Current Account Sustainability in Latin America Considering Nonlinearities

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Current Account Sustainability
in Latin America Considering
Nonlinearities
Por: Daniel Ordoñez-Callamand,
Luis F. Melo-Velandia,
Oscar M. Valencia-Arana
Núm. 987
2017

Current Account Sustainability in Latin America
Considering Nonlinearities∗
Daniel Ordo˜nez-Callamand†Luis F. Melo-Velandia‡
Oscar M. Valencia-Arana§
Abstract
We test current account sustainability based on the framework developed
by Hakkio and Rush [1991] and Husted [1992] using a two-regime threshold
vector error correction model. This methodology allows us to characterize
short-run nonlinearities in the current account. We estimate the model for
four Latin American economies: Chile, Brazil, Colombia, and Mexico. We
find a long-run relationship between the current account components, which
implies strong sustainability for Chile and Mexico and weak sustainability for
Colombia and Brazil. For the first two countries, the predominant regime
is associated with a current account surplus. In contrast, for Colombia and
Brazil, the prevailing regime corresponds to a situation in which there is a long-
run deficit. In general, the impulse response analysis shows that expenditure
and income shocks have positive and significant responses in the predominant
regime for both series.
Keywords. Threshold vector error correction; current account sustainability;
generalized impulse response function.
JEL Classification. C32, C52, F32.
∗The opinions expressed here are those of the authors and do not necessarily represent those of
the Banco de la Rep´ublica or those of its Board of Directors. The usual disclaimers apply.
†Research Assistant at Banco de la Rep´ublica (Central Bank of Colombia), email: ordonez-
d@javeriana.edu.co
‡Senior Econometrician at Banco de la Rep´ublica (Central Bank of Colombia), email:
lmelovel@banrep.gov.co
§Junior Research Economist at Banco de la Rep´ublica (Central Bank of Colombia), email: ovale-
nar@banrep.gov.co
1

1 Introduction
One of the policy makers’ main concerns is the magnitude and persistence of current
account deficits. In particular, it is important to know the level of sustainability of
the current account and its macroeconomic implications.
This study analyzes the sustainability of the current account in four Latin Amer-
ican countries under a nonlinear model. Latin American economies have been char-
acterized by an export orientation and high vulnerability to external shocks. The
dynamics of the current account of these countries show deficits of considerable and
persistent magnitudes. Moreover, these economies have experienced current account
reversals that caused large contractions in GDP and important macroeconomic ad-
justments.
Current account sustainability is also fundamental to understanding the effects
of recent drops in commodity prices. In most Latin American countries, this shock
led to a contagion effect on the economies in countries exporting such commodities.
There are two important implications to highlight: first, a contraction in external
revenues due to a fall in prices; and second, a drop in the trade-flow between these
countries. Both implications led to abrupt changes in relative prices (real deprecia-
tion) that were not reflected in significant improvements in the trade balance. On
the contrary, current account deficits became persistent or adjusted slowly at the
cost of lower economic growth.
In this study, we use a two-regime threshold vector error correction (TVEC) to
model the current account sustainability. We base the model on the notion of linear
cointegration with short-run nonlinearities. To the best of our knowledge, we are the
first to study the nonlinear sustainability of the current account from a multivariate
point of view. We estimate the model for four Latin American countries: Colombia,
Chile, Mexico, and Brazil.
The results show that the current account for Chile and Mexico is sustainable in
the strong sense between 1996 and 2016. For Colombia and Brazil, we find a long-
run relationship between income and expenditure of the current account for 1996
to 2015. However, this result suggests a long-run deficit that is consistent with the
notion of weak sustainability [Quintos, 1995].
TVEC estimation yields a predominant and non-predominant regime for each
2

country. Chile and Mexico’s non-predominant regimes are characterized by periods
in which expenditure exceeds income. These regimes are infrequent and of short
durations. Meanwhile, in Brazil and Colombia, the non-predominant regimes are
associated with periods where income is greater or very close to expenditure. Inter-
estingly in the case of Brazil, the non-predominant regimes remain for long periods
of time.1
The rest of the paper proceeds as follows. Section two presents a review of dif-
ferent methodologies to evaluate current account sustainability along with the theo-
retical model. Section three presents the empirical methodology. In section four, we
present the empirical results, and section five concludes.
2 Theoretical framework
2.1 Methodological Review
From a methodological perspective, researchers use two types of frameworks to eval-
uate current account sustainability. The first is accounting in the current account.
Under this approach, the current account is sustainable if the ratio of net external
assets as a percentage of GDP is stable or decreasing over time. Some approaches in
this vein consider the valuation effects of changes in the asset prices of international
portfolios and their effects on the current account dynamics, see for example Lane
and Milesi-Ferretti [2012] and Gourinchas and Rey [2007].
The second set of approximations are empirical and use both linear and nonlin-
ear models. The linear category includes univariate models as proposed by Trehan
and Walsh [1991] and Husted [1992]. They test whether the current account as a
percentage of GNP has a unit root. In this sense, the current account as percentage
of GNP is sustainable if the series is integrated of order zero. A disadvantage of this
methodology is that it assumes that the current account income and expenditure are
cointegrated with a cointegration vector given by (1,−1). We use a methodology
that does not impose the latter restriction.
1We define the non-predominant regime in line with unstable processes as those were the modulus
of the maximum eigenvalue of the companion matrix in the model (11) is greater than 1. Altissimo
and Violante [2001] provide a further discussion of ergodicity and stability in threshold models.
3

From the multivariate point of view, vector error correction models (VEC) of
current account income and expenditure are useful to explain the notion of sus-
tainability. Nevertheless, the dynamics of spreads, risk perceptions, and portfolio
decisions could be the most important determinants of nonlinearities in the current
account. An important aspect of assuming nonlinearities is that even if the current
account sustainability condition is fulfilled in the long term, persistent short-run
deficits can still compromise future sustainability [Raybaudi et al., 2004].
Nonlinearities are important from the policy making perspective because they
might change the characterization of current account sustainability. For example,
Chortareas et al. [2004] find statistical evidence suggesting external debt sustainabil-
ity in Latin American countries under nonlinear models despite the fact that most
traditional linear tests suggest the opposite.2
2.2 Theoretical Model
To evaluate current account sustainability, we test the intertemporal budget con-
straint following Hakkio and Rush [1991] and Husted [1992]. Recent empirical ap-
plications include that by ¨
Onel and Utkulu [2006], among others.
The framework is based on the intertemporal model of consumption. In particu-
lar, we assume an infinitely lived sovereign planner capable of borrowing and lending
in international markets using one-period financial instruments. The objective of the
central planner is to maximize the discounted sum of expected social utility subject
to the intertemporal constraint
max
{Ct,Bt}∞
t=0
E0
∞
X
t=0
βt[U(Ct)]
Yt+Bt=Ct+ (1 + rt)Bt−1,(1)
where Ctrepresents consumption, Btdenotes international borrowing, Ytis output,
rtis the one-period world interest rate, and (1 + rt)Bt−1represents the country’s
foreign debt.
2As Pippenger and Goering [2000] suggest, unit root and cointegration tests under threshold
processes have low power against nonlinear alternatives.
4

For simplicity, we assume an endowment economy with no investment. The
central planner chooses the paths of consumption Ctand international borrowing Bt
to maximize the present value of the expected utility. The Euler equation entails
Et
U(Ct)
U(Ct+1)=βEt(1 + rt+1) (2)
Since Yt−Ct=Xs
t−Mt, we can express the budget constraint in terms of the
trade balance as:
Bt+Xs
t=Mt+ (1 + rt)Bt−1(3)
Where Xs
tdenotes exports and Mtimports. Assuming rtis stationary around
a mean rwith r > 0, we can add and subtract rBt−1on the right hand side of
equation (3) and introduce the auxiliary variable Ft≡Mt+ (rt−r)Bt−1, which
represents deviations of the interest rate from its unconditional mean. Then, the
budget constraint can be rewritten as
Bt+Xs
t=Ft+ (1 + r)Bt−1(4)
Furthermore, assuming that Xs
tand Ftfollow random walks with drift 4Xs
t=
η1+ε1,t and 4Ft=η2+ε2,t, where ε1,t , ε2,t are independent white noise processes.
The first difference of equation (4) entails
4Bt+4Xs
t=4Ft+ (1 + r)4Bt−1(5)
Using forward-looking integration to solve for 4Bt, we have:
4Bt=
T
X
j=1 "1
1 + rj
4Xs
t+j− 4Ft+j#+1
1 + rT
4Bt+T(6)
Taking the limit as T→ ∞ and noting that both components (Xs
t, Ft) are random
walks, the changes in the foreign assets can be expressed as follows:
4Bt= (η1−η2)
∞
X
j=1 1
1 + rj
+

∞
X
j=1 1
1 + rj
(ε1,t+j−ε2,t+j)
+ lim
T→∞ 1
1 + rT
4Bt+T(7)
Using the convergence criteria for a geometric series, the term P∞
j=1 1
1+rjcon-
verges to 1
r. Therefore, the current account can be expressed as
5

4Bt=a+et+ lim
T→∞ 1
1 + rT
4Bt+T,(8)
where a=(η1−η2)
rand et=hP∞
j=1 1
1+rj(ε1,t+j−ε2,t+j)i.
Given that etis I(0) and assuming the limit term in (8) is equal to 0, if the
current account, ∆Bt, is I(0), the intertemporal budget constraint holds.
Current Account Sustainability Test
In practice, the current account can be expressed in terms of net exports and interest
rate payments by replacing equation (3) in (8) and assuming that the limit term is
zero:
∆Bt=MMt−Xs
t,(9)
where MMt≡Mt+rtBt−1and we assume that the series of exports Xs
tis I(1).
A necessary condition to show that ∆Btis I(0) is that Xs
tand MMtare jointly
CI (1,1) with cointegrating vector (1,−1). We can test the latter condition by
evaluating β= 1 in the following regression in a cointegration framework
MMt−βXs
t=a∗+e∗
t(10)
If there is no cointegration between Xs
tand MMt, the intertemporal budget con-
straint is not satisfied. On the other hand, if both series are cointegrated and β= 1,
then the current account is sustainable in strong sense. Finally, if the series are
cointegrated and β6= 1, the current account is sustainable in a weak sense.3
As Hakkio and Rush [1991] point out, weak sustainability is consistent with the
intertemporal budget constraint (solvency condition). However, in this case the
undiscounted value of debt grows to infinity and the incentive for the government to
default increases.
3 Empirical Methodology
Hansen and Seo [2002] first proposed the estimation for threshold vector error correc-
tion (TVEC) models using the maximum likelihood method. However, the properties
3Note that we normalize the coefficient of imports plus interest rate payments in equation (10).
Hence, our criteria for weak sustainability is the inverse of that proposed by Quintos [1995].
6

of the estimators of the model were not established. Alternatively, Seo [2011] pro-
posed the smoothed least squares estimation method (SLS) for TVEC models and
developed the asymptotic theory for both the least squares (LS) and the SLS method.
We adopt the latter estimation method.
Let xtbe a k-dimensional I(1) vector of a series that is cointegrated with a nor-
malized cointegrating vector α= (1, β0)0; then, the corresponding error correction
term can be written as zt(β) = x0
tα.
We can express the two-regime TVEC model as
∆xt=A0
1Xt−1(β) + A0
2Xt−1(β)I(zt−1(β)> γ) + t∀t∈[p+ 1, T ],(11)
where Xt−1(β)≡(1, zt−1(β),∆0
t−p)0with ∆t−pdenoting the vector of the lagged
difference terms (∆x0
t−1,∆x0
t−2, ..., ∆x0
t−p)0,A1and A2are (2 + kp)×kmatrices of
coefficients, γis the threshold parameter, I(·) represents the usual indicator function,
and tis an i.i.d sequence with E(t) = 0 and E(t0
t) = Σa positive definite matrix.
Considering all available observations, we can rewrite the full model in (11)
y= [(X(β), Xγ(β)) ⊗Ik]λ+, (12)
where stacks t,X(β) is the matrix that stacks Xt−1(β), and Xγ(β) stacks
Xt−1(β)I(zt−1(β)> γ), ystacks ∆xt,λis equal to vec((A0
1, A0
2)0), and vec is the
operator that stacks the columns of a matrix.
We can obtain the SLS estimator by replacing I(zt(β)> γ) with a function
κ(st(β, γ )), where st(β, γ) is given by st(β, γ) = zt(β)−γ
hand h→0 as T→ ∞.
Furthermore, the function κ(·) must satisfy
lim
n→−∞ κ(n) = 0,lim
n→∞ κ(n)=1
In addition to the last two conditions, the function κ(·) must also fulfill certain
technical requirements, such as those imposed in Seo and Linton [2007].
We obtain the smoothed model by replacing Xγ(β) with Xγ(β)∗in (12), where
the latter is the matrix that stacks Xt−1(β)κ(st−1(β, γ)). Then, the SLS estimator
is defined as
Argmin
θ∈Θ
ST(θ) where ST(θ) := (y−[(X(β), Xγ(β)∗)⊗Ik]λ)0(y−[(X(β), Xγ(β)∗)⊗Ik]λ),
7

where θ= (β0, γ, λ0)0and Θis a compact parameter space.
Hansen and Seo [2002] solve the previous optimization problem in two stages. In
the first stage, they consider a grid search for the parameters (β0, γ).4In the second
stage, given this parameters, we can obtain the estimator of λusing LS.
Under some assumptions, Seo [2011] shows that the asymptotic distribution of
the SLS estimator is
T h−1
2(ˆ
β−β)
T1
2h−1
2(ˆγ−γ)⇒σv
σ2
q 1
0BB01
0B
1
0B01!−1BdW
W(1) 
√T(ˆ
λ−λ)⇒N 0,E 1It−1
It−1It−1⊗Xt−1X0
t−1−1
⊗Σ!,
(13)
where Tis the sample size, ⇒denotes convergence in distribution, Wdenotes a
standard Brownian motion, and the last k−1 components of x[T s]
√Ts∈[0,1] converge
to a Brownian motion vector Bwith covariance matrix Ω. On the other hand, ˆσ2
v
and ˆσ2
qare given by
ˆσ2
v=1
TX
t 1
2√hXt−1(ˆ
β)0A2
dκ(st−1(ˆ
β, ˆγ))
dst−1
ˆt!2
ˆσ2
q=h
2TQT kk (ˆ
θ),
(14)
where QT kk is the diagonal element associated with γof the Hessian matrix
QT(θ) = ∂2ST(θ)
T ∂θ∂ θ0.
Note that the asymptotic distribution of (β0, γ) depends on the smoothing pa-
rameter h, which has to fulfill certain assumptions.5We use h= ˆσEcT−1
2log Tas
in Wang et al. [2016] and Seo [2011]. Furthermore, we must also consider that the
vectors ( ˆ
β0,ˆγ)0and ˆ
λ0are asymptotically independent, so constructing the confidence
intervals for the parameters in ˆ
λis straightforward.
4The grid for β0can be centered around a preliminary estimate, such as that obtained from a
linear VEC model.
5See Seo [2011].
8

4 Empirical Results
4.1 Data
Our data covers the period between the first quarter of 1996 through the second
quarter of 2016 for Chile and Mexico, and until the last quarter and the third quar-
ter of 2015, for Colombia and Brazil, respectively.
Following Herzberg [2005], we consider the current account components directly
to test for sustainability. This disaggregation has been fundamental in explaining
the current account dynamics in Latin American countries because factor income
and remittances serve as buffers for export fluctuations.
We construct the current account income and expenditure for each country by
considering the sum of goods and services, primary and secondary income records
of the current account, including debit and credit records, respectively. Income and
expenditure are measured as a percentage of GDP.6 7
4.2 Results
Our modeling strategy consists of five steps. In the first step, we test for the presence
of unit roots in the series of current account income and expenditure. The second
step is to test the existence of a cointegration relationship between the aforemen-
tioned series. In the third, step we perform a test to choose between a TVEC model
and the usual VEC model. Then, we estimate the TVEC model and we show an
analysis of the model residuals in the fourth step. Finally, we compute the general-
6We consider GDP instead of GNP since the total production that occurs outside the countries’
borders is not significant. On average, the ratio between GNP/GDP is around 94% for Colombia,
93% for Brazil, 95% for Mexico, and 93% for Chile during 1996 −2015.
7The series that we use in the empirical exercise are not exactly the same implied by the theoret-
ical framework. However, the exports and imports of goods and services are accounted in primary
income (credit and debit). Moreover, interest payments are part of the current account records. In
addition, exports and imports plus interest payments represent a high percentage of current account
income and expenditure, respectively. More precisely, exports represent between 77% and 97% of
the current account income, while imports plus interest payments represent between 63% and 99%
of the expenditure through all quarters. On average, they represent 84% and 89% for Colombia,
90% and 83% for Chile, 90% and 85% for Mexico, and 93% and 79% for Brazil. Considering these
characteristics, the current account series that we use in the empirical exercise are consistent with
the theoretical framework developed in section 2
9

ized impulse response function (GIRF) of the nonlinear model as the last step.8
We begin our analysis by testing for the presence of unit roots in the series of
current account income and expenditure for each country. For this purpose, in Table
1, we report the results for the variance ratio statistic proposed in Breitung [2002].
The null hypothesis of the test is that the series has a unit root, while the alternative
implies that the series is stationary.
Table 1: Breitung [2002] Unit Root Tests
Chile Mexico Colombia Brazil
Expenditure 0.047 0.075 0.061 0.030
Income 0.043 0.083 0.037 0.028
Authors’ calculations. *, **, and *** indicate significance at
the 10%, 5 %, and 1% levels, respectively. H0:ytis I(1)
Ha:ytis I(0).
Second, we conduct a test to confirm the existence of a cointegration relationship
between current account income and expenditure. In Table 2, we present the results
of two rank tests used to examine cointegration as proposed by Breitung [2001]. We
correct both a Kolmogorov-Smirnov type (κ∗statistic) and a Cramer-Von Mises type
(∗statistic) to account for the correlation between the two series, as in Breitung
[2001]. These tests are considered over the traditional cointegration tests following
the results of Pippenger and Goering [2000], who showed that the latter have low
power under threshold processes. The null hypothesis of the test is that the series
under consideration are not cointegrated. Based on our results, we find statistical
evidence to reject the null hypothesis of no cointegration in all cases at traditional
levels of significance.
8It is worth noting that each step assumes that the previous step has a certain result. For
example, the cointegration step requires that the series are non-stationary.
10

Table 2: Breitung [2001] Cointegration Tests
κ∗-Statistic ∗-Statistic
Chile 0.201∗∗∗ 0.006∗∗∗
Mexico 0.266∗∗∗ 0.005∗∗∗
Colombia 0.222∗∗∗ 0.008∗∗∗
Brazil 0.223∗∗∗ 0.009∗∗∗
Authors’ calculations. *, **, and *** indicate
significance at the 10%, 5 %, and 1% levels,
respectively. H0:x1, x2are not cointegrated
Ha:x1, x2are cointegrated.
Third, we compute the Hansen and Seo [2002] two-regime threshold cointegration
test in VEC models. Under the null hypothesis, we can approximate the data gener-
ating process by a linear VEC model, while we consider a two-regime TVEC model
under the alternative. Given the results in Table 3, we reject the null hypothesis of
a linear VEC model at the 5% level of significance in all cases.
Table 3: Hansen Test Results for TVEC Models
Chile Mexico Colombia Brazil
Statistic 32.39 34.29 33.02 35.28
P-value 0.00 0.03 0.01 0.03
Authors’ calculations. P-values calculated using a resid-
ual based bootstrap method. H0:V EC Ha: two-regime
T V E C.
The results of the Hansen and Seo [2002] test confirm the presence of nonlin-
earities in the VEC representation of the cointegration relationships in each of the
countries. For this reason, we conduct the estimation for the TVEC model described
in section 3.
11

Table 4: Estimation Results for the Cointegrating Coefficients
Chile Colombia Mexico Brazil
β1.026 1.178 1.069 1.232
St Dev 0.011 0.033 0.040 0.023
Authors’ calculations. St Dev denotes the standard
deviation.
Table 4 presents the estimation results for the cointegrating coefficients of the
TVEC models.9This implies a long-run relationship between current account in-
come and expenditure in all countries. In these cases, the current account is sus-
tainable. In particular, there is strong sustainability for Chile and Mexico since the
null hypothesis that β= 1 cannot be rejected at the 1% significance level. On the
other hand, there is weak sustainability in Colombia and Brazil since this hypothesis
is rejected.
To evaluate the proposed models, we consider several diagnostic tools, including
the multivariate portmanteau and normality tests suggested in L¨utkepohl [2005], as
well as the multivariate autoregressive conditional heteroskedasticity (ARCH) tests
in Tsay [2014]. On the other hand, to evaluate the stability of the models, we re-
port the maximum eigenvalues of the companion matrix for both regimes of the
TVEC models. Additionally, we evaluate the remaining nonlinearity in the residu-
als using the [Broock et al., 1996] (BDS) test. We report the results of these tests
in Appendix B, which shows no evidence of misspecification in the estimated models.
In Figure 1, we present the current account income and expenditure dynamics for
Chile, Mexico, Colombia, and Brazil. Both series are measured as a percentage of
GDP. Additionally, we show the estimated error correction term (EC) and threshold
(ˆγ). We define the EC as (Expendituret−ˆ
βI ncomet). The threshold determines
the transition between regimes (predominant and non-predominant).10
For Chile and Mexico, the predominant regimes are periods where the EC is below
the threshold. On the other hand, for Colombia and Brazil, the predominant regimes
occur when the EC exceeds the threshold. The periods of the non-predominant
regime are plotted in grey areas.
9Appendix A presents the threshold parameters and the short-run coefficient matrices.
10We report ˆ
βand ˆγin Table 4 and Table 5 of Appendix A, respectively.
12

Figure 1: Error Correction Dynamics
●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●●
−0.1 0.0 0.1 0.2 0.3 0.4 0.5
Error Correction−Chile
96/01 98/10 01/07 04/04 07/01 09/10 12/07 15/04
0.00 0.02 0.04 0.06 0.08 0.10
Error Correction−Mexico
96/01 98/10 01/07 04/04 07/01 09/10 12/07 15/04
−0.05 0.00 0.05 0.10 0.15 0.20 0.25
Error Correction−Colombia
96/01 98/10 01/07 04/04 07/01 09/10 12/07 15/04
−0.05 0.00 0.05 0.10 0.15
Error Correction−Brazil
96/01 98/10 01/07 04/04 07/01 09/10 12/07 15/04
Expenditure Income ECT Threshold Non−predominant Regime
The model equation is described in (11), ECT denotes the error correction term x0
tˆα, threshold denotes ˆγ, the
non-predominant regimes are those where the modulus of the maximum eigenvalue of the companion matrix is
greater than 1.
13

4.2.1 Chile
Chile’s current account has remained in balance for most of the years in the sample,
as in the top-left panel of Figure 1. This is partly due to the fact that the levels of
public sector external indebtedness have been relatively low through the last 20 years.
The Chilean economy is characterized by high imports of hydrocarbons and cop-
per exports. The behavior of the current account from 2004 onwards can be explained
by positive shocks to the terms of trade due to an increase in international copper
prices. Figure 1 suggests that this shock temporarily reversed during the financial
crisis of 2007-2008, but was offset by the subsequent fall in oil prices.
The terms of trade remained high until 2011, when they began a gradual decline
that persists until today. The latter effect is associated with the reduction of global
demand (mainly in China), along with the reduction in the quality of copper exports.
The TVEC model identifies the non-predominant regime when the error correc-
tion term is above the threshold. For the Chilean economy, the non-predominant
regime is associated with periods in which current account expenditure exceeds cur-
rent account income. These periods were frequent and of short duration in the late
1990s, during which Chile had large capital inflows (1996-1997) that generated cur-
rent account deficits. They were followed by contractionary monetary policies, low
domestic liquidity, and a reduction in the terms of trade that put more pressure on
the current account. On the other hand, the gradual decline in the international price
of copper along with the increase in mining investments and strong growth in private
domestic demand explain the other non-predominant periods during 2012-2013.
4.2.2 Mexico
The evolution of current account expenditure and income for the Mexican economy
appears in the top-right panel of Figure 1. We can analyze the dynamics of the
external expenditures by accounting for the changes in consumption and investment
explained by shocks to the terms of trade. These shocks are highly associated with
oil production and exports along with the trade balance with the U.S.
Similar to Chile, the non-predominant regime in Mexico is related to periods
where current account expenditure exceeds income. These periods occurred in the
late 1990s and coincided with a contraction in the U.S. economy, stagnant non-oil
14

exports, and weaker domestic demand. The current account deficit in the late 1990s
was financed mostly by foreign direct investment (FDI), primarily in financial sector
investments. More recently, a fall in the international price of oil partly explains the
brief non-prevalent period during 2015-2016.
4.2.3 Colombia
The lower-left panel in Figure 1 shows the evolution in current account expenditure
and income for Colombia. Unlike Chile and Mexico, the Colombian current account
deficit has been historically persistent. This is reflected in the estimation results for
the cointegration vector in Table 4, which suggest a long-run deficit. In this case, the
non-predominant regime corresponds to periods where the current account income
and expenditure were very close.
Colombia accumulated imbalances in the external sector in the second half of the
1990s. This led to an economic adjustment between the end of the 1990s and the be-
ginning of the 2000s. Following the adjustment, Colombia experienced an economic
downfall and a temporary current account surplus. The other periods of the non-
predominant regime observed during 2004-2005 are associated with improvements in
the terms of trade, mainly from higher external demand in Venezuela.
Finally, the price of oil declined significantly in 2014. This led to a persistent
negative shock to the terms of trade, which explains the increase in the current ac-
count deficit from then onward.
4.2.4 Brazil
The lower-right panel of Figure 1 shows the dynamics of Brazil’s current account.
We can explain the dynamics by considering three historical phases.
The first phase begins in 1995 with the implementation of the ”Real Plan” and
ends in 2002. During this period, the current account deficits increased and reached
a maximum of 4.32% of GDP in 2002. The second phase occurred from 2004 to 2010
and was characterized by economic policies aimed to expand the domestic market
and improve international trade conditions. This is reflected in current account sur-
pluses since there were increases in commodity prices and in the export volume to
15

South American trading partners.
The third phase covers the period between 2010 and 2015 and is characterized by
persistent current account deficits. This occurred for two reasons. First, a decline in
the international trade of manufactured goods in response to the 2008 international
financial crisis; second, a sharp increase in domestic demand generated by favorable
terms of trade conditions in the previous years.
The estimated model suggests a non-predominant regime in the second phase.
This regime was characterized by a surplus or balance in the current account. Similar
to the case of Colombia, we found statistical evidence of a long-run deficit.
4.3 Generalized impulse response function
In this section, we evaluate the response of current account income and expendi-
ture to a shock in both series by conducting a generalized impulse response function
(GIRF) analysis as proposed by Koop et al. [1996]. The advantage of the GIRF over
the traditional impulse response function is that it accounts for nonlinear dynamics
and allows for asymmetries related to the shock size and the shock sign, as well as
different behaviors depending on when the shock occurs.
For a given horizon (h), a given shock size (δ), and a given history (ω), the GIRF
is defined as
GI RF (h, δ, ω) := E[yt+h|δ, ω]−E[yt+h|ω] (15)
We can interpret the expectations of the equation above as the optimal forecasts
of yt+hat time twith and without a shock of size δ. For nonlinear models, we can
calculate these expectations as in Granger and Ter¨asvirta [1993].
In our empirical exercise, the estimated GIRF includes all observations in the
sample as histories. We also considered the following set of shocks: nδi
σio, where σi
is the standard deviation of the i−th residual series taken from an evenly spaced grid
between [−3,3] with grid distance of 0.1, i=expenditure,income. We calculate the
expectations in equation (15) using Monte Carlo methods, assuming normal distri-
bution for all countries except Brazil. In this case, we employed bootstrap methods
considering the non-normality of the residuals.11
11 Table 10 reports the results of the normality tests.
16

The GIRF distribution can show multimodal behaviors in nonlinear models. We
therefore considered high density regions (HDR), as proposed by Hyndman [1995].12
We evaluate the response of current account income and expenditure to positive
shocks between 1 and 3 standard deviations. We compute the GIRF for each country
for predominant and non-predominant regimes and report the results in Appendix C.
In each figure, the horizontal and vertical axes represent the time horizon and the
magnitude of the response, respectively. The responses are given as a percentage
of GDP. We considered 95% (light grey) and 90% (dark grey) regions for the HDR
boxplots of the GIRF. The black points outside the boxes identify outliers.
4.3.1 Chile
In general, the response to both shocks is positive and statistically significant as
Figure 2 and Figure 3 of Appendix C show. Moreover, the magnitude of the re-
sponse is very similar in both the predominant and non-predominant regimes. In
particular, for current account expenditure shocks, the magnitude of the responses
in both series stabilizes around 2% in 5 years. However, the responses in income and
expenditure to an income shock are slightly higher (3%) and have greater uncertainty.
Overall, the results suggest a short-term reversal from deficit (non-predominant
regime) to surplus periods (predominant regime). A possible explanation is the coun-
tercyclical economic policy in the Chilean economy. This allows for macroeconomic
buffers that soften the business cycle.
4.3.2 Mexico
We find that the responses to current account expenditure shocks are asymmetri-
cal and statistically significant when these shocks occur in the predominant regime
(Figure 4 of Appendix C). On the other hand, with respect to income shocks, the
response in both series is positive and significant. The responses to both shocks are
similar (less than 1%) in magnitude.
12HDR are such that for a given confidence level α, the probability that the random variable
falls within the region is greater than 1 −α. Furthermore, HDR satisfy two properties: first, given
a confidence level, the region occupies the smallest possible volume in the sample space. Second,
every point inside the region has a density at least as large as every point outside the region.
17

Conditioning over the non-predominant regime (Figure 5 of Appendix C), we find
that the responses of expenditure and income to expenditure shocks are not signif-
icant and show multimodal behavior after 3 years. The responses of both series to
income shocks are again not significant.
4.3.3 Colombia
As Figure 7 of Appendix C shows, the response to an expenditure shock in periods of
current account deficits (predominant regime) is positive and statistically significant
for both income and expenditure. The magnitude varies between 3% and 1%.
Furthermore, the responses to income shocks in the predominant regimes are
significant at 10%. The expenditure responses are slightly smaller than income re-
sponses. The latter is uplifting since this might suggest that income shocks can
generate pressure on the balance in current account deficit scenarios.
Moreover, the results in Figure 6 of Appendix C indicate that the responses to
both shocks are only statistically significant in the first period after the shock during
a current account surplus (or balance).
4.3.4 Brazil
For Brazil, we find that an expenditure shock has a positive effect on both series
in current account deficit periods (predominant regime), as Figure 9 of Appendix C
shows. In this case, the magnitude of the response for both current account compo-
nents ranges from 1 to 3% over a 5-year horizon.
However, unlike the other countries, the responses of income and expenditure
to an income shock are not statistically significant. Furthermore, as Figure 8 of
Appendix C shows, the responses of both series to expenditure shocks are only sig-
nificant up to the third year in periods of surplus (or balance). In the case of an
income shock, the responses in both series are positive but only significant one or
two periods after the shock.
18

4.4 Brief summary of GIRF results
In the case of Chile and Mexico, the predominant regime is characterized by a cur-
rent account surplus, while for Colombia and Brazil, this regime is characterized
by a current account deficit. Moreover, when the current account expenditure and
income shocks occur in the predominant regime, the response of the current account
components is positive, significant, and permanent for Chile, Colombia, and Mexico.
In Brazil, we find that the response to income shocks is not statistically significant.
The magnitude of these responses varies between 5% and 1% of GDP, except for
Mexico, whose response is less than 1% of GDP.
On the other hand, the response to income and expenditure shocks in the non-
predominant regime is not statistically significant in Mexico and Colombia. In Chile,
the response to these shocks is almost equal to the response when the shock occurs
in the predominant regime. For Brazil, the response is temporal and only significant
for expenditure shocks.
5 Concluding remarks
In this study, we examine current account sustainability in a nonlinear framework by
estimating a two-regime TVEC model for Chile, Colombia, Mexico, and Brazil. We
find a long-run relationship between the current account components, which suggests
strong sustainability for Chile and Mexico and weak sustainability for Colombia and
Brazil.
In this context, strong and weak sustainability imply that the current account
components have a common trend. In the strong case, a unit shock in expenditures
is followed by an equivalent response in income in the long run. However, in the weak
case, the response has a different magnitude. For Colombia and Brazil, we find that
this response is less than one. Therefore, if expenditure increases by 1%, income will
increase by less than 1% in the long term. Then, despite the long-run relationship
between the current account components, the economy accumulates external imbal-
ances over time.
The results of the model also indicate that the first regime is associated with
current account surplus periods while the second is associated with current account
deficits. For Chile and Mexico, the first regime associated with current account
19

surplus is predominant, while current account deficit periods are few and of short
duration.
On the other hand, the regime related to current account deficit prevails for
Colombia and Brazil. Despite this imbalance, there is a long-run relationship since
both series are cointegrated. This result suggests a long-run deficit in the current
account.
In the short run, the responses of both current account components to expendi-
ture shocks are positive and significant for all countries in the predominant regime.
However, in this regime, the response to income shocks is generally not significant for
Brazil. In the non-predominant regime, we find that only in Chile are the responses
to both shocks significant beyond two quarters.
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22

Appendix A Estimation Results
The two-regime TVEC model can be written as
∆xt=A0
1Xt−1(β) + A0
2Xt−1(β)I(zt−1(β)> γ) + t
where Xt−1(β)≡(1, zt−1(β),∆0
t−p)0with ∆t−pdenoting the vector of the lagged
difference terms (∆x0
t−1,∆x0
t−2, ..., ∆x0
t−p)0,zt(β) = x0
tα, and α= (1, β0)0.
Table 5: Estimation Results for Threshold Parameter
Chile Colombia Mexico Brazil
γ0.028 -0.033 0.002 -0.006
St Dev 0.066 0.236 0.245 0.007
Authors’ calculations. St Dev denotes the standard
deviation.
Table 6: Estimation Results for the TVEC(3) Model for Chile
A1A2
Expenditure Income Expenditure Income
Est St Dev Est St Dev Est St Dev Est St Dev
ECt−1-0.20∗∗ 0.08 -0.03 0.08 0.03 0.21 0.06 0.20
Expenditure{t−1}0.12 0.13 0.06 0.12 -1.07∗∗∗ 0.40 -0.44 0.39
Income{t−1}-0.15 0.16 -0.23 0.16 0.91 0.92 -0.04 0.90
Expenditure{t−2}0.00 0.13 -0.20 0.12 -0.43 0.41 -0.16 0.40
Income{t−2}-0.12 0.16 0.12 0.16 -1.41∗∗ 0.63 -1.16∗0.61
Expenditure{t−3}-0.19 0.12 -0.31∗∗∗ 0.12 -0.62 0.54 0.23 0.52
Income{t−3}-0.08 0.16 0.28∗0.16 -0.65 0.46 -0.65 0.45
Authors’ calculations. *, **, and *** indicate significance at the 10%, 5 %, and 1% levels, respectively.
Est denotes the estimated coefficient, St Dev denotes the standard deviation, and EC denotes the
error correction term (z).
23

Table 7: Estimation Results for the TVEC(5) Model for Mexico
A1A2
Expenditure Income Expenditure Income
Est St Dev Est St Dev Est St Dev Est St Dev
ECt−1-0.40∗∗ 0.18 -0.19 0.17 -0.43 0.59 -0.19 0.55
Expenditure{t−1}0.06 0.26 0.24 0.24 6.72∗∗∗ 2.36 5.39∗∗ 2.21
Income{t−1}-0.27 0.30 -0.28 0.28 -8.50∗∗∗ 3.04 -7.02∗∗ 2.85
Expenditure{t−2}-0.19 0.26 -0.02 0.24 9.92∗∗∗ 2.82 8.01∗∗∗ 2.65
Income{t−2}0.18 0.29 0.06 0.27 -10.39∗∗∗ 2.90 -8.54∗∗∗ 2.72
Expenditure{t−3}-0.03 0.26 -0.07 0.24 6.53∗∗∗ 1.36 5.52∗∗∗ 1.28
Income{t−3}-0.02 0.28 0.00 0.26 -7.14∗∗∗ 1.52 -5.96∗∗∗ 1.43
Expenditure{t−4}-0.14 0.25 0.10 0.24 2.80 1.84 1.81 1.72
Income{t−4}-0.12 0.27 -0.32 0.26 -2.48 1.82 -1.59 1.71
Expenditure{t−5}-0.08 0.25 -0.08 0.23 -4.11∗2.17 -3.20 2.03
Income{t−5}0.00 0.27 0.04 0.26 4.58∗2.38 3.56 2.23
Authors’ calculations. *, **, and *** indicate significance at the 10%, 5 %, and 1% levels, respectively.
Est denotes the estimated coefficient, St Dev denotes the standard deviation, and EC denotes the
error correction term (z).
Table 8: Estimation Results for the TVEC(6) Model for Colombia
A1A2
Expenditure Income Expenditure Income
Est St Dev Est St Dev Est St Dev Est St Dev
ECt−1-0.63∗∗ 0.25 -0.25 0.20 0.56∗∗ 0.26 0.28 0.21
Expenditure{t−1}-0.26 0.31 0.02 0.25 0.17 0.34 -0.05 0.27
Income{t−1}-0.76∗∗ 0.36 -0.71∗∗∗ 0.28 0.74∗0.39 0.69∗∗ 0.30
Expenditure{t−2}-0.75∗∗∗ 0.28 -0.87∗∗∗ 0.22 0.69∗∗ 0.31 0.79∗∗∗ 0.25
Income{t−2}0.51 0.40 0.16 0.31 -0.68 0.41 -0.10 0.32
Expenditure{t−3}0.22 0.48 -0.18 0.38 -0.17 0.50 0.14 0.39
Income{t−3}-1.06∗0.57 -0.72 0.45 0.91 0.60 0.63 0.47
Expenditure{t−4}-0.88∗∗∗ 0.33 -0.88∗∗∗ 0.26 0.59 0.37 0.88∗∗∗ 0.29
Income{t−4}0.67 0.51 0.49 0.40 -0.56 0.55 -0.47 0.43
Expenditure{t−5}1.13 0.73 0.46 0.57 -1.21 0.76 -0.39 0.59
Income{t−5}-1.95∗∗ 0.81 -1.19∗0.64 1.80∗∗ 0.84 0.97 0.66
Expenditure{t−6}-0.02 0.37 -0.40 0.29 0.11 0.41 0.68∗∗ 0.32
Income{t−6}-0.79 0.62 -0.29 0.49 0.62 0.65 0.10 0.51
Authors’ calculations. *, **, and *** indicate significance at the 10%, 5 %, and 1% levels, respectively.
Est denotes the estimated coefficient, St Dev denotes the standard deviation, and EC denotes the error
correction term (z).
24

Table 9: Estimation Results for the TVEC(6) Model for Brazil
A1A2
Expenditure Income Expenditure Income
Est St Dev Est St Dev Est St Dev Est St Dev
Const 0.01∗0.01 0.01 0.01 -0.01 0.01 -0.01 0.01
ECt−10.33∗∗ 0.14 0.26∗0.16 0.08 0.28 0.32 0.31
Expenditure{t−1}-0.19 0.31 0.14 0.35 -0.51 0.48 -0.84 0.53
Income{t−1}-0.15 0.26 -0.18 0.29 0.39 0.48 0.49 0.54
Expenditure{t−2}0.16 0.35 0.16 0.39 -0.44 0.52 -0.78 0.58
Income{t−2}-0.52∗0.28 -0.42 0.31 0.64 0.49 0.80 0.55
Expenditure{t−3}0.74∗∗ 0.36 0.62 0.40 -1.21∗∗ 0.51 -1.34∗∗ 0.57
Income{t−3}-1.05∗∗∗ 0.29 -0.78∗∗ 0.33 1.03∗∗ 0.52 1.16∗∗ 0.57
Expenditure{t−4}-0.90∗∗ 0.39 -1.13∗∗∗ 0.43 0.28 0.50 0.54 0.55
Income{t−4}0.29 0.30 0.49 0.33 -0.20 0.46 -0.43 0.51
Expenditure{t−5}-0.77∗0.44 -0.19 0.48 0.70 0.53 -0.08 0.59
Income{t−5}0.40 0.31 0.11 0.35 -0.58 0.46 -0.27 0.51
Expenditure{t−6}-1.22∗∗∗ 0.42 -1.23∗∗∗ 0.46 1.11∗∗ 0.49 1.35∗∗ 0.54
Income{t−6}0.68∗∗ 0.31 0.81∗∗ 0.34 -0.54 0.45 -1.00∗∗ 0.50
Authors’ calculations. *, **, and *** indicate significance at the 10%, 5 %, and 1% levels, respectively.
Est denotes the estimated coefficient, St Dev denotes the standard deviation, and EC denotes the error
correction term (z).
25

Appendix B Diagnostic Results
Table 10: ARCH, Normality, and Portmanteau Tests for the Residuals of the TVEC
Models
Chile Mexico Colombia Brazil
Statistic Pval Statistic Pval Statistic Pval Statistic Pval
ARCH
LM 8.18 0.61 9.58 0.48 6.12 0.81 6.39 0.78
Rank-Based 5.97 0.82 14.99 0.13 11.16 0.35 11.91 0.29
Corrected Q 54.88 0.06 55.20 0.06 28.83 0.91 38.05 0.56
Normality
JB 5.14 0.27 2.70 0.61 3.95 0.41 15.69 0.00
Portmanteau
Lag 20 59.89 0.62 53.73 0.56 49.20 0.58 46.11 0.70
Authors’ calculations.
Table 11: Maximum Eigenvalues of the Companion Matrix of the TVEC Models
A1A1+A2
Chile Mexico Colombia Brazil Chile Mexico Colombia Brazil
1.00 1.00 1.26 1.04 1.32 1.27 1.00 1.00
0.83 0.92 1.26 1.04 1.32 1.13 0.94 0.92
0.83 0.76 1.03 1.00 1.15 1.13 0.84 0.92
0.68 0.76 1.03 0.97 1.00 1.00 0.84 0.91
0.68 0.73 1.01 0.97 0.91 0.96 0.84 0.91
Authors’ calculations. Reported modulus for the five maximum eigenvalues.
26

Table 12: BDS Test for Residuals of the TVEC Models
Expenditure Income
Chile 0.21 0.63
Mexico 0.06 0.95
Colombia 0.89 0.22
Brazil 0.78 0.04
Authors’ calculations. Reported p-values
at embedding dimension 2, epsilon value
equal to 1.5 standard deviations.
27

Appendix C Generalized impulse-response func-
tions
Figure 2: GIRF for the Predominant Regime in Chile
−0.10 0.00 0.05 0.10
Shock in Expenditure − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Income − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Expenditure − Response in Income
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Income − Response in Income
Value
1 3 5 7 9 12 15 18
28

Figure 3: GIRF for the Non-predominant Regime in Chile
−0.10 0.00 0.05 0.10
Shock in Expenditure − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Income − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Expenditure − Response in Income
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Income − Response in Income
Value
1 3 5 7 9 12 15 18
29

Figure 4: GIRF for the Predominant Regime in Mexico
−0.03 −0.01 0.01 0.03
Shock in Expenditure − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.03 −0.01 0.01 0.03
Shock in Income − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.03 −0.01 0.01 0.03
Shock in Expenditure − Response in Income
Value
1 3 5 7 9 12 15 18
−0.03 −0.01 0.01 0.03
Shock in Income − Response in Income
Value
1 3 5 7 9 12 15 18
30

Figure 5: GIRF for the Non-predominant Regime in Mexico
−0.2 −0.1 0.0 0.1 0.2
Shock in Expenditure − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.2 −0.1 0.0 0.1 0.2
Shock in Income − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.2 −0.1 0.0 0.1 0.2
Shock in Expenditure − Response in Income
Value
1 3 5 7 9 12 15 18
−0.2 −0.1 0.0 0.1 0.2
Shock in Income − Response in Income
Value
1 3 5 7 9 12 15 18
31

Figure 6: GIRF for the Non-predominant Regime in Colombia
−0.2 −0.1 0.0 0.1 0.2
Shock in Expenditure − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.2 −0.1 0.0 0.1 0.2
Shock in Income − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.2 −0.1 0.0 0.1 0.2
Shock in Expenditure − Response in Income
Value
1 3 5 7 9 12 15 18
−0.2 −0.1 0.0 0.1 0.2
Shock in Income − Response in Income
Value
1 3 5 7 9 12 15 18
32

Figure 7: GIRF for the Predominant Regime in Colombia
−0.10 0.00 0.05 0.10
Shock in Expenditure − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Income − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Expenditure − Response in Income
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Income − Response in Income
Value
1 3 5 7 9 12 15 18
33

Figure 8: GIRF for the Non-predominant Regime in Brazil
−0.10 0.00 0.05 0.10
Shock in Expenditure − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Income − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Expenditure − Response in Income
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Income − Response in Income
Value
1 3 5 7 9 12 15 18
34

Figure 9: GIRF for the Predominant Regime in Brazil
−0.10 0.00 0.05 0.10
Shock in Expenditure − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Income − Response in Expenditure
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Expenditure − Response in Income
Value
1 3 5 7 9 12 15 18
−0.10 0.00 0.05 0.10
Shock in Income − Response in Income
Value
1 3 5 7 9 12 15 18
35

ogotá -