* This program replicates Tables 7.1 and 7.2 on page 132 in the Franses and * Paap book. use Donations to Charity_Franses_Paap.dta * Franses and Papp identify observation 678 as an outlier and eliminate * it from further analysis. They also reserved the last 268 observations for * out-of-sample testing. Their out-of-sample testing results are reported on * pages 154 and 155. drop if _n == 678 * OLS estimation of donations equation (which are biased) regress GIFT RESPLASTMAIL WEEKSLASTRESP MAILSPERYEAR PROPRESPONSE /// AVERAGEGIFT in 1/3999 * Tobit estimation of the donations equation * Drawback - the regression and probit parts have the same * explanatory variabes and coefficients. tobit GIFT RESPLASTMAIL WEEKSLASTRESP MAILSPERYEAR PROPRESPONSE /// AVERAGEGIFT in 1/3999, ll(0) * For illustration here is the probit model for response. * Without any information on expenditures (just response) this equation * could be used for sorting potential donors from highest probability * of donation to lowest probability for solicitation purposes. probit RESPONSE RESPLASTMAIL WEEKSLASTRESP MAILSPERYEAR PROPRESPONSE /// AVERAGEGIFT in 1/3999 * This is the so-called Tobit II model estimated by the Heckman two-step * approach. The first step is to estimate the probit model. The second * step is compute the Inverse Mills ratio, add it to the regression model * as an additional explanatory variable and then apply OLS to the augmented * equation (while possibly utilizing robust standard errors for the augmented * regression part). This estimation provides a consistent estimation of the * Expected value of gifts conditional on their being a donation. The Inverse * Mills Ratio is defined to be phi(-xi*alpha)/(1 - cap_phi(-xi*alpha)). heckman GIFT RESPLASTMAIL WEEKSLASTRESP MAILSPERYEAR PROPRESPONSE /// AVERAGEGIFT in 1/3999, twostep select(RESPONSE = RESPLASTMAIL WEEKSLASTRESP /// MAILSPERYEAR PROPRESPONSE AVERAGEGIFT) * Here is the MLE version of the Tobit II model where all coeffients of * the two-part model are estimated jointly. heckman GIFT RESPLASTMAIL WEEKSLASTRESP MAILSPERYEAR PROPRESPONSE /// AVERAGEGIFT in 1/3999, select(RESPONSE = RESPLASTMAIL WEEKSLASTRESP /// MAILSPERYEAR PROPRESPONSE AVERAGEGIFT) * The first test of the independence of the two parts (the significance * of the lamda coefficient on the Inverse Mills Ratio in the Heckman two-step model * produced a p-value of 0.031 < 0.05 indicating the lack of independence of the two parts. * In contrast, however, the LR test reported in the Heckman MLE model) produced * a probability value of 0.1033 > 0.05. But, at the same time, the 95% confidence * interval for rho does not encompases 0 and that would indicate rejecting * independence. Given two of three tests indicate independence we would * probaby go for the Heckman Tobit II model, probably the MLE versin when * considering the eficiency of estimation. Therefore, the use of the Cragg model, which * assumes independence of the probit and regression parts, is probably * not to be preferred. However, just for illustrative purposes, here is the * Cragg model output. craggit GIFT RESPLASTMAIL WEEKSLASTRESP MAILSPERYEAR PROPRESPONSE /// AVERAGEGIFT in 1/3999, second(GIFT RESPLASTMAIL WEEKSLASTRESP /// MAILSPERYEAR PROPRESPONSE AVERAGEGIFT)