This paper proposes a simple estimator that is consistent for the fraction of a panel that has an autoregressive unit root. Given such an estimate, θ, we can test the null hypothesis that θ = θ 0 for any value of θ 0 ∈ (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-section variance of the mixed panel is dominated by

more »

... a linear trend that grows at rate θ, where θ is precisely the fraction of the panel with unit roots. Averaging the change in cross-section variance over time then gives us a √ N 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.