estimate cumulative fixed effects

This paper addresses fixed-effect estimation in linear panel data models by proposing a distribution-free adaptive shrinkage estimator. The method minimizes mean squared error within a broad class of shrinkage estimators—achieving, for the first time, shrinkage optimality without distributional assumptions. It accommodates time-varying fixed effects and arbitrary serial dependence structures, while adaptively shrinking estimates by jointly modeling cross-sectional and temporal correlations. The estimator admits a closed-form expression and is computationally efficient, supporting one-period-ahead forecasting. Monte Carlo simulations and empirical applications demonstrate substantial improvements in noise reduction and predictive accuracy over conventional shrinkage approaches—particularly under weak distributional assumptions or strong serial correlation.

This paper addresses inference failure of fixed-effects M-estimators in three-dimensional panel data (e.g., sender × receiver × time) and network data, arising from Nickell bias, incidental parameter bias, and degenerate limiting distributions. Unlike two-dimensional panels, we first systematically characterize the heterogeneous asymptotic behavior of fixed-effects estimators under three-way structures: asymptotic unbiasedness holds only in special settings, whereas most configurations suffer severe bias and nonstandard limiting distributions. To resolve this, we develop an explicit bias-correction formula based on high-dimensional fixed-effects bias decomposition—applicable to both linear and nonlinear models, weakly exogenous regressors, and multi-way additive unobserved effects (e.g., two-way, directed/undirected network, and bipartite structures). Our method substantially improves confidence interval coverage and test power, delivering the first unified, consistent, and feasible inferential framework for complex networked panel data.

Existing methods for panel data with interactive fixed effects (i.e., factor structures) suffer from severe estimation bias and distorted confidence intervals when factors are weak. This paper proposes a robust estimator with improved convergence rate and constructs a bias-aware confidence interval, achieving the first uniformly valid inference with respect to factor strength—thereby overcoming the theoretical breakdown of conventional approaches under weak factors. Our method operates within a minimax linear estimation framework and incorporates a nuclear-norm constraint to correct initial estimation errors in the interactive effects. Monte Carlo simulations demonstrate substantial gains in inferential accuracy under weak factors, near-lossless estimation efficiency under strong factors, and stable coverage rates at nominal levels across the full spectrum of factor strengths—delivering both robustness and efficiency.

This paper addresses computational bottlenecks in linear panel models with grouped fixed effects, where conventional methods rely on non-convex or combinatorial optimization and require prespecifying an upper bound on the number of groups. We propose a three-step estimation procedure that neither requires prior knowledge of the number of groups nor involves complex optimization: (1) consistent estimation of slope parameters; (2) agglomerative clustering based on pairwise differencing to consistently identify the true group structure; and (3) mixed OLS within the identified groups. Theoretical results accommodate time dimension $T$ growing at any polynomial rate in $N$, ensuring consistent group identification and asymptotically efficient estimation of common parameters—achieving the same efficiency as the infeasible regression using true groups. An empirical re-examination of the income-democracy relationship demonstrates the method’s robustness and computational efficiency.

This paper addresses asymptotic inference for interactive fixed-effects estimators in unbalanced panel data under random missingness. Recognizing that existing literature lacks a systematic characterization of how missingness proportions and patterns affect estimation, we derive the asymptotic normality of the estimator under general missing-data mechanisms—establishing the first rigorous theoretical foundation for this setting. We propose a robust inference procedure based on principal component analysis (PCA) that remains valid under high missingness rates. Monte Carlo simulations confirm the method’s reliability even with substantial missingness and demonstrate the robustness of Bai (2009) and Moon–Weidner (2017) frameworks under conditionally random missingness. Applying our approach to reassess the causal effect of democratization on economic growth, we robustly identify a statistically significant positive impact. Our results enhance both the statistical credibility and empirical applicability of interactive fixed-effects models in realistic settings with missing data.

This study addresses the limitation of traditional approaches that estimate social contextual spillover effects along a single dimension, thereby neglecting the multidimensional interaction between overlap content and duration as well as their endogenous heterogeneity. The authors propose a multidimensional causal treatment framework that conceptualizes spillover effects as the joint causal influence of both observable and unobservable characteristics shared across life courses, innovatively decomposing them into combinations of content and duration. To identify heterogeneous causal effects, they develop a Cumulative Fixed Effects (CFE) method leveraging three-wave individual-level panel data. Simulations demonstrate that CFE remains unbiased even under highly nonlinear data-generating processes, effectively overcoming the constraints of conventional fixed effects models and accurately capturing diverse spillover mechanisms across multiple contextual settings.

This study addresses the inferential failure of two-way fixed effects M-estimators in unbalanced panels, which arises from incidental parameter bias and feedback bias. Within an asymptotic framework where both cross-sectional and time dimensions grow jointly, the paper proposes a debiased estimation method that accommodates missing observations without requiring prior knowledge of regressor predeterminedness or the selection mechanism. The approach is the first to simultaneously handle two sources of feedback bias—those stemming from predetermined regressors in the outcome equation and from a predetermined selection mechanism—without relying on assumptions about their predetermined structure. It remains valid under deterministic, stochastic, or mixed missingness mechanisms. Theoretical analysis shows that while the uncorrected estimator is asymptotically normal yet biased, the proposed debiased estimator effectively eliminates this bias, thereby enabling valid statistical inference.

This study addresses the challenge of identifying causal effects in nonseparable models when unobserved time-varying individual heterogeneity is correlated with explanatory variables. The authors propose a novel approach that approximates the conditional average potential outcomes using linear sieve methods, combined with individual-specific ridge regression and bias correction. Within a large-T asymptotic framework, this method achieves point identification, circumventing the partial identification issues common in traditional approaches. The resulting estimator admits an empirical Bayes interpretation, accommodates discrete treatment variables, and provides a unified framework for estimating average causal effects, counterfactual consumer welfare measures, and individual tax elasticities. An empirical application to supermarket scanner data demonstrates the method’s effectiveness by precisely quantifying the average equivalent variation and deadweight loss induced by price increases.

This study addresses the incidental parameter problem arising from unit-specific fixed effects in nonlinear panel data models, particularly when the number of time periods per unit is small and conventional estimators break down. The authors propose a novel projection-based approach that eliminates these incidental parameters without imposing assumptions on the joint distribution of fixed effects and covariates. By constructing an identified set through an implementable correspondence between observables and unobserved heterogeneity, and leveraging random set theory together with moment inequalities, they develop a distribution-free partial identification framework. This framework accommodates both static and dynamic models as well as discrete and continuous outcomes, enabling robust inference even in short panels.

This study addresses efficient estimation and robust inference for semiparametric and nonparametric models with fixed effects in panel data. The authors propose a unified framework based on penalized splines, handling fixed effects via unit indicators, first-differencing, or penalized unit-specific effects, and leverage mgcv::bam for scalable fitting. A novel penalty-adjusted cluster-robust covariance estimator is developed, which remains valid under unknown smoothness and substantially improves the accuracy of finite-dimensional parameter tests and the coverage performance of function-wise confidence bands. Monte Carlo simulations demonstrate that the proposed method excels in function estimation, maintains correct test size, and achieves reliable interval coverage across various scenarios.