Table A D.1 displays estimates of standard errors (SE) of the reported VSL estimates required to use the meta-analysis approach presented in Chapter 4. As can be seen from Table A D.1, only a fraction of the studies reports these. If not reported, the standard error can be estimated based on information about reported confidence intervals (CI)1. If this information is also not available, it is also possible to impute this information, for example based on information about sample size and relationship with standard errors reported by the other studies. There are a number of options for imputation in the literature (Viscusi, 2019[1]). In this study a Bayesian imputation method is used to recover missing SE error estimates.
Following the Bayesian imputation method and based on the cumulative distribution function (CDF) of the VSL estimates, the standard errors (SEs) of VSL estimates are assumed to be randomly missing. Therefore, observed information is used to impute the missing SEs. Information on the observed 2 474 SEs is used to impute the missing 1 634 SEs by fitting Bayesian models (McElreath, 2018[2]). The estimation for each model is based on four parallel Markov chains sampled by the No-U-Turn Sampler (NUTS), and each chain has 2 000 draws with 2 000 iterations to tune. A simple Bayesian linear regression model is used where the mean of the is assumed to be a linear function of the only regressor . Figure A D.1 shows that this method yields imputed SE values that closely follow the observed values and is therefore considered a valid approach.
