Verbeek 5ed. Chapter 4 - Heteroskedasticity and Autocorrelation
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name: SN
log: \5iexample4_s.smcl
log type: smcl
opened on: 5 Jun 2020, 20:25:24
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. * Solomon Negash - Examples
. * Verbeek(2017). A Giude To Modern Econometrics. 5ed.
. * STATA Program, version 16.1.
. * Chapter 4 - Heteroskedasticity and Autocorrelation
. ******************** **** *********************
. * Table 4.1 OLS results linear model
. u "Data/labour2.dta", clear
. reg labor wage output capital
Source | SS df MS Number of obs = 569
-------------+---------------------------------- F(3, 565) = 2716.02
Model | 198943126 3 66314375.3 Prob > F = 0.0000
Residual | 13795026.5 565 24415.9761 R-squared = 0.9352
-------------+---------------------------------- Adj R-squared = 0.9348
Total | 212738152 568 374539 Root MSE = 156.26
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labor | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
wage | -6.741904 .5014054 -13.45 0.000 -7.72675 -5.757057
output | 15.40047 .3556333 43.30 0.000 14.70194 16.09899
capital | -4.590491 .2689693 -17.07 0.000 -5.118793 -4.062189
_cons | 287.7186 19.64175 14.65 0.000 249.1388 326.2984
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. predict u, r
. g u2=u^2
. reg u2 wage output capital
Source | SS df MS Number of obs = 569
-------------+---------------------------------- F(3, 565) = 262.05
Model | 6.9733e+12 3 2.3244e+12 Prob > F = 0.0000
Residual | 5.0117e+12 565 8.8702e+09 R-squared = 0.5818
-------------+---------------------------------- Adj R-squared = 0.5796
Total | 1.1985e+13 568 2.1100e+10 Root MSE = 94182
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u2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
wage | 228.8569 302.2172 0.76 0.449 -364.7495 822.4632
output | 5362.207 214.3544 25.02 0.000 4941.179 5783.236
capital | -3543.509 162.1186 -21.86 0.000 -3861.938 -3225.081
_cons | -22719.51 11838.87 -1.92 0.055 -45973.09 534.0697
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. * Table 4.3 OLS results loglinear model
. g lnlabor=log(labor)
. g lnwage=log(wage)
. g lnoutput=log(output)
. g lncapital=log(capital)
. reg lnlabor lnwage lnoutput lncapital
Source | SS df MS Number of obs = 569
-------------+---------------------------------- F(3, 565) = 1011.02
Model | 656.747035 3 218.915678 Prob > F = 0.0000
Residual | 122.338812 565 .21652887 R-squared = 0.8430
-------------+---------------------------------- Adj R-squared = 0.8421
Total | 779.085847 568 1.37163001 Root MSE = .46533
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lnlabor | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnwage | -.9277643 .0714046 -12.99 0.000 -1.068015 -.7875133
lnoutput | .9900474 .0264103 37.49 0.000 .938173 1.041922
lncapital | -.0036975 .0187697 -0.20 0.844 -.0405644 .0331695
_cons | 6.17729 .2462105 25.09 0.000 5.69369 6.660889
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. * Table 4.4. Auxiliary regression White test
. predict uh, r
. g uh2=uh^2
. g lnwage2=lnwage^2
. g lnoutput2=lnoutput^2
. g lncapital2=lncapital^2
. reg uh2 lncapital c.lnwage##c.lnoutput c.lnoutput#c.lncapital c.lnwage#c.lncapital lnwage2 lnoutpu
t2 lncapital2
Source | SS df MS Number of obs = 569
-------------+---------------------------------- F(9, 559) = 7.12
Model | 46.3960128 9 5.15511253 Prob > F = 0.0000
Residual | 404.532757 559 .723672195 R-squared = 0.1029
-------------+---------------------------------- Adj R-squared = 0.0884
Total | 450.92877 568 .793888679 Root MSE = .85069
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uh2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------------+----------------------------------------------------------------
lncapital | 1.142053 .3758217 3.04 0.002 .4038578 1.880248
lnwage | -1.299008 1.752744 -0.74 0.459 -4.741778 2.143762
lnoutput | -.9037247 .5598545 -1.61 0.107 -2.0034 .195951
|
c.lnwage#c.lnoutput | .1380382 .1625628 0.85 0.396 -.1812704 .4573467
|
c.lnoutput#c.lncapital | -.1916048 .0368665 -5.20 0.000 -.2640187 -.119191
|
c.lnwage#c.lncapital | -.2517789 .1049671 -2.40 0.017 -.457957 -.0456008
|
lnwage2 | .1927418 .2589536 0.74 0.457 -.3158992 .7013828
lnoutput2 | .1381977 .0356469 3.88 0.000 .0681794 .2082159
lncapital2 | .0895375 .0139874 6.40 0.000 .0620631 .1170118
_cons | 2.544613 3.002783 0.85 0.397 -3.353504 8.44273
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. * Table 4.5 OLS results loglinear model with White standard errors
. reg lnlabor lnwage lnoutput lncapital, r
Linear regression Number of obs = 569
F(3, 565) = 544.73
Prob > F = 0.0000
R-squared = 0.8430
Root MSE = .46533
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| Robust
lnlabor | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnwage | -.9277643 .0866604 -10.71 0.000 -1.09798 -.7575484
lnoutput | .9900474 .0467902 21.16 0.000 .8981434 1.081951
lncapital | -.0036975 .037877 -0.10 0.922 -.0780944 .0706995
_cons | 6.17729 .2938869 21.02 0.000 5.600045 6.754534
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. * Table 4.6 Auxiliary regression multiplicative heteroskedasticity
. g lnuh2=log(uh2)
. reg lnuh2 lnwage lnoutput lncapital, r
Linear regression Number of obs = 569
F(3, 565) = 4.92
Prob > F = 0.0022
R-squared = 0.0245
Root MSE = 2.2404
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| Robust
lnuh2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnwage | -.0610507 .3291281 -0.19 0.853 -.7075147 .5854133
lnoutput | .2669502 .1378352 1.94 0.053 -.0037818 .5376821
lncapital | -.3306879 .0910089 -3.63 0.000 -.5094449 -.1519308
_cons | -3.253832 1.110527 -2.93 0.004 -5.435097 -1.072566
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. * Table 4.7 EGLS results loglinear model
. predict xb, xb
. g w = 1/(exp(xb))
. reg lnlabor lnwage lnoutput lncapital [weight=w]
(analytic weights assumed)
(sum of wgt is 16,475.1465694904)
Source | SS df MS Number of obs = 569
-------------+---------------------------------- F(3, 565) = 1074.48
Model | 700.868865 3 233.622955 Prob > F = 0.0000
Residual | 122.847468 565 .217429147 R-squared = 0.8509
-------------+---------------------------------- Adj R-squared = 0.8501
Total | 823.716333 568 1.45020481 Root MSE = .46629
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lnlabor | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnwage | -.8555786 .0718764 -11.90 0.000 -.9967562 -.7144009
lnoutput | 1.034611 .0273057 37.89 0.000 .9809776 1.088244
lncapital | -.0568635 .0215757 -2.64 0.009 -.099242 -.0144851
_cons | 5.895357 .2476376 23.81 0.000 5.408954 6.38176
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. * Figure 4.2 Actual and fitted consumption of ice cream
. use "Data/icecream.dta", clear
. reg cons income price
Source | SS df MS Number of obs = 30
-------------+---------------------------------- F(2, 27) = 0.98
Model | .008509865 2 .004254932 Prob > F = 0.3876
Residual | .117013493 27 .004333833 R-squared = 0.0678
-------------+---------------------------------- Adj R-squared = -0.0013
Total | .125523358 29 .004328392 Root MSE = .06583
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cons | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
income | .0002135 .0019687 0.11 0.914 -.003826 .004253
price | -2.030037 1.473893 -1.38 0.180 -5.054216 .994143
_cons | .9002396 .4550343 1.98 0.058 -.0334136 1.833893
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. predict xb, xb
. twoway (scatter cons time) (line xb time), title("Figure 4.2 Actual and fitted consumption of ice
cream, March 1951-July 1953", size(*.65)) ytitle(Consumption) xtitle(Time) legend(off)
. graph export figure4_2.png, replace
(note: file figure4_2.png not found)
(file figure4_2.png written in JPEG format)
. * Figure 4.3 Ice cream consumption, price and temperature/100
. g temp100 = temp/100
. twoway (line temp100 time) (line cons time, lpattern(dash_3dot)) (line price time, lpattern(dash)
), title("Figure 4.3 Ice cream consumption, price and temperature/100", size(*.65)) ytitle() xtit
le(Time) legend(ring(0) position(6) cols(3) size(vsmall))
. graph export figure4_3.png, replace
(note: file figure4_3.png not found)
(file figure4_3.png written in JPEG format)
. * Table 4.9 OLS results
. tsset time
time variable: time, 1 to 30
delta: 1 unit
. reg cons income price temp
Source | SS df MS Number of obs = 30
-------------+---------------------------------- F(3, 26) = 22.17
Model | .090250523 3 .030083508 Prob > F = 0.0000
Residual | .035272835 26 .001356647 R-squared = 0.7190
-------------+---------------------------------- Adj R-squared = 0.6866
Total | .125523358 29 .004328392 Root MSE = .03683
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cons | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
income | .0033078 .0011714 2.82 0.009 .0008999 .0057156
price | -1.044413 .834357 -1.25 0.222 -2.759458 .6706322
temp | .0034584 .0004455 7.76 0.000 .0025426 .0043743
_cons | .1973149 .2702161 0.73 0.472 -.3581223 .752752
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. estat dwatson
Durbin-Watson d-statistic( 4, 30) = 1.021169
. * Figure 4.4 Actual and fitted values (connected) of ice cream consumption
. predict xb2, xb
. twoway (scatter cons time) (line xb2 time), title("Figure 4.2 Figure 4.4 Actual and fitted values
of ice cream consumption", size(*.65)) ytitle(Consumption) xtitle(Time) legend(off)
. graph export figure4_4.png, replace
(note: file figure4_4.png not found)
(file figure4_4.png written in PNG format)
. * Table 4.10 EGLS (iterative Cochrane-Orcutt) results
. prais cons income price temp, corc
Iteration 0: rho = 0.0000
Iteration 1: rho = 0.4006
Iteration 2: rho = 0.4008
Iteration 3: rho = 0.4009
Iteration 4: rho = 0.4009
Iteration 5: rho = 0.4009
Iteration 6: rho = 0.4009
Iteration 7: rho = 0.4009
Cochrane-Orcutt AR(1) regression -- iterated estimates
Source | SS df MS Number of obs = 29
-------------+---------------------------------- F(3, 25) = 15.40
Model | .047040596 3 .015680199 Prob > F = 0.0000
Residual | .025451894 25 .001018076 R-squared = 0.6489
-------------+---------------------------------- Adj R-squared = 0.6068
Total | .072492491 28 .002589018 Root MSE = .03191
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cons | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
income | .0032027 .0015461 2.07 0.049 .0000186 .0063869
price | -.8923963 .8108501 -1.10 0.282 -2.562373 .7775807
temp | .0035584 .0005547 6.42 0.000 .002416 .0047008
_cons | .1571479 .2896292 0.54 0.592 -.4393546 .7536504
-------------+----------------------------------------------------------------
rho | .4009256
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Durbin-Watson statistic (original) 1.021169
Durbin-Watson statistic (transformed) 1.548837
. * Table 4.11 OLS results extended specification
. reg cons income price temp l.temp
Source | SS df MS Number of obs = 29
-------------+---------------------------------- F(4, 24) = 28.98
Model | .103387183 4 .025846796 Prob > F = 0.0000
Residual | .021406049 24 .000891919 R-squared = 0.8285
-------------+---------------------------------- Adj R-squared = 0.7999
Total | .124793232 28 .004456901 Root MSE = .02987
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cons | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
income | .0028673 .0010533 2.72 0.012 .0006934 .0050413
price | -.8383021 .6880205 -1.22 0.235 -2.258307 .5817025
|
temp |
--. | .0053321 .0006704 7.95 0.000 .0039484 .0067158
L1. | -.0022039 .0007307 -3.02 0.006 -.0037119 -.0006959
|
_cons | .1894822 .2323169 0.82 0.423 -.2899963 .6689607
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. * Figure 4.6 US$/EUR and US$/GBP exchange rates, January 1979-December 2001
. u "Data/Forward5.dta", clear
. tsset dateid01
time variable: dateid01, 01jan1979 to 01dec2001, but with gaps
delta: 1 day
. twoway (line exusbp dateid01) (line exuseur dateid01), ytitle() xtitle(Date) tlabel(#15, angle(fo
rty_five)) title("Figure 4.6 US$/EUR and US$/GBP exchange rates, January 1979 - December 2001", si
ze(*.65)) legend(off)
. graph export figure4_6.png, replace
(note: file figure4_6.png not found)
(file figure4_6.png written in JPEG format)
. * Figure 4.7 Forward discount, US$/EUR and US$/GBP, January 1979-December 2001
. g diff1 = exusbp - f1usbp
. g diff2 = exuseur - f1useur
. twoway (line diff1 dateid01) (line diff2 dateid01), ytitle() xtitle(Date) tlabel(#15, angle(forty
_five)) title("Figure 4.7 Forward discount, US$/EUR and US$/GBP, January 1979-December 2001", size
(*.65)) legend(off)
. graph export figure4_7.png, replace
(note: file figure4_7.png not found)
(file figure4_7.png written in JPEG format)
. log close
name: SN
log: \5iexample4_s.smcl
log type: smcl
closed on: 5 Jun 2020, 20:25:56
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