Show me the Model

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Antonio Fatas wrote

Show me the modelMost of the commentary one reads these days about the negative consequences of the policies set by central banks (low-interest rate and quantitative easing) are not backed by any economic model that I know.[skip]
But what is the economic model that can provide a theoretical justification to an environment where the central bank can significantly affect equilibrium asset prices and interest rates for a prolonged period of time and without causing inflation?  I have not seen it yet.
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When we teach the effects of monetary policy we tend to use economic models that have a Keynesian flavor to it, with some form of price rigidity and where changes in the nominal interest rate by central banks have a short-run impact on real interest rates (as inflation moves slowly). But this only works in the short run, while prices are rigid."

Emphasis mine.   OK I shall do so below (it will be a sketch of a model).

I claim that I can think up an economic model with rational agents which has any behavior I choose.  Thus I consider "Show me the model" a challenge which I can't honorably ignore.

I also like to argue that the insights which macroeconomists think they have obtained from models always and invariably are implied by the simplifying assumptions which no one claims are realistic.  

First, before going on, I note that my objection to current Fed policy is that I think that they should promise to keep the target federal funds rate essentially zero until inflation is over 4% and not until either inflation is over 2.5% or unemployment is under 6.5%.  Also I object to QE 3 because I think they should buy only agency issued mortgage bonds issued the day before the purchase and that they should buy 100% of them.  That is I want Fed policy to have the effect which I claim it can have.

Second note Fatas's equivocation.  He mentions "quantitative easing," he asks for a model in which "the central bank can," but when he discusses existing models he discusses only "changes in the nominal interest rate".  Quantitative easing has vanished, because it is not considered in standard models. The absense of quantitative easing in standard models is a reason to not rely on standard models, not a reason to dismiss arguments about the effect of quantitative easing.

Third note that Fatas implicitly asserts that there is only one nominal interest rate when he writes "the nominal interest rate." In fact there are thousands of nominal interest rates on debt with different maturities and defult risks.

Clearly the Fed can affect risk premia permanently by changing the amount of risky asset which private investors hold.  It is also easy to obtain such an effect in standard asset pricing models.  This means that central banks can subsidize sectors.  It is clear that the Fed is attempting to do exactly this by buying RMBS (residental mortgage backed securities).  It is clear that, even without nominal rigidity of any kind, the Fed could affect the economy if it could purchase RMBS issued by profit seeking firms for prices much higher than the market price.  This would be a subsidy to mortgage lending.  In a flexible price real business cycle type model, it would cause higher investment in housing and lower investment in plant and equipment.

This would have effects which would be modest unless the Fed's purchases were huge -- say $ 85 billion a month.  Actually the effects need not be modest even for less huge purchases.  If you add Marshallian (Romer 86) type spillovers caused by equipment investment but not by housing investment, then the Fed policy could cause a permanently lower GDP growth rate in a model with perfect foresight and flexible prices.  In general, I would strongly oppose such a policy.  I strongly support it now, because the economy is in a liquidity trap so housing investment doesn't crowd out other investment.  But the claim that central banks can't influence the real economy permenently is clearly based on absolutely false assumptions about what central banks are doing.

OK finally the last bolded "if".  In the USA the Fed can't buy RMBSs issued by a profit seeking firm. They can only buy Federal agency issued RMBS.  The weak link in the chain linking Fed policy and the real economy is the FHFA which is legally obliged to minimize the cost (soon to maximize the profit) to the Treasury of the Fannie Mae/Freddie Mac, but whose actions are more easily understood if the aim were to minimize GDP.  But models are magic and I can assume that the scales will fall from Ed DeMarco's eyes in my model.

OK so the model would be a totally non standard model in which there is a housing sector and in which the nominal mortgage interest rate is higher than an equal maturity nominal default risk free rate.  Then this risk premium has effects and Fed purchases of RMBS have portfolio balance effects.  It is totally conventional for macroeconomists to assume that there is no housing sector.  I think this is just one of many many reasons why standard macroeconomic models are not useful.