This paper proposes a model for, and investigates the consequences of, strong spatial dependence in economic variables. Our findings echo those of the corresponding “unit root” time series literature: Spatial unit root processes induce spuriously significant regression results, even with clustered standard errors or spatial HAC corrections. We develop large‐sample valid unit root and stationarity tests that can detect such strong spatial dependence. Finally, we use simulations to study strategies for valid inference in regressions with persistent spatial data, such as spatial analogues of first‐differencing transformations. Regressions from Chetty, Hendren, Kline, and Saez (2014) are used to illustrate the issues and methods.

Standard extreme value theory implies that the distribution of the largest observations of a large cross section is well approximated by a parametric model, governed by a location, scale and shape parameter. The extremes of a panel of independent cross sections are all governed by the same parameters as long as the underlying distribution as well as the size of the cross sections are time invariant. We derive inference about these parameters, and tests of the null hypothesis of time invariance, under asymptotics that do not require the number of extremes or the number of time periods to increase. We further apply Hamiltonian Monte Carlo techniques to estimate the path of time-varying parameters. We illustrate the approach in four examples of U.S. data: damages from weather-related disasters, financial returns, city sizes and firm sizes.