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.

Japan in NOT a Market Monetarist Success Story

Annoyingly (starting a post with that word is strangely entertaining), Scott Sumner has once again claimed that the increase in Japanese inflation that we have seen over the last few years provides vindication for Market Monetarism. Perhaps most infuriating was his magical ability to know that the thing that has caused the increase in inflation (which is really very modest, which I will address shortly) is the Bank of Japan's monetary stimulus program: "and monetary stimulus did get [Japan] out of deflation."

The real question here is what would actually enable Sumner to reasonably make this claim (news flash, it is not the evidence, which in this case agrees with both the Keynesian and Market Monetarist view). This is where I once again delve into philosophy of science, but don't worry, this is very general. As economics is quasi-experimental in that policy experiments can be conducted, but the system can never be closed, a good method for testing a hypothesis is something along the lines of what Jason Smith has suggested: "any system can become an effective closed system if your instrumental variables move faster (move a greater magnitude in a shorter period of time) than your unobserved variables."

That is, all we need to do is have Japan engage in a massive monetary stimulus in order to see if monetary stimulus works in liquidity trap conditions. Oh, wait... Yes, as it turns out, Japan has been doing massive monetary stimulus, so I guess we have our ideal (if not perfect) experiment. Evidently the massive expansion of the monetary base in Japan has led to inflation. Market Monetarists win!

No. It's extremely important to note that the lukewarm response of inflation to the monetary stimulus is completely consistent with a Keynesian analysis in which the improved labor market has increased inflation via the Phillips curve and that the inflation has little or nothing to do with the monetary stimulus. How do we know which one of these models is more accurate in this case? We can easily use one of Scott Sumner's pet models and see if it squares with his predictions -- then we could have a slightly more testable prediction than 'increasing monetary base growth leads to increased inflation' which doesn't actually specify how structural the supposed relationship is (and allows Scott to get away with his terrible declaration of victory).

It must first be understood that Scott can claim his prediction is correct even though the increase in the Japanese monetary base has been much quicker than the increase in nominal GDP, which is evidence in and of itself against monetary policy effectiveness. However, because Sumner's prediction was simply that the monetary stimulus would cause an increase in inflation (never mind the magnitude), the apparent failure of Market Monetarism to explain Japan can be ignored.

Fortunately for those of us who aren't trying to be dishonest (I'm growing tired of giving people the benefit of the doubt), Sumner has given us a model. Namely, he has frequently argued that velocity is a positive function of the nominal interest rate. With this, we can look at the nominal interest rate in Japan (noting that it has been relatively constant since the Bank of Japan began monetary easing) and the velocity of the monetary base in Japan (noting that it has fallen precipitously since Abenomics began) and see if Sumner's model, which predicts relatively constant velocity at constant interest rates, fits with reality.

Evidently it doesn't. Now, Scott will likely defend himself by saying he doesn't pretend to have an explanation for why real money demand would have risen so sharply in Japan since the nominal money supply began increasing sharply, but the fact remains that the nominal and real monetary base should not track each other so closely if market monetarism were indeed correct. In fact, Sumner has repeatedly said that expectations of more NGDP growth (in this case equivalent to more inflation) would make demand for the monetary base fall. I agree with this theory, but this is evidently not what has happened in Japan -- the Japanese situation is simply incongruous with his position.

Of course, Scott only predicted that inflation and monetary base growth would be positively correlated, not that the degree of correlation would be somewhat constant. Any positive inflation response is thus a positive result for Market Monetarism!

Believe it or not, NK models are not Market Monetarist

Today on Twitter, Nick Rowe deployed a couple of the tricks his commonly like to use when arguing against New Keynesians who think (rightly) that the NK model suggests that, when the Wicksellian natural rate is negative, fiscal stimulus is 1) warranted and 2) will not be offset by the central bank.

Notably, Nick said

"accommodate fiscal stimulus" = "no longer trying to target 2% inflation"

Assume NK [is] true. Current BoC r > ZLB > ELB (as defined by BoC)

 Of course, Nick should know (from numerous posts in which I have written about this same issue) that the New Keynesian IS curve implies that expansionary fiscal policy raises the natural real interest rate, which means that, if inflation is currently below target, fiscal stimulus can raise it to target without requiring an appropriately sized interest rate cut (which may not be possible).

This is where the biggest fault in Nick's argument is -- he suggests that, as long as the nominal interest rate is currently above the zero lower bound (or the 'effective lower bound'), a New Keynesian central bank can keep inflation on target. Essentially, he is arguing that, since the current interest rate set by the Bank of Canada is above zero, the Wicksellian natural rate (defined as the interest rate at which inflation is on target) must be above zero.

This assumption is just plain wrong, but I will slightly alter Nick's actual argument into something that I think is much better (and probably what he meant, but was unable to articulate given Twitter's stringent limits on tweet length). In a New Keynesian model, the central bank can raise the Wicksellian natural rate by deliberately setting future nominal interest rates lower than they otherwise would be (this is called forward guidance). Because of this, all a central bank need do to keep current inflation on target is to lower the path of the nominal interest rate.

Now the argument makes a lot more sense; Nick is suggesting that 1) the Bank of Canada is responsible for inflation being below target because they refuse to use forward guidance and 2) since inflation is exactly where the Bank of Canada wants it, fiscal policy will simply be offset.

The issues that I have with this argument are two-fold:

First, the regime I just described on behalf of Nick is not consistent with an inflation targeting regime because the central bank is supposed to deliberately raise future inflation above target in order to put current inflation on target. This is what forward guidance does in New Keynesian models and, as such, represents an important break from actual inflation targeting.

Second, the empirical failure of forward guidance is well documented and is commonly referred to as the 'forward guidance puzzle.' For instance, Del Negro et al. 2012 note that "[DSGE models] appear to deliver unreasonably large responses of key macroeconomic variables to central bank announcements about future interest rates ... Carlstrom et al. (2012b) shows that the Smets and Wouters model would predict an explosive inflation and output if the short-term interest rate were pegged a the ZLB between eight and nine quarters" [1].

Thus, not only is forward guidance not consistent with keeping inflation on target in the medium term, it is probably nowhere near as effective at raising the Wicksellian natural rate as basic DSGE models would suggest which severely limits my edited version of Nick's original argument. As it turns out, the Bank of Canada is probably either self-constrained by a refusal to do an adequate amount of forward guidance or otherwise constrained by a lack of effective tools to raise the natural rate up to a level at which inflation would be on target. In this case, it is perfectly reasonable to suggest that not offsetting loose fiscal policy is not inconsistent with the Bank of Canada's inflation target.

[1] Del Negro, Marco & Giannoni, Marc & Patterson, Christina, 2012.
"The forward guidance puzzle,"
Staff Reports 574, Federal Reserve Bank of New York, revised 01 Dec 2015.

Expectations

The most common way to 'model' expectations when making a DSGE model is to assume that agents' expectations are rational -- i.e. 'model consistent.' To the extent that the modeler believes (wrongly) that the model is structural and wants to develop a quantitative model or the modeler doesn't care if the model is structural and only wants to write a logically consistent model, rational expectations are perfectly reasonable.

For instance, if I have just derived the consumption Euler equation given a budget constraint in which real government bonds can be traded intertermporally and log utility, I will find have the following equation governing consumption behavior:
$$(1)\ \frac{1}{c_t} = \beta E_t \frac{1}{c_{t+1}}\left(1+r_t\right)$$
Ignoring the fact that this is far from a complete model, it immediately becomes clear that, in order to determine the value of consumption this period, it is also necessary to determine the expected value of consumption in the next period. Since, in this model, the representative consumer has decided upon this consumption function itself, so it can simply extrapolate forward to determine what it 'expects' to consume in the future.

In my mind, there is nothing fundamentally wrong with this and, so long as you ban explosive solutions in real variables (something that is an extremely important part of Blanchard-Kahn), you can easily find equilibrium solutions to DSGE models. Different heterodox economists (and occasionally Noah Smith, who is so happy trashing mainstream econ that a casual observing might not notice that he has a PhD in economics and is a card-carrying member of the economic orthodoxy) have made their own critiques of rational expectations, but within the realm of qualitative DSGE models, I personally find the typical criticism of "but expectations aren't actually formed that way" somewhat excessive -- the model has other aspects that are more inaccurate, like the fact that there is no income distribution and all workers are paid the same wage, but no one seems to care about that.

The real issue with rational expectations comes from (guess who) market monetarists. Nick Rowe famously called monetary policy 99% expectations (and then corrected himself in comments on one of my post by arguing that monetary policy is 100% expectations) and Scott Sumner will happily evade any theoretical argument that monetary policy is ineffective at the zero lower bound by invoking the central bank's ability to create expected inflation simply by saying that it will occur.

See, when your only requirement of expectations is that they are model consistent, you can essentially argue that the only thing a central bank needs to do in order to change expectations of a nominal variable (which it controls in equilibrium, which is the long run -- and I don't mean 'solution to the model' when I say equilibrium, I mean steady state) is to start targeting that variable at the desired level. The real world equivalent of this would be the hypothetical scenario in which the Federal Reserve announced tomorrow that it will target 4% inflation from now on and inflation instantly jumps up to a 4% annualized rate for the quarter, thus causing a large boom and ending the liquidity trap.

Why can't this happen? Because, in order to achieve that target -- in order to be 'credible' -- the Fed has to have an effective tool to create that inflation. Open market operations don't count because it is empirically ineffective and the nominal interest rate doesn't count because it can't be cut significantly (plus the nominal interest rate would go up in this scenario anyway). The problem could be similarly phrased as 'there are multiple equilibria consistent with a rate increase, how do we know whether we will get the one with deflation or the one with immediately higher inflation?' If this sounds like John Cochrane's brand of Neo-Fisherism, don't worry; it is.

Sumner, by suggesting that the Fed can change expected inflation at will, is arguing right along with Cochrane that the second equilibrium is possible -- all the Fed need do is announce a higher inflation target to get there. Meanwhile, Cochrane is left puzzling about equilibrium selection given a set of concrete steppes. The answer is clear: central banks can obviously choose the equilibrium themselves, thus stimulating the economy and escaping the liquidity trap.

No. The fundamental problem here is that Cochrane understands the model while Sumner doesn't (OK this may not necessarily be true, but Sumner has repeatedly admitted his lack of use of DSGE, so I don't think I'm that far off). In Cochrane's paper, 'The New Keynesian Liquidity Trap,' the central bank does ultimately control the final inflation rate using a Taylor Rule (the coefficient may be zero in his baseline simulation, but the model is still stable, so my point still stands), but there are still multiple equilbria at the end of the liquidity trap, so, so long as the inflation target remains constant at $t=\infty$, the central bank remains unable to simply announce an end to the liquidity trap.

Naturally, this made me curious about the effect of a mid-liquidity trap increase in the inflation target in a perfect foresight model (my modeling tools preclude me from doing stochastic models with the zero lower bound unfortunately). Here are the results:

Temporary increase in the inflation target from period 15 to period 50

No change to inflation target

As you can see, in the basic New Keynesian setup, increasing the inflation target halfway through a natural rate-decline induced liquidity trap and allowing that increase to persist for another 30 periods after the liquidity trap has ended is partially effective, at least in a perfect foresight model, which ignores expectations altogether (the liquidity trap lasts from period 10 until period 20). 

So, evidently, changes in the inflation target (as long as they are accompanied by corresponding changes in the policy rule) can be effective, even if they are temporary and start after the liquidity trap has begun. The difference here, though, is that I have insured that the inflation rate will converge to the target, since the model is perfect foresight, so my point above remains valid; absent the ability to guarantee that, once the inflation target is revised upwards, inflation will converge to the new equilibrium (assuming there are multiple equilibria, one of them being a persistent liquidity trap), the ability of central banks to dodge liquidity traps by announcing changes in target inflation rates (or some other change to inflation expectations) is both unclear and entirely at the mercy of one's priors.

How Would You Know?

How would you know if central banks were impotent at the zero lower bound?

You would have them target some nominal variable and then see if they can achieve that target. Wait, every central bank that I can think of off the top of my head does this: the Federal Reserve, BOJ, BOC, BOE, and the ECB. So, given that all of these central banks have had limited success at keeping inflation on target, monetary policy seems to have been pretty impotent.

Even if we restrict the analysis to countries that adopted the inflation target during the zero lower bound period (i.e. the BOJ and the Federal Reserve), we would find the same result: since the new target was adopted, in both cases 2% inflation, the target variable has been consistently below target.

Of course, all the market monetarists will respond by basically saying that inflation is always on target, so the recent experience only means that central banks are liars. This proposition is so ridiculous that I refuse to comment further on it.

For the remaining sane people in the room, the failure of inflation targeting central banks to have inflation on target is an indication of the ineffectiveness of monetary policy at the zero lower bound. Specifically, chronically low inflation means that the ability of central banks to loosen monetary policy (whatever the heck that means, everyone please stop referring to undefined terms like the 'stance' of monetary policy) has been severely limited over the last 8 years.

Actually, I do want to comment a little bit on the aforementioned ridiculousness. If your view is consistent with any empirical outcome, then it is unfalsifiable and should probably be ignored. Then again, this is probably true for the majority of economics, which is why your opinions, along with those of Post Keynesians, Austrians, and probably yet other heterodox school that I have never heard of, still exist.

Why can't we (unfortunately, I might add) reject market monetarism based on the last 8 years? Because if we did that, we'd also have to reject all the good theories like the Phillips curve, sticky prices at the individual firm level, Marshallian labor markets, etc.

Market Monetarism

My list of questions and/or criticisms that I don't think have been properly addressed for/of Market Monetarists has increased to such a degree that I think the best way to deal with everything is just to write one blog post and send it to a Market Monetarist (probably Nick Rowe, who seems to be the most reasonable one, from my experience, and probably the only one who will bother to respond).

Natural Rate Hysteresis:

The Wicksellian natural rate is completely forward looking in sticky price NK models (with either Calvo or Rotemberg pricing). Does switching to something like Taylor Contracts for the price level or nominal wage result in a backward looking natural rate? If not, why do you think that there is natural rate hysteresis (theoretical explanation, please. I don't care if you think you see it in the data, because the natural rate is unobservable).

Falsification:

What, if anything, would you have to observe in the data to determine that liquidity traps genuinely exist? Apparently low inflation despite high monetary base growth (i.e., money demand at unprecedented levels) since 2009 doesn't convince you, so what would?

Concrete Steppes:

Since central banks don't commit to monetary policy in the very long run (or, if they do, the commitment doesn't suggest anything quantitative), is it not reasonable to conclude that deliberately communicated actions by a central bank (forward guidance can be included here) are necessary for actual changes in monetary policy? 

NGDP Targeting:

In sticky price models, NGDPLT does not prevent the zero lower bound from binding when there are large persistent negative shocks to the real natural rate. Does wage stickiness remove this problem? If so, what evidence is there for wage stickiness (I mean, there has to be a reason why the profession switched to sticky prices and I'm fairly certain that reason is usually stated as 'there's no evidence for a high degree of wage stickiness').

Liquidity Traps:

Imagine we're in a multi-period version of Krugman (1998) in which the CIA constraint is not binding and will not bind for the next five periods. Do you agree that any current OMO will be completely useless? Of course, the central bank can simply increase the money supply five periods in the future (when it once again has control over the price level) and recursively set the nominal interest rate to be greater than zero, so there is a way out when the liquidity trap is finite. But, in the real world, the length of the liquidity trap is not set in stone. What if this is the case, so the central bank has no idea how far in the future it must induce expectations of the money supply to be higher in order to escape the liquidity trap. In this case, would you agree that the only reliable way to escape the liquidity trap is to decrease the current money supply until the CIA constraint binds?

Fiscal Policy:

I'm assuming you would agree that, ceterus paribus, fiscal stimulus raises the real natural rate. Given this, what reason do you have to oppose fiscal stimulus at the zero lower bound -- I know you don't think monetary policy is impotent in this case, but, given the possibility that us Keynesian's are right, what's wrong with a higher natural rate (and, correspondingly, a higher nominal interest rate), especially since we all agree that monetary policy is effective off of the zero lower bound. Similarly, why support austerity if it lowers the natural real rate; what's wrong with making the job of a central bank easier?

Money Demand:

Does your preferred money demand function more closely resemble MIUF (in which the nominal interest rate can never actually hit zero, lest money demand be infinite) or CIA (in which a zero nominal interest rate implies indeterminate money demand, which means that OMO's are completely useless as long at the nominal interest rate equals zero)?

History Dependence in the Natural Rate

One of the pet claims of Market Monetarists is that the Federal Reserve's failure to cut the nominal interest rate quickly enough in 2008 caused the natural interest rate to become negative in 2009 -- basically that the natural rate is history dependent. This claim does not immediately seem suspect; after all, if you cause a recession in the current period by setting the nominal interest rate above the natural rate, then it only makes sense that simply reversing that decision in the next period will not close the output gap.

The problem with this is that it is ignorant of what the Wicksellian natural rate actually is: expected inflation plus the real natural rate (which is completely independent of monetary policy, unless you believe in hysteresis, which, as far as I know, no Market Monetarists do). To argue that setting the interest rate above the natural rate in the current period results in a reduction in the natural rate in the next period is to argue that the current nominal interest rate affects the inflation rate expected to prevail two periods from now.

So, either agents are backward looking (which no market monetarists, who generally like the EMH, believe to my knowledge) or monetary policy affects potential output. Also take note that a lower natural real rate is either consistent with higher current potential output (which would mean that current tight money raises potential output in the next period) or lower future output (which would mean that current tight money causes potential output two periods in the future to fall).

Given the forward looking nature of the natural rate, it should be clear that the only way that a central bank can influence the natural rate is by changing the expected path of future interest rates relative to the expected path of future real natural interest rates (I guess Woodford is smarter than some Market Monetarists might like to admit).

Then what actually happened in 2008? Evidently the Fed allowed expectations of future interest rates to exceed expectations of future natural rates, something that they could not have prevented by cutting the nominal interest rate further in 2008 and something that could not have been prevented without a large increase in inflation expectations -- which could not have happened under a 2% inflation targeting regime or an NGDPLT regime that would be broadly consistent with 2% inflation.

Note: before you take issue with my last statement, I simulated a simple New Keynesian model in which the real natural rate goes negative for five periods under two different regimes. In one, NGDP is banned from being off-target and, in the other, the central bank sets the nominal interest rate equal to the (nominal) natural rate. In both cases, the only thing that prevented the zero lower bound from binding was an increase in the inflation target and/or the equilibrium growth rate of NGDP; NGDPLT on its own can't circumvent the zero lower bound problem.

If you want proof, I have all the pictures here (it may not be immediately clear what each one means, be careful not to misinterpret).

Extended Response to Nick Rowe

Nick Rowe on Twitter earlier today:

If [a] central bank targeted the price of peanuts, would we blame recessions on bad peanut harvests? Or blame [the] central bank for not raising [the] target price?

It depends. It depends on how quickly the central bank finds out about the bad peanut harvest, how quickly the new policy can be enacted, and how effectively the central bank can control the price of peanuts.

Suppose no one know about the size of the peanut harvest until the following period. In this case, the central bank, which we will assume can completely control the price of peanuts for the time being, is not culpable for the recession that occurs because the price of peanuts is too low. The central bank could not have known that the price level (of peanuts) at which output remained at potential was higher than they otherwise thought, so they cannot be blamed for the recession that ensues.

If, on a slightly different note, the central bank faces a delay in policy implementation, it may not be able to act quickly enough to prevent a recession; they can raise the target price with a delay, but there will still be a recession in the meantime and the central bank is not culpable.

Alternatively, assume that the central bank knows about the bad harvest in real time and doesn't face a policy lag, but, for some reason, is unable to set the price of peanuts any higher. In this case, the central bank can't be blamed either -- there is nothing it can do to prevent it from happening, so the correct culprit for the recession is the bad peanut harvest.

Generally, assuming there are no significant lags in information or implementation, the central bank would be to blame for not preventing the recession. The only time that the blame really shouldn't fall on a central bank is when it can't control the price (of peanuts) -- in this case, central bank impotence is to blame for the recession, not actions taken by the central bank.

With that aside, now we can go about determining when central banks are impotent.

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.

I Don't understand Market Monetarist Logic

So the typical market monetarist view on business cycles is that low NGDP causes low RGDP. Let $p$ indicate whether or not NGDP is lower than normal and $q$ indicate whether or not RGDP is lower than normal. The market monetarist contention can be represented as such:

$$ p \rightarrow q $$

If a central bank successfully targets inflation, then NGDP should track RGDP (because NGDP growth is always equal to RGDP growth plus the inflation target). This looks like

$$ q \rightarrow p $$

These two statements don't seem to make sense when paired with each other... According to market monetarists, low NGDP caused the great recession, but, because of the inflation targeting regime in the US, low RGDP causes low NGDP... Do market monetarists think that the great recession caused itself? Their logic seems to imply either that recessions come from something like multiple equilibria when central banks target inflation or that they just can't happen because in inflation targeting regimes, NGDP doesn't fall unless RGDP does and RGDP doesn't fall unless NGDP does, so neither ever fall. If they think that inflation targeting produces multiple equilibria, then why don't they say so? If the multiple equilibria logic is correct, then they shouldn't be strictly advocating and NGDP target; they should be telling everyone to switch to any target that doesn't make NGDP depend of RGDP...

This is all extremely confusing. 

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.