Wednesday, June 8, 2022

The Phillips Curve

Behold the Phillips curve, one more statistical correlation treated as an eternal verity that our inflationary era has just undermined. 

From 2007 to 2019, the standard observation was "The Phillips curve has become flat." Large changes in unemployment correspond to very little change in inflation, or small changes in inflation correspond to huge changes in unemployment, depending on which causal (mis) reading of the correlation you choose. To the optimist, allowing a tiny bit of inflation could dramatically reduce unemployment. To the pessimist, it would take immense unemployment to do anything about inflation, should we have to.

Then came the pandemic. Unemployment shot up with no change in inflation, right on the curve. 

Then came the inflation. The Phillips curve woke up. It's almost vertical! (The scales of the two axes are different). 

Much Fed and commentator thinking relies on the Phillips curve. It's the central way interest rates affect inflation, in conventional thinking. High interest rates raise real interest rates lower aggregate demand cause unemployment which causes via the Phillips curve, lower inflation. 

Clearly, something is very wrong here. Maybe expectations shift. Maybe supply shocks do matter after all. Surely one should start with a serious dynamic Phillips curve, as most macro literature does. Maybe the Phillips curve is flexible up but sticky down, and the natural rate shifts around.  Maybe prices are sticky until they aren't. As Bob Lucas showed long ago, the slope of the Phillips curve depends on the volatility of inflation. Countries with volatile inflation get no output boost from additional inflation. Thousands of epicycles can be added, and this post is a bit of an invitation to do so. Or maybe the Phillips curve was just a correlation after all, hiding a deeper reality. (My view, but for another blog post). 

In the meantime, it's another good warning not to take statistical correlations too seriously, and certainly not as causally as we tend to do. Such as inflation will always be 2%. Such as real interest rates are on a permanent downward trend? 

This time of inflation will lead us to rewrite an awful lot of macroeconomics. 


  1. I wasn't alive in the 1970's, but it certainly was a seminal period in economic history. What we have now looks an awful lot like the 1970s, with a lot of the same ex post explanations being offered about why inflation is so high.

  2. Of course the Phillips curve is flat when somebody makes inflation constant at x % per year. Changes in unemployment would be exclusively due to supply shocks.

    Then comes COVID -- unexpected, though temporary, overall negative supply shock + [huge] overall positive demand shock, bigger than expected, I think, and yup, inflation rises.

    The only surprise in the data to me is how quickly expectations adjusted - near vertical is near vertical.

    1. How did I get to be anonymous? I'm Frank.

  3. I'd say the general lesson is that you should be deeply suspicious of "new" theories that happen to correspond with what you desire to be true.

  4. The bottom one-third to one-half of the labor force is experiencing the best job markets in more than 50 years. PCE core near 5% and cooling off.

    Orthodox macroeconomists are in hysterics over the present rate of inflation, but perhaps 50 million to 80 million Americans are enjoying better prospects in the workforce.

    I wonder if a 5% rate of inflation is a reasonable exchange for tight labor markets.

    1. Apparently not tight enough.

      32% employment to population ratio now compared to the high 40-45% range from 1980-2000.

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  6. Have you read the Fiat Standard? Seems much of modern monetary theory was made up to justify government policy.

    Shortages have little to do with price changes beyond suppliers not adjusting the price fast enough. Simlarly, unemployment has little to do with price changes. The real cause of the phillips curve is poverty: people work more when they are poor. Inflation leads to poverty, which leads people to work more.

    In COVID times we saw this clearly: when people were flush with government cash, we saw the great resignation. As the money runs out, we'll see more people looking for jobs. Whether they find them or not is a function of labor-suppliers (aka: employees) lowering their prices fast enough.

  7. I took economics in the mid 70s and there was talk that the Phillips curve "shifted" to try to explain why things didn't fit.

    But a more fundamental question is whether the Phillips curve even exists outside a few cherry picked periods? I've looked at inflation / unemployment graphs in the past and seen a lot of random scatter plots having little resemblance to a curve.

  8. "This time of inflation will lead us to rewrite an awful lot of macroeconomics."

    Start with this - page #1 - Interest is often construed to be the cost of borrowing. This is technically not accurate. Interest is the cost of time associated with any non-simultaneous transaction.

    For instance, if I may be willing to pay you $20,000 for a car delivered to you today, but only $18,000 for the same car delivered to me a year from now. Effectively I am charging you interest on the money I am giving to you now for a car to be delivered at a later point.

    1. Page #2 - The most efficient political economy is an autocracy - the king determines how much "stuff" each individual gets. All trades have a 100% success rate.

      The 2nd most efficient political economy utilizes three party trading. All trades have a 50% success rate.

      The 3rd most efficient political economy utilizes two party trading (what we have now). All trades have a 25% success rate.

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    1. So the replacement is what?

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    3. After Keynesian Macroeconomics - Thomas Sargent & Robert Lucas

      "Should this intellectual arbitrage prove successful, it will suggest important changes in the way we think about policy. Most fundamentally, it will focus attention on the need to think of policy as the choice of stable rules of the game, well understood by eco- nomic agents. Only in such a setting will economic theory help predict the actions agents will choose to take. This approach will also suggest that policies which affect behavior mainly because their consequences cannot be correctly diagnosed, such as monetary instability and deficit financing, have the capacity only to disrupt. The deliberate provision of misinformation cannot be used in a systematic way to improve the economic environment."

      To get to stable monetary policy rules of the game, you also need stable fiscal policy rules of the game such that the two are never at loggerheads.

      One method is fiscal neutrality / surplus (government does not borrow or print money).

      Another is equity sold by government Treasury (government does not borrow or print money).

      In both cases, monetary policy focused solely on price stability is achieved.

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  10. "This time of inflation will lead us to rewrite an awful lot of macroeconomics."
    -- This is highly unlikely, but it may see many PhDs reconsider the NK DSGE model structure.

    (1) the so-called new Keynesian Phillips Curve is not causal;
    (2) inflation, πₜ , is explained by a simple linear monetary function:
    πₜ = b₀ + b₁ ΔMₜ₋₄ + b₂ ΔMₜ₋₆ + εₘ ₜ ,
    πₜ is the current period "Median Consumer Price Index" (Percent Change at Annual Rate, Quarterly, Seasonally Adjusted) (= MEDCPIM158SFRBCLE)
    ΔMₜ₋ₙ = (Mₜ₋ₙ - Mₜ₋ₙ₋₄)/(Mₜ₋ₙ₋₄) is M2, "Percent Change from Year Ago of (Billions of Dollars), Quarterly, Seasonally Adjusted" (= M2SL) lagged by n calendar quarters.
    Coefficient values are: b₀ = 1.58363 (significant, p < 0.05); b₁ = 0.030635 (not significant, p > 0.05); b₂ = 0.173525 (significant, p < 0.05).
    r² = 0.897 F-stat = 34.86 (F-crit = 19.37; k=2, n=11) DOF = 8
    Eleven quarterly observations: 2018:Q1 through 2022:Q2.

    (3) The time sequence of events is important to the explanation of πₜ as a function of two events: (A) the onset of the pandemic in 2020:Q1, (B) the lock-down decisions by states and the federal government in 2020:Q2, (C) the action of the FRB-FOMC to floor the FFR at ZLB and ramp-up QE, (D) federal fiscal stimulus. Events (A) and (B) were two shocks that increased the unemployment and decreased incomes. Events (C) and (D) were monetary and fiscal 'shocks', respectively, that had the effect of causing a jump in M2 and sustained growth in M2 at double-digit year-over-year rates quarterly. The Phillips Curve is not relevant under such conditions and the coefficient of the second term on the right-hand side of the standard simplified version of the NKPC is not statistically different from zero during this period. I.e., while the plot of πₜ versus uₜ suggests that πₜ is inversely proportional to uₜ during the latter of half of the period, there is no causal linkage between those two variables--it is mere happenstance arising from the sequence of events (A)-(B) and (C)-(D).

    (4) The output gap, xₜ , is related to the unemployment rate, uₜ , by Okun's Law in the form: xₜ = c₀ - c₁[uₜ- uₜ*] + εᵤ ₜ , where xₜ = logₑ( Yₜ / Ȳ ₜ), where Yₜ is GDP, and Ȳ ₜ is Potential GDP, in period t. r² = 0.8 for 1967:Q1 < t < 2009:Q2 with c₀ = c₀' and c₁ = c₁', and for 2009:Q1 < t < 2022:Q1 with c₀ = c₀'' and c₁ = c₁''. The coefficients of Okun's Law change at 2009:Q1, for reasons probably having to do with the FRB-FOMC institution of QE1 and QE2 and the aftermath of the 2008:Q3-2009:Q1, but this is mere supposition on my part at this juncture.

    Data source re: para. (2):
    FRED graph -- Monthly data is converted to a quarterly average value; quarterly data is taken as is. The multi-variate OLS was performed in MS Excel using the LINEST function with the intercept calculated , and statistics displayed:
    LINEST(πₜ , ΔMₜ₋₄ ... ΔMₜ₋₆, true(),true()), t ϵ [2018:Q2, 2022:Q2].

  11. "A New Way of Forecasting Recessions", Edward E. Leamer
    WORKING PAPER 30247; DOI 10.3386/w30247; ISSUE DATE July 2022

    On page 36 of 36pp, a chart illustrating the variation of annual inflation (ordinate) vs. unemployment rate (abscissa):
    "Figure 22 The Phillips Curve in the 1960s, 1970s and 1980s"

    The remainder of the paper presents the author's proposed new method of statistically determining the (a) the time remaining between the present period and the period of on-set of the next recession, and (b) probability of a recession occurring given the yield curve, unemployment rate and inflation rate in the current period. The author notes that an inversion of the U.S. Treasury yield curve, measured by the difference between the 13-week T-bill yield and the 10-yr T-note yield, is more predictive than either the unemployment rate or the inflation rate. Inversion of the U.S. Treasury yield curve has in the past been a product of efforts by the FRB's FOMC to curb monetary expansions by reducing commercial bank holdings of reserves. Changes in the unemployment and inflation rates have in the past lagged FOMC open market activities that raise the Fed Funds rate. It follows that short-term rates (e.g., 13-month T-bill rate) vs. long-term rates (e.g., 10-year T-note yield) will be a leading indicator relative to the unemployment rate or the inflation rate, if past behaviour is indicative of future behaviour.

    Examination of the historical record indicates that the FOMC has tended to commence tightening monetary policy when the unemployment rate passed below the non-cyclical rate of unemployment from above. Those episodes of tightening of the monetary policy tended to continue well past the point where the unemployment rate passed the non-cyclical rate of unemployment from below, stopping only when it became apparent from other indicators that business activity had turned from expansion to contraction (i.e., onset recession). The historical records indicate that the rate of inflation typically continued advancing until about the middle of a recession period when it then commenced to decline. This year's statements from the Chairman of the FRB indicate that the FOMC tightening of monetary policy through the open market activities and setting of the Fed Funds rate will not be discontinued until the FOMC sees the rate of inflation turning down towards the FOMC's fixed target rate for inflation. If the FOMC holds to this course, a "soft-landing" is almost surely precluded.

    The present paper discusses the forecast of onset of recession periods and the techniques related to such forecasting.


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