Spatial autoregressive (SAR) models

Stata now fits SAR models. SAR may stand for either spatial autoregressive or simultaneous autoregressive. Regardless of terminology, SAR models allow spatial lags of the dependent variable, spatial lags of the independent variables, and spatial autoregressive errors. Spatial lags are the spatial analog of time-series lags. Time-series lags are values of variables from recent times. Spatial lags are values from nearby areas.

SAR models are fit with the new commands spregress, spivregress (for endogenous covariates), and spxtregress (for panel data).

The models are appropriate for area (also known as areal) data. Observations are called spatial units and might be countries, states, districts, counties, cities, postal codes, or city blocks. Or they might not be geographically based at all. They could be nodes of social network. Spatial models estimate direct effects -- the effects of areas on themselves -- and estimate indirect or spillover effects -- effects from nearby areas.

Stata provides a suite of commands for working with spatial data and a new [SP] manual to accompany them. When spatial units are geographically based, you can download standard-format shapefiles from the web that define the map. With a single command, you can make spillover effects proportional to the inverse distance between areas or restrict them to be just from neighboring areas. And you can create your own custom definitions of proximity.

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