Unravelling the nexus between energy prices and exchange rate in Malaysia: Fresh insights from a non-linear perspective using threshold cointegration analysis

Abstract

This paper proposes a nonlinear threshold cointegration framework to study how energy prices affect Malaysia's nominal exchange rate, considering the money supply, income, and interest rate. The study employs a threshold cointegration approach utilizing threshold autoregressive and momentum threshold autoregressive models. The momentum threshold vector error correction model determines the short-run adjustment of exchange rate deviation from the long-run equilibrium level. The findings reveal that the nonlinear adjustment process to capture the short-run deviation in the long-run equilibrium path is primarily influenced by energy prices, money supply, and interest rates. These results highlight the importance of considering the impact of energy prices on exchange rate policies when formulating and implementing economic policies in Malaysia. The findings can also be valuable for decision-makers to comprehend the future dynamics of exchange rates and make well-informed decisions.

1. Introduction

The puzzling phenomena of exchange rate determination remain mystified from its inception. The earliest and most significant factors in determining the exchange rate are the monetary fundamentals, which claim that monetary fundamentals disclose limited information in the short run [1]. Since then, there has been conflicting empirical evidence on the ability of monetary fundamentals to explain changes in the exchange rate. However, it is generally agreed upon that over an extended period, the monetary fundamentals can manage the dynamics of the nominal exchange rate [[2], [3], [4]]. Researchers' primary focus in exchange rate modelling is still on monetary models. Still, the failings of macroeconomic fundamentals have prompted them to look for other methods for estimating the exchange rate in the short run.

The in-depth analysis of the literature highlighted that numerous factors can be investigated to examine the exchange rate. These factors include the choice of significant determinants, sample period, and linear or nonlinear model [5]. A crucial aspect of macroeconomic analysis and market surveillance is the evolution of the exchange rate over a certain period. It has been challenging for market practitioners and academicians to determine exchange rates for a different time frame. There are two distinct periods during which the exchange rate determination can be divided: the long and short run [6]. The short-run determination refers to the period of tick by tick, daily, and monthly. In comparison, the long-run determination refers to the monthly, quarterly, and annual periods. Thus, the researchers attempt to determine the exchange rate that must make various choices among different horizons, diverse factors, and techniques.

Besides, several methods are available for evaluating the exchange rate's dynamic behavior over the long and short terms. The validation of monetary models provides limited evidence on the exchange rate adjustment dynamic using linear techniques. These traditional linear methods cannot explain the complex nonlinear patterns and dynamics of exchange rates [7]. The complex problem of nonlinear patterns in determining exchange rates has led researchers to employ nonlinear approaches. The economic crises like the OPEC decision-making, the global financial crisis (2008–2010), the geopolitical major events of 2006, and the Asian financial crisis (1997–1998), which resulted in an oil shock, give the empirical rationale for the nonlinear pattern of exchange rates [8]. These crises may result in structural breaks and a nonlinear foreign exchange response that distorts linear assumptions. The nonlinear dynamics of the exchange rate have been extensively supported by earlier studies [7,9].

Nevertheless, past studies used models that impose nonlinear symmetry methods. Meanwhile, the preferences of an asymmetric policy cannot be explored using symmetric adjustment models. Therefore, it is necessary to examine the impact by employing a nonlinear adjustment model, which enables the determination of the speed of adjustment that may capture the nominal exchange rate equilibrium.

In emerging and developing economies, the exchange rate has remained an integral subject of debate for the past few decades. Emerging economies are usually more volatile and contain higher liquidity risk than developed economies due to low trading volume [10]. As Malaysia is a small and open economy, the financial crisis has affected it more severely, which may directly affect the exchange rate. The unique regimes of exchange rates in Malaysia make it more complex than other emerging countries [11]. In Malaysia, macroeconomic policies are developed to address the balance in core objectives such as economic growth, economic stability, and equity.

Meanwhile, fiscal and monetary policy meet the objectives of development and stabilization. In Malaysia, the formulation of fiscal policy concentrates more on ethnic and political dimensions, whereas monetary policy focuses on two policy objectives: exchange rate stability and price stability. Fiscal reforms in Malaysia have grown considerably more slowly than monetary policy reforms and financial restructuring [12].

Nevertheless, the political factor's influential role must be addressed, particularly during the financial crisis. In contrast, an informal commitment toward the stability of the exchange rate might initiate policy dilemmas when confronting external shocks in the future. The external shock or global externalities are captured through trade transmission channels that influence exporting commodity currencies like Malaysia.

The previous studies documented that macroeconomic fundamentals endogenously determine the exchange rate. However, identifying exogenous shock by monetary fundamentals, which would help examine the exchange rate behavior, is impossible. The exogenous shock is captured through the trade transmission channel, which affects the exporting commodity currency through multiple channels. It implies that export-oriented economies are majorly affected by the global commodity prices through its effect on wages and the demand for non-traded goods. Moreover, in a small and open economy (like Malaysia) that relies on commodities for earnings via export, a boom in the global commodity market would usually result in a balance of payment surplus and growth of foreign reserves, which exert more pressure on the demand for domestic currency. Hence, it shows that commodity economies, with their global trade arrangement, are a good experience for exchange rate determination [7,13]. Thus, the determinants that jointly capture the endogenous and exogenous shock are significant for determining exchange rates in long-run and short-run dynamics.

Oil price is considered an important energy commodity that would impact the global commodity market. The previous studies demonstrated that oil price changes are an exogenous shock to commodity economies. Besides, Malaysia is one of Southeast Asia's prominent export-led commodity economies and the second-largest oil-producer economy [14]. [15] reports that Malaysia's crude oil and petroleum products are among the country's top export commodities. According to Ref. [16], an increase in energy prices by 1 dollar raised oil-related revenues by RM 300 million, eventually appreciating the ringgit. It indicates a higher share of petroleum products in a trade, which makes it an important determinant of the exchange rate. However, there should be a caveat: The Malaysian economy usually trades petroleum products in USD. The Malaysian economy has experienced a sharp decline in economic performance due to fluctuations in energy prices globally that may adversely impact the current account balance and lead to the depreciation of the local currency [17]. Thus, it is necessary to re-evaluate the energy price-exchange rate nexus to determine the long-run and short-run dynamics of the exchange rate.

Considering the fact [4], demonstrated that the monetary fundamentals cannot quickly explain the exchange rate movement. Previous studies examined the macroeconomic fundamentals and exchange rate nexus in the Malaysian context over the long run [18,19]. However, the validity of the association between the exchange rate and macroeconomic determinants in a short period would remain debatable in Malaysia. It shows that macroeconomic fundamentals may not adequately perform through foreign exchange adjustments due to global uncertainty [20]. To capture the impact of the uncertain event on the exchange rate, there is a dire need to explore the significant determinants to examine the Malaysian exchange rate for the period of short-run dynamics.

This paper is an extended study of [21,22]. Both studies endogenously highlighted macroeconomic fundamentals' role in exchange rate determination over long and short-run dynamics. However, the monetary fundamentals cannot identify the exogenous shocks in the short run, especially in an export-oriented economy. In addition, these studies used linear methodologies to determine exchange rate dynamics. Exchange rate deviation has nonlinear behavior. Thus, there is a need to apply the nonlinear testing procedures for nonlinear adjustment in the exchange rate dynamics. Discussing the papers' similarities and differences, we extend their proposed models in noteworthy directions. Our paper provides threefold contributions to the existing body of literature. First, this study incorporates exogenous determinants based on economic theory to examine the exchange rate dynamics, along with macroeconomic fundamentals as endogenous factors of an export-driven Malaysian economy. The most prominent determinant to show the exogenous shock is energy price. Energy price changes are an observable exogenous shock to commodity economies [23]. In addition, energy price as an external shock affects the small and emerging economies larger than the developed economies, which mostly experience currency depreciation [24,25].

This raises the basic question: Are the exchange rate dynamics affected by macroeconomic fundamentals endogenously or along with energy price as an exogenous shock? To answer this question, there is a dire need to investigate the macroeconomic fundamentals and energy prices to examine the exchange rate behavior using nonlinear techniques in long-run and short-run dynamics. Second, we examine the monetary and reduced form monetary models to account for short-run adjustment of exchange rate deviation from their long-run equilibrium paths. Third, past empirical shreds of evidence used a linear adjustment model that cannot capture asymmetric policy preferences. We employ a nonlinear adjustment model of the threshold cointegration approach that allows for a speedy adjustment in the exchange rate. In this way, we broaden the prior studies of the Malaysian exchange market by considering energy prices and macroeconomic fundamentals by using the nonlinear framework covering a longer period to elucidate the dynamics of the exchange rate in Malaysia. Our study attempts to fill the gap with the inclusion of energy price along with macroeconomic fundamentals for nonlinear adjustment of exchange rate dynamics in the long-run and short-run horizons using a nonlinear framework of threshold cointegration in the context of Malaysia.

This study is organized as follows: A literature review is presented in Section 2, which reviews the nexus between exchange rate and macroeconomic fundamentals and energy prices. Section 3 shows the data and methodology. The results and discussions are explained in Section 4, and the paper is summarized in Section 5.

2. Literature review

Energy prices act as a driving force in exchange rate determination for long and short periods. Theoretically, the wealth effect and portfolio are the two transmission channels that considerably influence the exchange rate [26]. The theory postulates that the impact of energy prices can be significantly different for oil-importing and oil-exporting countries [24]. For oil-importing countries, the increase in energy prices would increase trade deficits, leading to currency depreciation. Oil-exporting countries take advantage of increased energy prices through a wealth transfer channel. The wealth transfer from oil-importing countries to oil-exporting countries is favorable for trade surpluses and foreign reserves and will eventually appreciate the currency. The empirical results of [7] found a significant relationship nexus between energy price and exchange rate between 2010 and 2017 in Malaysia [27]. exhibits a positive link between energy price and nominal exchange rate and finds that an increase in energy price may depreciate domestic economies of oil-importing countries in the long and short run.

On the other hand [28], examined the negative link between energy prices and exchange rates during 2003–2010 in G20 economies [29]. also supported the currency appreciation in oil-exporting economies using a Markov switching approach [30]. demonstrated a negative energy price-exchange rate nexus in 12 countries of the Asian region, excluding Japan and Hong Kong, from 2006 to 2016 at a daily frequency [31]. documented that Malaysia is an oil-exporting economy, although its share among oil-exporting economies is relatively small. A recent study by Ref. [32] found that imports of oil products increased after the global financial crisis, which caused the current account deficit in Malaysia. According to Ref. [33], significant dependence has been observed on oil-abundant economies' energy prices and exchange rates. Hence, the empirical results provide ambiguous signs in the long-run and short-run in the context of Malaysia.

Besides [11], confirmed a positive association between relative money supply and exchange rate in the long run. Likewise [34,35], found a positive nexus between exchange rate and relative money supply in the long run. The results reveal that a rise in money supply would increase the purchasing power, which induces demand-pull inflation in an economy, thereby leading to a decline in export demand, ultimately depreciating the currency [36]. demonstrated that a price rise may appreciate the exchange rate through an expansionary money supply. According to Ref. [37], an expansionary money supply may appreciate the domestic currency due to uncovered interest rate parity (UIRP) conditions. Under UIRP, an increase in interest rates would cause foreign capital to flow in and increase demand for domestic currency. Hence, past studies confirm mixed evidence to show the relative money-nominal exchange rate nexus [1,38].

Empirical studies have debated a strong link between income and exchange rates [39]. In the long run, a negative association between variables was found using quarterly data from 1980Q1 to 1995Q1 among the five ASEAN countries. A similar result has been found by Ref. [21], who found a negative relationship between relative income and exchange rate. The economic theory validates the evidence that increases in relative national income against foreign income create excess upward pressure for money and appreciate the value of a domestic currency. By contrast [40], observed a positive association between income and exchange rate from 1970 to 2007 in eleven African countries. The result is supported by Ref. [34], who confirmed a robust positive link between income and exchange rate and implies that an increase in income may increase imports, leading to a trade deficit and depreciating the currency. Meanwhile [36], examined the long-run and short-run dynamics of a positive and insignificant relationship between relative income and the nominal exchange rate using monthly data from 1995 to 2013.

In addition, the interest rate is considered an important determinant of monetary policy. The accelerating interest rate shows an expansion in the policy rate, which led to a depreciation of the baht against the USD and British Pound between 2003 and 2011 in Thailand [41]. Numerous researchers found a similar empirical finding, supported by the theory that an increase in interest rate differential would decrease domestic currency demand and depreciate the domestic currency 34]. [42] demonstrates a robust positive connection between Ghana's interest rate and exchange rate from 2007 to 2020. The findings found a difference in the short-run dynamics of the exchange rate. They found that a rise in the interest rate differential would engage foreign investors for investments that ultimately appreciate the currency against foreign currency. However, the study of [43] examined that there was insignificant evidence to show the relationship between an ER nexus using the frequency domain Granger causality test.

Earlier studies have primarily focused on the macroeconomic fundamentals in the long run [2,3]. However, these fundamentals cannot examine the exchange rate in the short run. Thus, our study provides worthy contributions to the body of knowledge by exploring two issues. The first issue investigates that the linear models cannot capture the nonlinear behavior of exchange rates. Hence, there is a need to apply nonlinear testing procedures for such adjustments in exchange rate dynamics. Therefore, our paper applied the threshold approach for nonlinear adjustment of exchange rate dynamics over long and short horizons. The second issue focuses on the role of energy prices that cannot be ignored in a small and open economy and identifies the exogenous shock to improve exchange rate determination through a nonlinear approach in short-run dynamics. Thus, the second issue investigates the significant relationship between the exchange rate, macroeconomic fundamentals, and energy prices in Malaysia's long- and short-run dynamics.

3. Model estimation and methodology

3.1. Model estimation

This paper examines the impact of energy price, money supply, income, and interest rate on the nominal exchange rate between 1994 and 2017 in the long and short run. Numerous studies focused on linear monetary models, whereas our study expanded the studies of [21,22] by incorporating energy prices and the monetary model using a nonlinear threshold technique. This study is comprehensive as it employs the robust techniques of cointegration [44] and the nonlinear threshold approach [45]. Thus, using the nonlinear framework for the reduced-form monetary model of energy price inclusion with monetary fundamentals is interesting. Thus, the underlying models can be expressed as follows;

$${\mathit{ln}NER}_t={\beta }_1{\mathit{ln}MSMY}_t+{\beta }_2{\mathit{ln}MSUS}_t+{\beta }_3{\mathit{ln}IPMY}_t+{\beta }_4{\mathit{ln}IPUS}_t+{\beta }_5{\mathit{ln}IRMY}_t+{\beta }_6{\mathit{ln}IRUS}_t+{\epsilon }_t$$ (1)

$${\mathit{ln}NER}_t={\beta }_1{\mathit{ln}MSMY}_t+{\beta }_2{\mathit{ln}MSUS}_t+{\beta }_3{\mathit{ln}IPMY}_t+{\beta }_4{\mathit{ln}IPUS}_t+{\beta }_5{\mathit{ln}IRMY}_t+{\beta }_6{\mathit{ln}IRUS}_t+{\beta }_7{\mathit{ln}EP}_t+{\epsilon }_t$$ (2)

where ln NER represents the nominal exchange rate, ln MSMY, ln MSUS, ln IPMY, ln IPUS, ln IRMY, ln IRUS, and ln EP refer to money supply (Malaysia), money supply (USA), income (Malaysia), income (USA), interest rate (Malaysia), interest rate (USA), and energy price, respectively. This paper has taken a direct quote (MYR/USD) for the bilateral exchange rate wherein a positive (negative) relationship shows an upward (downward) movement in the exchange rate that leads to depreciation (appreciation) of Malaysian currency (against the dollar). The end-of-month convention has been used for monthly observation. The current study relaxes all the restrictions on the coefficients of the explanatory variables. Table 1 presents an explanation of variables and sources of data.

Table 1.

Description and sources of variables.

Variable	Details	Source
Nominal exchange rate (NER)	Nominal exchange rate, MYR/USD (end of month)	BNM
Money Supply, Malaysia (MSMY)	M3 proxy for money supply (end of month)	DOSM
Money Supply, USA (MSUS)	M3 proxy for money supply (end of month)	FRED
Income, Malaysia (IPMY)	The proxy of industrial production is used for income (end of month)	DOSM
Income, USA (IPUS)	The proxy of industrial production is used for income (end of month)	FRED
Interest Rate, Malaysia (IRMY)	3-months interbank rate is used on monthly basis (end of month)	BNM
Interest Rate, USA (IRUS)	Federal funds rate is used as proxy of interest rate (end of month)	FRED
Energy Prices (EP)	OPEC basket price per barrel (end of month)	OPEC

Note: This table explains the formulation of all variables and sources of data. BNM stands for Bank Negara Malaysia, DOSM represents the Department of Statistics Malaysia, FRED represents Federal Reserve Economic Data, and OPEC represents the Organization of the Petroleum Exporting Countries.

3.2. Methodology

To verify the integration order, this study uses unit root tests such as the ADF test [46], the KPSS test [47], and the structural break unit root test ]. The study also employed the BDS test proposed by Ref. [48], signifying a nonlinear behavior of the variables. The ADF test is expressed in Eq. (3).

$${\Delta lnNER}_t={\alpha }_0+\delta {lnx}_{t-1}+{\sum }_{i=1}^m{\alpha }_i{\Delta lnx}_{t-\mathrm{i}}+{\epsilon }_t$$ (3)

where m stands for the optimal lag length, Δ stands for the first difference operator, and α0 for the constant coefficient. εt represents the error term in year t. The KPSS test has the characteristics to solve the problem of low power in the classical testing framework, expressed in Eq. (4).

$${lnx}_t={\mathrm{\xi }}_t+e_t$$ (4)

where, ξt = ξt-1+ vt; lnNER ∼ (0, σ2). If the variance (σ2) is significantly zero for all t, then series of lnxt is stationary [49]. consider the breakpoint to observe the stationarity of observed variables as per Eq. (5).

$${\Delta \mu }_t=\mathrm{\rho }{\mu }_{t-1}+{\sum }_{i=1}^k{\lambda }_i{\Delta \mu }_{t-i}+{\upsilon }_t$$ (5)

Additionally, BDS tests were employed to identify the nonlinear dynamics. The null hypothesis of independent and identical distribution (iid) allows the detection of non-random behavior in data. The statistical expression of the BDS test is explained in Eq. (6).

$$V_{m,\epsilon }=\sqrt{T}\frac{C_{m,\epsilon }-C_{1,\epsilon }^m}{s_{m,\epsilon }}$$ (6)

where $s_{m,\epsilon }$ represent the standard deviation of the expression $\sqrt{T}\left(C_{m,\epsilon }-C_{1,\epsilon }^m\right)$ that can be accessed consistently by Ref. [50]. The BDS statistic expression follows normal distribution of mean zero and variance 1 properties, N (0, 1), in Eq. (7).

$$V_{m,\epsilon }\stackrel{d}{\to }N\left(0,1\right)$$ (7)

At 5% significance level, the iid null hypothesis can be rejected, when $\left|V_{m,\epsilon }\right|$ > 1.96.

Additionally [44], jointly ascertain the [[51], [52], [53], [54]] test statistics. The results are more efficient and accurate whenever BH cointegration is used instead of other traditional cointegration tests. According to the BH cointegration null hypothesis, the variables have no cointegrating relationship (Ho). The BH cointegration expressions are explained in Eqs. (8), (9).

$$EG-JOH=-2\left[\ln \left(p_{EG}\right)\right]$$ (8)

$$EG-JOH-BO-BDM=-2\left[\ln \left(p_{EG}\right)+\left(p_{JOH}\right)+\left(p_{BO}\right)+\left(p_{BDM}\right)\right]$$ (9)

where p_EG, p_JOH, p_BO, and p_BDM represent the individual cointegration tests of the p-value significance level. We also employ the Dynamic Ordinary Least Square (DOLS) method suggested by Ref. [55]. The DOLS technique is an extension of the OLS technique by incorporating leads and lags of explanatory variables to resolve the issues of autocorrelation, endogeneity, and small sample bias [55]. The DOLS estimator can be structured in the following Eq. (10) and Eq. (11) for both models.

$$lnNER={\beta }_0+{\beta }_1\mathit{ln}{MSMY}_t+{\beta }_2\mathit{ln}{MSUS}_t+{\beta }_3\mathit{ln}{IPMY}_t+{\beta }_4\mathit{ln}{IPUS}_t+{\beta }_5{lnIRMY}_t+{\beta }_6{lnIRUS}_t+\sum _{k=-p}^n{\gamma }_{1k}{\Delta lnMSMY}_{t-k}+\sum _{k=-p}^n{\gamma }_{2k}{\Delta lnMSUS}_{t-k}+\sum _{k=-p}^n{\gamma }_{3k}{\Delta lnIPMY}_{t-k}+\sum _{k=-p}^n{\gamma }_{4k}{\Delta lnIPUS}_{t-k}+\sum _{k=-p}^n{\gamma }_{5k}{\Delta lnIRMY}_{t-k}+\sum _{k=-p}^n{\gamma }_{6k}{\Delta lnIRUS}_{t-k}+{\mu }_t$$ (10)

$$lnNER={\beta }_0+{\beta }_1\mathit{ln}{MSMY}_t+{\beta }_2\mathit{ln}{MSUS}_t+{\beta }_3{lnIRMY}_t+{\beta }_4{lnIRUS}_t+{\beta }_5{lnEP}_t+\sum _{k=-p}^n{\gamma }_{1k}{\Delta lnMSMY}_{t-k}+\sum _{k=-p}^n{\gamma }_{2k}{\Delta lnMSUS}_{t-k}+\sum _{k=-p}^n{\gamma }_{3k}{\Delta lnIRMY}_{t-k}+\sum _{k=-p}^n{\gamma }_{4k}{\Delta IlnIRUS}_{t-k}+\sum _{k=-p}^n{\gamma }_{5k}{\Delta lnEP}_{t-k}+{\mu }_t$$ (11)

$$\Delta {\mu }_t={{\rho }^{+}I}_t{\mu }_{t-1}+{\rho }^{-}\left(1-I_t\right){\mu }_{t-1}+\sum _{i=1}^kɗ\Delta {\mu }_{t-i}+{\upsilon }_t$$ (12)

All the parameters are explained above. Where β0 denotes the constant term. Where -p symbolizes lead values. According to this model, it is assumed that there is no dependent relationship between cross-sections.

3.3. Threshold approach (TAR and M-TAR)

The nonlinear threshold cointegration, which includes the momentum threshold autoregressive (M-TAR) and threshold autoregressive (TAR) models, was proposed by Ref. [45]. The nonlinear adjustment of the short-run deviation towards the long-run equilibrium path and the long-run cointegrating relationship are estimated using the threshold approach.

Where I_t represent Heaviside indicator function:

$$TAR:I_t=\{\begin{array}{c}1if{\mu }_{t-1}\ge \tau \\ 0if{\mu }_{t-1}<\tau \end{array}$$ (13)

The alternative rule of MTAR suggested by Ref. [45], which is used for the following Heaviside indicator in Eq. (14).

$$MTAR:I_t=\{\begin{array}{c}1if\Delta {\mu }_{t-1}\ge \tau \\ 0if\Delta {\mu }_{t-1}<\tau \end{array}$$ (14)

Eq. (12) and Eq. (13) expressed the TAR model and Eq. (12) and Eq. (14) expressed the M-TAR model. τ in Equations (13), (14) refers to a threshold value proposed by Ref. [56]. If both If ${\mu }_{t-1}$ and $\Delta {\mu }_{t-1}$ surpass the threshold (τ), then ${\mathrm{\delta }}^{+}{\mu }_{t-1}$ represents the adjustment coefficient. In contrast, the adjustment coefficient is ${\mathrm{\delta }}^{-}{\mu }_{t-1}$, if ${\mu }_{t-1}$ and $\Delta {\mu }_{t-1}$ are less than the threshold (τ). The threshold vector error correction model (TVECM) is used to account for the short-run divergence of the exchange rate in the long-run equilibrium path once long-run cointegration among the variables is established. The short-run dynamics for the nominal exchange rate that is examined by the monetary fundamentals are displayed in the following statement.

$$\Delta \mathit{ln}\text{NER}={\mathrm{\alpha }}_0+{{\rho }^{+}\mathrm{I}}_{\mathrm{t}}{\mathrm{\mu }}_{\mathrm{t}-1}+{{\rho }^{-}\mathrm{I}}_{\mathrm{t}}{\mathrm{\mu }}_{\mathrm{t}-1}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{\lambda }}_{\mathrm{i}}\Delta {\mathit{ln}\text{NER}}_{\mathrm{t}-\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{\phi }}_{\mathrm{i}}\Delta {\mathit{ln}\text{MSMY}}_{\mathrm{t}-\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\partial }_{\mathrm{i}}\Delta {\mathit{ln}\text{MSUS}}_{\mathrm{t}-\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{\gamma }}_{\mathrm{i}}\Delta \mathit{ln}{\text{IPMY}}_{\mathrm{t}-\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{ɤ}}_{\mathrm{i}}\Delta {\mathit{ln}\text{IPUS}}_{\mathrm{t}-\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{ƥ}}_{\mathrm{i}}\Delta {\mathit{ln}\text{IRMY}}_{\mathrm{t}-\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{\theta }}_{\mathrm{i}}\Delta \mathit{ln}{\text{IRUS}}_{\mathrm{t}-\mathrm{i}}+{\mathrm{\upsilon }}_1$$ (15)

where, ρ + and ρ − denotes the parameters of the speed of adjustment for ΔlnNER from its long-run equilibrium path. ⍺ denotes constant term. ΔlnMSMY represents the money supply (Malaysia), ΔlnMSUS represents the money supply (USA), ΔlnIPMY represents income (Malaysia), ΔlnIPUS represents income (USA), ΔlnIRMY represents the interest rate (Malaysia), and ΔlnIRUS represents the interest rate (USA) that may Granger cause the exchange rate in a short period of time. When the joint coefficients of the past macroeconomic fundamentals change i.e., φ, ∂, γ, ɤ, ƥ, and θ were significant then it would cause the exchange rate in the short term. ʋ₁ denotes white noise disturbance term of Model 1.

In Model 2, the connection among the nominal exchange rate and macroeconomic fundamentals (such as the money supply and income of Malaysia and the USA) and the energy price is expressed in Eq. (16).

$$\Delta \mathit{ln}\text{NER}=\mathrm{\alpha }+{{\rho }^{+}\mathrm{I}}_{\mathrm{t}}{\mathrm{\mu }}_{\mathrm{t}-1}+{{\rho }^{-}\mathrm{I}}_{\mathrm{t}}{\mathrm{\mu }}_{\mathrm{t}-1}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{\lambda }}_{\mathrm{i}}\Delta {\mathit{ln}\text{NER}}_{\mathrm{t}-\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{\phi }}_{\mathrm{i}}\Delta {\mathit{ln}\text{MSMY}}_{\mathrm{t}-\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\partial }_{\mathrm{i}}\Delta {\mathit{ln}\text{MSUS}}_{\mathrm{t}-\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{ƥ}}_{\mathrm{i}}\Delta \mathit{ln}{\text{IRMY}}_{\mathrm{t}-\mathrm{i}}+{\sum }_{\mathrm{i}=1}^{\mathrm{k}}{\mathrm{\theta }}_{\mathrm{i}}\Delta \mathit{ln}\text{IRUS}+{\sum }_{i=1}^k{\mathrm{\vartheta }}_i\Delta {lnEP}_{t-i}+{\mathrm{\upsilon }}_2$$ (16)

All the parameters are explained above. ΔlnEP represents that energy price may Granger cause the nominal exchange rate in the short run. When the joint coefficients of the past macroeconomic fundamentals change i.e., φ, ∂, ƥ, θ, and ϑ were significant then it would Granger cause the exchange rate in the short period of time. ʋ₂ denote white noise disturbance term of Model 2.

4. Results and discussion

The descriptive summary of variables is presented in Table 2. The money supply (USA) has the highest mean value, followed by money supply (MYS) and interest rate (USA & MYS). The income (USA & MYS) shows greater volatility due to the collapse of several financial institutions during the global financial crisis in 2008, followed by interest rates (USA & MYS).

Table 2.

Descriptive statistics.

Variable	Mean	Standard Deviation	Minimum	Maximum	Skewness	Kurtosis
lnNER	1.230	0.157	0.894	1.501	−0.680	2.577
lnMSMY	26.030	0.575	25.012	26.894	0.091	1.472
lnMSUS	29.538	0.425	28.877	30.258	0.015	1.773
lnIPMY	5.331	7.359	−17.600	28.900	−0.137	3.828
lnIPUS	1.901	4.239	−15.330	8.560	−1.814	7.402
lnIRMY	4.032	1.864	2.030	11.150	1.933	6.304
lnIRUS	2.589	2.331	0.050	6.850	0.284	1.398
lnEP	1.231	0.702	2.270	4.880	−0.049	1.780

Note: lnNER represent log of nominal exchange rate, lnMSMY represent log of money supply of Malaysia, lnMSUS represent log of money supply of USA, lnIPMY represent log of income of Malaysia, lnIPUS represent log of income of USA, lnIRMY represent log of interest rate of Malaysia, lnIRUS represent log of interest rate of USA, and lnEP represent log of energy price.

Table 3 rejects the null hypothesis of independently and identically distributed data at the 5 % level. The finding suggests that nonlinear models are expected to better detect nonlinearities in exchange rate dynamics than linear models supported by Refs. [57,58].

Table 3.

Univariate and multivariate BDS statistics.

m	Univariate BDS Statistics								Multivariate BDS Statistics
	lnNER	lnMSMY	lnMSUS	lnIPMY	lnIPUS	lnIRMY	lnIRUS	lnEP	Model-1	Model-2
2	0.184	0.203	0.207	0.111	0.173	0.198	0.191	0.187	0.131	0.126
3	0.309	0.345	0.351	0.196	0.289	0.336	0.326	0.318	0.220	0.210
4	0.393	0.444	0.453	0.248	0.364	0.431	0.417	0.408	0.275	0.260
5	0.447	0.513	0.524	0.275	0.409	0.495	0.477	0.467	0.303	0.285
6	0.484	0.561	0.575	0.284	0.435	0.538	0.515	0.507	0.313	0.293

Note: Series p-values are ‘0.0000’. m represents embedding dimensional points.

Table 4 documents the results of the unit root and finds the unit root in a series with structural breaks. All variables seem stationary or integrated in the same order I (1). The findings indicate that Malaysia has experienced the AFC and GFC. The empirical findings of the structural break provide evidence that the Malaysian exchange rate is more affected by the Asian financial crisis [59]. Furthermore, optimal lag length criteria are presented in Table 5, and 12 lags have been chosen using the AIC criterion. Past studies also support the idea that AIC performs better among all criteria [60]. Subsequently, Table 6 presents the combined cointegration results and indicates the existence of long-run cointegration based on [61] statistics. The results are from the past studies of [22,34]. The result is also supported by Ref. [32]. A plausible justification of this association suggests that Malaysia is an export-led economy with a high trade openness rate, which helps its economy to improve its balance of payment position, which ultimately appreciates the Malaysian currency against the US Dollar.

Table 4.

Unit root test results.

Variable	ADF		KPSS		ZA				Decision
	I (0)	I (1)	I (0)	I (1)	I (0)	Time break	I (1)	Time break
lnNER	−1.679	−16.167a	0.24a	0.092	−3.065	1997/M11	−16.677a	1998/M02	I (1)
lnMSMY	−1.129	−13.777a	1.955a	0.149	−2.616	2006/M10	−13.916a	2013/M05	I (1)
lnMSUS	0.949	−13.305a	2.015a	0.195	−4.359	2004/M12	−9.272a	1997/M10	I (1)
lnIPMY	−3.446	−7.483a	0.43a	0.0099	−4.002	2009/M10	−15.819a	2009/M02	I (1)
lnIPUS	−2.316	−8.286a	0.426a	0.027	−3.984	2009/M08	−8.871a	2009/M04	I (1)
lnIRMY	−1.691	−9.604a	0.831a	0.060	−6.201	1998/M08	−10.379a	1998/M07	I (1)
lnIRUS	−1.533	−5.977a	1.399a	0.087	−2.997	2001/M01	−9.428a	2000/M08	I (1)
lnEP	−1.537	−15.252a	1.566a	0.073	−4.072	2014/M05	−10.381a	2008/M07	I (1)

Note:

^aIndicates 1% significance level, ADF denote Augmented Dickey and Fuller test, KPSS denote Kwiatkowski, Phillips, Schmidt and Shin test, ZA denote Zivot and Andrews test.

Table 5.

Results of lag length criteria.

Model	Model-1	Model-2
AIC	−15.637a [12]	−25.196a [12]
SIC	−12.513a [1]	−22.707a [1]
HQC	−13.188a [4]	−23.440a [4]

Note:

^aShow a lag order selection criterion. AIC, SIC, and HQC refers the Akaike information criterion, Schwarz information criterion, and Hannan-Quinn information criterion, respectively.

Table 6.

Bayer and hanck cointegration test.

	Model-1		Model-2
Type of Test	Test statistic	Cointegration	Test statistic	Cointegration
Combined approach
EG-JOH	20.354*	Yes	22.298*	Yes
EG-JOH-BO-BDM	33.158*	Yes	40.739*	Yes
Significance level	Critical Values (EG-JOH)		Critical Values (EG-JOH-BO-BDM)
1%	15.3		29
5%	10.3		19.7
10%	8.2		15.7

Note: *, ** and *** represents the significance level at 1%, 5% and 10%, respectively. Brackets [] shows p-value.

The DOLS results to capture the long-run elasticities of variables are shown in Table 7. The outcome for both models indicates a long-term relationship between the exchange rate and its explanatory variables, meaning that the null hypothesis cannot be rejected at a 5% significance level. The result is consistent with a recent study by Ref. [42]. Additionally [34], provided evidence of a connection between the government tax, energy, money supply, interest rate differential, and exchange rate. The theoretical transmission channel supports the reduced form monetary model through the portfolio balance effect channel in the long run.

Table 7.

Dynamic ordinary least square results.

Variables	Model 1	Model 2
Constant	−6.144a(0.908)	−8.754a (1.207)
lnMSMY	−0.455a (0.040)	−0.328a (0.070)
lnMSUS	0.624a (0.057)	0.633a (0.082)
lnIPMY	0.006a (0.002)
lnIPUS	−0.017a (0.003)
lnIRMY	0.074a (0.021)	−0.016a (0.015)
lnIRUS	0.004 (0.006)	0.024a (0.005)
lnEP		−0.079a (0.029)
TB	0.466a (0.077)	0.219a (0.059)
Hansen Parameter Instability
Lc Statistic	0.003 [0.2]	0.003 [0.2]
JB	0.785 [0.675]	3.086 [0.214]

Note:

^aIndicates 1 % level of significance. The standard error and p-value displays in () and [], respectively. DOLS represent dynamics OLS regression with deterministic trend (TB), and leads and lags is 12, Lc shows Hansen parameter instability statistics, JB represent Jarque-Bera test for normality.

The long-run elasticities for both models are also included in Table 7. At the 1% level, there is a negative correlation between Malaysia's money supply and exchange rate. It implies that a 1% increase in Malaysia's money supply causes the exchange rate to go lower, appreciating the currency's value by 0.455 for Model 1 and 0.328 for Model 2, respectively. Conversely, for Models 1 and 2, a 1% increase in the US money supply will result in a 0.624 and 0.633 depreciation of the Malaysian Ringgit, respectively. The findings demonstrate that the uncovered interest rate parity (UIRP) theory remains valid when an expansionary monetary shock leads the currency to appreciate rather than depreciate. It also indicates that rising domestic interest rates do not encourage foreign investors to borrow from the domestic economy. Nevertheless, the findings contradict the findings by Ref. [38], which can result from an application of different proxies of money supply, for instance, M1 and M2.

Furthermore, Malaysia's coefficient of income is positive over a long period, whereas the coefficient for the United States is negative. Contrasting to the assumptions of the macroeconomic model, this suggests that the theory of export-led growth does not hold. According to the monetary model, an increase in the real income gap caused an excessive demand for local currency, which caused the home currency to appreciate. On the other hand, the results imply that raising income enhances the trade balance, which causes the value of the home currency to rise. Nonetheless, the value of the local currency declined due to the reduction in excess demand. Similarly [62], contended that conditions for export-led growth would be necessary for real income to rise. Thus, the findings are supported by Ref. [34], who found that rising income increased imports, which worsened the position of the trade balance in African countries.

Moreover, Malaysia's interest rate is statistically significant and consistent with theoretical expectations for Model 1. A rise in interest rates is correlated with a 0.07 percent increase in the nominal exchange rate. In a flexible-price form, the outcome aligns with monetary theory, which emphasizes that a rise in interest rates would reduce demand for local currency and cause it to depreciate. The results support the UIRP theory, which states that a higher interest rate will cause the currency's value to decline. These findings can also be seen as a sign of strong consumer demand for imported goods, which would raise imports while decreasing exports into the economy and eventually lead to a trade deficit. Since there is a significant demand for trading currencies, this action will put upward pressure on trading currencies and negative pressure on domestic currencies. Rising interest rates are, therefore, a sign of anticipated economic inflation, which could eventually lead to a depreciation of the Malaysian currency.

However, in the sticky-price version of Model 2, the interest rates in the USA and Malaysia are statistically significant and in line with the theory of the monetary approach. The currency would gain (the exchange rate would decrease) by 0.02% for every 1% increase in the Malaysian interest rate. The Malaysian Ringgit would benefit from a 1% increase in US interest rates, even if it would devalue the foreign currency. According to the monetary method of determining exchange rates, a rise in interest rates would motivate investors to invest in the local economy, possibly leading to an appreciation of the Malaysian Ringgit. The findings suggest that, over the long term, price rise is entirely regulated by the money supply. The outcome agrees with the earlier research of [42].

However, at a 1% significance threshold, energy prices substantially adversely impact the exchange rate. It suggests that a 1% increase in energy prices resulted in a 0.08% long-term increase in the currency's value. The empirical result corresponds with the channel of portfolio balance. According to the argument, increasing energy prices caused a wealth transfer from oil-importing to oil-exporting countries, which impacted the current account balance. The balance of payments and foreign exchange reserves have been beneficially influenced by the current account balance, which continually strengthens the native currency [63]. It implies that the oil sector provides between thirty and forty percent of the country's budget and is essential to Malaysia's economy. The result is in line with [64], who indicate that following the collapse of the crude oil market, Malaysia's government revenue will drop from 19% to 13%. The results of adverse relationships have been supported by earlier research by Refs. [29,31], which shows that higher energy prices will result in rising currency values in countries that export oil. On the other hand, the result of [65] proved that energy prices have a favorable effect on exchange rates.

At a 1% level, the break dummy's coefficient is significantly positive for both models. The positive coefficient for Model 1 and Model 2 showed that the currency's value decreased by 0.47 and 0.22, respectively. The positive coefficient implies that the currency crisis depreciates the domestic currency. The currency crisis can negatively affect the currency due to capital outflows from the domestic market that reduce the demand for domestic currency [66]. This result is also consistent with [67], who elaborates that the crisis came from Thailand, which confronted the speculative attack in mid-1997, resulting in the depreciation of the currencies of South-East Asian economies. From July 1997 to January 1998, the Malaysian currency experienced heavy selling pressure against the USD.

Table 8 exhibits the results of TAR and MTAR. In TAR estimation, the threshold value of both models is zero, which is deterministic by nature. The long-run equilibrium convergence is confirmed by point estimates, indicating that positive deviation convergence is faster than negative deviation convergence for both models. Furthermore, the F-joint value (9.243) is less than 10% of the critical value for Model 1, implying that no long-run cointegrating relationship exists between macroeconomic fundamentals and the nominal exchange rate. For Model 2, the F-joint value (10.694) is above the critical value at the 10% level, which allows us to reject the null hypothesis of no cointegration. The result implies the presence of a long-run link among variables in Malaysia. The F-equal values (1.148) and (1.284) reject the null hypothesis of symmetry adjustment for both models [56]. is also used to examine the consistent M-TAR in the case of the non-zero threshold value. In the consistent M-TAR model, the estimated threshold values are 0.014 and 0.013 for Models 1 and 2, respectively. It shows that positive deviation convergence is higher than negative deviation for both models. For both models, F-joint statistics values (16.713) and 18.040 are greater than the critical value at the 10% level for Models 1 and 2, respectively, demonstrating that the null hypothesis of no cointegration is rejected. The results imply that both models highlight the long-run cointegrating relationship between the nominal exchange rate and its determinants. In addition, the findings support the evidence of asymmetry adjustment at the 10% level. Hence, the results indicate an asymmetric adjustment mechanism among variables, as supported by past studies [[68], [69], [70]].

Table 8.

Enders-siklos cointegration test results.

Parameter	TAR		MTAR
	Model-1	Model-2	Model-1	Model-2
$\tau$	0	0	0.014	0.013
${\rho }^{+}$	−0.259 (0.061)	−0.289 (0.064)	−0.409 (0.071)	−0.416 (0.069)
${\rho }^{-}$	−0.169 (0.079)	−0.193 (0.081)	−0.107 (0.063)	−0.114 (0.067)
$F_{Joint}$	9.243 [10.784]	10.694a [10.115]	16.713a [12.849]	18.040a [12.034]
$F_{Equal}$	1.148a [1.105]	1.284a [1.153]	15.162a [6.514]	14.929a [6.557]
Long run Cointegration	$\times$	$\surd$	$\surd$	$\surd$
Asymmetry Effects	$\surd$	$\surd$	$\surd$	$\surd$

Note:

^aDenote significance at 10% level. Numbers in parenthesis ( ) is standard errors and brackets [ ] is Ender-Siklos (2001) bootstrap critical value with 10,000 simulations.

Table 9 reports the findings of asymmetric adjustments of variables by considering a general to a specific approach. The empirical findings show that the money supply and exchange rate are strongly negatively correlated at the current value (ΔlnMS) and lag four (ΔlnMSt-4) for Model 1, and at the current value (ΔlnMS), lag one (ΔlnMSt-1), and lag four (ΔlnMSt-4) for Model 2 in the short run. The elasticity estimates show that a rise in the money supply would appreciate the currency. The result suggests that an expansionary money supply may put upward pressure on the local currency. The results are similar to the studies of [40], who found that currency appreciated following an expansionary money supply.

Table 9.

The m-tvecm estimates.

Variables	Model-1		Model-2
Constant	0.006*	(0.001)	0.007*	(0.002)
${\Delta \mathit{ln}\text{NER}}_{t-3}$	0.242*	0.053)	0.286*	(0.052)
${\Delta \mathit{ln}\text{NER}}_{t-4}$	−0.102***	(0.054)	−0.116**	(0.054)
${\Delta \mathit{ln}\text{NER}}_{t-11}$	0.050***	(0.029)	0.053***	(0.028)
${\Delta \mathit{ln}\text{NER}}_{t-12}$	0.280*	(0.056)	0.384*	(0.058)
$\Delta \mathit{ln}\text{MSMY}$	−0.939*	(0.030)	−0.948*	(0.031)
${\Delta \mathit{ln}\text{MSMY}}_{t-1}$			−0.067**	(0.031)
${\Delta \mathit{ln}\text{MSMY}}_{t-3}$	0.250*	(0.057)	0.299*	(0.058)
${\Delta \mathit{ln}\text{MSMY}}_{t-4}$	−0.124**	(0.058)	−0.137**	(0.059)
${\Delta \mathit{ln}\text{MSMY}}_{t-7}$			0.070**	(0.031)
${\Delta \mathit{ln}\text{MSMY}}_{t-12}$	0.379*	(0.058)	0.480*	(0.059)
${\Delta \mathit{ln}\text{MSUS}}_{t-3}$			−0.429**	(0.211)
${\Delta \mathit{ln}\text{MSUS}}_{t-11}$	−0.421**	(0.205)	−0.311	(0.215)
${\Delta \mathit{ln}\text{MSUS}}_{t-12}$			−0.200	(0.209)
${\Delta \mathit{ln}\text{IPMY}}_{t-11}$	−0.0003	(0.000)
${\Delta \mathit{ln}\text{IPUS}}_{t-5}$	0.001	(0.001)
${\Delta \mathit{ln}\text{IRMY}}_{t-2}$			−0.004***	(0.002)
${\Delta \mathit{ln}\text{IRMY}}_{t-5}$	−0.009*	(0.002)	−0.010*	(0.003)
${\Delta \mathit{ln}\text{IRMY}}_{t-6}$	0.004***	(0.002)	0.005**	(0.002)
${\Delta \mathit{ln}\text{IRMY}}_{t-7}$	−0.005**	(0.002)	−0.003	(0.002)
${\Delta \mathit{ln}\text{IRUS}}_{t-6}$	0.007**	(0.003)
${\Delta \mathit{ln}\text{IRUS}}_{t-8}$			0.006**	(0.003)
${\Delta \mathit{ln}\text{IRUS}}_{t-10}$			−0.005	(0.003)
${\Delta \mathit{ln}\text{EP}}_{t-7}$			0.017**	(0.007)
${\Delta lnE\mathrm{P}}_{t-8}$			−0.009	(0.007)
$\Delta$ TB	−0.021	(0.013)	−0.014	(0.013)
${\rho }^{+}$	−0.063**	(0.028)	−0.098*	(0.031)
${\rho }^{-}$	−0.066***	(0.039)	−0.064	(0.042)
H01: φ1 = φ2 = φ3 = φ4 = φ5 = φ6 = 0	1014.579*	[0.000]	1061.273*	[0.000]
H02: ∂1 = ∂2 = ∂3 = 0			26.998*	[0.000]
H03: ƥ1 = ƥ2 = ƥ3 = ƥ4 = 0	22.342*	[0.048]	25.193*	[0.000]
H04: θ1 = θ 2 = 0			4.674***	[0.097]
H05: ϑ1 = ϑ2 = 0			6.418**	[0.040]

Note: *, **, and *** denotes 1%, 5% and 10% level of significance, respectively. Numbers in ( ) shows standard error. [] represent p-value.

Meanwhile, appreciation of the currency, in turn, decreases exports and increases imports, which ultimately deteriorates the current account. The findings are supported by Refs. [38,71], who pointed out that Malaysia's expected sign of money supply is negative. By contrast [36], applied an ARDL model for Uganda's small and open economy and found that fiscal expansion would induce depreciation pressure on the currency.

By contrast, the response of the exchange rate caused by domestic money supply indicates a positive relationship at three lag (ΔlnMSt-3) and seven lag (ΔlnMSt-7) for Model 1 and 3 (ΔlnMSt-3), seven lag (ΔlnMSt-7), and 12 lag (ΔlnMSt-12) for Model 2. In the short run, a positive rise in the domestic money supply would lead to currency depreciation. The empirical findings suggest that expansionary monetary policy is necessary for confirming the stability of the exchange rate in an economy. A similar finding was observed by Ref. [31]. In addition, the joint Wald test statistics of domestic money supply indicate that the zero-restriction null hypothesis (H01) is strongly rejected at a 1% level for both models. It shows that the domestic money supply of Malaysia's granger causes Malaysia's exchange rate to increase in the short run, as supported by Ref. [22]. The existence of a short-run causal relationship from the money supply to the exchange rate is supported by Ref. [71].

Furthermore, the coefficient of foreign money supply is significantly negative at a 5% level in the short run. The findings indicate that a rise in foreign money supply will appreciate the Malaysian currency at lag 11 (ΔlnMSt-11) for Model 1 and at lag 3 (ΔlnMSt-3) and lag 11 (ΔlnMSt-11) for Model 2. The negative elasticity implies that the expansionary money supply of the USA would lead to a weakening of the dollar against the ringgit. The findings are consistent with those of [3,31], who demonstrate a negative connection between foreign money supply and exchange rate in the short run. The null hypothesis of foreign money supply (H02) is strongly rejected at a 1% level, indicating that the USA money supply granger-cause exchange rate for both models in the short-run, which is supported by Ref. [72] in Malaysia.

Moreover, the estimated coefficients of the Malaysian interest rate are negative and significant at lags 5 (ΔlnIRMYt-5) and 7 (lnIRMYt-7) for Model 1. In contrast, they are significant at the 1% level for Model 2 at lag 2 (ΔlnIRMYt-2) at lag 5 (ΔlnIRMYt-5). However, an increase in the Malaysian interest rate at lag 6 (ΔlnIRMYt-6) for Model 1 and Model 2 at 10 % and 5 % levels, respectively, would depreciate Malaysia's currency in the short run. Although the domestic interest rate behavior indicates appreciation and depreciation of currency at different lags, one observes the high intensity and magnitude of currency appreciation in Malaysia's short run. It implies that the high-interest rate encourages savings while discouraging market investments and businesses' reluctance to borrow money from banks. Resultantly, the increase in interest rate affects the pattern of consumer spending. The results align with [40,73] but contrast with the results of [36].

Moreover, the null hypothesis (H03) of the joint Wald statistic of interest rate in Malaysia is rejected, confirming the short-run Granger causality from the domestic interest rate to the exchange rate in Malaysia. The inflow of international capital leads to currency appreciation. The currency appreciation results in a rise in the consumption of imports and a decrease in exports in the Malaysian economy.

In addition, the foreign interest rate at lag 6 (ΔlnIRUSt-6) and lag 8 (ΔlnIRUSt-8) shows a positive and significant effect on the Malaysian exchange rate for Model 1 and Model 2, respectively. The result implies that an increase in the federal funds rate encourages spending by making borrowing cheaper in the short run. Moreover, the null hypothesis (H04) of the joint Wald statistic of Malaysia's interest rate is rejected for both models. The result confirms that foreign interest rates affect exchange rates in the short run. Moreover, the null hypothesis (H04) of the joint coefficient of the lagged foreign interest rate is rejected at a 10% significance level for Model 2, indicating the causation between the foreign interest rate and the exchange rate in the short run. The Granger causality findings are supported by Refs. [3,74].

Moreover, the empirical results highlight no significant relationship between domestic and foreign income and the exchange rate in the short run for Model 1. In addition, the energy price coefficient indicates a positive impact on the exchange rate at a 5% level for Model 2. In the short run, the rise in energy prices would depreciate the currency by 0.02%. The result implies that the central bank reinvests its revenues in US dollar assets, resulting in the US dollar appreciating in the short run because of the wealth. The wealth transfer channel justifies the energy price and exchange rate nexus relevance. In the short run, the wealth can be accumulated as foreign reserves (US dollar assets), strengthening the US dollar (nominal appreciation), and depreciating the exporter currency. The extensive literature supported the evidence that oil-exporter economies may prefer to reinvest their wealth in US dollar assets in the short run [75,76]. [77] documented that the increase in energy prices provides no significant evidence of an appreciation of the currency in oil exporters as determined by theoretical considerations. The joint Wald null hypothesis (H05) of zero restriction is rejected at a 5% level, demonstrating the short-run causation effect from energy price to exchange rate in the short run.

For Model 1, the results show that the exchange rate's positive and negative short-run deviations from its long-run equilibrium path are being corrected by 6% and 7% each month. For a positive deviation from the exchange rate equilibrium path, it will take eight months, and for a negative deviation, it will take seven months. At the same time, the full adjustment to equilibrium would take about 17 to 14 months. In addition, negative divergence adjustment is faster than positive divergence in the short run. Model 2's positive deviation adjustment is about 10% at a 1% level. The results show that monthly short-run adjustments correct the disequilibrium while complete adjustment takes almost ten months for equilibrium. The high speed of adjustment confirms the validity of Model 2. Thus, the result implies that the monetary fundamentals have greater potential to adjust negative deviation changes, while the positive deviation in the exchange rate is due to the trade transmission channel and that half of the disequilibrium can be removed from its exchange rate equilibrium path in five months.

Table 10 presents the M-TVECM diagnostic and stability test for both models. R-square and Durbin-Watson (D-W) statistics imply no sign of spurious regression in both models. The R-square of Model 1 indicates that macroeconomic fundamentals accounted for 80% of the variance, whereas the reduced monetary model accounted for 82% of the maximum variability. Notably, embedded energy prices in monetary fundamentals show greater explanatory power to determine exchange rates in the short run. Further, Table 10 presents the residual diagnostic tests. The result reveals no autocorrelation problem, and the variances of the residuals are homogenous for both models. Fig. 1 shows the CUSUM plot of both models is significant at a 5% level, signifying that all the coefficients in both models are stable and robust over the sample period.

Table 10.

M-TVECM diagnostic and stability tests.

Model Diagnostic and Stability	Model-1	Model-2
Adjusted R-squared	0.80	0.82
Durbin-Watson statistic	2.10	2.16
F-Stat	62.909 [0.000]	51.388 [0.000]
Serial Correlationa	1.506 [0.471]	2.784 [0.249]
Heteroskedasticityb	83.595 [0.060]	74.752 [0.111]
CUSUMc	Stable	Stable

Notes:

^aBreusch–Godfrey Serial Correlation Lagrange Multiplier (LM) test.

^bAutoregressive conditional Heteroskedasticity (ARCH) test.

^cCumulative Sum of Recursive Residual (CUSUM).

Fig. 1.

Plot of cumulative sum of recursive residual (CUSUM).

Over 10 months, the Cholesky one SD response functions of exchange rate are plotted for the money supply, income, interest rate, and energy price at a 5% significance level. Fig. 2 shows a negative link between Malaysia's exchange rate and its money supply. The response is sharp in the first two, fourth, and fifth periods of Malaysia's money supply. It increases gradually, implying that the currency appreciates due to the strong effect of the interest rate under the UIRP theory [40]. Meanwhile, the exchange rate response is positive, indicating a positive shock to the USA's money supply. In the first two months of the US money supply, the response is immediate, but after that, it moves slowly upward and downward but is positive.

Fig. 2.

Plots of impulse response function.

Further, the response of impulses to Malaysia's income positively impacts the exchange rate. The increase in income (Malaysia) shows a steep increase in the first three periods; after that, the response graph gradually decreases until the seventh period but is still positive. At the same time, the response of impulses to the income of the USA shows an initially positive relationship until the fifth period, after which there is a negative relationship. The fluctuation in income (in Malaysia and the USA) suggests that a greater number of monetary transactions create a surplus demand (supply) of currency, which results in an appreciation (depreciation) in the value of a currency. The findings are supported by Ref. [78]. In addition, the interest rate of Malaysia shocks provides an essential outcome for the direct link for the first two months. Later, it reflects a sharp increase in the response graph. It implies that the interest rate acts as a catalyst for exchange rate stability. Nonetheless, the interest rate in the USA has shown an inverse relationship with the exchange rate when less deviation is observed. Moreover, the response to energy prices shows a fixed effect during an early period of 2 months, and subsequently, it illustrates a downward trend consistently. The findings are supported by Refs. [29,31].

5. Conclusion and policy implications

The main goal of this paper is to examine the explanatory power of energy price by incorporating the money supply, income, and interest rate on the nominal exchange rate using a nonlinear threshold approach in Malaysia over the period from 1994M01–2017M12. The empirical findings reveal a substantial long-run connection between the nominal exchange rate and its determining factors for both models using Bayer and Hank cointegration. Using DOLS, the findings uncover that Malaysia's money supply and the USA's income appreciate the currency. In contrast, the USA's money supply, Malaysia's income, Malaysia's interest rate, and structural breaks depreciate the domestic currency. The results indicated that a rise in money supply would expand Malaysia's external debt, investment, and real interest rates in the long run. In addition, a rise in income will depreciate the currency, which is consistent with neoclassical growth theory. According to theory, a rise in income induces higher import bills and increases trade deficits in an economy. That, in turn, will increase the capital flights and decrease the demand for local currency, which leads to the depreciation of local currency. Importantly, the money supply was revealed to be the long-run contributing factor to exchange rate dynamics.

We employed Enders and Siklos' approach to TAR and MTAR, which confirmed the long-run cointegrating relationship and asymmetric adjustment mechanism in the MTAR model comprising a non-zero threshold adjustment value. Hence, the threshold error correction model is evaluated by employing the MTAR approach. The results revealed that money supply, interest rate, and energy price would granger cause exchange rates in the short run. It advocates the adjustment of the short-run dynamics of the exchange rate, which is more rapid in both directions. In the reduced-form model, the domestic currency appreciates due to the nominal exchange rate's response to a positive shock. The asymmetric error term adjustment indicates that the monetary fundamentals would adjust all disequilibrium in the long-run equilibrium position. Meanwhile, the role of energy price as an exogenous shock appears to be significantly higher, and disequilibrium would be adjusted within 10 months.

As Malaysia is a commodity-driven export economy, rising energy prices cause accumulation in foreign currency reserves that put upward pressure on demand for local currency, ultimately leading to an appreciation of the Malaysian currency. The results reveal that the Malaysian exchange rate reacts to positive shocks instead of negative shocks due to increased energy prices. It also indicates that the Malaysian exchange rate is more prone to overvaluation than undervaluation. The same situation was observed in the Asian financial crisis (AFC) when misalignment appeared due to currency overvaluation. An appreciated currency will adversely impact the current account deficit, the rise in foreign debt, and the risk of speculative outbreaks at adverse costs. Meanwhile, a devalued currency holds the concept of export-led growth.

Malaysian policymakers should coordinate both fiscal and monetary policy, taking the concept of inflation into account when it is necessary to cope with rising exchange rates. In addition, monetary policy must be designed to normalize the money supply in the economy. Monetary policy should concentrate on massive variations in the exchange rate that might encourage speculative effects and weaken the stability of the currency demand function. Concerning this aim, exchange rate policies should focus on offsetting the required elasticity to confirm competitiveness and appropriate stability to escalate confidence in the local currency and the inherent fundamentals that support the currency's worth over time. The central bank should persist to enhance its foreign exchange reserves as a cushion against adverse external shocks that would impact the exchange rate. In addition, central banks should also practice a lean approach to wind policy by arbitrating in the FX market to stabilize currency fluctuations and the real economy regardless of the impact of financial stability. Besides, the central bank should focus on the wealth effects that may help manage the current account balance, stabilizing the exchange rate. In addition, concerning the wealth transmission channel, the government of Malaysia can establish a wealth fund that must be independent to deal with the energy price revenue during periods of price hikes or plunges. This policy is important because it can take corrective measures for energy price changes. Formulating suitable strategies to mitigate the risk of positive and negative oil shock impacts on the Malaysian economy is necessary. In addition, the nonlinear performance of the energy price and the exchange rate helps stakeholders make rational investment decisions. The investor can also decide to uncover the best-performing stock and discover the right time for investment. Finally, the detailed regulatory implications can be exhibited through a diagram to see a broader and deeper picture of the explanation. Thus, Fig. 3 explains the regulatory implications in detail.

Fig. 3.

Regulatory implications.

Regardless of the novel contributions to the existing research knowledge, this paper has few limitations and some challenging avenues for potential research work. The prominent limitation is the availability of microstructure data in determining exchange rates. As more data becomes available, one could further investigate the exchange rate determinants and test whether the results deviate from the current study. Subsequently, the availability of recent data on macroeconomic performance and the forex exchange market will further complement the exchange rate determination in the long-run and short-run. Future research prospects in this field will use high-frequency data (1 h or 1-min frequency) to uncover the dynamics of examining exchange rates. It can be realized by explaining the exchange rate forecasting with macroeconomic fundamentals employing the interpretive and revolutionary AI approaches. Recently, the outbreak of COVID-19 had a larger effect on Malaysia's GDP. Furthermore, it was a sudden and sustained decrease in crude oil prices, which eventually brought down the country's earnings. Thus, there is a dire need for an in-depth evaluation of macroeconomic fundamentals and oil prices to explore the dynamics of exchange rates, particularly during the COVID-19 pandemic, which will offer an interesting research avenue.

CRediT authorship contribution statement

Shamaila Butt: Writing – original draft, Methodology, Data curation. Muhammad Ramzan: Supervision, Project administration, Formal analysis, Conceptualization. Wing-Keung Wong: Project administration. Muhammad Ali Chohan: Writing – original draft. Ayman Hassan Bazhair: Writing – original draft.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.