Abstract:
Economists and economic policymakers believe that households' and firms' expectations of future inflation are a key determinant of actual inflation. A review of the relevant theoretical and empirical literature suggests that this belief rests on extremely shaky foundations, and a case is made that adhering to it uncritically could easily lead to serious policy errors.
Nobody thinks clearly, no matter what they pretend. ...That's why people hang on so tight to their beliefs and opinions; because, compared to the haphazard way they're arrived at, even the goofiest opinion seems wonderfully clear, sane, and self-evident.
Dashiell Hammett, The Dain Curse (1928)
Mainstream economics is replete with ideas that "everyone knows" to be true, but that are actually arrant nonsense. For example, "everyone knows" that:
None of these propositions has any sort of empirical foundation; moreover, each one turns out to be seriously deficient on theoretical grounds.1 Nevertheless, economists continue to rely on these and similar ideas to organize their thinking about real-world economic phenomena. No doubt, one reason why this situation arises is because the economy is a complicated system that is inherently difficult to understand, so propositions like these--even though wrong--are all that saves us from intellectual nihilism. Another, more prosaic reason is Stigler's (1982) equally nihilistic observation that "it takes a theory to beat a theory."
Is this state of affairs ever harmful or dangerous? One natural source of concern is if dubious but widely held ideas serve as the basis for consequential policy decisions.2 In this note, I examine one such idea, namely, that expected inflation is a key determinant of actual inflation. Many economists view expectations as central to the inflation process; similarly, many central banks consider "anchoring" or "managing" the public's inflation expectations to be an important policy goal or instrument. Here, I argue that using inflation expectations to explain observed inflation dynamics is unnecessary and unsound: unnecessary because an alternative explanation exists that is equally if not more plausible, and unsound because invoking an expectations channel has no compelling theoretical or empirical basis and could potentially result in serious policy errors.3
I'm always a little dubious about an appeal to expectations as a causal factor; expectations are by definition a force that that you intuitively feel must be everpresent and very important but which somehow you are never allowed to observe directly.
R. M. Solow (1979)
The usual argument for viewing expected inflation as a key driver of actual inflation goes something like this.
If correct, such a view has important practical and policy consequences. For an inflation forecaster, observed (imperfect) measures of expected inflation might usefully inform inflation projections and permit one to explain past inflation developments. For a central bank with a price-stability mandate, monitoring measures of inflation expectations can provide an important gauge of how well the monetary authority is meeting its goal, while attempts to shape the public's inflation expectations through central bank communications and policy actions will represent time well spent. In particular, to the extent that post-1990 inflation dynamics reflect the effect that the conduct of monetary policy has had on inflation, there should be an active attempt by policymakers to preserve the relevant features of this policy regime. But what real evidence do we have for this view?
Pure economics has a remarkable way of pulling rabbits out of a hat--apparently a priori propositions which apparently refer to reality. It is fascinating to try to discover how the rabbits got in; for those of us who do not believe in magic must be convinced that they got in somehow.
J. R. Hicks (1946)
Two of the earliest theoretical arguments for assigning an explicit role for inflation expectations in a Phillips curve relation are found in Phelps (1967) and Friedman (1968). In addition, Lucas and Rapping (1969) derived an aggregate supply function in which a correlation between inflation and real activity would arise through a price expectations mechanism, while Lucas's imperfect information model (which was described opaquely in a 1972 article and somewhat more accessibly in a 1973 paper) implied an inflation equation in which a change in (rationally) expected inflation would pass through one-for-one into the intercept of the Phillips curve. Finally, a later generation of rational expectations models that started from the assumption of less-than-fully flexible prices or wages gave rise to the so-called new-Keynesian Phillips curve, which differed from previous models in assigning a role to the current expectation of next period's inflation rate (as opposed to last period's expectation of the current inflation rate).
What are the merits of each theoretical approach? Phelps simply asserted that the intercept of the Phillips curve would shift one-for-one with expected inflation; to the extent that a theoretical argument was vouchsafed, it was based on the notion that "...the supply of labour [should be] independent of the real and money rates of interest and hence independent of the expected rate of inflation," as "...otherwise, every steady-state of fully anticipated inflation would be associated with different 'levels' of output, employment and the real wage." Hence, Phelps's argument was basically founded on the idea that nominal variables should not permanently affect real variables, though here the real variable in question was the real interest rate.
Friedman's derivation was superficially simpler than Phelps's--unlike the latter's paper, Friedman's paper contains no equations--but was arguably better grounded in theory. Specifically, Friedman posited that workers entered the wage bargain with a concern over anticipated real wages (the concern with real wages is of course a reasonable one if money illusion is absent) while firms' hiring decisions were based on actual real wages (no distinction was made between the consumption and product wage). Hence, by reducing the ex post real wage, a surprise increase in prices could yield higher employment. But a fully anticipated price increase would be fully reflected in nominal wages, thereby leaving the real wage (or any other real variable) unchanged.
Lucas and Rapping formulated a model in which price expectations affect labor supply by influencing households' substitution between goods and leisure across time. Specifically, the model assumes that a rise in (expected) real interest rates boosts labor supply today (the cost of current leisure, in terms of foregone future consumption, goes up). Critically, the model also assumes adaptive expectations in the price level, along with less than one-for-one adjustment in nominal interest rates.
A little later, Lucas (1972) constructed a model in which agents use observed market prices in order to assess how much of a given disturbance is "purely monetary" as opposed to having resulted from a shock to a real variable. The basic idea is tied to the notion that producers might mistake an absolute (money) price change for a relative price change; the theoretical problem that the paper attempts to solve is why one producer's mistake in a particular direction isn't simply offset in the aggregate by a different producer's mistake in the opposite direction. (The paper does so by appealing to a sort of "islands economy" that is similar to a modelling strategy employed by Phelps in other work.) What is often called the "Lucas supply function" or "Lucas surprise supply function" refers to an aggregate supply or Phillips curve relation of this form.4
Finally, the subsequent development of the new-Keynesian Phillips curve represented an attempt to integrate rational expectations into a model where some sort of exogenously specified contracting mechanism or the assumed presence of adjustment costs yielded nominal rigidities. Given the models' assumed competitive structure, these nominal rigidities would in turn cause current inflation to depend on expected future inflation.5
Even without appealing to empirical arguments (that will be done in the following section), it is clear that none of these models makes a strong or even especially plausible theoretical case for including expected inflation in an inflation equation.
It should also be pointed out that all of these models give pride of place to short-run expected inflation, in the sense that current inflation is influenced by a one-period-ahead expectation (the main difference across models is whether the short-run expectation is last period's expectation of the current inflation rate or this period's expectation of next period's inflation rate).11 This fact sits uneasily with the observation that in policy circles--at least in the United States--much more attention is paid to long-run inflation expectations, as it is the "anchoring" of these expectations that is viewed as being the wellspring of desirable economic outcomes and (as an empirical matter) as the source of important changes in U.S. inflation dynamics over the past 50 years.12 Moreover, while it turns out to be possible to append anadaptive-learning mechanism to several of these models in order to derive an inflation equation where long-run inflation expectations do play a critical role (see section 5, below), such a mechanism turns out to carry subtly different policy implications.
Don't interfere with fairy tales if you want to live happily ever after.
F. M. Fisher (1984)
It is an irony of history (or perhaps a testimony to the power of pure thought) that, when Phelps and Friedman sought to justify their proposed theoretical specifications, they were faced with the uncomfortable fact that empirical Phillips curves appeared to be remarkably stable. The sensible explanation that both authors advanced was that this seeming stability was actually the result of existing models' having been estimated over a period in which actual and expected wage and price inflation had remained within a relatively narrow range. (Oddly, neither author appealed to the gold standard to make his case.) While one could quibble with the view that inflation (and other influences on inflation, like trend productivity and unemployment) had actually been all that stable over the first part of the 20th century, there was no question that the sustained inflation increases of the 1960s and 1970s appeared to be associated with outward shifts of estimated Phillips curves. Ex post, these developments were seen as a stunning victory for the prediction that expected inflation was an important determinant of actual inflation.13
It is worth noting, however, that the direct evidence for an expected inflation channel was never very strong. Most empirical tests concerned themselves with the proposition that there was no permanent Phillips curve tradeoff, in the sense that the coefficients on lagged inflation in an inflation equation summed to one14 Relatedly, the invocation of an adaptive expectations mechanism in numerous theoretical contextsled many to simply associate the presence of lagged inflation terms in empirical Phillips curves models with a role for "expectations" in some loose sense.15 Perhaps the closest (and, for the time, most econometrically sound) attempt at a direct test was made by McCallum (1976), where he used instrumental variables techniques to assess the role of expected price inflation in a wage equation.16 (These techniques are similar in spirit to those employed in the 1990s to estimate new-Keynesian models; hence, they suffer from the same sorts of problems--discussed below--that attend empirical estimates of those models.)
In addition, the various theoretical models that assumed a role for expected inflation tended to carry other empirical implications that were clearly at variance with the data. For example:
Similarly, the documented empirical deficiencies of the new-Keynesian Phillips curve are legion.
Leaving aside the results of econometric tests of particular models (and given that there is good evidence that many prices actually are sticky), doesn't it seem intuitively plausible that firms fixing their price over some period would worry about future costs or demand conditions--that is, about any relevant developments that could materialize over the period in which their price is held constant? Perhaps, but perhaps not.
This last point is particularly important given that one of the few shreds of empirical evidence that we do have suggests that it is long-run expectations that are most relevant for inflation dynamics. As figure 2 demonstrates, there is a suggestive low-frequency correlation between an estimate of inflation's long-run stochastic trend and survey measures of long-run expected inflation.23 The stability of inflation's long-run trend after the mid-1990s--more precisely, the fact that the trend appears almost completely invariant to changes in economic conditions--is perhaps the most remarkable feature of the U.S. inflation process at present; at a minimum, it represents a significant departure from the experience of the 1970s and 1980s (see the dashed line in figure 3, which plots the stochastic trend for price inflation over a longer period).24
Of course, the correlation that is apparent in figure 2 provides, at best, only circumstantial evidence of a causal relationship in which expectations determine the long-run properties of inflation; it could equally well reflect a situation where respondents to these surveys are making reasonably plausible inflation forecasts in response to observed changes in actual inflation. In addition, further evidence against a causal relationship is provided by the fact that in recent years, movements in these survey measures (as well as in long-run inflation expectations from TIPS yields) appear not to be mirrored by changes in trend inflation (this casual observation is confirmed by Rudd, 2020, using more-formal estimation techniques).25
A reasonable reader's reaction to the preceding discussion might be: "So what? No model is going to describe reality all that well, and a convincing theory of aggregate supply--or of inflation dynamics generally--has eluded students of macroeconomics since the field's inception. So your criticisms really just amount to ill-tempered pettifogging."
What I believe such a response misses is that the presence of expected inflation in these models provides essentially the only justification for the widespread view that expectations actually do influence inflation. In other words, rather than simply serving as a plausible postulate that, once invoked, allows a theorist to analyze other interesting questions, the expected inflation terms in these models have been reified into a supposed feature of reality that "everyone knows" is there. And this apotheosis has occurred with minimal direct evidence, next-to-no examination of alternatives that might do a similar job fitting the available facts, and zero introspection as to whether it makes sense to use the particular assumptions or derived implications of a theoretical model to inform our priors (particularly when the ancillary assumptions of the model are so incredible and when the few clear predictions it makes are so wildly at odds with the available empirical evidence).
It is far, far better and much safer to have a firm anchor in nonsense than to put out on the troubled seas of thought.
John Kenneth Galbraith (1958)
If expected inflation isn't a key determinant of actual inflation, how might we try to explain the observed evolution of postwar U.S. inflation dynamics?
First, consider figure 4, which plots inflation's stochastic trend (the black dashed line) together with the estimated stochastic trend for unit labor cost growth (the blue line).26 The similar contours of the two lines certainly seems to indicate that the long-run behavior of price inflation and labor cost growth is linked.
Second, the fact that inflation's stochastic trend manifests its last persistent level shift after the 1990-1991 recession also seems relevant, in that it suggests that "whatever happened" to inflation might be more related to its actual level's having been kept low rather than to any "credibility" that the Fed gained as an inflation fighter following the Volcker disinflation. Put differently, a trend inflation rate of around four percent was associated with highly persistent inflation dynamics--both in the late 1960s and in the 1980s--while a two-percent trend inflation rate was not.
Another way of stating this point is that an important feature of inflation dynamics after the mid-1990s appears to be the lack of a strong wage-price spiral (or of any significant year-to-year feedback between wage growth and inflation). This is true despite large (but ultimately transitory) increases in actual inflation--for example, headline PCE inflation averaged 3 percent over the three years leading up to the 2007-2009 recession.27 It seems unlikely that well-anchored long-run inflation expectations were the root cause of this stability, inasmuch as this belief also leads to the conclusion that workers were willing to ignore noticeable (and reasonably sustained) changes in the cost of living when deciding on the wage rate that they were willing to accept, simply because they believed that eventually inflation would return to some long-run average pace.28
An observation about the actual nature of the "wage bargaining process" is helpful at this point. Outside of a few unionized industries (which now account for only about 6 percent of employment), a formal wage bargain--in the sense of a structured negotiation over pay rates for the coming year--doesn't really exist anymore in the United States. In a world where most employment is "at will," changes in the cost of living will enter nominal wages as part of an employer's attempt to retain workers: If employers pay their workers a wage that falls too far behind the cost of living, they will start to see more quits, which will in turn force them to raise the wages they pay to existing workers (and those they offer to new hires). But there is no real scope for direct negotiation.29
In situations where inflation is relatively low on average, it also seems likely that there will be less of a concern on workers' part about changes in the cost of living--that is, a smaller proportion of quits will reflect workers' attempts to offset higher consumer prices by finding a better-paying job. But this is a story about outcomes, not expectations: Workers don't behave this way because they expect to see low inflation in the future, but rather because they don't view their recent wage increases as appreciably lagging actual changes in the cost of living.30
On this latter point the experience of the 1960s and 1970s is telling. As one study of wage determination over this period argued, "there appears to be some threshold at which the rate of change in living costs becomes a pervasive factor of which account has to be taken in wage decisions," and that "[i]t is when the upward movement of prices quickens, and extends substantially throughout the whole range of consumer goods and services, that wages begin to respond directly to price movements." That threshold was apparently reached around the mid-1960s, when the rate of increase in the CPI moved up to around 3 percent, with "the advance extending to most of its components" and with the food at home component rising by 5 percent.31
Hence, the current (post-1995) state of inflation dynamics could reflect a situation where inflation simply does not enter workers' employment decisions--people no longer (or don't often) quit a job because their wages aren't keeping up with the cost of living (which is not to say that they won't do so if they believe that they can get higher pay elsewhere--money is money, after all--and especially when conditions in the labor market reduce the likelihood of undergoing a prolonged spell of unemployment before finding a better-paying job). This situation is different to one where an adaptive expectations channel is operative--under the alternative interpretation, expectations are irrelevant in the sense that there is no attempt to leapfrog or make up for anticipated inflation "in advance" by negotiating a higher nominal wage. Rather, the current period represents one in which inflation isn't on workers' "radar screens" anymore (or is at least is only a very tiny blip), which in turn yields an outcome where current price inflation does not respond (much) to past inflation (because inflation is not a major factor in wage determination).32
Even if one is not willing to concede that inflation expectations are utterly irrelevant, it is still necessary to explain why it would be that long-run expectations appear to be the ones that pin down actual inflation. It turns out to be possible to come up with an explanation along these lines, but it takes a bit of doing.
First, assume that the "true" inflation equation has a role for short-run expected inflation (say because these expectations influence wage-setting behavior--or simply take your pick from one of the theoretical models described in section III). Specifically, assume that the world is described by a version of a Phelps-Friedman Phillips curve:
| $$\displaystyle \pi_t = \beta (U_t-U_t^*) + (1-\phi) \pi_{t-1} + \phi E_{t-1} \pi_{t} + \zeta Z_t + e_t ,$$ | (1) |
Now assume that that agents use the following inflation forecasting rule to formulate their one-period-ahead inflation expectation:
| $$\displaystyle E_t \pi_{t+1} = c_{0,t} + c_{1,t} \pi_t ,$$ | (2) |
| $$\displaystyle E_{t-1} \pi_{t} = c_{0,t-1} + c_{1,t-1} \pi_{t-1} .$$ | (3) |
| $$\displaystyle \pi^{LR}_{t-1} = \frac{c_{0,t-1}}{1 - c_{1,t-1}} .$$ | (4) |
Substituting the forecasting rule (3) into the Phelps-Friedman specification (1) yields
| $$\displaystyle \pi_t = \beta (U_t-U_t^*) + (1-\phi) \pi_{t-1} + \phi [ c_{0,t-1} + c_{1,t-1} \pi_{t-1} ] + \zeta Z_t + e_t ,$$ | (5) |
| $$\displaystyle \pi_t = \beta (U_t-U_t^*) + (1-\phi+\phi c_{1,t-1}) \pi_{t-1} + (\phi-\phi c_{1,t-1}) \pi^{LR}_{t-1} + \zeta Z_t + e_t .$$ | (6) |
If correct, such a description of the world would carry two important implications.
What this second point suggests is that the observed stability of both observed long-run inflation expectations and inflation's stochastic trend is consistent with a situation in which agents no longer update their perceived law of motion for inflation (put differently, a gain close to zero will weaken the statistical evidence for a unit root in actual inflation). This state of affairs will in turn be reasonable so long as the forecast errors that result from setting expectations in this manner are relatively small--or, if large, not very persistent. It also doesn't preclude continued attention to inflation on the part of households--they are still making forecasts--but rather requires them to see no pressing need to revise or update the "parameters" of their forecasting rule. Finally, a situation like this is also not at odds with actual inflation developments playing a limited role in workers' employment decisions, since "on average" a steady rate of nominal wage increases (even one that implies a pace of real wage increases that lags trend productivity growth) will still ensure that workers' earnings won't fall too far out of line with the cost of living.
Importantly, this explanation lines up with another salient fact: Agents--specifically households--still appear to pay attention to inflation in other contexts. In particular, there is a strong correlation between consumer sentiment and actual inflation, even since the mid 1990s; likewise, actual inflation appears to influence short-run expected inflation (and even long-run expected inflation to a more-limited degree).34 Again, these observations are consistent with the notion that agents see no reason at present to make large changes to their view of the inflation process ("updates to their forecasting rule"), but they also hint at the mildly disturbing possibility that inflation might not be quite as far off households' radar screens as we might hope.35
Few things are harder to put up with than the annoyance of a good example.
Mark Twain, The Tragedy of Pudd'nhead Wilson (1894)
At present, an inflation analyst generating inputs to policy decisions should be mainly concerned with the possibility that inflation's stochastic trend is once again starting to react to changes in actual economic conditions, as such a situation could be a harbinger of a return to a regime with high inflation persistence. However, if the preceding description of inflation dynamics is correct, movements in measures of short-term or long-term expected inflation will probably not provide a very accurate real-time indicator of whether this situation is starting to emerge--and, by extension, whether actual inflation is starting to become a material factor in agents' decisionmaking.36 Similarly, statistical estimates of inflation's long-run trend are likely to suffer from the usual endpoint problems that plague filtering exercises. So is there anything else that analysts or policymakers might try to monitor?
One development to watch for would be any evidence that a renewed concern with price inflation was starting to affect wage determination--either in statistical form (for example, if reduced-form models of wage growth that assumed a stable long-run trend were to see errors emerge that appeared to be correlated with actual inflation) or in the form of anecdotes. To the extent possible, we might also try to determine whether quit rates were starting to rise in a manner that was less tied to the state of the labor market and more correlated with consumer price developments, or whether wage increases for new hires were starting to rise appreciably relative to wage increases for workers in continuing employment relationships (the argument being that wages for new hires are more flexible and hence more responsive to economic conditions). Unfortunately, these are developments that would probably only become clear over a span of several years, not over a few months or quarters.
Another practical implication is rhetorical. By telling policymakers that expected inflation is the ultimate determinant of inflation's long-run trend, central-bank economists implicitly provide too much assurance that this claim is settled fact. Advice along these lines also naturally biases policymakers toward being overly concerned with expectations management, or toward concluding that survey- or market-based measures of expected inflation provide useful and reliable policy guideposts. And in some cases, the illusion of control is arguably more likely to cause problems than an actual lack of control.
Interviewer: What was your intention?
R. Crumb: I don't know. I think I was just being a punk.
Thomas Maremaa, "Who Is This Crumb?" New York Times, October 1, 1972
Related to this last point, an important policy implication would be that it is far more useful to ensure that inflation remains off of people's radar screens than it would be to attempt to "re-anchor" expected inflation at some level that policymakers viewed as being more consistent with their stated inflation goal.37 In particular, a policy of engineering a rate of price inflation that is high relative to recent experience in order to effect an increase in trend inflation would seem to run the risk of being both dangerous and counterproductive inasmuch as it might increase the probability that people would start to pay more attention to inflation and--if successful--would lead to a period where trend inflation once again began to respond to changes in economic conditions.38
This sort of concern is not merely academic. Empirical estimates of PCE price inflation's long-run trend typically yield point estimates that are slightly below the Federal Reserve's stated longer-run target of two percent (Rudd, 2020). Hence, even if anchored long-run inflation expectations actually are the reason that trend inflation is currently stable, it appears that the level at which they are anchored isn't fully aligned with the Federal Reserve's policy goal.
A related issue is more pragmatic. In some ways, the situation that arises from a focus on long-term inflation expectations is similar to one in which a policymaker seeks to target a single indicator of full employment--for instance, the natural rate of unemployment. Like the natural rate, the long-run expectations that are relevant for wage and price determination cannot be directly measured, but instead need to be inferred from empirical models. Hence, using inflation expectations as a policy instrument or intermediate target has the result of adding a new unobservable to the mix. And, as Orphanides (2004) has persuasively argued, policies that rely too heavily on unobservables can often end in tears.
One might also be uneasy about policymakers' relying too heavily on the assumption that inflation's long-run trend will remain stable going forward so long as measured long-run inflation expectations do. Even if every one of my preceding arguments is judged by the reader to be completely unconvincing, it nevertheless remains the case that we have nothing better than circumstantial evidence for a relationship between long-run expected inflation and inflation's long-run trend, and no evidence at all about what might be required to keep that trend fixed (beyond that it might involve keeping actual inflation from moving up too much above two percent on a sustained basis). Given the huge boon to stabilization policy that results from a stable long-run inflation trend, actions that might jeopardize that stability would appear to face an unusually high cost-benefit hurdle.
The best lack all conviction, while the worst
Are full of passionate intensity.
W. B. Yeats, "The Second Coming" (1920)
Consider the following Gedankenversuch.
Say you had never heard of Phelps or Friedman, and only knew that the stochastic trend for inflation (and labor costs) last shifted noticeably following a recession that occurred after a period when actual inflation had been running at four percent. You then came across some survey measures of long-run expected inflation that roughly showed the same one-time level shift. Would you be convinced enough by this evidence to conclude that long-run inflation expectations were an important factor driving inflation dynamics? Or would you be skeptical of this conclusion because it is basically derived from a single observation (with later observations providing no evidence at all), and because one could just as easily explain these facts with an appeal to the notion that agents were simply making forecasts of inflation that were roughly correct on average? How would you also explain that a recession permanently reduced trend inflation when actual inflation was four percent, but never did so thereafter?
Or would you justify the view that expectations "matter" by pointing to the inflation experience of the 1960s and 1970s, even though that period provides no actual evidence that workers or firms tried to boost their wages or raise their prices in anticipation of future price or cost changes? After all, history really only tells us that lags of actual inflation seem to enter inflation equations to a greater or lesser degree over time, not that expectations do or did; thinking that these lags of inflation are present because they are a proxy for some kind of forecast is more a habit of mind than anything solidly grounded in fact.
Alternatively, if you view the theoretical arguments as dispositive, exactly how would you explain to a fellow economist why it is that you see an important role for expected inflation in inflation dynamics? Would you make a halfhearted appeal to Phelps and Friedman? Would you feel a little guilty doing so, knowing that these authors either assumed such a role for expectations (Phelps) or motivated it with a theoretical mechanism whose basic predictions are clearly wrong (Friedman)? If not, then how would you explain that, in reality, only long-run inflation expectations seem even vaguely related to actual inflation? And if you tied your explanation to some sort of "wage bargaining" mechanism, what existing institutional feature of the economy would you point to in order to justify it? Would you instead try to fall back on the new-Keynesian Phillips curve, whose theoretical derivation is even harder to take seriously and whose empirical justification is close to nonexistent?
And would you feel the slightest bit nervous (or chagrined) about any of it?
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