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Impact of Training on Earnings and Optimal Period of Training by

Chew Soon Beng (NTU), Nicholas Groenewold (Western Australia) and Rosalind Chew (NTU)

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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.

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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.

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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

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2RRegressor 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)

EDOL0.0817(1.69)

EDNL0.1110(1.94)

EDSE0.0447(0.96)

EDPR0.0370(0.78)

QUAL0.0188(2.25)

LS0 (S0) 0.5117(20.83)

0.4864(18.78)

0.5050(20.18)

0.5037(20.35)

Obs 821 939 821 821 821

0.4703 0.2073 0.4219 0.4721 0.4729

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Summary of Table 1

Regressions 4 or 5 show that Gender is significantly positive and Education is significantly positive too.

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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.

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Regressors

Equation

1 2 3 4 5

CONST3.4321(18.98)

3.1944(16.02)

3.4815(20.01)

3.4457(19.57)

3.4537(19.73)

AGE-0.0013(-1.01)

-0.0013(-1.01)

-0.0013(-1.03)

-0.0012(-0.98)

-0.0013(-1.02)

GENDER0.1429(5.04)

0.1429(5.04)

0.1724(7.18)

0.1808(7.28)

0.1933(7.36)

MARITAL

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)

C30.0447(1.07)

0.2824(3.05)

C4-0.2377(-2.56)

0.2566(2.84)

C50.0189(0.62)

C60.1499(1.32)

0.3877(2.72)

C70.0040(0.10)

0.2417(2.64)

C80.2377(2.56)

QUAL0.0165(1.95)

DUR-0.0000(-0.60)

0.0002(1.13)

0.0005(1.63)

DURSQ-0.0000(-1.32)

0.0000(-1.73)

LS00.5204(20.85)

0.5204(20.85)

0.5118(20.83)

0.5145(20.87)

0.5054(20.41)

Obs 821 821 821 821 821

0.4751 0.4751 0.4700 0.4704 0.4737

Optdur 250 240

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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.

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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

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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

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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

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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.

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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.

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Regressors Equation 1 Regressors Equation 2

Regressors Equation 3

CONST3.5152(18.16) CONST

3.2269(15.95) CONST

3.3651(17.63)

AGE-0.0014(-1.10) AGE

-0.0012(-0.92) AGE

-0.0014(-1.11)

GENDER0.1853(7.07) GENDER

0.1947(7.40) GENDER

0.1713(6.26)

MARITAL0.0194(0.88) MARITAL

0.0221(1.01) MARITAL

0.0118 (0.55)

DURATION0.0005(1.58) QUAL

0.0172(2.03) QUAL

0.0157(1.86)

DURATION2

0.0000(-1.74) DURATION

0.0005(1.67) DURATION

0.0007(2.29)

QUAL0.0148(1.74)

DURATION2

0.0000(-1.70)

DURATION2

0.0000(-2.43)

TAKE1-0.0324(-1.28) ABC1

0.0166(0.61) J100

0.4016(4.47)

TAKE20.0701(2.47) ABC2

0.0085(0.31) J200

0.3136(3.66)

TAKE30.0457(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)

J7000.1006(0.58)

J8000.2624(2.73)

J10000.1034(1.02)

J99990.2896(3.52)

LS00.5016(20.25) LS0

0.5020(20.21) LS0

0.4824(19.10)

Obs 821 821 821

0.4818 0.4755 0.4976

Opt Dur 231 250 241

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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)

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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

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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.

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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.

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So optimal d depends

(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)

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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

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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.