Spatial Unit Roots

Princeton University, Princeton NJ

Investigators

Abstract

When data series, such as inflation or unemployment rates are highly correlated over time, it is difficult to establish the direction of causation. Not accounting for such high correlation over time leads to wrong conclusions. Economists have therefore developed methods to correct for such correlation when drawing conclusions from data that are highly correlated over time. There are no methods to correct for strong correlation among economic variables that are measured at different locations, such as income, housing prices, or crime rates, across different US commuting zones. This research develops new methods to correct for strong correlation among economic variables across space to help researchers make correct inference. The research develops a formal framework to study such effects, derives tests to detect strong spatial correlation, and suggest methods to restore valid conclusions from strongly correlated spatial data. Since strongly correlated spatial data is quite common, this research could have important implications for how to draw correct empirical conclusions in the social sciences and beyond. The results of this research will improve policy making that involves consideration of space, such as housing and crime policies in US urban areas. This research uses four projects to investigate the consequences of "unit root"-type strong spatial dependence. The suggested methods echo corresponding concepts and results in the time series literature: The project suggests a model for general spatial "unit-root"-type I(1) processes; it then establishes a Functional Central Limit Theorem justifying a large sample Gaussian process approximation for such I(1) processes. The I(1) model is then generalized to a spatial "local-to-unity" model that exhibits long-range, stationary dependence as well as characterize the large sample behavior of regression inference with spatial I(1) variables and establish that spurious regression is as much a problem with spatial I(1) data as it is with time series I(1) data. Finally, the research develops asymptotically valid spatial unit root and stationarity tests, inference for the local-to-unity parameter, and suggest strategies for obtaining valid inference in regressions with persistent (I(1) or local-to-unity) spatial processes. Besides contributions to the econometrics literature, the results of this research will improve policy making, especially urban policies, where spatial dependence tends to be very strong. The results will also help establish the US as a global leader in spatial econometrics. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.