## 14 May 2016

### Non-Walrasian Macro

The typical framework used by economists to make models renders generating monetary non-neutrality nigh impossible without the use of dubious assumptions like price adjustment costs or the existence of a 'Calvo fairy' that chooses at random when a firm can or cannot change its price.

Otherwise, it is posited, the firm would just set its price to whatever level is consistent with full employment at all times, rendering monetary policy useless at doing more than simply changing the inflation rate. Brushing aside possible empirical issues with this contention, this poses significant political problems for many economists; if monetary policy is impotent at all times, then either the economy is always at 'potential' thus rendering all intervention unnecessary, or the only viable means of economic stabilization is fiscal. As both of these options are highly undesirable to everyone who doesn't work at the St. Louis Federal Reserve of the University of Chicago, the problem must be solved.

This is when most of the profession turned to finding microfoundations for price stickiness (only to find that none of them are consistent with the actual behavior of individual prices, but never mind that) and thus New Keynesian economics was born. We now have the expectations augmented Phillips curve, in all its reduced form glory derived from a set of specific if highly unrealistic assumptions about the world. There is one point of interest here, however: if you remove both rational expectations and the dynamic aspect of the model, the basic three equation New Keynesian model reduces to IS-LM with sticky instead of completely stuck prices -- think Krugman's 1998 paper.

Evidently we spent 20 years trying to develop a model that has the exact same insight into the economy as we were able to get from a much simpler model from 1936 (Occam's razor, anyone), but at least this one can pretend to be quantitative (Smets-Wouters). Now I will not pretend to minimize the advantages of utility maximization when it comes to analyzing situations; sometimes it really helps to use utility maximization when you cannot simply draw an upward and downward sloping curve and call it a day (hooray for OLG models!), but when it comes to qualitative models of the business cycle, nothing beats IS-LM (say what you will about the consumption function, just have Y = a*G, for all I care).

Maybe it's time we took this all in a different direction, though. The main reason we went on the rabbit trail of New Keynesianism to get back to IS-LM was because of Walrasian ideas about supply and demand. That is, by some force of magic the market will determine the equilibrium price instantly (hence the rule that quantity supplied equals quantity demanded). But does this really make sense? even assuming individual firms knew the exact shape of their demand curve, is it reasonable to assume that they would be able to determine what (nominal) price to set so that their relative price is at the profit maximizing level? Or, more succinctly, how do firms magically know what price to set if there is no real Walrasian auctioneer?

But if we don't ignore tatonnement -- that gradual approach of a price to its equilibrium level -- then we naturally get Phillips curves everywhere, as firms slowly increase prices to fend of excess demand and lower wages to head off excess supply (of course wage bargaining is two sided but bear with me). In fact, replacing $D=S$ in models with $\dot{p} = \alpha(D-S)$ could circumvent the entire need for New Keynesian models; let the nominal rigidities run wild as freshwater economists cower in fear of non-Walrasian macro.

Not only would this alleviate the need for New Keynesian models, it would replace them with much simpler that are what I would like to call 'semi-microfounded.' That is models would have the typical upward and downward sloping curves -- who needs calculus -- and then have a specification for how tatonnement occurs. For instance, a labor market would have a labor demand equation: $L_d = -a W$ and a labor supply equation $L_s = b W$. Then tatonnement would be $\dot{W} = \alpha(L_d - L_s)$. Did the equilibrium wage move? Oh no, I guess we'll have to find it since uncle Walras can't just tell us what it is any more.

This is in some sense an effective field theory approach. We think that the rate of change of the price depends on supply and demand (where $D \approx S$), then we'd say:
$$\frac{dp}{dt} = a_{0} + a_{1} (D - S) + a_{2} (D - S)^{2} + b_{1} \frac{d}{dt} (D - S) + \cdots$$
where the $a$'s have units of time and the $b$'s are dimensionless.