Sunday, September 25, 2022

WSJ stability oped -- full text

Now that 30 days have passed, I can post the full text of "Nobody Knows How Interest Rates Affect Inflation" in the Wall Street Journal August 25. A previous post has a summary with pretty pictures. 


A grand economic experiment is under way. Can the Federal Reserve contain inflation without raising interest rates much higher than they are now?

Conventional wisdom says that as long as interest rates are below the rate of inflation, inflation will rise. Inflation in July was 8.5%, measured as the one-year change in the consumer price index. The Fed has raised the federal funds rate only from 0.08% in March to 2.33% in August. According to the conventional view, that isn’t nearly enough. Higher rates are needed, now.

This conventional view holds that the economy is inherently unstable. The Fed is like a seal, balancing a ball (inflation) on its nose (interest rates). To keep the ball from falling, the seal must quickly move its nose.

In a newer view, the economy is stable, like a pendulum. Even if the Fed does nothing, so long as there are no more shocks, inflation will eventually peter out. The Fed can reduce inflation by raising interest rates, but interest rates need not exceed inflation to prevent an inflationary spiral. This newer view is reflected in most economic models of recent decades. It accounts for the Fed’s projections and explains the Fed’s sluggish response. Stock and bond markets also foresee inflation fading away without large interest-rate rises.

So which view is correct? In normal times, it’s hard to tell. Whether seal or pendulum, inflation and interest rates move up or down together in the long run, and they jiggle around each other in the short run.

Advocates for the conventional view argue that the Fed raised interest rates too little in response to inflationary shocks in the 1970s. Only when the Fed raised interest rates substantially above inflation for several years in the early 1980s, provoking two deep recessions, did inflation finally subside. The sooner we get to it, they say, the better.

Advocates for the stable view point to recent decades of steady inflation at zero interest rates in the U.S., Europe and Japan. When deflation appeared and central banks couldn’t move rates much below zero, conventional analysts warned of a “deflation spiral.” It never happened. Why should an inflation spiral break out now?

In both theories, expected inflation matters: If people expect higher inflation next year, they buy or raise prices today. The central assumption behind the unstable inflation-spiral theory is that people expect next year’s inflation to be pretty much the same as last year’s inflation—what economists call “adaptive expectations.” A driver who looks in the rearview mirror to judge where the road is will quickly veer off to one side or another.

The central assumption behind the stable theory is that people think more broadly about future inflation. They’re not clairvoyant, but they don’t ignore useful information and aren’t much worse at forecasting inflation than, say, Fed economists are. If a driver looks forward through the windshield, even a dirty windshield, the car tends to get back on the road.

Economists don’t know for sure whether the economy is stable or unstable, whether inflation can fade away without interest rates substantially above inflation. In that light, the Fed’s actions make some sense. If you really don’t know how interest rates affect inflation, it’s natural to raise rates slowly. Inflation may subside on its own. If not, you can keep raising rates.

If inflation fades, the conventional view will be seriously undermined. If it spirals, absent other shocks, the new view is in trouble. But a good experiment requires everyone to leave the test tube alone. Unfortunately, we are likely to see some new shock: a virus, a war, a financial crisis or a fiscal blowout. Inflation will then rise or fall for reasons having nothing to do with spirals, stability and interest rates.

Mr. Cochrane is a senior fellow at Stanford University’s Hoover Institution and an adjunct scholar of the Cato Institute. His book “The Fiscal Theory of the Price Level” is out in January.


Economists wondering what the heck I'm talking about and where are the equations should read "Expectations and the Neutrality of Interest rates."


  1. The article neatly sums up the conundrum facing the profession. In the traditional (now "Volcker") camp, high real interest rates are required to moderate final demand that will in turn moderate the rate of inflation of prices of final private goods and services. This is the view currently being pressed by the Powell FOMC. The terminal state for this view is economic recession and less than full employment (i.e., high rates of involuntary unemployment). The World Bank has expressed the view that the collective responses by central banks to the Powell FOMC's program of raising the U.S. short term interests, in order to contain imported inflation that results when the U.S. dollar appreciates rapidly (as it has been doing in response to the short-term U.S. interest increases) and drives down the value of their own domestic currencies, will be a deeper global recession and higher involuntary unemployment. From the FOMC's perspective, "it's our dollar, but your problem." This is not new, nor unexpected (cf., 1997-8 Asian Crisis). J. Powell has stated without equivocation that this is the FOMC's policy and strategy, invoking the ghost of 'Volcker-past' to underline their serious commitment to wrestle inflation down come what may, a la Paul Volcker 1980.

    The contrary view is that inflation is the result of excessive monetary stimulus through 2020-2021 via 'helicopter drops', generous employment subsidies and income supports, and via open-market operations (through the NY FRB). This view holds that as the expansionary fiscal and monetary policies naturally wind down with the passing of the pandemic-induced economic shock, inflationary pressures will subside of their own. This camp's adherents point to the the relatively low steady inflation rate that followed the 2007-9 recession through to the end of 2019, irrespective of FOMC interest rate policy during that interlude.

    Theory is a mixed bag. The Fisher Relation between the rate of interest, the rate of inflation, and the real rate of interest along with new Keynesian DSGE models of the economy inform us that as the interest rises, the rate of inflation increases in lock-step to maintain a constant real rate of interest. The seal vs the professor analogy of stable equilibrium vs unstable equilibrium is too simplistic. New Keynesian DSGE models are too complex to yield simple intuitive insights. The reduced 2-equation NK model is still too complex to yield broadly applicable conclusions. The conditional expectation terms cannot simply be replaced by AR(1) analogues. The resulting analytical solutions fail to yield useful results relevant to real world circumstances. But, the "all models are wrong, yet some are useful" observation keeps the NK DSGE models in active circulation.

    J. Powell and his fellow members of this year's FOMC have decided to cut the Gordian Knot, come what may. The issue decided for now, we are left with the problem of coping with the consequences ('shocks') of that decision. Those least prepared will those most harmed.

    1. " The Fisher Relation between the rate of interest, the rate of inflation, and the real rate of interest along with new Keynesian DSGE models of the economy inform us that as the interest rises, the rate of inflation increases in lock-step to maintain a constant real rate of interest."

      New Keynesian models are defined by the presence of nominal rigidity on prices and/or (nominal) wages which all breaks short run monetary neutrality. The central bank moving the nominal interest rate is going to have real effects in that setting, so the story you're telling can only be verified in the long run in those models.

      And I am not sure I would regard this long-run prediction of New Keynesian models too seriously, especially since money is usually thrown into them as an afterthought, but it's at least a non crazy idea to think of it as a sensible approximation in the long-run.

    2. Yes, that is true if one assumes that the price setting firms set prices because either (1) their number came up (Taylor), or, (2) they were randomly selected based on a lottery which has a Poisson distribution (Calvo) that then allowed the firm to change its prices. The presumption in both Phillips Curve variants is that there is an external force that determines either the schedule (Taylor) or the Poisson arrival rate (Calvo) and that in each case the processes are stationary and time invariant. In practice, as we have seen this year and last year, firms do not face rigid 'menu costs' during periods when prices are rising rapidly. From a business perspective, it would be inconceivable to have to await the outcome of a lottery in order to be permitted to change product/service prices. It would be runious for a business not to change prices when costs are changing rapidly. The Calvo and Taylor models are academic constructions that presume to micmic real world phenomena. And many economists merely assert that their ideosyncratic DSGE models include "Calvo" "sticky-price" features. This gives the economist a conventional Phillips Curve Euler equation, but it rarely tells us whether the Phillips Curve is based on practical experience or merely conventional academic modelling practice. We also know that commodity prices quickly change, from week to week, month to month, and day to day. Prices are set by the highest cost producer's marginal cost (e.g., in extractive industries). "Menu costs" are effectively nil. While I appreciate having the distinction between "short run" and "long run" effects pointed out, I wouldn't equate the Fed Funds Rate (nominal) minus the conditional expectation of the next period rate of inflation with the real rate of interest. Stephen Williamson ('New Monetarist' blog) defines the rate of interest as \beta multiplied by the ratio of the marginal utility of consumption in perod t+1 to the marginal utility of consumption in period t. Since all factors in this definition are denominated in the commodity consumed, the rate of interest so-defined is the real rate of interest. It's one definition. Another is that expounded by K. Wicksell, the so-called "natural rate of interest". The Euler equation derived from the household's optimization of its cost function subject to the initial endowment budget state equation, need not incorporate Fisher's Relation if the state equation is rendered in real terms rather than nominal terms. Permutations and combinations on the basic structure gives rise to the behaviour that the economist wishes to study or theorize. Based on experience in business, I would derate the notion of "menu costs" being an impediment to price changes.

  2. Nothing's changed in > than a century. Irving Fisher calls it an exact science. Interest it the price of credit. The price of money is the reciprocal of the price level. Hence, inflation control depends upon money control. The rate-of-change in money flows is decelerating:

    Long-term money flows, proxy for inflation (underweights vt)

    01/1/2022 ,,,,, 1.998
    02/1/2022 ,,,,, 2.011
    03/1/2022 ,,,,, 1.633
    04/1/2022 ,,,,, 1.409
    05/1/2022 ,,,,, 1.326
    06/1/2022 ,,,,, 1.237
    07/1/2022 ,,,,, 1.232
    08/1/2022 ,,,,, 1.241
    09/1/2022 ,,,,, 1.155
    10/1/2022 ,,,,, 1.141 sell commodities
    11/1/2022 ,,,,, 0.906
    12/1/2022 ,,,,, 0.594
    01/1/2023 ,,,,, 0.603
    02/1/2023 ,,,,, 0.543
    03/1/2023 ,,,,, 0.459
    04/1/2023 ,,,,, 0.441
    05/1/2023 ,,,,, 0.391
    06/1/2023 ,,,,, 0.325
    07/1/2023 ,,,,, 0.300


    This is an interesting conversation on shrinking the Federal Reserve balance sheet. I wonder what are the views of John Cochrane on the necessities (or lack thereof) of doing so.

  4. Rational expectations can fit into the Unstable view too. If we have inflation this year because the Fed helped finance government overspending, that's an indication that we'll probably have inflation next year because the Fed *will continue* to behave that way and help finance government overspending. To reform its reputation, the Fed needs to show a regime change, a reform in attitude. That's tough unless the Fed shows it's willing to induce a recession.

    1. J. Powell in his recent remarks (Sept. /22) has indicated that the FOMC members are prepared to accept a recession if it brings the rate of inflation down to the FOMC's preferred target rate of inflation (now defined as 2.5%/yr).

      If one is a believer in the Phillips Curve, and holds that the central bank can utilize the Phillips Curve 'effect' to control inflation, then reducing the employment rate (increasing the unemployment rate) will cause a concommitant reduction in the rate of inflation. Central bankers must believe in the Phillips Curve 'effect'. It's axiomatic.

  5. We're witnessing, in the London, U.K., financial derivatives market, the limits to dogmatic "inflation fighting". The U.S Dollar zone imposes its own constraints on what the FOMC can effectively achieve through manipulation of the Bank Rate. Inflation may turn out to be the least-worst alternative if the FOMC's determined pursuit of ever-increasing rate hikes tips financial markets into a series of financial crises here and abroad. It may be felt that the banking reforms undertaken since the 2008-9 financial crash will insulate U.S. financial markets from the worst of a financial contagion, and that may turn out to be true to some extent; but the inter-connectedness of financial markets in the U.S. Dollar zone should constrain the FOMC from excessive zelousness to "fight inflation" down to 2%/annum. Or, so one might hope would be the case. Experience in 2007-8, and the 1980s and the 1990s Asian financial crisis does not auger well.

    Events this week in the U.K. derivatives market provide a cautionary signal. Inflation is not the worst outcome, however much Chmn. Powell may declare it to be so. There are worse outcomes to be had. Financial market failures being just one out of many that dogmatic pursuit of an inappropriate central bank policy risks creating.

  6. There is a 74% correlation between the change in M2 over a year and the federal deficit over that year. If you're wondering what drives expansion of the money supply, look no further than the federal deficit. The Fed's games with interest don't account for much.

    Given that the denominator for inflation calculations is the money supply, I would suggest looking closer at the relationship between the deficit and M2.

    Converting levels of M2 and the deficit to rates, we can see very clearly that the deficit rate (deficit/M2) is going to drive inflation in the long run, and gives us a clearer view of the effects of the quality of the economy.

  7. Interest rates are a useful control knob which has been used by many nations with some success to align inflation with targets. But they are as effectual as the gentian violet in Catch-22 when the real cause is government spending, with worse to come as IRA 2022 hits.

  8. In your article "Expectations and the Neutrality of Interest rates", on page 34, you state "In an instant dt only a fraction λdt of producers may change prices." This is incorrect, if it is assumed that the process in the Calvo version of the Phillips Curve is based on a Poisson distribution with parameter λ for the arrival rate or instance density. λdt is the probability of one arrival or instance occurring in the time interval dt. The probability of N arrivals in a time interval of length T is given by w(r) = probability(N = r) = exp( -λ.T).( λ.T)^r / r!

    Taking the limit as T goes to zero of exp( -λ.T).( λ.T)^r / r! gives
    prob(N=r) = ( λ.dt)^N / N! = o(dt^N).

    If N = 2, then prob(2 = r) = o(dt^2) which is negligible in ordinary differential calculus. If N = 1, then prob(1 =r) = o(dt) = λ.dt. Prob(0 = r) = 1 - λ.dt + o(dt), where o(dt) ~ (λ.dt)^2.

    The error enters as a result of the calculation of the expected number of events in the interval dt. EN = λ.dt exp(λ.dt) ~ λ.dt, but dt~0 which gives EN~0 for small λ which must be the case for a Calvo sticky-price process.

    Ref.: Cox, D. R., and Smith, W. L. Queues. London, U.K., 1961: Methuen's Monographs on Statistical Subjects.

  9. “All signs point to an economy that is clearly in excess demand. The clear implication is that further rate increases are warranted.” Bank of Canada Governor, Tiff Macklem.

    "More needs to be done to bring inflation down meaningfully and persistently. I anticipate additional rate hikes into early next year." FRB Governor, C. Waller.

    "Inflation remains stubbornly and unacceptably high, and data over the past few months show that inflationary pressures remain broad based." FRB Governor, L. Cook.

    The foregoing quotations taken from remarks by three central bank governors on Thursday, Oct. 7th, indicate that these decision-makers are in no doubt whatsoever over the efficacy of the rising short-term interest rate to tame 'inflationary pressures' and 'excess demand' in the economies they have monetary policy making authority for (as far as that goes).

    One interesting feature of the simplified continuous time two-equation new Kenyesian DSGE model shows up when the model equations are transformed from the time domain to the frequency domain via application of the Laplace Transform. There is a technique to determine the steady-state solution to the state-space equations using the Laplace transforms of those equations: Multiply the transformed equation by s, the frequency domain transform of variable t in the time domain, and take the limit as s goes to zero. The result is the steady-state value of the variable in the time domain. For the case where the interest, i(t) - r = {\pi}*, the target inflation rate, a constant, the steady-state rate of inflation, {\pi}, equals the target rate of inflation, despite the resolvent having one unstable root. This suggests that for economies for which the simplified continuous time two-equation NK DSGE model applies, the central bank governors could usefully avoid much strife and trouble simply by setting the interest rate to r + {\pi}* and then sitting back and waiting for the system dynamics to resolve the transient state. This result comports with your more involved analysis satisfactorily.

    Evidently, the central bankers quoted above have very high pure time rates of discount, i.e., r >>0, whereas K. Arrow puts the pure time rate of discount, r, in the range of 1%/year when determining the discount factor {\beta} in the present value of the representative household's utility of consumption policy {U[c(t)]} 0> 1%/yr for the model economies' values of r ~ 1%/yr. The emotive remarks of the central bank governors seem to point in this direction.


Comments are welcome. Keep it short, polite, and on topic.

Thanks to a few abusers I am now moderating comments. I welcome thoughtful disagreement. I will block comments with insulting or abusive language. I'm also blocking totally inane comments. Try to make some sense. I am much more likely to allow critical comments if you have the honesty and courage to use your real name.