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

## Monday, November 10, 2014

### A dirty little secret

 Shhh...I told you *nothing!*
There's been a lot of talk lately about the so-called "Neo-Fisherite" proposition that higher nominal interest rates beget higher inflation rates (and vice-versa for lower nominal interest rates). I thought I'd weigh in here with my own 2 cents worth on the controversy.

Let's start with something that most people find uncontroversial, the Fisher equation:

[FE]  R(t) = r(t) + Π (t+1)

where R is the gross nominal interest rate, r is the gross real interest rate, an Π is the expected gross inflation rate (all variables logged).

I like to think of the Fisher equation as a no-abitrage condition, where r represents the real rate of return on (say) a Treasury Inflation Protected Security (TIPS) and (R - Π) represents the expected real rate of return on a nominal Treasury. If the two securities share similar risk and liquidity characteristics, then we'd expected the Fisher equation to hold. If it did not hold, a nimble bond trader would be able to make riskless profits. Nobody believes that such opportunities exist for any measurable length of time.

Let me assume that the real interest rate is fixed (the gist of the argument holds even if we relax this assumption). In this case, the Fisher equation tells us that higher nominal interest rates must be associated with higher inflation expectations (and ultimately, higher inflation, if expectations are rational). But association is not the same thing as causation. And the root of the controversy seems to lie in the causal assumptions embedded in the Neo-Fisherite view.

The conventional (Monetarist) view is that (for a "stable" demand for real money balances), an increase in the money growth rate leads to an increase in inflation expectations, which leads bond holders to demand a higher nominal interest rate as compensation for the inflation tax. The unconventional (Neo-Fisherite) view is that lowering the nominal interest leads to...well, it leads to...a lower inflation rate...because that's what the Fisher equation tells us. Hmm, no kidding?

The lack of a good explanation for the economics underlying the causal link between R and Π is what leads commentators like Nick Rowe to tear at his beard. But the lack of clarity on this dimension by a some writers does not mean that a good explanation cannot be found. And indeed, I think Nick gets it just about right here. The reconciliation I seek is based on what Eric Leeper has labeled a dirty little secret; namely, that "for monetary policy to successfully control inflation, fiscal policy must behave in a particular, circumscribed manner." (Pg. 14. Leeper goes on to note that both Milton Friedman and James Tobin were explicit about this necessity.)

The starting point for answering the question of how a policy affects the economy is to be very clear what one means by policy. Most people do not get this very important point: a policy is not just an action, it is a set of rules. And because monetary and fiscal policy are tied together through a consolidated government budget constraint, a monetary policy is not completely specified without a corresponding (and consistent) fiscal policy.

When Monetarists claim that increasing the rate of money growth leads to inflation, they assert that this will be so regardless of how the fiscal authority behaves. Implicitly, the fiscal authority is assumed to (passively) follow a set of rules: i.e., use the new money to cut taxes (via helicopter drops), finance government spending, or pay interest on money. It really doesn't matter which. (For some push back on this view, see Price Stability: Is a Tough Central Banker Enough? by Lawrence Christiano and Terry Fitzgerald.)

When Neo-Fisherites claim that increasing the nominal interest rate leads to inflation, the fiscal authority is also implicitly assumed to follow a specific set of rules that passively adjust to be consistent with the central bank's policy. At the end of the day, the fiscal authority must increase the rate of growth of its nominal debt (for a strictly positive nominal interest rate and a constant money-to-bond ratio, the supply of money must be rising at this same rate.) At the same time, this higher rate of debt-issue is used to finance a higher primary budget deficit (just think helicopter drops again).

Well, putting things this way makes it seem like there's no substantive difference between the two views. Personally, I think this is more-or-less correct, and I believe that Nick Rowe might agree with me. I hestitate a bit, however, because there may be some hard-core "Neo-Wicksellians" out there that try to understand the interest rate - inflation dynamic without any reference to fiscal policy and nominal aggregates. (Not sure if this paper falls in this class, but I plan to read it soon and comment on it: The Perils of Nominal Targets, by Roc Armenter).

If the view I expressed above is correct, then it suggests that just limiting attention to (say) the dynamics of the Fed's balance sheet is not very informative without reference to the perceived stance of fiscal policy and how it interacts with monetary policy. Macroeconomists have of course known this for a long time but have, for various reasons, downplayed the interplay for stretches of time (e.g., during the Great Moderation). Maybe it's time to be explicit again. Let's help Nick keep his beard.

1. David: I need to think about this a little more, but my I *think* we are on the same page.

"When Monetarists claim that increasing the rate of money growth leads to inflation, they assert that this will be so regardless of how the fiscal authority behaves."

Yes, but if the increased rate of money growth is permanent (or doesn't decrease below the initial growth rate at some future time), that tells you how the fiscal authority must behave. Because the Present Value of seigniorage profits (at least in nominal terms) will be higher.

For example, if new money is paid as interest on old money, so "the central bank increases the rate of interest" means the same as "the central bank increases the (base) money growth rate" (which has no fiscal consequences for the rest of the government budget constraint) then sure that would (at least eventually) increase the inflation rate. And I'm pretty sure that's what's going on in John Cochrane's "Interest on reserves' paper. (My post on this: http://worthwhile.typepad.com/worthwhile_canadian_initi/2014/10/john-cochranes-monetary-policy-with-interest-on-reserves.html

But the trouble comes if you take a Woodfordian model, where there is no stock of base money (well, strictly there is, but people can hold either positive or negative balances at the central bank, with interest on those balances, and the positive and negative balances sum to zero in aggregate) it gets trickier.

Personally, I blame the Neo-Wicksellians, for thinking about central banks as setting an interest rate. That way lies madness, and Neo-Fisherites. So you have to start thinking about whether individual agents could coordinate on an equilibrium where the central bank holds the nominal interest rate fixed. Schmitt-Gruhe and Uribe just assume they do, "stability" be damned!

My beard is greying fast.

1. Nick,

I'm pretty sure we agree on the first part. And since I am old school, I do have trouble wrapping my mind around the concept of monetary policy in the absence of money.

However, in terms of the Schmitt-Groehe and Uribe paper, why don't you just "reverse engineer" things in terms of quantities instead of prices? If I recall correctly, the do have an interest-bearing government liability floating around. Rather than pegging the interest rate on that security, just ask how the quantity of that object would have to behave over time and how the fiscal authority would have to finance such an operation (they also assume lump-sum taxes).

I'm not sure how this relates to your concern for "stability" of equilibria. I presume that your concern should remain, although possibly you believe that explicitly targeting quantities is somehow more robust.

2. David: "However, in terms of the Schmitt-Groehe and Uribe paper, why don't you just "reverse engineer" things in terms of quantities instead of prices? If I recall correctly, the do have an interest-bearing government liability floating around."

That was my initial thought. My initial hunch was that their model was basically the same as John Cochrane's, so that the central bank raising R meant a growing stock of B. But then I noticed that B0 could be positive, negative, or zero. And that the simplest case was where B0=0. So that wouldn't work. Plus B seemed to play no role whatsoever in their results. So I then figured it's really a Woodfordian model structure, and they were just *assuming* that inflation adjusted to reconcile the Fisher equation with the nominal interest rate. Because that's the only perfect foresight equilibrium.

My new post (on collective speeding) tries to explain why it is not individually rational for firms to coordinate on that unstable equilibrium.

2. Drs. Andolfatto and Rowe,

With regard to "a consolidated budget constraint", I understand that the Treasury is Uncle Sam's left pocket and the Fed his right pocket.

But what constrains Uncle Sam's spending, considering that he has a single wallet with various sections in it for convenience or confusion? He can fill any of those wallet accounts with how ever much money as he wishes.

Left Coast Bernard

1. Left Coast:

Nothing constrains Uncle Sam's spending in *nominal* terms. You can print as much money as you want, but if it becomes worthless as a result, what good is that?

The limits to printing money (seigniorage) are the same as the limits to any form of taxation.

2. I agree with David.

3. David and Nick,
To show inflation causal relationship, we need a true accounting equation derived from NIPA sector accounts:

Md*Vd= R- NIC = P*Q

Where
Md = actual money demand in GDP production money flows
Vd = money demand velocity among sector money flows in production
R = total sector income receipts
NIC = total sector non-investment/non-consumption spending such as
interest payments, transfer payments, debt payments, etc.

Md = RGDP, Vd = (R-NIC)/RDGP = P (price level)

The gap between R and NIC is the causal factor to effect price level P. In other words, the larger gap (i.e. more total sector spending R, less total sector non-production spending NIC), the higher price level P

Note there are quite differences from QTM equation: MV=PQ
1. Use money demand Md (not money supply) in NIPA accounts
2. Money demand velocity (Vd) is calculated by aggregation of all money flows between sectors for exchanging goods, services or NIC spending. It is not axiomatically defined as PQ/M
3. No axiomatic assumption about relationship : “money supply (Ms) = money demand (Md)” or money supply increase will cause money demand increase in GDP production.

4. Accounting equations are equivalent functions (not just equivalent function output values)

4. Layman trying to decipher your post - let me start with your conclusion, that both sides of the debate are saying essentially the same thing. What is that thing, precisely? The layman hearing of the debate is that the sides say opposite things about the impact of Fed interest rate policy on inflation (Cochrane's short vs long term distinction aside, which may be a resolution and maybe behind what you are saying here, but can you be more explicit?).

And, you frame the question differently - namely you state the Monetarist in terms of growth in money supply vs the Neo Fisherite in terms of interest rates. Presumable there is an equivalence between money supply and interest rates given the way the Fed implements interest rate policy - is that fair to say?

And finally, can you be more explicit about why the budgetary response to increasing interest rates has to be what you indicate above?

1. Andy,

Take your second paragraph. Yes, there exists a theoretical equivalence (at least in the models I am familiar with).

Take you first paragraph. If what I just said is true, then yes, they are saying the same thing, just in different ways. Some caution, however. In some of these theories, money and bond supplies have no role to play.

Finally, what I said about the budgetary response just follows from a simple "quantity theory of money." To get higher inflation, you need to have the money supply grow faster. This is done by creating new money and injecting it in the system as transfers (negative taxes, or helicopter drops).

Does this help?

2. The crucial part is how the demand-side uses the money after transfers.
The money use can be categorized into 4 spending types at macro level of accounting: investment(I), consumption(C), NIC(non-I, non-C) and non-GDP (i.e. money transfers, but not into GDP production money flows such as stock markets, etc.)

Regardless of increasing or decreasing money supply/interesting rate, it would not get inflation if our income-spending gap (i.e. R-NIC, see explanation in my previous post) is smaller like current lowinflation economic condition. We have higher NIC spending based on NIPA accounting data, which drags the inflation. P= (R-NIC)/RGDP in NIPA accounting identity.

The inflation “blackhole” is in NIC and non-GDP spending in demand side after money transfers from supply side.

5. There seems to be a maintained assumption that the monetary authority has an obligation to prevent the sovereign fisc from defaulting. (And the assumption is clearly contrary to fact in certain cases, such as when there are multiple sovereigns involved, as in the case of the ECB) Otherwise, the sovereign fisc is just like any other debtor -- possibly "too big to fail," but the same could be true of private debtors. If the sovereign fisc is just another debtor, then I think the old monetarists win and the neo-Fisherites lose, because there's nothing, except expected monetary policy, to tie down the price level in the long run. So there's no reason to expect the inflation rate to be stable, unless the monetary authority acts (or is expected to act) to maintain stability. If it permanently sets the interest rate wrong and is expected to keep doing so, you get instability.

In practice, in most cases, I think there's a "soft obligation" on the part of monetary authorities to prevent fiscal default. So they can play a game of chicken where they bring the fisc to the brink of default. But implicit in their ability to play such a game is that there remains the perception of a nonzero probability of actual default (as opposed to hyperinflation as the only out for a bankrupt fisc). So, at least, fiscal policy doesn't have quite as much power over the long-run price level as it would in the idealized "hard obligation to avoid default" case.

Interesting (and it just has occurred to me writing this comment) to consider that maybe fiscal policy should include the behavior of private "too big to fail" debtors. For the relevant purposes, fiscal policy would be the actions of any debtor that the monetary authority is expected to protect from default in the long run.

1. Andy,
A risk-taking central bank effectively has two functions. One is as supplier of reserves and LOLR. The second is as an intermediary. The intermediary function subjects it to the risk of losses. Just as a TBTF bank, these losses would have to be covered via fiscal policy in the form of foregone seigniorage or an out-right reccapitalization. The central bank can elect to finance the lost seigniorage with zero-cost reserves. However, financing it with interest-bearing reserves just creates more losses.

In the end, I don't see much difference between a TBTF bank and the central bank's risk asset balance sheet. Both are fiscal risk, both fiscal risks can be underwritten by reserve issuance.

2. Andy,

If the sovereign fisc is just another debtor, then I think the old monetarists win and the neo-Fisherites lose, because there's nothing, except expected monetary policy, to tie down the price level in the long run.

I'm not sure I understand this statement. In any case, my post was trying to bridge the (apparent) gap between Old Monetarist and Fisherite interpretations of monetary policy. I don't think it's a matter of one side "winning" over another.

3. I'm saying you've only bridged the gap if the central bank is committed to preventing the fisc from defaulting. Otherwise fiscal policy is not directly relevant to the value of money. And the neo-Fisherites end up on the wrong side of that unbridged gap, because what matters is just the supply and demand for money, and a choice of lower interest rates by the central bank is always a choice of more money supply (except if all money is created by paying interest on old money, which is an odd case).

4. Andy,

Oh, I see what you're saying now.

The Fed is only permitted by law to buy and sell treasury debt (or treasury insured securities, like agency MBS). Imagine a world with no treasury debt. How would the Fed inject money into the economy? In my view, treasury support is needed. The treasury has to issue the bonds that the Fed buys. And conversely, if contractions in the money supply are wanted or needed, and if asset sales are not sufficient (say because they have lost value), then again, treasury support is needed, regardless of how committed the Fed might be. No?

5. As I understand it, the Fed can also create money by lending to banks at the discount window. But I'll acknowledge that the Treasury can potentially set limits on the Fed's ability to create and destroy money. I'd question, though, how relevant is a theory that depends on those limits' being binding.

For example, as you note, there is a potential limit on how much base money the Fed can destroy, so there might be a minimum quantity of base money that must remain. But the real demand for base money tends to rise, more or less exponentially, over time, so eventually, presumably, the demand for any given fixed quantity of base money would be sufficient to bring the price level arbitrarily low. So in the long run the "minimum quantity of base money" constraint won't be binding on the Fed unless as long as its preferred average inflation rate is nonnegative.

6. David. Fyi u made zerohedge this morning.

1. Hilarious. Angry populist denounces direct and butally frank culturally significant Fraser Valley-speak.

News release: Right away, this year. The Federal Reserve Bank of St. Louis acknowledged reception of Dr. Andalfatto's resignation today. The president said that in no uncertain terms could the term 'dickhead' be used to insult well known and loved yet so angry conspiracy theorists.

Bullard added that in the St. Louis Fed, only co-authors were allowed to call each other 'morons'.

7. Good post, interesting discussion Dave and Nick. Tusin tuck.

8. It's good to see the clarification on the importance of the assumption about the fiscal rule.

One question.

When you assume that the fiscal rule targets the nominal growth of government debt, is that the growth of the face value or of the market value? In particular, what happens when you have long term debt? If government debt is mostly term debt, we would expect a permanent increase in the nominal interest rate to result in an immediate fall in the market value of that debt. Does the Neo-Fisherite result require that the fiscal response is a large one-off primary deficit to offset this?

1. Nick,

I suppose I was implicitly assuming a steady state, in which case the nominal face value and market value would grow at the same rate.

I think you are correct. A surprise permanent increase in the interest rate would cause a decline in the market value of outstanding debt. To be honest, I'm not sure off-hand what sort of fiscal actions would have to take place to anchor the real value of total debt (short and long term). Should be easy to work out though. Can assign this as homework? ;)

9. David:

"When Neo-Fisherites claim that increasing the nominal interest rate leads to inflation, the fiscal authority is also implicitly assumed to follow a specific set of rules that passively adjust to be consistent with the central bank's policy. At the end of the day, the fiscal authority must increase the rate of growth of its nominal debt"

What would happen if the fiscal authority did the opposite, and tried to reduce its debt by cutting spending and raising taxes? Would the higher interest rate still lead to higher inflation in this case or not? This might be a silly question, I'm just not sure what you meant. Thanks.

1. This is not a silly question at all! In fact, I think it's a very important question. Why don't you read the Christiano and Fitzgerald paper I cite above? They touch on this issue, and provide references for further reading.