Transcript No Slide Title

DURBIN–WU–HAUSMAN SPECIFICATION TEST
reg LGEARN S EXP ASVABC MALE ETHBLACK ETHHISP
Source |
SS
df
MS
-------------+-----------------------------Model |
65.490707
6 10.9151178
Residual | 121.216936
533 .227423895
-------------+-----------------------------Total | 186.707643
539
.34639637
Number of obs
F( 6,
533)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
47.99
0.0000
0.3508
0.3435
.47689
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.0883257
.0109987
8.03
0.000
.0667196
.1099318
EXP |
.0227131
.0050095
4.53
0.000
.0128724
.0325538
ASVABC |
.0129274
.0028834
4.48
0.000
.0072633
.0185916
MALE |
.2652878
.042235
6.28
0.000
.1823203
.3482552
ETHBLACK |
.0077265
.0715863
0.11
0.914
-.1328994
.1483524
ETHHISP |
.0536544
.0937966
0.57
0.568
-.1306019
.2379107
_cons |
.4002952
.1663149
2.41
0.016
.0735821
.7270083
------------------------------------------------------------------------------
When we regressed the logarithm of earnings on years of schooling and other regressors
using EAEF Data Set 21, we obtained the output shown above.
1
DURBIN–WU–HAUSMAN SPECIFICATION TEST
reg LGEARN S EXP ASVABC MALE ETHBLACK ETHHISP
Source |
SS
df
MS
-------------+-----------------------------Model |
65.490707
6 10.9151178
Residual | 121.216936
533 .227423895
-------------+-----------------------------Total | 186.707643
539
.34639637
Number of obs
F( 6,
533)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
47.99
0.0000
0.3508
0.3435
.47689
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.0883257
.0109987
8.03
0.000
.0667196
.1099318
EXP |
.0227131
.0050095
4.53
0.000
.0128724
.0325538
ASVABC |
.0129274
.0028834
4.48
0.000
.0072633
.0185916
MALE |
.2652878
.042235
6.28
0.000
.1823203
.3482552
ETHBLACK |
.0077265
.0715863
0.11
0.914
-.1328994
.1483524
ETHHISP |
.0536544
.0937966
0.57
0.568
-.1306019
.2379107
_cons |
.4002952
.1663149
2.41
0.016
.0735821
.7270083
------------------------------------------------------------------------------
In some data sets the schooling variable is known to be subject to serious measurement
error. Sometimes it accounts for as much as 10 percent of the variance in the schooling
data.
2
DURBIN–WU–HAUSMAN SPECIFICATION TEST
reg LGEARN S EXP ASVABC MALE ETHBLACK ETHHISP
Source |
SS
df
MS
-------------+-----------------------------Model |
65.490707
6 10.9151178
Residual | 121.216936
533 .227423895
-------------+-----------------------------Total | 186.707643
539
.34639637
Number of obs
F( 6,
533)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
47.99
0.0000
0.3508
0.3435
.47689
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.0883257
.0109987
8.03
0.000
.0667196
.1099318
EXP |
.0227131
.0050095
4.53
0.000
.0128724
.0325538
ASVABC |
.0129274
.0028834
4.48
0.000
.0072633
.0185916
MALE |
.2652878
.042235
6.28
0.000
.1823203
.3482552
ETHBLACK |
.0077265
.0715863
0.11
0.914
-.1328994
.1483524
ETHHISP |
.0536544
.0937966
0.57
0.568
-.1306019
.2379107
_cons |
.4002952
.1663149
2.41
0.016
.0735821
.7270083
------------------------------------------------------------------------------
If that is the case, the OLS coefficient of schooling will tend to be downwards biased and
one should consider using the instrumental variables approach to fit the regression model.
3
DURBIN–WU–HAUSMAN SPECIFICATION TEST
ivregress 2sls LGEARN EXP ASVABC MALE ETHBLACK ETHHISP (S=SM SF SIBLINGS
LIBRARY)
Instrumental variables (2SLS) regression
Number of obs =
540
Wald chi2(6) = 230.09
Prob > chi2
= 0.0000
R-squared
= 0.3454
Root MSE
= .47574
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.111379
.0473785
2.35
0.019
.0185189
.2042391
EXP |
.0258798
.0080659
3.21
0.001
.010071
.0416887
ASVABC |
.0092263
.007939
1.16
0.245
-.0063339
.0247866
MALE |
.2619787
.0426492
6.14
0.000
.1783878
.3455696
ETHBLACK | -.0121846
.0817591
-0.15
0.882
-.1724295
.1480604
ETHHISP |
.0457639
.0948904
0.48
0.630
-.1402179
.2317457
_cons |
.2258512
.3862189
0.58
0.559
-.5311239
.9828263
-----------------------------------------------------------------------------Instrumented: S
Instruments:
EXP ASVABC MALE ETHBLACK ETHHISP SM SF SIBLINGS LIBRARY
Here we have used SM, mother's years of schooling, SF, father's years of schooling,
SIBLINGS, number of brothers and sisters, and LIBRARY, a dummy variable equal to 1 if
anyone in the household had a library card and 0 otherwise, to instrument for S.
4
DURBIN–WU–HAUSMAN SPECIFICATION TEST
ivregress 2sls LGEARN EXP ASVABC MALE ETHBLACK ETHHISP (S=SM SF SIBLINGS
LIBRARY)
Instrumental variables (2SLS) regression
Number of obs =
540
Wald chi2(6) = 230.09
Prob > chi2
= 0.0000
R-squared
= 0.3454
Root MSE
= .47574
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.111379
.0473785
2.35
0.019
.0185189
.2042391
EXP |
.0258798
.0080659
3.21
0.001
.010071
.0416887
ASVABC |
.0092263
.007939
1.16
0.245
-.0063339
.0247866
MALE |
.2619787
.0426492
6.14
0.000
.1783878
.3455696
ETHBLACK | -.0121846
.0817591
-0.15
0.882
-.1724295
.1480604
ETHHISP |
.0457639
.0948904
0.48
0.630
-.1402179
.2317457
_cons |
.2258512
.3862189
0.58
0.559
-.5311239
.9828263
-----------------------------------------------------------------------------Instrumented: S
Instruments:
EXP ASVABC MALE ETHBLACK ETHHISP SM SF SIBLINGS LIBRARY
The Stata command is 'ivregress 2sls', followed by the dependent variable, then a list of
explanatory variables not being instrumented, and finally, in parentheses, the variable(s)
being instrumented, followed by an = sign, followed by a list of instruments.
5
DURBIN–WU–HAUSMAN SPECIFICATION TEST
ivregress 2sls LGEARN EXP ASVABC MALE ETHBLACK ETHHISP (S=SM SF SIBLINGS
LIBRARY)
Instrumental variables (2SLS) regression
Number of obs =
540
Wald chi2(6) = 230.09
Prob > chi2
= 0.0000
R-squared
= 0.3454
Root MSE
= .47574
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.111379
.0473785
2.35
0.019
.0185189
.2042391
EXP |
.0258798
.0080659
3.21
0.001
.010071
.0416887
ASVABC |
.0092263
.007939
1.16
0.245
-.0063339
.0247866
MALE |
.2619787
.0426492
6.14
0.000
.1783878
.3455696
ETHBLACK | -.0121846
.0817591
-0.15
0.882
-.1724295
.1480604
ETHHISP |
.0457639
.0948904
0.48
0.630
-.1402179
.2317457
_cons |
.2258512
.3862189
0.58
0.559
-.5311239
.9828263
-----------------------------------------------------------------------------Instrumented: S
Instruments:
EXP ASVABC MALE ETHBLACK ETHHISP SM SF SIBLINGS LIBRARY
Here we have just one variable being instrumented, S, and four instruments, SM, SF,
SIBLINGS, and LIBRARY.
6
DURBIN–WU–HAUSMAN SPECIFICATION TEST
reg LGEARN S EXP ASVABC MALE ETHBLACK ETHHISP
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.0883257
.0109987
8.03
0.000
.0667196
.1099318
ivregress 2sls LGEARN EXP ASVABC MALE ETHBLACK ETHHISP (S=SM SF SIBLINGS
LIBRARY)
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.111379
.0473785
2.35
0.019
.0185189
.2042391
The instrumental variable estimate of the schooling coefficient is larger than the OLS one.
The reason may be that measurement error in S may indeed be a problem, causing the OLS
estimate to be downwards biased.
7
DURBIN–WU–HAUSMAN SPECIFICATION TEST
reg LGEARN S EXP ASVABC MALE ETHBLACK ETHHISP
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.0883257
.0109987
8.03
0.000
.0667196
.1099318
ivregress 2sls LGEARN EXP ASVABC MALE ETHBLACK ETHHISP (S=SM SF SIBLINGS
LIBRARY)
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.111379
.0473785
2.35
0.019
.0185189
.2042391
However, another possibility is that the difference is purely random. Note that the IV
estimate has a relatively large standard error.
8
DURBIN–WU–HAUSMAN SPECIFICATION TEST
reg LGEARN S EXP ASVABC MALE ETHBLACK ETHHISP
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.0883257
.0109987
8.03
0.000
.0667196
.1099318
ivregress 2sls LGEARN
ASVABC
MALE LIBRARY
ETHBLACK ETHHISP (S=SM SF SIBLINGS
cor S EXP
SM SF
SIBLINGS
LIBRARY)
(obs=540)
|
S
SM
SF SIBLINGS LIBRARY
------------------------------------------------------------------------------------------+--------------------------------------------LGEARN |
Coef.
z
P>|z|
[95% Conf. Interval]
SStd.
| Err.
1.0000
-------------+---------------------------------------------------------------SM |
0.3616
1.0000
S |
.111379 SF.0473785
2.35
.2042391
|
0.3935
0.62410.019
1.0000 .0185189
SIBLINGS | -0.2287 -0.3251 -0.2851
1.0000
LIBRARY |
0.1742
0.2762
0.2587 -0.0723
1.0000
This is because SM is only weakly correlated with the instruments. In general, the weaker
the correlation between the instrument(s) and the variable being instrumented, the greater
is the population variance of the coefficient.
9
DURBIN–WU–HAUSMAN SPECIFICATION TEST
reg LGEARN S EXP ASVABC MALE ETHBLACK ETHHISP
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.0883257
.0109987
8.03
0.000
.0667196
.1099318
ivregress 2sls LGEARN EXP ASVABC MALE ETHBLACK ETHHISP (S=SM SF SIBLINGS
LIBRARY)
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.111379
.0473785
2.35
0.019
.0185189
.2042391
The Durbin–Wu–Hausman test may enable us to discriminate between these two
possibilities.
10
DURBIN–WU–HAUSMAN SPECIFICATION TEST
ivregress 2sls LGEARN EXP ASVABC MALE ETHBLACK ETHHISP (S=SM SF SIBLINGS
LIBRARY)
Instrumental variables (2SLS) regression
Number of obs =
540
Wald chi2(6) = 230.09
Prob > chi2
= 0.0000
R-squared
= 0.3454
Root MSE
= .47574
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.111379
.0473785
2.35
0.019
.0185189
.2042391
EXP |
.0258798
.0080659
3.21
0.001
.010071
.0416887
ASVABC |
.0092263
.007939
1.16
0.245
-.0063339
.0247866
MALE |
.2619787
.0426492
6.14
0.000
.1783878
.3455696
ETHBLACK | -.0121846
.0817591
-0.15
0.882
-.1724295
.1480604
ETHHISP |
.0457639
.0948904
0.48
0.630
-.1402179
.2317457
_cons |
.2258512
.3862189
0.58
0.559
-.5311239
.9828263
-----------------------------------------------------------------------------Instrumented: S
Instruments:
EXP ASVABC MALE ETHBLACK ETHHISP SM SF SIBLINGS LIBRARY
Here we have just one variable being instrumented, S, and four instruments, SM, SF,
SIBLINGS, and LIBRARY.
11
DURBIN–WU–HAUSMAN SPECIFICATION TEST
ivregress 2sls LGEARN EXP ASVABC MALE ETHBLACK ETHHISP (S=SM SF SIBLINGS
LIBRARY)
Instrumental variables (2SLS) regression
Number of obs =
540
Wald chi2(6) = 230.09
Prob > chi2
= 0.0000
R-squared
= 0.3454
Root MSE
= .47574
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
z
P>|z|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.111379
.0473785
2.35
0.019
.0185189
.2042391
EXP |
.0258798
.0080659
3.21
0.001
.010071
.0416887
ASVABC |
.0092263
.007939
1.16
0.245
-.0063339
.0247866
MALE |
.2619787
.0426492
6.14
0.000
.1783878
.3455696
ETHBLACK | -.0121846
.0817591
-0.15
0.882
-.1724295
.1480604
ETHHISP |
.0457639
.0948904
0.48
0.630
-.1402179
.2317457
_cons |
.2258512
.3862189
0.58
0.559
-.5311239
.9828263
-----------------------------------------------------------------------------Instrumented: S
Instruments:
EXP ASVABC MALE ETHBLACK ETHHISP SM SF SIBLINGS LIBRARY
. estimates store EARNIV
To implement the DWH test using Stata, you first fit the IV version, and follow with the
command ‘estimates store‘ followed by a name for the IV regression (here ‘EARNIV’).
12
DURBIN–WU–HAUSMAN SPECIFICATION TEST
reg LGEARN S EXP ASVABC MALE ETHBLACK ETHHISP
Source |
SS
df
MS
-------------+-----------------------------Model |
65.490707
6 10.9151178
Residual | 121.216936
533 .227423895
-------------+-----------------------------Total | 186.707643
539
.34639637
Number of obs
F( 6,
533)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
47.99
0.0000
0.3508
0.3435
.47689
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.0883257
.0109987
8.03
0.000
.0667196
.1099318
EXP |
.0227131
.0050095
4.53
0.000
.0128724
.0325538
ASVABC |
.0129274
.0028834
4.48
0.000
.0072633
.0185916
MALE |
.2652878
.042235
6.28
0.000
.1823203
.3482552
ETHBLACK |
.0077265
.0715863
0.11
0.914
-.1328994
.1483524
ETHHISP |
.0536544
.0937966
0.57
0.568
-.1306019
.2379107
_cons |
.4002952
.1663149
2.41
0.016
.0735821
.7270083
-----------------------------------------------------------------------------. estimates store EARNOLS
You then fit the OLS version, and follow with the command 'estimates store’ followed by
a name for the OLS regression (here, 'EARNOLS').
13
DURBIN–WU–HAUSMAN SPECIFICATION TEST
reg LGEARN S EXP ASVABC MALE ETHBLACK ETHHISP
Source |
SS
df
MS
-------------+-----------------------------Model |
65.490707
6 10.9151178
Residual | 121.216936
533 .227423895
-------------+-----------------------------Total | 186.707643
539
.34639637
Number of obs
F( 6,
533)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
47.99
0.0000
0.3508
0.3435
.47689
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.0883257
.0109987
8.03
0.000
.0667196
.1099318
EXP |
.0227131
.0050095
4.53
0.000
.0128724
.0325538
ASVABC |
.0129274
.0028834
4.48
0.000
.0072633
.0185916
MALE |
.2652878
.042235
6.28
0.000
.1823203
.3482552
ETHBLACK |
.0077265
.0715863
0.11
0.914
-.1328994
.1483524
ETHHISP |
.0536544
.0937966
0.57
0.568
-.1306019
.2379107
_cons |
.4002952
.1663149
2.41
0.016
.0735821
.7270083
-----------------------------------------------------------------------------. estimates store EARNOLS
. hausman EARNIV EARNOLS, constant
To perform the test, you give the command 'hausman’ followed by the name you gave to the
IV regression, then the name of the OLS regression, followed by a comma, and then
‘constant’, as shown.
14
DURBIN–WU–HAUSMAN SPECIFICATION TEST
reg LGEARN S EXP ASVABC MALE ETHBLACK ETHHISP
Source |
SS
df
MS
-------------+-----------------------------Model |
65.490707
6 10.9151178
Residual | 121.216936
533 .227423895
-------------+-----------------------------Total | 186.707643
539
.34639637
Number of obs
F( 6,
533)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
540
47.99
0.0000
0.3508
0.3435
.47689
-----------------------------------------------------------------------------LGEARN |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------S |
.0883257
.0109987
8.03
0.000
.0667196
.1099318
EXP |
.0227131
.0050095
4.53
0.000
.0128724
.0325538
ASVABC |
.0129274
.0028834
4.48
0.000
.0072633
.0185916
MALE |
.2652878
.042235
6.28
0.000
.1823203
.3482552
ETHBLACK |
.0077265
.0715863
0.11
0.914
-.1328994
.1483524
ETHHISP |
.0536544
.0937966
0.57
0.568
-.1306019
.2379107
_cons |
.4002952
.1663149
2.41
0.016
.0735821
.7270083
-----------------------------------------------------------------------------. estimates store EARNOLS
. hausman EARNIV EARNOLS, constant
(If the constant does not have the same meaning in the IV and OLS regression, omit the
comma and ‘constant’. The constant will then not be included in the comparison of the
coefficients.)
15
DURBIN–WU–HAUSMAN SPECIFICATION TEST
---- Coefficients ---|
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
|
EARNIV
EARNOLS
Difference
S.E.
-------------+---------------------------------------------------------------S |
.111379
.0883257
.0230533
.0464029
EXP |
.0258798
.0227131
.0031667
.0063889
ASVABC |
.0092263
.0129274
-.0037011
.0074527
MALE |
.2619787
.2652878
-.0033091
.0076842
ETHBLACK |
-.0121846
.0077265
-.019911
.0405924
ETHHISP |
.0457639
.0536544
-.0078904
.018018
_cons |
.2258512
.4002952
-.174444
.3513736
-----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from ivregress
B = inconsistent under Ha, efficient under Ho; obtained from regress
Test: Ho: difference in coefficients not systematic
chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=
0.25
Prob>chi2 =
0.9999
The last command produces the test statistics shown above. In the top left corner the IV
and OLS estimates of the coefficients are compared. IV is column (b), OLS column (B).
16
DURBIN–WU–HAUSMAN SPECIFICATION TEST
---- Coefficients ---|
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
|
EARNIV
EARNOLS
Difference
S.E.
-------------+---------------------------------------------------------------S |
.111379
.0883257
.0230533
.0464029
EXP |
.0258798
.0227131
.0031667
.0063889
ASVABC |
.0092263
.0129274
-.0037011
.0074527
MALE |
.2619787
.2652878
-.0033091
.0076842
ETHBLACK |
-.0121846
.0077265
-.019911
.0405924
ETHHISP |
.0457639
.0536544
-.0078904
.018018
_cons |
.2258512
.4002952
-.174444
.3513736
-----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from ivregress
B = inconsistent under Ha, efficient under Ho; obtained from regress
Test: Ho: difference in coefficients not systematic
chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=
0.25
Prob>chi2 =
0.9999
H0: Assumption B.7 is valid
The null hypothesis is that there is no violation of Assumption B.7. If it is true, there will be
no significant difference in the estimates.
17
DURBIN–WU–HAUSMAN SPECIFICATION TEST
---- Coefficients ---|
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
|
EARNIV
EARNOLS
Difference
S.E.
-------------+---------------------------------------------------------------S |
.111379
.0883257
.0230533
.0464029
EXP |
.0258798
.0227131
.0031667
.0063889
ASVABC |
.0092263
.0129274
-.0037011
.0074527
MALE |
.2619787
.2652878
-.0033091
.0076842
ETHBLACK |
-.0121846
.0077265
-.019911
.0405924
ETHHISP |
.0457639
.0536544
-.0078904
.018018
_cons |
.2258512
.4002952
-.174444
.3513736
-----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from ivregress
B = inconsistent under Ha, efficient under Ho; obtained from regress
Test: Ho: difference in coefficients not systematic
chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=
0.25
Prob>chi2 =
0.9999
H0: Assumption B.7 is valid
The IV estimator b will be consistent under both the null hypothesis and the alternative. The
OLS estimator B will be consistent (and unbiased), and more efficient than the IV estimator
under the null hypothesis, but it will be inconsistent if the null hypothesis is false.
18
DURBIN–WU–HAUSMAN SPECIFICATION TEST
---- Coefficients ---|
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
|
EARNIV
EARNOLS
Difference
S.E.
-------------+---------------------------------------------------------------S |
.111379
.0883257
.0230533
.0464029
EXP |
.0258798
.0227131
.0031667
.0063889
ASVABC |
.0092263
.0129274
-.0037011
.0074527
MALE |
.2619787
.2652878
-.0033091
.0076842
ETHBLACK |
-.0121846
.0077265
-.019911
.0405924
ETHHISP |
.0457639
.0536544
-.0078904
.018018
_cons |
.2258512
.4002952
-.174444
.3513736
-----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from ivregress
B = inconsistent under Ha, efficient under Ho; obtained from regress
Test: Ho: difference in coefficients not systematic
chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=
0.25
Prob>chi2 =
0.9999
H0: Assumption B.7 is valid
If the null hypothesis is true, there was no need to use IV and it is actually undesirable
because it will be less efficient than OLS.
19
DURBIN–WU–HAUSMAN SPECIFICATION TEST
---- Coefficients ---|
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
|
EARNIV
EARNOLS
Difference
S.E.
-------------+---------------------------------------------------------------S |
.111379
.0883257
.0230533
.0464029
EXP |
.0258798
.0227131
.0031667
.0063889
ASVABC |
.0092263
.0129274
-.0037011
.0074527
MALE |
.2619787
.2652878
-.0033091
.0076842
ETHBLACK |
-.0121846
.0077265
-.019911
.0405924
ETHHISP |
.0457639
.0536544
-.0078904
.018018
_cons |
.2258512
.4002952
-.174444
.3513736
-----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from ivregress
B = inconsistent under Ha, efficient under Ho; obtained from regress
Test: Ho: difference in coefficients not systematic
chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=
0.25
Prob>chi2 =
0.9999
H0: Assumption B.7 is valid
If the null hypothesis is false, however, IV is preferred because the OLS estimates will be
inconsistent.
20
DURBIN–WU–HAUSMAN SPECIFICATION TEST
---- Coefficients ---|
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
|
EARNIV
EARNOLS
Difference
S.E.
-------------+---------------------------------------------------------------S |
.111379
.0883257
.0230533
.0464029
EXP |
.0258798
.0227131
.0031667
.0063889
ASVABC |
.0092263
.0129274
-.0037011
.0074527
MALE |
.2619787
.2652878
-.0033091
.0076842
ETHBLACK |
-.0121846
.0077265
-.019911
.0405924
ETHHISP |
.0457639
.0536544
-.0078904
.018018
_cons |
.2258512
.4002952
-.174444
.3513736
-----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from ivregress
B = inconsistent under Ha, efficient under Ho; obtained from regress
Test: Ho: difference in coefficients not systematic
chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=
0.25
Prob>chi2 =
0.9999
H0: Assumption B.7 is valid
Under the null hypothesis, the test statistic has a chi-squared distribution with degrees of
freedom usually equal to the number of coefficients being compared. However under
certain conditions the number of degrees of freedom may be smaller.
21
DURBIN–WU–HAUSMAN SPECIFICATION TEST
---- Coefficients ---|
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
|
EARNIV
EARNOLS
Difference
S.E.
-------------+---------------------------------------------------------------S |
.111379
.0883257
.0230533
.0464029
EXP |
.0258798
.0227131
.0031667
.0063889
ASVABC |
.0092263
.0129274
-.0037011
.0074527
MALE |
.2619787
.2652878
-.0033091
.0076842
ETHBLACK |
-.0121846
.0077265
-.019911
.0405924
ETHHISP |
.0457639
.0536544
-.0078904
.018018
_cons |
.2258512
.4002952
-.174444
.3513736
-----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from ivregress
B = inconsistent under Ha, efficient under Ho; obtained from regress
Test: Ho: difference in coefficients not systematic
chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=
0.25
Prob>chi2 =
0.9999
H0: Assumption B.7 is valid
 2 (7)crit, 5%  14.07
In this case there are 7 degrees of freedom. The test statistic is lower than the critical value
of chi-squared at the 5 percent significance level.
22
DURBIN–WU–HAUSMAN SPECIFICATION TEST
---- Coefficients ---|
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
|
EARNIV
EARNOLS
Difference
S.E.
-------------+---------------------------------------------------------------S |
.111379
.0883257
.0230533
.0464029
EXP |
.0258798
.0227131
.0031667
.0063889
ASVABC |
.0092263
.0129274
-.0037011
.0074527
MALE |
.2619787
.2652878
-.0033091
.0076842
ETHBLACK |
-.0121846
.0077265
-.019911
.0405924
ETHHISP |
.0457639
.0536544
-.0078904
.018018
_cons |
.2258512
.4002952
-.174444
.3513736
-----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from ivregress
B = inconsistent under Ha, efficient under Ho; obtained from regress
Test: Ho: difference in coefficients not systematic
chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=
0.25
Prob>chi2 =
0.9999
H0: Assumption B.7 is valid
 2 (7)crit, 5%  14.07
Thus we do not reject the null hypothesis. As far as we can tell, there is no significant
measurement error.
23
DURBIN–WU–HAUSMAN SPECIFICATION TEST
---- Coefficients ---|
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
|
EARNIV
EARNOLS
Difference
S.E.
-------------+---------------------------------------------------------------S |
.111379
.0883257
.0230533
.0464029
EXP |
.0258798
.0227131
.0031667
.0063889
ASVABC |
.0092263
.0129274
-.0037011
.0074527
MALE |
.2619787
.2652878
-.0033091
.0076842
ETHBLACK |
-.0121846
.0077265
-.019911
.0405924
ETHHISP |
.0457639
.0536544
-.0078904
.018018
_cons |
.2258512
.4002952
-.174444
.3513736
-----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from ivregress
B = inconsistent under Ha, efficient under Ho; obtained from regress
Test: Ho: difference in coefficients not systematic
chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=
0.25
Prob>chi2 =
0.9999
H0: Assumption B.7 is valid
 2 (7)crit, 5%  14.07
This is almost certainly the right conclusion in this case, because the schooling histories of
the respondents in the NLSY have been recorded with great care.
24
DURBIN–WU–HAUSMAN SPECIFICATION TEST
---- Coefficients ---|
(b)
(B)
(b-B)
sqrt(diag(V_b-V_B))
|
EARNIV
EARNOLS
Difference
S.E.
-------------+---------------------------------------------------------------S |
.111379
.0883257
.0230533
.0464029
EXP |
.0258798
.0227131
.0031667
.0063889
ASVABC |
.0092263
.0129274
-.0037011
.0074527
MALE |
.2619787
.2652878
-.0033091
.0076842
ETHBLACK |
-.0121846
.0077265
-.019911
.0405924
ETHHISP |
.0457639
.0536544
-.0078904
.018018
_cons |
.2258512
.4002952
-.174444
.3513736
-----------------------------------------------------------------------------b = consistent under Ho and Ha; obtained from ivregress
B = inconsistent under Ha, efficient under Ho; obtained from regress
Test: Ho: difference in coefficients not systematic
chi2(7) = (b-B)'[(V_b-V_B)^(-1)](b-B)
=
0.25
Prob>chi2 =
0.9999
H0: Assumption B.7 is valid
 2 (7)crit, 5%  14.07
However, if the test statistic is not significant, this does not necessarily mean that the null
hypothesis is true. It could be that it is false, but the instruments used in IV are so weak
that the differences between the IV and OLS estimates are not significant.
25
Copyright Christopher Dougherty 2012.
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Introduction to Econometrics, fourth edition 2011, Oxford University Press.
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2012.11.16