## 20 April 2016

### 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!

## 17 April 2016

### 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.

## 15 April 2016

### More Issues With Neo-Fisherism

I always seem to be about a day late to the party, nevertheless I guess I'll present a little bit of a defense of the mainstream view before I get immensely busy.

I would first like to point out one issue that I have with both Stephen Williamson's and John Cochrane's attempt to show that even backward looking Phillips curves have Neo-Fisherian attributes. To my knowledge (that is, to the extent that they explained their models in their posts), Cochrane always retained perfect foresight in the Euler equation and Williamson always retained rational expectations, regardless of their model of inflation expectations. As this is integral to the model result, I expect that they would at least be up front about this assumption. Alas, no.

Neo-Fisherians, like most New Keynesians, have the disturbing habit of completely ignoring the money supply -- which they implicitly assume moves in a different way in response to changes in the nominal interest rate than most New Keynesians implicitly assume (note that I am not precluding Neo-Fisherians from being New Keynesians, the two are not necessarily exclusive, as Cochrane and Williamson have argued multiple times). Thus, I think it is at least important to frame this argument through the lens of a money demand function with interest elasticity.

As my only intention here is to highlight money supply dynamics, the model will involve completely flexible prices and focus solely on two periods.Variables in the current period will appear as $x$ while variables in the future period will appear as $x'$. Additionally, the final price level is fixed at $\bar p$. The money demand function is
$$m - p = -\alpha i$$
where $m$ is the money supply, $p$ is the price level, $\alpha$ is the interest elasticity of money demand, and $i$ is the nominal interest rate. The Euler equation is
$$i = p' - p$$
All variables, except $i$, are in logs.

In this model, the central bank sets the money supply $m$ and the future money supply $m'$, which determines $p$, $p'$, $i$, and $i'$.

Solving the model for $p$ given $m$, $m'$, and $\bar p$ yields:
$$p = \frac{m + \alpha \left[\frac{m' + \alpha \bar p}{1+\alpha}\right]}{1+\alpha}$$
If the central bank holds $m'$ constant and increases $m$, then $p$ will rise less than one for one with the $m$, which, given the money demand function, implies a lower nominal interest rate. This is, in essence, the conventional wisdom; the central bank engages in a temporary open market operation which raises the current inflation rate and lowers the nominal interest rate.

This result can be changed depending on how the central bank chooses $m'$. In fact, the central bank can set $m'$ such that the price in $p$ more than offsets the rise in $m$, thus giving the Neo-Fisherian result which, (warning, massive tangent) is rather ill-defined.

Williamson likes to define it in a way that favors the Neo-Fisherian argument but doesn't necessarily fit with his claim that raising the nominal interest rate results in higher inflation. Namely, he argues that, as long as a model suggests that a permanent increase in the nominal interest rate will eventually result in higher inflation, that that model is Neo-Fisherian. To me, this argument  (which I'll grant I haven't quoted from him, so if I am building a straw man feel free to call me out on it) sounds like saying "as long as a model has an Euler equation, has rational expectations, and has flexible prices (or equivalently has sticky prices but bans explosive solutions), that model is Neo-Fisherian." This works well with his definition, I suppose, but 1) I don't like his definition, 2) it doesn't necessarily mean that inflation will rise immediately very quickly, and 3) it doesn't say anything about non-permanent increases in the nominal interest rate.

In my opinion, a Neo-Fisherian result is one in which a temporary positive shock to the nominal interest rate delivers an immediate or almost immediate increase in inflation that is not offset by deflation in the periods preceding the higher inflation. Thus, I will happily admit that higher inflation and higher nominal interest rates are mutually consistent in the long run, but I will not concede that the way to get higher inflation immediately is to raise the nominal interest rate. As of yet, I do not believe any Neo-Fisherian has adequately made this argument (tangent over).

I digress, different paths for the money supply are consistent with different results for inflation and expected inflation, but a non-permanent increase in the money supply gives the conventional result of higher inflation and a lower nominal interest rate. However, if the central bank increases the future money supply by more than the current money supply, it is possible that the observed result will appear Neo-Fisherian: that is, $p$ increases more than $m$, which is consistent with immediately higher inflation and a higher nominal interest rate (lower demand for real balances). Is this really what Neo-Fisherians believe happens on the event of an interest rate increase? This weird higher nominal interest rate, lower real money supply, higher nominal money supply result is really strange and I highly doubt it happens with regularity. In fact, between 1956 and 2008, the only time that this consistently happened (with the monetary base to nominal GDP ratio replacing $m-p$ and the monetary base to real GDP ratio replacing $m$) was the late 1960's to early 1980's:
Given this reality, it should be possible to include that Neo-Fisherism is indeed not part of the current monetary policy regime (assuming the Federal Reserve has not abandoned the Taylor principle and the treasury is still Ricardian).

## 12 April 2016

### 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.