Monday, September 8, 2014

Theories of Inflation and the European Predicament

How do macroeconomists think about inflation? To get a grip on this, it's useful to dig into the history of economic thought. Long ago, in the mid-1970s, when I had no idea what formal economics was about (and, you might say, nothing much has changed), I had heard about "wage-price spirals." A web search will give you plenty of descriptions of what we might charitably call the "wage-price spiral theory" of inflation. Here's one that's as good as any:
When an economy is operating at near full employment and people have money to spend, demand for goods and services increases. To meet the demand, companies expand their businesses and hire more workers. However, at near full employment, most workers already have jobs. So companies have to lure workers with higher wages, which, of course, increases the companies' costs, explains the website Biz/ed. The workers then push for higher wages to meet the higher prices and expected price hikes, which increases company costs again. Theoretically, this continues in an inflationary spiral until a loaf of bread costs the proverbial wheelbarrow full of cash.
You'll notice that the behavior of governments and central banks doesn't enter into the story. Apparently a wage-price spiral is a self-fulfilling dynamic process which could start under any conditions and continue forever - unless something is done about it. In the 1970s, some policymakers thought the solution to a perceieved wage-price spiral problem was (naturally) wage-price controls. For example, Richard Nixon tried a 90-day wage-price freeze, and the government of Canada imposed wage-price controls for a much longer period of time. Such controls were advocated by economists like John Kenneth Galbraith, who perhaps wasn't taken so seriously by most academics, but even mainstream macroeconomists such as James Tobin could sometimes find "incomes policies" attractive.

In current academic circles, there isn't much talk about wage-price spirals, though of course some ideas never die. Perhaps the primary achievement of the Old Monetarists - principally Milton Friedman - was to convince people that inflation control is the job of central banks, and that wage-price controls only produce inefficiencies (though experience with those policies was pretty convincing as well). So, if inflation control is the job of the central bank, and we think there is something wrong with the inflation rate, we know who to blame. Of course, Friedman seems to have failed to give central banks useful instructions for implementing inflation control. He argued that there is a direct link between money growth and long-run inflation, that monetary disturbances are a primary determinant of fluctuations in real GDP, and that "fine-tuning" is inappropriate. So, Friedman reasoned, the appropriate monetary policy is:
...that the monetary authority go all the way in avoiding such swings by adopting publicly the policy of achieving a steady rate of growth in a specified monetary total. The precise rate of growth, like the precise monetary total, is less important than the adoption of some stated and known rate. I myself have argued for a rate that would on the average achieve rough stability in the level of prices of final products, which I have estimated would call for something like a 3 to 5 per cent per year rate of growth in currency plus all commercial bank deposits or a slightly lower rate of growth in currency plus demand deposits only. But it would be better to have a fixed rate that would on the average produce moderate inflation or moderate deflation, provided it was steady, than to suffer the wide and erratic perturbations we have experienced.
Like wage and price controls, targeting of monetary aggregates was tried (in the 1970s and 1980s, primarily) and it failed. The relationships among monetary aggregates, inflation, and real economic activity proved to be highly unstable, causing Old Monetarist prescriptions to work poorly. That doesn't stop the proponents of Old Monetarism -a dwindling breed- from trying. We can still find work involving searches for the elusive ideal monetary aggregate or searches for the elusive stable money demand function.

So, if inflation control through money growth targeting works poorly, what to do then? Some central banks opted to target inflation directly or, more generally, there was some recognition that the central bank should take nonneutralities of money into account, and Taylor wrote down a simple rule of thumb that would allow for that. The Taylor rule was subsequently enshrined in New Keynesian models, along with an updated version of the Phillips curve.

The Phillips curve appears to be the modern version of the wage-price spiral. Typically, that's how the inflationary process is described for the lay person. For example, here's from a recent blog post in The Economist:
The American economy, we wrote in July, almost certainly has less room to grow than it used to. Estimates of the economy's potential output, or how much it can produce at a given time without serious inflationary pressure building, have been revised down substantially by the Congressional Budget Office and other economists studying the issue.
That was from a piece on potential output in the United States, but what I am interested in is the part about "serious inflationary pressure." Apparently there is more inflationary pressure the lower is the output gap - the difference between "potential" output and actual output. Clearly the writer(s) of this blog post subscribe to a Phillips curve theory of inflation. The Old Monetarists (Friedman) and modern structuralists (Lucas) may have thought they debunked Phillips curve thinking, but it's remarkably persistent. How come?

If you think a stable money demand function is hard to find, try to find a Phillips curve in the data. As with the money demand function though, nothing stops a committed Phillips curve adherent. Whether by finding the right combination of inflation measure and output gap measure, judicious use of Bayesian estimation, or whatever, by hook or by crook a Phillips curve can indeed be uncovered in the data. But, as I outline here, it's hard to make a case that the Phillips curve is helpful for thinking about inflation, its causes, and what to do about it. For example, Phillips curves are not useful in forecasting inflation (see this paper by Atkeson and Ohanian.).

Diehard Phillips curve folks, in extreme states of denial, will insist that the output gap is a latent variable, and thus the existence of low inflation implies that the output gap must be high. Indeed, from the blog post in The Economist, quoted above, if we take potential output to be defined by the behavior of the inflation rate (as seems to be implied by the quote), we should be able to back out a measure of of the output gap from the actual inflation rate. I'm pretty sure that, if you do that exercise, you will come up with nonsense.

But perhaps the Phillips curve - even as complete fiction - has been useful, if for nothing else than to permit agreeement among policymakers. In the recovery phase of a business cycle downturn, supposing the nominal interest rate and the inflation rate are low, an appeal to the Phillips curve can help in obtaining agreement to "tighten," i.e. to raise the policy rate. Even though inflation is low, it can be argued that "inflation pressure" exists, inflation threatens, and tightening should occur before it is too late. Old Monetarists, Old Keynesians, and New Keynesians alike, might find reasons to agree on that. Indeed, I think we can write down models where this would be self-fulfilling, and that type of reasoning - though it may actually be wrong - could yield the right policy decision. The policy decision would be right in the sense that it would avoid the bad equilibrium (bad in the sense of not achieving the central bank's inflation target) that converges to the zero lower bound and low inflation forever - see this paper by Jim Bullard.

So, what does this have to do with Europe? Here's what's happened to the average of inflation rates across countries in the Euro zone:
The inflation rate has fallen dramatically, and is now well below the ECB inflation target of 2%. As well, long bond yields (in this case of 10-year bonds) are down sharply:
Today's 10-year German bond yield is even lower than when I constructed this chart - it's 0.95%, relative to 2.375% for a 10-year U.S. Treasury bond.

The recent European experience might look familiar to someone who lived in Japan, say over the period 1990-1995. Here's CPI inflation in Japan:
And here's the 10-year bond yield for Japan:
There are some differences of course, for example it took longer for the inflation rate and bond yield to fall in Japan, but the experience is roughly similar.

What is the mandate of the ECB? From the ECB's web site:
The ECB’s main task is to maintain the euro's purchasing power and thus price stability in the euro area.
In case it's not clear to you what that means, there is an explanation here. Apparently price stability means that inflation rates between 0% and 2% are more or less OK, negative inflation rates are not OK, and maybe 1.8% is more OK than 0.8%. Suffice to say, though, that the ECB is changing policy, or about to change policy, on several dimensions, so it appears to think that the inflation you see in the first chart is definitely not OK, or projected to be not OK. Draghi's press conference after the policy change makes it clear that he's worried about a decline in inflation expectations, which you can see in breakeven rates on European government bonds.

So, since it appears the ECB wants to increase the inflation rate in the Euro zone, how does it intend to to it? First, the ECB has reduced its policy rates. The interest rate on the ECB's main refinancing operations was reduced to 0.05%, and the interest rate on deposits at the ECB was reduced to -0.20%. The refinancing rate is important, as the ECB does not typically intervene directly in an overnight market as is the case, for example, in the United States, but by lending to financial institutions, and the key lending facility is "main refinancing." The ECB has also taken the unusual step of charging for the privilege of holding reserves at the ECB, i.e. the ECB currently has a -0.20% lower bound rather than a zero lower bound. People - Miles Kimball among them - who think that relaxing the zero lower bound on the nominal interest rate will solve the world's problems get very excited about this. Second, there is a central bank credit program about to get underway, i.e. TLTROs (targeted long-term refinancing operations), which is central bank lending to European financial institutions with attached incentives to encourage these institutions to lend to the private sector. Third, there are planned asset purchases by the ECB - quantitative easing (QE) - with some of the specifics to be worked out later. Again, Draghi answers some questions about this in his press conference. It seems the asset purchases will take two forms: asset-backed securities and covered bonds. A covered bond is basically a collateralized bond, secured by a specified set of assets on the issuer's balance sheet, rather than being subject to the usual seniority rules in bankruptcy proceedings.

What theory of inflation could we use to think about the ECB's change in policy? Though some deflation-scare stories sound something like old wage-price spriral stories in reverse, let's dismiss that. What about Old Monetarism? It's reported in the press conference that M1 in the Euro area was growing at 5.6% in July, and that wouldn't alarm a quantity theorist, I think. However, belief in the Phillips curve is certainly consistent with what the ECB is doing, or proposing to do. Real economic activity is deemed to be weak, so a Phillips curve adherent might think that has something to do with the low rate of inflation in the Euro zone. Then, if we follow Old or New Keynesian prescriptions, conventional monetary easing - lower nominal interest rates - should increase output and inflation. Unconventional easing (QE and relaxing the zero lower bound) could be added to the Keynesian mix, given the zero-lower-bound problem.

But what if we think more carefully about the key elements of the "easing" program?

Starting with the last policy change first - ECB asset purchases (QE) - we might ask why this might matter. The press conference I think makes clear what I have in mind. Draghi says:
So QE is an outright purchase of assets. To give an example: rather than accepting these assets as collateral for lending, the ECB would outright purchase these assets. That’s QE. It would inject money into the system.
Then later:
Let me also add one thing, because the ABS may sound more, I would say novel, than they are in the ECB policy-making, and indeed, the modality is novel, because we would do outright purchases of ABS, but the ABS have been given as collateral for borrowing from the ECB for at least ten years, so the ECB knows very well how to price and how to treat the ABS that’s accepted, especially since we have, - and this is in a sense another dimension that makes any precise quantification difficult at this point in time - we have narrowly defined our outright purchase programme to simple and transparent ABS.
So, you might ask why it would make a difference if the ECB purchases a given asset outright, vs. extending a loan to a financial institution with the asset posted as collateral. Why would there be a bigger effect - and on what - in the first case relative to the latter?

Next is the TLTRO. Details of this program can be found here and here. This is basically an incentive program for lending by ECB financial institutions, tied to main refinancing operations - a kind of subsidized lending program. There's no particular link to inflation, unless we think there is some mechanism by which more credit - or credit reallocation - matters for inflation.

Finally, let's look at the ECB's interest rate policy, which I want to spend some time on. There are two parts to this. The first is conventional easing, which in the case of the ECB is a drop in its main refinancing rate - the rate at which it lends to financial institutions. The second is unconventional - a drop in the interest rate on reserves to a lower negative rate. The key worry here is that the ECB becomes trapped in a state with low inflation and low nominal interest rates forever, and can't get out. Note that this is a policy trap, not the "deflationary trap" that some people worry about. This is what Jim Bullard discusses in this paper. It's well known that conventional Taylor rules can have poor properties, and can lead to policy traps of this type. If inflation is low, the central bank lowers the nominal interest rate, which leads to lower inflation in the long run due to the Fisher effect. Ultimately, the economy converges to a steady state at the zero lower bound with inflation lower than what the central bank wants, and it can't get out unless the policy rule changes. Further, note that relaxing the zero lower bound won't help. If the central bank charges negative interest on reserves, this only lowers the inflation rate at the low-inflation steady state.

Could a central bank actually get into a low-inflation policy trap and not figure it out? The Japanese case shows us that central bankers can be very stubborn. In the case of Europe, here's what's been happening to the overnight interest rate and the inflation rate over time:
And here's the same data as a scatter plot:
You can see that there is substantial variation in the real ex post interest rate, but the Fisher relation shows up in the scatter plot, just as it does for the United States. Given this, and the first four charts in this post, it might enter your mind that Europe might be going in the same direction that Japan did 20 or more years ago.

How could we think about monetary policy in this context? Our goal is to determine what it takes to increase the inflation rate in an economy, taking into account short run effects, and the Fisher effect, which will dominate in the long run. One model that captures some of what we might be interested in is a segmented markets model. I'm going to use it because it's simple, and the key implications may not be so different if we were to include other types of short-run monetary non-neutralities. A very simple segmented markets model is in this paper by Alvarez, Lucas, and Weber. The details of what I did are in these notes that I've posted.

In the model, there are many households which each live forever. Each has a fixed endowment of goods each period, and sells those goods in a competitive market for cash. Goods are purchased from other households subject to cash-in-advance. There are two types of households - traders and non-traders. A trader can trade in the bond market each period, and holds a portfolio of money and bonds. Non-traders do not trade in the bond market, and hold only cash. The central bank intervenes by way of open market operations, the result being that an open market purchase of government bonds initially affects only the traders. There is a nonneutrality of money, which comes about because of a distribution effect of monetary policy. An open market purchase will increase the consumption of traders in the short run, and it is the consumption of traders that determines bond prices. Thus, when the open market purchase of bonds occurs, this tends to increase consumption of traders and nominal and real interest rates go down. But standard asset pricing implies that there is a Fisher effect - higher anticipated inflation implies a higher nominal interest rate.

In my notes, I work out the local dynamics of this economy. I don't worry about liquidity traps as I'm interested in what happens when the central bank gets off the zero lower bound. If the central bank experiments with random open market operations, it will observe the nominal interest rate and the inflation rate moving in opposite directions. This is the liquidity effect at work - open market purchases tend to reduce the nominal interest rate and increase the inflation rate. So, the central banker gets the idea that, if he or she wants to control inflation, then to push inflation up (down), he or she should move the nominal interest rate down (up).

But, suppose the nominal interest rate is constant at a low level for a long time, and then increases to a higher level, and stays at that higher level for a long time. All of this is perfectly anticipated. Then, there are many equilibria, all of which converge in the long run to an allocation in which the real interest rate is independent of monetary policy, and the Fisher relation holds. A natural equilibrium to look at is one that starts out in the steady state that would be achieved if the central bank kept the nominal interest rate at the low value forever. Then, in my notes, I show that the equilibrium path of the real interest rate and the inflation rate look like this:
There is no impact effect of the monetary "tightening" on the inflation rate, but the inflation rate subsequently increases over time to the steady state value - in the long run the increase in the inflation rate is equal to the increase in the nominal rate. The real interest rate increases initially, then falls, and in the long run there is no effect on the real rate - the liquidity effect disappears in the long run. But note that the inflation rate never went down.

We could add things to this model - liquidity effects on the real rate from scarce safe assets, real effects of monetary policy on aggregate output, etc., and I don't think the basic story would change. The story is that a sustained increase in the inflation rate is not possible unless the nominal interest rate goes up. Further, note that the real interest rate goes up temporarily in the process, and with a more fully developed model, there may be pain associated with that. Of course, in economics free lunches are always hard to find. If we think that higher inflation in the long run is good for us, it's hard to imagine there wouldn't be some cost to getting there.

Tuesday, August 19, 2014

Secular Stagnation: Useful Ideas or Hot Air?

There is an ebook available on "Secular Stagnation: Facts, Causes, and Cures," which consists of a set of papers by a group of economists, brought together in an attempt to understand secular stagnation, and how we might address the problem, if it is one. Some of the papers are summaries of published or unpublished research, while others are more speculative.

What is secular stagnation? Apparently it's frequently on the lips of some people, but according to Barry Eichengreen,
...while the term ‘secular stagnation’ was widely repeated, it was not widely understood. Secular stagnation, we have learned, is an economist’s Rorchach Test. It means different things to different people.
I think the problem here is that an idea cannot be understood if it's not an idea. The people who claim that the idea exists - principally Larry Summers and Paul Krugman - trace it to Alvin Hansen's "Economic Progress and Declining Population Growth," from 1939. Nicholas Crafts summarizes what Hansen had to say:
The first time around, ‘secular stagnation’ was a hypothesis famously articulated by Alvin Hansen ... Hansen argued that the US economy faced a crisis of underinvestment and deficient aggregate demand, since investment opportunities had significantly diminished in the face of the closing of the frontier for new waves of immigration and declining population growth. It was as if the US was faced with a lower natural rate of growth to which the rate of growth of the capital stock would adjust through a permanently lower rate of investment.

As we all know, these fears were completely without foundation – the delusions of a hypochondriac rather than the insightful diagnosis of a celebrated economist.
I think we could go even further than that. Not only were Hansen's writings the "delusions of a hypochondriac," but we would have a hard time making sense of his arguments in the context of the modern theory of economic growth, and what we know about the causes of growth and the reasons for differences in standards of living across countries. Suffice to say that a re-reading of Alvin Hansen won't enlighten us as to what we should expect from the world economy over the next twenty years or so.

But, what about the contents of this ebook? There are really two parallel notions of stagnation discussed in these contributed papers. For convenience, I'll call these growth stagnation and Keynesian stagnation. The growth stagnation idea appears to take conventional economic growth theory as a basis for how we should think about future economic growth, in the U.S. and in the world. From Hsieh and Klenow, empirical work on economic growth tells us that we can account for 10-30% in income differences across countries by differences in human capital, about 20% by differences in physical capital, and 50-70% by differences in TFP (total factor productivity). This should also apply to the time series. So if, for example, we are pessimistic about future TFP growth in the U.S., we then have a strong reason to be pessimistic about future real GDP growth in the U.S. On one side of the argument, Robert Gordon is a pessimist. Gordon points out that TFP growth was much lower after 1970 than in the period from 1920-1970, and he is confident that the average rate of TFP growth we experienced for 1970-2014 will persist for the next 25-40 years. Further, he is worried about four "headwinds," i.e. demographics, education, inequality, and government debt. Basically, a smaller fraction of the U.S. population will be working, educational attainment in the U.S. has plateaued and the quality of U.S. education may be in decline, inequality in incomes has increased and may continue to do so, and there are reasons to think that government debt could increase relative to GDP.

If reading Gordon's entry in this volume is inclined to make you depressed, Joel Mokyr's piece is a great pick-me-up. He says:
There is nothing like a recession to throw economists into a despondent mood. Much as happened in the late 1930s, many of my colleagues seem to believe that ‘sad days are here again’. Economic growth as it was experienced by the world through much of the 20th century, they tell us, was a fleeting thing. Our children will be no richer than we are. Some of the best economists of our age, including Larry Summers, Paul Krugman, and my own colleague Robert J. Gordon, are joining the chorus of the doomsayers. It is said that we are faced by headwinds that inevitably will slow down growth and perhaps condemn us to secular stagnation. There is no denying that the population of the world is getting older, and that the fraction of people working (and supporting the aged) is falling everywhere except in Africa. The ‘big pushes’ driven by millions of married women taking jobs and the huge increase in college graduates that drove post 1945 growth were one-off boons, but they are no more. Growing inequality exacerbates demography. Slow growth is here to stay, say the secular stagnationists.

What is wrong with this story? The one word answer is ‘technology’. The responsibility of economic historians is to remind the world what things were like before 1800. Growth was imperceptibly slow, and the vast bulk of the population was so poor that any disruption in food supply caused by a harvest failure could kill millions. Almost half the babies born died before reaching the age of five, and those who made it to adulthood were often stunted, ill, and illiterate. What changed this world was growth driven by technological progress. Starting in the late 18th century, innovations and advances in what was then called ‘the useful arts’ slowly began improving life, first in Britain, then in the rest of Europe, and eventually in much of the rest of the world. The story has been told many times over, but as Nobelist Robert Lucas once wrote, once you start thinking about it, it’s hard to think of anything else.
So, we should stop moaning, and recognize that life is pretty good and likely to get much better.

Mokyr's point is that there is much important scientific advance happening right under our noses, and that this new science will be applied in many ways that we might find hard to imagine from our 2014 viewpoint, just as Alexander Graham Bell would have a hard time imagining an I-phone. Further, the effects of current and future innovations on economic welfare may not be measured well. For example, information has become much more accessible in myriad ways that make us better off, but not all of that is captured in GDP.

Technological change does create economic problems that we need to deal with, though. It is now well-understood that an important factor in the increase in the dispersion in income in the U.S. in the last 30 years or more has been technological change. This change can bring huge rewards to innovators while depreciating particular types of human capital. For example, David Autor has written about the hollowing out of the skill-distribution because information technology makes middle-level skills obsolete. This then becomes a challenge for U.S. education. Indeed, better access to public education at all levels is a possible remedy for the income-distribution problem that Gordon seems to be concerned with.

In terms of the growth stagnation story, there is nothing in this volume that sheds new light on the growth process, and would permit us to confidently project stagnation in the medium to long term, in the U.S., or in the world. We know a lot about how TFP, human capital accumulation, and physical capital accumulation, work to produce growth in per capita incomes, but we perhaps know little about the actual process of innovation, and how to predict it.

The idea that seems to have spurred the publication of this volume, however, is not growth stagnation, but Keynesian stagnation. But Keynesian stagnation does not appear - at least to me - to be in the Keynesian tradition. Keynesians have been quite comfortable with the idea that mainstream growth theory could guide our thinking about "long-run" issues, while sticky-price and sticky-wage economics could guide our thinking about "short-run" issues. For example, Robert Solow provided us with the foundation for modern growth theory, but also wrote (with Paul Samuelson) a classic paper on how to exploit the Phillips curve tradeoff. Similarly, Mike Woodford took a several-generations-later version of Solow's growth model (with credit to Cass, Koopmans, Brock, Mirman, Kydland, and Prescott, along the way), put in some sticky prices and monetary policy, and convinced central bankers that it would be a good idea to use such a model to think about short-run monetary policy. New Keynesian models have the property that monetary policy is non-neutral in the short run, but the mechanics of the basic growth model take over in the long run.

This is definitely not what Larry Summers and Paul Krugman have in mind. Here's the basic hypothesis, as stated by Summers:
Unfortunately, almost all work in both the New Classical and New Keynesian traditions has focused on the second moment (the variance) of output and employment. This thinking presumes that, with or without policy intervention, the workings of the market will eventually restore full employment and eliminate output gaps. The only questions are about the volatility of output and employment around their normal levels. What has happened in the last few years suggests that the second moment is second-order relative to the first moment – the average level of output and employment through time.
I'll take "New Classical and New Keynesian traditions" to be represented by the ideas of Mike Woodford - prices and/or wages are sticky in the short run, and in the long run the world works according to the Solow/Cass/Koopmans/Brock/Mirman/Kydland/Prescott growth model. But what Summers sees is a world that is not at "full employment" even in the long run. He doesn't say this, but presumably he thinks that price rigidity and/or wage rigidity can persist indefinitely.

So what's the problem? Summers points out that the real rate of interest has declined over time, and argues - in typical New Keynesian fashion - that this has created a zero-lower-bound problem. The actual real rate has fallen, but it should be lower than it is (the "natural rate" is lower than the actual real rate), but monetary policy cannot lower the real rate further, because the short-term nominal interest rate is at its lower bound of zero. Summers argues that this problem could persist long into the future. Stagnation is then essentially a nagging output gap, that monetary policy cannot correct in the "usual" fashion. Paul Krugman is basically on the same wavelength.

If you are a young macroeconomist, you might be thinking of Summers and Krugman as some creaky dinosaurs blowing hot air. Where is your model, Summers and Krugman, you might say. Well, Eggertsson and Mehrotra have fleshed out a theory that they think captures what Summers and Krugman are trying to get at. The Eggertsson and Mehrotra chapter in this volume is a summary of a formal academic paper that I discussed in this post. The gist of that blog post is that Eggertsson and Mehrotra - as with Eggertsson/Krugman, which is closely related - focus on the wrong problem. The key inefficiency in their model arises from a credit friction, but they are focusing their attention on the secondary zero-lower-bound inefficiency that the credit friction creates. Basically, the problem is insufficient government debt, and the solution is straightforward.

Now we are getting somewhere. The contribution in this volume from Cabellero and Farhi gives a nice synopsis of safe asset shortages and why such shortages produce the low real interest rates we have been observing. Before the financial crisis, high savings in the world combined with financial innovation created a high demand for safe assets - as stores of wealth, as collateral, and for exchange in asset markets. Governments can supply safe assets, but the private sector can also do it. So, if governments do not increase their outstanding debt in the face of an increased demand for safe assets, then the price of safe assets rises and real interest rates fall. This creates a profit opportunity for the creation of safe private assets. Indeed, asset-backed securities could perform such a role. But the financial crisis showed us that, in the face of poor regulation, the capacity of the private sector to produce safe assets can be limited. Further, when the private sector builds up a stock of "safe" assets which proves not be safe, the ensuing destruction and loss of trust can result in persistent inefficiencies.

The private sector is rebuilding its capacity to produce safe assets, but changes in private sector regulation are also serving to increase the demand for safe assets. For example, the liquidity coverage ratio included in Basel III banking regulation will create an additional demand for safe assets by commercial banks. Though there are things that central banks can do in the face of safe asset shortages (as I show here and here), a safe asset shortage is basically a fiscal problem. The safe asset shortage is reflected in binding financial constraints that imply the economy is non-Ricardian. Government debt matters, and an expansion in the stock of government debt can be welfare improving. Presumably this also implies a lower net cost of financing government projects, meaning that a safe asset shortage provides an opportunity for the government to finance education and infrastructure on the cheap. Note that we can come to that conclusion without ever invoking stickiness, multipliers, fallacy-of-this, or fallacy-of-that.

An interesting feature of this paper is that it captures some of Larry Summers's concerns about monetary policy and financial stability. In the model, when there is a shortage of safe assets, low real interest rates can create incentive problems in asset markets. Basically, creating safe private assets is profitable when the real interest rate is low, but misrepresenting unsafe assets as safe ones is potentially even more profitable. Conventional monetary easing acts to reduce the real interest rate, and therefore aggravates incentive problems. Indeed, if incentive problems are severe enough, a safe asset shortage induces a situation in which the central bank should not push the nominal interest rate to zero.

The editors of this volume, Coen Teulings and Richard Baldwin, seem convinced that the potential for secular stagnation, whatever it may be, requires some radical rethinking of policy approaches. I don't think so. While there is much we don't know about how economies work, and we continue to learn, normal economics is certainly not at a loss in dealing with the problems we face, or will face.


Monday, August 4, 2014

The ON RRP Facility and Post-Liftoff Fed Policy

[See some related ideas in a post by John Cochrane.]

When the FOMC ultimately decides that short-term nominal interest rates in U.S. financial markets should rise, a lot will have changed since pre-financial crisis times. Principally, the Fed's balance sheet is about 5 times larger, total reserves have increased from about $10 billion on average in 2007 to about $2.8 trillion currently, and the Fed now pays interest on reserves.

Any central bank with a significant quantity of excess reserves outstanding overnight operates within a floor system, in which the interest rate on overnight liabilities of the central bank determines the overnight interest rate - in a financial system with no significant frictions. In the case of the U.S. Federal Reserve System, the frictions make all the difference, and create a thorny monetary policy problem for liftoff from essentially-zero overnight nominal interest rates.

The Fed's problem would be easy in a financial system like that in Canada, for example. In normal times, the Bank of Canada operates under a channel system. It targets an overnight interest rate, which is subject to an upper bound, which is the rate at which the Bank lends to financial institutions (the "Bank rate"), and a lower bound, which is the deposit rate for financial institutions at the Bank - the counterpart of the interest rate on reserves, or IOER in the U.S. Typically, the Bank rate is set at 0.25% above the target, and the deposit rate at 0.25% below the target. The idea is that no financial institution would borrow from another one at a rate above the Bank rate, nor would it lend to another financial institution at a rate below the Bank's deposit rate, so arbitrage will keep the target rate between the upper and lower bounds. Here's a chart showing the actual overnight rate in Canada:
Typically, the Bank pretty much nails its target. For example, in the chart, the target since mid-2010 has been 1%, and there has been little variability in the actual overnight rate around the target. An important point to note here is that lending and borrowing at the overnight rate is secured - this is a repo market.

Though normally the Bank of Canada operates a channel system, from April 21, 2009, to June 1, 2010, there was a floor system in Canada. Over this period, the Bank's deposit rate and the target rate were both set at 0.25%, with the Bank rate at 0.50%. Commensurate with that configuration of policy rates, the Bank also kept a positive quantity of reserves in the financial system overnight:
In Canada, there are no reserve requirements on banks. Overnight reserves would be zero, but for some slippage due principally to bad timing. For example, a financial institution could receive a large payment near the end of day, in which case it would be convenient to hold this as reserves overnight (no idea what was going on in early 2012). During the floor system period, you can see that the Bank of Canada targeted the quantity of overnight reserves at $3 billion - what the bank thought was sufficient reserves so that the floor of 0.25% would bind. With a floor system in place, there are sufficient reserves overnight such that arbitrage dictates that the overnight interest rate is equal to the interest rate on reserves.

But, you might say, that's not what has been happening in the United States since the financial crisis. There is a very large quantity of excess reserves in the U.S. financial system, and the IOER has been set at 0.25% since late 2008, but the fed funds rate - the overnight rate the FOMC currently focuses on - looks like this:
So, typically, fed funds have been trading below the IOER, and the interest rate differential has tended to increase over time. Over the last year, fed funds have typically been trading at 15 basis points or more lower than the IOER. Clearly, something is inhibiting arbitrage. What is it?

When Congress amended the Federal Reserve Act to permit payment of interest on reserves by the Fed, it specified that government-sponsored enterprises (GSEs) could not receive these payments. The key GSEs that matter in this respect are Fannie Mae, Freddie Mac, and the Federal Home Loan Banks (FHLBs). Most people know what Fannie Mae and Freddie Mac are up to, but most economists I have run into had no idea until recently what a FHLB is. The FHLB system was set up during the Great Depression as a housing finance vehicle. There are twelve FHLBs, each with a district (much like Fed districts, though FHLB districts are not identical to Federal Reserve districts) and member financial institutions. The members each hold nontradeable stock in the FHLB, and the primary activity of a FHLB is issuing tradeable securities to finance lending to member institutions. This lending is typically secured by mortgages, and the intention seems to be to direct financing toward low-income mortgage borrowers. FHLBs also hold a relatively small portfolio of mortgages, purchased outright. As is the case with Fannie Mae and Freddie Mac, FHLBs have reserve accounts with the Fed and, since GSEs receive zero interest on those reserve balances while commercial banks and other financial institutions currently receive interest at the current IOER rate of 0.25%, there would appear to be gains from trade.

GSEs which would otherwise hold reserve balances overnight could lend overnight on the fed funds market to commercial banks, for example. Those commercial banks could then hold the funds as reserves overnight, earning 0.25%, pay the GSEs x%, where 0 < x < 0.25, make a profit, and the GSEs and commercial banks would be better off as a result. Indeed, frictionless arbitrage would dictate that the GSEs would get all of the gains from trade, with x = 0.25. Why is this arbitrage activity, between GSEs and financial institutions with interest-bearing reserves important? Given that the U.S. financial system is awash in reserves, we might predict that there would be little reason for any financial institution to borrow on the fed funds market overnight, so that most fed funds activity should currently just be arbitrage. Indeed, Afonso et al. estimate that about 75% of lending on the fed funds market was accounted for by FHLBs, by the end of 2012.

But why is the arbitrage not perfect, or even close to it? Financial institutions that receive interest on reserves also face balance sheet costs associated with borrowing on the fed funds market. For example, deposit insurance premia depend on total assets, and there are capital requirements and other restrictions on commercial banks. As a result, the cost of fed funds borrowing is idiosyncratic - it will depend on a bank's size, and on the composition of its portfolio, for example. Of particular note is that branches of foreign banks in the U.S., because they do not have domestic retail deposits, do not pay deposit insurance premia, so they have a cost advantage over domestic banks in borrowing on the fed funds market. What would we predict then? Branches of foreign banks should be borrowing fed funds from FHLBs. Again, Afonso et al. estimate that, by the end of 2012, about 60% of borrowing on the fed funds market was being done by foreign-owned banks.

Liftoff?
Once liftoff occurs, presumably with a stock of reserves in the financial system that is on the order of what it is currently, what would happen if the Fed adhered to its existing operating strategy? One might expect that, as the IOER increased, the fed funds rate would follow. Perhaps the current margin of about 15 basis points between the IOER and the fed funds rate would be maintained. Perhaps that margin would increase. It's hard to say, given our imperfect understanding of what explains the margin in the first place. One might also ask: who cares about the margin anyway? Surely the overnight rate that is critical to most financial market participants is the IOER? Maybe in this idiosyncratic floor system we should be ignoring fed funds market activity, as that is just about arbitrage between GSEs and foreign-owned banks?

There are other alternatives, though. The New York Fed has been conducting experiments using an overnight reverse repurchase agreement (or ON RRP) facility. A reverse repo for the Fed consists of a loan, typically overnight, to the Fed, secured by collateral (typically Treasury securities) from the Fed's asset portfolio. But why would the Fed need to post collateral on a loan? Surely the Fed is good for it? But, if the Fed were to borrow unsecured, we would call that reserves. If the Fed borrows by way of reverse repos, then it is permitted to pay interest to anyone, including GSEs, and it can also borrow from financial institutions that do not hold reserve accounts. Indeed, to enlarge the set of financial institutions that can hold interest-bearing Fed liabilities, the New York Fed has approved an expanded list of counterparties which includes domestic commercial banks, foreign-owned banks, GSEs (including some FHLBs) and money market mutual funds (which do not have reserve accounts). ON RRP activity by the Fed is shown in the next chart:
We should then think of ON RRPs simply as reserves by another name. Relative to regular reserves, the only difference is that reserves are unsecured while ON RRPs are secured, but since the Fed is the borrower, that's irrelevant. The only relevant difference between reserves and ON RRPs is that, while some financial institutions (e.g. commercial banks) can hold both reserves and ON RRPs and earn interest on both, some financial institutions (GSEs) hold reserves at 0% interest and ON RRPs with positive interest, and some other financial institutions (e.g. money market mutual funds) cannot hold reserves at all, but can hold ON RRPs.

But, given that the ON RRP facility now exists, what to do with it? To figure this out, it helps to understand how policy would work in the liftoff phase in the absence of ON RRPs. Given the size of the Fed's portfolio, total liabilities of the Fed - in this case currency and reserves - is essentially fixed in nominal terms. For a particular IOER, asset prices, the prices of goods and services, and quantities, including the fraction of Fed liabilities held as reserves, adjust so that consumers and financial institutions are willing to hold the total stock of Fed liabilities. If the Fed sets a higher IOER, then everything adjusts, and presumably the fraction of Fed liabilities consisting of reserves will increase.

Now, throw ON RRPs into the mix. There are different ways in which the Fed could intervene in the repo market. For example, the Fed could decide on a quantity of borrowing on a particular day, and then conduct an auction among its counterparties. However, what the Fed seems to ultimately envision is a "fixed rate, full allotment" allocation mechanism, according to which a rate is set, and the fed accepts whatever is forthcoming at that rate. So far, full allotment appears not to have been attempted, as the ON RRP experiments conducted by the New York Fed, beginning in January of this year involved putting per-counterparty caps on takeup, with a fixed rate of .05%. Caps were increased over time, to $10 billion per counterparty in April 2014. As you can see in the last chart, outstanding ON RRPs in the last few months have come in mostly between $200 billion and $300 billion - on average somewhat less than 10% of total interest-bearing Fed liabilities.

Given a setting for IOER, there will in general be some critical value for the spread between the IOER and the ON RRP rate such that takeup is zero below that rate, and positive above it. From the New York Fed's experiments, it seems we are safe in assuming that this critical spread is at least 20 basis points. Further, suppose the spread is lower than the critical value, and the ON RRP rate increases with IOER held fixed. What happens? Fed liabilities will in general be more attractive, and ON RRPs will be more attractive relative to either reserves or currency. We would expect that short-term market interest rates would increase (not IOER of course), and more Fed liabilities would be held in the form of ON RRPs, with less held as reserves and currency. For example, perhaps some FHLBs which would formerly have been lenders on the fed funds market would now hold ON RRPs. This would reduce reserves and activity on the fed funds market.

Clearly, given the IOER, the ON RRP rate can be sufficiently high that reserves go to zero. That is, we know that if the ON RRP rate exceeds IOER, then no financial institution would wish to hold reserves. But, it's possible that reserves could go to zero with the ON RRP rate less than IOER, if there is sufficient demand for ON RRPs from the GSEs and money market funds. Further, with sufficient interest-bearing Fed liabilities in the system, it is possible that the ON RRP rate could be high enough that fed funds market activity could dwindle essentially to zero. We know that much of current fed funds market activity is just the result of arbitrage between GSEs and banks that earn interest on reserves, and this arbitrage activity would go away with a sufficiently high ON RRP rate.

Concerns
So, now that we have thought through how a system with three primary Fed liabilities - currency, reserves, ON RRPs - might work, what potential concerns might there be with such a framework?

1. There is potentially a lot going on here. How will the FOMC communicate monetary policy actions to the public in a simple and clear fashion? This was one of the subjects of discussion at June FOMC meeting (see the minutes):
Most participants agreed that adjustments in the rate of interest on excess reserves (IOER) should play a central role during the normalization process. It was generally agreed that an ON RRP facility with an interest rate set below the IOER rate could play a useful supporting role by helping to firm the floor under money market interest rates. One participant thought that the ON RRP rate would be the more effective policy tool during normalization in light of the wider variety of counterparties eligible to participate in ON RRP operations. The appropriate size of the spread between the IOER and ON RRP rates was discussed, with many participants judging that a relatively wide spread--perhaps near or above the current level of 20 basis points--would support trading in the federal funds market and provide adequate control over market interest rates. Several participants noted that the spread might be adjusted during the normalization process. A couple of participants suggested that adequate control of short-term rates might be accomplished with a very wide spread or even without an ON RRP facility. A few participants commented that the Committee should also be prepared to use its other policy tools, including term deposits and term reverse repurchase agreements, if necessary. Most participants thought that the federal funds rate should continue to play a role in the Committee's operating framework and communications during normalization, with many of them indicating a preference for continuing to announce a target range. However, a few participants thought that, given the degree of uncertainty about the effects of the Committee's tools on market rates, it might be preferable to focus on an administered rate in communicating the stance of policy during the normalization period. In addition, participants examined possibilities for changing the calculation of the effective federal funds rate in order to obtain a more robust measure of overnight bank funding rates and to apply lessons from international efforts to develop improved standards for benchmark interest rates.
To clarify what is going on here, if the Fed continues to announce policy in terms the fed funds market, this would require that the ON RRP rate be set sufficiently low relative to the IOER so that the fed funds market remains active. Use of the ON RRP facility has some advantages in this context. It works against segmentation in financial markets and thus gives interest-bearing Fed liabilities a broader reach, and it also puts a floor under the fed funds rate. The higher the ON RRP rate relative to the IOER, though, the less fed funds market activity there would be, and the greater the fraction of the interest-bearing Fed liabilities consisting of ON RRPs. Indeed, if the ON RRP rate were equal to the IOER, this might imply that most of the stock of Fed interest-bearing liabilities would be in the form of ON RRPs, as it is less costly for the GSEs and money market funds - which cannot earn interest on reserves - to intermediate ON RRPs than it is for commercial banks to intermediate reserves. Presumably the money market funds would expand and the commercial banks would contract.

2. A large ON RRP facility could eliminate fed funds market activity. Some people might ask why we should care. Borrowing on the fed funds market is unsecured, so each fed funds contract reflects idiosyncratic risk. In general, the "fed funds rate" is not a rate - it's a distribution. And in times of financial stress, the dispersion in that distribution can be substantial. You can see that in Figure 3 of this paper by Afonso et al. To get some idea of how risky the average fed funds market trade is, consider the margin between the fed funds rate and the 1-month T-bill rate in the next chart:
You can see that, even in normal times, there is a subsantial amount of risk in the fed funds market, and risk went up substantially during the financial crisis. We can certainly make a case that a central bank should be targeting an essentially risk-free overnight rate. Other central banks, including the Bank of Canada and Bank of England, see fit to target a repo rate.

In addition to the fact that the fed funds market is risky, a second problem is that the measured effective fed funds rate does not include all fed funds market trade, but only exchange through brokers. A large fraction of fed funds market activity is over-the-counter, and therefore goes unmeasured. There are indirect ways of measuring activity on the fed funds market, but these are problematic.

A third problem with the fed funds market is that central bank intervention in this market is unwieldy. In pre-financial crisis times, the New York Fed would attempt to hit a given fed funds rate target by predicting, on a given day, the demand for reserves, and then supplying the quantity of reserves that would satisfy demand at the target interest rate. This has lead to substantial fluctuations in the effective fed funds rate around the target, particularly during times of high financial market volatility. During the financial crisis, in addition to the problem that the fed funds rate was a questionable measure of the tightness of monetary policy (due to risk), the New York Fed seems to have had significant difficulty hitting the target.

All of these problems highlight the advantages of the ON RRP facility, and of the ON RRP rate as a permanent target for the FOMC. ON RRP activity is secured, so the ON RRP rate is essentially risk-free, and hitting a given ON RRP rate target is trivial using fixed-rate full-allotment. The Fed would simply fix a rate, and then accommodate forthcoming demand at that rate.

3. A dual system, with IOER above the ON RRP rate, would be more costly than it needs to be. Because holding interest-bearing Fed liabilities is more costly for domestic commercial banks than for foreign owned banks, GSEs, and money market funds, the Fed has to pay a premium to get banks to hold reserves. Thus, the Fed could achieve a given level of monetary accommodation, at lower cost, if the IOER is equal to the RRP rate, than if there were no ON RRP facility. This is roughly what Jeremy Stein is getting at:
You’re saving the taxpayer a little bit of money. You might say one job you give to the Fed is to fund its balance sheet as cheaply as possible.

4. A large ON RRP facility could make the financial system less stable. Sheila Bair, for example, has argued that a fixed rate full allotment ON RRP facility would create a kind of escape route for the liability-holders of financial intermediaries to run to in the event of perceived financial distress.
Even a relatively minor market event could encourage a massive flow of funds to the Fed while contributing to a flow away from other short-term borrowers.
Students of money and banking history might find that argument curious. To quote from the original Federal Reserve Act, Congress wanted to
... provide for the establishment of Federal reserve banks, to furnish an elastic currency, to afford means of rediscounting commercial paper, to establish a more effective supervision of banking in the United States, and for other purposes.
The idea behind "furnishing an elastic currency" was to provide an escape route. The recurrent banking panics during the National Banking era (1863-1913) were essentially shortages of retail media of exchange. The ability of the banking system to supply media of exchange was impaired during panics, and this disrupted payments and aggregate economic activity. Unfortunately, the National banking system was not designed to take up the slack. With the Federal Reserve System in place, however, the Fed could act to make up for the financial disruption during a panic by supplying more currency, either through discount window lending or open market purchases. Disruption associated with repo runs is not so different. Repos are liquid assets - media of exchange - which are provided by private financial intermediaries. In times of financial stress, as during the recent financial crisis, the repo market can be disrupted. In such circumstances, it is the job of the central bank to take up the slack. One way to do this would be through a ON RRP facility. The private sector could be having a difficult time finding liquid assets, and the Fed could supply them through the ON RRP facility.

So, in conclusion, the ON RRP facility seems neither mysterious nor scary, and could play an important role in U.S. monetary policy in the future.

Tuesday, July 15, 2014

Monetary Policy: Canada and the United States

Since the financial crisis, monetary policy has been strikingly different in Canada and the U.S. The first chart shows overnight nominal interest rates - the overnight money market rate in Canada and fed funds rate in the U.S.
The fed funds rate has been below 0.25% since late 2008, but the Bank of Canada achieved liftoff in mid-2010, and the overnight rate in Canada has been at 1% since then. What about central bank balance sheets?
In Canada the size of the balance sheet increased modestly during the last recession, then declined somewhat. Currently total assets held by the Bank of Canada are slightly less than 5% of GDP. But, as is well-known, successive rounds of quantitative easing (QE) have increased the size of the Fed's balance sheet substantially, to close to 25% of GDP. As is also well-known, QE has lengthened the average maturity of the assets on the Fed's balance sheet. Currently, about 2/3 of the Fed's Treasury security holdings exceed 5 years to maturity, and the Fed holds a large quantity of long-maturity mortgage-backed securities. The next chart shows the composition of the Bank of Canada's portfolio of Canadian government debt.
In contrast to the Fed, which has reduced its holdings of Treasury bills to zero, the Bank of Canada still holds a large fraction of its assets as T-bills, though this fraction has come down since before the financial crisis. However, most of the shift in the Bank of Canada's portfolio was out of T-bills and into government bonds with maturity less than three years. Before the financial crisis, the Bank held about 2/3 of its portfolio of government debt in maturities less than three years, and that is roughly the case currently.

So, since the end of 2007, the Bank of Canada has increased the size of its balance sheet by a small amount, and lengthened the maturity of its government securities, also by a very small amount. There's really not much going on relative to the large QE intervention that occurred in the U.S., which included the purchase of a large quantity of asset-backed securities. Thus, the conventional view, given the currently higher overnight nominal interest rate in Canada, would be that Canadian monetary policy is substantially tighter than in the U.S. So, if I were a strong believer in the persistent real effects of monetary policy, if I thought that lower nominal interest rates meant higher inflation, and if I think that QE works as advertised, I might think that: (i) real economic activity should be depressed in Canada relative to the U.S., and (ii) inflation should be lower in Canada than in the the U.S. Is that what happened? First, real GDP:
The U.S. lost some ground to the U.S. during the recession, but growth in the recovery phase has been roughly similar. Next, the PCE deflator:
Again, there is a level effect in Canada vs. the U.S., relative to 2007Q4, but in the recovery phase the PCE inflation rate is roughly the same in the two countries, though somewhat higher in Canada in the last couple of years.

So, if you were to ask your average macroeconomist to back out monetary policy in Canada and the U.S. by looking at the last two charts, that person might tell you that it was about the same. But we know it wasn't.

I have seen a lot of stories recently about the effects of monetary policy on asset prices - bubbly talk, basically. If we take those stories seriously, we might expect to see more asset value appreciation in the U.S. than in Canada. In the stock market, that is certainly the case. The next chart shows the S&P 500 index, and a comparable measure for Canada.
But, not so for the housing market (these house price measures are not really comparable - Case/Shiller compared to a new house price index for Canada; but that's the best I could do):

So, maybe monetary policy - conventional or unconventional - isn't as big a deal as some people think it is.

Monday, June 2, 2014

Depreciation

From a post by Brad DeLong on Krusell and Smith's comment on Piketty's "Capital in the Twenty-First Century:"
As time passes, it seems to me that a larger and larger fraction of Piketty's critics are making arguments that really make no sense at all--that I really do not understand how people can believe them, or why anybody would think that anybody else would believe them. Today we have Per Krusell and Tony Smith assuming that the economy-wide capital depreciation rate δ is not 0.03 or 0.05 but 0.1--and it does make a huge difference...
From page 43 of Piketty's book:
This depreciation is substantial, today on the order of 10 percent of GDP in most countries...

Sunday, June 1, 2014

Change of Venue

I will shortly be taking up a full-time position in the Research Department of the Federal Reserve Bank of St. Louis. The Federal Reserve System has always been good to me, in spite of the grief I give the Fed from time to time. I'm looking forward to working with a first-class group of economic researchers, under superb leadership. We all intend to collectively move the institution forward to even bigger and better things.

Readers should not notice much difference in what I do here. I have to be a little more careful, I have to respect blackout periods around FOMC meetings, and sometimes I'll know things that I'm not permitted to tell you. You'll notice a disclaimer at the top of the page. That's essentially what appears (except for the "potshots") in the published work of Fed employees. The idea here is the same. What I write here need have nothing to do with the St. Louis Fed's position, the Federal Reserve System's position, the Board of Governors position, etc., on anything. But I don't intend to shy away from discussing policy issues.

Tuesday, May 13, 2014

Secular Stagnation and Forgotten Monetary Economics

Since Larry Summers's talk at the IMF in November, there has been some blog discussion of "secular stagnation." The secular stagnation idea seems to have originated with Alvin Hansen (AER, 1939), but I assure you that reading that will not enlighten you as to why we may or may not have entered a period of secular stagnation.

I have been as puzzled as anyone about secular stagnation and what it might mean, and I'm not sure that Paul Krugman's latest post on the topic helps much. There are three dimensions of aggregate economic data that Krugman wants us to think about, and he argues that these reflect aspects of secular stagnation. The first is the decline in the real rate of return on short-term government debt that has occurred since 1980. On this, I think it helps to broaden our perspective a bit, and look at a longer time series. The next chart shows the 3-month T-bill rate, minus the pce inflation rate (year over year) for the period 1948-2014.
If we take this as a measure of the real interest rate, we can see the decline in the real rate from 1980 to the present, which Krugman wants to draw our attention to. But, given the fact that the average real rate over the sample we're looking at is 1.13% (as shown in the chart) the 1980-2000 period is not the best benchmark we could choose, as the real rate was well above the sample average for most of that period. The real rate has certainly been low - on average - since 2000, but it was also low in the 1950s and the 1970s. So, in terms of this measure of the real rate, the low real rates we have been observing are not unprecedented, and there appears to be no particular reason for us to extrapolate low real rates into the future for a long period of time. Indeed, there are good reasons to think that the real rate should continue to increase. This is important, as it seems to be a key part of the Summers/Krugman narrative on secular stagnation. Summers and Krugman think that there is something that will keep the real rate low for an extended period of time and that - in Old Keynesian or New Keynesian fashion - this requires an extended period of time during which the central bank's nominal policy interest rate should be at the zero lower bound.

The other two aspects of the data that Krugman wants to focus on are the drop in household debt since the last recession, and the drop in the growth rate of the population aged 20-64. Through back-of-the-envelope calculations, Krugman translates what he sees in the data into a drop in the demand for consumption and investment of 7% of GDP, which I'm assuming he thinks will persist indefinitely. Of course, if we look at these observations through the lens of conventional long-run economics, the view for the future is anything but gloomy. Krugman is thinking that the increase in the savings rate as the result of low household debt, and the drop in the working-age population growth rate are bad news. But the Solow growth model - which forms the basis for modern growth theory, and which we teach to undergraduates (see Chapter 7 of this fine intermediate macro book) - tells us that an increase in the savings rate and a decline in the population growth rate will lead to a short run increase in the growth rate of per capita real income and a long run level increase in per capita real income. That seems like a good thing. So Krugman must have some kind of unconventional long-run economics in mind. But what is it?

I've been meaning to read "A Model of Secular Stagnation," by Gauti Eggertsson and Neil Mehrotra (E/M), which Gauti posted last month, but other things got in the way. E/M seems to have Krugman's blessing, and Simon Wren-Lewis provides some explanation, for those who might not be familiar with what E/M are doing. As far as I know E/M is the only attempt at making rigorous economic sense of what Summers and Krugman have been talking about.

So what is in the paper? E/M construct a 3-period-lived overlapping generations (OG) model to address the problem. Stripping their model down to essentials, suppose the population at each date consists of the young, the middle-aged, and the old, and that the total population grows at rate g. To start with, this is an endowment economy in which the young and old are endowed with nothing, and each middle-aged person has an endowment of y units of a perishable consumption good. Each person wants to consume in all periods of life, has time-separable utility, and discount factor B. Assuming that there are no assets in this economy - no money, no government bonds, no capital - the only exchange in this model is in a credit market in which the young are borrowers and the middle-aged are lenders. The young borrow, pay back their loans in middle-age, and use the returns on their loans to the young to consume in old age.

E/M add to this a borrowing constraint. There is an exogenous quantity d, which is the maximum amount that a borrower can commit to repay in the next period. Then they follow Woodford in treating this as a "cashless economy" in which zero money balances are held at all dates, and there are prices of goods in terms of money that support that equilibrium. Then, in a fashion familiar to everyone who has seen short-run New Keynesian models, wage/price rigidity is imposed - here in the form of permanent wage rididity - and then the model behaves much like in Eggertsson and Krugman's paper, except in a long run context. There are paradoxes of thrift, toil, and flexibility, more government spending is a good thing, etc.

For what I want to do, a 3-period OG model is not the best vehicle, as it has "startup" problems. Once we introduce other assets, it won't have nicely behaved equilibria. The following model will give us almost exactly the same thing as the E/M model does, but it's more tractable. Suppose an initial group of old people (who will come in handy later) who live only one period, with everyone else being two-period-lived. At each date there is a group of young and a group of old, and the total population grows at rate g. There is heterogeneity in each generation. A fraction a of economic agents are lenders who receive y units of the consumption good when young and 0 when old, and a fraction 1-a of borrowers who receive 0 when young and y when old. We'll assume log utility and discount factor B, as in E/M.

Unconstrained Cashless Economy
Without other assets in this economy, we just have a sequence of two-period Fisherian economies in which there is an intragenerational credit market with real interest rate r. With no borrowing constraints, the equilibrium interest rate is

(1) r = (1-a)/aB - 1

So, the real interest rate is determined by the discount factor and the ratio of borrowers to lenders. We can have a very low real rate if there are many lenders and few borrowers.

Constrained Cashless Economy
Now impose a binding borrowing constraint d on what a borrower can repay in old age. Then, the real interest rate is

(2) r = [(1-a)d(1+B)]/(Bya) - 1

So, in this case, the real interest rate is lower the lower is d, i.e. the tighter is the borrowing constraint. This is of course standard behavior in models with borrowing constraints - e.g. incomplete markets models.

E/M want to argue - in standard Woodford fashion - that for economic agents to be content with holding zero money balances in equilibrium, we must have

r >= -i/(1+i),

where i is the inflation rate. So if r is very low, then i must be very high so that the real rate of return on money does not exceed the real rate of interest.

So, now we have a problem. Woodford constructed his cashless economies so as to focus his attention on a sticky price friction. In doing so he was implicitly (or sometimes explicitly) stating that other types of monetary frictions do not matter much, or were safely ignored for the problems he was interested in. To show that a cashless economy made sense technically, Woodford constructed simple examples where this works, for example with money in the utility function (and separability) or by taking the "cashless limit" in an economy where money is used in transactions. It's not clear how this works in the context of this OG model, as of course these models were constructed and used, for example by Samuelson and Peter Diamond, as models in which outside assets (money and government debt) could matter.

Indeed, there are two potential inefficiencies that exist in this model (depending in part on how we define inefficiency). One is due to the borrowing constraint - a standard credit friction. The other is a standard dynamic inefficiency. And both of those frictions are things that we often use, in various contexts, to motivate a role for government and central bank liabilities.

Monetary Economy
Following up on that thought, suppose that we introduce a fixed stock of money, M, which is the collective endowment of the first period old. Then, we can construct equilibria in which this money is valued. But, the "cashless" equilibria we already worked out (equations 1 and 2) are also equilibria - what we call the "nonmonetary equilibria," for which money is not accepted in exchange because it is not accepted in exchange, and it thus has zero value. But what we are interested in are monetary equilibria, and we will restrict attention to stationary ones - equilibria where consumption allocations are constant across generations.

First, in the unconstrained case with no borrowing constraint, in the monetary equilibrium we are interested in,

(3) r = -i/(1+i) = g,

and this equilibrium exists if and only if

(4) B(1+g) > (1-a)/a

Then, either the monetary equilibrium exists, and it's Pareto optimal, or (4) does not hold, in which case the nonmonetary equilibrium is Pareto optimal. So, without the borrowing constraint, a fixed stock of money solves the dynamic inefficiency problem.

Next, suppose that there is a binding borrowing constraint. Then the real interest rate is the same as in equation (3), in the absence of other assets. But, suppose we introduce money, as before, as a fixed stock M of cash balances initially endowed to the old in the first period. As well, suppose the government can issue one-period government debt, and can tax lump-sum. But the government has some constraints on how it can tax, in that the young and old can be taxed differently, but all members of the same generation bear the same tax. So, suppose the government issues b units of government debt per young person each period, makes a lump-sum transfer b to each young person, and pays off the government debt (which is a perfect substitute for private loans) by taxing each old person lump-sum. Then, suppose that the government sets the level of government debt per young person at

b = y/[(1+g)(1+B)]

forever. If (4) holds, there exists a Pareto-efficient equilibrium with valued money, no matter how small d is, as that equilibrium has zero lending. It's the same equilibrium allocation we supported with no borrowing constraint and money as the only asset. If (4) does not hold, then we can obtain a Pareto efficient equilibrium in which money is not valued if the government sets the debt quantity according to:

b = (aBy)/[(1-a)(1+B)]

What's going on here? E/M write down a model with two inefficiencies: a dynamic inefficiency, and a credit friction. With sufficient flexibility in taxation, the government can solve both inefficiency problems with the appropriate provision of government liabilities. Why all the fuss with wage rigidity and zero-lower-bound "paradoxes" is not clear.

Another Model of Secular Stagnation
I can see what E/M and Summers/Krugman might be getting at though. The fact that real rates of return have been low since the financial crisis may be important, and could make a big difference for how monetary policy should proceed going forward. What elements would we want in such a model so that it can enlighten us about what is going on? It seems we would like to explain at a fundamental level why the real interest rate is low. This may reflect particular credit frictions, but we want to be explicit about what they are. Also, we would like to see a sufficient array of assets in this model. Perhaps some of these assets are used as collateral, which appears to have been important during and after the financial crisis. We also want to include the assets and liabilities that appear on both sides of the central bank's balance sheet. Otherwise, how can we analyze monetary policy in a sensible way? We also want the model to say something about liquidity traps in a low-real-interest-rate world.

I've got just the thing. The elements of the desired model I've sketched are right up the New Monetarist alley. We think of our research program originating, in part, with the work that Neil Wallace and his Minnesota students and coauthors did in the late 1970s and 1980s. Those people worked with various OG models - like the one that E/M study, and the one I was playing around with above. Of course we long ago moved on to other things. There's much current monetary research that uses versions of the Lagos-Wright model. I like this framework, not because it tells us much of anything new about monetary exchange, but because it admits a whole array of interesting financial and credit market behavior in a highly-tractable way. You can do much more with it than with an OG model.

So, here's an example. I didn't know until I read E/M that I had constructed a secular stagnation model, but according to them, that's exactly what my quantitative easing paper is. In that model there are banks, there's monetary policy, there's a collateral constraint (endogenous!), and you can have a negative real interest rate at the zero lower bound with positive inflation. There can be secular stagnation, in that the low real rate can persist forever, due to a shortage of collateral, and that collateral shortage is reflected in low output and inefficient exchange. The collateral shortage persists because of stupid fiscal policy, and the shortage can be mitigated with QE by the central bank. Cool, right? I think Krugman actually loves the thing, but can't bear to say it.