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# ec20-newlec9 - Econometrics Lecture#9b Dummy Variables I 1...

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1 Econometrics Lecture #9b: Dummy Variables I

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2 Dummy Variables A dummy variable is a variable that takes on the value 1 or 0 Examples: male (= 1 if are male, 0 otherwise), south (= 1 if in the south, 0 otherwise), etc. Also called “binary” variables Mean of a dummy: share in the “1” category. What about in a regression?
3 A Dummy Independent Variable Consider a model with one continuous variable ( x ) and one dummy ( d ) : y = β 0 + δ 0 d + 1 x + u 0 can be interpreted as an intercept shift The difference in average y between the “1” and “0” categories at x = 0 To interpret dummy coefficients: examine expected value (or predicted value of estimates) If d = 0, then E[ y|x; d=0] = 0 + 1 x If d = 1, then E[ y|x; d=1]= 0 + 0 + 1 x

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4 Example of δ 0 > 0 x y δ 0 β 0 y = ( 0 + 0 ) + 1 x y = 0 + 1 x slope = 1 d = 0 d = 1 slope = 1
For example… Interpret the estimated slope coefficients: Ln(wage) = b 0 0.26*female+0.12yrsed Either: male-female wage gap is 26%, holding constant education (or the male- female wage gap at 0 years of education) Yrsed = b 0 + 0.5*white + 0.08*birthyear Holding constant birth year, whites average 0.5 years of education than non-whites

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6 Multiple Categories Any categorical variable can be turned into a set of dummy variables: Race, industry, region, etc. There will always be A base group is represented by the intercept, and With m categories there will be m – 1 dummy variables; Coefficient on each dummy variable interpreted as intercept shift relative to the excluded group If there are a lot of categories, it can make sense to group some together Example: top 10 ranking, 11 – 25, etc.
Multiple categories example: region Categorical variables can be entered as controls in regressions by putting in dummies for all but one category Ex: Region = {North, South, East, West} Construct… In STATA, e.g., tab region, gen(regdum) Estimate = north Not 0 North 1 North i D

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ec20-newlec9 - Econometrics Lecture#9b Dummy Variables I 1...

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