Impact of Exchange Rate on Trade Balance of India: Evidence from Threshold Cointegration with Asymmetric Error Correction Approach

Abstract

In this research, we investigate the dynamic relationship between the trade balance and exchange rate in the case of India using threshold cointegration and an asymmetric error-correction model. Empirical results validate that the long-run dynamic relationship between the trade balance and exchange rates is asymmetric. In the short run, the trade balance responds only due to positive deviations in the exchange rate. In contrast, in the exchange rate model, the exchange rate reacts only due to negative deviations in the trade balance. In addition, the results exhibit that the adjustment following variation in the exchange rate seems higher than the adjustment in the trade balance in the short run. Besides, the results indicate that the speed of adjustment due to the positive and negative shocks differs in the trade balance and the exchange rate models. Further, the uni- directional Granger causality result suggests that the trade balance substantially affects the exchange rate. However, the Granger causality effect of the exchange rate on the trade balance seems minimal. Finally, our results validate the impact of momentum equilibrium adjustment path asymmetric effects between the trade balance and exchange rate, indicating that the adjustment path is asymmetric in the long run. Therefore, policy planners in India should consider the asymmetric adjustment between these two drivers to overcome trade balance discrepancies in the short and long run.

JEL Codes: F40, F41, C22, C32, C12

Keywords

Trade balance exchange rate non-linear threshold cointegration asymmetric error-correction causality

Introduction

The relationship between the trade balance and the exchange rate has stirred much interest, particularly in the floating exchange rate era. Exchange-rate movements continually affect imports and exports, directly impacting the trade balance of any economy. International trade theory defines domestic currency depreciation (or devaluation) as directly affecting a country’s trade balance. Moreover, it is expected that improvements to the trade balance do not immediately change at the time of currency depreciation, which indicates that the exports and imports of previous years have long-term consequences for and cumulative impacts on the current trade balance (Arize et al., 2017). Therefore, any exchange-rate volatility has an immediate and cumulative effect on the trade balance (Dogru et al., 2019; Martin, 2016). The current account imbalance and its adverse impact on the exchange rate are serious concerns for a developing economy like India. Since the devastating global financial crisis (GFC) in 2008, there has been an emphasis on evaluating current account deficits (CADs) and their associated negative consequences for most developed and developing economies (Behera, 2015a, 2015b, 2016).

Some scholars claim that the CAD significantly contributes to global financial crises (Blanchard & Milesi-Ferretti, 2009; Caballero et al., 2008; Obstfeld & Rogoff, 2009; Portes, 2009). The high and unsustainable CAD threatens a growing economy and can surmount efforts towards debt insolvency in the long run (Behera, 2017). A high and persistent CAD occurs due to several factors in an open economy model. These can trigger unwarranted impacts on the balance of payments (BOPs) of a country. One significant factor contributing to the deterioration of the CAD is exchange-rate fluctuation. Therefore, exchange-rate dynamics and their effect on the BOPs are vital issues to any emerging economy.

The pioneering Marshall–Learner (M–L) stability condition is usually applicable when measuring the effects of currency depreciation or devaluation on the trade balance of a country.¹

The M–L conditions require the estimation of export and demand models (Arize et al., 2017). Analysing export demand is tedious as it requires a proxy of world income, world export prices and effective exchange rates for all trading partners. However, some studies have employed this approach (Arize, 1990; Warner & Kreinin, 1983). For instance, Arize (1990) used the export and demand approach to investigate the export behaviour of seven developing countries in Asia (India, Indonesia, Korea, Malaysia, Pakistan, the Philippines and Thailand) from 1973 to 1985. Following the M–L condition, the devaluation of home currency can improve the trade balance in the long run. The M–L condition states that depreciation in the exchange rate facilitates exported goods to become competitive abroad. Further, a devaluation in the exchange rate improves the competitiveness of exports and reduces imports (Bahmani-Oskooee, 2001).

Nevertheless, scholars often claim that the exchange rate policy’s depreciation may not always work well to reduce the trade deficit (e.g., in the case of resource-dependent economies). For instance, Auty (2001) found that resource-rich countries underperformed compared to resource-deficient countries. Similarly, Van der Ploeg (2011) and Smith (2014) further explain that resource-rich developing economies cannot successfully transform their depleting exhaustible resources into other productive assets. The relationship between the trade balance and the exchange rate is found to be linear in the literature. Additionally, most researchers assume that the relationship between the trade balance and the exchange rate is linear. For instance, Bahmani-Oskooee (2001), Singh (2002) and Kennedy (2013) used Engle–Granger and Johansen–Juselius cointegration techniques to investigate whether real depreciation has a favourable long-run effect on the trade balance. Other scholars have suggested cointegration analysis to determine the long-run relationship between the trade balance and exchange rate. Arize (1994) and Bahmani-Oskooee (2001) used the Johansen–Juselius cointegration technique (traditional cointegration technique) to examine the long-run equilibrium relationship between the trade balance and exchange rate. Further, previous studies (Arize, 1994; Bahmani-Oskooee, 2001) explain that currency depreciation policies recover the trade balance of emerging countries. Similarly, subsequent studies used the full information maximum likelihood (FIML) estimator developed by Johansen and Juselius (1990), as well as the autoregressive distributed lag (ARDL) bounding test approach of cointegration developed by Pesaran et al. (2001) to evaluate the relationship between the trade balance and exchange rate. For instance, Sun and Chiu (2010) and Ng et al. (2008) found a positive relationship between the trade balance and exchange rate and concluded that currency depreciation improves the trade balance. Similarly, Doojav (2018) found that exchange rate depreciation improves trade balance in the short and long run in the case of Mongolia.

The large CAD of the Indian economy pre-1990 was a severe concern for economists and policymakers. In 1991, the CAD reached a high of 3% of the GDP, and foreign exchange reserves were depleted to the extent that the import bill could not be financed (even for three weeks), leading to the major BOPs crisis. To address this problem, the Indian Government implemented several initiatives following the guidelines of the International Monetary Fund (IMF) in 1991. Accordingly, under the exchange rate management system, the fixed exchange rate system was switched to a managed float exchange rate system to curb the trade deficit, promote export and attract foreign capital with non-resident deposits. Due to these initiatives, the CAD eventually moderated 1–2% of the GDP until 2007–2008, including a surplus from 2001 to 2002 and 2003 to 2004. However, from 2008 to 2012, the CAD increased due to a deceleration in the export sector, growth in oil and gold imports and a rise in investment income payments coupled with a slowdown in investment income receipts. Therefore, the CAD as a percentage of GDP increased again to 4.8% in 2012–2013, whereas the CAD decreased to 2.7% of the GDP in 2018–2019. However, prolonged CAD is challenging because they pressure foreign reserves and increase the burden of debt service. The Indian economy inevitably grew more rapidly following trade and financial liberalisation in 1991. Therefore, it is necessary to investigate possible transmission mechanism channels and the dynamic nexus between India’s exchange rate and trade balance post-1991.

Much of the extant literature focuses on the notion that the relationship between the exchange rate and trade balance is linear and non-linear. Further, most studies use linear adjustment to explain the long-run relationship between the exchange rate and trade balance and assume that this relationship is linear (Arize, 1994; Bahmani-Oskooee, 2001; Ng et al., 2008; Sun & Chiu, 2010). In contrast, few studies additionally examine the non-linear and asymmetrical relationship between the exchange rate and trade balance (Arize et al., 2017; Bussiere, 2013; Dedeoglu & Ogut, 2017; Frankel et al., 2012; Jibrilla & Tijjani, 2015). Using an asymmetric model, Bhat and Bhat (2021) validate no evidence of the J-curve phenomenon in India. Enders and Siklos (2001) found that the assumption of linear adjustment may be misleading because it leads to model misspecifications, while the actual relationship between the trade balance and exchange rate deviates from linearity.

Moreover, scholars have recognised that crucial macroeconomic parameter exhibits non-linear adjustment through business cycles. The literature investigating possible non-linear transmission between the exchange rate and trade balance is scant, particularly for India. This motivates us to explore the pairwise non- linear dynamics of adjustment between India’s trade balance and exchange rate from 1993 to 2017, including the period following the trade liberalisation in 1991. Following Balke and Fomby (1997) and Enders and Siklos (2001), we investigate the non-linear behaviour between the trade balance and exchange rate adjustment in India using the regime-switching threshold models. Therefore, this is an entirely new way of exploring non-linear dynamics that impact the exchange rate on trade. This is supposed to be different from the previous existing (Aziz, 2008; Ng et al., 2008; Singh, 2002; Sun & Chiu, 2010) that have established the linear means of the symmetrical transmission mechanism between the trade balance and the exchange rate.² Furthermore, investigating causality and non-linear dynamics in the open economy models using asymmetric econometric approaches may help to highlight the actual speed of adjustments and transmission mechanism between the trade balance and exchange rate in India.

The major empirical findings of the article are summarised below. First, the empirical results reveal that the long-term relationship between the trade balance and exchange rate in India is asymmetrical. Further, we find that the adjustment speed is substantially slower in trade balance during positive versus negative deviations in the exchange rate from long-run equilibrium. This indicates that adjustments in the trade balance are faster when the exchange rate appreciates. Second, in the bivariate empirical modelling setup, we examine the one-to-one asymmetrical relationship between the trade balance and exchange rate in India using two separate empirical specifications of the models by altering the dependent and independent variables following the Enders and Siklos (2001) threshold autoregression mechanism. The empirical results suggest that the trade balance responds to positive deviations in the exchange rate. In contrast, the exchange rate responds to negative deviations in the trade balance in the short run. However, the results reveal that positive deviations in the exchange rate are quite responsive and that the speed of adjustment is high, indicating that any discrepancies in the trade balance can be adjusted quickly. Third, the empirical results demonstrate the one-way direction of Granger causality between the trade balance and exchange rate in India. This suggests that the trade balance Granger causes the exchange rate. Fourth, the results substantiate the evidence of asymmetric momentum equilibrium adjustment between the trade balance and the exchange rate, indicating a non-linear relationship between the trade balance and the exchange rate in India. Therefore, the main findings of the current research can have significant policy implications for policymakers in emerging economies like India.

The remainder of the article is organised as follows. Second section discusses an overview of the Indian BOP and the exchange rate movement; third section summarises previous studies’ findings; and fourth section discusses the data and empirical methodology used to investigate the asymmetric adjustment between the trade balance and exchange rate in India. The penultimate section discusses the empirical results, and the last section presents the study’s main findings and policy implications.

Brief Overview of Indian BOP and the Exchange-rate Movement

The CAD, supply side shocks, oil price shocks and their impact on exchange rate volatility have always been a concern for emerging economies like India. The CAD issue has been under the radar since the late 1970s when countries experienced large swings in the CAD due to a sharp increase in oil prices and changes in exchange-rate regimes. Further, the Indian economy’s massive trade deficit has been a major concern among economists and policymakers in the last two decades. Historically, India has run a CAD, primarily driven by a merchandise trade deficit partially balanced by net exports of services and net receipts in secondary income (transfers) accounts. India’s external sectors deteriorated during British colonial rule, but the country has remained one of the world’s top 10 exporters. India experienced a sharp decline in merchandise trade from 2.5% in 1949–1950 to a mere 0.5% by the late 1980s (Singh, 2002). Moreover, India faced an external-balance-of-payment crisis in 1991 due to a negative invisible balance, led by a sharp increase in investment income payments and reduced remittance receipts.

The decline in exports compelled India to shift towards a market-oriented economy through massive trade liberalisation measures to promote trade, capital flows, and economic growth. However, the merchandise trade deficit has been the leading factor behind the CAD in India. India’s invisible trade account exhibited a negative balance from 1969–1970 to 1972–1973 and again in 1991. After trade liberalisation in 1991, especially since 2004, India has experienced a significant increase in merchandise trade deficit facilitated by a high rise in oil imports. Moreover, according to the RBI report, India’s CAD was at US$15.8 billion (2.4 % of GDP) in Q1 of 2018–2019 compared with US$15.0 billion (2.5% of GDP) in Q1 of 2017–2018. Further, a widening of the CAD due to the more considerable increase in merchandise imports relative to exports on a year-on-year (YOY) basis was primarily due to a higher trade deficit at US$45.7 billion compared with US$41.9 billion a year ago. Nevertheless, net service receipts increased by 2.1% on a YOY basis, mainly due to net earnings from software and financial services. In 2012 and 2013, when the crude oil price peaked in global markets, the deficit was at 4.2% and 4.8%, respectively. Low crude oil prices have kept the CAD in check, as the invisible account has been mainly stable. With strong support from the capital account and foreign exchange reserves, CAD continuously declined from 2014 to 2017–2018. In summary, after trade liberalisation in 1991, the trade balance was dramatically affected by the volatility in the exchange rate, which motivated us to explore the dynamic linkage between the exchange rate and trade balance in India post-1991.

Figure 1 shows India’s trade balance and exchange rate movement from 1993 to 2017. Moreover, the trade balance shows fluctuation and a sudden drop in approximately 2008. This indicates that due to the GFC in 2008—and its contagion effect that spread to emerging markets—India faced a severe trade deficit, facilitating a severe BOP crisis in 2008. This consequence again created the alarming situation that often occurred before the 1990s. The lower panel of Figure 1 reflects India’s exchange rate movement from 1993 to 2017. The figure shows that the exchange rate was quite volatile before 2008. However, after 2012–2013, the real exchange rate consistently increased, which indicates that the Indian currency was depreciating to the major trading countries’ currencies.

Figure 1.

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

A Brief Review of the Literature

After the 2000s, a plethora of research examines the relationship between exchange rates and trade balance from a theoretical and empirical perspective. The theoretical relationship can be explained from the standpoint of the elasticity approach based on the familiar M–L condition. The M–L condition requires estimating the export and import demand models (Arize et al., 2017). For instance, some studies have employed the export and import demand approach (Goldstein & Khan, 1978; Warner & Kreinin, 1983) to evaluate the relationship between the exchange rate and trade balance. Following theoretical developments, studies by Haynes and Stone (1982) and Himarios (1989) examined the direct relationship between the trade balance and exchange rate from a cross-cultural perspective. These studies used export minus import, or export volume divided by import volume, in place of the trade balance to examine the nexus between the exchange rate and trade balance across different countries. For instance, some studies (Arize et al., 2017; Dedeoglu & Ogut, 2017; Dogru et al., 2019; Sharma & Pal, 2018) suggest cointegration analysis to determine whether there is a long-run relationship between the exchange rate and trade balance across different countries.

Nevertheless, some existing studies obtained a positive relationship between the trade balance and exchange rate (e.g., Bahmani-Oskooee, 2001; Sun & Chiu, 2010). A positive relationship facilitates the devaluation of the currency, which can reduce the trade deficit. In contrast, other studies have still failed to find, or only minimally found, a relationship between the trade balance and exchange rate (Hatemi & Irandoust, 2005; Wilson & Tat, 2001). However, some previous studies have investigated the relationship between the trade balance and exchange rate, finding symmetrical and linear adjustments between these two variables. For example, Bahmani-Oskooee and Gelan (2018), Kennedy (2013), Onafowara (2003), Singh (2002) and Bahmani-Oskooee (2001) found a linear and positive relationship between the trade balance and exchange rate. This suggests that the behaviour of the trade balance relative to the exchange rate is assumed to be the same for currency appreciation or depreciation. The linear relationship between trade balance and the exchange rate is based on the standard linear unit-root test and linear cointegration approaches. However, Enders and Siklos (2001) point out that such a narrow conclusion based on the assumption of the linear-model specification may be misleading when there is a possibility of non-linear dynamics of adjustment between variables. Therefore, the linear relationship may fail to appropriately identify the actual co-movement between the trade balance and exchange rate and could completely ignore the reactions of specific business cycles.

Arize et al. (2017) find that asymmetry arises when positive and negative deviations revert to the mean, or the reversion speed differs between positive and negative deviations from equilibrium. However, following the linear and symmetric assumption, the use of the linear models has led to the consequences of the equivalent adjustment occurring in the positive and negative deviation, a notion that warrants further evaluation. In contrast, several scholars (e.g., Arize & Malindretos, 2012; Sollis et al., 2002) have argued that economic and financial variables are non-linear and could be asymmetric. As explained earlier, utmost care must be taken when interpreting the empirical results that assume a symmetric relationship between the trade balance and exchange rate, which may lead to bias and flawed empirical inferences. Therefore, taking into account the essence of nonlinearity for the economic and financial variables like the exchange rate and trade balance in India, this article investigates the dynamic relationship between these variables using the familiar threshold cointegration approaches. Further, applying asymmetric modelling to examine the dynamic nexus between the trade balance and exchange rate enables an exploration of the possibility of asymmetric movement. Besides this, the dynamics in the speed of adjustment between the trade balance and exchange rate could lead to notable empirical findings for an emerging economy like India. Using the threshold cointegration and asymmetric error-correction modelling approaches to examine the dynamic nexus and asymmetric speed of adjustment between the trade balance and exchange rate in India represents a novel attempt at filling the existing gap in the literature.

Data and Methodology

To investigate the relationship between the trade balance and exchange rate, we use monthly data over the period of 1993–4 to 2017–12. This specific period is considered because India converted its fixed exchange rate to a managed float rate system after trade liberalisation in 1991. The Indian Government also introduced several other liberalising measures, including significant tariff reduction, abolishing quantitative restrictions on non-consumer goods, flexible exchange rates, a liberal set of foreign direct investment (FDI) rules and new current account convertibility. Similarly, financial-sector reforms have included the gradual liberalisation of interest rates, the development of money and capital markets, and operational flexibility for banks to manage their liabilities subject to transparency and prudential norms. A significant surge in export performance due to favourable worldwide factors, exchange rate devaluation and large-scale deregulation significantly affects the trade balance in India.

The trade balance in India is defined as exports divided by imports. Similarly, the real exchange rate is proxied by the 36-currency, trade-weighted, real effective exchange rate. All data are extracted from the Handbook of Statistics on India’s economy, RBI. The study uses linear versus threshold cointegration with the error-correction mechanism to evaluate the long-run equilibrium relationship between the exchange rate and trade balance (Balke & Fomby, 1997; Enders & Granger, 1998). Besides this, we apply various econometrics tests to validate the existence of nonlinearity in the trade balance (denoted as TB hereafter) and exchange rate (denoted as ER hereafter), variables. All variables were converted into a natural logarithm before estimation to avoid a skewed distribution in the dataset.³ Descriptive statistics of the variables are given in Table 1.

Table 1.

Correlations, Descriptive Statistics, Unit-Root Test Results for Trade Balance (TB) and Exchange Rate (ER).

	TB	ER
TB	1		−0.66
ER	−0.66		1
Statistics	Level (TB.)	1st Diff (∆X)	Level (ER.)	1st Diff (∆ER.)
Mean	−0.130	–	2.023	–
SD	−0.131	–	0.026	–
Minimum	−0.323	–	1.979	–
Maximum	0.028	–	2.093	–
Total obs.	297		297
ADF with trend	−5.331	−12.860***	−2.820	−14.704***
ADF with drift	−2.274	−12.878***	−1.708	−14.704***

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Notes: The critical values are −3.45, −2.87 and −3.13 (ADF test, including trend) and −3.45, −2.87 and −2.57 (ADF test, including drift) at the 1%, 5% and 10% levels of significance, respectively (MacKinnon, 1996).

*** denotes significance at the 1% level.

TB: trade balance (defined as the value of exports divided by imports); ER: exchange rate (proxied by the 36 currencies trade-weighted real effective exchange rate).

From an econometric perspective, the first step of the study examines the stochastic properties of the variables while there is evidence of structural breaks. The study applies several econometric procedures to check the presence of unit roots of the variables using various unit-root tests, specifically while there is evidence of single and double structural breaks in the time series data. Inevitably, different macroeconomic and financial parameters are not free from the impact of various supply side and demand shocks. Therefore, it is necessary to check whether external shocks can affect different macroeconomic and financial parameters. Further, due to structural breaks in data and variables, using unit-root tests solely based on assumptions of linearity in the time series data and macroeconomic variables, the slope coefficient may change, giving biased results. Therefore, the study uses various unit-root tests that consider structural breaks in the time series data to examine the probable evidence of structural breaks. Following the evidence of structural breaks, the subsequent empirical interest is to explore the long-run relationship (cointegration) between variables. Second, the study applies familiar econometric procedures to investigate linear and asymmetric cointegration using standard threshold autoregressive (TAR) models. Third, the study uses the asymmetric error-correction model (AECM) to explore the non-linear dynamics of adjustments between variables. As previously discussed, critical economic and financial variables like trade balance and exchange rate in India could behave non-linearly due to various financial shocks, structural shifts in the economic policies following trade liberalisation in 1991, and the oil and gold crisis (among others). Therefore, following the previous literature (Arize et al., 2017; Balke & Fomby, 1997; Dedeoglu & Ogut, 2017; Enders & Granger, 1998; Jibrilla & Tijjani, 2015), we use the asymmetric cointegration and AECM model to explore the non-linear long-run equilibrium relationship between the trade balance and exchange rate. The three standard econometrics methodologies are discussed below.

Unit-root Test in the Presence of Structural Breaks

As macroeconomic data are always subject to breaks either in slope or trend, therefore, it is imperative to examine the evidence of structural breaks while determining the order of their integrations. Without such detection of breakpoints evident from different shocks, modelling procedures will be exposed to inadequacy and biased inferences. Hence, we use the kind of test that captures the dynamics of time series properties and reveals the correct order of integration of the variables. To do so, unlike traditional ADF test, which in its regression equation does not include evidence of breaks (Perron, 1989), Perron and Vogelsang (1992) additive outlier (AO) and innovational outlier (IO) tests are deemed to be a fit to capture the possible multiple structural breaks in the data. According to Perron and Vogelsang (1992), the AO considers evidence of sudden breaks, whereas IO revolves around capturing breaks that unfold gradually over time. The most interesting part of appropriating either AO or IO depends on the transition path, which comes from break structures. To estimate the AO model, first, the deterministic part of the data is removed by utilising regression as follows:

y_{t} = μ + δ D U_{t} + η_{t}

(1)

where DU_t = 0 if t ≤ TB .⁴ Further, the AO model is specified to capture changes in the mean of {y_t}^T₁, when B (1< TB < T). Then by using the already estimated errors in the next structural breaks, evidence is tested by the following equation:

η_{t} = \sum_{i = 0}^{k} ω_{i} D T B_{t - i} + ρ η_{t - 1} + \sum_{i = 0}^{k} C_{i} Δ η_{t - 1} + ε_{t}

(2)

where estimated errors from Equation (1) are indicated by η_t.

TB shows a possible break date, and DTB becomes one conditional upon t = TB+1 and 0 otherwise. Then the study estimated Equations (1) and (2) by the OLS procedure to evaluate the possible evidence of structural breaks in the data by considering the number of break years. Moreover, if the value of t-statistc on ρ is significantly different from zero, the null will be outrightly rejected. So, suppose we follow the alternative hypothesis. In that case, the variable (e.g., trade balance) will be treated as stationary with breaks which further indicates temporal changes in the structure of the variable owing to the strong presence of breaks. In contrast, if the value of t-statistics on ρ is statistically significant, the variable has a unit root. At the same time, permanent change occurs in the long run due to the evidence of breaks.

Unit Roots in the Presence of Double Structural Breaks

For a more robust detection of further multiple breaks period that is significantly evident in time series data, Clemente et al. (1998) tests are employed. Clemente et al. (1998) test is an extension of Perron and Vogelsang (1992) and remodified Equations (1) and (2) as:

y_{t} = μ + δ_{1} D U_{1 t} + δ_{2} D U_{2 t} + η_{t}

(3)

η_{t} = \sum_{i = 0}^{k} ω_{1 i} D T B_{1 t - i} + \sum_{i = 0}^{k} ω_{2 i} D T B_{2 t - i} + ρ η_{t - 1} + \sum_{i = 1}^{k} C_{i} η_{t - i} + ε_{t}

(4)

where DU_jt takes the value fo conditinal upon t > TB_j (j = 1,2) and 0 otherwise. And DTB_jt is said to be one when t become TB_j + 1 and zero, otherwise. TB₁ and TB₂ times in, which means it gets transformed.

To test the null hypothesis, the deterministic portion of the variable has been discarded by running OLS on Equation (3). Further, in connection with Equation (4), other possible evidence of structural breaks is estimated by assuming that there is a presence of unit root in the model. Hence, subject to the testing of the existence of unit root as proposed by the null hypothesis, the rejection of null will be supported with the help of significant ρ of the t-statistic. Therefore, the results of multiple breaks will be established, whereas temporary movements and permanent effects are associated with single and multiple breaks. Likewise, the non-significant ρ will confirm the evidence of the non-stationarity of the variable. Even the structure of the variable can be permanently changed conditionally upon sudden shocks.

Threshold Unit-root Test

Most macroeconomic variables are subject to structural breaks, which may have threshold effects. Hence, using traditional linear unit root tests to determine the order of the integrations is inappropriate. Therefore, the study applies the Caner and Hansen (2001) threshold unit-root test to examine the variables’ order of integration and stationarity properties. Another benefit of the Caner and Hansen (2001) test is that it considers nonlinearity and asymmetric effects in time-series data. Unlike traditional unit-root tests (i.e., ADF and PP), the test developed by Caner and Hansen (2001) is more robust. The TAR model that Caner and Hansen (2001) developed is based on a two-regime model. The TAR model is discussed as follows:

Δ T B_{t} = {θ^{'}}_{1} x_{t - 1} 1_{{z_{t - 1} (λ)}} + {θ^{'}}_{2} x_{t - 1} 1_{{z_{t - 1} \geq}} + ε_{t}

(5)

where TB denotes a dependent variable (e.g., trade balance) for t = 1, …, T, and x_t_–1 = (TB_t_–1 r^'_tΔTB_t_–1 … TB_t_–k)'); 1_{.} represents the indicator function; ε_t is the independently and identically distributed error term; z_t = TB_t_–1 r^'_tTB_t_–m for some delay parameter; m ≥ 1 is the threshold variable; and r_t represents the vector of deterministic components, including an intercept and a possible linear time trend. The autoregressive order is k, and k ≥ 1. In this case, the value of the threshold is unknown, and it takes the values of the interval λ ϵ Λ = [λ₁, λ₂], where λ₁ are λ₂ are selected and satisfies P (z_t ≤ λ₁) = π₁ > 0 and P (z_t ≤ λ₂) = π₂ > 1. Further, it is typical to assume π₁ and π₂ are symmetrical so that π₂ = 1 – π₁. Generally speaking, the respective components of θ₁ and θ₂ can be written as

θ_{1} = (\begin{matrix} ρ_{1} \\ β_{1} \\ α_{1} \end{matrix}), θ_{2} = (\begin{matrix} ρ_{2} \\ β_{2} \\ α_{2} \end{matrix}),

where ρ₁, ρ₂, β₁, β₂ are scalars and α₁, α₂ are k × 1 vectors. Therefore, ρ₁ and ρ₂ measure the slope coefficients of TB_t_–1, whereas β₁ and β₂ measure the slope coefficients of the deterministic components (TB_t_–1, …, ΔTB_t_–k) in a two-regime model. The TAR model in Equation (5) is estimated using the least-squares method.

Following Caner and Hansen (2001), the current study examines whether the threshold effect exists in the data by considering the null hypothesis (i.e., H₀: θ₁ = θ₂). Further, Caner and Hansen (2001) formulated a standard Wald test to examine evidence of the threshold effect in the time series, as follows:

W_{T} = T (\frac{{\hat{σ}}_{0}^{2}}{{\hat{σ}}^{2}} - 1)

(6)

where ${\hat{σ}}^{2}$ represents the residual variance of the TAR model, and ${\hat{σ}}_{0}^{2}$ represents the residual variance of the linear model following the null hypothesis. Caner and Hansen (2001) advocated that the critical values cannot be estimated in the strong presence of the data’s non-stationary and asymptotic features. Therefore, a bootstrap method proposed by Caner and Hansen (2001) is applied for the same⁵. Caner and Hansen’s (2001) threshold unit-root test results are reported in the fifth section of this article.

Threshold Cointegration Analysis

The linear form of cointegration (Engle & Granger, 1987) does not take care of asymmetries present in the data due to a series of breaks and nonlinearity. Therefore, the study prefers incorporating Enders and Siklos’s (2001) cointegration with regime switching mechanism to evaluate asymmetric adjustment effects between the trade balance and exchange rate. The empirical specification which formulates the regime-switching cointegration between the trade balance and the exchange rate is discussed below:

T B_{t} = α_{1} + β_{2} E R_{t} + ε_{1 t}

(7)

where TB and ER represent the trade balance and real exchange rate in India.

The standard empirical specification of the regime-switching cointegration is discussed below:

Δ {\hat{ξ}}_{t} = ρ_{1} I_{t} {\hat{ξ}}_{t - 1} + ρ_{2} (1 - I_{t}) {\hat{ξ}}_{t - 1} \sum_{i = 1}^{P} φ_{i} Δ {\hat{ξ}}_{t - i} + μ_{t}

(8)

I_{t} = {\begin{matrix} 1 if {\hat{ξ}}_{t - 1} \geq τ \\ 0 if {\hat{ξ}}_{t - 1} \leq τ \end{matrix} for TAR model

(9)

I_{t} = {\begin{matrix} 1 if Δ {\hat{ξ}}_{t - 1} \geq τ \\ 0 i f Δ {\hat{ξ}}_{t - 1} \leq τ \end{matrix} for MTAR model

(10)

where I represent the heavy-side indicator, p denotes lags; ρ₁, ρ₁ and φ_i, represent coefficients, and τ denotes the threshold value. Besides, ${\hat{ξ}}_{t}$ represents the estimated residual factors in the model. Equation (9) is attributed to TAR specification. In contrast, the momentum TAR (MTAR) model is defined in Equation (10). Further, TAR specifically evaluates residuals that are characterized by deep asymmetrical manoeuvres (Enders & Granger, 1998; Enders & Siklos, 2001). The MTAR specification, on the other hand, encapsulates dynamic asymmetries of the estimated errors when adjusting the irrespective of directions. Chen and Tsay’s (1993) technique is appropriate for approximating the required consistent threshold candidate value. Equations (9) and (10) are further framed to estimate the consistent-TAR (C-TAR) and consistent-MTAR (C-MTAR) models for drawing the threshold values. An F-test is used to test cointegration (H₀: ρ₁ = ρ₂ = 0) against (H₀: ρ₁ = ρ₂ ≠ 0) the alternative hypothesis for C-TAR or C-MTAR with asymmetric adjustments.

Asymmetric Error-correction Model (AECM) with Threshold Cointegration

After finding evidence for cointegration, Engle and Granger (1987) further developed an error-correction mechanism to identify the speed of adjustment between variables. Balke and Fomby (1997) and Enders and Granger (1998) further developed nonlinearity in the adjustment techniques by decomposing the typical error correction model into negative and positive components. The paramount rationale of employing AECM is to scrutinize whether cumulative positive and negative exchange rate deviations alter the trade balance asymmetrically in India and delineate it in the following forms.

\begin{array}{l} Δ T B_{t} = θ_{t b} + δ_{t b}^{+} E_{t - 1}^{+} + δ_{t b}^{-} E_{t - 1}^{-} + \sum_{J = 1}^{J} α_{t b J}^{+} Δ T B_{t - j}^{+} + \sum_{J = 1}^{J} α_{t b J}^{-} Δ T B_{t - j}^{-} + \\ \sum_{J = 1}^{J} β_{t b J}^{+} Δ E R_{t - j}^{+} + \sum_{J = 1}^{J} β_{t b J}^{-} Δ E R_{t - j}^{-} + ϑ_{t b t} Δ E R_{t} \\ = θ_{e r} + δ_{e r}^{+} E_{t - 1}^{+} + δ_{e r}^{-} E_{e r}^{-} + \sum_{J = 1}^{J} α_{e r J}^{+} Δ E R_{t - j}^{+} + \\ \sum_{J = 1}^{J} α_{e r J}^{-} Δ E R_{t - j}^{-} + \sum_{J = 1}^{J} β_{e r J}^{+} Δ T B_{t - j}^{+} + \sum_{J = 1}^{J} β_{e r J}^{-} Δ T B \end{array}

(12)

The subscript t denotes time, and j represents the time lags in the variables. All the lagged variables in the first difference form (i.e., ΔTB_t _{– j} and ΔER_t _{– j} ) are decomposed into positive and negative components indicated by ⁺ and ⁻. For instance, ΔTB⁺_t _{– j} is equal to TB_t _{– 1} – TB_t _{– 2} if TB_t _{– 1}>–TB_t _{– 2} and equal to zero otherwise. Further, TB_t _{– 1} is equal to TB_t _{– 1} – TB_t _{– 2} if TB_t _{– 1}<– TB_t _{– 2} and equal to zero otherwise. Similarly, ΔER⁺_t _{– j} is equal to ER_t _{– 1} – ER_t _{– 2} if ER_t _{– 1}>–ER_t _{– 2} and equal to zero, otherwise; and ER_t _{– 1} is equal to if ER_t _{– 1}<–ER_t _{– 2} and zero otherwise.⁶

Empirical Results

Descriptive Statistics and Unit Root Test

The correlation, descriptive statistics and unit-root results of the variables are reported in Table 1. The results reveal a negative correlation between the trade balance and the exchange rate in India. The average values of the trade balance and exchange rate are −0.130 and 2.023, respectively. This shows that, on average, after the 1990s, the trade balance in India was negative, whereas the exchange rate rose and continually depreciated. The empirical results suggest that the trade balance shows depressing volatility, while the exchange rate shows an upward trend in volatility. Initially, we used the ADF unit-root test to evaluate the order of the integration of the variables. The results show that both variables have unit roots at the level. However, the unit root problem is eliminated at the first difference, indicating the variables’ I(1) process.

The critical problem that emerges from the ADF test is that the ADF test is not correctly taking care of possible structural instability due to various macroeconomic shocks and volatility in time series data. Inevitably, because of different external, supply and demand side shocks in an emerging economy like India, we cannot rule out the possibility of structural breaks in the time series data. Therefore, to address the issues of structural breaks, we apply the AO model in this study.⁷

Considering the evidence of multiple breaks determined endogenously, the study anticipates not accepting the null hypothesis that ignores the numerous breaks in the time series data and variables. Hence, verifying unit roots with multiple breaks endogenously determined can have more robust evidence than one break (Ben-David et al., 2003; Lumsdaine & Papell, 1997; Maddala & Kim, 2003). The double-break unit-root test and figures are depicted in Table 2 and Figures 2 and 3 of the TB and ER. The empirical findings of the double break in TB are significantly negative, indicating that unanticipated shocks have adverse and permanent effects. The TB is stationary around the mean (swaps in 2005:1 and 2013:3). Correspondingly, for the exchange rate, the significant structural breakpoint is evident in 2010:2. The empirical findings exhibit double and single structural breaks in the trade balance and exchange rate in India. Followed by the authentication of multiple breaks with non-stationarity of the TB and ER, symmetry and asymmetry cointegration have been applied.

Table 2.

AO Model Results for Two-break Test.

Variables	δ₁	δ₂		First Break	Second Break
TB	−0.111***	−0.006***	−0.379***	2005: Jan	2013: March
	[−19.173]	[3.590]	[−3.293]
	(0.000)	(0.000)	(0.000)
ER	0.473***	−0.006	−0.100***	2010: Feb	2012: March
	[12.767]	[−1.529]	[3.629]
	(0.000)	(0.127)	(0.000)

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Notes: Structural break year dummy variable coefficients δ. *** p<.01, ** p<.05, * p<.10. Values in [ ] and ( ) represent t-statistics and p values, respectively.

Figure 2.

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Figure 3.

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Before applying further tests to examine cointegration, we conducted a series of nonlinearity tests to explore the significant evidence of nonlinearity in the TB and ER variables. The results of nonlinearity tests are reported in Table 3. The Broock-Dechert-Scheinkman (BDS) test of temporal dependence following Broock et al. (1996) rejects the null of non-linear temporal dependence and accepts the existence of non-linear dependence in TB and ER. The neural network linearity test (Teraesvirta et al., 1993) and the WNN test (White and Lee test; Lee et al., 1993) for neglected nonlinearity in time-series models reveals substantial evidence of nonlinearity in ER versus TB in India. Further, the RUN test that Bradley (1968) developed to detect non-randomness in the series rejects the null hypothesis of randomness and accepts that a series like ER and TB are not random at the 5% significance level. Moreover, considering the evidence of nonlinearity in both variables, the study applies non-linear threshold unit-root tests to examine the order of integration in the TB and ER variables.

Table 3.

Nonlinearity Test Results.

BDS	ER				TB
ε	0.28	0.57	0.86	1	0.28	0.57	0.86	1
m = 2	−1.44	0.4	0.75	0.93	58.9	40.58	30.25	24.43
m = 3	6.69	2.45	1.96	1.63	74.7	48.66	33.64	25.95
m = 4	7.65	2.99	1.63	1.24	95.3	58.71	36.93	27.07
m = 5	11.08	4.48	1.93	1.29	129	71.32	40.48	27.91
m = 6	15.81	4.54	1.74	1.16	178	88.91	44.73	28.96
m = 7	−5.11	3.69	1.43	0.84	264	113.93	50.01	30.19
m = 8	0.4	4.43	1.08	0.53	411	147.28	56.29	31.48
		F-statistic		p value		F-statistic		p value
NNT		0.49		0.61		3.6***		0.00
WNN		0.51		0.59		3.65***		0.02
RUN		SN		p value		SN		p value
RUN				0.37		−4.21		2.45

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Notes: The BDS (Broock-Dechert-Scheinkman; Broock et al., 1996) represents a test for linear temporal interdependence. The m represents the embedding dimension, and ε denotes the radius of the comparison ball in terms of the standard deviation of the series. NNT represents the neural network linearity test (Teraesvirta et al., 1993); WNN represents the White and Lee test (Lee et al., 1993) for neglected nonlinearity in time series models; and the RUN (Bradley, 1968) test is used to detect non-randomness in the series. SN depicts the standard normal test.

Utilising the Cancer and Hansen (2001) test, the threshold effects of TB and ER are presented in Tables 4 and 5. In Table 4, the top panel indicates the results using the region λ = [0.15, 0.85] and the bottom panel shows the region λ = [0.10, 0.90]. The results of the threshold unit-root test indicate that the null of nonlinearity can be rejected at the 5% significance level (in the top panel, when the lag order m is set at 2 and 3). However, the results reported in Table 5 suggest significant evidence of a threshold effect in the ER variable in the bottom region λ = [0.10, 0.90] at different delays only, with orders starting from 1 to 3. The upper region with λ = [0.15, 0.85] does not reject the null of linearity in ER at different delay orders. The threshold effect in the trade balance and exchange rate are presented in Figures 4 and 5.

Table 4.

The Bootstrap Threshold Test for TB.

M	Wald Test	Bootstrap			p values
λ = [0.15, 0.85]	Wald Test	10% CV	5% CV	1% CV	p values
1	28.89	31.51	34.56	41.32	0.17
2	33.66	31.37	34.34	40.92	0.05
3	41.94	31.52	34.38	40.73	0.00
λ = [0.10, 0.90]
1	26.19	31.86	34.72	41.49	0.30
2	23.68	31.81	34.61	40.22	0.48
3	35.29	31.66	34.44	40.01	0.03

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Note: λ indicates the threshold value, and m represents lag order.

Table 5.

The Bootstrap Threshold Test for ER.

m	Wald Test		Bootstrap		p values
λ = [0.15, 0.85]	Wald Test	10% CV	5% CV	1% CV	p values
1	43.31***	32.31	35.80	42.94	0.00
2	38.91**	32.42	35.34	41.70	0.02
3	33.29*	32.33	35.32	42.05	0.07
λ = [0.10, 0.90]
1	3.21	9.76	11.71	16.37	0.87
2	7.42	9.68	11.83	16.40	0.37
3	1.97	9.67	12.02	16.87	0.97

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Note: λ indicates the threshold value, and m represents lag order.

Figure 4.

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Figure 5.

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Further, the empirical results reject the null of linearity at different lag orders in both regions at the 5% significance level, indicating evidence of a threshold cointegration between variables during the study period from 1993 to 2017. The evidence of nonlinearity and threshold effects suggests that both variables are non-stationary (see Tables 6 and 7). Following Cancer and Hansen’s (2001) test, the empirical results reveal that the test statistics for one-sided Wald test statistics are less than 1% critical values, which represents a failure to reject the null hypothesis of the non-stationary series. Further, the individual test statistics t₁ and t₁ cannot be used to reject ρ₁ = 0 or ρ₂ = 0, indicating that the trade balance and exchange rate are non-stationary.

Table 6.

Unit-root Test for the Threshold Autoregressive Model of TB.

m	One Wald Test		t–1 Test			t–2 Test
m	W_1T	1% CV	t-stat	1% CV	p value	t-stat	1% CV	p value
1	6.339	16.04	0.822	3.55	0.56	2.37	3.50	0.10
2	9.158	15.80	2.484	3.58	0.09	1.72	3.51	0.27
3	8.783	15.34	1.983	3.50	0.18	2.20	3.48	0.13
4	5.973	15.55	0.190	3.50	0.53	2.26	3.45	0.12
5	9.850	15.64	2.118	3.50	0.15	2.31	3.52	0.11
6	7.156	15.67	2.035	3.49	0.18	1.73	3.47	0.26
7	8.189	15.66	2.809	3.54	0.05	0.54	3.47	0.65
8	5.026	15.63	0.443	3.50	0.68	2.19	3.46	0.14
9	6.633	15.60	1.430	3.54	0.36	2.14	3.51	0.14
10	10.148	15.64	1.494	3.50	0.34	2.88	3.49	0.04

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Note: m = delay order, W_1T = one side Wald statistic, 1% CV = 1% critical value, p value = Bootstrap p value.

Table 7.

Unit-root Test for the Threshold Autoregressive Model of ER.

m	One Wald Test		t–1 Test			t–2 Test
m	W_1T	1% CV	t-stat	1% CV	p value	t-stat	1% CV	p value
1	3.15	15.84	1.77	3.54	0.26	−0.24	3.51	0.85
2	7.42	15.98	2.66	3.57	0.07	0.57	3.49	0.65
3	1.97	16.30	1.00	3.60	0.52	0.98	3.49	0.52
4	0.88	16.20	0.46	3.62	0.68	0.81	3.58	0.58
5	1.52	16.74	0.78	3.58	058	0.95	3.55	0.53
6	0.98	16.87	–0.77	3.66	0.91	0.99	3.53	0.52
7	0.90	16.83	–2.06	3.69	0.98	0.95	3.52	0.54
8	1.08	17.20	0.84	3.70	0.58	0.59	3.60	0.64
9	1.92	16.93	–0.92	3.70	0.93	1.38	3.64	0.39
10	2.61	16.96	1.27	3.67	0.43	0.98	3.53	0.53

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Note: m = delay order, W_1T = one side Wald statistic, 1% CV = 1% critical value, p value = Bootstrap p value.

Results of the Asymmetric Cointegration

The asymmetric (non-linear) cointegration between variables can be tested using TAR models. Moreover, four types of threshold models—TAR, MTAR, C-TAR and C-MTAR—are used to check the non-linear cointegration between the trade balance and exchange rate in India. The estimated results are reported in Table 8. Further, all the non-linear models specify a maximum of 12 lags to address the serial correlation problem. We have used AIC, BIC and Ljung–Box Q statistics to check the correct specification of the models. Besides, results reveal that all the empirical models are free from serial correlation issues.

Table 8.

Results of Engel–Granger and Asymmetric Cointegration.

Item	E-G	TAR	C-TAR	MTAR	C-MTAR
Lag	3	3	3	3	3
Threshold		0	0.066	0	0.013
ρ₁⁺ †	−0.243***	−0.17***	−0.213***	−0.109**	−0.055
	(−4.316)	(−2.87)	(−3.238)	(–1.785)	(−0.816)
ρ ₁ ^–	__	−0.142**	−0.122***	−0.192***	−0.207***
		(−2.529)	(−2.33)	(−3.498)	(−4.073)
Diagnostic Test
AIC	−3.536	−1031.309	−1032.538	−1032.367	−1034.913
BIC	−3.498	−1009.228	−1010.457	−1010.285	−1012.832
Q_LB.(4)		0.188	0.195	0.166	0.137
Q_LB.(8)		0.284	0.30	0.276	0.227
Q_LB.(12)		0.033	0.025	0.043	0.039
Hypothesis Testing
H₀: No symmetric cointegration	−3.884***	6.47***	7.103***	7.015***	8.333***
H₀: No asymmetric cointegration		0.135	1.103	1.177	3.701**
H₀: p value		[0.714]	[0.247]	[0.279]	[0.055]
Total obs.	297	297	297	297	297
Coint. obs.	293	293	293	293	293

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Notes: † For the Engle–Granger cointegration test, ρ₁ refers to ρ in Equation (8). For the Engle–Granger cointegration test, the critical values are −2.572, −1.941 and −1.615 at the 1%, 5% and 10% levels, respectively. Q_LB.(p) denotes the significance level for the Ljung–Box Q statistic; it tests serial correlation based on p (lag) autocorrelation coefficients (p = 4,8, 12). ϕ is the threshold cointegration test with the critical values from Enders and Siklos (2001). F is a standard F-test on the asymmetry of the price transmission. Numbers in the brackets and square brackets are t-values and p values. *** p<.01, ** p<.05, * p<.10.

Following Chen and Tsay’s (1993) procedures, we have estimated the threshold models. Empirical results report that the threshold values for C-TAR and C-MTAR models are −0.066 and 0.013, respectively. Further, empirical results suggest evidence of asymmetric cointegration between TB and ER. The threshold model selection criteria based on the AIC and BIC criterion for the trade balance and exchange rate are shown in Figure 6. Figures 7 and 8 portray the asymmetric effect (threshold value) of the non-linear (asymmetric) models (TAR and MTAR).

Figure 6.

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Figure 7.

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Figure 8.

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

The null hypothesis of linear cointegration is rejected at the usual significance level indicated by Φ between the trade balance and exchange rate [Φ (H₀: ρ₁ = ρ₂ = 0)] in the C-TAR specification, which in other words, strongly supports threshold cointegration between TB and ER. After finding support for threshold cointegration between the variables, we examine whether the long-run equilibrium adjustment is asymmetric. However, the C-MTAR model outrightly rejects the evidence of linear adjustment (H₀: ρ₁ = ρ₂) with the usual significance level,⁸ and strongly supports the evidence of long-run asymmetrical equilibrium adjustment. Hence, the TB and ER react differently to positive and negative deviations from their equilibrium path.

Further, based on the estimates of the C-MTAR model, positive and negative shock values are −0.055 and −0.207. From this point estimations, it is explicit that the speed of adjustment to converge into the long-run equilibrium is more expeditious for negative than positive shocks. Moreover, results show that positive deviations take around 5.5% per month while negative deviations get hold of 20.7% per month independently to converge into long-run equilibrium. More intuitively, approximately negative deviations get exhausted in 18 months (1/0.055 =18.18 months), and positive deviations in just 5 months (1/0.207 = 4.83 months).⁹ Aforementioned put forward a considerable nether momentum of convergence in the trade balance for positive (above threshold) deviations from long-term equilibrium versus negative (below threshold) deviations in the exchange rates. Therefore, the results show that the deficit in the trade balance adjustments seems faster when the exchange rate appreciates than when the exchange rate depreciates. Taken together, the results reveal that threshold cointegration and asymmetric adjustments are present in all specified threshold models. Further, the study has used the C-MTAR model rather than the C-TAR model to investigate the asymmetric speed of adjustment between variables.¹⁰ Additionally, we use Equations (11) and (12) following Chen and Tsay’s (1993) methods of AECM to evaluate the causal effect between variables.

Results of the Asymmetric Error-correction Model

Our results validate the evidence that the TB and ER are asymmetrically cointegrated. The evidence of asymmetric cointegration further suggests a need to assess the one-to-one asymmetric relationship and speed of adjustment between variables using the AECM. The one-to-one correspondence and asymmetric adjustment between the bi-variate framework can be efficiently addressed by alerting the dependent and independent variables in two separate AECMs. Table 9 presents the estimated results while we alter the dependent and independent variables in two different AECMs. In the trade balance AECM model, the results show that the coefficients α^–₁, α⁺₄, α^–₄ and β^–₁, δ⁺ are significant at the 5% level. Similarly, in the exchange rate AECM model, the five coefficients (α^–₄, β⁺₂, β^–₁, β^–₂, δ^– ) are significant at the 1% level, while the other three coefficients are significant at the 5% level. For the estimated equations, the R² statistics are 0.103 and 0.296, respectively. Moreover, based on the AIC and BIC statistics, the model specification fits better for the trade balance AECM than the exchange rate AECM.

Using F-tests, we evaluate the Granger causality hypothesis in the AECM. For the trade balance AECM, the F-statistic values for the first and second hypotheses are 2.588 and 1.174, respectively. However, the results reveal that only one F-statistic is statistically significant. This indicates that the trade balance affects the exchange rate considerably in one direction. Similarly, the results reveal that using F-statistics to validate the first hypothesis produces a result not significantly different from zero in the exchange rate AECM. However, to validate the second hypothesis, the estimated F-statistic is 6.477 and substantially different from zero at the 1% level. This suggests that the trade balance affects the exchange rate. More specifically, this indicates that the previous year’s exchange rate substantially affects the current year’s trade balance. Therefore, in the short run, the exchange rate of current and prior periods likely substantially impacts the trade balance during the current period.

The asymmetric transmission mechanism between the trade balance and exchange rate can be examined using several hypotheses. Initially, the first hypothesis indicates the distributed lag asymmetric effect between the variables. To empirically validate and generate detailed insights concerning the transmission mechanism between trade balance and exchange rate, eight F-tests can be performed based on the AECM techniques.¹¹ The reported F-statistic value is 0.892, and it is not statistically significant. This suggests the impact of lag variables does not have an asymmetric effect on each other in the one-to-one correspondence models.

The second hypothesis (H₀₅) evaluates the asymmetric cumulative impact between the two variables. Results reported in Table 9 suggest evidence of a cumulative asymmetric effect from TB to ER. Further, the results reveal no significant evidence of an asymmetric cumulative impact from ER to TB, even if the specified lag varies from 0 to 4. Therefore, the asymmetric effect of the distributed lag between TB and ER is absent. In contrast, the results reveal the presence of cumulative asymmetric impacts from the trade balance to the exchange rate in India.

Table 9.

Results of the AECM with Threshold Cointegration.

Item	TB		ER
Item	Coefficients	t-statistics	Coefficients	t-statistics
Θ	0.002*	1.717	−0.002	−0.311
α1⁺	0.083	0.736	−0.568	−0.755
α2⁺	−0.155	−1.373	0.525	0.699
α3⁺	−0.046	−0.422	0.29	0.04
α4⁺	−0.225**	−2.067	0.469	0.648
α1^–	0.269**	2.564	−0.625	0.925
α2^–	−0.063	−0.589	0.205	−0.881
α3^–	−0.037	−0.342	0.424	0.284
α4^–	0.196*	1.85	−0.426***	4.604
β1⁺	0.011	0.696	−0.245***	−4.006
β2⁺	0.025	1.55	0.664***	−2.316
β3⁺	0.019	1.192	−0.251**	−2.406
β4⁺	0.019	1.251	−0.22**	−2.18
β1^–	0.035**	2.106	−0.394***	−3.614
β2^–	0.008	0.503	−0.49***	−4.564
β3^–	0.001	0.048	−0.092	−0.86
β4^–	0.012	0.796	−0.136	−1.332
δ⁺	−0.026**	−2.317	0.005	0.062
δ^–	−0.002	−0.27	−0.198***	−3.578
R2	0.103	—	0.296	—
AIC	−2126.373	—	−1020.714	—
BIC	−2052.838	—	−947.179	—
QLB (4)	0.960	—	0.680	—
QLB (8)	0.802	—	0.216	—
H01: α1⁺= α1^– = 0 for all lags	2.588***	[0.01]	0.359	[0.94]
H02: βi⁺= βi^–= 0 for all lags	1.174	[0.32]	6.477***	[0.00]
H03: α2⁺= α2^–	0.253	[0.62]	0.892	[0.35]
H04: β4⁺= β4^–	0.076	[0.78]	0.265	[0.61]
H05: Σ⁴i =1 αi⁺ = Σ⁴i =1 αi^–	6.148***	[0.01]	0.01	[0.92]
H06: Σ⁴i =1 βi⁺ = Σ⁴i =1 βi^–	0.158	[0.69]	0.01	[0.92]
H07: δ⁺= δ^–	3.014**	[0.08]	5.107***	[0.02]

Source: Authors own computations using the datasets of the Handbook of Statistics on Indian Economy, RBI.

Notes: ***p<.01, **p<.05, *p<.10, p values are in brackets.

The last hypothesis (H₀₇: δ⁺ = δ^–) evaluates the momentum equilibrium adjustment path asymmetries between the trade balance and exchange rate in India. The estimated values of the F-test are positive and significantly different from zero. This supports momentum equilibrium adjustment path asymmetries between India’s trade balance and exchange rate. Therefore, this indicates that the reaction to deviations is not the same in the short-term and long-term. Moreover, the positive error-correction term (δ⁺) in the trade balance model is negative and statistically significant. Furthermore, the results reveal that in the ER model, the estimated coefficient of the negative error-correction term (δ^–) is −0.198 and statistically significant. Therefore, this indicates that, in the trade balance and exchange rate AECM, the speed of adjustment differs following negative and positive shocks. Moreover, the results exhibit that magnitude and speed of adjustment to correct the trade balance discrepancies is 2.6% in a month, following a positive deviation in the exchange rate in the short run. Therefore, measured in response time, it takes approximately 38.5 months for positive deviations in the exchange rate to digest any disturbances in the trade balance. Similarly, in the exchange rate AECM, the magnitude of the error-correction coefficient suggests that the exchange rate significantly responds to negative deviations in the trade balance by 19.8% in a month in the short term. Therefore, it takes approximately 5.05 months for negative deviations in the trade balance to balance any instability in the exchange rate. In the short run, towards restoring stability in the exchange rate, negative deviations have a much higher reaction speed from long-term equilibrium than positive deviations. Similarly, in correcting trade-balance discrepancies in the short run, positive divergences involve a higher adjustment rate than negative deviations in return to long-term equilibrium.

Conclusions and Policy Implications

This article investigates the asymmetric dynamics of the inter-relationship between TB and ER in India using threshold cointegration and the AECM approaches by considering monthly data from 1993:04 to 2017:12. The empirical results support notions that the relationship between TB and ER is asymmetric. The asymmetric cointegration results reveal a lower speed of convergence in the trade balance following a positive deviation than negative deviations in the exchange rate, indicating that a deficit in trade-balance adjustments is faster when the exchange rate appreciates than during periods when the exchange rate depreciates. Besides this, the results support the momentum adjustment path asymmetries between TB and ER in India. Furthermore, results exhibit that the speed of digesting positive and negative shocks differs in the TB and ER models.

Using the AECM, results reveal that any discrepancies in the trade balance significantly respond only to positive deviations in the exchange rate in the short run. In contrast, instability in the exchange rate substantially responds only to negative deviations in the trade balance. Moreover, our results reveal that positive deviations are highly responsive in the short run and adjust quickly if there are any discrepancies in the TB. Similarly, in the exchange rate AECM, the negative divergence involves a substantially faster speed of adjustment than the positive deviations. Therefore, negative variations in the trade balance quickly adjust for any instability in the ER in the short run. Further, our results reveal a one-way direction of Granger causality between TB and ER, indicating that TB Granger substantially causes ER.

There is a possibility that apart from the trade balance and exchange rate, several other factors, such as interest rate, price index and trade policy, can affect the transmission mechanism between TB and ER. Moreover, the analysis could be extended by examining the impact of exchange rates on trade balance across a group of developing countries. Therefore, using the panel threshold model may be worthwhile investigating the asymmetric transmission mechanism between TB and ER across emerging economies by including other institutional and macroeconomic factors. However, we leave the analysis of these dimensions for future research.

We find that trade balance and exchange rate are asymmetrically related, and there is a one-to-one asymmetric adjustment between them. Therefore, understanding the asymmetric relationship, asymmetrical adjustment and asymmetrical causality between TB and ER could substantially help policymakers, global investors and the governments of developing countries like India. Specifically, for example, the empirical findings from this article can provide guidance around financial factors when the Indian Government is concerned about import substitution or export promotion policies in the country. The findings from our analysis suggest that TB and ER are non-linearly related, and their adjustment process is asymmetrical. Moreover, we find that the trade balance and exchange rate are asymmetrically related and significantly affected by negative and positive shocks, and the speed at which they revert to equilibrium varies. Therefore, from a policy perspective, Indian policymakers should consider the non-linear behaviour between macroeconomic parameters such as trade balance and exchange rate to overcome trade balance discrepancies in the short versus the long run. Taken together, the findings from this article suggest that the use of linear models does not provide an adequate description of the current trends in the trade deficit due to the asymmetric movements of the exchange rate, particularly after India’s liberalisation period.

Footnotes

Acknowledgements

We would like to thank anonymous journal reviewers for giving us constructive comments to improve the article significantly. We would also like to thank the Editors and Managing Editors of the journal for providing inputs to revise the article following the referees’ valid suggestions.

Declaration of Conflicting Interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Ethical Approval

This article does not contain any studies with human participants or animals performed by any authors.

Funding

The authors received no financial support for the research, authorship, and/or publication of this article.

Notes

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