Methods

With Tim Salimans and Kamlesh Kumar, I am exploring the MHT model's empirical implementation.

Abbring, Jaap H., and Tim Salimans (2011), “The likelihood of mixed hitting times”, Mimeo.

We present a method for efficiently computing the likelihood of a mixed hitting-time model that specifies durations as the first time a latent Lévy process crosses a heterogeneous threshold. This likelihood is not generally known in closed form, but its Laplace transform is. Our approach to its computation relies on numerical methods for inverting Laplace transforms that exploit special properties of the first passage times of L ́evy processes. We use our method to implement a maximum likelihood estimator of the mixed hitting-time model in MATLAB. We illustrate the application of this estimator with an analysis of Kennan’s (1985) strike data.

[estimates strike data]

 

Abbring, Jaap H., Kamlesh Kumar, and Tim Salimans (2012), “Estimating mixed hitting-time models with the generalized method of moments”, In progress.

In this companion paper, we study the asymptotic properties of a generalized method of moments estimator of a mixed hitting-time model that specifies durations as the first time a latent Lévy process crosses a heterogeneous threshold. The estimator builds on Abbring's (2012) characterization of the conditional duration distribution implied by this model in terms of its Laplace transform. We implement the estimator in MATLAB and illustrate its application.

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