[BINARY DEPENDENT VARIABLE ESTIMATION WITH STATA]

Transcription

1 Tutorial #3 This example uses data in the file dta under Tutorial folder. It contains 753 observations from a sample PSID data on the labor force status of married women in the U.S in The variables of our interest are: 1. inlf =1 if in labor force, 1975 =0 if not in labor force, kidslt6 = # kids < 6 years 3. kidsge6 = # kids age= woman's age in yrs 5. educ =years of schooling 6. city=1 if live in SMSA 7. unem= unemployment rate in county of residence 8. huswage=husband's hourly wage, 1975 This data set is used in the textbook: Introductory Econometrics: A Modern Approach, second edition, by Jeffrey M. Wooldridge. The goal is to estimate the effect of husband s wage on labor force participation of married women. Let s see an example of Linear Probability Model. reg inlf kidslt6 kidsge6 age educ unem city huswage Source SS df MS Number of obs = 753 F( 7, 745) = Model Prob > F = Residual R-squared = Adj R-squared = Total Root MSE = inlf Coef. Std. Err. t P> t [95% Conf. Interval] kidslt kidsge age educ unem city huswage _cons The coefficient of huswage implies that 1 USD increase in hourly wage of husband leads to 1.3% drop in probability of being in the labor force for married women. However, when we look at the graph which is generated by the following code. predict inlfhat (option xb assumed; fitted values). scatter inlfhat huswage

2 Fitted values husband's hourly wage, 1975 Obviously for some husband wage categories, we predict more than 1 which is not sensible. Let s try probit and logit models which overcomes this problem.. probit inlf kidslt6 kidsge6 age educ unem city huswage LR chi2( 7) = Log likelihood = Pseudo R2 = kidslt kidsge age educ unem city huswage _cons logit inlf kidslt6 kidsge6 age educ unem city huswage Logistic regression Number of obs = 753 LR chi2( 7) = Log likelihood = Pseudo R2 = kidslt kidsge age educ unem city huswage _cons

3 The following table reports OLS, probit and logit models respectively.. esttab m1 m2 m3 kidslt *** *** *** (-8.41) (-7.84) (-7.53) kidsge (-1.18) (-1.32) (-1.31) age *** *** *** (-4.91) (-4.88) (-4.82) educ *** 0.144*** 0.239*** (6.32) (6.12) (5.95) unem (-0.39) (-0.38) (-0.39) city (0.08) (0.23) (0.17) huswage ** ** ** (-3.19) (-3.20) (-3.13) _cons 0.706*** (4.32) (1.30) (1.28) N These models are not comparable in terms of magnitude of the coefficient, but they all have the same sign for each coefficient. For getting the marginal effect in probit and logit models mfx command is used in STATA. The code is the following (1) (2) (3) inlf inlf inlf reg inlf kidslt6 kidsge6 age educ unem city huswage eststo m1 probit inlf kidslt6 kidsge6 age educ unem city huswage mfx eststo m4 logit inlf kidslt6 kidsge6 age educ unem city huswage mfx eststo m5

4 . esttab m1 m4 m5, margin kidslt *** *** *** (-8.41) (-7.82) (-7.50) kidsge (-1.18) (-1.32) (-1.31) age *** *** *** (-4.91) (-4.89) (-4.82) educ *** *** *** (6.32) (6.12) (5.96) unem (-0.39) (-0.38) (-0.39) city (d) (0.08) (0.23) (0.17) huswage ** ** ** (-3.19) (-3.20) (-3.13) N Marginal effects; t statistics in parentheses (d) for discrete change of dummy variable from 0 to 1 * p<0.05, ** p<0.01, *** p<0.001 Now, the coefficients are comparable and indeed very close to each other. Likelihood Ratio Test in STATA Let s examine to models (1) (2) (3) inlf inlf inlf. probit inlf kidslt6 kidsge6 age educ unem city huswage. probit inlf kidslt6 kidsge6 age educ unem city huswage exper expersq LR chi2( 7) = Log likelihood = Pseudo R2 = kidslt kidsge age educ unem city huswage _cons eststo l1

5 LR chi2( 9) = Log likelihood = Pseudo R2 = kidslt kidsge age educ unem city huswage exper expersq _cons eststo l2. lrtest l1 l2 Likelihood-ratio test LR chi2( 2) = (Assumption: l1 nested in l2) We reject the null hypothesis that exper and expersq are statistically not different from 0 which means that model 2 fits data better than model 1. WALD TEST For running this test, we first estimate the unrestricted model and then test whether the restrictions hold in the following way.. quietly probit inlf kidslt6 kidsge6 age educ unem city huswage exper expersq. test exper expersq ( 1) exper = 0 ( 2) expersq = 0 chi2( 2) =

6 LAGRANGE MULTIPLIER TEST In order to conduct this test, we need to download user-written testomit & enumopt commands.. findit testomit. findit enumopt For this test, we first estimate the restricted model and then conduct the test in the following way.. quietly probit inlf kidslt6 kidsge6 age educ unem city huswage. predict lfprob, score. testomit exper expersq, score(lfprob) probit: score tests for omitted variables Term score df p exper expersq simultaneous test This test also is in line with the results of previous tests which tells us that exper and expersq are statistically significant in determination of labor market status.

7 GOODNESS OF FIT with BINARY D.V. - Pseudo R 2 : reported with the regression output -% correctly predicted : estat class command after running the regression. probit inlf kidslt6 kidsge6 age educ unem city huswage Iteration 0: log likelihood = Iteration 1: log likelihood = Iteration 2: log likelihood = Iteration 3: log likelihood = LR chi2( 7) = Log likelihood = Pseudo R2 = kidslt kidsge age educ unem city huswage _cons estat class Probit model for inlf True Classified D ~D Total Total Classified + if predicted Pr(D) >=.5 True D defined as inlf!= 0 Sensitivity Pr( + D) 79.91% Specificity Pr( - ~D) 48.31% Positive predictive value Pr( D +) 67.06% Negative predictive value Pr(~D -) 64.61% False + rate for true ~D Pr( + ~D) 51.69% False - rate for true D Pr( - D) 20.09% False + rate for classified + Pr(~D +) 32.94% False - rate for classified - Pr( D -) 35.39% Correctly classified 66.27%.