Testing Purchasing Power Parity in Cambodia: Time-Varying Trade Weights in Constructing Real Effective Exchange Rate

The purchasing power parity (PPP) is generally accepted as the exchange rate projection between two countries relative to their inflation rate. However, despites many researches in the past years, the answer to whether the PPP holds, remains an on-going debate. The prior researches are criticized for their heavy reliance on the bilateral exchange rate which consists of short time-series or uses multilateral or real effective exchange rate (REER) constructed by the fixed trade weight. Finally, the implementing of only the most popular unit-root or stationary tests such as ADF and PP deems to diagnose with certain weaknesses, for instance, size distortion ascending from the heteroscedasticity. The main purpose of this study, therefore, is to study whether the PPP holds in Cambodia? In this paper, an alternative stationary test known as the KPSS test is incorporated with the stationary test thereof. Avoiding the aforementioned problem, the time-varying trade weights of Cambodia from 1995 to 2019 is employed to construct the total data points or months of 295 REER from January 1995 to July 2019 instead. The result indicates that the PPP theory holds in Cambodia based on the result generated by the ADF test modeled with constant and trend. The test result thereof also indicates that the REER of Cambodia has a mean reverting process.


INTRODUCTION
The Purchasing Power Parity (PPP) theory assumes the measure of two countries' purchasing power of a basket of goods equals to one another. However, if this assumption fails to hold, the implication can be drawn and extrapolated that the change of demand of a basket of goods in either country must have been altered. In accordance to the PPP theory, one of the major explanation to this phenomenon is the market imperfection resulted from tariffs, quotas and the transaction cost, etc. Thereof, to measure the purchasing power of a basket of goods or services, the exchange rate between that two countries is a vital indicator on which serious attention have to be paid. When the price of the same or identical product between two countries are not the same, the arbitrage opportunity is formed. Meaning that with the assumption of no transaction cost, goods or services can be bought low in one country and sold high in another. The exercising of the arbitrage opportunity results in the exchange rate appreciation in the country with low-priced goods or services, subsequently, correcting the purchasing power parity of the two countries to the same level.
Consequently, if the PPP theory holds in a country, the policymakers can exploit its significant benefit and apply to regulate and manage the variation of the exchange rate. Studying the PPP, therefore, begins by generating real bilateral exchange rate (RER) or the constructing real multilateral exchange rate, also known as real Controversial discussion has been contended around the whether the PPP hold or not, some of which argues on the length of the time series whether or not it is long enough to capture the impact. Second, researchers argue between the implementing of the bilateral exchange rate and the multilateral exchange rate, which one would affect the conclusion of the PPP theory? Third, the trade share, which is used to construct the REER, should be fixed at a particular time period or should use the time-varying trade weights? The three major controversial discussions above are all considered in this study. The main purpose of this paper, thus, is to demine whether the PPP holds in Cambodia or not. Giving the purpose of the study, time-varying trade shares of Cambodia is employed to construct the monthly REER from the January 1995 to July 2019. Additionally, three stationary tests such as Augmented Dickey and Fuller (ADF), Phillips-Perron (PP) and Kwiatkowski, Phillips, Schmidt and Shin (KPSS) tests are applied on the constructed REER.

LITERATURE REVIEW
The purchasing power parity (PPP) theory is a generally accepted model for the exchange rate projection between two countries, proportional to the inflation rates in the long-run. Researchers, however, are caught in the dilemma with regard to the validity of the theory and the most feasible methods for studying the aforementioned theory. For instance, recent studies by Taylor (2000) and Shiller (2013) emphasis the validity issues of the PPP theory in predicting the exchange rates over short time-intervals. Many existing studies, likewise, also evidenced against the correlation between the relative price levels of two countries and the movement of two currencies over a short time-interval, witnessing the deviation from PPP. In contrast, in the long-run, the existing literatures appears to be in favor of the theory and recommends that the PPP theory is likely to hold. Giving market forces may bring the exchange rates to their PPP levels (Cassel, 1916;Keynes, 1923;Gailliot, 1970;Frankel, 1978;Ohno, 1990). Some recent researches, on the other hand, asserts that PPP theory is invalid, subsequently, contradicting to the preceding studies by Friedman andSchwartz. (1963), Frenkel (1981), Hakkio (1984), Mark (1990), and Rogoff (1996) which researches lend significant support to the PPP theory as a long-run hypothesis in the international economics.
Recent researches asserts that inconsistent findings related to the PPP theory resulted from the variability of price indices between the two countries that are used to measure the inflation rates and the study period (Shiller, 2013;Hyrina and Serlestis, 2010). The failure of the PPP theory in determining exchange rate movements during the investigations attributed to the differences between the observed countries with respect to their economic conditions and policies. The deviations in price levels for nontraded goods of both economies and between international and domestic markets, are also important aspects that suggest the violation of the PPP theory.
In an attempt to address the issues identified in the prior studies that were not in favor of the theory, the later studies adjusted the methodologies and employed new economic techniques, yet those further empirical analyses produced mixed results (Hyrina and Serlestis, 2010). Hyrina and Serlestis (2010) have classified the testing procedures of the PPP theories in six different categories, from tests on null hypothesis in early studies by Isard (1977), Krugman (1978) and , to testing using a non-linear econometric technique by Sercu et al. (1995), as well as testing using panel-based unit-root developed by Levin et al. (2002) and Im et al. (2003).
The period of the observation, on the other hand, becomes a key aspect in the analysis of whether the PPP theory holds, due to different economic context. A number of studies were undertaken to test the theory before and after the Bretton Woods.  concludes the validity of the PPP theory in the 1920s and the collapse of the theory during the transition to the flexible exchange rate regime following the collapse of Bretton Woods in the 1970s. It was argued by Hakkio (1984) who used cross-country tests and supported that the theory worked better in the 1970s than in the 1920s. Enders (1988) performed a test using the Autoregressive Integrated Moving Average (ARIMA) Model to compare between 1960-1971 and 1973-1986. The study found mixed evidences for the PPP hypothesis during the Bretton Woods System and the flexible exchange rate period. "The point estimates of the longrun real exchange rates for Canada, Japan, and Germany did not significantly differ from unity. Point estimates for all countries indicates that real exchange rates are convergent. All confidence intervals, however, are sufficiently large that the null hypothesis that the real rate follows a random walk, cannot be rejected" (Enders, 1988). Frankel (1986Frankel ( , 1990, additionally, pointed out main concerns in previous studies regarding the PPP tests. First, the insufficient data points for the analysis and the types of tests could affect the results of the theory as the predictors of the exchange rate movements. Thus, employing a larger dataset, often extending to a century, and obtaining data for a panel data set for many countries are expected to address the weakness of the PPP tests (Frankel, 1986;Abuaf and Jorion, 1990). Observing a more extended time interval is likely to yield a favorable result to the PPP theory. Klaassen (1999), adopting the Markov regime-switching model, found the evidence in favor of the PPP in the long-run during the post-Bretton Woods period. However, this study emphasized a contradicting result to the research by Hyrina and Serlestis (2010), testing the PPP theory for a sample of 23 countries over a century, which eventually rejected the claims of the theory. The second approach was supported by Frankel and Rose (1996) and Papell (1997). Frankel and Rose (1996) found a strong statistical correlation between the exchange rate differential and the inflation differential through the analysis of a 45-year annual panel data set of 150 countries. Another study using a "wide-sample" panel analysis highlighted the importance of cross-sectional dependence on the outcome of testing a unit root in panels of real exchange rates (O'Connell, 1998).
Furthermore, concerning over the reliance on the unit-root to test for the PPP may lead to size distortion bias relative to the heteroscedasticity. Su et al. (2014) employs the bootstrapped KSS a robust model to counter the problem thereof and applies to test PPP of 61 countries from 1994 to 2012. The result counters the PPP theory. Tsong (2011), in contrast, adopts the nonlinear ESTAR process to test the stationary of the unit-root test. The result indicates that the model performs even better than KSS. After implementing the model on 15 countries in Asia, the result suggests in favor of PPP. Likewise, Bec et al. (2004) implements SETAR model on the monthly real exchange rate data of five European countries also provides evidence to support the PPP. Cavaliere (2004) and Cavaliere and Taylor (2007), on the other hand, have tested the unit-root under the time-varying variance. Both have attached great important in developing a robust model to deal with the variance change.
Giving the suspecting of PPP breakdown through the implementation of the unit-root tests on the real effective exchange rate constructed by trade share that fixed at a single base year, Bahmani-Oskooee, et al. (2009) introduces and implements the stationary test on REER for 52 countries using the time-varying trade weight. As a result, the research method indicates that the breakdown of PPP is somewhat sensitive to the use of time-varying trade weight. In Cambodia, however, no research has ever offered evidence of PPP holds in Cambodia yet. Thereof, the construct of REER using the time-varying trade weights has not yet been conducted and tested in Cambodia yet. For instance, the studies by Joyeux andWorner in 1998 andTang in 2009 which detail of the research result is discussed as the following. Joyeux and Worner (1998) applied the cointegration technique to test whether PPP hypothesis holds in the long-run between Cambodia and Thailand. The sample periods are based on the monthly data over a 6-year period from 1991:1 to 1997:4 whom sample periods are considerably short. Since testing the absolute PPP theory involves examining if the logarithm of the real exchange rate follows the mean reversion, the absolute version of long-run PPP would allow the real exchange rate to be difference from zero in the short-run, but it would require real exchange rate to be a zero mean stationary process. As for Cambodia and Thai markets, however, are quite similar in which the information and transportation costs are not possible to ignore, the relative PPP is a more relevant concept. Consistent with the author's anticipation, the relative version of PPP existed between Cambodia and Thailand as suggested by the empirical data. Liew and Tang (2009a) also used the monthly observations from 2001:M5 to 2009:M2, a relatively long period of time span, to examine the validity of PPP hypothesis for an East Asia transition economy, namely Cambodia. After performing the Johansen's multivariate cointegration test, the empirical results showed that the long-run PPP was verified in Cambodia because the nominal exchange rate and price levels were cointegrated. Even though the studies carried out by Joyeux and Worner (1998) and Liew and Tang (2009a) found supporting evidence of PPP in Cambodia, there are two limitations of their studies as argued by Liew and Tang (2009b). The former concerned with the two methods that they employed to test whether or not PPP hold, in which there is no clear advantage of one method to another. The later drawback is that both works utilized single bilateral exchange rates without taken into consideration the other bilateral exchange rates; therefore, the test results tend to support PPP hypothesis in Cambodia. To bridge the gap of the second shortcoming, Liew and Tang (2009b) reinvestigated the validity of PPP hypothesis in Cambodia by using nine bilateral exchange rates between Cambodia and her trading partners from 1991:M1 to 1997:M4. In their study, the ADF and PP test failed to reject the null hypothesis of unit root, implying that PPP did not hold in Cambodia. Furthermore, to uncover the potential bias of using a relatively small sample size (which was only 94 observations), the authors further applied panel unit root test to validate the hypothesis of PPP. Unfortunately, the panel unit root test's results were also failed to find supporting evidence of the PPP in Cambodia. Their empirical result contradicted to the previous findings by Joyeux and Worner (1998) and Liew and Tang (2009a).
Refering to the result of Joyeux and Worner (1998) and Liew and Tang (2009a), the drawbacks of both researches are the application of short time period, use only bilateral nominal exchange rate between Cambodia and some of her trading partners and employ only the stationary test such as ADF and PP tests. Attempting to deal with the time-varying variance and filling the gap of the preceding studies, the current research will employ longer time series, 1995:M1-2019M7, use multilateral or real effective exchange rate based on time-varying trade weights, and introduce a complimenting KPSS test in addition to the ADF and PP test.

METHODOLOGY
This section will be separated into to two main parts. The first part is the construction of the real effective exchange rate which was introduced by Bahmani-Oskooee in 1995. The second part is the reviewing of the econometric theory relating to the unit root or stationary test which will be applied on the constructed real effective exchange rate to determine whether mean-reverting process of the series does exist or not.
Generating real effective exchange rate, four main steps are carried out. In the first step, the bilateral exchange between Cambodia Riel and her main trading partners of which ten countries including Thailand Baht, Hong Kong Dollar, China Yuan, Vietnam Dong, Singapore Dollar, South Korea Won, Japan Yen, Malaysia Ringgit, Indonesia Rupiah and United States of America Dollar, is constructed. The exchange rate quotation between Cambodia or Khmer Riel (KHR) and her main trading partners' currency are not available, but the exchange quotations between each country currency and US Dollar are available, thus cross exchange rate between Khmer Riel and each trading partner can be calculated. Each bilateral exchange rate is denoted by EX i 's and defined as number of units of trading partner i's currency per unit of KHR. If the real effective exchange rate increases, the Cambodian riel is appreciated. In the second step, the nominal bilateral exchange rates found in step one are adjusted with each trading partner's consumer price index (CPI) with 2010 as based year (2010=100). The real bilateral exchange rate, denoted as REX i , is indicated below,

Augmented Dickey-Fuller (ADF) Test
A number of unit-root tests had been published by Dickey and Fuller in 1979 to check whether a selected data of time series under investigation has a unit root/non-stationary or has no unit root/stationary or not. A stationary data exhibits a mean-reverting process in general. The fundamental estimation of the Dickey-Fuller (DF) test is an estimation of first order autoregressive (AR) model of the form: y t =β 1 +β 2 t+β 3 y t-1 +ε t (1) Where y: Time series variable, β i : Parameters or coefficients, i = 1,2,3, t: Time trend, ε: Residual or error term which is assumed to be i.i.d The equation (1) can be written in another form, Where β 3 *=β 3 -1 The DF had imposed an assumption on the DF test that the residual terms are serial uncorrelated. In case, the predicted error terms in equation (2) are serial correlated which violates the assumption of the DF test, the estimated result of the test is not consistent. Worth noted that the null hypothesis of the Dickey-Fuller test is β 3 = 1 and the alternative hypothesis is |β 3 | <1. If the null hypothesis is failed to be rejected, the has a unit root or non-stationary. In contrast, the y t is stationary or has no unit root, if the null hypothesis is rejected (Dickey and Fuller, 1979).
To solve the problem of the serial correlation of the error term, Dickey and Fuller had developed another test known as the Augmented Dickey-Fuller (ADF) test. The ADF test is conducted by running the following form of a regression while keeping the stated hypotheses as the DF test. The null hypothesis states that the series has a unit root while the alternative hypothesis states that the series has no unit root or stationary.
Where y: Time series data, ∆: First difference operator, β 1 , β 2 , δ and: Parameters or coefficients, t: Time trend, ε: Error term or residual term, i.i.d The determination of the optimal lags length of the regression model (3) is the most crucial task to do in conducting the ADF test. Since small lags length of this model would not produce a white noise error or residual term, and the estimated standard error of each respected parameter would also not be well-estimated.
The optimal lags length can be defined by using the information criteria such as Akaike Information Criterion (AIC) or Schwarz Information Criterion (SIC). The hypotheses of ADF test, null and alternative hypotheses, are presented below: The null hypothesis of δ = 0 is failed to reject when the critical value of t-test which can be extracted from the DF table is smaller than the t-statistic which implies that the time series under investigation has a unit root or non-stationary. The hypothesis is rejected or the alternative hypothesis of δ < 0 is accepted in case that t-statistic is greater than the critical t-test which can be interpreted that the time series is stationary or has no unit root (Dickey and Fuller, 1979).

Phillips-Perron (PP) Test
The lags of the first different terms of the regressors have been added to the regression model (1) in order to solve the problem of serial correlation of the residual or error term which produces inconsistency of the estimated result as had been conducted by the Dickey and Fuller. A later more comprehensive theory of unit root test had been developed by Phillips and Peron in 1988.
The PP test is conducted by running exactly the same form of regression model as the DF test. The model indicated in equation (4) below, Despite the regression model of the two tests, PP and DF, are exactly in the same form, instead of adding lag of the first difference terms of regressors into the regression equation in order to get rid of serial correlation of the residual term problem. A nonparametric adjustment of the t-statistic, which assumed in the DF test, is transformed into the Phillips-Peron Z-statistic instead. However, the asymptotic of Z-distribution and t-distribution is applied to the PP and DF respectively (Phillips and Perron, 1988).

Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) Test
In 1992, Kwiatkowski, Phillips, Schmidt and Shin (KPSS) developed a unit-root test on an observable time series. The null-and alternative hypotheses of the KPSS unit root test are completely opposite from the ADF and PP tests since the nullhypothesis of stationary around a deterministic trend is test against the alternative hypothesis of a non-stationary or unit root. The KPSS statistic is derived by predicting the residual or error term from the Ordinary Least Square (OLS) regression as show below, The residual terms are assumed to be stationary error. t is a time trend and r t is a random walk which has the following form, Where the u t are assumed to be independent and identically

EMPIRICAL RESULTS
Two main parts are presented in this section. The first part describes the movement and the descriptive statistics of the real effective exchange series. Significantly, this study tries to explain whether during the investigation period, Cambodia's Riel is under-or over-valued. The month or the point at which the Riel is defined to be under-valued when the index of real effective exchange rate at specific month or point is less than index of 100. In contrast, Riel is over-valued when the REER at a point is more than 100. Additionally, the estimated result of unit-root tests: ADF, PP, and KPSS is shown in the second part.     Figure 2 also indicates that the REER series are not distributed as the normal distribution since the null-hypothesis of normal is rejected because the probability value of the Jarque-Bera is lower than 1 percent significant level.

CONCLUSION
The reason of PPP theory does not hold in real world is feasibly due to some constraint. First, the length of the time-series is too short. Second, the exchange rate used is a bilateral exchange rate. Although, in some cases, the multilateral or real effective exchange rate is used. The construction is still based upon the fixed trade weight which is inadequate to demonstrate the actual situation of the trade structure that keeps changing prominently every year. Equally important, the unit root tests implemented in the prior studies were ADF and PP tests. The forgoing problems are attempted to tackle in this study. In accordance to the result of the ADF test of the model with constant and trend, which is implemented on the constructed monthly REER from January 1995 to July 2019 using each respected year trade weights from 1995 to 2019, indicates that the theory of PPP holds in Cambodia.
Additionally, this study also demonstrates that the reason PPP does not hold is not due to the unit root tests because regardless of the implementation of the KPSS test, the PPP theory would still breakdown. As a matter of fact, the large time-series data and time-varying trade weight of REER series could probably be the concerning reasons corresponding to the justification of PPP theory holds in Cambodia.
Last but not least, the National Bank of Cambodia (NBC) can implement the REER process as the fundamental measure to keep track, manage the variation of the exchange rate and subsequently, formulate the strategic planning related to the monetary policy to ensure price stability and achieve sustainable economic development.
As for the school of thought, the later study that strives to extend the coverage of the study to understand the PPP theory in Cambodia, the structural break of REER should indeed be included and implemented. Provided that the REER implemented in this study shows many structural breaks as demonstrated in Figure 1.
If the structural breaks are controlled and the estimated result from the unit-root tests: ADF, PP and KPSS tests which is applied on the REER with time-varying trade shares indicates that PPP still holds in Cambodia, this result would be a new discovery for the study of PPP in other countries around the world.

Sponsoring Organization
The CamEd Business School, Cambodia.