Reference no: EM13186240

A data set contains data on the years of formal training, training qualifications, years of work experience, and hourly earnings in rupees in 2010 for a sample of 100 refrigeration mechanics in India. Most refrigeration mechanics acquire their skills through informal apprenticeships and have no formal training. Some have one year of formal training and earn the Refrigeration Mechanic Certificate if they pass the test at the end. Some take a second year of formal training and earn the Refrigeration Mechanic Diploma if they pass the test at the end. Trainees may continue to the second year of training only if they have passed the test at the end of the first year.

Dummy variables RMC and RMD are defined as follows:

RMC = 1 for those who have had at least one year of formal training and have passed the test for the Refrigeration Mechanic Certificate, but have not passed the test for the Refrigeration Mechanic Diploma. RMC = 0 otherwise. RMD = 1 for those who have had two years of formal training and have passed the test for the Refrigeration Mechanic Diploma. RMD = 0 otherwise.

Three regressions are performed:

(1) The logarithm of hourly earnings on EXP, number of years of work experience, and TRAINING, number of years of formal training.

(2) The logarithm of hourly earnings on EXP, RMC, and RMD.

(3) The logarithm of hourly earnings on EXP, TRAINING, RMC, and RMD.

The regression results are shown in the table (standard errors in parentheses; RSS = residual sum of squares.)

(1) (2) (3)

EXP 0.030

(0.005)

0.028

(0.005)

0.029

(0.005)

TRAINING 0.200

(0.020)

- 0.100

(0.045)

RMC - 0.18

(0.04)

0.10

(0.05)

RMD - 0.30

(0.06)

0.20

(0.08)

constant 2.00

(0.60)

2.24

(0.61)

2.10

(0.70)

R2 0.35 0.40 0.42

RSS 105.0 100.0 95.0

(a)  Provide an interpretation of the coefficient of TRAINING in regression (1) and a mathematical justification for your interpretation.(see Dougherty (2011) p 200-201)

(b)  Provide an interpretation of the coefficient of RMD in regression (2) and a mathematical justification for your interpretation. (See box 5.1 in Dougherty(2011))

(c) Provide an interpretation of the coefficient of RMD in regression (3) with a brief explanation.

(d)  Someone asserts that the earnings of diploma-holders are no higher than those of certificate-holders. Explain what you would need to do to test this hypothesis. (Note: Start by considering a new dummy variable NQ (no qualification) equal to 1 for those who do not possess either the RMC or the RMD, and equal to 0 if RMC = 1 or RMD = 1.)

(e)  Someone else asserts that the extra earnings of a diploma-holder, compared with those of a certificate-holder, are equal to the extra earnings of a certificate-holder compared with the earnings of those with no formal training. Explain what you would need to do to test this hypothesis.

(f) Someone else asserts that the TRAINING variable is sufficient and that adding the dummy variables in specification (3) does not improve the explanatory power of the model. Test this hypothesis at the 1% level using an F-test.