The first, by Marc Dordal-i-Carreras, Olivier Coibion, Yuriy Gorodnichenko, and Johannes Wieland, is called "Infrequent but Long-Lived Zero-Bound Episodes and the Optimal Rate of Inflation." One benefit of a higher inflation target is to reduce the occurrence of zero lower bound (ZLB) episodes, so understanding the welfare costs of these episodes is important in calculating an optimal inflation target. The authors explain that in standard models with a ZLB, normally-distributed shocks result in short-lived ZLB episodes. This is in contrast with the reality of frequent but long-lived ZLB episodes. They build models that can generate long-lived ZLB episodes and show that welfare costs of ZLB episodes increase steeply with duration; 8 successive quarters at the ZLB is costlier than two separate 4-quarter episodes.
If ZLB episodes are costlier, it makes sense to have a higher inflation target to reduce their frequency. The authors note, however, that the estimate of the optimal target implied by their models are very sensitive to modeling assumptions and calibration:
"We find that depending on our calibration of the average duration and the unconditional frequency of ZLB episodes, the optimal inflation rate can range from 1.5% to 4%. This uncertainty stems ultimately from the paucity of historical experience with ZLB episodes, which makes pinning down these parameters with any degree of confidence very difficult. A key conclusion of the paper is therefore that much humility is called for when making recommendations about the optimal rate of inflation since this fundamental data constraint is unlikely to be relaxed anytime soon."The second paper, by Emi Nakamura, Jón Steinsson, Patrick Sun, and Daniel Villar, is called "The Elusive Costs of Inflation: Price Dispersion during the U.S. Great Inflation." This paper notes that in standard New Keynesian models with Calvo pricing, one of the main welfare costs of inflation comes from inefficient price dispersion. When inflation is high, prices get further from optimal between price resets. This distorts the allocative role of prices, as relative prices no longer accurately reflect relative costs of production. In a standard New Keynesian model, the implied cost of this reduction in production efficiency is about 10% if you move from 0% inflation to 12% inflation. This is huge-- an order of magnitude greater than the welfare costs of business cycle fluctuations in output. This is why standard models recommend a very low inflation target.
Empirical evidence of inefficient price dispersion is sparse, since there is relatively minimal fluctuation in inflation in the past few decades, when BLS microdata on consumer prices is available. Nakamura et al. undertook the arduous task of extending the BLS microdataset back to 1977, encompassing higher-inflation episodes. Calculating price dispersion within a category of goods can be problematic, because price dispersion may arise from differences in quality or features of the goods. The authors instead look at the absolute size of price changes, explaining, "Intuitively, if inflation leads prices to drift further away from their optimal level, we should see prices adjusting by larger amounts when they adjust. The absolute size of price adjustments should reveal how far away from optimal the adjusting prices had become before they were adjusted. The absolute size of price adjustment should therefore be highly informative about inefficient price dispersion."
They find that the mean absolute size of price changes is fairly constant from 1977 to the present, and conclude that "There is, thus, no evidence that prices deviated more from their optimal level during the Great Inflation period when inflation was running at higher than 10% per year than during the more recent period when inflation has been close to 2% per year. We conclude from this that the main costs of inflation in the New Keynesian model are completely elusive in the data. This implies that the strong conclusions about optimality of low inflation rates reached by researchers using models of this kind need to be reassessed."