arXiv 8 Oct 2026 · Econometrics
arXiv:2610.12350 · PDF · Extracted main text
The Information Matrix (IM) test is a natural specification check for likelihood-based models, yet cross-sectional implementations are often badly sized, confound neglected heterogeneity with distributional misspecification, and require third derivatives. We develop the panel information matrix (PIM) test for models with fixed effects. Explicit fixed effects isolate functional-form misspecification from time-invariant unobserved heterogeneity. Although the profile maximum likelihood estimator inherits incidental-parameter bias of order $O(1/T)$, the leading bias of the profile PIM is of order $\sqrt{n}/T$, so it is asymptotically negligible whenever $n/T^2\to 0$, which includes the rectangular regime $n/T\toconst$, and stabilizes under parabolic asymptotics $n/T^2\toρ\in(0,\infty)$. This robustness arises because the indicator fluctuates at rate $\sqrt{n}$ rather than $\sqrt{nT}$. The same rate argument makes third-derivative corrections asymptotically unnecessary, so the test uses only first- and second-order likelihood derivatives. Simulations confirm that asymptotic PIM critical values suffice in moderately long panels, even when Wald tests for $θ$ are badly sized, while a parametric bootstrap largely removes size distortions when $ρ>0$.
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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 | Horowitz, Joel L (1994) Bootstrap-based critical values for the information matrix test | 0.950 | 7 | 4 | 86% |
| 2 | White, Halbert (1982) Maximum likelihood estimation of misspecified models | 0.874 | 6 | 3 | 67% |
| 3 | Jinyong Hahn and Guido Kuersteiner Bias reduction for dynamic nonlinear panel models with fixed effects | 0.843 | 5 | 4 | 60% |
| 4 | Martin Schumann and Thomas A. Severini and Gautam Tripathi (2023) The role of score and information bias in panel data likelihoods self | 0.754 | 7 | 5 | 43% |
| 5 | Jerzy Neyman and Elizabeth L. Scott Consistent estimation from partially consistent observations | 0.737 | 3 | 3 | 67% |
| 6 | Chesher, Andrew (1984) Testing for neglected heterogeneity | 0.737 | 3 | 2 | 100% |
| 7 | Lancaster, Tony (1984) The covariance matrix of the information matrix test | 0.737 | 3 | 2 | 100% |
| 8 | Higgins, Ayden and Jochmans, Koen (2024) Bootstrap Inference for Fixed-Effect Models | 0.727 | 13 | 4 | 38% |
| 9 | Jinyong Hahn and Whitney K. Newey Jackknife and analytical bias reduction for nonlinear panel models | 0.721 | 8 | 5 | 38% |
| 10 | Aguirregabiria, Victor and Mira, Pedro (2007) Sequential Estimation of Dynamic Discrete Games | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 45 scored citations.