Applied Quantitative Methods Lecture 10 Dummy Variables Maximum

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 Race (white, black, hispanic) Marital status (single, married, divorced, widowed) Type of school attended (general, occupational, technical)

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

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

Binary Variable (Cont. ) § Intercept effect Marginal effects of education (β 1) and experience (β 2) on wages are the same for migrants and non-migrants TE Epstein & Radu (2009) Migrants: Mig = 1 Non-migrants : Mig = 0

Binary Variable (Cont. ) § Intercept effect

Binary Variable (Cont. ) § Slope effect (interaction term)

Binary Variable (Cont. ) § Slope effect (interaction term) § Migrants (Mig = 1 & Educ. Mig = 1) § Non-migrants (Mig = 0 &Educ. Mic = 0)

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 Mig. Temp = 0, if non-migrant 1, if permanent migrant Mig. Perm = 0, if non-migrant

Multiple Categories (Cont. ) § Wage equation § Population w/r to migration status Non-migrants: Mig. Temp = 0, Mig. Perm = 0 Temporary migrants: Mig. Temp = 1, Mig. Perm = 0 Permanent migrants: Mig. Temp = 0, Mig. Perm = 1

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

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

Multiple Dummy Variables § Wage equation 1, if male Male = 0, if female 1, if married Mar. Stat = 0, if single § Married female § Married man

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

Dummy Variable as Dependent (Cont. ) § Using OLS to estimate a model with binary dependent variable 1) 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

Maximum Likelihood § Focusing example Sample: X 1 = 4, X 2 = 6 Parameter: μ – population mean. X~ N(μ; 1) § Obtaining estimate for μ

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

Maximum Likelihood (Cont. ) § Normal distribution § For σ = 1 & X 1 = 4, X 2 = 6 § Likelihood function for μ § Log- Likelihood function

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

Maximum Likelihood (Cont. ) § Population model § Density function for distribution of Yi - Disturbances are normally distributed § Likelihood function for β 1, β 2, and σ

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

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

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

Probit Model (Cont. )

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

Probit Model: Interpreting Coefficients § Indirect interpretation of the coefficients

Probit Model: Interpreting Coefficients

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