Description

1 attachmentsSlide 1 of 1attachment_1attachment_1.slider-slide > img { width: 100%; display: block; }

.slider-slide > img:focus { margin: auto; }

Unformatted Attachment Preview

Economics 122B

Applied Econometrics II

Fall 2020

Homework 2

Due by 4pm on 5/14/2020

Derivations

Problem 1: Given the model y = X? + ? with E(?|X) = 0 and V ar(?|X) = ?,

please derive the expected value and covariance matrix of the estimator

?? GLS = (X 0 ??1 X)?1 X 0 ??1 y.

(1)

If you are given X and y only, is this estimator feasible? Discuss what you may need

to do, listing the steps in the process explicitly.

Problem 2: Given the model y = X? + ? with E(?|X) = 0 and V ar(?|X) = ?,

please derive the expected value and covariance matrix of the OLS estimator. Is

OLS biased in this setting? Is it efficient? If you are unwilling to place additional

assumptions about the form of heteroskedasticity, how can you estimate the standard

errors of the OLS estimator? Please discuss.

This material is in your class notes. However, your understanding of the

material is essential, so do not copy blindly make sure you understand

the steps and the main ideas.

Application

Problem 3: Generate a covariate matrix X of dimension n × k, where n = 250 and

k = 2. The first column in X should be a column of ones and the other column can

be generated from a normal distribution with variance 10. Let ? = (0.5, 1)0 and let

? 2 = 1. Simulate y from the model y = X? + ?, where ? ? N (0, ? 2 In ). Estimate ?

by ordinary least squares and produce the forecast point estimates y?f for Xf = X.

Also produce the standard errors of your forecast and plot your point and interval

estimates of your forecast in a graph. [Hint: see your class notes.] Provide details on

your calculations and also submit your computer code.

For this exercise, you can use any software you are comfortable with, but

program the steps yourself, following the theoretical derivations presented

in class.

Purchase answer to see full

attachment

Tags:

economics

OLS

Derivations

User generated content is uploaded by users for the purposes of learning and should be used following FENTYESSAYS.COM ESSAY’s honor code & terms of service.