Currency harmonisation in the Southern African Development Community: a pathway to addressing the PPP puzzle

Nominal exchange rate (NER) between any two economies is dictated by the macroeconomic fundamentals of such economies, and its behaviour is particularly governed by the macroeconomic policies in each of these economies. One notable factor dictating the NER dynamics is the purchasing power parity (PPP). Expectedly, PPP has been widely accepted as the yardstick for most exchange rate models since the demise of the Bretton Woods system in 1971. The PPP hypothesis posits that in the long-run, bilateral NER between two national currencies must converge to an equilibrium level commensurate with the relative price levels in the countries involved. That is, bilateral real exchange rate (RER)—obtained by deflating bilateral NER by the associated relative prices—has a tendency to revert to its mean value in the long-run.

At the heart of the PPP doctrine lies the so-called ‘law of one price’ (LOP) which asserts that in competitive markets (free of transaction costs and barriers to trade), identical goods expressed in a common currency must be sold at the same price across countries (Krugman et al. 2018). Therefore, if parity holds for a continuum of individual goods in the reference basket (i.e., LOP holds), then there must be a higher likelihood that goods market arbitrage stimulates parity in the general price level (Krugman et al. 2018, Rogoff, 1996, Taylor and Taylor, 2004).

Despite its widely accepted theoretical background, the verdict as to whether or not the PPP hypothesis holds in practice has not been unanimously supported by empirical data thus far—herein, lies the so-called ‘PPP puzzle’. Prior research has attributed this sparse empirical consensus to a number of factors, including transaction costs (Alba and Papell, 2007, Engel and Rogers, 1996, 2001, Lopez and Papell, 2007, Wu et al. 2011, Yilanci and Eris, 2013); short data span (Abuaf and Jorion, 1990, Lothian and Taylor, 1996, Murray and Papell, 2002, 2005, Taylor, 2001); low statistical power problem (Abuaf and Jorion, 1990, Frankel, 1985, Lothian and Taylor, 1996, Murray and Papell, 2005); heterogeneities among the cross-sectional units (Al-Gasaymeh and Kasem, 2015, Alba and Papell, 2007, Cheung and Lai, 2000, Wu et al. 2011).

To this end, a growing number of studies have argued that geographical proximity could facilitate trade via lower transportation costs and thus enhance the validity of the PPP hypothesis in practice (the so-called ‘border effect’). Moreover, one well-documented solution to the short sample problem in the absence of long-horizon data is the use of panel test techniques which permits cross-section variation (Alba and Papell, 2007, Lothian and Taylor, 1996, Taylor, 2003); while accounting for nonlinearities in the data could circumvent the low power problem (Arize, 2011, De Villiers and Phiri, 2022, Kapetanios and Shin, 2008, Kapetanios et al. 2003, Kruse et al. 2012, Otero and Smith, 2017, Taylor, 2001). Meanwhile, a differential consideration of country groups premised on their homogenous characteristics-including, inter alia, economic conditions and geographic location has been explored in the literature (Al-Gasaymeh and Kasem, 2015, Alba and Papell, 2007, Cheung and Lai, 2000, Christidou and Panagiotidis, 2010, Huang and Yang, 2015, Papell and Theodoridis, 2001, Wu et al. 2011). These potential heterogeneities between diverse groups of economies manifest through the failure of the PPP hypothesis to hold in cross-country settings. In response to spuriously unfavourable empirical evidence of PPP hypothesis due to country heterogeneity, revelations have emerged incriminating the ‘numéraire currency’ effect. That is, the choice of the numéraire currency plays a crucial role in the empirical validation of the PPP hypothesis. Briefly, the literature is replete with evidence indicating more support for long-run PPP when other currencies (e.g., European currencies), rather than the USD, are adopted as the base currency (see e.g., Huang and Yang, 2015, Papell and Theodoridis, 2001).^{Footnote 1} Surprisingly, almost all of these studies have been exclusively confined to the experience of advanced economies (Coakley and Fuertes, 2000, Huang and Yang, 2015, Papell and Theodoridis, 2001).

The SADC region presents an intriguing case study, not solely due to its status as Africa’s largest economic bloc but also due to the unique policy-level challenges it faces. This study, therefore, addresses these critical issues impacting the SADC economies. First, SADC envisages to achieve macroeconomic convergence, stable and harmonised exchange rate systems (Zerihun and Breitenbach, 2016, 2018), and ultimately creating a Monetary Union as enshrined in a number of regional agreements, including the SADC Protocol on Trade. Despite successfully establishing the SADC Free Trade Area (FTA) in 2008, as one facet for deepening economic integration, the regional body has missed its targets of establishing a monetary union (in 2016) and adopting a single currency (in 2018). It is the lack of consensus on the validity of PPP, coupled with our resolve to contribute to the debate on the potential existence of an optimum currency area (OCA) in SADC that particularly motivates this study. While experiences from the eurozone offer excellent lessons for SADC policymakers, the underlying heterogeneities between these two sets of economies call for an explicit investigation of OCA theory in SADC via testing for convergence in macroeconomic fundamentals—PPP.

Moreover, the primary advantage of using the ZAR relative to the other regional currencies resides in the fact that South Africa is the largest economy in the region and is naturally the largest regional trading partner for the other member states. Notably, the ZAR is the official settlement currency for the regional cross-border real-time gross settlement system in the SADC region (SADC-RTGS) and indeed, the second-highest denominated currency (after the USD) in intra-SADC transactions, accounting for over 35% of the region’s cross-border payments. Therefore, investigating the empirical validity of the PPP, while taking into account the numéraire currency effect, is of peculiar significance for SADC as it can serve as a valuable framework for selecting a common currency for the proposed currency union in the region. Moreover, despite the extant PPP literature, there is still a significant gap in reconciling empirical evidence with the PPP theoretical predictions in Africa in general, and SADC region in particular. Consequently, monetary policymakers in the region continue to pursue exchange rate policies largely premised on the assumption that PPP holds. This is lamentable, as it can lead to the adoption of misleading policies that may not successfully address the underlying issues causing the exchange rate discrepancies.

To sum up, in an attempt to reconcile the PPP puzzle, this paper therefore conducts a horse race to investigate the contribution of the numéraire currency and the border effects to the puzzle between the standard specification of ‘the US dollar as the numéraire currency’ versus the unconventional consideration of ‘the ZAR as a numéraire currency’. Monthly time-series observations spanning the period 1990:01–2022:04 window are drawn from 14 SADC member states, thus producing a spatially wider and temporally longer frame of reference than has been considered in prior literature. This, coupled with the use of a broader spectrum of testing methodologies employed is a notable advancement in the PPP literature in Africa in general, and the SADC region in particular. To our knowledge, no study has thus far systematically advanced this relevant modelling choice especially in the context of less developed economies.

Our central results can be succinctly stated as follows. First, while our empirical estimates do not show impressively consensual evidence of long-run mean-reverting behaviour in the USD-based rates, we do find overwhelming statistical support of PPP from the ZAR-based rates in the SADC economies. Thus, accounting for the numéraire currency and the border effects cast some hope in solving the PPP puzzle. While novel to the SADC context, these findings are consistent with the results obtained elsewhere (Alba and Papell, 2007, Engel and Rogers, 1996, 2001, Lopez and Papell, 2007, Wu et al. 2011, Yilanci and Eris, 2013). Second, further enquiry suggests that the speed of reversion of the ZAR-based real exchange rate (RER) to parity is significantly faster than the USD-based rates, implying that the USD-based rates are affected by a series of persistent, real shocks unlike shocks to the ZAR-based rates which are merely transitory. By and large, our findings reflect increasing levels of intra-SADC trade due to the reduced trade barrier and ease with which information regarding prices and profit opportunities is transmitted within the trading block. More importantly, the latter two findings suggest that fundamental macroeconomic variables determining real exchange rates within SADC states sufficiently share similar stochastic trends. This implies the existence of an OCA both between member states and within the region at large as Zerihun and Breitenbach (2016) and Zerihun and Breitenbach (2018) suggest. Lastly, the empirical results and conclusions thereto are remarkably robust to the use of both linear and nonlinear exponential smooth transition autoregressive (ESTAR), panel unit root tests, and cointegration techniques. In this regard, our empirical approach therefore reinforces the notion that the failure to establish the PPP relationship in the early research is not entirely due to the low test power problem, but rather the short-span problem (Ghysels and Perron, 1993, Papell and Theodoridis, 2001, Taylor, 2003).

The rest of the paper runs in the following fashion. In the next section, we offer a cursory review of the empirical literature on PPP in Africa. ‘Materials and Methods’ formally discusses the econometric method employed and the data leveraged in the analysis. ‘Empirical results and discussions’ presents the baseline results and the related robustness checks are presented in ‘Further robustness checks’. ‘Conclusion and policy implications’ concludes the exercise.

Theoretical literature

The PPP theory has had its ebbs and flows over the past century. The literary work regarding the relationship between exchange rate and relative price indexes (i.e., PPP theory) was first introduced in the 1910s and gained popularity in the early 1970s with the advent of floating exchange rates and gyrations in relative prices and exchange rates. Despite being formally coined by a Swedish economist Cassel (1918), the term ‘purchasing power parity’ has a far longer history dating back to the scholars of the Salamanca School in 16th-century Spain. Nevertheless, Cassel was the first economist to formulate a systematic framework that clearly established PPP as an operational theory, and the first to empirically test it. Since then, there has been a plethora of literature exploring the empirical validity of the theory, but have generated contrasting results (Balassa, 1964, Gailliot, 1970, Officer, 1976).

The influential theoretical works of Gustav Cassel (see e.g., Cassel, 1916, 1918, 1920) are the pioneering studies to highlight how exchange rates adjust to changes in the relative prices. There are typically three closely related, albeit quite distinct interpretations of the PPP doctrine that have been advanced within international trade theory. The first interpretation claims that deviations in monetary factors, is the sole determinant of the exchange rate of any importance. The second variation on the interpretation of the theory is rather dogmatic and asserts that monetary factors in any two countries will exactly determine the equilibrium exchange rate. The last interpretation claims that monetary factors are the primary determinants of exchange rate but accommodates key secondary factors, including barriers of trade (e.g., tariff and non-tariff barriers, transportation costs), expectations, and capital flows (Gailliot, 1970, Holmes, 1967). The third interpretation of the PPP is attributed to Cassel and is probably the most widely accepted among international economists. The central tenet of Cassel’s argument is that monetary factors are primary determinants of long-run exchange rate between any two currencies under a flexible exchange-rate regime.

By virtue of assigning the determination of the foreign-exchange rate solely to the money market, without allowing any explanatory role to the goods market and goods prices, some proponents of the monetary approach (e.g., Frenkel, 1976, Holmes, 1967) have argued that the original PPP formulation by Cassel is actually an application of the quantity theory of money (QTM) into international trade theory. The most cogent articulation of such attribution of views to Cassel was put forward by Frenkel (1976) who argued that Cassel’s formulation was originally focused on relative quantities of money. The approach was later translated into a relationship between domestic and foreign prices through the application of the quantity theory of money. Cassel’s original formulation in 1916 focused on the relative quantities of money. This approach was later translated into a relationship between prices through the application of the QTM. Conceptually, however, it is apparent that in Cassel’s computation of equilibrium exchange rates, prices only served as a proxy for underlying monetary conditions. The determination of exchange rates does not appear to depend, neither explicitly nor implicitly, on international goods arbitrage. Nevertheless, Frenkel (1976, pp. 203) contended that translating the theory from a relationship between currencies into a relationship between prices through the QTM seems to have been counterproductive.

However, some economists have faulted such interpretation of Cassel’s formulation of PPP theory. For instance, Michaely (1982) lamented that Cassel’s theory may have been misconstrued. He argued that it is obvious that the goods prices, which are the fundamental component in the model rather than a ‘proxy’ for money, are the ultimate determinants of exchange rate in Cassel’s formulation. The quantity of money is incorporated into the model only for the following two reasons. First, under certain conditions, it is the quantity of money that determines prices. As Cassel (1918, 1920) argued, the PPP theory is applicable only when the disturbance originates with a change in the quantity of money and not any other significant changes. Second, price data paucity may necessitate the use of quantity of money to proxy changes in price levels (Cassel, 1916, Michaely, 1982). Thus, Cassel’s formulation implied that the quantity of money is actually a proxy for relative prices and not the other way round as was interpreted by Frenkel (1976). This is indeed evident in Cassel’s 1916 prominent article on which Frankel’s arguments were based:

“Given a normal freedom of trade between two countries, A and B, a rate of exchange will establish itself between them and this rate, smaller fluctuations apart, will remain unaltered as long as no alteration in the purchasing power of either currency is made and no special hindrances are imposed upon the trade. But as soon as inflation takes place in the money of A, and the purchasing power of this money is, therefore, diminished, the value of the A-money in B must necessarily be reduced in the same proportion. (…) when two currencies have been inflated the new normal rate of exchange will be equal to the old rate multiplied by the quotient between the degrees of inflation of both countries.” –Cassel (1916, pp. 62).

By and large, Cassel’s formulation can be taken to imply that divergence of the exchange rate from parity signals a state of disequilibrium, and necessitates adjustments in either prices or the exchange rate until parity is restored. The adjustment mechanism operates through international goods arbitrage, which leverages price disparities between any two markets. Specifically, by buying at lower prices and selling at higher ones, arbitrageurs take advantage of these discrepancies until prices are equalised. That is, the PPP doctrine predicts that if one country has higher inflation than another, the higher-inflation country’s currency is expected to depreciate relative to the lower-inflation country’s currency. The concept that PPP could be valid due to international goods arbitrage is linked to the LOP (Taylor and Taylor, 2004).

In summary, Cassel’s PPP theory has profoundly shaped the perception of many international economists towards the world, and it is no wonder Dornbusch and Krugman (1976) alluded that ‘under the skin of any international economist lies a deep-seated belief in some variant of the PPP theory of the exchange rate’. Meanwhile, Rogoff (1996) cautioned that such intimate belief in PPP theory needs to be complemented by empirical evidence, stating:

“While few empirically literate economists take PPP seriously as a short-term proposition, most instinctively believe in some variant of purchasing power parity as an anchor for long-run real exchange rates. Warm, fuzzy feelings about PPP are not, of course, a substitute for hard evidence.”

Empirical literature

On the empirical front, the literature exploring the practical validity of the PPP theory has been extensive. However, the evidence reported by these studies is largely conflicting or at best inconclusive. Some studies find compelling evidence supporting the validity of the theory (Coakley and Fuertes, 2000, De Villiers and Phiri, 2022, Huang and Yang, 2015, Kargbo, 2003, 2004, Kyei-Mensah, 2023, MacDonald, 1993, Nagayasu, 1998, Papell and Theodoridis, 2001, Vo and Vo, 2023, Zerihun and Breitenbach, 2018). However, other empirical studies have found that PPP does not hold in practice (Guglielmo and Luis, 2013, Gyamfi and Appiah, 2019, Olayungbo, 2011). Contrary to the above empirical findings, others have found mixed results where PPP is said to hold for some set of countries and fail in others (e.g., Alba and Papell, 2007, Arize, 2011, Arize et al. 2010, Bahmani-Oskooee et al. 2017, Bahramian and Saliminezhad, 2021, Chang et al. 2006, Christidou and Panagiotidis, 2010, Engel and Rogers, 1996, 2001, Huang and Yang, 2015, Iyke and Odhiambo, 2017, Lopez and Papell, 2007, Olaniran and Ismail, 2023, Papell and Prodan, 2020, Wu et al. 2011, Xie et al. 2021, Yilanci and Eris, 2013). Specifically, empirical evidence suggests that the verdict on the validity of PPP is highly sensitive to: (i) model specification (i.e., econometric tools employed); and (ii) sample selection bias (i.e., temporal or geographical space under investigation).

By leveraging time series cointegration techniques on annual observations, Guglielmo and Luis (2013) fail to reject the null hypothesis of a unit root in all their 44 Sub-Saharan countries over the 1970–2012 time frame, pointing to the non-existent PPP evidence. Again, in their recent work employing nonlinear unit root tests and nonlinear cointegration techniques over monthly observations spanning 1970:01–2017:01 period, Gyamfi and Appiah (2019) cast doubt on the existence of long-run PPP relationship in all of the 16 African economies under investigation.

On the contrary, a number of studies offer some comforting evidence in support of the PPP hypothesis on the African scene. For example, Kargbo (2004) exploits Johansen’s multivariate cointegration and error correction modelling techniques to probe the empirical validity of the PPP hypothesis in 35 African economies whose yearly data was uniformly available for the 1958–2002 period. By and large, Kargbo (2004) established overwhelming statistical evidence for the long-run PPP relationship in all of the countries under scrutiny. In a closely related study employing the same econometric techniques, albeit featuring parallel market exchange rates and CPI and covering 30 African countries during the 1960–97 period, Kargbo (2003) provides similar supporting evidence attesting the validity of the PPP hypothesis in Africa. In an attempt to reconcile these estimates with the traditional literature, Kargbo (2006) also applies Johansen’s cointegration and error correction modelling methods on both official and parallel market bilateral NERs and the GDP deflator series of 40 African economies over the 1958–2003 period. Indeed, they find robust evidence of the long-run PPP relationship in both samples. It is salient to note that the positive support of the PPP doctrine in the context of parallel market exchange rates and relative prices was first witnessed through the lens of panel cointegration method employed by Nagayasu (1998) in his study of 16 African economies spanning the 1981–1994 period.

Arize et al. (2010) estimated a system of cointegration equation to establish the presence of the long-run relationship between NER and relative prices in 14 African economies from which they established robust statistical evidence of the PPP relation in 11 of these economies. Their further analysis suggests that the half-life deviations from PPP were below the 3–5 year consensus advocated by Rogoff (1996). Meanwhile, Arize (2011) investigated the PPP hypothesis in 66 less developed economies via both linear stationarity and nonlinear unit root tests exploiting monthly observations of real effective exchange rates (REER) for the 1980:01–2009:10 window. They establish the mean reverting tendency of the REERs in 9 of the 20 African economies considered. In the same vein, Yilanci and Eris (2013) also adopted Fourier linear and nonlinear unit root test schemes for 33 African countries. At best, they conclude that PPP is supported in approximately over 60% of these economies.

Yet, Chang et al. (2006) utilised a battery of conventional univariate unit root tests in parallel with a highly dynamic nonlinear (logistic) unit root test (due to Leybourne et al. 1998). The latter test provides favourable PPP evidence for 6 out of the 22 economies considered whereas the conventional tests lead to type I error in five of these cases. Similarly, Chang et al. (2010) consider a panel of 15 countries from the Common Market for Eastern and Southern Africa (COMESA), and SADC regions using monthly data spanning the 1994:12-2008:07 time frame. Besides the conventional univariate and panel unit root tests, the authors also deploy the Seemingly Unrelated Regressions Augmented Dickey-Fuller (SURADF) test to robustly ascertain the PPP hypothesis. Although the conventional univariate and panel unit root tests overwhelmingly fail to reject the unit root null hypothesis in all of the sample, the SURADF found satisfactory support of PPP in only 3 of the 15 countries considered in their sample. Likewise, Bahmani-Oskooee et al. (2014) investigated the tendency of RER series to move in sync with relative prices using quarterly data from 20 African countries over the 1971q1-2012q4. They find co-movements between these series in half of the economies considered, suggesting that the PPP hypothesis is valid in such countries. Meanwhile, using the same sample window and countries, Bahmani-Oskooee et al. (2017) employed a different econometric approach, vis-à-vis the quantile unit root test, and concluded that the doctrine was partially supported in only 5 of the 20 countries considered.

Motivated by the proposed monetary integration in SADC, Zerihun and Breitenbach (2016) and Zerihun and Breitenbach (2018) have set out to test the hypothesis of whether or not the region forms the optimal currency area (OCA). In both of these studies, they exploit the same sample space (11 SADC states) over the sample period consisting of monthly observations between 1995:01-2010:08. In Zerihun and Breitenbach (2016), they exploit two nonlinear stationarity tests—the Fourier stationarity test and the Broock, Dechert and Scheinman (Broock et al. 1996, BDS) test— whereas Zerihun and Breitenbach (2018) leverage Johansen’s multivariate cointegration and panel cointegration techniques. Taken together, both studies lend firm support of the PPP equilibrium in SADC suggesting that the region indeed meets the OCA requirements premised on the PPP benchmark. Nevertheless, the authors openly caution readers to interpret their results judiciously due to the short sample period explored.

In another interesting article, Akinboade and Makina (2006) consider the PPP dynamics between South Africa against the country’s four key trading partner currencies, namely the US dollar, the pound sterling, the euro and the Japanese yen. Indeed, they establish support for the co-movement of exchange rates and the relative prices in their sample. In the same spirit, Mangani (2012) investigates the mean reverting behaviour of RER series for Malawi relative to the country’s 18 key trading partners using both traditional and nonlinear unit root tests over the 1994:01–2010:12 window. Overall, he offers some intriguing evidence pointing to a partial support of the PPP hypothesis in eleven of these economies, particularly driven by the border effects. Meanwhile, Iyke and Odhiambo (2017) test the validity of PPP between two SADC countries—Lesotho and Zambia—against the US using annual observations over the period 1955–2010. Interestingly, they found favourable PPP evidence for Lesotho but none for Zambia.

Summarising literature gaps

Earlier empirical literature on the validity of the PPP hypothesis mostly focuses on advanced economies rather than emerging markets or low- and middle-income countries, triggering potential concerns as to whether these findings suffer from the infamous sample-selection bias. The lack of empirical evidence on the latter set of economies is primarily due to data paucity, leading to the ‘survivorship bias’. Nevertheless, akin to the research conducted elsewhere, the scanty research on PPP in Africa has generally yielded mixed results. Thus, the debate on the empirical validity of the PPP hypothesis remains subject of ongoing controversy. This warrants further contributions on the subject.

Previous studies examining the empirical validity of the PPP hypothesis in SADC have one common setback. Specifically, prior studies extensively used major currencies (particularly the US dollar) as the numéraire currency and grossly neglected the border effect and the numéraire currency effect.^{Footnote 2} This greatly undermines the generalisability and credibility of their findings. The only notable exception thus far, however, is the recent contribution by Zerihun and Breitenbach (2018). While their primary focus resides in the application of the Johansen’s multivariate cointegration technique on the USD-based exchange rates, they briefly designate South Africa as the numéraire country in their attempt to establish the robustness of the benchmark estimates. Yet again, their analysis is typically guilty of the short sample problem, which the authors openly caution policymakers not to take their recommendations at face value.

Against this backdrop, and addressing the gaps identified in the empirical literature, the contribution this study to the PPP debate is fourfold. First, contrary to the prevailing literature, the current study sets out to investigate the numéraire currency effect in the empirical validity of the PPP theory. Understanding that fundamental macroeconomic variables that determine real exchange rates in SADC states to share a common trend is crucial as it can serve as a useful framework for choosing a common currency for the prospective currency union in the region. Second, by virtue of deploying the ZAR in parallel with the US Dollar as numéraire currencies—unlike the mainstream literature—the present study tests the well-known conjecture that geographical proximity reinforces the empirical validity of the PPP hypothesis. Our working hypothesis is that geographical proximity (and FTA) should help to mitigate transaction costs (e.g., transportation costs, tariffs and non-tariff barriers, and information costs), and thus stimulate faster price convergence within the trading block. Thus, this line of enquiry reasonably assumes that SADC member states are homogenous on economic (e.g., exchange rate regimes—Zerihun and Breitenbach, 2018), and social and cultural spectra (affecting e.g., taste—which ensures homogeneity in the composition of the consumption basket).

Third, the central conclusion from the preceding literature review is that a ‘one-size-fits-all’ approach to testing the empirical validity of the PPP hypothesis is likely to produce unsatisfactory results and, consequently, lead to ill-advised policy implications. In particular, neither linear nor nonlinear stationarity test scheme has successfully emerged as a holy grail modus operandi to the PPP investigation. Indeed, the same applies for the choice between univariate and panel tests. Therefore, in contrast to other studies, this paper considers a wider spectrum of econometric tests including both univariate and panel, as well as linear and nonlinear test schemes. From an econometric viewpoint, the latter implies that we do not rely on the performance of any single test scheme and thus yield more robust results. Our final point of departure from the previous literature is that we reasonably employ high-frequency time-series observations spanning the period 1990:01–2022:04 to achieve a relatively longer data span than has been considered in prior literature in the context of SADC. This is not only important as it overcomes the infamous power problem (Papell and Theodoridis, 2001, Taylor, 2003), but also crucial in providing a long-run perspective on the subject—which is of utmost significance to policymakers.

This study aims to empirically assess the validity of the PPP theory in the SADC region over the period 1990:01-2022:04. We begin by discussing the theoretical underpinnings of the study, followed by conducting a series of univariate unit root and stationarity tests on the variables to investigate their order of integration. Next, we estimate the number of years required for a PPP deviation to permanently decay by 50% in response to a unit shock, and then test for unit root in a panel setting. Lastly, the study also employs nonlinear unit root tests and cointegration analysis for robustness checks.

Theoretical background

In this section, the study’s theoretical foundation is laid forth in accordance with prominent research by Cassel (1918), Cassel (1920), Officer (1976), Dornbusch (1985), and Taylor (2013). As stated earlier, the LOP forms the central building block of the PPP theory (Taylor and Taylor, 2004). Therefore, to fully grasp the market forces that drive the outcomes predicted by the PPP theory, we must first delve into the LOP. The LOP states that once prices are expressed in a common currency, a standard good i should sell for the same price in any two markets:

where S, P_t, and ({P}_{t}^{* }) denote NER, and consumer price index (CPI) at time t in the domestic and the foreign market, respectively. Thus, holding all else equal, distortions in the bilateral NERs should be commensurate with the deviations in the relative prices between the two markets:

The underlying assumption is that markets and goods in the two economies are integrated and perfectly competitive such that any price differentials between the domestic and the foreign markets will be equalised by international arbitrage. This constitutes the variant of PPP commonly referred as the ‘absolute’ version. Formally, it is crucial to distinguish between the PPP theory and the LOP. On the one hand, in its absolute form, PPP posits that the exchange rate between any two countries is proportional to the ratio of their aggregate price levels. Thus, under the PPP theory, P_t and ({P}_{t}^{* }) represent aggregate price levels, and the exchange rate is determined simultaneously with price levels in each country. On the other hand, the LOP applies to specific commodities, indicating that P_t and ({P}_{t}^{* }) are the prices of identical goods in different markets, while the exchange rate is determined exogenously. The unrestricted estimable version of equation (2) can be obtained by taking the logarithm of both sides and adding a constant (β₀) and a stochastic error term ϵ_t:

where s_t, p_t and ({p}_{t}^{* }) are respective logarithms of S, P_t, and ({P}_{t}^{* }). Tests of the absolute PPP involve estimating equation (3) or its restricted version given as:

However, the absolute PPP version does not represent the real-world setting in that the majority of the tradable goods are differentiated products and thus reference baskets may differ across countries. Such discrepancies in the reference baskets are taken into account in the ‘relative’ variant of PPP, which defines the bilateral RER, R, as:

Taking the natural logarithm of Equation (5), we obtain:

The PPP doctrine requires price convergence between the domestic and the foreign country as long as the prices are indexed in a common currency and that deviations (if any) should only be transitory. This implies that the real exchange rate in equation (6) can be expressed as:

where (s=ln S), ({p}_{t}=ln {P}_{t}), and ({p}_{t}^{* }=ln {P}_{t}^{* }). When PPP holds, the real exchange rate r_t is generated from an I(0) process. Therefore, in order to test for PPP hypothesis, we subject the RER series, r_t, to a battery of unit root and stationarity tests.

Univariate unit root tests

This study employs three unit root and stationarity tests: the Augmented Dickey-Fuller (due to Dickey and Fuller, 1981, Said and Dickey, 1984, henceforth, ADF), the Phillips and Perron (1988, henceforth, PP) and the Kwiatkowski et al. (1992, henceforth, KPPS) test. Because we are unable to determine, a priori, whether the appropriate specification includes only an intercept term or its counterpart with a trend, our analysis considers both cases.

The ADF test

To test for stationarity properties in the RER series, we first employ the ADF test of unit root (Said and Dickey, 1984). The univariate ADF test of nonstationarity considers the following systems of equations:

where models (8) and (9) respectively denotes mean-stationarity and trend-stationarity series, in which ϵ_t is white noise. Therefore, the null hypothesis of a unit root in the RER series, r, implies that γ = 0. Thus, we test:

against the alternative hypothesis that the series are I(0)

This is evaluated using the standard t-statistic ({t}_{gamma }=hat{gamma }/se(hat{gamma })), where γ is the slope coefficient of the first-order autoregressive parameter in model (8) or (9), while (se(hat{gamma })) is the associated standard error. The rejection of the null hypothesis in favour of the alternative provides evidence that the PPP hypothesis holds. In our empirical application, the optimal lag length, k, sufficient to eliminate any serial correlation in the residual is determined endogenously using the Akaike Information Criterion (AIC).^{Footnote 3}

The PP test

In order to complement the ADF test results, we employ another univariate unit root test borrowed from Phillips and Perron (1988)—the PP test. This test derives the t-statistic where the asymptotic distribution of the test is not affected by the serial correlation. Thus, the PP test adopts the following statistic:

where ρ₀ is a consistent estimate of the error variance in models (8) and (9), f₀ denotes an estimator of residual spectrum at zero frequency, and S is the standard error of the regression. The critical values of the PP test are the same as those of the ADF test.

The KPPS test

Kwiatkowski et al. (1992) propose another alternative unit root test which, unlike the former two, is based on the residuals and considers the null hypothesis of stationarity against the alternative of a unit root. Specifically, the KPPS test considers the following equation:

where ϵ_t is a stationary process and x_t = x_t−1 + μ_t is a random walk process in which ({mu }_{t} sim iid(0,{sigma }_{mu }^{2})). That is, we test:

against the alternative hypothesis that the series are not I(0)

The lag order for the KPSS test is assumed to be homogeneous, and in our application, it is set at lag 12 in each case.

Half-life of PPP deviations

The stationarity test techniques outlined above are not informative regarding the speed of convergence of RER series towards their long-run equilibrium PPP trajectory. To gain more insight into the PPP puzzle, we seek to estimate the half-life deviation from PPP which is the expected amount of time it takes for the magnitude of response to a unit shock to the RER series to dissipate by 50% (Rogoff, 1996).^{Footnote 4} Specifically, we compute point estimates of the half-life of deviations from PPP using the coefficient on the first-order autoregressive parameter in the ADF model. Our preferred specification for this exercise is the model with a constant term and a time trend (i.e., model (9)). Thus, the half-life is approximated from the following equation (Murray and Papell, 2002, Taylor, 2001):

in which γ is the autoregressive coefficient in equation (9).

Panel unit root tests

As stated earlier, in order to further overcome the low power of the univariate unit and stationarity tests as those outlined above, we proceed to employ a battery of panel tests of unit root. Econometrically, the rationale for the panel unit root and stationarity tests is to augment the cross-sectional dynamic to the temporal dimension by considering a panel of RER series (in lieu of individual time series) so as to increase the amount of information thereby increasing the statistical power of the test (Taylor, 2003). Empirically, the absence of a long-run PPP relationship in a bilateral setting does not necessarily imply the exchange rates in a multi-country setting would also exhibit nonstationary behaviour (Enders and Hum, 1994, Zerihun and Breitenbach, 2018). Hence, our application of the panel unit root tests constitutes an appraisal of a modified version of the traditional PPP referred to as the generalised PPP (GPPP) (Enders and Hum, 1994). This lends further insight into our enquiry of the existence of an OCA in SADC (Zerihun and Breitenbach, 2016, 2018).

More specifically, we employ the following six panel unit root and stationarity tests to the RER series: the Choi (2001, henceforth, FT test), Pesaran (2007, henceforth, PES test), Im et al. (2003, henceforth, IPS test), Levin et al. (2002, henceforth, LLL test), Harris and Tzavalis (1999, henceforth, HT test), and Breitung and Das (2005, henceforth, BD test). A shortlist of papers that have employed these statistical techniques in the realm of PPP hypothesis includes, inter alia, Wee and Lee (2022), Al-Gasaymeh and Kasem (2015), Huang and Yang (2015), Bahmani-Oskooee et al. (2014), Wu et al. (2011), Chang et al. (2010), Murad and Hossain (2018) and Alba and Papell (2007). It is salient to note that whereas the first three tests accommodate panels with gaps, the latter three require strongly balanced panels. Therefore, we employ the former tests on the full sample, albeit unbalanced panel of the 14 SADC countries covering the entire period under scrutiny. Next, we deploy all six tests on a sub-sample spanning 1991:11-2017:02 which precludes Lesotho, Mozambique, Namibia, and Tanzania whose data starts from at least 1994:11. Furthermore, we consider both detrended and demeaned series in order to obtain more robust results.

Variables and data sources

This study leverages monthly bilateral NER of 14 SADC member states: Angola, Botswana, Democratic Republic of Congo, Eswatini, Lesotho, Madagascar, Malawi, Mauritius, Mozambique, Namibia, Seychelles, South Africa, Tanzania, and Zambia with two numéraire currencies—the United States dollar (USD) and the South African rand (ZAR)—and a measure of relative prices.^{Footnote 5} The relative price series are given by the ratio of the price index in each of the base countries—United States and South Africa—to the comparable index in the domestic country, proxied by the CPI. The respective NER and CPI series are the end-of-period and period average statistics, respectively, drawn from the International Monetary Fund’s International Financial Statistics database. The CPI data are benchmarked at the 2010 prices.

Our sample period generally spans from January 1990: except for Tanzania; Lesotho and Namibia; and Mozambique whose data is only available from December 1994, January 2002, and January 2004, respectively. The start of the sample period roughly coincides with the signature date of the Declaration and Treaty establishing the SADC from its predecessor body, the Southern African Development Coordination Conference (SADCC), in 1992. For Botswana, Lesotho, Mauritius, Namibia, South Africa, and Zambia, the data extend to April 2022 (the latest available). The data for the rest of the countries extend at least beyond February 2017 as presented in Table 1 hereunder.^{Footnote 6} As is apparent from the table, our sample includes 214–388 data points, giving us sufficiently long time series to circumvent the infamous problem of ‘small sample distortions’ that undermines the power of univariate unit root tests. To this end, Comoros and Zimbabwe are precluded from the analysis due to data paucity during a significant part of the sample period. Specifically, the CPI data for Comoros is only available between December 1999 and October 2014, while the NER series for Zimbabwe is unavailable in the database prior to February 2019.

Before presenting the empirical results, we examine the variables used in this study through summary statistics and visual plots. Following this, we discuss our findings from the two econometric approaches considered: univariate unit root tests and panel unit root tests for the PPP hypothesis. Recall that we consider two numéraire currencies: the US dollar and the South African rand. The latter not only seeks to verify whether the validity of the PPP hypothesis is sensitive to the choice of the numéraire currency in the African context, but more importantly tests the hypothesis that PPP is enhanced by geographical proximity between the domestic country and the numéraire country. Hence, for each test, we present two sets of results corresponding to the two numéraire currencies. Note, however, that our analysis does not explicitly incorporate a separate variable to capture the distance between the home and the numéraire countries. Furthermore, the section discusses the results for the half-life deviations from PPP.

Summary statistics and visual inspection of variables

Table 1 provides a full menu of summary statistics of the RERs under both numéraire currencies. It is apparent that Zambia has the lowest average value of RERs followed by Botswana for both numéraire currencies, while Madagascar has the highest mean of RERs followed by Tanzania and the Democratic Republic of Congo. Looking at the skewness results, the RERs for the majority of the economies are symmetrically distributed around the mean. Furthermore, the Jarque-Bera statistics suggest that the bilateral RER series for all countries follow a non-normal distribution. Indeed, the normality test results are statistically significant at conventional levels.

Next, Figs. 1, 2 provide a visual examination of the RER series generated from the two numéraire currencies. A decrease in the RER series denotes a real depreciation of the domestic currency against its numéraire counterpart. A number of features in the data stand out. First, the majority of the RER series seem to maunder in a fashion reminiscent of the random walk process. Also, notice that there is little discernible evidence of explosive behaviour in RER series nor is there any obvious deterministic time trend. Yet, for most countries, the RER series are also characterised by a highly degree of persistence, albeit, slow-moving process. By and large, it is unclear whether the appropriate specification includes an intercept term only or its counterpart with a trend. Such uncertainty justifies our decision to include both cases. The associated sample correlograms for each of the RERs are shown in Figure A1 of the Appendix. They generally reveal that, in each case, only the first partial autocorrelation coefficient is significantly different from zero at the 5% significance level.

Real exchange rates in SADC member states: USD.

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Real exchange rates in SADC member states: ZAR.

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Univariate unit root tests results

The univariate unit root test results for the evidence of PPP hypothesis (or the lack thereof) are presented in Table 2. The upper panel of Table 2 considers the USD as the numéraire currency while the lower panel presents results for the ZAR as the numéraire currency. The results from the ADF test with an intercept term only are denoted as τ_A1 while those containing both the constant term and a trend are denoted as τ_A2. Likewise, the comparable statistics from the PP, and KPSS tests are respectively denoted as τ_P1 and τ_P2, and τ_K1 and τ_K2.

USD-based bilateral RER and PPP

When considering the USD as the numéraire currency, the three tests suggest that ignoring the trend term find favourable evidence of stationarity in 50% of the SADC countries considered. Particularly, for the ADF and PP tests with a constant term only, we reject the null hypothesis of a unit root for the RER series of Angola, the Democratic Republic of Congo, Lesotho, Madagascar, and Namibia at conventional levels of significance. Meanwhile, under the same specification, the KPSS test suggests that failure to reject the null hypothesis of stationarity for these five series amounts to committing type II error, and actually finds statistical evidence that the dollar RER series for Eswatini and Mauritius are actually stationary. For a consideration of the detrended series: the ADF and PP tests reject the null hypothesis of a unit root in six countries: Angola, the Democratic Republic of Congo, Lesotho, Madagascar, Malawi, Namibia, and Seychelles, all at conventional levels of significance. However, the KPSS test for the detrended series fails to reject the null of stationarity only for the Democratic Republic of Congo and Seychelles. Overall, our dollar-indexed bilateral RER series appear to be characterised by a trend-stationary process. By and large, our conservative estimates from the three univariate unit root tests indicate that the dollar-based RER series support the PPP hypothesis only in 7 (Angola, Democratic Republic of Congo, Lesotho, Madagascar, Malawi, Namibia and Seychelles) out of the 14 SADC states under examination. Our results are, however, at odds with the finding by Chang et al. (2010) who reveal no support of PPP in their 15 SADC and COMESA economies under consideration using the same univariate unit root tests considered in this paper. This could be attributed to the short span of their sample and ill-advised model specifications without consideration of the time trend.

What is more intriguing is that after taking the first difference of the series, all three tests unanimously point to stationarity of all the series except for Lesotho and Namibia where the KPSS test rejects the null hypothesis of stationarity, albeit at 10% significance level. The differenced series are plotted in Figs. 3 and 4.

Real exchange rates in SADC member states (1st difference): USD.

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Real exchange rates in SADC member states (1st difference): ZAR.

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ZAR-based bilateral RER and PPP

Now we turn to the consideration of the ZAR as the numéraire currency. Unlike the Dollar-based RERs discussed above, there is no obvious evidence that the ZAR-based rates are level or trend stationary processes as the incorporation of a stochastic trend does not necessarily improve the test results as previously level-stationary (with intercept only) series are rendered non-stationary when the trend term is accounted for. This is especially true when we consider the ADF test. Specifically, considering the demeaned series only, the tests suggest that the RER series of the Democratic Republic of Congo, Malawi, Mozambique, Namibia, Seychelles, and Tanzania are level-stationary. However, the inclusion of the trend term to the RER series shows evidence that 6 of the previously level non-stationary series, vis-à-vis Angola, Botswana, Eswatini, Madagascar, Malawi, and Mauritius, are actually trend-stationary at conventional levels of significance. Moreover, the test on detrended series finds no evidence of a unit root in eight RER series. Therefore, taken together, our conservative estimates using the ZAR-based bilateral RERs show favourable support of PPP hypothesis in all the SADC states considered for this latter exercise except for Lesotho. Again, all the univariate unit root tests on the first-differenced series of the ZAR-based RERs seem to provide robust evidence of stationarity at conventional levels.

The strong evidence in support of the PPP hypothesis in the SADC countries when we consider one of the region’s currencies, namely the ZAR, as the numéraire currency intuitively points to the evidence that PPP is indeed enhanced by geographical proximity (Al-Gasaymeh and Kasem, 2015, Alba and Papell, 2007, Engel and Rogers, 1996, 2001, Lopez and Papell, 2007, Wu et al. 2011). That is, considering a numéraire country that is geographically closer to the domestic market cast some hopes in solving the PPP puzzle. Indeed, this piece of evidence also generally confirms the assertion that the choice of a numéraire country plays a crucial role in PPP studies (Papell and Theodoridis, 2001).^{Footnote 7} These results particularly corroborate those of Mangani (2012) who considered RER series for Malawi against the country’s 18 key trading partners and documented partial support of PPP for countries geographically closer to Malawi. Similar results have been observed elsewhere by Alba and Papell (2007) who considered a panel of 84 USD-based RER series and found, among others, that PPP holds for countries closer to the US and indeed that panels of African (and Asian) countries did not support the hypothesis. In the same token, while Al-Gasaymeh and Kasem (2015) find no statistical support for PPP in the Middle East economies, they do reveal favourable evidence for PPP for the Latin American economies as the latter set of countries are geographically close to the USA.

Indeed, a closer examination of the ZAR-based RERs lends some interesting support to the notion of the border effects on the validity of PPP hypothesis. For instance, it is fascinating to note that two of the countries (i.e., Botswana and Zambia) which show no support for the PPP hypothesis based on the USD rates, offer overwhelming support for PPP under the ZAR-based RERs. Nevertheless, the evidence of the border effects does not entirely enjoy much support due to the non-existent PPP evidence for one of South Africa’s closest neighbours: Lesotho.

Furthermore, the analysis of the ZAR-based RER series also gives a glimpse into the effects of a monetary union on the validity of the long-run PPP (Bleaney, 1992, Christidou and Panagiotidis, 2010, Lopez and Papell, 2007, Zerihun and Breitenbach, 2018). Specifically, Eswatini, Lesotho, Namibia, and South Africa constitute the Common Monetary Area (CMA) under the auspices of the Multilateral Monetary Agreement signed in February 1992. Notwithstanding, the ZAR is a legal tender that is widely used and accepted in the other three CMA member states. Moreover, the three countries rely heavily on trade with South Africa and thus their fixed and predictable exchange rate with the ZAR enhances cross-border trade (Van Zyl et al. 2003). Furthermore, traditional wisdom suggests that the adoption of a single currency is more likely to enhance the validity of the long-run PPP (Rose, 2000). Indeed, a critical look at the CMA members under the ZAR-based RERs, particularly those of Eswatini and Namibia, suggests that the monetary union enhances the validity of the PPP.^{Footnote 8} Nevertheless, the weight of this argument is again partially undermined by the non-mean-reverting behaviour of Lesotho’s RER series, which also echoes the mixed finding of Huang and Yang (2015) in their study of the Eurozone countries.

To sum up, the favourable evidence for the ZAR-based PPP analysis relative to the USD-based rates also point to the convergence of consumption preferences within the SADC region which is enhanced by the cultural homogeneities across the region (Engel, 1993, Krugman et al. 2018). The implication of these results is that intra-SADC international arbitrage is not possible in the SADC states as any gains or losses in cross-border competitiveness by the economies are gradually corrected, ceteris paribus.

Results for half-life deviations

Table 3 reports the point estimate of the half-lives of PPP deviations alongside their 95% confidence intervals. By and large, these results indicate that for the majority of the SADC economies, the USD-based RERs take a relatively longer time to adjust towards their mean-reverting process compared to the ZAR-based rates (see also Fig. 5). Specifically, our estimates suggest that the time it takes for a unit shock to the USD-based RERs to dissipate by 50% is approximately 14.38 months (1.20 years), while conservative estimates indicate that this speed can take as long as 68.21 months (5.68 years). Our estimates of the average half-life for these economies roughly collaborate the finding by Chang et al. (2010) estimated using the panel SURADF method.^{Footnote 9} Indeed, the estimated 5.68-year half-life upper bound for the USD-based rates is roughly in sync with the documented consensus of 3–5 years (Murray and Papell, 2002, Rogoff, 1996). On the other hand, the ZAR-based RERs yield an average speed of parity reversion of under 1 year (11.47 months). However, an average half-life upper bound estimate for the ZAR-based rates is 33.97 months (2.83 years) which roughly coincides with the documented consensus lower bound of 3 years. In a nutshell, these results indicate that shocks to the USD-based RERs appear to be more persistent than shocks to the ZAR-based rates since there is 10% chance that the true half-life of parity reversion of the USD-based rates take ~2.85 years longer than the ZAR-based rates.

Estimated half-lives of parity deviations.

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Panel unit root test results

Table 4 hereunder reports the results for all the panel unit root tests for both numéraire currencies. By and large, it is apparent from Table 4 that the panel unit root tests offer overwhelming evidence in support of the PPP hypothesis in the SADC region for both numéraire currencies. More specifically, all the panel tests reject the null hypothesis of a unit root at 1% level for both numéraire currencies and both the entire sample as well as the 1991:11-2017:02 sub-sample, suggesting the validity of the PPP hypothesis. These results largely collaborate our baseline estimates and more importantly augment the test power. Nevertheless, the only exception to this is when we subtract cross-sectional means during the full sample analysis in which the FT and IPS tests fail to reject the unit root null. In the interim, the PES test provides support for PPP at 5% level of significance. Overall, while our results are at odds with the evidence documented by Chang et al. (2010), but they do collaborate with other estimates obtained on the African scene (see e.g., Nagayasu, 2002, Wu et al. 2011, Zerihun and Breitenbach, 2016) as well as those obtained from industrialised countries (see e.g., Abuaf and Jorion, 1990, Alba and Papell, 2007, Lopez and Papell, 2007). More crucially, our results thereby confirm the existence of an OCA in SADC premised on the GPPP insight (Enders and Hum, 1994, Zerihun and Breitenbach, 2016, 2018), and thus provide a green light for the proposed SADC monetary union.

To further anchor confidence in our baseline estimates, this section draws from the nonlinear unit root test techniques as well as cointegration analysis.

Nonlinear unit root tests

It is now a well-established fact that PPP holds as a long-run phenomenon (see e.g., Rogoff, 1996). However, it is also well-known that such long-run data may undergo remarkable changes in terms of trade and international friction (Arize, 2011, Boundi-Chraki and Tomé, 2022, Chang, 2016, De Villiers and Phiri, 2022, Kapetanios et al. 2003, Kruse et al. 2012). A second potential source of nonlinear dynamics in the adjustment towards the long-run PPP stems from the failure of the rational expectations assumption to hold as economic agents would have varying beliefs regarding the equilibrium NER level; and third, nonlinearities may arise due to the potential effects of central bank interventions in the foreign exchange markets (Arize, 2011).

Expectedly, a heated debate is still ongoing regarding the process of adjustment towards such a long-run PPP, and a plethora of literature has cast doubt on the credibility of the linear unit root tests. As such, we seek to verify the robustness of our baseline results by availing ourselves to the nonlinear unit root tests drawn from Kapetanios et al. (2003, henceforth, KSS) and Kapetanios and Shin (2008, henceforth, KS).^{Footnote 10} The KSS and KS techniques adopt the unit root null hypothesis against the alternative of a globally stationary ESTAR process. As Otero and Smith (2017) document, the primary difference between the two techniques is that the KSS test is based on ordinary least-squares detrending procedure whereas the latter approach is based on the generalised least-squares detrending.

Table 5 presents the results of the nonlinear unit root tests. Here, it is apparent that under both numéraire currencies, the KSS test gives more favourable support for the rejection of the unit root null compared to the KS test. Yet, the ZAR-based RERs enjoy more support for the PPP hypothesis relative to the USD-based rates. Specifically, of the 14 SADC member states considered under the USD-based RERs, at best, we find support for the PPP hypothesis in only nine countries. Moreover, even for these few countries that enjoy favourable PPP support under the USD-based rates, such evidence for most of these countries is by and large statistically weak. Meanwhile, under the ZAR-based, the nonlinear unit root tests provide affirmative evidence of the PPP hypothesis in 12 of the 13 member states. All in all, it is quite comforting to note that the nonlinear unit root test results largely conform to the spirit of the baseline conclusions in ‘Empirical results and discussions’. This conclusion is robust to different optimal lag selection procedure including the fixed optimal lag selection method, and endogenous lag selection techniques such as the AIC and Schwarz information criterion. The results from this exercise should not be taken for granted as they not only confirm our baseline conclusions from the linear unit root tests, but more importantly also demonstrate the conjecture that the lack of support for the PPP hypothesis in prior literature using conventional (linear) unit root tests is not primarily due to a statistical artefact, namely the low power of the tests, but rather due to the short spans of data employed in such analyses (Ghysels and Perron, 1993, Papell and Theodoridis, 2001, Taylor, 2003).

Cointegration analysis

Next, we exploit the cointegration analysis to check if the series generated by the sum of NER and foreign prices {s + p*} in equation (7) is cointegrated with the domestic price sequence {p} (Enders, 2015). This study borrows the test procedure from Johansen and Juselius (1990, henceforth, JJ-test) which examines the restrictions imposed by cointegration on the unrestricted VAR model.^{Footnote 11} It is salient to note that unlike the Engle and Granger (1987) test which is flawed due to its sensitivity to variable ordering, the JJ-test is not only immune to the variable ordering problem, but more importantly allows for a multivariate case configuration (of prices and exchange rates); as it accommodates short-run deviations of the variables while allowing the variable system to revert to the long-run equilibrium as per the PPP hypothesis (Kargbo, 2004, Zerihun and Breitenbach, 2018). Thus, the results reported in this analysis are those from the JJ-test VAR system estimated with the maximum likelihood trivariate model.

Before implementing the JJ-test, we set out to establish the statistical properties of the NER and CPI series (Zerihun and Breitenbach, 2018). This is a prerequisite step so as to verify that the series are integrated in the same order (Enders, 2015, Kargbo, 2004, Nagayasu, 2002, Zerihun and Breitenbach, 2018). For this task, we employ the ADF test of stationarity in which the optimal lag length is selected via AIC out of the 12 maximal lags specified. The results indicate that all the series are generated by I(1) processes. The only exceptions to this are the NER series for Angola (for both numéraire currencies) and the Namibian CPI series and its ZAR-based NER. As such, we do not perform the JJ-test for these two countries as the series are integrated of different order (Enders, 2015). To conserve space, the results of the unit root test of the nominal series and price indices can be accessed from the authors via a written request. It is interesting to note that our finding that (log) NER series are pure random walk processes dates back to Mussa (1979) and Adler and Lehmann (1983), and is consistent with recent literature (see inter alia Kargbo, 2004).

The results for the JJ-test for both numéraire currencies are reported in Table 6. Here, we report the trace statistic for the rank (r) associated with different coefficient matrices. The JJ-test considers the null hypothesis of no cointegrating relationship between NER and relatives price series. From Table 6, we establish the presence of two cointegrating relationships among variables in seven economies, for each numéraire currency considered. Specifically, our results suggest that for the USD-based bilateral NER, we reject the null hypothesis of no cointegration for Botswana, the Democratic Republic of Congo, Malawi, Mauritius, Seychelles, Tanzania, and Zambia. These results are statistically significant at 5% level. That is, we find sufficient evidence that any deviations in the USD-based NER series will be commensurate with the inflation differentials in the seven aforementioned countries. These findings reaffirm the validity of PPP hypothesis established earlier by the unit root tests except in the case of Botswana and Zambia where PPP was initially declared non-existent by the univariate unit root tests.

Similarly, a consideration of the ZAR-based exchange rates suggests the presence of a long-run PPP relationship in Madagascar, Malawi, Mauritius, Mozambique, Seychelles, Tanzania, and Zambia. Interestingly, the JJ-test verdict for all of these economies concurs with the unit root test results, enhancing our confidence in the baseline results. Overall, these results confirm the tendency of NER series and prices to revert to their long-run equilibrium paths as prescribed by the PPP theory. More importantly, our results reaffirm the verdict that the fundamental macroeconomic variables determining real exchange rates in SADC states sufficiently share similar trends, implying that region forms an OCA (Enders and Hum, 1994, Zerihun and Breitenbach, 2016, 2018).

Conclusion

Despite the intuitive appeal of the PPP theory, a vast body of empirical research has produced conflicting verdicts on its validity. The paper adds nuance to the PPP literature primarily by conducting a horse race between considering the ZAR as a numéraire currency against the traditional practice where the US dollar is designated as the numéraire currency. We find sufficient statistical evidence suggesting that the empirical validity of PPP is influenced by the numéraire currency and border effects. Importantly, further evidence indicates that the ZAR-based RERs take significantly shorter time to converge towards their equilibrium PPP paths compared to the USD-based rates, suggesting that shocks to the USD-based RERs are rather more persistent than shocks to the ZAR-based rates which are merely transitory.

Implications

The findings presented in this study are important not only for researchers in international economics but also for monetary policymakers, asset managers, and investment practitioners. Based on our empirical results, we propose the following policy suggestions. First, the finding that the fundamental macroeconomic variables determining real exchange rates in SADC states sufficiently share similar trends implies that the region conforms to OCA criteria. This reaffirms the region’s structural preparedness for the implementation of the proposed monetary union and the subsequent adoption of a single currency. Therefore, in light of this, we recommend that SADC should proceed with this transformative process, as the region is well-positioned to thrive under a monetary union and a single currency regime.

Second, our finding of strong evidence for mean-reversion in ZAR-based rates confirms that macroeconomic fundamentals in the SADC region are harmonised and insulated against foreign shocks. This enhanced economic resilience within the SADC region strengthens its bargaining power in the global market, fostering the bloc’s agenda of achieving a fully integrated internationally competitive region. SADC policymakers are therefore advised to leverage their collective economic weight in international negotiations to secure favourable trade agreements with the outside world. Third, the validity of the long-run PPP in SADC, coupled with the significantly shorter half-lives, implies that any short-run deviations in the balance of payments will eventually return to their equilibrium path in response to market forces. We therefore recommend minimal (if any) central bank interventions in the foreign exchange market to avoid distorting the PPP condition.

Fourth, we recommend that monetary authorities across SADC should maintain inflation rates in line with their key trading partners to avoid the detrimental effects of devaluation or internal deflation. That is, policymakers are advised to implement deliberate strategies to tame domestic inflation and ensure it does not significantly outpace that of their trading partners. This may include adopting effective monetary policies (e.g., adopting inflation targeting) and implementing structural reforms aimed at reinforcing domestic productivity and international competitiveness. Fifth, given the validity of PPP in the SADC member countries, it is imperative that monetary authorities in these economies proactively use the PPP theory as a model for exchange rate determination and as a tool to assess the (dis)equilibrium status of their currency and monitor discrepancies between domestic and foreign inflation rates. These countries are therefore advised to leverage the PPP theory to ascertain the amount of domestic or foreign price-level adjustment required to maintain an equilibrium exchange rate. Despite the positive prospects of PPP in the SADC region, these economies are unlikely to achieve unlimited gains from arbitrage in intra-SADC goods trade. Lastly, asset managers and investment practitioners in SADC are recommended to capitalise on the short-run mean-reverting nature of exchange rates implied by PPP to develop long-term investment strategies by pinpointing currencies that significantly drift from their PPP levels and benefit from their long-term anticipated correction towards the equilibrium. Moreover, asset managers are also advised to use PPP to adjust their global asset allocation strategies, prioritising investments in countries with currencies that are significantly undervalued relative to their PPP levels, in anticipation of higher future returns as the currencies eventually revert back to the long-run equilibrium.

Study limitations and potential areas of future research

Although the current study has produced robust empirical evidence supporting the impact of the border effect on PPP in the context of SADC region, the analysis suffers from one key limitation that can be explored by future research. The restricted data availability precludes us from explicitly incorporating a variable to capture the distance between the numéraire countries and the rest of the SADC countries. Including this variable may either reinforce our conclusion of the border effect or yield different results and conclusions, and its impact on the speed of convergence of real exchange rates towards their equilibrium PPP remains to be explored. Future research can exploit this window to deepen our understanding of the border effect to further reveal the empirical validity of the PPP theory.