Scott Sumner asked how Market Monetarism is different from the new Keynesian economics.
There is a lot of difference between Market Monetarism and the new Keynesian mainstream of a backward-looking Taylor rule.
Those new Keynesians who favor adjusting policy interest rates to target the forecast for the growth path of nominal GDP as a policy regime are not the mainstream. But certainly they still count as new Keynesians.
So what is left?
Market Monetarists favor allowing market forces to determine all interest rates at all times.
We do not favor having the central bank "set" any interest rate or especially to make commitments as to what those interest rates will be in the future.
For example, Market Monetarists do not favor keeping the Federal Funds rate near zero for an extended period of time, one or two years, or even until unemployment falls below 6.5% or inflation rises above 2.5% in the medium run.
Market Monetarists especially don't favor quantitative easing as a means to lower long term interest rates.
The theoretical framework of Market Monetarism is that spending on output depends on the quantity of money and the demand to hold it. And the quantity of money should be adjusted according to the demand to hold money given a level target for nominal GDP.
Sumner did discuss the new Keynesian focus on interest rates, but is it really true that new Keynesians focus on the difference between a policy rate and the Wicksellian natural rate?
As for the difference Sumner emphasizes, the use of "the market" as an indicator of monetary policy, I think that is less essential. I have a longstanding interest in index futures convertibility, but I have never believed that it is practical to use stock prices or commodity prices to judge the proper level of base money.