Inflation and 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.