1BINARY VARIABLES
When modeling certain relationships, it may be necessary to recognize the possibility that certain
events may change the nature of the relationships among the variables included in a regression
model by changing either the slope or the intercept or both. For example, an event such as war
may change the relationship between consumption and income. Also, gender discrimination may
cause differences in the coefficients of the earnings regressions for men and women. Likewise, a
strike or bad weather may alter the relationship between a firm’s advertisement expenditure and
its sales revenue. In other words, it is quite conceivable that the intercept or slope coefficients
may change over time if time series data are used. Likewise, it is quite conceivable that the
intercept and slope coefficients may be different for different groups if cross section data are
used. Such changes in the slope, intercept or both are referred to as structural changes, since they
entail changes in the structure of the model.
To examine the impacts of such events on regression relationships econometricians often use
qualitative independent variables, commonly referred to as binary variables, dummy variables or
indicator variables. As we shall see below, such variables assume only two possible values, 0 or
1.
We shall now examine how binary variables can be used to capture the following situations:
(i)
changes in the intercept
(ii)
changes in the slope
(iii)
changes in both the intercept and the slope
Each of these situations will be discussed in turn.
USING BINARY VARIABLES TO CHECK FOR CHANGES IN THE INTERCEPT
In a regression model relating consumption and income using time series data we may examine
the impact of war on the intercept by creating a binary variable D which assumes the value 1
when the period is a wartime period and 0 when it is a peacetime period. Thus, we specify the
following regression:
y
i
=β
0
+β
1
x
i
+β
2
D
i
+ε
i
where y and x denote consumption and income, respectively;
D is a binary variable (D=0 for
peacetime period and D=1 for wartime period).
Since D=0 for peacetime period, the regression for peacetime period will, in fact, be:
y
i
=β
0
+β
1
x
i
+β
2
0+ε
i
i.e. y
i
=β
0
+β
1
x
i
+ε
i
, which has intercept β
0
and slope β
1
Since D=1 for wartime period, the regression for the wartime period will, in fact, be:
y
i
=β
0
+β
1
x
i
+β
2
1+ε
i
i.e. y
i
= (β
0
+β
2
)+β
1
x
i
+ε
i
, which has intercept (β
0
+β
2
) and slope β
1
1
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View Full DocumentClearly, the slope for the wartime regression is the same as the slope for the peacetime
regression. However, the two intercepts are different. Thus, by introducing a binary variable in
this manner we can test whether the intercept has changed. Should the coefficient, β
2
, of the
binary variable turn out to be significant at a reasonable level of significance it is concluded that
the intercept has changed.
USING BINARY VARIABLES TO CHECK FOR CHANGES IN THE SLOPE
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 Winter '09
 Ogwang
 Econometrics, Regression Analysis, binary variable, binary variables

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