1. Introduction

Exchange rate stability is an important indicator of a country’s economic strength. India followed ‘fixed exchange rate’ regime till the economic crisis of 1991. After March 1992, it started following the policies of liberalization and structural adjustment program making Rupee partially convertible on the current account. Since then, India has registered tremendous fluctuation in Rupee exchange rate figures owing to increasing trade and financial relationship of India with its major trading partner’s viz. USA, Europe and China.

USA, China and EU represent an interesting case for research as these countries are increasingly becoming closely related to India through both commodity and capital flows. According to Department of Commerce of India, for the calendar year 2012-2013, EU became the largest trading partner of India; China had been relegated to the third position which was then followed by USA. Hence, trade of India with these countries has had phenomenal influence on fluctuation of Rupees over the years.

Indo-US relationship has gone through a remarkable transformation in the new millennium. Trade and commerce has been a crucial component of the rapidly expanding and multi- faceted relations between India and US all these years. According to Embassy of India, from modest $5.6 billion in 1990, the bilateral trade in merchandise goods increased to $62.9 billion in 2012 representing an impressive 1023.2% growth in a span of 22 years. From 2001 to 2012, exports to and imports from U.S. registered a continuous rise; the figures surged by 488.38 % and 316.07% respectively. India - U.S. bilateral merchandise trade stood at $44.06 billion in the period January – August 2013 with the surge in India’s merchandise exports to and imports from U.S.by 3.62% and 9.55% respectively when compared to the same period previous year. Closer business ties have generated a fivefold increase in bilateral trade since 2000. On the investment front, USA covers almost every sector in India which is open for private participants; USA has 5.75% share in FDI equity inflows to India from April 2000 to August 2013 and is categorized as the fifth largest investor in India. Thus, the twenty-first century India-U.S. strategic relations are at the threshold of unprecedented developments.

The development of trade between European Union countries and India has been a top priority lately. India is not only the world's largest democracy, but is one of the fastest growing economies in the world and therefore with the increasing India’s global presence, Europe has found India to be a very important strategic partner in the new millennium and the economic and financial relationship between the two countries has increased manifold. During 2003-2011, the value of trade between the European Union (EU) and India nearly tripled from €28.10 billion to € 80.2 billion, in fact, EU-India trade amounted to about 9.9 percent of India’s total bilateral trade in 2012 – pushing the EU into the forefront as India’s leading trade partner. Bilateral trade between India and the EU was valued at €75.8 billion in 2012 versus €80.2 billion in 2011, representing a decline of 5.49% owing to sovereign debt crisis. India’s exports to EU and imports from EU recorded a decline of 5.1% and 4.7% respectively YOY in 2012. The EU is also one of the largest sources of Foreign Direct Investment for India, FDI inflows from the EU into India increased from €7.5 billion in 2010 to €14.19 billion in 2011. India’s investment into the EU also rose from €0.48 billion in 2010 to nearly €2 billion in 2011. In 2012-2013, EU exports to India and imports from India totaled to €38.596 billion (decrease 10.3 percent year-on-year) and €37.08 billion (down 4.1 percent from the year before) respectively on account of the increased uncertainty and panic in Euro zone, but despite this, EU still stands as India’s largest trading partner.

Among the most encouraging recent developments in India’s and China’s economy is India – China ties which has shown a significant improvement with the passage of time. According to Embassy of India, India and China officially resumed trade in 1978. India-China bilateral trade which was as low as US$ 2.92 billion in 2000 reached US$ 51.8 billion in 2008, making China India’s largest trading partner in goods, replacing the United States of America. By the end of 2009, as a result of the world economic downturn, bilateral trade dropped to US$ 43.27 billion (a decline of 16.54%). However, in 2010 bilateral trade recorded a growth of 43% compared to the year-ago period with India’s exports and imports registering a rise of 52% and 38% respectively. India’s exports to China for 2012 reached US$ 18.8 billion, recording a decline of more almost 20% y-o-y, whereas, imports touched a total of US$ 47.75 billion, recording a decline of more than 5% over the figure for 2011. Thus, these plunging figures reflect the trends of the global economic slowdown marked by lower consumption and slower growth in trade volumes.

These changing trade and financial relationships of India with its major trading partners make the study all the more imperative to aid financial practitioners in enhancing their investment performance by suggesting proper asset allocation, and policy makers in understanding the nature of and interaction between the variables in order to frame more realistic policies.

Therefore, the present study aims at understanding the financial and economic relations of India with USA, China and Europe by checking the validity of International parity conditions like Relative Purchasing Power Parity, Covered Interest Rate Parity, Uncovered Interest Rate Parity, Fisher effect and Forward rate hypothesis. These international parity conditions establish the relationship between the values of two or more currencies and their respective economic conditions.

In the next section the paper reviews the existing literature on international parities. Section 3 explains the methodological framework of the paper, while section 4 tests the stationarity of data. Individual parities are empirically tested in section 5 and joint parities in section 6. The final section concludes the paper.

2. Literature Review

International Parity Conditions have received considerable empirical scrutiny to understand the relationship of different countries across the globe. Numerous researches have been conducted in past to verify if the law of one price and various forms of PPP hold good. One of the studies conducted by J.Hodgson and P.Phelps argued that a change in prices does not affect the exchange rate, though with a long time lag ^[1], whereas Rogalsi and Vinson found that a change in prices gets immediately reflected in the exchange rate movements as the forex markets are perfect and reflect all the available information with immediate effect ^[2]. But a substantial body of literature witnesses failure of PPP because of impact of interest rates and other variables on exchange rates.

But studies by Mishkin ^[3], Adler and Dumas ^[4], Abuaf and Jorion ^[5] found evidence of significant deviations from the relationship between interest rate differential and exchange rate as well, persisting for lengthy periods. The work of Adler and Lehman provided evidence against their result even over the long term ^[6]. A research by Hakkio found that the relationship between interest rate differentials and exchange rates is not perfect in the long run but it supports the use of inflation differentials to forecast long run movements in exchange rates because of interaction between goods and assets market ^[7], and thus, comes into existence – “the Fisher Effect”.

Weber ^[8], King and Watson ^[9], Koustas and Serletis ^[10] and Rapach ^[11] rejected long run relationship of inflation with respect to real interest rates using the framework of Fisher and Seater ^[12] and a large number of OECD countries. Engsted ^[13], Koustas and Serletis ^[10], Atkins and Serletis ^[14] and Rapach ^[11], among others, formally tested for cointegration and also found no support for cointegration between inflation and nominal interest rates. On the other hand, Evans and Lewis ^[15], and Crowder and Hoffman ^[16], among others, found evidence in favor of cointegration with post war United States data.

There also exists enormous Literature on whether the forward exchange rate is an unbiased predictor of the future spot rate or not; Frenkel and Poonawala found that the bias in forward exchange rate were smaller for emerging currencies than for the currencies of advanced country and concluded that the time varying exchange risk premium may not be the explanation of the traditional findings of bias – because the currency of the emerging markets are comparatively more risky than advanced country currencies and therefore would carry a higher risk premium ^[17]. Azouzi, Kumar & Aloui examined the relationship between future spot rates and forward exchange rates using USD-TND (Tunisian Dinar) data and revealed that the UFER hypothesis is rejected ^[18]. But, Hall et al. also addressed empirical violation of the forward rate unbiasedness theory and the findings strongly support the forward rate unbiasedness hypothesis without violating the efficient market theory ^[19].

Recently, a growing body of literature advocates joint validity of the international parity conditions to allow more channels of interaction between the variables. Nikolaos Mylonidis and Dimitrios Sideris examined the financial relations between USA and Canada by examining the validity of various international parity conditions like PPP, UIP, CIP and forward market efficiency hypothesis using joint modeling framework, the paper reported evidence for joint validity of PPP & CIP between USA & Canada reflecting high links between their commodity & capital markets. In contrast to the results of other researches, this research provides affirmative evidence in favor of both PPP and CIP ^[20].

In the Indian context, little work has been done to test International Parity Conditions. Vij ^[21], Sharma and Mitra ^[22], Frenkel and Poonawala ^[17] used forward premium specification to test the UFH in Indian forex market and found that forward rate is not an unbiased predictor of the future spot rate, thereby rejecting UFH in India. Surbhi Jain and N.R. Bhanumurthy examined the issue of integration of financial markets in India in the post-1991 period and found that there is a strong integration of the domestic call money market with the LIBOR. Though, the study found that there is a long-term co-movement between domestic foreign exchange market and LIBOR, it is not robust due to frequent intervention by the Central Bank in the foreign exchange market ^[23]. Abdul Rashid and Kalbe Abbas examined joint validity of PPP and UIP and stated that nominal exchange rate of domestic country, prices levels and interest rates of domestic and foreign country move together in the long run. Thereby, the equilibrium exchange rate may be determined according to PPP and UIP for South Asian economies ^[24]. Renu Kohli examined mean-reversion in the real exchange rate for India after change in exchange rate regime in 1993 and the results indicate that sources of disturbance to the real exchange rate are monetary ^[25].

International Parity conditions have grabbed little attention in India; therefore this paper aims to bridge this gap by employing the parity conditions jointly to delve deeply into the interaction between the variables like interest rate, inflation rate & forward rates in different economic conditions and together their influence on the exchange rate market.

3. Data and Methodology

The validity of the 5 doctrines is checked by employing single cointegrating framework and joint modeling framework using monthly data from January 2001 to October 2013 for the countries viz. India, China, USA and European Union. The variables taken into account are 3 month forward exchange rate, bilateral nominal exchange rate, consumer price indices and 91 days Treasury bill rates. German 91 day Treasury bill rates (Bubills) are taken in place of European 91 day Treasury bill rates on account of non-availability of the data. All the variables are expressed in natural log. The monthly data of all the variables is taken from International Financial Statistics except forward exchange rates, nominal exchange rates and Bubills. 3-month Forward INR/USD rates are retrieved from Reserve bank of India, 3-month Rupee/Euro forward rates are taken from New York foreign exchange market and financial times and since China had pegged currency regime for a long time so its forward rates were fixed. The nominal exchange rates data is obtained from Pacific exchange rate service. 3 month Bubills data till 2006 has been acquired from International Financial Statistics, from 2007-2010 the data has been taken from Bloomberg (Code: GETB1) and from 2011 onwards the data is sourced from FxGlory.

The Johansen ^[26] cointegration is considered to examine the long run relationship between these parity conditions, but the actual cointegration analysis begins with the verification of integration consistency of the variables by using conventional unit root and stationarity test. Thus, Augmented Dickey-Fuller (ADF) test ^[27] and Phillips-Perron (PP) test ^[28] are used. The equations of Augmented Dickey Fuller test (eq.1) and Phillip – Perron test (eq.2) are as follows.

(1)

(2)

Once the Unit Root Tests are applied, then, the two major objectives of the research i.e. the extent to which International Parity conditions like RPPP, CIP, UIP, Fisher effect and Forward rate market hypothesis hold for the examined period using single cointegrating vector framework and, joint testing of these parities under joint modeling framework are addressed.

The long run VECM:

(3)

Where,

D_t= a (p, 3) matrix of dummy variables

τ_i= a (P, P) matrix of short run dynamic coefficients

ε_t = a (P, 1) vector of error terms

π = a (p, p) matrix of long run dynamic coefficients.

In the absence of international capital mobility and trade restrictions, there exists theoretical relationship between prices, forward exchange rates, spot exchange rates and interest rates which are defined by international parity conditions. These parities except forward rate hypothesis have been categorized in two forms i.e. strong and weak form. The distinction between the strong and weak form has been made on the basis of the cointegrating coefficient of the independent variable. If the coefficient is -1 then the parity is said to hold in strong form and if the coefficient is anything other than -1 i.e. δ then the parity holds in weak form (Wherein, δ has a negative value).

H₁: Relative purchasing power parity: states that the country with higher inflation should see its currency depreciate

Strong Form: S_t = P_t^d - P_t^f

Weak Form: S_t = δ (P_t^d - P_t^f)

H₂: Fisher Effect: Country with higher inflation should witness hike in its interest rates

Strong Form: i_t^d - i_t^f = (P_t^d - P_t^f)

Weak Form: i_t^d - i_t^f = δ (P_t^d - P_t^f)

H₃: Covered interest rate parity: Forward rates should incorporate the interest rate differential

Strong Form: F_t-S_t = (i_t^d - i_t^f)

Weak Form: F_t-S_t = δ (i_t^d - i_t^f)

H₄: Uncovered interest rate parity: Country with higher interest rates should anticipate depreciation in its expected exchange rate.

E(ΔSt) = i_t^d - i_t^f

Strong Form: i_t^d = i_t^f, E(ΔSt)

In the event, the interest rates of both the countries should positively cointegrate and depreciation in the expected spot rate should be a stationary series and the coefficient of i_t ^f should be 1 for UIP to hold in strong form.

Weak Form: i_t^d = δ i_t^f

In the event the interest rates of both the countries should positively cointegrate and depreciation in the expected spot rate should be a stationary series and the coefficient of i_t ^f should be δ for UIP to hold in weak form.

According to Mylonidis, N. and Sideris, D., E (ΔS_t) is the function of gap between the log of nominal exchange rate St and the log of equilibrium exchange rate S_t^eq with the proportion of constant θ which relates this gap to the expected change in the nominal exchange rate ^[20].

E (ΔS_t) = - θ (S_t - S_t^eq)

Thus, larger the deviation of nominal exchange rate from the hypothetical long run equilibrium exchange rate, the lower the expected exchange rate depreciation in the future periods to restore the equilibrium condition. Furthermore, due to the PPP relationship, equilibrium exchange rate is a function of domestic and foreign price levels.

S_t ^eq= P_t^d – P_t^f

H₅: Forward rate hypothesis: studies whether current forward exchange rate is a good predictor of future spot rate of exchange or not.

F_t= S_t+3

Since exchange rate determination is not affected by the actions of importers and exporters or investors alone but by both, therefore, Dornbusch suggested the following condition for nominal exchange rate determination ^[29].

H₆: Purchasing Power Parity and Uncovered Interest Parity –At times PPP and UIP are rejected when they are tested individually, but, when tested jointly they are found to be valid because exchange rate is affected by both goods and assets market, so the combined effect on the exchange rate is estimated as:

St = (P_t^d – P_t^f) – (1/ θ) (i_t^d– i_t^f).

This section of the study deals with the joint restrictions on both the cointegrating vectors under consideration. In order to put a restriction on weak form of parity in joint modeling framework, it is important that the particular parity in concern should be valid at least in weak form under single cointegration framework because the coefficient used under joint testing in weak form is the one that is derived from cointegration test run for individual parity conditions. The required coefficient in all the strong form of parities is 1.

From hypothesis H₇ - H₁₀ (Table 1), first of all, Strong form of one parity is cointegrated with strong form of another parity, if there is cointegration found between both the parities then it is suggested that the parities are valid in strong form, but if the results show no cointegration then strong form of one parity and weak form (if the parity is valid in weak form when tested individually) of another are cointegrated, if there exists cointegration between the two parities then the results confirm validity of one parity in strong form and other parity in weak form, but again if the results show no cointegration then weak form of both the parities are tested together for their validity check.

Table 1. Parity Equations

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4. Unit Root Test

Testing whether in an autoregressive statistical model of a time series, the autoregressive parameter is one or not using the results of the two tests i.e., Augmented Dicky fuller test (Table 2) and Phillips Perron Test (Table 3).

Consumer price index of India is found to be a non stationary series as inflation rose tremendously because food prices were stoked by drought and also the reason that it imports crude oil whose prices were on a continuous rise along with the increase of indirect taxes; index numbers of industrial production also improved, indicating rise in employment numbers which led to demand exceeding supply, thereby causing rise in inflation. CPI in China was very much in control but took to the fuelling path post 2008, allowing it to be tagged as a non stationary variable owing to China’s current account surplus; China had to print its currency to sell to the foreigners to buy Chinese products. Inflation in Europe rose spectacularly and at a much faster rate than in India till 2009 because of rising production costs and a firm foothold in the international arena, but when the sovereign debt crisis unfolded in Euro zone in 2010, the European government cut spending and raised taxes to heal their finances which weakened the economy, caused businesses to curb investment and lay off more staff, and thus, reported a drop in the inflation numbers. CPI numbers in USA were not as high as in India and Europe but the figures did rise making the data non stationary, inflation rose in USA also because of rising energy prices that is imported and due to adjusting monetary policy put in place to achieve employment targets.

91 day Treasury rates in India also contained Unit root because interest rates have been continuously adjusted to tame the rising inflation levels. Treasury rates in China are found to be stationary on account of contained inflationary pressures for most part of the decade. Treasury rates in Germany also contain unit root because till 2004 the interest rates were deliberately kept low in order to provide boost to the business activities, but after that interest rates rose on account of increasing inflation, and in 2009, rates saw a fall in its figures due to recessionary pressures. Treasury rates are found to be unsteady in USA also for the decade considering two major events like WTC attack and subprime crisis.

Table 2. ADF Test

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Rupee spot rates with respect to all the 3 currencies i.e. Dollar, Yuan and Euro are found to be non stationary owing to increasing economic and financial relationship of India with its major trading partners. Rupee forward rates with respect to Dollar, Yuan and Euro are also non stationary because of increased usage of these derivative instruments to hedge against the risk of currency fluctuations rendering unsteadiness to its nature.

Table 3. Phillips Perron test

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5. Restrictions on Individual Vectors

Testing the validity of all the parities to establish relationship between interest rates, spot exchange rates, 3 month forward exchange rates and inflation rates; and thus, understanding the relationship of India with its major trading partners (Table 4).

Table 4. Single Cointegration Framework

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H₁: Purchasing Power Parity (PPP)

There exists an inverse relationship between the spot INR/CNY rate and inflation differential of India-China indicating violation of RPPP because it is observed that sometimes increased inflation in China resulted in appreciation of Yuan and a fall in the CPI numbers led to plunged Yuan value against Dollar. The primary reason that catalyzed this inverse relationship is that china deliberately held down Yuan’s exchange rate to keep its exports cheap and fuel growth, but the rising inflation had customers fuming in the country leaving Chinese leaders with little choice but to allow the Yuan to appreciate at a faster pace against dollar.

For India-Europe, there is an inverse cointegration between spot INR/EUR rate and inflation differential i.e. the value of Rupee depreciated with the corresponding increase in the inflation numbers in Europe, thus, violating PPP. The possible reasons can be attributed to impressive growth of EU-India trade which doubled from €28.6 billion in 2003 to over €55 billion in 2007 and India gets its maximum imports from EU which caused weakening of Rupee. In 2012, India’s exports to EU registered an increase of 97.66% since 2005, amounting to €37.3 billion. EU exports to India have also increased by almost 83% amounting to €39.30 billion during the same period. Though the export growth figures were better in India but still imports in India from Europe were more than its exports to Europe, which put a downward pressure on the value of Rupees.

Relationship between Spot INR/USD rate and inflation differential of USA and India is found to be inverse, alluding that with the increase in inflation in India its currency appreciated, thereby violating RPPP for the given period. The reason is India’s exceeding export numbers to its import numbers from USA (in 2010, India’s exports to US reached $24.5 billion and US exports to India accounted for $21.4 billion). It was in August 2011 that the crisis took its toll on INR, with the flight of foreign funds to safer haven currencies and better investment opportunities, the INR had no other choice but to fall. But for the larger part of the study period, rupee was comfortably trading strongly against dollar, and thus resulted in an inverse relationship. After studying the effect of prices on exchange rate, understanding the impact of prices on interest rates also becomes prominent to completely study the exchange rate relationships, and thus comes into picture the testing of Fisher effect.

H₂: Fisher Effect

Cointegration results suggest validity of Weak Fisher effect in Rupee/Yuan case in the given period for real interest rates are not equal in India and China, thus violating the condition which is necessary for the absolute fisher effect condition to hold. Nominal interest rates are affected by factors other than inflation such as supply of and demand for money in the economy, monetary policy, and different economic conditions. During the period of 2001-2008, India set a firm foothold in the International market and constantly grew which resulted in increase in demand for capital to flourish and expand businesses, and thus led to higher interest rates. The falling interest rates in China during this period (deliberately kept to low to encourage businesses) also contributed to the higher interest rate differential. Payne and Ewing evaluated the Fisher effect for nine developing countries wherein, India was one of the countries and there was no evidence of Fisher effect for India ^[30].

As with Rupee/Euro again, Fisher effect stands valid in a very weak form for the study period. Indian economy has grown manifolds since 2001 and when the economic growth of India picked up momentum then the demand for Rupees went up putting upward pressure on interest rates. Towards the end of the decade, part of Europe was engulfed in sovereign debt crisis, there was a lot of uncertainty around and its effect could also be felt in India; the lenders cut down on their lending or demanded higher interest rates from individuals or companies as compensation for the higher default risks that arose at the time of uncertainties, or did both.

Cointegration results violate the Fisher effect condition in India-USA in view of the fact that India was booming in this stage wherein business activities in the country were growing tremendously, consumption was rising and so was the standard of living, giving way to the rising stock market indices which touched an all time high in 2006. But, the entire decade was the worst for U.S economy, a sharp reversal from a long period of prosperity that led economists and policymakers to fundamentally rethink the foundation of the USA’s growth. The decade began with the world trade centre attack and, in 2007 USA was hit hard by subprime crisis.

Thus, inflation does impact interest rates in China and EU. Therefore, when impact of interest rates is checked on exchange rates; inflation has a part to play. Now further the study discusses impact of interest rates on exchange rates.

H₃: Covered Interest Parity (CIP)

For India - China, CIP stood valid in its weakest form. Jayanth R. Varma conducted a study regarding the validity of CIP and concluded that CIP is violated on account of structural barriers and institutional factors. Another possible reason for the failure of strong CIP is that due to India’s constant attempt to tame rising inflation, its interest rates went through constant turbulence, thereby creating speculative opportunities for profitable arbitrage ^[31].

CIP is rejected in India-Europe. Though European economy has been an open economy encouraging globalization and although it is far from the closed market that it was twenty years ago, India still places restriction on goods and capital flows that hinder trade with the EU. The other reason for failure of CIP is that exchange rate is not only affected by interest rate differential but also by inflation differential; as a general rule, a country with a consistently lower inflation rate exhibits a rising currency value as its purchasing power increases relative to other currencies. Favorable terms of Trade for Europe over the years (exports > imports) also affected exchange rate determination, resulting in increased demand for Euro (an increase in the currency's value). CIP would have existed had the cost of converting forward Rupee rate to forward Euro rate eradicated all the profit from the transaction.

For India-USA, CIP is again rejected, reflecting no financial integration between the two countries. With the higher interest rates in India compared to USA, Rupee appreciated in the long run. Investors from USA when invested in India, the demand for rupee increased and rupee appreciated in response, thus indicating that forward exchange rates did not incorporate the difference in interest rates for the two countries and arbitrage opportunity existed due to favorable commodity and capital flows for India. On the contrary, Vipul Bhatt and Arvind Virmani carried out a research – Global integration of India’s money market: interest rate parity in India, wherein, they argued that the short-term (up to 3 month) money markets in India are getting progressively integrated with those in the USA even though the degree of integration is far from perfect ^[32].

A deviation from CIP is Uncovered Interest Rate Parity (UIP), wherein the transaction is uncovered because the investor does not sell the currency forward, thus, remaining uncovered to any risk of the currency deviation.

H₄: Uncovered Interest Parity (UIP)

UIP fails to hold in all the three cases because neither the interest rates of India cointegrated with that of China, Europe and USA nor was Δs_t ^eq a stationary series. UIP is violated on account of no relationship between the interest rates of two countries. The basic assumptions of UIP (like no transaction costs, no taxes and no capital controls) do not hold in the practical world, so the transaction expenses, taxes levied on the profits, and imperfect capital mobility gave away the opportunity to the arbitragers to earn profit. The other reason considered for the failure of UIP is that European securities, Chinese securities, and USA securities are not perfect substitutes of Indian securities, and if there are any, it is impossible for investors to have perfect knowledge about it.

Vipul Bhatt and Arvind Virmani conducted a study - Global integration of India’s money market: interest rate parity in India and found results similar to this research concluding failure of UIP ^[32]. Studying interest rates, inflation and exchange rate relationship does not suffice the purpose. Forward rate hypothesis also forms an integral part of international parity conditions as it spells out whether foreign exchange markets are efficient or not.

H₅: Forward Rate Hypothesis

A positive cointegrating relationship is found to be existent between the forward INR/CNY rate and future spot INR/CNY rate with the coefficient -1.000164, signifying that the forward INR/CNY rate is perfectly able to predict spot INR/CNY rate. The reason for validity of FRH can be attributed to the fact that China’s currency had been pegged strongly against US dollar over the years. A positive cointegrating relationship holds between the forward INR/EUR rate and spot INR/EUR rate with the coefficient -1.000384, implying that the forward INR/EUR rate is able to predict the future spot INR/EUR rate in proportion of -1.000384 which is close to 1, and therefore, strong form of unbiased forward hypothesis is valid. In India - USA, again a significant cointegrating relationship is found between the forward exchange rate and future spot exchange rate with the coefficient as -0.99960 indicating - with 1 unit increase in forward INR/USD rate, the spot INR/USD rate value depreciates by 0.99960 times which is close to 1. Thus, Forward rates are an unbiased predictor of the future spot exchange rate.

Therefore it can be said that forward rates fully reflect available information about the exchange rate expectations because the news about economic factors such as changes in domestic and foreign quantities of money, real incomes, and real interest rates is available 3 months prior when the forward rate is first determined. In contrast, a research conducted by Rohit Vishal Kumar and Soumya Mukherjee with respect to the validity of FRH in context of INR/USD found that Forward rate hypothesis was valid in weak form ^[33].

Two parities can be tested in single cointegration framework by specifying individual restriction on the dependent parity, therefore; the next hypothesis uses two parities and restriction on one cointegrating vector. The parities have been tested jointly in single cointegration model.

H₆: PPP & UIP

In all the three cases, PPP fails to hold jointly but UIP holds in weak form. When PPP and UIP were tested alone, both the parity conditions failed to hold for all the three trading partners, but when both the conditions are tested jointly, UIP is found to be valid, thus exhibiting that UIP is not by itself a stationary series but when combined with a linear combination of prices. Thus, the long term interaction between goods and assets market should not be ignored.

6. Joint Restrictions on both the Cointegrating Vectors

The joint modeling of the conditions allows for possible interaction in the determination of price, interest rates, and exchange rates in the commodity and capital markets (Table 5). The joint modeling of international parity condition sheds further light on each individual parity condition, thereby increasing the probability of establishing well- defined results.

H₇: PPP & CIP

For Rupee/Yuan, when PPP and CIP were tested individually, it was found that PPP failed to hold and CIP stood valid in weak form. The parities in their strong forms in joint modeling framework also pressed no cointegration button, but there exists a cointegrating relationship when strong form of PPP and Weak CIP are tested. The reason for the joint validity in the strong form is that exchange rate is affected by both trade and financial relationship existent between the two countries.

Table 5. Joint Modeling Framework

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Cointegration violates the validity of SPPP and SCIP under joint modeling framework for India – Europe. These conditions have not been tested in weak forms because when PPP and CIP were tested individually, both PPP and CIP failed to hold. This means that the cost of hedging exchange risk did not eliminate the higher returns that accrued from investing in rupee which offered higher interest rate due to high inflation.

No cointegration exists between the two parities for India – US suggesting rejection of both the parities in strong form. These parities have not been tested in weak form in joint modeling framework because they were rejected in individual form also. When higher inflation differential causes rupee to appreciate against dollar then PPP is violated. India has a lot of untapped potential and USA has been increasingly utilizing that potential to the best of its benefit by investing in Indian stocks and infrastructure; this created demand for rupee and ultimately appreciated Indian currency despite high inflation for most part of the study period. CIP fails on theoretical grounds as arbitrage opportunity existed for traders because forward rates are also found to be appreciating on account of increasing economic growth irrespective of higher interest rates in India.

H₈: PPP & Fisher Effect

For India-China, when PPP and fisher effect were tested individually, the results revealed validity of fisher effect in weak form and rejection of PPP, but when tested jointly in their strong forms, the result shows that both the parities are evident; this is because inflation rates and interest rates are the two very important factors that affect exchange rates. Thus, it is argued here that when difference in interest rates is brought about only by the changes in inflation rates then depreciation of rupee is equal to the rising inflation rate differential between the two countries.

For India – Europe, the two parity conditions are violated in the strong form under joint testing but stand valid when SPPP and Weak fisher effect are tested. This means that factors like Psychological barriers, legal constraints, transaction costs, taxes, political risk, and currency risk prevent capital from freely flowing across borders to take advantage of real interest differential. PPP failed to hold individually but holds under joint testing structure because exchange rate is affected by inflation rate when it interacts with other macro-economic variables.

When Purchasing power parity and fisher effect were tested individually, they both were rejected in India with respect to USA, therefore joint testing of both the parities is carried out and the result indicates violation of both the parities under the joint framework also. These parities cannot be tested in weak form under joint modeling framework because they were rejected under the single cointegrating framework on theoretical grounds. PPP failed because despite increased inflation, INR/USD rate appreciated, and strong form of fisher effect is also violated as increase in inflation differential caused interest rate differential to fall.

H₉: PPP & Forward Rate Hypothesis

Strong purchasing power parity and forward rate hypothesis are jointly valid in all the three cases. 3 months forward rate is an unbiased predictor of the spot exchange rate when rise in inflation differential causes spot exchange rate to depreciate as much as increase in the inflation differential, and vice versa. When traders know that the depreciation in currency would be equal to rise in inflation differential then forward rates would absorb all that expectation and would be able to accurately predict spot exchange rate.

H₁₀: CIP and Fisher Effect

When CIP and fisher effect were tested individually in India with respect to China, they both were evident in weak form, therefore their strong forms are tested jointly, and there is no cointegration between the two parities reflecting violation of their strong forms, but cointegration results suggest validity of Weak form of CIP and strong form of fisher effect. This means that when rise in inflation rate differential is equal to the rise in interest rate differential then the interest rate differential causes 3 months forward exchange rate to depreciate not exactly equal to the rise in inflation differential but in some proportion of that. The reason behind the failure of strong CIP is that forward rates had been fixed for spot Yuan rate which was pegged to Dollar, and whatever fluctuations took place, they were due to changes in Indo-US relationship and therefore interest rates did not play a big role in bringing about a change in forward rates.

But for India – Europe and India-USA, both the parities are found to have cointegration suggesting their validity in strong form. When inflation is contained in the interest rates, the investors avoid investing in that particular currency because inflation erodes all the earnings of the corporate, and thus, higher interest rates are offset by depreciating currency and covered interest arbitrage is eradicated when interest rate differential is equal to the inflation differential.

7. Conclusion

The present study re-examined the validity of the five key parity relations (PPP, UIP, CIP, and Fisher Effect and Forward rate hypothesis) of India with China, Europe and USA. The study argued that testing the aforementioned conditions in a Joint testing approach is appropriate because it allows for dynamic interactions in the determination of prices, interest rates and exchange rates. The results reveal affirmative evidence in favor of India-China and India- Europe suggesting that inflation, interest rates, forward rates together affect the determination of Rupee-Yuan and Rupee-Euro exchange rates. In Rupee - Dollar case, interaction among the variables fails to validate the parities because the economic growth in the last decade wasn’t so impressive for the US economy. It proves to be one of the worst economic periods for the country.

The analysis affirms that higher returns of the Chinese traders from Indian securities were partially eliminated by the cost of hedging exchange risks given the percentage rise in inflation was equal to the percentage rise in Rupees (depreciation), but for US and European investors, covered arbitrage was eradicated only when interest rate differential was equal to inflation differential. Forward exchange rates proved to be a great tool to identify the spot exchange rate direction. Companies that imported goods from china felt pressure on their margins as magnificent rise in imports (Yuan deliberately kept weak to make its exports cheaper) from china depreciated rupee. The evidence also suggests that Indian firms/companies that export to Europe struggled when higher interest rates were accompanied by higher inflation in India (Joint validity of Strong Fisher Effect and SCIP) because higher interest rates got adjusted in forward Rupee/Euro rates, and depreciated forward rates indicated depreciation in spot rates, which led to increased capital and labor costs. This forced exporters to price the products higher (Joint validity of PPP and Forward rate hypothesis) and made the exports expensive, and thus, affected the export volumes unfavorably in 2012-2013. The Euro zone sovereign debt crisis increased uncertainty prevailing in the financial markets in late 2010, but INR depreciation was only felt in August 2011. Given the falling growth of GDP in India, high inflation, policy paralysis exhibited by the central government, the investors started pulling their money out of Indian economy and invested in safe haven. However, Indian companies attracted importers from USA as a consequence of miserable US economic conditions, implying that India enjoys trade surplus with USA.

The paper also provides further scope to study - the variables of which country are acting as the driving forces for the system and are casting the shadow of barriers on Indian currency. Not much empirical work is available on the main structural models of exchange rate determination with respect to India and the present study confirms that the parity conditions are key relationships that can be used to predict movements of Rupee-Yuan and Rupee-Euro rates. The findings present picture of India’s unprecedented economic expansion in the entire decade because the eastern economies became the producers and the western economies became the consumers, but, with US banking crisis followed by Euro zone crisis, India witnessed a clear fall in foreign inflows, growth numbers and Rupee value. Despite these recessionary pressures, the fundamentals of the Indian economy are very strong no matter how difficult things were post 2011 because India outperformed US stock market and other major stock indices around the world and sustained weak economic conditions during global economic meltdown. Taking a slightly longer view, the Indian economy has been doing pretty well from 1994, very well from 2003, and especially so from 2005 and with the improvement in governance and infrastructure in India, the economy presents a bright future outlook.

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