Thursday, April 7, 2016

Fiscal Theory of the Price Level, Helicopters, and Central Bank Balance Sheets

Last week, I attended a conference on the fiscal theory of the price level (FTPL) in Chicago. Eric Leeper claims that I'm actually a closet FTPL person, and seems to have thought I belonged there, which is certainly fine with me. The assignment was to talk about research ideas. Some people had papers, and some (like me) didn't. My slides are posted here.

Here's the idea. The FTPL came out of research done by Eric Leeper, Mike Woodford, Chris Sims, and John Cochrane, among others, beginning in the early 1990s, so this stuff has been around for quite a while. Indeed, there are precedents in the work of Sargent and Wallace, and Aiyagari and Gertler in the 1980s, for example. Sometimes FTPL practitioners seem to be shooting for an alternative quantity theory. Under the quantity theory of money - Old Monetarism basically - we were supposed to think that the demand for money was a stable function of some small set of observable economic variables, so that the supply of money by the central bank would determine the price level and inflation. Under the FTPL it's the quantity of government debt (or in some versions the quantity of consolidated government debt - including the central bank's liabilities) that's important, and it's also important that the counterpart of "demand" for this debt need not be stable. The FTPL starts with the consolidated government's intertemporal budget constraint and, typically, writes it (after some manipulation) with the real quantity of government debt outstanding on the left-hand side (nominal debt divided by the price level), and the expected discounted value of government surpluses on the right-hand side. Therefore, if the stuff on the right-hand side of this equation is given, the nominal quantity of government debt determines the price level. Alternatively, the expected discounted value of future government surpluses is the analog of the demand for money in the quantity theory of money, so reductions in the future government promises backing the government's debt will reduce the demand for government debt and its current value - increase the price level - given the supply of government debt in nominal terms.

John Cochrane provides some intuition in terms conventional asset pricing. That is, think of the expected discounted future government surpluses as analogous to the payoffs on any asset, and the real value of government debt as the value of the asset, and it all makes sense. That's not even an analogy - the intertermporal consolidated government budget constraint can literally be rewritten as an asset pricing equation.

OK, so where does this theory go then? Sometimes the FTPL people got sidetracked with issues such as whether the consolidated government budget constraint is a constraint or an equilibrium relationship, whether the government is similar to, or different from, a private household, in terms of its budget constraint, etc. Some of that discussion was unproductive for this research program, I think. Also, one might get the idea from this literature that central banks cannot fundamentally be independent, and that the fiscal authority is always in the inflation driver's seat, which I don't think is the right way to think about the fiscal-monetary interaction. But, the fiscal-monetary interaction is the message of the theory, and that's very interesting. For example, central banks have recently been engaged in quantitative easing policies, which sometimes look like conventional fiscal debt-management. That might be viewed as central banking jumping into the fiscal driver's seat.

So, what's in my slides? There are three parts to this: (i) a model with minimal government; (ii) a model with open market operations; (iii) a non-Ricardian model with a government debt shortage. The models are very simple, with no uncertainty. The minimal government (MG) model and open market operations (OMO) models are simple cash-in-advance setups with fixed endowments - output and consumption are fixed, and we're only going to be concerned with determining inflation and the price level. The non-Ricardian (NR) model has production.

Start with the MG model, and consider this a thought experiment. The basic idea is to show that we can set up a central bank with no connection to fiscal policy, and this central bank will have no problem determining the price level and inflation. There are households in this economy, and they have fixed endowments each period, but can't consume their own goods and can only trade subject to cash-in-advance - they need currency to buy goods. There is a role for the government, but it's minimal, i.e. the government grants a monopoly to a central bank to issue currency, and I'm supposing the government can costlessly enforce the monopoly. The government also issues shares in the central bank to the households, and constrains the central bank to turn over its profits, period-by-period, to its shareholders. The central bank can issue currency and reserves as liabilities, and uses the liabilities to finance lending to the households. Reserves cannot be used in retail transactions - purchases of goods - and they bear interest, otherwise people would not hold them. Reserves are convertible into currency, one-for-one, and vice-versa. I've assumed away banks, so reserves are just debt instruments of the central bank that anyone can hold.

The MG central banking structure has something in common with what was envisioned by the framers of the 1913 Federal Reserve Act, or with how the European Central Bank works. That is, money is injected through central bank lending rather than open market operations. We could add details like private banks and collateralized lending, but those things don't matter for the general ideas here.

What does the central bank do in the MG model? The model is dynamic, but think in terms of one-time policy decisions that give a stationary equilibrium - a constant inflation rate, and a constant quantity of reserves, in real terms. The central bank fixes the nominal interest rate it charges on its loans at a constant R forever. This does two things. First, it determines the spread the central bank earns on lending financed with currency issue, though the central bank makes zero profits intermediating loans by issuing reserves, as the interest rate on reserves is R in equilibrium. Second, through standard asset pricing, R determines the inflation rate - that's just Irving Fisher. This is an economy in which the real rate is a constant (we'll relax this later). Finally, the the central bank sets the nominal path for its profits, and the nominal path for its total liabilities. And that does it. This determines the initial price level, the inflation rate, and how the stock of central bank liabilities is split between reserves and currency.

Then, in the MG equilibrium, increasing R increases the inflation rate one-for-one, and the central bank can produce as much inflation as it wants. Holding all the other elements of central bank policy constant, a level increase in the stock of nominal outside money is irrelevant for prices and inflation. This just increases the quantity of reserves. That's a liquidity trap result, but you get the liquidity trap no matter what R is. Further, the growth rate in total outside money is disconnected from inflation. While the nominal stock of currency grows at the inflation rate in equilibrium, the total stock of central bank liabilities need not.

The key thing here is that the central bank determines prices and inflation without any fiscal support. If the idea you got from the FTPL is that fiscal policy is necessary to determine the price level and inflation, that's not correct.

Next, go to the OMO model in which the central bank buys and sells government debt, and there is a fiscal authority that can tax households lump sum. Otherwise the model is the same as MG, except now the central bank's profits are turned over to the fiscal authority. Here, we'll suppose that the fiscal authority determines on its own the real transfers over time that are required to support the government debt. At the first date, the fiscal authority issues debt, some of which the central bank purchases by issuing outside money (reserves and currency), and the fiscal authority then rebates the proceeds of the debt issue to households. Then, the fiscal authority levies future taxes to pay the interest on the government debt, which will be constant in equilibrium, so we can think about what is going on. This economy is Ricardian, so the present value of the fiscal authority's transfers is zero. But as in the MG economy, transfers with a positive present value are generated from the central bank's activities. Those transfers are determined by R, and we'll assume that fiscal policy is constant (government debt held constant in real terms) and does not depend on R.

In the OMO economy, monetary policy works much as in the MG economy. Inflation is determined in a Fisherian fashion, and the central bank can have a large balance sheet, but if there are positive reserve holdings forever, having more outside money in this economy has no effect. Given R, the extra money is held as reserves. Further, "helicopter drops" cannot produce more inflation. Given all the other features of policy, if the fiscal authority increases transfers - in real terms, say - then in this Ricardian economy that has no effect. Further, there will be no effect on prices if the central bank purchases the extra debt issued with outside money. The money will just be held as reserves - it's irrelevant whether the increase in transfers is financed with reserves or government debt. Indeed, the central bank could issue currency to finance the transfers, and this will just be converted into reserves and held that way - nothing happens.

In terms of the FTPL, the point here is that FTPL results are derived simply from assumptions that imply that the fiscal authority is in the inflation driver's seat. Here, I've just made natural assumptions about central bank independence and, again, the central bank determines the price level and can have as much inflation as it wants.

Now that we've got those basic ideas nailed down, we can get more sophisticated and think about an economy - the NR economy - with exchange involving secured credit and currency. This works a bit like a cash goods/credit goods model. Here government debt serves as collateral in credit transactions. If the collateral constraint binds, this implies that government debt carries a liquidity premium, and the real interest rate will be low. Then the economy is non-Ricardian. More government debt will relax the collateral constraint and improve efficiency, but we'll assume that the fiscal authority behaves suboptimally, and the central bank responds to that.

So, what happens?

1. If the collateral constraint binds, this implies the central bank should set R > 0 at the optimum. The friction that makes the real interest rate low implies that the central bank should not be at the zero lower bound.
2. Given R, expansion in the central bank's balance sheet is again neutral - swapping reserves for government bonds does not matter, provided these two assets serve equally well as collateral.
3. A policy of increasing transfers financed with government debt, with a permanent expansion in government debt, is beneficial policy, as this relaxes the collateral constraint. But it doesn't matter if this is financed by an increase in outside money (a helicopter drop). If so, the extra money is held as reserves. Further, this action doesn't increase inflation - it reduces inflation. If the central bank wants to increase inflation, it has to raise R. Neo-Fisher again.
4. If reserves are worse collateral than government debt (true in practice, basically, if we think of collateral as, in part, supporting bank liabilities) then a balance sheet expansion by the central bank is bad - it just tightens collateral constraints. This increases inflation alright, but there's a welfare loss.

So, the conclusions are:

1. FTPL forces us to think seriously about fiscal/monetary interaction, and that's very important. But fiscal support is not necessary for monetary policy to work, nor is it useful to think of fiscal policy determining inflation on its own - the central bank can indeed be independent.
2. Fiscal/monetary interaction becomes really important when we start thinking about the liquidity properties of government debt.
3. Helicopter drops? Forget it. This is not some cure-all for a low-inflation problem.
4. QE can be harmful, as it soaks up useful collateral and replaces it with inferior assets.
5. Neo-Fisherian denial is not good for you. Central banks that want to increase inflation need to increase nominal interest rates.


  1. Why do reserves exist in the MG and OMO models? And why would you say they are part of "outside money" (since they are no different from loans)? If the central bank decided to have zero reserves always, so that outside money was 100% currency, wouldn't the quantity theory return?

    1. "Why do reserves exist in the MG and OMO models?"

      Because I put them in there. Seriously, the idea is that this is a starting point. The reserves don't have a useful role to play, which is also going to be true of government debt in that stripped-down model. You can think about adding details and considering what else might be important.

      "why would you say they are part of "outside money""

      They're central bank liabilities, and can be converted one-for-one into currency. Looks just like the reserves the my employer issues, which we would call outside money.

      "wouldn't the quantity theory return?"

      Sure, in this model that's exactly what happens.

    2. Two things, Dr Williamson. First, a smaller government means less collateral which is already scarce, and even lower rates. I almost think you want investors to fund government with negative interest rates! Sounds like Draghi. Second, since bond collateral already is binding, why did you say it will bind. It is already destroying the savings of most Americans. Low long bond rates are engineered into the system when you have too much demand for long bonds. That is obviously what is happening now, not just in the future.

  2. I am going to study these models as son as I can, as I am quite interested. Anyway, all your models have currency. What would happen without the cash in advance constraint, i.e. in a cashless model? Wouldn't that make the FTPL reappear? Of course, this is just a theoretical curiosity, as for at least some godos cash is still used.

    1. This is a model with currency and credit (cash-in-advance, sort of):

      This one is built on Lagos-Wright, with a lot of stuff going on - banks, retail transactions using currency and bank deposits, things that look like repos:

      "cashless" models are a problem, as it's hard to think about central banking as we know it. But I'm working on something where I build up something in layers, starting with a cashless model, so as to understand what is going on in some NK models, particularly with respect to zero lower bound policies. For example, in a cashless model, you can have secured credit, and a binding collateral constraint, just as in the last model in the slides. That's interesting.

  3. The FTPL is just an inferior version of the Backing Theory of money. The backing theory says that the value of money is determined on the same principles as bonds, which is to say, by the assets and liabilities of the issuer. This means, for example, that if a government has a large stock of land or other fixed assets, then it can go ahead and run deficits without causing inflation, as long as the government has enough land to back the money it has issued.

    1. A bond issuer can't unilaterally default on its bonds without consequences, especially when they're secured bonds. But a government can safely "default" thru currency devaluation, either stealth or explicit.

      And Mike, does the discounted value of its future tax revenues count as an asset? Cos that's an awesome asset to have, eh?

    2. A government can't implicitly default on its debt by way of inflation and devaluation without consequences. If a government does that, the bondholders are likely to think it will do it again.

    3. And you could say: well, but a government doesn't have to go to court to default on its debts. But, the government of Argentina has been in court about its defaults.

  4. Dr Williamson, my head is spinning. I apologize for that.

    1. I was thinking that the ECB wants negative rates which will finance Germany. Heck, Germany may not even have to collect taxes. They will just get investors to pay them for bonds to be used as collateral. I wrote about that and the link is by my name.

    2. Hoover and Mellon were hated SOB's, run out of town in the Great Depression. Mellon said this: "...liquidate labor, liquidate stocks, liquidate farmers, liquidate real estate... it will purge the rottenness out of the system. High costs of living and high living will come down. People will work harder, live a more moral life. Values will be adjusted, and enterprising people will pick up from less competent people." **This sounds like what the Fed did in 2008, and Market Monetarists, who somehow support the thinking of this buffoon, austerity, etc, clearly oppose the destruction of the money supply that occurred in 2008. I suppose you are not a MMer, just a New Monetarist. Therefore, you must think like Mellon. I think that is bad, really bad. But you obviously don't, if I interpret you correctly. I would like to know why? And I would like to know why the Market Monetarists don't hate Mellon!!

  5. I think the FTPL counter-argument to your MG model is that the central bank setting the nominal path for its "profits" is actually the same thing as fiscal policy.

    I think if you interpret the FTPL argument properly, any change in the net nominal quantity of government liabilities constitutes *fiscal* policy. From this perspective, the dividends the central bank pays are liabilities it creates out of thin air, and thus having the central bank set its own profits is equivalent to it setting fiscal policy.

    On the other hand, simply changing the size of the balance sheet is *monetary* policy, and in a frictionless model it doesn't do anything at all.

    1. Typically the FTPL seems to have a problem with the central bank "profits." That often gets swept under the rug. I interpret some of what was said in the FTPL literature (and it's a pretty murky literature) as saying that the fiscal authority must be determining the price level. That doesn't seem to be right. You can call the central bank profits whatever you want, but if the central bank determines the profits, I think I would call that monetary policy.