R代写-EC421

EC421: Advanced Econometric Methods - Spring 2021
Problem Set 4. Due 6:00pm (Eastern Time), Monday, 4/19 Wednesday, 4/21.
1. Let y1; y2; :::; yn be a random sample of positive data (yi > 0) from a population of with the
density function
f(y; ) =
1

ey=; y > 0
f(y; ) = 0; y 0
where > 0. This is the density of the exponential distribution. Note that it is easy to show
that E(yi) = and var(yi) = 2:
(a) Write down the log-likelihood function for this data.
(b) Derive b; the maximum likelihood estimator of :
(c) Prove that b is a consistent estimator. [Hint: compute the bias and variance of b and
show that they converge to zero as n grows.]
(d) Compute the Fisher information of : What is the Cramer-Rao lower bound for the
variance of unbiased estimators of ?
(e) Is b an e¢ cient estimator?
2. Wooldridge 7.7. Note: Equation (7.29) is the empirical example included in the lecture notes
in the Linear Probability Model section of the notes.
3. Wooldridge 8.5
4. Wooldridge 17.5
5. Wooldridge 17.7
6. Wooldridge 7.C13 parts (i)-(v) (dont do part (vi))
7. Wooldridge 17.C1
8. Wooldridge 17.C10 parts (i), (ii), (iii), (iv) and (x) only.