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12 Cards in this Set
- Front
- Back
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How can we make a linear model more flexible (showing different type of graphical relationships)?
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We can consider using 3 different types of models:
1. Logarithmic 2. Quadratic 3. Interaction Terms |
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What is the Logarithmic model?
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100*change in logY is 'approximately equal to' a %change in Y
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Give an example of a logarithmic regression model:
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predicted logY= predicted log of wage
X1= education thus: predicted log wage = predicted value of Bo+predicted value of B1 (education) |
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Can you interpret the model you created?
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each additional year of education is associated with a constant %change in wages
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why does the specification of the log wage work the way it does (in the sense that you now interpret with a % change rather than a unit change)?
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given regular values of wage such as
1 1.051 2.72 7.39 7.77 the associated log values are 0 .05 1 2 2.05 - moving from 1 --> 1.051 is little more than a 5% change and moving from 0 -->.05 is roughly 5% as well. But it does NOT work well for LARGE changes. |
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There are three different logarithmic specifications listed in table 2.3 in Woodridge, what are they?
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1. level - level
2. log - level 3. Log - Log |
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explain the specification 'level - level'
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dependent variable = y
independent variable = x interpretation of B1: change in E[Y]=B1changeX or in other words: 'if you increase x by one value, it changes expected value of Y by B1' |
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explain the specification 'log - level'
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dependent variable = log(y)
independent variable = x interpretation of B1: the percentage change in expected Y = B1change in X. then multiply B1 by 100 |
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explain the specification 'log - log'
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dependent variable = log(y)
independent variable = log(x) interpretation of B1: (*%change in Y & %change in X) So a 1% change in X you would expect a B1 % change in Y (do not multiply the B1 by 100 in this case, the percentage is already there b/c it is logged) |
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Explain why we might use the second listed 'more flexible' model: Quadratic Term
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a quadratic term allows you to model an increasing (then/or decreasing) marginal effect of X on Y, in a linear specification
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An example of a quadratic term question: How would you write the following?: Suppose that you believe experience in the labor market increases wages more so at lower levels of experience than at higher levels of experience
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wage exp Edu exp^2
25 1 4 1 36 2 4 4 45 3 4 9 56 4 4 16 58 5 4 25 61 6 4 36 61.5 7 4 49 Betas Bo Intercept 9.928571429 B1 exp 15.73214286 B2 Edu 0 B3 exp^2 -1.196428571 If B1 and B3 (which are the same data except B3 is squared) show that B1>0 (+) and B3<0 (-) then the quadratic is concave |
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Explain why we might use the third listed 'more flexible' model: Interaction Terms
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Interaction terms allow you to model the partial effect of X on Y to depend upon another variable; including an interaction term (combining by multiplication) allows you to do this
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