Elsevier

Economics Letters

Volume 123, Issue 1, April 2014, Pages 75-78
Economics Letters

A simple and effective misspecification test for the double-hurdle model

https://doi.org/10.1016/j.econlet.2014.01.022Get rights and content

Highlights

  • Testing for misspecification in the double-hurdle model is an important task.

  • Diagnostic testing can be carried out effectively by a conditional moment test.

  • Information matrix equality provides the necessary moment conditions.

  • Bootstrap correction is indispensable for overcoming finite-sample issues.

  • Monte Carlo evidence shows that the test has good size and power properties.

Abstract

The commonly-used version of the double-hurdle model rests on a rather restrictive set of statistical assumptions, which are very seldom tested by practitioners, mainly because of the lack of a standard procedure for doing so, although violation of such assumptions can lead to serious modelling flaws. We propose here a bootstrap-corrected conditional moment portmanteau test which is simple to implement and has good size and power properties.

Section snippets

Introduction and motivation

The double-hurdle model is a commonly used model for dealing with double censoring. This model is well suited for analysing situations where a sample selection effect occurs and a corner zero solution is possible in the optimisation process by the individual. As such, it has been used in countless applications, such as labour market studies, in which the dependent variable is the number of hours worked (the classic reference here is  Blundell et al. (1987)), migrant remittances (Bettin et al.,

Our proposed test

The test we propose builds on a conditional-moment approach originally proposed by  Smith (1987), supplemented with a bootstrap correction to improve its poor finite-sample properties, as suggested by Horowitz (1994). A similar strategy was recently proposed by Lucchetti and Pigini (2013), who focused on testing the bivariate normality assumption in the bivariate probit and sample selection models.

This test uses the fact that, under correct specification, the information matrix equality implies

Monte Carlo study

Before going into the details of our Monte Carlo experiment, a word of warning is necessary. Numerical optimisation of the double-hurdle log-likelihood may be difficult in some cases for two reasons: first, as is well known among practitioners, the log-likelihood may be bimodal, especially in smaller samples2; moreover, the maximal value of ρ may, in finite

Conclusions

Testing for misspecification in the double hurdle model is an important task that can be carried out very effectively by a conditional moment test.

Since the routine estimation technique is maximum likelihood, the relevant moment conditions can be chosen from those stemming from the information matrix equality. However, a bootstrap correction is absolutely indispensable. Moreover, the choice of the actual moment conditions to use in practice may be an issue.

In this article, we propose two

References (12)

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The authors wish to thank, without implicating them for remaining errors, Chiara Gigliarano and an anonymous referee for their useful comments.

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