Garett Jones  

Future money and today's NGDP

The Autobiography of Malcol... Questions for Austrians...

In times of trouble, I often turn for comfort to the Cagan money demand model.  Philip Cagan, who passed away in June of this year, was a monetarist who moved the ball down the court.  Back in the 50's, he gave us a new and better set of reasons for thinking that future monetary policy impacts today's economy.

Here's his story: Today's demand for real, liquid buying power (the money supply divided by the level of prices, M/P) depends partly on inflation in the near future.  If inflation's high, you want to hold less money--you'd rather hold real assets that won't lose value in an inflation. 

Sure, you as one person can dump your money holdings by selling (!) them to someone else.  But for the economy as a whole, the money supply is pinned down by government (and some other stuff I'm leaving out--remember, you never want to see everything in perspective).  So if there's inflation in the future, the only way people can reduce their real buying power today is for the price level to rise.  Future inflation causes a price increase today.

But here's the thing: Cagan doesn't just assume that inflation is caused by money growth---he proves it.  There's a little arithmetic to it, but the story is this: Today's price level depends partly on today's money supply, and partly on tomorrow's price level.

But tomorrow's price level depends on both tomorrow's money supply and the price level in the even more distant future, which depends partly on money in the still more distant future.  And so onward, forever.

The result?  Today's price level depends mostly on the future supply of money.

So if word gets out that the money supply will be higher than expected two years from now, in Cagan's story that pushes up prices today.  And longer-lasting increases in future money have a bigger impact on prices than one-off increases (like the burst of money printed around Y2K).

Economists have a lot of stories about why expectations matter, how beliefs about future government policy influence things today.  But Cagan's money demand model did more than that: It gave us a new reason to think that a credible Federal Reserve---one that makes their future intentions clear, and sticks to those plans--creates macro stability today.  

Implication: Countries that seriously debate big changes in their monetary policy--even for the better--create macro instability right now. 

And the Cagan model is a great starting point for thinking about why the Fed's new monetary policy rule will start pushing up nominal GDP fairly soon...even if it takes years for the mortgage purchases to add up to much of anything.  Expected money matters today.

Coda: Congratulations to Scott Sumner on his deserved and underacknowledged victory. 

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CATEGORIES: Monetary Policy , Money

COMMENTS (10 to date)

Cagan's name is not one I hear mentioned often but his views are certainly interesting. Maybe this is implied, but is it correct to presume under this view that the price level is based on future expectations of the money supply rather than known outcomes?

Two other questions related to implications of the model:
1) If the Fed Chairman and other voting members only serve limited terms, can they credibly commit to certain policies beyond their term limits? If so, how?

2) If the gov't cannot control M2 (within a couple percent) over periods of at least several years, could the Fed's actions actually destabilize future expectations by implying a wider range of outcomes?

Yancey Ward writes:


5-10 years from now, Sumner will hope everyone forgets his role.

Garett Jones writes:


1. That's why the Fed makes almost all decisions with supermajority votes: it's a sign of credible long-run commitment.

The vote for this new rule was 11-1, so even if quite a few FOMC members drop out over the next few years (for instance, because of political pressure from the GOP), they've still got enough votes to keep this truck moving. 11-1 was big news on credibility.

My guess is that when the history of this era is written, we'll find that Bernanke and perhaps a few other FOMC members spent a lot of time building an 11-1 consensus, precisely because they care about the long-run credibility of the process.

The difficulty of building credibility and the importance of retaining credibility are at the heart of modern macro policy, so it's surely in the minds of FOMC members.

2. Possible; but with the many market-based indicators of future inflation, both the public and the Fed will be able to see some signs of destabilization. And note that the new program is reasonably rule-based, which reduces some kinds of uncertainty.

More importantly, the "M" in the Cagan model should be read broadly when applying it to the real world: It's a stand-in for "liquid wealth," which in today's world might mean home equity lines of credit, T-bills, and commercial paper.

That's part of the reason the New Keynesians largely gave up on using money as an indicator of the stance of monetary policy: It was always hard to know which kind of "money" had a reliable relationship with the price level. Instead, money is used as a metaphor in basic models, useful for forming ideas, but used only cautiously in practice.

Ritwik writes:

So, does the change in expected future money cause inflation expectations to change, or the price level to change?

In any model where the price level is flexible to respond to expectations,why aren't inflation expectations zero?

Garett Jones writes:


1. Today's price level is a weighted average of the expected future money supply.

2. If the expected future money supply grows (say 10% per yr) the expected price level grows: as time passes, you're throwing the small numbers out of the average and giving more weight to bigger numbers. Short kids leave, tall kids enter, class height rises.

The arithmetic is in the slides I linked to; also a Yale student has some nice Cagan PowerPoints doing the math showing how permanent money growth causes persistent inflation.


Thanks for the response. Thinking a bit more about expectations of the future broad money supply, there appears to be at least a couple ways in which the Fed's recent action will shrink future supply:
1) Extension of zero-rate to 2015 should create a fall in the yield curve, thereby reducing future interest income on Treasuries.
2) By swapping low-paying reserves for higher-yielding MBS, the Fed is reducing interest income to the financial sector. (Since the Fed's profits are transferred to the Treasury, the money supply falls)

If the magnitude of shifts in expectations arising from these effects is comparable to that from a rising MB, might the Fed's new policy have only a minimal impact on NGDP?

(Note: I recognize there are many other means by which the Fed's policy can alter expectations of future money supply in both directions.)

Charles R. Williams writes:

If the fed controls money, then money is defined in such a way as to be economically irrelevant. If money is defined in a relevant way, then the fed has little control over it. Cagan was theorizing in a different economic universe (the 1950's) where the fed has effective control over money.

If we define money very broadly as liquid assets, then the private economy creates the money supply it needs through the process of financial intermediation. When the fed creates excess reserves by buying T-bonds, it is simply sucking financial intermediation activity in-house. Absent a collapse of the banking system, this will have no first order effects on the economy. There can be second order effects through expectations but these are unlikely to be both strong and positive.

Ritwik writes:


I did read the arithmetic but the dM/M = dP/P condition necessary for any general class of quantity theoretic results is built into Cagan's price level function. He doesn't use the naive M=kP type function, that is only one of the various class of functions that has the dM/M= dP/P property. I don't think Cagan has 'proved' anything.

My intuition is - if the money supply streams of the future are perfectly anticipated, then irrespective of the way the price level depends on them, the price level should be a martingale. I will work out the arithmetic when I get some more time, but I think the fact that Cagan's price level function depends on future money supplies does not change the fact that it does not handle forward looking rational expectations. Cagan's equation has more sophisticated algebra, but its intuition is strictly of the naive quantity theory sorts.

I may be wrong, so I will work on this some more. But to pre-specify any relation between the price level and the money supply that has the dM/M = dP/P property built into it is to cheat.

Kent J. Lyon writes:

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Bob Layson writes:

If a long lived with and slowly growing supply of commodity money is used throughout a world economy, where there is net saving and innovation, then expectations will be of most prices (set in conventional unit masses of the commodity) to gently fall. And they will. All without any need for a central bank or a policy, credible of otherwise. All that is needed is a common practice.

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