Hiroyuki Kasahara, Hirokazu Matsuyama, Katsumi Shimotsu, Shota Takeishi
arXiv 29 Sep 2026 · Econometrics
arXiv:2609.36824 · PDF · Extracted main text
Ignoring unobserved heterogeneity in duration models biases parameter estimates and invalidates inference, but testing for it is non-regular: the null hypothesis lies on the boundary of the parameter space and some parameters are unidentified under the null. These features render standard asymptotic theory inapplicable. This paper develops an EM test for unobserved heterogeneity in censored Weibull duration models, building on the EM approach of Li, Chen, and Marriott (2009). The test statistic has an asymptotic null distribution equal to the square of max{0, N(0,1)}, hence critical values require neither simulation nor bootstrap, and the test accommodates covariate-dependent censoring of arbitrary form. Monte Carlo simulations compare the EM test with the likelihood ratio test (LRT) of Cho and White (2010), information matrix tests, and Lagrange multiplier tests. The EM test has empirical size close to the nominal level for sample sizes of 500 or more, where the LRT remains markedly conservative and the other tests over-reject. Its size-adjusted power is comparable to that of the LRT and higher than that of the other tests. Because size adjustment requires knowledge of the data-generating process and is unavailable in practice, the EM test attains higher power than the LRT in most designs as the tests would actually be applied. In an application to the Stanford Heart Transplant data, the EM test rejects homogeneity in every covariate specification, whereas the LRT's conclusion depends on a user-chosen set of admissible parameter values and on the specification.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Li, P., Chen, J., and Marriott, P (2009) Non-finite Fisher Information and Homogeneity: An EM Approach | 1.000 | 6 | 5 | 100% |
| 2 | Cho, J. S. and White, H (2010) Testing for Unobserved Heterogeneity in Exponential and Weibull Duration Models | 0.985 | 23 | 7 | 96% |
| 3 | Hansen, B (1996) Inference When a Nuisance Parameter is not Identified under the Null Hypothesis | 0.843 | 3 | 3 | 100% |
| 4 | Lancaster, T (1984) The Covariance Matrix of the Information Matrix Test | 0.737 | 3 | 2 | 100% |
| 5 | Sharma, S (1987) Specification Diagnostics for Econometric Models of Duration, UCLA Department of Economics Discussion Paper | 0.737 | 3 | 2 | 100% |
| 6 | Heckman, J. and Singer, B (1984) A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data | 0.737 | 3 | 2 | 100% |
| 7 | Kalbfleisch, J. D. and Prentice, R. L (2002) The Statistical Analysis of Failure Time Data | 0.693 | 6 | 1 | 100% |
| 8 | Chesher, A (1984) Testing for Neglected Heterogeneity | 0.644 | 2 | 2 | 100% |
| 9 | Han, A. and Hausman, J (1990) Flexible Parametric Estimation of Duration and Competing Risk Models | 0.644 | 2 | 2 | 100% |
| 10 | Khan, S. and Tamer, E (2007) Partial Rank Estimation of Duration Models with General Forms of Censoring | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 43 scored citations.