WPS6475


Policy Research Working Paper                             6475




    Duration Dependence and Change-Points
    in the Likelihood of Credit Booms Ending
                                 Vitor Castro
                                Megumi Kubota




The World Bank
Europe and Central Asia Region
Poverty Reduction and Economic Management, Macroeconomics 1 Unit
June 2013
Policy Research Working Paper 6475


  Abstract
  Whether the likelihood of a credit boom ending is                                  their duration and that these events have become longer
  dependent on its age or not, or whether the respective                             over the past decades. In addition, the paper extends the
  behavior is smooth or bumpy are important issues to                                baseline Weibull duration model in order to allow for
  which the economic literature has not given attention                              change-points in the duration dependence parameter.
  yet. This paper tries to fill that gap, exploring those                            The empirical findings support the presence of a
  issues with a proper duration analysis. Credit booms                               change-point: increasing positive duration dependence
  are identified considering two criteria well established                           is observed in booms that last less than eight to ten
  in the literature: (i) the Mendoza-Terrones criteria                               quarters, but it becomes decreasing or even irrelevant for
  and (ii) and the Gourinchas-Valdes-Landarretche                                    longer events. Analogous results are found for those credit
  criteria. A continuous-time Weibull duration model is                              boom episodes that are followed by systemic banking
  employed over a group of 71 countries for the period                               crisis (bad credit booms). The findings also show that
  1975q1–2010q4 to investigate whether credit booms                                  credit booms are, on average, longer in industrial than in
  are duration dependent or not. The findings show that                              developing countries.
  the likelihood of credit booms ending increases over



  This paper is a product of the Poverty Reduction and Economic Management, Macroeconomics 1 Unit, Europe and Central
  Asia Region. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution
  to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://
  econ.worldbank.org. The authors may be contacted at vcastro@fe.uc.pt and mkubota@worldbank.org.




          The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development
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                                                        Produced by the Research Support Team
      Duration dependence and change-points in the
            likelihood of credit booms ending



                 Vitor Castroa,*                                           Megumi Kubotab
      University of Coimbra and NIPE                                          The World Bank




Keywords: Credit booms, duration analysis, Weibull model, duration dependence, change-
points
JEL Codes: C41,E32, E51
Sector Board: EPOL




a,*
  Castro: University of Coimbra, Faculty of Economics, Av. Dias da Silva, 165, 3004-512 Coimbra, Portugal;
University of Minho, Economic Policies Research Unit (NIPE), Campus of Gualtar, 4710-057 Braga, Portugal;
vcastro@fe.uc.pt; tel.: +351 239 790543; fax: +351 239 790514. b Kubota: The World Bank, Poverty and
Economic Management, Macroeconomics 1 Unit, Europe and Central Asia (ECA). 1818 H Street, NW,
Washington, DC 20433, USA; mkubota@worldbank.org; tel: +1 202 473 4844. The views expressed in this
paper are those of the author and do not necessarily reflect those of the World Bank or its Board of Directors.
1. Introduction
      The rapid build-up in domestic credit can have deleterious effects on economic

activity. Understanding the dynamics of credit is important to evaluate not only the behavior

of the economic activity but also the financial system. The literature argues that recessions are

more likely, the longer an economy builds up booms in financial markets —more specifically,

booms in credit markets (Brunnermeier and Sannikov, 2012). In addition, there is evidence

that the probability of banking distress increases the longer the duration of credit booms are

(Barajas, Dell’Ariccia and Levechenko, 2009).

       The empirical literature shows that credit expansions can lead to higher growth

(Levine, 2005) but also heighten aggregate volatility and the likelihood of banking crisis

(Reinhart and Kaminsky, 1999; Demirguc-Kunt and Detragiache, 2002). Credit booms are

typically the result of result of surges in private capital inflows (Bruno and Shin, 2012;

Calderón and Kubota, 2012; Obstfeld, 2012). These surges lead to a rapid build-up of

leverage which, in turn, may lead to financial fragility (Borio and Disyatat, 2011; Gourinchas

and Obstfeld, 2012). A massive rising of inflows of foreign capital may lead to excessive

monetary and credit expansions (Sidaoui et al., 2011), increase the vulnerability associated to

currency and maturity mismatches (Akyuz, 2009), create distortions in asset prices (Agnello

and Sousa, 2011; Agnello et al., 2012a) and, consequently, bubbles in stock and market prices

and overvaluation of the real exchange rate (Magud et al., 2012).

       Duration analysis has been widely used to examine the length of business cycle

phases. Diebold and Rudebusch (1992) conduct a duration analysis to evaluate the

stabilization process of the economic activity during the post war period. In the same line,

Vilasuso (1995) employs nonparametric change-point tests to examine the duration of the

business cycle in the United States. Castro (2010) also conducts a duration analysis over a

panel of industrial countries and finds evidence that supports that the longer an expansion or

contraction, the more likely it is for that phase of the cycle to come to an end. Claessens, Kose

and Terrones (2011) apply the Weibull duration model to financial cycles and find that the

longer a financial downturn (as measured by the length of peak-to-trough phases in credit,

housing prices and equity prices), the more likely this downturn is likely to end.


                                               2
       Hence, understanding the duration of a credit boom is of crucial importance given its

consequences on the financial sector and economic activity. For instance, Barajas,

Dell’Ariccia and Levchenko (2009) and Dell’Ariccia et al. (2012) examine whether the

duration of credit booms is important in predicting future financial crisis or not. In fact, the

literature finds that the duration (as well as the amplitude) of the credit booms is a robust

predictor of those booms that end up in a systemic banking crisis.

       The main goals of this paper are: first, to investigate whether the likelihood of credit

boom episodes ending depends on its own length of time, i.e. whether they are duration

dependent or not; and, second, to analyze whether there are breaks in its behavior employing

a Weibull duration model with change-points. Castro (2012) adapts the Weibull model with

change-points proposed by Lara-Porras et al. (2005) to examine the duration of the business

cycle phases. Therefore, we follow his strategy in employing a continuous-time Weibull

model with change-points to analyze the duration of credit booms.

       Our paper uses the quarterly gross capital flows data for 71 countries from 1975q1 to

2010q4. Following Rothenberg and Warnock (2011), Forbes and Warnock (2011), and

Calderón and Kubota (2012a, 2012b), we argue that the dynamics of capital flows and credit

markets along the business cycles are better captured using quarterly data.

       The identification of credit boom episodes follows the work undertaken by Calderon

and Kubota (2012b). Given that there is no single criterion to identify credit booms, they use:

(i) the Mendoza and Terrones (2008) criteria (MT-criteria) and (ii) and the Gourinchas,

Valdes and Landarretche (2001) criteria (GVL-criteria). The first criterion identifies a credit

boom when the deviation of the real credit per capita from its trend exceeds 1.75 times its

standard deviation, whilst the second one considers that a credit boom takes place if the

deviation of the ratio of credit to GDP from its trend exceeds 1.5 times its standard deviation

or the (year-on-year) growth in the credit-GDP ratio exceeds 20 percent. The paper also

differentiates regular booms vis-a-vis those that end up in a systemic bank crisis or bad credit

booms. Empirical evidence shows that not all credit booms end in a full-blown banking crisis

and that a large share of them are followed by a soft landing (Tornell and Westermann, 2002;

Barajas et al. 2009; Calderón and Servén, 2011). Consequently, we define bad credit booms

                                               3
as credit booms followed by a systemic banking crisis (Barajas et al., 2009; Calderón and

Kubota, 2011).

       We start by estimating a basic continuous-time Weibull model to investigate whether

the likelihood of credit booms ending depends on its own age and concluded that, in fact, it

does depend: credit booms are affected by positive duration dependence. We then extend the

baseline Weibull duration model to allow for change-points in the duration dependence

parameter —as implemented in Lara-Porras et al. (2005) and Castro (2012). The basic

Weibull model assumes that the behavior of duration dependence is smooth (i.e. either

constant, increasing or decreasing) over time, whereas the degree of likelihood of a credit

boom ending as it gets older may change after certain duration. The empirical findings indeed

support the presence of a change-point: increasing positive duration dependence is observed

in booms that last less than eight to ten quarters, but it becomes decreasing or even non-

relevant for longer events (according to the GVL-criteria). This evidence is robust to the

criteria used to define credit booms (MT or GVL-criteria) and the sub-group of countries

(industrial or developing) or time period (pre or post-1990) considered. Analogous results are

found for those credit booms that end up in a systemic banking crisis (bad credit booms).

       The main messages of this paper are: first, that the evidence of true duration

dependence is helpful in predicting credit boom episodes. The evidence of positive duration

dependence implies that the risk of a credit boom ending in any particular time increases over

time. If credit booms are characterized by positive duration dependence, then the duration

analysis provides information which is useful in predicting turning points in the economy.

Consequently, our finding of duration dependence provides evidence of predictability of

credit booms. Second, our results with change-points suggest the presence of a breaking-point

in credit boom episodes. The predictability of credit booms can be improved if they last less

than 2 to 2 ½ years, according to the MT-criteria and GVL-criteria, respectively. However,

the longer the credit boom persists – more than 2 or 2 ½ years – less predictable its end

becomes, because the likelihood of their end is no longer dependent on its age, but probably

depends on other time-varying random factors. Finally, we also find robust evidence of

positive duration dependence for bad credit booms. In this case, the risk of a credit boom

                                              4
ending up in a banking crisis increases over time. Additionally, the analysis with change-

points also suggests the presence of a breaking-point in credit boom episodes followed by

systemic banking crisis.

         Thus, our findings indicate the ending of a credit boom depends positively on the

length of its life span. For the MT-criteria they also show that the mean duration of credit

booms is higher in industrial countries than in developing countries, therefore, credit boom

episodes are more persistent, on average, in industrial countries than in developing countries.

The empirical evidence provided by the estimation of the Weibull model with change-points

also supports the presence of (increasing) positive duration dependence. These results imply

that, on average, the duration of credit booms lasts within 2 to 2 ½ years in the last decade for

MT-criteria and GVL-criteria, respectively. Specifically, the duration with the MT-criteria

lasts within 2.5 years for all and developing countries in the pre-1990 period while within 3 ¾

years for industrial countries for the post-1990 period. The case of GVL-criteria duration

becomes slower: 2.5 to 3 ¾ years.

         All these results represent remarkable new findings in this field of the research and an

important contribution to the literature and to a better understanding of the behavior of credit

booms.

         The rest of the paper is organized as follows. Section 2 reviews the existing literature

on credit booms and duration analysis. Section 3 presents the econometric models. Section 4

describes the data and the methodology. The empirical analysis and the discussion of the

results are presented in Section 5. Finally, Section 6 concludes.



2. Literature Review

         This section reviews the theoretical and empirical literature of the drivers and

consequences of credit booms and their duration. We first outline some empirical facts and

theoretical arguments about the creation of credit booms. Then we review the few existing

papers on the importance of the duration of credit booms when predicting financial and

economic downturns. Finally, we review some of empirical applications of duration analysis

in the economics literature.

                                                5
       Rapid growth of domestic credit can take place in an economy due to the deepening of

financial intermediaries (Levine, 2005), upswings in credit demand during normal output

recoveries, and excessive cyclical fluctuations —or the so-called credit booms (Elekdag and

Wu, 2011). In turn, credit booms are triggered, according to the literature, by (positive)

productivity shocks, financial reforms, and surges in capital inflows (Dell’Ariccia et al. 2012).

In fact, Mendoza and Terrones (2012) find that 20-50 percent of the peak of credit booms in

industrial and emerging market economies is preceded by productivity surges, financial

reforms, and massive capital inflow episodes. Elekdag and Wu (2011) add that loose

monetary policy in industrial and emerging economies may have contributed to the build-up

of credit booms prior to the 2008-9 global financial crises. They also corroborate the findings

in the literature that longer credit booms are related to lower credit standards, deteriorating

balance sheets among banks and corporations, and warning signs of overheating —such as,

strong domestic demand, widening current account deficits, massive inflows of foreign

finance and rising asset prices.

       Minsky (1986) suggested that a benign economic environment —characterized by

high growth and low output volatility— would increase speculative investor euphoria and

lead to excess risk taking. Debt would exceed what agents can pay-off from their proceeds,

thus leading to a financial crisis. As the credit bubble bursts, banks will curtail credit not only

to sub-prime borrowers but also to those that can afford to borrow, and the economy will

subsequently enter into a spiral of recession.

       Recent theoretical efforts show that financial frictions can severely affect real

economic activity. Brunnermeier and Sannikov (2012) build a dynamic stochastic general

equilibrium model where shocks are amplified and propagated through leverage and asset

prices. Their model introduces a mechanism through which agents respond to exogenous

declines in macroeconomic risk by increasing leverage (i.e. rapid increase in credit).

Consequently, low exogenous risk environment (a feature of the Great Moderation period)

would be conducive to a greater build-up of systemic risk. In this setting, low fundamental

risks (as signaled by low output volatility) leads to higher leverage (that is, longer and sharper

credit expansions). In turn, the leverage build-up will lead to abrupt macroeconomic

                                                 6
contractions. To put it simply, they argue that financial crises and, hence, recessions are more

likely to take place, the longer an economy builds up booms in financial markets —and, more

specifically, booms in credit markets.

       Understanding the genesis and drivers of financial booms is important due to their

devastating consequences on real economic activity. Claessens, Kose and Terrones (2012)

provide an analysis of the linkages between real and financial cycles and, more specifically,

the influence of financial booms (either in credit or asset prices) on the duration and

amplitude of recessions and recoveries in real economic activity. They find that boom-bust

financial cycles are highly synchronized with real cycles and, consequently, affect the

duration and strength of recessions and recoveries. In particular, recessions associated with

financial disruptions —that is, credit crunches and/or housing price busts— tend to be longer

and deeper, and their ensuing recoveries are slightly shorter and stronger when combined with

booms in financial markets. As financial disruptions are associated with longer and deeper

recessions, recoveries associated with credit or housing price booms are associated with

stronger output growth. Levine (2005) shows that credit expansions can lead to higher growth

although these expansions may heighten aggregate volatility and the likelihood of banking

crisis (Reinhart and Kaminsky, 1999; Demirguc-Kunt and Detragiache, 2002).

       Barajas, Dell’Ariccia and Levchenko (2009) examine empirically the nature of credit

booms —especially those that end up in a full blown banking crisis. They suggest that the

probability of banking distress will increase the longer a credit boom in an economy is.

Gourinchas and Obstfeld (2012) argue that financial crises in advanced and emerging market

economies over the last century have been preceded by financial booms —that, typically, take

the form of rapid growth of domestic credit and large appreciation of the domestic currency.

Schularick and Taylor (2012) confirm this result for 14 advanced countries over the period

1870-2008. They argue that failures in the operation, regulation and/or supervision of the

financial system have led to recurrent episodes of financial instability. In turn, these episodes

are the outcome of "credit booms gone wrong." Barajas et al. (2009), in addition, show that it

is not only the amplitude of the credit boom but also its duration that help predict future



                                               7
systemic banking crisis. In sum, understanding the duration of credit boom is of crucial

importance given its consequences on the financial sector and economic activity.

       The literature argues that credit booms do not always end up in systemic crises. For

instance, Tornell and Westermann (2002) that the probability of a systemic banking crisis in a

given country i at time T, conditional on a lending boom, is around 6 percent. Barajas et al.

(2009) find that approximately 16 percent of lending booms have preceded systemic banking

crises and that this likelihood will rise to 23 percent if non-systemic episodes of financial

distress are included. In addition, they find that there are size and duration thresholds above

which credit booms inevitably are followed by a crisis —approximately 40% of credit booms

that last between 9 and 12 years end up in a crisis, whereas all credit booms over 13 years will

invariably are followed by financial turmoil. These findings suggest that hard landing does

not necessarily follow a boom in credit markets —especially so for shorter booms. However,

longer booms (especially those over 12 years) may reflect either excessive risk taking or

cronyism. In the light of these empirical findings, it might be important to distinguish whether

the effects of surging capital inflows may be differ when explaining the incidence of credit

booms that end up in a crisis (i.e. bad credit booms) from those credit booms followed by a

soft landing (which we can denote as "good" credit booms).

       Capital inflows and credit booms. Capital flows play an important role in driving

credit booms —with the probability of credit booms being preceded by surges in capital

inflows being larger among emerging market economies than among industrial countries

(Elekdag and Wu, 2011). In particular, the sharp movements in capital flows – as a result of

the recent globalization process – have put the emphasis of the analysis on the link between

those flows and developments in domestic financial markets. Recent theoretical research has

modeled the linkages between capital flows and banking leverage through the mechanisms

that leads to rising gross flows of foreign financing in the banking sector (Bruno and Shin,

2012). They tend to show that gross capital flows move in the opposite direction of risk

premia in capital markets, reflecting the sensitivity of bank leverage to risk premia.

       Furceri et al. (2011) examine the relationship between capital inflows and credit in a

dynamic perspective. They calculate the dynamic response (IRFs) of domestic credit to

                                                8
capital inflow shocks using an annual data from 1970 to 2007 for developed and emerging

market economies and show that in the event of a capital inflow shock, the ratio of credit to

GDP tends to increase during the first two years following the shock but the effect is reversed

in the medium-term. They also find that the macroeconomic policy stance of the country may

help mitigate the short-term effect of these shocks.

       Calderon and Kubota (2012) use quarterly data for a wide array of countries to

examine the dynamic relationship between gross inflows and credit booms. They find that an

increase in gross capital inflows is more likely to predict subsequent credit booms. They also

show that not all types of gross inflows have the same predictive ability: while surges in

equity-type flows have no relationship or, at best, reduce the probability of build-ups in credit,

a massive inflow of debt-type securities would raise the likelihood of credit booms.

       On the other hand, the literature shows that these surges in capital inflows lead to a

rapid build-up of leverage which, in turn, may lead to financial fragility (Borio and Disyatat,

2011; Gourinchas and Obstfeld, 2012). A massive rising inflows of foreign capital may lead

to excessive monetary and credit expansions (Sidaoui et al., 2011), increase the vulnerability

associated to currency and maturity mismatches (Akyuz, 2009), create distortions in asset

prices (Agnello and Sousa, 2012a; Agnello et al., 2012a) and, consequently, lead to stock and

housing price bubbles as well as an overvaluation of the real exchange rate (Magud et al.,

2012). Recent empirical efforts show that the flexibility of the exchange rate arrangement

may act as counteract the impact of gross inflows on credit expansions. Magud et al. (2012)

show that surges of capital inflows in countries with less flexible monetary arrangements lead

to a more rapid credit expansion and to a shift towards foreign currency. As shown in Calvo

et. al (2004, 2008), the vulnerability to capital inflow reversals is greater in countries with

more inflexible exchange rate regimes. These reversals, in turn, could potentially trigger

credit busts and asset price deflation with deleterious effects on real economic activity.

       These studies explore deeply the links between credit booms, capital flows, crises and

the respective outcomes, but neglect the issue of their duration, which is another important

dimension to understand the credit booms behavior. Moreover, as the historical analysis



                                                9
shows in the presence of several events of credit booms, with similar outcomes but different

durations, the issue of their duration analysis gains even more relevance.

           Having flourished in the engineering and medical fields, duration analysis rapidly

spread out to other sciences. In economics, it started to be employed in labor economics to

assess the duration of periods of unemployment. 1 It has also been widely used in the analysis

of the duration of the business cycle phases. 2 A basic Weibull model is usually employed in

those studies with the aim of finding duration dependence in the phases of the business cycle,

i.e. whether the likelihood of expansions and recessions ending is dependent on its age or not.

However, this model assumes that the behavior of duration dependence is smooth over the

entire duration of the event, which may not be true. Given this limitation, Castro (2012)

adapts the Weibull model with change-points proposed by Lara-Porras et al. (2005) to the

analysis of the duration of the business cycle phases. This author shows that positive duration

dependence in expansions is no longer present when they last more than ten years, which

proves the presence of a change-point in the duration of economic expansions.

           Other studies also show the presence of duration dependence in different dimensions

of the economy. For instance, Bracke (2011) and Cunningham and Kolet (2011) show that the

likelihood of housing booms and busts ending is positively dependent on their age. More

recently, Agnello et al. (2012b) provide some evidence indicating that fiscal consolidations

are also duration dependent.

           Due to its properties, this kind of analysis is also suitable for studying the duration of

credit booms. Hence, we employ a continuous-time Weibull model to investigate the presence

of duration dependence in a large group of countries over the last decades. Additionally, we

also control for the presence of change-points in the structure of the model. In the next

section, we describe the application of these models to the study of the duration of credit

booms. This analysis represents an important contribution to the economic literature in this

field and it intends to contribute to a better understanding of the behavior of credit booms.



1
    See Allison (1982) and Kiefer (1988) for a review of the literature on duration analysis.
2
    See, for example, Sichel (1991), Zuehlke (2003), Davig (2007) and Castro (2010, 2012).


                                                          10
3. Econometric Models

    This section describes the duration analysis techniques conducted in our empirical paper –

more, specifically, the basic Weibull model and a Weibull model with change-points.

3.1. Duration analysis

       We start by assuming that the duration variable is defined as the number of periods

(quarters) a credit boom is taking place. If T measures the time span between the beginning of

a credit boom and its end, then t1, t2,…,tn will represent its observed duration. The probability

distribution of the duration variable, T, can be specified by the cumulative distribution

function, F(t)=Pr(T<t), and the corresponding density function is f(t)=dF(t)/dt. Alternatively,

the distribution of T can be characterized by the survivor function, S(t)=Pr(T≥t)=1-F(t),

which measures the probability that the duration of a credit boom phase is larger or equal to t.

       A particularly useful function for duration analysis is the hazard function such as:



                                                                                              (1)


which measures the rate at which credit boom spells end at time t, given that they lasted until

that moment. In other words, it measures the probability of exiting from a state in moment t

conditional on the length of time in that state. This function helps characterizing the path of

duration dependence. For instance: (i) if dh(t)/dt>0 for t=t*, there is positive duration

dependence in t*; (ii) if dh(t)/dt<0 for t=t*, then there is negative duration dependence in t*;

and (iii) if dh(t)/dt=0 for t=t*, there is no duration dependence. Therefore, when the derivative

of the hazard function with respect to time is positive, the probability of a credit boom ending

in moment t, given that it has reached t*, increases with its age. Thus, the longer the credit

boom is, the higher the conditional probability of its end will be.

       From the hazard function, we can derive the integrated hazard function such that:



                                                                                              (2)


and compute the survivor function as follows:


                                                11
                                                                                              (3)


While different parametric continuous-time duration models can measure the magnitude of

duration dependence and the impact of other time-invariant variables on the likelihood of an

event ending, the most commonly used functional form of the hazard function is the

proportional hazard model as:



                                                                                              (4)


where h0(t) is the baseline hazard function that captures the data dependence of duration and

represents an unknown parameter to be estimated, β is a (K×1) vector of parameters that need

to be estimated and x is a vector of covariates. The proportional hazard model can be

estimated without imposing any specific functional form to the baseline hazard function (the

so called "Cox model"). Given the inappropriateness of this procedure (in particular, for

studying duration dependence), a popular alternative imposes a specific parametric form for

the function h0(t) (i.e. the "Weibull model").



3.2. The basic Weibull model

       The Weibull model is characterized by the following (baseline) hazard function as:



                                                                                              (5)


where p parameterizes the duration dependence, t denotes time, γ is a constant, p>0 and γ>0.

If p>1, the conditional probability of a turning point occurring increases as the phase gets

older, i.e. there is positive duration dependence; if p<1 there is negative duration dependence;

finally, there is no duration dependence if p=1. In this last case, the Weibull model is equal to

an Exponential model. Therefore, by estimating p, we can test for duration dependence in

credit boom phases.



                                                 12
       If we plug the Weibull specification for the baseline hazard function as expressed by

equation (5) in the proportional hazard function denoted by (4), we get:



                                                                                              (6)


Hence, the corresponding survivor function can be written as:



                                                                                              (7)


       This model can be estimated by Maximum Likelihood, and the log-likelihood function

for a sample of i=1,…,n boom episodes is given by:




                                                                                              (8)


where ci indicates when observations are censored. If the sample period under analysis ends

before the turning point has been observed, then observations will be censored (i.e. ci=0);

when the turning points are observed in the sample period, the observations are not censored

(in which case, ci=1).



3.3. A Weibull model with change-points

       While the basic structure of the log-likelihood function for the Weibull model allows

us to analyze the presence of duration dependence in credit boom phases, we also move a step

further in that we assess the extent to which the likelihood of a boom ending as it gets older

changes after a certain duration. Thus, we allow for the possibility of a structural break in the

Weibull model and conjecture that the parameters of the baseline hazard function (p and γ)

can change at a certain point (i.e. the "change-point") in time. In particular, we expect that the

degree of duration dependence, p, changes after the event has lasted more than a certain time.

Consequently, we do not only expect that the likelihood of a credit boom phase ending


                                               13
increases over time, but also that if it has lasted more than a certain time, the likelihood of

ending may change significantly after that point, that is, the magnitude of duration

dependence may decrease or increase from that point onwards.

       We propose a Weibull model for credit boom phases with change-points that follows

the general model framework developed by Lara-Porras et al. (2005) and Castro (2012) for

cases where the Weibull distribution, or the respective parameters characterizing the baseline

hazard function, varies over time for different intervals, but remain constant within each

interval. For simplicity, let us re-write equation (5) as:



                                                                                               (9)


where γ=λp. Hence, the survival function becomes:



                                                                                              (10)


Denoting g(t)=lnH(t) and considering a change point, τc, and two intervals, t0<t≤τc and

τc<t≤tT, g(t) can be expressed as:



                                                                                              (11)


with j=1,2. Due to the fact that the continuity of g(t) in the change-point, Ï„c has to be verified,

we must impose that:



                                                                                              (12)


Solving this equation with respect to p2, we get:



                                                                                              (13)


Consequently, in the case of the survival time ending in the first interval, we have that:


                                                 14
                                                                                               (14)


and, similarly, for the following survival time ending in the second interval:



                                                                                               (15)


        Considering the i-th spell (or individual), we get:



                                                                                               (16)


where di=1 if t0<t≤τc, di=0 if τc<t≤tT, and i=1,2,...,n (i.e. the number of spells).

        For H(ti,xi)=exp[g(ti)+β′xi], the hazard function is given by:



                                                                                               (17)


and the corresponding survivor function can be expressed as:



                                                                                               (18)


Therefore, the log-likelihood function can be written as:



                                                                                               (19)


                       p1             p ln(λ1t c )
where g ' (t ) = d i      + (1 − d i ) 1            . This model is estimated by Maximum Likelihood,
                       ti             ti ln(λ2t c )

given a particular change-point Ï„c. The relevance of the change-point is evaluated by testing

whether there is a statistically significant difference between p1 and p2, i.e. whether the

duration dependence parameter changes significantly between the two sub-periods.




                                                   15
4. Data and Methodology

       This section describes the definition and sources of the data for our empirical

assessment and the strategy to identify credit booms. Then we show the descriptive statistics

for the episodes and duration of credit booms and identify the duration of credit booms.

       To proceed with the duration analysis, we collected quarterly data for 71 countries (23

industrial economies and 48 emerging market economies) from 1975q1 to 2010q4 on real

credit. The measure of credit considered in our analysis is the deposit money bank claims on

the private sector taken from the line 22d of the IMF's International Financial Statistics (IFS).

We express the amount of credit in real terms by dividing the nominal credit by the CPI index

(at the end of the quarter). Other measures of credit considered in this study are the ratio of

real credit to GDP and the leverage of the banking system. The latter indicator is computed as

the ratio of private credit to bank deposits where deposits are measured as the sum of demand

and time deposits (IFS lines 24 and 25, respectively).

       However, our aim is to identify credit booms to compute the respective duration.

Defining a credit boom is not easy because there is no consensus in the literature on the best

methodology to identify them. Some studies use the amount of real credit provided by the

banking system; others use the bank lending normalized by either total population or the

amount of goods produced in the real economy. In this study we decided to focus on the

criteria used by Calderón and Kubota (2012) for their analysis on the effects of surges in

private capital inflows over credit booms. In their paper they consider the following criteria

from the literature on credit booms: (i) Mendoza and Terrones (2008) or MT-criteria; and (ii)

Gourinchas, Valdes and Landarretche (2001) or GVL-criteria, which is later implemented and

updated by Barajas, Dell'Ariccia and Levchenko (2009).

       In the criteria defined by Mendoza and Terrones (2008) to identify credit booms, an

episode of credit boom takes place whenever the amount of credit extended by the banking

system to the private sector grows by more than its experience during a typical cyclical

expansion. The amount of real credit per capita, lit , is the key variable to identify a boom in
                     ~
lending. They denote lit as the deviation of (the log of) real credit per capita from its long-run



                                               16
                                         ~
                                                  ()
trend (or its cyclical component), and σ lit as its corresponding standard deviation. In this

study, we follow Mendonza and Terrones' (2008) strategy in computing the long-run trend of

real credit per capita using the Hodrick-Prescott (HP) filter.

          A country is considered to have experienced a credit boom if it has one or more
                                        ~        ~
                                                            ()
subsequent quarters where the condition lit > ϕσ lit holds. The factor ϕ is a threshold factor

set by Mendonza and Terrones (2008) at 1.75. We adopted this factor as a basis for our

analysis, but we also consider other values of Ï• (1.5 and 2.0) to evaluate the robustness of

                                                         ˆ , takes place in the quarter that
our results. Note that the peak date of the credit boom, t
                        ~
                               { ~
maximizes the deviation lit − ϕσ lit     ( )} from the set of contiguous quarters while it satisfies the
                             ˆ has been determined, the starting period of the credit boom t S
condition stated above. Once t
                                                           ~
                                                                  {    ( )} while the final period of
                                                                       ~
is such that t S < tˆ and it yields the smallest value for lit − ϕ S σ lit

                                    < tˆ and also yields the smallest value for {l − ϕ σ (l )} where
                                                                                 ~        ~   F
the boom t F is such that t F                                                           it         it


Ï• S = Ï• F = 1.

          For robustness, we also consider the GVL-criteria to identify credit booms. This

method identifies a credit boom by looking at the growth of credit in the economy as proxied

by the bank credit to the private sector as a percentage of GDP, L/y. Thus, Gourinchas et al.

(2001) define a credit boom as an episode where the deviation of the ratio L/y from a country-

specific trend in country i at period t (with the trend being calculated up to that period t)

exceeds a determined threshold. In particular, a credit boom takes place if the ratio of private

credit to GDP meets either of the following two conditions: (i) the deviation of L/y from its

estimated trend, say L/y, is greater than 1.5 times its standard deviation and the year-on-year

growth rate of L/y exceeds 10 percent, and/or (ii) the year-on-year growth rate in the ratio L/y

exceeds 20 percent. 3 We also adopted this procedure but, like in the MT-criteria, we

considered other thresholds in a robustness analysis: 1.75 and 2.0.


3
    According to Barajas et al. (2009), the starting and final quarter of the identified credit boom is defined
accordingly. The beginning of the episode is the earliest year in which L/y is greater than ¾, its standard
deviation and the annual growth rate of L/y exceeds 5 percent, or the annual growth rate of L/y exceeds 10


                                                       17
           These methodologies offer some differences. The MT-criteria uses the real credit per

capita to identify booms in credit markets whereas the GVL-criteria use the ratio of credit to

GDP. Both criteria use the HP-filter to compute the trend in credit and apply a rolling variant

of the filter that takes information up to the moment where the deviation is computed.

Thresholds are country-specific rather than based on the cross-sectional distribution of

countries. Like Calderón and Kubota (2012), we use quarterly information on credit, which,

as they argue, is more appropriate to assess cyclical movements and volatility associated to

crisis episodes. 4

           We collect quarterly information on real credit provided by the banking system to the

private sector for 71 countries from 1975q1 to 2010q4 to identify the credit boom episodes

according to the two criteria outlined above. Table 1 presents some descriptive statistics for

the number of episodes identified (Obs.), their mean duration (Mean), standard deviation

(S.D.), minimum (Min.) and maximum (Max.). Industrial and developing countries and

different periods of time are also considered in this analysis.



                                            <Insert Table 1 around here>



           Using the MT-criteria we are able to identify 123 credit boom episodes over our entire

time dimension -- of which 32 episodes took place in industrial economies and 91 in

developing countries. Over time, most episodes of lending booms occur in the 1990s (50). On

the other hand, when we use the GVL-criteria, we are able to identify a larger number of

episodes (231), especially in the period 2000-2010 (98). 5 Most of them also occur in the

group of developing countries (180).



percent. Analogously, the end quarter of the boom is determined if either the year-on-year growth rate of L/y
becomes negative, or L/y falls below ¾ times its standard deviation and its growth rate is lower than 20 percent.
4
    The HP-filter is used to compute the trend, where the value of Lagrange multiplier employed in the
maximization problem is λ=1600 (for quarterly data) rather than the value of 100 used in the MT-criteria to
decompose the annual data.
5
    This means that the GVL criteria allow us to identify many episodes of credit booms in the run-up to the recent
global financial crisis.


                                                         18
           By organizing the data in spells – where a spell represents the number of years that a

credit boom lasts and it is denoted by Dur – we are able to compute their mean duration. 6

According to the MT-criteria, credit booms last on average around 6.1 quarters, but they last

longer in the group of industrial countries (7.5) than in the group of developing countries (5.6)

– see Table 1. According to the GVL-criteria they tend to last a bit more (about 8.5 quarters),

either for industrial or developing countries. Whether there is any significant difference or not

in the duration of credit booms between these groups of countries is something that we will

test below in the empirical analysis. In particular, we will test whether there is a significant

difference in the average duration of credit booms, as well as in the duration dependence

parameter (p) between these two groups of countries. This will be done by including the

dummy D_Indus in the model, which takes the value of 1 for industrial countries and 0

otherwise. Moreover, some separate regressions for each of these groups will also be

considered.

           Additionally, we observe in Table 1 that the average duration of credit booms has

increased over the last decades, independently of the criteria used. Whether this evidence is

statistically solid is another issue that we will explore in the empirical analysis using dummies

for each decade (Dec70, Dec80, Dec90, Dec00). Following Castro (2012), we also consider a

kind of a trend variable for the credit boom spells, labeled as Event, to check whether their

duration has become gradually longer or shorter over time. This variable reports the order or

observation number of each event over time and for every single country: it is equal to 1 for

the first event, 2 for the second, and so on. If the coefficient on this variable is significantly

smaller (larger) than zero, phase durations get longer (shorter) over time or, better, from spell

to spell.



5. Empirical Analysis

           This section investigates whether there is positive duration dependence in credit boom

episodes using quarterly data from 1975q1 to 2010q4 for both industrial and developing

countries (23 and 48, respectively). We also conduct a test whether there is positive duration
6
    The variable Dur corresponds to t_{i} in the model described in the previous Section.


                                                         19
dependence in bad credit booms followed a systemic banking crisis. We analyze the results

from the basic Weibull duration model and the model with change-points. Finally, we conduct

a series of robustness checks.

5.1. The baseline model

          The empirical evidence that emerges from the estimation of the basic Weibull model

presented in sub-Section 3.2 is summarized in Tables 2 and 3. These tables are divided in two

blocks, one for each criterion used to define credit booms: the MT-criteria and the GVL-

criteria. We start by recalling that the estimate of p measures the magnitude of the duration

dependence and γ corresponds to the estimate of the constant term. A one-sided test is used to

detect the presence of positive duration dependence (i.e. whether p>1) and the sign '+'

indicates significance at a 5% level.

          The results reported in Table 2 provide strong evidence of positive duration

dependence for credit booms, either using the MT-criteria or the GVL-criteria. This means

that the likelihood of a credit boom ending increases as the time goes by. This is robust for all

regressions presented in this table although significant differences arise in the dynamic path

of this likelihood between the MT-criteria and the GVL-criteria. The probability of credit

booms ending at time t, provided that they lasted until that period grows over time at an

increasing rate according to the MT-criteria, but at a decreasing rate according to the GVL-

criteria. 7 For instance, p is in most of the cases statistically greater than 2 when the MT-

criteria is used, therefore, the statistical analysis of the second-order derivative of the baseline

hazard function indicates the presence of constant positive duration dependence in credit

booms. On the other hand, p is lower than 2 in most cases when the GVL criteria are used;

that is, there is evidence of a decreasing duration dependence in the GVL-defined credit

booms. Our result is in line with the shorter mean duration of the credit booms identified by

the MT-criteria, as observed above in the descriptive statistics. Nevertheless, we should

emphasize that positive duration dependence is present in the duration of credit booms

independently of the criteria used to identify them.

7
    See Castro (2010, 2012) for details on the analysis of the second-order derivative of the baseline hazard
function.


                                                      20
                                           <Insert Table 2 around here>



           We assumed that credit booms may have a length from one quarter to the maximum

observable in our sample although, according to our characterization, their minimum duration

is higher than one (it is two – see Table 1). Therefore, our duration analysis evaluates whether

truncating the booms at their minimum duration affects the results or not. Consequently, the

hazard rate must be identically zero for the first quarter and some non-zero value thereafter.

Truncation is made at the minimum observable durations: d0=min(di)-1, where min(di) is the

shortest boom observed in the sample (two, in our case). This means that the survival function

is now:



                                                                                            (20)


           Truncation is allowed for in the regressions presented in Column 2 of Table 2, but the

results are not affected by this "small" truncation. This implies that positive duration

dependence is still present in credit booms regardless the criteria used to define these booms.

In general, results in the duration research are generally not sensitive to the choice of this

minimum observable duration and the qualitative conclusions tend to be identical in any

case. 8 Thus, we will carry on with our analysis without taking into account this intricacy in

the model.

           In the regressions presented in column 1, we also assume that the population of

individual spells is homogeneous, i.e. each credit boom is under the same risk of ending.

Given that this may not represent the reality, the regressions in column 3 allow for the

presence of unobserved heterogeneity or frailty. In statistical terms, a frailty model is similar

to a random-effects model for duration analysis: it represents an unobserved random

proportionality factor that modifies the hazard function of an individual spell and accounts for

heterogeneity caused by unmeasured covariates or measurement errors. In order to include

8
    See, for example, Sichel (1991), Layton and Smith (2007) and Castro (2010, 2012).


                                                        21
frailty in the Weibull model, the hazard function expressed by equation (6) is modified as

follows:



                                                                                              (21)


where v is an unobserved individual-spell effect that scales the no-frailty component. The

random variable v is assumed to be positive with unity mean, finite variance (θ) and

independently distributed from t and x. The survival function becomes:



                                                                                              (22)


       Since the values of v are not observed, we cannot estimate them. Therefore, we follow

Lancaster (1990) and assume v follows a Gamma distribution with unity mean and variance θ.

Consequently, the frailty survival function can be written as:



                                                                                              (23)


the frailty hazard function becomes:



                                                                                              (24)


and the corresponding log-likelihood function can be expressed as:



                                                                                              (25)


       The variance parameter (θ), which measures the presence (or absence) of unobserved

heterogeneity, is an additional parameter that needs to be estimated. As θ is always greater

than zero, the limiting distribution of the maximum-likelihood estimate of θ is a normal

distribution that is halved or chopped-off at the zero-bound. Therefore, the likelihood ratio

test (LR test) used to detect its presence is a `boundary' test that takes in account the fact that



                                                22
the null distribution is not the usual chi-squared with one degree of freedom, but rather a

mixture of a chi-squared with no degrees of freedom and a chi-squared with one degree of

freedom (Gutierrez et al., 2001). The results show some evidence of unobserved

heterogeneity, as corroborated by the p-value of the LR test reported at the bottom of column

3: at a 5% level we do not reject the presence of frailty either using the MT-criteria or GVL-

criteria. This can be due to the omission of some relevant conditionings. According to Jenkins

(2005, p. 81) omitted variables are one reason for the presence of frailty in the model. Hence,

in the next regressions we will control for that problem including some additional regressors

in the equation. 9

          In particular, frailty can be linked to the presence of individual country-specific effects

in the model. Therefore, in the regressions in column 4 we add country-dummy variables to

the equation. In this case, the test for pooling, i.e. the LR test, is used to assess whether the

model controlling for country-specific effects is preferred to simple pooling. The p-value of

the LR test reported at the bottom of column 4 supports the existence of those effects.

However, Claessens et al. (2011, p.17) points out that having only a limited number of

observations/spells per country – which is our case – fixed effects may have to be ruled out.

In fact, we had some difficulties in achieving convergence when country-dummies are

included in the model, especially when other regressors are used. Hence, we decided to

simplify the analysis considering only two sets of countries that present some homogeneity

inside each group, but that are heterogeneous between then: industrial and developing

countries. This procedure (partially) solves the problems faced with the use of country-

dummies – controlling for eventual individual or group heterogeneity – and allow us to test

for differences in the mean duration of credit booms between those two groups of countries.

          Thus, in Column 5, we add the dummy variable D_Indus to the model. We observe

that the coefficient associated to this variable is negative and statistically significant when the

MT-criteria are considered. This suggests that, on average, credit booms tend to last longer in


9
    We should stress that when we tried to control for frailty with those additional regressors the model did not
achieve convergence. Therefore, we conduct our analysis with the more parsimonious structure for the Weibull
model.


                                                        23
the group of industrial countries. 10 However, when the GVL-criteria is used no significant

differences are found in the mean duration of credit booms between industrial and developing

countries. These two findings are well in line with what we have observed in the descriptive

statistics (see Table 1).

           Another issue that can be analyzed here is whether the duration dependence parameter

is the same for industrial and developing countries or not. To analyze this issue, we start by

replacing the parameter p by p+ΔpD_Indus in the regressions presented in column 6 to

directly estimate that difference (i.e. Δp); in column 7, we also include the dummy D_Indus.

When the MT-criteria is used, we observe a significant difference in the the duration

dependence parameter between those two groups of countries (column 6), however, that

difference becomes statistically insignificant when the dummy D_Indus is added to the

equation (see column 7). This means that the main difference between them is in the mean

duration of credit booms and not in the duration dependence parameter: evidence of positive

duration dependence is found for both groups of countries, as shown in the regression in

column 7 or even in the separate regressions for industrial and developing countries presented

in columns 8 and 9, respectively. However, despite the duration dependence parameter begin

statistically similar, our findings indicate the presence of increasing duration dependence in

the first group and constant duration dependence in the second. Hence, the rate at which credit

booms end in the group of industrial countries is slightly higher, even though the difference is

not statistically significant.

           When we employ the GVL-criteria, no significant differences are observed either in

the duration dependence parameter or in the mean duration of credit booms between those

groups of countries. Nevertheless, we should note that: (i) like in the MT-criteria, the rate at

which credit booms end in the group of industrial countries is slightly higher than in the group

of developing countries (even though this difference is not significant); (ii) but, unlike the

MT-criteria, we observe constant positive duration dependence in the first group (instead of

increasing) and decreasing (instead of constant) positive duration dependence in the second.

This conclusion is corroborated in the separate regressions presented in columns 8 and 9.
10
     Note that a negative coefficient means a lower probability of the event ending over time, i.e a longer duration.


                                                          24
           In sum, our findings show that credit booms are duration dependent. In particular, they

show that the likelihood of these events ending increases over time, at an increasing rate if

they are defined using the MT-criteria, but at a decreasing rate if the GVL-criteria is used

instead. Moreover, with the MT-criteria we also observe that the mean duration of credit

booms is higher in the group of industrial countries than in the group of developing countries.

           As we are using a continuous-time duration model, there is no scope to include

regressors that vary over time, but it is possible to consider a few that remain constant over

each spell. The dummy D_Indus, included in some regressions above, is one example. Other

possible regressors are the trend variable Event for spells and the dummies for the decades

(Dec80, Dec90, Dec00). These additional regressors are included in the first two regressions

presented in Table 3 to collect for possible time effects. The results confirm the presence of

positive duration dependence (increasing with the MT-criteria and decreasing with the GVL-

criteria) and a lower likelihood of credit booms ending for industrial countries (with the MT-

criteria). Moreover, the negative coefficient on Event shows that credit booms have become

longer from spell to spell, but its effect has not proved to be statistically significant, When

controlling for time-effects using dummies for the decades, however, we are able to unveil

significant effects. The results indicate that the likelihood of a credit boom ending indeed

decreases over time, especially in the 1900s and 2000s. To collect this effect more precisely,

we created another dummy to group these two decades: D90_10. This dummy takes the value

of one for the period between 1990 and 2010, and zero otherwise. Both regressions presented

in column 3 confirm that, on average, credit booms have indeed become longer after 1990. 11

This implies that longer credit booms may be associated to increasing financial globalization.

The rapid expansion of global asset trade —as observed by the increased financial

globalization over the last 25 years— has led to rising gross inflows and higher levels of

activity in credit markets. Claessens et al. (2012) show that greater financial openness reduces

the duration of downturns in credit markets and that it may also increase the duration of credit

booms. Hence, we can infer that the greater duration dependence can be perceived as a


11
     These findings are also in line with what we have observed in the descriptive statistics (see Table 1)


                                                           25
consequence of the increasing globalization process, deeper integration and liberalization of

some markets and economies and higher capital mobility observed since the 1990s.



                                            <Insert Table 3 around here>



           Similarly to what we did above for the groups of industrial and developing countries,

we also analyze here whether the duration dependence parameter is the same or not before

and after 1990. Hence, we replace the parameter p by p+ΔpD90_10 in the regressions

presented in column 4 to directly estimate that difference (i.e. Δp); in column 5, we also

include the dummy D90_10. We observe a significant difference in the duration dependence

parameter between those two periods (column 4) and that difference remains significant when

the dummy D90_10 is included, especially in the GVL-criteria (see column 5). However, the

coefficient on the dummy loses its statistical significance. Hence, the main difference between

these two periods is more in the duration dependence parameter than in the mean duration of

credit booms. In fact, separate regressions in columns 6 and 7 for the pre- and post-1990

periods, respectively, show that the difference in the constant parameter γ is negligible while

the difference in the duration dependence parameter is substantial, especially when the GVL-

criteria is considered. This might mean that this second criteria is more sensitive to the higher

duration of credit booms in the last few years. In fact, the GVL-criteria allow us to identify

many episodes of credit booms in the run-up to the recent global financial crisis as well as

booms that have occurred during the recovery that followed the recent crisis. Moreover, with

these criteria we observe the presence of constant positive duration dependence in the pre-

1990 period and decreasing duration dependence in the post-1990 period, which reflects the

higher propensity for longer credit booms in the recent years. 12 As a result, the recent

financial globalization leads to longer trough-to-peak cycles in credit —and more specifically,

longer credit booms, especially in industrial countries.


12
     However, this evidence is not so clear when the MT-criteria is used: both duration dependence parameters (for
pre- and post-1990 periods) present evidence of increasing duration dependence and their difference is not
statistically significant (see columns 5 to 7).


                                                        26
           Are all credit booms alike? Looking at the duration dependence of bad credit booms.

           We test whether there is a positive duration dependence in bad credit booms. It is clear

from the literature that not all credit booms end in crisis —most of them are followed by soft

landing (Tornell and Westermann, 2002; Barajas et al. 2009; Calderón and Servén, 2011).

More specifically, it is likely that one out of four credit boom episodes will end with a

currency or a banking crisis (Mendoza and Terrones, 2012). Table 4 provides these results for

bad credit booms followed a systemic banking crisis.

           Independently of the criteria used, we robustly find the presence of positive duration

dependence for bad credit booms —which evolves at a constant pace over time.

Consequently, bad credit booms have a greater propensity to end over time. This evidence is

even more robust when we estimate the model with a change-point. Here, our findings show

that the likelihood of bad credit booms ending increases at a faster pace for those that last less

than 10 quarters. For those episodes with longer duration, their respective likelihood increases

at a decreasing rate. This implies that they tend to persist for a bit longer once they pass that

threshold. The difference between the parameters (pâ‚‚-pâ‚?) is also statistically significant which

supports the suitability of the change-points Weibull model to the analysis of the duration of

bad credit booms.

           Regarding the effect of the additional regressors, we are not able to find any

significant impact. The coefficients on D_Indus, Event and D90_10 fail to be statistically

significant. Hence, there are not significant differences in the level of the duration dependence

coefficient between industrial and developing countries (column 2) or pre- vis-à-vis after

1990 (column 4). 13

           Thus, our results show the presence of positive duration dependence and of a change-

point in the duration of bad credit booms, independently of the criteria used to define them

(MT or GVL) and the sub-group of countries (industrial or developing) or time period (pre- or

post-1990) considered. Therefore, we robustly find that bad credit booms also tend to die out

within two years and a half.

13
     We also controlled for decade dummies. The estimated coefficients for these dummies were not statistically
significant.


                                                       27
                                           <Insert Table 4 around here>



5.2. The model with change-points in duration dependence

           The results presented in Tables 2 and 3 rely on the assumption that the magnitude of

the duration dependence parameter is invariant whatever the duration of the credit booms

spells is. In Figure 1, we plot the survivor functions for credit booms for all countries,

industrial and developing countries and pre- and post-1990 periods, regarding the two

concepts to define credit booms (the MT and GVL-criteria). It is clear that the probability (or

proportion) of a credit boom surviving after duration ti substantially decreases as they become

older. This sharp decline is consistent with the existence of positive duration dependence.

Moreover, the survivor functions quickly fall until ti=8 – for all the cases considering the MT-

criteria – and until ti=10 (for all and developing countries and for the pre-1990 period) or

ti=15 (for the industrial countries and for the post-1990 period) – for the cases considering the

GVL-criteria – but, and these evolve at a slower pace. This highlights the possibility of breaks

in duration dependence and it is necessary to have a more flexible framework allowing for

change-points in the Weibull distribution at Ï„c=8 (MT-criteria) and Ï„c=10 or Ï„c=15 (GVL-

criteria). In fact, Figure 1 suggests that the magnitude of duration dependence parameter

might be lower when credit booms are longer than those values and the likelihood of their

ending can significantly change above those thresholds. 14 Thus, there is significant evidence

to suspect that change-points in the duration of credit booms may indeed exist.



                                           <Insert Figure 1 around here>

14
     Another signal of the existence of a break-point in duration dependence for credit booms is provided by the
slope of the survivor functions. For example, in the case of the full sample, our computations show that the
average slope, considering the MT-criteria (GVL-criteria), is equal to -0.128 (-0.090) for booms that are shorter
than 8 (10) quarters and -0.020 (-0.013) for those that last longer than 8 (10) quarters. Putting it differently, when
credit booms have a duration shorter than 8 (10) quarters, each additional quarter of duration, on average,
increases the likelihood of they ending by about 12.8 (9.0) percentage points. In contrast, when they have a
length longer than 8 (10) quarters, each additional quarter of duration rises the likelihood of they ending by only
2.0 (1.3) percentage points. Similar conclusions were reached for the sub-samples. The respective computations
are available upon request.


                                                         28
           In order to test for the presence of differences in the duration dependence parameter,

we consider a Weibull model with change-points. For each criterion, we estimate two

dependence duration parameters, one for the first duration-period (p1) and another one for the

second duration-period (p2), and evaluate the statistical significance of the difference between

the two (p2-p1). 15,16 The results are reported in Table 5.

           In column 1, we estimate a simple equation without covariates. In column 2, we

control for differences in the average duration of credit booms between industrial and

developing countries and to account for the possibility of their duration change over time.

Columns 3 and 4 present the results of separate regressions for industrial and developing

countries, respectively, controlling for time-effects. In column 5, the dummies for the time-

effects are replaced by the dummy for the post-1990 period. 17 Finally, columns 6 and 7

present separate regressions for the pre- and post-1990 periods, respectively, controlling for

group-effects.



                                             <Insert Table 5 around here>



           As expected, the results presented in Table 5 show that the duration dependence

parameter indeed varies with the duration of the credit boom spells. In particular, the

magnitude of the duration dependence parameter is always significantly lower when credit

booms are longer than 8 or 10 quarters, considering they are defined by the MT-criteria or

GVL-criteria, respectively. Remarkably, the difference between the parameters after and

before the respective change-point (p2-p1) is always negative and statistically significant,




15
     The estimates for the two constant terms are γ1=λ1p1 and γ2=λ2p2.
16
     The delta method is used to compute the respective standard-errors.
17
     As it very complex to control, at the same time, for change-points and different duration dependence
parameters for the pre- and post-1990 periods, we use instead the dummy D90_10 and estimate separate
regressions for both periods to control for those time differences.


                                                          29
independently of the criteria used to define credit booms. 18 In particular, considering the MT-

criteria, increasing positive duration dependence is observed in credit booms that last less than

8 quarters, while decreasing (or constant) duration dependence characterizes those booms that

last more than that threshold. Consequently, our findings show that there is significant

evidence of credit boom episodes ending within two years. With the GVL-criteria, even

though increasing duration dependence is observed for booms that last less than 10 quarters,

when their length is longer, duration dependence is no more present, i.e. the likelihood of

ending is no longer dependent on their age. Indeed, while the parameter p1 is statistically

significant in all specifications, p2 does not seem to exhibit statistical significance. As a result,

independently of the criteria used, we robustly find that there is a change-point in the duration

of credit booms. Moreover, all these results hold even when country/group-effects and time-

effects are controlled for.

           After controlling for change-points, we are still observing that the average duration of

credit booms is significantly higher in the group of industrial countries and that its duration

has increased over the last two decades (see, in particular, columns 2 and 5). As our final

exercise, we control for the presence of change points in each group of countries (columns 3

and 4) and time-periods (columns 6 and 7) separately. Independently of the criterion or

subgroups used, all results show the presence of a change-point, therefore, this confirms our

simple plotted charts in Figure 1. Overall, the results are similar to the ones obtained with the

full sample except for developing countries. When the MT-criteria is used for developing

countries (column 4), we confirm the presence of (increasing) duration dependence for credit

booms that last less than 8 quarters, however, duration dependence is no longer present for

those booms that last more than that threshold.

           Thus, our results conclude that there is strong evidence supporting the presence of a

change-point in the duration of credit booms, independently of the criteria used to define them

(MT or GVL) and the sub-group of countries (industrial or developing) or time period (pre- or


18
     Even though Figure 1 is clear about the location of the change-points, we tried other quarters as change-points,
but unsurprisingly this difference was never statistically significant in those cases. Those additional results are
not reported here to save space but they are available upon request.


                                                          30
post-1990) considered. Therefore, our findings show strong evidence that the life of credit

booms dies out within two years regardless of any criteria, sub-group of countries and time

period used.



5.3. Robustness checks

       The MT-criteria identifies a credit boom when the deviation of the real credit per

capita from its trend exceeds 1.75 times its standard deviation. The GVL-criteria considers

that a credit boom takes place if the deviation of the ratio of credit to GDP from its trend

exceeds 1.5 times its standard deviation or the (year-on-year) growth in the credit-GDP ratio

exceeds 20 percent. For robustness purposes, we consider different and reasonable values for

those parameters and check whether our findings are robust to those changes or not.

Accordingly, for the MT-criteria, we replace the parameter Ï•=1.75 by Ï•=1.5 and Ï•=2.0 and

for the GVL-criteria, we consider Ï•=1.75 and Ï•=2.0 instead of Ï•=1.5. Table 6 presents the

results of these robustness checks for both criteria with different parameters. For this analysis,

we select the more representative equations from the regressions presented above for both the

basic Weibull model and the Weibull model with change-points.



                                    <Insert Table 6 around here>



       Starting with the MT-criteria and considering the basic Weibull specification (columns

1 and 3 in Table 6), the results support our empirical findings: there is evidence of increasing

duration dependence using either the 1.5 or 2.0 thresholds. These results also confirm that

industrial countries are characterized by longer credit booms and that their length has

increased over the last couple of decades. This evidence is also supported by the Weibull

specifications with change-points (columns 2 and 4). Most importantly, we corroborate the

presence of a change-point in credit booms at the same 8 quarters threshold as increasing

positive duration dependence is found for shorter booms while their duration dependence is




                                               31
constant for longer ones. Consequently, the difference in the duration dependence parameters

is statistically significant either at Ï•=1.5 or Ï•=2.0.

       The results for the GVL-criteria are not different from the ones obtained above: (i) the

basic Weibull specifications (regressions 5 and 7) confirm the evidence of decreasing duration

dependence; (ii) there are no significant differences between industrial and developing

countries; (iii) credit booms became longer over the last decades; (v) the presence of a

change-point is confirmed (the difference pâ‚‚-pâ‚? is statistically significant either for Ï•=1.75 or

Ï•=2.0); (vi) increasing duration dependence is observed for those booms that last less than 10

quarters although, once again, no duration dependence is found for longer events. As a result,

our robustness analysis confirms our empirical findings.



6. Conclusions

       This paper analyzes whether credit booms are duration dependent and investigates the

presence of change-points in the likelihood of their ending. It represents an avenue of research

that, to the best of our knowledge, remains vastly unexplored in the empirical literature of

credit booms. We employ a continuous-time duration model over a group of 71 countries

from 1975q1 to 2010q4 to investigate whether the likelihood of credit booms ending indeed

depends on its own age and to check the presence of change-points in its behavior. The credit

booms considered in this analysis were identified using two criteria well established in the

literature: the Mendoza-Terrones and the Gourinchas-Valdes-Landarretche criteria.

       The main message of this paper is that there is robust evidence of positive duration

dependence in credit booms. This finding provides information of the predictability of credit

boom episodes. It implies that the risk of credit booms coming to an end in a particular year

increases over time.

       Our results also show that these events have become longer over the last decades,

which means an increase in the persistence of credit boom phases over time. Moreover, the

findings provided by this study also indicate that credit booms are, on average, longer in

industrial than in developing countries.


                                                32
        Additionally, the baseline Weibull duration model was extended to allow for breaks or

change-points in the duration dependence parameter. While the basic Weibull model assumes

that the behavior of duration dependence is smooth (i.e. either constant, increasing or

decreasing) over time, the degree of likelihood of a credit boom ending as it gets older may

change after a given duration. The empirical findings indeed support the presence of a

change-point: increasing positive duration dependence is observed in booms that last less than

eight to ten quarters, but it becomes decreasing or even non-relevant for longer events

(according to the GVL-criteria). This evidence is robust to the criteria used to define credit

booms (MT or GVL criteria) and the sub-group of countries (industrial or developing) or time

period (pre- or post-1990) considered. This represents a striking finding in this field of the

literature that certainly contributes to a better and deeper understanding of the credit booms

behavior. Moreover, it can also contribute to a timely formulation of policies that can help

fine-tuning the trade-off between credit and economic growth.

        We also show that those credit booms that end up in a crisis (bad credit booms) also

exhibit evidence of positive duration dependence and the presence of a change-point: the

likelihood of bad booms ending increases at an increasing rate for those that last less than 10

quarters; for those that last longer the respective likelihood also increases but at a decreasing

rate.

        While providing valuable information on the duration of credit booms, the present

paper opens new avenues for further work. For instance, given that the selection of the

change-point is exogenously determined by a sensible graphical analysis of the survivor

function, an interesting extension of this piece of research would be to incorporate a discrete

latent variable in the standard Weibull model. This would make the selection of the change-

point endogenous, thereby, representing a challenging and promising approach to be

considered in the future.

        Finally, we observed that longer credit booms tend to be less dependent on its age – as

shown by the Weibull model with change-points. Hence, it is likely that other time-varying

factors might be considered to explain its duration. This means that the study of the duration

of credit booms can also be extended with the application of discrete-time duration models

                                               33
that allow for the inclusion of those time-varying covariates. That is another dimension of the

problem that is beyond of the scope of this paper but to which the authors are carefully

addressing in another paper.




                                              34
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                                            39
List of Tables

  Table 1: Descriptive statistics for the episodes and duration of credit booms
 Dur                                          Obs.            Mean              S.D.             Min.            Max.
   MT (2008) criteria
 All countries                                123              6.05             2.8               2               17
 Industrial countries                          32              7.44             2.83              4               16
 Develping countries                           91              5.56             2.63              2               17
 D_Indus                                      123              0.26             0.44              0                1
 Event                                        123              1.52             0.77              1                5
   1975-1979                                   12              4.67             2.31              2                8
   1980-1989                                   30              5.63             2.22              2               10
   1990-1999                                   50              6.46             3.23              2               17
   2000-2010                                   31              6.32             2.61              2               12

   GVL (2001) criteria
 All countries                                231              8.53             5.88              2               35
 Industrial countries                          51              8.51             5.28              2               27
 Develping countries                          180              8.54             6.05              2               35
 D_Indus                                      231              0.22             0.42              0                1
 Event                                        231              2.23             1.24              1                7
   1975-1979                                   16              5.69             2.89              2               12
   1980-1989                                   41              5.98             3.05              2               16
   1990-1999                                   76              8.93             5.42              2               27
   2000-2010                                   98              9.77             6.95              2               35


Notes : This table reports the number of episodes (Obs.), the mean duration (Mean), the standard deviation (S.D.), the
minimum (Min.) and the maximum (Max.) duration for credit boom spells. The data are quarterly and comprises 79
countries over the period 1975q1-2010q4. Credit booms are identified using the works of Mendoza and Terrones (2008)
and Gourinchas et al. (2001). The MT-criteria identifies a credit boom when the deviation of the real credit per capita from
its trend exceeds 1.75 times its standard deviation. The GVL-criteria considers that a credit boom takes place if the
deviation of the ratio of credit to GDP from its trend exceeds 1.5 times its standard deviation or the (year-on-year) growth
in the credit-GDP ratio exceeds 20 percent. Note that this criteria was more recently applied and updated by Barajas,
Dell'Ariccia and Levchenko (2009).
  Table 2: Duration dependence in credit booms: basic Weibull model estimation
  MT-criteria           (1)                  (2)                 (3)                  (4)                 (5)                  (6)                 (7)                  (8)                 (9)
          γ               0.0113 ***           0.0137 **           0.0048 **            0.0056              0.0118 **            0.0105   **         0.0148 **            0.0027              0.0148 **
                        [0.0042]             [0.0058]            [0.0021]             [0.0060]            [0.0047]             [0.0044]            [0.0067]             [0.0018]            [0.0068]
          p                2.320 +,i            2.236 +,c           2.903 +,i            4.724 +,i           2.387 +,i            2.431   +,i         2.275 +,c            2.784 +,i           2.275 +,c
                         [0.189]              [0.209]             [0.235]              [0.390]             [0.218]              [0.235]             [0.245]              [0.326]             [0.245]
          ∆p                                                                                                                     -0.212   **          0.510
                                                                                                                                [0.111]             [0.403]
        p+∆p                                                                                                                      2.219   +,c         2.784 +,i
                                                                                                                                [0.202]             [0.321]
          θ                                                         0.337 **
                                                                  [0.147]
       D_Indus                                                                                               -0.564 **                                -1.701 **
                                                                                                            [0.237]                                  [0.805]
    LogL                  -84.78             -288.72               -81.96              -18.15                -80.81             -287.31             -285.42               -15.28              -64.66
    LR test                                                         0.022               0.000
    SBIC                  179.18              587.07               178.36              397.21               176.07              589.05               590.08                37.50              138.35
    Spells                  123                 123                   123                 123                 123                 123                  123                    32                  91

  GVL-criteria
          γ               0.0245 ***           0.0338 ***          0.0033 **            0.0269 **           0.0241 ***          0.0243 ***           0.0263 ***           0.0177 **           0.0263 ***
                        [0.0043]             [0.0073]            [0.0013]             [0.0124]            [0.0042]              [0.042]            [0.0049]             [0.0077]            [0.0049]
          p                1.627 +,d            1.513 +,d           2.931 +,i            2.348 +,i           1.627 +,d            1.621 +,d           1.593 +,d            1.772 +,c           1.593 +,d
                         [0.080]              [0.092]             [0.242]              [0.130]             [0.079]              [0.081]             [0.087]              [0.187]             [0.087]
          ∆p                                                                                                                      0.037               0.179
                                                                                                                                [0.072]             [0.203]
        p+∆p                                                                                                                      1.657 +,d           1.772 +,c
                                                                                                                                [0.094]             [0.184]
          θ                                                         1.062 ***
                                                                  [0.215]
       D_Indus                                                                                                0.056                                   -0.397
                                                                                                            [0.171]                                  [0.469]
    LogL                 -231.73             -667.37              -213.16             -171.29              -231.67              -673.75             -673.47               -47.90             -183.36
    LR test                                                         0.000               0.001
    SBIC                  474.34             1345.62               442.64              777.97               479.67             1353.49              1368.70              103.66               377.10
    Spells                  231                 231                   231                 231                 231                 231                  231                   51                 180

Notes: Estimations for the duration of credit booms considering the Mendoza and Terrones (2008) criteria (first block) and Gourinchas et al. (2001) criteria (second block). Heteroscedasticity
and serial autocorrelation robust standard errors clustered by country are reported in square brackets; ***, **, * - statistically significant at 1%, 5% and 10% level, respectively; â?º indicates that p is
significantly higher than one using a one-sided test with a 5% significance level; d, c, and i indicate decreasing, constant and increasing positive duration dependence, respectively; â–³p is the
estimated difference in the duration dependence parameter between Industrial and Developing countries; p +Δp is the value of the duration dependence parameter for the Industrial countries.
The Schwartz Bayesian Information Criterion (SBIC) is computed as follows: SBIC= 2(-logL+(k/ 2)logN) , where k is the number of regressors and N is the number of observations (spells).
Truncation at the minimum values of Dur is used in the regressions presented in column 2. In column 3, the p-value of the LR test for unobserved heterogeneity/frailty gives assesses if the
estimated variance (θ ) is different from zero. In column 4, the p-value of the LR test analyses the statistical significance of country-specific dummy variables (pooling test), that is, LR=-
2(logL_{r}-logL_{u}) , where r and u correspond to the restricted and unrestricted models, respectively. Columns 8 and 9 present separate regression results for the Industrial and Developing
countries, respectively
  Table 3: Duration dependence in credit booms: basic Weibull with time-effects
 MT-criteria           (1)                (2)                 (3)                (4)                 (5)                (6)                 (7)
         γ               0.0125 *           0.0171 **           0.0137 **          0.0101   ***        0.0097    *        0.0094 *            0.0103 **
                       [0.0067]           [0.0073]            [0.0058]           [0.0039]            [0.0057]           [0.0056]            [0.0044]
            p             2.388 +,i          2.478 +,i           2.450 +,i          2.609   +,i         2.624    +,i       2.624 +,i           2.393 +,i
                        [0.215]            [0.194]             [0.204]            [0.198]             [0.273]            [0.274]             [0.237]
         ∆p                                                                        -0.220   **         -0.241
                                                                                  [0.100]             [0.296]
        p+∆p                                                                        2.389   +,i         2.383    +,i
                                                                                  [0.209]             [0.228]
      D_Indus            -0.576 **           -0.519 **          -0.497 **          -0.489   **         -0.489    **        -0.237             -0.579 **
                        [0.235]             [0.223]            [0.234]            [0.230]             [0.229]             [0.304]            [0.289]
       Event             -0.037
                        [0.179]
       Dec80                                 -0.357
                                            [0.291]
       Dec90                                 -0.774 ***
                                            [0.284]
       Dec00                                 -0.588 **
                                            [0.268]
       D90_10                                                   -0.439 **                                0.046
                                                               [0.203]                                 [0.611]
   LogL                 -80.78              -77.65              -78.46            -283.72             -283.72             -26.04             -51.94
   SBIC                 180.81              184.17             176.17              586.69              591.50              63.30             117.07
   Spells                 123                 123                  123               123                   123                42                 81

 GVL-criteria
         γ               0.0269 ***         0.0387 ***          0.0374 **          0.0177   **         0.0167    ***      0.0152 ***           0.184 ***
                       [0.0056]           [0.0104]            [0.0072]           [0.0033]            [0.0065]           [0.0057]            [0.0039]
            p             1.627 +,d          1.772 +,d           1.756 +,d          2.117   +,c         2.143    +,c       2.167 +,c           1.666 +,d
                        [0.080]            [0.078]             [0.082]            [0.111]             [0.202]            [0.196]             [0.088]
         ∆p                                                                        -0.442   ***        -0.475    **
                                                                                  [0.077]             [0.219]
        p+∆p                                                                        1.675   +,d         1.668    +,d
                                                                                  [0.080]             [0.088]
      D_Indus             0.023               0.112              0.125              0.135               0.136               0.378              0.071
                        [0.176]             [0.168]            [0.164]            [0.161]             [0.161]             [0.265]           [0.0173]
       Event             -0.047
                        [0.175]
       Dec80                                 -0.092
                                            [0.224]
       Dec90                                 -0.876 ***
                                            [0.267]
       Dec00                                 -1.156 ***
                                            [0.246]
       D90_10                                                    -0.962 ***                             0.079
                                                                [0.139]                               [0.434]
   LogL                 -231.41            -214.90             -216.55            -656.48            -656.47              -43.36             -170.60
   SBIC                  484.60             462.46              454.87            1334.74            1340.16               98.85              356.68
   Spells                  231                231                   231              231                  231                 57                174

Notes : See Table 2. △p is the estimated difference in the duration dependence parameter between the pre- and post-1990 periods; hence, p +Δp is the value
of the duration dependence parameter for the the period post-1990; Columns 6 and 7 present separate regression results for the pre- and post-1990
periods, respectively.
  Table 4: Duration dependence in bad credit booms
 MT-criteria          (1)                (2)                (3)                (4)                (5)                (6)
        γ1              0.0156 *           0.0154             0.0108             0.0161             0.1409 ***         0.1853 ***
                      [0.0076]           [0.0096]           [0.0069]           [0.0191]           [0.0098]           [0.0467]
            γ2                                                                                      0.2316 ***         0.3954 ***
                                                                                                  [0.0763]           [0.1142]
            p1           2.086 +,c          2.141 +,c          2.147 +,c          2.272 +,c          2.457 +,c          2.491 +,i
                       [0.235]            [0.313]            [0.254]            [0.515]            [0.280]            [0.276]
         p2                                                                                          1.003              1.118
                                                                                                   [0.253]            [0.340]
         ∆p                                -0.028                                -0.127
                                          [0.443]                               [0.567]
        p+∆p                                2.114 +,c                             2.146 +,c
                                          [0.314]                               [0.270]
        p2-p1                                                                                       -1.454 ***         -1.373 ***
                                                                                                   [0.398]            [0.445]
      D_Indus                              -0.427             -0.464             -0.408                                -0.334
                                          [1.031]            [0.459]            [0.470]                               [0.407]
       Event                                                   0.312
                                                             [0.458]
       D90_10                                                                     -0.134                                -0.306
                                                                                 [1.262]                               [0.370]
   LogL                 -34.15            -108.17             -33.15            -107.68            -106.61            -105.77
   SBIC                  75.83             231.39              81.34             234.17             224.50             234.10
   Spells                   43                 43                 43                  43                43                  43

 GVL-criteria
        γ1              0.0081 **          0.0093 **          0.0091             0.0101             0.1037   ***       0.4141    ***
                      [0.0033]           [0.0047]           [0.0060]           [0.0123]           [0.0072]           [0.0971]
            γ2                                                                                      0.1068   ***       1.2637    *
                                                                                                  [0.0146]           [0.6613]
            p1           2.022 +,c          1.949 +,c          2.033 +,c          2.039 +,c          2.682   +,i        2.686    +,i
                       [0.150]            [0.181]            [0.155]            [0.417]            [0.344]            [0.350]
         p2                                                                                          1.475   +,d        1.505    +,d
                                                                                                   [0.223]            [0.221]
         ∆p                                 0.339                                 0.014
                                          [0.299]                               [0.438]
        p+∆p                                2.288 +,c                             2.053 +,c
                                          [0.239]                               [0.157]
        p2-p1                                                                                       -1.208 ***         -1.181 ***
                                                                                                   [0.445]            [0.450]
      D_Indus                              -0.683              0.147              0.249                                 0.212
                                          [0.773]            [0.374]            [0.357]                               [0.326]
       Event                                                  -0.154
                                                             [0.399]
       D90_10                                                                     -0.404                                -0.287
                                                                                 [1.252]                               [0.392]
   LogL                 -40.72            -144.15             -40.48            -144.01            -141.99            -141.66
   SBIC                  89.23             303.86              96.53             307.48             295.66             302.77
   Spells                   49                 49                 49                  49                49                  49

Notes : See Tables 2 and 3. â–³p is the estimated difference in the duration dependence parameter between industrial and developing countries (column 2)
and the pre- and post-1990 periods (column 4); hence, p+Δp is the value of the duration dependence parameter for industrial and the post-1990 period,
respectively; p2-p1 is the estimated difference in the duration dependence parameters in the model with a change-point.
The change point is located at 10 quaters of duration for both criteria.
  Table 5: Duration dependence in credit booms: basic Weibull with change-points
  MT-criteria           (1)                 (2)                  (3)                 (4)                  (5)                 (6)                 (7)
        𝛾1               0.1513   ***        0.2269   ***         0.2118   ***         0.258   ***        0.2340   **          0.2969   ***        0.7370   ***
                        [0.0052]            [0.0210]             [0.0743]            [0.0357]            [0.0984]             [0.0478]            [0.1291]
        𝛾2                0.181   ***        0.3546   ***         0.4597   *          0.4607   *          0.3800   *           0.3577   **         3.8444
                        [0.0183]            [0.0412]             [0.2431]            [0.2567]            [0.2080]             [0.1439]             [4.120]
        �1                2.833   +,i         2.890   +,i          4.616   +,i         2.662   +,i         2.888   +,i          2.683   +,i         3.026   +,i
                         [0.218]             [0.219]              [0.668]             [0.215]             [0.219]              [0.311]             [0.279]
        �2                1.457   +,d         1.653   +,c          1.867   +,c         1.479               1.628   +,c          2.206   +,c         1.567   +,c
                         [0.232]             [0.277]              [0.387]             [0.373]             [0.278]              [0.436]             [0.313]
     �2 − �1            -1.376   ***        -1.237   ***         -2.743   ***        -1.183   ***        -1.259   ***         -0.477              -1.459   ***
                         [0.306]             [0.337]              [0.795]             [0.422]             [0.334]              [0.547]             [0.430]
       D_Indus                                -0.466   **                                                  -0.459   **          -0.245              -0.533   **
                                             [0.189]                                                      [0.190]              [0.295]             [0.229]
        Dec80                                 -0.327                1.024 **           -0.488
                                             [0.314]              [0.438]             [0.334]
        Dec90                                 -0.618   **          -0.088              -0.598 **
                                             [0.288]              [0.302]             [0.310]
        Dec00                                 -0.567   *            0.267              -0.683 **
                                             [0.292]              [0.384]             [0.320]
       D90_10                                                                                               -0.353 *
                                                                                                           [0.183]
    LogL                 -283.98             -278.77              -70.66              -203.05             -279.22              -92.08              -186.57
    SBIC                  582.41              596.03              165.59               437.68              587.32              202.86               395.10
    Spells                  123                 123                   32                   91                  123                 42                   81

 GVL-criteria
        𝛾1               0.1167   ***        0.1797 ***           0.1168 ***          0.1695   ***        0.1805               0.2300 ***          0.1704   ***
                        [0.0034]            [0.0197]             [0.0216]            [0.0105]            [0.1751]             [0.0368]            [0.0094]
        𝛾2               0.1436   ***        0.3527 ***           0.2433              0.3151   ***        0.3633               0.5584              0.4747   ***
                        [0.0135]             [0.952]             [0.2089]            [0.0740]            [0.7174]             [0.4510]            [0.1588]
        �1                2.346   +,i         2.426 +,i            2.328 +,c           2.388   +,i         2.429 +,i            2.364 +,i           2.002   +,c
                         [0.135]             [0.140]              [0.306]             [0.130]             [0.141]              [0.216]              [0.120
        �2                1.001               1.128                1.008               1.098               1.112                1.145               0.957
                         [0.093]             [0.102]              [0.278]             [0.109]             [0.102]              [0.286]             [0.126]
     �2 − �1            -1.345   ***        -1.297 ***           -1.320 ***          -1.290   ***        -1.317 ***           -1.219 ***          -1.043   ***
                         [0.170]             [0.181]              [0.510]             [0.167]             [0.181]              [0.413]             [0.126]
       D_Indus                                 0.065                                                        0.069                0.321               0.018
                                             [0.140]                                                      [0.139]              [0.277]             [0.155]
        Dec80                                 -0.079               -0.076              -0.080
                                             [0.277]              [0.593]             [0.301]
        Dec90                                 -0.801 ***           -1.588 ***          -0.644 **
                                             [0.296]              [0.543]             [0.330]
        Dec00                                 -0.976 ***           -1.254 ***          -0.966 ***
                                             [0.279]              [0.541]             [0.312]
       D90_10                                                                                               -0.838 ***
                                                                                                           [0.146]
    LogL                -650.35              -637.66             -138.88             -497.31              -638.32              -136.07            -509.91
    SBIC                1317.03              1313.43              305.28             1030.98              1309.30               292.36            1040.46
    Spells                 231                  231                   51                180                    231                  57               174


Notes : See Tables 2 and 3. p 2-p 1 is the estimated difference in the duration dependence parameters. Columns 3 and 4 present separate regression results for
the Industrial and Developing countries, respectively. Columns 6 and 7 present separate regression results for the pre- and post-1990 periods, respectively.
The change-point is located at duration equal to 8 quarters in all regressions considering the MT-criteria. For the GVL-criteria, it is located at duration equal
to 10 quarters, except for the Industrial countries and post-1990 period which is located at 15 quarters of duration.
  Table 6: Robustness checks with different thresholds
                                                MT-criteria                                                                   GVL-criteria
                              𝜑 = 1.5                                 𝜑 = 2.0                            𝜑 = 1.75                                  𝜑 = 2.0
                      (1)                 (2)                 (3)                  (4)              (5)                 (6)                  (7)                  (8)
        𝛾1            0.0223 ***          0.2641    ***        0.0140 *            0.3763    ***     0.0364 ***         0.1785    ***         0.0358 ***          0.1800 **
                     [0.0078]            [0.0269]             [0.0079]            [0.0599]          [0.0095]           [0.0095]              [0.0097]            [0.0199]
        𝛾2                                0.3972    ***                            0.8366    **                         0.3221    ***                             0.3174 ***
                                         [0.0959]                                 [0.3314]                             [0.0701]                                  [0.0786]
        �1              2.330 +,i           2.601   +,i         2.506 +,i            2.968   +,i      1.781 +,d           2.410   +,i          1.767 +,d            2.389 +,i
                       [0.146]             [0.157]             [0.237]              [0.221]          [0.077]             [0.146]              [0.079]              [0.159]
        �2                                  1.683   +,c                              1.720   +,c                          1.193                                     1.216
                                           [0.263]                                  [0.317]                              [0.162]                                   [0.196]
     �2 − �1                              -0.918   ***                             -1.247   ***                         -1.217   ***                              -1.173 ***
                                           [0.313]                                  [0.393]                              [0.199]                                   [0.212]
      D_Indus           -0.475 ***          -0.434   ***        -0.557 **            -0.528   **       0.040              -0.011                0.085                0.044
                       [0.181]             [0.154]             [0.253]              [0.212]          [0.186]             [0.151]              [0.198]              [0.165]
       Dec80            -0.305              -0.274              -0.939               -0.347           -0.033              -0.010               -0.056               -0.039
                       [0.285]             [0.304]             [0.349]              [0.376]          [0.219]             [0.268]              [0.234]              [0.279]
       Dec90            -0.592 **           -0.480   *          -0.740 **            -0.542   *       -0.881 ***          -0.795   ***         -0.883 ***           -0.800 ***
                       [0.261]             [0.264]             [0.352]              [0.308]          [0.273]             [0.300]              [0.264]              [0.288]
       Dec00            -0.485 **           -0.464   *          -0.471 **            -0.448   *       -1.174 ***          -1.008   ***         -1.145 ***           -0.983 ***
                       [0.246]             [0.262]             [0.230]              [0.255]          [0.244]             [0.274]              [0.248]              [0.276]
   LogL               -109.24             -360.20               -57.48             -211.36          -193.95             -583.03              -179.82              -542.22
   SBIC                248.81              755.78              142.09               454.38           419.95            1208.81                391.14             1121.21
   Spells                  157                 157                  92                   92              209                 209                  191                  191


Notes : See Tables 2, 3 and 4. Odd columns report the results from the basic Weibull model estimation, while even columns show the results from the Weibull model
with a change-point; the change-point is located at duration equal to 8 and 10 quarters for the MT-criteria and GVL-criteria, respectively.
    List of Figures



    Figure 1. Survivor functions for credit booms according to criteria, groups and periods.
                                            MT-criteria
                                                               All countries                                                                                        Industrial countries                                                                                Developing countries
            1




                                                                                                                                                                                                                          1
                                                                                                                  1
                    .75




                                                                                                                                                                                                                                  .75
                                                                                                                          .75
Proportion Surviving




                                                                                                                                                                                                              Proportion Surviving
                                                                                                      Proportion Surviving
         .5




                                                                                                                                                                                                                       .5
                                                                                                               .5
            .25




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                                                                                                                  .25
            0




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                                                                                                                  0


                           0   1   2       3   4   5    6   7 8 9 10 11 12 13 14 15 16 17 18 19 20                                 0   1   2       3   4   5    6   7 8 9 10 11 12 13 14 15 16 17 18 19 20                                 0   1   2       3   4   5    6    7 8 9 10 11 12 13 14 15 16 17 18 19 20
                                                            Duration of credit booms                                                                                Duration of credit booms                                                                                 Duration of credit booms




                                                                                                                                                                     Pre-1990 period                                                                                         Post-1990 period
                                                                                                                     1




                                                                                                                                                                                                                           1
                                                                                                                             .75




                                                                                                                                                                                                                                   .75
                                                                                                         Proportion Surviving




                                                                                                                                                                                                               Proportion Surviving
                                                                                                                  .5




                                                                                                                                                                                                                        .5
                                                                                                                     .25




                                                                                                                                                                                                                           .25
                                                                                                                     0




                                                                                                                                                                                                                           0
                                                                                                                                   0   1   2       3   4   5    6   7 8 9 10 11 12 13 14 15 16 17 18 19 20                                 0   1   2       3   4   5    6    7 8 9 10 11 12 13 14 15 16 17 18 19 20
                                                                                                                                                                    Duration of credit booms                                                                                 Duration of credit booms




                                                                                                                                                       GVL-criteria
                                                               All countries                                                                                        Industrial countries                                                                                    Developing countries
             1




                                                                                                                     1




                                                                                                                                                                                                                             1       .75
                     .75




                                                                                                                             .75




                                                                                                                                                                                                                 Proportion Surviving
 Proportion Surviving




                                                                                                         Proportion Surviving




                                                                                                                                                                                                                          .5
          .5




                                                                                                                  .5




                                                                                                                                                                                                                             .25
             .25




                                                                                                                     .25




                                                                                                                                                                                                                             0
             0




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                           0           5           10        15        20        25    30   35   40                                0           5           10        15        20        25    30   35   40                                0           5           10         15        20        25    30   35   40
                                                            Duration of credit booms                                                                                Duration of credit booms                                                                                 Duration of credit booms




                                                                                                                                                                     Pre-1990 period                                                                                         Post-1990 period
                                                                                                                     1




                                                                                                                                                                                                                             1
                                                                                                                             .75




                                                                                                                                                                                                                                     .75
                                                                                                         Proportion Surviving




                                                                                                                                                                                                                 Proportion Surviving
                                                                                                                  .5




                                                                                                                                                                                                                          .5
                                                                                                                     .25




                                                                                                                                                                                                                             .25
                                                                                                                     0




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                                                                                                                                   0           5           10        15        20        25    30   35   40                                0           5           10         15        20        25    30   35   40
                                                                                                                                                                    Duration of credit booms                                                                                 Duration of credit booms