ECON4150 - Introductory Econometrics Seminar 4
Stock and Watson EE8.2
April 28, 2015
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
1 / 20
Current Population Survey
data on labor force characteristics of the population, including the level of
employment, unemployment, and earnings
this subset consider young workers aged 25 to 34 in 2012.
7440 individuals.
FEMALE: 1 if female; 0 if male
YEAR: Year
AHE : Average Hourly Earnings
BACHELOR: 1 if worker has a bachelor degree; 0 if worker has a high school degree
AGE: age of individual, from 25 to 34, young workers
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
2 / 20
clear all
cd M:\pc\Desktop\courses\introductory_econometrics\seminar_4
use "cps12.dta"
cap log close
log using EE8_2.log , replace
set more off
pause on
//describe the data
describe
//summary statistics
summ
summ
Variable |
Obs
Mean
Std. Dev.
Min
Max
-------------+-------------------------------------------------------year |
7440
2012
0
2012
2012
ahe |
7440
19.80026
10.68632
2.136752
91.45602
bachelor |
7440
.531586
.4990349
0
1
female |
7440
.424328
.4942738
0
1
age |
7440
29.64772
2.839661
25
34
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
3 / 20
a)
reg ahe age female bachelor, r
Linear regression
Number of obs
F( 3, 7436)
Prob > F
R-squared
Root MSE
=
=
=
=
=
7440
539.54
0.0000
0.1801
9.6782
-----------------------------------------------------------------------------|
Robust
ahe |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------age |
.510286
.0395409
12.91
0.000
.4327747
.5877973
female | -3.810305
.2239148
-17.02
0.000
-4.249241
-3.371368
bachelor |
8.318628
.2237329
37.18
0.000
7.880048
8.757208
_cons |
1.866198
1.175373
1.59
0.112
-.4378656
4.170261
-----------------------------------------------------------------------------. estimates store rega
.
.
>
>
>
>
>
.
/*
If Age increases from 25 to 26 or from 33 to 34, earnings are predicted to in
crease by $0.510 per hour.
These values are the same because the regression is a linear function relating
AHE and Age.
*/
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
4 / 20
b
gen lnahe=ln(ahe)
reg lnahe age female bachelor, r
Linear regression
Number of obs
F( 3, 7436)
Prob > F
R-squared
Root MSE
=
=
=
=
=
7440
623.31
0.0000
0.1964
.47823
-----------------------------------------------------------------------------|
Robust
lnahe |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------age |
.0255179
.0019619
13.01
0.000
.0216721
.0293637
female | -.1923376
.0112614
-17.08
0.000
-.2144132
-.170262
bachelor |
.4377833
.0112003
39.09
0.000
.4158275
.4597391
_cons |
1.941423
.0590018
32.90
0.000
1.825763
2.057083
-----------------------------------------------------------------------------.
estimates store regb
.
. /* earnings are predicted to increase in both cases by 100%*0.0255=2.55%.
>
These values, in percentage terms, are the same because the regression
>
is a linear function relating ln(AHE) and Age.
> */
.
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
5 / 20
c
gen lnage=ln(age)
reg lnahe lnage female bachelor, r
Linear regression
Number of obs
F( 3, 7436)
Prob > F
R-squared
Root MSE
=
=
=
=
=
7440
624.31
0.0000
0.1966
.47817
-----------------------------------------------------------------------------|
Robust
lnahe |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------lnage |
.7529408
.0576153
13.07
0.000
.6399984
.8658831
female | -.1923558
.0112593
-17.08
0.000
-.2144271
-.1702844
bachelor |
.4376637
.0111993
39.08
0.000
.4157099
.4596175
_cons |
.1495315
.1953385
0.77
0.444
-.2333873
.5324504
-----------------------------------------------------------------------------. estimates store regc
.
.
. /*
>
If age goes from 25 to 26, the percentage increased is approximated by ln(26
> /25) = 0.0392, then 3.92%.
>
The predicted increase in earnings is 100% * 0.75 * (0.0392) = 2.9
>
If age goes from 35 to 36, the percentage increased is approximated by ln(36
> /35) = 0.0290, then 2.90%.
>
TheStock
predicted
increase in earnings
is the Econometrics
100% * 0.75
and Watson EE8.2
ECON4150 - Introductory
Seminar*4 (0.0290) = 2.1%. April 28, 2015
6 / 20
d
gen agesquared=age^2
reg lnahe age agesquared female bachelor, r
Linear regression
Number of obs
F( 4, 7435)
Prob > F
R-squared
Root MSE
=
=
=
=
=
7440
469.24
0.0000
0.1967
.47816
-----------------------------------------------------------------------------|
Robust
lnahe |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------age |
.1040449
.0457314
2.28
0.023
.0143984
.1936913
agesquared | -.0013284
.0007728
-1.72
0.086
-.0028433
.0001864
female | -.1923983
.0112589
-17.09
0.000
-.214469
-.1703276
bachelor |
.4374121
.0112096
39.02
0.000
.4154381
.4593862
_cons |
.791882
.6712609
1.18
0.238
-.5239793
2.107743
-----------------------------------------------------------------------------. estimates store regd
/* Age increases from 25 to 26, the predicted change in ln(AHE) is
(0.104 * 26 - 0.0013 * 26^2) - (0.104 * 25 - 0.0013 * 25^2) = 0.036.
Earnings are predicted to increase by 100%*0.036=3.6%.
Age increases from 34 to 35, the predicted change in ln(AHE) is
(0.104 * 35 - 0.0013 * 352) - (0.104 * 34 - 0.0013 * 342) = 0.012.
Earnings are predicted to increase by 100%*0.012=1.2%.
*/
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
7 / 20
e
/*
>
The regressions of questions (c) and (b) differs with respect the choice of
> one regressor.
>
The dependent variable is the same ln(ahe).
>
Then, we can make a choice comparing the two regression using the adjusted
> R squared.
> */
quietly reg lnahe lnage female bachelor, r
display "adjusted R2_c = " e(r2_a)
adjusted R2_c = .19623914
quietly reg lnahe age female bachelor, r
display "adjusted R2_b = " e(r2_a)
adjusted R2_b = .19605996
// adjusted R2_c = .19623914 > adjusted R2_b = .19605996
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
8 / 20
f
/* The regression in (d) includes an extra regression when compared with regre sion (b).
The dependent variable is the same ln(ahe).
Then, we can make a choice comparing considering just the t-statistics of agesquared */
reg lnahe age agesquared female bachelor, r
Linear regression
Number of obs
F( 4, 7435)
Prob > F
R-squared
Root MSE
=
=
=
=
=
7440
469.24
0.0000
0.1967
.47816
-----------------------------------------------------------------------------|
Robust
lnahe |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------age |
.1040449
.0457314
2.28
0.023
.0143984
.1936913
agesquared | -.0013284
.0007728
-1.72
0.086
-.0028433
.0001864
female | -.1923983
.0112589
-17.09
0.000
-.214469
-.1703276
bachelor |
.4374121
.0112096
39.02
0.000
.4154381
.4593862
_cons |
.791882
.6712609
1.18
0.238
-.5239793
2.107743
-----------------------------------------------------------------------------/*
coefficient on agesquared is not statistically significant different
from zero
at a 95% level (|t| = |-1.72| < 1.96).
This suggests that (b) is preferred to (d).
*/
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
9 / 20
g
. /*
Choice of regressors is different but same dependent variable.
Check the adjusted Rsquared
*/
quietly reg lnahe age agesquared female bachelor, r
display "adjusted R2_d = " e(r2_a)
adjusted R2_d = .19627256
quietly reg lnahe lnage female bachelor, r
display "adjusted R2_c = " e(r2_a)
adjusted R2_c = .19623914
// adjusted R2_c = .19623914 < adjusted R2_d = .19627256. d preferred
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
10 / 20
h
// first store the predicted values from the different regressions
quietly reg lnahe age female bachelor, r
predict lnahe_b_hat
quietly reg lnahe lnage female bachelor, r
predict lnahe_c_hat
quietly reg lnahe age agesquared female bachelor, r
predict lnahe_d_hat
// then sort
sort age
// graphs
two (line lnahe_b_hat age if female==0 & bachelor==0 , lwidth(medthick) lpattern(solid) lcolor(blue)) ///
(line lnahe_c_hat age if female==0 & bachelor==0 , lwidth(medthick) lpattern(solid) lcolor(red)) ///
(line lnahe_d_hat age if female==0 & bachelor==0 , lwidth(medthick) lpattern(solid) lcolor(black)) ///
, scheme(s1color) legend(pos(7) ring(0) label(1 "regression_b") label(2 "regression_c")label(3 "regression_d"))
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
11 / 20
2.6
Fitted values
2.7
2.65
2.75
2.8
h
2.55
regression_b
regression_d
24
26
regression_c
28
30
32
34
age
/*
very similar fitted values.
The quadratic specification (regression_d)more curvature than the log-log one (regression_c).
for a female with a high school diploma similar but
shifted (by the amount of the coefficient on the dummy variable female) lines,
*/
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
12 / 20
i
gen fembac=female*bachelor
regress lnahe age agesquared female bachelor fembac, robust
Linear regression
Number of obs
F( 5, 7434)
Prob > F
R-squared
Root MSE
=
=
=
=
=
7440
382.92
0.0000
0.1984
.4777
-----------------------------------------------------------------------------|
Robust
lnahe |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
-------------+---------------------------------------------------------------age |
.1043224
.04568
2.28
0.022
.0147766
.1938682
agesquared | -.0013316
.0007719
-1.73
0.085
-.0028447
.0001815
female | -.2423732
.0166376
-14.57
0.000
-.2749877
-.2097587
bachelor |
.4004463
.0148482
26.97
0.000
.3713396
.4295531
fembac |
.0898571
.0225592
3.98
0.000
.0456346
.1340796
_cons |
.8037409
.6706449
1.20
0.231
-.510913
2.118395
------------------------------------------------------------------------------
/*
>
The coefficient on the interaction term
>
fembac allows the effect of Bachelor on ln(AHE) to be different accordingly
> to the gender of the individual
> */
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
13 / 20
i
/*
> Alexis, predicted value: 0.104 * 30 - 0.001 * 30^2 - 0.242 + 0.401 + 0.090 +
> 0.804 = 3.273
> Jane predicted value: 0.104 * 30 - 0.001 * 30^2 - 0.242 + 0.804 = 2.782
>
> Predicted diff Alexis-jane= 3.273 - 2.782 = .491
>
> Bob 0.104 * 30 - 0.001 * 30^2 + 0.401 + 0.804 = 3.425
> Jim 0.104 * 30 - 0.001 * 30^2 + 0.804 = 3.024
>
> Predicted diff Bob - Jim = 3.425 - 3.024 = 0.401
>
> the diff - diff is the interaction term .491 - 0.401 = 0.09
>
> */
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
14 / 20
j
. // interaction term and then F statistic
gen agefem = age * female
gen agesquaredfem = agesquared * female
regress lnahe age agesquared agefem agesquaredfem female bachelor fembac, r
Linear regression
Number of obs
F( 7, 7432)
Prob > F
R-squared
Root MSE
=
=
=
=
=
7440
275.77
0.0000
0.1993
.47749
------------------------------------------------------------------------------|
Robust
lnahe |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
--------------+---------------------------------------------------------------age |
.0202458
.0601672
0.34
0.737
-.097699
.1381905
agesquared |
.0001442
.0010166
0.14
0.887
-.0018486
.0021369
agefem |
.1925467
.0923517
2.08
0.037
.0115112
.3735821
agesquaredfem | -.0033832
.0015605
-2.17
0.030
-.0064421
-.0003242
female |
-2.94933
1.355778
-2.18
0.030
-5.607039
-.2916208
bachelor |
.4007629
.0148487
26.99
0.000
.3716552
.4298706
fembac |
.0886023
.0225717
3.93
0.000
.0443554
.1328492
_cons |
1.987056
.8833646
2.25
0.025
.2554111
3.718701
-------------------------------------------------------------------------------
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
15 / 20
j
test agefem agesquaredfem
( 1)
( 2)
agefem = 0
agesquaredfem = 0
F(
2, 7432) =
Prob > F =
4.14
0.0160
> the effect of Age on earnings (in log) is statistically(at the 5% but not 1% l
> evel) different
> between men and women
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
16 / 20
k
gen agebac = bachelor * age
gen agesquaredbac = bachelor * agesquared
regress lnahe age agesquared agebac agesquaredbac female bachelor fembac, r
Linear regression
Number of obs
F( 7, 7432)
Prob > F
R-squared
Root MSE
=
=
=
=
=
7440
273.66
0.0000
0.1987
.47768
------------------------------------------------------------------------------|
Robust
lnahe |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
--------------+---------------------------------------------------------------age |
.0373728
.0646696
0.58
0.563
-.0893979
.1641435
agesquared | -.0002287
.0010931
-0.21
0.834
-.0023716
.0019142
agebac |
.1283798
.0912705
1.41
0.160
-.0505362
.3072958
agesquaredbac | -.0021153
.0015424
-1.37
0.170
-.0051387
.0009082
female | -.2423161
.0166376
-14.56
0.000
-.2749306
-.2097017
bachelor | -1.529426
1.340231
-1.14
0.254
-4.15666
1.097807
fembac |
.0899989
.0225708
3.99
0.000
.0457537
.1342442
_cons |
1.810172
.9490109
1.91
0.057
-.0501582
3.670502
-------------------------------------------------------------------------------
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
17 / 20
k
test agebac agesquaredbac
( 1)
( 2)
agebac = 0
agesquaredbac = 0
F(
2, 7432) =
Prob > F =
Stock and Watson EE8.2
1.30
0.2725
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
18 / 20
k
test agebac agesquaredbac
( 1)
( 2)
agebac = 0
agesquaredbac = 0
F(
2, 7432) =
Prob > F =
1.30
0.2725
/*
Pvalue is larger than 0.05, even larger than 0.10, so that we can not reject t
he null
hypotesys that the two coefficent are both 0. Thus, there is not statistical s
ignificant evidence
of a different effect of Age on ln(AHE) for high school and
college graduates
*/
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
19 / 20
l
/*
Gender and education are significant predictors of earnings,
significant interaction effects between:
--- age and gender
--- gender and and education
*/
log close
Stock and Watson EE8.2
ECON4150 - Introductory Econometrics Seminar 4
April 28, 2015
20 / 20