Validity of Purchasing Power Parity (PPP) Hypothesis in the Ecowas (1980

Abstract

This study investigates the validity of a purchasing power parity (PPP) hypothesis in the ECOWAS. Secondary data on real exchange rates, domestic inflation rates, and foreign inflation rates were sourced from the World Development Indicators of the World Bank (2018). Unit root tests, Panel unit root tests, and panel cointegration tests were used to investigate the validity of the PPP hypothesis in the ECOWAS. The study found that the PPP hypothesis is valid individually in all the ECOWAS member countries. The results from the panel unit root tests also confirm the validity of the PPP hypothesis in the ECOWAS. Specifically, the LLC with individual intercept (t = −5.97117, p < 0.0000), IPS with individual intercept (t = −3.30564; p < 0.0000), Fisher ADF with individual intercept (t = −3.43996; p < 0.0003), and Fisher PP with individual intercept (t = −5.91557; p < 0.0000) while the panel cointegration test rejects the validity of the PPP hypothesis. Therefore, the study suggests that the ECOWAS can cautiously forge ahead with the implementation of their economic integration policies and programs in the sub-region.

Keywords

PPP hypothesis panel unit root tests panel cointegration test ECOWAS

Introduction

Establishing the validity of a purchasing power parity (PPP) hypothesis is one of the major ways of assessing if countries are tending toward economic integration. As a result, the concept of the PPP hypothesis has been attracting the increasing attention in the last three decades in the field of international trade and finance because of its use for international comparison of economies and social indicators (Taylor & Taylor, 2004). PPP hypothesis can be described as the equalization of prices when converted to a common currency, with a unit of purchasing power, say one American dollar, it should be possible to purchase the same equal bundle and quality of goods or services anywhere in the World, with arbitrage (Neary, 2004). Once prices are converted to a common currency, national price levels should equalize (Bacchiocci & Fanelli, 2005). It also implies that the long-run domestic and foreign price levels are equal when they are measured in the same currency (Copeland, 2000; Duarte, 2001; Pakko & Pollard, 2003; Rogoff, 1996). Furthermore, PPP hypothesis implies that the prices of identical goods in different countries should equal after adjusting for the rate of exchange between currencies (Pakko & Pollard, 1996). Thus, PPP measures the relative purchasing power of currencies across countries based on the market exchange rate and domestic price indices of the countries (Olagunju, 2010).

The PPP hypothesis is known to be the by-product of the law of one price (LOP) which states that if prices are converted to the same currency, the price of any similar tradable goods (goods traded in the world market) as against non-tradable goods will be the same in every country engaged in international trade if the transaction costs are zero. If there are any price differentials, they will be eliminated by arbitrage (Taylor & Taylor, 2004). Also, Lamont and Thaler (2003) stated that if the same asset is selling for two different prices simultaneously, then arbitrage will step in, correct the situation and make themselves a profit. Thus, price differentials between countries are not sustainable in the long run. Commodity arbitrage will wipe such differential away and prices will be equalized between countries and in the process, the exchange rate will also be changed.

A number of exchange rate policies have been adopted in West Africa to improve the external competitiveness of the ECOWAS as well as expedite actions toward economic integration and introduction of a single currency in the region. To a large extent, these policies have their roots in the empirical validity of the PPP hypothesis, which implies price level equality across the various integrating countries. As a result, countries in West Africa are being viewed as an interesting group by those who hold unto the bipolar view because there exists the fixed exchange rate regime and floating exchange rate regime among ECOWAS member countries as they move toward implementing full economic integration. Specifically, studies such as (Boyer, 1978; Broda, 2004; Fleming, 1962; Friedman, 1953b; Henderson, 1979; McKinnon, 1981; Mundell, 1963; Ramcharan, 2007) argued that in a world of increasing international capital mobility, only the two extreme exchange rate regimes are likely to be sustainable either a permanently fixed exchange rate regime or a freely floating exchange rate regime.

Furthermore, studies have used the PPP hypothesis to explain the long-run relationship between the exchange rate of two currencies and the price levels of the integrating countries with mixed results. For instance studies such as Cushman (2008) and Crowder (1996) reject the validity of PPP in the long run. While studies by Cheung and Lai (1993), Cheung, Lai, and Bergman (2004), Arize, Malindretos, and Nam (2010), and Arize, Malindretos, and Ghosh (2015) suggested the validity of PPP in the long run. The few existing studies on the validity of PPP in West Africa, have all neglected the existence of bi-polar exchange rate regimes as a major influence in the formation of economic integration in the ECOWAS. Hence, this study intends to investigate the validity of the PPP hypothesis in view of the prevailing fixed and flexible exchange rate regimes in the ECOWAS (1980–2017).

Literature Review

The concept of the PPP hypothesis has long been the subject of an ongoing and lively debate in economics and some of the central problems which the has analyzed in this regard over the past three decades have only recently been resolved, while others still remain on the research agenda and still other puzzles have only recently come into the agenda (Taylor & Taylor, 2004). Therefore, based on the theoretical background literatures, Laurentiu (2013) posits that, the concept of the PPP hypothesis is based on the LOP, which implies that in the absence of transaction costs and official trade barriers, identical goods will have the same price in different markets when the prices are expressed in the same currency.

Sarno and Taylor (2002) examined the relationship between PPP and the real exchange rate using the unit root tests and cointegration test. The study found that PPP might be viewed as a valid long-run international parity condition when applied to bilateral exchange rates obtained among major industrialized countries, and the mean reversion in real exchange rate displays significant non-linearity. While the study by Václav (2010) empirically examined the validity of the relative PPP hypothesis in the EU member states using the univariate (linear and non-linear) and multivariate (panel) unit root tests. The univariate non-linear unit root tests revealed that the relative version of PPP holds for the majority of new EU member states while panel unit root tests and robustness tests based on decomposition using various specifications and country’s characteristics show clear-cut evidence that economic growth and openness are important determinants giving additional support to PPP.

Furthermore, Aloy, Boutahar, Gente, and Peguin-Feissolle (2011) examined the relationship between PPP and the long memory properties of real exchange rates. The study used a three-step testing methodology and found that most of the bilateral real exchange rates under study are not mean reverting and that the non-linear adjustment is far from being prominent and that only few bilateral real exchange rate exhibit true long memory mean-reverting properties. Also, Brissimis, Sideris, and Voumvaki (2005) tested the long-run PPP under exchange rate targeting using both VAR and cointegration techniques. The study produced biased estimate due to the omission of policy effects which are found to be significant only for Greece while for France, the test result provided evidence bearing on the effectiveness of the competitive deflation strategy pursued by the French authorities. Laureti (2001), on the other hand, confirmed that the higher the degree of economic integration, the higher the correlation between changes in the exchange rates and inflation.

The study by Chang, Chou, Lee, and Tang (2011) revisited the long-run PPP with asymmetric adjustment for G7 countries using the threshold cointegration tests. The study found a strong evidence of long-run PPP in G7 countries, with the exception of Canada. The adjustment mechanism was also asymmetric. While, Beckmann (2013) used the VAR, ECM, and dynamic stochastic simulation to examine the non-linear adjustment, PPP and the role of nominal exchange rates and prices. The result from the study indicates the nominal exchange rate is responsible for the non-linear mean-reverting behavior in real exchange rates which mainly drives overall adjustments. Similarly, the study also confirmed recent results that half-life times of real exchange rate shocks are significantly smaller than the consensus benchmark of 3–5 years.

Also, Hussein (2015) used the Engle and Granger cointegration test to empirically test for the validity of the PPP theory for the Canadian dollar and the US dollar exchange rates. The result of the study showed that there is no cointegration between actual exchange rates and PPP rate, suggesting that there is no long-run relationship between the Canadian dollar and the US dollar exchange rates. However, Laurentiu (2013) used the augmented DF unit root tests and two steps cointegration Engle and Granger test to examine the validity of PPP during the great financial crisis. The study found evidence in favor of PPP during the crisis period for the UK pound at 1 percent confidence interval, while for the euro and Japanese yen were both at a 5 percent confidence interval. Furthermore, for the Engle and Granger cointegration test, the study also provided evidence of PPP holding in the long run only for the euro at a 5 percent confidence interval during the crisis period.

In the same vein, Huang and Yang (2015) used the Pesaran panel unit root test to examine the relationship between European exchange rate regimes and PPP in eleven European countries. The study provided an evidence for mean reverting in the real exchange rate is much weaker in the post-1998 euro period than in the pre-euro. This was in contrast to the result obtained for the four countries not using euro: Norway, Sweden, Switzerland, and the UK. Thus, the evidence for the mean reverting in the real exchange rate is strong in both pre- and post-euro (post-1998) periods.

Furthermore, Christidou and Panagiotidis (2010) used unit root test and panel unit root tests (Pesaran, 2007) and stationarity test (Hadri & Kurozumi, 2008) to investigate PPP and the European single currency. The result obtained from the panel estimate is inconclusive. The panel stationarity test failed to support PPP while the panel unit root tests fail to reject PPP for the whole sample and for the period before the introduction of a single currency. Similarly, Morley and Lo (2015) used the Bayesian method of non-linear threshold to investigate the non-linear exchange rate dynamics and PPP persistence. The result for the exchange rate from the G7 countries suggest the general support for non-linearity in exchange rate with the strength of the evidence depending on which country pair is been considered.

However, Huang and Yang (2015) found that contrary to the widely believe that following the adoption of the euro, the long run PPP hypothesis is more likely to hold within the euro countries was rejected. This is because the mean-reverting in the real exchange rates is much weaker in the post-1998 euro period than in the pre-euro period. However, the study also found that four countries not using the euro such as Norway, Sweden, Switzerland and the UK showed the evidence of mean reverting in real exchange rates is very strong in both pre- and post-euro periods.

The study by Yildirim (2017) test the validity of the PPP hypothesis between Turkey and its major trading partners of the EU, Russia, China and the US. The study found that non-linear unit root tests showed stronger evidence in favor of the validity of the PPP hypothesis when compared to the conventional unit root test only if non-linearities in real exchange rates are correctly specified. Furthermore, the study reveal that the real exchange rates of the countries having some form of trade liberalization are more likely to behave as linear stationary process. In the same vein, Ma, Li, and Park (2017) shows the validity of the PPP hypothesis among the East Asian countries of China, Japan and South Korea using the quantile unit root and quantile cointegration tests.

Furthermore, Arize et al. (2015) used the fully modified OLS, cointegration tests and ECM to investigate PPP symmetry and proportionality from 116 countries. The result from the long-run cointegration analysis, short-run dynamics and half-lives, all provided evidence for long-run PPP. The symmetry condition is largely supported and when imposed on prices, the proportionality condition is supported in a majority of cases. While, Bahmani-Oskooee, Chang, and Lee (2015) examined the validity of the PPP hypothesis among eleven emerging market economies. The study adopted a panel stationarity test with both sharp and smooth breaks and found that the methodology adopted provided a strong support for the validity of PPP among the eleven emerging market economies which was contrary to the empirical results of several univariate unit root tests.

The study by Arize et al. (2010) used multivariate ECM to estimate cointegration, dynamic structure and the validity of PPP in African countries. The result from the long-run cointegration analysis, short-run error correction models, persistence profile analysis and variance decomposition all confirmed the validity of PPP in these moderate to high inflation countries. However, estimates of the half-life deviation from PPP are found to be outside the range suggested by Rogoff (1996). Also, Mishra and Sharma (2010) used the panel unit root tests to investigate the real exchange rate behavior and optimum currency area in East Asia. The study found some supportive evidence for GPPP which in turn, provided support for the feasibility of the optimum currency area in East Asia. However, the presence of asymmetries in the process, through which countries adjust to shocks in the system indicate that still higher level of economic integration is required to strengthen the case of a currency union. More importantly, the overall results appear to be invariant to the choice of a base currency and therefore it provided support to the argument that both US dollar and Japanese yen are important for East Asia while considering the case of a currency union.

Similarly, Su, Chang, and Tsangyao (2011) examined the validity of PPP for fifteen Latin American countries using the stationarity test with a Fourier function. The empirical result from the univariate unit root tests indicate that PPP does not hold for these fifteen countries under study. However, a stationarity test with a Fourier function indicate that PPP is valid individually for four of these fifteen Latin American countries and they are Brazil, Chile, Ecuador and Uruguay. In the same vein, Yusuf and Nasim (2011) used the unit root and cointegration tests to investigate the linkages between goods and assets markets in West African countries. The study showed that few African countries support PPP with the both bivariate and multivariate approach. Also, Bahmani-Oskooee, Kutan, and Zhou (2008) used the ADF and KSS unit root tests to examine whether or not real exchange rate follows a non-linear mean-reverting process in developing countries. The study found that the unit root test supported the PPP theory twice in many developing countries as the ADF unit root test. Suggesting that non-linear adjustment toward PPP in developing countries is an important phenomenon. The countries characteristics indicate that PPP holds more often for high inflation countries and for countries with high flexibility in their exchange rates.

In the same vein, Olagunju (2010) used the unit root tests, cointegration test, and VAR to empirically examine the PPP hypothesis in West Africa. The study found the evidence of the validity of PPP among the ECOWAS countries using the panel VAR while the VAR result for individual countries showed the absence of the validity of PPP which implies an inconclusive result. While, Olayungbo (2011) examined the validity of the PPP hypothesis and the degree of conformity to PPP in sixteen selected sub-Saharan African countries for the period of 1980 to 2005 using both ADF and panel unit root tests. The study found that only five countries from the selected sixteen countries had no unit root problem in their exchange rates. Hence, in the light of economic integration, only the five countries could go ahead with the elimination of all trade barriers that could enhance economic integration.

Methodology

This study is based on the theory of optimum currency area pioneered by Kenen (1969), McKinnon (1963), Mundell (1961) and on Alesina and Barro (2002) who operationalize the optimum currency area theory and added new elements to Mundell’s optimality criteria in their empirical study where competitive firms produce output using a production function as stated in Dixit and Stiglitz (1977), Spence (1976). The output of firm i is given by:

Y_{i} = {A L}_{i}^{1 - α} . \sum_{j = 1}^{N^{I} + N^{I I}} X_{j i}^{α}

(3.1)

where A > 0 is a productivity parameter, $L_{i}$ is firm i’s employment of labor, 0 < α < 1, $X_{j i}$ is the amount of intermediate input of type j used by firm i, and N is the number of types of intermediate goods available. From equation (3.1), there are two countries, where country I produces the intermediate good $\begin{matrix} j & = & 1 & , & . & . & . & , & N^{I} \end{matrix}$ and country II produces the intermediate goods. $\begin{matrix} j & = & N^{I} & + & 1 & , & . & . & . & , & N^{I} & + & N^{I I} \end{matrix}$ Intermediate inputs are differentiated goods and, to simplify this set up, there is no overlap in the range of goods produced by the two countries. A country that is larger in terms of number of products is assumed to be larger in the same proportion in terms of labor: $\frac{N^{I}}{L^{I}} = \frac{N^{I I}}{L^{I I}}$ and the ratios are normalized to 1. Within each economy, labor markets are perfectly competitive; however, there is no migration across borders.

Also, there is free trade and no transaction costs for shipping goods within each country. However, the shipping of an intermediate good across country borders entails transaction costs. For each unit of intermediate goods shipped from country I to country II or the reverse, 1 –– b units arrive, with 0 < b < 1. Also, each firm maximizes profit, taking as given the real wage rate, W, and the price, $p_{j}$ , of each type of intermediate good. The prices are all measured in units of the final product and the first-order conditions for the choices of intermediate inputs are:

\begin{array}{l} {A α L}_{i}^{1 - α} X_{j i}^{α - 1} = p_{j}, j = 1 \begin{matrix} , & . & . & . & , \end{matrix} N^{I} \\ {A α L}_{i}^{1 - α} X_{j i}^{α - 1} = (\frac{p_{j}}{1 - b}), j \\ = N^{I} + 1 \begin{matrix} , & . & . & . & , \end{matrix} N^{I} + N^{I I} \end{array}

(3.2)

Every producer of final goods will use all $N^{I} + N^{I I}$ varieties of the intermediate inputs as long as all of the prices are finite and b < 1. The final output is a homogenous good that can be used for consumption or to produce intermediate goods. Since consumable goods are identical and their transportation entails no cost hence, their prices are the same everywhere and are normalized to one.

Prices of intermediate goods produced by both country I and II depend on the extent of their factor endowment. If there is only one potential producer in each sector, the constant-elasticity demand function implied by the Spence-Stiglitz formulation determines the price of each intermediate good to be. $\frac{1}{α}$ More generally, other forms of imperfect competition will lead to mark-up price, $p_{j} = μ_{j}$ with 1 < $μ_{j}$ $\frac{1}{α}$ . Substituting the markup price into equation (3.2) determines the quantities of intermediate good j demanded by firm i in country I:

\begin{array}{l} X_{j i} = {(A α / μ^{I})}^{1 / (1 - α)} . L_{i}, j \\ = 1 \begin{matrix} , & . & . & . & , \end{matrix} N^{I}, \\ X_{j i} = {[(A α / μ^{I I}) . (1 - b)]}^{1 / (1 - α)} . L_{i}, j \\ = N^{I} + 1 \begin{matrix} , & . & . & . & , \end{matrix} N^{I} + N^{I I} \end{array}

(3.3)

Aggregating over firms lead to the level of aggregate output in country I where:

\begin{array}{l} Y^{I} = A^{1 / (1 - α)} α^{α / (1 - α)} L^{I} \\ [{(\frac{1}{μ^{I}})}^{α / (1 - α)} N^{I} + {(\frac{1 - b}{μ^{I I}})}^{α / (1 - α)} N^{I I}] \end{array}

(3.4)

From the perspective of incentives to use the intermediate inputs, markup pricing $(μ^{I I} > 1)$ and trading cost (b > 0) have similar and reinforcing effects. The monetary value of these imported goods is determined by multiplying the quantity of intermediates by $μ^{I I} / (1 - b) :$

The value of intermediate goods imported by country I from II is given as follows:

p_{i m I \leftarrow I I} = {(A α)}^{1 / (1 - α)} {(\frac{1 - b}{μ^{I I}})}^{α / (1 - α)} N^{I} N^{I I}

(3.5)

The corresponding value of the exports of intermediate goods from country I to country II is obtained after multiplying by $μ^{I} / (1 - b)$ and obtain the following value:

p_{e x I \to I I} = {(A α)}^{1 / (1 - α)} {(\frac{1 - b}{μ^{I}})}^{α / (1 - α)} N^{I} N^{I I}

(3.6)

Equations (3.5) and (3.6) imply that balanced trade in intermediate goods results if $μ^{I} = μ^{I I}$ . Otherwise, any net surplus or deficit in the trade of intermediate goods is matched by an equal size net deficit or surplus in the trade of final products.

The only firms in country I that makes profits in equilibrium are the monopolistic producers of intermediate goods numbered $j = 1 \begin{matrix} , & . & . & . & , N^{I} \end{matrix}$ . The ownership rights in these firms are assumed to be distributed evenly across the households of country I. In this case, country I has a representative household, whose net income and consumption correspond to gross output less the production of intermediates plus the country’s net surplus in intermediate trade with country II. The resulting equation for consumption per person is given below as:

\begin{array}{l} \frac{C^{I}}{N^{I}} = A^{1 / (1 - α)} α^{α / (1 - α)} . \\ {\begin{cases} {(\frac{1}{μ^{I}})}^{1 / (1 - α)} . [(μ^{I} - α) . N^{I} + α . (μ^{I} - 1) Χ {(1 - b)}^{α / (1 - α)} . N^{I I}] \\ + (1 - α) . {(\frac{1 - b}{μ^{I I}})}^{α / (1 - α)} . N^{I I} \end{cases}} \end{array}

(3.7)

If $μ^{I} = μ^{I I} = μ$ , then equation (3.7) is simplifies as:

\begin{array}{l} \frac{C^{I}}{N^{I}} = A^{1 / (1 - α)} α^{α / (1 - α)} . (μ - α) . \\ {(\frac{1}{μ})}^{1 / (1 - α)} Χ [N^{I} + {(1 - b)}^{α / (1 - α)} . N^{I I}] \end{array}

(3.8)

For a given country size and trading costs, the distorting element in the model comes from the markup pricing of the intermediate goods in the two countries. A social planner for the world, who takes as given the sizes of countries and bears the costs of trade b, would price each of these goods at marginal costs, 1. Output denoted by ${(Y^{I})}^{*}$ , would then be higher than before, corresponding to settingin $μ^{I} = μ^{I I} = 1$ equation (3.4):

\begin{array}{l} {(Y^{I})}^{*} = A^{1 / (1 - α)} α^{α / (1 - α)} N^{I} . \\ {N^{I} + {(1 - b)}^{α / (1 - α)} . N^{I I}} \end{array}

(3.9)

If the markup ratios are the same in the two countries, $μ^{I} = μ^{I I} = μ$ , then the short fall of production due to markup pricing is given from equations (3.4) and (3.9) by:

\frac{Y^{I}}{{(Y^{I})}^{*}} = {\frac{1}{μ}}^{α / (1 - α)} < 1

(3.10)

In this model, consumption per person (and, hence, the utility of the representative consumer) would be maximized if the entire world consisted of one country, because cross-border transaction costs would then be eliminated.

Suppose, this study consider two countries, i and j, which naturally trade a lot because they are close together, speak the same language, or have other characteristics that reduce trading costs. Then, this study wishes to consider whether this pair of countries would be especially motivated to reduce the financial costs of trading by adopting a common currency which is the highest form of economic integration. To achieve economic integration depends on whether the marginal effects of 1 – b on $C^{I}$ , which equation (3.7) shows to be positive, rises or falls as 1 – b increases.

\frac{{\partial C}^{I}}{\partial (1 - b)} ~ {(1 - b)}^{(2 α - 1) / (1 - α)}

(3.11)

Hence, the second derivative is positive or negative depending on whether $α$ is or less than one-half. If $α > \frac{1}{2}$ , then the intermediates are relatively close substitutes, and the dominant effect is that a lowering of b saves on the trading costs incurred (which are more important when the volume trade is large). If $α < \frac{1}{2}$ , then the intermediates are poor substitutes, and the dominant effect involves the high marginal product of intermediates when the trading cost is high. Thus, to get the expected results whereby countries that naturally trade a lot would particularly benefit from using a common currency.

To introduce nominal elements and a possible role for monetary policy, Alesina and Barro (2002) used a simple setting in which the nominal process of the intermediate goods involve some stickiness, whereas the prices of the final goods are flexible. For goods produces in country I, $p_{j} (j = 1 \begin{matrix} , & . & . & . & , \end{matrix} N^{I})$ be the nominal price of the jth intermediate good and p be the nominal price of final goods (and, hence, consumer goods), all of which sell at one price. The study assume that p is determined through some stochastic process by country I’s monetary authority. If the nominal prices of the intermediate goods were flexible, the preceding analysis would go through, with the relative price of each good, $p_{j} / p$ , equated to the markup ratios, $μ^{I}$ .

Suppose, however, that the producer of intermediate goods in each sector j sets the nominal price $p_{j}$ one period in advance. Then, to find the nominal price that the provider would choose, then, the study have to know the probability distribution of p. As a first approximation, the price will be set as:

p_{j} \approx μ^{I} . S p

(3.12)

where $S p$ is one-period-ahead expectation of p. If p exceeds $S p$ , then $p_{j} / p = μ^{I} . (S P / p)$ falls correspondingly below the intended markup level, $μ^{I}$ , and the demand for country I’s intermediates rises.

Country II uses a different currency and denominates its prices, $p_{j}^{*} (j = N^{I} + 1 \begin{matrix} , & . & . & . & , \end{matrix} N)$ and $p^{*}$ , in units of that currency. It is assume that $p^{*}$ is determined through some stochastic process by country II’s monetary authority. It is also assume that the nominal exchange rate, E, between the currencies of countries I and II is flexible and adjusts so that the standard PPP condition holds:

E = \frac{p}{p^{*}}

(3.13)

This condition is consistent with the assumption that final product is homogenous and internationally tradable with zero transaction costs.

As in country I, the nominal, the nominal price of each of country II’s intermediate goods, $p_{j}^{*}$ for $j = N^{I} + 1 \begin{matrix} , & . & . & . & , N, \end{matrix}$ is set one period in advance. The price-setting formula is analogous to that given in equation (3.12):

p_{j}^{*} \approx μ^{I I} . S p^{*}

(3.14)

Therefore, $p^{*}$ if exceeds ${S p}^{*}$ , then $p_{j}^{*} / p^{*} = μ^{I I} . ({S p}^{*} / p^{*})$ falls correspondingly below the intended markup level, $μ^{I I}$ , and the demand for country II’s intermediates rises. Note that the nominal price in country I’s money of each of country II’s intermediate goods is given by:

$p_{j} = {S p}_{j}^{*}$ , for.

j = N^{I} + 1 \begin{matrix} , & . & . & . & , N \end{matrix}

(3.15)

The PPP hypothesis condition in equation (3.13) implies accordingly that the relative price of each of these goods is:

p_{j} / p = p_{j}^{*} / p^{*}

(3.16)

Thus, buyers in both countries face the same relative prices for the intermediate goods produced in country II and for the intermediate goods produced in country I.

Model Specification on the Validity of the PPP Hypothesis in the ECOWAS

Drawing from the theoretical framework, this study consider the LOP which relates exchange rates and price level as the foundation of this study.

In that regard, the LOP states that for any good i:

P_{i} = {E P}_{i}^{*}, i = 1, \dots, N .

(3.17)

where $P_{i}$ is the domestic-currency price of good i

$P_{i}^{*}$ is the foreign currency price of good i

$E_{}^{}$ is the exchange rate defined as the home-currency price of foreign currency

$i_{}^{}$ denotes the type of product (i = 1, …, N)

The absolute PPP implies that the nominal exchange rate between two currencies is equal to the ratio of national price levels. Following Rogoff (1996) absolute PPP requires:

\sum P_{i} = E \sum P_{i}^{*}, i = 1, \dots, N .

(3.18)

E = \frac{P_{i}}{P_{i}^{*}} i = 1, \dots, N .

(3.19)

Also, the relative PPP hypothesis states that the exchange rate should bear a constant term proportional to the ratio of national price levels, in the form of:

E = \frac{{k P}_{i}}{P_{i}^{*}}

(3.20)

Where k is the constant parameter.

PPP hypothesis, implies a constant real exchange rate (Q):

Q = \frac{{E P}_{i}}{P_{i}^{*}}

(3.21)

Taking the logarithms of both sides of the equations (3.19) and (3.20), we then obtain:

e_{} = c_{} + p^{*} - p_{}

(3.22)

where $e_{}, p^{*}, p_{}$ are the logarithms of $E_{}, P^{*}, P_{}$ and $c_{} = {\ln (k) = 0}_{}$ under absolute PPP. Under either of the variation of PPP, a change in the ratio of price levels implies a proportionate change in the nominal exchange rate, such that:

Δ e = Δ p^{*} - {Δ p}^{}

(3.23)

Equation (3.23) states that the percentage change in the nominal exchange rate is equal to the difference between the inflation rates in the domestic and the foreign country. Following the logarithms to equation (3.22), the linear version of the PPP relationship has been stated as:

e_{t} = α_{0} + α_{1} p_{t} + α_{2} p_{i}^{*} + U_{t}

(3.24)

The panel version of equation (3.24) is stated as follows:

e_{i t} = α_{0} + α_{1} p_{i t} + α_{2} p_{i t}^{*} + U_{i t}

(3.25)

where $e_{i t}$ the logarithm of the nominal exchange rate is expressed in terms of the domestic price of foreign exchange, $p_{i t}$ and $p_{i t}^{*}$ are the natural logarithm of the domestic and foreign prices, respectively.

Therefore, to establish the validity of the PPP hypothesis, the study employ the use of unit root tests, cointegration test, panel unit root tests, and panel cointegration test respectively to validate the existence of PPP among ECOWAS countries.

Analysis and Interpretation of Results

This section presents the results testing the validity of PPP hypothesis in the ECOWAS using both the country specific unit root tests, cointegration test, as well as, the panel unit root tests and the panel cointegration test. The style of presentation and analysis is simply tabulation of results and at the end of which a brief discussion and econometric significance of the estimated results are made.

Tests for the Country-Specific Validity of the PPP Hypothesis in the ECOWAS

Following the linear version of the PPP hypothesis as stated in equation (3.24), the results of the test for the individual country specific validity of the PPP hypothesis in the ECOWAS are presented in Table 1 using the Augmented Dickey-Fuller (ADF) test, Phillips-Perron (PP) test, Kwiatkowski-Phillips-Schmidt-Shin (KPSS) test and Unit Root with Breakpoint (URB) test. Therefore, Table 1 showed that the PPP hypothesis is valid for Benin republic using the ADF test (t = −3.1914; p < 0.05), KPSS test (t = 0.7223, 0.1467; p < 0.05), and URB test (t = −7.5747, −5.6239; p < 0.01). The results obtained in respect of the validity of the PPP hypothesis for Benin Republic is applicable to all other CFA member countries since they all operate the same fixed exchange rate regimes except Guinea-Bissau which later joined the CFA in 1997. Thus, the PPP validity in respect of Guinea-Bissau was confirmed using PP test (t = −2.8973; p < 0.10), KPSS test (t = 0.7994, 0.2511; p < 0.01) and URB test (t = −7.0760, −6.8529; p < 0.01).

Furthermore, Table 1 revealed that the PPP hypothesis is valid for Cape Verde using the ADF test (t = −2.6744; p < 0.10), PP test (t = −3.6842, p < 0.01; t = −3.2099, p < 0.10) and KPSS test (t = 0.3877, 0.1310; p < 0.10) while the PPP hypothesis is valid in the Gambia using KPSS test (t = 0.7023 & 0.1460; p < 0.05) and URB test (t = −5.6139; p < 0.01) respectively. Also, the study revealed that the PPP hypothesis is valid in Ghana using PP test (t = −3.8760, −5.8220; p < 0.01), KPSS test (t = 0.9315, 0.2303; p < 0.01), and URB test (t = −7.3732, p < 0.01; t = −5.3148, p < 0.05). However, the study confirmed the validity of the PPP hypothesis in Guinea is only observed using KPSS test (t = 0.8810, p < 0.01; t = 0.1750, p < 0.05) only.

In the same vein, Table 1 revealed that the PPP hypothesis is valid in Liberia using the PP test (t = −4.5905, −5.3175; p < 0.01), KPSS test (t = 0.4769, 0.1687; p < 0.05) and URB test (t = −5.9906, −7.2243; p < 0.01), and also, confirmed that the validity of the PPP hypothesis in Nigeria was achieved using the KPSS test (t = 0.9251, 0.2259; p < 0.01) only. Finally, this study supports the validity of the PPP hypothesis in Sierra Leone using the PP test (t = −3.0598; p < 0.05), KPSS test (t = 0.8704, 0.2451; p < 0.01) and URB test (t = −5.3178, −11.7764; p < 0.01).

Therefore, given the country specific validity of the PPP hypothesis as shown in Table 1 and in view of the economic integration initiatives of the ECOWAS member. The findings of the study supports the assertion that ECOWAS could forge ahead with the planned economic integration initiatives among its member countries.

Tests for the Validity of the PPP Hypothesis in the ECOWAS Using Panel Unit Root Tests

Following the panel version of the PPP hypothesis as specified in equation (3.25), the results for the panel validity of the PPP hypothesis using the panel unit root tests on the pooled exchange rates of all the ECOWAS members countries are presented in Table 2. The Levin, Lin and Chu (LLC) panel unit root test, Im, Pesaran and Shin (IPS) panel unit root test, Fisher’s Panel ADF and PP tests as well as Hadri LM test were used to test the validity of the PPP hypothesis in the panel data. Since the characteristics of the 15 ECOWAS countries involve in this study are likely to be homogenous in nature, hence the need to confirm the validity of the PPP hypothesis using all the aforementioned panel unit root techniques.

The results presented on Table 2 confirmed the validity of the PPP hypothesis using the panel unit root tests which showed that the pooled exchange rates of the ECOWAS member countries are stationary at levels using the panel unit root tests. Specifically, the LLC with individual intercept (t = −5.97117, p < 0.0000), IPS with individual intercept (t = −3.30564; p < 0.0000), Fisher ADF with individual intercept (t = −3.43996; p < 0.0003), Fisher PP with individual intercept (t = −5.91557; p < 0.0000). This findings of the validity of the PPP hypothesis is in line with earlier studies such as (Arize, Malindretos, & Ghosh, 2010, 2015; Coakley & Snaith, 2004; Mishra & Sharma, 2010; Sugimota, 2009). However, the Hadri LM test rejects the validity of the PPP hypothesis.

Table 1.

Tests for the Country-Specific Validity of the PPP Hypothesis in the ECOWAS

	Augmented Dickey-Fuller (ADF) Test			Phillips-Perron (PP) Test			Kwiatkowski-Phillips-Schmidt-Shin (KPSS) Test		Unit Root with Breakpoint (URB) Test
ECOWAS Member Countries	With Intercept	With Trend and Intercept	None	With Intercept	With Trend and Intercept	None	With Intercept	With Trend and Intercept	With Intercept	With Trend and Intercept
Benin	−3.1914**	−1.6666	0.6745	−2.4260	−2.5601	0.9113	0.7223**	0.1467**	−7.5747*	−5.6239*
Burkina Faso	−3.1914**	−1.6666	0.6745	−2.4260	−2.5601	0.9113	0.7223**	0.1467**	−7.5747*	−5.6239*
Cape Verde	−2.6744***	−2.1066	0.5927	−3.6842*	−3.2099***	1.1284	0.3877***	0.1310***	−3.9065	−3.9498
Cote d’Ivoire	−3.1914**	−1.6666	0.6745	−2.4260	−2.5601	0.9113	0.7223**	0.1467**	−7.5747*	−5.6239*
The Gambia	−0.7074	−2.1096	0.9064	−2.0111	−2.3271	1.9543	0.7023**	0.1460**	−3.2016	−5.6139*
Ghana	−2.2878	−0.9403	−1.1739	−3.8760*	−1.2089	−5.8220*	0.9315*	0.2304*	−3.2016	−5.6139*
Guinea	−1.2620	−0.8587	1.4062	−1.9176	−1.8076	1.6163	0.8810*	0.1750**	−2.5841	−2.0094
Guinea−Bissau	−2.6353	−3.1142	0.7608	−2.8973***	−0.5653	0.8089	0.7994*	0.2511*	−7.0760*	−6.8529*
Liberia	−0.3366	−1.2881	0.5674	−4.5905*	−5.3175*	0.2229	0.4769**	0.1687**	−5.9906*	−7.2243*
Mali	−3.1914**	−1.6666	0.6745	−2.4260	−2.5601	0.9113	0.7223**	0.1467**	−7.5747*	−5.6239*
Niger	−3.1914**	−1.6666	0.6745	−2.4260	−2.5601	0.9113	0.7223**	0.1467**	−7.5747*	−5.6239*
Nigeria	−1.2830	1.0236	−0.2459	−1.8534	−0.9622	1.1284	0.9251*	0.2259*	−1.9739	−1.9739
Senegal	−3.1914**	−1.6666	0.6745	−2.4260	−2.5601	0.9113	0.7223**	0.1467**	−7.5747*	−5.6239*
Sierra Leone	−0.7852	−2.3900	0.9980	−3.0598**	−0.6644	1.3402	0.8704*	0.2451*	−5.3178*	−11.7764*
Togo	−3.1914**	−1.6666	0.6745	−2.4260	−2.5601	0.9113	0.7223**	0.1467**	−7.5747*	−5.6239*
Critical Values
1% = *	−3.752946	−4.416345	−2.669359	−3.632900	−4.243644	−2.632688	0.739000	0.216000	−4.949133	−5.347598
5% = **	−2.998064	−3.622033	−1.956406	−2.948404	−3.544284	−1.950687	0.463000	0.146000	−4.443649	−4.859812
10% = ***	−2.638752	−3.248592	−1.608495	−2.612874	−3.204699	−1.611059	0.347000	0.119000	−4.193627	−4.607324

Source: Author’s computation.

Table 2.

Panel Validity of the PPP Hypothesis in the ECOWAS

Levin, Lin and Chu Test					Im, Pesaran and Shin Test			Fisher ADF Test				Fisher PP Test				Hadri LM Test
Variable	Individual Intercept	Individual Intercept with Trend	None	Individual Intercept		Individual Intercept with Trend	Individual Intercept		Individual Intercept with Trend	None	Individual Intercept		Individual Intercept with Trend	None	Individual Intercept		Individual Intercept with Trend
Exchange Rates	-5.97117	−1.20557	1.93057	−3.30564		−0.19265	−3.43996		−0.26927	3.07334	−5.91557		−0.24182	3.72809	12.1685		10.4177
(P-Value)	(0.0000)	(0.1140)	(0.9732)	(0.0005)		(0.4236)	(0.0003)		(0.3939)	(0.9989)	(0.0000)		(0.4045)	(0.9999)	(0.0000)		(0.0000)

Source: Author’s computation.

Test for the Validity of the PPP Hypothesis in the ECOWAS Using the Panel Cointegration Tests

The Pedroni panel cointegration tests was conducted on the pooled exchange rates, domestic inflation rates (as proxy for domestic price) and foreign inflation rates (for the purpose of this study, inflation rates of the US and France were used as proxy for foreign prices) of all the ECOWAS member countries. Table 3 presents the Pedroni panel cointegration tests which supports the validity of the PPP hypothesis in the ECOWAS with only four statistic as shown by panel-rho statistic (t = −2.625006; p < 0.0043) and panel-pp statisctic (t = −3.367056; p < 0.0004), weighted rho-statistic (t = −2.650040; p < 0.0040) and weighted pp-statistic (t = −3.685697; p < 0.0001) while the remaining Pedroni statistic reject the validity of the PPP hypothesis in the ECOWAS leading to an inconclusive result. The findings of cointegration test is in line with earlier study by (Agyapong & Adam, 2012) which revealed that the PPP hypothesis is inconclusive in the ECOWAS.

Conclusion and Recommendation

In conclusion, the study found that all the ECOWAS member countries individually satisfy the condition for the validity of the PPP hypothesis given the stationarity of their real exchange rates at levels. In the same vein, the panel unit root tests showed some degree of validity of the PPP hypothesis among in the ECOWAS when both the fixed and flexible exchange rate regimes were pooled together in a panel. However, the Pedroni panel cointegration tests reject the validity of the PPP hypothesis because few pedroni cointegration statistic support long-run cointegration in the ECOWAS exchange rates.

Therefore, given the individual country validity of the PPP hypothesis in the ECOWAS, the study suggests that the ECOWAS can cautiously forge ahead with the implementation of their economic integration initiatives in view of the prevailing exchange rate regimes in the ECOWAS.

Table 3.

Pedroni Panel Cointegration Test with Individual Intercept

	Statistic Probability	Weighted Statistic Probability
Panel v-Statistic	−1.664457 0.9520	−1.271937 0.8983
Panel rho-Statistic	−2.625006 0.0043	−2.650040 0.0040
Panel PP-Statistic	−3.367056 0.0004	−3.685697 0.0001
Panel ADF-Statistic	−1.100184 0.1586	−0.673956 0.2502
Group rho-Statistic	0.015850 0.5063
Group PP-Statistic	−1.357663 0.0873
Group ADF-Statistic	0.596974 0.7247

Source: Author’s computation.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

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Validity of Purchasing Power Parity (PPP) Hypothesis in the Ecowas (1980–2017)

Abstract

Abstract

Keywords

Introduction

Literature Review

Methodology

Model Specification on the Validity of the PPP Hypothesis in the ECOWAS

Analysis and Interpretation of Results

Tests for the Country-Specific Validity of the PPP Hypothesis in the ECOWAS

Tests for the Validity of the PPP Hypothesis in the ECOWAS Using Panel Unit Root Tests

Tests for the Country-Specific Validity of the PPP Hypothesis in the ECOWAS

Panel Validity of the PPP Hypothesis in the ECOWAS

Test for the Validity of the PPP Hypothesis in the ECOWAS Using the Panel Cointegration Tests

Conclusion and Recommendation

Pedroni Panel Cointegration Test with Individual Intercept

Footnotes

Declaration of Conflicting Interests

Funding

References