This article proposes a novel estimator for regression coefficients in clustered data that explicitly accounts for within-cluster dependence. We study the asymptotic properties of the proposed estimator under both finite and infinite cluster sizes. The analysis is then extended to a standard random coefficient model, where we derive asymptotic results for the average (common) parameters and develop a Wald-type test for general linear hypotheses. We also investigate the performance of the conventional pooled ordinary least squares (POLS) estimator within the random coefficients framework and show that it can be unreliable across a wide range of empirically relevant settings. Furthermore, we introduce a new test for parameter stability at a higher (superblock; Tier 2, Tier 3,...) level, assuming that parameters are stable across clusters within that level. Extensive simulation studies demonstrate the effectiveness of the proposed tests, and an empirical application illustrates their practical relevance.

翻译：本文提出了一种针对聚类数据回归系数的新型估计量，该估计量明确考虑了聚类内依赖性。我们研究了在有限和无限聚类规模下该估计量的渐近性质。随后将分析扩展至标准随机系数模型，推导了平均（共同）参数的渐近结果，并建立了针对一般线性假设的Wald型检验。此外，我们在随机系数框架下研究了传统混合普通最小二乘（POLS）估计量的表现，证明其在广泛的经验相关设定中可能不可靠。进一步地，我们提出了一种针对更高层级（超区块；第二层、第三层……）参数稳定性的新检验方法，其假设参数在该层级内的各聚类间保持稳定。大量模拟研究验证了所提检验方法的有效性，实证应用则揭示了其现实意义。