PURCHASING POWER PARITY BASED ON CAPITAL ACCOUNT, EXCHANGE RATE VOLATILITY AND COINTEGRATION: EVIDENCE FROM SOME DEVELOPING COUNTRIES
AHMED, Mudabber
*Abstract
One of the most important and recurrent concept in international macroeconomics is Purchasing Power Parity (PPP) hypothesis. PPP has been used as a theory of domestic price determination under fixed exchange rate regime and a theory of exchange rate determination under flexible exchange rate regime. The main purpose of this study is to examine how well the PPP theory fit to the developing countries. The purpose is accomplished through conducting a battery of tests – non-regression based, regression based and co-integration based. An important feature of the study is that test of PPP which relies on capital account is also carried out. In general our findings do not support the PPP theory. PPP is not supported even if we rely on capital account in derivation of PPP.
Only the relative version of PPP as a theory of price determination in Pakistan does have some empirical support. The paper also discusses potential reasons for empirical failure of PPP in developing countries.
JEL classifications: F30; F31; F40
Keywords: Purchasing Power Parity; Uncovered Interest Rate Parity;
Real Exchange Rate; Random Walk Process; Unit Root Test.
1. Introduction
One of the most important and recurrent concept in international macroeconomics is Purchasing Power Parity (PPP) hypothesis. It has
* Mudabber, Ahmed, Associate Professor, Department of Economics, University of Chittagong, Chittagong - 4331, Bangladesh. Email:
been used as a theory of domestic price determination under fixed exchange rate regime and a theory of exchange rate determination under flexible exchange rate regime. According to PPP theory same basket of goods should sell for the same price in different countries when measured in a common currency. The PPP theory can be exemplified by presenting two versions, namely, absolute and relative versions. International macroeconomists employ this concept one way or the other and this study is devoted to a comprehensive examination of it1.
Literature on testing validity of PPP in developed countries has grown immensely over the last two decades. But literature on testing relevance of PPP in developing countries is still in its early stages.
Previous literature on developing economies mainly tested PPP by employing F-tests and no attempts were made to analyze the possible causes for their findings2. Moreover, in the previous studies different PPP versions relied for their derivations on items which appear on the current account of the balance of payments. This paper extends the previous efforts at least in three important ways: First, a simple but useful non-regression based approach to test relevance of PPP is carried out. Second, this study relies for PPP derivations on items which appear not only in the current account but also in the capital account. Third, a simple procedure for testing cointegration with a known cointegrating vector (not blindly estimating a cointegrating vector) is applied.
Three major South Asian Association for Regional Co-operation (SAARC) countries viz. Bangladesh, India, and Pakistan are selected as cases for this study. They share many common features with other developing countries. All these economies have gone through either fixed exchange rate regime or managed floating regime. All the three countries, at various times during 1980s and 90s, have adopted IMF structural adjustment policies. The experience of these countries is
1 To know about the origin of PPP see Cassel (1928), Myhram (1976), Frenkel (1978), Officer (1982).
2 See Genberg (1978), and Qureshi (1992/93) for example.
sufficient, we believe, to make meaningful conclusions regarding the relevance of the PPP hypothesis in developing economies.
The rest of the paper is organized as follows: Section 2 outlines the model and methodology. Section 3 gives a brief discussion about the data set used in the present paper. Section 4 discusses the empirical findings. Section 5 concludes.
2. Mode l and methodology
This study employs both regression and non-regression based (exchange rate volatility ) tests to examine the validity of PPP theory.
Suppose P, P* and S be the home price, foreign price and nominal exchange rate respectively. According to PPP theory we can write
Pt = St Pt* (1)
If the exchange rate is fixed and home country is small compared to foreign country then foreign price will determine the home price.
But if the exchange rate is flexible we can write (1) alternatively as
St = Pt / Pt* (2)
The above two equations represent PPP theory in absolute versions as they deal with absolute price levels. However, we derive the relative version of (1) in the following way3:
Taking natural log in both sides of (1)
lnPt = lnSt + lnPt* (3) and lnPt-1 = lnSt-1 + lnPt-1* (4)
Subtracting (4) from (3), we have
∆pt = ∆st + ∆pt* (5) where ∆ is the first difference operator and pt = lnPt, st = lnSt, and p*t = lnP*t . Similarly relative version of (2) is
3 See Genberg (1978) and Hallwood and MacDonald (1994).
∆st = ∆pt - ∆pt* (6) Stochastic representation of equation (3) and (5) are the following:
pt = α + ßpt* + ut (7)
∆pt = a + b∆pt* + ut (8) if PPP theory holds, ß and b should be equal to unity. In the equations (7) and (8), α+ ut or a + ut amounts to st or ∆st where ut is a white noise process.
Stochastic representation of equation (2) and (6) are the following:
st = α + ßpt + ß*pt* + ut (9)
∆st = a + b∆pt + b*∆pt* + ut (10) If PPP holds it is expected that ß = b =1 and ß* = b* = -1 and the constants are equal to zero. An F test is appropriate to test the above mentioned hypothesis.
The above derivations of PPP rely on current account items only, and this is how the approach has been motivated by most of the earlier studies. But recently researchers opine that PPP may be thought of in terms of certain parity conditions that relate to the capital account4. Applying the uncovered interest parity condition we have
∆set+1 = it – it* (11) where ∆set+1 expected proportionate change in exchange rate to prevail in period t+1, it and i*t are home nominal interest rate and foreign nominal interest rate respectively. We know real interest rate is nominal interest rate less expected inflation rate
rt = it - ∆pet+1 (12)
rt* = it* - ∆pe*t+1 (13)
4 See Hallwood and MacDonald (1994, pp.119-20) for details about this methodology.
where r is real interest rate and ∆pet+1 expected inflation rate to prevail in period t+1. Substituting (12) and (13) in (11) and rearranging
∆set+1 = (r–r*) + (∆pet+1–∆pe*t+1) (14) By assuming that real interest rates are equalized across countries we get
∆set+1 = ∆pet+1 – ∆pe*t+1 (15) equation (15) is slightly modified version of relative PPP. The variables are now expected rather than actual. But expected values are not observable. However, we can employ rational expectations theory to overcome the problem. Actual change in exchange rate and change in price levels can be written as expected value plus a surprise, which is truly random and unpredictable.
∆st+1 = ∆set+1 + εt+1 (16)
∆pt+1 = ∆pet+1 + ζt+1 (17)
∆p*t+1 = ∆p*et+1 + ζ*t+1 (18) substituting (16) (17) and (18) in (15) and rearranging
∆st+1 - ∆pt+1 + ∆p*t+1 = εt+1 - ζt+1 + ζ*t+1 = ηt+1 (19)
∆qt+1 = ηt+1 (20)
qt+1 - qt = ηt+1 (21)
where qt = st - pt + p*t . Equation (21) says that q follows a random walk. The equation can be estimated in the following form:
qt = α + βqt-1 + ηt (22)
where ηt is a white noise process. Our null hypothesis is α= 0 and ß =1 and rejection of this implies PPP hold if we rely on capital
account.
Non-regression based evidence can be checked by focusing on visual evidence: how closely the nominal and real exchange rate move together i.e. by looking the exchange rate volatility. The real exchange rate is defined as
Q = SP* / P (23)
Rearranging we get
S = QP / P* (24)
If PPP holds, it is expected that Q = 1 (or a constant) i.e., movement of nominal exchange rate should not influence real exchange rate in the same direction. If price ratio P*/P increases then S must fall to keep Q constant. But If S rises along with rise in P*/P then Q rises and PPP does not hold.
3. Data
The data used in this study are taken from the IMF, International Financial Statistics (IFS). Quarterly observations comprising the period 1975:Q1-2003:Q4 for India and Pakistan, and 1976:Q2- 2003:Q4 for Bangladesh are used to estimate the models. The US data is taken as foreign variables. Exchange rate is defined as the domestic currency price of one unit of foreign exchange (i.e. US dollar). The study uses a similar data set, sample period, and framework for all countries, as far as it is allowed by the availability of data.
4. Empirical Evidence
We start our empirical analysis with non-regression based evidence. In figures 1-3, the relationship between real and nominal exchange rates is shown. In figure 1, real and nominal exchange rates move closely together in case of India (a correlation coefficient of 0.97). Thus the nominal appreciation or depreciation is seen to be a real appreciation or depreciation. In case of Pakistan, we can divide the sample period 1975:1 to 2003:4 into two sub-periods: from 1975:1 to 1981:4 when the exchange rate was fixed, from 1982:1 to 2003:4 when exchange rate was flexible.
We see no correlation between real and nominal exchange rates during the fixed exchanged rate regime. But during the flexible exchange rate regime they move together (a correlation coefficient of 0.94). In case of Bangladesh the relationship is rather weak (a correlation coefficient of 0.78) but they move more or less in the same direction.
Figure 1: Indian rupee and US dollar: Movement of real (Q) and nominal (S) exchange rates
1 9 7 5 1 9 7 8 1 9 8 1 1 9 8 4 1 9 8 7 1 9 9 0 1 9 9 3 1 9 9 6 1 9 9 9 2 0 0 2
2 . 0 0 2 . 2 5 2 . 5 0 2 . 7 5 3 . 0 0 3 . 2 5 3 . 5 0 3 . 7 5 4 . 0 0
Q S
Figure 2: Pakistani rupee and US dollar: Movement of real (Q) and nominal (S) exchange rates
1 9 7 5 1 9 7 8 1 9 8 1 1 9 8 4 1 9 8 7 1 9 9 0 1 9 9 3 1 9 9 6 1 9 9 9 2 0 0 2
2 . 2 5 2 . 5 0 2 . 7 5 3 . 0 0 3 . 2 5 3 . 5 0 3 . 7 5 4 . 0 0
4 . 2 5 Q
S
Figure 3: Bangladeshi taka and US dollar: Movement of real (Q) and nominal (S) exchange rates
1 9 7 6 1 9 7 9 1 9 8 2 1 9 8 5 1 9 8 8 1 9 9 1 1 9 9 4 1 9 9 7 2 0 0 0 2 0 0 3
2 . 0 0 2 . 2 5 2 . 5 0 2 . 7 5 3 . 0 0 3 . 2 5 3 . 5 0 3 . 7 5 4 . 0 0
4 . 2 5 Q
S
Our broad conclusion from this evidence would be that law of one price does not hold in a floating or managed floating regimes and we can identify two potential reasons behind it: First, over the period demand in Bangladesh, India and Pakistan shifted away from domestic traded goods to foreign traded goods. This created excess demand for foreign goods and excess supply of domestic traded goods. So P*/P increased but it was not offset by nominal exchange rate appreciation.
Second, we can exploit the thesis of Balassa-Samuelson to provide an explanation of the empirical failure of PPP in developing countries. Balassa (1964) observed that productivity is higher in the traded goods sector of developed country (taking the USA as DC) compared with developing countries (India, Bangladesh and Pakistan) but productivity is similar in the non-traded goods sector.
A weighted average basket of traded and non-traded goods will be cheaper in low wage country – in the developing country. Given that nominal exchange rate is determined by relative prices of traded and non traded goods, there will be a divergence between nominal and real exchange rates. An implication of the divergence between nominal and real exchange rates is that a given amount of dollar converted into rupee or taka at the nominal exchange rate will buy a larger basket of commodities in Bangladesh, India or Pakistan than in the USA. This is inconsistent with PPP.
Let us now move to regression based evidence. A careful examination of data on exchange rate shows that Pakistan operated under strictly fixed rate regime from 1975: Q1 to 1981:Q4 and therefore equations (7) and (8) was estimated for that period.
Equations (9), (10) and (22) was estimated for the period 1982:Q1 to 2003:Q4. Only relative version of PPP under fixed exchange rate regime is supported by data (See table 2)5. Neither absolute version nor relative version of PPP is supported by India and Bangladesh data (see table 1 and 3). Estimated results of equation (22) reveals that PPP is not supported even if we rely on capital account in
5 These findings do not corroborate the findings of Qureshi (1992/93).
derivation of PPP. Real exchange rate follows a random walk process in all the three countries.
Table 1: Regression based test of PPP in India
Equation Constant Estimated coefficient of F- statistic
(P- Value) p* ∆p* p ∆p qt-1
(9) 1.095 -0.887 - 1.397 - - 46220.97 (0.000) (10) 0.0217 - -0.720 - 0.141 - 15.079 (0.000)
(22) 0.0183 - - - - 0.996 2.142 (0.122)
Table 2: Regression based test of PPP in Pakistan
Equation Constant Estimated coefficient of F- statistic
(P- Value)
p* ∆p* p ∆p qt-1
(7) -1.511 1.243 - - - - 1172.53 (0.000)
(8) 0.0180 - 0.640 - - - 1.855 (0.172)
(9) -2.286 0.457 - 0.817 - - 67492.29 (0.000) (10) 0.030 - -0.055 - -0.340 - 11.571 (0.000) (22) -0.0367 - - - 1.013 2.420 2.420 (0.1101)
Table 3: Regression based test of PPP in Bangladesh Equation Constant Estimated coefficient of F-
statistic (P- Value)
p* ∆p* p ∆p qt-1
(9) -0.541 0.556 - 0.378 - - 52208.35 (0.000) (10) 0.012 - -0.055 - 0.123 - 27.522 (0.000)
(22) 0.039 - - - - 0.995 1.477 (0.1507)
Finally we move to co-integration based test of PPP following Hamilton (1994). Most of the cointegration testing procedures are based upon a two step procedure of estimating a cointegrating vector and then check whether the residuals are stationary6. In order for a set of variables to be cointegrated, they must have the same order of integration, i.e., the variables should have a unit root. In general any
6 Adler and Lehman (1983), Abuaf and Jorion (1990), Patel (1990) and Fraser et al. (1991) applied this procedure to test PPP.
linear combination of them should also have a unit root. But according to Engel and Granger (1987) there is a possibility that certain linear combinations of them might be stationary. In this study, we conduct a simple procedure for testing cointegration with a known cointegrating vector.
We test whether the PPP restriction (s - p + p*) is a cointegrating vector. The procedure is to run a battery of unit root tests. In table 4 variables p, p* and s are tested for a unit root with 8 extra lags and trend. All the three variables in all three countries pass the test for the presence of a unit root. Finally, the proposed PPP restriction is tested for the presence of a unit root. Again the proposed PPP restriction passes the test for the presence of a unit root. So no evidence of cointegration among p, p* and s is found.
Table 4: Cointegration based test of PPP in India, Pakistan and Bangladesh
Variables Estimated Test Statistic (Unit root tests) India Pakistan Bangladesh
p -2.905 -1.820 -2.070
p* -1.150 -1.150 -2.411
s -2.087 -2.689 -2.993
s – p + p* -1.270 0.267 -0.281
The critical value of the test statistic at 5% level is -3.45 and is taken from table 8.5.2 of Fuller (1976). Eight lags and trend is employed in the tests.
Several factors may be identified for failure of PPP: First, construction of an appropriate price index is an important factor. In Bangladesh, India and Pakistan most of the items included in CPI are domestically traded goods or non-traded goods. PPP version of exchange rate considers the price ratio of traded commodities only.
Second, some times expected future monetary development determine current exchange rate. In such case exchange rate moves ahead of price development – equation (9) and (10) will not hold.
Third, we should turn our attention on the underlying assumptions of the law of one price. Some of the underlying assumptions of law of one price such as homogeneous nature of traded goods, no barrier to
trade, no transactions cost, no movement of capital can be put into questions. For example, US trade with Bangladesh, India and Pakistan comprises of non-agricultural commodities and they are not homogeneous in nature.
5. Summary and Conclusion
The main purpose of this paper has been to examine the validity of Purchasing Power Parity theory in some developing countries. The purpose is accomplished through conducting a battery of tests – non- regression based, regression based and cointegration based. An important feature of the study is that test of PPP which relies on capital account is also carried out. In general our findings do not support the PPP theory. PPP is not supported even if we rely on capital account in derivation of PPP.
Only the relative version of PPP as a theory of price determination in Pakistan does have some empirical support. Choice of appropriate price index, change in demand structure, productivity change, monetary development, and structural and institutional impediments to competitive markets are some factors responsible for glaring failure of PPP in the developing countries.
This finding has a significant policy implication. The policy maker should be aware of the fact that PPP should not be employed as a theory of exchange rate determination. It should not be employed as a theory of price determination either in the developing countries.
Construction of a price index with appropriate weight on traded goods deserves attention in developing economies.
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