Meta-analyzing the price puzzle

Meta-analysis is the analysis of the literature on, say, the estimate of a particular elasticity. This is common in medical studies, where each individual study has usually little statistical significance, but aggregating them may give the results more power. In Economics, there are few meta-analyses (although there is a society on the topic) as study samples are statistically much more sound and each study takes so much time that there is little incentive to do a lot o the same topic. Yet, this happens for some themes.

One such theme is the price puzzle: many vector-autoregression models show that a monetary contraction is immediately followed by a rise in the price level, which is rather counter-intuitive. Marek Rusnák, Tomáš Havránek and Roman Horváth found 70 articles from 31 countries providing 210 estimates of the response at five horizons. Can one then simply do a statistical analysis on these estimates? That is not so easy, as there may be a publication bias. As the puzzle is now well documented, journal editors are not particularly interested in studies that demonstrate it again. The authors claim that there is such a bias, but I have to confess I do not understand how they come to that conclusion.

The price puzzle is on average present, and prices eventually decrease as suggested but all theories. But there is substantial variance in the results, which the authors show can be explained by what variables are included or what variant of a vector-autoregression is run. This unfortunately confirms my frustration with this field: there is a dizzying array of methods and specifications that yield different results, and it is impossible to tell which one is right. Maybe we need a bit more theory to discipline this.