LN+6+Interactive+Terms

LN+6+Interactive+Terms - Empirical Methods II (API-202A)...

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Empirical Methods II (API-202A) Kennedy School of Government Harvard University 1 Lecture Notes 6 Non-linear Relationships – Interactive Terms Non-linear regression can take on more than one form: 1. Logs and Quadratics (last class) The predicted change in Y associated with a change in X 1 depends on the value of X 1 2. Interaction between two variables – i.e. X1*X2 (dummies and/or non-dummies) The predicted change in Y associated with a change in X 1 depends on the value of another variable X 2 Example of dependence on another variable : Does the data suggest that the relationship between wages and years of experience is the same for men and women? Wages = 0 ˆ 1 ˆ Female + 2 ˆ Education + ˆ . reg wage female educ, robust Regression with robust standard errors Number of obs = 526 R-squared = 0.2588 ------------------------------------------------------------------------------ | Robust wage | Coef. Std. Err. t P>|t| [95% Conf. Interval] -------------+---------------------------------------------------------------- female | -2.273362 .2702033 -8.41 0.000 -2.804179 -1.742545 educ | .5064521 .0598956 8.46 0.000 .3887867 .6241176 _cons | .6228168 .7286843 0.85 0.393 -.8086909 2.054324 ------------------------------------------------------------------------------ Note: To simplify the presentation we will use wages and not Log (wages) as LHS variable. QUESTION #1 : Can we answer our question with this regression?
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Empirical Methods II (API-202A) Kennedy School of Government Harvard University 2 To answer our question we need to: i) Create a new RHS variable that results from the interaction between the dummy variable female and the variable educ (education or years of schooling). Let’s see how this works with our data set: . gen fem_educ=female*educ . list educ female fem_educ in 1/5 +--------------------------+ | educ female fem_educ | |--------------------------| 1. | 11 1 11 | 2. | 12 1 12 | 3. | 11 0 0 | 4. | 8 0 0 | 5. | 12 0 0 | +--------------------------+ ii) Estimate the following SR: Wages = 0 ˆ 1 ˆ Female + 2 ˆ Education + 3 ˆ Female * Education + ˆ o 1 ˆ no longer represents the predicted change in Y given a one-unit change in X. Why not? o We can no longer interpret the magnitude of the coefficients in isolation since we cannot change gender and “hold the variable female*education constant.”
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Empirical Methods II (API-202A) Kennedy School of Government Harvard University 3 How do we interpret the relationship between educations and wages in this regression?
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This note was uploaded on 04/12/2009 for the course HKS API202A taught by Professor Levy during the Spring '09 term at Harvard.

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LN+6+Interactive+Terms - Empirical Methods II (API-202A)...

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