Inflation and economic growth Noticeable works about the impact of inflation on economic growth are dated back to the 90s.

For example, Barro (1995):


  the impact effects from an increase in average inflation by 10 percentage points per year are a reduction of the growth rate of real per capita GDP by 0.2-0.3 percentage points per year and a decrease in the ratio of investment to GDP by 0.4-0.6 percentage points.


He also shows outliers there:



Bruno and Easterly, “Inflation Crises and Long-Run Growth” (1998), reiterate that extreme situations matter for growth:


  growth falls sharply during discrete high inflation crises, then recovers rapidly and strongly after inflation falls.


Since after these papers, no highly cited paper on topic appeared. Though there's Acemoglu et al., “Institutional Causes, Macroeconomic Symptoms” (2003), which is relevant in another sense.

In a recent survey (2012), the Bank of England mentions without a reference that


  The consensus seems to be that
  above a threshold of around 3%–4%, inflation imposes welfare
  costs, while the plausible gains from reducing inflation below
  about 2% are unlikely to outweigh the advantages of a positive
  inflation target.
  There is even less guidance in the literature on the optimal
  level of inflation in developing and emerging countries,
  though Balassa-Samuelson effects imply that optimal
  inflation in these countries should be a little higher than in
  industrialised countries.


Apart from cross-country evidences, rare country studies are available. The IMF on India (2014):


  Our findings suggest that, on average, there is a negative long-run relationship between
  inflation and economic growth in India. We also find statistically-significant inflation-growth threshold effects in the case of states with persistently-elevated inflation rates of above 5.5 percent. 


Does the current academic consensus remain with Barro's 1995 paper? Are there any new estimates of the impact of inflation, threshold levels of inflation, and changes in inflation on long-term economic growth?
Macro regressions, especially annual ones, have in general two flaws:


They have small sample problems and
They have no proper identification


In order to circumvent problem #1, people often assume that the DGP process behind different countries are the same, increasing observations from perhaps 60 to 600.

In order to attack #2, many people add timing assumptions. However, this is still no clear identification, these are still assumptions.

To see the issue: Imagine high inflation at $t-5$, and low growth at $t$. Using a standard timing assumption, the former caused the latter. However, we like to think about agents as forward looking. Can we be certain that expectations w.r.t. the latter didn't influence the former?

Especially because of #2, this type of regressions have lost popularity. Also, there is not really much more to do. 

tl;dr: No important new results that I know of.