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EMET2007 Lecture 9 for Wattle - EMET2007/6007 Econometrics...

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EMET2007/6007 Econometrics I: Econometric Methods Professor Rodney W. Strachan, ANU qualitative variables 8 st May 2013 Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 1 / 53
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RODNEY: TURN ON THE RECORDING! Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 2 / 53
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Multiple Regression Analysis with Qualitative Information Introductory Econometrics: A Modern Approach by Je/rey M. Wooldridge, 4e This will be Chapter 7 Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 3 / 53
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Variable/Data types: Categorical or qualitative: Separates observations into groups. E.g., gender, race Ordinal: Has a clear ordering. E.g., °Like± > °Dislike±, or °Agree strongly± > °Agree± > °Neither agree nor disagree± > °Disagree± > °Strongly disagree± Interval: The distance between 1 and 2 is the same distance as between 5 and 6, but there is no real zero. That is, 2 is not twice as big as 1. E.g., Time 10pm and 8pm, Temperature (OK ignoring 0 o Kelvin) Ratio: has a real zero. E.g., height, weight, wealth, Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 4 / 53
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This lecture will be largely about how to incorporate categorical/qualitative and ordinal variables into regression analysis Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 5 / 53
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Multiple Regression Analysis with Qualitative Information Qualitative Information Examples: gender, race, industry, region, rating grade, . . . A way to incorporate qualitative information is to use dummy variables They may appear as the dependent or as independent variables A single dummy independent variable wage = β 0 + δ 0 female + β 1 educ + ε δ 0 = the wage gain/loss if the person is a woman rather than a man (holding other things ²xed) Dummy variable: female = 1 if the person is a woman female = 0 if the person is a man Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 6 / 53
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Alternative interpretation of coefficient: i.e. the difference in mean wage between men and women with the same level of education: Intercept shift Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 7 / 53
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For the same level of education, the expected wage of a male is di/erent to the expected wage of a female The expected wage of a male is ( female = 0) E ( wage j educ ) = β 0 + β 1 educ The expected wage of a female is ( female = 1) E ( wage j educ ) = β 0 + δ 0 + β 1 educ The di/erence is then E ( wage j educ , female ) ° E ( wage j educ , male ) = δ 0 Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 8 / 53
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The coe¢ cient δ 0 captures the di/erence in the expected y from the base category: in this case the base category is °men± If δ 0 < 0 then by virtue of being a male, a man with the same level of education as a woman can expect a higher wage than the woman. An interesting and important hypothesis, then, is H 0 : δ 0 = 0 H 1 : δ 0 6 = 0 OR H 0 : δ 0 ± 0 H 1 : δ 0 < 0 Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 9 / 53
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Dummy variable trap Putting too many dummies in and so inducing perfect multicollinearity For example, wage = β 0 + δ 0 female + δ 1 male + β 1 educ + ε This model cannot be estimated (perfect collinearity) female + male = 1 Lecture 9 (qualitative variables) EMET2007/6007 8 st May 2013 10 / 53
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