Estimating Large Correlation Matrices for International Migration
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, the...
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Veröffentlicht in: | arXiv.org 2016-05 |
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Format: | Artikel |
Sprache: | eng |
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Zusammenfassung: | 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. |
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ISSN: | 2331-8422 |