The Duration of the Exchange Rate and Financial Account
Regimes: A Multiple Destinations Model Approach∗
Raul Razo-Garcia†
Carleton University
This Draft: March 2008
Abstract
This research analyzes the duration of the policy mix comprising an intermediate exchange rate regime and closed financial account. A multiple destinations model, augmented
to incorporate unobserved heterogeneity, is proposed to explore the duration dependence of
this policy and investigate the role played by domestic and international factors on the length
of the spells. Our analysis is novel because we overcome the potential endogeneity between
the two policies by analyzing the duration of the policy mix, allow for multiple destinations
and control for unobserved heterogeneity using parametric and semiparametric techniques.
The evidence favors the multiple destination model over the single destination version. So
the latter hides interesting factors affecting the duration of the policy mix and overestimates
the probability of survival. Regarding the probability of moving to a new policy we found
that it depends on the elapsed duration. The deepness of the financial system, GDP per
capita, size, the general acceptance of capital controls and the interaction between the feasibility of an intermediate exchange rate and a dummy variable for emerging markets are the
most important determinants of the duration.
∗
I am highly indebted to my advisor Barry Eichengreen for his continuous guidance, encouragement, and
support. I want also thank Kenneth Train for his comments on this paper and Carmen Reinhart and Nancy Brune
for proportionating their data. Financial support from CONACYT and UC-MEXUS is gratefully acknowledged.
All errors, however, are my own.
†
Department of Economics, C870 Loeb Building 1125 Colonel By Drive, Ottawa, Ontario, K1Y 3P1, Canada.
Email: rrazogar@connect.carleton.ca
1
1
Introduction
The evolution of the international monetary system in the past 140 years can be divided into
four different episodes: the Gold Standard, the Interwar period, the Bretton Woods System
and the Post-Bretton Woods era. In each of these episodes the reaches of the trilemma of
the monetary policy are evident.1 During the Gold Standard, for example, most countries
forwent monetary independence in order to gain exchange rate (hereafter, ER) stability and
capital mobility.2 Something different occurred during the interwar period when ER stability
was sacrificed to tailor monetary policy toward domestic goals. The disastrous macroeconomic
performance and the international economic disintegration experienced between the two World
Wars called for a new international monetary order. As a result delegates from 44 nations
gathered in Bretton Woods, New Hampshire, United States, and signed the Bretton Woods
agreement in July 1944. This new monetary order, designed to promote price stability and full
employment, was characterized by fixed-but-adjustable ER and capital controls. This in turn
allowed policymakers to keep their monetary independence and to have a stable ER. In 1973,
the Bretton Woods system collapsed and this in turn opened the way to a new era of greater
ER flexibility.
The abandonment of the fixed-but-adjustable parity system brought with it not only changes
to the spectrum of exchange rate regimes (hereafter, ERR) but also changes to the set of financial
account (hereafter, FA) policies that countries could rely on (i.e. capital controls).3 Since then
a vast majority of countries, both advanced and developing, have shown a strong preference to
deal with greater ER flexibility (not necessarily a fully flexible regime) before starting or accelerating the liberalization of the FA. As a byproduct, the policy mix comprising an intermediate
regime and capital controls (hereafter, IC) became one of the most popular arrangements among
policymakers in the last thirty five years (see figure 1).4
Not surprisingly, during this sequencing process of policies an important number of countries
have moved away from the IC combination. This paper asks what factors determine the timing
of that shift (i.e. the duration of the regime). To answer that question, however, we need to
1
See Obstfeld, Shambaugh, and Taylor (2004a) and Obstfeld, Shambaugh, and Taylor (2004b) for empirical
evidence of the constraints of the trilemma along history and Obstfeld and Taylor (2005) the role of the trilemma
on the evolution of the international financial system.
2
In spite of the golden points.
3
We have observed countries implementing a great variety of ER arrangements currency boards (e.g. Argentina
and Hong Kong), dollarization (e.g. El Salvador), currency unions (e.g. Euro Zone), de facto pegs (e.g. Thailand
before the Asian crisis), crawling pegs (e.g. Brazil and Mexico), managed floating (e.g. Mexico after the tequila
crisis) and floating regimes (e.g. New Zealand), among others.
4
This trend is more evident for advanced and emerging markets. For all the other countries, the mix of hard
pegs and capital controls has also been a popular option.
2
recognize the existence of another dimension in the analysis: the presence of multiple destinations
(i.e. regimes). The reason is that policymakers choose not only the timing of the shift but also the
arrangement they will adopt next.5 For example, some of countries that moved away from the IC
policy mix continued their process towards a more flexible ER, others started the liberalization
of FA, and some others moved back in terms of ER flexibility implementing a hard peg. In the
specific case of emerging markets, these experienced a series of crises that pushed some of them
to implement more flexible ERR and others to reconsider the pace of FA liberalization.
The importance of the existence of multiple destinations in the analysis of duration may be
better understood through an example. Imagine a country abandoning an intermediate ERR.
This economy can move in terms of ER flexibility in opposite directions, to a hard peg or a
floating regime. Before answering the question of what determines that shift, we must ask
whether the factors that lead to implement a hard peg are the same as those that cause an exit
to a flexible arrangement. We argue that even if the set of determinants are the same in these
two situations, the magnitude of their effects may vary across the possible destinations.
Thus, if we recognize the existence of multiple destinations in the duration analysis of policy
mixes another question surges; how the marginal effects of the explanatory variables on the
duration vary across destinations? Our belief is that answering these two questions will help
not only to improve our understanding of the duration of these policies but will also enhance
our understanding of their sequencing and therefore of the developments of the international
monetary system.
Recognizing that the duration analysis involves these two dimensions, when to move and
in what direction, implies that the naive one destination model, commonly used in this area
of research, does not serve to answer both questions.6 To overcome this problem we employ
a duration model that recognizes the existence of multiple destinations. In particular, the
empirical model we propose is equivalent to the simplest of the multiple destinations models;
a competing risks model.7 Such models have been used to analyze the duration of various
economic phenomena but not to analyze the duration of ER arrangements and capital controls.
Our analysis is novel, relative to the existent work in the ERR and capital controls literature,
in several ways. First, we allow multiple destinations. Second, rather than oversimplifying the
5
In some situations, policymakers have no choice but to abandon the current exchange rate regime. Even in
those situations our argument on the need to recognize the existence of multiple destinations is still valid.
6
Going back to our example in which a country is moving from a soft peg, in that framework the single
destination model would pool the hard pegs and floating regimes in one destination.
7
A traditional multiple destinations model is the medical competing risks model. A patient could die of lot
of things (hearth attack, cancer, etc...). Another example would be the duration of marriage, where one risk is
death of one of the spouses and the other is divorce.
3
Figure 1: Evolution of the de facto Exchange Rate Regimes (Reinhart and Rogoff) and Financial
Openness Index (Brune)
A
A. Exchange Rate Regime Evolution (Reinhart and Rogoff)
100%
Freely Float
90%
80%
70%
60%
50%
40%
30%
20%
10%
No Flexibility
I
II
III
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2007
2004
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0%
XIV
B. Financial Openness Index (Brune)
100%
Completely
p
y Open
p
90%
80%
70%
60%
50%
40%
30%
20%
10%
Completetely Closed
I
II
III
IV
V
VI
VII
VIII
IX
X
2005
2003
2001
1999
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1995
1993
1991
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1987
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1981
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0%
XI
Notes: Reinhart and Rogoff’s classification comprises the following arrangements: I) No separate legal tender,
II) Pre announced peg or currency board arrangement, III) Pre announced horizontal band that is narrower
than or equal to +/ − 2%, IV) De facto peg, V) Pre announced crawling peg, VI) Pre announced crawling band
that is narrower than or equal to +/ − 2%, VII) De factor crawling peg, VIII) De facto crawling band that is
narrower than or equal to +/ − 2%, IX) Pre announced crawling band that is wider than or equal to +/ − 2%,
X) De facto crawling band that is narrower than or equal to +/ − 5%, XI) Moving band that is narrower than or
equal to +/ − 2% (i.e., allows for both appreciation and depreciation over time), XII) Managed floating, XIII)
Freely floating, and XIV) Freely falling. Intermediate regimes comprise regimes (IV)-(XI)
Brune’s index is the sum of eleven components related to the capital flows: I) controls on inflows of invisible
transactions proceeds from invisible transactions (repatriation and surrender requirements); II) controls on
outflows of invisible transactions (payments for invisible transactions and current transfers); III) controls on
inflows of invisible transactions from exports; IV) controls on inflows pertaining to capital and money market
securities; V) controls on outflows pertaining to capital and money market securities; VI) controls on inflows
pertaining to credit operations; VII) controls on outflows pertaining to credit operations; VIII) controls on
inward direct investment; IX) controls on outward direct investment; X) controls on real estate transactions; and
XI) provisions specific to commercial banks
4
currency spectrum in fixed versus floating regimes, as is commonly done in the literature, we
allow for three arrangements; hard pegs, intermediate and floating regimes. Third, we study the
duration of the policy mix consisting of the ERR and the openness of the FA. This improvement
is consistent with recent efforts to recognize and control for the interaction between the choice
of the ERR and the imposition of capital controls. Fourth, we investigate the role played by
unobserved factors on the duration of the policy mix.
Using data from 1965 to 2006 for advanced and developing countries, we obtain that financial
development, institutional framework (proxied by GDP per capita), relative size, the international acceptance of capital controls and the interaction between an emerging market dummy
variable and the feasibility of intermediate ERR are the main factors affecting the duration of
the IC policy mix. The results show that large economies with underdeveloped financial systems
exhibit lower survival rates. As expected, the development of the general legal systems and institutions (proxied by GDP per capita) is an important requirement for a country to lift capital
controls. Additionally, the evidence indicates that the probability of survival depends on the
elapsed duration. For example, when a Log-logistic baseline function is assumed the chances of
moving toward a new regime exhibits an inverted U-shape.
Interestingly, emerging markets are found to be different, relative to the rest of the world, in
many aspects. First, despite of their deep integration to the international capital markets they
are attracted by the soft pegs. Second, consistent with the ”fear of floating thought”, initiated
by Calvo and Reinhart (2002), these countries prefer to liberalize the FA rather than allowing
the ER to freely float. Finally, emerging economies need to accumulate foreign reserves in order
to maintain for a longer period of time an intermediate ERR. The last two results support the
rejection of the ”bipolar view” hypothesis for these type of economies (e.g. Eichengreen and
Razo-Garcia 2006).8
Regarding the advantages of using a multiple destinations model over the single destination
version, we find that the former fits the data much better and that the latter masks interesting
factors affecting the duration of the policy mix. For example, countries that eventually move to a
hard peg and closed FA policy mix are at a higher risk of abandoning the current regime relative
to the countries moving to any other destination. We also find that the competing risks model
does a better job estimating the probability of survival and hazard functions. In particular, our
8
The advocates of this hypothesis state that the middle ground of the ERR spectrum is disappearing in favor
of the two corners, hard pegs and floating, as the countries integrate to the world capital market. Bubula and
Ötker-Robe (2002), Masson (2001), Masson and Ruge-Murcia (2005), and Eichengreen and Razo-Garcia (2006)
have tested this argument using different de facto ER classifications. The consensus is to the rejection of the
hypothesis.
5
estimates indicates that the single destination model overestimates the probability of survival
(underestimate the hazard function).
Two robustness checks are carried out to verify the sensitivity of the results to the specification of the baseline function and the presence of unobservable characteristics. First, we estimate
the model using four different types of multivariate proportional hazards; Exponential, Weibull,
Gompertz and Log-logistic. Second, given the potential misspecification of the random process
for unobserved heterogeneity and its consequences in the estimated parameters we estimate the
model using parametric and semiparametric techniques. In both cases, the qualitative results
do not change.
The rest of the paper is structured as follows. In Sections 2 and 3 we briefly describe the
evolution of the ERR and the liberalization of the FA, respectively. In section 4 we analyze
the tendencies of the bivariate classification of the ERR and capital controls. Next, in section
5 we describe the econometric model, while in section 6 we present the results. Some policy
implications, mainly regarding to the Chinese economy, are described in section 7. Final remarks
are contained in section 8.
2
Evolution of the Exchange Rate Regime
A key issue in the analysis of ERR is how to classify these arrangements. The two choices are
the de jure and de facto classifications. While the former is generated from regimes reported by
countries (i.e. official regimes) the latter is constructed on the basis of the behavior of market
ER and other macroeconomic variables (e.g. international reserves). Since our investigation
deals with the duration of the implemented policy mix we utilize de facto arrangements.
Three de facto ERR classifications have been constructed recently: Levy-Yeyati and Sturzenegger (2005), Bubula and Ötker-Robe (2002), and Reinhart and Rogoff (2004). We opted to use
Reinhart and Rogoff’s (RR) natural classification for the following reasons. First, when multiple ER coexist RR use data from black or parallel markets to classify the arrangement under
the argument that market-determined dual or parallel markets are important, if not better,
barometers of the underlying monetary policy.9 Second, RR introduce a ’freely falling’ category
to distinguish for periods of very high inflation and uncontrolled depreciation.10 Third, this
classification is available for a longer period of time.
9
Under official peg arrangements dual or parallel rates have been used as a form of back door floating.
A country exchange rate arrangement is classified as ”freely falling” when the twelve-month inflation rate is
equal or exceeds 40 percent per annum or the six months following an exchange rate crisis where the crisis marked
a movement from a peg or an intermediate regime to a floating regime (managed or freely floating). For more
details on this classification see the Appendix in Reinhart and Rogoff (2004)
10
6
The countries included in the empirical analysis are grouped into three categories; advanced,
emerging and ’developing’ countries. The definition of advanced countries coincides with that of
industrial countries in the IMF International Financial Statistics data set. Countries included
in the Emerging Market Bond Index Plus (EMBI+), the Morgan Stanley Capital International
Index (MSCI), Singapore, Sri Lanka and Hong Kong SAR are defined as emerging markets.
All the other countries for which we have data are classified as ’developing’ countries.11 The
resulting sample consists of 22 advanced countries, 32 emerging markets and 141 of ’developing’
countries.12
Simple plots provide evidence that some countries in the early seventies and before the
collapse of the Bretton Woods system started to move away from hard pegs13 to experiment
with intermediate14 and floating regimes.15 Figure 2 documents this tendency. Among the
advanced economies this trend is more evident. In fact, by the end of the 80s the hard pegs had
almost disappeared from the industrialized world (figure 2, panel B). The adoption of the euro
in 1999, however, reverted that trend.
While emerging markets also moved to soft pegs, they did so at a much slower pace. In fact,
the intermediate regimes still accounted for more than half of the emerging countries sub sample
in 2006. A possible argument to explain this behavior is that many of these economies lack
essential preconditions for the operation of alternatives regimes. Among developing countries,
the prevalence of intermediate regimes also increased but at a rate much slower than the emerging
countries. Where these regimes accounted for less than 20 per cent of the developing sub sample
in 1973, they accounted for half of that sub sample in 2006. Finally, these countries have shown
a higher attraction toward hard pegs.
The trend just described is consistent with the rejection of the ’bipolar view’ and with the
idea that intermediate regimes are still a viable option for non-industrialized countries. The
importance of soft pegs in the currency spectrum over the past 35 years makes these type of
arrangements an ideal candidate to analyze the determinants of its survival. In particular, we are
interested in quantifying the effect of variables such as inflation, stock of international reserves,
11
Although we classify this group as developing countries there are some countries, as Monaco and Malta, that
do not fit that description.
12
A list of the countries included in the analysis is provided in the Appendix.
13
Our definition of hard pegs includes regimes with no separate legal tender, pre-announced peg or currency
board, and pre-announced horizontal band that is narrower than or equal to plus/minus 2%. De facto pegs are not
classified as hard pegs because there is no commitment by the monetary authorities to keep the parity irrevocable.
14
Includes de facto pegs, de facto crawling band that is narrower than or equal to +/-2%, pre-announced
crawling band that is wider than or equal to +/-2%, de facto crawling band that is narrower than or equal to
+/-5%, moving band that is narrower than or equal to +/-2% (i.e., allows for both appreciation and depreciation
over time), pre-announced crawling peg, pre-announced crawling band that is narrower than or equal to +/-2%,
and de facto crawling peg.
15
Includes managed floating and freely floating arrangements.
7
level of development, among others, on the probability that the intermediate regime will end,
given survival to t.
3
Evolution of the Openness of the Financial Account
Given the lack of a de facto classification for the openness of the FA we rely on Nancy Brune’s
de jure financial openness index (BFOI).16 This index aggregates eleven components related to
capital flows.17 For the purposes of this paper we have updated Brune’s index for 2005 and
2006. For simplicity and to obtain a reasonable number of spells for different policy mixes, two
FA regimes are assumed; closed and open. Countries with a BFOI greater than 3 are classified
as open FA regimes.18
This binary classification shows a clear rise in capital mobility since 1973 (figure 3). The
fraction of countries with open FA rises most among advanced countries, followed by emerging
markets and developing economies. Although some countries were already financially open in
the early 70s, the divergence between advanced countries and the rest of the world, if anything,
has widened over time. A significant movement toward higher capital mobility started in the late
70s in developed economies and ten years later in emerging countries. By 1994 the industrialized
world had moved virtually all the way to fully open FA. Among developing countries, we see
that they have delayed this process for some years. In fact, a significant fraction of emerging
and developing countries still maintained restrictions on capital flows in 2006. Eichengreen and
Razo-Garcia (2006) argue that the preconditions for rapid FA liberalization were and are absent
outside of the industrialized world. So in order to move further in the FA liberalization process,
emerging markets and developing countries need to strengthen macroeconomic policies, financial
systems, prudential supervision and regulation, transparency, and corporate governance. This
coincides with the main conclusions emerging from the literature on financial crises of the 1990s.
4
Evolution of the Bivariate Classification of the Exchange Rate
Regime and Liberalization of the Financial Account
In the two previous sections we observed a trend towards greater ER flexibility and a continued
rise in capital mobility. However, since we did not look at the joint evolution of the ERR and
capital controls it was not possible to verify whether the timing of these two processes match,
16
Excluding the exchange rate structure component.
See notes figure 1.
18
A value of 3 corresponds to the 66th percentile of the financial openness index.
17
8
or if such reforms were implemented in sequential manner. To do so, we study the evolution of
the bivariate classification of the ERR and the openness of the FA.
Figure 4 combines data on these two policies. One thing that comes through clearly from this
figure is that the date on which the movement towards greater ER flexibility started does not
coincide with the start of the liberalization of the FA. Instead, this binary classification shows
that a sequencing process has been taking place in the last 35 years. The first stage of this process
initiated a few years before the collapse of the Bretton Woods system, when a significant share
of countries moved from a hard peg and closed FA to intermediate regimes (panel A). However,
during this initial stage there is no clear intention to remove capital controls. As a result, the
IC policy mix became one of the most popular arrangements implemented around the world.19
The next stage in this sequencing process is characterized by a removal of the limits on capital
flows.
Important insights can be obtained when one makes the same analysis separately for advanced countries, emerging markets and developing economies. First, immediately after the
collapse of the Bretton Woods system, the IC policy mix became the most popular arrangement
among advanced and emerging countries. Contrary to this, developing countries have preferred
to maintain a hard peg with a closed FA. In fact, it was not until the early 90s when the IC
mix began to be a more accepted policy among these economies. Second, at the end of the 80s
the majority of the advanced economies were ready to liberalize the FA. Within this subgroup
we see a dominant movement toward an intermediate ERR and open FA. Among developing
countries, a similar trend is observed but with less intensity. Third, by the late 90s the advanced
countries have moved virtually all the way to fully open FA and in doing so have abandoned the
intermediate ERR in favor of either hard pegs or floating rates.
Beyond the importance of the IC policy mix in the evolution of the international monetary
system there are three additional aspects supporting our choice to analyze this policy. The first
one is the absence of left-censored spells for this arrangement. If we had left-censored spells
we would have to resort to stationary assumptions to build up the likelihood function. In other
words, the presence of left-censored spells implies that the econometrician needs to make some
assumptions regarding the flows into, and out, of the regime. Secondly, the number of spells
for the IC policy mix is reasonable. Third, the majority of the spells are concentrated in the
post-Bretton-Woods era. It is possible that the main determinant of the duration of the hard
peg ERR and closed FA policy mix was the Bretton Woods system by itself (and the restrictions
imposed by it) and not other macroeconomic variables.
19
Closely followed by the soft pegs and closed FA.
9
Figure 2: Evolution of the de facto Exchange Rate Regimes (Reinhart and Rogoff)
10
Hard Pegs
Intermediate
Floating
Freely Falling
Hard Pegs
Intermediate
C. Emerging Market Countries
Floating
2006
2003
2000
1997
1994
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0%
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20%
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40%
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15.0
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60%
1949
20.0
1946
80%
1943
25.0
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100%
1946
B. Advanced Countries
1943
A. All Countries
Freely Falling
D. Other Countries
30.0
80.0
70.0
25.0
60.0
20.0
50.0
40.0
15.0
30.0
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Intermediate
Floating
Freely Falling
Hard Pegs
Intermediate
Floating
Freely Falling
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open
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closed
1983
C. Emerging Market Countries
1980
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10.0
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open
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11
1965
Figure 3: Evolution of the de facto Capital Controls
B. Advanced Countries
25.0
90.0
70.0
20.0
15.0
50.0
10.0
30.0
5.0
10.0
0.0
closed
D. Other Countries
80.0
20.0
70.0
60.0
50.0
40.0
30.0
5.0
20.0
10.0
0.0
Figure 4: Evolution of the Policy Mix: ERR and FA Openness
A. All Countries
B. Advanced Countries
100%
25.00
80%
20.00
60%
15.00
Intermediate and
Closed
40%
10.00
Hard Peg and
Closed
5.00
20%
Intermediate and
Open
Intermediate and
Closed
Hard Peg and
Closed
HP Open
Fall Closed
Int Closed
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Float Closed
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Fall Closed
C. Emerging Market Countries
Int Closed
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Int Open
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HP Closed
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D. Other Countries
30.00
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60.00
50.00
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40.00
15.00
Intermediate and
Closed
30.00
10.00
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5.00
In summary, along history countries have used their ER and FA policies to cope with domestic
and international shocks. In spite of the discretionary use of these two policies we can identify a
common sequence during the post-Bretton Woods era. This ’typical’ sequence is characterized
first by a closed FA and a hard peg combination, then a move toward greater ER flexibility
(intermediate ERR and closed CA) and finally a move toward a more open FA.
5
Empirical Duration Model with Multiple Destinations
Since the work of Klein and Marion (1997) on the duration of fixed ER few attempts have
been undertaken to understand the determinants of survival of different ERR.20 Regardless of
the important contribution of these papers to the field, we found three important limitations
on them. First, there is in general an oversimplification of the ERR spectrum in fixed versus
floating arrangements when the data show that intermediate regimes are still a valid option
for the non-industrialized world. Second, the common concern in the application of duration
models to ER arrangements has been with the exit of countries from one ERR to any another
arrangement; a single destination state pooling all the possible ER destinations. It is surprising
that none of the current studies allow for multiple destinations. In fact, the decision or the need
to exit an ERR is accompanied by the choice of the arrangement that will be adopted next.
Third, from the ’bipolar view’ argument and the trilemma of monetary policy we know that
there exists a connection between the level of capital mobility and the ERR. Thus, to analyze
the duration of the ER arrangements the interaction (endogeneity) between the openness of the
FA and the ERR must be acknowledged.21
To deal with these issues we propose a multiple destinations model. Special emphasis is
placed on the role played by macroeconomic conditions prevailing before the abandonment of
the regime. Three potential destinations are identified: i) hard peg and a closed FA (hereafter,
HPC); ii) intermediate ERR and open FA (hereafter, IO); and iii) flexible rate and closed FA
(hereafter, FC).22 To verify the robustness of the results the model is augmented to incorporate
unobserved heterogeneity. An additional sensitivity analysis is carried out to verify the impact of
the distributional assumptions imposed on the unobservable characteristics by using parametric
and semiparametric techniques.
20
See Wälti (2005) and Klein and Shambaugh (2006)
Obstfeld, Shambaugh, and Taylor (2004b), Razo-Garcia (2008a), von Hagen and Zhou (2006), and Walker
(2003) analyze empirically this issue.
22
The other potential destinations, hard-peg-ER-open-FA and floating-ER-closed-FA, has zero or just a few
transitions during the sample period.
21
13
5.1
The Multiple Destinations Model
The empirical model proposed is the simplest of the multiple destination models; the competing
risks model. While the implementation of this type of models is not new in the duration analysis
of economic phenomena it has become more familiar in the past few years. Research on the
duration dependence of unemployment, retirement, hospital length stay or brand loyalty, among
other subjects, have made use of such models.
Han and Hausman (1990), Foley (1997), Addison and Portugal (2001) study unemployment
duration allowing multiple destinations. While the former allow two risks, new jobs and recalls,
Foley and Addison and Portugal assume inactivity (out of the labor) and employment as the
two possible destinations.23 In a similar spirit Butler, Anderson, and Burkhauser (1989) analyze
the duration of retirement assuming two potential risks, return to work or death.24 In health
economics, Picone, Wilson, and Chou (2003) resort to a competing risks model to identify
factors influencing hospital lengths of stay and post-hospital destinations of Medicare patients.
The potential destinations assumed by them are skilled nursing facilities, home health agencies,
inpatient hospital rehabilitation units or in-hospital death.25 In marketing, researchers have
employed this type of duration models to analyze brand loyalty (brand choice). Popkowski
Leszczyc and Bass (1998), for example, propose a multiple destinations model for brand choice
of ketchup assuming four brands. They focus on the transition from one brand to the others
and the possibility of staying. In all these cases the evidence supports the multiple destinations
model. Regarding the survival of the ER arrangements or capital controls we are not aware of
any study utilizing a multiple destinations model.
A first attempt to analyze the duration of ERR is found in Klein and Marion (1997). These
authors examine the duration of pegs in 16 Latin American countries plus Jamaica motivated
by a belief that there exists a trade-off between the cost associated with the defense of the peg
(e.g. overvaluation or undervaluation of the ER) and the costs associated with the abandonment
of the parity (e.g. political cost). Using a similar set of countries Blomberg, Frieden, and Stein
(2005) analyze the government ERR choice, constrained by politics. Mathematically, these
authors examine the likelihood of abandoning the peg in time t+1, given the survival of the
regime to t (hazard rate). They collapse the spectrum of ERR in two possible arrangements,
23
An appealing characteristic of the model proposed by Addison and Portugal (2001) is the allowance for
defective risks. The reason is that some destination states may be unreachable for some individuals so the
probability of moving to that state is zero for them and therefore the risk is defective. Foley focuses on the
determinants of the unemployment duration in Russia Addison and Portugal analyze the case of Portugal.
24
These authors allow for semiparametric unobserved heterogeneity (gaussian) and correlation among the heterogeneity components associated with the competing risks.
25
These authors control for the unobservable factors in a non-parametric way.
14
fixed and flexible. Their results provide statistical support for negative duration dependence
(i.e. the longer a country has been on a currency peg the less likely it is to abandon it).
5.2
The Empirical Model
Now we describe the empirical model in which we rely on. This section is based on the work of
Lancaster (1990). Suppose that there are K possible destination states and define each of them
as k, k = 1, 2, ..., K. These destinations must be mutually exclusive and they have to exhaust the
possible destinations. For example, a country pegging its currency can continue to be pegging,
move to a soft peg or switch to a floating regime. Let us think of time to exit as a continuous
random variable, T , and consider a large number of countries entering state k at a time we
shall identify as T = 0.26 In fact, for country ith we must define k different continuous duration
random variables Tik (one for each risk or destination regime). Only the smallest of all these
durations Ti = min Tik and the corresponding destination are observed. All the other durations
are censored given that risk k is materialized (i.e. Tik > Ti for k 6= min Tik ). Estimating
erroneously a single destination model under the presence of multiple risks is equivalent to
assume that the random variables Tik are independent. Nevertheless, since the Tik s are affected
by the agents’ behavior and unobservable characteristics (heterogeneity) this assumption looks
very unrealistic and might led to incorrect inference (van den Berg, 2005).
Define the instantaneous rate of exiting for state k per unit time period at t, known as the
transition intensity for state k, as
P r(t ≤ T ≤ t + dt, Dk ; T ≥ t, X)
dt →0
dt
θk (t; X) = lim
k = 1, 2, . . . , K
(1)
where P r(t ≤ T ≤ t+dt, Dk ; T ≥ t, X) is the probability that a country departs from the current
arrangement to state k in the short interval (t, t + dt) given that the state is still occupied at
t, f (·) and F (·) are the probability density function and the cumulative density function of the
random variable T , and Dk is a vector containing K binary variables dk assuming the value
of one if state k is entered and zero otherwise. So Dk is a vector of zeros except for the k th
row which is equal to one. In this framework, the hazard function is the sum of the transition
intensities over the destination states
K
X
P r(t ≤ T ≤ t + dt; T ≥ t, X)
f (t)
=
=
θk (t; X)
dt →0
dt
1 − F (t)
θ(t; X) = lim
(2)
k=1
26
Note that in this model we have K + 1 random variables conformed by the random variable T and K statedummy variables.
15
The last equality in (2) indicates that the total of the survivors at t who exit on the following
period is the sum over k of those who leave for destination k. In other words, since the potential
risks (destinations) are mutually exclusive events their densities (transition intensities) are added
to obtain the conditional probability of exiting the current regime. These competing risks,
however, may be correlated due to the unobserved heterogeneity present in each transition
intensity.
Let S(t; X) denote the probability of survival to t, P r(T ≥ t) = 1 − F (t). From a well known
relationship between the hazard and the survivor functions we obtain the following equation
S(t; X) = exp
n
Z
−
t
o
n
o
θ(s; X)ds = exp − Λ(t; X)
(3)
0
where Λ(t; X) is the integrated hazard function. Then, S(t; X)θk (t; X)dt might be interpreted
as the probability of departure to state k within the period (t, t + dt)27
P r(t ≤ T < t + dt, Dk ; X) = S(t; X)θk (t; X)dt
(4)
The empirical counterpart of S(t; X)θk (t; X) is the fraction of an entering cohort who exit for
state k between t and t + dt.28
Two types of spells contribute to the likelihood function; completed and censored. A country
observed to exit for regime k at time ti contributes P r(exit f or k at time ti ) which can be
rewritten in terms of the transition intensities and survivor functions. From equations (2), (3)
and (4) we obtain the contribution of non-censored spells to the likelihood function
(
−
P r(t < Ti < t + dt, Dk ; Xi ) = exp
Z tX
K
)
θk (u; Xi )du θk (t; Xi )dt
(5)
0 k=1
A spell censored at time ti contributes the probability of being alive at that time (i.e. the
survival function). Thus, the likelihood function is29
L(Γ) =
" K
n
Y
Y
i
27
28
#
dk,i
P r(t < Ti < t + dt, Dk ; Xi )
exp
n
− Λi (t; Xi )
o1−PK
k=1 dk,i
(6)
k=1
S(t|X)θk (t; X)dt=P(survival to t) × P(departure to k in (t, t + dt)|survival to t).
Note that the intensity transition θk is equal to πkSfk and not to fSk as it would be if θk were the hazard
function. In this case, fk (t) = −dSdtk (t) , πk fk (t) is the probability that a country exit the regime on period t and
went to state k and S k (t) is the probability of survival to t conditional on the event that when departure occurs
is to state k, P r(T ≥ t|when exit occurs it is to k, X).
"
#
"
# PK
n
o dk,i
n
o 1− k=1 dk,i
Q
Q
K
29
L(Γ) = n
− Λi (t)
exp − Λi (t)
.
i
k=1 θk (t; Xi ) exp
16
where Γ is a vector of parameters and dk,i is a binary variable equal to one when transition is
for state k and equal to zero otherwise.
5.3
Baseline Functions
Once the empirical model has been set the next step is to specify the functional form of the
transition intensities, θk . This implies that we need to decide whether the transition probabilities
will increase, decrease or stay constant over time. A common assumption in the literature is to
assume time-independent transition intensities. However, since we do not know if the probability
of departing to an FC policy mix, or any other state, in the short interval (t, t+dt), given survival
to t, is constant over time this assumption seems somewhat restrictive a priori. To verify the
sensitivity of the results to this assumption we estimate the model using different functional
forms for the transition intensities. To do so, we first assume a proportional ”hazard” model
θk (t, x) = f1 (x)f2 (t)
(7)
where f1 and f2 are the same functions for all countries. As before, t represents the duration of
the regime, x is a vector of explanatory variables that shift the transition intensities, and β is a
vector of coefficients associated with these variables.
The specification of θk (t) consists of two terms. The first is a description of the way in which
the transition intensities change, at a given point in time, between countries with different
characteristics, f1 (x) = exp{x0 k βk }.30 The second term is known as the baseline hazard, which
is a functional form for the time dependence, f2 (t). Note that the transition intensities for two
different entities with regressor vectors x1 and x2 are in the same ratio,
f1 (x1 )
f1 (x2 ) ,
for all t. We
estimate the model assuming the following baseline functions
f2,k (t) = exp{β0 }
f2,k (t) = exp{β0 }αk tαk −1
f2,k (t) = exp{β0 } exp{γk t}
Exponential Model
(8)
Weibull Model
(9)
Gompertz Model
(10)
With the first two baseline functions, Weibull and Gompertz, we allow the transition intensities,
and therefore the hazard function, to increase or decrease monotonically over time. Specifically,
in the Weibull model the transition intensities rise or fall monotonically if αk > 1 (positive dura30
Exponentiation prohibits the prediction of negative hazard rates and does not put restrictions on the parameters.
17
tion dependence) or αk < 1 (negative duration dependence), respectively.31 On the other hand,
in the Gompertz model the hazard and the transition intensities rise (decrease) monotonically if
γk > 0 (γk < 0). The exponential model is nested within the Weibull and the Gompertz models
when α = 1 or γ = 0, respectively. Thus, for the Exponential model the transition intensity
does not depend on the elapsed duration.
Anticipating a possible non-monotonic behavior of the transition intensities we also consider
a Log-logistic model
θk (t; x) =
exp{β0 + x0 k βk }αk tαk −1
1 + exp{β0 + x0 k βk }tαk
(13)
This specification is more flexible relative to the proportional ’hazard’ model because it displays
a non-monotonic behavior for some parameterizations. For α > 1, θk (t; x) exhibits an inverted
h
i
1
α
U-shape increasing from zero at t = 0 to a single maximum at t = exp{βα−1
and then
]
0
0 +x k βk }
approaching to zero as t → ∞. For α ≤ 1 the transition intensity decreases monotonically.32
5.4
Unobserved Heterogeneity
We adjust the model described above for unobserved heterogeneity. Heterogeneity arises when
different countries have potentially different duration distributions. In that case, the waiting
times are generated by different stochastic processes. Although we control for systematic differences across countries on the transition intensities by the inclusion of a vector of observable
characteristics, X, there might be significant unmeasured (unobserved) differences among them.
Neglecting unobserved heterogeneity affects the probability of staying in a given regime and
therefore a spurious state dependency might result. Specifically, not controlling for unobserved
factors implies that countries with the same level of covariates are identical. If this is not the
case, the model would be misspecified. To analyze the importance of unobserved heterogeneity
we estimate a mixed proportional ’hazard’ model and a mixed Log-logistic model.
Given the potential misspecification of the random process for unobserved heterogeneity and
its consequences on the estimated parameters (i.e. biased estimates) we estimate the competing
31
For the Weibull model the hazard function and the probability of survival to time t are
θ(t; X) =
K
X
αk exp{x0k βk }tαk −1
(11)
k=1
S(t; X) = exp
n
−
K
X
exp{x0k βk }tαk
o
(12)
k=1
Specifically, if α = 1 then θk (t; x) decreases monotonically from exp{β0 + x0 k βk } at t = 0 to zero as t → ∞.
If α < 1, θk (t; x) diminishes monotonically from ∞ at the origin to zero as t → ∞.
32
18
risks model using parametric and semiparametric methods.33 Our semiparametric approach is
analogous to Butler, Anderson, and Burkhauser (1989).34
Common in the literature is to assume multiplicative heterogeneity
θk (t; Xi , νk ) =f1 (Xi )f2 (t)h(νk )
θk (t; Xi , νk ) =
(14)
exp{β0 + X0ik βk }αk tαk −1
h(νk )
1 + exp{β0 + X0ik βk }tαk
(15)
where h(νk ) is an increasing function of a time-invariant residual to be regarded as a realization
of a random variable Vk . The realization of this random term, νk , is both unknown and varies
over the population of interest. Equations (14) and (15) are the modified transition intensities
for the proportional hazard and the Log-logistic models, respectively. Let ν = ν1 , . . . , νK
be the vector of unobserved multiplicative heterogeneity assumed to have a joint distribution
denoted by G(ν; X). We can rewrite equations (3) and (5) conditioned on νk
(
P r(t ≤ T < t + dt, Dk ; Xi , ν) = θk (t; Xi , νk ) × exp
−
Z tX
K
)
θk (u; Xi , νk )du
(16)
0 k=1
(
−
P r(T ≥ t; Xi , ν) = exp
Z tX
K
)
θk (u; Xi , νk )du
(17)
0 k=1
To construct the likelihood function, however, we need the unconditional counterparts of the
marginal probabilities, equation (5), and the probability of survival.35 These probabilities are
obtained by integrating out the random term ν
Z
∞
P r(t ≤ T < t + dt, Dk ; Xi ) =
Z
∞
···
P r(t ≤ T < t + dt, Dk ; Xi , ν)g(ν; Xi )dν
Z ∞
Z ∞
P r(T > t; Xi ) = Λ(t; X) =
···
P r(T ≥ t|Xi , ν)g(ν; Xi )dν
−∞
(18)
−∞
−∞
(19)
−∞
which involves an K-fold integral. A simple case is one in which the K elements of ν are
independent gamma distributed variables (the case we describe in the next section). In that
case the K-fold integral decomposes into a product of K integrals and the risks are implicity
assumed to be independent.
33
Assuming a distribution for the unobserved heterogeneity terms is not necessarily a source of bias but it is
always preferable to implement a less restrictive model.
34
A modified version of Heckman and Singer (1984) approach.
35
Unconditional respect to the heterogeneity term.
19
5.4.1
Parametric Estimation of the Unobserved Heterogeneity
A general specification of unobserved heterogeneity allows for risk-specific random components.
Let h(ν) = ν and G(ν; Xi ) be the joint cumulative distribution function of the random vector
ν conditional on Xi . The first set of models, adjusted for unobserved heterogeneity, that we
estimate assume that the K elements of ν are independent gamma distributed random variables.
Hence, following Lancaster (1990)
m
S k (t; X)
Z
∞
Z
∞
···
=
−∞
Z
exp −
−∞
t
1
θk (t; Xi , ν) g(ν; Xi )dν =
1
2
0
(20)
σ
k
[1 + σk2 Λm
k (t; X)]
where the superscript ”m” refers to the corresponding functions for the mixture distribution and
Rt m
Λm
(t)
=
k
0 θk (s; X)ds is the integrated transition intensity for state k. Similarly, the mixture
transition intensity can be written as the ratio of the conditional hazard at the mean of the
marginal distribution of G(ν; X) divided by the increasing function [1 + σk2 Λkm (t; X)]
θkm (t; x) =
θk (t; x)
1 + σk2 Λkm (t; X)
(21)
With equations (20) and (21) we can derive the likelihood function
L(Γ) =
" K
n
Y
Y
i
where S
m
#
m
θkm (ti ; Xi )dk,i S k (ti ; X)
(22)
k=1
Q
R
Q
R P
m
t
t m
K
K
dk ds =
m (s; X)dk ds =
(s;
X)
θ
exp
−
θ
= exp − 0 K
k=1 S k (t; X).
k=1
k=1 k
0 k
Note that the likelihood function is a product of K likelihoods, one for each destination (or
failure). Moreover, the likelihood function involving a specific destination is exactly the same
likelihood you would obtain by treating all other types of failure (destinations) as censored
observations.
In this framework the presence of unobserved heterogeneity can be easily tested. If there is
no heterogeneity the variance of the K states should be jointly equal to zero. Under the null,
the true model would be equal to the one presented in section 5.2.
5.4.2
Semiparametric Method to Account for Unobserved Heterogeneity
To check the sensitivity of the results to the Gamma and independence assumptions imposed
in the previous section we resort to a semiparametric estimation technique. In this framework
the unmeasured heterogeneity is controlled for in a manner similar to Butler, Anderson, and
20
Burkhauser (1989) strategy. Contrary to Heckman and Singer (1984), who assume that the
distribution of the unobservable heterogeneity term is explicitly discrete, Butler, Anderson,
and Burkhauser consider that the discrete distribution is a numerical approximation of the
true distribution. This semiparametric estimation technique allows correlated competing risks
without imposing any distributional assumption on G(ν; X).
Let h(ν) = exp(ν). As before, to derive the likelihood function we need the unconditional
counterparts of the equations (16) and (17). Integrating out these probabilities over all possible
values of ν we obtain
Z
∞
P r(t ≤ T < t + dt, Dk ; Xi , ν)g(ν; Xi )dν
···
P r(t ≤ T < t + dt, Dk ; Xi ) =
≈
∞
Z
LK
X
l1 =1
lK =1
···
Z
∞
τl1 ,...,lk P r(t ≤ T < t + dt, Dk ; Xi , ν = q)
Z
P r(T ≥ t; Xi ) =
≈
(23)
−∞
−∞
L1
X
∞
···
P r(T ≥ t; Xi , ν)g(ν; Xi )dν
−∞
L1
X
LK
X
l1 =1
lK =1
(24)
−∞
···
τl1 ,...,lk P r(T ≥ t; Xi , ν = q)
n
o0
n
o0
where g(ν; Xi ) is the prior distribution of the residuals, ν = ν1,l1 , . . . , νK,lK , q = q1,l1 , . . . , qK,lK
is a vector of integration points, Lk is the number of integration points related to the random
effect of destination K and
(
τl1 ,...,lk = w1,l1 · · · wK,lK g(q1,l1 , . . . , qK,lK ) exp
2
q1,l
1
2
+ ··· +
2
qK,l
K
)
(25)
2
The approximation is obtained by Gauss-Hermite numerical integration using w0 s as the integration weights.36 In the Appendix is proven that
L1
X
···
l1 =1
LK
X
τl1 ,...,lk = 1
(26)
lK =1
In this framework, the following likelihood function is maximized
L(Γ; X) =
N
Y
"
P
1− K
k=1 dk,i
P r(T ≥ t|Xi )
#
P r(t ≤ T < t + dt, Dk |Xi )
dk,i
i=1
36
More details about the Gauss-Hermite numerical integration are relegated to the Appendix.
21
(27)
subject to (23), (24), and (26).
6
Variables and Results
6.1
Variables
The source of the variables is included in the Appendix. The variables controlling for observed
heterogeneity are inflation, GDP per capita, trade openness, stock of international reserves
(normalized by M2), financial development, size relative to the U.S.A. (in terms of GDP),
SpillER and SpillFA. We also control for type of country (dummy variables for advanced and
emerging market countries) and regional fixed effects.
SpillER is the proportion of countries in our sample implementing an intermediate ERR
and SpillFA is the fraction of countries in the sample with a closed FA. Frieden, Ghezzi, and
Stein (2000) and Broz (2002) use a variable similar to SpillER to control for the feasibility of
the ER arrangement. The idea is to capture the ”climate of ideas” regarding the appropriate
ERR. That is, the choice of an ER arrangement may be related to the degree of acceptance
of that regime in the world. This being true, then if most of the countries are implementing
an intermediate arrangement it would be more feasible to maintain that regime. Therefore, we
expect a positive association between SpillER and the duration of the IC policy mix. Same logic
applies to SpillFA.
Optimum currency area (OCA) theory holds that variables such as low openness to trade,
large size and low geographical concentration of trade are associated more frequently with more
flexible regimes. The argument is that a higher volume and greater geographical concentration
of trade increase the benefits from a less flexible regime, reducing transaction costs. Trade
openness may be associated with the FA liberalization in two ways. On one hand, trade openness
is commonly seen as a prerequisite to open the FA. On the other hand, a high level of trade
openness can make capital controls less effective.37 Hence, higher trade openness should be
associated with a higher propensity to remove capital controls. For the IC policy mix this
means that an ambiguous relationship between the openness to trade and the duration of this
arrangement is expected. For example, if the preconditions to implement a hard peg do not
exist in a country willing to move in that direction then a soft peg might be a good alternative
to reduce the transaction costs associated with the international trade. In that case, the higher
the level of trade openness is the higher the hazard (lower survival) would be for countries
eventually moving to a more open FA. Continuing with OCA theory, smaller economies have a
37
Typically overinvoicing of imports or underinvoicing of exports.
22
higher propensity to trade internationally leading to a higher likelihood of pegging. No empirical
or theoretical correlation is expected between the size of an economy and the openness of the
FA, so the main effect of this variable on the duration of the IC policy mix is expected to come
from the ERR side.
The stock of international reserves is aimed to control for a ’life-jacket’ effect. In particular,
we want to check whether the stock of foreign exchange reserves helps to maintain a soft peg (i.e.
longer duration). To the extent that a high level of international reserves is seen as prerequisite
for defending less flexible regimes, a negative association between the flexibility of the ER and
the stock of international reserves is expected (i.e. longer duration of the IC policy mix or a
lower probability of survival conditional on the fact that the new regime involves a hard peg).
Countries with underdeveloped financial systems do not count with the instruments needed
to conduct open market operations and as a consequence are expected to adopt less flexible
regimes. Since financial development and innovation reduce the effectiveness of capital controls,
countries with more developed financial systems should exhibit a higher propensity to open the
FA. Thus, a negative relationship between financial development (M 2/GDP ) and the duration
of the IC policy mixture is expected.
Inflation can play two different roles regarding the ERR. On one hand, countries can choose
a less flexible regime as a commitment mechanism to assist them in maintaining credibility for
low-inflation monetary policy objectives.38 On the other hand, defending an intermediate or
a fixed ERR in a high inflation country might be a difficult and a costly task. Regarding the
FA and its relationship with inflation, previous research suggests that governments compelled
to resort to the inflation tax are more likely to utilize capital controls to broaden the tax base.
Hence, a negative correlation between inflation and the openness of the FA is expected. The
overall effect of inflation on the duration dependence of the IC policy mix is therefore uncertain.
If the costs of maintaining an intermediate regime under a high inflation environment are lower
than the low-inflation credibility benefits then a longer duration of the policy mix would be
expected.
Regarding the ERR and its expected correlation with institutions, Hausmann, Panizza, and
Stein (2001) claim that the ability to adopt a freely floating regime is closely related to the level of
development.39 So, countries with better institutional framework (i.e. developed countries) are
more inclined to adopt flexible arrangements. What then about the expected association between
38
For example, before the tequila crisis in 1994 Mexico resorted to a crawling peg (intermediate regime) to
mitigate inflation.
39
The rationale for this argument is based on the observed differences of the ratio of ER volatility to reserves
and the ratio of reserves to M2 between advanced, emerging markets and other developing countries.
23
the openness of the FA and the institutional framework? As we mentioned above, to move further
in the FA liberalization process, the economies need to develop the general legal systems and
institutions (e.g. prudential supervision and regulation). Also, as explained by Eichengreen and
Leblang (2003), democratic countries have more recognition of rights, including the international
rights, of residents who have a greater ability to press for the removal of restrictions on their
investment options.
Finally, given the close integration of emerging economies to the international capital markets
we analyze whether international reserves and the general acceptance of both the intermediate
regimes and capital controls affect the transition intensities of these countries in a different way
relative to the rest of the world. To do so, we include interactions between an emerging market
dummy variable and international reserves, SpillER and SpillFA. With the exception of the
dummy variables, SpillER, and SpillFA, all the other variables are lagged by one period.
6.2
Duration of the Intermediate Regime and Closed Capital Account
Our sample consists of 155 spells with an average and median duration of 9 and 7 years, respectively, and standard deviation of 7.5 (see table 1).40 The longest spell observed lasted 34 years
(Morocco) while the shortest just 1 year (14 spells). Only two countries moved to a floating ER
and open FA policy mix (Czech Republic in 1996 and Dominican Republic in 2003). These two
spells were discarded due to the small number of transitions observed during the sample period.
Hence, we identify three possible destinations if a country decides to leave the IC policy mix: 1)
HPC, 2) IO and 3) FC. Fifty spells are censored to the right. As we mentioned above, the left
censoring problem is not present for any of the spells included in the sample. As we mentioned
above, the left censoring problem is not present for any of the spells included in the sample.
Overall and destination-specific descriptive statistics are shown in table 1. Some stylized
facts can be drawn from that table. First, countries that move to a HPC policy combination
exhibit, on average, the lowest level of financial development across the three destinations. In
addition, countries that move to a hard peg (HPC) do it when the feasibility or acceptance
of capital controls is high. Second, it seems that economies with developed financial markets,
highest stock of international reserves, GDP per capita and level of trade openness liberalize
the FA first rather than allowing the ER to freely float. Small countries are, on average, less
attracted to lift capital controls. As expected, countries remove capital restrictions when the
general acceptance of controls is low (i.e. lower level of SpillFA across the three destinations).
40
The table with the spells, duration and countries is contained in the Appendix (table A-4).
24
Third, countries moving to some form of floating with capital controls are on average the largest
economies in our sample and the ones with the lowest level of international reserves. Fourth,
consistent with OCA theory, countries with the highest level of trade openness prefer less flexible
ER arrangements. In our sample, countries implementing intermediate regimes have the highest
level of international trade integration. Fifth, while countries that eventually move to a HPC
policy mix have the lowest average duration (4 years), countries that shift to an IO arrangement
exhibit the highest duration. The latter fact support the argument that it takes a long time to
prepare the ground to liberalize the FA. Sixth, a single destination model would hide all these
interesting facts.
The asymmetry between the three possible destinations can be clearly observed plotting the
empirical transition intensities and the probabilities of survival.41 Panel A in figure 5 shows
the empirical hazard and the survival rate. The transition intensities and the proportion of
surviving countries that move at the end of the spell to destination k are presented in panels B
to D. Due to the limited number of spells these plots should be taken with caution. At least the
transition intensity associated with regime HPC presents a very different behavior relative to the
hazard function and the other two transitions. Contrary to the empirical hazard, which exhibits
neither negative nor positive duration dependence in the first 15 years, the transition intensity
associated with the HPC policy exhibits positive duration. Hence the chances of departing to
the HPC arrangement in the short interval (t, t + dt), given survival to t, increases over time.
Similarly, the subgroup that eventually moved to a floating regime (i.e. FC policy) presents
positive duration dependence. Finally, among the countries eventually removing all capital
restrictions, the transition intensity related to the IO mixture indicates that the probability of
abandoning the current regime in the first 15 years of the spell is small. This means that it
takes about 15 years or so to prepare the ground to liberalize the FA.
Given the flexibility of the multiple destinations model and the asymmetric behavior shown
by the empirical transition intensities we estimate a ’hybrid’ model with baseline-specific destination functions. Since the empirical intensities for the IO and FC destinations are non-decreasing
over time (panels C and D in figure 5) we assume, in this specific model, Weibull transition
intensities for these two destinations. Given the non-monotonic behavior of the HPC transition
intensity, panel B in figure 5, we assume that the probability of moving toward a HPC policy mix
given survival to time t is better described by a Log-logistic transition intensity. This ’hybrid’
multiple destinations model is compared to model in which all transition intensities are assumed
to be Log-logistic.
41
These are nonparametric empirical hazard, survival or transition intensities.
25
Figure 5: Empirical Hazard and Transition Intensities
Panel A: All Spells
Proportion Surviving
Hazard
0.7
1
0.9
06
0.6
0.8
0.5
0.7
0.6
0.4
0.5
0.3
0.4
0.3
0.2
0.2
0.1
0.1
0
0
1
3
5
7
9
11
13
time
15
17
19
21
23
1
25
3
5
7
9
11
13
time
15
17
19
21
23
25
Panel B: Hard Peg - Closed FA
Proportion Surviving
Transition Intensities
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
1
3
5
7
9
11
13
15
17
19
21
23
25
1
2
3
4
5
6
7
8
9
10
11
12
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
time
13 14
time
15
16
17
18
19
20
21
22
23
24
25
Panel C: Intermediate - Open FA
1
1
0.9
0.9
0.8
0.8
07
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
13 14
time
i
15
16
17
18
19
20
21
22
23
24
1
25
2
3
4
5
6
time
Panel D: Float - Closed FA
1.2
1
0.9
1
0.8
0.7
0.8
0.6
0.6
0.5
0.4
0.4
0.3
0.2
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
time
26
1
2
3
4
5
6
7
8
9
10
11
12
13 14
time
15
16
17
18
19
20
21
22
23
24
25
Table 1: Descriptive Statistics
Variable
Duration
Inflation
M2/GDP
(Reserves/M2)
GDP per capita*
Relative Size
Trade Openness
SpillER
SpillK
Advanced
EM
Asia
Mean
All Spells
Std. Dev.
Min
Duration
27
Inflation
M2/GDP
(Reserves/M2)
GDP percapita*
Relative Size
Trade Openness
SpillER
SpillFA
Advanced
EM
Asia
To Hard-Peg ERR and Closed FA.
Mean
Std. Dev.
Min
Max
To Intermediate ERR and Open FA
Mean
Std. Dev.
Min
Max
9
8
1
34
4
4
1
18
11
8
1
32
0.116
0.390
0.360
0.395
0.021
0.700
0.437
0.675
0.148
0.290
0.252
0.124
0.290
0.455
0.560
0.065
0.432
0.077
0.144
0.357
0.455
0.435
-0.030
0.062
0.005
0.010
0.000
0.022
0.188
0.503
0.000
0.000
0.000
0.705
1.692
5.049
2.496
0.521
2.176
0.535
0.886
1.000
1.000
1.000
0.111
0.240
0.283
0.243
0.029
0.562
0.349
0.828
0.133
0.233
0.233
0.148
0.175
0.280
0.410
0.094
0.422
0.094
0.074
0.346
0.430
0.430
-0.030
0.067
0.005
0.011
0.000
0.074
0.188
0.560
0.000
0.000
0.000
0.705
0.849
1.129
1.735
0.486
1.810
0.477
0.886
1.000
1.000
1.000
0.117
0.481
0.468
0.768
0.016
0.801
0.458
0.663
0.300
0.225
0.125
0.125
0.349
0.793
0.757
0.033
0.394
0.042
0.095
0.464
0.423
0.335
0.013
0.062
0.048
0.018
0.000
0.219
0.361
0.530
0.000
0.000
0.000
0.638
1.692
5.049
2.496
0.152
1.928
0.535
0.853
1.000
1.000
1.000
Number of Spells
Variable
Max
155
30
To Flexible ERR and Closed FA
Mean
Std. Dev.
Min
Max
Mean
40
Censored
Std. Dev.
Min
Max
9
6
1
22
10
9
1
34
0.140
0.374
0.260
0.444
0.037
0.523
0.408
0.754
0.189
0.405
0.351
0.124
0.262
0.227
0.537
0.091
0.360
0.048
0.111
0.397
0.498
0.484
0.003
0.082
0.024
0.018
0.000
0.079
0.350
0.560
0.000
0.000
0.000
0.583
1.242
1.004
2.084
0.521
1.818
0.494
0.886
1.000
1.000
1.000
0.101
0.421
0.395
0.140
0.009
0.837
0.498
0.529
0.000
0.292
0.292
0.107
0.284
0.217
0.158
0.026
0.456
0.029
0.074
0.000
0.459
0.459
0.000
0.119
0.006
0.010
0.000
0.022
0.359
0.503
0.000
0.000
0.000
0.476
1.500
1.143
0.809
0.172
2.176
0.509
0.883
0.000
1.000
1.000
Number of Spells
Notes: † In thousands of 2000 $US
37
48
6.3
Results
An outstanding result is the similarity of the estimated coefficients across models with timedependent transition intensities; Gompertz, Weibull and Log-logistic.42 In these models the
empirical hazard, transition intensities and survival functions indeed depend on the elapsed
duration. An important difference between the proportional hazard models (i.e. Weibull and
Gompertz) and the Log-logistic model has to do with the behavior of the hazard function.
While the Weibull and Gompertz models exhibit monotonically increasing hazards (positive
duration) the estimated Log-logistic hazard exhibits an inverted U-shape. That is, with the
Log-logistic the chances of exiting the regime increase over the first years of the spell and then
decreases monotonically. With the Gompertz and Weibull baseline functions the probability of
moving to a new regime, given survival until time t, increases with the elapsed duration. Given
the robustness of our analysis to the baseline functions we just comment the results obtained
using the Log-logistic parameterization. For the other three models, Weibull, Gompertz and
Exponential, the estimations are presented in the Appendix, tables A-6 to A-8.
A second major result has to do with the role played by unobservable factors in the transition intensities and therefore in the survival function. In general, the results are not severely
affected by unobservable characteristics. The major impact is reflected on the magnitude of
the coefficients. Additionally, there is a small change in the significance of the estimates when
heterogeneity is controlled for in the multiple destinations model.
Log-Logistic Model
In the first three columns of table 2 we present the estimated coefficients for the single
destination model assuming no heterogeneity, gamma heterogeneity and semiparametric heterogeneity, respectively. The estimated coefficients allowing for multiple destinations, but not
controlling for unobservable factors, are shown in the next three columns (model [4]). The results controlling for heterogeneity (model [5]) are presented in columns 7-9. Finally, in the last
four columns we show the estimated coefficients using the ’hybrid’ multiple destinations model
(model [6]) and a restricted model in which the coefficients for every explanatory variables are
equalized across destinations (model [7]).43
42
The divergence exhibited by the Exponential model may be due to the implausible time-independent assumption imposed over the transition intensities and therefore in the hazard function.
43
The ’hybrid’ model uses a log-logistic transition intensity for the HPC destination and Weibull transitions
for the other two destinations, IO and FC. Let βj,k be the parameter associated with covariate j in destination
k. The restricted model sets βj,k = βj,l for j 6= l where l, j = {HP C, IO, F C}.
28
In this paper we argue that the marginal effects of the factors determining the duration of
the IC policy mix vary across destination states. Comparing the results of the single destination
models [1]-[3] and the competing risk versions [4]-[6] we verify that this is true. For example,
the single destination model indicates that the probability of moving to any other regime, given
survival until period t, increases with inflation. Now if we compare this result with the multiple
destinations model we observe that inflation indeed increases the probability of moving to a new
regime but increases more the likelihood of departing for those countries eventually moving to
a more open FA (i.e. a transition to an IO regime). A similar argument can be formulated for
all the variables included in the estimation.
A more formal way to prove that both models are different is through a likelihood ratio
test. The last line of the table shows the results of this test. Controlling or not for unobserved
characteristics we reject the null hypothesis that both models are equivalent. The rejection of
the null hypothesis provides support to the multiple destinations model and indicates that the
marginal effects of the exogenous variables on the duration indeed vary across destinations.
To answer the question of whether the probability of moving to a new regime exhibits a
U-shape we test if the α coefficients are greater than one.44 In all the cases this scale parameter
is greater than 2 and statistically greater than one at conventional levels. In particular for model
[5], multiple destinations with heterogeneity, the scale parameters are equal to 3.156, 2.862 and
2.709 for the HPC, IO and FC policy destinations, respectively. These numbers imply that the
estimated transition intensities and the hazard function exhibit an inverted U-shape. This can
be verified in figure 6.45 The hazard (survival) function, which is the sum of the three transition
intensities, increases (decreases rapidly) during the first years of the regime and then starts to
decrease (decreases at a slower pace).
Comparing the duration dependence obtained through the single and multiple destination
models we find that the former overestimates (underestimates) the probability of survival (hazard), figure 7. The bias may be so large that the probability of survival calculated with the single
destination model is two times greater than the probability calculated with the competing risks
model. So, policy analysis is severely affected when a single destination model is used.
Now we answer the question of what are the effects of the covariates in the overall and
destination-specific survival functions, S(t) and S k (t). Recall that S k (t) is the probability of
44
In the Gompertz (Weibull) model we test whether the γ (α) parameter is different from zero (one) or not.
If this parameter is different from zero (one) that would mean that the hazard function depends on the elapsed
duration.
45
To obtain the transition intensity k (k = {HP C, IO, F C}) we only use the observations from countries
that moved to destination k. The transition is just the average transition intensity per period of time among the
countries moving to destination k.
29
survival to t conditional on the event that when departure occurs is to state k. Figure 8 shows
S(t) and S k (t) for different values of the covariates. The four different lines represent 0, 0.4, 0.8
or 1 standard deviation from the original value for each exogenous variable.
Five variables are statistically different from zero at standard confidence levels in at least
two transition intensities: the development of the financial system (M 2/GDP ), GDP per capita,
relative size (Size), fraction of countries with a closed FA (SpillFA) and the interaction between
SpillER and the emerging market dummy variable. The results show a positive association
between the duration of the IC mix and the development of the financial system. Thus, economies
with underdeveloped financial systems have lower (higher) survival rates (hazards) relative to
the countries with developed financial system. Now, analyzing the probability of survival across
destinations we find that there are noticeable differences. The estimated coefficient associated
with our measure of financial development suggest that in the first 15 years of the spell the effect
on the probability of survival, S(t), is mainly driven by an important increase (decrease) in the
transition intensity (probability of survival) of the HPC destination. Specifically, countries that
eventually adopt an HPC arrangement and have an underdeveloped financial system exhibit a
lower (higher) survival rate (transition intensity) relative to the countries departing to the other
two destinations. Additionally, the behavior of the survival functions associated with the IO
and FC regimes suggest that countries with developed financial systems take a long time to
liberalize the FA or allow the ER float.
As expected, among the countries that eventually open its FA (i.e. IO regime) the ones with
higher GDP per capita exhibit a higher risk of abandoning the IC policy mix.46 . This suggests
that the development of general legal systems and institutions, proxied by GDP per capita, is
crucial for a country to open its financial markets. Conversely, for the subgroup of countries
exiting toward an HPC or FC regimes the ones with a better development of legal systems
and institutions present lower chances of abandoning the current regime. So, economies with a
strong preference toward intermediate regimes must develop a strong institutional framework in
order to maintain the regime.
Larger economies, relative to the U.S., are associated with a lower probability of survival
of the IC mix (first row of figure 9(a)). Again, the picture looks different when one makes the
analysis for each S k (t). Interestingly, if there is any change in the policy it is more plausible
to observe it within the subgroup of countries that eventually shift to a hard peg or a floating
regime. This result supports the ’bipolar view’ for the the industrialized countries.
The feasibility of capital controls is also an important determinant of the duration. In
46
For these countries the probability of survival is lower than 0.5 in the first five years of the spell.
30
particular, when the general acceptance of capital controls is high (i.e. high SpillFA) we observe
significantly shorter spells. At first glance, this result looks counterintuitive, but it is not. The
reason is that countries eventually moving to HPC or FC (i.e. limit capital mobility) exhibit a
higher (lower) exposure (survival rates). So, if there is any change in the policy mixture there
is a high chance of observing a move to one of the corners of the currency spectrum without
lifting capital controls. In other words, the more accepted the capital controls are, the longer
will be the period in which capital controls are implemented (rapid transition to regimes that
limit capital mobility, HPC and FC, relative to the countries that liberalize the FA moving to
an IO regime).47
Surprisingly, the general acceptance of the intermediate regimes (SpillER) does not play an
important role in the survival of the IC policy mixture. This can be verified in the plots of the
marginal effects (SpillER’s row, first column of figure 9(a)).48 Although the overall survival rate
do not change with SpillER the transition intensities and the destination-specific survivals do
change. This is the kind of asymmetries hidden in the single destination model and that makes
the competing risks model a better choice to analyze the duration of the ERR and capital
controls. As expected, when the general acceptance of soft pegs is high the countries with lower
survival rates are the ones that keep a soft peg but eventually choose to open their FA. Note
that even when the policymakers decided to abandon the IC mix, they did so by implementing
a policy combination that includes a soft peg (i.e. they shift to a IO policy mix). This result is
reinforced by the negative relationship between SpillER and the transition intensities associated
with the HPC and FC destinations. Thus, the higher SpillER is, the lower is the chance of
moving to a hard peg or a more flexible ER arrangement.
In line with OCA theory, among the economies moving to an HPC policy mix the ones with a
high level of trade openness exhibit lower survival rates. Also note that only the trade openness
coefficient for the HPC transition intensity is statistically significant. Inflation decreases the
probability of survival. From model [5] inflation has it biggest impact on the IO transition
intensity and is significant only for this destination. Results regarding inflation are slightly
different in the ’hybrid’ model [6].
Is it true that emerging markets are different to the rest of the world when we talk about the
duration of the IC arrangement? The answer is yes. We can clearly see this through the coefficients associated with the interaction of the emerging market dummy variable with some other
47
If we add up the transitions associated with the HPC and FC regimes we can obtain the hazard of keeping a
closed FA but abandoning the soft peg.
48
Since the transition intensities exhibit different signs, the effects of these on the hazard offset each other.
Recall that the hazard function is equal to the sum of the transition intensities.
31
variables. Three are the main findings. First, while these economies are closely integrated to the
international capital markets they love the intermediate arrangements, interaction with SpillER.
This interaction shows that emerging economies are very sensitive to the general acceptance of
soft pegs. In fact, this destination is the most sensitive to the interaction (50.376 vs 25.473 or
-3.3). Second, supporting the ’fear of floating’ argument, emerging economies prefer to remove
capital controls or implement a hard peg rather than moving to a floating regime (interaction
with SpillFA). This result is in part due to the relatively high importance of this interaction on
the IO transition intensity. Third, emerging markets with a high level of international reserves
have longer spells, interaction with Reserves/M 2. This interaction is statistically significant at
the 1 per cent level just for the IO transition intensity and greater than the estimates for the
other two destinations. Hence, when emerging markets start to build up their stock of foreign
reserves the chances of moving to a new regime increase significantly for the countries eventually
lifting capital controls but keeping a soft peg (i.e. transition toward IO). The last two results
are encouraging since they are consistent with the ’fear of floating’ though initiated by Calvo
and Reinhart (2002).
7
Policy Implications
A good example reflecting the complex interaction between the ERR and the openness of the
FA is the current debate on China’s appropriate reforms. As Eichengreen (2005) emphasizes the
ultimate question for China is ”not whether it will move to a more flexible currency but when,
and how it will get from here to there.” A more flexible regime would permit China to tailor
monetary policy to buffer the economy against shocks. At the same time, liberalizing the FA
would pose significant risks for the Chinese economy given the weakness of its financial system.
For example, the removal of capital restrictions may cause an outflow of deposits from Chinese
banks, destabilizing the financial system. Also, in a poor regulated environment capital inflows
could be misallocated and currency mismatches on the balance sheets of financial and corporate
sectors might surge. Under this situation China decided in July 2005, as was suggested by some
scholars (e.g. Eichengreen, 2005 and Prasad, Rumbaug, and Wang 2005), to move toward a
more flexible regime.49 Despite the transition to a more flexible regime, China is still classified
49
There are still some doubts about the current Chinese ERR. The greater flexibility of the ER could smooth
the FA liberalization process by preparing the domestic markets to deal with the effects of higher capital flows.
A more flexible ERR creates stronger incentives for developing the foreign exchange market and for currency risk
management. Additionally a more flexible rate avoids one-way bets and thereby prevents speculators from all
lining up on one side of the market creating losses in the event that expectations of revaluation or devaluation
are disappointed.
32
as a country implementing an IC policy mix.50 The question that arises now is what follows
next for China?
Eichengreen (2005) and Prasad, Rumbaug, and Wang (2005) suggest an improvement in the
regulation of financial institutions (i.e. better institutions) and a further development of the
financial system in order to move forward in the process to liberalize the FA. That is exactly
what the multiple destinations model implies. On one hand, our findings indicate that countries
implementing an intermediate ERR with limits on capital mobility need to improve the quality
of the institutional framework in order to move further in the liberalization of the FA. On the
other hand, the results indicate that countries with underdeveloped financial markets find it
harder to both maintain a soft peg and remove capital controls.
In recent years the world economy has been expanding, on average, at a rate slightly higher
than 4.0% per year. That is because emerging countries like China, India, Russia, and Brazil have
been growing at extraordinary rates. As a result, the ratio of the aggregate GDP of advanced
economies relative to the world economy has decreased during the same period. In 2008, for
example, China overtook Germany as the world’s third-largest economy (see figure 9). Similarly,
Russia’s economy overtook Spain and Canada last year, while Brazil also overtook Canada. This
tendency will eventually affect the optimal ER and FA policies of these countries. As China’s
economy catches up, first Japan and then the U.S., the importance of the exporting sector in
the overall economy might decrease and this in turn can make a flexible ERR a more attractive
alternative. Another possibility that we could foreseen is the adoption of a common currency
(a hard peg) in that region. The reason is that the degree of economic integration among
the Asian economies rises the benefits from a currency union. Our results support these two
potential trends. Specifically, the estimates show that large economies, currently implementing
a soft peg and limits on capital mobility, are at higher risk of moving to the ends of the currency
spectrum rather than moving to a more open FA.
Along with the growing importance of some emerging markets in the global economy is
the significant accumulation of international reserves. Countries such as China, Russia and
Brazil have increased lately their stock of foreign reserves (see figure 10). One of the most
common arguments to explain this behavior is that countries distrust the IMF so they have
been accumulating reserves for rainy days. At the end of 2007 China’s international reserves
were $1.5 trillion dollars or 29 per cent of China’s M2 stock. In the same year Russia, Brazil,
Korea and India also built up an important amount of foreign reserves. Beyond this amassment
process these four emerging economies have another thing in common; they have limits to capital
50
Reinhart and Rogoff classification indicates that China has been de facto pegging since 1992.
33
mobility. In addition, three of these four economies have implemented a soft peg during this
process.51 Our findings are consistent with this preference toward intermediate regimes from
emerging countries (interaction of the emerging market dummy variable and the foreign reserves),
however, our model predicts that these accumulation process will eventually put pressure to
liberalize the FA. In other words, among the emerging countries that eventually moved from an
IC regime to an IO (intermediate ERR and open FA) policy mix the countries with highest stock
of foreign reserves were at higher risk (i.e. exhibited a higher transition intensity and therefore
a lower probability).
Finally, it is not a secret that the development strategy followed by China, and some of its
neighbors, has relied on heavily in the ER. In fact, it is argued that Pacific Asian countries
are formally or informally managing their currencies with respect to the U.S. dollar in similar
fashion as they did during the Bretton Woods system. Dooley, Folkerts-Landau, and Garber
(2003) described this regional policy as a Bretton Woods system II. This behavior is in line with
our specific emerging market finding regarding the feasibility of intermediate regimes. Since the
regional acceptance of intermediate regime is high, it will take a longer period of time to observe
the Chinese economy moving toward a more flexible ER relative to the time it would take if the
acceptance of soft pegs was low. This reinforces the argument that China’s next step should be
the removal of capital controls in the medium run (after improving the quality of institutions
and developing further the financial system).52
51
52
With the exception of Brazil, country that has been implementing a de facto managed float.
This does not necessarily mean a full liberalization of the FA.
34
Figure 6: Estimated Hazard, Survival and Transition Intensities: Multiple Destinations Model
0.25
Figure 7: Single Destination versus Multiple Destinations: Hazard and
Survival Functions
0.25
Hazard
Transition Intensity: Hard Peg-Closed
Transition Intensity: Intermediate-Open
Transition Intensity: Float-Closed
0.2
Hazard One Destination
Hazard Multiple Destination
0.2
0.15
0.15
0.1
0.1
0.05
0.05
35
0
0
5
10
15
20
25
30
35
40
1
Survival
Survival: Hard Peg-Closed
Survival: Intermediate-Open
Survival: Float-Closed
0.8
0
1
5
10
15
20
25
30
35
40
Survival One Destination
Survival Multiple Destination
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
0
5
10
15
20
Years
25
30
35
40
0
5
10
15
20
Years
25
30
35
40
Figure 8: Marginal Effects on the Survival
Survival Function
Hard Peg-Closed
1
Floating-Closed
Intermediate-Open
1
1
1
Inflation
0.8
0.5
0.5
0.6
0.5
0.4
0.2
0
0
10
20
30
40
M2/GDP
1
0
0
10
20
30
0
40
0
1
10
20
30
40 0 0
1
1
0.5
0.5
10
20
30
40
10
20
30
40
10
20
30
40
20
30
40
0.8
0.6
0.5
0.4
0.2
0
1
Reserves/M2
10
20
30
40
0
0
0
10
20
30
40
0
1
1
0.8
0.8
0.8
0.6
0.6
0.6
0.4
0.4
0.4
0.2
0.2
0.2
0
0
1
0
10
20
30
40
1
10
20
30
40
0
10
20
30
0.5
10
20
30
0
10
20
Years
30
1
0.5
0.5
40
Original
0
40
0
1
0
10
20
30
40
0
1
0.5
0
40
1
0
0
10
20
30
40
0
10
20
Years
30
Plus 0.4 SD
40
0
1
10
0.5
0
0
0
0
30
0.5
0
40
20
0.5
0
1
0
0
10
0
0
0.5
0.5
1
GDP per capita
36
(Reserves/M2)*EM
0
0
10
20
Years
30
40
0
Plus 0.8 SD
(a) Inflation, M2/GDP, (Reserves/M2)*EM, Reserves/M2 and GDP per capita
Plus 1 SD
10
20
Years
30
40
Figure 8: Marginal Effects on the Survival (con’t)
Hard Peg-Closed
Size
Survival Function
1
1
0.5
0.5
0.5
0.5
Trade Openness
0
10
20
30
0
40
0
0
0
10
20
30
40
0
10
20
30
10
20
30
40
0
1
10
20
30
40
0
10
20
30
40
0
10
20
30
40
0
10
20
30
40
1
1
1
0.5
0.5
0.5
0.5
0
0
10
20
30
40
0
0
10
20
30
40
0
1
1
1
0.5
0.5
0.5
0
10
20
30
0
40
1
1
0.5
0.5
0
10
20
30
40
10
20
30
40
20
30
40
0
10
20
30
40
1
0
0.5
0
0
1
10
20
30
40
1
0.5
0.5
0
0
1
10
0
0
0
0
0
0
1
10
20
30
40
1
0.8
SPillK
37
0
40
1
0
SpillER
Floating-Closed
1
0
SpillER*EM
Intermediate-Open
1
0.6
0.5
0.5
0.4
0.5
0.2
0
0
0
0
10
20
30
40
Years
0
10
20
Years
Original
Plus 0.4 SD
30
40
0
10
20
30
40
0
Years
Plus 0.8 SD
(a) Size, Trade Openness, SpillER, SpillER*EM and SpillK
Note: These plots are obtained by increasing the original data by 0.4, 0.8 and 1 standard deviation.
Years
Plus 1 SD
Table 2: Single and Multiple Destination Models: Log-logistic Baseline
α
Inflation
M2/GDP
Reserves/M2
(Reserves/M2)*EM
GDP per capita
Size
38
Trade Openness
SpillER
SpillER*EM
SpillFA
SpillFA*EM
Advanced
EM
Asia
Constant
One Destination
Multiple Destinations
Multiple Destinations
Heterogeneity
No Heterogeneity
Semiparametric Heterogeneity
No
Gamma
Semi
HPC
[1]
[2]
[3]
[4]
Destinations
IO
FC
[4]
[4]
HPC
[5]
Destinations
IO
FC
[5]
[5]
2.337 ∗
2.337 ∗
2.491 ∗
2.396 ∗
2.229 ∗
2.432 ∗
3.156 ∗
2.862 ∗
2.709 ∗
(0.178)
(0.191)
(0.195)
(0.363)
(0.285)
(0.308)
(0.393)
(0.318)
(0.316)
2.225 ∗∗∗ 2.225
2.709 ∗∗∗
0.927
4.092 ∗∗∗ 2.707
2.022
5.617 ∗
1.577
(1.160)
(3.721)
(1.448)
(2.023)
(2.108)
(2.119)
(2.244)
(2.223)
(2.676)
-3.082 ∗
-3.082 ∗
-3.096 ∗
-9.402 ∗
-2.471 ∗
-3.630 ∗
-8.010 ∗
-3.410 ∗
-5.160 ∗
(0.769)
(0.600)
(1.381)
(3.238)
(0.969)
(1.483)
(3.336)
(1.122)
(1.651)
-0.131
-0.131
0.021
-0.683
-0.193
-0.244
-0.731
-0.382
0.466
(0.331)
(0.435)
(0.468)
(1.209)
(0.327)
(0.719)
(0.961)
(0.399)
(0.869)
3.422 ∗∗ 3.421 ∗∗∗ 2.968 ∗∗∗
-0.928
7.059 ∗
-0.515
-0.125
7.484 ∗
1.528
(1.612)
(1.888)
(1.794)
(5.106)
(2.288)
(3.327)
(5.608)
(2.444)
(4.257)
0.425
0.425
0.722
-8.540 ∗
1.122 ∗∗∗ -0.825
-5.854 ∗∗ 1.287 ∗∗ -1.740
(0.516)
(0.475)
(0.591)
(3.399)
(0.597)
(0.986)
(2.583)
(0.644)
(1.375)
7.873 ∗
7.873 ∗
7.581 ∗
24.089 ∗
5.483
11.836 ∗
17.719 ∗
4.902
16.247 ∗
(2.770)
(2.740)
(2.932)
(7.389)
(5.114)
(4.492)
(6.665)
(5.165)
(4.943)
0.916 ∗∗ 0.916
1.065
2.879 ∗
1.059 ∗∗∗ 0.448
2.122 ∗∗ 1.185
0.732
(0.433)
(0.639)
(0.577)
(0.999)
(0.639)
(0.777)
(1.030)
(0.795)
(1.006)
-3.368
-3.366
-4.264
0.329
19.686
-1.051
-4.856
16.445
-2.548
(4.672)
(2.251)
(5.038)
(6.943) (12.843)
(8.652)
(7.214) (12.380) (11.396)
2.003
1.997
3.218
-7.410
34.376
16.487
-3.300
50.376 ∗∗ 25.473 ∗∗
(7.081)
(2.388)
(7.914)
(11.246) (21.281)
(16.401) (11.388) (21.560) (11.636)
10.344 ∗ 10.346 ∗ 13.203 ∗
22.754 ∗
6.813
14.239 ∗
27.239 ∗
7.128
17.891 ∗
(2.471)
(1.788)
(2.647)
(6.008)
(5.487)
(5.033)
(5.948)
(5.372)
(5.636)
-1.016
-1.021
-0.641
7.439
19.558 ∗∗
-5.257
8.501
29.684 ∗
-8.061
(4.008)
(3.006)
(4.571)
(22.734)
(8.852)
(8.458) (20.402)
(8.929)
(6.420)
-1.956 ∗
-1.956 ∗∗∗ -2.273 ∗
7.691 ∗∗ -1.178
-0.378
3.944
-1.699
1.160
(0.833)
(1.023)
(0.968)
(3.516)
(1.091)
(1.453)
(2.942)
(1.165)
(1.728)
-1.184
-1.178
-1.759
-4.388
-31.226 ∗∗
-2.521
-7.785
-45.616 ∗
-3.824
(5.618)
(2.016)
(6.233)
(21.649) (15.140)
(12.825) (19.396) (15.181)
(8.774)
-0.690
-0.690
-0.764
-0.353
-0.961
-0.398
-0.682
-1.325
-0.615
(0.429)
(0.568)
(0.505)
(0.869)
(0.673)
(0.616)
(1.090)
(0.931)
(0.741)
-10.204 ∗ -10.207 ∗ -13.818 ∗
-21.576 ∗ -20.084 ∗
-15.739 ∗ -24.798 ∗ -20.792 ∗ -19.002 ∗∗
(3.641)
(1.953)
(3.837)
(6.968)
(9.141)
(6.791)
(6.930)
(8.838)
(8.267)
σg2
0.000
Total Number of Spells
158
t(α)†
7.513
158
6.998
158
7.641
3.841
158‡
4.309
4.656
Likelihood Ratio: 126.04
5.486
158‡
5.861
5.290
Multiple Destinations Hybrid
§
Semiparametric Heterogeneity
HPC
[6]
Destinations
IO
FC
[6]
[6]
Multiple Destinations
No Heterogeneity
Restricted model
[7]
3.203 ∗
2.787 ∗
3.321 ∗
(0.392)
(0.289)
(0.288)
0.877
7.112 ∗
7.647 ∗
(2.099)
(1.839)
(2.034)
-10.439 ∗
-1.532 ∗∗∗ -5.104 ∗
(3.675)
(0.850)
(1.320)
-0.865
0.069
-0.248
(1.168)
(0.221)
(0.838)
6.438
11.645 ∗
-0.927
(5.054)
(2.103)
(2.901)
-6.575 ∗∗ 0.915 ∗∗∗ -3.058 ∗
(2.979)
(0.498)
(0.939)
19.691 ∗
3.174
18.244 ∗
(7.896)
(4.858)
(3.496)
2.615 ∗
0.781
0.630
(1.021)
(0.625)
(0.768)
-3.546
21.224 ∗∗
-9.006
(7.896)
(9.809)
(8.737)
-10.209
29.709 ∗∗∗ 30.285 ∗∗∗
(11.979) (15.562)
(15.577)
28.268 ∗
5.199
13.521 ∗
(6.451)
(4.255)
(4.907)
-1.406
23.109 ∗
-6.109
(18.990)
(6.938)
(8.440)
5.446
0.491
3.152 ∗
(3.472)
(1.057)
(1.263)
1.541
-32.403 ∗
-6.666
(18.416) (11.265)
(12.527)
-0.139
-1.477 ∗
-1.457 ∗
(1.182)
(0.636)
(0.535)
-26.014 ∗ -22.319 ∗
-15.138 ∗∗
(7.636)
(6.863)
(6.664)
1.846 ∗
(0.141)
1.351
(1.166)
-2.350 ∗
(0.697)
-0.084
(0.229)
1.785
(1.631)
0.347
(0.437)
5.792 ∗
(2.111)
0.735 ∗∗
(0.366)
-1.975
(4.111)
2.296
(6.158)
8.328 ∗
(2.141)
-0.525
(3.654)
-1.450 ∗∗
(0.724)
-1.231
(4.935)
-0.452
(0.351)
-9.921 ∗
(3.081)
158‡
6.184
158‡
6.008
5.618
5.290
Likelihood Ratio: 114.04
Notes: *, **, *** denote coefficients statistically different from zero at 1%, 5% and 10% significance levels, respectively. In models [4] and [5] ”HPC” stands for hard peg ERR and
closed FA, ”IO” for intermediate ERR and open FA, and ”FC” stands for floating ERR and closed FA.
† The t-statistic testing if the alpha is different from one.
‡ The number of spells in for destinations HPC, IO and FC are 30, 40, and 38 spells, respectively. We also have 50 right-censored spells
The likelihood ratio test whether the multiple destination model is equivalent to the single destination model (restricted). Let βj,k be the parameter associated with covariate j in
destination k. The restricted model sets βj,k = βj,l for j 6= l where l, j = {HP C, IO, F C}.
§ The ’hybrid’ model uses a Log-logistic transition intensity for the HPC destination and Weibull transitions for the other two destinations.
8
Conclusions
For many years a vast majority of countries, both advanced and developing, used a combination
of soft pegs and limits on capital mobility as their de facto policy arrangement. In terms of
the sequencing of the two policies we have observed, during the post-Bretton Woods system,
a strong preference by policymakers to deal first with higher ER flexibility and then with a
more open FA. We argue that the importance of this mixture of policies in the evolution of
the international monetary system and our need to know more about its sequencing make the
analysis of the duration of a policy mix comprised by an intermediate ERR and a closed FA a
necessity in this area of research.
In this paper, we analyze the duration of that policy mix. Specifically, we try to answer the
question of what factors determine the timing of moving to a new regime (i.e. the duration of the
arrangement). We argue that in order to correctly answer this question we must acknowledge
the presence of multiple destinations (i.e. regimes), a dimension that has been completely
disregarded in the literature. With the recognition of multiple destinations another question
arises; how the determinants of the duration vary across the potential destinations.
To answer these two questions a simple competing-risks model, augmented to incorporate
unobserved heterogeneity, is proposed. In particular, we analyze the duration of 155 spells
in advanced, emerging and developing countries from 1965 to 2007. The evidence favors the
multiple destination model over the single destination version. Specifically, we find that the the
latter masks interesting factors affecting the duration of the policy mix and overestimates the
probability of survival. Regarding the probability of moving to a new policy the results show
that it depends on the elapsed duration.
The development of the financial system, GDP per capita, relative size, the general acceptance of capital controls, the feasibility of the intermediate ERR, and an emerging market
dummy variable are the exogenous variables with the highest explanatory power. The results
show that large economies with underdeveloped financial systems exhibit lower survival rates.
Based on our data set, emerging markets behave differently in many aspects. First, when we
interact the emerging market binary variable and the general acceptance toward soft pegs we
found that these type of countries are more sensitive to the general acceptance of the soft pegs.
Second, emerging economies accumulate foreign reserves in order to maintain an intermediate
ERR for a longer period of time (interaction with Reserves/M2). Third, emerging markets prefer
to open the FA rather than moving toward floating regime (interaction with SpillFA).
Surprisingly, the unobserved heterogeneity does not affect neither the direction of the effects
39
Figure 9: Evolution the Shares of Domestic GDP relative to the World GDP
A. Advanced Countries 35
30
25
20
15
10
5
US
U.S.
Germany
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
0
Japan
B. Advanced and Emerging Markets
9
8
7
6
5
4
China
3
2
1
Germany
Canada
Spain
Brazil
China
2007
2006
2005
2004
2003
2002
2001
2000
1999
1998
1997
1996
1995
1994
1993
1992
1991
1990
0
Russia
of the covariates on the survival, hazard and transition intensities nor their statistical significance. The main role played by unobservable factors is with respect to the magnitued of the
estimated coefficients. The results are robust to the econometric specification of the baseline
functions.
Some future work is needed to analyze the duration of the HPC and FC polixy mixtures.
For these alternatives an assumption about the transition from one policy mix to the others is
needed in order to overcome the presence of left censored spells. Since in this paper we could
not directly disentangle the effects of each covariate in the duration of the ERR or the duration
capital controls future work is needed on this. Razo-Garcia (2008b) analyzes the duration of
the hard pegs, intermediate and floating regimes controlling for the potential endogeneity of the
openness of the FA.
40
Figure 10: International Reserves Accumulation
Panel A: International Reserves in U.S. Dollars
1600000
1400000
Brazil
China
India
Japan
Korea
Russia
1200000
1000000
1200000
800000
1000000
800000
600000
600000
400000
400000
200000
200000
0
0
1990
1992
1994
1996
1998
2000
2002
2004
2006
Panel B: Ratio International Reserves relative to M2
90
80
Brazil
China
India
Japan
Korea
Russia
70
60
50
40
30
20
10
0
1990
1992
1994
1996
1998
2000
2002
2004
2006
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44
A
A.1.
Data
Country Definition
See section 2 for details on the definition of Advanced, Emerging and ”Other” Countries groups.
Table A-3: Countries in the Sample
Advanced Countries
Australia
Austria
Belgium
Canada
Denmark
Finland
Emerging Markets
Argentina
Brazil
Bulgaria
Chile
China
Colombia
Czech Republic
Ecuador
Egypt, Arab Rep.
Other Countries
Albania
Algeria
American Samoa
Andorra
Angola
Anguilla
Antigua & Barbuda
Armenia
Aruba
Azerbaijan
Bahamas, The
Bahrain
Bangladesh
Barbados
Belarus
Belize
Benin
Bermuda
Bhutan
Bolivia
Bosnia & Herzegovina
Botswana
Brunei
Burkina Faso
Burundi
Cambodia
Cameroon
Cape Verde
A.2.
France
Germany
Greece
Iceland
Ireland
Italy
Japan
Luxembourg
Netherlands
New Zealand
Norway
Portugal
San Marino
Spain
Sweden
Switzerland
United Kingdom
United States
Hong Kong
Hungary
India
Indonesia
Israel
Jordan
Korea, Rep.
Malaysia
Mexico
Morocco
Nigeria
Pakistan
Panama
Peru
Philippines
Poland
Russian Federation
Singapore
South Africa
Sri Lanka
Thailand
Turkey
Ukraine
Venezuela
Central African Rep.
Chad
Comoros
Congo, Dem. Rep.
Congo, Rep.
Costa Rica
Cote d’Ivoire
Croatia
Cyprus
Djibouti
Dominica
Dominican Rep.
El Salvador
Equatorial Guinea
Eritrea
Estonia
Ethiopia
Fiji
Gabon
Gambia, The
Georgia
Ghana
Grenada
Guatemala
Guinea
Guinea-Bissau
Guyana
Haiti
Honduras
Iran, Islamic Rep.
Iraq
Jamaica
Kazakstan
Kenya
Kiribati
Korea, Dem. Rep.
Kuwait
Kyrgyz Republic
Lao PDR
Latvia
Lebanon
Lesotho
Liberia
Libya
Lithuania
Macedonia, FYR
Madagascar
Malawi
Maldives
Mali
Malta
Marshall Islands
Mauritania
Mauritius
Mayotte
Micronesia
Moldova
Monaco
Mongolia
Montenegro (Serbia)
Mozambique
Myanmar
Namibia
Nepal
Netherlands Antilles
New Caledonia
Nicaragua
Niger
Oman
Palau
Papua New Guinea
Paraguay
Puerto Rico
Qatar
Romania
Rwanda
Samoa
Sao Tome & Principe
Saudi Arabia
Senegal
Serbia
Seychelles
Sierra Leone
Slovak Republic
Spells
In table A-4 we report the spells used in the estimation of the models.
45
Slovenia
Solomon Islands
Somalia
St. Kitts
St. Lucia
St. Vincent
Sudan
Suriname
Swaziland
Syrian Arab Republic
Tajikistan
Tanzania
Togo
Tonga
Trinidad and Tobago
Tunisia
Turkmenistan
Uganda
United Arab Emirates
Uruguay
Uzbekistan
Vanatu
Vietnam
Yugoslavia,
Zambia
Zimbabwe
Table A-4: Closed Financial Account and Intermediate Exchange Rate Policy Mix Spells
Hard Peg-Closed
Country
46
Benin
Burkina Faso
Burundi
Cameroon
Central African Rep.
Chad
Chile
Congo, Rep.
Cote d’Ivoire
Ecuador
Finland
France
France
Gabon
Indonesia
Jamaica
Japan
Korea, Rep.
Mali
Mauritania
Nepal
Niger
Philippines
Senegal
Sri Lanka
Suriname
Swaziland
Swaziland
Togo
Turkey
Intermediate-Open
Start Year Duration
1973
1973
1969
1973
1973
1973
1979
1973
1973
1970
1967
1968
1970
1973
1970
1989
1971
1973
1973
1972
1992
1973
1965
1973
1989
2000
1982
1994
1973
1970
2
2
5
2
2
2
4
2
2
6
3
4
1
2
2
7
7
9
2
1
15
2
1
2
18
5
4
9
2
6
Country
Armenia
Austria
Azerbaijan
Botswana
Cambodia
Costa Rica
Croatia
Cyprus
Denmark
Ecuador
Egypt, Arab Rep.
El Salvador
Finland
France
Greece
Hungary
Iceland
Indonesia
Ireland
Israel
Italy
Jamaica
Jordan
Macedonia, FYR
Malta
Mauritius
Mexico
Netherlands
Nicaragua
Paraguay
Portugal
Romania
Singapore
Slovak Republic
Slovenia
Spain
Sudan
Sweden
Uganda
Venezuela
Float-Closed
Start Year Duration
1996
1989
2001
1998
2003
1992
2003
2004
1988
1994
1994
1992
1990
1988
1994
2001
1994
1982
1992
1998
1988
1991
1996
2002
2004
1995
1991
1977
1995
1989
1991
2002
1973
2002
1999
1992
1999
1988
1993
1995
1
18
6
19
2
9
9
32
17
1
23
3
18
17
10
20
11
8
14
14
6
1
8
8
32
20
4
7
3
4
19
2
1
10
8
19
10
16
4
2
Country
Algeria
Algeria
Argentina
Australia
Brazil
Brazil
Chile
China
Colombia
Congo, Dem. Rep.
Dominican Rep.
El Salvador
Greece
Guinea
Haiti
Iceland
Indonesia
Iran, Islamic Rep.
Italy
Japan
Korea, Rep.
Madagascar
Malaysia
Moldova
Myanmar
New Zealand
Paraguay
Philippines
Philippines
Poland
Suriname
Syrian Arab Rep.
Thailand
Turkey
Turkey
United Kingdom
Zimbabwe
Censored
Start Year Duration
1972
1987
1980
1982
1976
1998
1999
1980
1983
1974
1982
1982
1981
1999
1992
1976
1973
1976
1975
1977
1997
1985
1997
1997
1982
1984
1981
1983
1997
1999
1981
1981
1997
1980
2000
1972
1983
8
14
2
8
8
5
12
7
19
3
16
18
16
9
8
12
1
3
3
5
18
4
22
3
9
12
17
14
13
5
8
12
20
9
3
1
3
Country
Albania
Algeria
Angola
Argentina
Azerbaijan
Bangladesh
Belarus
Burundi
Cape Verde
China
Colombia
Ethiopia
Fiji
Ghana
Guinea
Guinea-Bissau
Guyana
Honduras
India
Kazakstan
Lao PDR
Libya
Macedonia, FYR
Malawi
Malaysia
Moldova
Morocco
Mozambique
Myanmar
Nepal
Pakistan
Papua New Guinea
Peru
Philippines
Poland
Russian Federation
Rwanda
Samoa
Sierra Leone
Sri Lanka
Sudan
Tanzania
Thailand
Tonga
Tunisia
Ukraine
Vietnam
Zimbabwe
Start Year Duration
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
1992
1991
2006
2006
2006
1999
1998
2006
2006
2006
2006
2006
2006
1998
2006
2006
2006
1971
2006
1992
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
2006
2001
5
12
2
4
2
17
4
23
8
14
22
17
5
6
5
9
10
22
31
11
12
13
2
3
1
7
34
12
13
12
25
17
1
7
2
8
3
5
1
16
4
13
7
6
33
8
5
1
A.3.
Data Sources
Table A-5: Definition and Source of Variables
Variable
POLITY
XCONST
DURABLE
INFLATION
FINDEV
OPENNESS
GDPCAP
SHARE
GOVSIZE
Source
Polity IV project
Polity IV project
Polity IV project
IFS Line 64
WDI
WDI
WDI
DOT (IMF)
WDI
Definition or Transformation
Political Regime
Executive Constraints
Political Regime Durability
Annual Inflation
Money + Quasi Money (% of GDP)
Exports plus imports over GDP
GDP per capita (constant 2000 US$)
% Total Exports with Main Partner
General Government Final
Consumption Expenditure (% of GDP)
MONEY
FOREIGN LIABILITY
FINLIA
RESERVES
M2
RESM2
BORER
IFS Line 34
IFS Line 16c
RRER
Reinhart and Rogoff
KBrune
Nancy Brune
Chinn-Ito
Chinn and Ito
B
IFS Line 1L
IFS Lines 34 and 35
Bubula and Ötker-Robe
Foreign Liability to Money
Total Reserves - Gold
Money plus Quasi Money
Reserves/M2
De facto Exchange Rate Regime
Classification
De facto ”Natural” Exchange Rate
Regime Classification
Financial Openness Index (excluding
Exchange Rate Regime
Capital restrictions (k3)
Duration Models with Multiple Destinations
In this part we show the derivation of some of the equations presented in section 5. It is straightforward
to derive equation (11) from Weibull transition intensity and equation (2) so we omit the proof to save
space. Equation (12) is derived using the following well known fact
S(t) = exp
n
Z
−
θ(r)dr
0
47
t
o
then plugging the Weibull transition intensity into the previous equation we get
S(t) = exp
n
−
Z tX
K
αk rαk −1 exp{x0k βk }dr
o
0 k=1
= exp
n
− αk
K
X
exp{x0k βk }
Z
n
−
K
X
rαk −1 dr
o
0
k=1
= exp
t
exp{x0k βk }tαk
o
k=1
C
Gaussian-Hermite Numerical Integration
Gauss-Hermite quadrature is often used for numerical integration. In this paper we deal with the unobserved heterogeneity by replacing the continuous integrals included in equations 23 and 24 with a set
of discrete points at which the integrand is evaluated. In particular, we use the Gauss-Hermite formula
based on Hermite polynomials to deal with the integration interval (−∞, ∞). Specifically, our estimation method is based on the semiparametric approach proposed by Butler, Anderson, and Burkhauser
(1989). In spirit, this approach is similar to the non-parametric maximum likelihood method proposed
by Heckman and Singer (1984). The main difference between the two methods is that the latter assume
a discrete distribution for the unobserved heterogeneity, g(ν), while Butler, Anderson, and Burkhauser
(1989) assume that the discrete distribution is a numerical approximation of the true distribution (which
might be continuous). Then unconditional probability of leaving the current regime to destination k in
(t, t + dt) can be approximated in the following way:
Z
∞
Z
P r(t ≤ T < t + dt, Dk |Xi ) =
∞
···
P r(t ≤ T < t + dt, Dk |Xi , ν)g(ν; Xi )dν
(A-28)
)"
(
)
#
(
Z ∞
Z ∞
X ν2
X −ν 2
exp
P r(t ≤ T < t + dt, Dk |Xi , ν)g(ν; Xi ) dν
=
···
exp
2
2
−∞
−∞
"
(
)
#
LK
L1
X
X
X ν2
···
wl1 · · · wlK exp
≈
P r(t ≤ T < t + dt, Dk |Xi , ν)g(ν; Xi )g(ν; Xi )
2
l1 =1
lK =1
"
(
)
#
LK
L1
X
X
X ν2
≈
···
wl1 · · · wlK exp
g(P r(t ≤ T < t + dt, Dk |Xi , ν); Xi ) πli,k
1 ,...,lK
2
−∞
≈
−∞
l1 =1
lK =1
L1
X
LK
X
l1 =1
···
τl1 ,...,lk πli,k
1 ,...,lK
lK =1
2
P ν2
ν12
νK
where πli,k
= P r(t ≤ T < t + dt, Dk |Xi , ν),
2 = 2 + . . . + 2 , g(ν; Xi ) is the prior distribution of
1 ,...,lK
P ν2 the residuals and τl1 ,...,lk = wl1 · · · wlK exp
argument can be applied
2 g(νl1 , . . . , νlK ; Xi ). A similar
P ν2 i,k
to derive equation (24). The approximations rely on the assumption that exp
2 g(νl1 , . . . , νlK ; Xi )πl1 ,...,lK
can be approximated with negligible error by a multivariate Taylor Series of order mK, where m is a
P 2
P ν2 finite integer, in each of its arguments. The normalization exp
is used because the exp − ν2
2
is the basis of Gaussian integration over the range minus to plus infinity. As is clearly stated in Butler,
Anderson, and Burkhauser (1989) the number of integration points is determined by the accuracy of the
P ν2 i,k
approximation of exp
2 g(νl1 , . . . , νlK ; Xi )πl1 ,...,lK . If this is true, the likelihood function can be
approximated with negligible error and the resulting estimates can be treated as maximum likelihood
estimates, with asymptotic variance-covariance equal to the inverse Hessian.
The maximum likelihood is constrained by equation (26). Proving this constraint is straightforward
48
and comes from the fact the joint distribution is a proper density function
Z ∞
Z ∞
···
g(ν; Xi )dν = 1
−∞
−∞
Then, following the same argument as before
Z
∞
Z
∞
···
1=
−∞
g(ν; Xi )dν ≈
−∞
L1
X
···
l1 =1
=
L1
X
"
(
wl1 · · · wlK exp
X ν2
2
lK =1
···
l1 =1
C.1.
LK
X
LK
X
)
#
g(νl1 , . . . , νlK ; Xi )
τl1 ,...,lk
lK =1
Centered Moments of the Heterogeneity Terms
The moments of the heterogeneity random variables are:
E(νk ) =
L1
X
···
l1 =1
V(νk ) =
L1
X
L1
X
l1 =1
ρ(νk , νm ) = p
τl1 ,...,lk × qk,lk
···
LK
X
τl1 ,...,lk × qk,lk − E(νk )
2
(A-30)
lK =1
···
LK
X
τl1 ,...,lk × qk,lk − E(νk ) qm,lm − E(νm )
(A-31)
lK =1
Cov(νk , νm )
(A-32)
V(νk ) × V(νm )
for k, m = 1, . . . , K
C.2.
(A-29)
lK =1
l1 =1
Cov(νk , νm ) =
LK
X
Results Using Different Baseline Functions
49
Table A-6: Single and Multiple Destination Models: Weibull Baseline
One Destination
Heterogeneity
No
Gamma
[1]
[2]
Semi
Multiple Destinations
No Heterogeneity
HPC
Destinations
IO
FC
Multiple Destinations
Semiparametric Heterogeneity
HPC
Destinations
IO
[3]
[4]
[4]
[4]
[5]
[5]
α
1.554 ∗ 2.082 ∗
(0.109) (0.305)
2.876 ∗
(0.165)
1.940 ∗
(0.290)
1.884 ∗
(0.236)
1.996 ∗
(0.237)
3.126 ∗
(0.404)
2.813 ∗
(0.308)
Inflation
0.838
1.746
(0.978) (1.267)
-1.908 ∗ -2.701 ∗
(0.567) (0.842)
-0.047 -0.109
(0.156) (0.258)
0.658
2.644
(1.279) (1.892)
0.249
0.403
(0.376) (0.465)
4.685 ∗ 6.756 ∗
(1.536) (2.683)
0.733 ∗ 0.799 ∗∗
(0.304) (0.420)
-1.520 -2.635
(3.511) (4.470)
2.585
2.212
(5.134) (6.747)
6.750 ∗ 9.351 ∗
(1.794) (2.578)
-0.117 -0.728
(2.905) (3.967)
-0.969 -1.736 ∗∗
(0.621) (0.777)
-1.264 -1.290
(4.074) (5.328)
-0.258 -0.578
(0.299) (0.412)
-7.675 ∗ -9.513 ∗
(2.592) (3.452)
4.162 ∗
(1.305)
-2.872 ∗
(1.100)
0.116
(0.289)
3.089 ∗
(1.469)
-0.178
(0.463)
5.630 ∗
(2.216)
1.313 ∗
(0.538)
-0.893
(4.665)
-4.563
(6.659)
13.895 ∗
(2.915)
-2.149
(3.709)
-0.426
(0.710)
2.404
(5.129)
-0.446
(0.392)
-16.533 ∗
(3.775)
0.571
(1.779)
-8.826 ∗
(2.772)
-0.811
(0.993)
-2.043
(4.451)
-9.697 ∗
(3.223)
24.762 ∗
(6.608)
2.629 ∗
(0.629)
5.525
(4.578)
-9.105
(8.968)
22.673 ∗
(5.743)
5.521
(21.479)
9.146 ∗
(3.101)
-1.700
(20.300)
0.014
(0.636)
-23.042 ∗
(6.017)
M2/GDP
(Reserves/M2)
(Reserves/M2)*EM
GDP per capita
50
Size
Trade Openness
SpillER
(SpillER)*EM
SpillK
(SpillK)*EM
Advanced
EM
Asia
Constant
[5]
3.290 ∗
(0.284)
0.675
6.976 ∗
7.282 ∗
(1.305)
(1.844)
(2.142)
-8.138 ∗
-1.594 ∗∗∗ -4.935 ∗
(2.956)
(0.848)
(1.303)
-0.415
0.056
-0.255
(0.736)
(0.258)
(0.848)
3.574
11.709 ∗
-0.405
(5.327)
(2.165)
(2.841)
-3.999 ∗∗∗
0.947 ∗∗∗ -2.978 ∗
(2.454)
(0.491)
(0.967)
16.024 ∗
3.094
17.435 ∗
(6.430)
(5.140)
(3.505)
2.373 ∗
0.779
0.389
(0.781)
(0.654)
(0.747)
-11.339 ∗∗
21.764 ∗∗
-5.818
(5.449)
(9.890)
(8.791)
-5.311
29.637 ∗∗∗ 28.984 ∗∗
(10.460)
(15.750)
(15.119)
23.845 ∗
6.176
14.009 ∗
(5.965)
(4.839)
(5.169)
5.784
22.548 ∗
-5.611
(16.479)
(7.407)
(8.504)
1.010
0.236
3.217 ∗
(2.780)
(1.225)
(1.337)
-5.610
-32.130 ∗
-6.678
(15.776)
(11.373)
(12.415)
-0.633
-1.476 ∗∗
-1.393 ∗
(1.005)
(0.700)
(0.541)
-20.346 ∗
-23.114 ∗
-16.623 ∗
(6.713)
(6.949)
(6.840)
0.635 ∗∗∗
(0.355)
σg2
Total Number of Spells
t(α)†
3.383 ∗∗∗
2.118
(1.751)
(1.752)
-1.551 ∗∗
-2.371 ∗
(0.760)
(1.205)
-0.044
-0.274
(0.213)
(0.709)
6.547 ∗
-0.307
(1.871)
(2.560)
0.932 ∗∗∗ -0.477
(0.482)
(0.775)
4.174
6.495 ∗
(4.018)
(2.890)
0.808
0.389
(0.511)
(0.665)
14.671
-0.842
(10.457)
(6.759)
32.175 ∗∗∗ 13.544
(18.415)
(12.551)
5.036
12.217 ∗
(4.287)
(4.314)
17.641 ∗
-3.554
(7.515)
(6.683)
-0.766
-0.347
(0.964)
(1.180)
-28.581 ∗∗
-2.618
(13.080)
(9.952)
-0.791
-0.169
(0.565)
(0.507)
-16.310 ∗∗ -14.011 ∗
(7.408)
(5.482)
FC
158
5.083
158
3.546
158
11.337
3.238
158‡
3.740
4.200
5.262
158‡
5.887
5.290
Likelihood Ratio:
140.62
Likelihood Ratio:
147.72
Notes: *, **, *** denote coefficients statistically different from zero at 1%, 5% and 10% significance levels, respectively. In models [4][5] ’HPC’ stands for hard peg ERR and closed FA, ’IO’ for intermediate ERR and open FA, and ’FC’ for floating ERR and closed FA.
† The t-statistic testing if the alpha is different from one.
‡ The number of spells for destinations HPC, IO and FC are 30, 40, and 38, respectively. We also have 50 right-censored spells
The likelihood ratio test whether the multiple destination model is equivalent to the single destination model (restricted). Let βj,k be
the parameter associated with covariate j in destination k. The restricted model sets βj,k = βj,l
for j 6= l where l, j = {HP C, IO, F C}.
Table A-7: Single and Multiple Destination Models: Gompertz Baseline
One Destination
Heterogeneity
No
Gamma
[1]
[2]
Semi
[3]
γ
0.102 ∗ 0.162 ∗
(0.018) (0.043)
Inflation
0.950
1.546
1.320
(1.013) (1.131)
(1.050)
-2.175 ∗ -2.998 ∗
-2.734 ∗
(0.632) (0.925)
(0.722)
-0.057 -0.138
-0.141
(0.187) (0.257)
(0.205)
0.604
1.739
1.819
(1.278) (1.663)
(1.335)
0.295
0.457
0.422
(0.385) (0.490)
(0.412)
4.827 ∗ 6.454 ∗
5.810 ∗
(1.678) (2.443)
(1.856)
0.782 ∗ 0.805 ∗∗
0.677 ∗∗∗
(0.310) (0.406)
(0.376)
-1.703 -3.151
-2.987
(3.613) (4.145)
(3.792)
2.601
3.090
3.047
(5.526) (5.583)
(5.693)
6.887 ∗ 7.899 ∗
7.568 ∗
(1.892) (2.077)
(1.839)
0.235
0.663
0.745
(3.159) (3.154)
(3.575)
-0.928 -1.423 ∗∗∗ -1.463 ∗∗
(0.632) (0.809)
(0.672)
-1.567 -2.504
-2.642
(4.405) (4.242)
(4.700)
-0.147 -0.310
-0.354
(0.300) (0.381)
(0.319)
-7.135 ∗ -7.126 ∗
-7.489 ∗
(2.714) (2.926)
(2.682)
M2/GDP
(Reserves/M2)
(Reserves/M2)*EM
GDP per capita
51
Size
Trade Openness
SpillER
(SpillER)*EM
SpillK
(SpillK)*EM
Advanced
EM
Asia
Constant
σg2
Total Number of Spells
0.147 ∗
(0.019)
Multiple Destinations
No Heterogeneity
HPC
Destinations
IO
FC
Multiple Destinations
Semiparametric Heterogeneity
HPC
Destinations
IO
FC
[4]
[4]
[4]
[5]
[5]
[5]
0.133 ∗
(0.058)
0.120 ∗
(0.026)
0.141 ∗
(0.031)
0.293 ∗
(0.061)
0.282 ∗
(0.032)
0.380 ∗
(0.034)
0.470
(1.740)
-7.077 ∗
(2.623)
-0.592
(0.952)
-2.272
(4.329)
-7.663 ∗
(2.895)
20.638 ∗
(6.274)
2.312 ∗
(0.639)
2.040
(4.322)
-5.752
(8.423)
18.332 ∗
(4.887)
5.913
(19.426)
7.060 ∗
(2.781)
-3.002
(18.351)
0.005
(0.631)
-17.593 ∗
(5.123)
2.901 ∗∗∗
1.986
(1.616)
(1.582)
-1.884 ∗
-2.441 ∗∗
(0.792)
(1.223)
-0.022
-0.292
(0.210)
(0.712)
5.131 ∗
0.073
(1.757)
(2.478)
0.865 ∗∗∗ -0.222
(0.483)
(0.746)
3.596
5.828 ∗∗
(4.060)
(2.886)
0.780
0.407
(0.529)
(0.666)
14.698
-1.714
(10.337)
(6.030)
27.280 ∗∗∗ 14.185
(18.434)
(11.792)
5.578
11.485 ∗
(4.287)
(3.900)
14.458 ∗∗
-1.324
(7.248)
(6.154)
-0.474
-0.499
(0.950)
(1.171)
-23.822 ∗∗∗ -4.737
(12.850)
(9.248)
-0.603
0.065
(0.575)
(0.503)
-15.330 ∗∗ -11.854 ∗
(7.326)
(4.887)
0.565
2.500
6.363 ∗
(1.198)
(1.579)
(1.849)
-3.910
-5.431 ∗
-7.790 ∗
(2.484)
(1.051)
(1.414)
-0.414
-0.111
-0.549
(0.782)
(0.222)
(1.107)
4.476
4.475 ∗
-3.578
(3.694)
(1.939)
(3.115)
-2.112
1.993 ∗
0.913
(1.907)
(0.623)
(0.816)
10.837 ∗∗
9.476 ∗∗
16.018 ∗
(4.899)
(4.628)
(3.267)
0.679
1.260
1.076
(0.643)
(0.644)
(0.765)
-16.540 *
27.335 *
-13.519
(4.419)
(10.170)
(9.703)
9.503
10.396
19.021
(7.643)
(24.684)
(15.281)
17.295 ∗
11.178 ∗
10.902 ∗∗
(4.866)
(4.419)
(5.233)
12.238
11.601 ∗
-1.099
(15.176)
(9.494)
(7.225)
-1.993
-1.933
-1.590 ∗
(2.169)
(1.064)
(1.411)
-17.416
-13.830 ∗
-4.752
(14.349)
(16.611)
(11.361)
-0.078
-1.403 ∗∗∗ -0.978 ∗∗∗
(0.667)
(0.854)
(0.596)
-11.288 ∗∗ -26.079 ∗
-8.174
(5.205)
(7.128)
(7.228)
0.435
(0.282)
158
158
158
158‡
158‡
Likelihood Ratio:
124.46
Likelihood Ratio:
128
Notes: *, **, *** denote coefficients statistically different from zero at 1%, 5% and 10% significance levels, respectively. In models [4][5] ’HPC’ stands for hard peg ERR and closed FA, ’IO’ for intermediate ERR and open FA, and ’FC’ for floating ERR and closed FA.
‡ The number of spells for destinations HPC, IO and FC are 30, 40, and 38, respectively. We also have 50 right-censored spells
The likelihood ratio test whether the multiple destination model is equivalent to the single destination model (restricted). Let βj,k be
the parameter associated with covariate j in destination k. The restricted model sets βj,k = βj,l
for j 6= l where l, j = {HP C, IO, F C}.
Table A-8: Single and Multiple Destination Models: Exponential Baseline
One Destination
Heterogeneity
Inflation
M2/GDP
(Reserves/M2)
(Reserves/M2)*EM
GDP per capita
Size
Trade Openness
52
SpillER
(SpillER)*EM
SpillK
(SpillK)*EN
Advanced
EM
Asia
Constant
No
Gamma
Semi
HPC
[1]
[2]
[3]
[4]
0.780
0.780
0.780
(0.946)
(0.633) (1.001)
-1.177 ∗
-1.178
-1.178 ∗
(0.566)
(0.902) (0.585)
0.038
0.038
0.038
(0.187)
(1.207) (0.191)
0.622
0.623
0.623
(1.211)
(1.005) (1.075)
0.297
0.297
0.297
(0.365)
(0.717) (0.369)
2.767 ∗∗∗ 2.768 ∗∗ 2.768 ∗∗∗
(1.629)
(1.372) (1.581)
0.484 ∗∗∗ 0.484
0.484
(0.296)
(1.641) (0.307)
-1.257
-1.260
-1.260
(3.309)
(1.412) (3.185)
1.617
1.623
1.624
(4.950)
(3.015) (4.769)
5.856 ∗
5.855 ∗
5.855 ∗
(1.747)
(0.985) (1.618)
-0.463
-0.459
-0.459
(2.948)
(2.094) (2.656)
-0.829
-0.829
-0.829
(0.604)
(0.691) (0.617)
-0.528
-0.534
-0.534
(3.982)
(2.429) (3.672)
-0.215
-0.215
-0.215
(0.286)
(0.559) (0.313)
-6.012 ∗
-6.009 ∗ -6.751 ∗
(2.487)
(1.654) (2.317)
σg2
Total Number of Spells
Multiple Destinations
No Heterogeneity
Destinations
IO
[4]
0.487
2.229
(1.622)
(1.576)
-5.119 ∗
-0.561
(2.169)
(0.676)
-0.382
0.084
(0.913)
(0.214)
-2.079
4.213 ∗
(4.233)
(1.712)
-5.687 ∗
0.758 ∗∗∗
(2.386)
(0.452)
15.261 ∗
1.188
(5.050)
(4.014)
1.793 ∗
0.525
(0.571)
(0.488)
0.891
13.873
(4.221)
(9.772)
-5.868
17.043
(7.682)
(17.135)
15.182 ∗
4.075
(4.102)
(4.044)
-1.409
10.649
(15.560)
(6.891)
5.129 ∗∗
-0.243
(2.387)
(0.890)
3.178
-16.213
(14.877)
(12.017)
-0.048
-0.790
(0.606)
(0.573)
-14.380 ∗
-13.216 ∗∗∗
(4.447)
(6.891)
Multiple Destinations
Semiparametric Heterogeneity
FC
HPC
[4]
[5]
1.629
(1.404)
-1.089
(1.032)
-0.136
(0.685)
-0.561
(2.277)
-0.241
(0.681)
2.985
(2.705)
-0.088
(0.632)
-0.589
(5.276)
7.917
(9.042)
9.797 ∗
(3.482)
-4.632
(5.212)
-0.315
(1.079)
0.631
(7.273)
0.004
(0.463)
-10.187 ∗
(4.333)
Destinations
IO
[5]
0.487
2.229 ∗∗∗
(1.469)
(1.358)
-5.119 ∗
-0.561
(1.970)
(0.664)
-0.382
0.084
(0.809)
(0.219)
-2.079
4.213 ∗
(3.933)
(1.563)
-5.687 ∗
0.758
(2.212)
(0.468)
15.261 ∗
1.188
(4.567)
(3.586)
1.793 ∗
0.525
(0.565)
(0.493)
0.891
13.873
(3.879)
(8.832)
-5.868
17.043
(7.300)
(15.427)
15.182 ∗
4.075
(3.730)
(3.737)
-1.409
10.649 ∗∗∗
(14.323)
(6.213)
5.129 ∗∗
-0.243
(2.229)
(0.883)
3.178
-16.213
(13.744)
(10.813)
-0.048
-0.790
(0.607)
(0.553)
-13.638 ∗
-13.958 ∗∗
(4.029)
(6.289)
FC
[5]
1.629
(1.286)
-1.089
(1.040)
-0.136
(0.707)
-0.561
(2.119)
-0.241
(0.611)
2.985
(2.507)
-0.088
(0.642)
-0.589
(4.810)
7.917
(8.123)
9.797 ∗
(3.186)
-4.632
(4.724)
-0.315
(0.943)
0.631
(6.586)
0.004
(0.467)
-12.521 ∗
(3.989)
(0.000)
158
158
158
158‡
158‡
Likelihood Ratio:
110.58
Likelihood Ratio:
104.64
Notes: *, **, *** denote coefficients statistically different from zero at 1%, 5% and 10% significance levels, respectively. In models [4][5] ’HPC’ stands for hard peg ERR and closed FA, ’IO’ for intermediate ERR and open FA, and ’FC’ for floating ERR and closed FA.
‡ The number of spells for destinations HPC, IO and FC are 30, 40, and 38, respectively. We also have 50 right-censored spells
The likelihood ratio test whether the multiple destination model is equivalent to the single destination model (restricted). Let βj,k be
the parameter associated with covariate j in destination k. The restricted model sets βj,k = βj,l
for j 6= l where l, j = {HP C, IO, F C}.