ECMT2150 INTERMEDIATE ECONOMETRICS Week 2 Tutorial
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ECMT2150 INTERMEDIATE ECONOMETRICS
Week 2 Tutorial
Linear Regression and OLS
1. Which of the following models are (or can be transformed into) linear regression models?
a. yi = β0 +β1xi(2) +ui
b. yi = β0 +β1 ln xi +ui
c. lnyi = β0 +β1xi +ui
d. yi = β0 exp(β1xi +ui )
e. yi = β0 +β1(3)xi +ui
f. yi = β0 + β1 (1⁄xi ) +ui
2. Suppose someone has given you the following regression results:
y(ˆ)t =2.6911 - 0.4795xt
where y is the coffee consumption in Australia (cups per person per day); x is the retail price of coffee ($ per kilo); and t is the time period.
[Let us assume for simplicity that this is a demand curve. Note that demand and supply side factors will jointly determine the relationship between price and quantity, so estimating a demand equation can be complicated.]
a. What is the interpretation of the intercept in this example? Does it make economic sense?
b. How would you interpret the slope coefficient?
c. Is it possible to tell what the true least squares line is? That is, can you find β0 and β 1?
d. The price elasticity of demand is defined as the percentage change in the quantity demanded for a percentage change in the price. That is, the elasticity of 
. Note that 
is just the slope of y with respect to x. From the above regression results, can you determine the elasticity of demand for coffee? If not, what additional information do you need?
3. (Computer Exercise) Use the data in WAGE2 to estimate a simple regression explaining monthly salary (wage) in terms of IQ score (IQ). IQ (intelligence quotient) tests were developed over 100 years ago and attempt to measure a person’s innate cognitive ability (IQ tests are sometimes referred to as tests of ‘general intelligence’). There is a substantial body of research which examines whether IQ is related to a range of outcomes such as occupational status, income and even criminal activity. In this exercise we consider whether and how IQ affect the wage people earn in the labour market.
a. Report the average, minimum and maximum values, and the standard deviation for wage, education and IQ in the sample (IQ scores are standardized so that the average in the population is 100 with a standard deviation equal to 15).
b. Estimate a simple regression model where a one-point increase in IQ changes wage by a constant dollar amount. Use this model to find the predicted increase in wage for an increase in IQ of 15 points. Does IQ explain most of the variation in wage?
c. Now, estimate a model where each one-point increase in IQ has the same percentage effect on wage. If IQ increases by 15 points, what is the approximate percentage increase in predicted wage?
d. Do you think the simple regression captures a causal effect of IQ on the wage? Explain.
4. (Wooldridge Question 3.4) The median starting salary for new law school
graduates is determined by:
log(salary) = β0 +β1 LSAT + β2 GPA + β3 log(libvol) + β4 log(cost) + β5rank + u,
where LSAT is the median LSAT score for the graduation class, GPA is the median college GPA for the class, libvol is the number of volumes in the law school library, cost is the annual cost of attending law school, and rank is a law school ranking (with rank = 1 being the best).
i. Explain why we expect β5 < 0.
ii. What signs do you expect for the other slope parameters? Justify your answers.
iii. Using the data in LAWSCH86 (you do not need to do any regression), the estimated equation is
log(salary) = 8.34 + .0047 LAST + .248 GPA + .095 log(libvol)
+.038 log(cost) - .0033 rank
n = 136, R2 = .842
What is the predicted ceteris paribus difference in salary for schools with a median GPA different by one point? (Report your answer as a percentage.)
iv. Interpret the coefficient on the variable log(libvol).
v. Would you say it is better to attend a higher ranked law school? How much is a difference in ranking of 20 worth in terms of predicted starting salary?
2023-09-21
Linear Regression and OLS