Welcome to Econ 421
Introduction to Econometrics
Bing Ma
UMBC
What is Econometrics?
economic measurement
Much more than that:
Estimate economic relationships
Test economic theories
Evaluate and implement government and
business policy
Forecast
Non-experim

Inference in Multiple
Regression Models
Inference
Just as we did in Simple Regression
Models, we are going to compute
confidence intervals and perform
hypothesis tests in Multiple Regression
Models.
The idea is the same as before: but now
we can perform t

Further Issues
Further Issues
Specification error
Include an irrelevant variable
Omit a relevant variable
Multicollinearity
Heteroskedasticity
Autocorrelation
1
Include an irrelevant variable
True model:
Estimated model:
OLS estimators still unbiased;
Not

Extensions
Functional Form
One of the assumptions of the CLRM is that the
model is linear in the parameters, but we may
have nonlinear variables.
Models with nonlinear variables are useful to
accommodate many economic applications.
1
Logarithms
Sometimes,

The Multiple Regression Model
The Multiple Regression Model
Until now: 2 variables Y and X want to say something
about E(Y|X), or about the relationship between X and Y.
However, most of the time there is more than one
variable that affects Y.
Amount of t

INFERENCE IN
SIMPLE REGRESSION MODELS
Inference
Questions:
In the CAPM model (Problem Set 3), we estimated:
And found the following estimates for Microsoft
According to the theory, should be equal to zero.
Moreover, Microsoft is riskier than the market po

The Simple Regression Model
The Simple Regression Model
Until now:
1 variable X
We wanted to say something about the
population mean of X.
Now:
2 variables X, Y
We want to say something about the
population mean of one variable (Y) given
another variable

INTRODUCTION TO ESTIMATION
AND INFERENCE
Population X Sample
E(X), Var(X), Cov(X,Y), XY = population
Estimate the population parameters, using a
sample
Random Sample:
For a random variable Y, repeated draws from the
same population can be labeled as Y1, Y

STATISTICS REVIEW
Basic Concepts
Random experiment
Sample space
Random variables
Discrete. E.g.: number of children
Continuous. E.g.: height of Econ 421
students
1
Probability Functions
Probability density function (PDF)
Discrete:
E.g.: roll 1 dice.
X = c

Review of Econ 421
Statistics Review
Probability functions:
PDF
CDF
Joint PDF and CDF
Marginal PDF
Conditional PDF
Independence
1
Statistics Review
Features of Probability Distributions
Expected Value
Variance
Standard Deviation
Covariance
X, Y independen