Homework 4 Solutions
Ryan Abman, Chris Severen, Dan Argyle
February 24, 2014
1
Asymptotic Normality to Consistency
A) Consistency is a basic requirement of an estimator. As long as our estimator is co
Homework 3 Solutions
Ryan Abman, Chris Severen, Dan Argyle
February 13, 2014
1
MLE
A) Seeing as how cfw_Xt n is a sequence of independent and identically distributed (iid) exponential random
t=1
varia
Key Topics
Probability Concepts
Understand and verify the following implications, with X = fx1 ; : : : ; xn g,
E (ut jX ) = 0 ) E (ut jxt ) = 0 ) E (ut ) = 0
E (ut jxt ) = 0 ) E (xt ut ) = 0
You shoul
Economics 241B
Exercise 6
1.
Asymptotic Behavior of Hypothesis Tests
Your eldwork requires that you test H0 :
a.
You know that under H0 ,
p
n Bk
k
=
k
vs. H1 :
k
6=
d
k
p
! N (0; Avar (Bk )
k.
(1)
\
A
University of California
Department of Economics
D. Steigerwald
Economics 241B
Exercise 3
1.
Let (X1,Xn) be an independent and identically distributed sample of exponential
random variables with param
Homework 1 Solutions
Ryan Abman, Chris Severen, Dan Argyle
January 21, 2014
1
Scaling and R2
A) In this context, you would explain to the board member that R2 measures the proportion of test score
var
University of California
Department of Economics
D. Steigerwald
Economics 241B
Exercise 7
1.
Consider the population model (in deviation-from-means form)
Yt X t* U t ,
in which X t* is latent. The obs
University of California
Department of Economics
D. Steigerwald
Economics 241B
Exercise 2
1.
Consider the bivariate regression model
Yt X t U t ,
in which the regressor is exogenous and all observatio
University of California
Department of Economics
D. Steigerwald
Economics 241B
Exercise 5
1.
We will investigate the following claim (which appears in nearly this form in
Studenmund)
If an equation th
241B Lecture
Ergodic Stationarity
The key concept in extending analysis to time series, is a stochastic process. A
stochastic process is simply a formal name given to a sequence of random variables.
I
Homework 2 Solutions
Ryan Abman, Chris Severen, Dan Argyle
January 30, 2014
1
Distribution of estimator
A) Rejecting the null hypothesis tells us (with a fairly high degree of certainty) that the popu
Economics 241B
Population Regression Models
A starting point for work in econometrics is to select a variable of interest,
often termed the dependent variable, most frequently denoted Yt . The phrase
Economics 241B
Endogeneity Bias - The Example of Working
The classic illustration of the biases created by endogeneity dates to Working in
1927. Consider the simple model of demand and supply (for coe
Heteroskedasticity-Consistent Standard Errors
Hayashi 2.5
Goal:
accurate standard error estimates with heteroskedasticity
Scalar model
V ar ^ =
(
P
xt u t ) 2
P 2 2
xt
martingale dierence sequence ass
Conditional Expectation Functions
Econometrics II
Douglas G. Steigerwald
UC Santa Barbara
D. Steigerwald (UCSB)
Expectation Functions
1 / 23
Overview
Reference: B. Hansen Econometrics Chapters 1 and 2
Population Regression Models
Econometrics II
Douglas G. Steigerwald
UC Santa Barbara
Winter 2011
D. Steigerwald (UCSB)
Population Models
Winter 2011
1 / 12
Overview
Reference: F. Hayashi Econometrics
University of California
Department of Economics
Doug Steigerwald
Econometrics
Economics 241B
Course Goals:
To provide training in linear regression models, with special focus on the issues of endogen
Economics 241B 2014 Final
Question 1
An ongoing debate concerns the economic returns to schooling. The goal is to ensure that
the observed correlation between schooling and wage rates is not due to co
ECON 241B
Additional Problems
Question 1 Winter 2011 Q1
You wish to estimate the eect of unemployment on criminal behavior in Gotham City. In
your model, Crimet , is a function of the unemployment rat
Homework 5 Solutions
Ryan Abman, Chris Severen, Dan Argyle
February 27, 2014
1
The Studenmund Claim
A) Because Yt is strictly stationary, E(Yt ) does not depend on t. Thus E(Yt ) = E(Yt1 ) = 0. Theref
Homework 6 Solutions
Ryan Abman, Chris Severen, Dan Argyle
March 5, 2014
1
Asymptotic Behavior of Hypothesis Tests
A) Note that our test statistic is:
Bk k
n(Bk k )
=
SE (Bk )
Avar(Bk )
1 1
where Avar
Economics 241B 2014 Final
Question 1
An ongoing debate concerns the economic returns to schooling. The goal is to ensure that the
observed correlation between schooling and wage rates is not due to co
ECON 241B
Additional Problems
Question 1 Goes with HW6 (from Dougs old HW)
Consider the model:
Yt = 01 Xt1 + 02 Xt2 + Ut
t = 1, . . . , n
(1)
where Ut i.i.d.N (0, 2 ) while Xt1 and Xt2 are scalars suc
Homework 7 Solutions
Ryan Abman, Chris Severen, Dan Argyle
March 14, 2014
1
Instrumental Variables
A) To show that 1 can be written as a function of the average wage for law degree holders and non law
Economics 241B
Exercise 4
1.
Asymptotic Normality to Consistency
You undertake a research project on carbon sequestration with a colleague from
the geology department. He defers to you as the expert o
Economics 241B
Problem Set 1
1.
Scaling and R2
You are studying student test scores. To determine the impact of teachers on
test scores, you regress student specic test scores against: parents income
Economics 241B
Review of Limit Theorems for Sequences of Random Variables
Convergence in Distribution
The previous denitions of convergence focus on the outcome sequences of a random variable. Converg
Economics 241B
Modes of Convergence
We have concentrated on the (exact) nite-sample distribution for the OLS estimator. The nite-sample theory breaks down if one of the following three
assumptions is
241B Lecture
Application: Returns to Scale in Electricity Markets
We work from Nerlove (1963): a classic study of returns to scale in a regulated
industry.
The Electricity Supply Industry
In 1963, the
241B Lecture
Generalized Least Squares
One classic assumption (1.4) states that the errors have a spherical conditional
covariance matrix,
E (U U 0 jX ) = 2 I:
Today we relax the assumption and allow