# Semi-Parametric Empirical Best Prediction for small area estimation of unemployment indicators

## TL;DR

This paper introduces a semi-parametric approach for small area estimation of unemployment rates, improving accuracy and computational efficiency by avoiding strict distributional assumptions and heavy integral calculations.

## Contribution

It proposes a semi-parametric empirical best predictor that estimates the distribution of random effects from data, enhancing small area unemployment estimation.

## Key findings

- Effective in small sample areas with limited data
- Reduces computational burden compared to traditional methods
- Provides accurate estimates with bias correction

## 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-of-sample 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.