How do partly omitted control variables influence the averages used in meta-analysis in economics?

Meta regression analysis is used to extract the best average from a set of N primary studies of one economic parameter. Three averages of the N-set are discussed: The mean, the PET meta-average and the augmented meta-average. They are affected by control variables that are used in some of the primary studies. They are the POCs, partly omitted controls, of the meta-study. Some POCs are ceteris paribus controls chosen to make results from different data samples comparable. They should differ. Others are model variables. They may be true and should always be included, while others are false and should always be excluded, if only we knew. If POCs are systematically included for their effect on the estimate of the parameter, it gives publication bias. It is corrected by the meta-average. If a POC is randomly included, it gives a bias, which is corrected by the augmented meta-average. With many POCs very many augmentations are possible. The mean of all augmented meta-averages is also the mean of the N-set. If it has a publication bias so do the average augmented meta-averages.