Abstract
This article proposes a simple estimator that is consistent for the fraction of a panel that has an autoregressive unit root. Given such an estimate, , we can test the null hypothesis that θ = θ0 for any value of θ0 ϵ (0, 1]. The test is asymptotically standard normal and is valid whether or not the panel is cross-sectionally correlated. The main insight is that in a panel in which some units are stationary and some have unit roots, the cross-sectional variance of the mixed panel is dominated by a linear trend that grows at rate θ, where θ is precisely the fraction of the panel with a unit root. Averaging the change in cross-sectional variance over time then gives a consistent estimate of θ as N, T → ∞. Simulations show that the estimator has good finite-sample properties when T ≥ 100, even with N as small as 30.
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