Nonlinear Models Give No Escape From R*

The dynamic stochastic general equilibrium (DSGE) model literature is ever-growing, and new features are being continuously added. This makes it difficult to make generalizations about the literature. However, from a macro modelling perspective, we are mainly interested in models that might be used by a central bank to set interest rates. Even if we are not central bankers ourselves, we presumably want to understand how central bankers see their policy lever as working.

In an earlier article (link), I discussed how all linear models end up with a notion that there is a "neutral" interest rate at any given time -- a policy rate which does not lead the economy to accelerate in one direction or another. If we add standard assumptions made by neoclassical economists, we can get to the concept of r* -- which is a steady state neutral rate. (If we are away from that steady state, the neutral rate within a linear model at any given time is determined by the deviations of other values from their steady states.)

The implication is that if we take a linearisation of any DSGE model that meets standard rules for acceptability for neoclassical economists, we end up with a model that has an embedded r*. This means that most of our analytical effort in the real world is coming up with a good estimate of r* (and the steady state levels other variables that are supposed to be driving the economy). There is a not immediately obvious implication: if r* estimates behave in a pathological fashion, we have reasons to question any of those linearisations. Since my argument is that this is exactly what is happening, this would be worrisome for DSGE model fanciers.

The question then arises: can a transition to a nonlinear model reduce the dependence upon r*? My argument is that this is not the case, at least for models that we can hope to fit to observed data.

Interest Rate Neutrality at a Point in Time

The premise for my discussion is straightforward: imagine you are a central banker, who insists that an inflation target is to be hit. We will assume that the economy is is some form of non-pathological steady state, and so interest rate policy works as is conventionally expected. 

We assume that we are conventional economists, and assume that the real policy rate (r(t)) matters, and that the inflation rate does not do pathological things that cancels out movements in the nominal interest rate. As such, at a fixed time point t, we can set the real interest rate r(t)

I discussed various technical issues with this viewpoint in the previous article. One angle that pedantic people might latch onto is the story that central banks have reaction functions within DSGE models, and do not set the interest rate one period at a time. However, as a I noted in the linked article on linear models, we can add a constant to any reaction function to get control over the current period's interest rate.

I am ignoring the issue of the zero lower bound; whether or not a particular real rate is achievable is not the concern, rather the effect on the model output when the real rate is achieved. 

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