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Testing the Number of Components in Finite Mixture Normal Regression Model with Panel Data

Yu Hao, Hiroyuki Kasahara

arXiv 6 Oct 2022 · Econometrics

arXiv:2210.02824 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper develops the likelihood ratio-based test of the null hypothesis of a M0-component model against an alternative of (M0 + 1)-component model in the normal mixture panel regression by extending the Expectation-Maximization (EM) test of Chen and Li (2009a) and Kasahara and Shimotsu (2015) to the case of panel data. We show that, unlike the cross-sectional normal mixture, the first-order derivative of the density function for the variance parameter in the panel normal mixture is linearly independent of its second-order derivatives for the mean parameter. On the other hand, like the cross-sectional normal mixture, the likelihood ratio test statistic of the panel normal mixture is unbounded. We consider the Penalized Maximum Likelihood Estimator to deal with the unboundedness, where we obtain the data-driven penalty function via computational experiments. We derive the asymptotic distribution of the Penalized Likelihood Ratio Test (PLRT) and EM test statistics by expanding the log-likelihood function up to five times for the reparameterized parameters. The simulation experiment indicates good finite sample performance of the proposed EM test. We apply our EM test to estimate the number of production technology types for the finite mixture Cobb-Douglas production function model studied by Kasahara et al. (2022) used the panel data of the Japanese and Chilean manufacturing firms. We find the evidence of heterogeneity in elasticities of output for intermediate goods, suggesting that production function is heterogeneous across firms beyond their Hicks-neutral productivity terms.

Citation extraction

60
references
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distinct cited
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1Kasahara, H. and Shimotsu, K (2015) Testing the number of components in normal mixture regression models self0.8749467%
2Chen, J. and Li, P (2009) Hypothesis test for normal mixture models: The EM approach0.8434375%
3Kasahara, H., Schrimpf, P., and Suzuki, M (2022) Identification and estimation of production function with unobserved heterogeneity self0.81142100%
4Kasahara, H. and Shimotsu, K (2019) Testing the Order of Multivariate Normal Mixture Models self0.7374275%
5Ackerberg, D. A., Caves, K., and Frazer, G (2015) Identification properties of recent production function estimators0.64422100%
6Hartigan, J (1985) Failure of log-likelihood ratio test0.64422100%
7Kasahara, H. and Shimotsu, K (2012) Testing the number of components in finite mixture models self0.5112250%
8White, H (1982) Maximum likelihood estimation of misspecified models0.5112250%
9Gandhi, A., Navarro, S., and Rivers, D. A (2020) On the Identification of Gross Output Production Functions0.51121100%
10Chen, J (1995) Optimal rate of convergence for finite mixture models0.51121100%

Showing the top 10 of 63 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Identification and Estimation of Production Function with Unobserved Heterogeneity Hiroyuki Kasahara Vancouver School of Economics University of British Columbia [email removed] Paul Schrimpf Vancouver School of Economics University of British Columbia [email removed] Michio Suzuki Tohoku University Cabinet Office, Government of Japan [email removed]0.64422