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Test of neglected heterogeneity in dyadic models

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  • Hahn, Jinyong
  • Moon, Hyungsik Roger
  • Shi, Ruoyao

Abstract

We develop a Lagrange Multiplier (LM) test of neglected heterogeneity in dyadic models. The test statistic is derived by modifying Breusch and Pagan (1980)’s test. We establish the asymptotic distribution of the test statistic under the null using a novel martingale construction. We also consider the power of the LM test in generic panel models. Even though the test is motivated by random effects, we show that it has a power for detecting fixed effects as well. Finally, we examine how the estimation noise of the maximum likelihood estimator affects the asymptotic distribution of the test under the null, and show that such a noise may be ignored in large samples.

Suggested Citation

  • Hahn, Jinyong & Moon, Hyungsik Roger & Shi, Ruoyao, 2025. "Test of neglected heterogeneity in dyadic models," Journal of Econometrics, Elsevier, vol. 252(PB).
    • Handle: RePEc:eee:econom:v:252:y:2025:i:pb:s0304407624000824
    DOI: 10.1016/j.jeconom.2024.105736
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    References listed on IDEAS

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    1. Yuzo Honda, 1985. "Testing the Error Components Model with Non-Normal Disturbances," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(4), pages 681-690.
    2. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 239-253.
    3. Jinyong Hahn & Hyungsik Roger Moon & Connan Snider, 2017. "LM Test of Neglected Correlated Random Effects and Its Application," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(3), pages 359-370, July.
    4. Chesher, Andrew D, 1984. "Testing for Neglected Heterogeneity," Econometrica, Econometric Society, vol. 52(4), pages 865-872, July.
    5. Kuersteiner, Guido M. & Prucha, Ingmar R., 2013. "Limit theory for panel data models with cross sectional dependence and sequential exogeneity," Journal of Econometrics, Elsevier, vol. 174(2), pages 107-126.
    6. Lancaster, Tony, 1984. "The Covariance Matrix of the Information Matrix Test," Econometrica, Econometric Society, vol. 52(4), pages 1051-1053, July.
    7. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    8. Newey, Whitney K, 1985. "Maximum Likelihood Specification Testing and Conditional Moment Tests," Econometrica, Econometric Society, vol. 53(5), pages 1047-1070, September.
    9. Engle, Robert F., 1984. "Wald, likelihood ratio, and Lagrange multiplier tests in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 13, pages 775-826, Elsevier.
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    Keywords

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    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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