## 10 June 2016

### Either the Model is Wrong or Market Monetarism is Wrong

The idea that the zero lower bound is not actually a significant constraint on the ability of monetary policy to raise nominal GDP is integral to Market Monetarism. If the zero lower bound actually represents that constraint that mainstream macro says it does, then nothing Scott Sumner has said about monetary offset in the last 8 or so years is right.

Thus the stakes are quite high and, ignoring the extremely clear evidence that open market operations are useless at the zero lower bound (just look at the velocity of the monetary base in any country at the zero lower bound), if we can demonstrate that monetary policy is impotent at the zero lower bound, then the battle is won.

Unfortunately Market Monetarists refuse to believe that plummeting base velocity is tantamount to proof that further monetary expansion is next to useless at the zero lower bound, so the only possible argument is theoretical and therefore necessarily inconclusive. Nevertheless, I can at least prove that whatever model Sumner et al. are appealing to is not mainstream in the least when it comes to liquidity traps.

The most potent example of this is the consumption Euler equation, written in log terms like this:
$$c_t = E_t c_{t+1} - \theta(i_t - E_t \pi_{t+1} - r^n_t)$$
Assuming $\theta=1$ and, in line with most of the New Keynesian literature, that there is no investment or government spending, it can be rewritten in terms of nominal GDP:
$$n_t = E_t n_{t+1} -(i_t - r^n_t)$$

This simple relationship shows exactly how the Market Monetarist policy prescription of nominal GDP level targeting fails to alleviate periods in which $r^n_t$ -- that is the real natural rate of interest -- is negative. If the central bank targets zero nominal GDP growth, for instance,  then any time $r^n_t < 0$ either current nominal GDP must fall below target or future nominal GDP must go above target. The only two ways to avoid recession are to either abandon nominal GDP level targeting or to use expansionary fiscal policy.

Since the Market Monetarist position is clearly at odds with this interpretation, it is evident that whatever model each Market Monetarist appeals to (whether it is Sumner's Musical Chairs 'model' or whatever Nick Rowe is currently using to tell everyone recessions are excess demand for the medium of exchange) is not consistent with the basic assumption of utility maximization and a budget constraint needed to derive the consumption Euler equation and, in the interest of having an argument in which we all aren't yelling past each other, that model should be made clear; what specifically is wrong about the Euler equation?