Bayesian-smoothed location quotients for small regions with credible intervals and specialisation probabilities

Abstract

Location quotients are widely used to benchmark the relative concentration of activity in a region against a reference economy, but they are often reported as point estimates without uncertainty and can be unstable for small regions and rare categories. This paper proposes a Bayesian-smoothed location quotient that shrinks noisy region–sector shares toward the benchmark share and reports uncertainty using posterior credible intervals. As an alternative to arbitrary threshold rules, we introduce a posterior probability of specialisation that directly quantifies the evidence that a region’s latent share exceeds the benchmark share. We also provide a short stability bound showing that the smoothed estimator has controlled one-unit sensitivity to perturbations in the underlying counts. A concise simulation study and an empirical illustration demonstrate improved stability and more cautious inference in sparse-count settings.

Keywords

• Location quotient
• empirical Bayes
• small area estimation
• uncertainty quantification
• regional statistics

References

1. 1] A. Agresti and B. A. Coull, Approximate is better than “exact” for interval estimation of binomial proportions, Am. Stat. 52 (2), 119–126, 1998.