Estimating Large Correlation Matrices for International Migration

TL;DR

This paper introduces a Bayesian estimator for large correlation matrices in international migration, addressing data sparsity and improving regional migration projections.

Contribution

It proposes a maximum a posteriori estimator with an interpretable prior to regularize and improve correlation matrix estimation from limited data.

Findings

The estimator outperforms Pearson and simple shrinkage methods in simulations.

It yields more accurate regional migration projections, narrowing Africa's and widening Europe's forecasts.

The method effectively regularizes sparse correlation estimates with limited data.

Abstract

The United Nations is the major organization producing and regularly updating probabilistic population projections for all countries. International migration is a critical component of such projections, and between-country correlations are important for forecasts of regional aggregates. However, there are 200 countries and only 12 data points, each one corresponding to a five-year time period. Thus a $200 \times 200$ correlation matrix must be estimated on the basis of 12 data points. Using Pearson correlations produces many spurious correlations. We propose a maximum a posteriori estimator for the correlation matrix with an interpretable informative prior distribution. The prior serves to regularize the correlation matrix, shrinking a priori untrustworthy elements towards zero. Our estimated correlation structure improves projections of net migration for regional aggregates, producing narrower projections of migration for Africa as a whole and wider projections for Europe. A simulation study confirms that our estimator outperforms both the Pearson correlation matrix and a simple shrinkage estimator when estimating a sparse correlation matrix.