Co-Integration Tests and the Long-Run Purchasing Power Parity: A Case Study of India and Pakistan Currencies

This is a study of the application of the purchasing power parity propositions to the interesting cases of India & Pakistan through the Co-integration me-thod. The results of the Co-integrations of both the nations demonstrate that the exchange rates are more in tandem with price movements supporting PPP theorem. This is interesting given the near-and-far off relationship between India and Pakistan owing to historical and contemporary factors which does not hold an irrational exchange rate. It is good for the two important developing nations to expand their economic and trade relationship which is a win-win situation for both countries. The study also points to the need of the two countries, with extensive poverty still in spite of their nearly seven decades’ history of their development, to better manage their economies and currencies, the latter from fall and fall, which is dimming the international standing of their currencies. The study is a modest contribution to the literature on the Purchasing Power Parity theory with reference to the “special” cases of India and Pakistan.


Introduction
It is a matter of interest for both the learned and the way to know how foreign exchange rate determined, which, among others, determine, what one has to pay for imports and get from exports. It is an interesting matter to investigate in respect of any currencies.

India and Pakistan Economies
India and Pakistan are the two neighboring Asian nations, between which there is a great deal of economic similarity, the two forming one under the colonial British Rule, until the bifurcation of the country in 1947 into India and Pakistan and their exchange rate. This paper addresses the long run PPP of India and Pakistan currencies and their exchange rate. There is a need for a good deal of comparative studies of India and Pakistan economies, but such studies appear, to be few and far between. It is needless to say, that the "value" of currencies, is a good reflection of the relative strength of their economies and the purchasing power (pp) of their currencies determine their rate of exchange or foreign exchange rate, say, if two currencies, Rs&$, are of equal by or purchasing power (PPP), then the rate of exchange of the two currencies is Rs&$, Rs1= $1. Though this is a very simplistic explanation, it is being held all over.
As can be seen from the (Table 1), India and Pakistan both are lower middle income group (MIG) of countries with a Per Capita Income > $1000 and <$2000. The two are poverty ridden to the extent of over 20 per cent of the respective populations of 1.316 billion and 199.10 million. India is a $ 2597 billion economy and Pakistan is a $ 304.9 billion economy. Significantly, India has an edge in terms of all parameters except the ease of doing business, where it takes 34days while only 19 days in Pakistan. The two nations' PPP-PCI is $5630 for India and $5090 for Pakistan [1] [2]. Thus, Pakistan needs to improve its socio-economic parameters in relation to India. With its within 19 days business permissions, as against India's 34 days, Pakistan offers a better business environment than India. On the whole, the transformation of India and Pakistan economies, in the last so many years, has been from low income countries to lower middle income (LMI) ones. And, under the impact of globalization, in the 21 st century, the efforts on economic development and higher growth rate are found enhanced.

Economic-Growth, Exchange Rates and Foreign Trade
The attempts of both India and Pakistan is to attain higher per capita income  is that the ratio of exchange of currencies is on par with their purchasing power.
In the case of India and Pakistan, Pakistan Rupee is of lower purchasing power vis-à-vis Indian Rupee, response of higher rate of inflation and large trade-gap.
In Table 1, India-Pakistan respective rates of Inflation are 3% and 6% -7% and the trade gaps 2% -3% and 6.4% of GDP. Whether the long-term exchange and 3Ps ratios of the two nation converge. This is the problem under investigation in this modest but significant piece of study concerning two South Asian neighbors, economically distant. In terms of Table 2, India-Pakistan trade is interesting.
Both India and Pakistan have trade imbalances, the rate of imports growth exceeding that of exports, and trade growth is mainly driven by imports. India however is on a string growth. The result a falling foreign exchange rate of the two countries. However, in the adverse situation, the two countries appear reluctant to have any significance bilateral trade. Pakistan has no data on its exports to India. India has a surplus its Pakistan trade with (X-M) but their values are (M > $0.5 billion) and (Xs = $2 billion) maximum so far.

The PPP Theory and Literature
"The PPP theory says that the rate of exchange between two currencies is equal   [8]. There are studies empirically testing the 3P proposition of price and exchange rate equality (P = E) [9] [10] [11] [12], which on the whole hold the PPP's proposition.
where S is the nominal exchange rate measured in units of domestic currency per unit of foreign currency, P is the domestic price level and P * is the foreign price level. The relative PPP hypothesis, on the other hand, states that the exchange rate should be proportionate to the ratio of the price level and does not compare domestic and foreign levels of purchasing power, but rather focuses on changes in this purchasing power. Relative purchasing power parity theory, therefore, states that the inflation rate differentials between two countries are offset through inverse changes in the nominal exchange rate so that the purchasing power ratio between the two remains constant [13].
where k is a constant parameter, since information on national price levels normally is available in the form of price indices rather than absolute price levels, absolute PPP may be difficult to test empirically.
The PPP theory has been tested for several countries using various statistical

The Role of Country Characteristics on Purchasing Power Parity
The distinction is to investigate whether trade, inflation and geographical (distance) contribute towards the validity of purchasing power parity in terms of trade, inflation and geographical (distance), to have a bearing on the theory.
Therefore, also for countries with similar or resembling characteristics. India and Pakistan in this respect are a good case study of the problem. The study [10] examines the validity of Purchasing Power Parity and investigates the market  [20] found evidence to support long-run PPP for Asian economies. However, [21] found mixed evidence of PPP from thirteen Asia Pacific economies. On the other hand, the results of [22] [23] [24] [25], and [26] for the G-6 and OECD countries, [27] for the industrial countries, [28] [29] for the OECD countries, [10] for the OECD, [30] for the G-10 countries, and, [31] for 17 developed countries. On the other hand, some studies have also shown that the real exchange rate is non-stationary, as done by [32] for the OECD countries, [33] for 65 developing countries, and [34] for eight Pacific countries and 15 developed countries, and so on. It is found that India and Pakistan are an untested field for PPP investigation. They make an interesting case study for PPP testing. It is important for them to know whether PPP holds for them for meaningful economic and trade relations. Hence, this study undertaking.

Data and Methodology
The data collected from different sources mainly from World Bank group is of time series for economy, trade and price movements for the period (2004-2014) (Appendix) enough period for a relationship to examine the time series properties. The unit root test of ADF test is used to examine the stationarity of the data. The unit root tests were first implement on level, and then on first difference of the data. If the series are of first order, then we may proceed to test the existence of the long-run relationship among these variables using Johansen cointegration test. If the maximum Eigen statistic and trace statistic greater than 5% critical value, then we rejected the null hypothesis. By using Econometric Views-E p < , y is a (trend-) stationary series, thus, the hypothesis of (trend-) stationarity can be evaluated by testing whether the absolute value of p is strictly less than one.
The unit root tests generally test the null hypothesis 0 : 1 H p = against the one-sided alternative 1 : 1 The test of weak PPP consists in testing the existence of a cointegration relationship between the nominal exchange rate and the price ratio. Let, where k is a constant parameter Rewrite Equation (2) in log form where t e , p and * p are the exchange rate, the domestic price, and the foreign price respectively, t denoted for time subscript and c is constant, t ε is the error term, if t ε is a stationary process with zero mean then PPP holds in the long run. However, if t ε is non stationary implying that deviation from PPP are cumulative and not ultimately self-reversing, then PPP fails in the long run. Then, the test of cointegration between the nominal exchange rate and the national price levels by estimating the following regression: where e is the nominal exchange rate, P, P * the domestic price, and the foreign price respectively and c = constant, β 1 , β 2 = coefficient, ε t = error term. For strong PPP to be valid β 1 should be positive and equal to one, β 2 should be negative and equal to 1 in order for PPP to hold. For relative PPP, β 1 and β 2 do not need to be equal to 1.

Cointegration Test
After a careful compilation of data, cointegration procedure, developed by Joh- tive, a long-term relationship means that the balance variables move together in time, so that any short-term deviations from long-term trend will be corrected.
These series are said to be cointegrated and therefore, a common root stochastic trend. Johansen-Juselius, procedure again, in the n-variable first order given by VAR.
By subtracting 1 t X − from each side of the equation, equation (9) can be rewritten as: where 1 t X − and t ε are (n × 1) vectors; A is an (n × n) matrix of parameters; I is an (n × n) identity matrix; and π is defined as ( ) The rank of π equals to the number of cointegration vectors, also, the model in equation (10) can be generalized to allow for a higher-order autoregressive process, The most important function is still the grade as equal to the number of independent cointegration vectors. As we know that the rank of a matrix is equal to the number of its characteristics which are different from zero, so the number of individual cointegration vectors in this model may be determined by checking whether the significance of the characteristic roots π . The test for the number of cointegration vectors can be accomplished with the help of two like hood ratios (LR) test on the track of statistics and maximum eigenvalue statistics as shown below: Trace Test: Maximum eigenvalue test: where I λ the estimated eigenvalues and T is the number of valid observations, the null hypothesis of traces of statistical tests that the number of individual cointegration vector is smaller than or equal to r against a general alternative which gives the result of not more than rcointegrating vectors the last λ max statistical tests the null hypothesis that there is vector r cointegrating against the alternative of r + 1 cointegrating vectors. In general λ max statistics is more

Results and Discussion
The result of ADF test in Table 3 shows that the null hypothesis of unit root for both countries cannot be rejected at 1% significant level when all the variables are in the level but can be rejected when they are tested at first difference, which means all the variables are stationary at first difference. However, the null hypothesis of stationary cannot be rejected when all variables are tested in their first differences. Thus, we concluded that all the series are I (1) process. All the series are I(1) process; the cointegration test can be implement and proceeded to examine the long-run relationship among the variables. Table 4 reports the results for the Johansen cointegration test which showed that there exists a cointegrating relationship between exchange rate, and price levels for

Conclusions and Recommendation
India and Pakistan are strange cases of countries which are geographically near, but which hold them apart economically swing to the bitterness of partition and the mass exodus of people and sad memories, and still on-going territorial disputes and armed conflicts over them.
But the economies of the trade bind them together, which is amply proved by this model note of research. The Note opens a new era of good trade and economic relations, according to the Results hold a brighter economic prospect for the two countries.
The results of cointegration tests show that there exists a co-integrating relationship between exchange rate, domestic and foreign price levels, lending support to the validity of PPP. The findings of PPP, hold valid for Pakistan and India implies that the Pakistan economy is integrated with the economy of India.
The important policy implication is a good case for a cross-border agreement for trade and investment between the two countries. To promote trade benefit for the two economies, there is a need for removal of trade barriers, and promoting economic trade and socio-cultural and people relationship on "give-and-like" basis, and mutual trust and friendship.
The new and high and fair minded United Arab Emirates (UAE), wherein people of different faiths and nationalities fully feel at home and safe, is a model for India-Pakistan relationship [35].
With the goods and services markets appearing quite integrated liberalization of financial markets may take place. If we envision this process of integration continuing, then there will be the prospect of multi-dimensional cooperation between the two nations. Also, the study indicates the need of the two countries to better manage their economies and guard their currencies from continuous depreciation which is not good for their international image "Fair" economic co-operation rather than conflict is bound to raise the global standing of the economies of the two countries and make them look as somewhat equitable societies, same mass poverty. Not the least, PPP which has its roots in the medieval mercantilist school of trade, is still found valid, as the nations are interdependent. The overall lesson and prescription of the study is for the two-warring neighborhood is hold the price-line, look after your currency values, promote thrift investment and growth and overall prosperity and environmental well-being.

Conflicts of Interest
The authors declare no conflicts of interest regarding the publication of this paper. Pakistan External Trade-annual change, percent-Imports