Impact of Training on Earnings
and Optimal Period of Training
by

Chew Soon Beng (NTU), Nicholas
Groenewold (Western Australia) and
Rosalind Chew (NTU)
1
Objectives


Based on ordinary least squares (OLS) regression
methods, the results show that the training programmes,
on the whole, have a positive impact on improving
salary. Most of the demographic variables such as age
and gender yield expected results similar to past
research, with the exception of marital status.
We also estimated the optimal period of training which is
in the region of 75 to 79 days.

2
Data Coverage: A survey was conducted in
2002;



ABC Institute conducts taining programmes
in many areas, ranging from basic education
to English, Maths, engineering, technical,
professional and to business areas such as
marketing, HR skills.
Questionnaires were sent to all participants
taking the programmes in 2000 and 2001.
The period of training ranges from two days
and to three years.
3
Profile of Participants
Gender which is captured by dummy
variable
 Marital status; single, married and others;
 Age: Below 25; 26-34; 35-45; above 46
 Education; No education; Primary;
Secondary; N-Level or O Level

4
2
RRegressor
Dependent Variable
LS1
LS1
S1
LS1
LS1
CONST
3.4773
(20.01)
6.9431
(116.47)
625.0810
(8.61)
3.4555
(18.84)
3.4874
(20.11)
AGE
-0.0013
(-1.04)
-0.0014
(-0.89)
-1.1394
(-0.65)
-0.0010
(-0.73)
-0.0013
(-1.01)
GENDER
0.1728
(7.20)
0.3890
(15.03)
254.8239
(7.91)
0.1740
(7.20)
0.1767
(7.37)
MARITAL
0.0156
(0.72)
0.0185
(0.73)
24.7863
(0.83)
0.0192
(0.88)
0.0195
(0.90)
EDOL
0.0817
(1.69)
EDNL
0.1110
(1.94)
EDSE
0.0447
(0.96)
EDPR
0.0370
(0.78)
0.0188
(2.25)
QUAL
LS0 (S0)
Obs
0.5117
(20.83)
0.4864
(18.78)
0.5050
(20.18)
0.5037
(20.35)
821
939
821
821
821
0.4703
0.2073
0.4219
0.4721
0.4729
5
Summary of Table 1

Regressions 4 or 5 show that Gender is
significantly positive and Education is
significantly positive too.
6
More Results

All courses are grouped into eight different
types in terms of similar courses of similar
duration, denoted from 1 to 8 as shown in
Table 2 and entered them each as a (0,1)
dummy variable.
7
GENDER
0.1429
(5.04)
0.1429
(5.04)
0.1724
(7.18)
0.1808
(7.28)
0.1933
(7.36)
MARITA
L
0.0170
(0.77)
0.0170
(0.77)
0.0143
(0.66)
0.0156
(0.72)
0.0227
(1.04)
C1
-0.0626
(-0.98)
0.1751
(1.70)
C2
-0.0250
(-0.72)
0.2127
(2.38)
C3
0.0447
(1.07)
0.2824
(3.05)
C4
-0.2377
(-2.56)
0.2566
(2.84)
C5
0.0189
(0.62)
C6
0.1499
(1.32)
0.3877
(2.72)
C7
0.0040
(0.10)
0.2417
(2.64)
0.2377
(2.56)
C8
0.0165
(1.95)
QUAL
-0.0000
(-0.60)
DUR
DURSQ
0.5204
0.5204
0.5118
0.0002
(1.13)
0.0005
(1.63)
-0.0000
(-1.32)
0.0000
(-1.73)
0.5145
0.5054
8
Table 2


In the first of these equations we take course 8 as the
default – course 8 includes long courses (1 to 3 years
which are technically/mechanically oriented). The results
show little change in the coefficients and significance of
the previous regressors.
If, instead, we take C4 as the default, we see that all
other course dummies have coefficients which are
positive and significant, implying that for given values of
the other regressors, the hairstyling course leads to a
lower post-training course.
9
Table 2
Taking the duration of each component of
C1 to C8 (where there is a range we take
the mid-point) and using this as a
regressor, we obtain the results reported in
equation 3 of Table 2.
 But DUR has the wrong sign

10
Table 2



It is possible that the relationship between
course duration and wage gain is non-linear as
has been found in earlier literature.
We test this proposition by including a squared
duration term; the results are reported in
equation 3 in Table 2. The results show a
positive coefficient on the linear term but a
negative one on the quadratic term;
We can estimate optimal period of training
11
Table 2
This optimal value is reported in the last
line of the table in the row titles “optdur”
 Optimal period is about 250 days if we
exclude QUAL in the equation. It is 240 if
QUAL is included

12
Results based on Tables 1 and 2

Wage gains of training are: negatively
related to age, higher for men than for
women, higher for married than for
unmarried participants, increase with prior
educational achievement and peak at a
course duration of about a year.

13
More Analysis





More questions are included in the regression:
Why took ABC courses;
Whether changed job due to taking ABC courses
Whether work actually used knowledge obtained
from taking ABC courses
We consider the contribution of each of these in
turn and, most importantly, assess the
robustness of our basic results to the inclusion of
these variables.
14
MARITAL
0.0194
(0.88)
MARITAL
0.0221
(1.01)
MARITAL
0.0118
(0.55)
DURATION
0.0005
(1.58)
QUAL
0.0172
(2.03)
QUAL
0.0157
(1.86)
DURATION
2
0.0000
(-1.74)
DURATION
0.0005
(1.67)
DURATION
0.0007
(2.29)
QUAL
0.0148
(1.74)
DURATION
2
0.0000
(-1.70)
DURATION
2
0.0000
(-2.43)
TAKE1
-0.0324
(-1.28)
ABC1
0.0166
(0.61)
J100
0.4016
(4.47)
TAKE2
0.0701
(2.47)
ABC2
0.0085
(0.31)
J200
0.3136
(3.66)
TAKE3
0.0457
(1.40)
ABC3
0.1978
(2.35)
J300
0.1271
(1.31)
TAKE4
-0.0106
(-0.43)
ABC4
0.0387
(1.18)
J400
0.3145
(3.75)
TAKE5
-0.0967
(-2.25)
J500
0.2276
(2.75)
J600
-0.0580
(-0.21)
J700
0.1006
(0.58)
J800
0.2624
(2.73)
J1000
0.1034
(1.02)
J9999
0.2896
(3.52)
15
Table 3
The TAKE2 (the respondent wanted to
change jobs) increases the post-training
wage, other things equal, while TAKE5 (
accompanying a friend or relative) has a
negative coefficient
 Optimal period does not change much
(231 days)

16
The third set of variables added and
reported in Table 3 is occupation. Most of
the dummy variables entered are
significant and positive
 The default is General Labour

17
Determining Optimal Period of
Training with Costs



Denote duration by d, maximand by V, salary by
S, real discount rate by r, ABC mark-up (the
extent to which trainers’ salaries are higher than
average) by m and class size by c. Then
If we assume that the salary gain St+i – St =
St+1(dt)-St for all t and that the real discount
rate is constant at r, we can simplify the above
to:
Vt = (St+1(dt) – St)((1-(1/(1+r)n)/r) –
(1+(1+m)/c).St.dt.
18







Maximise with respect to dt:
∂Vt/∂dt = (∂St+1/∂dt).((1-(1/(1+r)n)/r) – (1+(1+m)/c).St = 0 for a
maximum
Use the regression coefficients to write
(∂St+1/∂dt) = 0.6028 – (2)(0.0014)dt
substitute into the equation and solve for dt:
dt = (0.6028-(1+(1+m)/c).(St/20.8)/(((1-(1/(1+r)n))/r).12)))/0.0028
where we have made adjustment for the fact that we discount
annually but salaries are in terms of $ per month and duration is in
terms of days (12 months per year and 20.8 working days per
month). St was taken as the average for the sample and = 1320.
19
So optimal d depends



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(a) positively on the coefficient of d in the regression
(0.6028 in this case)
(b) negatively (absolutely, since the numerator may be
negative)) on the coefficient of the squared d term in the
regression (0.0014 in this case; it enters as 2x0.0014 in
the denominator of the formula above)
(c) negatively on m (m =trainer’s cost mark up rate;)
(d) positively on c (impact of training on earnings in
terms of number of years)
(e) negatively on r (r=real discount rate)
(f) negatively on n (c= class size)
20
Table 4
Table 4: Sensitive Test for Determining Optimal Period of Training
.m
c
r
N
Dstar
0.5
5
0.01
10
-44
0.5
5
0.01
20
79
0.5
5
0.02
10
-58
0.5
5
0.02
20
65
0.5
5
0.05
10
-103
0.5
5
0.05
20
18
0.5
8
0.01
10
-22
0.5
8
0.01
20
91
0.5
8
0.02
10
-34
0.5
8
0.02
20
78
0.5
8
0.05
10
-75
0.5
8
0.05
20
35
0.5
10
0.01
10
-14
0.5
10
0.01
20
95
0.5
10
0.02
10
-27
0.5
10
0.02
20
82
21
All these effects (except (a) and (b) which are set
at their actual values, can be varied)






Case 1: given m is 0.5, c is 5, r is 0.01 and n is 10, the optimal
period of training is negative, implying that the training programme is
not worth conducting. See Row 2 of Table 4;
Case 2: Given m is 0.5, c is 5, r is 0.01 and if n is 20, the optimal
period of training is 79 days; see Row 3 of Table 4;
Case 3: Given m is 0.5. c is 5 and n is 20 but r is 0.02. the optimal
period of training is now 65 days, shorter as predicted by the theory.
See Row 5 of Table 4;
Case 4: Given m is 0.5, r is 0.02, n is 20 but c is 8, the optimal
period of training is increased to 78 days; see Row 10 of Table 4;
Case 5: If r is 0.02, c is 8, n is 20 but m is 0.8, the optimal period of
training is down to 75 days.
Hence, it is reasonable to conclude that the optimal period of
training is around 65 to 78 days.
22