Seemingly Unrelated Cointegrating Regressions with Autoregressive Distributed Lag Dynamics: Estimation, Bounds Testing, and Cross-Equation Inference

<title>Abstract</title> <p> This paper develops a seemingly unrelated autoregressive distributed lag (SUR-ARDL) framework for estimating and testing cointegrating relationships in panels with small cross-sectional dimension. By embedding the Pesaran et al. (2001) error-correction specification within a Zellner (1962) SUR system, the estimator exploits cross-equation correlation for efficiency while the ARDL lag structure parametrically removes second-order endogeneity and serial correlation biases without semi-parametric corrections. Unlike the FM-SUR estimator of Wagner et al. (2020, Journal of Econometrics) and the FM-GLS estimator of Lin and Reuvers (2025, Oxford Bulletin of Economics and Statistics), the proposed estimator requires only the N × N contemporaneous error covariance rather than 2N × 2N long-run covariance matrices, eliminating the principal source of finite-sample distortion in these methods. We establish that the feasible GLS estimator achieves a mixed-normal limiting distribution, the SUR bounds F-statistic inherits the Pesaran et al. (2001) bounds property regardless of the integration order of regressors, and cross-equation Wald tests for poolability and coefficient equality attain chi-squared distributions. A Monte Carlo study with demonstrates RMSE reductions of relative to single-equation OLS, substantial power gains for the bounds cointegration test, reliable covariance estimation with zero invertibility and adequate size with bootstrap critical values. An application to the renewable energy-economic growth nexus in ASEAN countries shows that SUR-ARDL reduces standard errors, detects cointegration in Vietnam where single-equation methods fail, and reveals a two-cluster structure of adjustment speeds slow-adjusting fossil fuel producers versus fast-adjusting energy importers through cross-equation hypothesis tests unavailable to equation-by-equation methods. <bold>JEL Classification:</bold> C13, C32, C33, Q43. </p>