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Dummy (or Binary) Explanatory Variables
Supplementary Lecture Notes:
Spring 2007
Dummy variables are qualitative (nonnumerical measures) variables as opposed to quantitative (numerical measures).
A dummy
variable characterizes an observation in terms of one of two possible disjoint categories or ‘qualities’.
In other words, if X is a dummy
variable, then it is a qualitative variable with two categories. For example, X can represent gender where observations have the "quality"
of being male or the "quality" of being female.
X = gender
Î
X = male or
X = female
Some other examples of Dummy variables:
X = employment status
Î
X= employed
or
X = not employed
X = Home ownership status
Î
X = owns home
or
X = does not own home
X = Education
Î
X = college grad
or
X = noncollege grad
In general if X is a Dummy variable then either X exhibits a certain ‘quality’ or X does not exhibit that quality.
The categories or qualities are nonnumerical.
To deal with this, we impose a "quantification" or coding scheme so that the variable takes
on numerical values.
A dummy variable is assigned the value either 0 or 1.
These are numerical codes to distinguish between two
disjoint categories.
Consider the following model
E(Y) =
β
o
+
β
1
X
1
+
β
2
X
2
Where
Y
=
annual salary of professors ($)
X
1
=
teaching experience (years)
X
2
=
gender
= 1 if male and
0 if female
Recall that in general the beta coefficient on a variable, X, tells us the expected change in Y of a one unit change in X, assuming all other
X variables in the model are held constant, i.e., controlling for the other X variables in the model.
Thus
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 Spring '07
 Francisco
 Econometrics

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