A look at M. G. Dagenais' contributions (1969, 1973) on threshold regression models and at chapter 9 of S.M. Goldfeld and R.E. Quandt's book (1972) concerning switching regression models suggested to me that a new approach to estimating the threshold model by introducing slack variables might be possible. One of the main advantages of this new method is to simplify to a great extent the estimation of the likelihood function which is reduced partly to the problem of estimating a limited number of simple integrals for each iteration in the process of optimization.
In order to facilitate a better understanding of our approach, two main models will be reviewed in the next section: the twin linear probability model (which can be estimated either by OLS, by a combination of probit and OLS, or by the tobit approach) and the threshold model. A critical look at the empirical results obtained by Dagenais (1973) will also be made before closing this section.
Our new threshold model with slack variables is presented in section 3 and the main features of our new approach are summarized in the last section of this paper.
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