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.