## Tuesday, September 22, 2015

### Knut Was a Neo-Fisherian

In the midst of this Paul Krugman post, I found a description of Wicksellian dynamics:
As I’ve been trying to point out – and as others, notably Ben Bernanke, have also tried to point out – such monetary wisdom as we possess starts with Knut Wicksell’s concept of the natural interest rate. Try to keep rates too low, and inflation accelerates; try to keep them too high, and inflation decelerates and heads toward deflation.
So, I was thinking, what happens if we write that down and work it out?

To keep it simple, we'll just deal with a deterministic world. It's more or less New Keynesian, but a little different. To start, we have the standard Euler equation, which prices a one-period nominal bond - after taking logs and linearizing:

(1) R(t) = r* + ag(t+1) + i(t+1),

where R(t) is the nominal interest rate, r* is the subjective discount rate, a is the coefficient of relative risk aversion (assumed constant), g(t+1) is the growth rate in consumption between period t and period t+1, and i(t+1) is the inflation rate, between period t and period t+1. Similarly, the real interest rate is given by

(2) r(t) = r* + ag(t+1).

Assume there is no investment, and all output is consumed.

To capture Krugman's concept of Wicksellian inflation dynamics, first let r* + ag* denote the Wicksellian natural rate of interest, where g* is the economy's long-run growth rate. Krugman says that inflation goes up when the the real interest rate is low relative to the natural rate, and inflation goes down when the opposite holds. So, write this as a linear relationship,

(3) i(t+1) - i(t) = -b[r(t) - r* - ag*],

where b > 0. Then, from (2) and (3),

(4) i(t) = ba[g(t+1)-g*] + i(t+1),

which is basically a Phillips curve - given anticipated inflation, inflation is high if the growth rate of output is high.

Then, substitute for g(t+1) in equation (1), using (4), and write

(5) i(t+1) = -[b/(1-b)][R(t) - r* - ag*] + [1/1-b]i(t).

So this is easy now, as to determine an equilibrium we just need to solve the difference equation (5) for the sequence of inflation rates, given some path for R(t), or some policy rule for R(t), determined by the central bank.

First, suppose that R(t) = R, a constant. Then, from (5), the unique steady state is

(6) i = R - r* - ag*.

That's just the long-run Fisher relation - the inflation rate is the nominal interest rate minus the natural real rate of interest. But what about other equilibria? If 0 < b < 1, or b > 2, then in fact the steady state given by (6) is the only equilibrium. If 1 < b < 2 then there are many equilibria which all converge to the steady state.

Next, suppose that R(t) = R1, for t = 0, 1, 2, ..., T-1, and R(t) = R2, for t = T, T+1, T+2,..., where R2 > R1. This is an experiment in which the nominal interest rate goes up, once and for all, at time T, and this change in monetary policy is perfectly anticipated. In the case where 0 < b < 1, there is a unique equilibrium that looks like this:

So, inflation increases prior to the nominal interest increase, and achieves the Fisherian steady state in period T, and the growth rate in output and the real interest rate are low and falling before the nominal interest rate increase occurs.

We can look at the other cases, in which b > 1, and the dynamics will be more complicated. Indeed, we get multiple equilibria in the case 1 < b < 2. But, in all of these cases, a higher nominal interest rate implies convergence to the Fisherian steady state with a higher inflation rate. Increasing the nominal interest rate serves to increase the inflation rate. Keeping the nominal interest rate at zero serves only to keep the inflation rate low, in spite of the fact that this model has Wicksellian dynamics and a Phillips curve.

I'm not endorsing this model - just showing you its implications. And those implications certainly don't conform to "try to keep rates too low, and inflation accelerates; try to keep them too high, and inflation decelerates and heads toward deflation," as Krugman says. The Wicksellian process is built into the model, just as Krugman describes it, but the model has neo-Fisherian properties.

## Sunday, September 20, 2015

### The ZIRP Blues

Here's the time series of the fed funds rate and inflation rate in the United States, from the time Paul Volcker became Fed Chair:
Suppose an alien with a high IQ lands in my back yard. I show her this picture, and explain that the central bank moves the fed funds rate up and down so as to control inflation. Ms. Alien points out that the fed funds rate and inflation were in the neighborhood of 10% in August 1979. Now, 36 years later, the fed funds rate and the inflation rate are close to zero. So, says Ms. Alien, it looks like the central bank spent 36 years fighting the inflation rate down to zero.

Ms. Alien would be surprised to learn that most people are not happy with the current state of affairs. There are always exceptions, of course - in this case, John Cochrane. But popular views on current U.S. monetary policy fall basically into two camps:

1. Phillips curve A: These people think inflation is too low. But eventually the Phillips curve will re-assert itself, and inflation will rise of its own accord. When that happens, we can worry about liftoff - an increase in interest rates to hold inflation down.
2. Phillips curve B: These people also think inflation is too low, that, eventually, the Phillips curve will re-assert itself, and that inflation will rise of its own accord. But a Phillips curve B type thinks that we need to get ahead of the game. Milton Friedman told us that there are "long and variable lags" associated with monetary policy. If we wait too long, then monetary policy will be scrambling to keep up with higher inflation, and interest rates will need to climb at a high rate, at the expense of real economic activity.

The Phillips curve A group includes Summers, Stiglitz, and Krugman, who states that we should "wait until you see the whites of inflation’s eyes." Members of the Phillips curve A and B camps have to somehow come to grips with the Phillips curve we see in the recent data, which looks like this:
The line joins the points in the scatter plot in temporal sequence, roughly from right to left. Krugman's point in his piece is that the natural rate of unemployment (NAIRU) has been receding as we get closer to it. In this view, we're supposed to have faith that the Phillips curve looks like this:

An alternative to Phillips A/B is the neo-Fisherian view. As John Cochrane says:
But if a 0% interest rate peg is stable, then so is a 1% interest rate peg. It follows that raising rates 1% will eventually raise inflation 1%. New Keynesian models echo this consequence of experience. And then the Fed will congratulate itself for foreseeing the inflation that, in fact, it caused.
Cochrane's saying that central bankers have to come to terms with the Fisher effect. If the short-term nominal interest rate is low for a long time, we should not be surprised that the inflation rate is low. And John is quite happy with low inflation. While the Phillips curve A and B camps fight it out over how to get inflation up, and sing the ZIRP (zero interest rate policy) blues, he's hoping they never figure it out.

There's a more subtle idea in the quote from Cochrane above, which is that a neo-Fisherian could find common cause with the Phillips curve B camp. They could all agree to liftoff, the inflation rate could rise due to the Fisher effect, and the central bank "will congratulate itself for foreseeing the inflation that, in fact, it caused."

If you're wondering what central bankers are thinking, a nice summary of conventional views is in a speech by Andy Haldane, Chief Economist at the Bank of England. It's a long speech, by U.S. central banker standards, but certainly thorough. Much of the speech focuses on the "problem" of the zero lower bound (ZLB). In most of the monetary models we write down, and in the traditional thinking of central bankers, zero is a lower bound on central bank's policy interest rate. The ZLB is thought to be a problem as, once the central bank reaches it, its policy options are limited. If one takes this seriously, there are two responses: (i) stay away from the ZLB; (ii) get more creative about policy options at the ZLB.

How do we stay away from the ZLB? Haldane tells us why we're now seeing ZLB policies:
... by lowering steady-state levels of nominal interest rates, lower inflation targets ... increased the probability of the ZLB constraint binding.
He's saying that low inflation targets, i.e. average rates of inflation that are low, imply lower nominal interest rates. So,
... one option for loosening [the ZLB] constraint would simply be to revise upwards inflation targets. For example, raising inflation targets to 4% from 2% would provide 2 extra percentage points of interest rate wiggle room.
So this is entirely consistent with John Cochrane and the neo-Fisherians. If the central bank's inflation target is higher by two percentage points, then the nominal interest rate must on average be higher by two percentage points, and the chances that monetary policy will take us to the ZLB should be much smaller.

But, Haldane is certainly not a neo-Fisherian. He's more in the Phillips curve A camp, as this is his policy recommendation:
In my view, the balance of risks to UK growth, and to UK inflation at the two-year horizon, is skewed squarely and significantly to the downside.

Against that backdrop, the case for raising UK interest rates in the current environment is, for me, some way from being made. One reason not to do so is that, were the downside risks I have discussed to materialise, there could be a need to loosen rather than tighten the monetary reins as a next step to support UK growth and return inflation to target.
Haldane makes it clear that he thinks the way to "return inflation to target," i.e. 2%, is not to let the central bank's interest rate target go up. And, as I wrote here, it's not as if the UK data will make you a believer in the Phillips curve. Here's the policy problem the Bank of England faces:
The policy interest rate target is currently at 0.5% in the UK but, as in the U.S., the inflation target is at 2% and actual inflation is hovering around 0%.

Haldane discusses ways in which central banks can get creative when confronted with the ZLB. The options that have been discussed (and in some cases implemented by some central banks) are:

1. Quantitative Easing: The idea here is that, at the ZLB, purchases by the central bank of short-term government debt are essentially irrelevant, as there is no fundamental difference between short-term government debt and reserves at the ZLB. But, the central bank could purchase long-maturity government debt or other assets at the ZLB. Perhaps that does something? Post-Great Recession, the U.S. of course acquired a large portfolio of long-maturity Treasury securities and mortgage-backed securities, and maintains the nominal value of that portfolio of assets through a reinvestment policy that is still in place. Whatever the effects of U.S. QE programs, it's an inescapable reality that inflation is close to zero. But, even larger asset purchases were carried out by the Swiss National Bank, and the Bank of Japan. Here's what's happened in Switzerland:
In this case, both the policy rate and the inflation rate are well below zero. The Swiss National Bank has a goal of price stability, which it defines as less than 2% inflation. I'm not sure if they are OK with an inflation rate less than -1%.

The Bank of Japan began a program of "qualitative and quantitative monetary easing" in April of 2013. Here's the overnight interest rate and inflation rate time series for Japan:
I've included the whole 20-year period over which Japan's overnight interest rate was below 1%. Japan is, as you know, our stock example of what ZIRP produces. But what of the effects of the Bank of Japan's recent QE experiment? Don't be deceived by that burst of inflation in 2014. In April 2014, the consumption tax in Japan went up from 5% to 8%, and that feeds directly into the CPI - the prices in the index are measured after-tax. If we look at the CPI levels since the beginning of the QE program in April 2013, you can see that more clearly:
So, from April 2013 to July 2015, the CPI increased about 4%. If 3 percentage points of that is simply due to the consumption tax increase, then we're left with less than 1/2% per year in inflation since the QE program began. The Bank of Japan's inflation target is 2%, which it is missing by a wide margin on the low side, in spite of an increase in the monetary base in Japan that looks like this:
You can't blame John Cochrane for stating the following, with respect to the U.S.:
Even the strongest empirical research argues that QE bond buying announcements lowered rates on specific issues a few tenths of a percentage point for a few months. But that's not much effect for your \$3 trillion. And it does not verify the much larger reach-for-yield, bubble-inducing, or other effects.

An acid test: If QE is indeed so powerful, why did the Fed not just announce, say, a 1% 10 year rate, and buy whatever it takes to get that price? A likely answer: they feared that they would have been steamrolled with demand. And then, the markets would have found out that the Fed can’t really control 10 year rates. Successful soothsayers stay in the shadows of doubt.

I've written down a model of QE, in which swaps of short-maturity assets for long-maturity assets by the central bank can have real effects. Basically, this increases the stock of effective collateral in the economy, relaxes collateral constraints, and increases the real interest rate. It's a good thing. But, if the nominal interest rate is pegged at zero, this will lower the inflation rate.

2. Lower the lower bound: If the ZLB is a problem, possibly we can make the problem go away by relaxing the bound. In models we write down, the zero lower bound arises because it is costless to hold currency which, given current technological constraints, cannot bear interest. When the central bank has excess reserves outstanding in the financial system, if an attempt were made to charge financial institutions for the privilege of holding reserves with the central bank, these institutions would opt to hold currency instead - in some of our models. But, in the real world it is not costless to hold currency. Making interbank transactions using currency is impractical, as millions of dollars in currency takes up a lot of space, and because real resources would have to be expended in preventing theft. This implies that market nominal interest rates can be negative and, indeed, some jurisdictions have opted for negative interest rates on reserve balances held at the central bank. One of those, as you can see in the chart above, is Switzerland, where the inflation rate is now below 1%. Another is the Euro area:
European overnight interest rates have not gone as low as in Switzerland, nor is the inflation rate as low, but it's a similar picture - not much inflation.

Relaxing the lower bound meets with a difficulty similar to that for QE - in the long run, this just serves to make inflation lower. To see this, consider a very crude monetary model - cash-in-advance. There's a representative consumer who gets utility u(c) from consumption goods c, and suffers disutility v(n) from supplying n units of labor, which produces n units of consumption goods. Consumption goods must be purchased with cash. There are also one period bonds, which sell at a price q at the beginning of the period, and pay off one unit of cash next period. Cash and bonds are held across periods, and fraction t of cash holdings held between periods is stolen. Suppose for simplicity that thieves steal money and burn it. To make things easy, look at an equilibrium in which the money growth rate is a constant, i. Letting B denote the discount factor, in equilibrium the price of the bond is given by

(1) q = B/(1+i)

That's just the Fisher relation. There are no liquidity effects in this model, and in equilibrium the nominal interest rate is (roughly) given by

(2) R = p + i,

where p = 1/B -1 is the real interest rate. In equilibrium c = n, i.e. all output is consumed, and c is determined by

(3) v'(c) = [B(1-t)u'(c)]/(1+i)

What's the lower bound on the nominal interest rate. It's R* = - t, that is, it's determined by the cost of holding cash. And, if the nominal interest rate is at its lower bound, R*, then the inflation rate is

(4) i* = - p - t,

so lowering the lower bound only serves to decrease the inflation rate. You can add bells and whistles - reasons for the real interest rate to be low, endogenous theft of currency, short run non-neutralities of money, or whatever, and I think the basic idea will go through.

Another suggested approach to increasing the inflation rate, given ZIRP, is:

3. Helicopter Drops: The "helicopter drop" was a thought experiment in Milton Friedman's "Optimum Quantity of Money" essay. In the thought experiment, Friedman asks you to consider what would happen if the government sent out helicopters to spew money across the countryside. People would pick up the money, spend it, and prices would go up, etc. Surely, if inflation is perceived to be too low, and we're at a loss as to how to increase it, we should be thinking about this, the argument goes. Can't the government just send people checks and make inflation go up?

Paul Krugman has a suggestion along these lines, for Japan, though what he's suggesting is not Friedman's helicopter transfers (which increase the government budget deficit), but increases in spending on goods and services, financed by printing money:

What’s remarkable about this record of dubious achievement is that there actually is a surefire way to fight deflation: When you print money, don’t use it to buy assets; use it to buy stuff. That is, run budget deficits paid for with the printing press.
Actually, that's exactly what has been going on in Japan. The Japanese government has been running a deficit, the quantity of government debt outstanding is very large (in excess of 200% of GDP) and, as we can see in the chart above, the monetary base is growing at a very high rate. That's what printing money amounts to. But, the central bank can only control the total quantity of outside money in existence, not its composition. How outside money is split between currency and reserves is determined by the banks who hold the reserves and the private firms and consumers who hold the currency. The central bank can do all the money printing it wants, but if the new money sits as reserves, as appears to be happening, it's not going to have the effect that Krugman wants.

Increasing interest rates is hard for central bankers. A decrease in rates rarely produces any flack, but central banks have few supporters when they talk about rate increases. Media pieces like this one in the NYT and this one in the Economist propagate the idea that interest rate increases are fraught with peril. One example people like to use is tightening by the Swedish Riksbank in 2010-2011. Here's the relevant chart:
The tightening that occurred was an increase of 1.75 percentage points in the Riksbank's target interest rate, in quarter-point steps, from July 2010 to August 2011. In the realm of central bank tightening phases, this isn't a big deal. Compare it to the previous tightening phase in Sweden, or the 4.25 percentage point increase that occurred in the U.S. over the 2004-2006 period. But, the Riksbank caught hell from Lars Svennson as a result. The Riksbank seems to have more or less followed Lars's advice since, but as you can see it is now keeping company with other central banks, with a negative policy rate, and inflation close to zero - two percentage points south of its target.

What are we to conclude? Central banks are not forced to adopt ZIRP, or NIRP (negative interest rate policy). ZIRP and NIRP are choices. And, after 20 years of Japanese experience with ZIRP, and/or familiarity with standard monetary models, we should not be surprised when ZIRP produces low inflation. We should also not be surprised that NIRP produces even lower inflation. Further, experience with QE should make us question whether large scale asset purchases, given ZIRP or NIRP, will produce higher inflation. The world's central bankers may eventually try all other possible options and be left with only two: (i) Embrace ZIRP, but recognize that this means a decrease in the inflation target - zero might be about right; (ii) Come to terms with the possibility that the Phillips curve will never re-assert itself, and there is no way to achieve a 2% inflation target other than having a nominal interest rate target well above zero, on average. To get there from here may require "tightening" in the face of low inflation.

## Sunday, September 6, 2015

Paul Krugman concludes that "hiking rates now is still a really bad idea." So, his opinion is clear. What's not so clear is his argument, which is this:
When the Fed funds rate was 5 percent, there was room to cut if a rate hike turned out to be premature — that is, the risks of moving too soon and moving too late were more or less symmetrical. Now they aren’t: if the Fed moves too late, it can always raise rates more, but if it moves too soon, it can push us into a trap that’s hard to escape.
So, suppose we're in the pre-financial crisis era, and the fed funds rate is 5%. As a thought experiment, suppose the FOMC decided at its regular meeting to hike the fed funds rate target to 5.25%. Then, at its next meeting it decided that the previous hike was a mistake, and undid it, reducing the fed funds rate target to 5%. I think Krugman is telling us that, in those circumstances, ex post we would prefer the policy that stayed at 5% to the one that went up a quarter point and then back down. I think he's also telling us that, once we discover the mistake, the best policy would be to reduce the fed funds rate below 5%. That's the basis for the asymmetry argument he's making - there's no problem if you're at 5%, but when you're at zero (essentially), you can't correct the mistake. So, fundamentally, this argument revolves around the assumption that there is an economically significant difference between going up to 5.25% this meeting, then down to 5% at the next meeting, vs. having stayed at 5%.

If that's the crux of it, Krugman needs to do a better job of making the case. In terms of modern macroeconomic theory, we don't think in terms of "too early" and "too late." Policy is state-dependent, i.e. data-dependent.
The policymaker takes an action based on what he or she sees, and what that indicates about where the economy is going. The question is: What is Krugman's desired policy rule, and where would that lead us? What exactly is the nature of the "hard to escape" trap that might befall us? As is, Krugman's not giving us much to go on.

Addendum: Here's another thought. Krugman seems to like the "normal" world of 5% fed funds rate better than the zero-lower-bound world - because, as he says, the normal world allows you more latitude to correct "mistakes." So why wouldn't he use that as an argument for liftoff?

## Friday, September 4, 2015

### Tribes?

Paul Romer is worried that the field of macroeconomics is too tribal - somehow our behavior is impeding scientific progress.

Romer starts his post with two statements:
1.The model in Lucas (1972), Expectations and the Neutrality of Money, made a path breaking contribution to economic theory. It is comparable in importance to the Solow model and the Dixit-Stiglitz formulation of monopolistic competition.

2. The model in Prescott and Kydland (1982), “Time to Build and Aggregate Fluctuations”, has no scientific validity.
As Romer points out, the first statement concerns a modeling contribution, while the second has to do with empirical usefulness. But Romer thinks that how we - that is, macroeconomists in particular - think about those two statements should be revealing.

Most of us can read those two statements and know how the extended arguments are likely to play out. Of course, it helps to have been around for a while - anyone under 33 would not have been born in 1982, and would see Kydland/Prescott as ancient history. And Lucas (1972), though of course highly influential, does not show up on many PhD reading lists these days. But, even if we know the typical arguments, we would like to know more. Has the author of the statement got anything new to say? How do they flesh out the argument? I might think, for example, that the author of the second statement isn't just commenting on how Kydland-Prescott fits the data. Maybe he or she has something to say about the whole methodological approach. In any case, I'm curious. I would like to know. I'm open to persuasion. Indeed, that's what economists do - we try to persuade others, using whatever means possible. And a lot of that persuasion involves words - written and spoken. My ex-colleague Deirdre McCloskey, had a lot to say about this. Here's an excerpt:
I like that. Science is human persuasion, not mechanical demonstration. From reading Romer's stuff lately, I think he believes in mechanical demonstration. According to Romer, scientific progress should be obvious to some self-appointed group of elite scientists, and if we could just get rid of some of the clutter, we would be moving on much more quickly toward ultimate Romerian truth.

In spite of my reluctance, I'll play along with Romer. He says:
Think of some macroeconomist X that you know.
Fine. Some people would say I'm a macroeconomist, so I'll volunteer. Mr. X at your service. The next step is the following:
Consider these questions:

A. Would X agree that there is an objective sense in which statements 1 and 2 can be said to be either true or false?

B. Would X agree that a reasonable person could conclude that statements 1 and 2 are both true?

C. Would X be able to examine dispassionately the evidence for and against these two statements and evaluate them independently?
So, note that I'm going Romer one better. He's asking you to put words in someone else's mouth. That seems a little weird.

In answer to A: Stupid question. (i) Give me the rest of the argument, not just a blunt statement. I want you to try to persuade me. This is definitely not about true and false. What's true and false is something we'll never know - we're just scientists in the dark trying to figure things out. (ii) What you should be asking is: Are you persuaded? Maybe, after hearing the whole argument, I'm halfway-persuaded, but I have something I can add to the argument to make it more persuasive. Maybe I've got a clarifying question. Maybe I want the author to expand on the argument.

B: No idea. First I want to see if the authors of 1 and 2 are giving me what I think is a persuasive argument.

C: No. Dispassionate? Remember, we're talking about human persuasion here. Humans are passionate. If macroeconomists were not passionate about their work, working with them would be deathly dull. I would rather paint houses for a living. And why would we be thinking about 1 and 2 independently? Indeed, given the nature of the statements, we should be thinking about these things in the same context. How you argue one could have a lot to do with how you argue the other.

Where is Romer leading us? Well, he seems to want to make the case that we (macroeconomists) are "infected by tribalism." He also argues that physicists are not tribalists.

I've argued elsewhere that, taking macroeconomics in particular, that the field is much less factional than some people would like to claim. Emphasis on factionalism sometimes makes an interesting story for undergraduate macro students. In the old days, there was a conflict between Monetarists and Keynesians - Chicago vs. the east coast. In the 1970s there was a conflict between "saltwaters and freshwaters" - CMU/Minnesota/Chicago/Rochester vs. the east coast. But, as the technology has changed, and people and ideas have moved around, it's much harder to identify warring camps, or a war. You'll note that statements 1 and 2 concern very old ideas. Romer didn't give us, say, post-2000 statements along these lines. Why? Because he would have a hard time finding such things, except perhaps on the blogosphere, where people seem to love rehashing old - and long-ago resolved - disputes.

But, researchers in macro - as with researchers in other fields in economics - will split off into groups that are internally relatively homogeneous. That's how we make progress. Persuasion is hard. If we try to work in heterogenous groups in which we're constantly going back to first principles to justify what we're doing, we're not going to advance much. Sometimes we make the most progress in a group where we can agree on assumptions. I spend some of my time interacting with a group of monetary theorists who share a common view about research methods and direction, and we tend to share an evolving set of models. I've learned a lot from that, and from the continuing relationship with people in the group. And so what if two groups are having a dispute. That's just healthy competition.

So, within economics, is macro unusual? Of course not. Indeed, the whole emphasis of post-1970 macroeconomics is to do it like everyone else. Before 1970, no one would have been discussing macro and Dixit-Stiglitz in the same sentence. Should economics work like physics? Of course not. We're studying very different problems requiring very different methods. Why would you expect economists to behave like physicists?

What's my bottom line? Romer is just leading us through an unproductive conversation - one that's not going to persuade anyone of anything. Here's something that would be more fruitful. Romer's chief beef with the macro profession seems to be that we don't give him enough credit. The two characters who wrote the articles in statements 1 and 2 get plenty of credit. They are well-cited, and they have Nobel prizes. Romer also has plenty of citations, but seems to want something more. I'm not a close follower of research on economic growth, but I see growth papers sometimes, and my familiarity with this stuff is roughly that of your average macroeconomist. Romer made a couple of key contributions to the literature on economic growth early in his career, building on the seminal work of Solow and the optimal growth theorists - Cass and Koopmans for example. Romer's work, and Lucas's for example, was highly influential, and spawned a whole literature - endogenous growth theory.

The hope for this line of research was that we would gain an understanding of the forces behind technological change. This type of research, it was thought, could give us huge rewards. Some countries are extremely poor, while others are extremely rich. If we can figure out how to make the extremely poor extremely rich, this would be a huge payoff for macroeconomic research. My impression - and I could be entirely wrong - is that this line of research has been something of a bust. Most of the insight we have into economic growth and the sources of disparities in standards of living in the world comes mainly through the lens of the Solow growth model, and Solow's paper was published in 1956.

So, I think it is incumbent on Romer, if he wants more credit, and more recognition, to make the case for himself - for his older ideas - and to give us some new ideas. I'm willing to be persuaded, as I'm sure most macroeconomists are. But, arguments about "mathiness," "macro gone wrong," and unsubstantiated charges of dishonesty aren't persuading anyone, as far as I can tell.

## Wednesday, September 2, 2015

### More Historical Fiction

Reading Paul Krugman's recent blog post reminded me of this earlier post of his, which was much in the same spirit. Krugman wants to argue that the Old Keynesians - James Tobin in particular - had it right. This is Krugman's conclusion:
So how does the decade of the 1980s end up being perceived as a defeat for Keynesians? To see it that way you have to systematically misrepresent both what happened to the economy and what people like Tobin were saying at the time. In reality, Tobinesque economics looks very good in the light of events.

So what exactly was "Tobinesque economics?" Krugman points us to Tobin's 1980 Brookings paper. Early in that paper, Tobin tells us about his view of the inflationary process - how we got where we did in the 1970s:
...when the authorities have chosen policies supportive of continued inflationary growth of MV, they have not done so from ignorance of arithmetic, indifference to inflation, or, in my opinion, political pressure. They have done so, rightly or wrongly, mainly because of the perceived consequences of nonaccommodation on the real performance of the economy. The inertia of inflation in the face of nonaccommodative policies is the big issue.
Tobin's view was that there was substantial inertia in inflation, and that it was very costly to bring it down - a widely-held view at the time. But there were other ideas at the time as I discussed here. Tom Sargent, in particular, was emphasizing the policy relevance of modern macroeconomics for disinflation. According to Sargent, central bank commitment was important, and we could reduce the inertia in inflation if we had a credible commitment from the central bank to reduce it.

The picture that Krugman shows us from Tobin's paper is this one:
Krugman says that kinda sorta looks like what actually happened. I suppose a cat looks like a horse, because it has four legs. If you read Tobin's paper, he's using that figure to illustrate how bad he thinks disinflation through monetary measures could be. Look at it! After 7 years of monetary disinflation, the unemployment rate peaks at more than 10%, and it takes more than 12 years to get back to what Tobin thinks is the natural rate of unemployment, 6%. Tobin is using what he thinks is a conventional macroeconometric model. It's got adaptive expectations and a Phillips curve with what people then would have called a "high sacrifice ratio." You have to suffer a lot of unemployment to get a small reduction in inflation. Of course, Tobin's simulation looks nothing like what happened.

In Tobin's paper, after he shows us his simulation, he goes through some arguments about other factors that may not be in his model. Then, his punchline is this:
For these reasons,I think it would be recklessly imprudent to lock the economy into a monetary disinflation without auxiliary incomes policies. The purpose of these policies would be to engineer directly a deceleration of wages and prices consistent with the gradual slowdown of dollar spending. Macroeconomic policy and wage-price guideposts or controls would be concerted. Instead of issuing a monetary threat to everyone in general and to no one in particular, the government would seek the consent and cooperation of organized labor and business in a five-to-ten-year program to eliminate inflation at minimal cost in employment, production, and investment. The most promising incomes policy is to use tax-based incentives for complying with a sequence of gradually declining guideposts.

Tobin's telling us that it would be silly to disinflate through monetary policy alone. We need wage and price controls! So, how the 1980s was a victory for "Tobinesque economics," I have no idea. The Fed did what Tobin said they should not do, inflation did not have the inertia Tobin said it would have, and wage and price controls were thrown out with the policy trash. Further, the language of modern central banking is all about inflation targeting, commitment, and looking into the future. Tobinesque economics can only look good if you're not looking.

## Tuesday, September 1, 2015

### Intuitive Neo-Fisherism

John Cochrane's blog post, Whither Inflation, is excellent reading. Basically, John takes a mainstream New Keynesian model and shows how it has Neo-Fisherian characteristics - if the central bank raises the nominal interest rate, inflation increases. Noah Smith seems to find this interesting, but he's got some problems with it. I'm going to attempt to answer his questions.

First, Noah says:
What about the Volcker disinflation, when Fed interest rate hikes were followed by disinflation?
Volcker was Fed Chair from August 1979 to August 1987. During that period the time series for the fed funds rate and the pce (year-over-year) headline inflation rate looks like this:
The broad story in that picture is that Volcker began his 8-year term with high nominal interest rates and high inflation, and ended it with much lower nominal interest rates and much lower inflation. The scatter plot, with points joined in temporal sequence, looks like this:
In that chart, inflation and the fed funds rate more often than not are moving in the same direction. Volcker didn't do Cochrane's experiment in reverse - the fed funds rate comes down gradually during the disinflationary period - but I don't see an inconsistency between what we see in the above 2 charts and what is coming out of Cochrane's experiments with the NK model.

Second, Noah says:
...are we sure we want to think about interest rate policy as a series of interest rate pegs, each of which people believe will last forever?
Typically, in analyzing monetary policy, we want to study the operating characteristics of particular policy rules. That is, we specify the feasible set of actions a central bank can take under particular contingencies, specify a policy rule as a mapping from states of the world to actions by the central bank, and then ask how the economy functions under that rule. Cochrane's clearly interested in that, but he wants to show you a simple policy experiment so you can understand what's going on: Suppose the central bank increases the policy rate at a given point in time, permanently. What happens? This can help build your intuition so that you can handle the more difficult exercise of working out the optimal policy rule.

Finally, Noah says:
But the last reason we should be a little wary of the Neo-Fisherian idea is that it goes against our basic partial-equilibrium Marshallian idea of supply and demand.
For Noah, what's going on in the NK model is not intuitive. What does he mean? We can start by consulting an online dictionary:
Intuition: the ability to understand something immediately, without the need for conscious reasoning.
That fits closely with how an economist thinks about intuition. Over time, we accumulate knowledge of economic theory - models, basically - by working with them. For a lay person, partial equilibrium Marshallian supply and demand is not intuition. He or she has no clue about supply and demand. Sometimes Marshallian intuition works - for economists. I see a piece of economics that is unfamiliar, but I can recognize elements of supply and demand in it, and then I get the idea. But Cochrane is dealing with an issue that is dynamic, it's general equilibrium, it involves how the economic agents in the model think about the future. Why would I expect that static Marshallian intution would work? And if it doesn't seem to work, why should that make me "wary" of the idea? Looks like I have the wrong intuition, and I have some learning to do.

Here's some intuition. See if this works for you. Roughly, we can separate the short-term nominal interest rate into three components at any point in time:

R = F + L + r,

where R is the observed nominal interest rate, F is the Fisher effect (or inflation premium), L is the liquidity effect - the effect of monetary policy on the real interest rate - and r is the long-run real interest rate, which is determined by non-monetary factors (we'll neglect Tobin effects and such). Next, consider Cochrane's experiment. There is a one-time, permanent increase in the nominal interest rate. In some models we would have to worry about what actual monetary policy actions (asset swaps or settings for administered interest rates) would be required to support this market interest rate, but in the NK model Cochrane works with, that's not an issue. The central bank can set the nominal interest rate, and that will induce a dynamic path for F and L. I think most economists would have intuition for the long-run effect. In the long run, the increase in L induced by the increase in R is zero, and F increases one-for-one with R. In the long run, the Fisher effect dominates.

In the short run, L moves in the same direction as R. That's the non-neutrality of money in the sticky price NK model. Consumption declines on impact, and then grows over time, at a declining rate. If you have taken a PhD macro course (or even some undergrad macro courses ) you should have some modern macro intuition. That intuition tells you how consumption smoothing relates to asset pricing. In this instance, with the representative consumer facing growing consumption, the real interest rate will be higher than it would otherwise be (the liquidity effect) because the representative consumer would like to smooth consumption over time (by borrowing against the future), but cannot. But consumption growth is falling over time, so the liquidity effect (the increase in L) declines over time. This implies that, with R constant, the Fisher effect (the increase in F) must rise over time.

So, we have the liquidity effect - the increase in L - initially positive and converging over time to zero, and the Fisher effect - the increase in F - rising over time and converging to the increase in R. But what is the Fisher effect on impact? I think the intuition of some people would tell them this impact effect should be negative. That intuition might come from thinking about Phillips curves. Maybe this Phillips curve intuition exists because people are ignoring the empirical evidence. Maybe people have some familiarity with reduced form NK models. Typically, in those formulations - essentially what Cochrane has written down - Cochrane's equation (2) is a "Phillips curve." So, you could forgive people for using their Phillips curve intuition in an attempt to understand what is going on the standard NK model. But, as it turns out, their intuition doesn't help them in this case.

It's not clear why anyone would expect the impact effect of the increase in R on F to be negative, if he or she understands what is going on in the model. And, indeed, Cochrane shows us an example in which the impact effect on F is positive, though there are other equilibria in which the impact on F is negative - in those other equilibria, the liquidity effect has to initially be that much stronger.

What would happen in models where we actually include money? An example in which there are short-run nonneutralities - liquidity effects - is the class of segmented markets models. In these models, the first round effects of monetary policy affect only a segment of the population - those closely-connected to financial markets. Then, an open market operation affects people asymmetrically. One very simple model of this type is Alvarez, Lucas, and Weber (AER, 2000). In that model, there are two types of people, traders and non-traders. When an open market purchase by the central bank occurs, the traders receive a cash injection, which is a temporary increase in their wealth, so traders then consume more. This induces a liquidity effect, as it is the consumption of traders that determines the price of nominal bonds in this economy. Consumption is temporarily high for traders, so L is temporarily low, and this reduces R.

If we do Cochrane's policy experiment in Alvarez/Lucas/Weber (ALW), we can find an equilibrium in which the impulse responses look like Cochrane's. In response to a permanent increase in the nominal interest rate, the inflation rate increases over time, and ultimately the increase in F is equal to the increase in R. But in the ALW model, there is a path for money growth that is needed to support the permanent increase in the nominal interest rate. In ALW, the quantity theory of money holds in a very simply way - total output is constant, and the price level is proportional to the money stock. So, ALW tells us that, to support a permanently higher nominal interest rate, what is required is higher and rising money growth.

So, that's reassuring. Cochrane's results hold in a widely-used macro model, and they hold in other monetary models with liquidity effects. So, for people who know how those models work, the results should be intuitive.