Method of Analysis
Coefficients for normalized versions of the independent
variables were estimated by regressing the
dollar value ofthe goods purchased, the proxy for Ur,
on the UE and UA variables and the income covariate.
OLS regression could not be used in this analysis,
since the large proportion of invitees who did not attend
(69 percent) created a large number of zero values
in the dependent variable. Further, all the nonzero
values in the dependent variable were positive,
since it is impossible to make a negative purchase. A
dependent variable possessing these characteristics is
censored, and OLS regression fit on such variables is
biased because the residuals are not normally distributed.
We therefore employed Heckman's two-step selection
bias-corrected regression (Heckman 1974;
Maddala 1983). PROBIT was used to first estimate
the probability that an invitee entered the market.
This estimate also produces a variable called lambda
(the inverse Mills ratio), which was then included in
an OLS regression to compensate for biases introduced
by the dependent variable.
Heckman's procedure produces two sets of coefficients
for each independent variable. The first set describes
the effect ofthe independent variables on the
probability a purchase is observed. The second set describes
the effect ofthe independent variables on the
magnitude of a purchase, if it is observed. We therefore
used the first set of coefficients to test whether the
UA and UE variables affected the likelihood of purchase
and the second set to test whether the same variables
affected the amount spent.