INTRODUCTION TO ECONOMETRICS II
ECO 306
NOUN
93 category. Note that we do not make any prior assumption about the size, or even the sign, of the coefficients.
2.5.3.1 The Dummy Variable Trap
What would happen if you included a dummy variable for the reference category There would be two consequences.
i.
Were it is possible to compute regression coefficients, you would not be able to give them an interpretation. The coefficient b
1
is a basic estimate of the intercept, and the coefficients of the dummies are the estimates of the increase in the intercept from this basic level, but now there is no definition of what is basic, so the interpretation collapses.
ii.
The other consequence is that the numerical procedure for calculating the regression coefficients will breakdown, and the computer will simply send you an error message (or possibly, in sophisticated applications, drop one of the dummies for you. Suppose that there are m dummy categories, and you define dummy variables D1... Dm. Then, in observation i, ∑
because one of the dummy variables will be equal to 1 and all the others will be equal to 0. But the intercept
is really the product of the parameter
and a special variable whose value is 1 in all observations. Hence, for all observations, the sum of the dummy variables is equal to this special variable, and one has an exact linear relationship among the variables in the regression model. As a consequence the model is subject to a special case of exact multicollinearity, making it impossible to compute regression coefficients.
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