Econometrics 2013
Quiz 1, May 27
Quiz 1 (15 points)
Consider the linear production function Yi = β0 + β1Xi + ui, where Y is output and X is input,
respectively. Suppose that the following results were obtained from a sample with 9 observations:
・ Sample average of Y = 10
・ Sample average of X = 10
・ Sample variance of Y = 20
・ Sample variance of X = 40
・ Sample covariance of X and Y = 20.
Suppose that Gauss Markov assumptions hold here and answer the following questions.
1.
Using equation (2.19) from the textbook, show the expected value and the variance of the OLS
estimator of β1. (5 points)
2.
Calculate the OLS estimates of β0 and β1. (2 points)
3.
Calculate the R2 [Hint: R2 is equaled to the square of “coefficient of correlation”, r.] (1 point)
4.
Estimate the variance of error term, σ2, and Var (𝛽𝛽̂1 ). [Hint: See eq. (2.61).] (2 points)
5.
6.
Calculate the t statistic of the slope parameter. (1 point)
Test the null hypothesis that X has no effect on Y against the alternative that X has some effect
on Y, at the 5% and 1% significance levels. (2 points)
7.
Suppose that you can get the exact same summary statistics as above from a different sample
with 13 observations. Under the situation, what’s the answer of question 5 & 6? (2 points)
Due day: June 3 (submit in class)