Three Propagation Mechanisms in Lucas and Sargent with a Response from Brad DeLong

UPDATE (4/3/2022): Reupping this post with the response to my query sent by Brad DeLong.

I’m writing this post in hopes of eliciting some guidance from readers about the three propagation mechanisms to which Robert Lucas and Thomas Sargent refer in their famous 1978 article, “After Keynesian Macroeconomics.” The three propagation mechanisms were mentioned to parry criticisms of the rational-expectations principle underlying the New Classical macroeconomics that Lucas and Sargent were then developing as an alternative to Keynesian macroeconomics. I am wondering how subsequent research has dealt with these propagation mechanisms and how they are now treated in current macro-theory. Here is the relevant passage from Lucas and Sargent:

A second line of criticism stems from the correct observation that if agents’ expectations are rational and if their information sets include lagged values of the variable being forecast, then agents’ forecast errors must be a serially uncorrelated random process. That is, on average there must be no detectable relationships between a period’s forecast error and any previous period’s. This feature has led several critics to conclude that equilibrium models cannot account for more than an insignificant part of the highly serially correlated movements we observe in real output, employment, unemployment, and other series. Tobin (1977, p. 461) has put the argument succinctly:

One currently popular explanation of variations in employment is temporary confusion of relative and absolute prices. Employers and workers are fooled into too many jobs by unexpected inflation, but only until they learn it affects other prices, not just the prices of what they sell. The reverse happens temporarily when inflation falls short of expectation. This model can scarcely explain more than transient disequilibrium in labor markets.

So how can the faithful explain the slow cycles of unemployment we actually observe? Only by arguing that the natural rate itself fluctuates, that variations in unemployment rates are substantially changes in voluntary, frictional, or structural unemployment rather than in involuntary joblessness due to generally deficient demand.

The critics typically conclude that the theory only attributes a very minor role to aggregate demand fluctuations and necessarily depends on disturbances to aggregate supply to account for most of the fluctuations in real output over the business cycle. “In other words,” as Modigliani (1977) has said, “what happened to the United States in the 1930’s was a severe attack of contagious laziness.” This criticism is fallacious because it fails to distinguish properly between sources of impulses and propagation mechanisms, a distinction stressed by Ragnar Frisch in a classic 1933 paper that provided many of the technical foundations for Keynesian macroeconometric models. Even though the new classical theory implies that the forecast errors which are the aggregate demand impulses are serially uncorrelated, it is certainly logically possible that propagation mechanisms are at work that convert these impulses into serially correlated movements in real variables like output and employment. Indeed, detailed theoretical work has already shown that two concrete propagation mechanisms do precisely that.

One mechanism stems from the presence of costs to firms of adjusting their stocks of capital and labor rapidly. The presence of these costs is known to make it optimal for firms to spread out over time their response to the relative price signals they receive. That is, such a mechanism causes a firm to convert the serially uncorrelated forecast errors in predicting relative prices into serially correlated movements in factor demands and output.

A second propagation mechanism is already present in the most classical of economic growth models. Households’ optimal accumulation plans for claims on physical capital and other assets convert serially uncorrelated impulses into serially correlated demands for the accumulation of real assets. This happens because agents typically want to divide any unexpected changes in income partly between consuming and accumulating assets. Thus, the demand for assets next period depends on initial stocks and on unexpected changes in the prices or income facing agents. This dependence makes serially uncorrelated surprises lead to serially correlated movements in demands for physical assets. Lucas (1975) showed how this propagation mechanism readily accepts errors in forecasting aggregate demand as an impulse source.

A third likely propagation mechanism has been identified by recent work in search theory. (See, for example, McCall 1965, Mortensen 1970, and Lucas and Prescott 1974.) Search theory tries to explain why workers who for some reason are without jobs find it rational not necessarily to take the first job offer that comes along but instead to remain unemployed for awhile until a better offer materializes. Similarly, the theory explains why a firm may find it optimal to wait until a more suitable job applicant appears so that vacancies persist for some time. Mainly for technical reasons, consistent theoretical models that permit this propagation mechanism to accept errors in forecasting aggregate demand as an impulse have not yet been worked out, but the mechanism seems likely eventually to play an important role in a successful model of the time series behavior of the unemployment rate. In models where agents have imperfect information, either of the first two mechanisms and probably the third can make serially correlated movements in real variables stem from the introduction of a serially uncorrelated sequence of forecasting errors. Thus theoretical and econometric models have been constructed in which in principle the serially uncorrelated process of forecasting errors can account for any proportion between zero and one of the steady state variance of real output or employment. The argument that such models must necessarily attribute most of the variance in real output and employment to variations in aggregate supply is simply wrong logically.

My problem with the Lucas-Sargent argument is that even if the deviations from a long-run equilibrium path are serially correlated, shouldn’t those deviations be diminishing over time after the initial disturbance. Can these propagation mechanisms account for amplification of the initial disturbance before the adjustment toward the equilibrium path begins? I would gratefully welcome any responses.

David Glasner has a question about the “rational expectations” business-cycle theories developed in the 1970s:

David GlasnerThree Propagation Mechanisms in Lucas & Sargent: ‘I’m… hop[ing for]… some guidance… about… propagation mechanisms… [in] Robert Lucas and Thomas Sargent[‘s]… “After Keynesian Macroeconomics.”… 

The critics typically conclude that the theory only attributes a very minor role to aggregate demand fluctuations and necessarily depends on disturbances to aggregate supply…. [But] even though the new classical theory implies that the forecast errors which are the aggregate demand impulses are serially uncorrelated, it is certainly logically possible that propagation mechanisms are at work that convert these impulses into serially correlated movements in real variables like output and employment… the presence of costs to firms of adjusting their stocks of capital and labor rapidly…. accumulation plans for claims on physical capital and other assets convert serially uncorrelated impulses into serially correlated demands for the accumulation of real assets… workers who for some reason are without jobs find it rational not necessarily to take the first job offer that comes along but instead to remain unemployed for awhile until a better offer materializes…. In principle the serially uncorrelated process of forecasting errors can account for any proportion between zero and one of the [serially correlated] steady state variance of real output or employment. The argument that such models must necessarily attribute most of the variance in real output and employment to variations in aggregate supply is simply wrong logically…

My problem with the Lucas-Sargent argument is that even if the deviations from a long-run equilibrium path are serially correlated, shouldn’t those deviations be diminishing over time after the initial disturbance? Can these propagation mechanisms account for amplification of the initial disturbance before the adjustment toward the equilibrium path begins? I would gratefully welcome any responses…

In some ways this is of only history-of-thought interest. For Lucas and Prescott, at least, had within five years of the writing of “After Keynesian Macroeconomics” decided that the critics were right: that their models of how mistaken decisions driven by serially-uncorrelated forecast errors could not account for the bulk of the serially correlated business-cycle variance of real output and employment, and they needed to shift to studying real business cycle theory instead of price-misperceptions theory. The first problem was that time-series methods generated shocks that came at the wrong times to explain recessions. The second problem was that the propagation mechanisms did not amplify but rather damped the shock: at best they produced some kind of partial-adjustment process that extended the impact of a shock on real variables to N periods and diminished its impact in any single period to 1/N. There was no… what is the word?…. multiplier in the system.

It was stunning to watch in real time in the early 1980s. As Paul Volcker hit the economy on the head with the monetary-stringency brick, repeatedly, quarter after quarter; as his serially correlated and hence easily anticipated policy moves had large and highly serially correlated effects on output; Robert Lucas and company simply… pretended it was not happening: that monetary policy was not having major effects on output and employment in the first half of the 1980s, and that it was not the case thjat the monetary policies that were having such profound real impacts had no plausible interpretation as “surprises” leading to “misperceptions”. Meanwhile, over in the other corner, Robert Barro was claiming that he saw no break in the standard pattern of federal deficits from the Reagan administration’s combination of tax cuts plus defense buildup.

Those of us who were graduate students at the time watched this, and drew conclusions about the likelihood that Lucas, Prescott, and company had good enough judgment and close enough contact with reality that their proposed “real business cycle” research program would be a productive one—conclusions that, I think, time has proved fully correct.

Behind all this, of course, was this issue: the “microfoundations” of the Lucas “island economy” model were totally stupid: people are supposed to “misperceive” relative prices because they know the nominal prices at which they sell but do not know the nominal prices at which they buy, hence people confuse a monetary shock-generated rise in the nominal price level with an increase in the real price of what they produce, and hence work harder and longer and produce more? (I forget who it was who said at the time that the model seemed to require a family in which the husband worked and the wife went to the grocery store and the husband never listened to anything the wife said.) These so-called “microfoundations” could only be rationally understood as some kind of metaphor. But what kind of metaphor? And why should it have any special status, and claim on our attention?

Paul Krugman’s judgment on the consequences of this intellectual turn is even harsher than mine:

What made the Dark Ages dark was the fact that so much knowledge had been lost, that so much known to the Greeks and Romans had been forgotten by the barbarian kingdoms that followed. And that’s what seems to have happened to macroeconomics in much of the economics profession. The knowledge that S=I doesn’t imply the Treasury view—the general understanding that macroeconomics is more than supply and demand plus the quantity equation — somehow got lost in much of the profession. I’m tempted to go on and say something about being overrun by barbarians in the grip of an obscurantist faith…

I would merely say that it has left us, over what is now two generations, with a turn to DSGE models—Dynamic Stochastic General Equilibrium—that must satisfy a set of formal rhetorical requirements that really do not help us fit the data, and that it gave many, many people an excuse not to read and hence a license to remain ignorant of James Tobin.

Brad

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6 Responses to “Three Propagation Mechanisms in Lucas and Sargent with a Response from Brad DeLong”


  1. 1 LAL March 30, 2022 at 9:30 pm

    I’m sure there is something subtle im missing but I think the answer to both of your questions is yes. 1) it pretty much has to as you intuited, and my memory of all the smets-wouters type new keynesian dsge models have plots of impulse response functions that all trail off. But those functions are to a single impulse in the first time period, usually to one variable. the idea which we dont get to see as much in papers or the classroom is to overlay them and integrate them all in the real word of constant shocks. I think the new Keynesian models incorporate (in spirit) the propagation mechanisms a) via sticky prices which through Calvo pricing are thought to be a good proxy for staggered contracts (is that a John Taylor paper 197? Maybe 198?), and b) just seems like consumption smoothing to me which is still there in lots of representative agents models when they specify the utility function. 2) And yes those impulse response functions can draw damn near any shape you want them to with the right alphabet soup of parameters. I like John Cochrane’s derivation of the Fisher rule like world for his simplest version of the fiscal theory of the price level, but when he adds long term debt, sticky prices, etc. he gets the curves to bend the “right” way like we expect from conventional monetary policy…and he is able to describe the counteracting effects better than most people. He’s got those plots scattered all over his blog and book.

    The only search theory models i know much about are the new monetarist ones. I’ve seen in some of them the goal of monetary policy should actually be to exacerbate shocks, etc. steve williamson has a paper that does that…williamson 2007? Sorry too lazy to edit this comment or look up my references…

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  2. 2 Jonathan Haskel March 31, 2022 at 12:35 am

    Agree with the previous comment.To me, the key point is that, as I understand it, most macro forecasting models have the shocks wearing off as an imposed joint assumption about nominal rigidities and the shock being temporary. Cost of adjustment models are then invoked as an additional way of rationalizing slow adjustment and lagged effects. Amplification mechanisms, such as fire sales of deteriorating bank assets are usually reserved for special circumstances.

    Thanks so much for your very informative and interesting blog.

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  3. 3 LAL March 31, 2022 at 5:09 pm

    Synchronicity at work: Cochrane shows the exact graphs I was talking about in his post today: https://johnhcochrane.blogspot.com/2022/03/will-inflation-persist.html?m=0

    He also provides links to his paper and book in the post. I’m interpreting the acceleration of the price level in the last model he describes as an affirmative to your second question. But if that is not what you meant I would be interested in understanding your question better.

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  4. 4 David Glasner April 3, 2022 at 4:30 pm

    LAL, Many thanks for your comments and your link to Cochrane. I’m encouraged that you agree with me that adjustment mechanism posited by Lucas and Sargent in their paper does not straightforwardly imply any amplification of the initial disturbance but simply a kind of asymptotic adjustment over time to a new equilibrium path. Epicycles, anyone?

    Jonathan, Many thanks for your comment seconding LAL’s, and also for your kind words about this blog. Comments like yours certainly encourage me to keep posting.

    LAL, I had a quick look at Cochrane’s post. My off the cuff response to the fiscal theory of the price level, which I have not really tried to fully understand, is that for the supplier of the world’s dominant currency, whose dominance is literally unchallenged and likely unchallengable, the flow of seignorage is so great that the fiscal shock that Cochrane is positing is not a big deal.

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  5. 5 Frank Restly April 4, 2022 at 2:16 pm

    “My off the cuff response to the fiscal theory of the price level, which I have not really tried to fully understand, is that for the supplier of the world’s dominant currency, whose dominance is literally unchallenged and likely unchallengable, the flow of seignorage is so great that the fiscal shock that Cochrane is positing is not a big deal.”

    Because as Paul Krugman would say bigger is always better and might makes right?

    “Pride goeth before destruction, and a haughty spirit before a fall.” – Proverbs

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  6. 6 LAL April 5, 2022 at 10:27 am

    “ (I forget who it was who said at the time that the model seemed to require a family in which the husband worked and the wife went to the grocery store and the husband never listened to anything the wife said.) ”
    Interestingly enough Lucas (1980) does exactly that: Separates society into two classes of workers and shoppers. And I remember this analogy being passed around as recently at 2011, but I have another interpretation, that it is of a capitalist class and a working class. That seems standard in old Keynesian analysis like that of Kalecki, and even in Krugman and Delong’s recession paper where people are grouped into debtors and creditors. The irony being their charge against Lucas of thinking only in terms of a single representative agent when he has already spawned two generations of heterogenous agent models (in the new monetarist tradition).

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About Me

David Glasner
Washington, DC

I am an economist in the Washington DC area. My research and writing has been mostly on monetary economics and policy and the history of economics. In my book Free Banking and Monetary Reform, I argued for a non-Monetarist non-Keynesian approach to monetary policy, based on a theory of a competitive supply of money. Over the years, I have become increasingly impressed by the similarities between my approach and that of R. G. Hawtrey and hope to bring Hawtrey’s unduly neglected contributions to the attention of a wider audience.

My new book Studies in the History of Monetary Theory: Controversies and Clarifications has been published by Palgrave Macmillan

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