You are given the following data on 2,800 respondents in the Australian National Longitudinal Survey of Youths with Jobs in 1994:

 

 =          Hourly earnings in the respondent’s main job at the time of 1994 interview

= Educational attainment (highest grade completed)

 =     Mother’s and father’s educational attainment

=       Composite score on cognitive tests in the Vocational Aptitude Test

=       Gender

=       Ethnicity (aboriginal, Caucasian, “others”, that is not aboriginal

or Caucasian)

=       Whether the main job in 1994 was in the government sector or

the private sector

 

(a)   As a policy analyst, you are asked to investigate whether there is evidence of earning discrimination, positive or negative, by sex or ethnicity in (1) government sector, and (2) the private sector.  Explain how you would do this, giving a mathematical representation of the regression specification(s). Also illustrate your answer graphically.

 

(b)   You are asked to investigate whether the incidence of earnings discrimination, if any, is significantly different in the two sectors.  Explain how you would do this, giving a mathematical representation of your regression specification(s).

 

 

Question 2.

 

a)   Consider the Cobb-Douglas production function that relates output (Y) to capital (K) and labour (L) which can be written as:

 

.                       (7.1)

 

i)         Which type of nonlinear regression is the Cobb-Douglas production function described above? Give reasons to support your answer.

 

ii)                  Explain how the above production function can be linearised to be estimated by OLS technique. What are the meanings of the  and  in the transformed model?

 

b)     Consider the following two models,

 

                (7.2)

 

= .             (7.3)

 

Explain how you would use the Fisher’s test (F-test) to determine whether the linear model is the best or the nonlinear for the data?  Name any 3 approaches to nonlinear estimation.