by Aleksander Berentsen, Mariana Rojas Breu and Shouyong Shi
http://d.repec.org/n?u=RePEc:tor:tecipa:tecipa-371&r=dge
Many countries simultaneously suffer from high rates of inflation, low growth rates of per capita income and poorly developed financial sectors. In this paper, we integrate a microfounded model of money and finance into a model of endogenous growth to examine the effects of inflation and financial development. A novel feature of the model is that the market for innovation goods is decentralized. Financial intermediaries arise endogenously to provide liquid funds to the innovation sector. We calibrate the model to address two quantitative issues. One is the effects of an exogenous improvement in the productivity of the financial sector on welfare and per capita growth. The other is the effects of inflation on welfare and growth. Consistent with the data but in contrast to previous work, reducing inflation generates large gains in the growth rate of per capita income as well as in welfare. Relative to reducing inflation, improving the efficiency of the financial market increases growth and welfare by much smaller amounts.
It is difficult to find theory that give a large welfare gain from reducing inflation. This paper seems to achieve it by combining endogenous financial intermediation with endogenous growth. While empirics confirm its results by comparing high, medium and low-inflation countries, one can also ask whether welfare effects are significant within low-inflation regimes, say from 5% to 2%, instead of the traditional 10% to 0% (or Friedman Rule).
NEP-DGE Blog 
It has been even more difficult for theoretical models to generate any significant effect of inflation on the growth rate of income per capita than on welfare. In most models, increasing inflation from 0 to 10% reduces the growth rate by about 0.05 percentage points, while empirical studies point to a number that is one order of magnitude larger.
It seems that theoretical (quantitative) models have been looking at the wrong place! They should have looked at the role of money/banking in the innovation market instead of the consumption-goods market.