Qt732 Week 4 Question Paper

Assignment 4

QMT732

November 2014

Question 1
a) Consider the Cobb-Douglas production function:

log Yi  log 1   2 log X 2i   3 log X 3i  ui where Y= Output, X 2 = Labour input, X 3 = Capital input, u = stochastic disturbance term. Show that  2 and  3 give output elasticities of labour and capital. [Hint: just recall the definition of the elasticity coefficient and remember that a change in the logarithm of a variable is a relative change, assuming the changes are rather small]
(7 marks)
b) To answer this question, you have to refer to the production function in a). The regression output and additional information are given in Appendix 1. Use   5% .
i)

What is the estimated regression equation? Interpret the preceding equation.
iii) Test the hypothesis that  3  0 , you are not allowed to use t-test. [Hint: you have to use Restricted and Unrestricted models]. State the models for both restricted and unrestricted, the null and alternative hypotheses and explain the formula for the test.
[Hint: Define the RSS R , RSS UR , q, n-k in this model] iv) Test the hypothesis that this Cobb-Douglas production function has constant returns to scale. State the null and alternative hypothesis. You will need to choose the appropriate output from Wald test in Appendix 1
(23 marks)
Question 2
Consider a model on the demand for chicken in Malaysia. The annual data are for the years
1980-2008. The estimated regression is summarized as below:

ˆ  4.99  0.73LY  0.37LP  23.36D2002  36.25D2008  2.79(LY * D2002)
LC
 4.25(LY * D2008)  0.41(LP * D2002)  0.23(LP * D2008) where LC
= logarithm of chicken consumption per adult (kg)
LY
= logarithm of percapita income