Semiparametric estimation of duration models when the parameters are subject to inequality constraints and the error distribution is unknown

This paper proposes a semiparametric method for estimating duration models when there are inequality constraints on some parameters and the error distribution may be unknown. Thus, the setting considered here is particularly suitable for practical applications. The parameters in duration models are usually estimated by a quasi-MLE. Recent advances show that a semiparametrically efficient estimator[SPE] has better asymptotic optimality properties than the QMLE provided that the parameter space is unrestricted. However, in several important duration models, the parameter space is restricted, for example in the commonly used linear duration model some parameters are non-negative. In such cases, the SPE may turn out to be outside the allowed parameter space and hence are unsuitable for use. To overcome this difficulty, we propose a new constrained semiparametric estimator. In a simulation study involving duration models with inequality constraints on parameters, the new estimator proposed in this paper performed better than its competitors. An empirical example is provided to illustrate the application of the new constrained semiparametric estimator and to show how it overcomes difficulties encountered when the unconstrained estimator of nonnegative parameters turn out to be negative.