ECON 5340 Applied Econometrics
Homework #1
Due: Tuesday, September 24, 2013
#1. For the two-variable regression model, derive the ordinary least squares slope estimator when
the intercept is restricted to be zero. Compare the slope estimator to the standa
ECON 5340 Applied Econometrics
1
Qualitative Response Models
Qualitative response models.
explain a yes or no choice.
have the regressand as a dummy variable.
are not estimated with OLS techniques.
require maximum likelihood estimation.
include linear pro
Fall 2013
ECON 5340 Applied Econometrics Exam #2
True or False. Five points per question: 2 pts for a correct T/F and 3 pts for the explanation.
1. Measurement error in the dependent variable is more serious than measurement error in the
explanatory varia
Fall 2013
ECON 5340 Applied Econometrics Exam #2
True or False. Five points per question: 2 pts for a correct T/F and 3 pts for the explanation.
1. Measurement error in the dependent variable is more serious than measurement error in the
explanatory varia
Fall 2013
ECON 5340 Applied Econometrics Exam #1
1. The OLS slope estimator is more efficient when the variance of is high.
True or False. Five points per question: 2 pts for a correct T/F and 3 pts for the explanation.
2. The OLS slope estimator cannot b
ECON 5340 Applied Econometrics
1
The Nature of Regression Models
I cover quickly; read chapter 1 on your own
ll
Concepts:
Correlation vs. causation
Terminology & notation
Data types
2
Two-Variable Regression Analysis: Some Basic Ideas
Population regres
ECON 5340 Applied Econometrics
1
Two-Variable Regression Model: The Problem of Estimation
Ordinary least squares (OLS)
Graphical representation
Objective function
Normal equations
Solving the normal equations
Properties of the solution
e = 0
corr(X; e) =
ECON 5340 Applied Econometrics
1
Classical Normal Linear Regression Model
Normality assumption for u
Implications for the OLS estimator ^ 2
ui
i:i:d:N (0;
2
)
Why the normal distribution for u?
Analytical simplicitiy
Central limit theorem
Properties of
ECON 5340 Applied Econometrics
1
Two Variable Regression: Interval Estimation and Hypothesis
Testing
Interval Estimation
^ value is a point estimate
2
(^2
; ^ 2 + ) is an interval estimate with 1
condence level
Signicance vs. condence level
Pr( ^ 2
^ + )=
ECON 5340 Applied Econometrics
1
Extensions of the Two-Variable Regression Model
Units of Measurement
Interpreting ^ 2
Magnitude of the coe cients
Functional Forms
Linear (in the variables) model
Log-linear model
Exponential growth
Linear trend
Compari
ECON 5340 Applied Econometrics
1
Multiple Regression Analysis: Estimation
Three-Variable Model: Notation and Assumptions
Yi =
1
+
2 X2i
+
3 X3i
+ ui
Two new classical assumptions:
No perfect multicollinearity
Model is correctly specied
Gauss-Markov Theo
ECON 5340 Applied Econometrics
1
Multiple Regression Analysis: Inference
Normality Assumption
t statistic & distribution
F statistic & distribution
Large n & the central limit theorem
Jarque-Bera test
Hypothesis Testing for Individual Coe cients
Regressio
ECON 5340 Applied Econometrics
1
Dummy Variable Regression Models
Dummy Variables
Represented as Di
Di = f0 or 1g
Measure qualitative data
Examples:
Gender: D1i = M ale and D2i = F emale
Ethnicity: D1i = Caucasian, D2i = Latino, D3i = Asian, etc.
Regio
ECON 5340 Applied Econometrics
1
Multicollinearity
What is multicollinearity (MC)?
Multicollinearity is multivariate correlation amongst the explanatory variables
Perfect MC: Violates a classical assumption & OLS can be calculated
t
Imperfect MC: Typica
ECON 5340 Applied Econometrics
1
Heteroscedasticity
What is heteroscedasticity (Hd)?
Heteroscedasticity is a nonconstant error variance
E (u2 ) = var(Yi jXi ) =
i
2
i
Draw gure of PRF and error distributions
Hd more common with cross-sectional data
Ex
ECON 5340 Applied Econometrics
1
Autocorrelation
What is autocorrelation (AC)?
Autocorrelation (or serial correlation) refers to correlation across error terms
E (ui uj ) = cov (ui ; uj ) 6= 0
Draw gure of PRF and autocorrelated errors
AC more common w
ECON 5340 Applied Econometrics
1
Model Specication
Here we discuss whether the model is correct and address issues such as.
omission of a relevant variable (undertting a model),
inclusion of an irrelevant variable (overtting a model),
measurement error,
s
ECON 5340 Applied Econometrics
1
Panel Data
Panel data .
is the combination of cross-section and time series data.
is also known as longitudinal or pooled data.
increases your sample size and e ciency of your estimates.
allows you to identify eects such a