Basile, Landon-Lane, and Rockoff have a new paper on the Great Depression. They conclude:

The main finding is that as we move away from short-term government bonds on the "liquidity spectrum" we encounter rates that appear to have been sensitive to changes in monetary policy, although the mortgage rates were an exception.

They note that Keynes himself did not believe America was in a liquidity trap, though some of the American Keynesians did.

Here is a new paper from the Kansas City Fed, by Taeyoung Doh, summarized by the Fed bulletin as such:

Doh uses a preferred-habitat model that explicitly considers the zero bound for nominal interest rates. His analysis suggests that purchasing assets on a large scale can effectively lower long-term interest rates. Furthermore, when heightened risk aversion disrupts the activities of arbitrageurs, policymakers may lower long-term rates more effectively through asset purchases than through communicating their intentions to lower expected path of future short-term rates.

I hold the default belief that such policies could prove effective today. There's also the broader point that QE can work by stimulating AD, without having to push around long rates very much.