Good public policy needs to be evidence based. However, the evidence base is thin for many policy issues. How can policy makers best respond to such thin areas of research that are also quite likely to change over time? Our survey investigates the evolution of the econometric evidence base for 101 economic issues, drawing upon 42,578 effect sizes (mainly elasticities and correlations) from 4,300 econometric studies. We evaluate the performance of six approaches to early research assessment: the simple unweighted mean; the median; the Paldam, "divide by 2" rule of thumb; the unrestricted weighted least squares (WLS) weighted average; the PET-PEESE meta-regression correction for publication bias; the weighted average of the adequately powered (WAAP); and WAAP-WLS. Lowest prediction errors are found in the Paldam rule of thumb and WLS. WLS typically reduces the initial exaggeration of thin evidence by half.