Linear Regression: Inference Based on Cluster Estimates

TL;DR

This paper introduces a new estimator for regression coefficients in clustered data that accounts for within-cluster dependence, extending to random coefficient models and proposing tests for parameter stability, with extensive simulations and real data application.

Contribution

It presents a novel estimator for clustered data regression that explicitly models dependence and develops new tests for parameter stability, improving inference accuracy.

Findings

The proposed estimator outperforms traditional methods in clustered settings.

Conventional POLS estimator can be unreliable in random coefficient models.

New tests effectively detect parameter stability across hierarchical levels.

Abstract

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.