I am once again looking at one of John Cochrane's papers. He has written a new working paper, "The New Keynesian Liquidity Trap", in which he explains the rather strange properties of the New Keynesian models when they hit the Zero Lower Bound for interest rates. He also wrote an op-ed for the Wall Street Journal in which he questions the case for fiscal activism which is based on those models. I think this is a good example of the dysfunctional nature of mainstream economics - I agree with his analysis of the 'New Keynesian' models, but I think his policy views make very little sense.

**Disconnect Between Theory And Policy Discussion**

There were a number of responses to this article, including Paul Krugman, Noah Smith and Nick Rowe. They largely discuss the arguably more interesting topic of whether the lack of "demand" is the cause for the last recession and subsequent slow growth (Paul Krugman objected to how Cochrane stuck demand in scare quotes) versus an alternative explanation of uncertainty (presumably caused by President Obama). I did not see any discussion of the observations of the problems within the New Keynesian methodology, which was the actual theoretical content of the paper that allegedly triggered this latest round of arguments over fiscal policy.

This debate is a demonstration of the weaknesses of the approved methods of discussing economics within the mainstream. Mathematical models, with highly complex yet wildly unrealistic properties are postulated, but are not properly solved. Some observations are made about what a solution might look like, and then these observations are stretched into categorical commandments about economic policy in the real world. Other researchers then follow almost exactly the same procedure, but they manage to create a system for which the opposite of the given property holds, and they thus can dispute those policy prescriptions...

Why bother with the mathematical formalism if all we end up with is the equivalent of a late night dorm room argument about topics that will never be resolved?

**Problems With New Keynesian Models**

If we strip out the never-ending argument about the role of the government in the economy, John Cochrane's working paper offers an understandable explanation of New Keynesian modelling methodology (understandable assuming that you have a mathematical background...), and what the "Zero Lower Bound" research is all about.

I cannot attempt to cover all the details of the working paper. But to summarise the New Keynesian methodology:

- The New Keynesian modellers write down a complicated nonlinear optimsation problem, which is "microfounded".
- A linear model is generated from this nonlinear model. Incidentally, this step breaks the stock-flow consistency of the model, assuming that the nonlinear model was in fact stock-flow consistent.
- Solutions to this linear model are generated; and since the linear model is under-determined, some means of selecting the "correct" solution has to be decided upon. (These solutions are called "equilibria", which is a meaningless term mathematically in this context.)

John Cochrane follows "the rules of the game" (the standard ways of finding solutions in the literature) in discussing these model solutions. In order to get large fiscal multipliers at the Zero Lower Bound, a particular set of solutions had to be chosen. But it is possible to choose another set of solutions, which actually look more sensible, where fiscal policy is again largely ineffective. The belief is that central bank policy forces the selection of one solution or another. That is, central bank policy is not really aimed at affecting the path of the economy by setting the level of interest rate, rather it forces the current state of the economy to snap to a current level by somehow making it known that it will be following a particular rule for all eternity. (Yes, that does sound like third-rate mysticism.)

(By way of background, fiscal policy appears ineffective within DSGE models for three main reasons:

- monetary policy rules would cancel out any effect of fiscal policy;
- fiscal policy has to passively adapt to monetary policy as a result of the Inter-temporal Governmental Budget Constraint (IGBC);
- Ricardian Equivalence - households will save for higher future taxes if there is a loosening of fiscal policy in the present.

Correspondingly, the "multiplier" on fiscal spending is normally much lower than 1 within these models.)

He points out that the solution ("equilibrium") would be pinned down by the Fiscal Theory of the Price Level (explained further here). But the Fiscal Theory of the Price Level is based upon the IGBC, and that constraint disappears when the system is linearised, and so it does not appear when we follow the "rules" set down by New Keynesian economists to determine which solution to choose.

I am in agreement that fiscal policy would drive the selection of the solution. More generally, all of the global properties of the original nonlinear system are needed to determine the existence and uniqueness of solutions. This determination needs to be addressed before the linearisation step.

As I discussed in my previous article, I think the mathematical foundation of the IGBC is flawed. But even if we overlook that major issue, the problems that John Cochrane identifies appear to be the result of a poor specification of fiscal policy. Most of the solutions to the New Keynesian models exhibit runaway inflation (which is only tamed by central bank policy rules). But rising nominal GDP typically causes unforeseen fiscal tightening (more income and sales taxes, indexation of government benefits lags inflation by a year), which acts as a brake on inflation. Fiscal policy needs to be actively loosened to overcome these effects to allow the inflation to continue.