Testing Structural Break in the Relationship Between Exchange Rate and Macroeconomic Variables

Abstract

The article aims to study the relationship between those macroeconomic factors that the affect (INR/USD) exchange rate (ER). Time series data of 40 years on ER, GDP, inflation, interest rate (IR), FDI, money supply, trade balance (TB) and terms of trade (ToT) have been collected from the RBI website. The considered model has suggested that only inflation, TB and ToT have influenced the ER significantly during the study period. Other macroeconomic variables such as GDP, FDI and IR have not significantly influenced the ER during the study period. The model is robust and does not suffer from residual heteroscedasticity, autocorrelation and non-normality. Sometimes the relationship between ER and macroeconomic variables gets affected by major economic events. For example, the Southeast Asian crisis caused by currency depreciation in 1997 and sub-prime loan crisis of 2008 severely strained the national economies. Any global economic turmoil will affect different economic variables through ripple effect and this, in turn, will affect the ER of different economies differently. The article has also diagnosed whether there is any structural break or not in the model by applying Chow’s Breakpoint Test and have obtained multiple breaks between 2003 and 2009. The existence of structural breaks during 2003–2009 is explained by the fact that volume of crude oil imported by India is high and oil price rise led to a deficit in the TB alarmingly, which caused a structural break or parameter instability.

Keywords

Exchange Rate Macroeconomic Variables Regression Structural Break Mundell–Flemming Trilemma

Introduction

Exchange rate (ER) is the rate at which one country’s currency is exchanged for other country’s currency. Health of an economy is indicated by the stability of its ER. When the ER is stable, then exporters and importers can anticipate their gain and accordingly can invest in the forward market. If ER is dwindling, then foreign investors will be reluctant to invest and there will be frequent inflow and outflow of funds.

Maintaining a stable exchange is difficult and not always possible to ensure. According to Mundell–Flemming Trilemma, all the countries in the world through their monetary policies seek to attain three different objectives: (a) fixed ER regime to stabilize international trade (b) independent monetary policy, so that country can change interest rates (IRs) freely to tackle inflation and unemployment (c) free flow of foreign capital, so as to provide liquidity to international investors. However, it is not possible for any country to attain all the three objectives simultaneously and at least one objective will always be violated. If a country has a fixed ER regime then any attempt by the country to reduced unemployment through a fall in IR will cause foreign capital to move out of the country and hence demand for domestic currency will rise, leading to a rise in the ER. Developing countries face a chronic problem of increasing inflation demanding for any attempt to be initiated in the development path. As a remedial measure to curb inflation, if a country follows contractionary monetary policy, then rate of interest will increase and it will lead to huge inflow of foreign capital and ER will depreciate. Thus, we see that a nation can choose only one objective. With globalization and current account convertibility, volatility in the ER has increased over a period of time.

ER is a major factor in determining the direction and magnitude of foreign trade (Allen & Gale, 2004). Soon after the breakdown of Bretton Woods System and the adoption of floating ER system in 1973 till adjustable pegged ER system in 1977, the impact of fluctuation of ER onto the volume of international trade has been rendered to be an important subject for empirical investigation. Prior to the breakdown of the Bretton Woods system when most of the countries would follow a closed-door policy, the three different objectives could still be attained. The trade liberalization of India comprises three measures: (a) freer imports by removing restrictions on imports and introducing open general licence system (b) flexible ER (c) partial convertibility of the rupee by removing restriction on the purchase and sale of foreign exchange in a current account. With globalization, a major portion of international trade comprises foreign capital. Foreign capital movement is very sensitive to IR fluctuations and IR movement is linked to changes in monetary policy. With the current state of globalization, it is difficult that all the three above stated objectives can be simultaneously achieved by any economy. Hence, it has become more and more important to predict the movement of the ER and study the macroeconomic determinants of the ER. Macroeconomic variables, such as inflation rate (Inf), IR, foreign direct investment (FDI), money supply (MS), trade balance (TB) and terms of trade (ToT), FDI and gross domestic product (GDP) are considered to be heavily influencing ER. Moreover, these macroeconomic variables are unstable depending on extant economic conditions of any economy and may cause volati-lity in ER (Kocenda & Valachy, 2006). Figure 1 shows the volatile behaviour of the USD/INR ER.

Figure 1.

Source: Reserve Bank of India.

Sometimes the relationship between ER and macroeconomic variables gets affected by major economic events. For example, the Southeast Asian crisis caused by currency depreciation in 1997 and sub-prime loan crisis of 2008 severely strained the national economies (Corsetti, Pesenti, & Roubini, 1999). Any global economic turmoil will affect different economic variables through ripple effect and this, in turn, will affect the ER of different economies differently. The financial crisis of 2007–2009 caused a huge amount of outflow by the foreign institutional investors from India in order to meet their liquidity. This led to an increase in demand for USD as FIIs wanted to convert their rupee in USD and thus the ER depreciated. The energy crisis in 2003–2009 caused the oil price to increase significantly from USD 35 per barrel to USD 147 per barrel. As a result, India’s import bill inflated causing BOP deficit and ER depreciation. This was the direct impact of the energy crisis. The indirect impact was that with the increase in oil prices, domestic cost of production increased leading to inflation in the economy which led to higher export price. This again caused BOP deficit and subsequent depreciation in the ER. The Global recession in 2000 caused the domestic rate of interest to fall leading to drain out of foreign capital and resultant balance of payment deficit, which caused the ER to appreciate.

International business environment has seen extreme unpredictability in ERs and a series of worldwide financial crises during the last couple of decades. Majority of recent empirical models have neglected the potential existence of a long-term equilibrium relationship between ERs and macroeconomic variables, but theoretically and empirically as well, ERs are still subject to many controversies in the field of economics and international finance (Makin, 2004). Surprisingly, the relationship has remained an important question due to little attention paid to investigating in this aspect, especially in developing countries. The variability of ERs, both in the case of appreciation or depreciation, is directly connected to the economic performance of a country. Volatility of developing countries’ currencies depends on the pegging system and the implicit weight of the currency that a particular country pegs (Beckmann, Belke, & Kuhl, 2011).

Inflation is the increase in general price level of any economy and is usually measured by the wholesale price index (WPI) in India. As a general rule, an economy with a lower Inf exhibits a higher currency value and economies with a higher Inf exhibits depreciation in its currency value. Therefore, the relationship between inflation and ER is negative. When MS increases in the economy, there is an inflationary situation in the economy. When inflation increases, it decreases the value of the currency. Therefore, there is an inverse relationship between MS and ER. By manipulating IRs, central banks reign over inflationary pressure. Changing IRs impact currency value as well. Higher IR attracts inflow of foreign capital and causes the ER to rise. Lower IR tends to decrease ER. Therefore, the relationship between IR and ER is also negative.

TB is net of inflows and outflows of foreign currencies from exports and imports respectively. These inflows and outflows of foreign currencies are caused by international trade and services (Chong & Tan, 2007). TB constitutes of a current account, which includes merchandise, services, interests, dividends, unilateral transfers, etc. Outflows from imports more than inflows from exports lead to a deficit in the TB. When TB is negative, then demand for foreign currency is more, which lowers economy’s ER. Therefore, the relationship between TB and ER is positive.

ToT is expressed as a ratio of export prices to import prices and if export prices rise more than import prices, ToT moves favourably. This means that there is an increasing demand for country’s export. Rising revenues from exports increase demand for the economy’s currency and an increase in the ER. Therefore, the relationship between ToT and ER is also positive.

GDP is gross of all goods and services produced in the economy in an accounting year. When GDP is less, there is a budget deficit as well as inflation in the economy. When inflationary situation is there in the economy, rate of interest will rise causing an inflow of foreign capital and subsequently, the value of economy’s currency depreciates. Therefore, there is a positive relationship between GDP and ER. FDI increases when the rate of interest is attractive in that economy. When the rate of interest increases, it decreases the value of the currency of that economy. Therefore, there is a negative relationship between FDI and ER.

Thus we see that all the above macroeconomic variables influence ER. This study adds to the literature of ER by focusing on the macroeconomic factors affecting ERs in India and has tried to find out structural breaks in that relationship.

Review of Literature

Most of the literatures have focused on the relationship between international trade and ERs, but very few studies have investigated the relationship between macroeconomic factors and ERs and also testing structural break in that relationship. In addition, the majority of the previous work explored the relations in advanced economies.

Dooley, Isard and Taylor (1995) applied multivariate vector autoregression and cointegration modelling techniques to test for the short-run and long-run influences of gold prices on ERs conditional on other monetary and real macroeconomic variables and applied the resulting error correction ER equation to out of sample forecasting exercises. The results, emerged from the various empirical investigations conducted, state that gold price movements have explanatory power with respect to ER movements over and above the effects of movements in monetary fundamentals and other variables that enter standard ER models. Based on the concept of gold as ‘an asset without a country’ and the argument that changes in country preferences will be systematically reflected in the price of gold, these empirical findings can be interpreted as indirect evidence that ER movements are largely overlapping with events that change preferences for holding claims on different countries.

Husteda and MacDonald (1999) in a study examined the extent to which a number of currencies central to the Asian currency crisis were misaligned at the end of 1996. A well-known fundamental based ER model, the monetary approach to ER behaviour, is used to produce estimates of equilibrium ERs for a number of Asian currencies. The estimates were calculated using panel methods and it was seen to be consistent with the underlying model. Most significantly, very little evidence of misalignment is found to exist in 1996. The study suggested that the cause of the Asian crash cannot be attributed to traditional fundamentals.

Kashif (2000) estimated economic indicators that influence the ER and showed that the relation between Inf and ER expressed in terms of USD and Pakistani rupee is negative and insignificant.

Edwards (2001) investigated the dynamic association between ER regimes, capital flows and currency crises in emerging economies. The study draws on lessons learned during the1990s and deals with some of the most important policy controversies that emerged after the Mexican, East Asian, Russian and Brazilian crises. He concludes that under the appropriate conditions and policies, floating ERs can be effective and efficient.

Taylor (2001) discusses the failure of liberalized policies in Argentina. He says that Argentina has failed in maintaining the liberalized policies about capital flows and a stable currency. Argentina had an anti-inflation programme based on freezing the ER in the early 1990s. This means that the MS within the country and the supply of credit to firms are tied directly to international reserves. So if the country gets capital inflows, the supply of money and credit increases, leading to a substantial increase in domestic prices.

Basurto and Ghosh (2001) using a standard monetary model of ER determination showed that tighter monetary policy was, in fact, associated with an appreciation of the ER during the 1997 currency crises in three Asian countries and during the 1994 Mexican currency crisis.

Harberger (2004) studied the impact of economic growth on the real ER. He found that there is no systematic connection between economic growth and real ER. Husain et al. (2004) found in their study that little access to international capital is available for the weaker and less developed countries, so low rate of inflation and a higher level of durability is associated with fixed ER regime in those countries. However, they found no robust relationship between economic performance and ER regime in the developing economies. They also found that advanced economies may experience a durable and slightly higher level of growth rate without a higher level of inflation in the flexible ER regime.

Dua and Sen (2006) examined the interactions between real ER, level of capital flows, volatility of flows, fiscal and monetary policy indicators, and current account surplus for Indian economy for the period between 1993 and 2004 and found that determinants of the real ER include net capital inflows and their volatility (jointly), government expenditure, current account surplus and MS in terms of significant impacts.

Dua and Sinha (2007) explained the impact of the East Asian crisis on India’s ER. To examine this, an index of currency pressure was estimated for four countries—Thailand, South Korea, Malaysia and India—covering the period just before, during and after the crisis. A contagion model with panel data for these four countries was also estimated during the crisis period. On the basis of the panel data estimates, the study concludes that while India experienced some effects of the crisis but those were not substantive. This is partly attributed to the role of stabilization policy in India that included intervention in the foreign exchange market by the central bank, phased tightening of monetary policy and restrictions on capital flows.

Choi and Park (2008) investigated the relationship between IRs and ERs during the Asian crisis period using a VAR model and rejected the use of a tight monetary policy (high IRs) in stabilizing ERs.

Mirchandani (2009) in a paper identified several macroeconomic factors and had shown significant impact on the variability in economy’s ER, whereas Emmanuel (2009) examined the impact of the determinants, such as oil prices, foreign reserves, CPI and IRs, on ER and found only oil prices to have significant short-run impact on ERs.

Achsani (2010) in a paper reconfirmed that in case, the Inf in the countries is much higher, the relationship between the ER and Inf is negative.

In a study, Polodoo, Seetanah and Padachi (2011) investigated the impact of ER volatility on the macroeconomic performance of small island developing states (SIDS). Taking a sample of 15 SIDS, the study analysed econometrically the impact of ER volatility on major macroeconomic variables, namely economic growth, external trade and FDI on the SIDS. The paper first constructs the z-score measure, developed by Wolf et al (2003), as a measure of ER volatility and employed data spanning for the period 1999 to 2010 to analyse robust estimates in a static framework as well as in a dynamic and longitudinal data framework using the generalized method of moments. It also analysed the impact of ER volatility on macroeconomic performance of the economies. The OLS with robust standard errors results indicates that ER volatility impacts negatively on current account balance but positively on the growth rate of the economies studied. In a dynamic setting, however, ER volatility does not influence the macroeconomic variables.

In a study, Coudert et al. (2011) determined the impact of global financial turmoil on the ER policies in emerging countries. Spill-overs from advanced financial markets to currencies in emerging countries are likely to be exacerbated during crisis periods. To test this hypothesis, they assessed the ER policies by currencies volatility and investigated their relationship to a global financial stress indicator measured by the volatility on global markets. The possibility of non-linearities was introduced by running smooth transition regressions over a sample of 21 emerging countries from January 1994 to September 2009. The results confirmed that ER volatility does increase more than proportionally with the global financial stress for most countries in the sample and also evidence regional contagion effects spreading from one emerging currency to other currencies in the neighbouring area.

Chowdhury (2012) using an Autoregressive Distributive Lag model found that the ToT, government expenditure, IR differentials and trade openness are the significant determinants of ERs for Australia in the long run, whereas Kia (2013) found that for Canada, over long run, the real ER is a function of real MS, domestic and foreign IRs, real GDP, real government expenditure, deficit per GDP, domestic and foreign outstanding debt and commodity prices.

Srikant and Kishore (2012) in a paper identified that among the various macroeconomic factors, lagged values of a current account, relative MS, relative output and IR differential have a most significant impact in determining the ER. Amongst the factors that have minimal impact on ER are forward premium, capital account and RBI’s net interventions.

Ozer-Imer and Ozkan (2014) investigated the impact of the 2008–2009 global financial crisis on the co-movement of 16 currencies in the sample. It was analysed that volatilities increased at least twofold with the outbreak of the crisis and there is an inverse relationship between volatility and the duration of the crisis. The dynamic conditional correlations (DCCRs) usually increase with the onset of the crisis and they fluctuate smoothly afterwards, keeping the increased level.

Grossmanna, Loveb, and Orlovc (2014) employed a panel vector autoregressive model (PVAR) to study the dynamics of the overall ER volatility based on panel data for 29 economies using simulating impulse response functions since economic shocks may affect high-frequency and low-frequency components of volatility differently. Accordingly, the paper also estimated the dynamics of the most destabilizing (high-frequency) components of ER volatility, which are isolated using spectral methodology. The investigations revealed interesting dynamic interrelationships between macroeconomic as well as financial variables and ER volatility. Little evidence was found for a significant difference in the responses of macroeconomic and financial variables to the overall volatility vis-à-vis the high-frequency components thereof. The feedback effects from ER volatility to macroeconomic and financial variables are found to be much stronger for developing countries relative to developed economies. These findings were confirmed by variance decompositions and are largely immune to several robustness checks.

Khan (2014) argued that countries generally prefer a flexible ER to the fixed ER and wanted to determine that factors that are responsible for the frequent devaluation of the ER of Pakistan. He used simple linear regression to find the impact of inflation rate, oil price, IR, export and import on the variability of ER and used correlation analysis to find the interrelationship among the independent variables. His study showed that inflation and oil price has a positive impact on ER and IR, export and import affected ER negatively.

Farahan and Nushrat (2015) in a study proved that Bangladesh benefitted significantly with the adoption of the flexible ER. The macroeconomic variables that are responsible for appreciation and depreciation of currency for Bangladesh are import, export, inflation rate, FDI, trade deficit and ER. They emphasized that government regulation in managing a floating ER is mandatory.

Ramasamy and Abar (2015) determined the role of ER in determining the nature of hedging to minimize ER risk. In the study, they have concluded that countries which are relatively economically developed with less unemployment and corruption, macroeconomic variables such as inflation rate, the balance of payments and IR has a negative impact on ER. The result so obtained is in contrast to the existing theory and according to them, it might be because of psychological factors like investor’s sentiment which is not included as an independent variable in the study.

Mathew, Suvitha, and Rekha (2015) analysed the impact of various macroeconomic variables on fluctuation of ER in India and found that inflation rate, external debt, GDP and FDI have a strong positive correlation with ER whereas IR has a negative correlation during the study period 2004–2013 for India.

Khera and Singh (2015) studied the upward and downward movements of Indian rupee against USD and suggested measure to check devaluation of Indian currency. Among the macroeconomic factors, GDP and FDI have a positive correlation, whereas inflation, lending rate and current account deficit have a negative correlation with ER during the period 1991–2013.

Abdoh, Yusuf, Zulkifli, Bulot, and Ibrahim (2016) studied the impact of only three macroeconomic variables, namely IR, inflation and export, on ER fluctuation of select ASEAN countries (Thailand, Malaysia, Cambodia, Philippines, Brunei Darussalam, Laos, Cambodia, Singapore and Vietnam) and found that it is only export which has a significant role in ER fluctuation during the study period 2005–2014.

Onoh, Okechukwu, and Duruechi (2017) tried to find whether there exists any structural break in the ordinary ER in Nigeria by using F-statistics and found that the structural break was evident in the years 1992, 1995 and 2005. The robustness was checked by applying Quant Andrew test. It was seen that identified break date coincides with a period of persistent excess liquidity, which got increased by the monetization of excess crude receipts. Other contributory factors to the liquidity surfeit include the huge autonomous inflow of foreign exchange and pre-election spending. The effect of the identified structural break was accommodated in the modelling approach to ensure that the estimated parameters are unbiased. The short-run model revealed that a decline in the spread will lead to an increase in economic agents’ desire to hold cash, as the incentive for arbitrage transactions moderates. The preliminary analysis shows that the ER was robust enough in explaining developments in the foreign exchange market.

Data and Methodology

This study covers a period of 40 years from 1977–1978 to 2015–2016. Time series data of 40 years on ER, GDP, inflation, IR, FDI, MS, TB and ToT have been collected from RBI website. The description of the variables is as given in Table 1.

Table 1.

Descriptive Statistics of Variables

Variable	Mean	Median	Max	Min	SD	Skewness	Kurtosis
ER	33.20239	36.33235	67.07200	7.909200	18.36058	–0.00471	1.762187
GDP	31155.22	20912.92	121898.5	8102.490	28368.03	1.893665	6.087752
Inf	78.66574	69.40737	183.000	14.27714	53.54049	0.608455	2.171322
IR	8.681250	9.0000	12.0000	6.0000	2.093938	0.0600060	1.820680
FDI	74947.93	24367.00	244258.0	174.0000	90104.45	1.109047	3.074111
MS	25864.98	7586.717	127919.4	329.0600	36150.68	1.517185	4.081901
TB	–2008.044	–220.8915	–9.354000	–10348.44	3129.222	–1.390684	3.422039
ToT	105.1815	88.31592	278.9794	14.12383	82.63183	0.484149	1.827656

Source: Researchers own calculation.

In order to see the stochastic relationship between ER and macroeconomic variables, we have to run multiple linear regression using ordinary least square (OLS) estimation method. But before running regression, we have to check stationarity of variables. If variables are not stationary and we still run regression, then it will lead to a spurious regression, which means that we might get a relationship between two variables where it actually does not exists. If a time series data is made stationary, then it indicates that its statistical properties will also remain the same in the future and prediction becomes possible. Graphically, we can check whether variables are stationary or whether variables are following any particular trend. We can also go in for Augmented Dickey–Fuller (ADF) test to check whether any series is stationary or not using the following model:

y_{t} = y_{t - 1} + u_{t} ​

(1)

Using lag operator notation, we can rewrite the above equation as follows:

y_{t} = L y_{t} + u_{t} ​

(2)

y_{t} (1 - L) = u_{t} ​ ​

(3)

From Equation (3), we can get the characteristic equation (1 – z) = 0 and the root of this characteristic equation is z = 1. If the root falls outside the unit circle, that is, z > 1, then the series is non-stationary. The variables have been plotted in a single graph, as shown in Figure 2.

Figure 2.

Source: Researchers own calculation.

The results of Augmented Dickey–Fuller test are shown in Table 2.

From Table 2, we see that all the variables are non-stationary at level but stationary at first differencing. That is to say, the variables are difference stationary. After converting the dependent variable (ER) and all the independent variables (GDP, Inf, IR, FDI, MS TB and ToT) into their first differences, we have run multiple linear regression using OLS estimation method and have obtained the estimated equation as follows:

Table 2.

Unit Root Tests of ER and Other Macroeconomic Variables

Variable	ADF Test at Level (Max Lag Length = 2)				ADF Test at First Difference (Max Lag Length = 2)
Variable	Coefficient	Statistic	P-value	Inference	Coefficient	Statistic	P-value	Inference
ER	–0.147132	–1.725165	0.7209	Not rejected	–0.837523	–5.033644	0.0012	Rejected
GDP	0.132437	3.23559	1.0000	Not Rejected	–0.795249	–4.844954	0.0003	Rejected
Inf	–0.049453	–1.315445	0.8688	Not Rejected	–0.618785	–3.962621	0.0187	Rejected
IR	–0.070210	–1.030910	0.7326	Not Rejected	–0.968901	–5.797772	0.0000	Rejected
FDI	–0.080717	–0.632005	0.8467	Not Rejected	–1.149215	–5.557544	0.0001	Rejected
MS	–0.001338	–0.112566	0.9408	Not Rejected	–0.940596	–5.464257	0.0001	Rejected
TB	–0.001933	–0.045083	0.9483	Not Rejected	–0.519730	–2.0979240	0.0361	Rejected
ToT	–0.10085	–0.319675	0.9127	Not Rejected	–1.145397	–6.960123	0.0000	Rejected

Source: Researchers own calculation.

\begin{matrix} \hat{D E R} = \hat{α} + \hat{β 1} \times D G D P + \hat{β 2} \times D I N F \\ + \hat{β 3} \times D I R + \hat{β 4} \times D F D I + \hat{β 5} \times D M S \\ + \hat{β 6} \times D T B + \hat{β 7} \times D T o T \end{matrix}

(4)

In Table 3, we see that the majority of the independent variables or regressors have an insignificant impact on the dependent variable or regressand. This usually happens when there is a problem of multicollinearity, that is, a high correlation among the regressors. Existence of multicollinearity shrouds the robustness of the impact of individual regressor. In order to check whether there is any multicollinearity among the regressors or not, we go in for correlation analysis, as given in Table 4.

Table 3.

Dependent Variable: DER

Explanatory Variables	Expected Sign of Coefficient	Coefficient	Std. Error	T-statistic	P-value
Const.	?	9.998281	13.99971	0.71478	0.4838
DGDP	+	–0.00014	0.000205	–0.680623	0.5043
DINF	–	0.702589	0.169986	4.133214	0.0006***
DIR	–	–0.665113	0.693679	–0.958820	0.3497
DFDI	–	0.0000204	0.0000317	0.643421	0.5276
DMS	–	–0.000029	0.000169	–0.171332	0.8658
DTB	+	0.003144	0.001361	2.309674	0.0323**
DToT	+	–0.135714	0.039671	–3.420967	0.0029**
R² = 0.4465, Adj R² = 0.4305, F = 43.7898**, Durbin–Watson = 1.8656

Source: Researchers own calculation.

Note: * 10 per cent level of significance, **significance at 5 per cent level, ***significance at 1 per cent level.

Table 4.

Correlation Between Independent Variables

	DGDP	DINF	DIR	DFDI	DMS	DTB	DTOT
DGDP	1	0.899996	–0.40624	0.912741	0.962952	–0.8232	0.736513
DINF	0.899996	1	–0.5298	0.835951	0.965331	–0.94295	0.922724
DIR	–0.40624	–0.5298	1	–0.46098	–0.38236	0.300646	–0.66732
DFDI	0.912741	0.835951	–0.46098	1	0.881128	–0.80755	0.769049
DMS	0.962952	0.965331	–0.38236	0.881128	1	–0.93164	0.829842
DTB	–0.8232	–0.94295	0.300646	–0.80755	–0.93164	1	–0.85384
DTOT	0.736513	0.922724	–0.66732	0.769049	0.829842	–0.85384	1

Source: Researchers own calculation.

Here from Table 4, we see that correlation between inflation and MS is high (0.965331), this is because inflation is checked by controlling the supply of money and with inflation real MS falls. Thus MS and inflation are interrelated to each other. So out of these two variables, only one is to be dropped. The rule is to drop that variable whose p-value is high. As per Table 3, we see that p-value of the MS is high. So MS, as a regressor, is dropped from the analysis. We again run multiple linear regression to estimate the following equation, dropping MS as a regressor.

\begin{matrix} \hat{D E R} = \hat{α} + \hat{β 1} \times D G D P + \hat{β 2} \times D I N F \\ + \hat{β 3} \times D I R + \hat{β 4} \times D F D I \\ + \hat{β 5} \times D T B + \hat{β 6} \times D T o T ​ \end{matrix}

(5)

We obtain regression outputs as given in Table 5 from the above equation.

Therefore, the estimated equation can be written as follows:

\begin{matrix} \hat{D E R} = \underset{(0.886890)}{11.00133} - \underset{(- 1.176065)}{0.000165 * D G D P} \\ + \underset{{(4.248831)}^{* * *}}{0.698936 * D I N F} - \underset{(- 1.073556)}{0.698016 * D I R} \end{matrix}

\begin{matrix} + \underset{(0.735867)}{0.0000219 * D F D I} + \underset{{(2.610357)}^{* *}}{0.003229 * D T B} \\ - \underset{{(- 3.705001)}^{* * *}}{0.137620 * D T o T} \end{matrix}

(6)

where * respresents 10 per cent level of significance, ** 5 per cent level of significance, *** 1 per cent level of significance. The data is stationary at first difference so that is why DER,DGDP,DINF,DIR are taken which means DER is first difference of exchange rate, DGDP is first difference of GDP, DINF first difference of inflation rate, DIR, first difference of interest rate.

From Table 5, we see that only inflation, TB and ToT have significant impacts on ER. Inflation and ToT at the rate 1 per cent and TB have a significant impact at the rate 5 per cent on ER. Other regressors, such as GDP, IR and FDI have not significantly influenced ER during the study period. First, we have analysed the variables which have been found to have significant impacts on ER during this period and the variables which have been found not to have a significant impact on a ER, later on.

Table 5.

Dependent Variable: DER

Explanatory Variables	Expected Sign of Coefficient	Coefficient	Std. Error	T-statistic	P-value
Const.	?	11.00133	12.40440	0.886890	0.3857
DGDP	+	–0.000165	0.000140	–1.176065	0.2534
DINF	–	0.698936	0.164501	4.248831	0.0004***
DIR	–	– 0.698016	0. 650190	–1.073556	0.2958
DFDI	–	0.0000219	0.0000298	0.735867	0.4704
DTB	+	0.003229	0.001237	2.610357	0.0167**
DToT	+	– 0.137620	0.037144	–3.705001	0.0014***
R² = 0.3760, Adj R² = 0.3572, F = 38.3076**, Durbin–Watson = 1.729

Source: Researcher’s own calculation.

Notes: ** 5 per cent level of significance, ***1 per cent level of significance.

So far as the relationship between ER and inflation is concerned, we have obtained positive relationship instead of the expected negative relationship. This positive relationship is vouched by the fact that when there is a minimum level of inflation in the economy, producers get incentives to invest more and more in the economy in expectation of reaping out a higher return. When investment spate is there, foreign capital in terms of FDI and FPI also infuses into the economy. Foreign investment increases the demand for the Indian rupee leading to an appreciation of the ER.

Similarly, ToT is also found to have a significant negative impact instead of positive impact onto ER. This negative impact can be justified by the fact that India has remained essentially an exporter of primary products whose export demand is inelastic. This means that India is willing to export more even at a lesser price leading to a fall in export earnings and consequent deterioration in its ToT. This is a case of ‘immiserizing growth’. Here when export earnings fall, a supply of foreign exchange in relation to Indian rupee also falls. Demand for foreign exchange remaining same, when supply falls, ER appreciates.

TB has a significant positive impact, which is expected. During the study period, India has always faced a deficit in TB. In order to maintain equilibrium through an increase in export and a decrease in import, India has depreciated her currency. Thus, positive significant impact is justified. When we analyse the regressors, which do not have significant impacts on ER, we see that GDP has a negative impact on ER, instead of expected positive impact and FDI has a positive impact on ER, instead of expected negative impact.

The negative impact of GDP can be understood as when GDP increases, then output and income both increase. Exports increase because of increase in output and imports increase because of increase in income. Since, a propensity to import is much higher as compared to a propensity to export in any developing economy, like India, therefore when GDP increases then import increases much higher than the increase in exports. Thus a deficit in TB occurs. As a corrective measure, ER is to be depreciated.

The positive impact of FDI onto ER can be explained by the fact the FDI is usually invited by the government in import-competing industries. Moreover, foreign firms, in order to do away with tariff, prefer to invest in FDI rather than direct export. As a result, production of import-competing industries increases. Because of this increase in total production of import-competing industries, some raw materials are still left to be imported more. This leads to an increase in imports and in turn. From regression output (see Table 5), we see that only inflation, TB and ToT have significant impacts on ER. The model is a good-fit as expressed by the F-statistics (38.3076), which is significant at 5 per cent level. The model is also robust as 37.6 per cent of the variation in ER is explained by the variations in the regressors.

Now the model that we have considered is also to be checked whether it suffers from any residual diagnostic problem or not in the following section.

Results and Discussion

Heteroscedasticity

Under this diagnostic test, the assumption is that residuals are not heteroscedastic rather residuals are homoscedastic which means that the variance of the residual term is constant. Usually Goldfeld–Quandt test, Breusch–Pagan test, White’s test, etc., are applied. The approaches are based on splitting the total sample of length T into two sub-samples of length T1 and T2. The regression model is estimated on each sub-sample and the two residual variances are calculated as

s_{1}^{2} = \frac{\hat{u 1} \hat{u 1}}{(T 1 - K)} a n d s_{2}^{2} = \frac{\hat{u 2} \hat{u 2}}{(T 2 - K)}, r e s p e c t i v e l y . ​

(7)

The null hypothesis is that the variances of the disturbances are equal, which can be written as: H₀: σ₁² = σ₂^2-- against a two-sided alternative. The test statistic is simply the ratio of two variances where the larger is placed in the numerator. The test statistic is distributed as F (T₁ – k, T₂ – K) under the null hypothesis and the null of constant variance is rejected if the test statistic exceeds a critical value, as given in Table 6.

Table 6.

Heteroscedasticity Test of Residuals

F-statistic	1.102173	Prob F(6, 20)	0.3954
Observed R²	6.709192	Prob chi-square(6)	0.3486
Scaled explained SS	3.124764	Prob chi-square(6)	0.7930

Source: Researchers own calculation.

From the actual-fitted-residual graph (Figure 3), we do not observe any heteroscedasticity in the residual, which can be verified from Table 6 also. From this table, we see that observed R² is insignificant, meaning thereby that residuals are free from heteroscedasticity. Therefore the model is robust.

Figure 3.

Source: Researchers own calculation.

Serial Correlation

Under this diagnostic test, the assumption is that the residuals are not autocorrelated, that is, error term of one period is not correlated to the error terms of other periods. One way to interpret the test statistic is in the context of regression of time t error on its previous values, as follows:

U_{t} = ρ U_{t - 1} + V_{t} ​

(8)

Under Durbin–Watson or Breusch–Godfrey serial correlation test statistic, the null and alternative hypotheses are as follows:

H_{0} = ρ_{0} a n d H_{1} \neq ρ_{1} ​

The Durbin–Watson statistics is given by

D W = \frac{\sum_{t = 2}^{T} {(\hat{u_{t}} - \hat{u_{t - 1}})}^{2}}{\sum_{t = 2}^{T} \hat{u_{t}^{2}}} ​

Durbin–Watson or Breusch–Godfrey serial correlation tests can be applied to test whether residual suffers from autocorrelation or not, as given in Table 7.

Table 7.

Serial Correlation Test of Residuals

F-statistic	1.102173	Prob F(6, 20)	0.3954
Observed R²	6.709192	Prob chi-square(6)	0.3486

Source: Researchers own calculation.

From the table, we observe that the value of observed R² is insignificant, meaning thereby that there is no serial correlation or autocorrelation in the residuals. Therefore the model is robust.

Normality

Under this diagnostic test, the assumption is that the residuals are normally distributed, that is, U_t  N(0, σ²). Jarque and Bera (1981) test is applied to test whether coefficient of skewness and coefficient of excess of kurtosis are jointly zero. Skewness measures the extent of deviation of the error terms from the mean and kurtosis measures the peakedness of the distribution of error term. Coefficient of skewness is given by

b 1 = \frac{E (u 3)}{\sqrt{\sqrt[2]{(σ 2) 3}}} a n d b 2 = \frac{E (u 4)}{(σ 2) 2} ​

(9)

Given, these coefficients of skewness and excess kurtosis, the Jarque–Bera test statistics is given by

D - W = T [(b_{1}^{2} / 6) + {(b_{2} - 3)}^{2} / 24] ​

(10)

From Figure 4, we observe that the residuals are normally distributed as the probability of Jarque–Bera test statistic is insignificant. Therefore the model is robust.

Figure 4.

Source: Researchers own calculation.

Ramsey’s Regression Specification Error Test (RESET)

The model that we have considered is linear in nature. Sometimes the appropriate model may be a non-linear one, such as lin-log model, log-linear model and log-log model. If the appropriate model is non-linear but we have considered a linear model, then there will be regression specification error. We have checked specification error with the help Ramsey test as given in Table 8.

Table 8.

Ramsey’s Regression Specification Error Test

F-statistic	1.1831	Prob F(1, 20)	0.2914
Log likelihood ratio	6.652979	Prob chi-square(1)	0.1986

Source: Researchers own calculation.

In Table 8, both F and χ² versions of the test are presented, which are insignificant. It is seen that there is no apparent non-linearity in the regression equation. Therefore a linear model is appropriate.

Parameter Instability

We can check whether this model is stable or not with the help of the CUSUM test following recursive estimation as given in Figure 5. In Figure 5, we can see that the residual is within the two bounds, meaning thereby that the model is stable. But, sometimes because of major economic events, the model may suffer from parameter instability or structural break. Many such economic events as, Association of South East Asian Nation (ASEAN) currency crisis in 1997, Dotcom bubble in USA in 2000–2002, Energy crisis (oil price crisis) in 2003–2009, subprime mortgage loan crisis in

2007–2009 and European sovereign debt crisis in 2009, may have influenced the model, as a result of which the model may have suffered from parameter instability, as shown in Tables 9–15.

Figure 5.

Source: Researchers own calculation.

In order to check whether there is a structural break or not in the model during these periods, we have gone for Chow’s Breakpoint Test and have obtained multiple breaks between 2003 and 2009, as shown in Tables 9–15.

Table 9.

Chow’s Breakpoint Test (Break at 2003) Null Hypothesis: No Breaks at Specified Breakpoints

F-statistic	3.621209	Prob F(1, 13)	0.0217
Log likelihood ratio	29.20766	Prob chi-square(1)	0.0001
Wald statistic	25.34846	Prob chi-square(1)	0.0007

Source: Researchers own calculation.

Table 10.

Chow’s Breakpoint Test (Break at 2004) Null Hypothesis: No Breaks at Specified Breakpoints

F-statistic	4.151810	Prob F(1, 13)	0.0130
Log likelihood ratio	31.70371	Prob chi-square(1)	0.0000
Wald statistic	29.06267	Prob chi-square(1)	0.0001

Source: Researchers own calculation.

Table 11.

Chow’s Breakpoint Test (Break at 2005)

Null Hypothesis: No Breaks at Specified Breakpoints

F-statistic	4.157968	Prob F(1, 13)	0.0130
Log likelihood ratio	31.73136	Prob chi-square(1)	0.0000
Wald statistic	29.10577	Prob chi-square(1)	0.0001

Source: Researchers own calculation.

Table 12.

Chow’s Breakpoint Test (Break at 2006)

Null Hypothesis: No Breaks at Specified Breakpoints

F-statistic	3.167829	Prob F(1, 13)	0.0347
Log likelihood ratio	26.87528	Prob chi-square(1)	0.0004
Wald statistic	22.17421	Prob chi-square(1)	0.0024

Source: Researchers own calculation.

Table 13.

Chow’s Breakpoint Test (Break at 2007)

Null Hypothesis: No Breaks at Specified Breakpoints

F-statistic	3.998684	Prob F(1, 13)	0.0150
Log likelihood ratio	31.00675	Prob chi-square(1)	0.0001
Wald statistic	27.99097	Prob chi-square(1)	0.0002

Source: Researchers own calculation.

Table 14.

Chow’s Breakpoint Test (Break at 2008)

Null Hypothesis: No Breaks at Specified Breakpoints

F-statistic	4.600480	Prob F(1, 13)	0.0087
Log likelihood ratio	33.64799	Prob chi-square(1)	0.0000
Wald statistic	32.20336	Prob chi-square(1)	0.0000

Source: Researchers own calculation.

Table 15.

Chow’s Breakpoint Test (Break at 2009)

Null Hypothesis: No Breaks at Specified Breakpoints

F-statistic	3.998684	Prob F(1, 13)	0.0150
Log likelihood ratio	31.00675	Prob chi-square(1)	0.0001
Wald statistic	27.99097	Prob chi-square(1)	0.0002

Source: Researchers own calculation.

The existence of structural breaks at points 2003–2009 is explained by the fact that volume of crude oil import by India is high, roughly around 37 per cent of total import. With the increase in oil price rise from USD 25–30 per barrel in 2003 to USD 100 per barrel in 2007 to USD 147.3 in 2008, a deficit in TB increased alarmingly which caused parameter instability. With the onset of the global recession, output and production started declining and consequently, income declined and led to a fall in the demand for oil and the price started falling and oil price settled down.

Conclusion

From the above analysis, we see that our model consisting of the ER as a dependent variable and other macroeconomic variables as independent variables is robust. The model has suggested that only inflation, TB and ToT have influenced ER significantly during the study period. Other macroeconomic variables such as GDP, FDI and IR have not significantly influenced ER during the study period. The model stands for all residual diagnostic tests. The model does not suffer from residual heteroscedasticity, autocorrelation and non-normality.

In order to check whether there is any structural break or not in the model during these periods, we have gone for Chow’s Breakpoint Test and have obtained multiple breaks between 2003 and 2009, as shown in Tables 9–15. The existence of structural breaks in the years during 2003–2009 is explained by the fact that volume of crude oil import by India is high, roughly around 37 per cent of total import. With the increase in oil price from USD 25–30 per barrel in 2003 to USD 100 per barrel in 2007 to USD 147.3 per barrel in 2008, a deficit in TB increased alarmingly which caused parameter instability.

In this article, we have not considered factors such as the budget deficit, tax rates, employment rate, foreign debt, repatriation of profits by MNCs and change in the composition of international trade on ER. Moreover, we have not considered the capital account balance. There is a paradigm shift in the composition of foreign trade. Now services contribute towards a major ingredient of foreign trade and this influences ER as well. So services can also be considered as one of the regressors. Future researches can consider all these variables and carry our study to fill this gap.

Footnotes

Declaration of Conflicting Interests

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

Funding

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

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