## INTRODUCTORY ECONOMETRICS – REPLICATING EXAMPLES

### Chapter 6 – Examples

```-------------------------------------------------------------------------------------
name:  SN
log:  ~Wooldridge\intro-econx\iexample6.smcl
log type:  smcl
opened on:   8 Jan 2019, 01:36:36
**********************************************
* Solomon Negash - Replicating Examples
* Wooldridge (2016). Introductory Econometrics: A Modern Approach. 6th ed.
* STATA Program, version 15.1.

* Chapter 6  - Multiple Regression Analysis: Further Analysis
* Computer Exercises (Examples)
******************** SETUP *********************

*Table6.1  Determinants of College GPA
u bwght, clear
eststo: qui reg bwght cigs faminc
(est1 stored)
eststo: qui reg bwghtlb cigs faminc
(est2 stored)
eststo: qui reg bwght packs faminc
(est3 stored)
esttab *, se r2 nostar ti("Compare to Table6.1 'Effects of Data Scaling'")

Compare to Table6.1 'Effects of Data Scaling'
---------------------------------------------------
(1)          (2)          (3)
bwght     bwghtlbs        bwght
---------------------------------------------------
cigs               -0.463      -0.0290
(0.0916)    (0.00572)
faminc             0.0928      0.00580       0.0928
(0.0292)    (0.00182)     (0.0292)
packs                                        -9.268
(1.832)
_cons               117.0        7.311        117.0
(1.049)     (0.0656)      (1.049)
---------------------------------------------------
N                    1388         1388         1388
R-sq                0.030        0.030        0.030
---------------------------------------------------
Standard errors in parentheses
est clear

*Example6.1. Effects of pollution on housing prices
u hprice2, clear
//Standardizing the variables
foreach x of varlist price nox crime rooms dist stratio  {
egen z`x'= std(`x')
label var z`x' "`x' - standardized"
}
reg zprice znox zcrime zrooms zdist zstratio
Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(5, 500)       =    174.47
Model |  321.011232         5  64.2022464   Prob > F        =    0.0000
Residual |  183.988778       500  .367977557   R-squared       =    0.6357
-------------+----------------------------------   Adj R-squared   =    0.6320
Total |   505.00001       505  1.00000002   Root MSE        =    .60661
------------------------------------------------------------------------------
zprice |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
znox |   -.340446   .0445411    -7.64   0.000    -.4279568   -.2529352
zcrime |  -.1432828   .0307168    -4.66   0.000    -.2036327   -.0829328
zrooms |   .5138878   .0300302    17.11   0.000      .454887    .5728887
zdist |  -.2348385   .0430217    -5.46   0.000    -.3193642   -.1503129
zstratio |  -.2702799   .0299698    -9.02   0.000    -.3291622   -.2113976
_cons |   6.61e-09   .0269672     0.00   1.000    -.0529829    .0529829
------------------------------------------------------------------------------
//Compare the result to Example 4.5.
g ldist=ln(dist)
reg  lprice lnox ldist rooms stratio
Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(4, 501)       =    175.86
Model |  49.3987586         4  12.3496897   Prob > F        =    0.0000
Residual |  35.1834663       501   .07022648   R-squared       =    0.5840
-------------+----------------------------------   Adj R-squared   =    0.5807
Total |   84.582225       505  .167489554   Root MSE        =      .265
------------------------------------------------------------------------------
lprice |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnox |  -.9535388   .1167417    -8.17   0.000    -1.182902   -.7241751
ldist |  -.1343395   .0431032    -3.12   0.002    -.2190247   -.0496542
rooms |   .2545271   .0185303    13.74   0.000     .2181203    .2909338
stratio |  -.0524511   .0058971    -8.89   0.000    -.0640372    -.040865
_cons |   11.08386   .3181113    34.84   0.000     10.45887    11.70886
------------------------------------------------------------------------------

//Equation (6.7)
reg lprice lnox rooms
Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(2, 503)       =    265.69
Model |  43.4513652         2  21.7256826   Prob > F        =    0.0000
Residual |  41.1308598       503  .081771093   R-squared       =    0.5137
-------------+----------------------------------   Adj R-squared   =    0.5118
Total |   84.582225       505  .167489554   Root MSE        =    .28596
------------------------------------------------------------------------------
lprice |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnox |  -.7176736   .0663397   -10.82   0.000    -.8480106   -.5873366
rooms |   .3059183   .0190174    16.09   0.000      .268555    .3432816
_cons |   9.233738   .1877406    49.18   0.000     8.864885     9.60259
------------------------------------------------------------------------------

//Equation (6.12)
u wage1, clear
reg wage exper*
Source |       SS           df       MS      Number of obs   =       526
-------------+----------------------------------   F(2, 523)       =     26.74
Model |  664.266927         2  332.133463   Prob > F        =    0.0000
Residual |  6496.14736       523  12.4209319   R-squared       =    0.0928
-------------+----------------------------------   Adj R-squared   =    0.0893
Total |  7160.41429       525  13.6388844   Root MSE        =    3.5243
------------------------------------------------------------------------------
wage |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
exper |   .2981001   .0409655     7.28   0.000     .2176229    .3785773
expersq |  -.0061299   .0009025    -6.79   0.000    -.0079029   -.0043569
_cons |   3.725406   .3459392    10.77   0.000     3.045805    4.405007
------------------------------------------------------------------------------

*Example6.2. Effects of pollution on housing prices
u hprice2, clear
g ldis=ln(dist)
g roomsq = rooms^2
reg lprice lnox ldis rooms roomsq stratio
Source |       SS           df       MS      Number of obs   =       506
-------------+----------------------------------   F(5, 500)       =    151.77
Model |  50.9872375         5  10.1974475   Prob > F        =    0.0000
Residual |  33.5949875       500  .067189975   R-squared       =    0.6028
-------------+----------------------------------   Adj R-squared   =    0.5988
Total |   84.582225       505  .167489554   Root MSE        =    .25921
------------------------------------------------------------------------------
lprice |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnox |   -.901682   .1146869    -7.86   0.000     -1.12701   -.6763544
ldis |  -.0867814   .0432807    -2.01   0.045    -.1718159    -.001747
rooms |  -.5451128   .1654542    -3.29   0.001    -.8701839   -.2200417
roomsq |   .0622612    .012805     4.86   0.000      .037103    .0874194
stratio |  -.0475902   .0058542    -8.13   0.000     -.059092   -.0360884
_cons |   13.38548   .5664732    23.63   0.000     12.27252    14.49844
------------------------------------------------------------------------------

*Example6.3. Effects of attendance on final exam performance
u attend, clear
g priGPAsq = priGPA^2
g ACTsq = ACT^2
eststo stndfnl: qui reg stndfnl atndrte priGPA ACT priGPAsq ACTsq c.priGPA#c.atndrte
estout , cells(b(nostar fmt(3)) 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(25)
--------------------------------------
stndfnl
b/se
--------------------------------------
atndrte                         -0.007
(0.01023)
priGPA                          -1.629
(0.48100)
ACT                             -0.128
(0.09849)
priGPAsq                         0.296
(0.10105)
ACTsq                            0.005
(0.00218)
c.priGPA#c.atndrte               0.006
(0.00432)
Constant                         2.050
(1.36032)
--------------------------------------
R-squared                        0.229
N                                  680
--------------------------------------
est clear

*Example6.4. CEO compensation and frim perfromance
u ceosal1.dta, clear
eststo salary: qui reg salary sales roe
eststo lsalary: qui reg lsalary lsales roe
estout , cells(b(nostar fmt(3)) 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(25)
---------------------------------------------------
salary      lsalary
b/se         b/se
---------------------------------------------------
sales                            0.016
(0.00887)
roe                             19.631        0.018
(11.07655)    (0.00396)
lsales                                        0.275
(0.03325)
Constant                       830.631        4.362
(223.90489)    (0.29388)
---------------------------------------------------
R-squared                        0.029        0.282
N                                  209          209
---------------------------------------------------
est clear

*Example6.5. Confidence interval for predicted college GPA
u gpa2, clear
eststo regression: reg colgpa sat hsperc hsize c.hsize#c.hsize
Source |       SS           df       MS      Number of obs   =     4,137
-------------+----------------------------------   F(4, 4132)      =    398.02
Model |  499.030504         4  124.757626   Prob > F        =    0.0000
Residual |  1295.16517     4,132  .313447524   R-squared       =    0.2781
-------------+----------------------------------   Adj R-squared   =    0.2774
Total |  1794.19567     4,136  .433799728   Root MSE        =    .55986
---------------------------------------------------------------------------------
colgpa |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
sat |   .0014925   .0000652    22.89   0.000     .0013646    .0016204
hsperc |  -.0138558    .000561   -24.70   0.000    -.0149557   -.0127559
hsize |  -.0608815   .0165012    -3.69   0.000    -.0932328   -.0285302
c.hsize#c.hsize |   .0054603   .0022698     2.41   0.016     .0010102    .0099104
_cons |   1.492652   .0753414    19.81   0.000     1.344942    1.640362
---------------------------------------------------------------------------------
g sat0 = sat - 1200
g hsperc0 = hsperc - 30
g hsize0 = hsize -5
eststo prediction: reg colgpa sat0 hsperc0 hsize0 c.hsize0#c.hsize0
Source |       SS           df       MS      Number of obs   =     4,137
-------------+----------------------------------   F(4, 4132)      =    398.02
Model |  499.030503         4  124.757626   Prob > F        =    0.0000
Residual |  1295.16517     4,132  .313447524   R-squared       =    0.2781
-------------+----------------------------------   Adj R-squared   =    0.2774
Total |  1794.19567     4,136  .433799728   Root MSE        =    .55986
-----------------------------------------------------------------------------------
colgpa |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
------------------+----------------------------------------------------------------
sat0 |   .0014925   .0000652    22.89   0.000     .0013646    .0016204
hsperc0 |  -.0138558    .000561   -24.70   0.000    -.0149557   -.0127559
hsize0 |  -.0062785   .0086006    -0.73   0.465    -.0231403    .0105833
c.hsize0#c.hsize0 |   .0054603   .0022698     2.41   0.016     .0010102    .0099104
_cons |   2.700075   .0198778   135.83   0.000     2.661104    2.739047
-----------------------------------------------------------------------------------

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(25)
---------------------------------------------------
regression   prediction
b/se         b/se
---------------------------------------------------
sat                            0.00149
(0.00007)
hsperc                        -0.01386
(0.00056)
hsize                         -0.06088
(0.01650)
c.hsize#c.hsize                0.00546
(0.00227)
sat0                                        0.00149
(0.00007)
hsperc0                                    -0.01386
(0.00056)
hsize0                                     -0.00628
(0.00860)
c.hsize0#c.hsize0                           0.00546
(0.00227)
Constant                       1.49265      2.70008
(0.07534)    (0.01988)
---------------------------------------------------
R-squared                        0.278        0.278
N                                 4137         4137
---------------------------------------------------
est clear

*Example6.6. Confidence Interval for Future Collage GPA
u gpa2, clear
reg colgpa sat hsperc hsize c.hsize#c.hsize
Source |       SS           df       MS      Number of obs   =     4,137
-------------+----------------------------------   F(4, 4132)      =    398.02
Model |  499.030504         4  124.757626   Prob > F        =    0.0000
Residual |  1295.16517     4,132  .313447524   R-squared       =    0.2781
-------------+----------------------------------   Adj R-squared   =    0.2774
Total |  1794.19567     4,136  .433799728   Root MSE        =    .55986
---------------------------------------------------------------------------------
colgpa |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
sat |   .0014925   .0000652    22.89   0.000     .0013646    .0016204
hsperc |  -.0138558    .000561   -24.70   0.000    -.0149557   -.0127559
hsize |  -.0608815   .0165012    -3.69   0.000    -.0932328   -.0285302
c.hsize#c.hsize |   .0054603   .0022698     2.41   0.016     .0010102    .0099104
_cons |   1.492652   .0753414    19.81   0.000     1.344942    1.640362
---------------------------------------------------------------------------------
margins, at(sat = 1200 hsperc = 30 hsize = 5 )
Adjusted predictions                            Number of obs     =      4,137
Model VCE    : OLS
Expression   : Linear prediction, predict()
at           : sat             =        1200
hsperc          =          30
hsize           =           5
------------------------------------------------------------------------------
|            Delta-method
|     Margin   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
_cons |   2.700075   .0198778   135.83   0.000     2.661104    2.739047
------------------------------------------------------------------------------

display as text "Root MSE = "  e(rmse)
Root MSE = .55986384
predict u, res
gen u2 = u^2
mean u2
Mean estimation                   Number of obs   =      4,137
--------------------------------------------------------------
|       Mean   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
u2 |   .3130687   .0078993      .2975818    .3285556
--------------------------------------------------------------
display sqrt(.313)
55946403

//The 95% CI
display as text "Lower Bound = " 2.7 - 1.96*.56
Lower Bound = 1.6024
display as text "Upper Bound = " 2.7 + 1.96*.56
Upper Bound = 3.7976

*Example6.7. Predicting CEO log(salary)
u ceosal2.dta, clear

*Step 1
reg lsalary lsales lmktval ceoten
Source |       SS           df       MS      Number of obs   =       177
-------------+----------------------------------   F(3, 173)       =     26.91
Model |  20.5672434         3  6.85574779   Prob > F        =    0.0000
Residual |  44.0789697       173  .254791732   R-squared       =    0.3182
-------------+----------------------------------   Adj R-squared   =    0.3063
Total |  64.6462131       176  .367308029   Root MSE        =    .50477
------------------------------------------------------------------------------
lsalary |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
lsales |   .1628545   .0392421     4.15   0.000     .0853995    .2403094
lmktval |    .109243   .0495947     2.20   0.029     .0113545    .2071315
ceoten |   .0117054   .0053261     2.20   0.029      .001193    .0222178
_cons |   4.503795   .2572344    17.51   0.000     3.996073    5.011517
------------------------------------------------------------------------------
predict lsalaryhat, xb
predict uhat, residual

*Step 2
g euhat=exp(uhat)
mean euhat //The Duan smearing estimate (alpha_hat_0)
Mean estimation                   Number of obs   =        177
--------------------------------------------------------------
|       Mean   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
euhat |   1.135661   .0523938       1.03226    1.239062
--------------------------------------------------------------
g mhat=exp(lsalaryhat)
reg salary mhat,noc // The coef. as in equation 46.44
Source |       SS           df       MS      Number of obs   =       177
-------------+----------------------------------   F(1, 176)       =    562.39
Model |   147352711         1   147352711   Prob > F        =    0.0000
Residual |    46113901       176  262010.801   R-squared       =    0.7616
-------------+----------------------------------   Adj R-squared   =    0.7603
Total |   193466612       177  1093031.71   Root MSE        =    511.87
------------------------------------------------------------------------------
salary |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
mhat |   1.116857   .0470953    23.71   0.000     1.023912    1.209801
------------------------------------------------------------------------------

*Step 3
qui reg lsalary lsales lmktval ceoten
display _b[_cons]+_b[lsales]*log(5000)+_b[lmktval]*log(10000)+_b[ceoten]*10
7.0140771

*Step 4
qui reg salary mhat, noc
display 1.136*exp(7.013) //or
1262.0761
display 1.117*exp(7.013)
1240.9674

*Example6.8. PRedicting CEO salary
corr mhat salary,
(obs=177)
|     mhat   salary
-------------+------------------
mhat |   1.0000
salary |   0.4930   1.0000
u ceosal2.dta, clear
reg salary sales mktval ceoten
Source |       SS           df       MS      Number of obs   =       177
-------------+----------------------------------   F(3, 173)       =     14.53
Model |  12230632.6         3  4076877.52   Prob > F        =    0.0000
Residual |  48535332.2       173  280551.053   R-squared       =    0.2013
-------------+----------------------------------   Adj R-squared   =    0.1874
Total |  60765964.7       176  345261.163   Root MSE        =    529.67
------------------------------------------------------------------------------
salary |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
sales |   .0190191   .0100561     1.89   0.060    -.0008294    .0388676
mktval |   .0234003   .0094826     2.47   0.015     .0046839    .0421167
ceoten |   12.70337   5.618052     2.26   0.025     1.614616    23.79211
_cons |   613.4361   65.23685     9.40   0.000     484.6735    742.1987
------------------------------------------------------------------------------

log close
name:  SN
log:  ~Wooldridge\intro-econx\iexample6.smcl
log type:  smcl
closed on:   8 Jan 2019, 01:36:37
-------------------------------------------------------------------------------------
```