Monday, October 22, 2012

To log-linearize or not to log-linearize?

Some recent research has shown that there is a free lunch lying there for fiscal policy when interest rates are constrained by the zero lower bound, in particular Eggertsson-Krugman and Christiano-Eichenbaum-Rebelo: the fiscal multiplier is larger than one and a tax rate cut leads to an increase in employment. But there is also a fundamental principle in Economics: always be suspicious of free lunches.

Anton Braun, Lena Mareen Körber and Yuichiro Waki show that the research above is all humbug. The way these new-Keynesian models are built is by log-linearizing around a steady-state with stable prices. There are two problems with that: 1) the fact that prices do change implies that there is a resource cost in these models due to either price dispersion or menu costs, depending on how you model the source of price rigidity; 2) log-linearization by definition implies a unique equilibrium. The sum of the two means that the extent literature has been approximating around the wrong steady-state and possibly looking at the wrong equilibrium.

Why? The cost of price change alters the slope of the aggregate supply, and this depends on the size of the shocks hitting the economy, once you looks at a non-linear solution of the model. Policy outcomes then look much more like those from an environment where there is no zero lower bound for the interest rate. That is, a tax increase reduces employment and the fiscal multiplier is close to one. To possibly get the other, more published result, one needs to have a price markup in the order of 50%, which is wildly unrealistic.

What this shows is that linearization is a nasty assumption, especially when a non-linearity is central to your case. Also, this highlights that the models punt too much on why prices are rigid. Simple rules are not sufficient. But regular readers of this blog already knew that.


Vilfredo said...

I have seen Larry Christiano defend his works claiming that the equilibrium that Tony Braun finds is not learnable. I must say I found this rather odd, as the equilibrium exists when there is no ZLB, but suddenly when there is a ZLB it would not be learnable? There got to be some continuity as the economy slips into ZLB.

Anonymous said...

Vilfredo: this is the paper: pdf

Anonymous said...

Seriously, how could Krugman even think that non-linearities can be model as linearities? One of his major works actually shows that linearities do not work: link at IDEAS.

Anonymous said...

There is some excellent discussion of this post over at EJMR.