. reg lwage educ exper tenure married black south urban
Source
|
SS
df
MS
Number of obs = 935
-------------+------------------------------
F( 7, 927) = 44.75
Model |
41.8377619
7
5.97682312
Prob > F = 0.0000
Residual | 123.818521
927
.133569063
R-squared = 0.2526
-------------+------------------------------
Adj R-squared = 0.2469
Total |
165.656283
934
.177362188
Root MSE = .36547
------------------------------------------------------------------------------
lwage
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ |
.0654307
.0062504 10.47
0.000
.0531642 .0776973
exper |
.014043 .0031852 4.41
0.000
.007792 .020294
tenure |
.0117473
.002453 4.79
0.000
.0069333 .0165613
married | .1994171
.0390502 5.11
0.000
.1227801 .276054
black |
-.1883499
.0376666 -5.00 0.000
-.2622717
-.1144281
south |
-.0909036
.0262485 -3.46
0.001
-.142417 -.0393903
urban |
.1839121
.0269583 6.82
0.000
.1310056 .2368185
_cons |
5.395497
.113225 47.65
0.000
5.17329 5.617704
------------------------------------------------------------------------------
The approximate difference in monthly salary between blacks and nonblacks is -18.8% (strictly speaking, you should use the exact formula that we discussed in class), i.e. black men earn about 18.8% less than the nonblack men. The difference is statistically significant (t-stat.=3.92).
. reg lwage educ exper tenure married black south urban exper2 tenure2
Source
|
SS
df
MS
Number of obs = 935
-------------+------------------------------
F( 9, 925) = 35.17
Model |
42.2353257
9
4.69281397
Prob > F = 0.0000
Residual | 123.420958
925
.133428062
R-squared = 0.2550
-------------+------------------------------
Adj R-squared = 0.2477
Total |
165.656283
934
.177362188
Root MSE = .36528
------------------------------------------------------------------------------
lwage
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ |
.0642761
.0063115 10.18
0.000
.0518896 .0766625
exper |
.0172146
.0126138 1.36
0.173
-.0075403 .0419695
tenure |
.0249291
.0081297 3.07
0.002
.0089743 .0408838
married |
.198547
.0391103 5.08
0.000
.1217917 .2753023
black |
-.1906636
.0377011 -5.06 0.000
-.2646533
-.116674
south |
-.0912153
.0262356 -3.48 0.001
-.1427035
-.0397271
urban |
.1854241
.0269585 6.88
0.000
.1325171 .2383311
exper2 | -.0001138
.0005319 -0.21 0.831
-.0011576
.00093
tenure2 |
-.0007964
.000471 -1.69 0.091
-.0017208
.0001279
_cons |
5.358676
.1259143 42.56
0.000
5.111565 5.605787
------------------------------------------------------------------------------
The F-test for joint significance of exper2 and tenure2 is
. test exper2 tenure2
( 1) exper2 = 0
( 2) tenure2 = 0
F( 2,
925)
= 1.49
Prob > F = 0.2260
The p-value shows that the 2 variables are jointly insignificant at 20% significance level.
. reg lwage educ exper tenure married black south urban black_educ
Source
|
SS
df
MS
Number of obs = 935
-------------+------------------------------
F( 8, 926) = 39.32
Model |
42.0055468
8
5.25069335
Prob > F = 0.0000
Residual | 123.650736
926
.133532113
R-squared = 0.2536
-------------+------------------------------
Adj R-squared = 0.2471
Total |
165.656283
934
.177362188
Root MSE = .36542
------------------------------------------------------------------------------
lwage
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ |
.0671153
.0064277 10.44
0.000
.0545008 .0797298
exper |
.0138259
.0031906 4.33
0.000
.0075642 .0200876
tenure |
.011787
.0024529 4.81
0.000
.0069732 .0166009
married | .1989077
.0390474 5.09
0.000
.1222761 .2755393
black |
.0948086
.2553994 0.37
0.711
-.4064202 .5960375
south |
-.0894495
.0262769 -3.40 0.001
-.1410187
-.0378803
urban |
.1838523
.0269547 6.82
0.000
.130953 .2367516
black_educ | -.0226236
.0201827
-1.12 0.263 -.0622326
.0169854
_cons |
5.374817
.1147027 46.86
0.000
5.14971 5.599925
------------------------------------------------------------------------------
The coefficient on black_educ shows that the return to
education
for black men is -2.3% lower than the the return to education for
nonblack
men (6.7%) but the
difference is statistically insignificant (t-stat=1.12) at the usual
significance levels.
. reg lwage educ exper tenure south urban single_black married_bl married_nbl
Source
|
SS
df
MS
Number of obs = 935
-------------+------------------------------
F( 8, 926) = 39.17
Model |
41.8849359
8
5.23561699
Prob > F = 0.0000
Residual | 123.771347
926
.133662362
R-squared = 0.2528
-------------+------------------------------
Adj R-squared = 0.2464
Total |
165.656283
934
.177362188
Root MSE = .3656
------------------------------------------------------------------------------
lwage
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ |
.0654751
.006253 10.47
0.000
.0532034 .0777469
exper |
.0141462
.003191 4.43
0.000
.0078837 .0204087
tenure |
.0116628
.0024579 4.74
0.000
.006839 .0164866
south |
-.0919894
.0263212 -3.49 0.000
-.1436455
-.0403333
urban |
.1843501
.0269778 6.83
0.000
.1314053 .2372948
single_black | -.24082
.0960229
-2.51 0.012 -.4292677
-.0523723
married_bl | .0094484
.0560131
0.17 0.866 -.1004789
.1193757
married_nbl | .1889147
.0428777
4.41 0.000
.1047659
.2730635
_cons |
5.403793
.1141222 47.35
0.000
5.179825 5.627762
------------------------------------------------------------------------------
The estimated wage difference between married blacks and married
nonblacks
is 100*(.0094-.1889)=-18%, i.e. , on average, married black
men
earn 18% less than married nonblack men, holding all the other factors
fixed.
. reg sleep totwrk educ age age2 yngkid if male==1
Source
|
SS
df
MS
Number of obs = 367
-------------+------------------------------
F( 5, 361) = 14.28
Model |
12345920.8
5
2469184.17
Prob > F = 0.0000
Residual | 62412191.5
361
172886.957
R-squared = 0.1651
-------------+------------------------------
Adj R-squared = 0.1536
Total |
74758112.4
366
204257.138
Root MSE = 415.8
------------------------------------------------------------------------------
sleep
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
totwrk | -.1903699
.0261503 -7.28 0.000
-.2417959
-.1389439
educ |
-12.99377
8.09208 -1.61
0.109
-28.9073 2.919767
age |
6.766816 15.40098 0.44
0.661 -23.52009 37.05372
age2 |
-.0328957
.1815595 -0.18 0.856
-.3899428
.3241514
yngkid |
65.06551
63.65015 1.02
0.307
-60.10615 190.2372
_cons |
3665.397
332.4681 11.02
0.000
3011.58 4319.215
------------------------------------------------------------------------------
and the estimated equation for women is
. reg sleep totwrk educ age age2 yngkid if male==0
Source
|
SS
df
MS
Number of obs = 283
-------------+------------------------------
F( 5, 277) = 6.03
Model |
6141361.7
5
1228272.34
Prob > F = 0.0000
Residual | 56394191.8
277
203589.14
R-squared
= 0.0982
-------------+------------------------------
Adj R-squared = 0.0819
Total |
62535553.5
282
221757.282
Root MSE = 451.21
------------------------------------------------------------------------------
sleep
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
totwrk | -.1455954
.0294894 -4.94 0.000
-.2036472
-.0875436
educ |
-9.284323
10.30645 -0.90 0.368
-29.57323
11.00459
age
|
-29.544 19.86969 -1.49
0.138
-68.65878 9.570786
age2 |
.3651966
.2394761 1.52
0.128
-.1062278 .8366209
yngkid | -79.66814
104.5678 -0.76 0.447
-285.5166
126.1803
_cons |
4215.637
410.4392 10.27
0.000
3407.66 5023.613
------------------------------------------------------------------------------
There are notable differences in the two equations. For instance,
having
a young child leads to more sleep for men (by 1 hour and 5 minutes per
week) but less
sleep for women (by 1 hour and 20 minutes per week) although these
effects appear to be insignificant.
. reg sleep totwrk educ age age2 yngkid male male_twrk male_educ male_age male_age2 male_ykid
Source
|
SS
df
MS
Number of obs = 650
-------------+------------------------------
F( 11, 638) = 9.17
Model |
18775388.4
11
1706853.49
Prob > F = 0.0000
Residual | 118806383
638
186216.902
R-squared = 0.1365
-------------+------------------------------
Adj R-squared = 0.1216
Total |
137581772
649
211990.403
Root MSE = 431.53
------------------------------------------------------------------------------
sleep
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
totwrk | -.1455954
.0282032 -5.16 0.000
-.2009777
-.0902131
educ |
-9.284323
9.856919 -0.94 0.347
-28.64025
10.0716
age
|
-29.544 19.00306 -1.55
0.121
-66.86009 7.772096
age2 |
.3651966
.2290311 1.59
0.111
-.0845494 .8149425
yngkid | -79.66814
100.0069 -0.80 0.426
-276.0507
116.7144
male |
-550.2391
522.631 -1.05 0.293
-1576.524
476.0457
male_twrk | -.0447745
.0391405
-1.14 0.253 -.1216344
.0320854
male_educ | -3.709445
12.94949
-0.29 0.775 -29.13823
21.71934
male_age | 36.31082
24.83132 1.46
0.144
-12.45017 85.0718
male_age2 | -.3980923
.2965817
-1.34 0.180 -.9804865
.1843019
male_ykid | 144.7336
119.8545
1.21 0.228 -90.62328
380.0906
_cons |
4215.637
392.5375 10.74
0.000
3444.815 4986.458
------------------------------------------------------------------------------
. test male male_twrk male_educ male_age male_age2 male_ykid
( 1) male = 0
( 2) male_twrk = 0
( 3) male_educ = 0
( 4) male_age = 0
( 5) male_age2 = 0
( 6) male_ykid = 0
F( 6,
638)
= 1.67
Prob > F = 0.1248
The relevant degrees of freedom are (6,638) and we cannot reject the null at 5% significance level since the p-value of the test is .125 (>.05).
. test male_twrk male_educ male_age male_age2 male_ykid
( 1) male_twrk = 0
( 2) male_educ = 0
( 3) male_age = 0
( 4) male_age2 = 0
( 5) male_ykid = 0
F( 5,
638)
= 0.97
Prob > F = 0.4353
and we cannot reject the null at the usual significant levels.
. reg price bdrms lotsize sqrft
Source
|
SS
df
MS
Number of obs = 88
-------------+------------------------------
F( 3, 84) = 57.46
Model |
6.1713e+11
3
2.0571e+11
Prob > F = 0.0000
Residual | 3.0072e+11
84
3.5800e+09
R-squared = 0.6724
-------------+------------------------------
Adj R-squared = 0.6607
Total |
9.1785e+11
87
1.0550e+10
Root MSE = 59833
------------------------------------------------------------------------------
price
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
bdrms |
13852.52
9010.145 1.54
0.128
-4065.14 31770.18
lotsize | 2.067707
.6421258 3.22
0.002
.790769 3.344644
sqrft |
122.7782
13.23741 9.28
0.000
96.45415 149.1022
_cons |
-21770.31
29475.04 -0.74 0.462
-80384.66
36844.04
------------------------------------------------------------------------------
. reg price bdrms lotsize sqrft, robust
Regression with robust standard
errors
Number of obs = 88
F( 3, 84) = 23.72
Prob > F = 0.0000
R-squared = 0.6724
Root MSE = 59833
------------------------------------------------------------------------------
|
Robust
price
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
bdrms |
13852.52
8478.625 1.63
0.106
-3008.153 30713.2
lotsize | 2.067707
1.251424 1.65
0.102
-.4208879 4.556301
sqrft |
122.7782
17.72533 6.93
0.000
87.52942 158.027
_cons |
-21770.31
37138.21 -0.59 0.559
-95623.71
52083.09
------------------------------------------------------------------------------
The most important difference is associated with the variable
lotsize.
Its robust std. error is almost twice as large as the non-robust std.
error
making lotsize
less significant (t-stat. drops from 3.2 to 1.7). the std. errors and
the t-statistics for the other variables are less affected.
. reg lprice bdrms llotsize lsqrft
Source
|
SS
df
MS
Number of obs = 88
-------------+------------------------------
F( 3, 84) = 50.42
Model |
5.1550402
3
1.71834673
Prob > F = 0.0000
Residual | 2.86256399
84
.034078143
R-squared = 0.6430
-------------+------------------------------
Adj R-squared = 0.6302
Total |
8.0176042
87
.09215637
Root MSE = .1846
------------------------------------------------------------------------------
lprice
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
bdrms |
.0369585
.0275313 1.34
0.183
-.0177905 .0917075
llotsize | .1679666
.0382812 4.39
0.000
.0918403 .2440929
lsqrft |
.7002324
.0928653 7.54
0.000
.5155596 .8849051
_cons |
5.610714
.6512837 8.61
0.000
4.315565 6.905863
------------------------------------------------------------------------------
. reg lprice bdrms llotsize lsqrft, robust
Regression with robust standard
errors
Number of obs = 88
F( 3, 84) = 49.32
Prob > F = 0.0000
R-squared = 0.6430
Root MSE = .1846
------------------------------------------------------------------------------
|
Robust
lprice
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
bdrms |
.0369585
.0306011 1.21
0.231
-.0238952 .0978121
llotsize | .1679666
.0414734 4.05
0.000
.0854922 .2504411
lsqrft |
.7002324
.1038288 6.74
0.000
.4937575 .9067072
_cons |
5.610714
.7813144 7.18
0.000
4.056985 7.164443
------------------------------------------------------------------------------
It appears that the log transformation mitigated the heteroskedasticity in the data and the differences in the std. errors now are relatively small.
. reg lfp lnnlinc age educ nyc noc, robust
Regression with robust standard
errors
Number of obs = 872
F( 5, 866) = 26.39
Prob > F = 0.0000
R-squared = 0.1097
Root MSE = .47188
------------------------------------------------------------------------------
|
Robust
lfp
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnnlinc | -.1891899
.0370341 -5.11
0.000
-.261877 -.1165028
age |
-.0122417
.00178 -6.88 0.000
-.0157353
-.0087481
educ |
-.0098705
.0055969 -1.76 0.078
-.0208556
.0011145
nyc |
-.2482384
.0328051 -7.57 0.000
-.3126252
-.1838515
noc |
-.0013628
.0159004 -0.09 0.932
-.0325706
.029845
_cons |
3.141225
.3758997 8.36
0.000
2.403444 3.879006
------------------------------------------------------------------------------
We need to use heteroskedasticity-robust standard errors since we
derived
in class that the conditional variance of the errors depends on the
regressors.
The effects
of income, age and number of young children are strongly significant
for the labour force participation of the married women in the sample.
Note that the
number of children older than 7 years (noc) has no effect
on lfp. Including the square of age in the model produces the
following results
. reg lfp lnnlinc age age2 educ nyc noc, robust
Regression with robust standard
errors
Number of obs = 872
F( 6, 865) = 36.23
Prob > F = 0.0000
R-squared = 0.1568
Root MSE = .4595
------------------------------------------------------------------------------
|
Robust
lfp
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnnlinc |
-.2375937
.036336 -6.54 0.000
-.3089106
-.1662767
age |
.0782537 .0123883 6.32
0.000 .053939 .1025684
age2 |
-.0011104
.0001482 -7.49 0.000
-.0014013
-.0008195
educ |
-.0081101
.0054628 -1.48 0.138
-.0188319
.0026118
nyc |
-.2281682
.032189 -7.09 0.000
-.2913459
-.1649905
noc |
-.0547312
.0176621 -3.10 0.002
-.0893968
-.0200657
_cons |
1.968587
.4040262 4.87
0.000
1.175601 2.761573
------------------------------------------------------------------------------
It is interesting to see now that noc has a significant effect on lfp and age has a diminishing effect (inverted U-shape) on lfp. The marginal effects of age on lfp for a 20-year and a 50-year old women are .078-2*.0011*20=.034 and .078-2*.0011*50=-.032, respectively, i.e. the age effect switched from positive (for a 20-year old woman) to negative (for a 50-year old woman). Call the predicted probabilities yhat. Then,
. summarize yhat if yhat<0
Variable
|
Obs Mean
Std.
Dev.
Min
Max
-------------+--------------------------------------------------------
yhat
|
14 -.1027707 .0941968
-.3507182
-.0185634
. summarize yhat if yhat>1
Variable
|
Obs Mean
Std.
Dev.
Min
Max
-------------+--------------------------------------------------------
yhat
|
1
1.016574
. 1.016574 1.016574
the results show that there are 14 negative predicted probabilities and 1 predicted probability larger than 1.
. probit lfp lnnlinc age age2 educ nyc noc
Iteration 0: log likelihood = -601.61168
Iteration 1: log likelihood = -527.81439
Iteration 2: log likelihood = -526.37879
Iteration 3: log likelihood = -526.37677
Probit
estimates
Number of obs =
872
LR chi2(6) =
150.47
Prob > chi2 = 0.0000
Log likelihood =
-526.37677
Pseudo R2 =
0.1251
------------------------------------------------------------------------------
lfp
|
Coef. Std. Err.
z
P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
lnnlinc | -.7385525
.1323584 -5.58 0.000
-.9979702
-.4791347
age |
.2332357 .0398307 5.86
0.000 .155169 .3113024
age2
|
-.0033 .0004906 -6.73
0.000
-.0042616 -.0023383
educ |
-.0232248
.0162045 -1.43
0.152
-.054985 .0085353
nyc |
-.6431679
.095832 -6.71 0.000
-.8309951
-.4553406
noc |
-.1581265
.0501046 -3.16 0.002
-.2563297
-.0599234
_cons |
4.652659
1.407971 3.30
0.001
1.893087 7.41223
------------------------------------------------------------------------------
. predict yhat2, p
. summarize yhat2
Variable
|
Obs Mean
Std.
Dev.
Min
Max
-------------+--------------------------------------------------------
yhat2
|
872 .4607822
.1985681
.004972 .9493863
. dprobit lfp lnnlinc age age2 educ nyc noc
Iteration 0: log likelihood = -601.61168
Iteration 1: log likelihood = -527.81439
Iteration 2: log likelihood = -526.37879
Iteration 3: log likelihood = -526.37677
Probit
estimates
Number of obs = 872
LR chi2(6) = 150.47
Prob > chi2 = 0.0000
Log likelihood =
-526.37677
Pseudo R2 = 0.1251
------------------------------------------------------------------------------
lfp |
dF/dx
Std. Err. z
P>|z|
x-bar [ 95% C.I. ]
---------+--------------------------------------------------------------------
lnnlinc | -.2922545
.0523248
-5.58 0.000 10.6856 -.394809
-.1897
age | .0922943
.0157431 5.86 0.000
39.9553
.061438 .12315
age2 | -.0013058
.0001939
-6.73 0.000 1707.63 -.001686 -.000926
educ | -.0091904
.0064122
-1.43 0.152 9.30734 -.021758 .003377
nyc | -.2545096
.0378944
-6.71 0.000 .311927 -.328781 -.180238
noc | -.0625726
.0198295
-3.16 0.002 .982798 -.101438 -.023708
---------+--------------------------------------------------------------------
obs. P | .4598624
pred. P | .4492704 (at x-bar)
------------------------------------------------------------------------------
z and P>|z| are the test of the underlying
coefficient
being 0
Now the predicted probabilities are between 0 and 1 (the minimum is
.005 and the maximum is .95). The estimated marginal effects from the
two
models are fairly
similar.
. reg lwage educ exper tenure
Source
|
SS
df
MS
Number of obs = 935
-------------+------------------------------
F( 3, 931) = 56.97
Model |
25.6953242
3
8.56510806
Prob > F = 0.0000
Residual | 139.960959
931
.150334005
R-squared = 0.1551
-------------+------------------------------
Adj R-squared = 0.1524
Total |
165.656283
934
.177362188
Root MSE = .38773
------------------------------------------------------------------------------
lwage
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ |
.0748638
.0065124 11.50
0.000
.062083 .0876446
exper |
.0153285
.0033696 4.55
0.000
.0087156 .0219413
tenure |
.0133748
.0025872 5.17
0.000
.0082974 .0184522
_cons |
5.496696
.1105282 49.73
0.000
5.279782 5.713609
------------------------------------------------------------------------------
and generate variables for the square of the residuals (res2), fitted values (yhat), square and cube of the fitted values (yhat2 and yhat3). The RESET test is obtained as an F-test on yhat2 and yhat3 in the regression
. reg lwage educ exper tenure yhat2 yhat3
Source
|
SS
df
MS
Number of obs = 935
-------------+------------------------------
F( 5, 929) = 34.16
Model |
25.7240527
5
5.14481053
Prob > F = 0.0000
Residual | 139.932231
929
.150626728
R-squared = 0.1553
-------------+------------------------------
Adj R-squared = 0.1507
Total |
165.656283
934
.177362188
Root MSE = .38811
------------------------------------------------------------------------------
lwage
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ |
4.882578
18.34014 0.27
0.790
-31.11034 40.87549
exper |
.9994516
3.754893 0.27
0.790
-6.369604 8.368507
tenure |
.8721999
3.276544 0.27
0.790
-5.558086 7.302485
yhat2 |
-9.30392
36.02601 -0.26 0.796
-80.00571
61.39787
yhat3 |
.4490062
1.765325 0.25
0.799
-3.015481 3.913493
_cons |
210.8379
791.544 0.27
0.790
-1342.584 1764.26
------------------------------------------------------------------------------
. test yhat2 yhat3
( 1) yhat2 = 0
( 2) yhat3 = 0
F( 2,
929)
= 0.10
Prob > F = 0.9091
Since the p-value is very large, we cannot reject the null hypothesis that the model is correctly specified. The White test for heteroskedasticity is computed from
. reg res2 yhat yhat2
Source
|
SS
df
MS
Number of obs = 935
-------------+------------------------------
F( 2, 932) = 2.48
Model |
.308151255
2
.154075627
Prob > F = 0.0841
Residual | 57.8348912
932
.062054604
R-squared = 0.0053
-------------+------------------------------
Adj R-squared = 0.0032
Total |
58.1430424
934
.062251651
Root MSE = .24911
------------------------------------------------------------------------------
res2
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
yhat |
-2.325484
3.387548 -0.69 0.493
-8.973589
4.322621
yhat2 |
.1632434
.2489785 0.66
0.512
-.32538 .6518668
_cons |
8.407836
11.51798 0.73
0.466
-14.19635 31.01202
------------------------------------------------------------------------------
. test yhat yhat2
( 1) yhat = 0
( 2) yhat2 = 0
F( 2,
932)
= 2.48
Prob > F = 0.0841
Since the p-value is .084 we reject the null of homoskedasticity at
10% sign. level. Therefore, we can use the specification in equation
(3)
but we need to
compute heteroskedasticity-robust standard errors.
. reg lwage educ exper tenure IQ
Source
|
SS
df
MS
Number of obs = 935
-------------+------------------------------
F( 4, 930) = 52.04
Model |
30.2968781
4
7.57421953
Prob > F = 0.0000
Residual | 135.359405
930
.145547747
R-squared = 0.1829
-------------+------------------------------
Adj R-squared = 0.1794
Total |
165.656283
934
.177362188
Root MSE = .38151
------------------------------------------------------------------------------
lwage
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ |
.0555855
.0072675 7.65
0.000
.0413228 .0698481
exper |
.015425 .0033155 4.65
0.000
.0089182 .0219318
tenure |
.0123705
.0025519 4.85
0.000
.0073623 .0173787
IQ
|
.0054564 .0009704 5.62
0.000 .0035519 .0073608
_cons |
5.209858
.1201247 43.37
0.000
4.974111 5.445605
------------------------------------------------------------------------------
As expected, including a proxy for ability corrects for the upward bias in the estimate for return to education and it drops from 7.5% in part (i) to 5.6%.
. ivreg lwage exper tenure (educ=sibs)
Instrumental variables (2SLS) regression
Source
|
SS
df
MS
Number of obs = 935
-------------+------------------------------
F( 3, 931) = 18.89
Model |
13.3491054
3
4.4497018
Prob > F = 0.0000
Residual | 152.307178
931
.16359525
R-squared
= 0.0806
-------------+------------------------------
Adj R-squared = 0.0776
Total |
165.656283
934
.177362188
Root MSE = .40447
------------------------------------------------------------------------------
lwage
|
Coef. Std. Err.
t
P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
educ |
.1338815
.0291925 4.59
0.000
.0765909 .1911722
exper |
.0294039
.0076291 3.85
0.000
.0144317 .0443762
tenure |
.0113425
.0028705 3.95
0.000
.0057091 .0169759
_cons |
4.553756
.4680328 9.73
0.000
3.635235 5.472278
------------------------------------------------------------------------------
Instrumented: educ
Instruments: exper tenure sibs
------------------------------------------------------------------------------
Surprisingly, the return to education from the IV regression is
higher
than its OLS estimate from part (i). This points to some problems in
using
sibs as an
instrument for educ (see the discussion in Example 15.2 on
p.491 in the text).