From: Subject: Stata: Econometric Analysis by William Greene, Chapter 12 Date: Wed, 26 Sep 2007 00:23:09 -0500 MIME-Version: 1.0 Content-Type: multipart/related; type="text/html"; boundary="----=_NextPart_000_0000_01C7FFD3.6ADED800" X-MimeOLE: Produced By Microsoft MimeOLE V6.00.2900.3138 This is a multi-part message in MIME format. ------=_NextPart_000_0000_01C7FFD3.6ADED800 Content-Type: text/html; charset="Windows-1252" Content-Transfer-Encoding: quoted-printable Content-Location: http://www.ats.ucla.edu/stat/Stata/examples/greene/greene12.htm Stata: Econometric Analysis by William Greene, = Chapter 12
3D"UCLA 3DHome
Stat = Computing > Stata=20 > Textbook=20 Examples > Econome= tric=20 Analysis, Fourth Edition by Greene
3DSearch=20

Stata Textbook Examples
Econometric Analysis, Fourth Edition by = William=20 Greene
Chapter 12: Heteroscedasticity

use =
http://www.ats.ucla.edu/stat/stata/examples/greene/TBL5-1, clear

rename x1 age
rename x2 income
rename x3 exp
rename x4 ownrent
rename x5 selfemp

generate incomesq =3D income^2
drop if exp=3D=3D0
save chapter12
Table 12.1, page 500. OLS.
regress exp =
age ownrent income incomesq

      Source |       SS       df       MS              Number of obs =3D =
     72
-------------+------------------------------           F(  4,    67) =3D =
   5.39
       Model |  1749357.01     4  437339.252           Prob > F      =
=3D  0.0008
    Residual |  5432562.03    67  81083.0153           R-squared     =3D =
 0.2436
-------------+------------------------------           Adj R-squared =3D =
 0.1984
       Total |  7181919.03    71  101153.789           Root MSE      =3D =
 284.75

-------------------------------------------------------------------------=
-----
         exp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. =
Interval]
-------------+-----------------------------------------------------------=
-----
         age |  -3.081814   5.514717    -0.56   0.578    -14.08923    =
7.925606
     ownrent |   27.94091   82.92232     0.34   0.737    -137.5727    =
193.4546
      income |    234.347   80.36595     2.92   0.005     73.93593    =
394.7581
    incomesq |  -14.99684   7.469337    -2.01   0.049     -29.9057   =
-.0879859
       _cons |  -237.1465   199.3517    -1.19   0.238    -635.0541    =
160.7611
-------------------------------------------------------------------------=
-----
Figure 12.1, Residuals Against Income, page = 500.
rvpplot income, xlabel(0(2)12) xline(2 4 6 8 =
10) ylabel(-500(500)2000) yline(0 500 1000 1500)
Table 12.2, Least squares, page 506. See results for Table = 12.1=20 above.
Table 12.2, Davidson/MacKinnon(1), page = 506.
regress exp age ownrent income incomesq, =
robust

Regression with robust standard errors                 Number of obs =3D =
     72
                                                       F(  4,    67) =3D =
  12.51
                                                       Prob > F      =
=3D  0.0000
                                                       R-squared     =3D =
 0.2436
                                                       Root MSE      =3D =
 284.75

-------------------------------------------------------------------------=
-----
             |               Robust
         exp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. =
Interval]
-------------+-----------------------------------------------------------=
-----
         age |  -3.081814   3.422641    -0.90   0.371    -9.913434    =
3.749805
     ownrent |   27.94091   95.56573     0.29   0.771    -162.8091    =
218.6909
      income |    234.347   92.12261     2.54   0.013     50.46954    =
418.2245
    incomesq |  -14.99684   7.199027    -2.08   0.041    -29.36616   =
-.6275259
       _cons |  -237.1465    220.795    -1.07   0.287    -677.8551    =
203.5621
-------------------------------------------------------------------------=
-----
Table 12.2, White, page 506. The White standard errors are = just a=20 rescaling of the Davidson/MacKinnon(1) standard errors by = sqrt((N-k)/N). We=20 will use some matrix commands to perform the = computation.
matrix d =3D vecdiag(e(V))
matrix v =3D  cholesky(diag(d))
matrix s =3D sqrt((72-5)/72)*vecdiag(v)
matrix list s

s[1,5]
          age    ownrent     income   incomesq      _cons
r1  3.3016611  92.187776  88.866358  6.9445639  212.99053
Table 12.2, Davidson/MacKinnon(2), page = 506.
regress exp age ownrent income incomesq, =
hc2

Regression with robust standard errors                 Number of obs =3D =
     72
                                                       F(  4,    67) =3D =
  12.06
                                                       Prob > F      =
=3D  0.0000
                                                       R-squared     =3D =
 0.2436
                                                       Root MSE      =3D =
 284.75

-------------------------------------------------------------------------=
-----
             |             Robust HC2
         exp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. =
Interval]
-------------+-----------------------------------------------------------=
-----
         age |  -3.081814   3.447715    -0.89   0.375    -9.963482    =
3.799853
     ownrent |   27.94091   95.67211     0.29   0.771    -163.0214    =
218.9032
      income |    234.347   92.08369     2.54   0.013     50.54722    =
418.1468
    incomesq |  -14.99684   7.199538    -2.08   0.041    -29.36718   =
-.6265067
       _cons |  -237.1465   221.0889    -1.07   0.287    -678.4419    =
204.1488
-------------------------------------------------------------------------=
-----
Example 12.5, page 510. Uses whitetst and = bpagan=20 commands by Christopher F. Baum and Nichols J. Cox. Use findit = whitetst=20 to locate programs and download the program (see How can I = use the=20 findit command to search for programs and get additional help? for = more=20 information about using = findit).
whitetst

White's general test statistic :  14.32893  Chi-sq(12)  P-value =3D  =
.2802

bpagan income incomesq
=20
Breusch-Pagan LM statistic:  41.92031  Chi-sq( 2)  P-value =3D  =
7.9e-10
Table 12.3, page 515 OLS. See results for Table 12.1=20 above.
Table 12.3, page 515. In the sections below we will show how = to=20 manually compute each of the results from Greene. It is also possible = to=20 compute these results using the wls0 command. You can download=20 wls0 by typing findit wls0 (see How can I = use the=20 findit command to search for programs and get additional help? for = more=20 information about using findit).
wls0 exp =
age ownrent income incomesq , wvar(income) type(abse) noconst        =
  /* 12.3a */
wls0 exp age ownrent income incomesq , wvar(incomesq) type(abse) =
noconst        /* 12.3b */
wls0 exp age ownrent income incomesq , wvar(income incomesq) type(e2) =
noconst   /* 12.3c */
wls0 exp age ownrent income incomesq , wvar(income incomesq) =
type(abse) noconst /* 12.3d */
wls0 exp age ownrent income incomesq , wvar(income incomesq) =
type(loge2)        /* 12.3e */
wls0 exp age ownrent income incomesq , wvar(income incomesq) =
type(xb2)          /* 12.3h */
Table 12.3a, page 515, Proportional to = income.
regress exp age ownrent income incomesq [aw =
=3D 1/income]

(sum of wgt is   2.4956e+01)

      Source |       SS       df       MS              Number of obs =3D =
     72
-------------+------------------------------           F(  4,    67) =3D =
   5.73
       Model |  1266234.79     4  316558.697           Prob > F      =
=3D  0.0005
    Residual |  3703808.18    67   55280.719           R-squared     =3D =
 0.2548
-------------+------------------------------           Adj R-squared =3D =
 0.2103
       Total |  4970042.96    71  70000.6051           Root MSE      =3D =
 235.12

-------------------------------------------------------------------------=
-----
         exp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. =
Interval]
-------------+-----------------------------------------------------------=
-----
         age |  -2.935011   4.603331    -0.64   0.526     -12.1233    =
6.253276
     ownrent |   50.49364   69.87914     0.72   0.472     -88.9857     =
189.973
      income |   202.1694   76.78152     2.63   0.010     48.91285     =
355.426
    incomesq |  -12.11364    8.27314    -1.46   0.148    -28.62689     =
4.39962
       _cons |  -181.8706   165.5191    -1.10   0.276    -512.2481    =
148.5068
-------------------------------------------------------------------------=
-----
Table 12.3b, page 515, Proportional to = incomes.
regress exp age ownrent income incomesq [aw =
=3D 1/incomesq]

(sum of wgt is   9.9041e+00)

      Source |       SS       df       MS              Number of obs =3D =
     72
-------------+------------------------------           F(  4,    67) =3D =
   5.73
       Model |  818838.837     4  204709.709           Prob > F      =
=3D  0.0005
    Residual |  2393372.15    67  35721.9724           R-squared     =3D =
 0.2549
-------------+------------------------------           Adj R-squared =3D =
 0.2104
       Total |  3212210.99    71  45242.4083           Root MSE      =3D =
 189.00

-------------------------------------------------------------------------=
-----
         exp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. =
Interval]
-------------+-----------------------------------------------------------=
-----
         age |  -2.694185   3.807306    -0.71   0.482     -10.2936     =
4.90523
     ownrent |   60.44877   58.55089     1.03   0.306    -56.41929    =
177.3168
      income |    158.427   76.39115     2.07   0.042     5.949597    =
310.9044
    incomesq |  -7.249289   9.724337    -0.75   0.459    -26.65915    =
12.16057
       _cons |  -114.1089   139.6875    -0.82   0.417    -392.9263    =
164.7085
-------------------------------------------------------------------------=
-----
Table 12.3c, page 515, Proportional to e^2. = 
regress exp age ownrent income incomesq

(output omitted)

predict e, resid
generate ee=3De^2
regress ee income incomesq, noconst
(output omitted)

predict p1
regress exp age ownrent income incomesq [aw =3D 1/p1]

(sum of wgt is   8.8046e-04)

      Source |       SS       df       MS              Number of obs =3D =
     72
-------------+------------------------------           F(  4,    67) =3D =
   5.93
       Model |  1454610.68     4  363652.671           Prob > F      =
=3D  0.0004
    Residual |  4111300.41    67  61362.6927           R-squared     =3D =
 0.2613
-------------+------------------------------           Adj R-squared =3D =
 0.2172
       Total |  5565911.10    71  78393.1141           Root MSE      =3D =
 247.71

-------------------------------------------------------------------------=
-----
         exp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. =
Interval]
-------------+-----------------------------------------------------------=
-----
         age |  -2.999273   4.842381    -0.62   0.538    -12.66471    =
6.666161
     ownrent |   45.10975   73.42671     0.61   0.541    -101.4506    =
191.6701
      income |   211.7943   73.52172     2.88   0.005     65.04438    =
358.5443
    incomesq |  -13.12857   7.233661    -1.81   0.074    -27.56702    =
1.309876
       _cons |  -196.0429   169.4295    -1.16   0.251    -534.2255    =
142.1398
-------------------------------------------------------------------------=
-----
Table 12.3d, page 515, Proportional to abs(e). = 
generate abse=3Dabs(e)
regress abse income incomesq, noconst
(output omitted)

predict p2
regress exp age ownrent income incomesq [aw =3D 1/p2]

(sum of wgt is   4.3021e-01)

      Source |       SS       df       MS              Number of obs =3D =
     72
-------------+------------------------------           F(  4,    67) =3D =
   6.37
       Model |  1626419.83     4  406604.957           Prob > F      =
=3D  0.0002
    Residual |  4277725.69    67  63846.6521           R-squared     =3D =
 0.2755
-------------+------------------------------           Adj R-squared =3D =
 0.2322
       Total |  5904145.52    71  83156.9792           Root MSE      =3D =
 252.68

-------------------------------------------------------------------------=
-----
         exp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. =
Interval]
-------------+-----------------------------------------------------------=
-----
         age |  -3.038906   4.953024    -0.61   0.542    -12.92518     =
6.84737
     ownrent |   41.89772   75.32687     0.56   0.580    -108.4553    =
192.2508
      income |   214.7859   70.17436     3.06   0.003     74.71733    =
354.8545
    incomesq |  -13.41379   6.353738    -2.11   0.038    -26.09591   =
-.7316792
       _cons |  -199.6993   170.1115    -1.17   0.245    -539.2433    =
139.8448
-------------------------------------------------------------------------=
-----
Table 12.3e, page 515, Proportional to log(e^2). = 
generate logee=3Dlog(ee)
regress logee income incomesq
(output omitted)

predict p3
replace p3 =3D exp(p3)
regress exp age ownrent income incomesq [aw =3D 1/p3]

(sum of wgt is   2.8166e-02)

      Source |       SS       df       MS              Number of obs =3D =
     72
-------------+------------------------------           F(  4,    67) =3D =
  69.69
       Model |  2872576.04     4   718144.01           Prob > F      =
=3D  0.0000
    Residual |  690414.776    67  10304.6981           R-squared     =3D =
 0.8062
-------------+------------------------------           Adj R-squared =3D =
 0.7947
       Total |  3562990.82    71  50182.9693           Root MSE      =3D =
 101.51

-------------------------------------------------------------------------=
-----
         exp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. =
Interval]
-------------+-----------------------------------------------------------=
-----
         age |  -1.233683   2.551197    -0.48   0.630    -6.325894    =
3.858527
     ownrent |   50.94976   52.81429     0.96   0.338      -54.468    =
156.3675
      income |   145.3045    46.3627     3.13   0.003     52.76413    =
237.8448
    incomesq |   -7.93828   3.736716    -2.12   0.037     -15.3968   =
-.4797647
       _cons |  -117.8675   101.3862    -1.16   0.249    -320.2352    =
84.50027
-------------------------------------------------------------------------=
-----
Table 12.3f, page 515, First step of two-step=20 estimation.
generate loginc =3D log(income)
regress logee loginc=20
(output omitted)

predict p4
replace p4 =3D exp(p4)
regress exp age ownrent income incomesq [aw=3D1/p4]

(sum of wgt is   8.5730e-03)

      Source |       SS       df       MS              Number of obs =3D =
     72
-------------+------------------------------           F(  4,    67) =3D =
   5.69
       Model |  1356781.78     4  339195.444           Prob > F      =
=3D  0.0005
    Residual |  3991163.63    67  59569.6064           R-squared     =3D =
 0.2537
-------------+------------------------------           Adj R-squared =3D =
 0.2091
       Total |  5347945.41    71  75323.1747           Root MSE      =3D =
 244.07

-------------------------------------------------------------------------=
-----
         exp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. =
Interval]
-------------+-----------------------------------------------------------=
-----
         age |  -2.957872   4.762688    -0.62   0.537    -12.46424    =
6.548494
     ownrent |   47.35701   72.13892     0.66   0.514    -96.63288    =
191.3469
      income |   208.8759   77.19801     2.71   0.009     54.78803    =
362.9638
    incomesq |   -12.7688   8.083831    -1.58   0.119    -28.90419    =
3.366592
       _cons |  -193.3253   171.0833    -1.13   0.263    -534.8089    =
148.1583
-------------------------------------------------------------------------=
-----
Table 12.3g, page 515, ML. Uses the reghv command by = Jeroen=20 Weesie. Use findit reghv to find program and download the = program (see=20 How can = I use the=20 findit command to search for programs and get additional help? for = more=20 information about using findit). 
reghv exp =
age ownrent income incomesq, var(loginc)=20

Multiplicative heteroscedastic regression             Number of obs  =3D =
     72
Estimator: mle                                        Model chi2(5)  =3D =
 68.428
                                                      Prob > chi2    =
=3D   0.000
Log Likelihood              =3D  -482.324               Pseudo R2      =
=3D  0.0662
                                                      VWLS R2        =3D =
 0.2421
-------------------------------------------------------------------------=
-----
         exp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. =
Interval]
-------------+-----------------------------------------------------------=
-----
lp_mean      |
         age |  -1.705189   2.758016    -0.62   0.536    -7.110802    =
3.700424
     ownrent |   58.09752    43.5065     1.34   0.182    -27.17365    =
143.3687
      income |   75.93179   81.04202     0.94   0.349    -82.90765    =
234.7712
    incomesq |   4.397655   13.43429     0.33   0.743    -21.93306    =
30.72838
       _cons |  -19.21409   113.0557    -0.17   0.865    -240.7992     =
202.371
-------------+-----------------------------------------------------------=
-----
lp_lnvar     |
      loginc |   3.651688   .3987368     9.16   0.000     2.870178    =
4.433198
       _cons |   6.397951   .4840636    13.22   0.000     5.449203    =
7.346698
-------------------------------------------------------------------------=
-----
Table 12.3h, page 515, Proportional to (xb)^2. = 
regress exp age ownrent income incomesq=20
(output omitted)

predict p
generate p5 =3D p^2
regress exp age ownrent income incomesq [aw=3D1/p5]

(sum of wgt is   2.3408e-02)

      Source |       SS       df       MS              Number of obs =3D =
     72
-------------+------------------------------           F(  4,    67) =3D =
   8.54
       Model |  102540.932     4  25635.2329           Prob > F      =
=3D  0.0000
    Residual |  201093.219    67  3001.39133           R-squared     =3D =
 0.3377
-------------+------------------------------           Adj R-squared =3D =
 0.2982
       Total |  303634.151    71  4276.53734           Root MSE      =3D =
 54.785

-------------------------------------------------------------------------=
-----
         exp |      Coef.   Std. Err.      t    P>|t|     [95% Conf. =
Interval]
-------------+-----------------------------------------------------------=
-----
         age |   .7315878    1.43144     0.51   0.611    -2.125579    =
3.588755
     ownrent |  -.2846994   46.67003    -0.01   0.995    -93.43847    =
92.86907
      income |   136.8154   48.40296     2.83   0.006     40.20271    =
233.4281
    incomesq |  -6.207781    6.76926    -0.92   0.362    -19.71928    =
7.303718
       _cons |  -148.1926   64.74939    -2.29   0.025    -277.4329   =
-18.95225
-------------------------------------------------------------------------=
-----
Table 12.4, page 521, Maximum Likelihood Estimates. We will = again=20 use the reghv command shown above in Table = 12.3g.
reghv exp age ownrent income incomesq, =
var(income incomesq)=20

Multiplicative heteroscedastic regression             Number of obs  =3D =
     72
Estimator: mle                                        Model chi2(6)  =3D =
101.113
                                                      Prob > chi2    =
=3D   0.000
Log Likelihood              =3D  -465.982               Pseudo R2      =
=3D  0.0979
                                                      VWLS R2        =3D =
 0.9584
-------------------------------------------------------------------------=
-----
         exp |      Coef.   Std. Err.      z    P>|z|     [95% Conf. =
Interval]
-------------+-----------------------------------------------------------=
-----
lp_mean      |
         age |  -.3759981    .550001    -0.68   0.494     -1.45398     =
.701984
     ownrent |    33.3591   37.13479     0.90   0.369    -39.42375     =
106.142
      income |   96.82688   31.79803     3.05   0.002     34.50389    =
159.1499
    incomesq |  -3.801144   2.624785    -1.45   0.148    -8.945629    =
1.343341
       _cons |  -58.44412   62.09841    -0.94   0.347    -180.1548    =
63.26654
-------------+-----------------------------------------------------------=
-----
lp_lnvar     |
      income |    5.35449   .3750446    14.28   0.000     4.619416    =
6.089564
    incomesq |  -.5631181    .036122   -15.59   0.000    -.6339159   =
-.4923202
       _cons |  -.0415783   .8079218    -0.05   0.959    -1.625076    =
1.541919
-------------------------------------------------------------------------=
-----
Repo= rt an=20 error on this page=20

UCLA Researchers are invited to our Statistical = Consulting=20 Services
We recommend others to our list of Other Resources = for=20 Statistical Computing Help
These pages are Copyrighted (c) by = UCLA=20 Academic Technology Services=20

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