PRACTITIONERS CORNER: An Advantage of the Linear Probability Model over Probit or Logit
| Published date | 01 November 1988 |
| Date | 01 November 1988 |
| Author | Steven B. Caudill |
| DOI | http://doi.org/10.1111/j.1468-0084.1988.mp50004005.x |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 50,4(1988)
0305-9049 S3.00
PRACTITIONERS CORNER
An Advantage of the Linear Probability Model over
Probit or Logit
Steven B. Caudill
Linear probability models, logit models, and probit models are estimated
when the dependent variable in a regression model is a dummy variable.
Recent criticism of the linear probability model (LPM) has led to increased
use of logit analysis and probit analysis in this situation. However, the linear
probability model permits estimation of some parameters which cannot be
estimated in logit models or probit models.
Historically, the method of estimating regression models with dummy
dependent variables has closely followed the development of the computer.
At first, only the LPM model was an option. Logit and probit models were
prohibitively expensive to estimate. As the computer technology improved,
the linear probability model quickly lost favour. In his survey on qualitative
response models, Amemiya (1981) says of the linear probability model:
it has frequently been used in econometric applications, especially in the
early years, because of its computational simplicity. Though I do not
recommend its use in the final stage of a study, it may be used for the
purpose of obtaining quick estimates in a preliminary stage. [p. 1487]
Criticisms of the linear probability model are discussed by Maddala
(1983); the disturbances in the LPM are heteroscedastic, therefore least
squares is not efficient, the disturbances are not distributed normally, so there
exist nonlinear procedures more efficient than least squares, and predicted
probabilities from the LPM can lie outside the O-1 interval. The improved
computer technology, along with these well-known criticisms, have combined
to eliminate the LPM as a method of estimating dummy dependent variable
models. However, the LPM does serve a purpose in addition to the one
suggested by Amemiya. Some parameters can be estimated in linear prob-
ability models which cannot be estimated in logit or probit models.
The coefficients of some dummy variables can be estimated in the LPM,
but not in logit or probit models. Anderson (1987) has demonstrated that the
coefficient of observation-specific dummy variables cannot be estimated in
either logit or probit models. An observation-specific dummy variable takes
the value one for a single observation and zero for all others. The coefficients
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