It's not time to blow up the New Keynesian model

Scott Sumner wrote a blog post recently in which he questioned the validity of New Keynesian models. He listed five of it's predictions that he finds troublesome:

1. The NK model implies that higher taxes on wages can be expansionary. 

2. The NK model implies that higher capital gains taxes can be expansionary. 

3. The NK model implies that raising the aggregate wage level by government fiat can be expansionary. 

4. The NK model implies that an increase in the fed funds target can be expansionary. 

5. The NK model implies that an fiscal austerity can be expansionary, if done by slowing the growth in government spending

His first three claims are hardly criticisms applicable to New Keynesian theory in general, but they do accurately point out that New Keynesian models turn a bit wonky at the zero lower bound. It is the last two claims that are particularly nefarious.

The fourth claim is ignorant of the fact that Neo-Fisherian results are entirely dependent on the existence of multiple equilibrium which arise from ambiguous fiscal policy and the absence of monetary policy rules. Inflation should really be considered indeterminate during an interest rate peg (as it was until the Neo-Fisherians decided to implicitly assume active fiscal policy). Alternatively, a theory of money demand could be added to New Keynesian theory that could solve the problem than discretionary interest rate control policy creates.

Sumner refers to Nick Rowe's recent (and quite good) post on New Keynesian fiscal policy as evidence for his fifth attack on New Keynesian models. What he doesn't realize, though, is that what Nick Rowe describes in his post is not consistent with higher output. Actually, the government is causing potential output to change by moving government spending around. Lower government spending is consistent with lower potential output. To understand why, it is necessary to look at Real Business Cycle theory. In RBC models, permanent changes in government spending have real (supply side) effects that change output. These supply side effects are present in New Keynesian models, and in this case they move potential output around which, in turn moves the natural rate of interest around. Expected austerity does raise the natural rate of interest, but it does not actually raise output.

Contrasting his own views with those he associates with New Keynesian models, Sumner provides four characteristics of the "musical chairs model":

1. In the short run, employment fluctuations are driven by variations in the NGDP/Wage ratio. 

2. Monetary policy drives NGDP, [sic] by influencing the supply and demand for base money. 

3. Nominal wages are stick in the short run, and hence NGDP shocks cause variations in employment in the same direction. 

4. In the long run, wages are flexible and adjust to changes in NGDP. Unemployment returns to the natural rate (currently about 5% in the US.)

As I noted in my comment, this set of four characteristics is not a model. It can be made into a model perhaps, but it falls short of actually being a model. If someone were to write down the "musical chairs model" as Sumner describes it, it would likely closely resemble a New Keynesian model where the primary friction is changed from sticky prices to rigid nominal wages and the central bank uses the monetary base, rather than the nominal interest rate, as the instrument for monetary policy.

Naturally, this leaves Sumner with the task of coming up with a money demand function that is both empirically accurate and gets around the problems that I wrote about here and here so that he doesn't have to drop his assertion that monetary expansion, even at the zero lower bound, is always expansionary, rather than useless as most plausible models of money demand (and the empirical evidence) seem to suggest. I suggest Sumner add his money demand function to this model by Stephanie Schmitt-Grohe and Martín Uribe and see if it performs as well as New Keynesian models when put to the data.

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