Chapter 4
Multiple Regression Analysis: Inference
Derive F-test from restricted OLS estimator.
0 : =
is (k+1)x1 vector
R is a Jx(k+1) matrix
q is a Jx1 vector
This is a series of linear restrictions with the following form:
10 0 + 11 1 + + 1 = 1
20 0 +
Econ 508:
Heteroskedasticity and Autocorrelation
Juan Fung
MSPE
April 8, 2011
Juan Fung (MSPE)
Econ 508: Heteroskedasticity and Autocorrelation
April 8, 2011
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Heteroskedasticity
What is heteroskedasticity?
Recall the linear regression model,
Yi = 0
Econ 508: Discussion
28 Jan. 2011
Juan Fung
1
Review: Functions of discrete random variables
Lets go over some basic properties of the expectations operator.
Suppose X takes values in cfw_X1 , . . . , XN , with respective probabilities cfw_p1 , . . . , pN
Appendix C: Asymptotic Properties of Estimators
Consistency. Let Wn be an estimator of based on a sample of 1 , , of size n. Then, Wn is a
consistent estimator of if, for every >0,
(| | > ) 0
When Wn is consistent, is the probability limit of Wn:
( ) =
Chapter 3 / Appendix E
Functional Forms:
Example: Urban density functions
Typical functional form is:
(1) ln() = 0 + 1 +
Where y is population density, land value, or floor-area ratios, and x is distance from the central
business district.
Derivatives:
(
Econ 508, HW2
Due Friday 10 Feb., 2012
1
1. A problem of interest to health ocials (and others) is to determine the eects of
smoking during pregnancy on infant health. One measure of infant health is birth
weight; a birth weight that is too low can put an
Econ 508: Discussion
4 Feb. 2011
Juan Fung
1
Condence intervals and hypothesis testing for and 2
This is a quick review. By now, you should be very comfortable with this. It might be useful
to review the important sampling distributions from Econ 506: N,
Econ 508, HW3
Due Tuesday 28 Feb., 2012
1
1. Zellner and Revankar (ReStud, 1970) modeled a generalized Cobb-Douglas production
function that captures varying economies of scale (increasing, then decreasing in output). In standard Cobb-Douglas, costs incre
Economics 508 (MSPE)
Spring 2007
Anil K. Bera
UNIVERSITY OF ILLINOIS
Department of Economics
FIRST EXAMINATION
Friday, March 9, 2007
10:00am - 12:00 noon
Room: Huff 112
Amado/5
Name:
Student ID:
This is a. closed-book examination. Notations are as use
Econ 508, HW1
Due Friday 3 Feb., 2012
1
1. The data in 401K.RAW are a subset of data analyzed by Papke (1995) to study the relationship between participation in a 401(k) pension plan and the generosity of the plan.
The variable prate is the percentage of
Econ 508, HW3
Due Friday 17 Feb., 2012
1
1. The following model can be used to study whether campaign expenditures aect election outcomes:
voteA = 0 + 1 log(expendA) + 2 log(expendB) + 3 prtystrA + u,
where voteA is the percentage of the vote received by
Econ 508, HW5
Due Thursday 15 March, 2012
1
1. To test the eectiveness of a job training program on the subsequent wages of workers,
we specify the model
log(wage) = 0 + 1 train + 2 educ + 3 exper + u,
where train is a binary variable equal to one if a wo
Production and Cost Functions
Based on Ernst Berndt, The Practice of Econometrics.
Includes a favorite quote: _ has written a paper of tremendous scope. In doing it, he had a
great struggle with the data. He won a few points, the data won a few points, an
Dummy Variables and Nonlinearities
Example from text: wage regression.
To simplify, focus on just the single explanatory variable, education.
Separate equations for male (M) and female (F):
Male only: = 0 + 1 +
Female only: = 0 + 1 +
Common slopes, diff
Instrumental Variables
Introduction: Measurement error for a single explanatory variable:
= +
= real value of the explanatory variable no measurement error
x = observed value of the explanatory variable includes measurement error
= +
and ( , ) = 0
(,
Econ 508:
Correlation and Regression
Juan Fung
MSPE
February 11, 2011
Juan Fung (MSPE)
Econ 508: Correlation and Regression
February 11, 2011
1 / 17
Introduction: the purpose of correlation and regression analysis
Suppose you observe n realizations of two
Econ 508:
Simple RegressionInference and prediction
Juan Fung
MSPE
February 25, 2011
Juan Fung (MSPE)
Econ 508: Simple RegressionInference and prediction
February 25, 2011
1 / 19
From estimation to inference
Simple regression model
Recall from last time t
Econ 508:
Multiple Regression
Juan Fung
MSPE
March 4, 2011
Juan Fung (MSPE)
Econ 508: Multiple Regression
March 4, 2011
1 / 20
The multiple regression model
Multiple inuences
We can extend the simple regression model
Yi = 1 + 2 Xi + i ,
to capture other i
Econ 508:
Multiple Regression: t and F tests
Juan Fung
MSPE
March 18, 2011
Juan Fung (MSPE)
Econ 508: Multiple Regression: t and F tests
March 18, 2011
1 / 10
General tests of the parameters
Recall the multiple regression model
Yi = 0 + 1 X1 + + k Xk +
i
Econ 508:
Issues beyond heteroskedasticity and autocorrelation
Juan Fung
MSPE
April 22, 2011
Juan Fung (MSPE)
Econ 508: Issues beyond heteroskedasticity and autocorrelation pril 22, 2011
A
1 / 26
Outline
More violations of the classical assumptions
Qualit
Measurement Error in the Dependent Variable
= 0 + 1 1 + + +
y* = real value of the dependent variable no measurement error
y = observed value of the dependent variable includes measurement error
Measurement error:
0 =
= difference between observed and
Simultaneous Equations Models
Another application of the IV approach. So far have used it for:
1. Omitted variables a variable like ability that is omitted from an equation and is
correlated with the included variables. Potential solution is to find an in
Time Series Models
Focus first on errors:
( ) = 2
Typically assume homskedasticity.
Denote an entry of by , where s<t.
Typically assumed that is a function of |t-s|, but not of t or s alone. A stationarity
assumption.
Definitions:
Autocovariances:
( , )
Econ 508, HW6
Due Friday 13 April, 2012
1
1. The accelerator model of inventory investment is
invent = 0 + 1 GDPt + ut ,
1 > 0
(1)
where invent is real value inventories in the US, GDPt is real gross domestic product,
and invent is the change in inventori