Transcript Chapter 5 the effects of changing the reference category (EC220)

Christopher Dougherty
EC220 - Introduction to econometrics
(chapter 5)
Slideshow: the effects of changing the reference category
Original citation:
Dougherty, C. (2012) EC220 - Introduction to econometrics (chapter 5). [Teaching Resource]
© 2012 The Author
This version available at: http://learningresources.lse.ac.uk/131/
Available in LSE Learning Resources Online: May 2012
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THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
700000
600000
COST
500000
400000
300000
200000
100000
0
0
200
400
600
800
1000
1200
1400
N
Technical schools
Vocational schools
General schools
Workers' schools
In the previous sequence we chose general academic schools as the reference (omitted)
category and defined dummy variables for the other categories.
1
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
700000
600000
COST
500000
400000
300000
200000
100000
0
0
200
400
600
800
1000
1200
1400
N
Technical schools
Vocational schools
General schools
Workers' schools
This enabled us to compare the overhead costs of the other schools with those of general
schools and to test whether the differences were significant.
2
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
700000
600000
COST
500000
400000
300000
200000
100000
0
0
200
400
600
800
1000
1200
1400
N
Technical schools
Vocational schools
General schools
Workers' schools
However, suppose that we were interested in testing whether the overhead costs of skilled
workers’ schools were different from those of the other types of school. How could we do
this?
3
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
700000
600000
COST
500000
400000
300000
200000
100000
0
0
200
400
600
800
1000
1200
1400
N
Technical schools
Vocational schools
General schools
Workers' schools
It is possible to perform a t test using the variance-covariance matrix of the regression
coefficients to calculate the relevant standard errors. But it is a pain and it is easy to make
arithmetical errors.
4
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
700000
600000
COST
500000
400000
300000
200000
100000
0
0
200
400
600
800
1000
1200
1400
N
Technical schools
Vocational schools
General schools
Workers' schools
It is much simpler to re-run the regression making skilled workers’ schools the reference
category. Now we need to define a dummy variable GEN for the general schools.
5
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
COST = b1 + dTTECH + dVVOC + dGGEN + b2N + u
The model is shown in equation form. Note that there is no longer a dummy variable for
skilled workers’ schools since they form the reference category.
6
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
COST = b1 + dTTECH + dVVOC + dGGEN + b2N + u
Skilled Workers' School
COST = b1 + b2N + u
(TECH = VOC = GEN = 0)
In the case of observations relating to skilled workers’ schools, all the dummy variables are
0 and the model simplifies to the intercept and the term involving N.
7
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
COST = b1 + dTTECH + dVVOC + dGGEN + b2N + u
Skilled Workers' School
COST = b1 + b2N + u
(TECH = VOC = GEN = 0)
Technical School
COST = (b1 + dT) + b2N + u
(TECH = 1; VOC = GEN = 0)
In the case of observations relating to technical schools, TECH is equal to 1 and the
intercept increases by an amount dT.
8
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
COST = b1 + dTTECH + dVVOC + dGGEN + b2N + u
Skilled Workers' School
COST = b1 + b2N + u
(TECH = VOC = GEN = 0)
Technical School
COST = (b1 + dT) + b2N + u
(TECH = 1; VOC = GEN = 0)
Note that dT should now be interpreted as the extra overhead cost of a technical school
relative to that of a skilled workers’ school.
9
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
COST = b1 + dTTECH + dVVOC + dGGEN + b2N + u
Skilled Workers' School
COST = b1 + b2N + u
(TECH = VOC = GEN = 0)
Technical School
COST = (b1 + dT) + b2N + u
(TECH = 1; VOC = GEN = 0)
Vocational School
COST = (b1 + dV) + b2N + u
(VOC = 1; TECH = GEN = 0)
General School
COST = (b1 + dG) + b2N + u
(GEN = 1; TECH = VOC = 0)
Similarly one can derive the implicit cost functions for vocational and general schools, their
d coefficients also being interpreted as their extra overhead costs relative to those of skilled
workers’ schools.
10
COST
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
dT
Technical
b1+dT
b1
Workers’
dV
dG
Vocational
b1+dV
b1+dG
General
N
This diagram illustrates the model graphically. Note that the d shifts are measured from the
line for skilled workers’ schools.
11
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
School
Type
COST
N
TECH
VOC
GEN
1
Technical
345,000
623
1
0
0
2
Technical
537,000
653
1
0
0
3
General
170,000
400
0
0
1
4
Workers’
526.000
663
0
0
0
5
General
100,000
563
0
0
1
6
Vocational
28,000
236
0
1
0
7
Vocational
160,000
307
0
1
0
8
Technical
45,000
173
1
0
0
9
Technical
120,000
146
1
0
0
10
Workers’
61,000
99
0
0
0
Here are the data for the first 10 of the 74 schools with skilled workers’ schools as the
reference category.
12
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH VOC GEN
Source |
SS
df
MS
---------+-----------------------------Model | 9.2996e+11
4 2.3249e+11
Residual | 5.4138e+11
69 7.8461e+09
---------+-----------------------------Total | 1.4713e+12
73 2.0155e+10
Number of obs
F( 4,
69)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
74
29.63
0.0000
0.6320
0.6107
88578
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
Here is the Stata output for the regression. We will focus first on the regression
coefficients.
13
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
^ = 88,000 + 11,000TECH – 90,000VOC – 143,000GEN + 343N
COST
The regression result is shown written as an equation.
14
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
^ = 88,000 + 11,000TECH – 90,000VOC – 143,000GEN + 343N
COST
Skilled Workers' School
^
COST
= 88,000 + 343N
(TECH = VOC = GEN = 0)
Putting all the dummy variables equal to 0, we obtain the equation for the reference
category, the skilled workers’ schools.
15
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
^ = 88,000 + 11,000TECH – 90,000VOC – 143,000GEN + 343N
COST
Skilled Workers' School
^
COST
= 88,000 + 343N
(TECH = VOC = GEN = 0)
Technical School
(TECH = 1; VOC = GEN = 0)
^
COST
= 88,000 + 11,000 + 343N
= 99,000 + 343N
Putting TECH equal to 1 and VOC and GEN equal to 0, we obtain the equation for the
technical schools.
16
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
^ = 88,000 + 11,000TECH – 90,000VOC – 143,000GEN + 343N
COST
Skilled Workers' School
^
COST
= 88,000 + 343N
(TECH = VOC = GEN = 0)
Technical School
(TECH = 1; VOC = GEN = 0)
Vocational School
(VOC = 1; TECH = GEN = 0)
General School
(GEN = 1; TECH = VOC = 0)
^
COST
= 88,000 + 11,000 + 343N
= 99,000 + 343N
^
COST
= 88,000 – 90,000 + 343N
= –2,000 + 343N
^
COST
= 88,000 – 143,000 + 343N
= –55,000 + 343N
And similarly we obtain the equations for the vocational and general schools, putting VOC
and GEN equal to 1 in turn.
17
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
^ = 88,000 + 11,000TECH – 90,000VOC – 143,000GEN + 343N
COST
Skilled Workers' School
^
COST
= 88,000 + 343N
(TECH = VOC = GEN = 0)
Technical School
(TECH = 1; VOC = GEN = 0)
Vocational School
(VOC = 1; TECH = GEN = 0)
General School
(GEN = 1; TECH = VOC = 0)
^
COST
= 88,000 + 11,000 + 343N
= 99,000 + 343N
^
COST
= 88,000 – 90,000 + 343N
= –2,000 + 343N
^
COST
= 88,000 – 143,000 + 343N
= –55,000 + 343N
Note that the cost functions turn out to be exactly the same as when we used general
schools as the reference category.
18
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
700000
600000
500000
COST
400000
300000
200000
100000
0
0
200
400
600
800
1000
1200
1400
-100000
N
Technical schools
Vocational schools
General schools
Workers' schools
Consequently the scatter diagram with regression lines is exactly the same as before.
19
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH VOC GEN
Source |
SS
df
MS
---------+-----------------------------Model | 9.2996e+11
4 2.3249e+11
Residual | 5.4138e+11
69 7.8461e+09
---------+-----------------------------Total | 1.4713e+12
73 2.0155e+10
Number of obs
F( 4,
69)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
74
29.63
0.0000
0.6320
0.6107
88578
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
The goodness of fit, whether measured by R2, RSS, or the standard error of the regression
(the estimate of the standard deviation of u, here denoted Root MSE), is likewise not
affected by the change.
20
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH VOC GEN
Source |
SS
df
MS
---------+-----------------------------Model | 9.2996e+11
4 2.3249e+11
Residual | 5.4138e+11
69 7.8461e+09
---------+-----------------------------Total | 1.4713e+12
73 2.0155e+10
Number of obs
F( 4,
69)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
74
29.63
0.0000
0.6320
0.6107
88578
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
But the t tests are affected. In particular, the meaning of a null hypothesis for a dummy
variable coefficient being equal to 0 is different.
21
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH VOC GEN
Source |
SS
df
MS
---------+-----------------------------Model | 9.2996e+11
4 2.3249e+11
Residual | 5.4138e+11
69 7.8461e+09
---------+-----------------------------Total | 1.4713e+12
73 2.0155e+10
Number of obs
F( 4,
69)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
74
29.63
0.0000
0.6320
0.6107
88578
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
For example, the t statistic for the technical school coefficient is for the null hypothesis that
the overhead costs of technical schools are the same as those of skilled workers’ schools.
22
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH VOC GEN
Source |
SS
df
MS
---------+-----------------------------Model | 9.2996e+11
4 2.3249e+11
Residual | 5.4138e+11
69 7.8461e+09
---------+-----------------------------Total | 1.4713e+12
73 2.0155e+10
Number of obs
F( 4,
69)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
74
29.63
0.0000
0.6320
0.6107
88578
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
The t ratio in question is only 0.35, so the null hypothesis is not rejected.
23
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH VOC GEN
Source |
SS
df
MS
---------+-----------------------------Model | 9.2996e+11
4 2.3249e+11
Residual | 5.4138e+11
69 7.8461e+09
---------+-----------------------------Total | 1.4713e+12
73 2.0155e+10
Number of obs
F( 4,
69)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
74
29.63
0.0000
0.6320
0.6107
88578
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
The t ratio for the coefficient of VOC is –2.65, so one concludes that the overheads of
vocational schools are significantly lower than those of skilled workers’ schools, at the 1%
significance level.
24
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH VOC GEN
Source |
SS
df
MS
---------+-----------------------------Model | 9.2996e+11
4 2.3249e+11
Residual | 5.4138e+11
69 7.8461e+09
---------+-----------------------------Total | 1.4713e+12
73 2.0155e+10
Number of obs
F( 4,
69)
Prob > F
R-squared
Adj R-squared
Root MSE
=
=
=
=
=
=
74
29.63
0.0000
0.6320
0.6107
88578
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
General schools clearly have lower overhead costs than the skilled workers’ schools,
according to the regression.
25
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH WORKER VOC
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
154110.9
26760.41
5.759
0.000
100725.3
207496.4
WORKER |
143362.4
27852.8
5.147
0.000
87797.57
198927.2
VOC |
53228.64
31061.65
1.714
0.091
-8737.646
115194.9
_cons | -54893.09
26673.08
-2.058
0.043
-108104.4
-1681.748
-----------------------------------------------------------------------------. reg COST N TECH VOC GEN
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
Note that there are some differences in the standard errors. The standard error of the
coefficient of N is unaffected.
26
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH WORKER VOC
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
154110.9
26760.41
5.759
0.000
100725.3
207496.4
WORKER |
143362.4
27852.8
5.147
0.000
87797.57
198927.2
VOC |
53228.64
31061.65
1.714
0.091
-8737.646
115194.9
_cons | -54893.09
26673.08
-2.058
0.043
-108104.4
-1681.748
-----------------------------------------------------------------------------. reg COST N TECH VOC GEN
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
The one test involving the dummy variables that can be performed with either specification
is the test of whether the overhead costs of general schools and skilled workers’ schools
are different.
27
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH WORKER VOC
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
154110.9
26760.41
5.759
0.000
100725.3
207496.4
WORKER |
143362.4
27852.8
5.147
0.000
87797.57
198927.2
VOC |
53228.64
31061.65
1.714
0.091
-8737.646
115194.9
_cons | -54893.09
26673.08
-2.058
0.043
-108104.4
-1681.748
-----------------------------------------------------------------------------. reg COST N TECH VOC GEN
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
The choice of specification can make no difference to the outcome of this test. The only
difference is caused by the fact that the regression coefficient has become negative in the
second specification.
28
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH WORKER VOC
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
154110.9
26760.41
5.759
0.000
100725.3
207496.4
WORKER |
143362.4
27852.8
5.147
0.000
87797.57
198927.2
VOC |
53228.64
31061.65
1.714
0.091
-8737.646
115194.9
_cons | -54893.09
26673.08
-2.058
0.043
-108104.4
-1681.748
-----------------------------------------------------------------------------. reg COST N TECH VOC GEN
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
The standard error is the same, so the t statistic has the same absolute magnitude and the
outcome of the test must be the same.
29
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH WORKER VOC
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
154110.9
26760.41
5.759
0.000
100725.3
207496.4
WORKER |
143362.4
27852.8
5.147
0.000
87797.57
198927.2
VOC |
53228.64
31061.65
1.714
0.091
-8737.646
115194.9
_cons | -54893.09
26673.08
-2.058
0.043
-108104.4
-1681.748
-----------------------------------------------------------------------------. reg COST N TECH VOC GEN
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
However the standard errors of the coefficients of the other dummy variables are slightly
larger in the second specification.
30
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH WORKER VOC
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
154110.9
26760.41
5.759
0.000
100725.3
207496.4
WORKER |
143362.4
27852.8
5.147
0.000
87797.57
198927.2
VOC |
53228.64
31061.65
1.714
0.091
-8737.646
115194.9
_cons | -54893.09
26673.08
-2.058
0.043
-108104.4
-1681.748
-----------------------------------------------------------------------------. reg COST N TECH VOC GEN
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
This is because the skilled workers’ schools are less ‘normal’ or ‘basic’ than the general
schools and there are fewer of them in the sample (only 17, as opposed to 28).
31
THE EFFECTS OF CHANGING THE REFERENCE CATEGORY
. reg COST N TECH WORKER VOC
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
154110.9
26760.41
5.759
0.000
100725.3
207496.4
WORKER |
143362.4
27852.8
5.147
0.000
87797.57
198927.2
VOC |
53228.64
31061.65
1.714
0.091
-8737.646
115194.9
_cons | -54893.09
26673.08
-2.058
0.043
-108104.4
-1681.748
-----------------------------------------------------------------------------. reg COST N TECH VOC GEN
-----------------------------------------------------------------------------COST |
Coef.
Std. Err.
t
P>|t|
[95% Conf. Interval]
---------+-------------------------------------------------------------------N |
342.6335
40.2195
8.519
0.000
262.3978
422.8692
TECH |
10748.51
30524.87
0.352
0.726
-50146.93
71643.95
VOC | -90133.74
33984.22
-2.652
0.010
-157930.4
-22337.07
GEN | -143362.4
27852.8
-5.147
0.000
-198927.2
-87797.57
_cons |
88469.29
28849.56
3.067
0.003
30916.01
146022.6
------------------------------------------------------------------------------
As a consequence there is less precision in measuring the difference between their costs
and those of the other schools than there was when general schools were the reference
category.
32
Copyright Christopher Dougherty 2011.
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11.07.25