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1 UCEMA ECONOMETRIA APLICADA - Probit- El archivo MROZ.xls tiene datos de un un estudio clásico donde se trata de estimar una ecuación de salarios para mujeres. La primer etapa del estudio es determinar la probabilidad de participación de la mujer en el mercado laboral. Estime un modelo probit de selección y discuta la especificación y resultados. La data basica es: THE MROZ DATA FILE IS TAKEN FROM THE 1976 PANEL STUDY OF INCOME DYNAMICS, AND IS BASED ON DATA FOR THE PREVIOUS YEAR, OF THE 753 OBSERVATIONS, THE FIRST 428 ARE FOR WOMEN WITH POSITIVE HOURS WORKED IN 1975, WHILE THE REMAINING 325 OBSERVATIONS ARE FOR WOMEN WHO DID NOT WORK FOR PAY IN A MORE COMPLETE DISCUSSION OF THE DATA IS FOUND IN MROZ [1987], APPENDIX 1. THE DATA SET CONSISTS OF 753 OBSERVATIONS ON 19 VARIABLES: 1. LFP A dummy variable = 1 if woman worked in 1975, else 0 2. WHRS Wife's hours of work in KL6 Number of children less than 6 years old in household 4. K618 Number of children between ages 6 and 18 in household 5. WA Wife's age 6. WE Wife's educational attainment, in years 7. WW Wife's average hourly earnings, in 1975 dollars 8. RPWG Wife's wage reported at the time of the 1976 interview (not the same as the 1975 estimated wage). To use the subsample with this wage, one needs to select 1975 workers with LFP=1, then select only those women with non-zero RPWG. Only 325 women work in 1975 and have a non-zero RPWG in HHRS Husband's hours worked in HA Husband's age 11. HE Husband's educational attainment, in years 12. HW Husband's wage, in 1975 dollars 13. FAMINC Family income, in 1975 dollars. This variable is used to construct the property income variable. 14. MTR This is the marginal tax rate facing the wife, and is taken from published federal tax tables (state and local income taxes are excluded). The taxable income on which this tax rate is calculated includes Social Security, if applicable to wife. 15. WMED Wife's mother's educational attainment, in years 16. WFED Wife's father's educational attainment, in years 17. UN Unemployment rate in county of residence, in percentage points. This taken from bracketed ranges. 18. CIT Dummy variable = 1 if live in large city (SMSA), else AX Actual years of wife's previous labor market experience. gen princ=(faminc-ww*whrs)/1000. probit lfp wa kl6 k618 we princ Iteration 0: log likelihood = Iteration 1: log likelihood = Iteration 2: log likelihood = Iteration 3: log likelihood = Probit regression Number of obs = 753 LR chi2(5) = Prob > chi2 = Log likelihood = Pseudo R2 = lfp Coef. Std. Err. z P> z [95% Conf. Interval] wa kl k we princ _cons

La data basica es: THE MROZ DATA FILE IS TAKEN FROM THE 1976 PANEL STUDY OF INCOME DYNAMICS, AND IS BASED ON DATA FOR THE PREVIOUS YEAR, 1975.

2 ECONOMETRIA APLICADA UCEMA Ejemplos Estimación con Truncamiento y Censura Usamos datos de un ejemplo de Mroz THE MROZ DATA FILE IS TAKEN FROM THE 1976 PANEL STUDY OF INCOME DYNAMICS, AND IS BASED ON DATA FOR THE PREVIOUS YEAR, OF THE 753 OBSERVATIONS, THE FIRST 428 ARE FOR WOMEN WITH POSITIVE HOURS WORKED IN 1975, WHILE THE REMAINING 325 OBSERVATIONS ARE FOR WOMEN WHO DID NOT WORK FOR PAY IN A MORE COMPLETE DISCUSSION OF THE DATA IS FOUND IN MROZ [1987], APPENDIX 1. THE DATA SET CONSISTS OF 753 OBSERVATIONS ON 19 VARIABLES: 1. LFP A dummy variable = 1 if woman worked in 1975, else 0 2. WHRS Wife's hours of work in KL6 Number of children less than 6 years old in household 4. K618 Number of children between ages 6 and 18 in household 5. WA Wife's age 6. WE Wife's educational attainment, in years 7. WW Wife's average hourly earnings, in 1975 dollars 8. RPWG Wife's wage reported at the time of the 1976 interview (not the same as the 1975 estimated wage). To use the subsample with this wage, one needs to select 1975 workers with LFP=1, then select only those women with non-zero RPWG. Only 325 women work in 1975 and have a non-zero RPWG in HHRS Husband's hours worked in HA Husband's age 11. HE Husband's educational attainment, in years 12. HW Husband's wage, in 1975 dollars 13. FAMINC Family income, in 1975 dollars. This variable is used to construct the property income variable. 14. MTR This is the marginal tax rate facing the wife, and is taken from published federal tax tables (state and local income taxes are excluded). The taxable income on which this tax rate is calculated includes Social Security, if applicable to wife. 15. WMED Wife's mother's educational attainment, in years 16. WFED Wife's father's educational attainment, in years 17. UN Unemployment rate in county of residence, in percentage points. This taken from bracketed ranges. 18. CIT Dummy variable = 1 if live in large city (SMSA), else AX Actual years of wife's previous labor market experience Para ilustrar el problema de truncamiento podemos estimar un modelo donde las horas trabajadas sean función de kl6, k618, wa y we. Si ignoramos el problema de truncamiento y estimamos por OLS: regress whrs kl6 k618 wa we if whrs>0 podemos reestimar usando el comando truncreg teniendo en cuenta que hay observaciones en cero truncreg whrs kl6 k618 wa we if whrs, ll(0)

OF THE 753 OBSERVATIONS, THE FIRST 428 ARE FOR WOMEN WITH POSITIVE HOURS WORKED IN 1975, WHILE THE REMAINING 325 OBSERVATIONS ARE FOR WOMEN WHO DID NOT WORK FOR PAY IN 1975.

3 Los resultados de la estimación por OLS están sesgados hacia abajo. No pueden usarse para hacer inferencia. Censura: Tobit Podemos estimar un modelo para explicar el salario anual en función de wa kl6 k618 we Primero calculamos el salario anual gen wwa=(ww*whrs) reemplazamos los missings por cero replace wwa=0 if ww==0 regress ww wa kl6 k618 we Luego estimamos como un tobit, especificando que lww está censurada en cero ll(0) tobit wwa wa kl6 k618 we, ll(0) Podemos calcular los efectos marginales sobre probabilidad de tener un salario positivo mfx compute, predict (pr(0,.)) Luego podemos calcular el efecto de cada variable en el log del salario dado que el individuo no ha sido censurado mfx compute, predict (e(0,.))

por cero replace wwa=0 if ww==0 regress ww wa kl6 k618 we Luego estimamos como un tobit, especificando que lww está censurada en cero ll(0) tobit wwa wa kl6 k618 we, ll(0) Podemos

4 ECONOMETRIA APLICADA UCEMA Estimacion de una ecuacion de salarios con sesgo de selección Método de Heckman El archivo tiene datos de un ejemplo de Mroz, un estudio clásico donde se trata de estimar una ecuación de salarios para mujeres La primer etapa sería un probit de selección y la segunda un ols La data basica es: THE MROZ DATA FILE IS TAKEN FROM THE 1976 PANEL STUDY OF INCOME DYNAMICS, AND IS BASED ON DATA FOR THE PREVIOUS YEAR, OF THE 753 OBSERVATIONS, THE FIRST 428 ARE FOR WOMEN WITH POSITIVE HOURS WORKED IN 1975, WHILE THE REMAINING 325 OBSERVATIONS ARE FOR WOMEN WHO DID NOT WORK FOR PAY IN A MORE COMPLETE DISCUSSION OF THE DATA IS FOUND IN MROZ [1987], APPENDIX 1. THE DATA SET CONSISTS OF 753 OBSERVATIONS ON 19 VARIABLES: 1. LFP A dummy variable = 1 if woman worked in 1975, else 0 2. WHRS Wife's hours of work in KL6 Number of children less than 6 years old in household 4. K618 Number of children between ages 6 and 18 in household 5. WA Wife's age 6. WE Wife's educational attainment, in years 7. WW Wife's average hourly earnings, in 1975 dollars 8. RPWG Wife's wage reported at the time of the 1976 interview (not the same as the 1975 estimated wage). To use the subsample with this wage, one needs to select 1975 workers with LFP=1, then select only those women with non-zero RPWG. Only 325 women work in 1975 and have a non-zero RPWG in HHRS Husband's hours worked in HA Husband's age 11. HE Husband's educational attainment, in years 12. HW Husband's wage, in 1975 dollars 13. FAMINC Family income, in 1975 dollars. This variable is used to construct the property income variable. 14. MTR This is the marginal tax rate facing the wife, and is taken from published federal tax tables (state and local income taxes are excluded). The taxable income on which this tax rate is calculated includes Social Security, if applicable to wife. 15. WMED Wife's mother's educational attainment, in years 16. WFED Wife's father's educational attainment, in years 17. UN Unemployment rate in county of residence, in percentage points. This taken from bracketed ranges. 18. CIT Dummy variable = 1 if live in large city (SMSA), else AX Actual years of wife's previous labor market experience Además de variables generadas El ingreso no generado por la mujer en la flia gen princ=(faminc-ww*whrs)/1000 La edad al cuadrado: gen wasq=wa*wa La experiencia al cuadrado gen axsq=ax*ax El log del salario

IS BASED ON DATA FOR THE PREVIOUS YEAR, 1975.

5 gen lww=log(ww) Todas las variables estan en la base **La ecuacion de seleccion es un probit: probit lfp princ we ax axsq wa kl6 k618 **La de salarios un OLS con el IMR (hazard) para corregir el sesgo regress lww we ax axsq imr **A partir del probit se puede calcular la inversa del ratio de Mills (IMR), o como lo llama tambien stata el Non selection hazard H(z) = f(z) / (1 F(z)), (donde f() es la density y F() es la acumulada, evaluadas en cada punto de la muestra y el z es el forecast en indice del probit) El Mills es 1 / H(z), Entonces la inversa del Mills (IMR) es el hazard Todo esto se puede hacer junto con el comando heckman en dos etapas La sintaxis es: heckman lww we ax axsq, twostep select(lfp=princ we ax axsq wa kl6 k618 ) first nshazard(imr) La expresión es bastante intuitiva: - primero esta el ols - despues el two step indica que es por dos etapas (no por max verosimilitud que es la opción por defecto) - luego la ecuacion de selección entre paréntesis (el probit) - el first es para reportar la primera etapa (el probit) - el nshazard lo guarda en la variable imr Para confirmar el procedimiento, es posible hacer primero un probit y luego el ols usando el imr como variable adicional. Para calcular el IMR a mano partiendo del Probit Estimar el probit probit lfp princ we ax axsq wa kl6 k618 predecir el valor del indice (los xb) predict lfp_index, xb

es la density y F() es la acumulada, evaluadas en cada punto de la muestra y el z es el forecast en indice del probit) El Mills es 1 / H(z), Entonces la inversa del Mills (IMR) es el hazard Todo esto

6 Generar el IMR como cociente de la función de densidad (f()) y la acumulada (F()) gen imr=(normalden(lfp_index))/(normal(lfp_index)) o alternativamente (deberia dar lo mismo por las propiedades de las func de densidad y acum): gen imr=(normalden(-lfp_index))/(1-(normal(-lfp_index))) correr la regresion utilizando el imr como regresor adicional regress lww we ax axsq imr ****

las propiedades de las func de densidad y acum): gen

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