Sustainability of the Current Account in Developing Countries: A Fourier Wavelet-Based Unit Root Test

Abstract

The sustainability of the current account balance for five fragile economies—Brazil, Argentina, South Africa, India, and Türkiye (namely, BASIT)—is investigated. These countries’ economies operate under a time current account deficit almost all the time, a condition that causes fragility to external shocks; the following fallout from these shocks may risk not only the domestic economy but also the international economy, such as by clogging trade and income distribution. In this study, the sustainability of the current account in BASIT countries is examined via wavelet-based Kapetanios, Shin and Snell (WKSS) and Fourier wavelet-based KSS (FWKSS) unit root tests, in conjunction with linear unit root tests. Even though traditional unit root tests generally support the sustainability of a current account deficit for all countries, a non-linear unit roots test confirms the traditional tests for only India and South Africa. Results from the wavelet transform of non-linear unit root tests indicate the unsustainability of the current account balance, except in the case Türkiye. Moreover, the FWKSS test confirms WKSS.

1. Introduction

After the increasing globalization of the world, particularly in the 1980s, numerous developing countries’ balance of payments has predominantly been hindered due to current account deficits. Frequently, governments finance these deficits through external debt, short-run money flows, or a combination of both. Each of these three approaches may eventually lead to balance of payment crises, primarily due to insufficient domestic savings. Various economists posit that if the balance of deficit surpasses 5% of its gross domestic product (GDP), it significantly increases the likelihood of a balance of payments crisis [1,2]. Moreover, ref. [3] points out that an increasing current account deficit, undervalued domestic money, and falling exports may serve to create heightened economic vulnerability. This reflects a deviation from a balanced economy, calling for adjustments in economic policies to prevent potential economic crises. Nonetheless, the reliability of such a threshold as an accurate indicator for countries may be open to question, given the central importance of contriving productive strategies for financing the current account deficit. Another perspective to take account is that if the current account deficit is used to finance productive investment, it may potentially stimulate higher GDP growth than the growth rate of the current account deficit itself [4,5].

Against a theoretical background, the current account balance is generally associated with the business cycle in each country [6,7,8]. A high growth rate leads to a larger current account deficit, due to the fact that the high growth rate causes a higher national income, which stimulates rising consumption and investment that contribute to more imports from abroad. If a rise in imports is not accompanied by the same level of exports (although it varies depending on the economic structure of the countries—an increase in imports is usually greater than an increase in exports), this causes the current account deficit to rise to a critical level where economic agents start to worry about the sustainability of the current account. It is also true to state the opposite [9]. A lower growth rate in a country, or a negative growth rate, causes a decrease in aggregate demand. Thus, demand for imported goods falls. Therefore, the current account deficit tends to shrink and may even turn into a surplus.

Some episodes support this view in the BASIT (Brazil, Argentina, South Africa, India, and Türkiye) countries. (See Figure A1 in the Appendix A) Growth rates exceeded 1% in Brazil in 2018 and 2019. However, the growth rate turned negative, and the current account deficit was reduced to almost 59% in 2020. After COVID-19, the current account deficit increased with an increase in growth rate. The same argument can also be applied to the Indian economy. Indeed, the deficit turned into a surplus in 2020. After the economic crisis in 2001, Türkiye experienced high growth rates for 5–6 years, while the current account deficit hit records levels. With the 2008–2009 crisis, there was a serious decrease in the current account deficit as a result of the economic contraction, but with the expansion of the economy in the following years, the current account deficit tended to increase again.

Indeed, trade balance is closed in relation to macroeconomic policy. Assume a country suffers inflation and a current account deficit. To reduce rising prices, let the central bank adopt a contraction monetary policy. Hiking interest rates leads foreign investors to make investment in the country—raising capital inflows- which causes an appreciation of home country’s currency. Thus, imported goods are now chapter than domestic goods, so the country runs a larger current account deficit. Also, the appreciation of the home country’s currency brings about falling of exports, too. It promotes a deficit [10,11,12].

Furthermore, policymakers can follow two paths when the current account balance is deteriorating. First, they can continue the current policy. An increase in the current account deficit may raise investors’ concerns, leading to changing sentiments. In this case, if the current account deficit becomes unsustainable, an economic crisis may occur. In fact, it is not the size of the current account deficit but how to finance the deficit that is important. Although the current account deficit to GDP ratio hit 7.7% in New Zealand in 1997, the country did not experience an external crisis [13]. In addition, South Africa, despite having a serious and continuous current account deficit after 2003, did not experience an economic crisis, except for 2020 and 2021. However, in Türkiye, Brazil, Argentina, and India, current account deficits caused external crises or foreign exchange crises from time to time.

Second, a sharp current account reversal may occur. For this, one can resort to exchange rate devaluation in addition to quotas and more tariffs to restrict imports. These policies will cause serious changes in the decision-making processes of economic units and the disruption of previously made plans. For example, a reversal of the current account deficit may lead to diminishing both consumption and investment [8]. If the current account reversal is due to the devaluation of exchange rates, it will cause an increase in the prices of imported consumption and intermediate goods. In this case, the country will experience an inflationary process. In addition, the increase in the prices of investment and intermediate goods may cause a reduced investment demand and, thus, the reduced growth rate of the country. Furthermore, the devaluation will cause foreign investors to leave the country. This will create an upward pressure on exchange rates, too [8,14].

The deterioration of the trade balance also affects the main trade partners of the country. Due to the serious rise in the trade deficit, countries may sometimes implement various policies, such as increasing tariffs, imposing quotas, or allowing exchange rates to depreciate. In such cases, since these policies will make imported goods relatively more expensive, the demand for imported goods will decrease in the country. This will cause a decrease in the GDP of the countries that sell goods to the relevant country– the country implements protective policies. In fact, the trade balances of trade partners will also worsen. Another effect is that policies aimed at reducing the foreign trade deficit limit countries’ economic growth. This will reduce the demand for imported goods and, therefore, cause a decrease in the GDP of the countries with which imports are made [10,11,12].

For these reasons, sustainability of the current account is vital not only to the country itself but also to other countries, especially trade partners. Numerous studies have been dedicated to investigating the sustainability of the current account deficit for over half a decade. Refs. [15,16] assert the notion that a country’s current account deficit can be deemed sustainable, provided that the intertemporal budget constraint is satisfied. Under the conditions of the no-Ponzi game and finite sample constraint, the continuity of the current policy is contingent upon satisfying the intertemporal budget constraint. As demonstrated by [15,17,18], the sustainability of a current account within an economy can be evaluated through the stationarity of the ratio of the current account deficit to the gross domestic product (GDP). The underlying premise is that policymakers may exhibit reluctance to alter the prevailing current account policy in a country, as long as the economic growth rate, characterized by positive expansion, exceeds the augmentation of their current account deficit. This particular scenario suggests that the sustainability of the current account deficit can be evaluated effectively using unit root tests.

Investigating the sustainability of the current account by employing standard unit root tests such as the Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) unit root tests, and the Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) stationary test may not capture accurate results due to the probability of non-linearity in the current account deficit.

It is argued by [19] that the non-linearity of the current account is stimulated by three distinct channels. Initially, the phenomenon of the twin deficit may cause a state of non-linearity. Subsequently, transaction costs may contribute to the non-linearity. In conclusion, the liability of domestic countries may indeed promote non-linearity. The ultimate conduit could potentially result from foreign investors’ reluctance to purchase domestic assets when the indebtedness of the domestic country escalates. Consequently, traditional unit root tests lack the capacity to expose non-linearity effects, potentially leading to undesirable findings. Furthermore, traditional unit root tests neglect structural breaks (Some traditional unit root tests have been extended to uncover the break effects, such as the Zivot–Andrews, Perron, and NG unit root tests, but these approaches are still based on linear approximation. Further details can be found in [20,21,22].).

We contribute to the literature in three ways. Primarily, the most innovative methods are used in the analyses. Our novel unit root test comprehensively incorporates both wavelet and Fourier transformations concurrently. The transformation of wavelets effectively encapsulates both domain and frequency localization simultaneously. Furthermore, wavelet analysis has the capability to disclose genuine signals, and the computation process exhibits a high degree of simplicity. Moreover, Fourier transformation possesses the ability to examine seasonality, trends, and noise. This methodology also incorporates an indeterminate number of structural disruptions. In accordance with the findings presented by [23], it can be deduced that the Fourier wavelet-based Kapetanios, Shin, and Snell (FWKSS) test has more power than both the wavelet-based KSS (WKSS) and Kapetanios, Shin, and Snell (KSS) tests. Finally, this method considers non-linearity in the time series.

This study continues as follows. The literature review is in the next section. In the third section, we elucidate the phenomenon of the current account deficit in the context of BASIT (Brazil, Argentina, South Africa, India, and Türkiye) countries. In the fourth section, the current account deficit is explained for BASIT countries. Subsequently, an overview of the theoretical background will be clarified. Next, the summary of the theoretical background will be explained. In the succeeding section, the data and econometric methodology employed are explained. In the sixth section, we interpret the findings of the analysis. Finally, the study concludes.

2. Literature Review

Given that numerous countries grapple with imbalances in their balance of payments (BOPS), resulting in unfavorable outcomes for global trade, policymakers have been endeavoring to maintain a sustainable current account for over half a century. Numerous investigators have concentrated their research efforts on this subject, with myriad studies producing varied outcomes for BASIT countries, in the academic literature [24,25,26,27,28]. The most recent and critical research studies yield the following results.

Ref. [29], along with [30], discovered empirical support for the sustainability of the Turkish account. Ref. [29] employs a linear model; nonetheless, the non-linear model is contemplated in the alternative research. Refs. [31] and [32] assert the implementation of linear models in their respective papers, which ultimately lead to the conclusion of weak sustainability. Regrettably, scholars such as the authors of [33,34], along with those of [35], reject the sustainability of the current account in Türkiye. Aside from [34], most researchers demonstrate a preference for linear models. In their research, the authors of ref. [27] quantitatively determined the threshold value of the current account deficit. The argument is advanced that a 5% threshold on the current account holds significant implications for the Turkish economy. Should this value be exceeded, policymakers may contemplate effecting a policy reversal aimed at reducing the deficit. Ref. [36] employs the analytics tools of Fourier ADF (FADF) and Fourier KPSS tests to assess the sustainability of Türkiye’s current account. The implications of the non-linearity unit roots test suggest that the CAD/GDP remains stationary. Furthermore, ref. [37] applied a Fourier panel estimation for five Asian countries to conclude on the suitability of the current account.

According to [38], in contrast to Brazil, where the current account is sustainable, Argentina’s current account unfortunately remains unsustainable. Ref. [39] posited that by employing a filtration process to exclude smooth and sharp breaks from the data, the sustainability of the current account can be ensured for all BRICS nations, except South Africa. Ref. [40] could not locate evidence supporting the sustainability of the current account for both Brazil and Argentina.

Ref. [28] deduced that potentially misleading conclusions may be drawn for Brazil, Russia, India, China, and South Africa if non-linearity tests are overlooked. In their 2022 study, the authors of ref. [41] favor a non-binary method for analyzing the sustainability of the current account in 28 countries, inclusive of Türkiye, South Africa, India, and Brazil. In conclusion, both linear and non-linear models reject the sustainability of Brazil’s current account. In the context of the Turkish and Indonesian economies, the linear test does not refute the null hypothesis of a unit root, whereas the non-linear tests categorically dismiss it. For the Turkish and Indonesian economies, the linear test fails to reject the null hypothesis of the unit root; however, non-linear tests do reject it. Thus, non-linearity models offer empirical support for the sustainability of both countries. In conclusion, both the linear and non-linear models corroborate the sustainability of the existing account configurations in India.

3. Current Account Deficit in BASIT Countries

In the global context, developing countries, with the exception of China, require capital to ensure the continuity of economic growth. Owing to the insufficiency of their savings to finance their investments, governments typically increase their investment activity, thereby inducing budget deficits. Both the deficit in savings and investment and the budget deficit contribute to the deficit in the current account.

Thus, for developing countries to attain higher growth rates, they require substantial capital investment. However, this necessity often leads to a consequential economic encumbrance—a current account deficit. The augmentation of the current account deficit over time incites issues within the balance of payments, catalyzing both economic and particularly foreign exchange crises. To avert these crises, policymakers within these countries might consider modifying their economic strategy. Thus, establishing the sustainability of the current account is crucial for the design of economic policy in developing countries.

The current account balance to GDP is shown in Figure 1. At the beginning of the data range, it was in surplus in Argentina. This surplus turned into deficit after three years, probably due to the imbalanced fiscal deficit. The deficit reached 6.2% in 1980, and continuously decreased up to 1985. The current account balance increased to 3.89% of GDP. The deficit switched to positive in 1990, since there was an economic crisis and a structural change in economics. Until 2002, the current account ran a deficit again. The current account balance changed to positive one more time, and it continued up to the mortgage crisis. Starting from 2010, the account balance turned negative, and the deficit dropped to 5.16% in 2018. The deficit was close to zero in 2019 due to the declining in real GDP. It shifted to surplus in 2020 and this surplus kept up the following year because of COVID-19 and exchange rate depreciation. It was negative in the last year of the dataset.

The current account was negative between 1975 and 1983. In addition, it was relatively high, since the mean of the deficit was 4.4%. The deficit turned into surplus due to the economic crisis in 1984. The surplus became negative the following year, and the deficit went on until 2001. The deficit switched to positive again in 2001 due to the economic crises. After that, the current account ran a deficit. The deficit hit 5% in 2012. With the effects of COVID-19 the deficit decreased to 2% of GDP, but it reached 3% again in 2022.

At the beginning, the current account was negative, but it turned positive immediately in India. The surplus kept up for four consecutive years. But it switched to a deficit in 1980. After that, except for expect 5 years, the Indian economy ran a deficit. The current account balance was positive between 2001 and 2004. The current account balance started to deteriorate again in 2005, and it peaked at over 5% in 2012. The deficit lasted until the COVID-19 pandemic era. Even if there was a surplus in 2020, it switched to a deficit again in the remaining years.

The striking characteristic of the current account balance is negative in Türkiye, and it worsened after 2002. The current account balance ran a surplus only in seven years, which were mostly of economic and financial crises such as 1994, 1988, and 2001. Even though the national currency depreciated then that year, the current account was in surplus, but it turned to a deficit immediately, except in 1988 and 1989. These two years were consecutively positive. After the 2001 economic crisis, the transition to the Strong Economy Program started to overcome the economic and structural problems in Türkiye by assigning IMF and World Bank rules, which caused the deterioration of the deficit of the current account in Türkiye. The deficit reached almost 9% of GDP in 2011. Moreover, the average was around 4.1% between 2012 and 2018. The current account balance became positive in 2019 due to high depreciation in the national currency. It was again in deficit in the remaining years.

The feature of the current account balance in South Africa is that the country ran a surplus more than the other four countries. The current account deficit was really high in 1975 and 1976. İt turned into a surplus in 1977, and it kept it up for three more years. After that, the current account balance deteriorated again over the following four years. Starting from 1985, the current count balance was positive up to 1995. After that year, the surplus becomes negative until 2002. The surplus continued for only two years, and then there was a sharp decline in the current account balance in South Africa. There was then a deficit in the current account balance in South Africa except for 2020 and 2021.

Given that numerous countries grapple with imbalances in their balance of payments (BOPS), resulting in unfavorable outcomes for global trade, policymakers have been endeavoring to maintain a sustainable current account for over half a century. Numerous investigators have concentrated their research efforts on this subject, with myriad studies producing varied outcomes for BASIT countries in the academic literature. The most recent and critical research studies yield the following results.

4. Theoretical Background

The sustainability of the current account is contingent upon the correlation between saving and investment, which a crucial factor in upholding intertemporal budget constraint. In 1980, ref. [42] devised an innovative methodology for testing it that incorporated the use of time series analysis. The premise is that there should be a substantial correlation between investment and savings at low frequencies. In the extended model of intertemporal budget constraint that incorporates a zero growth rate, it is suggested that the intertemporal budget constraint should be upheld provided that the current account balance remains stationary. In 2002, ref. [17] provided mathematical evidence to support the aforementioned concept. Building upon the work of [15,16,17,43], it proposed simple yet comprehensive models for further exploration.

The principle of national income accounting posits that, within an economic framework, the aggregate of production (Q) and imports (M) should be equivalent to the cumulative sum of consumption (C), investment (I), public expenditure (G), and exports (X).

Q + M = C + I + G + X

(1)

In the academic vernacular, net export can be elucidated as X-M, which enables us to reconfigure Equation (1) as outlined below:

Q = C + I + G + NX

The net debt position of a given country, relative to other countries, can be defined as -B, where the said country is obligated to pay interest at the average rate of “r” to the rest of the world. Therefore, it is proposed that the Gross National Product (GNP) of the respective countries should correspond to parameters designated in Equation (2).

Q − rB = C + I + G + NX − rB

(2)

Consequently, we can conceptualize the current account balance (CAB) as

CAB ≡ NX − rB = (Y − C − G) − I = S − I

(3)

where Y and S refer to GDP and saving in a country, and since S ≡ Y − C − G.

Assuming no alteration in the international reserve and net error and omission, the net change in the capital account (KA) should be equivalent to the balance of the current account. Moreover, the capital account balance can be defined as the difference in the country’s net debt position from t − 1 to t.

B_t − B_t−1 ≡ KA_t = CA_t

(4)

Assuming a model premised on zero steady-state growth, it is necessary for all variables to manifest a zero growth rate. This results in no variation in a country’s credit standing on a global scale, thus inducing a current account balance equivalent to zero.

0 = B_t − B_t−1 = 0 = CA_t ⇾ 0 = NX − rB ⇾ NX = rB

(5)

The aforementioned equation elucidates the concept that the trade deficit must be equivalent to paying interest derived from credit. Combining Equations (4) and (5), the following expression is obtained:

B_t − B_t−1 = r_tB_t−1 − NX

(6)

Upon recursively solving Equation (6), the following equation is obtained:

$$B_{t-1}=-{\sum }_{j=0}^{\infty }{R}^{-\left(j+1\right)}E\left(N{X}_{t+j}∣I_{t-1}\right)+\underset{j\to \infty }{\lim }{R}^{-j+1}E\left(B_{t+j}∣I_{t-1}\right)$$

(7)

In the scenario where R_t is equivalent to 1 + r_t, $E\left(R_{t+j}∣I_{t-1}\right)$ equals R universally for each incremental time point (t). It serves as a set of information holding relevance at time (t), while maintaining that i is greater than or equivalent to 0. Given that the long-term budget constraint is fulfilled, the second term of the aforementioned equation is rendered zero. The stipulation necessitates that the intertemporal budget constraint remains applicable only when R_t oscillates as a stochastic process and is confined within the margins of 1 + δ and δ > 0. Therefore, the current account balance maintains stationarity (The case can be extended to any positive growth rate. See ref. [17] for further details.).

This theory implies the stability of the current account balance, consequently, and the scholarly literature has employed unit root tests to determine the sustainability of the current account for various countries. Nevertheless, an excessive number of unit root tests have been introduced over the years. In the subsequent section, various unit root tests are duly presented, which are employed in this paper.

5. Data and Econometric Methodology

As previously indicated, the objective of this research is to scrutinize the sustainability of the currency account deficit within BASIT countries. The annual data, which represents the ratio of the current account to GDP, encompasses the years 1975–2022, except Argentina. The dataset starts in 1976 for Argentina. Data are retrieved from the World Bank database. (The data for 2023 has not yet been released by the World Bank database, so the data finish in 2022.)

As presented by [17], unit root tests are used to probe the sustainability of the current account. Nevertheless, the accuracy of the results derived from traditional (linear) unit root tests might be compromised due to the non-linearity of the time series. As postulated in [44], the power of the conventional unit root is inversely proportional to the augmentation of frequency. In addition, frequent instances of structural breaks often precipitate non-linearity in time series analysis. This disruption can instigate policy changes, consequently altering the dynamic structure of the time series. Should a time series demonstrate non-linearity, it is worth noting that traditional unit root tests may not possess the ability to accurately discern the implications of non-linearity. Consequently, these unit root tests could potentially yield inaccurate conclusions.

Ref. [45] (2003) enhanced a non-linear unit root test, ensuring that the model incorporated an exponential smooth transition autoregressive (ESTAR) process. In the unit root test, the authors incorporated an exponential transition function.

$$∆x_t={\phi x}_{t-1}+\beta y_{t-1}\left[1-e^{\left(-\delta y_{t-d}^2\right)}\right]+{\epsilon }_t$$

(8)

The mathematical concept delineated within the square brackets refers to the exponential smooth transition equation; this function notably remains confined within the parameters of zero and one, as stated by [23]. The parameter remains unknown, despite the exhibition of β expression within Equation (8).

The term in the square brackets is the exponential smooth transition equation, and this function is bounded between zero and one [23]. β expression is exhibited in Equation (8), and the parameter is not known. To efficiently examine the exponential smooth transition equation, research was executed by [45]. The first-order Taylor approximation was implemented in Equation (8). So, the following expression can be tested:

$$∆x\_t=\mu x\_(t-1)^3+\vartheta \_t$$

(9)

As posited by [46], continuous wavelet transformation is not practical for all frequencies and data in the identified fields of economics and finance; hence, the discrete version proves to be a more suitable alternative. Upon employing the Haar filter to perform the wavelet transform in Equation (9), the following expression is obtained (for details and proof of asymptotic distribution that used the same with KSS, see [23,46]):

$$∆V_{1t}={\sum }_{j=1}^p\varnothing ∆1_{1,t-j}+\alpha V_{t-1}^3+u_t$$

(10)

In this context, V_1,t signifies the wavelet transformation, specifically the scaling coefficient. The application of the KSS test with wavelet transformation is used in the testing of α. In conclusion, ref. [23] incorporated the Fourier transformation of Equation (10), a process built upon the work of [47], thus yielding the FWKSS test.

$$∆V_{1t}={\sum }_{j=1}^p\varnothing ∆1_{1,t-j}+\alpha V_{t-1}^3+\gamma \sin \left({\displaystyle \frac{2\pi kt}{T}}\right)+{ϛ}_t$$

(11)

Herein, k, t, and T denote the quantity of frequency, trend, and the sample size, respectively. There are two important points of this test. The frequency count, ranging from 0 to 5, is automatically determined using the selected information criteria method. The second consideration is that if the parameter of the Fourier test is not statistically significant, the researchers should favor the WKSS test [23,48].

6. Empirical Results and Discussion

The descriptive statics are found in

Table 1. Current account balance to GDP.

	ARG	BRA	IND	TUR	ZAF
Mean	−1.009	−2.193	−1.152	−2.534	−0.830
Median	−1.407	−2.734	−1.254	−2.401	−1.028
Maximum	8.971	1.559	1.744	2.014	5.288
Minimum	−6.203	−6.014	−5.005	−8.870	−5.345
Std. Dev.	3.095	2.030	1.342	2.404	2.907
Variance	9.580	4.119	1.801	5.778	8.452

Source: Author’s calculation.

. In South Africa, the maximum mean observed is −0.83; conversely, the minimum mean value noted is −2.534% in Türkiye. The lowest share of the current account balance to GDP can be observed in Türkiye, which stands at −8.87%. In contrast, the highest share of the current account balance relative to GDP is recorded in Argentina, with 8.97%. While India exhibits the smallest degree of variability, the volatility of variance in Argentina and South Africa manifests at a distinctly higher level. Although Türkiye possesses the largest current account deficit at present, the fluctuation of its current account balance does not reach the levels seen in Argentina and South Africa.

The outcomes derived from the econometric methodologies will be meticulously appraised. The sustainability of the current account is examined first through traditional unit root tests, specifically the Augmented Dickey–Fuller (ADF), Phillips–Perron (PP), and Kwiatkowski–Phillips–Schmidt–Shin (KPSS) tests. These are conducted for drawing comparisons with the non-linear tests. (The details of the linear unit roots test are found in [49,50,51]. Moreover, critical values of the ADF and PP tests are retrieved from [52].)

Table 2. Traditional unit root tests.

Unit Root Test	ARG	BRA	IND	TUR	ZAF
ADF Test	−3.050 **(0)	−3.746 ***(4)	−2.794 *(0)	−4.244 ***(0)	−3.204 **(0)
PP Test	−3.098 **(3)	−2.655 *(0)	−2.730 *(4)	−4.452 ***(4)	−3.344 **(1)
KPSS Test	0.116	0.110	0.183777	0.254317	0.33341

Note: The Akaike Information Criterion (AIC) serves as the standard reference for the suitable selection of lags in all tests conducted. The number in parenthesis denotes the lag selected by the AIC. The symbols *, **, and *** denote the rejection of the null hypothesis at 10%, 5%, and 1%, respectively.

presents the outcomes derived from conventional unit root examinations. The proportion of Brazil and Türkiye’s current account balance to their GDP exhibits stationarity at a 1% significance level. Additionally, when applying the Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) tests, the data remain stationary for both Argentina and South Africa. In contrast, the KPSS test provides a contradictory indication, implying potential non-stationarity for these countries. Additionally, both the Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) tests barely report stationarity for India. The KPSS test yields congruent results when applied to other countries. In conclusion, determining the stationarity of the current account deficit presents a significant challenge.

Should a time series display non-linear properties, conclusions drawn from linear models could potentially lack accuracy. Consequently, inferring policy from linear models may possible result in inaccuracies. The Brock, Dechert, and Scheinkman non-linearity test (hereinafter referred to as the BDS test), established by [53], is used to assess the presence or absence of non-linearity in the time series under investigation. Before conducting the BDS test, the current account balances relative to GDP for all nations were adjusted using the suitable Autoregressive Process (AR(P)). According to

Table 3. BDS test.

Dimesion	ARGF	BRAF	INDF	ZFAF	TURF
m = 2	0.214321	0.210193	0.21172	0.157123	0.042469
	(0.025505) ***	(0.023862) ***	(0.024679) ***	(0.014183) ***	(0.005801) ***
m = 3	0.364438	0.359772	0.361534	0.284991	0.084805
	(0.041147) ***	(0.038975) ***	(0.040132) ***	(0.02612) ***	(0.012587) ***
m = 4	0.467023	0.463897	0.46513	0.390305	0.126953
	(0.049826) ***	(0.047771) ***	(0.048977) ***	(0.036047) ***	(0.020449) ***
m = 5	0.534986	0.534442	0.534747	0.474839	0.168855
	(0.052863) ***	(0.051294) ***	(0.052368) ***	(0.043549) ***	(0.029074) ***
m = 6	0.578162	0.580565	0.579786	0.542001	0.210448
	(0.051938) ***	(0.050997) ***	(0.051848) ***	(0.04869) ***	(0.038247) ***

Note: *** denotes the level of statistical significance at 1%. The predicted error stemming from the autoregressive process (AR(P)) is represented by Country F; for example, ARGF presents the predicted error forecasting in Argentina. The optimal AR(p) process is AR(1), with the exception of applications in Türkiye and South Africa. For Türkiye and South Africa, the values of P are three and two, respectively. The outcomes have been deduced based on the standard error of 0.7 units of distance in the time series analysis. The BDS tests are conducted using a standard error distance of 0.5 and 1 unit. The outcomes align precisely with the table; thus, they are omitted from the publication. Results are available upon request from the author.

, the BDS test strongly indicates a non-linear process for the CA/GDP for all countries examined, as evidenced by our data. Hence, three distinct non-linear unit root tests are conducted to obtain more suitable outcomes for the BASIT nations.

The initial non-linear unit root test executed is the Kapetanios, Shin, and Snell (KSS) test, as delineated by [45]. After the application of the KSS test, the wavelet adaptation of the KSS test is implemented. The outcomes of both the KSS and WKSS examinations are presented in

Table 4. Non-linear unit root tests (KSS and WKSS).

Country	ARG	BRA	IND	TUR	ZFA
KSS	−2.627(1)	−2.87 *(1)	−3.228 **(0)	−0.599(2)	−3.237 **(1)
WKSS TEST	−0.5007(3)	−0.04032(7)	−1.1626(7)	−4.3233 ***(3)	−0.81178(1)

Note: In all assessments, the Akaike Information Criterion (AIC) serves as the benchmark for the correct selection of lag. Parenthetical notation indicates the number of lags chosen by the Akaike Information Criterion (AIC). In the context of hypothesis testing, the notations *, **, and *** correspond to the rejection of the null hypothesis at significance levels of 10%, 5%, and 1%, respectively. The authors of [23] reported the critical values of the WKSS test.

. On the basis of the study findings, it is inferred that the ratio of the current account balance to the gross domestic product (CAB/GDP) is non-stationary in both India and South Africa. In addition, the null hypothesis is dismissed at a 10% significance level for Brazil. The assessment further illustrates that the ratio of the current account deficit to GDP remains non-stationary for the remaining two countries under consideration.

The wavelet transformation applied to the KSS test results suggests a differing conclusion in comparison with prior unit root tests. The ratio of the current account balance to GDP is notably stationary in Türkiye. Regrettably, the null hypothesis for other countries cannot be rejected. This suggests that the sustainability of their current trade system is uncertain, as underlined by the WKSS’s assertion that the CA/GDP ratio represents a non-stationary process. The wavelet transform resulted in disparate outcomes for Brazil, India, Türkiye, and South Africa.

Finally, the outcomes from the Fourier wavelet-based unit root test, as proposed by [23], are assessed. The outcomes from the Fourier wavelet KSS (FWKSS) tests reveal that the balance of the current account to GDP for all countries is non-stationary. This conclusion is based on the inability to reject the null hypothesis at even a 10% level for the other four countries, as shown in

Table 5. A new non-linear unit root test (FWKSS).

Country	ARG	BRA	IND	TUR	ZFA
FWKSS TEST	0.6214(8)	0.1630(7)	−1.336(8)	−1.166(3)	0.3415(7)
Frequnecy	4	4	5	3	2
T test	−3.340	−2.138	−1.978	1.368	−2.444

Note: In all examinations, the Akaike Information Criterion (AIC) serves as the standard for selecting the appropriate lag. The number of the lags selected by AIC is indicated in parentheses. Ref. [23] reported the critical values of the FWKSS test.

. In conclusion, except Türkiye, the novel unit root test suggests that the current account balance to GDP ratio in these countries is non-stationary. Given that the test statistic is less than 1.96, the results of the WKSS test should be favorably considered for Türkiye within this analytical context. The assumption that Türkiye’s current account deficit is non-stationary might indeed be erroneous, notwithstanding the null hypothesis. The FWKSS unit root test cannot reject the non-stationarity of the current account balance relative to GDP.

Conversely, the t-test results were found to be statistically insignificant, implying that the parameters of the Fourier transformation might also lack statistical significance. As per the recommendation of [23], this scenario necessitates the use of the WKSS test by the researcher. On the other hand, the t-test is not statistically significant. As [23] suggested, if the parameters of the Fourier transformation are not statistically significant, the researcher should use the WKSS test.

7. Conclusions and Policy Implications

For sustainable development and a high growth rate, many nations—particularly developing countries—require external resources, notably capital, as their internal savings are insufficient. Given that these nations are reliant on foreign capital, it is an unavoidable consequence that they will sustain long-term trade deficits. Nonetheless, if improperly financed, this deficit could precipitate economic crises. Within the realm of the literature, there are certain indicators that reflect the potential fragility of an economy. The prevalent consensus within academia suggests that policymakers should consider revising economic policies whenever the current account deficit surpasses 5% of the country’s GDP, as a measure to avoid impending financial crises.

Nonetheless, certain nations often exceed this threshold, yet for an extended duration, policymakers have not modified their economic strategies. Despite certain developing nations operating under substantial current account deficits, they possess the capacity to perpetuate their economic strategies without requiring any alterations. Consequently, the sustainability of current account deficits in BASIT nations is under investigation.

To analyze sustainability, traditional linear and non-linear unit root tests are conducted. Traditional unit root tests give evidence that these nations should primarily be able to maintain their current account deficits, with only a few exceptions. In contrast, results from the KPSS test suggest a different conclusion compared with the other two traditional unit root tests. The novel findings from the FWKSS (non-linear unit root test) suggest a paradigm shift: the current account deficit in four notable countries, Argentina, Brazil, India, and South Africa, appears unsustainable, thereby mandating an imperative review of their economic policies.

However, this imperative excludes Türkiye, thereby making it an exception among global policymakers. While Türkiye’s current account balance may be sustainable, it is imperative for policymakers to identify and establish more secure methods of financing to avert potential account crises. In the aftermath of the COVID-19 pandemic and the Russo-Ukrainian war, developing countries have experienced a reduction in short-term investments. This, coupled with the surge in energy and food prices, may precipitate a scarcity of foreign currency for policymakers. Consequently, this situation could potentially trigger detrimental foreign currency crises in Türkiye. Nevertheless, the global inflation rate has escalated following the COVID-19 pandemic, prompting nearly all central banks to incrementally raise interest rates with the aim of curtailing general prices. This strategy, in turn, has led to a decline in the worldwide growth rate. This scenario will ultimately result in a decreased current account deficit in numerous countries. However, once central banks start the reduction of interest rates, the current account deficit is likely to escalate once more.