David Beckworth directed me to a new paper by Roger Farmer and  Giovanni Nicolò, recently published in The Manchester School.

They develop a different type of Keynesian model, which replaces the Phillips curve with an equation describing NGDP growth expectations:

In contrast to the NK-Phillips curve, the third equation of the FM-model is a belief function. Following Farmer (1993, 2012), the functional form for the belief function that we use in this study is described by Equation (3.b),

(3.b) Et [xt+1] = γxt + (1 − γ)Et−1 [xt ] ,

where xt ≡ πt+(yt − yt−1) is the growth rate of nominal GDP. The belief function is a mapping from current and past observable variables to probability distributions over future economic variables and the functional form that we chose for the belief function, captured by Equation (3.b), asserts that agents’ expectations about future nominal GDP growth are adaptive. When we estimated the model, we found that the data strongly favour the parameter restriction, γ = 1 and in Section V we report the estimates of the FM-model under this restriction. When we incorporate this restriction into the belief function, our model implies that beliefs about future nominal income growth are equal to current nominal income growth. By modeling beliefs about future nominal income growth as a new fundamental we resolve both dynamic and static indeterminacy.

Their model does still use the other two standard NK equations:

The FM- and the NK-models that we estimate in our empirical work have two equations in common. One of these is a generalization of the NK IS curve that arises from the Euler equation of a representative agent. The other is a policy rule that describes how the Fed sets the fed funds rate.

This is great, but my dream model would go even further, eliminating interest rates, inflation and real GDP. I would replace interest rates with market NGDP growth expectations from an NGDP futures market.If that market did not exist, then I’d have the central bank estimate NGDP expectations using other market prices. For simplicity, I’ll assume an NGDP futures market does exist.

NGDP growth expectations would be determined by the monetary policy regime. An expansionary monetary policy would raise expected future NGDP. This is what Keynes presumably meant by an increase in “animal spirits”.The increase in NGDP expectations, aka animal spirits, would cause an increase in current NGDP. Another equation would link unexpected moves in current NGDP with employment because nominal wages are sticky in the short run.

The central bank’s dual mandate would be stable growth in NGDP and employment close to the natural rate. Both goals would be achieved via stable growth in NGDP (i.e. a “divine coincidence”). And that stable growth in NGDP would be achieved by pegging an NGDP futures contract price at a level where market participants expected stable growth in actual NGDP.

There would be no circularity problem, as the market would be predicting the instrument (monetary base) setting that led to on target NGDP growth. The central bank would not be responding to changes in NGDP futures prices.