We propose a country classification of economic growth currency crisis consequences based on the entropic analysis of the real exchange rate. We show that this ranking is highly correlated with the annual minimum rate of growth, a proxy used to quantify real currency crisis effects.currency crises; entropy; growth effects of currency crises

Matesanz Gómez, David

Ortega, Guillermo J.

English

Research Papers in Economics

Economic growth and currency crisis: 
A real exchange rate entropic approach 
 
 
David Matesanz Gómez
∗ 
Department of Applied Economics, Universidad de Oviedo, Spain 
 
 
Guillermo J. Ortega
∗∗  
Department of Physics, Universidad de Buenos Aires and CONICET, Argentina 
 
 
Abstract 
We propose a country classification of economic growth currency crisis consequences 
based on the entropic analysis of the real exchange rate. We show that this ranking is highly 
correlated with the annual minimum rate of growth, a proxy used to quantify real currency 
crisis effects. 
 
 
JEL CODES: C82, F31, F40 
KEYWORDS: currency crises, entropy, growth effects of currency crises
                                                 
∗ D. Matesanz, Avda. Cristo s/n 33006, Oviedo, Spain, Phone: +34-985-104847,  fax: +34-985-105050, E-
mail address: matesanzdavid@uniovi.es 
 
∗∗ G. J. Ortega, Ciudad Universitaria, Pabellón I, Buenos Aires, Argentina, Phone: +54-11-44576-3390, Fax: 
+54-11-4576-3357 E-mail address:  ortega@df.uba.ar 
  
I. Introduction 
 
Prediction and contagion of financial crisis has received much attention in recent years. The 
financial instability during the Nineties has caused intense exchange and banking crisis in 
developed and, especially, in developing countries. Most of the empirical literature has 
focused on identification, prediction and contagion of currency crisis, see Kaminsky, 
Lizondo and Reinhart (1998) and Abiad (2003) for two comprehensive surveys. In this 
literature, the macroeconomics effects of currency crisis have sometimes been forgotten in 
favour of constructing mechanism to anticipate the events called currency crisis.  
In general, characterization of currency crisis has been focused on the analysis of indicators 
that use variance of the macroeconomic series, such us real exchange rate, reserves, and/or 
interest rates for dating and defining the event of crisis. But, as pointed out by Ebrahimi et 
al. (1999), although variance plays a central role in characterizing and ranking economic 
variables, entropy seems to be a superior measure to extract underlying information in the 
economic data.  
Following the above ideas, we have applied entropy analysis to the real exchange rate 
(RER) time series with the objective of classifying countries that have suffered currency 
crisis during the nineties in terms of their real vulnerability. We compared ordering results 
from variance and entropy of the time series showing that entropy is a better statistic to 
characterize the impact of currency crisis. Our results could be interpreted as a first step in 
the search for new forms of dating and predicting currency crisis and contagion. In order to 
do this, we have analysed a sample of 28 countries during the period of 1990-2002, most of 
which have suffered the effects of financial and currency crisis in the last decade. For a 
complete list of date and crisis originating countries see for example table 1 and 2 in 
Kaminsky et al. (2003) or appendix B in Pérez (2005).  
II.  Methodology 
Entropy and variance has been widely used in economic literature as measures of dispersion 
and uncertainty, although variance (and other higher moments) are by far the most popular 
indexes still used because of their simplicity. Given a time series x = x1, x2, x3,...,xi,.., xn, 
where the index i refers to discretized time, the (sample) variance of the time series is 
defined as: 
n
x x
x Var
n
i
i ∑
=
−
= =
1
2
2
) (
) ( σ          (1) 
where x  is the sample mean and σ is the standard deviation. Variance measures average 
departures of the time series from its mean. 
On the other hand, following Shannon (1948), we can construct a probability distribution 
P(x) from the time series x itself, and define the entropy of P(x) as: 
 
[] i
N
i
i p p x H P H 2
1
log ) ( ) ( ∑
=
− = =
intervals
x        (2) 
 
where the sum is over the Nintervals; intervals that the full range of allowed values of x is 
partitioned. In this way,  pj is the  probability of each interval j of being “occupied”, and it 
is estimated as the number of xi of the time series that fall in the interval i, divided by the 
total number of intervals, that is, Ninterval. A value of Nintervals = 50 has been used in our 
calculations, although the results reported are rather insensitive to variations in Nintervals 
from 20 to 50. Due to the finite amount of data used in the analysis, we have also estimated 
errors on observed entropy calculations accordingly with Roulson (1999). The maximum 
error reported in the entropy calculations is 3 %.  Broadly speaking, entropy describes the extent to which the distribution is concentrated on 
small sets; thus, it can be regarded as a measure of disparity of the distribution from the 
uniform one. If entropy is low, the distribution is concentrated at a few values of x. Note 
that entropy gives a very different kind of information than variance. If the distribution is 
concentrated on several small sets, far from each other, the variance can be large, while the 
entropy is small. We can recast the above paragraph in the particular case of exchange rate 
movements. For example, rigid exchange rate decisions tend to concentrate variations 
around small values during tranquil periods, and crisis generally moves these variations 
toward much higher values. In this sense, variations in RER are concentrated around sets far 
from each other. On the other hand, more flexible exchange rate decisions allow larger 
departures, even during tranquil times, and the values taken by the time series are not 
concentrated, but on the contrary, seem to be more or less continuous. So, entropy could  be 
a good index to classify different exchange rate dynamics in different countries. Moreover, 
we shall show that an entropic ranking in the real exchange rate is highly correlated with 
countries economic growth decay after devaluations.  
 
III.  Empirical Analysis 
We have used returns from the monthly real exchange rates (rRER) time series, in 28 
countries, calculated as: 
rRERi = (RERi+1 – RERi)/ RERi  
where rRERi is the monthly real exchange rate (return) at month i. The period 1990-2002 
has been used, yielding a total of 156 data points for each country. RER is computed as the 
ratio of domestic consumer price to foreign price proxied by USA consumer price, and the 
result is multiplied by the nominal exchange rate of the domestic currency with US dollar. 
Data, including real Gross Domestic Product (GDP), has been drawn from International Financial Statistics form the IMF database available on-line 
(http://ifs.apdi.net/imf/logon.aspx). 
We have calculated entropy and variance in rRER in the 28 selected countries (see 
Appendix). Results are displayed in Figure 1, where countries in the x-axis are ordered 
following an increasing entropy criterion. The upper panel of Figure 1 shows entropy values 
(with error bars), as calculated by using Equation 2. The lower panel in the same figure 
shows variance calculations (Equation 1). Comparing both upper and lower panels in this 
figure, it is clear that a direct relation between both measures does not exist, although in 
some cases local similarities exist. For instance, Argentina is at the first place in both cases, 
with the lowest entropy and highest variance. Other countries seem to share both criteria; 
Indonesia, Brazil and Venezuela also are placed in the lower part of the plots, that is, they 
share high variance and low entropy.  
In general, we can see that lower values of entropy correspond to the principal originating 
crisis countries in the last decade (Argentina, Thailand, Mexico) and, on the other side, 
countries of the EU, and Australia, have the highest entropies. In fact, one may divide the x-
axis in developing countries, from Argentina to Philippines, and developed countries, from 
The United Kingdom to Australia with the unique exception of Chile, right in the middle of 
the EU group. Looking at the lower panel of Figure 1 it is evident that following a variance-
ordering criterion will not yield the same results. So, variance and entropy, unless similar, 
orders this group of countries in a quite different fashion. Is the entropic ordering 
information useful for the currency crisis empiric literature? And, in what sense? 
We have tried to answer partially these questions in two directions.  
Firstly, ordering countries by rRER entropy solely, automatically create clusters of 
countries with similar exchange rate behavior, even though they are not always time correlated. This fact may be demonstrated by calculating any appropriate measure of 
“distance” between the variables, as for example cross-correlation coefficient.   
In Figure 2 we have calculated Pearson’s correlation coefficient between rRER among pairs 
of countries, also ordered in both axis accordingly with the entropy criterion. High 
correlations (white squares) between countries in the upper and right corner of the graph are 
clearly seen, as is expected in those countries belonging to the EU. However, the last 
country, Australia, although with a similar entropy value to the EU countries, shows no 
correlation at all with them, as also in the case of Ireland and Chile. Ireland, although a 
country belonging to the EU has no correlation with these countries, but noneless, it is 
placed in this cluster by its entropy value. Chile, on the other hand, seems unexplained 
however from this unique analysis. 
Outside the EU cluster, one may identify several clusters of correlations, as is the case 
Asian countries, that is, Malaysia, Thailand, Korea and Indonesia, in the lower and left part 
of Figure 2. Noteworthy is the case of Singapore, an Asian country, which however is 
placed just besides the EU countries accordingly with its entropy value. Looking at its 
correlations, it is easy to conclude that its position is mainly due to its high correlation with 
the EU countries. As it the case of Chile, Philippines however, remains also in an 
unexplainable position.  
Most of the Latin American countries seem to be isolated with few correlations, with the 
exceptions of Brazil, correlated with Argentina, Colombia and Chile.  
One may conclude from the above analysis that the particular entropy value, although a 
univariate statistic, seems to correctly order countries regarding its economic liaisons, even 
though in some cases there no exist time correlations.  In second place, real exchange rate movements are at the heart of the economic activity, and 
in this way, it is expected that any appropriate ordering criterion in the exchange rate 
movement will be reflected in the overall economic performance. 
Currency and financial crisis have produced severe consequences in the economic activity 
in the group of countries we study. For instance, Argentine gross domestic product (GDP) 
dropped 11% after exchange rate collapse in 2002 and has shown a very low economic 
growth rate in the analyzed sample (around 2%). Indonesia dropped more than 13% during 
1998 after bath collapse in 1997, but its economic growth rate in period analyzed is above 
4%. In Europe, we can see that economic growth consequences of currency crisis are quite 
different. For instance, Spanish GDP dropped only 1% in 1993 after the peseta devaluation 
or Greece and Portugal in the same year with economic growth contraction around 1,5% 
(table 1).  
Empirical literature of currency crisis has no tried to explain relationships between the 
proper crisis and the intensity of its macroeconomic effects. In table 2, we have calculated 
the correlation coefficient between the minimum of the annual GDP in the time series of 
each country and its order in our two ordering criteria, variance and entropy. We have 
found that the entropic criteria better fits a direct relation between drops in the GDP and 
rRER entropy, with lower entropy directly related with major GDP losses. 
Also in table 2, we have calculated the same correlation coefficient but using this time the 
economic growth average rate to test if currency crisis affects to the capability of countries 
economic growth in the medium term. Results of this correlation show that by only using 
exchange rate time series we are able to say little about the potential real economic growth 
in the medium and long term. These results are coincident with that reported by Chou and 
Chao (2001), and clearly in contrast with Christopoulos (2004), unless we have used 
different methodology. Nevertheless, in our analysis signs in entropy and variance are what we expected and, again, explanation capability of the entropy as information measure is 
better than the variance in the exchange rate time series analysis
1.  
 
 
IV. Conclusions 
We have introduced a new criterion to characterize the effects of currency crisis based 
solely in the analysis of the real exchange rate returns time series. We used entropy to order 
a group of 28 developed and developing countries. As we have shown, ranking countries 
accordingly with the entropy value of the real exchange rate is highly correlated with the 
intensity of economic growth drops in periods with currency crisis events. We have tested 
the entropy against the variance order. As a conclusion regarding this point, entropy seems 
to be a good measure for analyzing real vulnerability consequences in currency crisis 
events, with low values of entropy in cases of countries that have suffered severe currency 
crisis in terms of output growth dropped. Moreover, our results give firm signs about which 
exchange rate dynamics are more prone to suffer currency crisis. In addition, we have 
shown that the ordering proposed also gives important information regarding economic 
liaisons between groups of countries, and may shed new light in the contagion issue, 
although there remains much more research to do on this issue.    
                                                 
1 We expected that low entropy coefficients, which have shown an important relationship with the intensity of 
the dropped in GDP, were related with low economic growth rate in the medium term. So, we expected a 
negative correlation sign. In variance order, we expected a positive correlation sign.  
VI. Acknowledgements 
We would like to thank, without implicating, International Economics Research Group in 
Oviedo University, especially to Pepe Rivero, Saúl de Vicente and Pedro Álvarez, for their 
generous support with their previous work in this area. G.O. thanks financial support from 
the Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina.  
 
References 
Abiad, A., 2003, Early-Warning Systems: a Survey and a Regime-Switching Approach, 
IMF Working Paper 32, 1-60. 
Chou, L. W. and C. C. Chao, 2001, Are currency devaluations effective? A panel unit root 
test, Economics Letters 72, 19-25. 
Christopoulos, D. K., 2004, Currency devaluation and output growth: new evidence from 
panel data analysis, Applied Economics Letters 11, 809-813. 
Ebrahimi, N., Maasoumi, E. and  E. S. Soofi, 1999, Ordering univariate distributions by 
entropy and variance, Journal of Econometrics 90 (2), 317-336  
Kaminsky, G., Lizondo, S. and C. M. Reinhart, 1998, Leading Indicators of Currency 
Crises, IMF Staff Papers 45, 1-56. 
Kaminsky, G., Reinhart, M. and C.A. Vegh, 2003, The Unholy Trinity of Financial 
Contagion, Journal of Economic Perspectives, American Economic Association 17(4), 51-
74. 
Pérez, J., 2005, Empirical identification of currency crises: differences and similarities 
between indicators, Applied Financial Economics Letters 1 (1), 41-46. Rigobon, R., 2003, On the measurement of international propagation of shocks: is the 
transmission stable?, Journal of International Economics 61, 261-283. 
Roulson, M.S., 1999, Estimating the errors on the measured entropy and mutual 
information, Physica D 125, 285-294. 
Shannon, C., 1948, A mathematical theory of communication, Bell Systems Tech. 27, 379-
423. 
 
 
Appendix 
 
The 28 countries included in this work are as follows (order by increasing entropy): 
 
Argentine (ARG), Malaysia (MAL), Thailand (THA), Mexico (MEX), Korea (KOR), 
Indonesia (INDO), Brazil (BRA), Venezuela (VEN), Peru (PER), India (INDI), Ecuador 
(ECU), Turkey (TUR), Colombia (COL), Singapore (SIN), Philippines (PHI), United 
Kingdom (U_K), Sweden (SWE), Italy (ITA), Ireland (IRE), Finland (FIN), Chile (CHI), 
Greece (GRE), Portugal (POR), Switzerland (SWI), Denmark (DEN), Spain (SPA), 
Norway (NOR), Australia (AUS)  
Table 1. Entropy, Variance, Gross Domestic Product (GDP), 1990-2002 
 
  Entropy 
coefficients 
Variance 
coefficients 
MIN 
GDP 
(1) 
AVM 
GDP (2) 
MAX 
GDP 
(3) 
STAD 
DEV 
GDP (4) 
            
ARGENTINE 1,16  0,141  -10,89  1,928  10,58  6,427 
MALAYSIA 2,58  0,031  -7,36  6,602  10  5,047 
THAILAND 2,77  0,038  -10,51  5,001  11,17  5,738 
MEXICO 2,77  0,043  -6,17  3,146  6,77  3,46 
KOREA 2,90  0,039  -6,85  6,146  9,49  4,331 
INDONESIA 2,98  0,088  -13,13  4,236  8,22  5,636 
BRAZIL 3,04  0,062  -0,54  2,337  5,85  2,035 
VENEZUELA 3,22  0,068  -8,88  1,688  9,73  5,305 
PERU 3,45  0,043  -3,67  3,209  12,82  4,391 
INDIA 3,72  0,023  0,91  5,434  7,59  1,846 
ECUADOR 3,76  0,043  -6,3  2,592  5,12  2,903 
TURKEY 3,76  0,047  -7,32  3,575  9,26  5,811 
COLOMBIA 4,01  0,026  -4,2  2,699  5,71  2,616 
SINGAPORE 4,22  0,017  -1,9  6,695  12,26  4,39 
PHILIPPINES 4,28  0,031  -0,58  3,138  5,85  2,212 
UNITED KINGDOM  4,39  0,024  -1,37  2,209  4,42  1,569 
SWEDEN 4,53  0,033  -1,74  1,869  6,76  2,686 
ITALY 4,55  0,030  -0,88  1,546  3,03  1,049 
IRELAND 4,57  0,057  1,93  7,102  11,57  3,117 
FINLAND 4,69  0,033  -6,26 1,875  6,29 3,684 
CHILE 4,73  0,021  -0,76  5,682  12,28  3,523 
GREECE   4,76  0,030  -1,6  2,417  4,39  1,774 
PORTUGAL 4,76  0,030  -1,37  2,884  8,45  2,291 
SWITZERLAND 4,78  0,032  -0,83  1,21  3,8  1,446 
DENMARK 4,78  0,029  0  2,071  5,47  1,414 
SPAIN 4,81  0,032  -1,03  2,731  4,91  1,547 
NORWAY 4,84  0,028  1,11  3,326  5,26  1,335 
AUSTRALIA 5,04  0,046  -0,59  3,285  5,3  1,57 
 
(1) Minimum annual GDP growth in the period sample 
(2) Annual average GDP growth in the period sample 
(3) Maximum GDP growth in the period sample 
(4) Standard Deviation of GDP in the period sample 
 
 
 
 
Table 2. Entropic and variance ordering correlation coefficient 
 
  Annual GDP minimum 
  
Annual GDP average 
 
 
Entropy 
Ordering 
Variance 
Ordering 
Entropy 
Ordering 
Variance 
Ordering 
      
Correlation coefficient  0.7211  0.5599  -0.2667  0.1436 
Slope 0.3551  0.2757  -0.0558  0.0301 
 
 
 Figure 1: Entropy (upper panel) and variance (lower panel) in 28 countries.  
Countries are ordered by increasing entropy. Errors bars have been calculated in entropy as explained in the 
text. 
 
  
 
 
 
 
 
Figure 2: Cross-correlation coefficient between rRER in pairs of countries.  
White squares means perfect linear correlation ( r=-1 or r=1) and black squares means absence of linear 
correlation (r=0). The x-axis and y-axis are countries ordered by the entropy criterion. Coefficients data could 
be obtained from the authors. 
 
 
 
 

A mathematical theory of communication,

Are currency devaluations effective? A panel unit root test,

Currency devaluation and output growth: new evidence from panel data analysis,

Early-Warning Systems: a Survey and a Regime-Switching Approach,

Empirical identification of currency crises: differences and similarities between indicators,

Estimating the errors on the measured entropy and mutual information,

Ordering univariate distributions by entropy and variance,

The Unholy Trinity of Financial Contagion,

Economic growth and currency crisis: A real exchange rate entropic approach

Economic growth and currency crisis: A real exchange rate entropic approach

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