Sticky Information and Model Uncertainty in Survey Data on Ination Expectations Sticky Information and Model Uncertainty in
Survey Data on Ination Expectations William A. Branch University of California, Irvine
February 8, 2005
Abstract
This paper compares models of heterogeneity in survey ination expecta-
tions. On the one hand, we specify two models of forecasting ination based on
limited information ows of the type developed in Mankiw and Reis (2002). We
present maximum likelihood results that suggests a sticky information model
with a time-varying distribution structure is consistent with the Michigan sur-
vey of ination expectations. We also compare these sticky information mod-
els to the endogenous model uncertainty approach in Branch (2004). Non-
parametric evidence suggests that model uncertainty is a more robust element
of the data.
JEL Classications: C53; C82; E31; D83; D84
Key Words: Adaptive learning, model uncertainty, survey expectations.
1
Introduction
Despite the prominence of rational expectations in macroeconomics there is consider-
able interest in its limitations. As an alternative some researchers propose modeling
agents as econometricians (Evans and Honkapohja (2001)). This adaptive learning
approach typically assumes agents have a correctly specied model with unknown
parameters. In many models agents optimal decision rules are functions of these
beliefs. This paper has beneted enormously from comments and suggestions by Bruce McGough and
Ken Small. Email: wbranch@uci.edu; Department of Economics, 3151 Social Science Plaza, Irvine, CA
92697; Phone: (949) 824-4221; Fax: (949) 824-2182.
1 Other approaches impose bounded rationality at the primitive level; see, for ex-
ample, Mankiw and Reis (2002), Ball, Mankiw, and Reis (2003), Branch, Carlson,
Evans, and McGough (2004) and Sims (2003). Of these the sticky-information model
of Mankiw and Reis (2002) yields important (and tractable) implications for macroe-
conomic policy. Mankiw and Reis (2002) replace the staggered pricing model of Calvo
(1983), which is employed extensively in Woodford (2003), with a model of staggered
information ows. Each period, each rm, with a constant probability, updates its
information set when optimally setting prices. The remaining rms are free to set
prices also, but do not update their information from the previous period. Impor-
tantly, this leads to a phillips curve with ination as a function of past expectations of
current ination rather than current expectations of future ination as in Woodford
(2003). Mankiw and Reis (2002) and Ball, Mankiw, and Reis (2003) show that this
implies greater persistence in response to monetary shocks.
In an innovative paper, Mankiw, Reis, and Wolfers (2003) seek evidence of sticky
information in survey data on ination expectations. They examine surveys of pro-
fessional forecasters and construct a data set based on the Michigan Survey of Con-
sumers. Their results show that these survey data are inconsistent with either rational
or adaptive expectations and may be consistent with a sticky-information model.
There is considerable interest in empirically inferring the methods with which
agents form expectations. In particular, there is compelling evidence that survey
expectations are heterogeneous and not rational. For example, Bryan and Venkatu
(2001 a,b) document striking dierences in survey expectations across demographic
groups. Carroll (2003) provides evidence that the median response in the Survey of
Consumers is a distributed lag of the median response from the Survey of Professional
Forecasters. Branch (2004), adapting Brock and Hommes (1997), develops a method-
ology for assessing the forecasting models agents use in forming expectations. In that
paper, evidence suggests survey responses are distributed heterogeneously across uni-
variate and multivariate forecasting models. Brock and Durlauf (2004) argue that if
agents are uncertain about the prevailing ination regime then this uncertainty may
manifest itself in agents switching between myopic and forward-looking predictors;
hence, model uncertainty is a key aspect of expectation formation.
1
This paper has three objectives: rst to characterize sticky information in survey
data in the sense that a proportion of agents do not update information each period;
second, to test whether these proportions are static or dynamic; third, to provide
evidence whether model uncertainty or sticky information is a more robust element
of the survey data. Carroll (2003) and Mankiw, Reis, and Wolfers (2003) provide
indirect evidence of limited information ows in expectation formation. This paper
elaborates on the nature of these ows in survey data. We also bridge the sticky
information and heterogeneous expectations literature by presenting evidence of both
model heterogeneity and limited information ows.
1
Other papers which show heterogeneity across forecasting models include Baak (1999), Chavas
(2000), and Aadland (2003).
2 This paper extends Branch (2004) by focusing on predictors which dier tempo-
rally rather than spatially. Our approach, like Mankiw, Reis, and Wolfers (2003), tests
for sticky information ows in agents survey expectations. We also extend Mankiw,
Reis, and Wolfers (2003) by proposing two formulations of sticky-information. The
rst is the Mankiw-Reis approach which we refer to as the static sticky information
model. The other approach assumes that expectations are formed by a discrete choice
between forecasting functions which dier by the frequency with which they are re-
cursively updated. Using data from the Survey of Consumers at the University of
Michigan, we provide evidence of sticky information by testing the sticky information
models against the full-information alternative. Maximum likelihood evidence shows
that: sticky information in survey data is dynamic in the sense that the distribution
of agents across predictors is time-varying; the distribution of agents is not geometric
so that, on average, the highest proportion of agents update information somewhat
infrequently. This last result is in contrast to an implication of the Mankiw-Reis
model which has the highest proportion of agents updating each period.
Our nal objective is to determine whether model uncertainty is a more robust
element of the survey data than sticky information. We address this issue by compar-
ing the Rationally Heterogeneous Expectations (RHE) model of Branch (2004) with
the sticky information models presented in this paper. In Branch (2004) agents are
uncertain about the correct model for the economy and so each period they make a
discrete choice between alternatives.
2
We (non-parametrically) estimate the density
functions implied by these models and compare the t to the histogram of the actual
survey data. We nd that neither the sticky information or the model uncertainty
approaches are statistically identical to the distribution of the survey data. However,
on average, the model uncertainty approach provides a better t than the sticky infor-
mation models. As a corollary to these non-parametric results, we show that a sticky
information model which lets the distribution of information across agents vary over
time provides a better t than the static version of Mankiw and Reis (2002).
These results are new and signicant. There is considerable interest by the mone-
tary policy literature in whether agents have limited information or uncertainty about
the true economic model. Our evidence suggests that model uncertainty plays a more
important part of survey data but that sticky information is a feature as well. Based
on the results of this paper, a high priority of future research should intertwine both
sticky information and model uncertainty. We present evidence which suggests that
during periods of high volatility agents uncertainty about the economic environment
is a key factor in expectation formation. During periods of low volatility, model un-
certainty is less critical and agents may be inattentive. One methodological novelty
of this paper is that it provides a measure of t in terms of a models ability to t
the evolution of the full distribution of survey expectations through time.
A few qualications are in order. We acknowledge, at the outset, that our re-
sults do not address whether there is heterogeneity across multivariate and univariate
2
Pesaran and Timmermann (1995) also nd evidence of model uncerta