# A two-stage random-effects estimator for meta-analyses of the value per statistical life

## TL;DR

This paper introduces a new method for combining estimates of the value per statistical life using a two-stage random-effects model.

## Contribution

The novel two-stage random-effects estimator improves statistical efficiency in meta-analyses of VSL estimates.

## Key findings

- The estimator performs best when within-group non-sampling error variances are homogeneous.
- The method compares favorably to other meta-analysis estimators in simulation experiments.
- The approach was demonstrated on a dataset of 113 VSL estimates from U.S. studies.

## Abstract

We developed and examined the performance of a two-stage random-effects meta-analysis estimator for synthesizing published estimates of the value per statistical life (VSL). The meta-estimation approach accommodates unbalanced panels with one or multiple observations from each independent group of primary estimates, and distinguishes between sampling and non-sampling sources of error, both within and between groups. We used Monte Carlo simulation experiments to test the performance of the meta-estimator on constructed datasets. Simulation results indicate that, when applied to datasets of modest size, the approach performs best when the within-group non-sampling error variances are assumed to be homogeneous among groups. This allows for two levels of non-sampling errors while preserving degrees of freedom and therefore increasing statistical efficiency. Simulation results also show that the estimator compares favorably to several other commonly used meta-analysis estimators, including other two-stage estimators. As a demonstration, we applied the approach to a pre-existing meta-dataset including 113 VSL estimates assembled from 10 revealed preference and 9 stated preference studies conducted in the U.S. and published between 1999 and 2019.