Chapter 12 - Examples
------------------------------------------------------------------------------------------
name: SN
log: ~Wooldridge\intro-econx\iexample12.smcl
log type: smcl
opened on: 15 Jan 2019, 17:38:45
. **********************************************
. * Solomon Negash - Replicating Examples
. * Wooldridge (2016). Introductory Econometrics: A Modern Approach. 6th ed.
. * STATA Program, version 15.1.
. * Chapter 12 Serial Correlation and Heteroskedasticity in Time Series Regressions
. * Computer Exercises (Examples)
. ******************** SETUP *********************
. *Example 12.1. Testing for AR(1) Serial Correlation in the Phillips Curve
. u phillips, clear
. qui reg inf unem
. predict us, res
. g us_1 = us[_n-1]
(1 missing value generated)
. reg us us_1
Source | SS df MS Number of obs = 48
-------------+---------------------------------- F(1, 46) = 24.34
Model | 150.91704 1 150.91704 Prob > F = 0.0000
Residual | 285.198412 46 6.19996547 R-squared = 0.3460
-------------+---------------------------------- Adj R-squared = 0.3318
Total | 436.115452 47 9.27905217 Root MSE = 2.49
------------------------------------------------------------------------------
us | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
us_1 | .5729695 .1161334 4.93 0.000 .3392052 .8067338
_cons | -.1133967 .359404 -0.32 0.754 -.8368393 .610046
------------------------------------------------------------------------------
. qui reg cinf unem
. predict ua, res
(1 missing value generated)
. g ua_1 = ua[_n-1]
(2 missing values generated)
. reg ua ua_1
Source | SS df MS Number of obs = 47
-------------+---------------------------------- F(1, 45) = 0.08
Model | .350024192 1 .350024192 Prob > F = 0.7752
Residual | 190.837382 45 4.24083071 R-squared = 0.0018
-------------+---------------------------------- Adj R-squared = -0.0204
Total | 191.187406 46 4.15624796 Root MSE = 2.0593
------------------------------------------------------------------------------
ua | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
ua_1 | -.0355928 .1238908 -0.29 0.775 -.2851216 .213936
_cons | .1941655 .3003839 0.65 0.521 -.4108388 .7991698
------------------------------------------------------------------------------
. *Example 12.2. Testing for AR(1) Serial Correlation in the Minimum Wage Equation
. u prminwge, clear
. qui reg lprepop lmincov lprgnp lusgnp t
. predict u, res
. g u_1 = u[_n-1]
(1 missing value generated)
. reg u lmincov lprgnp lusgnp t u_1
Source | SS df MS Number of obs = 37
-------------+---------------------------------- F(5, 31) = 1.98
Model | .007527192 5 .001505438 Prob > F = 0.1089
Residual | .023530328 31 .000759043 R-squared = 0.2424
-------------+---------------------------------- Adj R-squared = 0.1202
Total | .03105752 36 .000862709 Root MSE = .02755
------------------------------------------------------------------------------
u | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lmincov | .0375001 .0352123 1.06 0.295 -.0343159 .109316
lprgnp | -.0784656 .070524 -1.11 0.274 -.2223003 .065369
lusgnp | .2039325 .1951588 1.04 0.304 -.1940965 .6019614
t | -.0034662 .0040736 -0.85 0.401 -.0117743 .0048419
u_1 | .4805093 .1664442 2.89 0.007 .1410441 .8199745
_cons | -.8507721 1.092691 -0.78 0.442 -3.079329 1.377785
------------------------------------------------------------------------------
. reg u u_1
Source | SS df MS Number of obs = 37
-------------+---------------------------------- F(1, 35) = 6.89
Model | .00511108 1 .00511108 Prob > F = 0.0127
Residual | .02594644 35 .000741327 R-squared = 0.1646
-------------+---------------------------------- Adj R-squared = 0.1407
Total | .03105752 36 .000862709 Root MSE = .02723
------------------------------------------------------------------------------
u | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
u_1 | .4173219 .1589351 2.63 0.013 .0946666 .7399772
_cons | -.0008953 .0044883 -0.20 0.843 -.0100071 .0082165
------------------------------------------------------------------------------
. *Example 12.3. Testing for AR(3) Serial Correlation
. u barium, clear
. qui reg lchnimp lchempi lgas lrtwex befile6 affile6 afdec6
. predict u, res
. g u_1 = u[_n-1]
(1 missing value generated)
. g u_2 = u[_n-2]
(2 missing values generated)
. g u_3 = u[_n-3]
(3 missing values generated)
. reg u lchempi lgas lrtwex befile6 affile6 afdec6 u_1 u_2 u_3
Source | SS df MS Number of obs = 128
-------------+---------------------------------- F(9, 118) = 1.72
Model | 5.03370599 9 .559300665 Prob > F = 0.0920
Residual | 38.3936622 118 .325370019 R-squared = 0.1159
-------------+---------------------------------- Adj R-squared = 0.0485
Total | 43.4273682 127 .341947781 Root MSE = .57041
------------------------------------------------------------------------------
u | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lchempi | -.1431582 .4720253 -0.30 0.762 -1.077897 .7915804
lgas | .623307 .8859741 0.70 0.483 -1.131163 2.377777
lrtwex | .1786676 .3910343 0.46 0.649 -.5956868 .9530219
befile6 | -.0859236 .2510066 -0.34 0.733 -.5829851 .4111379
affile6 | -.1221207 .2546984 -0.48 0.632 -.6264928 .3822514
afdec6 | -.066829 .2743668 -0.24 0.808 -.6101499 .4764919
u_1 | .2214913 .0916573 2.42 0.017 .0399849 .4029977
u_2 | .1340412 .0921595 1.45 0.148 -.0484597 .3165421
u_3 | .1255427 .0911194 1.38 0.171 -.0548985 .3059838
_cons | -14.36915 20.65567 -0.70 0.488 -55.27299 26.53469
------------------------------------------------------------------------------
. test u_1 u_2 u_3
( 1) u_1 = 0
( 2) u_2 = 0
( 3) u_3 = 0
F( 3, 118) = 5.12
Prob > F = 0.0023
. *Example 12.4. Prais-Winsten Estimation in the Event Study
. u barium, clear
. tsset t
time variable: t, 1 to 131
delta: 1 unit
. local x "lchempi lgas lrtwex befile6 affile6 afdec6"
. eststo OLS: qui reg lchnimp `x'
. eststo PW: qui prais lchnimp `x'
. estout , cells(b(nostar fmt(2)) se(par fmt(3))) stats(rho N r2, fmt(%9.3f %9.0g %9.3f ) ///
labels(rho Observations R-squared )) varlabels(_cons intercept) varwidth(20) ti(Table 12.1 ///
Dependent Variable: log(chnimp))
Table 12.1 Dependent Variable: log(chnimp)
----------------------------------------------
OLS PW
b/se b/se
----------------------------------------------
lchempi 3.12 2.94
(0.479) (0.633)
lgas 0.20 1.05
(0.907) (0.977)
lrtwex 0.98 1.13
(0.400) (0.507)
befile6 0.06 -0.02
(0.261) (0.319)
affile6 -0.03 -0.03
(0.264) (0.322)
afdec6 -0.57 -0.58
(0.286) (0.342)
intercept -17.80 -37.08
(21.045) (22.778)
----------------------------------------------
rho 0.293
Observations 131 131
R-squared 0.305 0.202
----------------------------------------------
. est clear
. *Example 12.5. Static Phillips Curve
. u phillips, clear
. tsset year
time variable: year, 1948 to 1996
delta: 1 unit
. eststo OLS: qui reg inf unem
. eststo PW: qui prais inf unem
. estout , cells(b(nostar fmt(3)) se(par fmt(3))) stats(rho N r2, fmt(%9.3f %9.0g %9.3f ) ///
labels(rho Observations R-squared )) varlabels(_cons intercept) varwidth(20) ti(Table 12.2 ///
Dependent Variable: inf)
Table 12.2 Dependent Variable: inf
----------------------------------------------
OLS PW
b/se b/se
----------------------------------------------
unem 0.468 -0.716
(0.289) (0.313)
intercept 1.424 8.296
(1.719) (2.231)
----------------------------------------------
rho 0.781
Observations 49 49
R-squared 0.053 0.136
----------------------------------------------
. est clear
. *Example 12.6. Differencing the Interest Rate Equation
. bcuse intdef, clear
Contains data from http://fmwww.bc.edu/ec-p/data/wooldridge/intdef.dta
obs: 56
vars: 13 25 Jul 2005 15:25
size: 2,632
------------------------------------------------------------------------------------------
storage display value
variable name type format label variable label
------------------------------------------------------------------------------------------
year int %9.0g 1948 to 2003
i3 float %9.0g 3 month T-bill rate
inf float %9.0g CPI inflation rate
rec float %9.0g federal receipts, % GDP
out float %9.0g federal outlays, % GDP
def float %9.0g out - rec
i3_1 float %9.0g i3[_n-1]
inf_1 float %9.0g inf[_n-1]
def_1 float %9.0g def[_n-1]
ci3 float %9.0g i3 - i3_1
cinf float %9.0g inf - inf_1
cdef float %9.0g def - def_1
y77 byte %9.0g =1 if year >= 1977; change in FY
------------------------------------------------------------------------------------------
Sorted by:
. reg i3 inf def
Source | SS df MS Number of obs = 56
-------------+---------------------------------- F(2, 53) = 40.09
Model | 272.420338 2 136.210169 Prob > F = 0.0000
Residual | 180.054275 53 3.39725047 R-squared = 0.6021
-------------+---------------------------------- Adj R-squared = 0.5871
Total | 452.474612 55 8.22681113 Root MSE = 1.8432
------------------------------------------------------------------------------
i3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
inf | .6058659 .0821348 7.38 0.000 .4411243 .7706074
def | .5130579 .1183841 4.33 0.000 .2756095 .7505062
_cons | 1.733266 .431967 4.01 0.000 .8668497 2.599682
------------------------------------------------------------------------------
. predict u, res
. g u_1 = u[_n-1]
(1 missing value generated)
. reg u u_1
Source | SS df MS Number of obs = 55
-------------+---------------------------------- F(1, 53) = 32.13
Model | 63.9253768 1 63.9253768 Prob > F = 0.0000
Residual | 105.435729 53 1.98935339 R-squared = 0.3775
-------------+---------------------------------- Adj R-squared = 0.3657
Total | 169.361106 54 3.13631678 Root MSE = 1.4104
------------------------------------------------------------------------------
u | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
u_1 | .6225242 .1098185 5.67 0.000 .4022562 .8427922
_cons | .0153323 .1903397 0.08 0.936 -.3664407 .3971053
------------------------------------------------------------------------------
. reg ci3 cinf cdef
Source | SS df MS Number of obs = 55
-------------+---------------------------------- F(2, 52) = 5.57
Model | 17.8058166 2 8.90290831 Prob > F = 0.0065
Residual | 83.1753705 52 1.59952636 R-squared = 0.1763
-------------+---------------------------------- Adj R-squared = 0.1446
Total | 100.981187 54 1.87002198 Root MSE = 1.2647
------------------------------------------------------------------------------
ci3 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cinf | .1494892 .0921555 1.62 0.111 -.0354343 .3344127
cdef | -.1813151 .1476825 -1.23 0.225 -.4776618 .1150315
_cons | .0417738 .1713874 0.24 0.808 -.3021401 .3856877
------------------------------------------------------------------------------
. corr i3 i3_1
(obs=55)
| i3 i3_1
-------------+------------------
i3 | 1.0000
i3_1 | 0.8845 1.0000
. predict e, res
(1 missing value generated)
. g e_1 = e[_n-1]
(2 missing values generated)
. reg e e_1
Source | SS df MS Number of obs = 54
-------------+---------------------------------- F(1, 52) = 0.29
Model | .429432502 1 .429432502 Prob > F = 0.5944
Residual | 77.7882033 52 1.49592699 R-squared = 0.0055
-------------+---------------------------------- Adj R-squared = -0.0136
Total | 78.2176358 53 1.47580445 Root MSE = 1.2231
------------------------------------------------------------------------------
e | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
e_1 | .071925 .1342418 0.54 0.594 -.1974509 .3413009
_cons | -.041392 .1664432 -0.25 0.805 -.3753848 .2926007
------------------------------------------------------------------------------
. *Example 12.7. The Puerto Rican Minimum Wage
. u prminwge, clear
. tsset year
time variable: year, 1950 to 1987
delta: 1 unit
. eststo OLS: qui reg lprepop lmincov lprgnp lusgnp t
. eststo Newey: qui newey lprepop lmincov lprgnp lusgnp t, lag(2)
. eststo Pw: qui prais lprepop lmincov lprgnp lusgnp t
. estout , cells(b(nostar fmt(4)) se(par fmt(4))) stats(r2 r2_a N, fmt(%9.3f %9.3f %9.0g) ///
labels(R-squared Adj-R-squared N)) varlabels(_cons intercept) varwidth(20) ti(Dependent ///
Variables: log(prepop))
Dependent Variables: log(prepop)
-----------------------------------------------------------
OLS Newey Pw
b/se b/se b/se
-----------------------------------------------------------
lmincov -0.2123 -0.2123 -0.1477
(0.0402) (0.0457) (0.0458)
lprgnp 0.2852 0.2852 0.2514
(0.0805) (0.0996) (0.1165)
lusgnp 0.4860 0.4860 0.2557
(0.2220) (0.2791) (0.2317)
t -0.0267 -0.0267 -0.0205
(0.0046) (0.0058) (0.0059)
intercept -6.6634 -6.6634 -4.6529
(1.2578) (1.5364) (1.3765)
-----------------------------------------------------------
R-squared 0.889 0.751
Adj-R-squared 0.876 0.721
N 38 38 38
-----------------------------------------------------------
. est clear
. *Example 12.8. Heteroskedasticity and the Efficient Markets Hypothesis
. u nyse, clear
. reg return return_1
Source | SS df MS Number of obs = 689
-------------+---------------------------------- F(1, 687) = 2.40
Model | 10.6866231 1 10.6866231 Prob > F = 0.1218
Residual | 3059.73817 687 4.45376735 R-squared = 0.0035
-------------+---------------------------------- Adj R-squared = 0.0020
Total | 3070.42479 688 4.46282673 Root MSE = 2.1104
------------------------------------------------------------------------------
return | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
return_1 | .0588984 .0380231 1.55 0.122 -.0157569 .1335538
_cons | .179634 .0807419 2.22 0.026 .0211034 .3381646
------------------------------------------------------------------------------
. predict u, res
(2 missing values generated)
. gen u2 = u^2
(2 missing values generated)
. reg u2 return_1
Source | SS df MS Number of obs = 689
-------------+---------------------------------- F(1, 687) = 30.05
Model | 3755.56865 1 3755.56865 Prob > F = 0.0000
Residual | 85846.3039 687 124.95823 R-squared = 0.0419
-------------+---------------------------------- Adj R-squared = 0.0405
Total | 89601.8726 688 130.23528 Root MSE = 11.178
------------------------------------------------------------------------------
u2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
return_1 | -1.104132 .2014029 -5.48 0.000 -1.499572 -.7086933
_cons | 4.656501 .4276789 10.89 0.000 3.816786 5.496216
------------------------------------------------------------------------------
. *Example 12.9. ARCH in Stock Returns
. u nyse, clear
. qui reg return return_1
. predict u, res
(2 missing values generated)
. gen u2 = u^2
(2 missing values generated)
. g u2_1 = u2[_n-1]
(3 missing values generated)
. reg u2 u2_1
Source | SS df MS Number of obs = 688
-------------+---------------------------------- F(1, 686) = 87.92
Model | 10177.7166 1 10177.7166 Prob > F = 0.0000
Residual | 79409.7636 686 115.757673 R-squared = 0.1136
-------------+---------------------------------- Adj R-squared = 0.1123
Total | 89587.4802 687 130.403901 Root MSE = 10.759
------------------------------------------------------------------------------
u2 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
u2_1 | .3370623 .0359468 9.38 0.000 .2664834 .4076413
_cons | 2.947433 .4402342 6.70 0.000 2.083065 3.811801
------------------------------------------------------------------------------
. g u_1 = u[_n-1]
(3 missing values generated)
. reg u u_1
Source | SS df MS Number of obs = 688
-------------+---------------------------------- F(1, 686) = 0.00
Model | .006037885 1 .006037885 Prob > F = 0.9707
Residual | 3059.08133 686 4.45930223 R-squared = 0.0000
-------------+---------------------------------- Adj R-squared = -0.0015
Total | 3059.08737 687 4.45282004 Root MSE = 2.1117
------------------------------------------------------------------------------
u | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
u_1 | .0014048 .0381773 0.04 0.971 -.0735537 .0763633
_cons | -.0011708 .080508 -0.01 0.988 -.1592425 .156901
------------------------------------------------------------------------------
------------------------------------------------------------------------------------------
. log close
name: SN
log: ~Wooldridge\intro-econx\iexample12.smcl
log type: smcl
closed on: 15 Jan 2019, 17:38:47
------------------------------------------------------------------------------------------