Probit Regression is a technique used when
the dependent variable is dichotomous (0 or 1). Unlike OLS, the
methods used to estimate the parameters involve nonlinear approaches
such as maximum likelihood. The probit specification is based
on the Cumulative Normal Distribution. It assumes there exists
a theoretical index Z(i) which is not observed or measured, but
is linked to an explanatory variable X(i) which we have collected
data on. The problem which Probit Regression solves is how to
obtain estimates for the explanatory variable while at the same
time obtain information about the underlying unmeasured scale
of index X(i). Most computer programs perform this estimation
process very quickly, even when the data sets are in the thousands.
One of the more useful aspects of Probit regression is that
it outputs the probability of the event which will fall between
0 and 1 (0% to 100%). Therefore, given a set of independent variables,
you could predict the probability of the event occurring using
a Probit specification. This technique is designed around individual
(disaggregated) crosssectional data rather than time series data
like that found in macroeconomic models. Other similar models
are called Logistic Regression and Tobit Regression.
