Lost in Aggregation: Quantifying Measurement Error from Geographic Centroids

Due to privacy laws and regulations, microdata typically provide regional identifiers rather than exact coordinates. Researchers therefore often construct spatial variables from these aggregations, but the statistical implications depend on the research setting. We test measurement error in New South Wales property transactions by comparing coefficients based on exact‐coordinate spatial variables with those based on official geographic centroids under conventional econometric specifications. Spatial aggregation departs from the canonical classical and Berkson error models, which predict attenuation and precision loss, respectively. The resulting error can have a non‐zero conditional mean and correlate with the exact regressor, making the direction of bias ambiguous, with relative biases ranging from −79.2 to 45.6 per cent. The consequences of geographic aggregation depend on the variable and specification, so there is no simple bias‐variance trade‐off. We examine several spatial variables, focusing on distance to Sydney's central business district (CBD) and the number of shops within 1 km. Centroids of Statistical Area Level 1 (SA1), the most granular regional classification examined, reproduce the smooth CBD‐distance coefficients closely. Local shop‐count coefficients can differ even at this level, with larger deviations in the coarser Statistical Area Level 2 (SA2) and postcode classifications. We show how buffer sizes, subsampling and alternative proxies can be used as sensitivity checks for spatial aggregation. This paper provides methodological guidance to applied researchers using spatial variables in microdata, particularly in Australia.