### Abstract

Use of the likelihood ratio (LR) statistic is examined to test for the mixture assumption of geometric distributions. As the asymptotic null distribution of the LR statistic is not a standard chi-square due to the fact that there are a boundary parameter problem and a nuisance parameter not identified under the null, we derive it separately and also provide a method to obtain the asymptotic critical values. Further, the finite sample properties of the LR test are evaluated by Monte Carlo simulations by examining the levels and powers of the LR test. Finally, using Kennan's (1985) strike data in labor economics, we conclude that unobserved heterogeneity is present in the data, which cannot be captured by specifying a geometric distribution.

Original language | English |
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Pages (from-to) | 31-55 |

Number of pages | 25 |

Journal | Journal of Economic Theory and Econometrics |

Volume | 20 |

Issue number | 3 |

Publication status | Published - 2009 Sep 1 |

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### Keywords

- Geometric distribution
- Likelihood ratio statistic
- Mixture
- Strike data
- Unobserved heterogeneity

### ASJC Scopus subject areas

- Economics and Econometrics

### Cite this

*Journal of Economic Theory and Econometrics*,

*20*(3), 31-55.

**Testing for the mixture hypothesis of geometric distributions.** / Cho, Jin Seo; Han, Chirok.

Research output: Contribution to journal › Article

*Journal of Economic Theory and Econometrics*, vol. 20, no. 3, pp. 31-55.

}

TY - JOUR

T1 - Testing for the mixture hypothesis of geometric distributions

AU - Cho, Jin Seo

AU - Han, Chirok

PY - 2009/9/1

Y1 - 2009/9/1

N2 - Use of the likelihood ratio (LR) statistic is examined to test for the mixture assumption of geometric distributions. As the asymptotic null distribution of the LR statistic is not a standard chi-square due to the fact that there are a boundary parameter problem and a nuisance parameter not identified under the null, we derive it separately and also provide a method to obtain the asymptotic critical values. Further, the finite sample properties of the LR test are evaluated by Monte Carlo simulations by examining the levels and powers of the LR test. Finally, using Kennan's (1985) strike data in labor economics, we conclude that unobserved heterogeneity is present in the data, which cannot be captured by specifying a geometric distribution.

AB - Use of the likelihood ratio (LR) statistic is examined to test for the mixture assumption of geometric distributions. As the asymptotic null distribution of the LR statistic is not a standard chi-square due to the fact that there are a boundary parameter problem and a nuisance parameter not identified under the null, we derive it separately and also provide a method to obtain the asymptotic critical values. Further, the finite sample properties of the LR test are evaluated by Monte Carlo simulations by examining the levels and powers of the LR test. Finally, using Kennan's (1985) strike data in labor economics, we conclude that unobserved heterogeneity is present in the data, which cannot be captured by specifying a geometric distribution.

KW - Geometric distribution

KW - Likelihood ratio statistic

KW - Mixture

KW - Strike data

KW - Unobserved heterogeneity

UR - http://www.scopus.com/inward/record.url?scp=70449117631&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70449117631&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:70449117631

VL - 20

SP - 31

EP - 55

JO - Journal of Economic Theory and Econometrics

JF - Journal of Economic Theory and Econometrics

SN - 1229-2893

IS - 3

ER -