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# Y 2 3 1 x note that the marginal eects for the two

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Unformatted text preview: as the reference category. –  Male: create a variable that equals 1 when male and 0 when female (female is the reference category) –  Race: create 2 variables (1 if black, 0 otherwise; and 1 if other, 0 otherwise) leaving white as the reference category –  Region: create variables (1 if west, 0 otherwise; 1 if northeast, 0 otherwise; and 1 if midwest, 0 otherwise) leaving south as the reference category Dummy Variables •  One way of addressing non- lineari:es is to separate a variable out into many dummy variables. –  E.g. We do not expect years of educa%on to have the same eﬀect on income when going from 8 to 9 years as the eﬀect going from 15 to 16 years. –  E.g When tes:ng for a dosage eﬀect, you may want to know if going from 10mg to 20mg has the same eﬀect as going from 90mg to 100mg. •  Dummy variables are interpreted as changing the intercept term for certain groups. yi = b1 + b2 xi + b3di + ei yi = (b1 + b3 ) + b2 xi + ei if di = 1 yi = b1 + b2 xi + ei if di = 0 9 2.5 Dummy Variables 2/17/12 Functional form: yi = 1 + 2 xi + 3 di + ui where the dummy variable di Graphically is either 1 or 0. y 2 3 1 x Note that the marginal e↵ects for the two groups (implicitly deﬁned by the dummy variable) are equal but the constant terms di↵er. 2.6 Interac:on Terms Interaction Terms •  If Functional form:the slopes are diﬀerent for diﬀerent groups, when you put all of the groups together, you aren’t geong an accurate picture of the true yi = eﬀect. 1 + 2 x1i + 3 x2i + 4 (x1i · x2i ) + ui –  In an extreme case, if the eﬀect is posi:ve...
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