Semiparametric empirical best prediction for small area estimation of unemployment indicators

Abstract

The Italian National Institute for Statistics regularly provides estimates of unemployment indicators using data from the Labor Force Survey. However, direct estimates of unemployment incidence cannot be released for Local Labor Market Areas. These are unplanned domains defined as clusters of municipalities; many are out-ofsample areas and the majority is characterized by a small sample size, which render direct estimates inadequate. The Empirical Best Predictor represents an appropriate, model-based, alternative. However, for non-Gaussian responses, its computation and the computation of the analytic approximation to its Mean Squared Error require the solution of (possibly) multiple integrals that, generally, have not a closed form. To solve the issue, Monte Carlo methods and parametric bootstrap are common choices, even though the computational burden is a non trivial task. In this paper, we propose a Semi-Parametric Empirical Best Predictor for a (possibly) non-linear mixed effect model by leaving the distribution of the area-specific random effects unspecified and estimating it from the observed data. This approach is known to lead to a discrete mixing distribution which helps avoid unverifiable parametric assumptions and heavy integral approximations. We also derive a second-order, bias-corrected, analytic approximation to the corresponding Mean Squared Error. Finite sample properties of the proposed approach are tested via a large scale simulation study. Furthermore, the proposal is applied to unit-level data from the 2012 Italian Labor Force Survey to estimate unemployment incidence for 611 Local Labor Market Areas using auxiliary information from administrative registers and the 2011 Census.

Data-Driven Transformations in Small Area Estimation

“…The estimation of the random effects can be made completely non‐parametric by using a discrete mixture proposed by Marino et al . (). Another option, and the one that we study in this paper, is to find an appropriate transformation such that the model assumptions (in this paper the Gaussian assumptions of the EBP method) hold.…”

“…The estimation of the quantiles is facilitated by a nested error regression model using the asymmetric Laplace distribution for the unit level error terms as a working assumption. The estimation of the random effects can be made completely non-parametric by using a discrete mixture proposed by Marino et al (2018Marino et al ( , 2019. Another option, and the one that we study in this paper, is to find an appropriate transformation such that the model assumptions (in this paper the Gaussian assumptions of the EBP method) hold.…”

Empirical Bayes small area prediction under a zero‐inflated lognormal model with correlated random area effects

“…Jiang and Lahiri (2001) develop a rigorous theory for EB prediction under the unit-level logistic mixed effects model, where the parameters are estimated using simulated method of moments. Extensions of the logistic mixed effects model with a single normally distributed random effect have been developed to incorporate a semiparametric model for the random effects (Marino, Ranalli, Salvati, & Alfò, 2019) and temporal data (Hobza, Morales, & Santamaría, 2018). Pfeffermann, Terryn, and Moura (2008) combine the logistic mixed effects model with a unit-level linear mixed effects model to develop a unit-level small area model for zero-inflated data.…”

$$\ell _2$$-penalized approximate likelihood inference in logit mixed models for regional prevalence estimation under covariate rank-deficiency

“…The Poisson or negative binomial mixed models were applied to estimate small area counts or proportions by Berg (2010), Chambers et al (2014), , Tzavidis et al (2015) and Boubeta et al (2016Boubeta et al ( , 2017, among others. Marino et al (2019) propose a semiparametric approach allowing for a flexible random effects structure in unit-level models. Ranalli et al (2018) introduced benchmarking for logistic unit-level.…”