John Cochrane has written a very interesting paper on monetary policy under conditions of “abundant liquidity”, including substantial excess bank reserves and interest paid on those reserves (IOR). The central idea behind the paper is the fiscal theory of the price level (FTPL), which is a valuation equivalence relationship between the real values of government debt and expected primary budget surpluses. This theory seems like a remote contrast to the perspective of debt sustainability in a growing economy, but it is a coherent model, and Cochrane emphasizes the point that FTPL itself does not constitute a budget constraint.

The paper is here:

http://faculty.chicagobooth.edu/john.cochrane/research/papers/cochrane_policy.pdf

This post presents only some of the important ideas found there. The paper itself is more comprehensive in scope than can be easily summarized here. It is particularly interesting for the way in which it combines an abstract, somewhat controversial theory with analysis of close up monetary operations.

**Fiscal Theory of the Price Level (FTPL)**

With simplified notation (mine), here is the core valuation equation that underlies Cochrane’s use of FTPL:

B (t – 1)/P (t) = s (r) (t)

The left hand side of the expression is the real value of outstanding government debt – i.e. the nominal value of debt B deflated by the price level P.

The right hand side is the present value of expected future real primary government surpluses (s) at time (t) discounted at the real rate of interest (r).

Time subscripting is important. A one period model is included for simple illustration. For example, B (t – 1) is the nominal face value of debt issued yesterday (period (t – 1)) in the afternoon and maturing today (period (t)) in the morning. Interest on debt (including interest on reserves) is earned overnight from yesterday afternoon (t – 1) to this morning (t). Debt that matures in the morning of (t) is paid off by money that is “printed up” by the central bank. And that money is “soaked up” by new debt B (t) that is reissued in the afternoon of (t). The intra-day period from the morning to the afternoon of (t) then becomes important in Cochrane’s explanation of the consumption function under sticky prices.

The right hand side of the FTPL equation is the present value of expected future government primary surpluses, discounted at a fixed real interest rate of r. By definition, primary surpluses sufficient to pay interest are required to avoid a deficit and the issuance of net new debt. Any primary surplus amount remaining after the payment of interest is available to pay down outstanding debt.

The nominal quantity B (t – 1) is the maturity face value of the debt maturing today that was issued yesterday at less than face value, depending on the interest rate. For example, a treasury bill may be issued yesterday at a price of 99, maturing today at a (standard) face value of 100. B (t – 1) is the face value of 100 and not the issue discount price of 99.

**FTPL Intuition**

Again:

B (t – 1)/P (t) = s (r) (t)

The left hand side of the expression is the real value of outstanding government debt – i.e. the nominal value of debt B deflated by the price level P.

The right hand side is the present value of expected future real primary government surpluses (s) at time (t) discounted at the real rate of interest (r).

The intuition for FTPL is not easy:

“Equation (1) is not a budget constraint. It is a valuation equation, an equilibrium condition. Its ingredients include the household budget constraint and first-order conditions. It works the same way as the valuation equation by which stock prices adjust the present value of expected dividends. There is no budget constraint that forces the government to respond to a deflation in Pt by raising surpluses, any more than a stock price bubble forces a company to raise earnings to justify the stock price. And just as well, because there is a Laffer curve limiting surpluses, but there is no limit to deflation, so there must be some price at which (1) is violated while budget constraints can never be violated… Equation (1) has a natural aggregate demand interpretation. (Woodford 1995). If the real value of nominal debt is greater* than the present value of surpluses, then people try to spend their debt and money on goods and services. But collectively, they can’t, so this excess aggregate demand just pushes up prices until the real value of debt is again equal to the present value of surpluses. Aggregate demand is nothing more or less than demand for government debt. By the private-sector budget constraint the only way to spend more on everything else is to spend less on government debt. This equation also expresses a wealth effect of government debt.”

*typo in original text corrected

He seems to say that there is a point at which extreme moves in the price level would cause FTPL to fail (“be violated”) as an equivalence – similar to the way that extreme prices for stock prices may call into question conventional equity valuation methods.

The Fisher equation for nominal interest rates plays a supporting role. The nominal interest rate can be decomposed into the real interest rate and expected inflation. The FTPL valuation formula unpacks these components. This approach has become part of the recent “neo-Fisherian” debate about whether economists have the sign right when predicting the direction of effects from changes in the central bank’s policy interest rate. For example, the simple case under FTPL of an interest rate increase with flexible prices leads to an increase in the price level and inflation – the reverse of the monetary tightening effect that is normally expected when the central bank increases interest rates. The author addresses this issue in some detail by considering the effect of monetary policy when combined with expectations for fiscal policy.

**Bank Reserves**

Cochrane treats interest-paying reserves as a form of debt. Ironically, notwithstanding the title of the paper, bank reserves play no critical role in the FTPL model of monetary policy – in the sense that the price level is associated with the real value of debt and not the composition of that debt. The paper only declares that a liquidity environment featuring interest paying reserves is compatible with a “fiscal theory world” where such reserves are treated as debt. At the same time, he maintains that reserves which don’t pay interest (as was the case in the pre-2008 Fed) as well as non-interest paying currency pose no problem for a fiscal theory world, as those elements of the monetary base can be set aside from debt treatment and effectively ignored in the FTPL model. The treatment of currency is particularly refreshing, given the usual monetarist approach that fails to differentiate operational characteristics as between bank reserve balances and currency.

He acknowledges general skepticism about the old fashioned money multiplier idea. The paper recognizes that this idea is obviously inoperative at least in the case of abundant liquidity where interest is paid on reserves. In fact, it should be understood more comprehensively that it is false as an explanatory model for all bank lending decisions in all environments, other than for the limited purpose of tactical adjustments in short term reserve management operations, where low risk liquid assets require negligible amounts of bank capital underpinning. These reserve adjustment operations are separate from core risk lending decisions requiring such capital backing and which are based on the economic use of capital – not on the availability of reserves.

The abstraction of transaction activity at the high level of central bank reserves ignores the presence of the commercial banking system and the broader money supply that is the reason for those reserves. However, one can visualize central bank reserves in use as the ultimate form of payment for government debt operations – issuance, retirement, or rollover – and for consumption functions that operate in the model under sticky prices. Money is in the form of reserve balances with intra-day motion – then locked in at the end of the day after activity has settled. Including interest paying reserves within a seamless debt interpretation pretty much ensures that any monetarist flavor is secondary to the main theme. The quantity of reserves and the quantity of conventional Treasury debt rank equally in importance, when interest is paid on both.

**Monetary and Fiscal Policy**

Cochrane defines policy in accordance with the logic of FTPL:

“I define monetary policy as manipulating government debt without any change in taxes or spending surpluses. I define fiscal policy as taxing and spending, i.e. determination of the surpluses.”

**Monetary Policy – The Flexible Price Case**

The elementary monetary policy case assumes flexible prices, with no change in expected surpluses or the real interest rate.

For example, with the right hand fiscal policy side of the equation unchanged, the central bank can force the price level higher by increasing the aggregate nominal face value of debt B (t – 1).

That means increasing the nominal interest rate. For example, suppose the central bank increases the interest rate paid on reserves from 3 per cent to 4 per cent. This will force the interest rate on treasury bills higher in a similar way via the usual market arbitrage mechanism. And if Treasury sells new bills at 96 rather than 97 (roughly), it will have to sell more of them in order to raise the same aggregate amount of money, and that means the aggregate maturity face value (which is what appears in the FTPL equation) must increase. This does not mean it needs to change the standard 100 maturity value on an individual bill – just the quantity of bills issued.

Using the FTPL valuation formula, B (t – 1) is the maturity face value of a bill issued in period (t – 1), maturing in period (t). Define ‘i’ as the nominal interest rate set by the central bank, r the real rate fixed by assumption, and p the expected inflation rate. Then the issue price Q of the bills as a fraction of their maturity face value is:

Q = 1 / (1 + i) = 1 / ((1 + r) (1 + p))

(This is nothing more than standard formula for a discounted price, decomposed into its real and expected inflation (Fisher) components.)

And the aggregate value of those bills at issue = BQ

Cochrane:

“The real value that the government raised by debt sales B (t – 1) Q (t – 1) / P (t -1) is fixed by the time (t – 1) present value of real surpluses … the price level P (t – 1) is already determined by (1) at time (t – 1), independently of B (t -1). Thus, if the government sells more B (t – 1), it faces a unit-elastic demand curve; the nominal bond price Q (t – 1) falls one for one with the increase in nominal debt, because expected inflation E (t – 1) P (t – 1)/P (t) rises one for one. This operation is just like a share split or a currency revaluation. The government has complete power over units in this frictionless model, which means it can control expected inflation without changing anything real… Treasury next determines the quantity of debt it needs to sell to finance the current deficit. When it does so, it observes market interest rates. So, when interest rates rise and bond prices Q (t – 1) fall, the Treasury raises the face value of the debt B (t – 1) that decides to sell.”

And:

“establishes that the price level is determinate, even with no monetary frictions at all, so long as the government follows a policy that suitably controls nominal debt and primary surpluses.”

As an (ultra-simplified) example, suppose Treasury has a debt rollover funding requirement of $ 1 billion at (t – 1). It issues 1 day treasury bills to mature at time (t) at a nominal interest rate of 1 per cent. Because of the price discount, the required aggregate maturity face value to be issued will be approximately $ 1 billion + $ 28,000. At a rate of 2 per cent, the required aggregate face value will be about $ 1 billion + $56,000. While the aggregate discounted price of the debt remains $ 1 billion, the aggregate amount of the discount has increased, and so has the aggregate maturity face value. Treasury will calculate the quantity of bills of some standard maturity face value to finance the $ 1 billion. The quantity of bills will be greater at 2 per cent than at one percent, and that increase in quantity means the aggregate face value B (t -1) will be greater.

The case will be similar for bank reserves. Increasing the nominal interest rate from 1 per cent to 2 per cent will increase the aggregate interest accrual from one day to the next. In a model that assumes the effective term to maturity of reserves is 1 day, the face value interpretation of reserves includes starting “principal” plus the interest accrual for the period in question.

The case of a Treasury bond with coupon payments, involving a longer period, would be treated similarly to bank reserves, by accruing the value of coupon payments over the chosen time period to a future “face value equivalent”.

Monetary policy under flexible prices is a counterintuitive (“neo-Fisherian”) story when compared to what normally is expected from central bank interest rate changes in tightening or easing modes. For example, an increase in the nominal interest rate increases both the current price level and expected inflation under FTPL, assuming no change in surpluses. Such a rate increase is usually considered – and observed – instead to be a “tightening” of monetary policy, with the reverse consequences as predicted by FTPL. But Cochrane maintains that this is because the effects usually observed obscure the operation of accompanying expectations for fiscal tightening (through a change in surplus expectations) which at work in the background and that constitute the piece that does that actual tightening. He goes through a number of simulations of combined policy effects in the paper, for both flexible and sticky price cases, which I will not address in this post.

**Monetary Policy – the Sticky Price Case**

Under sticky prices, FTPL passes the effect of monetary policy nominal rate changes to the real rate component, with an effect on output rather than on the current price level. Real output increases, which again is unexpected when compared to the usual view. The sticky price and its real rate and output effects are assumed to be temporary, after which things revert to flexible prices. Like the case of flexible prices, monetary policy under sticky prices is a counterintuitive story based on what normally is expected from how central banks set interest rates in tightening or easing modes. Such a rate increase is usually considered to be a “tightening” of monetary policy. But Cochrane maintains again that this is because the usual effects obscure the idea that expectations for fiscal policy are at work in the background, in a tightening mode that dominates.

**Fiscal Policy as seen in FTPL – The Meaning of “Shocks to Real Surpluses” **

Fiscal policy can change the right hand side of the FTPL equation – the present value of real primary surpluses. This has potential effects on the price level under flexible prices or on the real interest rate under sticky prices.

Cochrane refers to “inflationary shocks to surpluses” as a core example. What is envisioned by the idea of an “inflationary shock to surpluses”?

First of all, an inflationary shock to surpluses is a shock that by definition reduces expected real surpluses. By construction, such a shock moves the surplus position incrementally closer to a position of real budget balance or deficit. Notwithstanding the surplus starting point, this sort of directional change is consistent with what a Keynesian perspective might consider to be differentially stimulative, if not inflationary (the same directional change as that of an expanded deficit). Second, by construction again, the idea of an inflationary shock to surpluses is kept initially separate from the idea of any change in monetary policy. The left hand and right hand sides of the FTPL equation are treated separately in this definitional and policy framework. Third, Cochrane is referring to a shock to real surpluses, because the basis for FTPL equilibrium is a real valuation. Fourth, the shock is to the future value of real surpluses. The real interest rate r, which is used to discount the future value of real surpluses to a present value, is not considered part of the defined shock. We know this because r becomes an “endogenous” variable of response when surpluses are shocked under sticky rates.

What is less clear from the paper is whether the defined scope for surplus shocks means changes to the expectation for nominal surpluses. Indeed, this may be the obvious intention that has everything to do with the right hand side of FTPL. But if so, it does not seem to be expressed very clearly. After all, it seems it should be possible for the future real value of a surplus to change if the expected price level changes, with no change in nominal value, and no change in the real discount rate.

Still, it would seem to be the case that nominal surplus shocks are to be considered as the standard source of real surplus shocks. It seems to be implied from Cochrane’s mention of the Laffer curve as being a limiting factor to the size of surpluses. But it is hard to say.

All that said, we will set aside the challenge of understanding how a surplus shock is supposed to translate directly to nominal terms, and just assume that it is a change in the expected future value of future real surpluses. Whatever the nominal mechanism, the FTPL narrative holds in real terms. (Ironically, the paper does go into a nominal description of the left hand side operation of the equation under a shock to real surpluses. See below.)

**Surplus Shocks – Real Value Interpretations**

Here is his actual description of the effect of an “inflationary shock” to real surpluses (i.e. a reduction in real surpluses).

First, the flexible price case:

“The left-most term is the real value of nominal debt coming due in the morning, which must be rolled over. With a constant real interest rate, the real value of debt sold in the evening declined when expected future surpluses declined, as the right-most term declined. To match that decline, the real value of debt coming due in the morning declined, as P (t) on the left hand side … rose…”

With flexible prices, the price level increases from P (t – 1) to P (t) so that the real value B (t – 1)/ P (t) declines in conjunction with the assumed decline in real surpluses. Monetary policy hasn’t changed, so the nominal interest rate hasn’t changed. Nor has the real rate (only the size of assumed future real surpluses).

The sticky price case:

“… The real value of debt coming due in the morning B (t – 1) / P (t) cannot decline. How can the real value of debt paid off in the morning stay the same, in the face of a decline in expected surpluses? The answer is that the real interest rate also declines, the bond price rises, so the lower expected surpluses now have the same real value and the bonds are rolled over.”

If monetary policy is unchanged (by assumption), B (t – 1) and the nominal interest rate are unchanged. And if the price level is unchanged, then the left hand side of the FTPL equation doesn’t change in value. That means the right hand side can’t change. But if the level of real surpluses changes, then something else must offset it. So with the assumed reduction in surpluses, that means the real rate of interest must decline in order to keep the right hand side value unchanged and preserve the equivalence of the two sides of the equation. Hence, a fiscal shock in the form of a surplus reduction becomes an inflationary shock – because the real rate component embedded in the nominal interest rate set by the central bank must decrease. With an unchanged nominal rate, expected inflation must increase (according to the Fisher relation) although the price level has not yet started to change.

Cochrane opines that this real rate adjustment as an easing of policy is counterintuitive when interpreted in an FTPL framework – given the reduced availability of surpluses to measure against outstanding debt. Indeed, one normally thinks of reduced availability in the sense of something becoming more expensive (i.e. the interest rate here) rather than less expensive. Conversely, a Keynesian interpretation would intuitively associate reduced surpluses the other way around – as fiscal easing (i.e. counter-counterintuitive relative to FTPL) – because reduced surpluses hand back monetary resources to the private sector.

**Surplus Shocks – Nominal Value Interpretations**

The author offers a nominal value interpretation for real value adjustment under the two price behavior scenarios. The descriptions quoted below are difficult to follow, but they cover the effects of an inflationary shock to surpluses (a reduction in surpluses) for each of flexible and sticky price cases, in nominal terms:

First, the nominal explanation for **flexible prices**:

“The same mechanism in nominal terms: We can imagine the government printing up money B (t – 1) to pay off debt at the beginning of period t, money which must be soaked up with bond sales by the end of time t … With flexible prices and a constant real interest rate, the real value of surpluses (is) fixed, and at the same nominal price level P (t – 1)* these would no longer soak up all the dollars. So at that price level, people tried to buy more goods with their excess dollars. In doing so, they pushed up goods prices until the lower real quantity of debt sold in the afternoon soaked up the excess nominal dollars brought in by B (t – 1).”

(* The paper actually refers to P (t), but the point here is that P (t) does not remain at the level of P (t – 1)).)

The context is the maturity of Treasury debt B (t – 1) issued yesterday afternoon, maturing today in the morning, with reissuance of new debt today in the afternoon. The government “prints up” money in the morning to pay for the debt maturity. Indeed, this corresponds to the actual case, as Treasury’s account at the central bank is debited on an intraday basis to pay for the bond maturity, which increases bank reserves (whether the holder of the maturing bond is a bank or a bank customer with a deposit account). The account is replenished on the same day (assuming coincident maturities and rollovers) with the proceeds of newly issued debt.

The final sentence in the paragraph needs close interpretation. The government issues new debt in the afternoon sufficient to “soak up” the money printed up in the morning. This is a straightforward nominal refinancing requirement, whatever the case for real values. Flexible prices allow for an increase in the price level “during the day”, and that becomes the change that permits the FTPL valuation equation to reach equilibrium in real terms. Thus, the inflationary shock to real surpluses causes the real value of both sides of the equation to decrease by the same amount. And “the lower real quantity of debt sold in the afternoon” is lower compared to what would have been the case in the morning.

The references to “morning” and “afternoon” reflect an assumed intra-day period of financial and commercial trading, where the B (t – 1) bonds issued in time period (t – 1) are paid off with cash in the morning, and the B (t) bonds that replace them are issued in the afternoon. In the interim, the money that was “printed up” to pay off the morning maturity is available for use in acquiring goods and services during the day until required to purchase the new replacement bonds issued in the afternoon. Consumers in acquiring goods and services drive up flexible prices from P (t -1) to P (t). The change in the price level by the end of the day ensures that the real value of debt declines in tandem with the real value of surpluses.

Second, the nominal explanation for **sticky prices**:

“But now prices cannot rise. People still have more newly-printed money in their pockets B (t – 1) than will be soaked up by debt sales. What happens? First, they try to buy more goods and services as before. With prices fixed one period in advance, this extra aggregate demand now leads to greater output, not higher prices. But the greater output does not soak up any money in aggregate. More money spent by the buyer is received by the seller, and at the end of the day the excess money B (t -1) relative to bond sales that will soak it up is still there. So, if money holders cannot bid up the price of goods, they bid up the price of bonds instead. Asset price inflation takes the place of goods inflation. The real interest rate decline / real bond price rise continues until the excess cash is now all soaked up by bond sales at an unchanged price level.”

The real value dynamic already tells us that an inflationary shock under sticky prices lowers the real rate of interest in order to offset the decline in real surpluses – because both sides of the FTPL equation remain unchanged in real equilibrium. The reference to “does not soak up any money in aggregate” means that even though the money from the morning bond maturity is spent during the day on consumption, that aggregate quantity of money does not disappear or get “soaked up” just because of that. It continues to exist in stock form – until it is “soaked up” by the flow of bond reissuance in the afternoon. However, this description omits to say that the nominal dynamic for the money flow is the same for both flexible and sticky prices, since the difference between the two cases only relates to how nominal money expenditure during the day affects the price level or the output level. The nominal quantity of money is the same in both cases – the quantity that the government “printed up” in the morning to pay for the bond maturity. That money is then applied as an expenditure flow during the day. And during the day, between expenditure flows, the nominal quantity of money in stock form remains unchanged. It continues to exist as a stock throughout the day, while circulating as a flow.

The nominal amount of the bond maturity in the morning B (t – 1) is the quantity of money spent on consumption during the day. The same quantity of money still exists in stock form after being used to buy goods and services, and so it is available to buy the bonds issued in the afternoon B (t). Under sticky prices, the real value of the B (t -1) money has increased from morning to afternoon, reflecting the increase in output it has purchased. Therefore, the real cost or real price of B (t) bonds issued in the afternoon has increased. And it follows that because the real bond price has increased, then the real rate of interest has declined. And that is the same real rate of interest used to discount the real surpluses on the other side of the FTPL equation.

(Admission: I am not certain of this last nominal explanation, either in Cochrane’s own words or in my attempted translation. It is a difficult one. It seems descriptive enough, but I fail to see a presumably critical connection between the nominal version and the assumption of a decline in real surpluses.)

**The Stock Split Analogy**

Under the FTPL model, the central bank’s role in setting the interest rate is analogous to a corporate stock split. For example, assuming no change in expected surpluses, an increase in the central bank rate under flexible prices causes an increase in the price level and expected inflation. This is analogous to a split in the number of “shares” of debt representing a given real value.

Conversely, Treasury’s role is analogous to that of a corporate issuer of new stock for purposes of real enhancement to the business of the corporation (such as investment). According to Cochrane’s model, Treasury intends to balance newly issued debt with an equal amount of expected future surpluses, so that the FTPL valuation equation remains in balance without any effect on the price level.

Cochrane:

“The Treasury thus wants to sell more debt B (t – 1) and communicate a simultaneous rise in promised real surpluses. By contrast, the Fed wants to communicate the opposite expectations: To raise interest rates, it wants the government to sell more debt B (t -1) with no implications about future surpluses.”

“Isolating the debt sales B (t – 1) in two distinct branches of the government is a great way to communicate different expectations of future surpluses of otherwise identical debt sales… In the same way, corporations market share splits, fully-diluting increases in shares outstanding with no changes in earnings and public offering increases in shares outstanding that are intended to fully correspond to changes in earnings with no dilutions in ways that convey the right expectations… As we think about better institutional design for monetary policy which we should really call coordinated monetary-fiscal policy better communicating the intended promises about future surpluses is a central issue.”

**How Interest is paid on Reserves **

(This aspect is not referenced directly in the paper.)

The analogous “face value” of debt B (t – 1) in the case of reserves is the nominal quantity of reserves outstanding yesterday (t – 1) plus the interest paid on reserves from yesterday to today (t). This is comparable to a 1 day treasury bill that accrues interest from the discounted purchase price to the maturity face value. And so, the FTPL equation should work for reserves in the same way as for Treasury bill debt, treating B (t – 1) as the “face value” amount that matures at time (t), issued at a discount at time (t – 1) in the one day model.

One way of delineating government debt operations is to consider a decomposition into two parts: debt issued as reserves by the CB, and debt issued in bill and bond form to entities other than the CB. A corresponding decomposed fiscal effect consisting of the payment of interest on reserves and the payment of interest on bills and bonds other than those held by the CB. In this approach, the central bank issues one (ultimate) form of debt and Treasury issues the other.

The central bank pays interest on reserves in the form of newly created reserves. The initial accounting entry is a credit to reserves and a debit to central bank equity (both accounts on the right hand side of the central bank balance sheet). Therefore, given this form of payment, it would appear that the nominal quantity of reserves should grow at the rate of nominal interest paid, other things equal.

But in fact, standard institutional arrangements for Treasury and the central bank mean that reserve growth is not a function of the payment of interest on reserves. To see this, we need to examine related monetary operations. The following description applies in general form to the Federal Reserve and the Bank of Canada, among others (but not to the ECB, which is in a unique situation with a multinational setting and a different balance sheet structure):

The central bank earns a profit roughly equal to the interest it receives on Treasury bonds less the interest paid on reserves and the cost of other operating expenses. That profit is remitted to Treasury. But the remittance of CB profit to Treasury is not the same as the full fiscal effect of its operations on Treasury. Treasury pays interest to the CB and receives profit from it, so that both flows must be included in the calculation of the net fiscal effect of the CB on Treasury.

From an operational and accounting perspective, the central bank processes interest payments from Treasury by debiting Treasury’s deposit account at the bank and crediting its own equity position. It remits profit to Treasury in a reverse procedure, debiting its own equity position and crediting Treasury’s deposit account. The net fiscal effect on Treasury is the combined effect of the bond interest outflow from Treasury and the profit inflow to Treasury.

Given the composition of the central bank’s profit as noted above, this net fiscal effect is equal to the cost of interest paid on reserves plus other CB operating expenses. This makes sense when considering the CB as the issuer of debt in the ultimate form of bank reserves.

This net fiscal cost is typically a deficit in respect of Treasury’s position with the central bank. Again, this makes sense when considering that the payment of interest on reserves is a fiscal cost for this ultimate form of debt.

Thus, central bank debt operations typically result in a marginal deficit for Treasury. That shows up directly as a net outflow from Treasury’s account with the CB.

However, because Treasury adheres to a cash management discipline in fiscal operations, it will replenish that net outflow through further bill or bond market borrowing (except for the case where a primary surplus is available to pay all or some of the interest.)

The full effect on the banking system configuration is that the initial addition to reserves that arose from the payment of interest on reserves is reversed back out of reserves by the issuance of additional Treasury debt that drains reserves in the usual way and replenishes the Treasury account. (The same thing happens in parallel with respect to central bank operating expenses that similarly show up as payments from central bank equity into bank reserve accounts. Treasury ends up draining that effect with more borrowing as well, since it is part of the full fiscal effect. )

Thus, the central bank’s payment of interest on reserves in the form of additional reserves is only an interim stage of “financing” the expense of paying interest on reserves. In final form, this financing consists of further Treasury debt issuance that drains and replaces the original reserve effect of the central bank’s interest payments. This all assumes “other things equal” – e.g. that interest expense is not covered instead in part or whole by a current primary surplus.

So the payment of interest on reserves in the form of additional reserves is only a temporary effect at the system level, normally replaced by the more permanent financing of interest on reserves in the form of additional Treasury debt borrowing. This leaves the central bank free to pursue reserve growth objectives through open market operations, independently from operational effects that would otherwise be completely arbitrary relative to such policy objectives. The obvious example of this is evident in the stated policy objectives of various Federal Reserve quantitative easing programs. There is no direct connection between any of those objectives and the notion that bank reserves should grow at the same rate as and according to the amounts paid in the form of interest on reserves paid and left in the form of reserves.

Nick Rowe has posed the question directly as to what people might or should expect for money growth when interest is paid on reserves, given that interest is paid initially in the form of new reserves. In fact, that initial step is quickly undone by standard fiscal operations. The central bank intends for the growth path of reserves to be what it determines in using open market operations – not by paying interest on reserves with new reserves. Market participants understand this – if not explicitly then implicitly. Indeed, it would be counterintuitive to expect a relationship between interest on reserves and money supply growth unless there were an explicit announcement of such an intention by the central bank – especially given the non-standard operational adjustment required to achieve such an objective. Indeed, none of the Fed’s quantitative easing programs have had anything to do with such an objective. As noted, the interest paying mechanism is neutral by institutional design in terms of its money effect, due to the cash management discipline treasury exercises through its own operating account at the central bank. Of course, alternative institutional arrangements can always be considered. But if the question is asked as to what people expect now, it is reasonable to consider the monetary system as it currently operates in answering the question.

**Conclusion**

It is an interesting and comprehensive paper, and I have only touched on some of the basics here. More complex modelling of combined monetary and fiscal effects is found in the paper. FTPL produces a counterintuitive “sign” for the directional effect of central bank interest rate changes. Cochrane’s explanation is that what we observe is not monetary policy acting alone, but monetary policy in conjunction with the dominant effects of fiscal policy working in the background. The core idea with respect to interest on reserves is that reserves can be treated as another form of debt, along with Treasury bills and bonds. The treatment of debt is seamless as between the two categories, which makes FTPL integration of IOR very natural. Abundant liquidity can be treated in the FTPL framework. The arbitrage process for the transmission of the central bank rate to the rest of the system works for either regime. The CB uses the scarcity of excess reserves to target the fed funds rate in one case and pays interest on abundant excess reserves in the other. And it doesn’t matter whether interest paid on reserves ends up in the form of additional reserves or more Treasury debt. The paper is an interesting blend of abstract theory and operational detail. It acknowledges the institutional separation of central bank and Treasury roles for monetary and fiscal policy, as delineated in the structure of the FTPL valuation equation. At the same time, clarity in the separate roles and their effects opens up the opportunity for greater coordination of fiscal and monetary policy.

**References**

John Cochrane:

http://faculty.chicagobooth.edu/john.cochrane/research/papers/cochrane_policy.pdf

http://johnhcochrane.blogspot.ca/2014/10/monetary-policy-with-interest-on.html

http://johnhcochrane.blogspot.ca/2014/11/the-neo-fisherian-question.html

Nick Rowe:

http://worthwhile.typepad.com/worthwhile_canadian_initi/2014/11/the-collective-speed-limit-game.html

Other:

http://monetaryrealism.com/treasury-and-the-central-bank-a-contingent-institutional-approach/

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54 Comments on "John Cochrane’s “Monetary Policy with Interest on Reserves”"

JKH,

I thought of two “models” (closed economy):

1. Non-growth model

Here, the output settles to some value in the future and stays there. The identity seems to be valid except that it has a singularity at r=0

2. Growth-model

Here for large growths, the identity breaks down because the series summation is infinity. Also, it is even possible to have a primary deficit if growth is high. So the series summation can possibly be negative! Of course no cause for concern as the idea of the debt being some present value of future primary surpluses is questionable. It is different from the question of whether the debt is sustainable or not.

I am thinking of nominal but similar conclusions can be made for real variables as well.

FTPL seems to turn it the other way round and use it as some determination of the price level, although I am not sure of this point.

Nick Rowe made the same point.

But it doesn’t apply here logically, IMO, because FTPL equivalence is based on specific expectation for surpluses – so there’s no reason to expect a model format that produces a non-convergent or indeterminate result. The aspect of surplus specific expectation simply overrides that as a rational expectation. And that’s why zero is not a problem.

As to whether FTPL is “right” – that is a larger overarching question I think. I’m still puzzled by it.

FTPL simply seems to ignore costs. Prices depend on demand and since fiscal expansion raises demand, prices do depend on fiscal policy but anything not talking of costs in pricing will obviously be wrong.

So it’s always possible to construct a non-convergent series

But it’s also always possible to construct a convergent one

Depending on “expectations”

And the answer to the question as to why it doesn’t work for r=0 is that there is no strong reason for the identity to work in the first place.

Of course, sustainability is important but that issue is slightly different, although related.

JKH,

Hehe 🙂

It’s a bit strange language they use when talking of present value of future surpluses and so on.

Imagine a simplest closed economy which reaches a state of no growth and with a budget balanced endogenously.

The surplus is zero. But the government has a debt: the public debt.

So the identity relating public debt and future surpluses makes no sense.

One can think of adding complications, but it makes little sense of thinking of present value of future surpluses

In your example, the surplus would be zero, but the primary surplus would be exactly equal (but opposite in direction) to the interest on debt. “Surplus” is Cochrane’s FTPL means primary surplus, so discounting the primary surpluses at the effective interest rate would indeed be exactly equal to the outstanding debt.

In fact, if you consider actual (primary) surpluses and the actual effective rate on public debt, then I think Cochrane’s equation is simply an identity (except in unstable cases). What makes it a theory is using expected values and equating the rate on public debt with the time preference rate. Which I guess means it can’t really be tested, as how do you measure these things? We could build a simple SFC model to show the economy you describe. Cochrane would then say it’s being driven by (validated) expectations of future surpluses. We might say it’s being driven by stock-flow norms. Who is to say these aren’t really the same thing?

On endogeneity of deficits, I’d guess that Cochrane typically thinks in terms of lump sum taxes, so it would be more natural for him to think in terms of exogenous deficits. Personally, I think this is OK sometimes, but that the mainstream tends to adopt this assumption rather uncritically.

Nick,

Take a simple SFC Model of Wynne Godley. Zero interest rate. In that the GDP settles at G/θ, where θ is the tax rate and G the expenditure. The public debt settles to some value dependent on propensities to consume out of income and wealth. The deficit in the equilibrium is 0. But the present value of the surpluses is 0 and not equal to the public debt.

One can add complications – bonds and bills – but I am not sure if we can get the identity.

OK. Minor complication here is that it works for r ≠ 0, although doesn’t for r = 0. Hmm.

Do you mean the identity holds for r 0, but not r =0? I think I agree that it doesn’t hold in your example with r=0. There may be other examples. But in general it does seem to.

Yeah that’s what I meant.

But now I realize another model where it doesn’t.

Consider a closed economy with growth. For g greater than r, the series summation of present values explodes. The public debt on the other hand is obviously finite.

I am not sure: Is that right?

i.e. present value is just the sum of future values in a finite series when r is 0 (for real valuation).

Ramanan,

Why doesn’t it work for 0?

There’s no rule that says future surpluses must be an infinite series.

Present value is just the sum of future values in a finite series.

(Nick Rowe assumed the same thing.)

Same point for your second example.

question:

Does FTPL real equivalence require corresponding nominal equivalence as a precondition?

Agreed.

That’s a specific example of the more general case of the empirical evidence that debt doesn’t have to be paid off in its entirety.

If it were that simple then the theory would appear to be foolish. I’m not sure that’s the full story though. Surely there is somebody on the FTPL team who can address that.

Cochrane seems to flirt with it by suggesting it’s a real valuation equation but not a budget constraint – whatever that means.

Meanwhile, I have a few questions of my own:

http://worthwhile.typepad.com/worthwhile_canadian_initi/2014/12/who-would-ever-lend-to-an-ftpler.html?cid=6a00d83451688169e201bb07c3f894970d#comment-6a00d83451688169e201bb07c3f894970d

I just found it an interesting paper to review.

Good point.

The assumption does seem to be that of retiring the public debt!

Will check the WCI link.

Chochrane’s Fiscal Theory of the price level is completly based on forcing the government to have an intertemporal budget constraint. This assumption is ad hoc and absurd.

Note that when Cochrane says “Equation (1) is not a budget constraint. It is a valuation equation, an equilibrium condition.” he is only talking about equation 1, the model as a whole does have an intertemporal budget constraint. That is why their are surpluses in the model!

What do you think of his analogy with a dividend model for stock valuation?

It’s a bit odd isn’t it, because why would bonds behave like equity?

But reading the paper I was thinking that a good analog for the government in the model is actually a special purpose vehicle set up by a corporation to hide leverage (Enron being the famuos example). Model households are supply constrained and the government basically acts as an off balance sheet way for households to leverage up. So you could think of this kind of SPV issuing equities or bonds as analagous to to government debt.

And since the model is based in the land of perfect infinite forsight, all the households know that the SPV is backed by their own wealth, so of course the value of any equity it issues is based on their ability to pay themselves back later in taxes, and the SPV can set any share price it wants by changing the amount of shares it offers.

But this sure doesn’t seem to have anything to do with reality.

Though maybe getting debt off households balance sheets is the whole point of Keynesianism, so this train of thought might be useful.

JKH,

While there are many similarities, there are a lot of differences as well. Note how Cochrane starts assuming the government can “control” its debt. It’s Monetarism in a different form.

I can’t quite pin down what Cochrane’s broad views are. I haven’t read enough of his work, but yes, he’s definitely leaning more towards Monetarism and some form of New Classical econ. If you read this National Affairs article from 2011 he makes several predictions that are practically Austrian – collapsing USD, high inflation, high interest rates, etc. What kind of a model leads to those conclusions? It would be nice to know the basic economic framework that Cochrane is using so we can all avoid it. 🙂

http://www.nationalaffairs.com/publications/detail/inflation-and-debt

His framework is the fiscal theory of the price level. It’s a big deal in itself. That’s why I got interested in his paper. It’s a theme that runs throughout his work.

In my view, it’s definitely not monetarism. He is critical of monetarism. Nick Rowe has done a bunch of posts on the theme of monetarism and FTPL as competing modes of thinking – partly in response to the Cochrane paper. And Nick knows monetarism pretty well I figure.

It’s got intersecting strands with other “schools”. Nick Edmonds and I noticed one of them.

JKH,

Yes critical of Monetarism but still has traces of it. The reason I said was that he uses phrases such as controlling the government debt and bringing government debt into prices. Warren Mosler thinks along similar lines – there was a comment he wrote in Mitchell’s blog that Friedman is almost right and that the government controls the public debt and not the money stock.

Godley and Lavoie’s book is different in which the public debt is endogenous and price has its own dynamics (such as depending on firms’ costs) in addition to depending on domestic demand and fiscal policy.

Looking for a first class take-down of FTPL, I googled:

“Marc Lavoie Fiscal Theory of the Price Level”

And got –

His critique of MMT

🙂

But seriously I’d be interested in seeing a stock flow consistent analysis of what “a shock to the present value of real surpluses is supposed to look like.

For those who think Cochrane practices a form of monetarism, Nick Rowe is on a rampage of late that doesn’t quite square with that:

http://worthwhile.typepad.com/worthwhile_canadian_initi/2014/12/who-would-ever-lend-to-an-ftpler.html

Ramanan,

I recall they do that at the nominal value level.

Do they do it for real values of deficits and debt also?

FTPL is real value.

Ramanan, it seems to me that the MMT economists hold that the deficit is endogenously determined by the response of automatic stabilization to changing conditions and that government cannot directly control the size of the deficit through the budget as many seem to presume. The amount of public debt creation reflects the size of the deficit, so the government doesn’t control the amount of public debt directly in this view.

I think that the MMT economists would say that the government can influence the size of the deficit exogenously through fiscal policy conducted by functional finance informed through iaw the sectoral balance macro approach to achieve something close to optimal growth, full employment, and price stability, mopping up residual unemployment with the MMT JG. And if a government imposes austerity as a matter of ideology, it is likely to provoke a deficit anyway when automatic stabilization kicks in owing to declining performance.

I didn’t see Warren’s quote at Bill’s place, or don’t recall it anyway. Is this what he was talking about? Or am I not understanding it correctly?

Tom,

The trouble is that MMTers try to have it both ways. I understand they say deficits are endogenously determined and so on but then say things which are the opposite. Will try to find the comment but since it’s a huge blog, difficult to search it out. Is there a way to search only comments?

I keep wondering about that too, Cullen. He’s a bond vigilante kind of guy, but on the other hand, has written a huge amount about the FTPL. It’s one of his core research areas. I am having a hard time seeing how you can square the circle between the predictions of 2011 and this paper.

It seems like he is of the idea “any deficit must cause runaway inflation”, but then this paper has Keysnesian ideas like “These are signs conventionally attributed to monetary policy, and the opposite of what one might expect for Fiscal policy. But they make sense: If the price level cannot adjust, the real value of one-period government debt cannot change. Hence, if expected surpluses decline, their discount rate, the real interest rate, must decline, and this decline raises output growth. ” It’s spending more today means output must go up in some situations.

Not only that, this paper is about abilities of a joint monetary-fiscal authority. I don’t see how you can think through this idea and not end up somewhere close to where we are.

Nice to see you tackling this one!

You mention longer dated Treasury bonds in the “Monetary Policy – Flexible Price Case”. To me, it seems that the existence of longer dated debt is the main reason we would not expect to see neo-Fisherite results in the real world.

As an extreme case, assume that all public debt is in the form of zero coupon bonds with a remaining term of ten periods. Then consider an unexpected permanent increase in the nominal interest rate, keeping real rates and expected surpluses the same. The nominal value of the debt, projected to the date of redemption, is unchanged. However, it is reduced for all dates before that (reflecting the higher nominal discount rate). With fully flexible prices, this implies an immediate fall in the price level, followed by higher inflation thereafter (reflecting the higher nominal interest rate). The new path of the price level crosses the old one at the redemption date of the outstanding debt.

In a sticky price world this translates into a period of deflation followed eventually by a period of inflation, which is a much less surprising result.

I don’t think Cochrane considers this. He does look at longer-dated debt at one point, but not in the context of this question. Other models, such as those used by Stephen Williamson, seem to avoid this result by assuming that fiscal policy reacts to a fall in nominal debt prices by cutting taxes to offset any effects.

A different issue:

I think it was you who pointed out somewhere in discussion with Nick Rowe that the neo-Fisherian theme had a post Keynesian feel to it in a certain sense – i.e. the idea that higher interest rates on government debt, taken in isolation, are expansionary. I had the same impression. Mosler’s MMT for example is obsessive about how this creates an increase to income on net financial assets held by the private sector. And you are familiar with how Godley and Lavoie referred to it. I think Nick R. felt it was quite a different thing. I don’t know.

Also, I believe Cochrane has mentioned in places something that sounds very much like a Chartalist-type argument for the role of taxation in supporting the value of money – and that this is pretty basic to the FTPL approach as well. I think Nick R. agreed with that.

Yes, it was me that made that observation. Nick felt that the PK focus was more on the income aspects of higher interest payments. I’d sort of agree with that, but one of the things that fascinates me in economics is the way that seemingly very different ideas can just be alternative ways of looking at the same thing. I think there are some key points where Cochrane’s approach is consistent with the results of G&L (and with MMT as you say) for essentially the same reasons, even though the frameworks could hardly be more different.

Nick,

My approach to this post was to try and summarize the core elements of Cochrane’s FTPL framework. I specifically excluded aspects related to the term structure of debt, the extension to New Keynesian models, and his suite of combined monetary / fiscal policy scenarios. There was just too much there to cover for the first go around.

So my examination of those parts was limited.

But it sounds like you may be right. Boiling it down, the paper seems to me to have an accrual accounting (and therefore accrual economics) flavor to it. I don’t recall thoughts of marked to marked accounting (or economics) jumping out at me. Maybe I just missed it. But I think your point is essentially one of understanding how FTPL works with respect to an existing term portfolio in a marked to market environment. It would seem to produce a category of PL and expected inflation jumps that are separate from the same analysis in the principal focus of funding the government at bond rollover dates.

JKH: A long post!

I reckon you are getting the intuition of FTPL.

The Laffer curve, in this context, simply puts a limit on how big the real tax revenue, or real surpluses, can be. If you put the income tax rate too high, it’s a big disincentive to earn income, so income tax revenue falls when you increase the tax rate.

Split a firm into two departments. The “production” department does the production, marketing, etc., and earns profits. The “finance” department issues stocks and bonds, pays dividends and interest, does stock splits and buybacks, and chooses the composition of financing between stocks and bonds. The “production” department is fiscal policy; the “finance” department is monetary policy/central bank.

“If you put the income tax rate too high, it’s a big disincentive to earn income, so income tax revenue falls when you increase the tax rate.”

Presumably this depends on the extent to which the tax is considered to be entirely ‘redistributive’. I.e. if you pay a high tax rate but think that you are getting most of it back in the form of, say public services and other benefits, then it would be less of a disincentive to you than if you thought most of the benefit was going to others without benefitting you in some way.

It also assumes that people have control over their income or their spending. I cant control what Im paid and I cant control what I need to spend to live. Others set those terms not me. I assume 75% or more of people are like me. If you make substantially more than you need to live then maybe you can voluntarily take a pay cut in an effort to deprive the govt of revenue, otherwise you are screwed.

Besides, the whole 100% tax rate is a ridiculous consideration. Imagine if a person who wanted to make a point about income inequality asked us to consider a time when one person made all the income.

The Laffer curve assumes zero tax revenue is achieved at a 100% tax rate. However it seems to me that if you paid 100% of your income in tax, and then received the whole, or most of, the amount (or value) back in some way via the government, then there would still be an incentive to earn income, so tax revenue would not fall to zero. So it seems that the Laffer curve is based on a questionable set of assumptions about how tax revenue is used.

Philippe: there’s a “free rider” problem. You get the public goods, whether you as an individual pay for them or not.

Thanks for having a look Nick.

Although I still don’t understand the point you make here (your comment at your blog):

“Plus, money usually pays a negative (real) rate of return, so PV(S) is undefined, because you are discounting at a negative interest rate, so the terms do not converge to zero as time goes to infinity.”

If the real rate is negative, then the present value of future real surpluses is greater than their future value. I don’t see the problem with that provided the surplus series is finite. And I don’t see why it shouldn’t be finite, since its just the expectation for the amount that will be sufficient to cover the real value of debt. What reason is there to expect an infinite series of surpluses in this circumstance?

JKH: I’m more used to thinking about (potentially) infinite sequences of surpluses or deficits.

Start with (something like):

1. B(t) = S(t+1)/(1+r) + B(t+1)/(1+r)

and since, similarly,

2. B(t+1) = S(t+2)/(1+r) + B(t+2)/(1+r)

Substitute 2 into 1 to eliminate B(t+1), then repeat for period 3, and so on, and you get:

n. B(t) = PV(S) + B(t+n)/(1+r)^n

Now, that second term on the RHS of that equation is a PITA. We normally assume it goes to 0, as n goes to infinity, because r > 0, and so the denominator goes to infinity. That’s the “no ponzi condition”. But if r < 1 the denominator goes to 0 instead, so the second term can go to infinity.

I ducked that question in my latest post on FTPL, by assuming that S(t) is constant, so PV(S) = S/r. But if r < 0, that means S < 0 too.

We get: M/P = S/r where both S and r are negative. Money is a (stable) Ponzi scheme. (Which it is, of course).