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6Interactions, Binary and Categorical Variables

# 6Interactions, Binary and Categorical Variables -...

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Interactions, Binary Variables and Categorical Variables PAM 3100 Professor Michael Lovenheim Fall 2010 PAM 3100 Interactions, Binary Variables and Categorical Variables

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Interactions in OLS Regressions Often, we think the joint effect of two variables is different than each variable separately. We can test explicitly for this by using interaction terms: Example Score = β 0 + β 1 Mother ed + β 2 Income + β 3 Mother ed * Income + u β 3 is the interaction of mother’s education and income. It measures how much more effect income has on test scores when mother’s education is high (or low), and conversely, how much more of an effect mother’s education has on test scores when income is high (or low). The partial effect of mother’s education on test scores is: Score Mother ed = β 1 + β 3 * Income The partial effect of Income on test scores is: Score Income = β 2 + β 3 * Mother ed PAM 3100 Interactions, Binary Variables and Categorical Variables
Interactions in OLS Regressions Example Score = β 0 + β 1 Mother ed + β 2 Income + β 3 Mother ed * Income + u A positive value of β 3 suggests that the effect of income on test scores is higher when mother’s education is higher. It also suggests the effect of mother’s education on test scores is higher when income is higher. β 3 > 0 suggests income and mother’s education are compliments in the production of test scores. β 3 < 0 suggests they are substitutes. Now, we must interpret β 1 and β 2 with care. β 1 is the effect of mother’s education on test scores when income is zero. β 2 is the effect of income on test scores when mother’s education is zero. Since income and mother’s education are not (or are rarely) zero, these have little direct use. PAM 3100 Interactions, Binary Variables and Categorical Variables

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Example: Beer Taxes and Beer Prices Independent Variable Beer Price (Cents) Beer Tax (Cents) 0.195 (0.255) Distance to Nearest -0.028 Lower Tax State (0.018) Distance-Tax Interaction 0.007 ** for Nearest Lower Tax State (0.002) Constant 798.523 ** (7.560) On the border, a 1 cent increase in beer taxes increases prices by 0.195 cents. Every mile you get further from the border, the pass-through of taxes to prices increases by 0.007 cents. At 100 miles, the pass-through is 0.195+0.007*100=0.195+0.7=0.895. Note every 1 mile increase in distance is associated with a -0.028 + 0.007*tax change in prices. PAM 3100 Interactions, Binary Variables and Categorical Variables
Regression Analysis With Qualitative Information It often is the case in economics and policy analysis that our variables are qualitative - that is, they describe something about the world that is not quantitative. Gender Race Whether a respondent receives a given government intervention Whether a respondent is married What educational degree a respondent has Unlike income, expenditures, prices, etc., these concepts are hard to express in terms of continuous variables.

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6Interactions, Binary and Categorical Variables -...

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