The Prior Uncertainty and Correlation of Statistical Economic Data

Empirical estimates of source statistical economic data such as transaction flows, greenhouse gas emissions or employment are always subject to measurement errors but empirical estimates of source data errors are often missing. This paper uses concepts from Bayesian inference and the Maximum Entropy Principle to estimate the prior probability distribution, uncertainty and correlations of source data when such information is not explicitly provided. In the absence of additional information, an isolated datum is described by a truncated Gaussian distribution, and if an uncertainty estimate is missing, its prior equals the best guess. When the sum of a set of disaggregate data is constrained to match an aggregate datum, it is possible to determine the prior correlations among disaggregate data. If aggregate uncertainty is missing, all prior correlations are positive. If aggregate uncertainty is available, prior correlations can be either all positive, all negative, or a mix of both. An empirical example is presented, which reports uncertainty and correlation priors for the County Business Patterns database.