panel cointegration testing

This paper addresses the challenge of identifying multiple long-run equilibrium relationships in large-dimensional unbalanced panel data (where $n gg T$). Existing methods typically assume a single long-run relationship and struggle to simultaneously eliminate short-run dynamic disturbances while ensuring stable identification of long-run structures. We propose the “Pooled Minimum Eigenvalue” (PME) method—a novel, fully data-driven approach that requires no pre-specified causal ordering and applies to generalized linear processes with interactive time-varying effects. PME constructs bias-corrected sequences via time-averages over non-overlapping subsamples and jointly estimates eigenvalues and eigenvectors of the long-run covariance matrix to consistently determine both the number and coefficients of long-run relationships. We establish its consistency and asymptotic normality under $n,T o infty$ with $T approx n^d$, $d > 1/2$. Monte Carlo experiments confirm its high accuracy in rank selection, low coefficient bias, small RMSE, and strong test power.

This paper addresses structural break detection in the cross-sectional mean of panel data. We propose a novel weighted least squares change-point test that constructs a cross-sectional mean sequence and estimates nuisance parameters to formulate a test statistic independent of bandwidth selection and long-run variance estimation; its limiting distribution is analytically tractable and robust under both weak and strong cross-sectional dependence. Theoretically, the method is proven to be consistent and asymptotically efficient. Monte Carlo simulations demonstrate excellent finite-sample size control and power. The key contribution lies in establishing, for the first time, a unified asymptotic inference framework that requires no bandwidth tuning and avoids covariance kernel estimation—enabling flexible weight design and substantially enhancing adaptability and practicality for complex cross-sectional dependence structures.

Conventional causal inference methods for panel data rely heavily on strong parametric assumptions—such as linearity and fixed effects—limiting robustness and generalizability. Method: This paper proposes a nonparametric, matching-based analytical framework specifically designed for time-series cross-sectional (TSCS) data. It introduces the first systematic dynamic matching approach for such data, integrating propensity score matching, covariate balance diagnostics, and interactive visualization (via ggplot2 and Shiny). Contribution/Results: The framework relaxes assumptions on functional form and individual homogeneity, enhances assumption robustness and result verifiability, and delivers comprehensive diagnostic reports alongside interpretability assessment tools. Implemented as an open-source R package, it has been empirically validated across sociology, economics, and medical research, improving transparency, reproducibility, and credibility of longitudinal causal effect estimation.

This paper addresses unit root and cointegration inference for functional time series in Hilbert spaces, focusing on identifying the number of common stochastic trends—i.e., the dimension of the nonstationary subspace—and conducting hypothesis tests for the nonstationary and stationary subspaces. We systematically extend classical unit root and cointegration theory to arbitrary-dimensional Hilbert spaces for the first time, proposing a projection-operator spectral analysis method that is asymptotically efficient, fully data-driven (requiring no prior dimension specification), and uniformly applicable to high-dimensional vector time series, dynamic functional factor models, and curve-valued time series. We further develop theoretically grounded dimension-selection criteria and valid test statistics with rigorous asymptotic properties. Empirical applications to the U.S. yield curve and labor market indices robustly identify key common nonstationary trends, demonstrating the method’s interpretability and practical utility for real-world high-dimensional functional time series.

This paper addresses the identification and estimation of dynamic random-coefficient linear models with individual heterogeneity in short panel data. Due to predetermined regressors—such as lagged dependent variables—point identification is infeasible under conventional approaches. We therefore propose a semiparametric identification framework grounded in moment inequalities and distributional constraints, which—novelty—systematically characterizes the non-point-identified sets for the mean, variance, and cumulative distribution function of the random coefficients, accommodating discrete, continuous, and unbounded outcomes. We further develop a computationally tractable estimation and inference procedure, applying it to PSID data. Empirically, we find substantial unobserved heterogeneity in U.S. household income persistence; this heterogeneity constitutes a key structural driver of divergent consumption and saving behaviors across households.

This study addresses the challenge of conducting valid statistical inference on unit-specific coefficients in panel data exhibiting latent group structure. The authors propose a novel inference framework that first clusters units into a small number of latent groups and then explicitly accounts for uncertainty in group membership. Their approach involves two key components: constructing test statistics based on the minimal value over confidence sets for group assignments, and correcting for bias induced by potential group misclassification while developing standard errors robust to such misclassification. Theoretical analysis and simulation results demonstrate that, compared to conventional unit-by-unit time series methods, the proposed procedure yields substantially narrower confidence sets—particularly for units with high error variance—while maintaining proper size control and coverage accuracy, thereby avoiding inferential distortions caused by ignoring group assignment uncertainty.

Traditional econometric approaches treat observational data as vectors, making it difficult to effectively capture the two-dimensional structure of matrix-valued data and its intrinsic long-run equilibrium relationships. This study proposes a novel matrix cointegrated error correction model that, for the first time, establishes a cointegration framework admitting an equivalent matrix autoregressive (MAR) representation. By preserving the native matrix form of the data, the model naturally accommodates both cointegrating relationships and dynamic adjustment mechanisms. It accurately characterizes long-run equilibria and short-run dynamics among variables while maintaining structural integrity, thereby offering both economic interpretability and methodological innovation.

This study addresses the issue of size distortion in weak exogeneity tests within dynamic linear models, which often arises due to omitted variables inducing reverse causality. To resolve this, the paper proposes a novel asymmetric Portmanteau test that avoids joint dynamic parametrization by constructing an asymmetric quadratic form statistic based on the sequential cross-correlation structure. This statistic effectively distinguishes between violations of weak exogeneity and genuine reverse causal effects, and under the null hypothesis, it follows an asymptotic normal distribution, thereby circumventing the size distortions inherent in conventional symmetric tests. An empirical application to economic policy uncertainty shocks reveals rejection of weak exogeneity; upon introducing control variables, the inflation response shifts from negative to positive, lending support to a supply-shock interpretation and demonstrating the practical utility of the proposed method.