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Lecture33-34

# Lecture33-34 - 132 Lecture 33 Dummy variables 1 We are...

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132 Lecture 33 - Dummy variables 1) We are going to return to the study of dummy variables. Recall that we showed that one should always use one less variable than the number of categories one is looking at. Recall also that the interpretation of the dummy variable coefficient is that it measures the change from the category that has been left out to the included category. Finally, recall that we said we would very rarely use a dummy variable that would take on more than 2 values. If we have more than 2 categories, it is better to use additional dummy variables. One simple point I would like to make here is that if we are using a multiplicative equation form and want to convert it into a linear form using logs, and if, in addition, one of the independent variables is a dummy variable, then we do not want to let the dummy variable take on the value zero and one since the log is not defined for the value of zero. . This is very easy to correct. Simply let the dummy variable take on the values one and e. Then the log of the dummy variable will take on the value zero and one. (Do you see why?) 2) De-seasonalization is a term that is used to correct for specific events that occur at certain times during the year, but not at others. For instance, consumption expenditure increases dramatically during the month of December. This, of course, has to do with the fact that holidays occur during this month. So, people will not be following their normal consumption patterns. If we were to look at consumption during December and generalize from what occurs during this month to the rest of the year, we would of course be badly off in our estimates. When we de-seasonalize data, we are removing the effects of these unusual events from the data. Suppose that we have quarterly data. We can de-seasonalize the data by including dummy variables for the quarterly periods. Since there are four quarters during the year, we will include three dummy variables. The coefficients then tell us the change in the dependent variable in one quarter compared to the omitted quarter. So, if the fourth quarter is the one we omit (Since this is the quarter in which consumption expenditure is likely to be unusual), then the coefficient on each of the remaining three dummy variables tells us the difference in consumption expenditure between that quarter and the fourth quarter. . The three dummy variables we would include in the regression equation are: X 1 = in quarter 1, 0 otherwise Y B B X B X X t t = + + + . ε t 1 1 = = X in quarter 2, 0 otherwise X 1 in quarter 3, 0 otherwise 2t 3t b) In our earlier discussion of dummy variables, we gave examples in which dummy variables were used to change the intercept of the line. But, dummy variables can also be used to change the slope of the line.

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