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Forecasting Macroeconomic Fundamentals in Economic Crises
Maurizio Bovi† & Roy Cerqueti‡∗
† Italian National Institute of Statistics (ISTAT)
Piazza dell’Indipendenza, 4, 00185, Rome, Italy
Tel.: +39 06 46733607; fax: +39 06 44482619. Email: mbovi@istat.it
† Sapienza University of Rome, Faculty of Economics
Via del Castro Laurenziano, 9, 00185, Rome, Italy
Email: maurizio.bovi@uniroma1.it
‡ University of Macerata, Department of Economics and Law
Via Crescimbeni 20, 62100, Macerata, Italy.
Tel.: +39 0733 2583246; fax: +39 0733 2583205. Email: roy.cerqueti@unimc.it
Abstract
Thepaperstudies the way economic turmoils influence the lay agents’ predictions of
macroeconomic fundamentals. The recent economic crises have, in fact, led several au-
thors to challenge the standard macroeconomic view that all agents are Muth-rational,
hence omniscient and homogeneous, forecasters. In this paper lay agents are assumed
to be heterogeneous in their predictive ability. Heterogeneity is modeled by assum-
ing that people have equal loss functions, but different asymmetry parameters. The
adopted methodological tools are grounded in the standard Operational Research the-
ory. Specifically, we develop a dynamic stochastic optimization problem, which is solved
by performing extensive Monte Carlo simulations. Results show that the less sophis-
ticated forecasters in our setting – the medians – never perform as muthians and that
second best (SB) agents do that only occasionally. This regardless the size of the crisis.
Thus, as in the real world, in our artificial economy heterogeneity is a structural trait.
More intriguingly, simulations also show that the medians’ behavior tend to be rela-
tively smoother than that of SB agents, and that the difference between them widens in
the case very serious crises. In particular, great recessions make SB agents’ predictions
relatively more biased. An explanation is that dramatic crises extend the available
information set (e.g., due to greater mass media coverage), and this leads SB agents,
who are more attentive to revise their forecasts than medians. The point is that more
information does not necessarily mean better forecasting performances. All considered,
thus, our simulations suggest a rewording of Ackoff’s famous phrase: it is not silly to
not look for an optimal solution to a mess.
Keywords: Dynamic stochastic optimization model, economic crisis, forecasting, heteroge-
neous agents, Monte Carlo simulations.
1 Introduction
Expectations of future events play a prominent role in economic decision making. Con-
sumers must think about the type of house to buy, the amount of education to pursue, the
∗Corresponding author.
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fraction of income to save, etc. Firms must decide where to locate factories and offices,
what products to develop and produce, etc.
Standard macroeconomic theory describes economic decisions as the result of optimizing
behavior of omniscient ”Muth-rational” agents (Muth, 1961). Muth-rational expectations
are a collection of assumptions regarding the manner in which economic agents exploit
available information to form their expectations. In its stronger forms, rational expecta-
tions operate as a coordination device that permits the construction of a representative
agent having representative expectations. Though homogeneous rational expectations are
still very commonly assumed in macroeconomics, recently the study of heterogeneous beliefs
has been gaining momentum in the literature. This for two main reasons.
First, differences in agents’ beliefs play an important role in macroeconomic analysis. For
instance, heterogeneity in predictions has been offered as an explanation for why mone-
tary policy shocks can have real and persistent effects on output growth due to i) limited
capacity for processing information (Reis, 2006 and 2009), Mackowiak and Wiederholt,
2009), ii) infrequent updating of beliefs (Mankiw and Reis, 2002) or iii) slow aggregate
learning arising from dispersed information (Lorenzoni, 2009). Mixed beliefs may also stem
for other reasons. Since the theoretical work of Brock and Hommes (1997), many authors
have examined the benefit of including predictor choice as an economic decision in models
with expectations formation (Chiarella and Khomin, 1999). Especially in the short run,
then, different models may generate different predictions. Nonetheless, by examining GDP
dynamics Bovi (2013) finds that, over a time-span of two decades, an easy-to-perform adap-
tive expectations model systematically outperforms other standard predictors. Though this
should reduce model uncertainty and thereby lead to increased homogeneity in expecta-
tions, data collected in surveys show that great variety in expectations persists even in this
situation. In our setting Bovi’s findings are important because they support the notion of
the enduring presence of disperse beliefs, in line with the real-world situation. According
to Curtin (2008), then, lay people may be interested in knowing about how inflation affects
their shopping trolley, or the unemployment rate in their specific labor market, but are less
interested in learning about the performance of the whole country or in aggregated macro
indicators which are difficult to apply to their daily life. Reis (2006, 2009) interprets this
kind of finding arguing that costs associated with the acquisition and use of information
may generate ”rational inattention”.
Second, the recent worldwide economic crisis has likely impinged on individuals’ predictive
ability and, accordingly, on the degree of consensus on expected macroeconomic dynamics
– different forecasting performances imply disperse beliefs and vice versa. In this regard,
theoretical models (e.g., van Nieuwerburgh and Veldkamp, 2006) suggest that macroeco-
nomic uncertainty and dispersion in beliefs should be greater during recessions. Patton and
Timmermann (2010) show supporting evidence of that. Moreover, a better understanding
of this kind of heterogeneity can help elaborate sharper tests of macroeconomic models for
which subjective beliefs are a driver of economic activity. Though the literature focusing on
the prediction of financial crises is flourishing (e.g., Niemira and Saaty, 2004; Sevim et al.,
2014), much less effort has been made to examine the impact of bad economic conditions
on agents’ predictive performance.
In this context, the focus of our work – and intended contribution – is to examine the
effects of deteriorated macroeconomic conditions on agents’ forecasting performances. The
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fundamental that agents must predict in these economic periods is the GDP growth rate .
Specifically, our economic environment is populated by agents featured by different predic-
tive ability caused by disparate attentiveness and/or information sets. Following Capistran
and Timmermann (2009), we synthesize this kind of heterogeneity by the asymmetry pa-
rameter – namely, θ – of LINEX loss functions.
Wefocus on three (groups of) individuals performing reiterate forecasting exercises.
Thefirstcluster is made up by ”muthians”, which are equipped with symmetric – i.e.: θ = 0
– LINEX loss functions. They are the benchmark forecasters because they are objectively
optimal. The term ”objectively optimal” captures the main feature of the muthian agent: it
commits (optimal) errors with zero mean (McAllister, 1991). Borrowing from the standard
macroeconomic theory, we also hypothesize that there is a bijection between zero-mean-
errors agents and muthian ones.
Then, we study ”second best” (SB) forecasters, who are able to minimize the distance be-
tween their asymmetric loss functions and that of the muthian. The reason for being SB
agents can be in the lack of sufficient information and/or the agents’ inability to perform at
any time as good as the omniscient muthian. SB agents may be though of as expert and/or
professional forecasters such as, e.g., econometricians.
Lastly, we examine ”median” forecasters. This last cluster is obtained by considering the
median of the empirical distribution of the distances between asymmetric and muthian loss
functions. Hence, median forecasters can be thought of as agents that structurally follow
neither muthian’s rationality nor its opposite. Similarly to what said to explain the dif-
ference between SB and muthian agents, median and second best forecasters are different
because the former have not sufficient skill/information/attention to perform at any time
as good as the latter. Medians may be meant as na¨ıve decision makers using rule-of-thumb
and/or heuristics (Kahneman, and Tversky, 1974; Bovi, 2009).
We analyze these three (groups of) agents in two alternative bad macroeconomic environ-
ments: one only moderately unfavorable, the other much more depressed. The logic is
that there is a relationship between the magnitude of the crisis and the agents’ forecasting
performance. In fact, a well established stylized fact suggests that the more severe the
recession, the greater the GDP growth rate volatility. This is not the end of the story, how-
ever, because the level of GDP volatility magnifies the level of the forecast error. The basic
logic of this latter sequence is easy to understand: a constant is obviously much simpler to
forecast than a highly volatile variable (see also Dietz, 2012).
The current crisis may be thought of as a sort of natural experiment to understand how
lay decision makers react to very dramatic years. In particular, due to its terrible recent
downturn, Greece is one of the most suitable cases, raising the following question: How do
Greeks perceive their own personal financial situation with respect to that of their coun-
try? Clearly, the representative citizen cannot by definition systematically drift apart from
that of the country where she lives, given that the nation-wide economic situation is the
(weighted) sum of the individual ones in the country. Yet, it may be hard to remain objec-
tive in the course of very deep and prolonged economic crises (Ackoff, 1997).
A unique dataset from the European Commission helps us digging into individuals’ per-
ceptions on economic situations. The dataset is based on monthly surveys from the Joint
Harmonised EU Programme of Business and Consumer Surveys (European Commission,
2007). These surveys aim at capturing the representative Greek response. Each month
1Other challenging questions can be addressed by examining some financial variables such as stock prices
and returns, volumes, and the like (see e.g.: Chiarella and He, 2001; Consiglio and Russino, 2007). However,
our research interest is to explore the expectations formation process on real macroeconomic fundamentals.
3
respondents answered, among others, the following two questions: ”How do you expect the
financial position of your household to change over the next 12 months?” and ”How do you
expect the general economic situation in the country to develop over the next 12 months?”
The responses are summarized in two indexes, one for each question, varying between +100
(all respondents answer ”It is getting a lot better”) and -100 (all respondents answer ”It is
getting a lot worse”).
Figure 1 shows the squared difference between the two indexes since 1985.
INSERT FIGURE 1 ABOUT HERE
Caption: Squared difference between the indices which summarize the answers of the
Greek citizens to the following two questions: ”How do you expect the financial position
of your household to change over the next 12 months?” and ”How do you expect the
general economic situation in the country to develop over the next 12 months?”.
Responses vary between +100 (all respondents answer ”It is getting a lot better”) and
-100 (all respondents answer ”It is getting a lot worse”). The considered period is 1985M1
- 2013M7.
Evidence as clearly as astonishingly shows that, hit by the sovereign debt crisis started in
2008, month-after-month for nearly two years, there was an unprecedented level of decou-
pling between the Greeks’ predictions of their own and their nation’s economic destiny. We
interpret this persistent misalignment between Greeks and Greece as supporting evidence
that greater political and economic turbulence makes it harder to maintain objectivity. In
turn, it may imply that during great recessions i) decision makers could behave less opti-
mally than in less extreme cyclical phases and that ii) heterogeneity may become wider. In
this paper we try to shed some light on this kind of issues.
Based on the above as well as on the existing evidence (Aizenman and Pinto, 2005), we
assume that the level of macroeconomic volatility increases with the gravity of the turmoil.
To learn the effects of deteriorated economic conditions on agents’ forecasting exercises
we develop a stochastic dynamic optimization problem. From the methodological point of
view, our paper belongs and intends to add to the field of the optimal control theory. The
reader can find a complete survey of deterministic mathematical control theory in Bardi
and Capuzzo Dolcetta (1997). The stochastic framework is described in Borkar (1989),
Fleming and Soner (1993), Krylov (1980), Yong and Zhou (1999). In general, according
to some authors, optimization theory is a particularly useful tool for doing macroeconomic
analysis (see e.g. Engels, 1992; Woodford, 2009; Consiglio and Staino, 2012). Modeling of
economic crises based on the optimization theory and operations research has already been
done by some scholars in a number of different frameworks. To cite only a few: Kirby (2007)
deals with the relationships between confidence in operations research and economic tur-
bulence; Bayram et al. (2014) develop a stochastic integer program to detect the strategies
of the so-called community development corporations, non-governmental/nonprofit entities
contrasting the crisis in the U.S. by investing in foreclosed properties. Rios-Rull (2001) is
somewhat closer to our paper in that he deals with the assessment the relationship between
business cycle and heterogeneity of beliefs by developing dynamic optimization models. The
mainaimofthepresentstudy, however, is the way poor macroeconomic performances affect
lay people’s predictions of real GDP dynamics.
From the operative standpoint, we present a constrained minimization problem where the
objective function is the distance between the muthian’s loss function and the asymmetric
one. The problem is solved with respect to time-dependent asymmetry parameters θ’s (the
”control variables”). These latter actually control the objective function and the dynamics
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