🤖 AI Summary
This study addresses the identification and estimation of common slope coefficients in quantile regression models with short panel data, accommodating unrestricted individual effects and temporally stationary disturbances. Under a stationarity assumption on the error term, the authors propose a two-step minimum distance estimator for fixed time dimension \(T\): first, a differencing identification strategy is constructed via intertemporal quantile regression projections, circumventing explicit estimation of individual effects; second, this restriction is leveraged to identify slope coefficients that are invariant across quantiles. The resulting estimator accommodates arbitrary within-individual serial correlation, achieves \(\sqrt{n}\)-consistency and asymptotic normality, and is accompanied by an analytical covariance estimator, a cluster-robust bootstrap procedure, and an overidentification test. Monte Carlo simulations demonstrate its excellent finite-sample performance across a range of data-generating processes.
📝 Abstract
This paper studies a linear panel model with an unrestricted individual effect and a time- stationary idiosyncratic disturbance. We first show that stationarity is a strong restriction in a quantile model. In a linear conditional quantile specification with quantile-dependent slopes, equality of the conditional residual distributions across periods generically forces the slope coefficient to be constant over the quantile index. Thus, a stationary-error model identifies a common location coefficient rather than a collection of quantile-specific slope effects. We then develop a fixed-T estimator of this common coefficient. For each period, we run a cross- sectional quantile regression of the outcome on the full history of regressors. Stationarity makes the quantile projection of the composite individual effect and disturbance common across the period-specific regressions. Differences between diagonal and off-diagonal blocks of the resulting projection coefficients therefore identify the common slope whenever T>=2. We combine all such restrictions by a two-step minimum-distance estimator. The estimator is root-n-consistent and asymptotically normal with fixed T, permits unrestricted dependence across periods within an individual, and does not estimate the individual effects. We provide a consistent analytic covariance estimator, a cluster bootstrap, and an overidentification test of the projection restrictions implied by stationarity. Extensive Monte Carlo experiments show adequate performance under various designs.