Opaque Information and Rare Disasters:
The Role of Transparency in Explaining Cross-Country
differences in the ERP∗
Lorenzo Prosperi
June 12, 2012
Abstract
A large literature have shown that the possibility that a rare disaster event occurs in the
economy is able to match the level of the ERP in developed countries. I show that global
disaster models are not able to explain the cross-section of the ERP in emerging markets. I
propose a variation to the original model of Barro (2006) where the economy is affected by
idiosyncratic disaster risk and information frictions play a role. Theoretically we do not need
idiosyncratic different disaster exposures but only different uncertainty level on the disaster
effects to match the cross-sectional variability in the ERP. I showed empirically that ERP are
strictly affected by information frictions deriving from institutional aspects such as corruption,
”rule of law” and quality of the government. The same results hold in an international asset
pricing model from the point of view of the US investor as in Lustig, Verdelhan (2007),
suggesting that these findings do not depend on the choice of the benchmark model.
JEL: E32, E44, G12
∗ I thank Christian Hellwig, Roberto Pancrazi, Michael Donadelli and Nicola Borri for the useful suggestions. All
errors are the author’s responsability.
1
Contents
I An Asset Pricing Model with Information Frictions and Disaster
Risk
5
1 The Barro’s Model
5
2 A simple model with uncertainty on disaster effect
2.1
2.2
10
The Assumptions of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.1 How the agent selects the information level . . . . . . . . . . . . . . . . . .
10
11
2.1.2 Asset Pricing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Towards an International Model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 The Ellsberg Paradox and Information Frictions . . . . . . . . . . . . . . .
14
20
22
II Empirical Evidence on the Role of Information Frictions and Disaster
23
3 The Data
23
4 Empirical Evidence for the Single Country Model
26
4.1
The Testing Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
26
5 Empirical Evidence in an International C-CAPM framework
5.1 The Testing Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
29
29
6 Limits
34
7 Conclusions
34
2
In the last decade developing countries are studied intensively by economics researcher and
by financial practicioneers due to their increasing importance in the global scenario and as an
investment opportunity. In particular stock market indexes of these countries have drammatically
outperformed with respect to developed countries offering excess returns around 17% against 3%
of developed in the last 20 years. Furthermore there is a lot of heterogeneity between asset returns
that has to be understood.
In economic research much effort has been devoted in order to understand the source of such
premia. In general we observe a clear standard direct relationship between mean and standard
deviation of asset returns, suggesting that, as usual, a risk based explanation holds. Nevertheless,
standard asset pricing models, like CAPM, fail in predicting the risk-premia since Jensen’s alpha
are usually very high (Donadelli, Prosperi 2012). An interesting point to address is whether
consumption based models offer a better insight on this issue. Recent literature on real business
cycle (Garciaa-Cicco et al. (2010) ) has shown that standard neoclassical models are able to explain
most of the stylized facts in price and quantities for these countries without employing the role of
policy and market failures. Nevertheless there is still a large debate in the literature on the ability
of these models to explain both quantities and prices at the same time.
A recent contribution to the literature is the paper of Barro (2006) on the role of rare disaster in
asset pricing, that has started a line of research where disaster process are included in DSGE models
to help matching model outcomes with stylized facts1 . The basic intuition of this model is that
price and quantities may be affected by the remote possibility of the occurrence of an extreme event
(such as the Great depression, wars) that is rarely observed in the data. Recent works have shown
that allowing for the presence of such event, we are able to explain theoretically the excess returns
(i.e. solving the Equity Premium Puzzle) and quantities, in particular Gourio (2012) showed that
disaster risk has a substantal effect on investment decision and hence on macroeconomic dynamics
when disaster probability is time-varying. This is an important result since it contraddicts previous
result of Tallarini (2000) that showed that relative variabilities and co- movements of aggregate
quantity variables are unaffected by the amount of risk or the degree of risk aversion. In this work
a consumption economy is studied, hence
Most of the work on disaster risk and asset pricing focus on US economy; an interesting point
is to understand if this class of models works also for other countries and in particular for emerging
markets. Emerging markets’ literature usually focus on soverreign defaults, events that usually
occurs in bad states of the world. Borri, Verdelhan (2010) show that there is a risk-based explanation of sovereign bond returns, expecially for emerging markets. Soverreign defaults usually occur
in bad states. These bad states in these countries usually correspond to similar condition in the
US; in particular this is true when a disaster occurs. If the investors are risk-adverse and business
cycles are correlated, sovereign risk premia are high.
In this work it is shown that the model presented in Barro (2006) is not able to explain the level
and the heterogeneity of excess returns for emerging markets. An additional source of variability
1 As
an example see Gabaix (2008), Gourio et al. (2011), Gourio (2012)
3
is required in order to explain the data; in the following information frictions are presented as a
possible candidate for solving our puzzle. The main idea that is developed through the paper is
that once a disaster occurs the country may be affected by idiosyncratic random disaster shock. In
this setup this idiosyncratic shock as zero mean and variance that is selected endogenously by the
agent. The assumption of zero mean correspond to assuming that idiosyncratic exposure to global
disaster is zero on average for each country. The reason for this assumption is to show that we
do not really need to assume heterogeneity in disaster process to have heterogeneity in the ERP.
Indeed assuming different disaster exposure doesn’t work when we consider geographically close
countries that perform very different levels in the ERP. Indeed the source of heterogeneity can be
simply the uncertainty linked to idiosyncratic shock. A simple comparative statics is sufficient to
show that this is a more realistic hypothesis.
Secondly, the consumer can choose a given level of information facing a cost that depends on
information frictions related to ability of the agent to have an estimate of the effect of a disaster in
a particular country. Agents try to make predictions about disaster effects in a particular country,
hence they need to process information in order to obtain accurate estimates. Institutional aspect
such as burocracy, absence of ”rule of law”, corruption influence the quality of the informations.
This implies that when the quality of information is low, is more costly to be informed, hence the
uncertainty linked to investor beliefs about disaster effects is higher. This implies that investor
will require an higher premium.
This model has some similarities in results with the recent literature on ”ambiguity aversion”.
The seminal work of Epstein, Schneider (2008) proposed a new model of information processing
when quality is difficult to judge. In such cases investors treat signals as ambiguous and update
beliefs in a non-standard bayesian framework. This has several implications on asset prices. The
most imporant results for our purposes an ”ambiguity” premia arises that is not related to covariance
with the market. If the quality of the information is perceived to be low, the asset is perceived
as if it has lower mean payoff, hence expected return increases regardless the covariance with the
market. Hence the premium on an asset that is uncorrelated with the other assets in the market
need not converge to zero with the asset’s market share.
A simple empirical evidence of this model is proposed, using information indexes from the
Quality of Government dataset. The results support the hypothesis of the model and are robust
to specification issues.
An interesting question is whether such results hold in an international setting. I tried to
answer to this question using empirical evidence. It is shown that the conditional factor model
presented in Lustig, Verdelhan (2007) performs poorly in explaining excess returns. Nevertheless
the intercepts of the model are positively correlated with the same information friction indexes
that work for the single country model. Hence information frictions on disaster effects positively
affects asset returns regardless the covariance of the asset with US consumption.
A simple modification of the single-country model, allowing for the presence of an interational
investor, is presented in section 2.2. In this presentation emerges that an important role in ex-
4
plaining asset prices is played by the covariance in the fundamentals of the economies in disaster
states, i.e. the contagion term. As this contagion term increases, investors will require an higher
premium. This contagion term appears in the intercept of the empirical analysis performed above
since disaster states are not observed in the last decades. A different question is how information
frictions affect asset returns in this setting. It emerges that it is not plausible to adopt the approach
of one-country model, hence we need additional assumption to have the same results of the one
country model. For future development, a discussion on the role of the literature about ”ambiguity
aversion” is presented. Ambiguity aversion could explain how information frictions, that affect
information quality, can affect positively the contagion term.
The paper is organized as follows. In section 1 the original model of Barro (2006) is presented
and discussed. It is also shown that this model fails in predicting the cross section of asset returns.
In section 2 a modification of the Barro’s model with idiosyncratic disaster components and information frictions is presented. Results are commented with a reference to the existing literature.
In 2.2 the model is modified in order to allow for an international investor. In the second part
empirical evidences are presented. Data sources are presented in section . Section 4 shows that
the hypothesis of our model holds empirically. Similarly the same results hold in an international
setting and empirical evidence is shown in 5.
Part I
An Asset Pricing Model with Information
Frictions and Disaster Risk
1
The Barro’s Model
In this section we briefly present the model in Barro (2006) and Barro (2009). We review the
main assumptions of this model.
Assumptions
• A consumer maximize a time-additivity utility function with iso-elastic utility
U ({ct }) =
∞
X
t=0
e−ρt
Ct1−θ − 1
1−θ
• Endowment Economy: In the economy there exists a stochastic production system. The
amount of fruit in period t is At , the productivity of the tree evolves according to
log(At+1 ) = log(At ) + γ + ut+1 + vt+1
5
where ut+1 ∼ N (0, σ 2 ) and vt+1 is the disaster process which has distribution:
(
vt+1 =
0
e−ρ
log(1 − b) 1 − e−ρ
where b is a random contraction size and ρ > 0. The distribution of b is assumed to be
exactly equal to the empirical distribution derived in Barro (2006) from time series on real
GDP per capita for 35 countries for the full twentieth century. An implicit assumption is
that the real probability distributions are reasonably similar across countries and stable over
time.
• An equity claim on period t + 1’s output is available. A ”risk free” asset is also available but
a default can occurr with positive probability in the case of disaster.
b
Rt+1
=





Rf
Rf
e−ρ
(1 − q)(1 − e−ρ )
Rf (1 − d)
q(1 − e−ρ )
where q is the probability of default and d is the stochastic default size that for simplicity is
assumed to be equal to b.
• Ct = At
∀t
From this set of assumptions, it is simple to derive analitycally the expected return on the one
period claim2
h
i
1
log (Et [Rt+1 ]) = ρ + θγ − θ2 σ 2 + θσ 2 − p E (1 − b)(1−θ) − 1
2
and the risk free asset
h
i
1
f
log Et [Rt+1
] = ρ + θγ − θ2 σ 2 − p (1 − q)E (1 − b)1−θ + qE (1 − b)(1−θ) + qE [b] − 1
2
Finally the Equity Risk Premia (ERP) can be derived by simply substracting the previous expressions
ERP θσ 2 + p(1 − q) E (1 − b)−θ − E (1 − b)1−θ − E [b]
(1)
Equation 1 expresses the ERP in this economy; the variance of the output and the coefficient
of risk aversion affects positively the ERP. If we ignore the last term the expression for the ERP
in 1 coincides with the one in Mehra (2003). Mehra, Prescott (1985) and Mehra (2003) showed
that using the usual calibration for the parameters of the model, we are not able to match the
2 We
skip the derivation since we will adopt the same procedure in the following section.
6
level of the ERP from the data, i.e. the Equity Premium Puzzle. Barro (2006) showed that with
the inclusion of ”the disaster term” in 1 we are able to obtain a level of the ERP that is relatively
close to the data.
Even if the Barro’s model is able to match the data for US, it fails in predicting the ERP for the
emerging markets and in most of the developed countries too. Donadelli, Prosperi (2012) showed
that emerging markets have outperformed developed countries in the last 20 years, compensating
the investors with an average premium of 17%. From the liberalization of most stock markets, a
large flow of investment has pushed up stock prices in these markets driven also by global easy
credit conditions.
It is easy to check that the model of Barro (2006) fails in explaining the first moment of the
ERP on two different dimensions: on the level and cross-sectionally . In table 1 are presented the
empirical and theoretical ERP for the portfolio of countries that has been used for the empirical
analysis of the next section3 . These data are quarterly data of the ERP from 1988 (with different
sample size. The main problem with considering financial data for emerging markets is that sample
size is small, hence we may be affected by business cycles4 .
As we can easily check, there is a large positive difference between empirical and theoretical
ERP of Barro (2006) and Mehra (2003) that appears evident also in figure 2. In particular for
emerging markets the difference between empirical ERP and 1 is in most of the cases around 20%
on annual basis and around 3% for developed countries. Secondly both models fails in explaining
cross sectionally the data. Indeed, not only emerging markets offered higher ERP than the ones
predicted by the models, but also perform high heterogeneity in levels. The only source of crosssectional heterogeneity of the two models is the volatility of consumption growth; this means that
two countries that have the same variability in consumption should have the same ERP. Obviously
this result is contraddicted by the data; for example, if we compare Malaysia, Mexico and Turkey
that have the same level of variability in consumption growth (5%) performed differently in the
stock markets (from 10% to 35% in the ERP).
A simple explanation of these results could be that the coefficient of risk aversion that is used
to compute the theoretical ERP (θ = 4) is too low for emerging markets. Table 1 tells that this is
not the case. Indeed the last line presents the level of θ that would explain empirical data. These
levels are obviously too high, meaning that the data cannot be explained by the risk aversion of
the investors.
Barro (2006) identified another potential source of heterogeneity in the data: the leverage. If
the equity shares represent a claim on only a part of GDP, the result on the ERP changes. In
particular the ERP is higher if the ratio of equity payments to consumption is procyclical. In
such a case 1 changes by the multiplicative factor (1 + λ), where λ is the debt-equity ratio, that is
assumed to be non stochastic and constant. Since the leverage change across countries, this may
explain the heterogeneity in the ERP5 . Unfortunately this cannot be the case. Kalemli-Ozcan et al.
3 Data
sources for the ERP and Real consumption are described in section 3
3 for further discussion.
5 Since λ ∈ [0, 1], surely leverage cannot explain the level since the difference are much higher.
4 See
7
(2012) documented that leverage is much lower in emerging markets than in developed ones, hence
leverage cannot explain the fact that emerging markets offer higher than developed countries.
Finally an alternative hypothesis is that the disaster risk has idiosyncratic components. Gourio
et al. (2011) proposed an international business cycle model with time varying aggregate disaster
risk where countries differ in their exposure to aggregate risk and this exposure is constant over
time. The exposure to time varying disaster is the source of heterogeneity in the excess return in
this model. In particular lower exposure to aggregate disaster produces lower risk-free rates and
lower excess returns. The authors show that the heterogeneity in the ERP can be explained by
different disaster exposures, that means that the large differences in the ERP in table 1 are due
to the existence of a larger exposure of emerging markets to global risk with respect to developed
countries. This argument can be strongly criticized. The critique is based on some considerations
about the results of Gourio et al. (2011). Firstly disaster exposures cannot differ too much when we
consider countries that belongs to the same geographical area. Since a disaster is defined as a large
aggregate shock on TFP growth and does not affect directly any other aspect of the economy, the
impact of such a shock cannot differ too much when there is geographical proximity. This implies
that countries belonging to the same geographical area should have very similar ERP. This result
is contraddicted by the data and this can be observed once again in table 1. Countries belonging
to the same geographical area still have very different ERP, for example Czech Republik offers
a premium of 17.6% much lower than in Russia (36.6%) or Hungary (20.8%). Similar anomalies
occur in Asian countries and Middle East.
In this work we try to identify an additional source of heterogeneity for the ERP that can
explain the cross-sectional variability in the data. The idea is that we don’t need to impose that a
global disaster have different idiosyncratic effect among countries to generate heterogeneity in the
ERP; indeed what we only need is that we have different level of information on the effect of a
disaster effect on a particular country. If we simply assume that the disaster process is stochastic
and the variance of the effect of the disaster change among the countries, we simply obtain a
sufficient level of heterogeneity. As we will see, assuming heterogeneity on the variance provides
more realistic results than assuming heterogeneity in the exposure. Furthermore we suggest that
different level of uncertainty on the disaster effect are related to frictions in acquiring informations
about the country, frictions that can be related to institutional characteristics.
8
9
Brazil
0.248
0.034
0.005
0.039
92.15
India
0.153
0.022
0.002
0.036
53.29
Morocco
0.117
0.037
0.005
0.040
28.28
Chile
0.201
0.033
0.004
0.039
14.73
Indonesia
0.222
0.044
0.008
0.042
47.19
Tunisia
0.147
0.016
0.001
0.035
43.89
Colombia
0.231
0.031
0.004
0.038
178.70
S. Korea
0.101
0.053
0.011
0.045
47.31
France
0.055
0.011
0.001
0.035
49.79
Mexico
0.210
0.055
0.012
0.047
91.76
Malaysia
0.109
0.050
0.010
0.044
28.00
Germany
0.063
0.011
0.001
0.035
60.15
Peru
0.244
0.032
0.004
0.038
71.20
Pakistan
0.111
0.042
0.007
0.041
34.37
Italy
0.024
0.018
0.001
0.036
-38.52
Czech Rep.
0.176
0.025
0.002
0.037
27.65
Philippines
0.114
0.010
0.000
0.035
298.77
Japan
-0.041
0.015
0.001
0.035
-67.63
Hungary
0.208
0.042
0.007
0.041
101.24
Thailand
0.121
0.048
0.009
0.044
76.65
UK
0.047
0.026
0.003
0.037
-0.49
Poland
0.048
0.019
0.001
0.036
531.51
Kenya
0.407
0.031
0.004
0.038
37.09
USA
0.059
0.017
0.001
0.035
44.66
Russia
0.366
0.067
0.018
0.052
73.24
S. Africa
0.115
0.025
0.002
0.037
113.50
Canada
0.080
0.016
0.001
0.035
88.88
0
Arg
5
10
Pol
Col Per
Chl Mex Hun
Czr
Bra
15
20
Phi
Pak
Mal
Kor
Ino
Ind
Chi
Rus
Tur
Tha
Ken
25
SAf
30
Jap
35
Can
FraGer UKUS
Ita
Tun
Mor
Jor
Egy
Figure 2: Difference Empirical vs Theoretical ERP in 1: Each point in the plot represents the difference between the empirical ERP
(line 1 table 1) and the theoretical ERP of Barro (line 4 table 1)
−0.1
0
0.1
0.2
0.3
0.4
Figure 1: Empirical vs Theoretical ERP: In the first line the empirical ERP for each country in the column dimension is presented. In
the second line we have instead the standard deviation of real consumption per capita for each country. Finally in the third and fourth
lines we have the theoretical ERP as in Mehra (2003) and Barro (2006) for a level of θ = 4. The last line show the implied θ from 1.
These are the levels of risk aversion that would explain empirical data. Sample: 1990-2009
ERP
σC
ERP (M&P)
ERP (Barro)
Implied θ
Argentina
0.259
0.068
0.018
0.052
53.88
China
0.021
0.019
0.001
0.036
0.48
Jordan
0.031
0.093
0.034
0.069
-4.76
Turkey
0.342
0.052
0.011
0.045
75.52
Egypt
0.292
0.016
0.001
0.035
150.23
2
A simple model with uncertainty on disaster effect
2.1
The Assumptions of the Model
The occurrency of a disaster may produce different effects according to the country we are
considering. In particular an agent doesn’t know ex ante which is the effect of a disaster in a
country where information is opaque. This uncertainty affects the level of the disaster but also it
may affect the recovery from the occurence of a disaster. In particular when the political situation
is not stable, information is controlled, corruption is diffuse, it is hard to make predictions about
the recovery. In the following we are going to ignore this second source of uncertainty. Following
Barro (2006), we simply assume that the once the disaster occurs, it only affects the level of output
but not the other parameters of the process.
In this model we are going to consider the possibility that the agent can select his level of
information on the country endogenously. A risk-adverse agent would like to invest resources in
acquiring informations in order to remove the uncertainty related to the investment.
In the following we will assume that there exists another component where a disaster occurs. Our
disaster process can be rewritten in this way
(
vt+1 =
0
e−ρ
log(1 − b) + ij
1 − e−ρ
where ij = µˆj . Once the disaster hits the country j, it is affected by global random shock b and
a deterministic exposure µˆj . Even if the idiosyncratic shock is fixed, from the agent point of view
it is assumed to be random. A natural question may arise about the rationality of the agent that
is considering as random an event that is deterministic. Indeed when the agent is infinitely living,
he should learn the natural non-randomness of the process. Nevertheless in the real world people
live a finite period and since disasters are rare by definition, they may not be able to observe the
realization of a disaster. The agent living ”under the veil of ignorance” will consider the idiosyncratic
component as random. From a theoretical point of view this hypothesis corresponds to assuming
that the agent has limited memory or similarly limited ability of processing informations. This
approach is very similar to the one adopted by the ”rational inattention” literature, where the
agents live in a full information world but, since their ability of processing information is limited
the resulting variance of the process is higher. Luo, Young (2010) show that the inclusion of
rational inattention in a linear quadratic utility model raises expected excess returns increasing
the volatility of consumption relative to the endowment.
Since the disaster exposure is non-random from the point of view of the agent, it is assumed
that ij ∼ N µj − 21 s2j , s2j 6 . It is assumed that µj − 12 s2j is the expected country specific effect of
a disaster, instead s2j represents the uncertainty about her personal estimate about these effect. As
6 The assumption of normality in idiosyncratic exposure is conceptually not satisfying since it gives positive
probability to negative or greater than one disaster exposures. Nevertheless is very helpful in the algebra since we
can use the properties of log normal distribution
10
we can see, in this general formulation we are considering the possibility that different countries
may have different level of exposure to the disaster (µj 6= µi ∀i =
6 j). For a matter of simplicity
we assume that µj is determined according to available informations that are indipendent from
the other variables of the model, i.e. from the history of the process {At } or previous disaster
realizations. Like in Barro (2006) it is mantained the hypothesis of constant disaster probability,
Gourio (2012) presented a model with time-varying disaster risk in a production economy that
affects total factor productivity and capital destruction. In this model correlation between output
and disaster probability are correlated endogenously creating a feedback effect from the production
side to financial variable. Even if this assumption produces more realistic results, the first moments
of the ERP do not change significantly, hence it would not change the results of our analysis.
Notice that the additional variance term in the mean of the process ij has the role of offsetting
the variance in the mean of the lognormal distribution. Indeed the expected value of the output is
Et [At+1 ] = At eγ+
σ2
2
e−p + (1 − e−p )E [1 − b] eµj
The expected value of the output does not depend on the variance of the disaster exposure.
2.1.1
How the agent selects the information level
In this model it is assumed that the agent can improve his level of uncertainty by informing
himself. Information activity increases understanding of the enviroment and reduces the variance
s2j . If information activity has no cost, he would select the lowest achievable level of uncertainty
that is zero, since the idiosyncratic exposure is deterministic. In general perfect knowledge is not
achievable by human being indeed we need more and more effort to have a precise understanding
of the effect of an event. This consideration reflects the fact that the agent will face increasing
costs in order to reduce s2j . In order to account for this we simply assume that the agent has to
renounce to a fraction of the consumption good defined in the following way
C(s2j ; τj )
=
s2j
s̄
!τj
(2)
where s̄ is a common upper bound limit for s2j , hence 0 ≤ s2j ≤ s̄. In 2 a crucial role in explaining
cross country differences is explained by the parameter τj . Since the argument of the power
function is less than one, as this parameter increases the fraction of the consumption good that
we have to invest for a given level of s2j increases. This parameter can be interpreted as the degree
of opaqueness or information frictions in the country where the agent wants to invest: this affects
the costs he will face in reducing the uncertainty of disaster’s effect.
The total amount of consumption good that the agent consume at time t is
Ct =
C(s2j ; τj )At
=
s2j
s̄
!τj
11
elog(At−1 )+γ+ut +vt
= exp τj log(s2j ) − log(s̄) + log(At−1 ) + γ + ut + vt
The last expression is easy to interpret, if the consumer decide not to investigate on the country’s
condition he will choose s2j = s̄ hence he will not incurr in any cost, indeed if he wants to decrease
his uncertainty he should renounce to part of the consumption good. Hence the agent faces a
trade-off in the choice of s2j that will be derived by the maximization of the per-period expected
utility given the equilibrium condition.
sj
1−θ
1
−1
Et Ct+1
1−θ
s.t.
Ct+1 = C(s2j ; τj )At+1
M ax
2
(3)
Removing the terms not depending on s2j , the objective function can be rewritten in the following
way
1
exp((1 − θ)τj log(s2j ))Et [exp((1 − θ)vt+1 )] =
1−θ
h
h
ii
1
=
exp((1 − θ)τj log(s2j )) e−p + (1 − e−p )Et e(1−θ)[log(1−b)+ij ] =
1−θ
θ(1−θ)s2
j
1
=
exp((1 − θ)τj log(s2j )) e−p + (1 − e−p )E (1 − b)1−θ e(1−θ)µj − 2
1−θ
In this setting we are assuming that the agent at time t select his level of uncertainty/information
Instead the economic effects, the disaster and information cost, occur in t + 1. With this assumption the intertemporal problem of choosing s2t is equivalent to a single-period problem hence
s2j,t .
s2j,t = s2j .
We now take a log trasformation of the objective function7
θ(1−θ)s2
j
(1 − θ)τj log(s2j )) − p + pE (1 − b)1−θ e(1−θ)µj − 2
If we assume that the country specific disaster effect is negligible, µj ≈ 0 and that the uncertainty s2j is not so high, we can approximate the exponential function using ex = (1 + x). It is easy
to verify that the first order condition of the maximization problem 3 is the following
s2j :
θ(1 − θ)
(1 − θ)τj
− pE (1 − b)1−θ
=0
2
sj
2
assume that the arbitrary length period approach to zero, this means that p → 0. Hence we can
(1−θ)2 s2
j
2
taylor-expand the log of the ”disaster” part around p = 0. Let’s define x = E (1 − b)1−θ e(1−θ)µj +
(1 − e−p )x
log e−p + (1 − e−p )x = log(e−p ) + log 1 +
e−p
p
e
|p=0 p = px
log (1 + (ep − 1)x) ≈ 0 +
p=0
1 + (ep − 1)x
log e−p + (1 − e−p )x ≈ −p + px
7 We
12
which leads to an analytical solution
s2j =
2τj
pθE [(1 − b)1−θ ]
(4)
Equation 4 has an intuitive interpretation: when the information cost associated to country j
increases, the agent has to accept a lower level of information, indeed if the probability of disaster p
increases he wants to get more information in order remove some level of uncertainty if the disaster
occurs. As before the role of θ is ambiguous.
This result holds when µj is negligible, in such a case 4 represents a good approximation for
the optimal level of information. Nevertheless it may be that the agent thinks that country j will
be affected by large idiosyncratic shock if the disaster occurs; if this is the case equation 4 is a bad
approximation. Nevertheless even if expected idiosyncratic is large, it does not affect the results.
Indeed computing the F.O.C. for the log transformation of the objective function, we obtain
s2j :
θ(1 − θ) (1−θ)µj − θ(1−θ)s2j
(1 − θ)τj
2
e
= pE (1 − b)1−θ
2
sj
2
|
{z
}
| {z }
2
(5)
f (sj ,µj )
g(s2j ,τj )
Comparative statics is possible by simply plotting the LHS, g(s2j , τj ), and the RHS, f (s2j , µj )
of the last equation as shown in figure 2.1.1. The curves have positive intersection in an unique
point. As we increase τj from 0.1 to 0.3 the g() curve shifts upwards, implying that an higher s2j
will be selected. This confirms the result in 4. As µj decreases from 0 to -0.01, the agent will select
a lower s2j implying that higher information level (lower s2j ) is selected.
In the next section we will see which implications this model has in terms of asset pricing.
13
0
−2
−4
−6
g(,tau) f(,mu)
−8
g(,0.1)
f(,0)
g(,0.3)
f(,−0.1)
0.0
0.2
0.4
0.6
0.8
1.0
s2
Figure 3: The Optimal Level of Information: The black and the red line correspond respectively
to the LHS and RHS of 5 for τj = 0.1 and µj = 0. Increasing τj to 0.3 shifts upwards the LHS,
indeed reducing µj to -0.01 shifts the RHS rightside. In both cases s2j increases.
2.1.2
Asset Pricing
One Period Claim
We can to check now the asset pricing implication of this model. In the following we derive
similar results to the paper of Barro (2006). We start by the fundamental pricing equation
"
0
−ρ
u (Ct ) = e
At+1 C(s2j ; τj )
u (Ct+1 )
Pt
#
0
Et
(6)
that can be rewritten
"
(C(s2j ; τj )At )−θ
−ρ
=e
Et
14
(C(s2j ; τj )At+1 )1−θ
Pt,1
#
θ h
1−θ i
P1,t = e−ρ At C(s2j ; τj )) Et C(s2j ; τj )At+1
where P1,t is the price of the one period claim. Rearranging we obtain
P1,t
θ
(1−θ)
At C(s2j ; τj ))
Et [exp ((1 − θ)(γ + ut+1 + vt+1 ))]
= e−ρ At C(s2j ; τj ))
= e−ρ At C(s2j ; τj )Et [exp ((1 − θ)(γ + ut+1 + vt+1 ))]
Substituting our definition of the cost functions and exploiting the properties of the log normal
distribution, we end up with
P1,t
(1 − θ)2 σ 2
=At exp −ρ + τj
− log(s̄) + (1 − θ)γ +
2
2 θ(1−θ)s
j
e−p + (1 − e−p )E (1 − b)1−θ e(1−θ)µj − 2
log(s2j )
(7)
Using 7 the gross expected return of one period claim is defined as follows
σ2
C(s2j ; τj )At eγ+ 2 Et [evt+1 ]
Et [C(s2j ; τj )At+1 ]
=
Et [Rt+1 ] =
(1−θ)2 σ 2
P1,t
e−ρ At C(s2j ; τj )e(1−θ)γ+ 2 Et e(1−θ)vt+1
= eρ−
θ2 σ2
2
+θσ 2 +θγ
h
i−1
Et [evt+1 ] Et e(1−θ)vt+1
Taking logs of the last expression and assuming that the arbitrary length period approach to
zero (see footnote 7).
log (Et [Rt+1 ]) = ρ −
θ(1−θ)s2
j
θ2 σ2
+ θσ 2 + θγ + pE [1 − b] eµj − pE (1 − b)1−θ e(1−θ)µj − 2
2
(8)
Risk Free Asset
Using the pricing equation we can price also the risk free asset.
b
(C(s2j ; τj )At )−θ = e−ρ Et (C(s2j ; τj )At+1 )−θ Rt+1
1 = e−ρ−θγ+
θ2 σ2
2
i
h
h
Rf e−ρ + (1 − e−ρ ) (1 − q)Et e−θ(log(1−b)+ij ) +
ii
h
+qE[1 − b]Et e−θ(log(1−b)+ij )
where we have assumed that d = b. As usual, taking logs of both sides and rearranging terms it is
possible to obtain log(Rf ).
15
log(Rf ) = ρ + θγ −
θ(1+θ)s2
j
θ2 σ2
+ p − p E (1 − b)−θ e−θµj + 2
((1 − q) + qE[1 − b])
2
b
We are now interested in computing Et [Rt+1
].
b
Et [Rt+1
] = Rf e−p + (1 − e−p ) (qE[1 − b] + (1 − q))
b
log Et [Rt+1
] = log(Rf ) − p + p(1 − qEb) = log(Rf ) − pqE[b]
(9)
Equity risk premium
The equity risk premium can be simply derived as a difference between 8 and 9.
ERPt s2j , µj
h
i
θ(1−θ)s2
j
=θσ + p E[1 − b]eµj − E (1 − b)(1−θ) e(1−θ)µj − 2
2
−θµj + θ(θ+1)s2j
−θ
2
(qE[1 − b] + (1 − q)) + qE[b] − 1
+E (1 − b)
e
(10)
We are interested in testing whether an increase in s2j affects positively the ERP . Due to the
fact that the disaster distribution is the empirical distribution provided by Barro, we are not able
t
t
in general to know the sign of ∂ERP
and ∂ERP
∂µj . Nevertheless using a standard calibration it is
∂s2j
possible to plot ERPt s2j , µj . In order to do so we adopted the calibration of Barro.
p = 0.017
γ = 0.025
σ = 0.02
ρ = 0.03
θ=4
q = 0.4
The plot of 10 as a function of s2j is presented in figure 2.1.2. As expected, as the variance
associated to information cost increases, the required premium increases.
Comparative Statics
We are also interested to know what happens when τj and µj increase. As τj increases, the agent
has to pay more to get informed, hence he will choose optimally an higher variance level, i.e. to be
less informed. This obviously implies an increase in the ERP. Indeed if µj decreases, it means that
the agent things that in country j a disaster will be more effective than in other countries. This
induces the agent to invest more resources on information to reduce the variance on her estimate
(i.e s2j decreases). Hence the increase in µj has two effect on the ERP: a direct effect from 10,
and an indirect effect from the FOCs of the information problem. Using the calibration of Barro
(2006), it turns out that an increase of the expected disaster exposure of country j induces the
agent to ask an higher premium. These comparative statics are shown in figure 2.1.2.
From this analysis a simple confirmation of our initial hypothesis appears. Let’s suppose that
we fix τ = 0 and we want to claim that different ERP for country j and k derive from different
disaster exposures. If this is the case the expectation of a disaster in a country j will be different
16
than the one in country k, µj 6= µk . Let’s take j = Cz.Republik k = Russia; we know that
ERPCzR = 0.176, ERPRus = 0.366. By looking at the bottom right of 2.1.2, we can check that
we should have µRus ≈ −0.332 µCzR ≈ −0.114. This means that once a disaster occurs output
falls by E(1 − b)eµj . Since from Barro’s calibration E(1 − b) = 0.71, it is simple to show that the
occurrence of a global disaster leads to the following expected fall in GDP
∆yt Rus
|
≈ −49.6%
yt Dis
∆yt CzR
|
≈ −36.8%
yt Dis
. This means that we need to assume that real GDP in Russia falls of 12.8% more than in Czech
Republik when a disaster occurs. Similar results hold for Hungary, once a disaster occurs the
expected real fall in GDP should be ≈ 39.9%, 10% difference with Russia. This is not plausible
for two countries belonging to the same geographical area. Indeed if we fix µj = µk = 0 this large
difference in ERP may be explained by τRus ≈= 0.7 and τCzR ≈= 0.4, that looks more realistic.
This comparative statics does not imply that differences in the ERP can be uniquely explained
by different level of uncertainty associated to disaster effects; indeed we do not want to rule out
the possibility that disasters have different effects in neighbor countries. Nevertheless this analysis
shows that different ERP can be related to information issues and not different disaster process,
this hypothesis will be tested in the next part. In the empirical part the possibility that different
countries may have different disaster exposure is not considered, it is assumed that µi = 0 ∀i, hence
the heterogeneity comes only from information frictions.
17
0.35
0.30
0.25
0.20
0.15
0.10
0.05
0.00
0.05
0.10
0.15
sigma2j
Figure 4: The ERP as a function of information level: In the figure the ERP is plotted as a function
of s2j according to 10.
This simple analysis suggests that difference in risk exposures like in Gourio et al. (2011)
are not sufficient to explain different level in the ERP, but it is sufficient to assume that the this
difference is explained mostly by the level of uncertainty on the disaster effect. More precisely in our
model different countries have ex post different exposure to the aggregate shock, but ex-ante this
difference is zero. Our analysis also suggests that where informations are costly the agent will ask
an higher premium for investing in the economy, due to the fact that the uncertainty is necessarly
higher. What we propose is that the cost of information is strongly related to institutional assets
of the economy such as the judicial indipendence, the functioning of the government, corruption
or whether there is a democracy or not. All these factors affect the opacity of informations and
the cost for the agent to be informed. In the next section we test empirically this hypothesis.
18
sigmaj
tauj
0.02
0.03
−0.35 −0.30 −0.25 −0.20 −0.15 −0.10 −0.05
Sigma Response to muj
0.01
Sigma Response to tauj
0.00
0.04
muj
tauj
0.02
0.03
ERP Response to muj
0.01
muj
−0.35 −0.30 −0.25 −0.20 −0.15 −0.10 −0.05
0.00
ERP Response to tauj
0.00
0.04
Figure 5: Comparative statics of s2j and the ERP from 10. The plot on the left represent the comparative statics of s2j w.r.t. τj and µj .
In analogous way on the RHS we have comparative statics of the ERP with respect to the same variables
sigmaj
0.15
0.10
0.05
0.07
0.06
0.04
0.03
0.05
ERP
ERP
0.5
0.4
0.3
0.2
0.1
0.0
0.4
0.3
0.2
0.1
0.0
19
2.2
Towards an International Model
The results of the previous section hold in a closed tree economy hence we are not considering
the possibility of investing in an asset that is not perfectly correlated with the consumption stream.
An interesting question is whether such a premium arises also in a model of international C-CAPM,
where the US investor has to invest in an emerging economy where the payoff is not correlated
with US consumption.
In order to understand how information and disaster risk affect asset pricing in an international
setting , the previous model can be modified in a simple way. A simple approach is ton focus on the
role of disaster in asset pricing, and derive conclusion on the role of information from the results.
It is assumed that the domestic agent can invest in the tree economy of country F ; here two output
F
processes AD
t and At have to be considered
D
D
D
D
logAD
t+1 = logAt + γ + ut+1 + vt+1
2
udt+1 ∼ N (0, σD
)
F
F
F
F
logAt+1
= logAF
t + γ + ut+1 + vt+1
2
uF
t+1 ∼ N (0, σF )
”Normal” output shocks are in general correlated with covariance σD,F . The disaster process
for both countries have a global component (the disaster in Barro (2006)) and an idiosyncratic
components that may be correlated
(
j
vt+1
=
0
log(1 − b) + ij
e−ρ
1 − e−ρ
j = {D, F }
where as before ij ∼ N µj − 21 s2j , s2j and cov(iD , iF ) = sD,F . Here the agent cannot select the
information level; the focus of this model is to identify the role of sD,F in asset pricing. Without
showing the algebra, using the pricing equation
u
0
(AD
t )
−ρ
=e
AF
t+1
0
D
Et u (At+1 )
Pt
it is possible to derive the prices and expected returns from a one-period claim in the foreign
country and the risk-free asset
2
F θ 2 σD
log Et Rt+1
+ θσD,F − pE (1 − b)1−θ E eiF −θiD + pE [1 − b] E eiF
= ρ + θγ D −
2
2 2
−θµD + θ(1+θ)s2D
b −θ
D θ σD
2
log Et Rt+1 = ρ+θγ −
+p−p E (1 − b)
e
((1 − q) + qE[1 − b]) −pqE [b]
2
20
Finally, using the properties of log-normal distribution8 , the ERP can be derived by substracting the two last expressions
n
h
i F
D
2 θ(1+θ)
ERPtD,F =θσD,F + p E[1 − b]eµD − E (1 − b)(1−θ) e(µ −θµ )+sD 2 −θsD,F
−θµD + θ(θ+1)s2D
−θ
2
e
+E (1 − b)
(qE[1 − b] + (1 − q)) + qE[b] − 1
(11)
Equation 11 appears to be very similar to 10, in particular assuming the output processes
to be identical in 11 we are back in 10. As in the previous analysis, what plays a role here is
the different idiosyncratic exposure µD and µF . Assuming that these components are zero, the
unique fundamentals of country F that affects his ERP, are the covariance in ”normal” times,
σD,F , and the covariance in disaster periods, sD,F that can referred as contagion term. Observe
that as the contagion term or σD,F increases, the ERP also increases. This result has a natural
interpretation; since the investor is risk-adverse he wants to diversify his portfolio and select assets
that are not correlated with domestic consumption stream in bad times. Hence if the covariance
between domestic consumption and foreign asset increases, he will ask higher excess returns.
This prediction of the model, that emerging markets are priced according to the covariance
with consumption growth in the US, σD,F , is usually confirmed by the data. Borri, Verdelhan
(2010) showed empirically that soverreign excess return of bonds compensate investors for taking
on aggregate risk. Lustig, Verdelhan (2007) showed the same result for currency trade returns.
Nevertheless it is important to notice that these authors focused their analysis in ”normal period”,
assuming that bad states do not change the fundamental relatonship between the economies. In this
model covariance between countries is time-varying, it may jump in disaster periods according to
sD,F . The phenomenon of financial contagion is studied in dept in Forbes, Rigobon (2002). These
authors showed that even during the most famous financial crisis (1997 Asian crisis, 1994 Mexican
devaluation) a phenomenon of contagion did not occurred, and the level of interdependence was
the same as in normal periods. This means that contagion phenomena occurr rarely, for example
in the case of global disasters.
As a remark for the empirical part this means that the covariance between consumption growth
and asset returns does not capture this contagion effect. Instead, the investor still ask for a premium
due to disaster, that empirically appears in the intercept of a conditional factor model.
It is now clear how disasters affects asset pricing in an international setting. It is not clear
8 It
is required to derive E eiF −θiD . First
1
zF,D = iF − θiD ∼ N (µF − θµD ) − (s2F − θs2D ), s2F + θ2 s2D − 2θsD,F
2
Now, using the properties of the log-normal distribution
h
i
F
D
2 θ(1+θ)
E eiF −θiD = e(µ −θµ )+sD 2 −θsD,F
Observe that when the two countries are the same, we obtain e(1−θ)µj −
21
θ(1−θ)s2
j
2
as in the expression 10.
how information quality should affect the contagion term or disaster exposure. In the last section
we have assumed that information activity allows to reduce the variance associated to investor
beliefs up to the natural idiosyncratic variance of disaster (that was assumed to be zero). Here
information activity can be devoted to evaluate the contagion terms, i.e. to understand real
connection between the economies when a disaster hits. Let’s denote the contagion term as the
sum of the true contagion term and and an additional term that we denote as information bias
sD,F = s̄D,F + ιD,F the first term is the true real connection between the economies in disaster
periods. Let’s suppose that s̄D,F = ιD,F = 0; this implies that covariances in disaster states is
uniquely determined by the global disaster process. Assume that we are considering two countries
belonging to the same geographical area, hence µD = µF = s̄D,F = 0 and real connections are only
determined by information bias.
Information activity has the role of reducing information bias to zero. If information actiity
is costly, the agent will minimize the information bias up to a natural information friction level.
Nevertheless, with respect to the previous section, we are not able to evaluate the sign of ιD,F . In
the last section we proved that ιD,F (that was equal to s2j ) was greater than 0 and increasing in the
cost of information τj , this result implies that ERP is increasing in τj . In order to obtain a similar
result with this model we should assume that when information frictions are high, the information
bias is positive, i.e. when the investor face information frictions, he consider asset returns of foreign
country to be more correlated with domestic consumption stream. But in general we are not able
to assume if information bias plays a role increasing or decreasing covariance in disaster states.
We need to make a behavioural assumption.
2.2.1
The Ellsberg Paradox and Information Frictions
In order to explain such beliefs we should depart from expected utility approach in a bayesian
framework. A simple explanation can be related to the so called ”ambiguity aversion” literature. In
this framework the agent doesn’t behave in a bayesian way when faces ambiguity alternatives. An
classical example is the Ellsberg Paradox. In this experiment the agent is invited to chose between
two urns of four balls: a ”risky urn” with 2 black and 2 white balls, an ”ambiguous urn” where he
is told only that it contains at least one ball of each color. The agent is invited to select an urn
an bet on their color. A typical bayesian agent probably adopt a prior such that he is indifferent
between betting on the ambiguous or risky urn. Instead in the real world agents typically select
the risky urn. A simple way to explain such behaviour is that the agent forms a subjective range of
probabilities about the composition of the ambiguous urn. He then evaluates bets by calculating
the worst-case expected utility. If he is betting on black, he will consider the ambiguous urn as
containing only one black ball, hence he will chose the risky one. The opposite holds if he decides
to bet on white.
This kind of behaviour can explain why information bias is increasing in information frictions.
In this model ambiguity relies on sD,F ; if information quality is poor the agent form a range
[r(τ ), R(τ )] of alternative values for sD,F . Suppose for simplicity that s̄D,F ∈ [r(τ ), R(τ )] . The
22
width of the range is increasing in the level of information frictions τ . Indeed if information quality
is poor, the agent cannot exclude unplausible values for s̄D,F . If the agent is ambiguity-adverse he
will consider the worst case to be the real one. As shown in Epstein, Schneider (2005) this implies
that the asset price for the one period claim is determined as follows
(
Pt =
min
sD,F ∈[r(τ ),R(τ )]
e−ρ+(γF −θγD )+
2
(σF2 +θ2 σD
) −θσ
2
F,D
×
io
h
F
D
2 θ(1+θ)
e−p + (1 − e−p )E (1 − b)1−θ e(µ −θµ )+sD 2 −θsD,F
(12)
Hence he will consider sD,F = R(τ ), or put differently, the information bias is
ιD,F = R(τ ) − s̄D,F
∂ιD,F
>0
∂τ
This simple argument helps in explaining empirical results in the international setup coincide
with the one-country model of the beginning of the section. Ambiguity aversion is able to explain
why information frictions lead to higher ERP.
Part II
Empirical Evidence on the Role of
Information Frictions and Disaster
In the previous section, we have presented a model where the uncertainty linked to the realization of a disaster affects the pricing of holding a one period asset in a tree economy with disaster
risk. In particular we have seen that frictions in acquiring informations affect positively the excess
returns. The reason is that the investor, that is risk adverse, wants to invest resources to decrease
his uncertainty. A consequence of this model is that investing in a country where informations are
not easily available, will induce the investor to ask for a premium.
3
The Data
In this section we present the dataset that has been used for the empirical analysis. The
portfolio of country is presented in table 1. Each emerging country has been selected according to
economic importance and data availability. Instead, the advanced economies are the G-7 countries
and no geographical relation between these countries exists. The main problem with our empirical
analysis is the sample size. Unfortunately financial data for emerging markets started in 1988.
This can be a problem since business cycle, that are usually very long in the emerging markets,
23
may affect the ERP. As an example Garciaa-Cicco et al. (2010) documented that in the period
1980-2005 only 1-1.5 cycles occurred. Even if low sample size may explain the high level of ERP
in our sample, it is not able to explain the heterogeneity in the data.
Developed Countries
Advanced
Canada
France
Germany
Italy
Japan
United Kingdom
United States
Emerging Countries
Latin America Eastern Europe
Argentina
Czech Republic
Brazil
Hungary
Chile
Poland
Colombia
Russia
Mexico
Turkey
Perù
Asia & FE
China
India
Indonesia
Korea
Malaysia
Pakistan
Philippines
Sri Lanka
Taiwan
Thailand
Sub-Saharan Africa
Kenya
Nigeria
South Africa
North Africa & ME
Egypt
Jordan
Morocco
Tunisia
Table 1: Portfolio of Countries
Equity Risk Premia
The data for the ERP have been downloaded from Datastream. For each country the Morgan
Stanley Total Return Index has been used for the return of the one-period asset. MSCI-TRI are
denominated in US dollars and it is computed by reinvesting dividends. For our purposes we are
interested in quarterly and annual data but the sample size differs across countries. Table 2 reports
the sample size of the MSCI for the selected countries. As we can check there is large heterogeneity
in the sample size. Time series start at different period in most of the cases due to the fact that for
emerging markets financial liberalization occurred at different periods in time. The entire analysis
has been developed by using all the data available for each country; this implies that parameters
have been estimated using different samples in order to obtain more robust estimates. This issue
may affect the result in the cross section analysis when we aggregate these estimates. This problem
is unavoidable since it is related to datta availability, but several robustness tests showed that this
isssue does not affect the result significantly. Finally, also the MSCI-TRI for a global portfolio of
countries has been download as a proxy for the market return that will be used in section 5.
In order to obtain the ERP, we need to substract each return by a corresponding risk free rate
denominated in US dollar. We choose the return from the 10 year Treasury Bond. There are two
reasons for this choice. First, since we are using quarterly and annual data, using the usual 1
month Tbill may lead to misleading results due to the mismatch in the maturity of the investment.
Second, since investing in stocks is conceived as a long term investment, we should compare with
a return from an asset with similar maturity. Nevertheless the choice of the risk-free rate is not
critical for our result. The analysis has been replied using the 1 month TBill and the results are
substantially unchanged.
24
Argentina
Q1/88 Q4/11
Hungary
Q1/95 Q4/11
S. Korea
Q1/88 Q4/11
Kenya
Q3/02 Q4/11
France
Q1/88 Q4/11
Brazil
Q1/88 Q4/11
Poland
Q1/93 Q4/11
Malaysia
Q1/88 Q4/11
Nigeria
Q3/02 Q4/11
Germany
Q1/88 Q4/11
Chile
Q1/88 Q4/11
Russia
Q1/95 Q4/11
Pakistan
Q1/93 Q4/11
S. Africa
Q1/93 Q4/11
Italy
Q1/88 Q4/11
Colombia
Q1/93 Q4/11
Turkey
Q1/88 Q4/11
Philippines
Q1/88 Q4/11
Egypt
Q1/95 Q4/11
Japan
Q1/88 Q4/11
Mexico
Q1/88 Q4/11
China
Q1/93 Q4/11
Sri Lanka
Q1/93 Q4/11
Jordan
Q1/88 Q4/11
UK
Q1/88 Q4/11
Peru
Q1/88 Q4/11
India
Q1/93 Q4/11
Taiwan
Q1/88 Q4/11
Morocco
Q1/95 Q4/11
USA
Q1/88 Q4/11
Czech Rep.
Q1/95 Q4/11
Indonesia
Q1/88 Q4/11
Thailand
Q1/88 Q4/11
Tunisia
Q3/04 Q4/11
Canada
Q1/88 Q4/11
Table 2: Sample size of MSCI TRI
Real Consumption per capita
In order to evaluate the theoretical ERP in 10 we need the real consumption expenditure for the
countries in table 1. We used the data from World Bank on Household Consumption Expenditure
per capita (constant 2000 US $)9 . These are annual data from 1988 to 2009 but for some countries
data start after 1988. In particular data for Argentina start in 1993 and data for Czech Republik,
Poland and Russia start in 1990. We have no data on consumption for Sri Lanka, Taiwan and
Nigeria, hence these countries have been excluded in the first part of the empirical analysis.
Disaster Data
The disaster data that are necessary for the computation of the moments E[1 − b] in 10 are
the same data used in Barro (2006). The dataset of Barro is composed by 60 episodes across 35
countries in the twentieth century where real gdp growth declined at least 15 %.
Real Consumption Growth in the US
In the following is presented an empirical evidence of the role of information frictions in a model
of international CCAPM. Following Lustig, Verdelhan (2007), for this analysis quarterly data from
1988 Q1 to 2011 Q4 on real consumption of durable and non-durable goods have been used. Data
have been extracted from the NIPA tables of the Bureau of Economic Analysis.
Information Friction Indexes
Finding a good proxy for information index that may affect asset pricing in the emerging market
can be really hard since these frictions are not easily measurable. Indeed difficulties in obtaining
informations are mostly related to institutional factors that are really country specific. In particular
it doesn’t exist an unique factor that affects information availability; this means, for example, that
corruption of public officials may be a source of friction in country i but not in country j where
frictions can be generated by the absence of judicial indipendence. Hence the selection of a good
index can be an hard task in particular when the dataset of possible candidate indexes is large.
9 Indicator
Code: NE.CON.PRVT.PC.KD
25
Indeed we have many alternative indexes that are available in the Quality of Government (QoG)
Dataset developed by the QoG institute. The QoG institute compiled both a cross-sectional and
a panel dataset with global coverage spanning the time period 1946-2009. The datasets draw
on a number of freely available cross-sectional data sources on corruption, bureaucratic quality,
and democracy together with many other characteristics related to the electoral systems, socioeconomic factors and human development10 . In the analysis we have used only the cross-sectional
dimension of this dataset, using the measurement of the index around year 2000. Still removing
one dimension we have 841 alternative indexes that can be used. In order to select among these
index we used a stepwise procedure to select the most significative indexes and among this group
we have selected a small group of indexes related to information frictions. The stepwise procedure
and the selected index will be described in the next section.
4
Empirical Evidence for the Single Country Model
As we have seen in section 2, the theoretical ERP expressed in 10 is a function of the variance
of consumption growth σ 2 , the coefficient of relative risk aversion θ, the probabilty of a disaster
p, the probability that a disaster leads to the default of the country q, the disaster realizations b
and the idiosyncratic disaster component µj and σj2 . Using the calibration of Barro, we can obtain
values for all the parameters except for µj and σj2 where a calibration for this parameters does not
exist. Hence the usual exercise of matching theoretical ERP with empirical ERP to evaluate the
performance of this model is not feasible in this setting. We are testing the performance of this
model by testing one of his implication. In particular, we have seen that as the cost of information
τj increases, also s2j increases. This means that if we could estimate s2j for each country, we could
check this relationship by regressing the implied variances with proxies for information frictions.
This approach has two limits. First, we are assuming that 10 holds exactly, this is not obviously
the case since it depends strongly on distributional assumption, on the closed economy hypothesis
and the functional form of the cost function. Nevertheless we are not interested in having an exact
relationship, we need only that the idiosyncratic variance affects positively the ERP. Second, we
are not considering any other element that could affect positively the ERP, such as exchange rate
premia or investment decision. This second limit should be object of future research.
In the following the procedure to test the hypothesis is presented in detail.
4.1
The Testing Procedure
In order to obtain the implied volatilities ŝ2j , according to what has been discussed in section
2, we assume that µj = 0 ∀j. This implies that using the standard calibration presented in section
2 and the empirical ERP on the left hand side of 10 we can simply evaluate ŝ2j ∀j by inverting
10. These volatilities are presented in the first column of table 3. The first thing to observe is
10 All
the informations about the QoG dataset are reported in the Teorell et al. (2010).
26
that for some countries the inverting procedure doesn’t achieve convergence; in particular this is
true for China, Jordan, Italy, Japan, UK. This s simply explained by the fact that the ERP for
these countries are lower than the ERP of Barro’s model (see table 1 and since the variance has to
be greater than 0 the procedure does not achieve convergence. In order to match empirical with
theoretical ERP of our model, we should allow µj to be greater than 0. This means that once
a global disaster hits, these country are less affected. In this section these countries have been
excluded from the analysis.
Second, emerging markets have much higher idiosyncratic variance, reflecting that the difference
in the ERP is higher in these countries.
Argentina
Brazil
Chile
0.0964
0.0998
0.0486
Hungary
Poland
Russia
0.0603
0.0813
0.1218
S. Korea
Malaysia Pakistan
0.0405
0.0267
0.0279
Kenya
Nigeria
S. Africa
0.0937
0
0.0404
France
Germany
Italy*
0.002
0.0037
0.0001
* No convergence achieved
Colombia
0.0751
Turkey
0.0824
Philippines
0.0303
Egypt
0.0698
Japan*
0.0001
Mexico
0.0782
China*
0.0001
Sri Lanka
0
Jordan*
0.0001
UK*
0.0001
Peru
0.075
India
0.031
Taiwan
0
Morocco
0.0243
USA
0.0035
Czech Rep.
0.044
Indonesia
0.0891
Thailand
0.0469
Tunisia
0.0366
Canada
0.0116
Table 3: Implied s2j from 10: The uncertainty level measured by s2j has been derived by inverting
10 and using the data on the ERP and Barro (2006) calibration.
Once derived the implied variance s2j we are interested in looking for indexes for information
frictions in the QoG dataset that are correlated with these estimates. First, we narrowed the choice
by using an automatic stepwise procedure that rank the indexes according to the t-statistic on the
slope coefficient of the following relation
ŝ2j = αk + γk Indkj + j
j ∼ N (0, σk2 )
(13)
Second, in this group 6 indexes has been choosen according to qualitative criteria such as data
source, quality of the data and according to information friction issues. We have implemented the
choice of the index also according to the second part of the empirical analysis. The indexes that
have been selected are described in the appendix 2.
The estimates of the coefficients of relation 13 are presented in table 4. Due to potential measurment error and low sample size, we have performed the estimation using a bootstrap tecnique;
hence estimated coefficients and standard error derive from a bootstrap with 100000 resampling.
Results indicates a clear significative negative relationship between the implied volatilities of our
model and the selected information indexes; indeed all the coefficients γk are significative at 1%
significance level suggesting that information frictions play a role in pricing the ERP. In particular,
27
CPI and wbfi_cce are indexes of perception of corruption (decreasing in the amount of perceived
corruption). Estimates on these indexes suggest that as corruption increases, agents will put more
effort in achieving valuable informations, since in a corrupted country information are not public but are shared only with a selected part of private agents. Instead fi_legprop and wbgi_rle
are indexes related to the confidence that agents have in the rules of the society and in judicial
competence. The uncertainty linked to legislative environment induce the agents to invest more
resources in private informations that are usually costly. Not surprising indexes such as eiu_dpc
that measure the societal consesus supporting democracy affect the uncertainty related to disaster
risk. A democratic system is usually a system where there is a social agreement in sharing public
relevant informations. Finally icrg_qog represents and index that relates together all the factors
that we have identified, in particular is affected by corruption, law and order and bureaucracy
quality.
Dependent variable
Intercept
CPI
ŝ2j
(1)
0.099***
(-0.014)
-0.011***
(-0.003)
fi_legprop
(2)
0.244***
(0.041)
(3)
0.057***
(0.005)
(4)
0.131***
(0.016)
(5)
0.4***
(0.052)
-0.023***
(-0.006)
wbgi_rle
-0.027***
(-0.005)
icrg_qog
-0.141***
(-0.026)
eiu_dpc
-0.022***
(-0.009)
wbgi_cce
R2
(6)
0.133***
(0.025)
-0.013***
(-0.004)
0.349
0.465
0.489
0.25
0.343
0.467
Table 4: Bootstrap Estimates of 13: Each bootstrap estimate has been implemented by 100000
resampling of the {ŝ2j , Indexkj } for each index k.
The analysis is supported also by the scatterplots of the points for each identified index that
are shown in figure 6. The inverse relationship is clear in each subplot.
The analysis strongly suggests that a relationship between information frictions and ERP exists.
Nevertheless this approach has some clear limits that have to be studied in detail. First, we are
only considering a closed economy and hence ignoring the fact that the cross-section in the implied
volatilities may reflect the existence of currency premia. These premia can be correlated with the
indexes that have used in the analysis. Currency trader may ask for a premium for investing in
a country where there are some sources of political turbolence. Bailey, Chung (1995) found some
evidence that equity market premium in Mexico is affected by political risk. The analysis can be
28
improved by simply including a proxy for the currency risk in 13 correcting for the presence of
correlation between the error term and the explanatory variable.
Second, we are ignoring the possibility that idiosyncratic disaster exposure may differ across
countries. An alternative way to avoid this problem would be to estimate using µj and σj2 by
using a GMM approach. Unfortunately, to use this approach we would need quarterly data for
real consumption growth in the emerging markets in order to have a sufficiently large sample size.
5
Empirical Evidence in an International C-CAPM framework
An interesting question would be also to understand whether the previous results hold in an
international settings. In section 2.2 a simple modification of the original model has been presented
where the consumption stream is allowed not to be perfectly correlated with the asset return. The
role of the covariance between fundamentals in ”normal” and ”disaster” states has been discussed.
Ambiguity aversion has been used to show that excess return can increase with information frictions
since the contagion term is affected. In the following empirical evidence of this result is presented.
5.1
The Testing Procedure
In order to test the hypothesis identified above, we are using the approach of Lustig, Verdelhan
(2007) that adopted a simple pricing procedure to the return from carry trade strategies for different
countries. The authors proposed a linear three-factors model where the selected factors are real
consumption growth of durable and non-durable goods and market return. The authors show that
this conditional model derives from an approximation of the fundamental pricing equation when
the utility function is the one introduced by Yogo (2006)
h
i1/[1−(1/ρ)]
u(C, D) = (1 − α)C 1−(1/ρ) + αD1−(1/ρ)
Ut =
h
i1/κ 1/[1−(1/σ)]
1−γ
(1 − δ)u(Ct , Dt )1−(1/σ) + δEt Ut+1
where Ct and Dt are real consumption of durable and non-durable goods. It can be shown that
this specification for the utility function nests the CARA specification adopted in section 2 in the
one country model and the Epstein-Zin formulation. They called this model EZ-DCAPM. The
authors have estimated the conditional models for their country and by sorting the conditional
betas by interest rate differentials they found that there exists a consumption-based explanation
for the returns from currency trade.
A similar approach can be adopted for our purposes. Estimating a conditional model like the
one adopted by Lustig, Verdelhan (2007) for our set of countries permits to extrapolate the timevarying component that affects the ERP and that are not correlated with our issues on information
29
0.14
0.14
Rus
0.12
Rus
0.12
0.1
0.1
Bra
Arg
Ken
s2j
Mex
Tur
0.08
Tur
0.08
Bra
Arg
Ken
Ino
Ino
Pol
Col
Pol
Mex
s2j
Egy
Hun
0.06
Hun
0.06
0.04
Chl
Tha
Czr
Tun
Chl
Tha
Czr
SAf Kor
Phi
Mal
0.02
Ind
Phi
Pak
Tun
Ind
Pak
Mor
Kor
SAf
0.04
Per
Egy
Col
Per
Can
Mal
Mor
0.02
Ger
Fra
0
US
Can
0
Ger
US
Fra
2
3
4
5
6
Corruption Perception Index
7
8
−0.02
4.5
9
0.14
5
5.5
6
6.5
7
Legal Structure and Property Rights
7.5
8
8.5
0.14
Rus
0.12
Rus
0.12
0.1
0.1
Bra
Ken
Ino
Bra
Arg
Ken
Ino
0.08
Col
Tur
0.08
Col
Pol
Mex
s2j
Per
Pol
Hun
0.06
s2j
Egy
Phi
0.02
Czr
Kor
Czr
Chl
Kor
Tun
Ind
Mal
Mor
SAf
Phi
Pak
Chl
Tha
SAf
Tun
Ind
0.04
Tha
0.04
Hun
0.06
Pak
Arg
Tur
Mex
Per
Egy
Can
Ger
US
Fra
0
Mal
Mor
0.02
−0.02
Can
0
−1.5
US Ger
Fra
−1
−0.5
0
0.5
1
1.5
−0.04
2
0
0.2
0.4
Rule of Law
0.14
0.6
0.8
ICRG Indicator Quality of Government
1
1.2
Rus
0.1
Bra
Arg
Tur
0.08
Mex
Per
0.1
Ken
Ino
Ken
Ino
Pol
Egy
Hun
0.06
Tha
Tur
Hun
0.06
Mor
Chl
Tha
Czr
Kor
Czr
SAf Kor
Tun
0.04
Ind
Pak
Pol
Mex
Col Per
Egy
Chl
SAf
Tun
0.04
Bra
Arg
0.08
s2j
Col
Phi
Rus
0.12
s2j
0.12
Pak
Mal
PhiInd
Mor
0.02
Mal
0.02
Can
0
1.4
0.14
4
5
6
7
Democratic & Political Culture
Can
Ger
US
Fra
3
8
9
0
−1.5
−1
−0.5
0
0.5
1
Control of Corruption
Fra
1.5
USGer
2
2.5
Figure 6: Scatterplots of {ŝ2j , Indexkj }. Each sublot represents the scatterplot of implied volatilities
and selected indexes for (from top left to right down) cpi, fi_legprop, wbgi_rle, icrg_qog, eiu_dpc,
wbgi_cce. In each subplot is plotted a line corresponding to the estimated parameters presented
in table 4.
30
frictions. Our empirical analysis relies on the assumption that information frictions τ are not timevarying and correlated with global (US) consumption growth. This could not be the case if the
government of the emerging countries control information flows depending on the fact that we are
in global boom or downturn.
In this analysis it is assumed that information frictions are constant over time. As discussed
in 2.2, this implies that in the estimation of the conditional model, contagion term affects the
intercept of the conditional fator model. The intercept for a particular country j represents the
extra premium that the US agent requires for investing in the country, that under our assumption is
correlated with the existence of information frictions. In the following the implemented procedure
is described.
Following Verdelhan, Lustig (2007) we have estimated the following relationship
D
R
M
ERPt,j = αj + βjN D ∆cN
+ βjD ∆cD
t
t + βj ERPt + ut,j
ut,j ∼ N 0, σj2
(14)
The data are quarterly data for the ERP for emerging markets and MSCI global, and quarterly
data of real consumption growth of durable and non durable good in the US described in section
3. As noted before, the sample size differs across country, but this doesn’t affect our results. The
estimation results are presented in table 5. As we can see, in the EZ-DCAPM an important role is
played by the market betas. As in Lustig, Verdelhan (2007) consumption betas are not significative
in most of the cases.
As standard literature on empirical asset pricing does, the scatterplot of actual vs predicted
ERP is presented in order to evaluate the performance of 14. On the x-axis of figure 7 we have
predicted ERP. Standard literature evaluate predicted ERP by running a second regression
E[ERPj ] = λ0 βˆj
where βˆj are the coefficient estimates of table 5. On the y-axis we have actual ERP, i.e. ERPjF =
ERPj,t ∀j. If the model predicts the real data, all the data points should be aligned on the 45
degree line. The figure clearly suggests that this is not the case, and that in the model 14 a large
role is played by the intercept; in particular this is true for emerging markets that means that
there is still a large share of current variability in the ERP to be understood. Similar results have
been presented in Donadelli, Prosperi (2012).
We want to test now the role of information frictions in predicting the ERP in our dataset.
A similar approach of the previous section has been used. As a first step a list of candidate
explanatory indexes has been selected by using a stepwise procedure based on the t-statistic of the
coefficient ρk of equation 15.
α̂j = δk + ρk Indkj + j
j ∼ N (0, σk2 )
(15)
Secondly, we selected among these candidates using the same criteria of the previous section. It
turns out that most of the selected indexes of the previous analysis has a significative impact also
31
Country
Argentina
Brazil
Chile
Colombia
Mexico
Peru
Czech Republic
Hungary
Poland
Russia
Turkey
China
India
Indonesia
Korea
Malaysia
Pakistan
Philippines
α̂j
0.046
[.058]
0.046
[.034]
0.042*
[.024]
0.043
[.034]
0.037
[.025]
0.020
[.04]
0.016
[.039]
0.014
[.036]
0.006
[.033]
0.094
[.06]
0.040
[.044]
-0.021
[.038]
-0.017
[.026]
0.059
[.042]
0.006
[.025]
0.014
[.018]
-0.020
[.04]
0.001
[.02]
β̂jN D
4.912
[6.651]
-2.090
[3.086]
-2.124
[2.289]
0.039
[3.195]
-0.363
[2.564]
2.429
[3.276]
3.055
[3.344]
1.081
[3.162]
2.812
[4.476]
-6.985
[7.869]
-3.775
[7.335]
-0.168
[4.413]
3.542
[2.637]
-0.164
[5.377]
1.656
[3.54]
0.519
[2.675]
8.533*
[4.57]
2.412
[3.536]
β̂jD
-1.217
[1.621]
1.80*
[1.078]
0.540
[.705]
-0.171
[1.109]
0.756
[.852]
0.665
[1.079]
-0.249
[1.142]
0.623
[1.158]
1.224
[1.025]
1.021
[2.107]
2.048
[1.889]
1.640
[1.159]
0.932
[.723]
-0.863
[1.572]
0.407
[.934]
0.026
[.679]
-0.548
[1.023]
0.223
[.814]
β̂jR
0.957**
[.372]
1.110***
[.304]
0.520***
[.181]
0.751**
[.278]
0.719***
[.193]
0.485*
[.291]
0.521***
[.191]
1.214***
[.233]
0.968***
[.245]
1.667***
[.468]
1.200***
[.444]
0.682**
[.281]
0.790***
[.178]
1.699***
[.413]
1.325***
[.292]
0.970***
[.193]
0.229
[.301]
0.997***
[.216]
Sri Lanka
Taiwan
Thailand
Kenya
Nigeria
South Africa
Egypt
Jordan
Morocco
Tunisia
France
Germany
Italy
Japan
United Kingdom
USA
Canada
Table 5: Estimation of 14
32
α̂j
-0.049*
[.023]
-0.017
[.029]
0.009
[.023]
0.008
[.031]
0.024
[.034]
0.012
[.03]
0.036
[.037]
-0.017
[.017]
0.009
[.026]
0.008
[.022]
0.001
[.01]
0.008
[.012]
-0.02*
[.011]
-0.026**
[.012]
-0.002
[.01]
0.001
[.005]
0.003
[.014]
β̂jN D
6.201*
[3.611]
5.616*
[3.038]
-0.683
[3.529]
7.702*
[4.096]
1.474
[4.495]
-1.206
[2.448]
-3.565
[3.221]
0.142
[1.725]
1.668
[2.434]
6.047**
[2.629]
0.876
[1.114]
-0.978
[1.407]
2.430**
[1.159]
1.773
[1.481]
0.158
[1.037]
0.888
[.702]
0.625
[1.635]
β̂jD
2.029
[1.267]
0.415
[.853]
1.562**
[.726]
1.879
[1.691]
-0.560
[1.389]
1.214
[.811]
1.444
[1.039]
1.072**
[.495]
0.128
[.741]
0.193
[.801]
0.009
[.346]
0.284
[.436]
0.216
[.373]
0.206
[.393]
0.380
[.274]
0.156
[.202]
0.304
[.451]
β̂jR
0.404
[.307]
0.700*
[.228]
1.096***
[.23]
0.426
[.383]
0.918**
[.379]
0.613***
[.196]
0.829***
[.212]
0.265**
[.11]
0.256**
[.128]
-0.267
[.186]
0.901***
[.093]
0.985***
[.113]
0.851***
[.103]
0.901***
[.136]
0.751***
[.069]
0.752***
[.053]
0.862***
[.101]
0.09
Rus
0.08
0.07
Bra
Ino
Arg
Ken
Actual ERP
0.06
Tur
Mex Pol
Per
Col
Egy
Chl
Hun
0.05
0.04
0.03
Tun
0.02
Czr Nig
Tha
Kor
SAf
Ind
Pak
Mal
Phi
Sri
Mor Tai
Can
US
Ger
Fra
UKChi
0.01
0
−0.01
−0.01
Jor
Ita
Jap
0
0.01
0.02
0.03 0.04 0.05
Predicted ERP
0.06
0.07
0.08
Figure 7: Predicted vs Actual ERP of 14
in this setup suggesting that information frictions have a large role in explaining the cross section
of the ERP, and this result does not depend on the choice of the benchmark model. In presenting
these results two different evidence have been used. First, as in 4 a bootstrap estimate of 15 for each
selected index has been implemented. Without reporting the estimate results, we show scatterplot
of αj , Indkj as an evidence of a the negative relationship. Second, following Lustig, Verdelhan
(2007) an analysis on portfolios is presented. The αj have been ranked according to the index of
interest and, from this ranking, we developed 8 portfolios of countries and we computed the mean
alpha for each portfolio. This approach has several advantages: it gives a clear cut indication of the
relationship between the alphas and information frictions but furthermore eliminates stock-specific
component of returns that are not related to information frictions.
The results are presented in figure 8 to 13. The plots suggest that corruption indexes (cpi
and control of corruption) still play a role in explaining the extra premium paid by us investor.
As before the index of democratic culture has explanatory power, suggesting that also political
issues are important. A similar interpretation is associated with the impact of fl_clindex. This is
a general index from the same data provider of fl_legprop that includes other potential source of
investment uncertainty. As before Rule of Law and Quality of Government are important; when
the legislative environment is uncertain the foreign investor has to spend resources on legal issues
and to avoid burocracy.
The portfolio analisys suggests that a negative correlation between the alphas and selected
33
indexes exists, but there is also some evidnece that this relationship is not clear inside the extremes
of the interval. This is explained using two considerations: first, our indexes are obviously not free
of measurement error; second, while the ERP are sample average in a sample of 20 years, the
indexes are measured cross sectionally in a given year11 . This problem does not appear in Lustig,
Verdelhan (2007) since the sorting variable is interest rate differential that is time-varying and
measured with much more precision.
6
Limits
In both sections 4 and 5 we found an empirical evidence of the role of information frictions in
affecting excess return in stock markets. Even if the results of the analysis is clear and shows that
there exists an inverse relationship between premia and information frictions, there may be some
endogeneity issues. Indeed the existence of an high premia (i.e. high αj or high s2j could be also
explained by low growth prospects or high probabilities of default in a different model with respect
to the one specified above. High probability of default may be correlated with information frictions
that in our case are proxied by institutional aspects of the society. More corrupted government
where transparency is low can explain low future economic growth or defaults implying higher
returns required by the investors. A simple way to check if this endogeneity issue really arise
would be to include a proxy for economic prospects (e.g. ratings) in the empirical analysis. By
regression estimates or by portfolio analysis it is possible to test if these results still holds. More
sophisticatedly the analysis presented here could be refined by considering the panel dimensions
of information indexes and ratings using panel data estimatation or portfolio analysis with double
sorting as performed in Borri, Verdelhan (2010).
As a final remark it is worthly to notice that our analisys is affected by selection bias since
the countries where information frictions are really important in affecting investment decisions are,
in most of the cases, systems where a market for publicy traded assets are not available, since a
dictatorship is in place.
7
Conclusions
I showed that the cross section of emerging markets excess returns can be explained by information frictions that strongly affects beliefs on the effects of a global disaster in a particular country.
Barro’s model fails in predicting the levels and the heterogeneity of excess returns. Attempts to
solve the issue arguing that emerging markets may have different disaster exposures (Gourio et al.
(2011)) fail when looking at the data: countries that are very close from a geographical point of
view should have very similar ERP, since idiosyncratic exposures should not change too much.
I argued that information frictions affecting ability of the agents in forming beliefs on disaster
effects, are able to explain empirical data. A simple modification of the disaster economy of Barro
11 The
analysis could also be repeated by using the panel dimension that the QOG dataset offers.
34
has been proposed, where in the disaster process a random idiosyncratic component is included.
The agent endogenously select the information level facing costs. I showed that when frictions
increase, also excess return increases, regardless the level of disaster exposure. Furthermore I have
extended the model in an international setting, allowing for the possibility that consumption is
not perfectly correlated with asset returns. Here an important role is played by the contagion
term, i.e the real connection between the two economies once a disaster hits. When agents face
ambiguity in the contagion term, they are not able to determine ex ante what are the comovements
between asset and consumption in disaster states. Adopting the approach of ”ambiguity aversion”
literature, it is simple to show that a premium arises and that such premium is an increasing
function in information frictions.
These relationship between information frictions and excess returns has been tested using financial data and the Quality of Government dataset. From the single countries model, corruption,
judicial quality and burocracy are powerful proxies for information frictions that empirically evaluate my hypothesis. Adopting the model and the approach of Lustig, Verdelhan (2007) I showed
that the same indexes are good explanatory variables even in an international setting. Hence the
empirical analysis confirm the role of information frictions in explaining excess returns.
Several ways to improve the analysis are possible. From the empirical point of view, several
robustness checks can to be implemented in order to show that an endogeneity issues do not
arise and also more sophisticated econometric analysis are possible. Indeed further extension
are really interesting: in particular understanding how information frictions affect quantities in a
dynamical context can be useful to understand the dynamics of recovery from really bad states.
Also I showed that ambiguity aversion arguments can play a role when information quality is poor.
Hence a general equilibrium model with production and ambiguity aversion offer a much more
general intuition on the role of uncertainty in the economy as the recent contribution of Bloom
(2007) has shown.
35
Figure 8: Corruption Perception Index
0.1
0.02
Rus
0.08
0.015
0.06
Arg Col Bra
Tur
Mex
Egy
Nig
0.02
Chl
0.005
Mean α
0.04
Estimated α
0.01
Ino
Per
CzrHun
Mal
Mor TunSAf
Tha
Ken
0
Phi
−0.02
Pak
Ger
Pol
Kor
Fra
US
Ind
UK
−0.005
Tai
Jor
Chi Ita
0
Can
−0.01
Jap
−0.04
−0.015
Sri
−0.06
2
3
4
5
6
Corruption Perception Index
7
8
−0.02
9
1
2
3
4
5
6
7
8
5
6
7
8
5
6
7
8
Portfolio
Figure 9: Economic Freedom
0.04
0.1
Rus
0.03
0.08
0.06
Arg Bra
Tur
Egy
Nig
0.02
Mor
0
Chl
Mex
Mean α
0.04
Estimated α
0.02
Ino
Col
Per
Hun
Mal Czr
SAf
Tha Kor
Tun
Ger
Pol Ken
Phi Fra
Can
0.01
0
US
UK
−0.01
−0.02
Ind
ChiPak
Jor
Ita
Jap
Tai
−0.02
−0.04
Sri
−0.06
−0.03
5
5.5
6
6.5
7
7.5
Economic Freedom of the World (chained)
8
8.5
1
2
3
4
Portfolio
Figure 10: Rule of Law
0.1
0.025
Rus
0.02
0.08
0.015
0.06
Ino
0.01
Estimated α
0.02
Bra
Mex TurEgy
Nig
Chl
0.005
Per
Mal
SAf
Mor
TunTha
Pol
Ken
CzrHun
Kor
Fra
Phi
0
−0.02
Pak
Mean α
Arg
Col
0.04
Chi
Ind Jor
Ger
US Can
UK
−0.01
Tai
Ita
Jap
−0.015
−0.04
−0.02
Sri
−0.06
−1.5
−1
−0.5
0
0.5
Rule of Law
0
−0.005
1
1.5
−0.025
2
1
2
3
4
Portfolio
36
Figure 11: ICRG - Quality of Government
0.1
0.025
Rus
0.02
0.08
0.06
0.015
Ino
Arg
Col Bra
Tur
Mex
Egy
Nig
0.02
Tha
Ken
Per
Czr
Hun Mal
Mor
PolKor Tun
SAf
Phi
0
−0.02
Ind
Jor
Pak
0.01
Chl
Ger
Fra
US
Can
UK
0.005
0
−0.005
Tai
Ita
Jap
Chi
Mean α
Estimated α
0.04
−0.01
−0.04
−0.015
Sri
−0.06
−0.8
−0.6
−0.4
−0.2
0
0.2
0.4
Good Governance
0.6
0.8
1
−0.02
1.2
1
2
3
4
5
6
7
8
Portfolio
Figure 12: Democratic Culture
0.04
0.1
Rus
0.03
0.08
0.06
Ino
Bra
Arg
Col
Tur
Mex
Nig
0.02
0.02
Chl
Egy
Per
Mor
Tha
Pol
Ken
Hun
SAf
Tun
−0.02
Tai
Ind
Jor
Pak
Czr
Mal
Kor
Fra
Phi
0
Mean α
Estimated α
0.04
UK
0.01
Ger
Can
US
0
Jap
−0.01
Ita
Chi
−0.04
Sri
−0.06
−0.02
3
4
5
6
7
Democratic Political Culture
8
1
9
2
3
4
5
6
7
8
Portfolio
Figure 13: Control of Corruption
0.1
0.04
Rus
0.08
0.03
0.06
Ino
Arg
Bra
Col
Tur Mex
Egy
0.02
Nig
Per
Tha Mor
Ken
Czr
Mal Hun
SAf
Tun
PolKor
Fra
Phi
0
−0.02
Pak
Ind
Chi
Jor
0.02
Chl
Mean α
Estimated α
0.04
Ger
US Can
UK
0.01
0
Tai
Ita
Jap
−0.01
−0.04
Sri
−0.06
−1.5
−1
−0.5
0
0.5
1
Control f Corruption
1.5
2
−0.02
2.5
1
2
3
4
5
Portfolio
37
6
7
8
Appendix 1-Description of selected indexes
cpi - Corruption Perception Index
Source: Heritage Foundation
Year: 2002
Corruption Perceptions Index (CPI) measures the level of corruption in 152 countries The CPI is
based on a 10-point scale in which a score of 10 indicates very little corruption and a score of 0
indicates a very corrupt government. In scoringfreedom from corruption, the authors convert each
of these raw CPI data to a 0-100 scale by multiplying the CPI scores by 10.
eiu_dpc - Democratic Political Culture
Source: Economist Intelligence Unit - Index of Democracy
Year: 2006
The Democratic Political Culture index measures the extent to which there is a societal consensus
supporting democratic principles.
fi_legprop - Legal Structure and Security of Property Rights
Source: Fraser Institute - Economic Freedom of the World
Year: 2002
The index ranges from 0-10 where 0 corresponds to ’no judicial independence’, ’no trusted legal
framework exists’, ’no protection of intellectual property’, ’military interference in rule of law’, and
’no integrity of the legal system’ and 10 corresponds to ’high judicial independence’, ’trusted legal
framework exists’, ’protection of intellectual property’, ’no military interference in rule of law’, and
’integrity of the legal system’.
fi_clindex Economic Freedom of the World Index (chained)
Source: Fraser Institute - Economic Freedom of the World
Year: 2002
The index is founded upon objective components that reflect the presence (or absence) of economic
freedom. The index comprises 21 components designed to identify the consistency of institutional
arrangements and policies with economic freedom in five major areas: size of government (fi_sog),
legal structure and security of property rights (fi_legprop), access to sound money (fi_sm), freedom
to trade internationally (fi_ftradeint),regulation of credit, labor and business (fi_reg). The index
ranges from 0-10 where 0 corresponds to ’less economic freedom’ and 10 to ’more economic freedom’.
This is the version of the index published at the current year of measurement, without taking
methodological changes over time into account.
38
icrg_qog - ICRG indicator of Quality of Government
Source: International Country Risk Guide - The PRS Group
Year: 2002
The mean value of the ICRG variables ”Corruption”, ”Law and Order” and ”Bureaucracy Quality”,
scaled 0-1. Higher values indicate higher quality of government.
wbgi_cce - Control of Corruption
Source: World Bank - Governance Indicators
Year: 2002-2008 (varies by country)
”Control of Corruption” measures perceptions of corruption, conventionally defined as the exercise
of public power for private gain. The particular aspect of corruption measured by the various
sources differs somewhat, ranging from the frequency of ”additional payments to get things done”,
to the effects of corruption on the business environment, to measuring ”grand corruption” in the
political arena or in the tendency of elite forms to engage in ”state capture”.
wbgi_rle Rule of Law - Estimate
Source: World Bank - Governance Indicators
Year: 2002-2006 (varies by country)
”Rule of Law” includes several indicators which measure the extent to which agents have confidence
in and abide by the rules of society. These include perceptions of the incidence of crime, the
effectiveness and predictability of the judiciary, and the enforceability of contracts. Together,
these indicators measure the success of a society in developing an environment in which fair and
predictable rules form the basis for economic and social interactions and the extent to which
property rights are protected
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