## INTRODUCTORY ECONOMETRICS – REPLICATING EXAMPLES

### Chapter 8 – Examples

```-------------------------------------------------------------------------------------
name:  SN
log:  ~Wooldridge\intro-econx\iexample8.smcl
log type:  smcl
opened on:   9 Jan 2019, 21:10:27
. **********************************************
. * Solomon Negash - Replicating Examples
. * Wooldridge (2016). Introductory Econometrics: A Modern Approach. 6th ed.
. * STATA Program, version 15.1.

. * Chapter 8  - Heteroskedasticity
. * Computer Exercises (Examples)
. ******************** SETUP *********************

. *Example 8.1. Log wage equation with Heteroskedasticity- Robust Standard Errors
. u wage1, clear
. g marrmale = (female==0 & married==1)
. g marrfem = (female==1 & married==1)
. g singfem = (female==1 & married==0)
. g singmen = (female==0 & married==0)

. eststo hetroskedastic: qui reg lwage marrmale marrfem singfem educ exper* tenur*
. eststo robust: qui reg lwage marrmale marrfem singfem educ exper* tenur*, robust
. estout , cells(b(nostar fmt(3)) se(par fmt(3))) stats(r2 r2_a N, fmt(%9.3f %9.3f %9.0g) ///

----------------------------------------------
hetroskeda~c       robust
b/se         b/se
----------------------------------------------
marrmale                    0.213        0.213
(0.055)      (0.057)
marrfem                    -0.198       -0.198
(0.058)      (0.059)
singfem                    -0.110       -0.110
(0.056)      (0.057)
educ                        0.079        0.079
(0.007)      (0.007)
exper                       0.027        0.027
(0.005)      (0.005)
expersq                    -0.001       -0.001
(0.000)      (0.000)
tenure                      0.029        0.029
(0.007)      (0.007)
tenursq                    -0.001       -0.001
(0.000)      (0.000)
Constant                    0.321        0.321
(0.100)      (0.109)
----------------------------------------------
R-squared                   0.461        0.461
N                             526          526
----------------------------------------------
. est clear

. *Example 8.2. Heteroskedasticity-Robust F Statistic
. u gpa3, clear
. eststo hetrosked: qui  reg cumgpa sat hsperc tothrs female black white if spring==1
. eststo robust: qui  reg cumgpa sat hsperc tothrs female black white if spring==1, robust
. estout , cells(b(nostar fmt(5)) se(par fmt(5))) stats(r2 r2_a N, fmt(%9.3f %9.3f %9.0g) ///

----------------------------------------------
hetrosked       robust
b/se         b/se
----------------------------------------------
sat                       0.00114      0.00114
(0.00018)    (0.00019)
hsperc                   -0.00857     -0.00857
(0.00124)    (0.00142)
tothrs                    0.00250      0.00250
(0.00073)    (0.00074)
female                    0.30343      0.30343
(0.05902)    (0.05914)
black                    -0.12828     -0.12828
(0.14737)    (0.11924)
white                    -0.05872     -0.05872
(0.14099)    (0.11139)
Constant                  1.47006      1.47006
(0.22980)    (0.22068)
----------------------------------------------
R-squared                   0.401        0.401
N                             366          366
----------------------------------------------
. est clear

. *Example 8.3. Heteroskedasticity-Robust LM Statistic
. u crime1, clear
. g avgsensq = avgsen^2
. eststo hetrosked: qui reg narr86 pcnv avgsen avgsensq ptime86 qemp86 inc86 black hispan
. eststo robust: qui reg narr86 pcnv avgsen avgsensq ptime86 qemp86 inc86 black hispan, r
. estout , cells(b(nostar fmt(5)) se(par fmt(5))) stats(r2 r2_a N, fmt(%9.3f %9.3f %9.0g) ///

----------------------------------------------
hetrosked       robust
b/se         b/se
----------------------------------------------
pcnv                     -0.13560     -0.13560
(0.04037)    (0.03362)
avgsen                    0.01784      0.01784
(0.00970)    (0.01012)
avgsensq                 -0.00052     -0.00052
(0.00030)    (0.00021)
ptime86                  -0.03936     -0.03936
(0.00869)    (0.00622)
qemp86                   -0.05051     -0.05051
(0.01443)    (0.01420)
inc86                    -0.00148     -0.00148
(0.00034)    (0.00023)
black                     0.32460      0.32460
(0.04542)    (0.05851)
hispan                    0.19338      0.19338
(0.03970)    (0.04030)
Constant                  0.56701      0.56701
(0.03606)    (0.04028)
----------------------------------------------
R-squared                   0.073        0.073
N                            2725         2725
----------------------------------------------
. est clear

. *LM Statistic  - not-robust (See Section 5-2)
. qui reg narr86 pcnv ptime86 qemp86 inc86 black hispan
. predict u, res
. reg u pcnv avgsen avgsensq ptime86 qemp86 inc86 black hispan

Source |       SS           df       MS      Number of obs   =     2,725
-------------+----------------------------------   F(8, 2716)      =      0.43
Model |  2.37155739         8  .296444674   Prob > F        =    0.9025
Residual |  1863.99804     2,716  .686302664   R-squared       =    0.0013
Total |  1866.36959     2,724  .685157707   Root MSE        =    .82843

------------------------------------------------------------------------------
u |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
pcnv |   -.003317   .0403699    -0.08   0.935    -.0824758    .0758418
avgsen |   .0178411    .009696     1.84   0.066    -.0011713    .0368534
avgsensq |  -.0005163    .000297    -1.74   0.082    -.0010987    .0000661
ptime86 |  -.0015647   .0086935    -0.18   0.857    -.0186112    .0154819
qemp86 |   .0004742   .0144345     0.03   0.974    -.0278295    .0287779
inc86 |   .0000103   .0003405     0.03   0.976    -.0006574     .000678
black |  -.0050861   .0454188    -0.11   0.911     -.094145    .0839729
hispan |  -.0020709   .0397035    -0.05   0.958    -.0799229    .0757812
_cons |  -.0033216   .0360573    -0.09   0.927    -.0740242    .0673809
------------------------------------------------------------------------------
. display as text "N*Rsq = " 2725*.0013
N*Rsq = 3.5425

. *LM Statistic  - robust
. foreach x of var avgsen avgsensq {
. qui reg `x'  pcnv ptime86 qemp86 inc86 black hispan
. predict r_`x', residual
. gen ures`x'= u*r_`x'
. }
. gen one=1
. reg one ures*, noc
Source |       SS           df       MS      Number of obs   =     2,725
-------------+----------------------------------   F(2, 2723)      =      2.00
Model |  3.99708536         2  1.99854268   Prob > F        =    0.1355
Residual |  2721.00291     2,723  .999266586   R-squared       =    0.0015
Total |        2725     2,725           1   Root MSE        =    .99963

------------------------------------------------------------------------------
one |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
uresavgsen |   .0277846   .0140598     1.98   0.048     .0002156    .0553537
uresavgsensq |  -.0010447   .0005479    -1.91   0.057     -.002119    .0000296
------------------------------------------------------------------------------

. display as text "N - SSR = " 2725 - 2721.0029
N - SSR = 3.9971

. *Example 8.4. Heteroskedasticity in Housing Price Equations
. u hprice1, clear
. reg price lotsize sqrft bdrms
Source |       SS           df       MS      Number of obs   =        88
-------------+----------------------------------   F(3, 84)        =     57.46
Model |  617130.701         3  205710.234   Prob > F        =    0.0000
Residual |  300723.805        84   3580.0453   R-squared       =    0.6724
Total |  917854.506        87  10550.0518   Root MSE        =    59.833

------------------------------------------------------------------------------
price |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lotsize |   .0020677   .0006421     3.22   0.002     .0007908    .0033446
sqrft |   .1227782   .0132374     9.28   0.000     .0964541    .1491022
bdrms |   13.85252   9.010145     1.54   0.128    -4.065141    31.77018
_cons |  -21.77031   29.47504    -0.74   0.462    -80.38466    36.84405
------------------------------------------------------------------------------

. predict u, res
. g u2=u^2
. reg u2 lotsize sqrft bdrms
Source |       SS           df       MS      Number of obs   =        88
-------------+----------------------------------   F(3, 84)        =      5.34
Model |   701213780         3   233737927   Prob > F        =    0.0020
Residual |  3.6775e+09        84  43780003.5   R-squared       =    0.1601
Total |  4.3787e+09        87  50330276.7   Root MSE        =    6616.6

------------------------------------------------------------------------------
u2 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lotsize |   .2015209   .0710091     2.84   0.006     .0603116    .3427302
sqrft |   1.691037    1.46385     1.16   0.251    -1.219989    4.602063
bdrms |    1041.76    996.381     1.05   0.299    -939.6526    3023.173
_cons |  -5522.795   3259.478    -1.69   0.094    -12004.62    959.0348
------------------------------------------------------------------------------

. display as text "LM = N*Rsq =" 88 * .1601
LM = N*Rsq =14.0888
. display chi2tail(3, 88*.1601)
.00278674

. reg lprice llotsize lsqrft bdrms
Source |       SS           df       MS      Number of obs   =        88
-------------+----------------------------------   F(3, 84)        =     50.42
Model |  5.15504028         3  1.71834676   Prob > F        =    0.0000
Residual |  2.86256324        84  .034078134   R-squared       =    0.6430
Total |  8.01760352        87  .092156362   Root MSE        =     .1846

------------------------------------------------------------------------------
lprice |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
llotsize |   .1679667   .0382812     4.39   0.000     .0918404     .244093
lsqrft |   .7002324   .0928652     7.54   0.000     .5155597    .8849051
bdrms |   .0369584   .0275313     1.34   0.183    -.0177906    .0917074
_cons |  -1.297042   .6512836    -1.99   0.050    -2.592191    -.001893
------------------------------------------------------------------------------
. predict lu, res
. g lu2=lu^2
. reg lu2 llotsize lsqrft bdrms
Source |       SS           df       MS      Number of obs   =        88
-------------+----------------------------------   F(3, 84)        =      1.41
Model |  .022620168         3  .007540056   Prob > F        =    0.2451
Residual |  .448717194        84  .005341871   R-squared       =    0.0480
Total |  .471337362        87  .005417671   Root MSE        =    .07309

------------------------------------------------------------------------------
lu2 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
llotsize |  -.0070156   .0151563    -0.46   0.645    -.0371556    .0231244
lsqrft |  -.0627368   .0367673    -1.71   0.092    -.1358526    .0103791
bdrms |   .0168407   .0109002     1.54   0.126    -.0048356     .038517
_cons |    .509994    .257857     1.98   0.051    -.0027829    1.022771
------------------------------------------------------------------------------

. display as text "LM = N*Rsq =" 88 * .048
LM = N*Rsq =4.224
. display chi2tail(3, 88*.048)
.23826999

. *Example 8.5. Special Form of the White Test
. u hprice1, clear
. reg lprice llotsize lsqrft bdrms
Source |       SS           df       MS      Number of obs   =        88
-------------+----------------------------------   F(3, 84)        =     50.42
Model |  5.15504028         3  1.71834676   Prob > F        =    0.0000
Residual |  2.86256324        84  .034078134   R-squared       =    0.6430
Total |  8.01760352        87  .092156362   Root MSE        =     .1846

------------------------------------------------------------------------------
lprice |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
llotsize |   .1679667   .0382812     4.39   0.000     .0918404     .244093
lsqrft |   .7002324   .0928652     7.54   0.000     .5155597    .8849051
bdrms |   .0369584   .0275313     1.34   0.183    -.0177906    .0917074
_cons |  -1.297042   .6512836    -1.99   0.050    -2.592191    -.001893
------------------------------------------------------------------------------

. predict u, res
. g u2=u^2
. predict y, xb
. gen y2 = y^2
. reg u2 y y2
Source |       SS           df       MS      Number of obs   =        88
-------------+----------------------------------   F(2, 85)        =      1.73
Model |  .018463986         2  .009231993   Prob > F        =    0.1830
Residual |  .452873375        85  .005327922   R-squared       =    0.0392
Total |  .471337362        87  .005417671   Root MSE        =    .07299

------------------------------------------------------------------------------
u2 |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
y |  -1.709221   1.163334    -1.47   0.145    -4.022241    .6037986
y2 |   .1451354   .1009925     1.44   0.154    -.0556647    .3459354
_cons |   5.046839   3.345002     1.51   0.135    -1.603921     11.6976
------------------------------------------------------------------------------

. display as text "LM = N*Rsq =" 88 * .0392
LM = N*Rsq =3.4496
. display chi2tail(2, 88*.0392)
.17820869

.*Example 8.6. Financial Wealth Equation
. u 401ksubs, clear
. keep if fsize==1
(7,258 observations deleted)
. g age25sq=(age-25)^2
. eststo OLS1: qui reg nettfa inc, r
. eststo WLS1: qui reg nettfa inc [aw=1/inc]
. eststo OLS2: qui reg nettfa inc age25sq male e401k, r
. eststo WLS2: qui reg nettfa inc age25sq male e401k [aw=1/inc]
. estout , cells(b(nostar fmt(5)) se(par fmt(5))) stats(r2 N, fmt(%9.3f %9.0g) labels(R-squared ///
Adj-R-squared)) varlabels(_cons Constant) varwidth(20) ti(Table 8.1 Dependent Variable: nettfa)

Table 8.1 Dependent Variable: nettfa
------------------------------------------------------------------------
OLS1         WLS1         OLS2         WLS2
b/se         b/se         b/se         b/se
------------------------------------------------------------------------
inc                       0.82068      0.78705      0.77058      0.74038
(0.10359)    (0.06348)    (0.09957)    (0.06430)
age25sq                                             0.02513      0.01754
(0.00434)    (0.00193)
male                                                2.47793      1.84053
(2.05836)    (1.56359)
e401k                                               6.88622      5.18828
(2.28658)    (1.70343)
Constant                -10.57095     -9.58070    -20.98499    -16.70252
(2.53027)    (1.65328)    (3.49519)    (1.95799)
------------------------------------------------------------------------
R-squared                   0.083        0.071        0.128        0.112
------------------------------------------------------------------------
. est clear

. *Example 8.7. Demand for Cigarettes
. u smoke, clear
. local x "lincome lcigpric educ age agesq restaurn"
. eststo OLS: reg cigs `x'
Source |       SS           df       MS      Number of obs   =       807
-------------+----------------------------------   F(6, 800)       =      7.42
Model |  8003.02506         6  1333.83751   Prob > F        =    0.0000
Residual |  143750.658       800  179.688322   R-squared       =    0.0527
Total |  151753.683       806  188.280003   Root MSE        =    13.405

------------------------------------------------------------------------------
cigs |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lincome |   .8802682   .7277832     1.21   0.227     -.548322    2.308858
lcigpric |  -.7508586   5.773343    -0.13   0.897    -12.08355    10.58183
educ |  -.5014982   .1670772    -3.00   0.003    -.8294597   -.1735368
age |   .7706936   .1601223     4.81   0.000      .456384    1.085003
agesq |  -.0090228    .001743    -5.18   0.000    -.0124443   -.0056013
restaurn |  -2.825085   1.111794    -2.54   0.011    -5.007462   -.6427078
_cons |  -3.639841   24.07866    -0.15   0.880    -50.90466    43.62497
------------------------------------------------------------------------------
. predict u, res
. gen lu2=ln(u^2)
. qui reg lu2 `x'
. predict lu2h, xb
. g e_lu2h=exp(lu2h)
. eststo GLS: reg cigs `x' [aw=1/e_lu2h]
(sum of wgt is 19.97738570454038)

Source |       SS           df       MS      Number of obs   =       807
-------------+----------------------------------   F(6, 800)       =     17.06
Model |   10302.646         6  1717.10767   Prob > F        =    0.0000
Residual |   80542.159       800  100.677699   R-squared       =    0.1134
Total |   90844.805       806  112.710676   Root MSE        =    10.034

------------------------------------------------------------------------------
cigs |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lincome |    1.29524   .4370118     2.96   0.003     .4374148    2.153065
lcigpric |  -2.940312   4.460144    -0.66   0.510    -11.69528    5.814656
educ |  -.4634463   .1201587    -3.86   0.000    -.6993099   -.2275828
age |   .4819479   .0968082     4.98   0.000     .2919197     .671976
agesq |  -.0056272   .0009395    -5.99   0.000    -.0074713   -.0037831
restaurn |  -3.461064    .795505    -4.35   0.000    -5.022588   -1.899541
_cons |   5.635463   17.80314     0.32   0.752    -29.31092    40.58184
------------------------------------------------------------------------------

. estout , cells(b(nostar fmt(5)) se(par fmt(5))) stats(r2 r2_a N, fmt(%9.3f %9.3f %9.0g)
> labels(R-squared Adj-R-squared)) varlabels(_cons Constant) varwidth(20)

----------------------------------------------
OLS          GLS
b/se         b/se
----------------------------------------------
lincome                   0.88027      1.29524
(0.72778)    (0.43701)
lcigpric                 -0.75086     -2.94031
(5.77334)    (4.46014)
educ                     -0.50150     -0.46345
(0.16708)    (0.12016)
age                       0.77069      0.48195
(0.16012)    (0.09681)
agesq                    -0.00902     -0.00563
(0.00174)    (0.00094)
restaurn                 -2.82508     -3.46106
(1.11179)    (0.79550)
Constant                 -3.63984      5.63546
(24.07866)   (17.80314)
----------------------------------------------
R-squared                   0.053        0.113
N                             807          807
----------------------------------------------
. est clear

. *Example 8.8. Labor Force Participation of Married Women
. u mroz, clear
. local x "nwifeinc educ exper* age kidslt6 kidsge6"
. eststo heterosked: qui reg inlf `x'
. eststo Robust: qui reg inlf `x', r

. estout , cells(b(nostar fmt(5)) se(par fmt(5))) stats(r2 N, fmt(%9.3f %9.0g) labels(R-squared ///

----------------------------------------------
heterosked       Robust
b/se         b/se
----------------------------------------------
nwifeinc                 -0.00341     -0.00341
(0.00145)    (0.00152)
educ                      0.03800      0.03800
(0.00738)    (0.00727)
exper                     0.03949      0.03949
(0.00567)    (0.00581)
expersq                  -0.00060     -0.00060
(0.00018)    (0.00019)
age                      -0.01609     -0.01609
(0.00248)    (0.00240)
kidslt6                  -0.26181     -0.26181
(0.03351)    (0.03178)
kidsge6                   0.01301      0.01301
(0.01320)    (0.01353)
Constant                  0.58552      0.58552
(0.15418)    (0.15226)
----------------------------------------------
R-squared                   0.264        0.264
----------------------------------------------
. est clear

. *Example 8.9. Determinants of Personal Computer Ownership
. u gpa1, clear
. g parcoll = ( fathcoll==1 | mothcoll==1)
. eststo heterosked: qui reg PC hsGPA ACT parcoll
. eststo Robust: qui reg PC hsGPA ACT parcoll, r

. estout, cells(b(nostar fmt(5)) se(par fmt(5))) stats(r2 N, fmt(%9.3f %9.0g) labels(R-squared ///

----------------------------------------------
heterosked       Robust
b/se         b/se
----------------------------------------------
hsGPA                     0.06539      0.06539
(0.13726)    (0.14149)
ACT                       0.00056      0.00056
(0.01550)    (0.01607)
parcoll                   0.22105      0.22105
(0.09296)    (0.08804)
Constant                 -0.00043     -0.00043
(0.49054)    (0.49588)
----------------------------------------------
R-squared                   0.042        0.042
----------------------------------------------
. est clear

. qui reg PC hsGPA ACT parcoll
. predict yhat, xb
. gen hhat = yhat*(1-yhat)
. reg PC hsGPA ACT parcoll [aw=1/hhat]
(sum of wgt is 628.1830743667747)

Source |       SS           df       MS      Number of obs   =       141
-------------+----------------------------------   F(3, 137)       =      2.22
Model |  1.54663033         3  .515543445   Prob > F        =    0.0882
Residual |  31.7573194       137  .231805251   R-squared       =    0.0464
Total |  33.3039497       140  .237885355   Root MSE        =    .48146

------------------------------------------------------------------------------
PC |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
hsGPA |   .0327029   .1298817     0.25   0.802    -.2241292     .289535
ACT |    .004272   .0154527     0.28   0.783    -.0262847    .0348286
parcoll |   .2151862   .0862918     2.49   0.014       .04455    .3858224
_cons |   .0262099   .4766498     0.05   0.956    -.9163323    .9687521
------------------------------------------------------------------------------

. log close
name:  SN
log:  ~Wooldridge\intro-econx\iexample8.smcl
log type:  smcl
closed on:   9 Jan 2019, 21:10:28
------------------------------------------------------------------------------------------
```

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