Econ 388 R. Butler
2014 revisions lecture13
I. BENCHMARKING TRAINING PROGRAMS: Training Affects over Salesman
Lifetimes: Your merge company has a sales force drawn from individuals who have
experience one of three sales training progams: the Covey (C ) program, the Dilbert (D)
program, and the Frodo (F) program. You have been asked to evaluate the effectiveness of
each training program on the basis of a random sample of sales people. For all three
programs, it is believed that age increases the effectiveness as a salesperson. Hence, the
“model” is that there is a relationship between sales and age (sales increase generally
increase with age as sales gain experience). You want to know how alternative training
programs affect that sales-age relationship. That is, how do the training programs affect the
slope and intercept of the sales-age regression line. The data is as follows:
[[[show them lec14trn.ppt….discuss that it looks like three separate regression lines]]]]
annual
sales
56
55
63
52
58
65
64
61
69
73
62
70
41
40
46
48
45
58
55
57
62
47
64
60
28
25
71
62
50
Age
21
28
33
33
38
43
48
53
53
58
63
67
23
30
33
42
43
43
45
48
58
29
66
67
19
23
67
56
45
training
C
C
C
C
C
C
C
C
C
C
C
C
D
D
D
D
D
D
D
D
D
D
D
D
F
F
F
F
F
Covey=1
others=0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Dilbert=1
others=0
0
0
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
age*Covy
age*Dilb
21
28
33
33
38
43
48
53
53
58
63
67
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
23
30
33
42
43
43
45
48
58
29
66
67
0
0
0
0
0
1
46
34
59
36
71
62
71
37
27
47
29
59
51
63
F
F
F
F
F
F
F
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
training.do (training.sas)
***STATA *****;
# delimit ;
* training.sha the impact of the 3 training programs;
infile ann_sale age covey dilbert age_cov age_dil using
"e:\classrm_data\training.txt", clear;
regress ann_sale age in 1/12;
regress ann_sale age in 13/24;
regress ann_sale age in 25/36;
regress ann_sale age;
regress ann_sale age covey dilbert age_cov age_dil;
test (covey = 0) (dilbert =0) (age_cov = 0) (age_dil = 0);
***SAS *****;
data one;
* training.sas the impact of the 3 training programs;
infile 'e:\classrm_data\training.txt';
/* use the following infile options if the data set is tab delimited:
infile 'e:\classrm_data\training.txt' delimiter='09'x dsd truncover;*/
input ann_sale age covey dilbert age_cov age_dil;
run;
data two; set one; if (1<=_N_<=12); run;
proc reg; model ann_sale= age ; run;
data three; set one; if (1<=_N_<=12); run;
proc reg data=three; model ann_sale= age;run;
data four; set one; if (1<=_N_<=12); run;
proc reg data=four; model ann_sale= age;run;
proc reg data=one; model ann_sale= age covey dilbert age_cov age_dil;
test covey, dilbert, age_cov, age_dil; run;
a) Running each of the three samples as separate regressions ...
b) are the intercepts different for each of these 3 training programs? How do we know that
they are statistically different or not?
b) are the slopes different?
c) how do you interpret these differences?
d) what is the best training program?
II. Difference in Difference Estimates Revisited (recall the presentation in lecture 1)
Empirical example(s)
III Chow Tests: All Purpose F-Statistics
2
When we want to test the simultaneous significance of more than 1 variable (in the
salesman training example above, are slopes and intercepts statistically distinguishable, after
accounting for natural sampling variability?), then we can use "F-tests." These are also
called Chow tests, after the first econometrican to call peoples attention to the usefulness of
these tests. The usefulness of this is fairly well discussed in the text; it can be used to test
any kind of linear restriction on the coefficients. These tests are simply F-statistic type of
tests generated by examining the residual sum of squares from a restricted and unrestricted
model. If the restrictions aren't important, then residual sums of squares from both the
restricted and unrestricted models ought to be about the same and their difference should be
close to zero. The Chow test exploits this fact with a vengeance, as we have seen with
previous lecture on this useful F-statistic. Now we will do some examples from the papers
you are working on this semester. Who will be first?
A. Class participants examples from your papers
IN SUMMARY, CHOW OR F-TESTS ARE LINEAR RESTRICTIONS ACROSS
PARAMETERS EITHER TO 1. TEST IF A SUBSET OF PARAMETERS ARE
SIGNIFICANTLY DIFFERENT (SAY FROM ZERO), OR 2. TEST IF THERE IS A
SHIFT IN PARAMETERS ACROSS REGIMES (MALE EARNINGS EQUATIONS ARE
DIFFERENT THAN FEMALE EARNINGS EQUATIONS).
B. TESTING FOR DIFFERENCES IN INTERCEPTS, OR SLOPES
# delimit ;
infile ann_sale age covey dilbert age_cov age_dil using
"e:\classrm_data\training.txt", clear;
regress ann_sale age covey dilbert age_cov age_dil;
test (covey = 0) (dilbert =0);
test (age_cov = 0) (age_dil = 0);
C. TESTING FOR DIFFERENCES BETWEEN GROUPS ( like the salesman
receiving different types of training)-- revisit the results for the salesman/age and training
example from the beginning of the lecture. Testing whether all slopes and all intercepts are
equal. An approach also useful for looking at male/female differences, white/non-white
differences, corporate/field office differences, exempt/non-exempt differences, and before
the program was implemented vs. after the program was implemented (whatever the
program was).
# delimit ;
infile ann_sale age covey dilbert age_cov age_dil using
"e:\classrm_data\training.txt", clear;
regress ann_sale age in 1/12;
regress ann_sale age in 13/24;
regress ann_sale age in 25/36;
regress ann_sale age;
regress ann_sale age covey dilbert age_cov age_dil;
test (covey = 0) (dilbert =0) (age_cov = 0) (age_dil = 0);
Two ways to do F-tests from these equations (either use the first four, or the fifth one with the test
statement.
3