* 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)