Suppose that the model of XXXXXXXXXXis formulated with an overall constant term and n − 1 dummy variables (dropping, say, the last one). Investigate the effect that this supposition has on the set of...

Week 6 notes.doc

How do you decide which independent variables?
If you want to read more about this, try Studenmund, A.H. Using Econometrics
Chapter 7. (either 3rd or 4th Editions)
1. Theory
Is the variable’s place in the equation certain and theoretically sound?
Most important!
2. T-test
Is the variable’s estimated coefficient significant in the expected direction
(one-sided test)?
3.
2
R
Does the overall fit of the equation improve when then variable is added to
the equation?
4. Bias
Do other variables’ coefficients change significantly when the variable is added
to the equation?
If all of these are true, then the variable belongs in the equation.



1. Intercept Dummy Variables
i = β0 + β1X + β2Di + ε

2. Seasonal Dummies (Multi-alternative Dummies)
Ø Dummy variables used to represent qualitative variables that take on more
than two alternatives

Use one less dummy variable than there are alternatives. Each dummy will
epresent one condition.
Dummy Variables
Ø A dummy variable that changes the constant or intercept term
Ø Y
2
3. Slope Dummies
Ø A dummy variable that changes the slope of the relationship between x
and y

4. Dummy Dependent Variables
Ø Dummy variable is used as the dependent variable






CAUTION: Don’t include too many dummies or you’ll have to explain each data point!

CAUTION: Don’t include a dummy that only takes a value of 1 for one data point and
zero for all other observations. This ‘one-time’ dummy acts to eliminate that observation
from the data set, improving the fit artificially.



Example #1: More than 2 categories (more than one dummy variable)

Education can be thought of as:
(1) not having earned a high school diploma,
(2) having earned only a high school diploma, and
(3) having more education than a high school diploma.

Then we use two dummies. We’ll call them D1 and D2.

D1=1 if you have only a high school diploma
0 otherwise

D2=1 if you have more education than a high school diploma
0 otherwise.

What are all the possibilities?

you have more than a high school degree D1= _____ and D2= ____

you have a high school diploma and nothing
eyond that

D1= ____ and D2= ____

you have not earned any diploma D1= ____ and D2= ____


3
Some ideas for using dummy variables:
• Could use dummy for seasonal changes if you have data where each case is at a
different time point.

Illustration #1: If the data has been recorded quarterly, you will need 3 dummy
variables.

D1 = { 1 in Quarter 1
0 otherwise

D2 = { 1 in Quarter 2
0 otherwise

D3 = { 1 in Quarter 3
0 otherwise


D1 D2 D3
Quarter 1
Quarter 2
Quarter 3
Quarter 4


Illustration #2: Dummy for Time Series Data
If you were interested to study the impact of a particular event on a given...