Correcting measures of relationship betweeen aggregate-level variables for both unreliability and correlated errors: An empirical example

Many social scientists conducting macro-level analyses use aggregate-level variables (weighted sums of the characteristics of the individuals within the macro-level units: e.g., means, percents, or rates) to describe macro-level units (e.g., schools, cities, or states). Researchers have long known that aggregate-level variables are likely to be more reliable than individual-level variables.