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

Saturday, July 27, 2019

Blanchard and Farmer on the Phillips Curve

In case you missed it, there's an interesting (and slightly wonkish) debate going on between Olivier Blanchard and Roger Farmer concerning the theoretical relevance of the Phillips curve. Roger fired the opening salvo by presenting a macroeconomic model he claims fits the data well and yet makes no use of the Phillips curve. Farmer, in Laplace-like fashion, declared "he had no use for that hypothesis." Blanchard predictably, and understandably, came to the defense of the orthodoxy:

If you've followed my writings over the years, you'll not be surprised to learn that I am sympathetic to Roger's position in this debate. Below, I explain why. I begin by summarizing the gist of the conventional view. I then present a simple model that has no "natural" rate of unemployment. It's not exactly Roger's model, but it captures what I think is the essential part of his argument.

Let me now review. According to conventional (e.g., New-Keynesian, but also other) theory, there exists a "natural rate of unemployment" that potentially moves around owing to "structural" factors. The long-run rate of inflation is assumed to be fixed by policy in some unspecified manner. In an economy free of any disturbances, actual (and expected) inflation correspond to the long-run inflation target and the unemployment rate corresponds to the natural rate of unemployment. There is also a "natural" (or "neutral") real rate of interest that corresponds to the natural rate of unemployment. Absent any economic disturbances, monetary policy is assumed to set "the" nominal interest rate to its natural rate (the natural real rate of interest plus the inflation rate).

The actual rate of unemployment fluctuates around this natural rate owing to "shocks" that influence the aggregate demand for goods and services. I like to think of these shocks as "news" shocks that cause expectations over the future profitability of investment to fluctuate over time (see, for example, here). It does not matter for my purpose here whether expectations react rationally or irrationally to this information flow. The important thing is when people collectively become more bullish over the future return to investment, the demand for investment rises (at the expense of other forms of storing value, like government paper). For this reason, I attach the conventional label "aggregate demand shocks."

In the conventional model, fluctuations in aggregate demand for fixed nominal interest rate generate a negative relationship between inflation and unemployment. Intuitively, if firms have a bullish outlook, they raise their product prices more aggressively against the higher expected demand, and they also recruit more aggressively as well, which sends the unemployment rate lower. Adjustments in the interest rate (via monetary policy) designed to stabilize the inflation rate would imply movements in the unemployment rate without any corresponding change in inflation. All of this is consistent with the model I present below.

What about the question posed by Blanchard above: "Does anybody doubt that if the Fed decreased (unemployment) to 1%, it would not lead to more inflation?"

It's not entirely clear what experiment he has in mind. An educated guess suggests he's thinking about the Fed temporarily reducing its policy rate, causing a temporary boom in aggregate demand, leading to a temporary increase in inflation and a temporary decline in unemployment, with everything returning to normal once the Fed returns its policy rate to its "neutral" level. My answer to his question is that probably few people doubt this is what is likely to happen. Accepting this, however, does not validate the notion that "low unemployment causes high inflation." (Note: I am not accusing Blanchard of suggesting this causal relation, but many if not most people interpret the Phillips curve in exactly this way).

What I would like to ask Blanchard is the following. What do you think would happen to inflation and unemployment if the central bank lowered its policy rate permanently? I think the answer to this question would illuminate the "natural rate" hypotheses assumed by theorists, as well as what they are implicitly assuming about the conduct of fiscal policy (i.e., how it reacts to the change in monetary policy).

Let me now describe a simple OLG model (a model taught to me by Blanchard via his textbook with Stan Fischer). I will keep the wonkishness to a minimum here. If you want the full-blown version, just email me and I'll send it to you.

Individuals live for two periods in a sequence of overlapping generations. There are young entrepreneurs and young workers. Young entrepreneurs expend recruiting effort to find suitable young workers. The probability of finding a match is increasing in recruiting effort. A match, if it is formed, produces output in the following period. In this sense, recruitment effort is like an investment: a current expense leads to an expected future payoff. For the entrepreneur, the expected payoff depends in obvious ways on the expected productivity of the match (news) and the worker's bargaining power.

Young entrepreneurs face a trade-off: they can devote their resources to recruitment investment, or toward purchasing an alternative store of value in the form of interest-bearing government money (or debt). For a given inflation rate and a given nominal interest rate (both determined by policy), the optimal recruiting intensity trades off the expected return to recruiting relative to the real (inflation adjusted) return on government debt. In a steady-state, the inflation rate in my model is determined by the rate of growth of nominal debt, which is injected into the economy as lump-sum social security payments. The interest expense on the debt is financed with a lump-sum tax on old entrepreneurs.

The aggregate recruiting effort (which I associate with job vacancies) determines the unemployment rate. The model generates a negatively-sloped Beveridge curve. The equilibrium unemployment rate is: (1) decreasing in the inflation rate; (2) increasing in the nominal interest rate; (3) increasing in the bargaining power of workers; and (4) decreasing in the level of "optimism."

There is no "natural" rate of unemployment in this model in the sense of the unemployment rate necessarily  reverting ("self-correcting") to a given "natural" rate over a long enough period of time. Monetary and fiscal policy in this model can result in many different "natural" rates of unemployment (and interest). So, in this model, it is indeed possible for policy to drive the unemployment rate to permanently low levels without any inflationary consequences (since inflation is determined by the rate of growth of nominal debt in the long-run).

I should add that the model can speak to the effect of worker bargaining power on inflation as well. A permanent increase in worker bargaining power has no effect on inflation--it simply increases the real wage (and unemployment). In terms of an impulse-response function following a surprise increase in bargaining power, the mechanism works as follows. The increase in bargaining power reduces the expected return to recruiting workers, hence reduces recruiting investment. There is a portfolio substitution out of private investment activities into government securities. The implied increase in the demand for real money balances has the effect of driving the price-level down (for a given stock of nominal debt and assuming no change in the policy rate). So, increased worker bargaining power is disinflationary in the short run, but has no effect on inflation in the long run.

Let me conclude. One purpose of this post was to demonstrate that models without a "natural rate" hypothesis are not that unconventional--I cobbled the model above based on what I learned from standard textbooks, after all. Roger has shown another way to do this that does not stray too far (in my view, at least) from conventional theory either. These models may or may not turn out to be useful ways for understanding basic elements of the macroeconomy and for informing policy--I do not yet know for sure. But I do believe they are worth exploring further and I commend Roger for leading the way!

Monday, July 15, 2019

Does the Phillips Curve Live in Europe?

There's been much talk about the Phillips curve lately, especially in the wake of Jay Powell's recent testimony before Congress. Many people are proclaiming the death of the Phillips curve. I think that many people making these proclamations are probably wrong--or, more likely--they are correct, but for the wrong reasons.

What exactly is being proclaimed dead here? Are people referring to the absence of any statistical correlation between inflation and unemployment? Or are they referring to the theory that the unemployment rate (beyond some "natural" rate) causes inflation? These are two conceptually different notions of the Phillips curve. The fact that the Phillips curve is "flat" does not in itself negate the Phillips curve theory of inflation. This is because monetary policy and other factors (like expected inflation) could shift the position of the curve over time.

My own preferred theory of inflation does not rely on the unemployment rate per se. I think that the long-run inflation rate is determined by monetary and fiscal policy and that fluctuations in "aggregate demand" can generate countercyclical movements in inflation and unemployment (or procyclical movements in inflation and employment in a "full-employment" economy). But this is not a post on the theory of inflation. It's just about the statistical properties of the Phillips curve in the European Monetary Union. (In my previous post I talked about the Phillips curve in the United States, see here.)

Restricting attention to the EMU is of some interest here because individual member countries do not have direct control over monetary policy (although some countries may have greater influence than others). If (say) the Austrian economy goes into recession, it's not like the ECB will cut its policy rate just for the sake of Austria. So, to the extent that unemployment rates across EMU members states are not perfectly correlated, one might be in a better position to identify a conventional Phillips curve relationship. Below, I report the Phillips curve for all 19 member states and for the EMU as a whole. In this data, the negative relationship seems apparent in all but a few cases. I'll leave it up to the reader to draw his or her own conclusions.

PS. Antoine Levy points me to his paper showing an even stronger relationship at the regional level; see here: http://economics.mit.edu/files/16976























Friday, June 21, 2019

The Phillips Curve in Recession and Recovery

The Phillips curve can mean one of two conceptually distinct things (which are sometimes confused). First, the Phillips curve may simply refer to a statistical property of the data--for example, what is the correlation between inflation and unemployment (either unconditionally, or controlling for a set of factors)? Second, the Phillips curve may refer to a theoretical mechanism--why does inflation and unemployment exhibit the statistical properties it does?

The presumption among many is that statistical Phillips curves tend to be negatively sloped, suggesting a trade-off between inflation and unemployment. A standard theoretical interpretation of this negative relationship is that a high level of unemployment means that aggregate demand is low, so that firms feel less inclined to increase the price of their goods and services. Conversely, when unemployment is low, aggregate demand is high, allowing firms to raise their prices at a faster rate.

The problem is that statistical Phillips curves are not always negatively sloped. In fact, sometimes they appear to be positively sloped. Over long periods of time, the data looks like a shotgun blast (i.e., zero correlation). In a recent empirical study, however, Blanchard (2016) claims that the Phillips curve is alive (though perhaps not so well) in the U.S. data. Among other things, he reports that:
  1. Low unemployment still pushes inflation up; high unemployment pushes it down. 
  2. The slope of the Phillips curve, i.e., the effect of the unemployment rate on inflation given expected inflation, has substantially declined. But the decline dates back to the 1980s rather than to the crisis. There is no evidence of a further decline during the crisis.
Some economists reason that the theoretical Phillips curve only appears flat these days because monetary policy is successfully keeping inflation close to target. If a central bank can hit its target inflation rate perfectly, then it's no surprise that measured fluctuations in unemployment will have no statistical relationship with inflation. There's probably something to this argument.

Whatever the explanation, it will have to account for what I think is an interesting asymmetry in the  statistical Phillips curve. In particular, the U.S. Phillips curve appears to be negatively sloped when unemployment is rising (as in a recession) and is either flat or even positively sloped when unemployment is falling (as in a recovery).

In what follows, I measure inflation as the monthly year-over-year change in the PCE, averaged at the quarterly frequency. The unemployment rate is the quarterly civilian unemployment rate. I look at U.S. data 1980:1 - 2019:1.  Here's what the data looks like.
I define "recession" as quarters in which the unemployment rate is trending up and "recovery" as quarters in which the unemployment rate is trending down. I divide the sample above into four recession-recovery subsamples. In effect, I plot the Phillips curve conditional on whether the unemployment rate is rising or falling. A full analysis should also control for monetary policy and inflation expectations, but I leave that for another day. Here is what I find.

Episode 1. Recession 1981:1 - 1982:4 and Recovery 1983:1 - 1990:2

Episode 2. Recession 1990:3 - 1992:3 and Recovery 1992:4 - 2000:4

 Episode 3. Recession 2001:1 - 2003:3 and Recovery 2003:4 - 2006:4



 Episode 4. Recession 2007:1 - 2009:4 and Recovery 2010:1 - 2019:1

So it seems that the Phillips curve is alive and well -- but only in recessionary periods. Recessions in the United States tend to be sharp and short-lived. The unemployment rate displays a well-known cyclical asymmetry (something that labor-market search theory accounts for in a natural way; e.g., see here). Whatever it is that drives the unemployment rate sharply higher seems to release a disinflationary force that is not immediately mitigated by monetary and fiscal policy.

At the same time, it seems that the Phillips curve is dead -- at least, once the dust has settled and the economy enters into its typical recovery and expansion phase. (Or does the Phillips curve only appear flat because monetary policy tends to tighten policy over the recovery phase?)

Policy Implications?

What does this imply about the conduct of monetary policy? Well, we have to be careful, of course. But to my eye, the evidence above suggests that the Fed need not worry about letting the unemployment rate decline as far as it wants during a period of economic expansion. The specter of a sharp spike in future inflation because unemployment is too low seems nowhere evident in the data (see also Bullard 2017). In addition, we do not know where the so-called "natural" rate of unemployment resides at any given point in time, assuming that such an object even exists.

In the present environment, I think one might even be inclined to let inflation fluctuate below the target rate--in other words, treat the target rate as a soft ceiling when the economy is expanding. Trying to induce inflation higher during an expansion phase seems strange (imprudent?) to me for a couple of reasons.

First, what is the point of purposely taking an action that could be construed as making the cost-of-living grow more rapidly over time? How is such an action to be justified, apart from fulfilling an apparent desire on the part of a small number of technocrats to maintain "credibility" of the "symmetric" inflation target? There may be ways to justify persistent inflation overshooting following a period of persistent undershooting (e.g., if the goal is price-level targeting). But the arguments I've heard made in this regard are probably too subtle to communicate effectively and persuasively. If so, then why not just let inflation fluctuate between 0-2%. It's not like we can measure it with precision in any case (a point former Vice Chair Stan Fischer was fond of repeating).

Second, modern day central banks were built for the purpose of keeping a lid on inflation--they were not built to promote it. The present projected trajectory of deficit-spending will almost surely, sooner or later (Japan notwithstanding), generate inflationary pressure. (If it doesn't, then please just keep cutting taxes and increasing spending.) So again, it seems that the Fed (and the U.S. economy) might be better served by viewing 2% inflation as a soft ceiling--something to defend only in the event that inflation begins to wander significantly and persistently away from 2% (or whatever number one has in mind) in normal times. Let the fiscal authority have the fiscal space it wants/needs as long as inflation remains low.

Recessions, when they hit, tend to appear suddenly and unpredictably. Forecasting the precise date of a recession is a mug's game. Estimating recession probabilities seems more art than science. Perhaps the best that monetary policy can do is to be prepared to act quickly and decisively when the unemployment rate starts rising rapidly. If recent history is a guide, a sharp recession is likely to release a strong disinflationary impulse (related theory paper). In the old days, we might have labeled this a "money demand shock." Today, it is more likely to be described as a "flight to safety shock"--i.e., the safety of U.S. dollars and Treasury securities. I don't think it's particularly helpful to say that high unemployment is causing low inflation--the direction of causality may working in the opposite direction (a high demand for money/debt is causing low inflation). But either way, the appropriate policy response likely entails an accommodating expansion in the supply of money/debt.


Saturday, May 25, 2019

Is the U.S. budget deficit sustainable?

The U.S. federal budget deficit for 2018 came in just shy of $800 billion, or about 4% of the gross domestic product (the primary deficit, which excludes the interest expense of the debt, was about 3% of GDP).
As the figure above shows, the present level of deficit spending (as a ratio of GDP) is not too far off from where has been in the 1970s and 1980s. It's also not too far off from where it was in the early 2000s (although, the peaks back then were associated with recessions).

Of course, the question people are asking is whether deficits of this magnitude can be sustained into the foreseeable future without economic consequences (like higher inflation). In this post, I suggest that the answer to this question is yes, but just barely. If I am correct, then any new government expenditure program will have to come at the expense of some other program, or be funded through higher taxes. Let me explain my reasoning.

The Arithmetic of Government Spending and Finance

I begin with some basic arithmetic (I describe here where theory comes in). Let G denote government expenditures and let T denote government tax revenue. Then the primary deficit is defined as S = G - T  ( if S  <  0, then we have a primary surplus ). The absolute magnitudes involved have little meaning--it turns out to be more useful to measure a growing deficit relative to the size of a growing economy. Let Y denote the gross domestic product (the total income generated in the economy). The deficit-to-GDP ratio is then given by (S/Y).  In what follows, I will assume that this ratio is expected to remain constant over the indefinite future (this is what a "sustainable" budget deficit means.)

Let D denote the outstanding stock of government "debt." For countries that issue debt representing claims to their own currency and permit their currency to float in foreign exchange markets, attaching the label "debt" to these objects--like U.S. Treasury securities--is somewhat misleading. The better analog in this case is equity. Companies that finance acquisitions or expenditure through equity do not have to worry about bankruptcy. They may have to worry about diluting the value of existing shareholders if they over-issue equity, or use it to finance negative NPV projects. The same is true of the U.S. federal government (but not state or local governments). The risk of over-issuing treasury debt is not default--it is share dilution (i.e., inflation).

Let R denote the gross yield on debt (so that R - 1 is the net interest rate). If we interpret D as currency, then R = 1 (currency has a zero net yield). If we interpret D as U.S. Treasury debt, then R = 1.025 (UST debt has an average net yield of around 2.5%). Note that in some jurisdictions today, government debt has a negative yield (so, R < 1 ) -- that is, government "debt" is in this case an income-generating asset!

Alright, back to the arithmetic. Let D' denote the stock of debt inherited from the previous period that is due interest today. The interest expense of this debt is given by (R - 1)D' (the interest expense of currency is zero). The primary deficit plus interest expense must be financed with new debt D - D', where represents the stock of debt today and D' represents the stock of debt yesterday. Our simple arithmetic tells us that the following must be true:

[1]  S + (R - 1)D' = D - D'

Let me rewrite [1] as:

[2] S = D - RD'

Now, let's divide through by Y in [2] to get:

[3] (S/Y)  = (D/Y) - R(D'/Y)

We're almost there. Notice that (D'/Y) = (D'/Y')(Y'/Y). [I want to say that this is just high school math...except that my son came to me the other night with a homework question I could not answer. If you're not good at math, I understand your pain. But if you need some help, don't be afraid to ask someone. Like my son, for example.]

Define n = (Y/Y'), the (gross) rate at which the nominal GDP grows over time. In my calculations below, I'm going to assume n = 1.05, that is 5% growth. Implicitly, I'm assuming 2-3% real growth and 2-3% inflation, but I don't think what I have to say below depends on what is driving NGDP growth. In any case, let's combine (D'/Y) = (D'/Y')(Y'/Y) and n = (Y/Y') with [3] to form:

[4] (S/Y)  = (D/Y) - (R/n)(D'/Y')

One last step: assume that the debt-to-GDP ratio remains constant over time; i.e., (D'/Y') = (D/Y). Again, I impose this condition to characterize what is "sustainable." Combining this stationarity condition with [4] yields:

[*] (S/Y)  = [1 - R/n ](D/Y)

Condition [*] says that the deficit-to-GDP ratio is proportional to the the debt-to-GDP ratio, with the factor of proportionality given by [1 - R/n ]. This latter object is positive if R < n and negative if R > n.

The Mainstream View

There is no such thing as "the" mainstream view, of course. But I think it's fair to say that in thinking about the sustainability of government budget deficits, many economists implicitly assume that R > n. In this case, condition [*] says that if the outstanding stock of government debt is positive (D > 0), then sustainable deficits are impossible. Indeed, what is needed is a sustainable primary budget surplus to service the interest expense of the debt.

The condition R > n is a perfectly reasonable assumption for any entity that does not control or influence the money supply: state and local governments, emerging economies that issue dollar-denominated debt, EMU countries that issue debt in euros, federal governments that abide by the gold standard or delegate control of the money supply to an independent central bank with a preference for tight monetary policy.

The only exception to this that a mainstream economist might make is for the case of "debt" in the form of currency. The seigniorage revenue generated by currency (zero-interest debt), however, is typically considered to be small potatoes. Consider the United States, for example. Let's interpret D as currency. Currency in circulation is presently around $1.7 trillion, almost 10% of GDP. So let's set (D/Y) = 0.10, R = 1, and n = 1.05 in equation [*]. If I've done my math correctly, I get (S/Y) = 0.0025, or (1/4)% of GDP. That's about $100 billion. This may not sound like "small potatoes" to you and me, but it is for a government whose expenditures in 2018 totaled about $4 trillion.

The New and Modern Monetarist View

I think of "monetarists" as those who view money and banking as critical factors in determining macroeconomic activity. I'm thinking, for example, of people like Friedman, Tobin, Wallace, Williamson and Wright (old and new monetarists) on the mainstream side and, for example, Godley, Minksy, Wray, Fullwiler on the MMT (and other heterodox) side. A common ground shared by new/modern monetarists is the view of treasury debt as a form of money; i.e., the difference between (say) U.S. Treasury debt and Federal Reserve money is more of degree than in kind. Consider, for example, the following two objects:
Can you spot the difference?  The first one was issued by the U.S. Treasury and the second one by the Federal Reserve (the promised redemption for silver has long since been suspended). The Fed is said to "monetize the debt" when it replaces the top bill with the bottom bill. Is it any wonder why the BoJ cannot create inflation by swapping zero-interest BoJ reserves for zero-interest JGBs? (In case you're interested, see my piece here.)

In any case, rightly or wrongly, U.S. government policy presently renders the treasury bill illiquid (in the sense that it cannot easily be used to make payments). Of course, while the treasury bill no longer exists in physical form, every U.S. person can acquire the electronic version of (interest-bearing) T-bills at www.treasurydirect.gov. Just don't expect to be able to pay your rent or groceries with your treasury accounts any time soon. (Though, as I have argued elsewhere, it would be a simple matter to integrate treasury direct accounts with a real-time gross settlement payment system.)

But even if treasury securities cannot be used to make everyday payments, they are still liquid in the sense of being readily convertible into money on secondary markets (and maybe one day, on a Fed standing repo facility, as Jane Ihrig and I suggest here and here). USTs are used widely as collateral in credit derivative and repo markets -- they constitute a form of wholesale money. Because they are safe and liquid securities, they can trade at a premium. A high price means a low yield and, in particular, R < n is a distinct possibility for these types of securities.

In fact, R < n seems to be the typical case for the United States.
The only exception in this sample is in the early 1980s -- the consequence of Volcker's attempt to reign in inflation.

But if this is the case, then the mainstream view has long neglected a source of seigniorage revenue beyond that generated by currency. Low-yielding debt can also serve as a revenue device, as made clear by condition [*] above. How much is this added seigniorage revenue worth to the U.S. government?

Let's do the arithmetic. For the United States, the (gross) debt-to-GDP ratio is now about 105%, so let's set (D/Y) = 1.0.  Let's be optimistic here and assume that the average yield on USTs going forward will average around 2%, so R = 1.02. As before, assume NGDP growth of 5%, or n = 1.05. Condition [*] then yields (S/Y) = 0.03, or 3% of GDP. That's about $600 billion.

$600 billion is considerably more than $100 billion, but it's still small relative to an expenditure of $4 trillion. And, indeed, since the budget deficit is presently running at around $800 billion, there seems little scope to increase it without inducing inflationary pressure. (Note: by "increase it" I mean increase it relative to GDP. In the examples above, the debt and deficit all grow with GDP at 5% per year).

Conclusion

What does this mean for fiscal policy going forward? The main conclusion is that the present rate of deficit spending and high level of debt-to-GDP is not something to be alarmed about (especially with inflation running below 2%). The national debt can, will, and probably should continue to grow indefinitely along with the economy. What matters more is how expenditures are directed and how taxes are collected. Of course, this should be done with an eye to keeping long-term inflation in check.

What deserves our immediate attention, in my view, is a re-examination of the mechanisms through which government spending (when, where and how much) is determined. This is not the place to get into details, but suffice it to say that one should hope that our elected representatives have a capacity to reason effectively, have a broad understanding of history, are willing to listen, and do not view humility and compromise as four-letter words or signs of personal weakness. If we don't have this, then we have much deeper problems to deal with than the national debt or deficits.

Once the spending priorities have been established, the question of finance needs to be addressed. If the level of spending is less than 2% of GDP, then explicit taxes can be set to zero--seigniorage revenue should suffice. However, if we're talking 20% of GDP then tax revenue is necessary (at least, if the desired inflation target is to remain at 2%). If the tax system is inefficient and cannot be changed, this may mean cutting back on desired programs. Ideally, of course, the tax system could be redesigned to minimize inefficiencies and distortions. But tax considerations are likely always to remain in some form and, because this is the case, they should be taken into consideration when evaluating the net social payoff to any new expenditure program.

Wednesday, March 27, 2019

Is the ZLB an economic or legal constraint?

The so-called zero-lower-bound (ZLB) plays a prominent role in modern (and even older) macroeconomic theories. It is often introduced in a paper or at conference as a fact of life -- an unavoidable property of the physical environment, like gravity. But is it correct to view it in this way? Or is the ZLB better thought of as legal constraint--something that can potentially be circumvented by policy?

The Financial Services Regulatory Relief Act of 2006 allows the U.S. Federal Reserve (the Fed) to pay interest on reserve accounts that private banks hold at the Fed. Specifically, the Act states that:
Balances maintained at a Federal Reserve bank by or on behalf of a depository institution may receive earnings to be paid by the Federal Reserve bank at least once each calendar quarter, at a rate or rates not to exceed the general level of short-term interest rates.
The effective date of this authority was advanced to October 1, 2008, by the Emergency Economic Stabilization Act of 2008.

It is not clear (to me, at least) whether the Act grants the Fed the authority to pay a negative interest rate on reserves. Note that if the interest-on-reserves (IOR) rate is set to a negative number, then banks would in effect be paying the Fed a "service fee" for the privilege of holding reserve balances with the Fed. But if the Fed is not legally permitted to use negative interest rate policy (NIRP), then the ZLB is obviously a legal constraint.

This legal constraint, however, may not be binding if the ZLB is also an economic constraint. In fact, the traditional explanation for the ZLB is the existence of physical currency bearing zero interest. The idea that arbitrage will effectively keep interest rates from falling below zero is deeply ingrained in the minds of economists. For example, Corriea, et. al. (2012) write:
Arbitrage between money and bonds requires nominal interest to be positive. This "zero bound" constraint gives rise to a macroeconomic situation known as a liquidity trap. It presents a difficult challenge for stabilization policy.
However, we know from recent experience that the ZLB appears not to be an economic constraint.  Several central banks today have set their deposit rates into negative territory:


There is currently over $10 trillion of government debt in the world yielding a negative nominal interest rate; see here. As of this writing, even long bonds like the German 10-year Bund are in negative territory.

Well, alright, so the ZLB is evidently not an economic constraint. But surely there is some limit to how low nominal interest rates can fall? This lower limit is called the effective lower bound (ELB). And economic theory is clear: if we're at the ELB in a recession, then monetary policy has done about as much as it can be expected to do.

But what exactly is the ELB? Is it -1%, -2%, -5%, or perhaps even lower? Economists like Miles Kimball believe it to sufficiently negative to warrant NIRP as an effective policy tool; see here (see also the discussion by Ken Rogoff in chapter 10 of his book). These arguments, however, did not seem to gain much traction. For example, in the present discussions concerning the Fed's new long-run monetary policy framework, the possibility of NIRP is not even mentioned. But perhaps it should be if the ELB is in fact significantly below zero. In what follows, I want to make my own (related) argument for why the ELB is probably a lot lower than most people think.

Suppose the Fed was to set the IOR to -10% (in a deep demand-driven recession, this would presumably be accompanied with a promise to raise the IOR at some point in the future). The traditional economic argument suggests that any security dominated in rate of return by cash would in this case be driven out of circulation.

The first thing we could imagine happening is banks attempting to convert their digital reserves into vault cash. Banks are presently holding over $1.6 trillion in reserves with the Fed. The largest denomination Federal Reserve note is $100. This is what $1 trillion in $100 bills apparently looks like:


That's about the size of a football field. Banks would not convert all of their reserves into cash--even if it was costless to do so--because they'd need about $20-30 billion or so to make interbank payments. Of course, managing all that cash would be far from costless. But there is a simpler reason for why banks would not make the conversion. The Fed could simply charge banks a 10% service fee on their vault cash.

Alright, well what effect is the -10% IOR rate going to have on the deposit rate (or fees) that banks offer (or charge) their depositors? Banks are not likely to pass the full cost on to their depositors, especially if they view the NIRP to be temporary, because they'll want to maintain their customer relationships.

But let us take the extreme case and suppose that NIRP is perceived to be permanent. Then surely deposit rates will decline (or bank fees will rise) significantly. Deposit rates may even decline to the point where depositors start withdrawing their money from the banking system. Banks may well let this source of funding go if they could borrow more cheaply from the Fed (banks would need to borrow reserves to honor the withdrawal requests of their customers). Of course, the Fed lending rate is also a policy variable and could, in principle, be lowered to negative territory as well.

But how realistic is it to imagine all or most bank deposits converted to cash? While this might be the case for small value accounts, it seems unlikely that the business sector would be able to manage its payments needs without the aid of the banking system. Even money market funds need to work through the banking system. I suppose one could imagine a new product created by (say) Vanguard in which they create a cash fund with equity shares redeemable for cash that is collected and stored in rented Las Vegas vault. But the moment the activity is intermediated, it becomes taxable. If the Fed is not permitted to tax (oops, charge a service fee) such entities, the fiscal authority could, in principle, implement a surcharge that is set automatically off the IOR rate in some manner.

I think in this way one can see how the ELB might easily be well below -5% (or more). This is probably low enough to allow us to disregard the ELB as a binding economic constraint. The relevant constraint is always a legal one. And laws can be changed if it is deemed to serve the public interest.

Keep in mind that in a large class of economic models, ranging from Keynes (1936) to New Keynesian, there is potentially much to be gained by eliminating the ZLB. If these models are wrong, then let's get rid of them. But if they're roughly correct, why don't we take their policy prescriptions seriously? Let's stop talking about the ZLB as if it's a force of nature. It is a policy choice. And if it's a bad policy choice, it should be changed.



Thursday, March 14, 2019

The Chicago Booth Survey on MMT

I want to say a few things about Chicago Booth's recent survey questions posed to a set of economists; see here. The survey asked how strongly one believes in the following two statements:

Question A: Countries that borrow in their own currency should not worry about government deficits because they can always create money to finance their debt.

Question B: Countries that borrow in their own currency can finance as much real government spending as they want by creating money.

Not surprisingly, most economists surveyed disagreed with both statements. Fine. But, not fine, actually. Because the survey prefaced the two questions with 

Modern Monetary Theory

as if the the two statements constitute some core belief of MMT.  

Was any MMT proponent included in the survey? Don't be ridiculous, of course not (there were a couple from MIT though--perhaps they thought this was close enough). How would a typical MMT proponent have answered these two questions? I am sure that most would have answered in the exact same way as other economists. If this is the case, then why does Chicago Booth preface the survey with MMT? There are many possibilities, none of which are attractive for Chicago Booth.

Let's consider Question B first. Or, better yet, let's not. This question is so ridiculous it hardly merits a response. Nobody believes that governments face no resource constraints.

O.K., so let's consider Question A, where some legitimate confusion may be present. Before I start though, I want to make clear that I don't purport to know the entire MMT academic literature very well. But I have done some reading and I have corresponded with some very smart, very thoughtful MMT proponents. I don't agree with many of their views, but I think I see how some of what they say is both valid and contrary to conventional thinking. At the very least, it seems worth exploring. What I am about to say is my own interpretation -- I am not speaking on behalf of MMTers.

Alright, so on to the question of whether deficits "matter." The more precise MMT statement reads more like this "A country that issues debt denominated in its own currency operating in a flexible exchange rate regime need not worry about defaulting in technical terms on its outstanding debt." That is, the U.S. government can always print money to pay for its maturing debt. That's because U.S. Treasury securities represent claims for U.S. dollars, and the government can (if it wants) print all the dollars it needs. 

Nobody disagrees with this statement. MMTers like to make it explicit because, first, much of the general public does not understand this basic fact, and second, this misunderstanding is sometimes (perhaps often) used to promote particular ideological views on the "proper" role of government.

Mainstream economists, like myself, like to point out what matters is not technical default but economic "default." An unexpected inflation whittles away the purchasing power of those caught holding old money as new money is printed to pay for whatever. I think it's clear that MMTers understand this too. This can be seen in their constant reference to an "inflation constraint" as defining the economic limits to government spending. I tried to formalize this idea in my previous blog post; see here: Sustainable Deficits.

But it's more complicated than this -- and in interesting ways, I think. Consider a large corporation, like General Motors. GM issues both debt and equity. The debt GM issues is denominated in dollars, so it can go bankrupt. But GM also issues a form of "money"--that is, is can use newly created equity to pay its employees or to make acquisitions.

Issuing more equity does not expose GM to greater default risk. Indeed, it may very well reduce it if the equity is used to buy back GM debt. If GM is thinking about financing an acquisition through new equity issuance, the discussion is not going to about whether GM can afford to print the new shares. Of course it can print all the shares it wants. The question is whether the acquisition is accretive or dilutive. If the former, then issuing new money will make the value of GM money go up. If the latter, then the new share issue will be inflationary (the purchasing power of GM shares will go down). In other words, "deficits don't matter" in the sense that the outstanding GM liabilities do not matter per se -- what matters is something more fundamental. Equity "over-issue" may not be desirable, but the phenomenon is symptomatic, not causal.

The U.S. government and Federal Reserve in effect issue equity. The government need not default on its debt. This is because U.S. Treasury debt is convertible into money (equity) and the Fed can do so if it so chooses. The question for the government, as with GM, is whether any new spending program is accretive or dilutive. If the economy is operating at less than full capacity, then this is like GM being presented with a positive NPV investment opportunity. The government can issue new money that, if used wisely, need not be inflationary.

There are limits to how far this can go, of course. And there was the all important qualifier "if used wisely." But this is exactly where the debate should be: how should our institutions be designed to promote the "best" allocation of resources?

I often hear that MMTers don't have a good theory of inflation. As if there is a good theory of inflation out there already. But I see in MMT a theory of inflation that overlaps (not entirely) with my own views expressed, say, here: The Failure to Inflate Japan. The MMT view seems to take a broader view over the set of instruments that monetary policy may employ to control inflation. We can have a debate about the merits of their views, but there's no reason to dismiss them outright or to pretend they don't have a theory of inflation.

Another complaint I hear: the MMTers don't want to produce a model. You know, it's true, there are not many mathematical models out there. So what? 

First, the lingua franca of policy making is English -- math is a part of a trade language. Economic ideas can be understood when expressed in the vernacular. It's also been helpful to me and others to attempt to "formalize" our thoughts in our trade language. But it seems to me that some of my colleagues can only understand an argument if it's posed in their trade language. This is a rather sad state of affairs, if true. 

Second, MMT, like any school of thought, is evolving over time and comes from a different tradition. Instead of demanding a model (now!), why not reach out and try to help formalize some of their ideas. You never know -- you may actually learn something in the process.

I could go on, but will stop here for now. 


Monday, March 11, 2019

Sustainable deficits

There's been much welcome discussion of late concerning the sustainability of government budget deficits and whether the size of the public debt is anything to worry about. I'm not going to answer this question for you here today. But what I would like to do is describe a framework that economists frequently employ to help organize their thinking on the matter. I want to begin with some simple arithmetic and then move on to a bit of theory. I'll let you judge whether the framework has any merit.

Let's start with some standard definitions.
G(t) = government spending (purchases and transfers) in year t.
T(t) = government tax revenue in year t.
R(t) = gross nominal interest rate on government debt paid in year t+1.
D(t) = nominal government debt in year t (including interest-bearing central bank reserves).

Now let's link these objects together using the following identity:

[1] G(t) + [R(t-1) - 1]*D(t-1) = T(t) + [D(t) - D(t-1)]

In words, the left-hand-side (LHS) of the identity measures the money needed to pay for government spending G(t) and the interest expense of the debt [R(t-1) - 1]*D(t-1), where [R(t-1) - 1] denotes the net nominal interest rate. The right-hand-side (RHS) of the identity measures the money collected by the government in the form of taxes T(t) and the money created through new nominal debt issuance [D(t) - D(t-1)].

I find it convenient to rewrite [1] as,

[2] G(t) - T(t) = D(t) - R(t-1)*D(t-1)

The LHS of [2] represents the primary government budget deficit. If the deficit is positive in period t, then the RHS of [2] tells us that the stock of debt in period t must be larger than the interest plus principal of the debt maturing from period t-1.

Next, define n(t) = D(t)/D(t-1), that is, the (gross) rate of growth of the nominal debt. Use this definition to write D(t-1) = D(t)/n(t) and substitute this expression into [2] to form,

[3] G(t) - T(t) = [1 - R(t-1)/n(t)]*D(t)

Let Y(t) denote the nominal GDP. Now define g(t) = G(t)/Y(t), τ(t)=T(t)/Y(t) and d(t) = D(t)/Y(t). Because I want to limit attention to "long run" scenarios, let me impose a stationarity restriction: g(t) = g, τ(t) = τ, d(t) = d, R(t-1) = R, and n(t) = n. Then we can write [3] as,

[4] g - τ = [1 - R/n]*d

Assuming d > 0, the identity [4] tells us that a sustained primary deficit is possible only if R < n. Recall that R represents the (gross) nominal interest rate on government debt and n represents the (gross) rate of growth of the nominal debt. Because of my stationarity assumption d = D(t)/Y(t), it follows that n also represents the (gross) rate of growth of the nominal GDP.

A lot of mainstream thinking on the matter of "fiscal sustainability" is rooted, I think, in the assumption that R > n. In the standard DSGE model (which abstracts from financial market frictions), the "real" interest rate R/n is pinned down by time-preference and productivity growth. This real interest rate is typically estimated to be a positive number. If this is the view one adopts, then condition [4] implies that budget deficits cannot be sustained into the indefinite future. It's not exactly made clear what might happen if deficit finance persists in such a case -- maybe inflation and/or default. Bond vigilantes. Something like that.

But this view is, at best, seriously flawed. First of all, as just an empirical matter, R < n seems like a better approximation than R > n. Here the year-over-year growth rate of nominal GDP and the one-year Treasury-bill rate for the U.S. economy since 1961,


Secondly, the standard DSGE model ignores the role that U.S. Treasury debt plays as an exchange medium in financial markets. The growth in the demand for Treasury debt has come from many sources over the past few decades. It is used extensively as collateral in credit-derivative and repo markets. Foreign countries have clamored to accumulate U.S. Treasuries as a store of value. Its demand was further enhance as a "flight to safety" asset during the financial crisis. And more recently, changes in financial regulations (Dodd-Frank and Basel III) have further spurred the demand for Treasuries (for example, they can be used to satisfy the Basel III liquidity-coverage-ratio requirement for banks).

Because of the special role played by nominally safe government debt in financial markets, it can trade at a premium. That is, agents and agencies are willing to hold "monetary" objects for reasons other than their pecuniary rate of return. This is why the nominal (and real) interest rate on safe government securities can be set lower than the "natural" rate of interest. If R < n, then the RHS of [4] corresponds to seigniorage revenue. (Note: seigniorage is not limited to the purchasing power created by zero-interest cash.)

Some of this discussion seems related to what the MMT folks are talking about. I'm not an expert in that area (am still reading up on it), but see, for example, Scott Fullwiler's article: The Debt Ratio and Sustainable Macroeconomic Policy. There's also this nice piece by (the more mainstream) Neil Mehrotra: Debt Sustainability in a Low Interest Rate World and, of course, Olivier Blanchard's AEA Presidential Address: Public Debt and Low Interest Rates.

Are there limits to how large a sustainable deficit might be? To answer this question, we need to go beyond the identities described above. Here's a simple theoretical restriction: Assume that the demand for real debt d is increasing in its real yield R/n. In undergraduate money-macro textbooks, we might say "assume that the demand for money is increasing in the interest rate paid on money." Note that for a given nominal interest rate R, this implies that the demand for real money balances is decreasing in the (expected) inflation rate. Let's denote this theory of money demand by the behavioral equation:

[5] d = L(R/n), with L increasing in R/n.

Combine the theoretical statement [5] with the identity in [4] to form a government budget constraint:

[6] g - τ = [1 - R/n]*L(R/n)

Now, to discover the limit of how large the deficit can get, imagine that the government wants to maximize the sustainable deficit through its choice of R/n (all that matters here is the ratio). What are the limits to seigniorage revenue?

The answer to this question has a standard "Laffer curve" property to it. Increasing R (or decreasing n) is bad because doing so increases the interest expense of the debt. On the other hand, it increases the demand for debt. Think of [1 - R/n] as the tax rate and L(R/n) as the tax base. Increasing R/n has competing effects. So, for example, increasing n has the effect of increasing the inflation tax rate. This is good for revenue purposes. But it also has the effect of decreasing the tax base (as people substitute out of government debt into competing securities). This is bad for revenue purposes. The revenue (primary deficit) maximizing interest/inflation rate equates these two margins. In short, economic behavior places a restriction on how much the government can finance its operations through money/debt issuance.

This is a very simple theory and it can be extended in many different and interesting ways. But the point of this blog post was first, to demonstrate how government budget identities can be combined with economic theory to form a meaningful government budget constraint and second, to demonstrate that there's nothing necessarily wrong or unsustainable about a government running a persistent budget deficit.


Postscript: March 12, 2019

I should have figured that Nick Rowe beat me to this post; see here. He also provides this nice Laffer curve diagram.

In the diagram above, r corresponds to my R and g corresponds to my n. I think I would have drawn the diagram with seigniorage revenue on the y-axis and the real interest rate (R/n) on the x-axis. Then (R/n)* would denote the seigniorage revenue maximizing real yield on government debt.

Nick points out that in the OLG model, the introduction of (say) land eliminates the possibility that R < n in equiilbrium. This is true only if government debt serves only as a store of value. My paper with Fernando Martin uses a standard macro model where debt has a liquidity role and coexists with a higher yielding alternative asset. It also has a diagram like Nick's (Figure 1).

A final thought. One often hears MMTers say something like "we replace the government budget constraint with an inflation constraint." I interpret this statement in the following way. Imagine setting the nominal interest rate to its lower bound R = 1 (I actually think it can go lower). Then the real rate of return on government debt (zero-interest money) is 1/n. If the real GDP is constant, then n represents the equilibrium inflation rate (in a model where we impose the additional market-clearing restriction). Assuming we are on the LHS of the Laffer curve, increasing the inflation rate increases the primary deficit. An inflation constraint n < n* then limits how large the primary deficit can be.