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“Assume that all new money is always paid as interest on old money.”???? Well in the real world it just isn't. Why make assumptions that are not realistic?

"I'm still trying to figure out if John Cochrane's model is really a monetarist model, even though he doesn't think it is."

Oddly enough, it had struck me that certain aspects of his model had a lot in common with post-Keynesianism, even though he would never admit it. The idea that an increase in the interest rate can be expansionary appears often in PK models (see e.g. all of Godley and Lavoie's Monetary Economics). The analysis and assumptions may be very different, but the reason for the result is essentially the same.

Ralph: because, if we assume that central banks do not make charitable donations (do not own a helicopter), that is the only "monetary policy" that has no fiscal consequences for the long run government budget constraint. So any other change in the money supply is called "fiscal policy". It's like MMT in that respect.

Nick E: but isn't that because setting a higher interest rate means a higher flow of disposable income, plus growing wealth, in PK models? That is a very different mechanism. Here it's a substitution effect.

It helps to remember that all New Keynesian models are monetary models in disguise. They typically do not explicitly model the demand for money--the money market is left totally implicit--but they are equivalent to a money-in-utility type model, where real money balances are additively separable in the utility function. There are two assumptions in the standard NK model with money that are interchangeable: 1) assuming that money is additively separable in utility, 2) assuming that causality runs from inflation to central bank's interest rate target. "Conventional" New Keynesian models assume (2), which is why they can get away with leaving the money market implicit. But failing to specify the money market creates ambiguity about what the central bank's policy mechanism actually is.

When the central bank sells a bond, it decreases the total stock of money and, because prices are sticky, also reduces real money balances m/p in the short run. Since m/p is in the utility function, households respond to this loss of wealth by wanting to sell off some bonds and buy more money, the effect of which is that households demand a higher interest rate to hold the market-clearing amount of bonds. When money is in the utility function and prices are sticky, monetary contraction causes higher interest rates in the short run and deflation/lower interest rates in the long run.

Unfortunately, the ambiguity of NK assumptions creates creates confusion. Cochrane thinks his model is about treasury behavior, but it's not. What he has actually done is assumed that (1) and (2) above are both false (as could be the case when money is not in the utility function). Cochrane assumes that the central bank simply dictates the nominal interest rate in the bond market, and that households are ambivalent to any kind of OMO that would be required to maintain that target (so if m/p falls in the short run, households don't react in any way). The higher interest rate means that future prices have to rise in order to equilibrate the output market (ie, to maintain the market clearing real interest rate).

So this is all about implicit money markets. If you think money is special (money-in-utility), then the treasury is basically irrelevant and raising the interest rate is contractionary in the short run. If you aren't totally sure that money actually exists, then of course you are also suspicious about the existence of the liquidity effect where monetary expansion lowers interest rates in the short run.

Hmm. Well, maybe, but this is how I see it.

Underlying those PK payment functions is an assumption that the private sector has a steady state level of real holdings of government debt. If the actual real level of holdings differs from that, then the private sector will save or dissave accordingly (not dissimilar to monetarist stories, but focussed on a wider class of financial asset). So given the nominal stock of government debt, an equilibrium price level is determined. The real peg may be described differently, but I'm not so sure it's so different. Cochrane just chooses to identify the equilibrium real asset balance with the expected value of future surpluses.

It can certainly appear in the short run through being an item of income, but it doesn't need to be counted as income to still have the same long run impact. You could describe it as a wealth effect, but I'm personally wary of that, because it raises distracting questions of what is real wealth.

I do though agree there's a lot of differences in the narratives.

Matthew: "It helps to remember that all New Keynesian models are monetary models in disguise."

I totally agree. Even if the central bank in a NK model sets a stupidly high nominal and real interest rate, there would be no recession if underemployed worker/firms could simply barter their way back to full employment, even if barter exchanges had to take place at sticky Calvo relative prices. They are implicitly models of a monetary exchange economy. When woodford talks about a "cashless" economy, he is wrong. Credits and debits at the central bank ARE used as medium of exchange, as well as unit of account. It's just electronic, interest-paying, cash, where you can hold both positive and negative balances. My old post on this.

"which is why they can get away with leaving the money market implicit"

Excuse me while I have a short rant. I always go ballistic when I hear the words "the money market". CAPS LOCK ON. Every market is a money market in a monetary exchange economy. That's what "money" means! End rant. Sorry.

I am going to reflect on the rest of your comment. But I think this is the monetary mechanism in NK models. There is central bank money, which pays interest set by the central bank, and individuals can hold either positive or negative amounts of that money, but the net supply of that money is always zero. (The positive balances always sum to the negative balances.)

Nick E: I'm also going to reflect on your comment.

Good comments all. Too much food for thought, this early.

"Assume that all new money is always paid as interest on old money. [Update: Any other change in the money supply has consequences for the long run government budget constraint, so is called "fiscal policy".]"

Still trying to figure this out. Are you implying something like this? Say that in 2084 the central bank will redeem all the outstanding notes, in exchange for real goods, at a price of 100 notes per real good (I'm stealing your wording from the previous post). So when the central bank issues a new note in the form of interest, what is happening is that the same real good now redeems 101 notes. It's not fiscal policy because the government doesn't have to have more real goods on hand in 2084 to redeem its note issue.

JP: no. For every $100 in currency I hold, the central bank prints $1 per year, and gives it to me. (Only it does this on a daily or continuous time basis.) So I earn 1% interest on currency, and the stock of currency grows at 1% per year. In a Quantity Theory model, we get a 1% inflation rate (assuming no growth in real Y, and no other changes).

Is this analysis compatible with greater-than-zero RGDP growth rates?

If the money growth rate is 0%, then we effectively have a gold standard, which seems economically undesirable in a growing (real terms) environment.

If the money growth rate is n% > 0%, then I don't think we fix the problems of deflation. An agent assuming g% growth rate (real terms) will think that next period's price level will be (n-g)% greater than the current period's, so it's to their benefit to hold a cash (monetary base) balance at n% and defer their purchase.

It would seem that actually achieving n% inflation would require something we're defining here as "fiscal policy", to increase the monetary base net of interest paid on itself.

In a world where potential real output Y is unchanging and interest is paid on money, it seems that any change of this interest rate is really just an accounting exercise; we get real effects only in that different actors follow different accounting rules.

Majromax: "Is this analysis compatible with greater-than-zero RGDP growth rates?"

Yes. I only made that assumption for simplicity of exposition.

But yes, in a growing economy, if you wanted 0% inflation, you would need positive growth in the money supply, and that would create seigniorage revenue. But *relative to that benchmark* everything else in my "model" should be the same. An *additional* 1% growth in the money supply, with 1% interest on money, would cause 1% inflation, and have no fiscal consequences.

Nick, sloppy reading on my part. So your original post, the "Sign Wars" one, was an attempt to explain Cochrane using his own model (or at least the one from his blog posts). And this one is an attempt to back out the same results in terms of a monetarist framework.

Ah, okay -- seigniorage revenue is expected in a growing economy. I hadn't understood that from the post itself.

With that understood, I think this is an interesting model for QE transmission. The US's currently-implemented QE "looks like" a high interest rate on base money over a short interval (the asset purchase period), combined with a promise of a negative (relative to the counterfactual) interest rate at some point in the future.

JP: Well, my "sign wars" post was more of a diversion. I hadn't read JC's paper when I posted it. This post is more of an attempt to interpret JC's paper, after having sort of read it. Sign Wars was New Keynesian; this post is more monetarist.

@ JP

It's not fiscal policy because the government doesn't have to have more real goods on hand in 2084

I think his point is that it is not fiscal policy because there is no treasury ledger involved in the act. It is all done via the central bank's balance sheet. That is also what he was referring to when he wrote:

[Update: Any other change in the money supply has consequences for the long run government budget constraint, so is called "fiscal policy".]

But I may be wrong. If so, maybe Nick can clarify.

The interest on reserves regime is an attractive extension of 30 years of financial and monetary innovation. It gives us interest-paying money, the end of monetary frictions, and the foundation of a more stable financial system in which government short-term debt drives out private short term debt, much as government notes drove out banknotes in the 19th century" -- John Cochran

Wrong. This is the economic law that applies to paying interest on interbank demand deposits held at the District Reserve banks (which are owned by the member commercial banks):

Gresham’s law is a statement of the “principle of substitution” as applied to money: a commodity (or service) will be devoted to those uses which are most profitable. It is another one of the paradoxes of money that, unlike articles in the market, the bad drives out the good.

Remunerating excess reserves emasculates the Fed's "open market power". The only tool at the disposal of the monetary authority in a free capitalistic system through which the volume of money can be controlled is legal reserves. Keynes's liquidity preference curve (demand for money), is a false doctrine. Interest rates are the price of loan-funds, not the price of money; the price of money is represented by the various price (indices) level. The money supply (& commercial bank credit), can never be managed by any attempt to control the cost of credit (i.e., thru pegging the interest rate on governments; or thru "floors", "ceilings", "corridors", "brackets", etc).

McCollum’s Rule is also a false doctrine. The monetary base is required reserves. Currency has no expansion coefficient, in fact, all increases in currency held by the non-bank public are offset by concurrent expansions in Reserve Bank credit (as outflows are contractionary). See: http://bit.ly/yUdRIZ

Quantitative Easing and Money Growth:
Potential for Higher Inflation?
Daniel L. Thornton FRB-STL

Friedman was dead wrong. Reserves are not a tax. Reserves are "Manna from Heaven". A brief “run down” will indicate just how costless, indeed how profitable – to the participants, is the creation of new money. If the Fed puts through buy orders in the open market, the Federal Reserve Banks acquire earning assets by creating new inter-bank demand deposits. The U.S. Treasury recaptures about 98% of the net income from these assets. The commercial banks acquire “free” legal reserves, yet the bankers complained that they didn't earn any interest on their balances in the Federal Reserve Banks.

On the basis of these newly acquired free reserves, the commercial banks created a multiple volume of credit & money. And, through this money, they acquired a concomitant volume of additional earnings assets. How much was this multiple expansion of money, credit, & bank earning assets? Thanks to fractional reserve banking (an essential characteristic of commercial banking) for every dollar of legal reserves pumped into the member banks by the Fed, the banking system acquired about 93 (c. 2006), dollars in earning assets through credit creation

Remunerating excess reserve balances induces dis-intermediation for the non-banks (an outflow of funds or negative cash flows). Since 1933 the term dis-intermediation only applies to the non-banks and not the money creating, deposit-taking, commercial banks. Dis-intermediation for the CBs is not predicated on the level of interest rates. The CBs could continue to lend even if the non-bank public ceased to save altogether. The lending capacity of the CBs is dependent upon monetary policy, not the savings practices of the public. The 1966 S&L credit crisis is the paradigm. I.e., raising the remuneration rate destroys the ability of the NBs to obtain wholesale money market funding - except at higher rates (in the borrow-short to lend-long savings-investment business model). I.e., it affects not just the cost of credit, but the availability of credit.

Lending by the CBs is inflationary. Lending by the NBs is non-inflationary, ceteris paribus. Lending by the NBs provides an outlet for savings (matching savings with investment). Whereas bank held savings are impounded within the CB system (the CBs create new money when they lend/invest, they do not loan out existing deposits, saved or otherwise). I.e., raising the remuneration rate to possibly 3 percent (as Yellen suggests), will produce stagflation and destabilize economic growth.

flow5: Gresham's Law does not work when the issuer of the bad money promises to redeem that bad money at par for good money. Because eventually people will return that bad money to the issuer.

It's not that the interest is recaptured, it's that the supply of loan-funds (voluntary savings), are idled, or lost to investment, indeed to any type of consumption or expenditure.

The remittance doesn’t change the higher percentage of bank held savings that is now trapped in the CB system. That is the bad is driving out the good (decreases the supply of loan-funds).

That's how stagflation was predicted in the late 50's (then we got 5 successive increases in Reg Q ceilings for the CBs exclusively – up until the NBs could no longer compete). I.e., the CBs began to buy their liquidity as opposed to following the old fashioned practice of storing their liquidity. The CBs, as a system, simply pay for what they already own.

The remuneration rate allows the CB system to out-bid the NBs. If the NBs had been the dominate counterparty with the “trading desk”, then the money stock would have grown pari passu with POMOs. Instead the OMOs were predominately asset swaps.


> Remunerating excess reserves emasculates the Fed's "open market power".

Define excess reserves? If you mean "in excess of regulatory requirements," then what makes that level economically special?

As Nick often points out, Canada does not have minimum regulatory reserve levels. Instead, it sets a deposit rate slightly below its target rate and a bank rate slightly above.

This system encourages banks to keep appropriate reserves on hand, because the opportunity cost for not doing so is essentially double the target rate (losing 0.75% on the deposit plus paying 1.25% at the bank rate). This further encourages using other banks to make up the shortfall (at an intermediate overnight rate).

The US Fed may be running into trouble in that its target rate is still exceptionally low, so the current IOR rate is above the target rate. This is obviously not an equilibrium situation.

The volume of excess reserves (not required reserves), isn't relevant. It's the remuneration rate that indirectly "absorbs' savings. Canada's not relevant either.

Economics is an exact science. Economic prognostications are infallible. Roc’s in MVt = roc’s in nominal-gDp (proxy for all transactions in Irving Fisher’s “equation of exchange”). Bankrupt U Bernanke was solely responsible for the Great-Recession.

Nick - or anybody:

From Cochrane's paper, page 6 top:

"To set an interest rate target, the government auctions bonds –it says “the nominal interest rate will be 5%. We sell nominal bonds at 1/0.95 dollars per face value. We will sell any amount demanded at that price.” Equation (6) then is a simple reading of private demand –if the government targets nominal interest rates at a level i, that equation tells us how many bonds Bt 1 will be demanded. It reassures us that a fi…nite amount will be demanded, and therefore the nominal interest rate target will work."

Is that right?

Shouldn't it be (1/(1 + .05)) instead of 1/0.95 ?

JKH: I think you are right. It's presumably a (mental) typo. Because, IIRC, each bond promises to pay $1 the following period.

"To set an interest rate target" That's impossible.

What's the Canadian web site that corresponds to FRED. I'll figure out how to target gDp for Canada.

One day you will be very embarrassed by such a question. I.e., Greenspan never tightened and Bernanke never eased.


Another one, top of page 31:

"Equation (1) has a natural “aggregate demand” interpretation. (Woodford 1995). If the real
value of nominal debt is less 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 e¤ect”of government debt."

Maybe this one is right, but I'm having a hard time with the signs. Equation 1 is the basic debt valuation equation with expected future surpluses. He includes QE type bank reserves in his definition of debt I think, so spending debt is spending money in part.

If the real value of debt starts out lower than the PV of future surpluses, why doesn't an increase in the price level reduce the real value of debt further?

This would make intuitive sense to me if the real value of debt started out higher than surpluses - but surely he couldn't have a mistake in that sense - so I must be missing something?

It's weird.

There's something in this fiscal backing theory that smells faintly like neo-chartalism - i.e. the idea that the value of money is backed by the power of taxation.

JKH: "Maybe this one is right,"

No, that one is wrong too. Well spotted. He (presumably) meant to say the opposite, because FTPL says the opposite. You aren't missing anything! (But it is extra hard to figure out a "sign wars" paper, when the author sometimes gets the sign wrong by mistake!

You should leave a comment on his blog post, just letting him know about this and the previous typo.

"There's something in this fiscal backing theory that smells faintly like neo-chartalism - i.e. the idea that the value of money is backed by the power of taxation."

There's nothing faint about it. If you do neo-chartalism logically, plus assume flexible prices, you get FTPL.

JKH: "He includes QE type bank reserves in his definition of debt I think, so spending debt is spending money in part."

Yes. You think right. And an open market operation is just swapping one type of government debt for another, in this perspective.

You are now, officially, a macroeconomist!



Nick, I really liked Matthew's comment, but I think your complaint about his discussion of the "money market" is slightly off base. In one sense you are right, the traditional definition of the term 'market' implies a setting where people swap things. In that case you are quite right, all markets are money markets. But I also think economists use "market" for a slightly different concept, which as far as I know does not have another term to describe it. Let me give you and example:

In Germany V soared and the Cambridge K plummeted in 1920-23. No surprise there. Let's say Germans went from holding 10% of GDP as cash to just 1% of GDP as cash. And let's say they did so because the opportunity cost of holding cash rose sharply. How would you describe that change? One possible description (Matthew's and mine) would be that the rise in the opportunity cost of holding cash affected the money market. If that's wrong, it doesn't make the effect go away. I suppose you could say "a rise in the opportunity cost of cash affected the real demand for money," or it affected the "real money stock." Fair enough. But then if we are going to be symmetrical, we can no longer say "abolishing property taxes would affect the housing market." We'd have to say that action affected the real stock of housing. After all, prices can change in a market without any transactions occurring. We know that because stock prices often change sharply when the stock exchange ("market") is closed, and no transactions occur. At least prices can change if you define 'price' as the point where Qs equals Qd. So while the "transactions" view of markets is the original meaning, it seems the meaning in economics is now wider, and if we are not going to use "market" we need a new term for the concept.

Or am I totally off base here? (quite possible.)

Scott: I like Matthew's comment too. My little rant about "the money market" was more of an aside. Because using those words misses an important distinctive thing about money -- it's the medium of exchange.

Yes, John Cochrane's FTPL does assume that money and bonds are perfect substitutes, rather than imperfect substitutes where the demand for money depends on the difference between their rates of return. And that's a problem.

But the rise in the opportunity cost of holding cash will affect all markets, because money, unlike houses, is traded in all markets. Talking about "the money market" puts undue focus on the bond market.

This gets back to our own disagreement about MOE vs MOA!

Isn't the model simply the converse of monetary offset?

and one more:


I think its a pretty fascinating paper - because of a number of the observations he makes about the nuts and bolts of the CB balance sheet and the way in which he integrates that with his economic theory.

Miami: I don't think so. Or maybe I misunderstand you.

JKH: I always get a good feeling when: the author makes some minor mistakes, like saying "above" where he meant to say "below", and a reader can spot those mistakes, and the author sees straight away they were mistakes. It means the paper makes sense (whether right or wrong), and the reader understands it. (I always wonder, if you took a bit of post-structuralist twaddle, added or deleted a few negatives at random, whether anyone would notice the difference.)

Not exactly the same but the intuition seems very similar. All else equal, raising rates means more interest income for the private sector. Changes to government spending due to changes to rates make fed policy credible.

monetary offset; cb will raise rates to prevent spending beyond whats appropriate for the target. private sector adjustment
converse offset; government will raise surplus to prevent spending beyond whats appropriate for the target. public sector adjustment

Of course that is a gross over simplification but it's about how interest rates affect planned surpluses/deficits. If expectations are just mapping spending plans onto the future.

Higher rates are successful if they make the government save. Lower rates are successful by making the government dis-save. It's an assumption that is required by New Keynesian models (according to the paper, if i remember correctly) to generate standard monetary policy results of the effect of changes to interest rates on AD.

isn't that how monetary policy is supposed to work for the private sector? why would it be different for the government sector?
i'm starting to think i must not get it. or maybe i don't get which part is the interesting part. (not an economist)

"And with sticky prices, if the central bank sets a higher interest rate this causes a boom."
If you add "unless the government changes its fiscal stance as a result" and, I think, I make more sense. (but probably not)



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