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Macroeconomic Expectations Of Households And Professional Forecasters

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Abstract

Economists have long emphasized the importance of expectations in determining macroeconomic outcomes. Yet there has been almost no recent effort to model actual empirical expectations data; instead, macroeconomists usually simply assume that expectations are "rational." This paper shows that while empirical household expectations are not rational in the usual sense, expectational dynamics are well captured by a model in which households' views derive from news reports of the views of professional forecasters, which in turn may be rational. The model's estimates imply that people only occasionally pay attention to news reports; this inattention generates "stickyness" in aggregate expectations, with important macroeconomic consequences. © 2001 the President and Fellows of Harvard College and the Massachusetts Institute of Technology
EpidemiologyQJE.tex
Macroeconomic Expectations of
Households and Professional Forecasters
Christopher D. Carroll
ccarroll@jhu.edu
Published in the Quarterly Journal of Economics, Volume 118, Number 1, February 2003
December 17, 2002
Abstract
Economists have long emphasized the importance of expectations in determining
macroeconomic outcomes. Yet there has been almost no recent effort to model ac-
tual empirical expectations data; instead,macroeconomists usually simply assume
that expectations are ‘rational.’ This paper shows that while empirical household
expectations are not rational in the usual sense, expectational dynamics are well cap-
tured by a model in which households’ views derive from news reports of the views
of professional forecasters, which in turn may be rational. The model’s estimates
imply that people only occasionally pay attention to news reports; this inattention
generates ‘stickyness’ in aggregate expectations, with important macroeconomic
consequences.
Keywords:inflation, expectations, unemployment, monetary policy
JEL Classification Codes: D84, E31
This paper is derived from a paper originally titled “The Epidemiology of Macroeconomic
Expectations” written in connection with the conference “The Economy As an Evolving
Complex System III” at the Santa Fe Institute in November 2001, honoring Kenneth
Arrow’s contributions to the Santa Fe Institute and to economics. A paper with the
original title will be published in the associated eponymous conference volume. That
companion paper examines a variety of alternative epidemiological models of expectations
transmission that generate results similar to those of the baseline model presented here.
IamgratefultoJason Harburger, Jennifer Manning, Jirka Slacalek, and Johanna Francis
forexcellent research assistance, to Robert Axtell, William Branch, Carl Christ, William
Dickens, Michael Dotsey, Joshua Epstein, Marvin Goodfriend, Daniel Leigh, Bennett
McCallum, Yash Mehra, Serena Ng, Athanasios Orphanides, Adam Posen, John Roberts,
Martin Sommer, and Alexander Wolman for valuable feedback, and to Richard Kwok
for guidance to the relevant epidemiology literature. Thanks also to seminar audiences
at Johns Hopkins University, Harvard University, the Center on Social and Economic
Dynamics at the Brookings Institution, the Federal Reserve Bank of Richmond, New
York U n ivers i ty, a nd theUniversityofCyprus for valuable feedback.
The data and econometric programs that generated all of the results in this paper are
available on the author’s website, http://www.econ.jhu.edu/people/carroll.
Department of Economics, The Johns Hopkins University, Baltimore MD 21218-2685.
I. Introduction
Ever since the traditional foundation of macroeconomics by John Maynard
Keynes [1936], economists have understood that macroeconomic outcomes depend
upon expectations. Keynes himself believedthateconomies could experience fluc-
tuations that reflected movements in ‘animal spirits,’ but the basis for most of
today’s macro models was laid in the rational expectations revolution of the 1970s.
Early critics of the rational expectations approach complained that, in the words of
Friedman [1979], such models lacked “a clear outline of the way in which economic
agents derive the knowledge which they then use to formulate expectations,” but
recent criticisms have focused on the difficulty rational expectations models have
in reproducing various features of macroeconomic data like the high persistence of
inflation (Fuhrer and Moore [1995]) and the apparent inexorability of the tradeoff
between inflation and unemployment (Ball [1994)]; Mankiw [2001]). The literature
has consequently begun to explore the implications for macroeconomic dynamics of
various alternative assumptions about expectations formation, most notably models
of learning, see Sargent [1993] or Evans and Honkapohja [2001] for surveys.
Remarkably, however, there has been almost no work testing alternative models
of expectations using actual empirical data on expectations. McCallum’s [2002]
recent survey, for example, does not discuss results from a single paper that exam-
ines empirical expectations data. This is not for lack of data: The University of
Michigan’s Survey Research Center has been collecting information on households’
expectations about inflation, unemployment, economic growth, interest rates, and
other macroeconomic matters for almost 50years,theConference Board has con-
ducted similar monthly surveys of households since the late 1970s, and the Survey
of Professional Forecasters and its antecedents have collected data since the 1960s.
While there has been some work testing (andusually rejecting) the rationality of
these expectations,1aside from an insightful paper by Roberts [1998] and an impres-
sive (and very recent) paper by Branch [2001] there appears to have been essentially
no work proposing and testing positive alternative models for how empirical expec-
tations are formed.2
This paper proposes and tests one such model. Rather than having full un-
derstanding of the ‘true’ macroeconomic model and constantly tracking the latest
statistics to produce their own macroeconomic forecasts, typical people are assumed
to obtain their macroeconomic views from the news media. Furthermore (and im-
portantly), not every person pays close attention to all macroeconomic news; in-
stead, individual people are assumed to absorb the economic content of news stories
probabilistically, so that it may take quitesome time for news of changed macroe-
1SeeCroushore [1998], Thomas [1999], and Mehra [2002] for surveys.
2Theonlyother even tangentially relevant papers I have found were by Fishe and Idson [1990]
who test a model of heterogeneousdemandfor information using two years’ worth of Michigan
Surveydata; a paper by Urich and Wachtel [1984] that tests rationality using survey data on
money supply forecasts; and a paper by Dua and Ray [1992] that models SPF data using an
ARIMA forecastingframework.
1
conomic circumstances to penetrate to all agents in the economy. Finally, the news
media in turn are assumed to report the views of professional forecasters, who may
themselves make rational forecasts. (The structure of the model was inspired by
simple models of disease from the epidemiology literature; see the companion pa-
perCarroll [forthcoming]) for more on the epidemiological foundations of the model
and for a demonstration that more elaborate “epidemiological expectations” models
generate results similar to those of thebaseline model presented here.)
The baseline model provides a simple equation for the evolution of mean expec-
tations that is very similar to an equation proposed in recent papers by Mankiw and
Reis [2001, 2003]. Indeed, the model presented here could be viewed as providing
microfoundations for the Mankiw and Reis equation. Another contribution is the
derivation of a particularly simple specialization of that equation suitable for em-
pirical work; this specialization turns outtoyield an equation like one estimated by
Roberts [1998], for which it can again be regarded as providing a microfoundation.
Finally, the model’s explicit assumption that people derive their expectations from
news reports (and the paper’s specific proposal for how to measure news coverage)
respond to Friedman’s [1979] criticism of the unspecified nature of the expectations
formation mechanism in rational expectations models.
The model is applied to estimate the evolution of inflation expectations and un-
employment expectations from the Michigan Survey of Consumers. For inflation,
the typical household is estimated to update expectations roughly once a year, while
unemployment expectations appear to be updated slightly more frequently. Fur-
thermore, in a horserace between a version of the model where people update their
expectations either to the rational forward-looking forecast or to the most recently
reported past statistics (the ‘adaptive expectations’ model), the data strongly prefer
the forward-looking version of the model. Thus, the results can be interpreted as re-
flecting a plausible middle ground between fully rational expectations and adaptive
expectations.
Afinal section briefly comments on the relationship between this model and
some of the relevant existing empirical literature, with particular emphasis on the
relationship of the model to sticky-price models and the model’s implications for
the relationship between credibility and monetary policy. The implications of the
model for macroeconomic dynamics are notaddressed here, because the papers by
Mankiw and Reis [2001, 2003] and Roberts [1995, 1997] address those questions and
are directly applicable. Mankiw and Reis show that their model can explain many
phenomena that are unexplained by fully rational models, including why disinfla-
tions are inevitably contractionary; why monetary policy affects the economy with
considerable lags; why rapid economic growth leads to rising inflation; and why pro-
ductivity slowdowns are associated with a rise in the natural rate of unemployment.
The ability to solve all of these puzzles seems a large dividend in exchange for the
small price of relaxing the assumption that all agents’ expectations are fully rational
(in the sense required by typical rational expectations models) at every instant.
2
II. The Model
Consider a world where most people form their expectations about future inflation
by reading newspaper articles. Imagine for the moment that every inflation article
contains a complete forecast of the inflation rate for all future quarters, and suppose
(again momentarily) that any person who reads such an article can subsequently
recall the entire forecast.
Assume that not everybody reads every newspaper article on inflation. Instead,
in any given period each individual faces a constant probability λof encounter-
ing and absorbing the contents of an article on inflation. Individuals who do not
encounter an article simply continue to believe the lastforecast they read about.
Thus, the framework is mathematically similar to the Calvo [1983] model of sticky
prices in which firms change their prices with probability p.
Call πt+1 the inflation rate between quarter tand quarter t+1,
πt+1 =log(pt+1 )log(pt),
where ptis the aggregate price index in period t.Ifwedefine Mtas the operator
that yields the population-mean value of inflation expectations at time tand denote
the Newspaper forecast printed in quarter tfor inflation in quarter stas Nt[πs],
we have that3
Mt[πt+1]=λNt[πt+1 ]+(1λ){λNt1[πt+1]+(1λ)(λNt2[πt+1]+...)}.(1)
The derivation of this equation is as follows. In period tafractionλof the
population will have absorbed the current-period newspaper forecast for the next
quarter, Nt[πt+1]. Fraction (1 λ)ofthepopulation retains the views they held in
period t1ofperiodt+1sinflation rate. Those period-t1viewsin turn can be
decomposed into a fraction λof people who encountered an article in period t1
and obtained the newspaper forecast of period t+1sforecast, Nt1[πt+1], and a
fraction (1 λ)whoretained their period-t2viewsabout the inflation forecast
in period t+1. Recursion leads to the remainder of the equation.
This expression for inflation expectations is identical to the one proposed by
Mankiw and Reis [2001, 2003], except that in their framework updating agents
compute their own forecasts under the usualassumptions of rational expectations.
Mankiw and Reis motivate their assumption that forecasts are updated only occa-
sionally by arguing that there may be costs to obtaining or processing information.
It is undoubtedly true that developing a reasonably rational quarter-by-quarter fore-
cast of inflation arbitrarily far into the future would be a very costly enterprise for
atypicalperson (for example, it might require obtaining an economics Ph.D. first!).
But Mankiw and Reis do not provide any formal model of information processing
3Here we are assuming that all newspapers report the same forecast for inflation; see Car-
roll [forthcoming] for a version that allows for the possibility that different newspapers print
different forecasts; that paper shows that results in such a model are similar to those presented
here.
3
costs that leads to their specification, and indeed it seems likely that a formal model
of processing costs might imply an updating process quite different from the Poisson
process Mankiw and Reis assume.4
The model proposed above can be regarded as a microfoundation for the Mankiw
and Reis equation (1). Its value as a microfoundation is illustrated in the usual way:
it provides additional testable implications that do not follow directly from the ag-
gregate specification. In particular, the baseline model implies that in periods when
there are more news stories on inflation, the speed of updating should be faster, an
implication that is borne out in the empirical work below. It also provides impli-
cations for the analysis of the underlying micro data from the Michigan survey.
In particular, Souleles [forthcoming] finds highly statistically significant differences
across demographic groups in macroeconomic forecasts; the model suggests exam-
ining whether those differences can be explained by information on demographic
differences in readership rates of newspapers, or more general data on differences in
the extent to which different groups pay attention to economic matters.
Of course, real newspaper articles do not contain a quarter-by-quarter forecast
of the inflation rate into the infinite future as assumed in the derivation of (1), and
even if they did it is very unlikely that a typical person would be able to remember
the detailed pattern of inflation rates far into the future. Furthermore, even if both
of these assumptions were true, equation (1) wound not be testable in its current
form because the available survey data report only households’ expectations about
inflation rates over the next year. In order to derive implications from the model
that are testable with these data, it turns out to be necessary to impose some
structure on households’ implicit views about the inflation process.
Suppose people believe that at any given time the economy has an underly-
ing “fundamental” inflation rate. Furthermore, suppose they believe that future
changes in the fundamental rate are unforecastable; that is, beyond the next period
the fundamental rate follows a random walk. Finally, assume that people believe
that the actual inflation rate in a given quarter is equal to that period’s fundamental
rate plus an error term twhich reflects unforecastable transitory inflation shocks
(reflected in the ‘special factors’ that newspaper inflation stories often emphasize).
Thus, the typical person believes that the inflation process is captured by
πt=πf
t+t
(2)
πf
t+1 =πf
t+ηt+1,(3)
.
.
..
.
.
where tis a transitory shock to the inflation rate in period twhile ηtis the per-
manent innovation in the fundamental inflation rate πf
tin period t.Nowassume
that consumers believe that values of ηbeyond period t+1, and values of beyond
period t,areunforecastable white noise variables; that is, future changes in the
4See Sims [2001] for a model grounded in information theory that provides a formal model of
decisionmaking under information-processing constraints.
4
fundamental inflation rate are unforecastable, and transitory shocks are expected
to go away.5
Before proceeding it is worth considering whether this is a plausible view of
the inflation process; we would not want to assume that people believe something
patently absurd. However, the near-unit-root feature of the inflation rate in the
post-1959 period is well known to inflation researchers; some authors find that a
unit root can be rejected for some measures of inflation over some time periods, but
it seems fair to say that the conventional wisdom is that at least since the late 1950s
inflation is ‘close’ to a unit root process. See Barsky [1987] for a more complete
analysis, or Ball [2000] for a more recent treatment.
Note that the unit root (or near unit root) in inflation does not imply that future
inflation rates are totally unpredictable, only that the history of inflation by itself is
not very useful in forecasting future inflation changes (beyond the disappearance of
the transitory component of the current period’s shock). This does not exclude the
possibility that current and lagged values of other variables might have predictive
power. Thus, this view of the inflation rate is not necessarily in conflict with
the vast and venerable literature showing that other variables (most notably the
unemployment rate) do have considerable predictive power for the inflation rate
(see Staiger, Stock, and Watson [2001] for a recent treatment).
If we were to assume that households were rational and made their own inflation
forecasts solely based on observed past inflation under the assumption of an inflation
process like (2)-(3), then the rational forecast would be a geometrically declining
weighted average of past inflation realizations; in this case rational expectations
would be identical to adaptive expectations (Muth [1960]). However, we will assume
that households believe that experts have some ability to directly estimate the past
and present values of through period tand ηthrough period t+1 (through deeper
knowledge of how the economy works, or perhaps some private information); thus
households can rationally believe that a forecast from a professional forecaster is
more accurate than a simple adaptively rational forecast that they could construct
themselves.
Suppose now that rather than containing a forecast for the entire quarter-by-
quarter future history of the inflation rate, newspaper articles simply contain a
forecast of the inflation rate over the next year. The next step is to figure out how
such a one-year forecast for inflation can be integrated into some modified version
of equation (1). To capture this, we must introduce a bit more notation. Define πs,t
as the inflation rate between periods sand t,converted to an annual rate. Thus,
for example, in quarterly data we can define the inflation rate for quarter t+1at
an annual rate as
πt,t+1 =4(logpt+1 log pt)
=4πt+1,
5Note that we are allowing people to have some idea about how next quarter’s fundamental
rate may differ from the current quarter’s fundamental rate, because we did not impose that
consumers’ expectations of ηt+1 must equal zero.
5
where the factor of four is required to convert the quarterly price change to an
annual rate.
Our hypothetical person’s view is that the true ex-post inflation rate over the
next year will be given by
πt,t+4 =πt+1 +πt+2 +πt+3 +πt+4
(4)
=πf
t+1 +t+1 +πf
t+2 +t+2 +πf
t+3 +t+3 +πf
t+4 +t+4
=πf
t+1 +t+1 +πf
t+1 +ηt+2 +t+2 +πf
t+1 +ηt+2 +ηt+3 +t+3 +
πf
t+1 +ηt+2 +ηt+3 +ηt+4 +t+4.
Define Ft[s]astheagent’s forecast (expectation) as of date tof s,foran agent
who updates his views from a news report in period t.Usingthis notation, the
assumptions made earlier about the stochastic processes for and ηimply that
Ft[t+n]=Ft[ηt+n+1]=0(5)
for all n>0. Applying the Ftoperator to both sides of (4) reveals that the
person’s forecast of the inflation rate over the next year is simply equal to four
times his forecast of the fundamental inflation rate for next quarter:
Ft[πt,t+4]=4Ft[πf
t+1]
=Ft[πf
t,t+1].
Now for an important conclusion: If people believe that the forecasts printed
in the newspaper embody the same view of the inflation process laid out in equa-
tions (2)-(3) and (5), then an identical analysis leads to the conclusion that (defining
the ‘newspaper expectations’ operator Ntsimilarly to the consumer’s expectations
operator):
Nt[πt,t+4]=4Nt[πf
t+1]
=Nt[πf
t,t+1].
Thus, from the consumer’s point of viewthenewspaper forecast contains only
asingle important piece of information: a projection of the fundamental inflation
rate over the next year, which the process(2)-(3) implies is the expected funda-
mental rate in all of the year’s constituent quarters and all subsequent quarters as
well. A consumer who reads the newspaper in period t,therefore, will update his
expectations to equal the corresponding newspaper forecasts:
Ft[πt,t+1]=Ft[πt,t+4 ]=Ft[πf
t,t+4 ]=Nt[πf
t,t+4 ]=Nt[πt,t+4].
The rightmost equality holds because the consumer assumes that for n>0,
newspaper has no information about t+nor ηt+n+1,soNt[t+n]=Nt[ηt+n+1 ]=0.
The next equality to the left holds because we assume that when the consumer
6
reads the newspaper his views are updated to the views printed in the newspaper.
The other two equalities similarly hold because Ft[t+n]=Ft[ηt+n+1]=0.
Now note a crucial point: the assumption that changes in the inflation rate
beyond period t+1 areunforecastable means that
Ft1[πt1,t+3]=Ft1[πt,t+4 ](6)
Ft2[πt2,t+2]=Ft2[πt,t+4 ](7)
...
An equation similar to (1) can be written for projections of the inflation rate
over the next year:
Mt[πt,t+4]=λFt[πt,t+4 ]+(1λ){λFt1[πt,t+4 ]+(1λ)(λFt2[πt,t+4]+...)},
and substituting (6)-(7) into this equation and replacing Ftwith Nton the as-
sumption that the newspaper forecasts are the source of updating information, we
obtain
Mt[πt,t+4]=λFt[πt,t+4 ]+(1λ){λFt1[πt1,t+3 ]+(1λ)(...)}
Mt[πt,t+4]=λFt[πt,t+4 ]+(1λ)Mt1[πt1,t+3 ]
Mt[πt,t+4]=λNt[πt,t+4 ]+(1λ)Mt1[πt1,t+3 ].(8)
That is, mean measured inflation expectations for the next year should be a
weighted average between the current ‘rational’ (or newspaper) forecast and last pe-
riod’s mean measured inflation expectations.Thisequationistherefore directly es-
timable, assuming an appropriate proxy for newspaper expectations can be found.6
Readers uncomfortable with the strong assumptions needed to derive (8) may
be happier upon noting that the equation
Mt[πt,t+4]=λNt[πt,t+4]+(1λ)Mt1[πt,t+4](9)
can be derived without any assumptions onconsumersbeliefs about the inflation
process; the difference between (8) and (9) is only in the subscript on the πterm
inside the Mt1operator. The assumptions made above were those necessary to
rigorously obtain Mt1[πt,t+4]=Mt1[πt1,t+3 ]. In practice, however, even a much
more realistic view of the inflation process would likely imply a very high degree of
correlation between the period-t1projection of the inflation rate over the year
beginning in quarter tand the period-t1projection of the inflation rate over the
year beginning in quarter t+1. Indeed, three of out of the four quarters (t+2,t+3,
and t+4)areidentical between the two projections; the only differences between
the two measures would have to spring from the consumer’s period-t1projection
of the difference between the inflation rates in quarters t+1and t+5.
6This equation is basically the same as equation (5) in Roberts [1998], except that Roberts
proposes that the forecast toward which household expectations are moving is the ‘mathematically
rational’ forecast (and he simply proposes the equation without constructing a microfoundation
that might produce it).
7
III. Estimation
Estimating equation (8) requires us to identify data sources for population-mean
inflation expectations and for ‘newspaper’ forecasts of inflation over the next year.
The University of Michigan’s Survey Research Center conducts a monthly survey
of households that is intended to be representative of the population of the United
States. One component of the survey asks households what they expect the inflation
rate to be over the next year.7Iwill directly use the mean inflation forecast from
this survey as my proxy for Mt[πt,t+4].
Identifying the ‘newspaper’ forecast for next-quarter inflation might seem more
problematic, but there is a surprisingly good candidate: The mean four-quarter
inflation forecast from the Survey of Professional Forecasters (henceforth, SPF).
The SPF, currently conducted by the Federal Reserve Bank of Philadelphia and
previously a joint product of the National Bureau of Economic Research and the
American Statistical Association, has collected and summarized forecasts from lead-
ing private forecasting firms since 1968. The survey questionnaire is distributed once
aquarter, just after the middle of the second month of the quarter, and responses
are due within a couple of weeks. The survey asks participants for quarter-by-
quarter forecasts, spanning the current and next five quarters, for a wide variety
of economic variables, including GDP growth, various measures of inflation includ-
ing CPI inflation, and the unemployment rate. For more details on the SPF, see
Croushore [1993].
As noted above, the typical newspaper article on inflation interviews some ‘ex-
perts’ on inflation. The obvious candidates for such experts are the set of people
who forecast the economy for a living, so the pool of interviewees is likely to be
approximately the same group of forecasters whose views are summarized by the
SPF. Hence, it seems reasonable to identify Ntwith the SPF inflation expectations
data.
III.1. Do the Forecasts Forecast?
There is a substantial existing literature ontheforecasting performance of various
measures of inflation expectations including the Michigan Survey, the SPF, and
an informal survey of economists known as the Livingston survey.8Early papers
(Turnovsky [1970], Bryan and Gavin [1986]) claimed to find statistically significant
biases in some of the survey measures, but a recent review by Croushore [1998] shows
7Specifically, households are asked whether they think prices will go up, stay the same, or fall
over the next year. Those who say ‘go up’ (the vast majority) are then asked ‘By about what
percent do you expect prices to go up, on the average, during the next 12 months?’ For more
details on the survey methodology, see Curtin [1996]).
8Unfortunately, the recent survey paper by Thomas [1999] largely neglects the SPF, and focuses
instead mainly on comparisons of the Michigan survey and the Livingston survey. Thomas finds
the median of the Michigan survey to be a better forecaster than its mean, but my model delivers
predictions only for the mean and not for the median, so I neglect themedianforecast in my
empirical work.
8
that some of those results were spurious (due to improper treatment of the data or
econometric problems), and that the results claiming to reject rationality of the SPF
fail to hold up when the sample period is updated to include data for the last ten or
fifteen years. Croushore specifically examines the CPI forecasts of both the Michigan
survey and the SPF, and in a ‘forecast improvement’ exercise finds evidence of
systematic bias in the Michigan survey but not in the SPF. Roberts [1997] also finds
that the Michigan survey’s inflation expectations measure fails standard rationality
tests.
These results are suggestive, but are not precisely targeted on the question we
are interested in: Whether the SPF forecast canbeviewedas‘morerational’ than
the Michigan forecast, and whether there is evidence that information moves from
the SPF forecasters to the Michigan households but not vice versa.
One of the simplest measures of forecast accuracy is the mean squared error. It
is reassuring therefore that over the time period for which both SPF and Michigan
forecasts are available, the ex post MSE of the SPF forecast is about 0.6 while the
MSE for the Michigan survey is almost twice as large, about 1.1. (These are calcu-
lated by taking the square of the difference between the respective mean forecasts
and the actual CPI core inflation over the corresponding time period.)
Anatural next question is whether each of the two surveys has meaningful fore-
casting power for future inflation, and if so, whether the SPF forecast is better. As
afirststep, consider the implications of the near unit root in inflation. High serial
correlation means that future levels of the inflation rate will be highly predictable
based on the recent past history of inflation. Hence it is not very impressive to
find that both surveys have highly significant predictive power for inflation (which
they do), since this result could hold even if the forecasts were both mindless ex-
trapolations of past inflation into the future. The interesting question is whether
the survey forecasts have predictive power for the future inflation rate beyond what
could be predicted based on past inflation data.
To ans wer th is question, Table I presents a regression of the actual inflation rate
over the next year on the Michigan and SPF measures of expected inflation, along
with the most recent annual inflation statistic available at the time the SPF and
Michigan forecasts were made. Both survey measures have highly statistically sig-
nificant predictive power for future inflation even controlling for the inflation rate’s
recent past history, but the SPF measure has substantially more predictive power.
The ‘horserace’ regression results indicate that the Michigan survey measure con-
tains no information that is not also included in the SPF measure, while the SPF
forecast has highly statistically significant predictive power that is not contained
in the Michigan survey.9Note that this result implies that the Michigan forecast
is prima facia irrational (using the usual definition in rational expectations mod-
9Amorestringent test would be whether the surveys can predict the change in the inflation
rate. See Carroll [2001] for this test, which again finds that both surveys have highly significant
predictive power but the SPF has more power. A more extensive evaluation of the forecasting
power of the indexes is provided in the archive of programs that generated all of the results in this
paper, available on the author’s website.
9
els), since the information that forecasters possessed that allowed them to make a
superior forecast was in principle also available to households. Thus, we can un-
ambiguously conclude that the SPF forecast is ‘more rational’ than the Michigan
forecast, and the difference is large in both statistical and economic terms.
Afinal preliminary check is suggested by the structure of the model, in which
expectations are assumed to spread from forecasters to households. This suggests
that the professional forecasts should Granger-cause the household forecasts, but
not vice versa. Table II shows that there is indeed statistical evidence of Granger
causality from the professional forecasts to household forecasts, but no Granger
causality in the opposite direction.
Of course, a finding that the SPF forecast is better than the Michigan fore-
cast does not necessarily imply that the SPF forecast is fully rational. However,
Croushore [1998] reports results for a battery of optimality tests proposed in the
Handbook of Statistics by Diebold and Lopez [1996]; the SPF fails only one of these
tests, the DuFour test, which is actually partly a test of the symmetry of the forecast
errors around zero. Since nothing in rational expectations theory requires errors to
be symmetrically distributed, this test is arguably of less interest than the other
tests. Finally, note that the question of the rationality of the SPF forecasts is logi-
cally separate from the enterprise here, which is to examine whether the Michigan
forecasts can be well modeled as updating toward the SPF forecasts. Rationality of
the SPF forecasts is interesting in and of itself, but is in principle an independent
question that can be addressed separately (as in Croushore [1998]).
III.2. Estimating the Stickiness of Inflation Expectations
We now turn to the main question, which is whether the Michigan survey data can
be reasonably well represented by the model (8).
To provi de a baseline for comparison, the first line of Table III presents results
for the simplest possible model: that the value of the Michigan index Mt[πt,t+4]is
equal toaconstant, α0.Bydefinition the ¯
R2is equal to zero; the standard error
of the estimate is 0.88. The last column of the table is reserved for reporting the
results of various tests that will be conducted as the analysis progresses. By way
of example, the test performed for the benchmark expectations-constant model is
whether the average value of the expectations index is zero, α0=0. Unsurprisingly,
this nonsensical proposition can be rejected with an overwhelming degree of statis-
tical confidence, as indicated by a p-value that says that the probability that the
proposition is true is zero.
We begin to examine the baseline model’s ability to explain the Michigan data
by estimating
Mt[πt,t+4]=α1St[πt,t+4 ]+α2Mt[πt1,t+3 ]+t,(10)
where St[πt,t+4]isthecorresponding SPF forecast. Comparing this to (8) provides
10
the testable restriction that α2=1α1or, equivalently,
α1+α2=1.(11)
Results from the estimation of (10) are presented as equation 1. The point
estimates of α1=0.36 and α2=0.66 suggest that the restriction (11) is very
close to holding true, and the last column presents formal statistical evidence on
the question: It shows that the statisticalsignificance with which the proposition
that α1+α2=1canberejected is only about0.18, so that the restriction is easily
accommodated by the data at the conventional level of significance of 0.05 or greater.
Estimation results when the restriction is imposed in estimation are presented in the
next row of the table, which provides our first unambiguous estimate of the crucial
coefficient: λ=0.27. Note that the Durbin-Watson statistic indicates that there is
no evidence of serial correlation in the residuals (a Q-test yields the same result),
which is impressive because the individual series involved have very high degrees of
serial correlation. This is evidence that the two variables are cointegrated, as would
be expected if one were a distributed lag of the other.
The point estimate λ=0.27 is remarkably close to the value of 0.25 assumed by
Mankiw and Reis [2001, 2003] in their simulation experiments; unsurprisingly, the
last column for equation 2 indicates that the proposition α1=λ=0.25 is easily
accepted by the data. This estimate indicates that in each quarter, only about one
fourth of households have a completely up-to-date forecast of the inflation rate over
the coming year. On the other hand, it also indicates that only about 32 percent
(= (1 0.25)4)ofhouseholdshave inflation expectations that are more than a year
out of date.
As noted above, Roberts [1998] estimated a similar equation, except that his
proposal was that expectations move toward the mathematically rational forecast
of inflation rather than toward the SPF measure. Since the ‘rational’ forecast is
unobservable, he used the actual inflation rate and instrumented using a set of
predetermined instruments, on the usual view that if the instruments are valid
the estimation should yield an unbiased estimate of the coefficient on the true but
unobservable rational forecast. However, this procedure is problematic if there
was anything thatthe‘rational’ forecaster did not know about the structure of the
economy and had to learn from realizations over time; as Roberts acknowledges, it is
also problematic if the structure of the economy changes over time. A final drawback
to this approach is that instrumenting can cause a severe loss of efficiency. Since
the theory proposed here is quite literally that household expectations move toward
the SPF forecast, there is no reason to instrument. In the end, however, Roberts’s
parameter estimates are similar to those obtained here, though with considerably
larger standard errors.
What equation 2 of Table III indicates is that if the data are forced to choose
an α1=1α2they are happy with that restriction, and that a model that imposes
the restriction has a highly statistically significant ability to fit the data. However,
we have not allowed the data to speak to the question of whether there is a better
representation of inflation expectations than (10).
11
The first avenue by which we might wish to let the data reject the specification
is to allow a constant into the equation. Equation 3 presents the results. The last
column indicates that the proposition thattheconstant term is zero can be rejected
at a very high level of statistical significance; on the other hand, the improvement
in fit that comes with a constant is rather modest: The standard error declines
from about 0.43 without the constant to about 0.35 with it. Compared with a raw
standard error for the dependent variable of about 0.88, this improvement in fit is
not very impressive, even if it is statistically significant.
Furthermore, if the model is to be treated as a structural description of the true
process by which inflation expectations areformed,thepresence of a constant term
does not make much sense. It implies, for example, that if both actual inflation and
the rational forecast for inflation were to go to zero forever, people would continue
to expect a positive inflation rate (of a bit under 2 percent) forever. It seems much
more likely that under these circumstances people would eventually learn to expect
an inflation rate of zero. This point can be generalized to show that if the actual
inflation rate and the rational forecast were fixed forever at any constant value,
people’s expectations would never converge to the true, constant inflation rate, but
instead would be perpetually biased (unless the true value happened to be exactly
equal to the unique stable point of the estimated equation).
Amorepalatable explanation for the presence of a constant term is that the
baseline model is not a perfectly accurate description of the process by which in-
formation is transmitted in the economy; inthiscaseestimation of the misspecified
model could result in a spuriously significant coefficient term. For example, Car-
roll [forthcoming] demonstrates that the presence of a significant constant term
could reflect the presence of some social transmission of inflation expectations via
conversations with neighbors (epidemiologically, the disease is locally communica-
ble), in addition to the news-media channel examined here.
Another plausible modification to the model is to allow for the possibility that
some people update their expectations to the most recent past inflation rate rather
than to the SPF forecast of the future inflation rate. Since most news coverage of
inflation is prompted by the release of past inflation statistics (and since the new
past number is often in the headline of the news article) one might argue that it
might seem more likely for people to update their expectations to the past inflation
rate than to a forecast of the future rate. This coresponds to what is usually called
amodelof‘adaptive expectations.’ As noted above, however, if people believe
that the true inflation process is as described in (2)-(3), this adaptive expectations
benchmark is also identical to the limited-information rational expectations fore-
cast (again, remember that we are assuming that households believe professional
forecasters know much more about the inflation process than is contained in its past
history, so updating households could still believe that the SPF forecast is better
than the adaptively rational forecast would be).
We can examine these possibilities by estimating an equation of the form
Mt[πt,t+4]=α1St[πt,t+4 ]+α2Mt1[πt1,t+3 ]+α3Pt[πt5,t1],(12)
12
where Pt[πt5,t1]represents the most recently published annual inflation rate as of
time t.
Results from estimating this equation are presented in the next row of Table III.
The past inflation rate is indeed highly statistically significant - but with a negative
coefficient! The negative coefficient makes no sense, as it implies that a higher
past inflation rate convinces people that the fundamental inflation rate is lower.
The final row of the table, however, shows that when a constant is included in
this regression, the past inflation rate is no longer statistically significant, while
the forecast of the future inflation rate remainshighlystatistically significant. This
seems to indicate that the significance of the past inflation rate is spurious, in
the sense that the past inflation rate is just proxying for the missing constant
term, which we have already acknowledged to be statistically significant. The last
row in the table shows, surprisingly, that even when the SPF forecast is entirely
absent, the lagged inflation rate has no explanatory power for the Michigan survey
after controlling for the survey’s own lagged value; furthermore, the Durbin-Watson
statistic suggests a substantial amount of negative serial correlation in the residuals
of this equation, in contrast with the baseline model.
In sum, it seems fair to say that the simple ‘sticky expectations’ equation (8)
does a remarkably good job of capturing much of the predictable behavior of the
Michigan inflation expectations index.10
III.3. Inflation News Coverage and Inflation Expectations
If we take literally the assumption that people derive their inflation expectations
from news stories, we should expect that when there are more news stories people
should be better informed. Figure I plots an indexoftheintensity of news coverage
of inflation in the New York Times and the Washington Post against the actual
inflation rate;11 unsurprisingly, the intensity of news coverage of inflation was high-
estinthe early 1980s when the actual inflation rate was very high, and inflation
coverage has generally declined since then. Note, however, that the actual inflation
10One further robustness test is presented in Carroll [2001]: Estimation of the model on monthly
rather than quarterly data. This gets around the timing problems caused by the fact that the
Michigan index for a quarter reflects interviews continuously throughout the quarter while the SPF
reflects forecasters’ views at a point in time roughly halfway through the quarter. Estimates of
the monthly λare roughly a third the size of estimates of the quarterly rate, as would be expected
if the quarterly estimates were unbiased.
11The index was constructed as follows. For each newspaper i
{New York Times,Wash i n g ton Post},foreach year tsince 1980 (when the Nexis index of
both newspapers begins), a search was performed for stories that began on the front page of
the newspaper and contained words beginning with the root ‘inflation’ (so that, for example,
‘inflationary’ or ‘inflation-fighting’ would be picked up). For each newspaper, the number of
stories was converted to an index ranging between zero and 1 by dividing the number of stories
in a given year by the maximumn number of inflation stories in any year. Thus, the fact that the
overall index falls to about 0.25 in the last part of the sample indicates that there were about
aquarterasmanyfront-page stories about inflation in this time period as there were at the
maximum.
13
rate fell farther and faster than the news index; evidently, inflation remained an
important story during the period when it was dropping rapidly.
The bottom panel of Figure I plots the SPF and Michigan forecasts since the
third quarter of 1981 when the SPF first began to include CPI inflation. One
striking feature of the figure is that during the high-news-coverage period of the
early 1980s, the size of the gap between the SPF forecast and the Michigan forecast
is distinctly smaller than the gap in the later period when there was less news
coverage of inflation.
Aformalstatistical test of whether greater news coverage is associated with
‘more rational’ household forecasts (in the sense of forecasts that are closer to the
SPF forecast) can be constructed as follows. Defining the square of the gap between
the Michigan and SPF forecasts as GAPSQt=(MtSt)2,anddefining the inflation
index as NEWSt,wecanestimate the simple OLS regression equation
GAPSQt=α0+α1NEWSt.(13)
Table IV presents the results. Estimated over the entire sample from 1981q3 to
2000q2 the regression finds a negative relationship that is statistically significant
at the 5 percent level after correcting for serial correlation. The second row shows
that that if the first year of the SPF CPI forecasts is excluded the negative rela-
tionship is much stronger and statistically significant at better than the 1 percent
level; however, aside from the possibilitythat the first few SPF CPI forecasts were
problematic in some way, there seems to be little reason to exclude the first year of
SPF data.
The finding that household inflation forecasts are better when there is more
news coverage is an indirect implication of the model under the assumption that
absorption of the SPF forecast is more likely when there is more inflation cov-
erage. The proposition that the absorption rate is higher when there are more
news stories can also be tested directly. Table V presents estimation results com-
paring the absorption rate estimated during periods when there is more news
coverage than average (NEWSt>mean(NEWS)) and less coverage than average
(NEWSt<mean(NEWS)). The estimate of λis almost 0.7 during periods of inten-
sive news coverage, but only about 0.2 during periods of less intense coverage; an
F-test indicates that this difference in coefficients is statistically significant at the 5
percent level (and nearly at the 1 percent level).
There are several strands of the existing literature that deserve comment at this
point. In two important recent papers, Akerlof, Dickens, and Perry [1996, 2000]
have proposed a model in which workers do not bother to inform themselves about
the inflation rate unless inflation gets high enough that ignorance would become
costly. Since periods of high news coverage have coincided with periods of high
inflation, this model is obviously consistent with the finding that mean inflation
expectations aremorerational during periods of high coverage. Indeed, in a way
the ADP models are deeper than the one proposed here, because they provide an
explanation for the intensity of news coverage which is taken as exogenous here:
14
The news media write more stories on inflation in periods when workers are more
interested in the topic.
These results can also be viewed as somewhat similar to some findings by
Roberts [1998], who estimates a model like (8), performs a sample split, and finds
the speed of adjustment parameter much larger in the post-1976 period than in the
pre-76 era. He interprets this as bad news for the model. However, the pre-76 era
was one of much more stable inflation (until the last years) than the post-76 era,
so the finding of a higher coefficient in the later years is very much in the spirit of
the tests performed above, and is therefore consistent with the interpretation of the
model proposed here.
IV. Unemployment Expectations
If the model of expectations proposed here is to be generally useful to macroe-
conomists, it will need to apply to other variables in addition to inflation. Another
potential candidate is unemployment expectations; in previous work (Carroll [1992],
Carroll and Dunn [1997]) I have found unemployment expectations to be a powerful
predictor of household spending decisions, and since household spending accounts
for two thirds of GDP, understanding the dynamics of unemployment expectations
(and any deviations from rationality) should have considerable direct interest.
Unfortunately, however, the Michigan survey’s question on unemployment does
not ask households to name a specific figureforthefuture unemployment rate; in-
stead, households are asked whether they expect the unemployment rate to rise, stay
the same, or fall over the next year. Traditionally, the answers to these questions
are converted into an index by subtracting the “fall” from the “rise” proportion.
This diffusion index can then be converted into a forecast of the change in the un-
employment rate by using the predicted value from a regression of the actual change
in unemployment on the predicted change.
That is, the regression
¯
Ut,t+4 ¯
Ut4,t =γ0+γ1MU
t
(14)
is estimated, where ¯
Ut,t+4 is the average unemployment rate over the next year
and ¯
Ut4,t is the unemployment rate over the year to the present, and MU
tis the
Michigan index of unemployment expectations. With the estimated {ˆγ0,ˆγ1}in hand
aforecast of next year’s unemployment rate can be constructed from
ˆ
¯
Ut,t+4 γ0γ1MU
t+¯
Ut4,t.(15)
When (14) is estimated, the coefficient on MU
tis has a t-statistic of over 8,
even after correcting for serial correlation. However, in a horserace regression of
the actual change in unemployment on the Michigan diffusion index and the SPF
forecast of the change in unemployment, the Michigan forecast has no predictive
power. Thus, as with inflation, it appears that on average people have considerable
15
information about how the unemployment rate is likely to change, but forecasters
know a lot more than households do.
Tabl e VI pre sents a set of regression results for the household unemployment
forecast that is essentially identical to the tests performed in Table III for inflation
expectations.
The point estimate of the speed of adjustment parameter in row 3 is α1=0.31;
the test reported in the last column of that row indicates that this is statistically
indistinguishable from the estimate of λ=0.25 obtained for inflation expectations.
In most respects, in fact, the model performs even better in explaining unemploy-
ment expectations than in explaining inflation expectations. For example, row 3
indicates that the equation does not particularly want a constant term in it, while
row 4 finds that the lagged level of the unemployment rate has no predictive power
for current expectations even when a constant is excluded.
Nonetheless, this evidence should be considered with some caution. The process
of constructing the forecast for the average future level of the unemployment rate,
while apparently reasonable, may be econometrically and conceptually problem-
atic. In particular, this method assumes that the amount by which unemployment
is expected to change on average is related to the proportion of people who expect
unemployment to rise or fall; in fact, there is no necessary linear relationship be-
tween these two quantities. Other econometric difficulties may come from the use of
constructed variables on both the left and right hand sides of the equation. I view
this model of unemployment expectations merely as secondary supporting evidence
for the expectations modeling strategy pursued here, and therefore am not inclined
to pursue these conceptual and econometricproblemsfurther, though they might
be worth pursuing in later work.
V. Discussion and Relationship to Existing
Literature
Apotential criticism of this paper might be that expectations of households are
unimportant for macroeconomic outcomes; instead, perhaps what matters are ex-
pectations of experts, which may be rational in the traditional sense. This is not a
plausible criticism with respect to unemployment expectations, given the powerful
influence that households’ unemploymentexpectations have on household spend-
ing (Carroll and Dunn [1997]); households’ consumption decisions surely depend
on their own views rather than the views ofothers. In the case of inflation expec-
tations, whether households’ expectations are important presumably depends on
whether sluggish household expectations are partly or largely responsible for the
costly nature of disinflations. This seems a good guess, since credible preannounced
disinflations should be costless (or nearly so) in an economy in which all agents have
rational expectations (Ball [1994)]). It seems likely that a good part of the influence
of household expectations on inflation comes through a labor market channel. Stan-
dard models of unemployment, either in the search literature or the efficiency wage
16
literature, almost always rely upon an assumption that households’ labor supply
decisions are made by judging the appeal of available or expected real wage offers.
It is an empirical fact that wage contractsareusually written in nominal terms, so
these models of cyclical and structural unemployment entail an implicit assumption
that households can translate nominal wage offers into real ones, which requires
them to have expectations about inflation. Since wages are around two thirds of
business costs, if households’ inflation expectations affect nominal wage outcomes
they must affect firms’ pricing decisions through the usual ‘wage-push’ channel.
The potential importance of household expectations provides a new perspective
on the ongoing debate about the importance of ‘credibility’ in monetary policy.
Credibility has usually been thought of in terms of the beliefs of policy experts
andprivate forecasters; for example, an extensive recent treatment in Bernanke et.
al. [1999] judges credibility of inflation targeting regimes by examining how quickly
professional forecasts converge to the stated target range. Indeed, some central
banks (such as the Bank of England and the Bank of Israel) have begun to officially
look at surveys of forecasters as well as yields on inflation indexed bonds as measures
of such “expert” opinion. However, empiricaltests of whether credibility matters for
monetary policy have produced mixed results; see, e.g., Posen [1995, 1998] or Debelle
and Fischer [1994], and for an insider’s perspective and an excellent summary of
the literature see Blinder [1998]. The results above, however, indicate that there
are substantial gaps between beliefs of forecasters and of households, so credibility
among experts may not be sufficient to achieve a desired inflationary outcome;
the views of the experts need to be communicated effectively to the population to
become effective.
In many cases the model is likely to yield similar, though not identical, conclu-
sions to those obtained from models with price stickiness. Consider, for example,
the finding of Ball, Mankiw, and Romer [1988] that the Phillips curve is steeper
when inflation is higher, which they attribute to a reduction in price stickiness at
high inflation rates (a further justification of such effects can be found in the recent
paper by Dotsey, King, and Wolman [1999]). If the newsworthiness of inflation fore-
casts depends on the level of inflation and λreflects the intensity of news coverage,
then very similar implications could be derived in this model. However, the two
interpretations could be distinguished if newsworthiness is related to the change in
inflation (as figure I suggests).
Arelated question is why it appears to be easier to end high inflations than mod-
erate ones (Sargent [1982, 1983]): Perhaps the attention of the population tends to
be intensely focused on government inflation-fighting policies during hyperinflations
(so λ=1andthemodel collapses to rational expectations), while attention may be
focused on other matters during attempts to end moderate inflations. Ball [1994)]
showsthat quicker disinflations seem to entail smaller sacrifices of output; again,
this could reflect the fact that the policies needed to achieve a quick disinflation are
more dramatic, and therefore more newsworthy, than in a gradualist approach. One
wayoftesting these ideas for more recent episodes would be to construct indices
of news coverage of inflation like those presented above for other countries during
17
disinflationary episodes.
Of course, the real world presumably combines some degree of price stickiness
and a degree of expectational stickiness. The results in Ball [1995] showing strong
interactions between credibility and price stickiness suggest that a model that com-
bines sticky expectations and sticky prices might generate results different from the
results obtainable with either feature alone; this would also be an interesting topic
for future research.
VI. Conclusions
Given the consensus among economists that macroeconomic outcomes depend criti-
cally on agents’ expectations, it is surprising that there has been very little effort to
test positive models of expectations usingthelargebodyofempirical expectations
data available from the Michigan Survey and the Conference Board.
This paper shows that a very simple model in which the typical household’s
expectations are updated probabilistically toward the views of professional fore-
casters does a good job of capturing much of the variation in the Michigan Survey’s
measures of inflation and unemployment expectations. In addition to fitting these
data, the model can be interpreted as providing microfoundations for the aggregate
expectations equation postulated recently by Mankiw and Reis [2001, 2003] and ear-
lier by Roberts [1998]. As those papers show, macroeconomic dynamics are more
plausible in a variety of dimensions, including the tradeoff between inflation and
unemployment, the reaction of the economy to monetary shocks, and the relation-
ship between productivity growth and unemployment, when expectations deviate
in this way from the rational expectations benchmark.
There are many directions in which research could fruitfully proceed from here.
First, the Michigan and Conference Board surveys contain many other expectational
variables that could be studied to see whether the specification proposed here is
widely applicable. Second, the model could be tested at the micro level using the
raw household-level data from the surveys. (One approach would be to extend
the model of Branch [2001], in which individuals choose among various alternative
predictors, to include the SPF forecast among the competing predictors). Third,
the implications of more sophisticated models of the spread of expectations in the
population can be examined (see Carroll [forthcoming] for a start). And much more
work remains to be done to investigate the empirical and theoretical properties of
macroeconomic models in which expectations are formed in this way.
Finally, it is clear that in order for this framework to be a complete and general
purpose tool, it will be necessary to develop a theory that explains the variations in
the absorption parameter λover time. For present purposes it was enough to show
that λis related to the intensity of news coverage, but that only pushes the prob-
lem one step back, to the need for a model of the extent of news coverage. Possibly
the approach offered in a recent paper by Sims [2001] could help; Sims examines
models of ‘rational inattention’ which imply that an agent with limited information
18
processing capacity should optimally ignore most macroeconomic data. The diffi-
culty with applying the Sims framework to consumers directly is that solving the
problem of deciding what to ignore is even harder than solving the full-information
rational expectations model. However, if the news media were viewed as the agents
who solve the information compression problem (since the information stream they
can convey is obviously limited), the Sims framework might provide a useful formal
model of how the news media go about deciding how much coverage to give to
economic matters.
The Johns Hopkins University
19
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and the U.S. NAIRU in the 1990s,” NBER Working Paper Number 8320.
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23
TABL E I
Forecasting Power Of Michigan and SPF Indexes
Dependent Variable: πt,t+4
Constant πt5,t1Mt[πt,t+4]St[πt,t+4 ]DWStat
¯
R2
0.070 0.083 0.732 0.46 0.52
(0.526) (0.145) (0.204)∗∗∗
0.480 0.220 1.036 0.52 0.64
(0.323) (0.153) (0.161)∗∗∗
0.437 0.219 0.027 1.015 0.52 0.64
(0.545) (0.152) (0.261) (0.241)∗∗∗
Mt[πt,t+4]istheperiod-tmean of the Michigan survey measure of household expectations for
inflation over the next year. St[πt,t+4]istheperiod-tmean of the Survey of Professional Forecasters
forecast of the inflation rate over the next year. πt5,t1is the inflation rate between quarter t5
and t1, the most recently available annual data available at time t.Thecolumnlabelled DW
Stat reports the Durbin-Watson statistic; similar results are obtained using the Box-Ljung Q
statistic. All equations were estimated over the 1981q3 to 2000q2 period. Errors are corrected for
heteroskedasticity and autocorrelation using a Newey-West [1987] procedure (a Bartlett modified
kernel) with 4 lags. Results were not sensitive to alternative lag length choices. One, two, and
three stars indicate, respectively, statisticalsignificance at the 10, 5, and 1 percent levels.
TABL E I I
Granger Causality Between Michigan and SPF Surveys
Independent variables
Eqn Dependent Sum of coefficients on Durbin-
number variable Constant St1..St8Mt1..Mt8Wat so n ¯
R2
1St0.53 1.13 0.25 2.02 0.87
(0.14) (0.00)∗∗∗ (0.32)
2Mt1.27 0.58 0.18 1.96 0.71
(0.01)∗∗∗ (0.05)∗∗ (0.01)∗∗∗
Mtis the Michigan household survey measure of mean inflation expectations in quarter t,Stis
the Survey of Professional Forecasters mean inflation forecast. p-values for exclusion tests are
in parentheses below coefficient estimates. All equations are estimated over the period 1981q3
to 2000q2 for which both Michigan and SPF inflation forecasts are available. Box-Ljung Q-tests
found no evidence of serial correlation in the residuals, so standard errors are not corrected for
serial correlation; a serial correlation correction does not change results. One, two, and three stars
indicate, respectively, statistical significance at the 10, 5, and 1 percent levels.
24
TABL E III
Estimating and Testing the Baseline Model
Estimating Equation Mt[πt,t+4]=α0+α1St[πt,t+4]+α2Mt1[πt1,t+3]+α3Pt[πt5,t1]+t
Durbin- Test
Eqn α0α1α2α3¯
R2Watso n StdErr p-value
Memo: 4.34 0.00 0.29 0.88 α0=0
(0.19)∗∗∗ 0.000
10.36 0.66 0.76 1.97 0.43 α1+α2=1
(0.09)∗∗∗ (0.08)∗∗∗ 0.178
20.27 0.73 0.76 2.12 0.43 α1=0.25
(0.07)∗∗∗ (0.07)∗∗∗ 0.724
31.22 0.51 0.26 0.84 1.74 0.35 α0=0
(0.20)∗∗∗ (0.08)∗∗∗ (0.09)∗∗∗ 0.000
40.49 0.67 0.15 0.79 2.26 0.40 α1+α2+α3=1
(0.09)∗∗∗ (0.08)∗∗∗ (0.05)∗∗∗ 0.199
51.26 0.50 0.25 0.01 0.84 1.72 0.35 α3=0
(0.27)∗∗∗ (0.08)∗∗∗ (0.11)∗∗ (0.05) 0.814
61.02 0.04 0.71 2.63 0.47 α2+α3=1
(0.04)∗∗∗ (0.05) 0.239
Mt[πt,t+4]istheMichigan household survey measure of mean inflation expectations in quarter
t,St[πt,t+4]istheSurvey of Professional Forecasters meaninflation forecast over the next year;
Pt[πt5,t1]isthe published inflation rate forthe most recent one-year period. All equations are
estimated over the period 1981q3 to 2000q2 for which both Michigan and SPF inflation forecasts
are available. All standard errors are corrected for heteroskedasticity and serial correlation using a
Newey-West procedure (a Bartlett kernel) with four lags. Results are not sensitive to the choice of
lags. Box-Ljung tests found no evidence of serial correlation for equations 1-6; the Durbin-Watson
is reported because it may be more familiar to most readers.
25
TABL E I V
Household Inflation Expectations Are More Accurate When There Is More News Coverage
Equation Estimated: GAPSQt=α0+α1NEWSt
Sample α0α1D-W Stat ¯
R2
1981q3-2000q2 0.94 1.03 1.01 0.08
(0.26)∗∗∗ (0.50)∗∗
1982q3-2000q2 1.22 1.72 1.08 0.14
(0.25)∗∗∗ (0.46)∗∗∗
GAPSQ is the square of the difference between theMichigan and SPF inflation forecasts. NEWS
is an index of the intensity of news coverage of inflation in the New York Times and the Wash-
ington Post from 1981 to 2000. All standard errors are corrected for heteroskedasticity and serial
correlation using a Newey-West [1987] procedure with four lags. Results are not sensitive to the
choice of lags. {***,**,*}={1percent, 5 percent, 10 percent}significance.
TABL E V
Updating Speed Is Faster When There Is More News Coverage
Durbin- Q-Test
Eqn Sample λWatso n p-value
1Allobs0.273 2.12 0.971
(0.066)∗∗∗
2NEWS
t>mean(NEWS) 0.699 1.57 0.216
(0.176)∗∗∗
3NEWS
t<mean(NEWS) 0.210 1.93 0.451
(0.077)∗∗
The equation is estimated in the form MtMt1=λ(StMt1)whichimposesthecondition
λ+(1λ)=1. Allstandard errors are corrected for heteroskedasticity and serial correlation
usingaNewey-West [1987] procedure with four lags. Results are not sensitive to the choice of
lags. {***,**,*}={1percent, 5 percent, 10 percent}significance.
26
TABL E V I
Estimating and Testing the Baseline Model for Unemployment
Estimating Equation Mt[Ut,t+4]=α0+α1St[Ut,t+4]+α2Mt1[Ut1,t+3 ]+α3Pt[Ut5,t1]+t
Durbin- Standard Test
Eqn α0α1α2α3¯
R2Watso n error p-value
Memo: 6.38 0.00 0.08 1.29 α0=0
(0.29)∗∗∗ 0.000
10.32 0.68 0.94 1.73 0.32 α1+α2=1
(0.07)∗∗∗ (0.07)∗∗∗ 0.111
20.31 0.69 0.94 1.72 0.32 α1=0.25
(0.07)∗∗∗ (0.07)∗∗∗ 0.375
30.03 0.32 0.68 0.94 1.74 0.32 α0=0
(0.18) (0.07)∗∗∗ (0.07)∗∗∗ 0.847
40.32 0.67 0.01 0.94 1.73 0.33 α1+α2+α3=1
(0.07)∗∗∗ (0.09)∗∗∗ (0.05) 0.112
50.04 0.32 0.67 0.01 0.94 1.72 0.33 α3=0
(0.18) (0.07)∗∗∗ (0.09)∗∗∗ (0.06) 0.855
Mt[Ut,t+4]isaforecast of the average unemployment rate over the next year in quarter tderived as
described in the text from the Michigan survey measure of unemployment expectations; St[Ut,t+4 ]
is the mean of the SPF unemployment forecast over the next four quarters; Pt[Ut5,t1]isthe
published unemployment rate for the most recent one-year period. All equations are estimated
over the period 1978q1 to 2000q2 for which both Michigan and SPF unemployment forecasts are
available. All standard errors are corrected for heteroskedasticity and serial correlation using a
Newey-West procedure with four lags. Results are not sensitive to the choice of lags.
27
FIGURE I
Inflation Versus News Stories
CPI Inflation
Inflation Articles Index
1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001
0.0
1.6
3.2
4.8
6.4
8.0
9.6
11.2
0.00
0.25
0.50
0.75
1.00
Inflation
News Stories
28
FIGURE II
Michigan Versus SPF Forecasts
Inflation Forecast
1981 1983 1985 1987 1989 1991 1993 1995 1997 1999 2001
2
3
4
5
6
7
8Michigan Forecast
SPF Forecast
29
... That is, it lacks a micro foundation. Carroll (2003) provided an answer to this question by formulating and testing a model where individuals read newspaper articles about economic forecasts, but "only occasionally pay attention to news reports" (Carroll 2003, p. 269). They are inattentive and consequently error-prone, a trait that generates "stickyness" in aggregate expectations. ...
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... These findings have held up over time (Dawes et al., 1989), and although they apply to experts, there is little reason to think that lay respondents would perform any better. In fact, professional forecasts of inflation consistently outperform those of lay households (Carroll, 2003;Verbrugge and Zaman, 2021). ...
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Using novel survey evidence on consumer inflation expectations disaggregated by personal consumption expenditure (PCE) categories, we document the paradox that consumers' aggregate inflation expectations usually exceed any individual category expectation. We explore procedures for aggregating category inflation expectations, and find that the inconsistency between aggregate and aggregated inflation expectations rises with subjective uncertainty and is systematically related to socioeconomic characteristics. Overall, our results are inconsistent with the notion that consumers' aggregate inflation expectations comprise an expenditure-weighted sum of category beliefs. Moreover, aggregated inflation expectations explain a greater share of planned consumer spending than aggregate inflation expectations.
... The obvious disadvantages of the latter, that dominates in macroeconomics for over fifty years, initiated the intensive search for more realistic models of expectations formation. In the nineties of the 20th century bounded rationality hypotheses were proposed with their multiple variants of adaptive learning (Sargent, 1993), sticky information (Mankiw & Reis, 2002), and epidemiological model (Carroll, 2003). Due to the limited length of this paper, we refrain from their detailed presentation. ...
... A blooming field of research is dealing with how people actually form inflation expectations (Andre et al. 2022;Carroll 2003;Coibion et al. 2018;Conrad et al. 2021). Besides personal experience media consumption is a major influence. ...
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