Scott Sumner Claims His Model is Wrong by Claiming His Model is Right

I wrote a blog post a couple of days ago wondering if nominal GDP targeting and inflation targeting are the exact same thing. I came away with two conclusions: if sticky consumer prices are the primary source of nominal rigidity, then the answer is yes and if sticky input prices and/or prices not included in the central bank's target price index are the primary source of nominal rigidity then the answer is no. Implicit in these two conclusions is that real GDP is always at potential under an inflation targeting regime in sticky-consumer-price models and that real GDP is not often at potential in sticky-input-price models.

So, where does Sumner fit in to this? Well, Sumner recently read this post on Canadian austerity in the 1990s by Stephen Williamson. He noticed that Williamson sees adherence to an inflation target as evidence against monetary offset, so he decided to write this wonderfully contradictory statement:

If you observe the inflation rate always being on target, then the central bank is successfully offsetting any fiscal action that would have otherwise moved AD and inflation.

Of course, this statement is perfectly sound a-cyclical inflation targeting results in a constant output gap of zero, but that's not the way that Scott Sumner sees the economy. Being a market monetarist, he believes that counter-cyclical inflation targeting is consistent with a constant output gap of zero. If an inflation target is optimal, then monetary offset did occur in Canada, but if a nominal GDP target is optimal, then monetary offset did not occur in Canada. Since even friction-less models suggest that the multiplier on government spending is greater than zero (pdf), it's pretty obvious that monetary offset did occur in Canada, but this basically discredits the already somewhat scarce theoretical evidence for market monetarism.

It seems that two of Sumner's strongest positions are not consistent with each other. Either monetary offset happens in an inflation targeting regime or nominal GDP targeting is optimal.

In Theory, Monetary Offset Doesn't Work

Monetary offset, one of the major aspects of Market Monetarism, is severely hindered by the application of some basic macroeconomic theory. Take the bond pricing equation at the heart of most of modern macro:

$$ c_t = \left[\frac{(1 + \rho)(1+E_t \pi_{t+1})}{1 + i_t}\right] E_t c_{t+1} $$

$ c_t $ is current consumer spending, which is chosen in order to maximize all expected future consumption. When the real interest that can be earned on saving or investment increases above its natural rate, $ \rho $, current consumer spending falls. In normal times, the central bank targets an inflation rate, $ \pi_t $, which anchors inflation expectations to that target, so any adjustment in the nominal interest rate, $ i_t $, directly changes current consumption. If the government decides to actively reduce its budget deficit which depresses GDP, the central bank can lower the nominal interest rate to offset this change. This is the theoretical explanation for monetary offset. 

When the nominal interest rate is at zero, the central bank can no longer lower the nominal interest rate to counteract the effects of austerity. It only has two options: somehow increase inflation expectations or promise to keep future interest rates low. This is exactly what the Federal Reserve has resorted to in the last few years. Quantitative easing has increased inflation expectations and forward guidance has given the promise of an extended period of low rates. Perhaps expanding the monetary base like there's no tomorrow can have some effect in both keeping rates low and increasing inflation expectations. Nevertheless, neither of these policies are proven to work either in theory or in practice. Central banks are, for all intents and purposes, ineffective at increasing consumption at the zero lower bound.

Central banks slowly lose what small ability to control the economy they have as the economy returns to its natural state on its own. Inflation expectations are bound to fall as consumption returns to its natural level. At the zero lower bound, the steady state expected inflation rate falls $ \frac{1}{1+\rho}-1 $. This at least partially explains the multi-decade long period of low inflation and zero nominal interest rates in Japan. As the economy returns to equilibrium, the central bank will be progressively more powerless to offset shocks, fiscal or otherwise.

The key problem with Market Monetarism in general is that it isn't grounded in any kind of model outside of conjecture around a simple version of AD-AS in which the central bank has the ability to achieve any inflation or nominal GDP target it chooses. The reality is, central banks are not omnipotent and aggregate demand is more than just a negative function of the price level.

Monetary Offset Is A Thing in New Keynesian Models (Sort of)

I was playing around with fiscal stimulus in a New Keynesian model (with capital) that I had written down in Dynare and I was surprised to see that increases in government spending (funded by lump sum transfers) caused deflation rather than inflation. Puzzled, I decided to remove the part of the Taylor Rule that reacts to the output gap and, as I had initially predicted, fiscal stimulus became inflationary and output increased more than in my first test.

The moral of the story is that the idea of monetary offset that Scott Sumner brought up (I think) is partially right: the effects of fiscal stimulus will be (partially) counteracted by the central bank. In my model, this happens not because the central bank is targeting inflation, but because it tightens monetary policy in response to increases in output above potential. Of course, in order to have fiscal stimulus completely counteracted by the central bank, I needed to put the output gap coefficient on the Taylor Rule upwards of 5 (rather than the normal 0.5), so complete monetary offset with Taylor Rules doesn't seem to work.

In a way, this partially affirms the pro-fiscal-stimulus crowd and the pro-monetary-stimulus crowd (I belong more to the latter). Fiscal stimulus does appear to work in the short term, but the central bank really has power over aggregate demand.

If anyone wants to check my analysis, here are the relevant model equations:

$$ y_t  = e^{z_t} k_t^\alpha n_t^{1-\alpha} $$
$$ z_t = \rho z_{t-1} + \epsilon_t^z $$
$$ k_{t+1} = (1-\delta) k_t + x_t $$
$$ w_t = c_t^\sigma n_t^\phi $$
$$ c_t^{-\sigma} = \beta E_t c_{t+1}^{-\sigma} \left(\frac{1 + i_t}{E_t \pi_{t+1}}\right) $$
$$ y_t = c_t + i_t + g_t $$
$$ g_t = \rho g_{t-1} + \epsilon_t^g $$
$$ w_t = mc_t (1-\alpha) e^{z_t} k_t^\alpha n_t^{-\alpha} $$
$$ r_t + \delta = mc_t \alpha e^{z_t} k_t^{\alpha -1} n_t^{1 - \alpha} $$
$$  \log\pi_t = \beta \log E_t \pi_{t+1} + \frac {(1-\theta)(1-\beta \theta)}{\theta} \left( \log mc_t - \log \left(\frac {\epsilon - 1}{\epsilon}\right)\right) $$
$$ \frac{1 + i_t}{E_t\pi_{t+1}} = 1 + r_t $$
$$ i_t = \beta^{-1} - 1 + \phi_\pi (\pi_t -1) + \phi_y (\log y_t - y^n) $$

Where $y_t$ is real GDP, $z_t$ is the TFP, $k_t$ is the capital stock, $w_t$ is the real wage, $ c_t $ is consumption, $x_t$ is investment, $g_t$ is government spending, $mc_t$ is the marginal cost, $r_t$ is the real interest rate, $\pi_t$ is the gross rate of inflation, and $i_t$ is the nominal interest rate.

Here is the response to a fiscal shock with a normal Taylor Rule:

Normal Taylor Rule Fiscal Shock

And here is the response to a fiscal shock where the Taylor Rule ignores the output gap:

Modified Taylor Rule