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Unformatted text preview: Interactions, Binary Variables and Categorical Variables PAM 3100 Professor Michael Lovenheim Fall 2010 PAM 3100 Interactions, Binary Variables and Categorical Variables 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 = + 1 Mother ed + 2 Income + 3 Mother ed * Income + u 3 is the interaction of mothers education and income. It measures how much more effect income has on test scores when mothers education is high (or low), and conversely, how much more of an effect mothers education has on test scores when income is high (or low). The partial effect of mothers education on test scores is: Score Mother ed = 1 + 3 * Income The partial effect of Income on test scores is: Score Income = 2 + 3 * Mother ed PAM 3100 Interactions, Binary Variables and Categorical Variables Interactions in OLS Regressions Example Score = + 1 Mother ed + 2 Income + 3 Mother ed * Income + u A positive value of 3 suggests that the effect of income on test scores is higher when mothers education is higher. It also suggests the effect of mothers education on test scores is higher when income is higher. 3 > 0 suggests income and mothers education are compliments in the production of test scores. 3 < 0 suggests they are substitutes. Now, we must interpret 1 and 2 with care. 1 is the effect of mothers education on test scores when income is zero. 2 is the effect of income on test scores when mothers education is zero. Since income and mothers education are not (or are rarely) zero, these have little direct use. PAM 3100 Interactions, Binary Variables and Categorical Variables Example: Beer Taxes and Beer Prices Independent Variable Beer Price (Cents) Beer Tax (Cents) 0.195 (0.255) Distance to Nearest0.028 Lower Tax State (0.018) DistanceTax 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 passthrough of taxes to prices increases by 0.007 cents. At 100 miles, the passthrough is 0.195+0.007*100=0.195+0.7=0.895. Note every 1 mile increase in distance is associated with a0.028 + 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....
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This note was uploaded on 01/30/2012 for the course PAM 3100 at Cornell University (Engineering School).
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