Econometrics (CIC2005)
Tutorial 10
Multiple Regression Analysis: OLS Asymptotic
Question 1.
In the simple regression model under MLR.1 through MLR.4, we argued that the slope
estimator, ˆ
β1, is consistent for β1. Using ˆ
β0= ¯y−ˆ
β1¯x1, show that ˆ
β0=β0. [You need
to use the consistency of ˆ
β1and the law of large numbers, along with the fact that β0=
E(y)−β1E(x1).]
Question 2.
Suppose that the model
pctstck =β0+β1funds +β2risktol +u
satisfies the first four Gauss-Markov assumptions, where pctstck is the percentage of a
worker’s pension invested in the stock market, funds is the number of mutual funds that the
worker can choose from, and risktol is some measure of risk tolerance (larger rsiktol means
the person has a higher tolerance for risk). If f unds and risktol are positively correlated,
what is the inconsistency in ˜
β1, is the slope coefficient in the simple regression of pctstck on
funds?
Question 3.
The data SMOKE contains information on smoking behavior and other variables for a random
sample of single adults from the United States. The variable cigs is the (average) number
of cigarettes smoked per day. Do you think cigs has a normal distribution in the U.S. adult
population? Explain.
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