Tutorial 12
Quantitative Methods for Economics
Tutorial 12
Katherine Eyal
TUTORIAL 12
25 October 2010
ECO3021S
Part A: Problems
1. State with brief reason whether the following statements are true, false or uncertain:
(a) In the presence of heteroskedasticity OLS estimators are biased as well as inefficient.
(b) If heteroskedasticity is present, the conventional t and F tests are invalid.
(c) If a regression model is mis-specified (e.g., an important variable is omitted), the OLS residuals will show a distinct pattern.
(d) If a regressor that has nonconstant variance is (incorrectly) omitted from a model, the (OLS) residuals will be heteroskedastic.
2. In a regression of average wages, (W , in Rands) on the number of employees (N ) for a random sample of 30 firms, the following regression results were obtained (t-statistics in parentheses):
W
=
7.5 + 0.009 N
(N/A)
W /N
= 0.008 + 7.8
(14.43)
R2 = 0.90
(16.10)
(1/N )
R2 = 0.99
(76.58)
(a) How do you interpret the two regressions?
(b) What is the researcher assuming in going from the first to the second equation?
Was he worried about heteroskedasticity? How do you know?
(c) Can you relate the slopes and intercepts of the two models?
(d) Can you compare the R2 values of the two models? Why or why not?
1
3. In 1914, the South African Robert Lehfeldt published what has become a well-known estimate of a price elasticity of demand that relied on a double logarithmic specification. Lehfeldt reasoned that variations in weather drive fluctuations in wheat production from one year to the next, and that the price of wheat adjusts so that buyers are willing to buy all the wheat produced. Hence, he argued, the price of wheat observed in any year reflects the demand for wheat. Consider the equation log(price) = β0 + β1 log(wheat) + u where price denotes the price of wheat, wheat denotes the quantity of wheat, and
1/β1 is the price elasticity of demand for wheat. Demonstrate that if the first four
Gauss-Markov assumptions
Tutorial 12
Katherine Eyal
TUTORIAL 12
25 October 2010
ECO3021S
Part A: Problems
1. State with brief reason whether the following statements are true, false or uncertain:
(a) In the presence of heteroskedasticity OLS estimators are biased as well as inefficient.
(b) If heteroskedasticity is present, the conventional t and F tests are invalid.
(c) If a regression model is mis-specified (e.g., an important variable is omitted), the OLS residuals will show a distinct pattern.
(d) If a regressor that has nonconstant variance is (incorrectly) omitted from a model, the (OLS) residuals will be heteroskedastic.
2. In a regression of average wages, (W , in Rands) on the number of employees (N ) for a random sample of 30 firms, the following regression results were obtained (t-statistics in parentheses):
W
=
7.5 + 0.009 N
(N/A)
W /N
= 0.008 + 7.8
(14.43)
R2 = 0.90
(16.10)
(1/N )
R2 = 0.99
(76.58)
(a) How do you interpret the two regressions?
(b) What is the researcher assuming in going from the first to the second equation?
Was he worried about heteroskedasticity? How do you know?
(c) Can you relate the slopes and intercepts of the two models?
(d) Can you compare the R2 values of the two models? Why or why not?
1
3. In 1914, the South African Robert Lehfeldt published what has become a well-known estimate of a price elasticity of demand that relied on a double logarithmic specification. Lehfeldt reasoned that variations in weather drive fluctuations in wheat production from one year to the next, and that the price of wheat adjusts so that buyers are willing to buy all the wheat produced. Hence, he argued, the price of wheat observed in any year reflects the demand for wheat. Consider the equation log(price) = β0 + β1 log(wheat) + u where price denotes the price of wheat, wheat denotes the quantity of wheat, and
1/β1 is the price elasticity of demand for wheat. Demonstrate that if the first four
Gauss-Markov assumptions