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Applied Quantitative Methods

Applied Quantitative Methods. Lecture 10 . Dummy Variables. Maximum Likelihood Estimation. December 1 st , 2010 . Qualitative Variables. Binary Gender (male – female) Facebook account (have – don’t have) Migration status (migrant – sedentary) Multiple categories

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Applied Quantitative Methods

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  1. Applied Quantitative Methods Lecture 10. Dummy Variables. Maximum Likelihood Estimation December 1st, 2010

  2. Qualitative Variables • Binary • Gender (male – female) • Facebook account (have – don’t have) • Migration status (migrant – sedentary) • Multiple categories • Race (white, black, hispanic) • Marital status (single, married, divorced, widowed) • Type of school attended (general, occupational, technical)

  3. Binary Variable • Dummy variable (zero-one, indicator) • 1, if a person is a migrant • Migration status = • 0, if a person is a non-migrant (sedentary) • 1, if male • Gender = • 0, if female • N!B! Name you dummy variable after the characteristic for category 1 • TE Male = 1, if a person is male; 0 – if female

  4. Binary Variable (Cont.) • Interpreting estimation results • 1, if a person had migration experience • Mig = • 0, if a person never had migration experience • Coefficient α – difference in wages of migrants and non-migrants • with the same level of education and experience • Conditional expectations • Assuming

  5. Binary Variable (Cont.) • Intercept effect • Marginal effects of education (β1) and experience (β2) on wages are the same for migrants and non-migrants • TE Epstein & Radu (2009) • Migrants: Mig = 1 • Non-migrants : Mig = 0

  6. Binary Variable (Cont.) • Intercept effect

  7. Binary Variable (Cont.) • Slope effect (interaction term)

  8. Binary Variable (Cont.) • Slope effect (interaction term) • Migrants (Mig = 1 & EducMig = 1) • Non-migrants (Mig = 0 &EducMic = 0)

  9. Multiple Categories • Migration status (permanent migrant – temporary migrant – non-migrant) • Reference (base) category • - Non-migrants as reference category • Two dummy variables: • 1, if temporary migrant • MigTemp = • 0, if non-migrant • 1, if permanent migrant • MigPerm = • 0, if non-migrant

  10. Multiple Categories (Cont.) • Wage equation • Population w/r to migration status • Non-migrants: MigTemp= 0, MigPerm= 0 • Temporary migrants: MigTemp = 1, MigPerm= 0 • Permanent migrants:MigTemp = 0, MigPerm= 1

  11. Dummy Variable Trap • Inclusion of dummy variable for non-migrants • 1, if non-migrant • NM = • 0, otherwise • Problem of perfect collinearity • Solutions • - omit one of three dummies (introduce reference category) • - eliminate intercept: αT , αP , αNM become intercepts

  12. Dummy Variable Trap • Inclusion of dummy variable for non-migrants • 1, if non-migrant • NM = • 0, otherwise • Problem of perfect collinearity • Solutions • - omit one of three dummies (introduce reference category) • - eliminate intercept: αT , αP , αNM become intercepts

  13. Multiple Dummy Variables • Wage equation • 1, if male • Male = • 0, if female • 1, if married • MarStat = • 0, if single • Married female • Married man

  14. Dummy Variable as Dependent • Wage equation • Decision to migrate • Pi is not observed, we observe only Migi being either 1 or 0

  15. Dummy Variable as Dependent (Cont.) • Using OLS to estimate a model with binary dependent variable • No normality of the error term ε • Implication: Standard errors are invalid for t and F tests • 2) Heteroskedasticity: εi depend on the values of regressors • 3) Predicted values from the model might be negative or more than 1

  16. Maximum Likelihood • Focusing example • Sample: X1 = 4, X2 = 6 • Parameter: μ – population mean. X~ N(μ; 1) • Obtaining estimate for μ

  17. Maximum Likelihood (Cont.) The complete joint density function for all values of μ with the peak at 5

  18. Maximum Likelihood (Cont.) • Normal distribution • For σ = 1 & X1 = 4, X2 = 6 • Likelihood function for μ • Log- Likelihood function

  19. Maximum Likelihood (Cont.) • For the sample of size n

  20. Maximum Likelihood (Cont.) • Population model • Density function for distribution of Yi • - Disturbances are normally distributed • Likelihood function for β1,β2, and σ

  21. Qualitative Choice Models • Linear probability model • Dummy variable as dependent • Predicting the probability that an individual with a particular set of personal characteristics would make a given choice

  22. Probit Model Assuming that probability is S-shaped function of Z Linear probability model p = Z Probit analysis: Logit analysis :

  23. Probit Model (Cont.) • Sensitivity- marginal effect of Z on probability p

  24. Probit Model (Cont.)

  25. Probit Model (Cont.) • TE Graduation • 1, if graduated from high school • Grad = • 0, if not graduated • Probit Grad Score SM SF

  26. Probit Model: Interpreting Coefficients • Indirect interpretation of the coefficients

  27. Probit Model: Interpreting Coefficients

  28. Next Lecture Topic: Instrumental Variables !Wooldridge, Chapter 15 Paper: Levitt, S.D. (1997). Using Electoral Cycles in Police Hiring to Estimate the Effect of Police on Crime. The American Economic Review, Vol. 87, No. 3, (Jun., 1997), pp. 270-290

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