Market Monetarism and Multiple Equilibria

I was reading Scott Sumner's recent post about Neo-Fisherism and I had an epiphany about Market Monetarism.

I have consistently taken issue with the likes of Sumner because of what I view as his confusion of policies and the results of policies, or rather his confusion of policies and observations. Case in point would be the post I was just reading, in which Sumner says

But how did the Swiss authorities make sure this decrease in interest rates had a contractionary impact? The answer is simple; they did a simultaneous, once and for all, massive appreciation in the SF.

This idea that the exchange rate is just something that the SNB can set (while setting interest rates) is terrifyingly stupid from a conventional viewpoint. In general monetary policy can be seen through one of two lenses: 1) the central bank sets the monetary base and everything else is endogenous or 2) the central bank sets the short term risk free interest rate and everything else (including the monetary base) is endogenous.

Sumner regularly flaunts this view by suggesting that a central bank can, for example, set the interest rate and set the exchange rate at the same time. This is where my epiphany comes in. What's really going on is that there are multiple equilibria. A cut in the nominal interest rate can either occur through an increase in the money supply (ceterus paribus) or a negative shock to money demand (ceterus paribus), but which occurs in a given scenario? Obviously it's almost always a combination of both -- the monetary base is rarely constant and neither is money demand, but absent the presence of a more complete model, what I just outlined has many possible equilibria.

Sumner's solution to this problem is, rather than more completely specify the model, to simply choose the equilibrium that is consistent with the facts and assert that the central bank is responsible for bringing that equilibrium about. Do I think this approach is valid? Not exactly. Nevertheless I am much more sympathetic to it than what I previously perceived from Sumner. Furthermore even some full models exhibit multiple equilibria -- like New Keynesian models in which the Taylor Principle is not followed -- meaning that Sumner's approach to, e.g., Neo-Fisherism, while not as 'correct' as a more analytical description of the possible equilibria is at most equally egregious to Cochrane's dubious equilibrium selection.

To put this in terms more conducive to Sumner's typical line of reasoning, low interest rates can either be consistent with high NGDP or low NGDP. In his view the central bank chooses which equilibrium prevails and that equilibrium selection is the 'stance' of monetary policy. I personally don't think that assuming central banks are capable of equilibrium selection without explicitly modeling it is a good thing, but at least it's better than just assuming central banks are capable of pegging whatever nominal variable to whatever they want regardless of the circumstances.

Sumner on Philosophy

"If my philosophy is wrong then my market monetarism is equally wrong."

Yes. 

See also this and this.

Austerity

Upon realizing that I could easily get the Cyclically Adjusted Primary Balance data from the IMF as well as Real GDP data from the OECD without expending an extreme amount of energy, I decided to add to the empirical findings that already exist about austerity. I also sought to answer some of the concerns that Scott Sumner likes to express about every attempt at drawing a correlation not provided by Mark Sadowski.

I composed one list that included the Euro Area and one that did not (only to make Sumner shut up) and ran a regression taking the change in the CAPB between 2009 and 2014 as the x variable and the growth of real GDP between 2009 and 2014 as the y variable. The first list included Austria, Belgium, Canada, the Czech Republic, Germany, Denmark, Spain, Finland, France, Greece, Ireland, Italy, Japan, the Netherlands, Portugal, the United States, and the United Kingdom while the second list only had the Czech Republic, Japan, the United States, and the United Kingdom. Note that all of the countries were either at the zero lower bound or otherwise in a liquidity trap (defined as a case in which lowering the nominal interest rate to zero could not have resulted in full employment).

The second list was too small to yield any useful data, but the first list suggested that the coefficient on the change in the CAPB is about $-1.27$, with a p value of $9.2274 \cdot 10^{-4}$ (t-stat is $-4.112416418$). The second list did have a negative coefficient of about $-0.35$, but 5 samples is really way too few to actually conclude anything (maybe this is one of the reasons Sumner wants to remove the Euro Area).

One interesting fact that I noticed, that anyone could check in about 5 minutes if they cared to download the publicly available spreadsheet of CAPB from the IMF, is that, at least between 2009 and 2014, contrary to what Sumner claims, the US did less austerity than Europe. How much less? This much: $-0.3359236583554$. That is, the CAPB increased by about a third of a percentage point less in the US than in the Euro Area. If you included the UK, it would be even worse.

Why don't I include countries like Iceland in my calculations? Simple: they did not go to the zero lower bound in 2009 and they were never close to the zero lower bound, thereby making their addition to a regression about the effect of austerity in a liquidity trap a complete waste of time.

I'm still not perfectly happy with this assessment because I wanted to use the real GDP to working age population ratio instead of simply real GDP, as it would have made the intercept for the regression a little bit less uncertain -- while steady state real GDP growth is indeed quite variable, adjusting for demographics seems to solve the problem most of the time. Unfortunately FRED has annoying limitations with graphs and data lists, so this is the best I could do without spending more than a day on this.

The main point here is that, excluding countries obviously not at the zero lower bound, austerity is highly negatively correlated with real GDP growth and this correlation persists, even if it is not significant, when you exclude the Euro Area.

'Low Interest Rates Are Contractionary'

I wanted to delve a little bit deeper into Scott Sumner's claim that low interest rates are contractionary. Unfortunately, the model he uses to prove this is complete nonsense, since it requires the central bank to control the money supply and the nominal interest rate at the same time to achieve the result. Because of this, I think a dynamic analysis is pertinent.

Consider a dynamic and slightly altered version of Scott's money demand model:

$$(1)\: m_t - p_t = y_t - \alpha i_t$$

where $m_t$ is the (log) money supply, $p_t$ is the (log) price level, $y_t$ is the (log) of output, and $i_t$ is the nominal interest rate. Since the model is dynamic, I will also add the Fisher relation and the Euler equation:

$$(2)\: i_t = r_t + E_t\pi_{t+1}$$

$$(3)\: y_t = E_t y_{t+1} - \sigma r_t$$

where $r_t$ is the real interest rate and $\pi_t$ is the inflation rate ($\pi_t = p_t - p_{t-1}$).

Currently this model lacks an aggregate supply curve, so, for the time being, I'll go with a vertical AS curve for simplicity: $y_t = 0$. The central bank also sets the money supply in period $t+1$ such that $p_{t+1} = \bar p$. In this case, what happens when the central bank increases the money supply?

Well, if we simplify the model slightly, we can reduce it to

$$(4)\: p_t = \frac{m_t + \alpha\bar p}{1 + \alpha}$$
That is, an increase in the money supply causes the price level to rise and the nominal interest rate to fall ($\frac{\partial p_t}{\partial m_t} = \frac{1}{1 + \alpha} < 1$) -- interestingly the conventional result.

Of course Scott is now screaming at me for committing the same sin as Krugman by fixing the future price level. Don't worry, I'll get to a more complex model, I just wanted to show that Sumner's result doesn't make sense in this pseudo-dynamic context (that, I might add, is already much better than his lazy static model. The same goes for Krugman's 1998 model, which was also dynamic).

If we relax the assumption that the price level is fixed in the next period, the model instead simplifies to
$$(5)\: p_t = E_t\frac{1}{1 + \alpha}\sum^\infty_{j=t}\left(\frac{\alpha}{1+\alpha}\right)^{j-t}m_j$$
From this we know that the current price level is a function of the discounted sum of expected money supplies. This is basic market monetarist stuff: if an increase in the money supply is expected to be immediately reversed, the price level will not rise. Keep note of the fact that, in contrast with most market monetarist assertions, an expected reversal far in the future has a highly diminished effect on the price level. Expected monetary tightening ten years from now is as good as useless.

The point here, though is that a central bank can effect a reduction in the nominal interest rate without increasing the current money supply -- it simply has to reduce expected money supply growth. My point here is that Sumner never brought this up, and, since his reasoning is based entirely on the static version of the model, he has no right to say that his model implies contractionary low interest rates.

Changing aggregate supply only makes the model more difficult to understand, but, if the aggregate supply curve became
$$(6)\: y_t = f(p_t)$$
it would then be possible to argue that expected monetary tightening has an adverse effect on the economy. At this point, though, I don't think anyone should care. Sumner may have been claiming this, but his model certainly didn't justify the claim, so he should have been ignored.

Central Banks Can't Control Money Demand!!!!!!!

After posting too many lengthy comments on Scott Sumner's blog a while back, I decided I was going to ignore his claims that high interest rates are "expansionary" because they increase velocity. I tried, but he has crossed the line. He has elevated his already excessive list of central bank abilities to also include the ability to control money demand as well as the money supply.

NGDP = MB*(Base Velocity), where V is positively related to nominal interest rates.

Thus if you cut interest rates without increasing the money supply, then V falls and policy becomes more contractionary.

Read that a few times to get the full point that Sumner is making. His money demand equation is, of course, perfectly fine; you'd have to be ignorant to not understand that velocity is a positive function of nominal interest rates (or, in my preferred terminology, money demand is decreasing in nominal interest rates). The problem comes in when Scott says "if you cut interest rates without increasing the money supply." When you read this, sirens should have begun screeching in your head; Scott's weird partial equilibrium analysis in which there are three things that determine the nominal interest rate (money demand curve, interest rate chosen by central bank, and money supply) may be "monetary economics 101" in his mind, but it's certainly not economics 101, in which a monopoly supplier of something can't control its price and its quantity.

I mean, come on, this should be obvious, but apparently someone with a PhD in economics can make such a mistake without being universally discredited. In Scott's world, all a central bank must do is apparently announce higher nominal interest rates as well as monetary expansion, and NGDP will go up by the desired amount. Well, duh, but the real world doesn't work that way; just because you can force the money demand curve to shift so that a higher money supply means a higher nominal interest rate by making the nominal interest rate and the money supply exogenous in a model doesn't mean that this is actually possible. Seriously, the effective argument that Scott is making here is "thus if you reduce NGDP, then NGDP falls which means that monetary policy has become more contractionary." I'm sorry, but there's seriously no excuse for this; Sumner really needs to start working with general equilibrium sometime before he just skips this misleading line of reasoning and goes straight to "NGDP should have been higher in 2009, if that Fed had simply done this, then a recession wouldn't have happened" (bear with me and pretend Scott hasn't said almost exactly this before).

Of course, a central bank can go about raising the nominal interest rate without changing the current nominal interest rate, but this requires expected increases in the money supply, which Scott never mentions (probably because of previously mentioned attachment to partial equilibrium). That is, if expected money supply growth increases, then so will expected inflation, but this is not the argument that Scott is making, he only talks about the current money supply and the nominal interest rate in his post, and I'm not willing to give him the benefit of the doubt. Beyond that, Sumner was using a one period model to do dynamic analysis (someone explain to me why he's so dedicated to partial equilibrium), which is a sin in and of itself and he would still be guilty of even if he secretly meant to say "thus if you reduce expectations of future money supply growth without increasing the current money supply, then velocity falls [money demand goes up] and policy becomes more contractionary."

The worst part is that I haven't seen anyone complain about this apparent lapse of understanding of basic economics, everyone seems to be obsessed with Sumner's alleged Neo-Fisherism. Everyone, that's not the issue, you don't need to be bothered about Sumner appealing to an extremely basic one period model that you all should agree with, you should be screaming that "central banks can't control money demand!!!!!!!!!!"

Objectives vs. Tools of Monetary Policy

In the comments of one of Nick Rowe's recent posts, Scott Sumner has accused me of confusing objectives and tools of monetary policy:

You are looking at the causal effects of QE, whereas it makes more sense to view QE as the effect of a tight monetary policy that drives rates to zero. If you do a more expansionary monetary policy, such as currency depreciation, then you do not need as much QE. QE is a defensive mechanism, monetary policy needs to be viewed in terms of the policy goals of the central bank, and in terms of whether it will do whatever it takes to reach those goals.

Basically, Scott is suggesting that quantitative easing isn't actually a monetary policy, and is instead the natural conclusion to what he does view as monetary policy -- currency depreciation. Here, Sumner provides an interesting set of definition for what constitutes monetary policy and, more generally, what can reasonably be considered exogenous to a central bank.

In his mind, exchange rates are basically exogenous to the extent that central banks try to influence them. This is evident from his implicit assertion that, if central banks are "doing whatever it takes to reach [their] goals," they will invariably reach those goals. Of course, this isn't necessarily news, everyone has know Sumner's opinion that central banks are nearly omnipotent for quite some time, but this time he has laid it out more directly.

According to Sumner, the evolution of any nominal variable over time can be completely controlled by a central bank and, as such, can be used as a point of criticism for that central bank: "monetary policy needs to be viewed in terms of the policy goals of the central bank." As such, the actual polices that central banks follow are completely irrelevant; it doesn't matter what the path of interest rates is, the correct judge of current Federal Reserve policy (for example) is whether or not inflation is on target.

Of course, I, along with I hope the majority of people, don't see monetary policy in this light. Sumner seems to have made a point of confusing monetary policy -- e.g., QE, interest rate setting, open market operations -- with whatever nominal variable he happens to care about at the moment -- in this case exchange rates. This separation is important; it allows us to understand more directly a central bank's goals and how it intends to achieve those goals.

Evidently, Scott could care less about the how and only wants us to focus on the goals. He basically has reduced his thinking about monetary policy to the point that he views NGDP as an instrument of the central bank -- effectively an exogenous variable -- rather than a variable that a central bank may act to control. This level of abstraction from the operation of monetary policy, in my opinion even more grievous than the New Keynesian obsession with the nominal interest rate, is what allows Market Monetarists to callously ignore every model that doesn't allow exogenous NGDP that says the zero lower bound actually represents a constraint on monetary policy.

If central banks could make NGDP exogenous, would they be able to make NGDP exogenous? Naturally, but no one should care about the answer to such a redundant question, yet this is effectively the answer that you get from Sumner; he'll simply assert that "the BOC can always depreciate the Canadian dollar. The zero bound is not an issue in Canada" (from an earlier comment on the same post). Naturally, we should all trust Sumner's clairvoyance on this issue, clearly no argument about monetary policy effectiveness is necessary (see my first comment on Nick Rowe's post, if you want one anyway) and we can rest assured that fiscal policy is never necessary.

Ideally, considering the ability of monetary policy to effectively deal with challenges should be at least of some consideration and, since monetary policy has proved theoretically capable of offsetting the demand-side effects of fiscal stimulus among other shocks, the only point at which this can be of much concern is the zero lower bound. Both Sumner's and Rowe's refusal to give theoretical arguments against me in this area is rather troubling, evidently just assuming monetary policy is effective in every circumstance is completely acceptable.

People Should Be More Honest With Charts

Recently, Scott Sumner wrote a blog post with this chart in it:

 I thought it would be interesting to see how well this relationship held over the period that Sumner didn't include in his chart. Here it is:

It's interesting to note that the relationship doesn't look so good when you look at the entire sample in which all of the data is available. This is aside from that fact that the idea that the NGDP/Wage ratio would track unemployment is part of basic neoclassical theory and has nothing to do with wage stickiness.

Start with a simple Cobb-Douglas production function with employment and capital:

$$(1)\: Y_t = F(K_{t-1},L_t) = K_{t-1}^\alpha L_t^{1-\alpha} $$

Assume that the firm maximizes profits, $Y_t - w_t L_t - r_{t-1} K_{t-1}$ and you get the following first order condition for labor:

$$(2)\: w_t = (1-\alpha)\left(\frac{Y_t}{L_t}\right) $$

Dividing by $Y_t$ will give the nominal wage to NGDP ratio (since the nominal wage to NGDP ratio is the same as the real wage to RGDP ratio), which is

$$(3)\: \frac{w_t}{Y_t} = \frac{1-\alpha}{L_t} $$

It's clear from this that, in a simple neoclassical model, the nominal wage to NGDP ratio is expected to be negatively correlated with employment and, therefore, positively correlated with unemployment -- which is coincidentally the exact thing that Scott's chart shows. Variations in the nominal wage to NGDP ratio are not, in fact, vindications of the musical chairs model.

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.

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