An Illustration of a Pitfall in Estimating the Effects of Aggregate Variables on Micro Units

TLDR

Researchers often merge aggregate market or policy data with micro‑level observations and rely on regression models that assume independent disturbances, an assumption that is generally inappropriate for grouped data. This note demonstrates the risk of spurious regression arising from such misspecification by analyzing a wage regression that includes aggregate state‑level characteristics. The authors illustrate this by estimating a wage regression on individual worker data that incorporates aggregate state characteristics as regressors. They find that ordinary least squares yields severely underestimated standard errors. © 1990 MIT Press.

Abstract

Many economic researchers have attempted to measure the effect of aggregate market or public policy variables on micro units by merging aggregate data with micro observations by industry, occupation, or geographical location, then using multiple regression or similar statistical models to measure the effect of the aggregate variable on the micro units. The methods are usually based upon the assumption of independent disturbances, which is typically not appropriate for data from populations with grouped structure. Incorrectly using ordinary least squares can lead to standard errors that are seriously biased downward. This note illustrates the danger of spurious regression from this kind of misspecification, using as an example a wage regression estimated on data for individual workers that includes in the specification aggregate regressors for characteristics of geographical states. Copyright 1990 by MIT Press.