National Bank of Poland December 2005

Warsaw, Poland

Inflation Expectations: Theoretical Models and Empirical Tests

Richard Curtin1*

The University of Michigan data on consumers’ inflation expectations has been

analyzed by a wide range of scholars for nearly fifty years. The empirical evidence has been
mixed about the extent to which inflation expectations are consistent with the rational
expectations hypothesis of traditional economic models or with the bounded rationality
postulate of the newer behavioral models. Even if expectation were rational, judgements
about the costs and benefits of continuously updating inflation expectations may result in
sticky or staggered information flows that may make expectations appear non-rational.
Importantly, sticky expectations, like sticky wages and sticky prices, can have a significant
impact on optimal monetary policy. The Michigan data on inflation expectations is used to
test a wide range of hypothesis surrounding these basic issues, utilizing cross-section, panel,
and time-series data. The analysis indicates that there exists considerable heterogeneity in
inflation expectations, that inflation expectations are forward looking, that consumers do not
efficiently utilize all available information, that negative changes in the inflation rate have
about twice the impact as positive changes, that there is evidence of staggered updating, and
that these findings do not result from offsetting errors across demographic groups.

Realism and Relevance

John Muth began his classic article on rational expectations by noting that survey data on
expectations were as accurate as the elaborate models of economists, and he noted that there
were considerable differences of opinion in the cross-sectional survey data (Muth, 1961). His basic
insight was that economic agents form their expectations so that they are essentially the same as
the predictions of the relevant economic theory. The assumption that expectations were formed
rationally was for Muth the natural extension of economic theory which already held that firms
rationally maximize profits and consumers rationally maximize utility. Nonetheless, Muth noted that
rationality was an assumption that could be tested by its systematic comparison with alternative
theories in explaining observed expectations.

Muth’s hypothesis has indeed sparked an enormous amount of research as well as wide
divisions between disciplines in how rationality should be conceptualized and how the hypothesis
should be tested. Economics views rationality in terms of the choices it produces (substantive or
full rationality), whereas other social sciences view rationality in terms of the process that is used
to make choices (procedural or bounded rationality). It was Friedman’s (1953) celebrated essay
on methodology that declared the validity of economic theories to be independent of their
psychological assumptions. Economists have accordingly focused on whether the postulate of

*Research Professor and Director Surveys of Consumers, University of Michigan. E-mail: curtin@umich.edu
unbounded or bounded rationality was the more productive theoretical construct in terms of its
predictive accuracy.

Compared with tests of utility maximization, expectations have the unique advantage that
they could be measured and subjected to empirical tests.2 The rigor of the tests of the rational
expectations hypothesis ranges from tests of bias and predictive accuracy to how efficiently every
possible piece of relevant information was used in forming the expectations. There is a virtual
absence of empirical tests of the assumptions surrounding utility maximization, including tests on
whether agents gather and process the relevant economic information and to use it efficiently to
maximize utility, and whether consumers know all the relevant facts at any given time or if there
exits informational heterogeneity.

There are some economist that take seriously the implicit assumptions that there are
negligible costs associated with collecting and processing all the relevant information and that all
agents know the correct dynamic model. When asked about the stringent assumptions surrounding
utility maximization, economists quickly allow that what those simplifying assumptions lack in
realism they make up for in predictive performance. The lack of such a recognition of Friedman’s
basic methodological points in the discussion of rational expectations is quite amazing.

It should not be surprising that the debate about the rational expectations hypothesis has
continued unabated in the nearly fifty years since Muth first published his theory. Perhaps it is as
Lovell (1986) lamented two decades ago in his review of empirical tests of the rational expectations
hypothesis, “...why should data spoil such a good story.” Indeed, the clear advantage of the rational
expectations hypothesis is its theoretical strength. The hypothesis has proved to be enormously
productive in transforming macroeconomic theory given that the rationality assumption enables the
powerful tools of optimization to systematically expand the depth and breath of economic theories.

While the empirical tests have generally not fully supported the hypothesis, the criteria for
acceptance are rigorous and the lack of evidence is comparable to that found in tests of the full
rationality postulate in many other aspects of economic theory. In contrast, while bounded
rationality has frequently been confirmed in empirical studies, research on bounded rationality has
not led to an integrated theoretical structure that could spark further theoretical advances. Indeed,
the findings attributable to bounded rationality have been generally classified as “anomalies” rather
than being incorporated into mainstream theory. The list of such anomalies includes the impact of
framing, asymmetry of gains and losses, relative reference points, anchoring, and confirmatory bias,
among other findings (Tversky & Kahneman, 1982; Earl, 1990; Thaler, 1991; Thaler, 1992; Rabin,
1998; Rabin & Schrag, 1999). Only recently has there been a concerted effort to incorporate a
more realistic account of expectations into mainstream economic theory rather than relegating them
to anomaly status.

2
Many economists have now reinterpreted Muth’s original hypothesis to apply at the micro rather than an the aggregate level
(Begg, 1982). They reasoned that given that utility maximization is assumed to be true for each individual, why should
rational expectations be exempted from micro testing? Some analysts have even claimed that the only appropriate test of
the rational expectations hypothesis would be based on panel data. Some have also argued that the aggregation involved
in time-series tests result in inconsistent estimates and masks offsetting individual differences (Figlewski and Wachtel, 1983;
Keane and Runkle, 1990).

2
Costs and Benefits of
Rational Expectations

Like most economic phenomena, inflation expectations can be integrated into mainstream
theory by the systematic recognition of the costs and benefits associated with rational expectations.
Rational expectations are costly to form and their benefits are derived from their use in economic
decisions. As long as there is any positive cost involved in collecting and processing information
using the relevant dynamic model, some agents will choose to sometimes hold less accurate
expectations. The terms “sticky information” or “rational inattention” have been used to describe
the impact of costs on the formation process (Mankiw and Reis, 2002; Sims 2003; Bacchetta and
Wincoop, 2005). These theories postulate that rational consumers may find the costs associated
with updating their expectations to exceed the benefits. At any given time some people will find it
worthwhile to incur the costs, especially if that information is critical to a pending decision. Most
of the time, however, rational inattention is the optimal course. Alternatively, agents may base their
expectations on imperfect information, which can be conceptualized as less costly than perfect
information. Whatever the cause, the process creates staggered changes in expectations, whereby
at any given time expectations reflect a combination of current and past information across different
people.

Disagreement across people in their expectations at any given time is taken as an indication
of such a process (Mankiw, Reis and Wolfers, 2004). Some have modeled the disagreements as
the result of factors other than costs, such as an epidemiological process in which “expert opinion”
spreads slowly through a population like the spread of a disease (Carroll, 2003) . Costs can also
be assumed to vary across demographic subgroups, as some encounter lower costs for acquiring
and using information, and other more economically active subgroups derive greater benefits from
updating their expectations more frequently. This interpretation of disagreements or inaccuracies
in expectations stands in contrast to the older and still more common interpretation that the very
existence of differences across demographic subgroups indicate non-rational expectations (Bryan
and Venkatu, 2001; Souleles, 2001).

Staggered changes could be created by a wide range of processes that either encourage
or discourage agents from updating their expectations. A common hypothesis hold that it is due
to asymmetric responses to economic information, with agents updating their expectations much
more quickly in response to bad news about inflation. Akerloff, Dickens and Perry (2001) suggest
that bad economic news is perceived by consumers to contain more potentially relevant information
about their financial situation. The volume of news also matters, especially the volume of bad
news, as well as news that represent a sharp and negative break from the past (Carroll, 2003).
Sims (2003) shows that based on information theory the tone and volume of economic reporting
affects expectations beyond the information contained in the reports. This added impact of news,
however, may be short-lived, usually lasting less than a few months (Doms and Morin, 2004).

It is not clear when the news media creates expectations and when its reporting simply
responds to ongoing changes in expectations. Like any other business, the news media caters to
consumers’ preferences (Hamilton, 2004). For example, large shifts in expectations for future
changes in the unemployment rate were found to change in advance of shifts in media reports
about unemployment (Curtin, 2003).

The same staggered information flows have been hypothesized to result from uncertainty
about the correct structural model of the economy. Since model uncertainty is costly to resolve, it

3
results in less frequent updating of expectations (Branch, 2005). Although the data that indicates
disagreement in expectations is similar to what could be expected to result from model uncertainty,
these two concepts are distinct. More importantly, the prevalence of disagreement may be much
more variable over time than uncertainty.

The models developed to capture the impact of staggered information are similar to
consumption models that incorporate the division between “rule of thumb” and rational consumers.
In this context, the switching models capture the difference between those that update their
expectations regularly and those that base their expectations on pre-existing information. Mankiw
and Reis (2003), Carroll (2003), and Khan and Zhu (2002) estimated that rather than continuously
updating their expectations, most people update their expectations only a few times a year.

Sticky information theories result in differences in inflation expectations across agents.

There are, however, other reasons to expect heterogeneity that represent more fundamental issues.
Conventional economic theory assumes that the same information is available to all agents and the
same models are used to generate expectations about the future. The result is that there is only
one rational expectation at any given time for a given information set. Thus, while staggered
information and model uncertainty may result in heterogeneity of expectations, there is no
theoretical basis for expecting heterogeneity among those that have recently updated their
expectations. The allowance of private information in addition to public and official information to
influence the formation of expectations would provide a theoretical reason for heterogeneity in
expectations. For example, the impact of private information has been found to be pivotal in the
formation of unemployment expectations (Curtin 2003).

Monetary Policy Implications

Of Staggered Information Flows

Whatever the cause, the presence of sticky information is hypothesized to be the key to
understanding dynamics of the macro economy. Sticky information has a long history in research
on forward-looking Phillips curves (Woodford, 2003). The sticky information has ranged from
staggered wage contracts, to staggered pricing models, and to staggered information flows.
Whatever the source, the existence of sticky information indicates the non-neutrality of monetary
policy.

While there is now a widespread belief that monetary policy can influence output and
employment, there is no consensus on the mechanisms that produce the impact. To be sure, if
inflation expectations were fully rational and the central bank was fully committed to price stability,
there would be no impact on output and employment. Non-neutrality derives from non-rationality
in expectations or from a lack of commitment to price stability on the part of the central bank.

The optimal situation is when the central bank enjoys widespread credibility and
expectations are fully rational, allowing the central bank to reduce inflation without any loss in
output or employment. Although central banks differ widely in the credibility they enjoy, even
among those that have the highest credibility economic losses cannot be completely avoided.

When those optimal conditions are not present, expected inflation can become self-fulfilling
due to what has been termed the “expectations trap” (Chari, Christiano and Eichenbaum, 1998;
Albanesi, Chari and Christiano, 2002; Leduc, Sill and Stark, 2003). The enticement into the trap

4
is the higher cost in terms of output and employment that would result following the choices already
made by households and firms in anticipation of higher inflation: consumers typically favor debt
whose repayment will be eroded by higher inflation, and firms typically raise prices in advance to
protect the real value of their profits. These actions would imply relatively larger future losses in
output and employment if the central bank adopted a policy aimed at price stability. Since the
actions already taken by both consumers and firms act to lower the costs of inflation, the central
bank is “trapped” into an accommodative policy that confirms the higher inflation expectations.

While full rationality and a fully committed central bank may seem too much to expect,
Woodford (2005) advanced the notion that the main conclusions for optimal monetary policy also
pertain to the assumption of near-rational expectations. While there is no accepted standard to
judge whether expectations are “near-rational,” the analysis of inflation expectations can help to sort
out the various properties of expectations.

This paper investigates a broad range of these issues, including whether inflation
expectations are backward or forward looking, whether there is any support for the staggered
information hypothesis, the interpretation of disagreement data, and some other methodological
issues. Prior to the analytic sections, the rational expectations model as well as the adaptation
models are defined. The analysis then turns to the analysis of household inflation expectations
collected by the University of Michigan, variously based on cross-section data, panel data, and
times-series data. Finally, the analytic results are discussed along with their implication for
monetary policies.

Theoretical Models of Expectations

Expectations are beliefs about the future. This definition was cited by Plato more than two
thousand years ago, and it remains to this day the generally accepted meaning of the term.3 The
formation of expectations depends on two factors: informational inputs (I) and the model or process
of transforming information into expectations (f). Let the expectation of the inflation rate (Pe) formed
by the ith individual be defined as:

Pt et −1 = f ( I t − 1 )

where the subscript t on Pe indicates the period for which the expectation applies, and the
expectation formed based on the information that was available in a prior period, denoted by et-1.
The two dominant specifications of this equation are the rational expectations hypothesis and the
extrapolative, adaptive, and error learning models, which I will refer to collectively as “adaptive”
expectations.

The format of the appropriate empirical tests of these two models is just as distinctive as
their assumptions about rationality. The adaptive expectations models define what information is
used and how it is used in the formation of expectations, including the availability and cost of
information as well as the capacity of individuals to effectively utilize the information. The empirical

3
Plato wrote that “...each man possesses opinions about the future, which go by the general name of expectations...” (Plato,
Laws 644c, 360 BC).

5
tests were designed to determine whether variations in expectations are related to these
hypothesized factors. In contrast, tests of the rational expectations hypothesis focus on whether
the observed expectations are unbiased future forecasts and whether all of the information was
used efficiently and optimally. In the former case, expectations are analyzed as the dependent
variable, while in the latter case expectations are viewed as an independent variable in the analysis.

This difference makes the comparison of the relative merits of the two models difficult. For
the adaptive expectations models, confirmation essentially entails finding a significant empirical
relationship between expectations and some informational inputs. Confirmation of the rational
expectations hypothesis, in contrast, requires the finding of unbiased and efficient future
predictions. In tests of adaptive expectations, any statistically significant finding is taken as
confirmation even if it accounts for a trivial proportion of the variance, whereas anything short of full
rationality requires the rejection of the rational expectations hypothesis. This asymmetry in the
evaluation of empirical evidence has stunted theoretical developments.

This situation is nowhere more important than in the assessment of the forward-looking
content of expectations. Adaptive expectations models are inherently bound to the past. Aside
from the special case where future outcomes are extrapolations of the past, no method is usually
hypothesized to test the forward-looking content of expectations. Indeed, by their very construction,
adaptive expectations models portray the formation process as a relatively transparent function of
past outcomes where individuals never fully learn from their past errors. Rational expectations
models, in contrast, place their entire emphasis on assessing the forward-looking information, but
do not posit any specific process for the formation of expectations. When empirically rejected, the
rational expectations framework provides no insight into which limitations on rationality proved to
be most important.

Adaptive Expectations. The various adaptive, extrapolative, and error learning models can
be summarized by the following autoregressive distributive lag representation:

Pt e = α + ∑ β j Pt e− j + ∑ γ j Pt − j + ε t
j j

where Pe is inflation expectations, P is the actual inflation rate, j is the lag length, and ε is the error
term, with the i subscript dropped for convenience. Variables other than the inflation rate that are
part of the relevant information could also be included in the equation. Defining the unique
characteristics of the various models involves the specification of coefficients β, γ, and ε.

Perhaps the most basic hypothesis is that expectations essentially represent random
responses to the survey questions, unrelated to either the past realizations of the variable or even
past expectations. In this case, the β, and γ coefficients would be hypothesized to be equal to zero,
so that variations in expectations about its mean (α) are simply equal to the error term.

The pure extrapolative model is obtained by setting the coefficients β equal to zero, so that
expectations solely depend on the lagged inflation rate. The most restricted version of this model
can be characterized as “static expectations,” where expectations simply depend on the most
recent realization. The more general version holds that expectations represent a weighted average
of past realizations. Under the extrapolative hypothesis, the γ coefficients are hypothesized to be
any positive fraction between zero and one.

6
 The adaptive or error learning hypothesis posits that consumers revise their expectations
for the following period based on the error in their expectations in the current period (Fisher 1930,
Cagan 1956, Friedman 1957, Nerlove 1958). In terms of the above equation, this implies that only
one lag of the actual and expectation variables are used, with the coefficient on the difference
between the expected and actual outcomes (the speed of the learning adjustment) hypothesized
as being positive with an upper bound of 1.0. By use of the Koyck (1954) transformation, however,
the adaptive expectations model can be shown to be equivalent to a weighted average of past
realizations.

Another approach has been to utilize error correction models, which postulate equality in
equilibrium between inflation expectations and the inflation rate. The basic error correction model
can be expressed by using one lag of the expectations variable and two lags of the actual inflation
rate, and fixing these coefficients at 1.0 to express the notion that the equilibrium rate of inflation
is equal to its expectation. The error correction equation thus relates the change in expectations
to past changes in the actual inflation rate as well as the error in the prior period’s expectation.

The reliance on information about past changes in inflation is the source of the most
important disadvantage of all adaptive expectations models because systematic prediction errors
result since expectations tend to underestimate (overestimate) the true change whenever the
underlying variable is trending upward (downward). In response to this deficiency, augmented
models have been proposed, which incorporate information on other variables that are assumed
to influence the formation of expectations. The use of this additional information can help to offset
the tendency toward systematic prediction errors.

Rational Expectations. The strong appeal of the rational expectations hypothesis is that
it avoids the bias toward systematic prediction errors by shifting its focus from the variable’s history
to its future realizations. The rational expectations hypothesis equates the expectation with the
expected value of the actual subsequent realization, conditional on all available information (Muth,
1961). Unbiased expectations under the rational expectations hypothesis require that the
coefficients α and β are zero and one, respectively, in the equation:

Pt = α + β Pt et − 1 + ε t
The strong test of rationality also requires that all of the available information has been efficiently
and optimally used in forming the expectation. This involves tests on the statistical properties of the
prediction errors to determine if they are consistent with those stipulated by the hypothesis
(orthogonality, efficiency, consistency, as well as unbiasedness). Tests of this assumption take the
form:
ζ t = α + ∑ β j Pt − j + ∑ γ j Z t − j + ε t

where ζ is the prediction error, the coefficients β and γ are expected to be zero, and the prediction
errors are serially uncorrelated. This expresses the notion that if any of the available information
was systematically related to the prediction errors, the information was not efficiently and optimally
incorporated into the formation of the original expectation.

7
Reification of Economic Data
In Tests of Expectations

Some economists seem to believe the only source of information about the actual inflation
rate is the official announcements by the government’s statistical agency. The assumption that
consumers only utilize official sources of economic information reflects the widespread tendency
toward the reification of economic data—that is, treating conceptual measures as if they had a
concrete existence. All economic data represent estimates of the underlying concepts, and some
price indexes are measured with more error than others. There is no evidence that consumers
revise their inflation expectations each time the government issues new monthly estimates, revises
old figures or revises its measurement methodology. More importantly, aside for those who have
their incomes or pensions indexed to official indexes, theory suggests that consumers will use
whatever measure that best reflects their own expenditures. It would make no sense for consumers
to take into account future prices that they will not face when making decisions.

The recent debate about whether tests on inflation expectations should be based on real
time data or revised data reflects this tendency toward the reification of data (Mehra, 2002;
Croushore and Stark, 1999; Keane and Runcle, 1989; Zarnowitz, 1985). The information set at any
given time is usually assumed to only include past data on the official inflation rate, usually outdated
by at least one month (the official release of U.S. data on the Consumer Price Index (CPI) for any
given month is by the middle of the following month). While economist may condition their forecasts
only on official data, consumers can be expected to actively use all the information available to
them to gauge ongoing changes in price trends. Rather than relying on official information,
consumers more often report and depend on private information.

If anything, consumers suffer from an overload of private information about prices. In

comparison to the official information which has been released once a month in nearly the same
format for decades, private information has increased substantially. The media has been
repeatedly reinvented to provide expanded information, from newspapers, to television, to 24/7
operations of cable news, the internet, and the self-proclaimed experts that now inhabit all media.
More importantly, people gain information on prices in every daily transaction in the marketplace.
This personal collection of information is typically reported by consumers to be the most critical to
the formation of their expectations.

One way of exploring the impact of private versus official information is to compare changes
in expectations with the official release dates. The key analytic issue is how to devise a proxy
measure of the unobserved inflation rate prior to the official announcement. This issue is easy to
solve: the best estimate of the current month’s inflation is the official inflation rate. And the
hypothesis could be easily tested: the current month’s price index should be dominated by last
month’s inflation index for the official information hypothesis to hold, and the current month’s price
index should dominate last month’s official release if private information dominates. As you
probably already know, such a test provides little support for the notion that consumers base their
expectations on the official announcement.

The last issue is which inflation rate is the most appropriate to use to model consumer
expectations? The inflation index most often favored by economists is a core rate that excludes
energy and food prices, and is either based on the consumer price index or the personal
consumption deflator. Consumers generally identify inflation with the overall consumer price index
or personal consumption deflator as they best capture the prices of the goods and services that

8
they actually purchase. This analyses included in this paper focus on changes in the overall
Consumer Price Index (CPI-u).

Data on Inflation Expectations

The University of Michigan has collected data on the inflation expectations of consumers
for more than fifty years. Two questions are now asked of all consumers about expected price
changes: the expected direction of change in prices and the expected extent of change. The
question on the expected direction of change has been asked in a comparable format since 1946,
while the question on the extent of change has been modified several times. In the 1940's and
1950's, the question simply asked whether prices would go up a little or go up a lot; from the 1960's
to the mid 1970's, the question included a series of fixed percentage intervals from which the
respondent was asked to choose; and from the mid 1970's to present, the question simply asked
the percent rate of inflation that the consumer expected. This paper focuses only on the monthly
data collected since 1978 for the open-ended question on inflation expectations.

There is a considerable degree of cross-section as well as time-series variation in

consumers’ responses. The variation in responses is due to a number of factors, including
differences in information and computational capacities, uncertainty about the correct dynamic
model, and measurement errors. These differences are discussed from several perspectives
based on cross-section, time-series, and panel data.

Cross-Section Variation in Responses

The unweighted distribution of responses across the surveys conducted between 1978 and
2005 covering about 200,000 cases is shown in Chart 1. The response codes from 1% to 5%
contain 54 percent of all the responses; including up to response code 10% adds another 16
percent, and including up to response code 15% adds another 4 percent for a total of 74 percent
of all responses. As a result, three quarters of all responses fell within the same range recorded
by the consumer price index over the same time period—the year-over-year change in the CPI
ranged from a low of 1.0% in 2002 to a high of 14.6% in 1980.

The upper tail of the distribution is quite long, although just 5 percent of all response codes
were above 15%, and only ½ of one percent of all responses indicated an expected inflation rate
of 50% or more. The lower tail of the distribution, in contrast, was sharply truncated, with just 3
percent of all responses expecting an overall decline in prices. The most distinctive, and perhaps
the most difficult to explain phenomena, was the comparatively large number in who expected a
zero inflation rate. Across the past quarter century, overall prices were anticipated to remain
unchanged by18 percent of all respondents. Yet, just 3 percent expected declines in prices.

One might have reasonably anticipated that the distribution of responses would not change
so abruptly at zero. The lumping of inflation expectations at zero seems to suggest that a negative
inflation rate incorporates some psychological aspects that consumers actively avoid, or perhaps
that consumers consider the underlying probability distribution discontinuous at zero. The
psychological hypothesis was more common in the decades following the depression of the 1930's
when consumers associated price declines with income declines, but in recent memory most
consumers have eagerly embraced whatever product price declines they encountered in the

9
marketplace. The single, and important, exception being home prices. Rather than a kink in the
underlying probability distribution, the lumping at zero may simply reflect rounding, with consumers
actually expecting a very low rate of inflation and not price declines.

The truncation does not reflect the averaging of a few surveys where expectations of
declines were common with the many more surveys where they were uncommon. Chart 2 shows
the response distribution for 1980, when inflation expectations were at their highest levels; Chart
3 shows the response distribution for 2001, when inflation expectations were at their lowest levels.
The same truncation in response is evident in both cases. The major difference is that the 1980
distribution is shifted to the right and has a greater dispersion of responses.4

Whatever the cause, the data clearly indicate a truncated lower tail rather than a normal
distribution. Importantly, the extent of the truncation provides important information for those
utilizing distribution assumptions to calculate a numerical estimate from qualitative response scales
on inflation expectations, as is commonly done among EU countries.5

Digit Preference

A close examination of the response distribution indicates the prevalence of certain digits,
namely 0, 5, 10, 15, 20, and so on up to 50. This tendency to favor certain digits has been termed
“digit preference.” Digit preference is a widespread phenomena, exhibited in nearly all responses
to open-ended numeric questions (Baker, 1992; Edouard and Senthilselvan, 1997). The questions
could ask about dollar amounts of income, assets, debts, product prices, or questions about
probabilities of the occurrence of certain events, from the weather to a variety of economic or
political outcomes, and even in response to attributes of the person such as weight. The typical
explanation of digit preference is that it represents “rounded” answers based on considerations of
the cost of providing more exact responses. Economists may favor a “near rationality”
interpretation whereby the rounding represents the level of precision that is associated with
differences that matter to the respondent.

An even closer inspection will reveal the prevalence of 3, 7, 13, 17, and so on. This reflects
coding rules implemented by the survey organization to provide a consistent means to code range
responses. All responses are recorded as integers, and the very few decimal responses are
rounded and coded as integers without any fractional values. The key part of the rule states that
coders should round .5 to the nearest odd number, e.g. 3.5 would be rounded to 3 and 4.5 rounded
to 5. This rule in combination of the prevalence of range responses produces the high prevalence
of the coded values 3, 7, 13 and so forth: for example, a response of 5% to 10% would be coded
7%, a response of 10% to 15% would be coded 13%. Overall, the number of range responses are
quite rare. Whenever a respondent would give a range response, it was always probed for a more

4
The larger variance that has often been associated with higher expected inflation rates in the literature, may be partially due
to the truncation of the distribution at zero.

5
Transforming the qualitative expectations into quantitative estimates has been done for inflation expectations with mixed
success. Different methods have been used to “quantify” qualitative measures of expectations, with the Carlson-Parkin
(1975) technique the most widely known. These techniques involve an assumption about the underlying and unobserved
distribution of expectations (typically assumed normal, but other distributional assumptions have been used) combined with
an assumption that across the entire time-series expectations are unbiased and equal realizations (although other identifying
assumptions are possible). See Batchelor (1986) and Pesaran (1987) for a review of these techniques.

10
exact point estimate in the Michigan surveys, but some respondents insisted that they could not
narrow the range to a single best integer estimate.

Digit preference and the frequency of range responses are usually considered survey
measurement errors, given that they result in less precise measures. Experiments have been
conducted with the data before rounding (from one decimal) and the characteristics of the response
distribution have been nearly identical to the rounded figures, as one would expect. Range
responses are likely to reflect uncertainty about the future course of inflation, or the lack of
information that a more precise answer would require (presumably due to its high cost).

Some have misinterpreted digit preferences as “focal points” in the distribution, and suggest
that this indicates that inflation expectations are more qualitative than quantitative in nature (Bryan
and Palmqvist, 2005). The near universal presence of digit preferences would mean that the same
conclusion would be equally as valid for measures of income, assets, prices, and so forth, meaning
that surveys could measure only qualitative variables. The stability of the same integers as “focal
points” in the distribution over time has been misinterpreted as indicating that the distribution of
responses was not responsive to changes in the inflation or policies pursued by the central bank.

Time Series Variation

Rather than focusing on cross-section data, most economists are more interested in how
the distribution changes from month-to-month. Given the pronounced skew in the distribution of
inflation expectations, it is no surprise that the mean of the distribution always exceeds the median.
Moreover, given that the long upper tail of the distribution is likely to represent measurement errors,
the median rather than the mean of the distribution may provide the better measure of central
tendency.6 Indeed, the difference between the mean and median was substantial, with the mean
being about 25% higher than the median, or 1.0 percentage points higher (see Chart 4). Over the
period from January 1978 to August 2005, the mean of the monthly distributions was 4.8% while
the median was 3.8%. Despite the difference in the levels, the time series correlation between the
mean and median was 0.98, indicating that either measure provided nearly identical time-series
information. The median inflation expectation is typically the measure of choice, and I will restrict
my focus to the median in this paper.

The interquartile difference, defined as the difference between the 25th and 75th percentiles,
can be used as an estimate of the variance in the monthly data.7 Over the 1978 to 2005 period,
the interquartile range averaged 4.7 percentage points, with the 25th percentile averaging 1.5
percentage points and the 75th percentile averaging 6.2 percentage points, meaning that half of all
respondents held expectations within that range. The time-series correlations were quite high, as
the correlation between the 25th percentile and the median was 0.91 and the correlation between
the 75th percentile and the median was 0.97 (see Chart 5).

6
There is a long standing debate about whether large estimates (say, five or more times the median or mean) should be
deleted and thus treated as missing data, or whether some information can be retained, namely that the respondent expected
a large increase, and the data should simply be truncated.

7
The correlation between the interquartile range and the variance of the mean was 0.82.

11
 The interquartile range provides some interesting information about trends in inflation
expectations. Increases in the variance occur abruptly, but decreases take place over an extended
time period. Perhaps the clearest example in the sudden increase in variance at the time of the first
war with Iraq in 1991. Following that increase, the variance of inflation expectation decreased
gradually over the next decade (see Chart 6). Central banks have interpreted this to indicate that
their credibility can be lost suddenly, which then takes a considerable period of time to re-establish.

What do the cross-section as well as time-series variations in inflation expectations

indicate? There have been some that have used these variations as a strong indicator of vast
measurement error, making the data worthless. Others, as I have already noted, interpret the
variations as a reflection of the costs of collecting and processing information which result in a
staggered updating across respondents. While the more extreme responses may well reflect
measurement errors, most of the disagreement or heterogeneity reflects the balancing of costs and
benefits of updating expectations. To explore these issues in more detail, repeated measures on
the same individuals is needed.

Panel Data on Expectations

The sample design of the monthly Surveys of Consumers includes a rotating panel. In the
rotating panel design, each monthly sample is composed of a new representative subsample as
well as a re-interview subsample of all respondents who were first interviewed six months earlier.
The design was chosen to enhance the study of change in expectations and behavior. In the
present context, the sample design means that for each respondent two measures of inflation
expectations were collected six months apart. In each interview, respondents were asked about
the expected inflation rate during the following twelve months. As a result, the two instances of the
question do not ask about identical time periods but do contain overlapping periods of six months.

This design enables a partial test of the hypothesis of staggered information flows. The
staggered information hypothesis suggests that in any given monthly survey only some of the
respondents would have updated their expectations. For this analysis, the sample was restricted
to range from January 1993 to August 2005, when the inflation rate was more stable, averaging
2.5%. More importantly, the average change in the actual inflation rate over all six month intervals
within this time period was nearly zero, or more exactly 0.0005 percentage points. In comparison,
the average change in inflation expectations among identical individuals was -0.247, or a decrease
of one-quarter of a percentage point. The negative change in inflation expectations probably
reflects the persistent declines in the inflation rate over the 1993 to 2005 period. Overall, given that
the consumer data on inflation expectations is collected as rounded integers, the two sources were
remarkably close.

The average absolute differences, however, clearly indicate much greater change in the
inflation expectations data among panel members. The average absolute differences was 0.48
percentage points for the change in the actual inflation rate and 2.8 percentage points for the
change in inflation expectations. This amounted to absolute changes in expectations that were
more than five times the change in the actual inflation rate.

A simple regression indicated that for each percentage point change in the actual
annualized rate of inflation during the prior six months, consumers changed their inflation
expectations by about half of a percentage point. This response indicates that consumers did not

12
fully update their inflation expectations, as would be suggested by the staggered information
hypothesis. Indeed, across all respondents from 1993 to 2005, 27 percent reported the same
inflation expectation in the two surveys. Among the 73 percent that updated their expectations, 35
percent reported a higher inflation expectation in the second interview and 38 percent reported a
lower inflation expectation.

Costs of Updating Expectations

Any observed change in inflation expectations over the six month period cannot be taken
as proof that inflation expectations were updated. The observed change may simply indicate
measurement error rather than true change. A noted advantage of panel surveys is that stable
sources of measurement error can be eliminated by taking the difference between the two interview
measures. Since it is usually assumed that measurement error reflects specific questions and
specific subgroups, by asking the same person the same question on two occasions, the
measurement error would be eliminated by taking the difference of the two responses.

This by no means eliminates all measurement error, but it does eliminate errors that are
likely to be associated with systematic bias. Random error in measurement remains, which
increases the variance of the measures. For example, if expectations were not updated,
measurement errors could create a difference where none had existed. Such random variations
increases the proportion of unexplained variance, but does not created biased estimates.

Based on the six-month differences, comparisons were made across selected demographic
subgroups that could be reasonably expected to differ in the costs of updating inflation
expectations. Education was selected given that the formation of inflation expectations is assumed
to critically depend on the ability of the respondents to gather and interpret information; gender was
selected since information gathered from personal shopping experience may provide an information
advantage to women8; age and income were selected since the economic situation and
experiences are likely to differ over the life cycle.

Given the purpose of the analysis is to identify groups with relatively high or low
heterogeneity, the overall sample mean was subtracted, with the analysis focused on the deviations
from the mean. Recall that the observed change in inflation expectations was one-quarter of a
percentage point, compared with the change in the actual CPI across all six-month intervals of zero
in the 1993 to 2005 period.

A second measure of relative heterogeneity is the ratio of individual differences to the

sample difference. Thus, whenever the ratio was above 1.0 for a particular subgroup, it would
indicate that they had proportionately higher heterogeneity than other members of the panel during
the same six-month interval. The sample consisted of 26,611 cases that had complete data on
both measures with the interviews conducted from 1993 to 2005.

Consider the results for gender as shown in Table 1. Men raised their inflation expectations
by +0.080 percentage points over the six month interval on average, nearly the exact opposite of

8
Persistent differences in inflation expectations between men and women have been documented in the past (Bryan and
Venkatu, 2001).

13
the -0.075 decline recorded by women. Recall that the overall sample mean was -0.247, so that
the positive deviation of +0.080 for men was closer to the average actual change in the CPI of 0.0.
The absolute differences were also offsetting, although the average absolute differences were
much larger: men recorded a smaller than average absolute error of -0.452 and women a larger
error of +0.424. The ratio data indicated that the error among men was 67.6% of the average and
for women it was 130.4% of the sample average. The difference was somewhat narrower with the
ratio of the absolute errors.

The differences by education level conform to the hypothesis that the costs of collecting and
processing relevant data decline as education increases. In the lowest education subgroup, the
average change in inflation expectations was 2.9 times as large as the average, while among the
highest education subgroup the change was just about half the average. The effects across
education subgroups was nearly linear and significant, with higher education groups exhibiting less
heterogeneity.

The results by age group indicated that both the youngest and oldest age groups exhibited
greater heterogeneity in expectations. The results, however, were not as large nor as consistent
as those recorded by education. Indeed, none of the average deviations were significant, and only
some of the absolute deviations proved to be significant. The results by income groups indicate
that the least heterogeneity among the top forty percent of the income distribution, and the largest
heterogeneity was among those in the lowest fifth of the income distribution.

Overall, the data provide some support for the hypothesis that the costs involved in
collecting and procession information play a role in the decision to update inflation expectations.
Among groups that faced higher costs, the level of heterogeneity was greater indicating less
frequent updating, most notably among the least educated; correspondingly, groups that faced
lower costs and higher benefits exhibited more frequent updating and less heterogeneity, most
strongly shown by upper income subgroups.

Staggered Information Flows

Although the two-wave panel data can not rigorously test theories of staggered information
flows, it can provide some guidance. The theory is typically expressed in terms of the delayed
response in updating expectations. Since the panel includes a measure of only one change in
expectations, an analysis of the timing of the updating of expectations over time is not possible.
Instead, the process can conceptualize in reverse: rather than postulating that a given change in
the actual inflation rate has a staggered impact on a series of future changes in expectations, it is
postulated that a given change in inflation expectations resulted from the staggered impact of a
series of past changes in the actual inflation rate.

Past changes in the actual inflation rate were used as predictors in a regression analysis
of the change in inflation expectations. For this analysis, the past change in the inflation rate was
defined as the difference between the monthly change in the CPI (at annual rates) at time t and t-1.
Since the measured change in inflation expectations occurred over a six month interval, changes
in the actual inflation rate within that six month interval would not unambiguously support the
hypothesis of staggered information flows. Changes in the actual inflation rate that occurred more
than six months ago could more reasonably be anticipated to support the hypothesis. As a result

14
12 lagged changes in the monthly inflation rate were entered into the regression. In addition,
dummy variables for the demographic characteristics discussed above were also included.

The results of the regression are shown in Table 2. While the first six lags of the actual
change in the inflation rate were significant contributors to the change in inflation expectations, this
could simply reflect normal updating not the staggered information hypothesis. Nonetheless, it is
worth noting that the pattern in the size of the coefficients: they increase in size from the first lag
to the fourth lag and reach a peak at the sixth lag. The significance of the seventh to the tenth lags
offer greater support for the hypothesis that staggered information flows have a significant impact
on expectations. It is of some importance to note that all of these variables combined explained
just 1% of the total variation in inflation expectations. So even if the data support the staggered
information hypothesis, the support is quite meager.

Asymmetric Impact of Information

The hypothesis that unfavorable information about inflation prompts widespread and prompt
responses in inflation expectations can be tested by a comparison of positive and negative changes
in the actual inflation rate with subsequent changes in expectations. For each six month interval
in the panel, the change in inflation expectations was compared with the change in the actual
inflation rate during the prior six months, with negative and positive changes entered separately.
The regressions included 26,611 cases from 1993 to 2005.

The estimated results were consistent with the hypothesis that increases in the inflation rate
had a much larger impact than declines on inflation expectations. The coefficient for an increase
in inflation was 0.117 (standard error of 0.020), nearly twice the size of the coefficient for declines
in inflation of 0.068 (standard error of 0.020). The estimate that negative news about inflation was
twice as powerful as positive news is consistent with prospect theory (Kahneman and Tversky,
1979).

The asymmetrical response of inflation expectations may mean that there is also an
asymmetrical response to changes in the perceived credibility of central banks. Increases in
inflation will more promptly diminish the credibility of central banks, but declines in inflation will only
slowly rebuild lost credibility.

Backward or Forward-Looking Expectations?

Tests of whether the formation of inflation expectations represents a backward or forward-

looking process have typically been examined in separate equations, with the analyst having the
responsibility to judge the comparative evidence. There is a way to nest both hypotheses in the
same reduced form equation by regressing current inflation expectations on both past and future
changes in the actual inflation rate. Strong support for the adaptive hypothesis would be
demonstrated if past but not future changes in the actual inflation rate were significant predictors,
while support for forward-looking expectations would be shown if future but not past changes in the
actual inflation rate were significant predictors. Many will recognize the resulting equation as simply
another method to test for “Granger causality” (Geweke, Meese and Dent, 1982). The estimated
equation was fitted from 1978 to 2005 was:

15
 4 4 4
p te = 0.895 + 0.291 ∑ Pt + j + 0.318 Pt − 0.089 ∑ Pt − j + 0172
. ∑ Pt e− j R 2 = 0.954
. ) j =1
(0.276) (0106 (0148
. ) (0151 . ) j =1 (0.252) j = 1

The data indicate that higher future changes in the inflation rate were positively associated with
increases in current expectations. The coefficients for the four-quarter lead (indicated by t ranging
from +1 to +4) in the rate of inflation were both positive and significant, at more than twice its
standard error. A separate chi-square test on their exclusion of the four-quarter lead was easily
rejected (p=0.006). In contrast, the coefficients for the four-quarter lag (indicated by t ranging from
-1 to -4) were clearly insignificant, thereby rejecting the adaptive hypothesis. Moreover, the
coefficients were negative, exactly the opposite of what the adaptive hypothesis would predict.

Expectations also incorporate contemporaneous information on the inflation rate, even

though the survey has always been completed well in advance of the announcement of the official
inflation rate. Unlike past changes in inflation, contemporaneous changes in inflation had the
anticipated positive impact on expectations. The significance of the contemporaneous inflation rate
indicates that consumers obtain information about current inflationary trends from sources other
than the official announcements.

Rational Expectations Hypothesis

Tests on whether the Michigan data on inflation expectations meet the rigorous criteria
imposed by the rational expectations hypothesis have been repeatedly conducted during the past
quarter century.1 The data has never given unequivocal support to the rational expectations
hypothesis, with the principle failing the lack of efficient use of all available information.2 3 Thomas
(1999:141-142) summarized his findings by noting that “...consensus household inflation forecasts
do surprisingly well relative to those of the presumably better-informed professional economists.”
Indeed, the median consumer forecasts of year-ahead inflation rates “...outperformed all other
forecasts in the 1981-1997 period on simple tests of accuracy as well as on tests for
unbiasedness.” Mehra (2002, page 35) also finds that Michigan’s median inflation expectations
outperforms the expectations of professional economists and forecasters: “They are more accurate,
unbiased, have predictive content for future inflation, and are efficient with respect to economic
variables generally considered pertinent to the behavior of inflation.” As I noted at the start of this
paper, it was finding such as these that originally motivated Muth to advance the rational
expectations hypothesis.

1
See Lott and Miller (1982), Gramlich (1983), Grant and Thomas (1999), Thomas (1999), Mehra (2002), Roberts (1997),
Badhestani (1992), Bryan and Gavin (1986), Noble and Fields (1982), Batchelor and Dua (1989),
2
Cukierman (1986) has suggested that this is not a clear violation of the rational expectations hypothesis, since households
may not always correctly distinguish between temporary and permanent shocks and thus their forecasts could exhibit serially
correlated errors.
3
Similar comparisons were done for year-ahead forecasts of the national unemployment rate. Curtin (1999, 2003) found that
consumers’ forecasts of the year-ahead unemployment rate outperformed those of professional forecasters as well as
forecasts from two prominent macroeconomic models.

16
 What I will focus on is the puzzle that consumers’ performance at forecasting the inflation
rate is comparable to forecasts by economists. This finding is more troublesome for those who
favor some form on the adaptation hypothesis, but it is also quite difficult to argue that the costs of
collecting and processing information is not significantly lower for economists than for consumers.
Only under the hypothesis that the costs are trivial would no significant differences between
economists and consumers be anticipated.

Another hypothesis is that the errors in consumer expectations are offsetting, and as a
consequence the test were misleading. Thus, the errors could be quite large, say a significant
underestimate among men is offset by a significant overestimate among women, or similar
offsetting shifts among education or age subgroups. To examine this issue, a number of
regressions were performed for a selection of demographic subgroups. Given that survey data
usually involve some aggregation errors, the regression was calculated using nonlinear least
squares to estimate a moving average error term, using a consistent estimate of the covariance
matrix that allows for serial correlation and heteroscedasticity. The overlapping forecast intervals
generated by the survey questions could produce serially correlated errors even among perfectly
rational agents (Croushore, 1998). In fact, a significant first order moving average error term was
found in all equations. The residuals are also tested for the inefficient use of information on
inflation, but no tests were attempted for the inefficient use of other relevant information (what is
called strong efficiency).

Regressions were estimated for men and women as well as different education and age
subgroups and the results are reported in Table 3. The regressions are based on quarterly
observations from 1978 to 2005. Given the rather small monthly sample sizes, to insure that
estimates for each subgroup were based on a sufficient number of cases, the independent monthly
samples were pooled into quarterly observations to calculate the median inflation expectations for
each subgroup.4

The results of the analysis indicated that rather than offsetting errors, the year-ahead
inflation expectations of each of the demographic groups were an unbiased estimate of the actual
inflation rate. The null hypothesis that inflation expectations were a biased estimate was rejected
for every demographic subgroup at the 95% confidence level: every constant term was
insignificantly different from zero, and every estimated coefficient on inflation expectations was
insignificantly different from one. Every equation had a significant estimate of the moving average
error term, but only among the least educated and the older respondents was there any evidence
of the inefficient use of information about the inflation rate that was available at the time their
expectations were formed.

These results have always been met with disbelief. Could it be that the costs of forming
unbiased inflation expectations are more manageable based on staggered updating? Does the
presumably lower cost and greater importance of private information play a more pivotal role in the
formation of expectations than suggested by current theories? Or is the accuracy of expectations
a property of groups and consensus forecasts? Could it be that the rational expectations
hypothesis is true at the macro but not at the micro level?

4
Insufficient data in the first half of the period made it impossible to code real household income in a consistent fashion and
so this variable was excluded from this analysis.

17
Concluding Comments

There are at least as many unresolved issues now as when the rational expectations
hypothesis was first advanced nearly a half century ago. Indeed, the findings from this analysis can
be summarized in much the same way as Muth did in his classic article: consumers’ inflation
expectations are forward looking, they are generally as accurate as the forecasts of economic
models, and they more closely correspond to the hypothesis of rational expectations than to the
backward-looking hypothesis of adaptation.

There is no doubt that people sometimes engage in adaptative behaviors, correct past
errors, or simply rely on extrapolation to form expectations. These shortcuts are used to help
reduce the costs involved in collecting and processing data. These costs result in staggered
changes in expectations. In turn, staggered or sticky expectations are the likely cause of the finding
that consumers do not take into account all available information when forming their expectations.
It is simply too costly given the expected benefit. These finding, however, do not contradict the
rational expectations hypothesis but act to incorporate the hypothesis more fully into the standard
economic framework.

Moreover, the finding that consumers are not fully rational in forming their inflation
expectations is as surprising as the finding that consumers do not fully maximize their utility! The
profession needs to accept what amounts to a simplifying assumption that is roughly consistent with
the evidence at the macro level. The acceptance should be based on its predictive performance,
not on the realism of the theory’s assumptions. To be sure, full rationality is unlikely to be observed
in everyday life among consumers nor even among economists. Analysis at the micro level still
needs to more fully incorporate aspects of bounded rationality and other innovations of behavioral
theory.

Most of the theoretical implication of rationality for monetary policy, however, may be closely
approximated by “nearly rational” expectations. Without a more exact and universal definition of
what “near rationality” means, that glass will be seen as half empty by some and half full by others.
It is that unresolved ambiguity that continues to makes monetary policy an interesting and
challenging task.

18
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21
 Table 1: Change in Inflation Expectations Over Six Month Interval Within Selected
Demographic Subgroups, Panel Data 1993 - 2005

Population Deviations from Sample Means Ratio to Sample Means

Subgroup e
∆P e
(Std Err) |∆P | (Std Err) ∆P e
(Std Err) |∆Pe| (Std Err)

All Households 0.000 (0.032) 0.000 (0.026) 1.000 (0.128) 1.000 (0.009)
Gender
Male 0.080a (0.038) -0.452a (0.031) 0.676b (0.152) 0.843b (0.011)
Female -0.075 (0.050) 0.424a (0.042) 1.304 (0.204) 1.147b (0.015)
Education
Less High School -0.476 a (0.209) 1.504a (0.179) 2.925b (0.847) 1.522b (0.062)
High School -0.176a (0.067) 0.368a (0.055) 1.713b (0.269) 1.128b (0.019)
Some College 0.078 (0.065) 0.086 (0.053) 0.683 (0.263) 1.030 (0.018)
College Degree 0.157a (0.050) -0.425a (0.041) 0.365b (0.203) 0.852b (0.014)
Graduate Studies 0.122a (0.059) -0.631a (0.048) 0.508b (0.240) 0.781b (0.017)
Age
18 - 34 -0.097 (0.069) 0.326a (0.058) 1.392 (0.280) 1.113b (0.020)
35 - 44 -0.037 (0.061) -0.084 (0.051) 1.151 (0.247) 0.971 (0.018)
45 - 54 0.075 (0.063) -0.255a (0.052) 0.696 (0.256) 0.911b (0.018)
55 - 64 0.119 (0.081) -0.203a (0.067) 0.519 (0.325) 0.929b (0.023)
65 or older 0.009 (0.086) 0.106 (0.072) 0.964 (0.346) 1.037 (0.025)
Household Income
Bottom Fifth -0.177 (0.130) 1.005a (0.109) 1.714 (0.528) 1.349b (0.038)
2nd Fifth -0.122 (0.093) 0.453a (0.078) 1.494 (0.378) 1.157b (0.027)
a b
Middle Fifth -0.172 (0.071) 0.098 (0.059) 1.696 (0.289) 1.034 (0.020)
rd a b
3 Fifth 0.111 (0.059) -0.248 (0.048) 0.552 (0.237) 0.914 (0.017)
Top Fifth 0.194a (0.048) -0.579a (0.039) 0.216b (0.194) 0.799b (0.014)

Note: The average actual change in the CPI-u inflation rate was 0.0 across all six-month intervals.
a
Significantly different than 0.0 at 95% confidence level.
b
Significantly different than 1.0 at 95% confidence level.

22
 Table 2: Impact of Lagged Changes in Actual Inflation
Rate on Change in Inflation Expectations, 1993 to 2005

Coefficient Std Error

Intercept -0.188 0.113

Monthly Change in CPI

Lag 1 0.107* 0.016
Lag 2 0.167* 0.019
Lag 3 0.238* 0.024
Lag 4 0.301* 0.027
Lag 5 0.331* 0.029
Lag 6 0.339* 0.030
Lag 7 0.252* 0.029
Lag 8 0.177* 0.029
Lag 9 0.128* 0.027
Lag 10 0.087* 0.025
Lag 11 0.024 0.020
Lag 12 0.007 0.017
Sex
Male (excluded)
Female -0.130* 0.064
Education
Less High School -0.560* 0.151
High School -0.241* 0.089
Some College (excluded)
College Degree 0.032 0.091
Graduate Studies -0.038 0.105
Age

18-34 -0.138 0.094

35-44 -0.103 0.094
45-54 (excluded)
55-64 0.078 0.112
65 or older 0.090 0.110
Income
Bottom Fifth 0.072 0.119
2nd Fifth 0.062 0.103
Middle (excluded)
4th Fifth 0.248* 0.092
Top Fifth 0.276* 0.093

RSQD Adjusted 0.01

Cases 26,611

*Significantly different than 0.0 at 95% confidence level

23
 Table 3: Tests of Rational Expectations Hypothesis Based on
University of Michigan’s Inflation Expectations Data, Quarterly Data 1978 - 2005
Unbiased | α=0 & β=1 Efficiency | δ=0 & φ=0
Pt = α + β Pt Et −4
et = δ + ϕ Pt − 5
Population Subgroup
χ2 for
α β Θ R2 δ φ R2
Ho
All Households -0.414 1.184 0.655* 1.538 0.030 -0.035
0.884 0.005
(0.533) (0.181) (0.108) [0.464] (0.158) (0.039)
Gender
Male -0.135 1.158 0.726* 3.861 -0.004 -0.024
0.893 0.000
(0.524) (0.177) (0.081) [0.145] (0.153) (0.037)
Female -0.605 1.181 0.588* 1.037 -0.011 -0.031
0.862 0.000
(0.594) (0.186) (0.145) [0.594] (0.170) (0.042)
Education
Less High School -0.323 1.148 0.574* 0.722 -0.551* 0.091*
0.800 0.051
(0.692) (0.221) (0.091) [0.697] (0.195) (0.033)
High School -0.482 1.208 0.611* 1.895 -0.121 0.001
0.866 0.000
(0.610) (0.189) (0.076) [0.388] (0.167) (0.037)
Some College 0.082 1.064 0.607* 1.946 -0.105 -0.009
0.850 0.000
(0.635) (0.208) (0.118) [0.378] (0.204) (0.056)
College Degree 0.113 1.049 0.568* 1.960 -0.048 -0.021
0.853 0.000
(0.514) (0.175) (0.172) [0.375] (0.187) (0.049)
Graduate Studies 0.061 0.998 0.712* 0.107 -0.027 -0.022
0.876 0.000
(0.588) (0.189) (0.081) [0.948] (0.195) (0.058)
Age
18 - 34 -0.139 1.068 0.556* 0.243 -0.032 -0.026
0.849 0.000
(0.589) (0.190) (0.128) [0.886] (0.199) (0.057)
35 - 44 -0.150 1.064 0.624* 0.181 0.004 -0.029
0.869 0.000
(0.585) (0.184) (0.129) [0.914] (0.194) (0.054)
45 - 54 -0.229 1.143 0.590* 1.739 -0.052 -0.017
0.866 0.000
(0.582) (0.187) (0.095) [0.419] (0.176) (0.041)
55 - 64 -0.153 1.233 0.647* 8.089* -0.318* 0.048
0.864 0.012
(0.569) (0.188) (0.071) [0.018] (0.158) (0.029)
65 or older 1.356 0.834 0.766* 8.538* -0.929* 0.179*
0.789 0.218
(0.774) (0.271) (0.074) [0.014] (0.175) (0.042)

Standard errors in parentheses; probability level of χ2 in brackets. All standard errors and covariances
calculated using the Newy-West procedure. All estimated equations included a moving average error
term. An asterisk indicates significance at the 0.05 percent level; significance tests on all coefficients
expect β were for differences from 0.0 and test on β were for differences from 1.0. R2 adjusted for
degrees of freedom.

24
 Chart 1: Year-Ahead Inflation Expectations:
Distribution of Responses, 1978 – 2004

20%

15%

10%

5%

0%
-20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50
Response Codes

Chart 2: Year-Ahead Inflation Expectations:

Distribution of Responses 1980

20%

15%

10%

5%

0%
-20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50

Chart 3: Year-Ahead Inflation Expectations:

Distribution of Responses 2001

25%

20%

15%

10%

5%

0%
-20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50

25
 Chart 4: Median and Mean Inflation Expectations
(Monthly Data, 1978 – 2005)

15%
Median Mean

12%

9%

6%

3%

0%
1978 1981 1984 1987 1990 1993 1996 1999 2002 2005

Chart 5: Inflation Expectations:

25th , 50th , and 75th Percentiles

18%
25th 50th (Median) 75th
15%

12%

9%

6%

3%

0%

-3%
1978 1981 1984 1987 1990 1993 1996 1999 2002 2005

Chart 6: Inflation Expectations:

Interquartile Range

12%
rng
10%

8%

6%

4%

2%

0%
1978 1981 1984 1987 1990 1993 1996 1999 2002 2005

26