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The first essay examines the econometric validity of Purchasing Power Parity in certain large developing economies using a panel unit root methodology.. By using these more powerful pane

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TWO ESSAYS IN INTERNATIONAL ECONOMICS:

AN EMPIRICAL APPROACH TO PURCHASING POWER PARITY AND THE MONETARY MODEL OF EXCHANGE RATE DETERMINATION

BY SHIDONG ZHANG

A dissertation submitted in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY

WASHINGTON STATE UNIVERSITY College of Business and Economics

AUGUST 2003

© Copyright by SHIDONG ZHANG, 2003

All Rights Reserved

UMI Number: 3110885

Copyright 2003 by Zhang, Shidong All rights reserved

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To the Faculty of Washington State University:

The members of the Committee appointed to examine the dissertation of

SHIDONG ZHANG find it satisfactory and recommend that it be accepted

ACKNOWLEDGMENT First, I would like to thank Dr Thomas Lowinger for his support and guidance

As the chairman of my dissertation committee, he guided me with his insightful

comments and suggestions Many ideas in this dissertation grew out of our discussions Without his help and encouragement, I could not have completed this dissertation

Second, I would like to thank Dr Susan He for all of her help She always offered constructive advice on the econometric model of this dissertation I also would like to

thank Dr Mahbub Morshed for his valuable comments

There are many other individuals without whose help and encouragement this

dissertation would not be possible Dr Robert Rosenman was particularly helpful during the early stages of my work Dr Emst Stromsdorfer assisted me in the writing of the dissertation His help is greatly appreciated

I also would like to thank the faculty and staff of the Department of Economics and wish them all the best I have had an excellent education experience in Washington State University for which I am grateful

Finally, I owe a debt of gratitude to my father, mother, my wife and her mother for all their love, support and encouragement

TWO ESSAYS IN INTERNATIONAL ECONOMICS:

AN EMPIRICAL APPROACH TO PURCHASING POWER PARITY AND

THE MONETARY MODEL OF EXCHANGE RATE DETERMINATION

Abstract

by Shidong Zhang, Ph.D

Washington State University

August 2003

Chair: Thomas Lowinger

This dissertation contains two essays Both essays address the econometric validity of certain exchange rate models

The first essay examines the econometric validity of Purchasing Power Parity in certain large developing economies using a panel unit root methodology As the

foundation of many international economic models, the Purchasing Power Parity has to

be empirically tested over long time periods Although increasing evidence shows that Purchasing Power Parity holds in developed countries, research on developing countries

is limited The goal of this essay is to find out whether the Purchasing Power Parity is

valid for some large developing countries One of the reasons that tend to invalidate the Purchasing Power Parity is that the test method often lacks power In the light of new

econometric methods, some more powerful tests have been developed and the panel unit root test is one of them By using these more powerful panel unit root tests, we conclude

that the Purchasing Power Parity holds in large developing economies even though their

direct economic relations are limited and the half-lives are shorter than in previous studies

The second essay investigates the validity of the monetary model of exchange rate

determination by applying multivariate time series methodology This essay uses

quarterly data for the following four countries namely Germany, Japan, the United States, and the United Kingdom for the 1973-1999 period It applies Johansen’s cointegretion method to test whether there exists a long run relationship between the exchange rate and

certain macro economic variables The test results strongly support the monetary model when the United States is excluded If the United States is included in the econometric tests, the support for the monetary model tends to be weaker One possible explanation is

that as a world currency, the U.S dollar’s domestic demand may differ from the world U.S dollar supply

TABLE OF CONTENTS

Pages ACKNOWLEDGEMENTS - - - Q0 HH HH HH HH khi cư nen iii

LIST OF FIGURES cccececeesecseceescneseseecnsenereeeseeseeeenseesereseceees x CHAPTER ONE

AN EMPIRICAL TEST OF PURCHASING POWER PARITY IN SELECTED

DEVELOPING COUNTRIES - A PANEL DATA APPROACH 1

1.2 REVIEW OF LITERATURE - - - -Q SH nv 10 1.3 METHOD OF ANALYSTS - -. QQ TQ HS min ven 18 1.3.1 THE AUGMENTED DICKY-FULLER TEST 19 1.3.2 THE PHILLIPS-PERRON TEST -.-.-<-<- 20 1.3.3 LEVIN AND LIN TEST - - - cQ HH vn se, 21 1.3.4 1M, PESARAN, AND SHIN TEST - -~<< << <2 26

1.5 TESTS AND RESULTS - - - - - - Ăn SH nh nh nỲ ng cuc 32 1.5.1 UNIVARIATE UNIT ROOT TEST RESULTS 32 1.5.2 LEVIN AND LIN TEST RESULTS - -<<s<5 33 1.5.3 IM, PERARAN, AND SHIN TEST RESULTS 37

TABLE OF CONTENT

Pages APPENDIX 1A TABLES -. Q TQ HH HH HH nY s vn 40 APPENDIX 1B MAJOR TRADE PARTNERS OF

SELECTED COUNTRIES - - - - - - - SH SH HH 46 APPENDIEX 1C FIGURES - Q TQ HS Ị HH HH vn 48

DETERMINATION 0 :cccecceceeececeeeeeeceeceeeececeeeceeeecen ens

2.3 REVIEW OF LITERATURE - - - - BS Sàn S11 se 65 2.4 COINTEGRATION METHODOLOGY - - S222 2< S << 71

2.6 EMPTRICAL RESULTS .- - - - SH SSnS Sa 78 2.6.1 UNIT ROOT TEST RESULTS - - - < + << << < << s2 78 2.6.2 COINTEGRATION TEST RESULTS - - - - 79 2.7 CONCLUSION - - QQ TQ HH HH HH nh nr ra S4 APPENDIX 2A TABLES Q ĐT HH HH HH cư cà 86 APPENDIX 2B FIGURES Q Q Q - Q ĐH HH H SH HH ng 94

LIST OF TABLES

1.1 Country Information

1.2 Exchange rate summary statIstics

ÓẮ

Ẻ 89 46266660400400008 0046060060 040090606600%e6e00601960606 900906166966 1.3 Consumer prices index summary stafISfICS - -. -c- cà 1.4 Real Exchange rate summary stafiStICS -.- ch và 1.5 Univariate Unit Root Test

1.6 Levin and Lin (LL) panel unit root =ÔÖÔÖÔÖ`Ö`.`.` S5B

L

1.7 Im, Pesaran, Shin (IPS) panel unit root test .-. -

2.1 The unit root test of US variables — ÚÔ.ỐỐ

2.2 The unit root test of first đifference of US variables

2.3 The unit root test of UK variables c2 sec se se 2.4 The unit root test of first điference of UK variables -

2.5 The unit root test of Japan variables .- -. -< << 2.6 The unit root test of first đifference of Japan variables

2.7 The unit root test of Germany variabÌes .- - - - << «<< «<< << << 2.8 The unit root test of first đifference of Germany variables

2.9 The choice the lag order 5¬ -“-“Öễ ˆ ẮÚ

2.10 Trace test result in Germany/US mođềel - - - << << << 2.11 Max-eigenvalue test result in Germany/US mođel -

2.12 Trace test result in Japan/US mođel - - - - - - + -< cà se sec 2.13 Max-eigenvalue test result in Japan/US modđel -

2.14 Trace test result in UK/US model SỐ .Ô.ÓÁÔ Ắ ỏ.ỏỀẺ.Š.Š.ỏÖ.`

40 4]

42

43

45

45

86

86

86

86

87

87

87

87

88

88

89

89

89 90

2.15 Max-eigenvalue test result in UK/US model - - - - - -

2.16 Trace test result in Germany/Umited Kingdom model -

2.17 Max-eigenvalue test result in Germany/United Kingdom model

2.18 Trace test result in Japan/Germany model ere eee eee eee eee ee eee Cee eee eee

2.19 Max-eigenvalue test result in Japan/Germany mođel

2.20 Trace test result in Japan/United Kingdom model

2.21 Trace test result in Japan/United Kingdom model

LIST OF FIGURES

1.1 Real exchange rate of Egypt -. . - SH nh nu nnn

1.2 Real exchange rate Of Ïndia - - - - - - - Ăn SH n1

1.3 Real exchange rate of MexICO - - Son Hs HH nen

1.4 Real exchange rate of NIB€T14 - - - - Q nọ HQ SH nỲ 1n HH ni

1.5 Real exchange rate of PakIstan - - - n1 ng

1.6 Real exchange rate of the PiÏippines -.-. -. QSSSsns*

1.7 Real exchange rate of the South A fca - - - HQ

1.8 Real exchange rate of the South Korea - - - - cv

1.9 Real exchange rate of Thailand - - - - - - << Sc nSSS n3 1x

1.10 Real exchange rate of Turkey - - - - cà sọ n n1 s2

2.1 Exchange rate of the United Kingdom - - 2-2 s2

2.2 Money supply of the United Kingdom -.-<-<-

2.3 GDP of the United Kingdom - 5S Ăn 2S 2n 1s 1 se

2.4 Interest rate of the United Kingdom -.-.- -. -<-<-

2.5 Inflation rate of the United Kingdom - co

2.6 Money supply of the United States cece ccc cecececeesceeeecsnceeneeeeees

2.7 GDP ofthe United States -QQQQ HH HH vn gà

2.10 Exchange rate of Japan

2.11 Money supply of Japan

2.12 GDP ofJapan

2.13 Interest rate of Japan

“““—.Ố

2.14 Inflation rate of Japan cece ccccneceeceeneneeenenenscecececeseneeaeeeeeaees

2.16 Money suppÌy of Germany - - -cQ cQn n HH HH gu na

2.17 GDP of Germany SG Ô

2.18 Interest rate of Germany -. Ăn cọ nọ nn nen sa

2.19 Inflation rate of Germany =““.-. ˆŠ Ô Ô Ô.Ô`

2.20 Variables trend—Germany/US model - . - << < <<

2.21 Variables trend—Japan/US model - - - - ~- << <<

2.22 Variables trend—UK/US model 3 — -ˆ

CHAPTER ONE

An Empirical Test of Purchasing Power Parity in Selected Developing

Countries - a Panel Data Approach This paper aims to test one of the most controversial theories in international

economics - Purchasing Power Parity (PPP) The Purchasing Power Parity theory in its

various versions relates the exchange rate between any two currencies to the relative price levels in the respective countries The implication is that a country with inflation

higher than that of her trading partners will tend to have a depreciating currency

Although at times (especially before the 1990’s) PPP has often failed to stand up to empirical tests and its theoretical content of exchange rate determination has been

questioned, PPP continued to be pervasive in macroeconomic models PPP is still implicit and also explicit in many models of exchange rate determination, and is also used as a

yardstick of the openness of an economy in macroeconomic models On the policy front, PPP-based benchmarks have been used to estimate exchange rates levels in a bid to

establish the need, the extent, and the direction of adjustment The pervasiveness of PPP

in economics has gone hand in hand with the literature on the empirical tests of the

theory Most of these tests have been done for developed countries and very few such

studies have been done for developing countries This paper tests the PPP theory for a panel of selected developing countries

at that time appears to be linked to the prohibition of usury by the Catholic Church By lending in a foreign currency, lenders could justify interest payments by reference to

movements in PPP’ The intellectual origins of PPP began in the early 1800s, with the writings of Wheatly and Ricardo The modern origin of purchasing power parity traces to

the debate on how to restore the world financial system after the gold standard collapse

during World War I In a series of influential articles, the Swedish economist Gustav

Cassel (1921,1922) promoted the use of PPP as a means of setting relative gold parities

Though purchasing power parity had been discussed previously by classical economists

such as John Stuart Mill, Viscount Goschen, Alfred Marshall, and Ludwig von Mises,

Cassel’s writings were the most influential and PPP calculations played an important role

in the debate over the after-war policies (Rogoff, 1996)

Today, various versions of PPP are used in a wide range of applications: from choosing the right initial exchange rate for a newly independent country, to forecasting

medium and long term real exchange rates, to trying to adjust for price differentials in international comparisons of income

The basic building block for any variation of the purchasing power parity is the so-called “ law of one price”(LOP), The law of one price states that for any good 1:

Where P;,, denotes the price of good i in terms of the domestic currency at time t, P”;¿ is

the price of good i in terms of the foreign currency at time t, and S, is the nominal

exchange rate expressed as the domestic price of the foreign currency at time t

According to equation (1.1), the absolute version of the LOP essentially postulates that a

given good should have the same price across countries if prices are expressed in terms of the same currency of denomination For some intensively traded commodities, such as gold, the absolute version of LOP holds well

Basically, the reason behind LOP is arbitrage If goods flow freely between

countries, which means world trade is free, then logically LOP will hold For example, if

the gold price in London is higher than that in Hong Kong, and gold traders can “move” gold “without barriers” from Hong Kong to London to make a profit until equalizing the

gold prices in the two markets However, for some goods, if there exist barriers in the world trade, arbitrage may not equalize the prices between international markets Some

reasons why LOP may not hold in certain cases are as follows:

1 Perfect substitutes

Clearly, the LOP will hold only if goods produced internationally are perfect substitutes If this is the case, then the condition of no profitable arbitrage can ensure the equality of prices in highly integrated goods markets The

assumption of perfect substitutability between goods across different countries is

crucial for LOP In general, however, product differentiation across countries can create a wedge between domestic and foreign prices of a product, which is

proportional to the freedom of trade of the good itself

Transportation costs and trade restrictions

The law of one price assumes that there are no transportation costs and no

differential taxes applied between any two markets This means that there can be

no tariffs on imports or exports, or any other types of restrictions on trade Since

transport costs and trade restrictions do exist in the real world this would tend to

drive prices for similar goods apart Transport costs could result in a good having

a lower price in the exporting market and more expensive in the importing market Similarly, an import tariff would drive a wedge between the prices of an identical good in two trading countries’ market, raising it in the import market relative to the export market price Thus, the higher are transport costs and trade

restrictions between trading countries, the less likely for the prices of goods to be equalized

Costs of non-tradable inputs

Many items that are homogeneous, nevertheless sell for different prices because they require a non-tradable input in the production process As an

example (Rogoff, 1996), consider why the price of a McDonald’s Big Mac hamburger sold in Switzerland is 5 times more than that in China One factor is

that the rent for restaurant space may be much higher in Switzerland and the restaurant will pass along its higher costs in the form of higher prices

and that group is unable to achieve the scale of trade needed to equalize the prices

for that product (Perhaps they face capital constraints and can’t borrow enough money to finance the scale of trade needed to equalize prices) In either case, given traders without information about prices will cause them not to be

equalized Thus, the law of one price may not hold for some products which implies that absolute LOP will not hold either

Other market participants

Notice that in the LOP equilibrium, it is the behavior of profit-seeking importers and exporters that forces the exchange rate to adjust to the LOP level

These activities would be recorded on the current account of a country’s balance

of payments Thus, it is reasonable to say that the LOP theory is based on current

account transactions It is estimated that there is approximately $ 1 trillion dollars worth of currency exchanged every day on international foreign exchange

markets, but on average, the total amount of world trade each year was less than

$100 billion dollars in year 2000 This means that the amount of daily currency transaction is more than ten fold the amount of daily trade in goods and services

This seems to suggest that primary effect on the daily exchange rate may be

caused by the actions of investors rather than of importers and exporters Thus, the participation of other traders in the foreign exchange market, who are

motivated by other concerns, may lead the exchange rate to a value that is not consistent with LOP

In addition to the above issues, some countries’ prices include value-added taxes,

whereas others do not Profit margins may differ across locations depending on

competition

Formally, by summing up over all the traded goods in each country, the absolute version of the PPP hypothesis requires:

where the weights in the summation satisfy » ,„¡#, =1 Alternatively, ¡f the price indices

are constructed by using a geometric index, then we must form the weighted sum after taking logarithms:

N where the geometric weights in the summation satisfy > „¡, =1 and lower case letters

denote logarithms The weights a, or y, are based on a national price index If the

national price levels are P; and Ph or, in logarithms, p, and Pp then we can use equations

(1.2) or (1.3) to derive the absolute PPP condition as:

From equation (1.4) it can be easily seen that the real exchange rate q,, defined here in logarithmic form is:

may be viewed as a measure of the deviation from PPP

The biggest problem with trying to implement absolute purchasing power parity, however, is that very few data are available for measuring it Governments do not

construct price indices for an international standard basket of goods In any case, such an index can lead a range of index number problems For, example, equation (1.2) and (1.3)

implicitly assume that the same weights are relevant in each country, whereas price index weights will typically differ across different countries and will also tend to shift through

time In practice, economists often assume that PPP should hold approximately, using the price indices of each country In the geometric index case, for example, we can rearrange (1.30) to yield:

where y, and 7,” denote the weights in the home and foreign price index respectively

Obviously, the greater the disparity between the relevant national price indices, the greater the apparent disparity from aggregate PPP even when the LOP holds for

individual goods However, because the geometric price indices are homogeneous of degree one, then differences in weights across countries will matter less when price impulses affect all goods and services more or less homogeneously An x percent

increase in all prices in the foreign country will lead to an x percent increase in the

foreign price level and the right hand side of equation (1.7) will be augmented by x and the change in the u, term will be zero Thus, assuming domestic prices are constant, an x percent appreciation of the domestic currency is required in order to restore equilibrium

A similar analysis may be applied when there exists non-traded goods and

services Suppose that the LOP applies only among traded goods An x percent increase

in all foreign traded goods prices may reflect a general price increase in the foreign country; other things equal, it implies an x percent appreciation of the domestic currency

If there is no change of the non-tradable goods in the foreign country, the general price increase will be less than x The appreciation of the domestic currency depends on the

general price increase and will be less than x As a result, while the LOP may not hold for

an individual good, the PPP could still hold

Another problem with the price index is that most countries use arithmetic rather than geometric price indices, although deviations from measured PPP arising from this source are not likely to be large Considerable differences may arise, however, where

price impulses impinge heterogeneously across the various goods and services in certain

economy and, in particular, where price inflation differs between the traded and non- traded goods sectors

Finally, the price indices compiled by government are relative to a base year, say

1970 equals 100 Because the indices give no indication of how large absolute PPP

deviations were for the base year, one must either assume that absolute PPP held on

average over some base period or else limit one’s attention to the relative PPP

In its relative version, the LOP postulates the relatively weaker condition that:

clearly, the absolute LOP implies the relative LOP, but not vice versa If price indices are

used, then equation (1.8) will become:

s+ P t— Piis the relative price of the foreign commodity basket in terms of the đomestic

basket Compared with equation (1.5), which is derived from the absolute PPP, equation (1.13) implies that the real exchange rate is not necessarily zero provided the relative PPP

holds

In testing the relative PPP, if the real exchange rate is a constant over time, it

means that the relative PPP holds instantaneously in the testing period However, this is

unlikely to be the case due to the volatility of the economy If the real exchange rate is not a constant, but is subject to a mean reverting process, it means that the relative PPP

violated in the short run but holds in the long run The test of whether PPP holds in the long run typically asks whether q, is stationary about a fixed mean

1.2 Review of the Literature

Does the PPP hold? In short run, obviously not Price levels are relatively stable (there is stickiness in nominal prices) However, nominal exchange rates fluctuate widely

since these rates are subject to volatile capital flows in addition to the flow of goods and services Therefore, purchasing power parity does not hold in the short run Whether

purchasing power parity holds as a long-run equilibrium relationship remains an

important empirical question that has implications for the sources of disturbances to real

exchange rates and for models of exchange-rate determination

Due to the importance of PPP in macro-international economics, the empirical evidence on PPP is very large, and the sophistication of the testing procedures has

developed with the advances in econometric techniques

The empirical work before the 1980s on testing PPP was based on estimates of equations of the following form:

where €, is a error term The null hypothesis is:

obtained estimates of B and B" very close to plus and minus unity on data for high

inflation countries However, test after test has rejected PPP for more stable monetary environments The problem with these early tests is that they did not investigate the

stationarity of the residuals If both nominal exchange rates and relative prices are non- stationary variables (and are therefore not cointegrated), then equation (1.14) is a

spurious regression, and conventional OLS-based statistical inference is invalid If the error term in equation (1.14) is stationary, however, then a long-run linear relationship may exist between exchange rates and relative prices, but conventional statistical

inference is still invalid because of the bias present in the estimated standard errors

Since the early 1980s the conventional tests of PPP have been criticized on the ground that exchange rates and prices are non-stationary series From the mid to late

1980s onward, a standard approach has been the augmented Dickey-Fuller (ADF) test for

*For the regression test, see Frenkel (1978, 1981), Krugman (1978), Roll (1979)

a unit root in the process driving the real exchange rate Rejection of the null hypothesis

of a unit root would be evidence in favor of long run PPP, since it would imply that deviations of the real exchange rate from its mean value are only temporary However, nearly all unit root studies have concluded that the null hypothesis of a non-stationary

real exchange rate cannot be rejected for most countries in the post-Bretton Woods era

The empirical failure of the unit root tests of PPP in post-Bretton Woods data is

largely due to the low power of the tests employed In finite samples, these unit root test procedures inevitably have limited power against alternative hypotheses with highly

persistent deviations from equilibrium Simulation exercises indicated that this problem is particularly severe for small samples For example, if 50 observations are generated by a

stationary univariate model with first order autocorrelation of 0.9, the ADF test procedure rejects the unit root hypothesis in only 8 percent of the replications Even with 100

observations, the ADF test procedure rejects the unit root hypothesis in only 29 percent

of the replications (Levin and Lin, 1993)

Sarno and Taylor (2002) examined the lack of power of the unit root tests of PPP

by using a simple Monte Carlo experiment They verified that: “even with a century of

data on the pound sterling-U.S dollar real exchange rate, we would have less than an even chance of rejecting the unit root hypothesis” (Lothian and Taylor, 1996) Moreover, even if the first order autocorrelation coefficient is 0.825 (the lower band from the panel

unit root test), to reject the null hypothesis of unit root with more than 50 percent

probability, we would still need something like 75 years of data On the other hand, most

of the empirical work on unit roots has been done before 1990’s, which means they had

at most 18 years data since the period of generalized floating began in 1973 Obviously

the reason for not rejecting the unit root is due to lack of power

Researchers reacted to the low power problem by using long-horizon data Edison

(1987) used an error-correction model to analyze dollar/pound data for the years 1890-

1978, and his result was a slightly weaker rejection of the PPP During the 1990s, more modern empirical methods were employed in analyzing the long horizon data, including

variance ratios, fractional integration, cointegration and error correction models These long horizon data studies almost invariably tended to find evidence of mean reversion in

the real exchange rate (Rogoff, 1996) In a study, Mollick (1999) analyzed the behavior

of the real exchange rate in Brazil over the longest possible period for which data are

available: 1885-1990, and found mixed results Formal tests cannot reject the hypothesis

of non-stationary behavior; however, time series identification favors a stationary

interpretation, and autoregressive processes for the real exchange rate yield extremely robust and satisfactory estimates Lothian and Taylor (1996) presented unit root test

results for the franc-sterling and dollar-sterling real exchange rates using annual time

series data spanning two centuries With the increased test power obtained by this large data sample, they were able to reject the unit root hypothesis using both ADF and

Phillips-Perron (PP) tests and they concluded that PPP is valid in the long run for the two

bilateral exchange rates considered In response to Cuddington and Liang’s (2000) criticism, Lothian and Taylor (2000) strengthened their belief in the PPP relation and a

faster estimation of the speed of mean reversion Andersson and Lyhagen (1999) utilized

a long memory panel unit root test to reanalyze some previous empirical studies, and in

some cases the test rejected the hypothesis of no cointegration between foreign and domestic prices where the other authors’ tests did not Shively (2001) applied an exact small-sample, point-wise most powerful invariant unit root test to annual, long-horizon

real exchange rate (for 21 real exchange rates data from 1900 to 1997) He found clear

and consistent evidence in favor of the purchasing power parity relationship

While the consensus among these long horizon studies is remarkable, they are

subject to some criticism One obvious drawback of the long horizon approach is that it blends fixed and floating exchange rate data In the long run, the exchange rate regime or

even the whole economy’s structure is subject to change If one does not take these structural changes into account, the results maybe not reliable

Due to the problems of the long horizon approach, it is necessary to devise a test

to provide a convincing test of the real exchange rate, especially during the post-Bretton Woods period

A reasonable approach to the problem is to increase the power of the unit root testing Because the data are limited, the best way is to consider the use of pooled cross-

section time series data as a means of generating more powerful unit root tests The most influential studies are Levin and Lin (1992, 1993), Im, Pesaran and Shin (1997) The test

developed by Levin and Lin (LL) can be seen as a natural extension of the Dickey and Fuller (1981) test for a unit root to a set of time series It extends the method previously

suggested by Quah (1990) and Breitung and Meyer (1991) In light of the criticism by

Pearan and Smith (1995) on the use of pooled regressions of the LL type, Im, Pearan and

Shin (IPS) allow for heterogeneity of the series under the alternative and do not make use

of traditional panel estimation techniques but propose a group-mean Lagrange multiplier test and a group-mean t-test based on the individual ADF test statistics The asymptotic

properties for both tests are derived assuming a diagonal path limit The simulation results suggest both tests have greatly increased the power of the unit root test

Based on advances in econometric method, Wu (1996) employed the Levin and Lin test to study eighteen developed countries using data from January 1974 through

April 1993 His results show that the null hypothesis that exchange rates during the post- Bretton Woods period contain a unit root can be decisively rejected These results are

robust in that they are not sensitive to the choice of price indices or the frequency at which the observations are sampled Frankel and Ross (1996) examined PPP based on a

panel data set of 150 countries and 45 annual observations, and verified the PPP relation

Lothian (1996) used panel data for the United States and 22 other OECD countries for the

years 1974-1990, and presented evidence that despite substantial short-term

perturbations, purchasing power parity actually performed much better than commonly

believed Papell and Theodoridis (1998), utilizing samples of data that begin in 1973 and end between 1982 and 1996 with the United States dollar and the German mark as base

currencies, found that as the sample is extended, the evidence of PPP strengthens with

panel, but not univariate, methods Koedijk, Schotman, Dijk (1998) investigated the PPP

among 17 industrialized countries between 1972 and 1996 rejected the unit root and their

result was free of benchmark currency Andersson and Lyhagen (1999) used a long memory panel unit root test and rejected the random walk hypothesis Fleissig and

Strauss (2000) implemented panel unit root test for OECD countries and supported the PPP

While there are many studies on developed countries, equal attention has not been paid to the developing countries In developing countries, PPP is of potential interest to policy makers for at least two reasons First, PPP can become a prediction model for

exchange rates and a criterion for judging over- and under-valuation of currencies

Second, many exchange rate theories employ some notion of PPP in their construction

Thus the quality of policy advice may depend on the validity of PPP in developing

countries Although the PPP tests have gained success in developed countries, there may

be questions as to the generalization of these results to developing countries The

potential problem lies in that there may be large deviations of the exchange rate from PPP

in developing countries than in developed countries Developing countries tend to have more government intervention and trade restrictions The economic structures of

developing countries tend to be more diverse and structural changes can be more

frequent Next, there are arguments for smaller deviations from PPP for developing

counties Developing countries experience more volatile price changes and therefore it is

expected that monetary factors overshadow real ones in PPP deviations In addition, more

frequent use of foreign exchange controls in developing countries may have led to less

speculation resulting in lower exchange rate volatility

Tang and Butiong (1994) examined the bilateral exchange rates of eleven

developing Asian countries during the period 1973-1990 using an error correction model They found strong evidence in support of the PPP being a long run constraint for five of

the countries Their study suggested substantial deviations from PPP in countries that had

relatively high foreign exchange speculation and capital movements Bahmani-Oskooee (1993) confirmed PPP for twenty-four developing countries of twenty-five examined Chinn (1998) used the Johansen procedure (1988) to examine whether the Asian

currencies were overvalued just prior to the crisis and found evidence for PPP in nearly

all cases Razzaghipour, Fleming and Heaney (2000) employed an error correction model

to study crisis countries Their results are consistent with PPP and are quite robust, as PPP effects are evident in the time series even when the 1997 crash period is included in

the analysis It should be pointed out that none of the above studies used panel unit root

methods Holmes (2000) tested for long-run relative purchasing power parity in a sample

of 27 African developing countries by an IPS t-bar test using quarterly data covering the period 1974-1997 His results supported the relative PPP in these developing Africa countries

Based on the research above, the question of the validity of PPP in developing

countries is far from resolved The reasons are:

1 The developing countries chosen for PPP testing usually are countries

concentrated in geographical proximity For developing countries, the economic ties among countries in a specific region tend to be much stronger than with

countries outside such a region First, the transportation costs are lower, which

results in more international trade Second, the capital flows among developing countries in a specific region are more intensive than that among countries in different regions Third, there are economic blocs in some regions, such as the

Southeast Asian countries, and there exists some International economic policy

coordination in these economic blocs As a result, PPP is more likely to hold in a regional test

2 Some of the studies utilized the error correction model for the PPP test Given the

limitation of post-Bretton Woods data, these tests are also subjected to lack of

power As Levin and Lin Said: “For panels of this size (between 250 individuals, with 25 to 250 time series observations per individual), existing multivariate time series and panel data procedures may not be computationally feasible or

sufficiently powerful, So that the [panel] unit root test procedures outlined in this paper will be particularly useful.”

The aim of this paper is to test if the purchasing power parity doctrine holds in

large developing countries that are geographically distant from each other, using the more powerful panel unit root test

1.3 Method of Analysis

As mentioned above, we don’t expect that the PPP will hold in the short run, and

in the long run, there is no decisive evidence that PPP holds for developing countries If

one does not consider exchange rate regime changes, the best way to test for the long run

purchasing power parity is to examine whether the real exchange rate is a stationary (mean reverting) stochastic process Due to lack of power, the usual univariate unit root test is not feasible, which leads us to find a better way to solve this purchasing power

parity puzzle

1.3.1 The Augmented Dickey-Fuller (ADF) Test

The most common way to test for a unit-root in a time-series is to apply the Augmented Dickey-Fuller (ADF) test Assume that we want to test for a unit-root in y

An intuitive way of doing so would be to estimate y, =y y;.1 + & and then test if 7#l1

This is also similar to the way the ADF test is carried out To derive the test equation, begin with:

Subtract y,.; from each side:

Ye — Yor =(¥- Dyer + & (1.16)

Then, if @ = 0, equation (1.17) can be rewritten as y, = y,1 + & which means that y, follows a random walk To actually test if » = 0, one should estimate equation (1.17) and

check the t-value of @ against a certain critical value If the (absolute) t-value is larger

than the (absolute) critical value we reject the null of a unit-root and conclude that the

series is stationary and thus can be employed in a model

The ADF approach controls for higher-order correlation by adding lagged

difference terms of the dependent variable y to the right-hand side of the regression:

Ay: = + y Yer + OAye1 + ỗaAyt2 + + SpAyep + & (1.18)

this augmented specification is then used to test:

in this regression, an important result obtained by Fuller is that the asymptotic

distribution of the t-statistic on y is independent of the number of lagged first differences employed in the ADF regression The problem with the ADF test is that it has a very low power That is, the test is likely to not reject the null of a unit-root even if the series is stationary

1.3.2 The Phillips-Perron (PP) Test:

Phillips and Perron (1988) proposed a nonparametric method of controlling for

higher-order serial correlation in a series The test regression for the Phillips-Perron (PP) test is the AR(1) process:

While the ADF test corrects for higher order serial correlation by adding lagged

differenced terms on the right-hand side, the PP test makes a correction to the t-statistic

of the y coefficient from the AR(1) regression to account for the serial correlation in

The correction is nonparametric since they use an estimate of the spectrum of ¢ at

frequency zero that is robust to heteroskedasticity and autocorrelation of unknown form The PP t-statistic is computed as:

¥,=(>.8é_,)/T (1.22)

t=j+l

where tp, sp are the t-statistic and standard error of B and s is the standard error of the test

regression The asymptotic distribution of the PP t-statistic is the same as the ADF t- Statistic, and it is also subjected to a lack of power

1.3.3 Levin and Lin (LL) test

Levin and Lin considered the use of pooled cross-section time series data as

means of generating more powerful unit root tests The test procedures are designed to evaluate the null hypothesis that each individual in the panel has integrated residuals

versus the alternative hypothesis that all individuals have stationary residuals Since the null hypothesis imposes a cross-equation restriction on the first-order partial

autocorrelation coefficients, these panel test procedures can yield much higher power than performing a separate unit root test for each individual This test allows the residual variance and the pattern of higher-order serial correlation to vary freely across

individuals Moreover, these tests are consistent in detecting alternative hypotheses in

which the first-order partial autocorrelation varies across individuals Thus, the test allows for heterogeneity across individuals in every respect except the presence or absence of a unit root In contrast to the nonstandard distributions of unit root test

statistics for a single time series, the panel test statistics have limiting normal

distributions

For practical purposes, the use of panel data to perform unit root tests applies

primarily relevant to a panel of moderate size (i.e between 10 and 250 individuals, with

25 to 250 time series observations per individual) For panels of this size, existing

multivariate time series and panel data procedures may not be sufficiently powerful

Suppose { yj } is a stochastic process for a panel of individuals i=1, , N, each of whom is observed over time periods t=1, ,T to determine whether this process contains

a unit root for each individual in the panel, we assume all individuals in the panel have identical first-order partial autocorrelation, but all other parameters of the disturbance

process are permitted to vary freely across individuals Thus, under the null hypothesis,

each individual time series has a unit root and the differenced data, Ay; = yit— Viti follows a stationary ARMA process for each individual Under the alternative hypothesis,

the process { yj }is stationary for each individual in the panel

Suppose the stochastic process { yi: } is generated by the following model,

AYin = Oo; + 5; Vint + Sit (1.23) The disturbance ¢;, is distributed independently across individuals and follows a

stationary invertible ARMA process for each individual, which is expressed as:

E, =D 9;64-5 +E ÿ”ữj (1.24)

J=0 The series { y; } may have an individual-specific mean, but does not contain a time trend, which is a reasonable assumption for testing PPP Both absolute PPP and relative PPP

require that the real exchange rate mean revert to a constant, and under relative PPP, the

constant is not necessarily zero The panel test procedure evaluates the null hypothesis

that 6; = 0 and ap; = 0 for all i=1, ,N against the alternative hypothesis that 5; < 0 and ơại

ER for all i=1, ,N

The test procedures of panel unit root can be summarized in four steps Step 1

eliminates the influence of aggregate effects by subtracting cross-section averages from each variable Step 2 and 3 can be performed to carry out separate ADF tests for each

individual in the panel Finally, step 4 computes the unit root test statistics

Step1: Subtract cross-section averages from the data

The LL test requires that the data be generated independently across individuals

This assumption can be relaxed to allow for a limited degree of dependence via a time-specific aggregate effect The influence of these aggregate effects can be

N

removed by subtracting the cross-section average y = > y,, from the observed

i=l data, which is equivalent to include time-specific intercepts in the regression model The removal of cross-section averages from the data does not affect the

limiting distributions of the panel unit root

Step2: Compute orthogonalized first differences and lagged levels for each individual, and normalize them by the estimated residual standard error

First, perform two auxiliary regressions of Ayj, and yi) with respect to the p;

lagged first differences and the intercept, and calculate the residuals é, and

¥,,_, from these regressions:

pi

Is}

pie

f=]

To control for heterogeneity across individuals, the estimated innovation

é,, and orthogonalized lagged level »,_, are normalized by the regression standard

error, which is:

asymptotically, the normalized innovations @,, will be independent and identically

distributed for all individuals i=1, ,N and time periods t=1, ,T

Step3: Estimate the ratio of long-run to short-run standard deviations for each

individual, and then calculate the average ratio for the panel Under the null

hypothesis, the normalized long-run variance is:

K is the lag truncation parameter, & i is consistent if K grows exponentially at a

rate less than T wz, = /(K +1) The ratio of the long-run standard deviation to

the innovation standard deviation s; = oy; / 6,i, and it can be estimated by:

The average standard deviation ratio can be estimated as follows:

the estimated average standard deviation ratio 5 will be used to adjust the mean of

the panel unit root test statistic

Step 4: Compute the panel test statistics

Under the null hypothesis, the normalized residual innovations @,, are

independent of the normalized lagged residuals ¥,_, for each individual in the Vit

panel This hypothesis can be tested by performing the following regression:

the average lag order for the individual ADF regressions Then the least squares

estimate 6 , the standard error of the regression ổ, „ the reported standard error

(RSE) of ễ, and the regression t-statistic for the null hypothesis that 6 =0 can be expressed as follows: