Believe those who are seeking the truth. Doubt those who find it. Andre Gide

## Wednesday, March 31, 2021

### A Natural Rate of Interest

This post was motivated by a conversation with Eric Lonergan. It began with a simple question: what should be the interest rate paid on reserves? I answered that according to theories I'm familiar with, reserves should earn the "natural" rate of interest, which I defined as the sum of population and productivity growth. So, assuming 2% "real" growth and 2% inflation, reserves (and government debt more generally) should be yielding around 4%.

I think it's fair to say most people did not find my answer very satisfying. So I thought I'd take a moment to explain how I arrived at it. I want to do so in the context of a model economy. Let me describe the model first. We can discuss its limitations and possible extensions later on.

Consider an economy where people live for two periods; they are "young" and then become "old." Let N(t) denote the population of young at date t. Assume that the population grows at (gross) rate n; that is, N(t) = nN(t-1). In this "overlapping generations" model, the population at date t is given by N(t)+N(t-1).

Individuals in this economy generate y units of perishable output (goods and services) when they are young. I'm going to treat y as fixed over time. This implies that the RGDP at date t is given by N(t)y and that the RGDP grows at rate n over time (there is no productivity growth). In what follows, I label n the "natural" rate of interest.

Suppose that people only value consumption when they are old. This poses an interesting economic problem. The young can produce goods that the old value, but the old have no way of paying for these goods. Private credit markets don't work here.

The cooperative solution is very simple: the young should "gift" their goods y to the old. If everyone followed this cooperative protocol, then the young of generation t would consume (in their old age) c(t+1) = N(t+1)y/N(t) = ny.

That is, by following this protocol, it's as if the young "deposit" their income y in a savings account that generates a (gross) real yield equal to n, the "natural" rate of interest.

Since private competitive markets cannot be expected to implement this socially-desirable outcome, what other mechanisms might be employed? In small communities, reciprocal gift exchange seems to work quite well. In the present context, the young look after their parents, expecting their children to return the favor, and so on.

Larger communities need to rely on other mechanisms. In the present context, a PAYGO social security system that taxes the young y and pays the old ny would do the trick.

The same outcome could be achieved through monetary exchange. Suppose the government lets all individuals open a central bank money account. The government creates (out of thin air) M dollars and credit the accounts of the "initial old" with M/N(0) dollars. Assume that M is kept constant over time. The old are expected to spend these dollars on a competitive spot market, where goods exchange for dollars at price p(t).

The equilibrium price-level is easy to derive in this example. At any date t, we have N(t-1) old people collectively holding M dollars. These M dollars will be spent (the old have no reason not to) on the goods available for sale, N(t)y. The market-clearing condition here is M = p(t)N(t)y at every date t. Because both M and y are constant, and because population N(t) is growing at rate n, it follows that the equilibrium price-level p(t) must be falling at rate n.

So, if we interpret M as "reserves" in this model economy, then reserves yielding the natural rate of interest would be consistent with economic efficiency. If reserves yield zero nominal interest rate, then efficiency requires some deflation. But the same outcome is possible if reserves were to yield a nominal interest rate n in a zero-inflation rate regime.

This result continues to hold for more general preferences. Suppose that people care about consumption when young and old. Then the young will only want to consume a fraction of their income. That fraction will depend on (among other things) the real rate of return they expect on their retirement savings. As it turns out, the so-called "Golden Rule" allocation requires that money/bonds yield the natural rate of interest.

Is this a good place to start thinking about Eric's question? It may be a good place to start, but we don't want to stop here. The analytical framework above is "bare bones." Among other things, my analysis implicitly assumes that there is no difference between reserves and government treasury securities. Does this matter? If it does, the reasons need to be spelled out. What modifications to the simple model above would imply that to meet a given social objective, it is desirable to have reserves yield less than treasury securities? In reality there is duration risk. But why does the Treasury issue bonds with different maturities in the first place? Moreover, why are these bonds purposefully rendered illiquid (for example, by discouraging the Fed from monetizing the entire bond issue or, at least, from setting up standing purchase facilities?). The answers to these questions are not immediately obvious to me. But they may be to you!

## Thursday, March 4, 2021

### Is it time for some unpleasant monetarist arithmetic?

The title of this post alludes to a paper written by Tom Sargent and Neil Wallace 40 years ago "Some Unpleasant Monetarist Arithmetic." The startling conclusion of this paper is that a central bank (limited to interest rate policy and/or open market operations) does not have unilateral control over the long-run rate of inflation. The result is made all the more powerful by the fact that it relies mostly on arithmetic and only minimally on theory.

So, what's the basic idea? First, begin with the fact that monetary and fiscal policy are inextricably linked via a consolidated government budget constraint. This implies that monetary policy will have fiscal consequences. In particular, interest-rate policy affects the interest expense associated with rolling over any given amount of government debt. The question is how the fiscal authority intends to finance interest expense. There are two basic ways it can to do this: (1) use primary surplus (increase taxes and/or cut spending); (2) issue debt. The first option is associated with what economists call a Ricardian fiscal policy; the second option is associated with a Non-Ricardian fiscal policy.

A central bank has no control over (1) or (2); these are determined by the tax and spend decisions made by the fiscal authority. Suppose the fiscal authority chooses (2). If so, then what is accomplished by increasing the policy rate? Ceteris paribus, it increases the rate at which nominal debt is issued. This is arithmetic. If nominal debt is money (and it is), then this must lead to higher inflation, not lower inflation.

The corollary here is that a central bank has no unilateral control over the long-run rate of inflation. A central bank may be permitted to choose a long-run inflation target, but only with the blessing of the fiscal authority. Canadians know this: the Bank of Canada and the Government of Canada meet every five years to review their joint inflation-control agreement. In other jurisdictions, the central bank simply assumes that fiscal policy will be conducted in a "responsible" manner (i.e., a manner that will not un-anchor long-run inflation expectations).

If the primary deficit is managed in a manner to anchor long-run inflation, then the central bank is left free to use interest rate policy for the purpose of stabilizing shocks to aggregate demand. To stabilize the inflation rate around target requires, in this context, that the central bank raises its policy rate aggressively against above-target inflation. (Hopefully, even the threat of such a response keeps inflation close to target. This is the so-called Taylor principle.)

The question monetary policymakers might want to mull over these days is whether this standard policy prescription is appropriate in an environment where the traditional fiscal support for inflation-targeting seems to be waning? I want to be clear here: I am not saying this is happening today or that it will happen in the future. I'm saying that it might happen and that if it does, monetary policy makers should have a contingency plan in place. What should this contingency plan look like?

So, to take a concrete example, suppose that the tax and spend decisions coming from Congress imply an elevated primary deficit for the foreseeable future. Perhaps there's been a "regime change" in thinking that transcends political parties so, no matter who controls Congress, the expectation is for elevated primary deficits for as long as we can see. (I am not suggesting this is good or bad, I'm just saying suppose.)

Next, suppose the economy is humming along at or near what anyone would call "full employment." And then suppose inflation rises to 3, 4, 5% or higher and stays there with no sign of ever wanting to return to the Fed's official 2% long-run inflation target. What should the FOMC do in this hypothetical scenario? (Again, consider this as the type of thought-experiment that is necessary to form a contingency plan -- I do not mean to suggest that this scenario is likely, only that it is possible--and not in a Dumb and Dumber way).

The monetary policy advice coming from a model like Sargent and Wallace (1981) might suggest something like this: For as long as Congress remains in a regime of high primary deficits

[1] Keep policy rate low, or even lower it, if possible; and
[2] Announce a temporarily higher inflation target (consistent with the new fiscal regime).

Recommendation [1] comes from Unpleasant Monetarist Arithmetic. Increasing the interest rate in this fiscal regime will only lead to higher inflation. Lowering the interest rate has the opposite effect. If recommendation [2] is not adopted, the monetary authority would have to explain (after every meeting) why it is missing its 2% inflation target. They might, of course, just say it's "temporary," but this would wear thin after a few years.

This advice is based on the assumption that everyone knows there's been a change in fiscal regime and that it will be persistent. What if no one is really sure of regime change or, if regime change, how long it might last?

The prudent thing to do in this more realistic case is to hedge your bets. In terms of [1], one might recommend raising the policy rate, but not by as much as would normally be done given the observed inflationary pressure. In terms of [2], one could probably get away with maintaining the long-run inflation target at 2% and legitimately explaining away deviations from target as "transitory."

Probably the last thing monetary policy should do under these circumstances is to raise the policy rate aggressively against inflationary pressure (as recommended by the Taylor principle). The Taylor rule works fine under a Ricardian fiscal policy. But it may backfire un a Non-Ricardian fiscal policy--this was the whole point of Sargent and Wallace (1981).

Tightening monetary policy might have the effect of bringing inflation down temporarily (this is consistent with the Sargent and Wallace model). But in reality (and in some models, like here and here), this would come at the cost of economic recession.

I can see no rationale for creating a recession to bring inflation down temporarily. But there may be a political-economy rationale for the threat of such a policy. That is, a Congress that does not trust future Congresses may want to create an independent (but accountable) central bank to pursue a low-inflation mandate and to do whatever it can with interest rate policy to achieve that mandate, even at the cost of recession. Future Congresses are in this manner obliged to behave in a Ricardian manner (so only temporary deficits permitted), which has the effect of anchoring long-run inflation.

Well, maybe. But I can't help but think of Dr. Strangelove here.

PS. I recently gave a talk on this that you can view here beginning at the 3 hour 12 minute mark.

## Sunday, February 21, 2021

### A Journey in Macroeconomic Thinking

I've been thinking a bit lately about theories of the business cycle (a lot of time for reflection in these days of COVID-19). At least, the way some of these theories have evolved over my lifetime and from the perspective of my own training in the field. From my (admittedly narrow) perspective as a researcher and advisor at a central bank, the journey beginning c. 1960 seems like it's taken the following steps: (1) Phillips Curve and some Natural Rate Hypothesis; (2) Real Business Cycle (RBC) theory; (3) New Keynesian theory. It seems like we might be ready to take the next step. I'll offer some thoughts on this at the end, for whatever they're worth.

There's no easy way to summarize the state of macroeconomic thinking, of course. But it seems clear that, at any given time, some voices and ways of thinking are more dominant than others. By the time the 1960s rolled around, there seemed to be a consensus that monetary and fiscal policy should be used to stabilize the business cycle. The main issue, in this regard, revolved over which set of instruments was better suited for the job. (See, for example, this classic debate between Milton Friedman and Walter Heller).

Central to macroeconomic thinking at the time was a concept called the Phillips Curve (PC). There is a subtle, but important, distinction to make here between the PC as a statistical correlation and the PC as a theory of that statistical relationship. In 1958, Phillips noticed an interesting pattern in the data: nominal wage growth seemed negatively correlated with the unemployment rate in the U.K. over the period 1913-48 (see diagram to the right). How to interpret this correlation? One theory is that when the unemployment rate is high, workers are easy to find and their bargaining position is weak, leading to small nominal wage gains. Conversely, when unemployment is low, available workers are scarce and their bargaining position is strong, leading to large nominal wage gains.

Then, in 1960, Paul Samuelson and Robert Solow wrote their classic piece "Problem of Achieving and Maintaining a Stable Price-Level: Analytical Aspects of Anti-Inflation Policy." Then, as is the case still now, the authors lamented the lack of consensus on a theory of price inflation. Various cost-push and demand-pull hypotheses were reviewed, problems of identification noted, and calls for micro-data to help settle the issue were made. They also mentioned Phillips' article and noted how the same diagram for the U.S. looked like a shot-gun blast (little correlation, except for some sub-samples). Then they translated the Phillips curve using price inflation instead of wage inflation. No data was sacrificed in this exercise; their "theory" was summarized with the diagram to the left.

I put "theory" in quotes in the passage above because the theory (explanation) was never clear to me. In particular, while I could see how an increase in the rate of unemployment might depress the level wage, I could not grasp how it could influence the rate of growth of wages for any prolonged period of time. This logical inconsistency was solved by the Phelps-Friedman natural rate hypothesis; see Farmer (2013) for a summary and critique.

The TL;DR version of this hypothesis is that the PC is negatively sloped only in the short-run, but vertical in the long-run. So, while monetary policy (increasing the rate of inflation) could lower the unemployment rate below its natural rate, it could only do so temporarily. Eventually, the unemployment rate would move back to its natural rate at the higher rate of inflation. This hypothesis seemed to provide a compelling interpretation of the stagflation (high inflation and high unemployment) experienced in the 1970s. It also seemed to explain the success of Volcker's disinflation policy in the 1980s. Nevertheless, uneasiness in the state of the theory remained and a new (well, nothing is ever completely new) way of theorizing was on the horizon.

By the time I got to grad school in the late 1980s, "real business cycle theory" was in vogue; see Charles Plosser's summary here and Bob King's lecture notes here

There was a lot going on with this program. A central thesis of RBC theory is that the phenomena of economic growth and business cycles are inextricably linked. This is, of course, is an old idea in economics going back at least to Dennis Robertson (see this review by Charles Goodhart) and explored extensively by a number of Austrian economists, like Joseph Schumpeter.

The idea that "the business cycle" is to some extent a byproduct of the process of economic development is an attractive hypothesis. Economic growth is driven by technological innovation and diffusion, and perhaps regulatory policies. There is no a priori reason to expect these "real" processes to evolve in a "smooth" manner. In fact, these changes appear to arrive randomly and with little or no mean-reverting properties. It would truly be a marvel if the business cycle did not exist.

The notion of "no mean-reverting properties" is important. It basically means that technology/policy shocks are largely permanent (or at least, highly persistent). If macroeconomic variables like the GDP inherit this property, then a "cycle"--the tendency for a variable to return to some long-run trend--does not even exist (and if you think you see it, it's only a figment of your imagination). For this reason, early proponents of RBC theory preferred the label "fluctuations" over "cycle." This view was supported by the fact that econometricians had a hard time rejecting the hypothesis that the real GDP followed a random walk (with drift). For example, here is Canadian GDP plotted against two realizations of a random walk with drift:

This perspective fermented at a time when the cost of computing power was falling dramatically. This permitted economists to study models that were too complicated to analyze with conventional "pencil and paper" methods. Inspiration was provided by Lucas (1980), who wrote:

Our task, as I see it…is to write a FORTRAN program that will accept specific economic policy rules as ‘input’ and will generate as ‘output’ statistics describing the operating characteristics of time series we care about, which are predicted to result from these policies.”

And so that's what people did. But what sort of statistics were model economies supposed to reproduce? Once again, it was Lucas (1976) who provided the needed guidance. The empirical business cycle regularities emphasized by Lucas were "co-movements" between different aggregate time-series. Employment, for example, is "pro-cyclical" (tends to move in the same direction as GDP) around "trend." These types of regularities can be captured by statistics like correlations. But these correlations (and standard deviations) only make sense for stationary time-series, and the data is mostly non-stationary. So, what to do?

Transforming the data through first-differencing (i.e., looking at growth rates instead of levels) is one way to render (much of) the data stationary. Another approach was made popular by Prescott (1986), who advocated a method that most people employ: draw a smooth line through the data, label it "trend," and then examine the behavior of "deviations from trend." Something like this,

It's important to note that Prescott viewed the trend line in the figure above as "statistical trend," not an "economic trend." To him, there was no deterministic trend, since the data was being generated by a random walk (so, the actual trend is stochastic). Nevertheless, drawing a smooth trend line was a useful way to render the data stationary. The idea was to apply the same de-trending procedure to actual data and simulated data, and then compare statistical properties across model and data.

The point of mentioning this is that no one involved in this program was conditioned to interpret the economy as "overheating" or in "depression." Growing economies exhibited fluctuations--sometimes big and persistent fluctuations. The question was how much of these observed fluctuations could be attributed purely to the process of economic development (technological change), without reference to monetary or financial factors? I think it's fair to say that the answer turned out to be "not much, at least, not at business cycle frequencies." The important action seemed to occur at lower frequencies. Lucas (1988) once again provided the lead when he remarked "Once one starts to think about growth, it is hard to think about anything else." And so, the narrow RBC approach turned its attention to low-frequency dynamics; e.g., see my interview with Lee Ohanian here

Of course, many economists never bought into the idea that monetary and financial factors were unimportant for understanding business cycles. Allen and Gale, for example, schooled us on financial fragility; see here. But this branch of the literature never really made much headway in mainstream macro, at least, not before 2008. Financial crises were something that happened in history, or in other parts of the world. Instead, macroeconomists looked back on its roots in the 1960s and embedded a version of the PC into an RBC model to produce what is now known as the New Keynesian framework. Short-run money non-neutrality was achieved by assuming that nominal price-setting behavior was subject to frictions, rendering nominal prices "sticky." In this environment, shocks to the economy are not absorbed efficiently, at least, not in the absence of an appropriate monetary policy. And so, drawing inspiration from John Taylor and Michael Woodford, the framework added an interest rate policy rule now known as the Taylor rule. Today, the basic NK model consists of these three core elements:

[1] An IS curve: Relates aggregate demand to the real interest rate and shocks.
[2] An Phillips Curve: Relates the rate of inflation (around trend) to the output gap.
[3] A Taylor Rule: Describes how interest rate policy reacts to output and inflation gaps.

I have to be honest with you. I never took a liking to NK model. I'm more of an Old Keynesian, similar to Roger Farmer (we share the same supervisor, so perhaps this is no accident). In any case, the NK framework became (and continues to be) a core thought-organizing principle for central bank economists around the world. It has become a sort of lingua franca in academic macro circles. And if you don't know how to speak its language, you're going to have a hard time communicating with the orthodoxy.

Of the three basic elements of the NK model, I think the NK Phillips Curve (which embeds the natural rate hypothesis) has resulted in the most mischief; at least, from the perspective of advising the conduct of monetary policy. The concept is firmly embedded in the minds of many macroeconomists and policymakers. Consider, for example, Greg Mankiw's recent piece "Yes, There is a Trade-Off Between Inflation and Unemployment."

Today, most economists believe there is a trade-off between inflation and unemployment in the sense that actions taken by a central bank push these variables in opposite directions. As a corollary, they also believe there must be a minimum level of unemployment that the economy can sustain without inflation rising too high. But for various reasons, that level fluctuates and is difficult to determine.

The Fed’s job is to balance the competing risks of rising unemployment and rising inflation. Striking just the right balance is never easy. The first step, however, is to recognize that the Phillips curve is always out there lurking.

The Phillips curve is always lurking. The message for a central banker is "sure, inflation and unemployment may be low for now, but if we keep monetary policy where it is and permit the unemployment rate to fall further, we will risk higher inflation in the future." I'm not sure if economists who write in this manner are aware that they're making it sound like workers are somehow responsible for inflation. Central banker to workers: "I'm sorry, but we need to keep some of you unemployed...it's the inflation, you see."

There is evidence that this line of thinking influenced the FOMC in 2015 in its decision to "lift off" and return the policy rate to some historically normal level; see my post here explaining the pros and cons in the lift-off debate. By the start of 2014, there was considerable pressure on the Fed to begin "normalizing" its policy rate. By mid 2014, the expectation of "lift off" likely contributed to significant USD appreciation and the economic weakness that followed. If I recall correctly, Vice Chair Stan Fischer started off the year by announcing that four rate hikes for 2015 were in order (as it turned out, the Fed only raised rates once--in December). To some observers, this all seemed very strange. After all, the unemployment rate was still above its estimated "natural" rate (5%) and inflation continued to undershoot its 2% target. What was going on?

What was going on was the Phillips curve. Here is Chair Yellen at the March 17-18, 2015 FOMC meeting (transcript available here):

If we adopt alternative B, one criterion for an initial tightening is that we need to be reasonably confident that inflation will move back to 2 percent over the medium term. For the remainder of this year, my guess is that it will be hard to point to data demonstrating that inflation is actually moving up toward our objective. Measured on a 12-month basis, both core and headline inflation will very likely be running below 1½ percent all year. That means that if we decide to start tightening later this year, a development that I think is likely, we will have to justify our inflation forecasts using indirect evidence, historical experience, and economic theory.
The argument from history and economic theory seems straightforward. Experience here and abroad teaches us that, as resource utilization tightens, eventually inflation will begin to rise. To me, this seems like a simple matter of demand and supply. So the more labor and product markets tighten, the more confident I’ll become in the inflation outlook. Because of the lags in monetary policy, the current high degree of monetary accommodation, and the speed at which the unemployment rate is coming down, it would, to my mind, be imprudent to wait until inflation is much closer to 2 percent to begin to normalize policy. I consider this a strong argument for an initial tightening with inflation still at low levels, and it’s one that I plan to make. But I also recognize and am concerned that, at least in recent years, the empirical relationship between slack and inflation has been quite weak.
Now, I don't want to make too much of this particular episode. Personally, I don't think it had a major impact on the recovery dynamic. But I do think it had an impact; in particular, the pace of improvement in labor market conditions temporarily slowed. It was an unforced error (as I think other members of the Committee sensed as well).

I think the lift-off episode has contributed to a general re-thinking of the Phillips curve and the natural rate hypothesis. The notion of an economy operating at "excess capacity" has always seemed a bit strange to me, let alone the idea that excess capacity as a cause of inflation (as opposed to a force operating on the price-level). Perhaps it is time to re-visit Milton Friedman's "plucking model."  Instead of drawing a smooth line through the center of a time-series, Friedman drew a line that defined a ceiling (a capacity constraint). Shocks to the economy manifest themselves as "downward plucks" (as if plucking on an elastic band).

The plucking model is consistent with the observed cyclical asymmetry in unemployment rate fluctuations. And labor market search models are a natural way to model that asymmetry. In case you're interested, I develop a super-simple (and dare I say, elegant) search model here to demonstrate (and test) the idea: Evidence and Theory on the Cyclical Asymmetry in Unemployment Rate Fluctuations, CJE 1997). See also my blog post here as well as some recent work by Ferraro (RED, 2018) and Dupraz, Nakamura and Steinsson (2019). I like where this is going!

One attractive feature of search models, in my view, is that they model relationship formation. Relationships provide a very different mechanism for coordinating economic activity relative to the canonical economic view of anonymous spot exchange in centralized markets. In a relationship, spot prices do not matter as much as the dynamic path of these prices (and other important aspects) over the course of a relationship (see my critique of the sticky price hypothesis here). The observation that retailers, in the early days of C-19, voluntarily rationed goods instead of raising prices makes little sense in anonymous spot exchange, but makes perfect sense for a merchant concerned with maintaining a good relationship with his or her customers. And merchant-supplier relationships can handle shortages without price signals (we're out of toilet paper--please send more!). In financial markets too, the amount of time that is spent forming and maintaining credit relationships is hugely underappreciated in economic modeling. Search theory turns out to be useful for interpreting the way money and bond markets work too. These markets are not like the centralized markets we see modeled in textbooks--they operate as decentralized over-the-counter (OTC) markets, where relationships are key. One reason why economies sometimes take so long to recover after a shock is because the shock has destroyed an existing set of relationships. And it takes time to rebuild relationship capital.

Notions of "overheating" in this context probably do not apply to labor market variables, although there is still the possibility of an overaccumulation of certain types of physical capital in a boom (what the Austrians label "malinvestment"). Any "overheating" is likely to manifest itself primarily in asset prices. And sudden crashes in asset prices (whether driven by fundamentals or not), can have significant consequences on real economic activity if asset valuations are used to support lines of credit.

Finally, we need a good theory of inflation. The NKPC theory of inflation is not, in my view, a completely satisfactory theory in this regard. To begin, it simply assumes that the central bank can target a long-run rate of inflation (implicitly, with the support of a Ricardian fiscal policy, though this is rarely, if ever, mentioned). At best, it is a theory of how inflation can temporarily depart from its long-run target and how interest rate policy can be used to influence transition dynamics. But the really interesting questions, in my view, have to do with monetary and fiscal policy coordination and what this entails for the ability of an "independent" central bank even to determine the long-run rate of inflation (Sargent and Wallace, 1981).

I know what I've described only scratches the surface of this amazingly deep and broad field. Most of you have no doubt lived through your own process of discovery and contemplation in the world of macroeconomic theorizing. Feel free to share your thoughts below.

## Wednesday, September 9, 2020

### Cochrane on debt II

Yesterday, I posted a reply to John Cochrane's Sept 4 post on the national debt. John alerted me to his Sept 6 update, which I somehow missed. Given this update (together with some personal correspondence), let me offer my own update.

John begins with an equation describing the flow of government revenue and expenditure. With a debt/GDP ratio of one, the sustainable (primary) deficit/GDP ratio is given by g - r, where g = growth rate of NGDP and r = nominal interest rate on government debt (I include Federal Reserve liabilities and currency in this measure). John assumed g - r = 1% (so about \$200B). In a post I published last year, I assumed g - r = 3% (so about \$600B); see here: Is the U.S. Budget Deficit Sustainable?

Two things to take away from these calculations. First, this arithmetic suggests that the U.S. federal government can easily run persistent primary budget deficits in the range of 1-3% of GDP. Not only does the debt not need to be paid off, but it can grow forever. Second, primary budget deficits are presently far in excess of this range. What does this imply?

Let's step back and think about John's equation. The arithmetic of the government "budget constraint" basically says this:

Deficit/GDP = [1 - (1+r)/(1+g)] x Debt/GDP

Note that a sustainable primary deficit is only possible if r < g. If r > g, then a primary surplus is needed to service the interest expense of the debt.

Students of monetary theory may recognize the expression above as a Laffer curve for inflation finance. That is, in the case of currency we have r = 0. Let g represent the growth rate of the supply of currency and assume a constant RGDP (so that g also measures the growth rate of NGDP). Finally, replace debt with currency, so that

Seigniorage revenue = [1 - 1/(1+g)] x Money/GDP

Again, this is just arithmetic. Economic theory comes in through the assumption that the demand for money is decreasing in the rate of inflation, g. If this is true, then an increase in g has two opposing effects: it increases seigniorage revenue by increasing the inflation tax rate, but it lowers seigniorage revenue because it decreases the inflation tax base. There is a maximum amount of seigniorage revenue the government can collect by printing money. That is, there are limits to inflation finance. (See also my post here.)

Now, I know John is fond of saying that Federal Reserve liabilities and U.S. Treasury securities are essentially the same thing (especially if the former exist mainly as interest-bearing reserve accounts). I happen to agree with this view. But then we can use exactly the same logic to characterize the limits to bond finance, recognizing that U.S. Treasury securities are essentially money. To this end, assume that the Debt/GDP ratio is an increasing function of (r - g). To make things a little simpler, let me continue to assume zero RGDP growth, so that g represents both inflation and NGDP growth. Finally, let me assume that r is a monetary policy choice (just as setting r = 0 for currency is a policy choice).

Next, we need a theory of inflation. In the models I work with, the rate of inflation in a steady state is determined by the growth rate of the nominal debt, g, which I also treat as a policy parameter. So, the magnitude r - g is policy-determined, at least, within some limits. By lowering r and increasing g, the government is making its securities less attractive for people to hold. But this just tells us that the demand for debt is lower than it otherwise might be--it does not tell us how large this demand is in the first place, or how it is likely to evolve over time owing to factors unrelated to r or g (e.g., regulatory demand, foreign demand, etc.).

So, with this apparatus in place, my interpretation of what worries John is the question of what happens if [1] the federal government finds itself near the top of the bond-seigniorage Laffer curve; and [2] a shock occurs that requires a large fiscal stimulus. Barring alternative forms of securing resources (e.g., through direct command/conscription), the government will not have the fiscal capacity to lay claim against the resources it needs. Printing more money/bonds here is not going to help even with zero interest rates. The ensuing inflation would simply put us on the right-hand-side of the Laffer curve -- the government's ability to secure resources would only diminish

Assuming I have captured at least a part of John's concern accurately, let me go on to critique it. To begin, there's nothing wrong with the logic I spelled out (I don't think). But I want to make a couple of points nevertheless.

First, the demand for U.S. government securities (D/Y) seems to be growing very rapidly and for a very long time now. We know, anecdotally, that the UST is used widely as collateral in credit derivatives markets and repo, that foreign countries view it as a safe asset, that investors value its safety, and that recent changes to Dodd-Frank and Basel III have contributed to the regulatory demand for USTs. The global demand for the U.S. dollar is, if anything, growing more rapidly than ever (re: the recent "dollar shortages" that resulted in the Fed opening its central bank swap lines). We don't know where this limit is, but judging by how low U.S. inflation is (together with low UST yields), it seems fair to day that there's still plenty of fiscal capacity. (And I want to stress that this has nothing to do with the ability of a country to pay back its debt -- I'm not sure why John keeps mentioning this while at the same time understanding that this debt is money).

I suspect that John is likely to agree with what I just said. Sure, there may be more room now, but how much more? With bipartisan concern for debt absent in Congress, with no sign of inflation in sight, with interest rates so low, how can we not hit this limit at some point?

My own view is that we are bound to hit this limit (though, economists like Simon Wren-Lewis have warned me not to discount the forces of austerity). The question is what happens once we hit that limit? I say we get USD depreciation and some inflation (not hyperinflation). John seems to be worried about hyperinflation after all, which he likens to a debt rollover crisis. I just don't see it. (Of course, if John is simply suggesting that the fiscal authority will continue to run persistently large deficits in the face of high inflation, then I agree with him. While I don't see this happening, who can say for sure?)

Finally, what happens if we're near the debt limit and there's a shock. Well, what type of shock exactly? The type of shock that hit us in 2008 is likely to increase the demand for debt, expanding fiscal capacity. So, here too, I'm not sure what form the debt crisis is supposed to take. It would be great to appeal to a model (but please, not one of Greece).

## Tuesday, September 8, 2020

### Cochrane on why debt matters

The stock of national debt is now larger than our annual national income in the United States. Is this something to worry about? Does it matter how big the debt-to-GDP ratio gets? Is there any limit to how large it can grow and, if so, what is it this limit and what factors determine it? A lot of people have been asking these questions lately. John Cochrane is the latest to opine on these questions here: Debt Matters

I'm not even sure where to begin. I suppose we can start with the famous debt clock pictured on the right. Whenever I look at the debt clock, I'm reminded of James Tobin who, in 1949 remarked:

The peace of mind of a conscientious American must be disturbed every time he is reminded that his government is 250 billion dollars in debt. He must be shocked by the frequent announcement that every newborn baby is burdened, not with a silver spoon, but with a debt of \$1700.

The national debt is now 100 times larger than it was in 1949. Society has somehow managed to hold itself together since then. At the very least, this suggests we need not pay attention to the debt clock. It does not, however, not mean we shouldn't pay attention to managing the debt. Ironically, worrying about the debt is, in a way, what permits us not to worry about it. The time to start worrying is when we and our elected representatives stop worrying about it. According to John, "The notion that debt matters, that spending must be financed sooner or later by taxes on someone, and that those taxes will be economically destructive, has vanished from Washington discourse on both sides of the aisle." That is, it may be time to start worrying.

I think there's an element of truth to this. For example, while it's true that the Reagan deficits were large, it's also true that there was strong bipartisan support for "doing something about the growing debt." And it wasn't just words. As Justin Fox reminds us, Congress increased taxes seven times between 1982-93. Well, what about Japan? As I explain here, Japan is a poster child for "worrying about the debt." To make a long story short, the debt-to-GDP ratio in Japan has stabilized (pre-Covid, at least), inflation is below target, and the fiscal authority keeps raising the sales tax. Rightly or wrongly, the Japanese "care" about the national debt--the effect of which is to keep fiscal policy "anchored."

But what exactly is there to fear if fiscal policy becomes "unanchored?" For a country like the United States, it seems clear that outright default will never happen. U.S. Treasury securities (USTs) are too important for global financial markets. A default may very well trigger a global financial meltdown. The only practical option is to continue rolling over the debt, principal and interest (the latter of which is very low these days). Is there a danger of "bond vigilantes" sending the yields on USTs skyward? Not if the Fed stands ready to keep yields low (related post here on yield curve control). And, in any case, even if the Fed raises (or is expected to raise) its policy rate, the U.S. Treasury can just continue to issue the bills necessary to make the scheduled payments. Treasury securities and Federal Reserve reserves are just different forms of interest-bearing money. To put things another way, the national debt need never be paid back--like money, it can be held in private wealth portfolios forever. The only question is on what terms it will be willingly held.

This last point gets to the question of what can be expected to happen if the debt gets too large (say, because the fiscal authority plans to run large primary budget deficits off into the indefinite future). Much will depend on the evolution of the global demand for USTs. If that demand stops growing while fiscal deficits run unabated, surely we can expect the U.S. dollar to weakened and the domestic price-level to rise. The former is likely to contribute to an export boom, which should serve to close the trade deficit (mitigating the adverse consequences of global imbalances). The latter is likely to promote the growth of nominal GDP.

Needless to say, an export boom and higher NGDP growth don't sound like disaster scenarios, especially in the current economic environment. John seems to worry that whatever happens, it's likely to happen suddenly and without warning. We know Naples is going down (in the manner of Pompeii c. 79AD), we just don't know when. But how does the lava flow correspond to the economic consequences of a debt crisis? (Keep in mind, we're not talking about a country that issues foreign-denominated debt.)

Should we be worried about hyperinflation? Evidently not, as John does not mention it (see also this nice piece by Francis Coppola). But he does mention something about fiscal capacity (the ability of the fiscal authority to exert command over resources). As I explain here, there are limits to how much seigniorage can be extracted in this manner. To put things another way, there are economic limits to how large the debt-to-GDP ratio can get. But reaching this limit simply means that the required tax (whether direct or indirect via inflation) is high--it does not mean disaster.

John concludes with the following warning: "The closer we are to that limit, the closer we are to a real crisis when we need that fiscal capacity and its no longer there." This is one of those sentences that starts your head off nodding in agreement. But then you think about it for a minute and wonder what type of "real crisis" he has in mind? If it's a financial crisis, the implied positive money-demand shock (flight-to-safety) is likely to increase fiscal capacity, not diminish it. A war perhaps? In these types of emergencies, the nation bands together and governments use other means to gather the resources necessary (e.g., conscription).

So, to conclude, I'm not saying that John is wrong. It's just not very clear in my mind how he imagines a U.S. debt crisis to unfold exactly. What is missing here is a model. This is odd because one of John's great strengths is model building. And so my conclusion is that it would be very interesting to follow the logic of his argument through the lens of one of his models. Let's see the model, John!

## Friday, September 4, 2020

### The Fed's new monetary policy framework

The Fed's much-anticipated new monetary policy framework is now public. Fed Chairman Jerome Powell outlined the policy framework last week in Jackson Hole; you can view his speech here. Overall, I thought Powell's delivery was very good. While there's room for improvement, I think the new framework is a step in the right direction (George Selgin provides a good critique here). There were three things in Powell's speech that stuck out for me. I discuss these below.

Shortfalls vs. Deviations

At the 22:30 mark, Powell reports what may very well be the most substantive change to the monetary policy statement. Here, he states that the FOMC will now interpret important macroeconomic time-series like GDP and unemployment as exhibiting "shortfalls" instead of "deviations" from some ideal or "maximum" level (a frustratingly vague concept).

The practical effect of this shift is to remove (or make less prominent) in the minds of FOMC members the idea that the economy is, or will soon be, "overheating" (i.e., embarked on an unsustainable path that can only end in misery for those most vulnerable to economic recession).

The idea of "deviation from (some) trend" seems like a plausible description of the postwar U.S. up to the mid-1980s. Severe contractions were usually followed by equally robust recoveries. However, this representation seems to break down since the "great moderation" that began in the mid-1980s. Since then, economic recessions have not been followed by above-average growth. Instead, each recession seems better described as a "growth shortfall." We're not entirely sure what accounts from this cyclical asymmetry, but it seems consistent with Milton Friedman's "plucking model." I think we can expect a stream of research resurrecting this old idea (see here, for example).

In any case, the upshot here is that, to the extent that "overheating" is no longer considered a serious threat, the FOMC will be less likely to implement "preemptive" policy rate hikes. This constitutes a tacit acknowledgement that the period leading up to "lift off" and what followed might have been handled better. As I wrote at the time (see my discussion here), standard Phillips Curve logic did not seem to support tightening (unemployment was above the estimated natural rate, inflation was below target, and inflation expectations were declining). But the Committee somehow talked itself into the need to "normalize," to act preemptively and not get caught "behind the curve." In fairness, monetary policy is always about balancing risks (in this case, the perceived risk of overheating). In the near future, less weight will be assigned to the risk of overheating.

The Maximum Level of Employment

At the 22:30 mark, Powell states "Of course, when employment is below its maximum level, as is so clearly the case now, we will actively seek to minimize that shortfall..."

I have a hard time not interpreting "maximum" here as "socially desirable." I think most people would agree that the 2008 financial crisis caused employment to decline below its maximum level. The workers rendered idle in that episode constituted a social waste, and the Fed was right to loosen monetary policy to stimulate economic activity in the face of recessionary headwinds.

But the recession induced by the C-19 is very different from standard recessions. This was laid out very clearly by St. Louis Fed President Jim Bullard on March 23, 2020: Expected U.S. Macroeconomic Performance during the Pandemic Adjustment PeriodAccording to Bullard, the temporary removal of some workers from their jobs is not, in this case, a waste of resources. The decline in employment in this case should be viewed as an investment in public health. That is, the maximum level of employment declined and its recovery is driven mostly by the contagion dynamic (as well as improvements in social distancing protocols, masking, testing, treatments, etc.). The role of monetary policy here is to calm financial markets (which the Fed successfully accomplished in March) and to aid the fiscal authority with its income maintenance programs. In short, the primary monetary/fiscal policy objective here is to deliver insurance, not stimulus.

Monetary stimulus is appropriate, however, to the extent that demand factors (e.g., individually rational, but a collectively irrational restraint on spending) are inhibiting the recovery dynamic. The evidence for this is usually assumed to be found in falling inflation and inflation expectations, and declining bond yields. And usually, this makes sense, because we usually assume that recessions are caused by collapses in aggregate demand (as in 2008-09). But what if the increase in the demand for money (safe assets in general) is driven by a collectively rational fear? We'd expect to see the exact same inflation and interest rate dynamic, but the role for stimulative monetary policy would be more difficult to justify (though the desirability for insurance remains).

So, maybe it is not so clearly the case now that employment is below or, at least, far below its "maximum" level. Note that a significant part of the decline in aggregate employment is coming from the leisure and hospitality sector:
Arguably, we do not want, at this stage of the pandemic, to promote the indoor dining experiences people enjoyed earlier this year. This activity will return slowly as economic fundamentals improve. The "full employment" level of employment in this sector is clearly below what it was in Jan 2020. But, to be fair, it is entirely possible, and perhaps even likely, that the level of employment even here is lower than the "full employment" level. It's very hard to tell by how much though.

Average Inflation Targeting

At the 24:00 mark, Powell explains how AIT will help anchor inflation expectations. Missing the inflation for a prolonged period of time will cause expectations to drift away from target and line up with the historical experience. This view of expectation formation is firmly rooted in the "adaptive expectations" tradition. That is, expectations are assumed to be formed by looking backward instead of forward

People sometimes claim that adaptive expectations are inconsistent with "rational" expectations. But this is not necessarily the case. In fact, it makes sense to use the historical record of inflation realizations to make inferences about the long-run inflation target if people are not sure of the monetary authority's true inflation target; see, for example, here: Monetary Policy Regimes and Beliefs

It's still not entirely clear to me whether FOMC members view AIT as a policy to pursue passively (i.e., let inflation creep up to and beyond target on its own) or actively (i.e., take explicit actions to promote an overshoot of inflation). If it's the former, then I'm on board with the idea. But if it's the latter, I am not. In particular, with the liquidity-trap-like conditions we're presently in, the Fed does not have the tools (or political will) to boost inflation persistently. It is likely to fail, just as the Bank of Japan failed. (I explain here why it's more difficult for a central bank to raise the inflation target than to lower it.) So, as I've advocated many times in the past, why not just declare 2% as a soft-ceiling and let fiscal policy do the rest?

My view rests on the belief that missing the inflation target from below by 50bp over the past eight years is not a significant macroeconomic problem (especially given how crudely inflation is measured). The FOMC did view it as a problem, but mainly, it seems, because of the embarrassment associated with missing its target. "We are a central bank. We have an inflation target. Central banks are supposed to hit their inflation targets. We need to hit our inflation target to remain credible." This is why earlier FOMC statements emphasized the Fed's "symmetric" inflation target. That did not work and so now we have AIT which, I'm afraid, might not work either. Happily (for those who want to see higher inflation), Congress seems comfortable with the idea of producing large budget deficits into the foreseeable future.

So, if we get higher inflation, it will largely be a fiscal phenomenon. The purpose of AIT is to accommodate any rise in inflation for the purpose of increasing inflation expectations and avoiding the specter of deflation (people often point to Japan as a case to avoid, by Japan seems to be doing fine as far as I can tell). There is the question of how the Fed would react should inflation rise sharply and persistently above 2%. Even if the event is unlikely, it would be good to state a contingency plan. In the past, the Fed could be expected to raise its policy rate sharply. But this event, should it transpire, will almost surely take place during an employment shortfall (since this is now the acknowledged new normal). The only prediction I'll make here is that the FOMC will have a lot of explaining to do in this event.