 6,615 lexpendB + 0,152 prtystrA Dependent Variable: VOTEA

C 45.07893 3.926305 11.48126 0.0000

LEXPENDA 6.083316 0.382150 15.91866 0.0000

LEXPENDB -6.615417 0.378820 -17.46321 0.0000

PRTYSTRA 0.151957 0.062018 2.450210 0.0153

Yes, 1% increases on expend A will probably increase vote for A. 1% increases on expend B will decrease vote for A.

(iv) t-test