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

Thursday, February 8, 2018

Fiscal theories of the price-level

This post is me thinking out loud about how fiscal considerations may influence the price-level.  The question of what determines the price-level is an old one. It's a question that economists struggle with to this day.

To begin, what do we mean by the price-level? Loosely, the price-level refers to the "cost-of-living," where cost is measured in units of money. Living refers to the flow of services consumed (destroyed) for the purpose of survival/enjoyment. (Note that the cost-of-living might alternatively be measured as the amount of labor one must expend per unit of consumption, but this would require a separate discussion.)

Measuring aggregate material living standards is challenging for two reasons. First, people consume a variety of goods and services. Suppose that the price of food goes up and the price of shelter goes down. Does the cost-of-living go up or down? Second, different people have different material needs/wants (and individual wants and needs change over time too). Statisticians do the best they can to address these complications by constructing "average consumption bundles" as done in the calculation of the Consumer Price Index (CPI). The following diagram plots the change in the price-level (the inflation rate) for several categories of goods and services:

In what follows, I'm going to abstract from inflation and focus only on the theory of the price-level (inflation is the rate of change in the price-level over an extended period of time). To this end, think of a very simple world where the real GDP (y) is fixed and determined exogenously (independent of monetary policy). Assume that the expected rate of inflation is zero. Then, by the Fisher equation, the nominal interest rate corresponds to the real interest rate. I want to think of this interest rate as being potentially influenced by monetary policy (I like to think of r as representing the real yield on treasury debt, where treasury debt possesses a liquidity premium.)

Perhaps the oldest theory of the price-level is the so-called Quantity Theory of Money (QTM). It seems clear enough that people and agencies are willing to accept and hold money because money facilitates transactions--it provides liquidity services. In the simplest version of the QTM, the demand for real money balances takes the form L(y), where L is increasing in y. The idea here is that the demand for liquidity is increasing in the level of aggregate economic activity (as indexed by y).

Next, the QTM assumes that the supply of money (M) is determined by the central bank. Let P denote the price-level. Then (M/P) denotes the supply of real money balances. The QTM asserts that the price-level is determined by an equilibrium condition which equates the supply of real money balances with the demand for real money balances. Mathematically,

[1] M/P = L(y)

Condition [1] can be explained as the consequence of the "hot potato" effect. The idea is that someone must be willing to hold the extant money supply. If M/P > L, then the money supply exceeds money demand. In this case, people will presumably try to dispose of their money holdings (by spending them on goods and services). People accepting money for payment will be thinking the same thing--they are willing to accept the money, but only selling their goods at a higher price. The "hot potato" effect ceases only when condition [1] holds. The same logic applies in reverse when M/P < L (with everyone wanting to get their hands on the potato).

Now, suppose that y varies over time. Then the QTM suggests that a central bank can keep the price-level stable at P0 by letting the money supply move in proportion to money demand; i.e., M = L(y)*P0. This is what is meant by "furbishing an elastic currency." This reminds us as well that interpreting money-price correlations in the data are tricky if money demand is "unstable."

O.K., so now let's see where fiscal policy fits in here. Let D denote the outstanding stock of government debt. If a central bank is restricted to create money only out of government debt, then we can write M = θD, where 0 < θ < 1 is the fraction of the debt monetized by the central bank. If the central bank wants to increase the money supply, it would conduct an "open market operation" in which it buys bonds for newly-issued money, resulting in an increase in θ. Note that the money supply may increase through changes in D for a constant θ.

Let B denote the bonds held by the private sector (i.e., not including the bonds held by the central bank). That is, B = (1 - θ)D. The interest expense of the public debt is given by rB. Note, while the treasury actually pays an interest expense rD, the interest payments to the central bank rM are remitted to the treasury, leaving a net cost equal to rB = r(D-M). Thus, the central bank is in a position to lower the interest expense of the public debt by monetizing a larger fraction of it (I discuss this in more detail here and here.) To the extent that the central bank influences r, it is also in a position to lower the interest expense by lowering r.

Now let's write down the government "budget constraint." Let T denote tax revenue (net of transfers) and let G denote government purchases (of goods and services). Then, assuming that default is not an option, the government budget constraint is given by,

[2] = G + rB

The difference T - G is called the primary budget surplus (deficit, if negative). So another way to read [2] is that the interest expense of the government debt must be financed with a primary surplus. Note that if r < 0, then the government is in a position to run a perpetual primary deficit. (The more general condition is r < g, where g is the growth rate of the economy, which I've normalized here to be zero.)
In most monetary models, the fiscal policy plays no role in determining the price-level. The reason for this lies in the implicit assumption that taxes are non-distortionary (e.g., lump-sum) and that the fiscal authority passively adjusts T to ensure that condition [2] holds.  This latter assumption is sometimes labeled a Ricardian fiscal regime. In a Ricardian regime, fiscal policy does not matter for the price-level. To see this, suppose that the central bank increases r. Then the fiscal authority increases T (or decreases G) with no change in the money supply or price-level. Or, imagine that the fiscal authority increases D. In this case, the central bank can keep the money supply constant by lowering θ, the fraction of debt it chooses to monetize. If so, then B will increase. In a Ricardian regime, the fiscal authority will again either increase T (or decrease G), leaving the price-level unchanged. 

But suppose fiscal policy does not behave in the Ricardian manner described above. To take an example, suppose that the fiscal authority instead targets T, or T-G, or (T-G)/P, etc. For concreteness, suppose it targets the real primary surplus τ = (T-G)/P.  In this case, condition [2] can be written as, 

[3] τ = r(B/P)

Condition [3] forms the basis of what is known as the fiscal theory of the price-level (FTPL); see Cochrane (1998). The idea is as follows. Imagine a world where there is no need for money (a cashless economy), so that condition [1] is irrelevant. Imagine too that the real rate of interest is determined by market-forces, so that r > 0 represents the "natural" rate of interest. Finally, imagine that the outstanding stock of debt D = B is nominal. Then the price-level is determined by condition [3] which, while resembling a government budget constraint, is in fact a standard stock-valuation equation. To see this, rewrite [3] as follows,

[4] (B/P) = τ/r

The right-hand-side of [4] represents the present value of a perpetual flow of primary government budget surpluses τ. The left-hand-side of [4] measures the real value of the government's debt. The equation [4] asserts that the real value of government debt is equal to the present value of the stream of primary surpluses. This is analogous to the way one might value the equity of a company that generates a stream of profits τ. 

Note that condition [4] looks a lot like condition [1]. We can use the same "hot potato" analogy to describe the determination of the price-level in this case. For example, suppose that (B/P) > τ/r. Then people and agencies will presumably want to sell the over-valued government debt (for goods and services). People are willing to accept these nominal claims, but only if they are sold more cheaply--that is, if the goods sold to acquire the bonds can be sold at a higher price. As before, this hot potato effect ceases only when condition [4] holds. 

I'm still not sure what to think about the FTPL. While I lean more toward the QTM view, I do believe that fiscal considerations can have an important influence on the price-level. The way I'm inclined to think about this, however, is as follows. 

Since nominal government debt represent claims against government money, it's not surprising that such debt inherits a degree of "moneyness." To the extent this is true, the measure of money M used in equation [1] should be expanded to include the liquid component of government debt. Let X < B denote the liquid component of government debt. There are a few ways to think about this. One obvious way is to imagine that the banking sector creates deposit liabilities out of X. Or we could imagine that X is accepted directly as payment for goods and services, at least, for a subset of agencies (China, for example, effectively exports goods and services for X). In any case, the appropriate measure of money is given by M + X. In the limiting case where X = B, the relevant money supply becomes the entire government debt D = M + B, so that condition [1] becomes, 

[5] D/P = L(y)

In a world where government debt becomes increasingly more relevant as an exchange medium than central bank money, control over the money supply is effectively transferred to the fiscal authority.  This is another sense, distinct from the FTPL, in which fiscal policy might influence the price-level. The difference boils down to the source of money demand -- is it primarily liquidity-preference, or is it because money/debt instruments are viewed as tax-backed liabilities?

There is, of course, much that I've left out here.  While the assumed invariance of real economic activity to monetary and fiscal policy is not a bad place to start for the question at hand, it is clearly not a good place to end. As well, the model should be extended to permit sustained inflation. All of this can be easily done and I'll try to come back to it later. 

Something I do not think is critical for the issue at hand is modeling private money creation (beyond the monetization of government debt modeled above). To the extent that banks monetize positive NPV projects, the money they create out of private assets (in the act of lending) creates value that is commensurate with additional liabilities created. In short, accretive share issuances (good bank loans) are not likely to  be dilutive (inflationary). Of course, the same is true of newly-issued government money if the new money is used to finance positive NPV projects (including the employment of labor in cases of severe underemployment). 


  1. Can’t see anything wrong with the Warren Mosler model which can be set out in about 100 words, and which I think he sets out in his “Soft Currency Economics”. It goes like this.

    The private sector wants a stock of state liabilities (base money and government debt). The more of that stock that the private sector has the more it will tend to spend, which raises demand. If the state issues MORE than the stock that the private sector wants, the state (i.e. central bank and or government) it will have to pay interest in order to stop the private sector trying to spend away the excess. Ergo the state could perfectly well issue a stock of liabilities such that it did not pay any interest and yet induced the private sector to spend at a rate that brings full employment.

    That’s about it.

    Re privately issued money (not something Mosler considers in so much detail), that will tend to cut interest rates because it costs private banks nothing to obtain that money, whereas under a "state money only" regime (i.e. full reserve banking) private banks can only obtain money by borrowing it or earning it. The right that private banks have to create or "print" money is actually a subsidy of private banks: one that should be banned. See:

  2. "In most monetary models, the fiscal policy plays no role in determining the price-level. The reason for this lies in the implicit assumption that taxes are non-distortionary (e.g., lump-sum) and that the fiscal authority passively adjusts T to ensure that condition [2] holds. This latter assumption is sometimes labeled a Ricardian fiscal regime. "

    Can you give some colour on the former assumption too? ie the assumption that taxes are non distortionary?

    1. Consider the Friedman rule. It prescribes using a lump-sum tax to finance interest on money (or, equivalently, to destroy zero-interest money at a rate that produces deflation). Without that lump-sum tax instrument, financing such a monetary policy would be more complicated.

  3. You write: "Something I do not think is critical for the issue at hand is modeling private money creation (beyond the monetization of government debt modeled above). To the extent that banks monetize positive NPV projects, the money they create out of private assets (in the act of lending) creates value that is commensurate with additional liabilities created. In short, accretive share issuances (good bank loans) are not likely to be dilutive (inflationary)."

    Shouldn't this be: As long as we can assume that banks only monetize positive NPV projects, then it is not critical to model private money creation.

    In short, if we don't trust the regulation of banks' asymmetric information to prevent banks from originating, monetizing and selling "bad" assets, then we need to model the macroeconomic effects of private money creation. Do you agree?

    Carolyn Sissoko

  4. Broadly speaking, I agree. On the other hand, I suppose this is the role that equity plays. Bank money takes the form of debt, the capital buffer could be used to absorb the losses that banks make on bad loans.

  5. "Bank money takes the form of debt"

    With the right regulation this would be a true statement. In fact, banks nowadays are allowed to commit to expand their deposits on demand -- and these commitments are treated in a FDIC resolution as equally as binding as deposits themselves. Thus, bank guarantees are arguably just as much "bank money" as bank debt itself. These guarantees go by various names: acceptances, letters of credit, liquidity facilities, etc. And they are usually drawn down, if at all, by troubled entities.

    The idea that the capital buffer is adequate to absorb losses on these guarantees was tested 2007-08 and found wanting for several very large banks.

    Carolyn Sissoko

  6. Sorry if I am imposing... The "hot potato" idea that people try to get rid of excess money, seems backwards to me. It seems like spending is driven by acquisition. So excess money would be idle until someone figures out something to spend it on. Perhaps investors behave differently, because they are always in the investment mindset.

    If increased money does not increase spending, velocity decreases in the exact proportion by which the money supply increased. But really, the existing money is circulating just as before, while the additional new money increase just sits idle on the side.

    This hearkens back to deep questions that marx and others have asked about surplus product. Steve Keen has a video titled "Dialectic as a foundation for a dynamic non-equilibrium monetary economics", where he explores this in depth. Specifically, he describes 2 different circuits of exchange between Money and Commodities. The C->M->C circuit is qualitative, and the M->C->M+ circuit is quatitative.(he explains this at 59:30 in the video). Investors ask how they can increase their quantity of money, through investment, while the average joe asks how he can qualitatively improve his comfort by exchanging his commodity of time for consumer goods.

    The overarching thesis of Keen's work is something he calls "debt deflation". I interpret this as not necessarily a decrease in price levels, but an increase in the burden and difficulty of that qualitative exchange of commodities for the averge Joe. Prices don't drop too far, because resources are controlled through debt and capture, but they don't rise either, because the economy is limited by sales, and more product is produced immediately, without overwhelming capacity to the point that competing firms increase prices.

    Inflation is complex. You do a good job of explaining some valuable ideas, I was just wondering if you had thoughts on Keen's work and others like him who try to start from a different conceptual angle.

    1. You're not imposing, thanks for your question. I think it's a good idea to explore different ways of thinking about the determinants of inflation. I have not read Keen's work in this area, though he has promised to send me a set of notes outlining his core macro model. Perhaps these will contain his theory of inflation too.

  7. One way private money might come into play is as follows:

    Rather than the conventional QTM or your extended D/P = L(y), the dominant stock-flow ratio might be something like (D + A) / P =L(y), where A is privately issued high quality liquid assets. Then if lending criteria are relaxed we might see an increase in A/P requiring a rise in P (to reduce D/P).

    This depends on the extent to which private label assets are seen as substitutes for public ones, something that is probably quite relevant to the period leading up and during the GFC.

    1. In the models of private money I've seen, something like the fiscal theory of the price-level is at work. Essentially, if A is used to finance a flow of output, then the supply of liabilities is matched by a corresponding flow of output (loosely, the supply of money increases in proportion to the supply of output, leaving the price level unchanged). I have an old set of notes here that may or may not be of help:

    2. Thank you for the notes. I like your conclusion, which seems to me consistent with the Kaldor critique of monetarism.

      In the context of the GFC, maybe a better model might be one where private lending is against a fixed supply of land, so growth in A is reflected in an increase in the value of land, rather than additional flow of output. Also, the growth of A needs to be driven by a loosening of financial constraints, rather than an increased desire to borrow. This means that the demand for land and hence the price is generally constraint by lending criteria.

  8. This is a good start in thinking about why we have central banks, whether we should have them, and the future role for central banks as transactions technologies change. Economically, what we should care about is the whole spectrum of consolidated government debt, from currency and reserves, through government debt of different maturities. Traditionally, central banking has evolved so that the typical arrangement is a more-or-less independent central bank with a monopoly on currency issue (and reserves too - they play an important role in payments arrangements), and the power to conduct swaps of its liabilities for the liabilities of the fiscal authority. And the fiscal authority makes decisions on debt management - what maturities and how much of each maturity of interest-bearing debt to issue. Historically, the power of the central bank comes from the special nature of its liabilities - determined mainly through its monopoly on currency issue. So here I'm going to differ with David - I think the competing private means of payment and debt instruments are very important. Quantity theory ideas are deeply embedded in how central bankers think about policy - typically open market purchases are thought to increase prices, and growth in the stock of central bank liabilities is thought to lead to inflation. Of course, recent history might make you think twice about that. But, government debt seems to play a special role without any explicit restrictions on the issue of private debt. For example, government debt is the dominant form of collateral in the repo market. So, liquidity is just a matter of degree. And some assets that are liquid in some markets are not liquid in others. For example, currency is useful in retail payments, but useless for interbank transactions. It's currently hard to draw the line between what we think is monetary policy and what we think is fiscal policy. For example, QE looks like debt management, so is that fiscal policy? And what if currency were eliminated (Ken Rogoff might be happy)? Could the central bank control inflation simply by pegging an interest rate on its own interest-bearing liabilities? What if we let the central bank issue a full spectrum of interest-bearing, tradeable securities? Would that be a good thing? We can make some guesses about these things, but there is currently little research that gives us answers.

    1. Excellent points and questions, Steve.

      I think we can all agree that liquidity is a matter of degree. One question I have in regard to this observation is whether any sensible theory of the price-level should recognize this fact, or whether it suffices to restrict attention to the supply of nominal outside assets (or even a subset of such assets, like government currency). Any thoughts on this?

    2. There's no good reason to restrict attention to any class of assets, as far as I can tell.

  9. Well, I am totally confused now.

    That said, I would like you to address some questions.

    We can now assume large federal deficits for as far as the eye can see, even if we ascend Mt. Everest with telescopes.

    So what should be monetary policy?

    The Bank of Japan has gone to QE, and now owns 45% on JGBs. No inflation. They appear to have deleveraged Japan in fact, if not in theory. Interest payments flow back to the Treasury. Is regular QE an option to retire growing federal debt?

    If the US has huge deficits in the future but also hits zero bound again, should it issue large very long term, very low-rate bonds? Japan and Germany can borrow interest free. If the US can, is that another way to deleverage? Issue zero-rate perma-bonds?

    Or should we dispense with the whole Treasury borrowing, Fed open markets operations and commercial banks, reserve ratios and "hope the banks lend" get-up, and go to straight money financed fiscal programs in the next recession? This would also avoid a huge pile up of federal debt and would be stimulative in fact.

    Is QE actually anti-inflationary? Some Dallas Fed bank research guys issued a paper once saying so. QE buys assets that back the federal government and currency.

    Yi Wen of St Louis Fed also wrote a paper that contended QE is anti-inflationary, as did some guys at the NY Fed. This is fascinating---why not buy back debt through QE if this is the case? Move the Fed into the Treasury (as Reagan wanted!).

    I would like for the monetary community to accept as a premise large federal deficits in perpetuity, and then come up with some monetary policies that might actually work.

    Tighter money could trigger a recession and lead to even larger deficits and plenty of misery.

    1. What confused you in what I wrote?

      You ask what monetary policy should be in light of future deficits. For U.S., Fed has a mandate to "do what ever it takes" to keep inflation near target and help out however it can in other areas (the dual mandate). I suspect this will mean raising rates going forward, but much depends on how fiscal policy and the real economy evolves.

      As for other questions on Japan, etc., maybe take a look at

  10. Well I am often confused, so let's pass on that, and go directly to monetary tools.

    Okay, for better or worse, the Fed will target 2% on the PCE (perhaps as a ceiling in real life), and then some real growth.

    But given chronic and large federal deficits, which tools are best?

    Raising interest rates might cause a recession (and then truly epic deficits) and will also balloon interest payments until the recession hits. During the recession, rates will probably hit zero.

    The Dallas Fed published a paper finding QE was anti-inflationary.

    “[T]he [Fed’s] quantitative easing programs, which created money to purchase mortgage-backed securities from the public, preserved price stability because that money is backed by the returns from real estate investments….
    Likewise, any money created to purchase government debt from the public at market prices is backed by the same primary surpluses that the public already expected would service that debt. As long as the expected primary surpluses backing existing government liabilities haven’t changed, there is no reason for the price level to change either.”
    ----Inflation Is Not Always and Everywhere a Monetary Phenomenon, authored by Antonella Tutino and Carlos E.J.M. Zarazaga.

    Yi Wen published a paper finding very little inflation impact from QE entitled, “Evaluating Unconventional Monetary Policies---Why Aren't They More Effective?

    Then we have an earlier report from the NY Fed, "The Macroeconomic Effects of Large-Scale Asset Purchase Programs" (authored by a trio, Han Chen, Vasco Cúrdia, and Andrea Ferrero). No inflation from QE.

    So the blunt question is: We know there will be huge---yuge--- federal deficits going forward. A trillion a year as a baseline. I guess $2 trillion in a recession.

    But if QE is not inflationary, why not buy back debt---indeed, why not buy back debt not only in a recession, but at the hint of a recession.

    The same way the Fed raises interest rates now, not due to inflation, but due to the hint of pending inflation. The Beige Books chronicle worker "shortages" in great detail, and Vasco Curdia says the Fed wants to get back to 4.75% unemployment.

    Why not heavy QE to forestall a recession, and alleviate taxpayer indebtedness? And possibly, hold down inflation (if you believe the Dallas guys).

    1. Let me try to answer your Q: given deficits, given QE not inflationary, why not monetize?

      I have written on this here
      and here

      You can read there the type of push back one gets.

      In any case, QE is likely to be inconsequential (small potatoes). The negative side of such an operation is mostly political - the optics of a large Fed balance sheet will invite criticism and potential legislation limiting Fed powers. Fed wants to stay clear of politics as much as possible.

      In terms of whether QE inflationary or not, a lot depends on whether fiscal policy is "Ricardian" or "non-Ricardian" going forward. The Dallas Fed conclusion above rests on assumption that fiscal policy will remain Ricardian. There is little to justify such an assumption, imo.

    2. Thanks for your reply. I will put on my reading glasses and give it a try.

  11. I don’t know this literature enough to know if this is discussed. I’ve always seen [4] as an inequality condition. It B/P at present prices are lower than present value deficits, the condition is not binding: The government is solvent and nobody cares, i.e. another model determines prices. If it is binding (think Zimbabwe), than [4] determines prices and the other model doesn’t matter.

    This opens up an interesting question: Because present value deficits are uncertain (random), there would be a level of debt close to [4] at present prices where prices come from two models according to the probability that we are at [4]. In other words, the effects of fiscal policy on prices grow as we get closer to [4] or the “insolvency point” at current prices.

    1. Right, I am used to interpreting as an inequality too. But FTPL uses GBC as a valuation equation.
      See also: