Nonlinear Fixed Effects Model
Nonlinear Fixed Effects Panel Data Model · Also known as: nonlinear FE model, NLFE, conditional fixed effects model, incidental parameters model
The nonlinear fixed effects model extends fixed effects panel estimation to outcomes governed by nonlinear response functions — such as binary, count, or censored outcomes — while absorbing unobserved individual heterogeneity through unit-specific intercepts. Key special cases include conditional logit for binary outcomes and Poisson fixed effects for count data.
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When to use it
Use a nonlinear fixed effects model when you have panel data, your outcome is binary, count-valued, or otherwise limited-dependent, and you need to control for unobserved time-invariant unit heterogeneity that is potentially correlated with the regressors. It is the appropriate estimator when within-unit variation is the primary source of identification and the outcome distribution is clearly non-Gaussian. Do not use it when the panel is very short (T = 2 or 3) and the outcome is binary — the incidental parameters bias is severe; bias-corrected probit or a linear probability fixed effects model may be preferable. Do not use it when there is no meaningful within-unit variation in key regressors (perfect collinearity with the fixed effects).
Strengths & limitations
- Controls for all time-invariant unobserved heterogeneity without specifying its distribution, unlike random effects.
- Conditional likelihood approach (logit, Poisson) fully eliminates the incidental parameters problem, yielding consistent estimates.
- Robust to correlation between the individual fixed effect and the regressors — a key advantage over random effects.
- Poisson fixed effects is remarkably robust and consistent even when the outcome is not truly Poisson-distributed, as long as the conditional mean is correctly specified.
- Naturally handles panel data with many units (large N) and moderately short panels.
- For probit and tobit, no exact sufficient statistic exists; conditional likelihood is unavailable and bias-corrected estimators are more complex.
- Units with no within-variation in the outcome (e.g., firms that never exit) are dropped from the conditional likelihood, potentially creating a selected sample.
- Does not identify the effect of time-invariant regressors — they are absorbed into alpha_i.
- With very short panels (small T) and binary outcomes, conditional logit still performs well, but many other nonlinear FE estimators face residual incidental parameters bias.
- Average marginal effects require additional computation and are less straightforward to interpret than OLS coefficients.
Frequently asked
Why can I not just use probit with dummies for each unit?
Adding unit dummies to a probit model estimates alpha_i jointly with beta. Because the number of alpha_i parameters grows with N, the maximum likelihood estimator of beta is inconsistent in short panels — this is the incidental parameters problem. The bias can exceed 100% in small T settings. Conditional or bias-corrected estimators avoid this.
What is the difference between conditional logit and random effects logit?
Conditional (fixed effects) logit conditions out alpha_i using a sufficient statistic, making no distributional assumption about the fixed effects and allowing them to correlate freely with the regressors. Random effects logit assumes alpha_i is independent of x_it and integrates it out. If the independence assumption fails, random effects logit is biased; the Hausman test can detect this.
Can I use Poisson fixed effects for non-count outcomes?
Yes. The Poisson pseudo-maximum likelihood (PPML) estimator is consistent whenever the conditional mean is correctly specified as exp(x_it * beta + alpha_i), regardless of whether the data are actually Poisson-distributed. It is widely used for trade flows and other non-negative continuous outcomes, including those with many zeros.
How do I handle time-invariant regressors with nonlinear fixed effects?
Time-invariant regressors are perfectly collinear with the unit fixed effects and cannot be identified. If identification of their effects is important, consider a correlated random effects (Mundlak) approach, which models the dependence between alpha_i and x_it through unit means while keeping time-invariant regressors in the model.
What should I do when many units are dropped from the conditional likelihood?
Units with no within-variation in the outcome (e.g., always zero, always one) contribute no information to the conditional likelihood and are excluded. Report how many units are dropped and compare their observable characteristics to retained units. If exclusion is systematic, interpret results cautiously; they apply to the subset of units that do exhibit outcome variation.
Sources
- Chamberlain, G. (1984). Panel data. In Z. Griliches & M. D. Intriligator (Eds.), Handbook of Econometrics (Vol. 2, pp. 1247–1318). Elsevier. link ↗
- Wooldridge, J. M. (2010). Econometric Analysis of Cross Section and Panel Data (2nd ed.). MIT Press. ISBN: 978-0262232586
How to cite this page
ScholarGate. (2026, June 3). Nonlinear Fixed Effects Panel Data Model. ScholarGate. https://scholargate.app/en/econometrics/nonlinear-fixed-effects-model
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
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