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BINARY_VARIABLES

# BINARY_VARIABLES - 1BINARY VARIABLES When modeling certain...

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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 0 1 x i 2 D i 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 0 1 x i 2 0+ε i i.e. y i 0 1 x i 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 0 1 x i 2 1+ε i i.e. y i = (β 0 2 )+β 1 x i i , which has intercept (β 0 2 ) and slope β 1 1

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Clearly, 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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BINARY_VARIABLES - 1BINARY VARIABLES When modeling certain...

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