Estimating large correlation matrices for international migration

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 × 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.

Growing up and moving out: Migration and the demographic transition in low- and middle-income nations

“…By comparing these with known migrant flow data produced by select countries with robust population tracking systems, Abel and Cohen (2019) suggested that closed demographic accounting approaches are the preferred method for estimating global bilateral migrant flows based on incomplete stock data. For our main analysis, we use the ‘demographic accounting, pseudo-Bayesian (closed)’ method, which is the one most well supported in Abel and Cohen (2019) and most like the method previously introduced by Azose and Raftery (2018) (for further discussion, see supplementary material , section 2 ). The result is estimates of the total number of outmigrants from each country to every other country within five-year periods between 1990 and 2015.…”

Partial correlation graphical LASSO

“…The space method of Peng et al (2009), similarly to PCGLASSO, uses an $$$ {L}_1 $$$ penalty on the partial correlations, but in combination with a function other than the log‐likelihood. Azose and Raftery (2018) introduced a separable prior on the marginal correlations. They argued that a key benefit of their prior is the ability to specify beliefs about correlations.…”

A Model of Dynamic Flows: Explaining Turkey’s Interprovincial Migration

“…A class of models that share the Bayesian nature of our model and also deal with migration can be found in Azose and Raftery (2015, 2018). The main aim of those models is to forecast country-level future net migration based on past migration via an autoregressive hierarchical model.…”

“…The main aim of those models is to forecast country-level future net migration based on past migration via an autoregressive hierarchical model. Azose and Raftery (2018) improve those forecasts by developing a procedure that estimates cross-country correlations in net migration rates. These models differ from ours in that explaining the determinants of migration is not part of their purpose.…”