Taylor = Wicksell + Fisher + Friedman

Note to all genuine historians of economic thought: yes, I know. There's real history, then there's Whig history, and then there's this blog post.

Knut Wicksell said that there is one rate of interest at which desired savings equals desired investment, so that aggregate demand equals aggregate supply. This is the long run equilibrium rate of interest. He called it the "natural rate of interest". He said that if the central bank set the rate of interest permanently above the natural rate of interest, this would reduce aggregate demand for goods permanently below aggregate supply, and cause a "cumulative process" in which the price level would fall without limit. And if it set the rate of interest permanently below natural rate, this would raise aggregate demand for goods permanently above aggregate supply, and cause a "cumulative process" in which the price level would rise without limit.

Irving Fisher said that you need to distinguish between the nominal and the real rate of interest. The (expected) real rate equals the nominal rate minus (expected) inflation. Savings and investment, and hence aggregate demand, depend on the (expected) real rate of interest, and do not depend on the nominal rate. So the long run equilibrium or natural rate of interest is a real rate of interest, and is independent of the rate of inflation. If the central bank sets a nominal rate of interest, that nominal rate of interest must equal the natural rate plus the (expected) rate of inflation, if we are to be in long run equilibrium.

Milton Friedman said that actual inflation depends on expected inflation, as well as on the gap between aggregate demand and aggregate supply. So if aggregate demand exceeds aggregate supply, actual inflation will exceed expected inflation. And he said that expected inflation will eventually catch up to any constant level of actual inflation. This means that if aggregate demand permanently exceeds aggregate supply, we won't just get rising prices, as Wicksell said; we will get ever-accelerating inflation.

John Taylor added Wicksell, Fisher, and Friedman together, and came up with the Taylor Principle. The Taylor Principle is designed for central banks which set a nominal rate of interest and want to keep inflation near to its target. The Taylor Principle says that if the rate of inflation rises by 1 percentage point above target, the central bank must raise the nominal interest rate by more than 1 percentage point, otherwise inflation will rise without limit. And if the rate of inflation falls 1 percentage point below target, the central bank must lower the nominal rate of interest by more than 1 percentage point, otherwise inflation will fall without limit. Here's why:

The central bank cannot observe the natural rate of interest, and will almost always get it wrong. Suppose the central bank sets the nominal rate of interest too low -- below the natural rate plus the (expected) rate of inflation. So the real rate of interest is below the natural rate, so aggregate demand exceeds aggregate supply, and so inflation rises without limit. As inflation rises, so does expected inflation. So the (expected) real rate of interest falls still further, so aggregate demand rises still further. To make inflation stop rising, and make it fall back towards the target, the central bank needs to raise the real rate of interest, which means raising the nominal rate of interest by more than inflation has increased above target.

Anyone who recognises the validity of the Taylor Principle implicitly recognises the validity of Wicksell's insight (as well as Fisher's and Friedman's insights). The Taylor Principle is designed to stop the Wicksellian cumulative process happening. The Taylor Principle is designed to make an otherwise unstable long-run equilibrium stable. If Wicksell was wrong, then so is the Taylor Principle.

Comments

[David Andolfatto]

If you read Howitt (JPE, 1992, Section VI, Figure 2), you'll see the "Taylor principle" in there. As far as I can tell (I may be wrong), this predates Taylor's statement of the result. So perhaps we should call it the "Howitt principle" from now on.

[Nick Rowe]

David: Good find! That makes sense, from my perspective. It's implicit in Wicksell, Fisher and Friedman. I wouldn't be surprised to find it in Friedman, somewhere, in some form. And I wouldn't be totally stunned to find it in Hayek even (though probably so awkwardly stated that you wouldn't recognise it until someone else said it more clearly!)

[Scott Sumner]

Nice post. Just out of curiousity, are you describing Friedman's natural rate theory, or the Keynesian NAIRU? It sounds kind of Keynesian to me. I thought he reversed causality, i.e. had unexpected inflation driving output.

[Nick Rowe]

Scott: Thanks. If I remember Friedman 68 correctly, I think he says it both ways round, though we do tend to associate Friedman with the "unexpected inflation causes output above natural rate" interpretation of the Phillips Curve as an expectations-augmented supply curve, and Phelps with the "output above the natural rate causes unexpected inflation" disequilibrium price-adjustment interpretation of the Phillips Curve.

I could have written Phelps instead of Friedman. But Friedman works better, because Friedman explicitly related his 68 analysis back to Wicksell.

[Greg Ransom]

Mises and Hayek pointed out that Wicksell's Bohm-Bawerkian account of the effect of below "natural" interest rates on production goods of different time lengths would unavoidably lead to systematic distortions the relative price / physical structure of the economy. And similarly, "real" rates set accurately at the "natural" rate would would in fact NOT give you a stable price level, e.g. if there were productivity gains in some sectors price levels would fall and relative prices would change, even given "neutral" money and a stable money supply.

In other words -- "micro" relations like relative prices, production structures, and the non-neutral effect of changing money supplies & "non-natural" interest rates must be taken seriously, and any pseudo-"Wicksellian" picture which pretends that these causal relations don't exist can't be taken seriously for scientific purposes.

"Knut Wicksell said that there is one rate of interest at which desired savings equals desired investment, so that aggregate demand equals aggregate supply. This is the long run equilibrium rate of interest. He called it the "natural rate of interest". He said that if the central bank set the rate of interest permanently above the natural rate of interest, this would reduce aggregate demand for goods permanently below aggregate supply, and cause a "cumulative process" in which the price level would fall without limit."

[Nick Rowe]

Greg: my own preferred definition of the "natural rate" is that rate which is consistent with stable prices. (Note, I did not say "would cause stable prices").

But, did Hayek ever enunciate anything like the Taylor Principle? Because, as I said above, I would not be totally stunned if he had.

[Jon]

The result is clear from monotonicity principles alone. e.g., the old Bode stability criteria for an LTI system was always that you need gain greater than one for all frequencies (timescales) over which there are undampened disturbances (shocks)--of course that old Bode criteria is not precisely right but good enough. In this sense, its only necessary to accept that there is a controllable relationship between inflation and the (nominal) interest-rate.

That latter idea predates Wicksell--I think you find that in Menger for instance (obviously discussed as the market-rate of interest). Indeed, surely this was present in the Banking-Currency school debate in the 1840s. Although the concern was to a first order about the quantity of money, it was understood that the problem was in equilibrating supply and demand, since even then the nominal-rate was understood as the price of money, I think this was already known. Well perhaps not, there was no transmission mechanism from the market-rate to the inflation-rate per se. Wicksell cast things in real-terms rather than nominal, but as your story goes that's a window dressing in some sense that others later removed to close the idea back to what we knew in the 1840s...

It seems to me easy to get wrong footed by the mere artifice of the language of the day. Of course I'm a very bad armchair historian, perhaps someone will set me right. Still, I see a story of rediscovery here.

[Kevin Donoghue]

"Irving Fisher said that you need to distinguish between the nominal and the real rate of interest. The (expected) real rate equals the nominal rate minus (expected) inflation. Savings and investment, and hence aggregate demand, depend on the (expected) real rate of interest, and do not depend on the nominal rate."

Keynes responded that if expected inflation rises, the spot price of goods should immediately jump to a level consistent with the higher expected future price, given the interest rate. From what I've seen of DSGE models (which is not much I admit) they seem to duck this issue by assuming that consumption goods cannot be stored for future use. Hicks was bothered by this too. As he said, the (unfrozen) fish market isn't obviously the most appropriate one to have in mind when you are thinking about macro.

Am I right in thinking that this problem is being dodged? I'm sure Scott Sumner, unlike Hicks, isn't bothered, since Scott's Keynes is full of it. But it bothers me because my Keynes is a rather deep thinker.

[David Beckworth]

Nick,

Great job integrating these ideas. This is a nice follow-up to Kocherlakota/Willamson discussion.

[anon]

"As he said, the (unfrozen) fish market isn't obviously the most appropriate one to have in mind when you are thinking about macro."

Presumably, there are substitution effects which keep the relative prices of storable vs. non-storable goods at a fairly constant ratio. It is similar to the Bela-Balassa effect in spatial economics (and international trade), where locations that are more productive in tradable goods have higher price levels for non-tradables and visa-versa.

[Nick Rowe]

Jon: " Still, I see a story of rediscovery here." That's what it's looking like.

Kevin, and anon: I don't think it matters for this point (at least not qualitatively, though it will quantitatively) whether fish can be frozen or not.

With fresh fish, a fall in the real interest rate leads to an increased consumption demand for fish, via the consumption-Euler equation. Individuals want to consume more fish now and less later.

With frozen fish, a fall in the real interest rate leads to an increased investment demand for fish (more gets frozen for future consumption) via the investment Euler equation. Individuals want to invest more fish now and less later.

Both increase the current demand for newly-produced fish, relative to planned future demand. The elasticities will presumably be different, though, so it matters qualitatively.

But there are two ways that expected inflation can rise: the future expected price level can rise, given the current price level; and the current price can fall, given the expected future price level.

David: thanks! Yes, it was obviously inspired by the Kocherlakota debate (which I now think is just starting to become very productive, by the way, and may just be starting to go into an area I wanted it to go, about loosening monetary policy even at the lower bound, with nominal interest rates rising even in the short run). But I didn't reference that debate explicitly, since I thought it stood on its own.

[Greg Ransom]

Right. Wicksell had more than one version of what constituted "stable prices". And it turned out these definitions were not compatible -- and they were not compatible with real world, heterogeneous production processes which take more or less time, and which change in their productive output across time.

And understandably, economists prefer to define the "natural rate" in a way that excludes the real world, but which works great in an unreal math construct. All the better to teach on a blackboard, all the better to fit in a textbook, all the better to fill a CV with publications, etc.

Nick wrote:

"Greg: my own preferred definition of the "natural rate" is that rate which is consistent with stable prices."

[Greg Ransom]

.. and all the better to create easily graded exams ..

[JP Koning]

Great post Nick.

With Mises/Hayek/Menger also coming out of the woodwork in the comments, I'd add Henry Thornton to the list of predecessors. In his 1804 book Paper Credit, Thornton pointed out that the inability of the Bank of England to raise its discount rate above 5%, when the rate of profit was 6,7,8%, would lead to a rise in prices. The 5% ceiling was set by usury laws. Makes me think of your analogy Nick... a hand balancing a stick hits a wall and can't compensate, but its not the zero percent minimum wall but the five percent maximum wall.

[Nick Rowe]

Greg: Yep. Wicksell, IIRC, makes a real dog's breakfast over defining the natural rate. Which is why my post isn't really history of thought.

What about replacing "stable prices" with "inflation being on target" (however that is defined by the central bank in question)? In other words, redefine the natural rate as that rate (or that time-path of rates) which is consistent with inflation staying at the central bank's target? It would not strictly be a nominal rate, if we did that, but that's OK. For Canada, it would be a nominal rate, minus CPI inflation, plus 2%.

JP: Thanks!

That's a lovely example of the zero lower bound, only now it's a 5% upper bound! What happened, historically? Did the usury laws get abolished? It also backs up what Jon said above.

It's not just Wicksell, in other words. This is broader than just a couple of theorists.

[David Andolfatto]

Nick,

"If Wicksell is wrong, so is the Taylor (Howitt) principle."

I think that most of us would agree that there exists an underlying logic to Wicksell's theoretical construct. I am wondering, however, what sort of empirical evidence people use to convince themselves that the phenomenon actually exists (obviously, one cannot simply appeal to the fact that central bankers believe in and use the Howitt-Taylor principle).

Anyway, just wondering. Perhaps others can help out here.

By the way, great post. I plan to draw on this material the next time I teach macro. (You should really write a book and save us a lot of trouble).

[Nick Rowe]

Thanks David. I ought to write a book, but I just can't get my act together to write anything other than blog posts.

Robert Waldmann gave the example of the Weimar hyperinflation, where the Reichsbank kept the interest rate fixed. That's a great example. But Japan still worries me as a possible contradiction, even though Scott and others think the BoJ is really targeting 0% inflation.

I expect empirical confirmation of the counterfactual would be estimated Taylor Rules during periods when inflation did not explode. If you find gamma exceeds one, and inflation remained fairly steady, that would also confirm the theory.

There's a problem with the empirics though. Suppose an inflation-targeting bank has strong credibility. So expected future inflation remains stuck at 2%, even though actual inflation fluctuates randomly around 2%. The central bank wouldn't need to respond strongly to inflation, because it only needs to respond strongly to inflation when expected inflation follows actual inflation, which never happens. We often can't observe credible threats, because they never need to be carried out. This is part of the "off-equilibrium path" stuff I've been nattering on about, which really defines what variable is exogenous and what is endogenous, i.e. what's the monetary policy instrument.

Or, you just have to do empirics on each of the components, and cross your fingers, hoping it all adds up right.

[Richard W]

Nick Rowe
' That's a lovely example of the zero lower bound, only now it's a 5% upper bound! What happened, historically? Did the usury laws get abolished? It also backs up what Jon said above. '

They were repealed in stages until fully abolished in 1854. It was really the arguments of Jeremy Bentham who started the ball rolling in Defence of Usury which critiqued Adam Smith's defence of interest rate restrictions. He sent a copy to Smith but he obviously disagreed because he did not make any substantial revisions to The Wealth of Nations after 1784.

Defence of Usury 1787, in which he proclaimed a laissez-faire position, and introduced his concept of utility, urging “that no man of ripe years and of sound mind, acting freely, and with his eyes open, ought to be hindered, with a view to his advantage, from making such bargain, in the way of obtaining money, as he thinks fit: nor, (what is a necessary consequence) any body hindered from supplying him, upon any terms he thinks proper to accede to.”

http://socserv2.mcmaster.ca./~econ/ugcm/3ll3/bentham/usury

[Kevin Donoghue]

Nick, I agree that Keynes's point doesn't invalidate your conclusion: "If Wicksell was wrong, then so is the Taylor Principle." That sounds right to me, though I'd hate to see it on an exam paper with "Discuss" after it.

You say: “But there are two ways that expected inflation can rise: the future expected price level can rise, given the current price level; and the current price can fall, given the expected future price level.”

That statement makes perfect sense to me, provided I think of p(t) and p(t+1) as simply two terms in a sequence. Where I have a problem is in understanding why anyone would want to think about a market that way. In my world, agents making deals in period t can't decide that it would be just as handy to change E[p(t+1)] as to change p(t). E[p(t+1)] is given and in an efficient market p(t) is determined on that basis by discounting.

To my way of thinking, talking about the expected rise in a flexible price is very tricky. The very moment it’s expected to rise, it rises. What's the expected inflation rate of gold, for example? Does the expected inflation rate change when the spot price goes up? To me it seems that particular inflation rate is a function of interest rates and costs of insurance. So the expected inflation rate is practically constant, no matter how volatile the market is.

I don’t suppose you dispute this, but I have the sense that it’s by losing sight of just such simple points that ‘scary smart’ guys like Cohrane and Kocherlokota make their very scary mistakes.

[Kevin Donoghue]

That's Cochrane and Kocherlakota, obviously.

[Nick Rowe]

Kevin: "That statement makes perfect sense to me, provided I think of p(t) and p(t+1) as simply two terms in a sequence. Where I have a problem is in understanding why anyone would want to think about a market that way. In my world, agents making deals in period t can't decide that it would be just as handy to change E[p(t+1)] as to change p(t). E[p(t+1)] is given and in an efficient market p(t) is determined on that basis by discounting."

(I forget how we came to this point, but nevertheless): that depends on what the "news" is. Take a very simple old monetarist flexible price model. The "news" is an announcement of a permanent doubling of the money supply. p(t) and E[p(t+1)] both double. Suppose instead that the news is that M will permanently double at t+1, but not today. Then E[p(t+1)] doubles,, while p(t) increases but by less than doubling. So expected inflation increases.

[Nick Rowe]

And if we modify that old monetarist model, to assume that prices are sticky in the short run, so that p(t) is unaffected by today's news, and prices adjust only slowly in response to excess demand or supply, then *all* the action must come from E[p(t+1)] adjusting to news.

[Kevin Donoghue]

"Suppose instead that the news is that M will permanently double at t+1, but not today. Then E[p(t+1)] doubles, while p(t) increases but by less than doubling. So expected inflation increases."

Is that because the "old monetarist flexible price model" you have in mind has adaptive expectations? The only way I can see partial adjustment being consistent with rational expectations is if there are storage costs or something like that, so that it just doesn't pay to bid p(t) all the way up to E[p(t+1)].

In the sticky-price case of course I have no objection to the notion of expected inflation. It makes perfect sense there. Where I think people can easily wander into nonsense is when they transplant an equation involving expected inflation into a flexible price model, failing to see that expected inflation is just {E[p(t+1)]/p(t)}-1, which ought to be very stable in such a model. It's the spot price, p(t), that soaks up all the volatility; see the FX market for example - the mother of all flexible-price markets.

But I'm certainly not saying that you suffer from that confusion. The victims are likely to be people who are very good at manipulating models and churning out papers, but spared the task of teaching undergraduates. They would do no great harm if they stuck to their epsilontics, but when they translate their equations into words they make no sense. At least that's my theory about how they end up saying the sky is green and then saying they never said any such thing.

With that I'll sign off. Thanks for another good post.

[Adam P]

"Is that because the "old monetarist flexible price model" you have in mind has adaptive expectations?"

No, it's because the old monetarist model also has a stable demand for real balances (basically an LM curve), and we tacitly assume that we start out in equlibrium. If prices double today with M as yet unchanged then real balances have halved, everyone tries to accumulate money and firms can't sell their product.

Price move a bit because the expected inflation reduces the demand for real balances but you wouldn't expect it to halve it.

[Nick Rowe]

Kevin: "Is that because the "old monetarist flexible price model" you have in mind has adaptive expectations?"
No, I was assuming RE in that case. We know that E[P(t+1)] doubles, so there will be inflation from t to t+1, which reduces the real demand for money, which causes p(t) to increase.