Prospects for a Monetary Union in the East Africa Community: Some Empirical Evidence

This paper examines G-PPP and business cycle synchronization in the East Africa Community with the aim of assessing the prospects for a monetary union. The univariate fractional integration analysis shows that the individual series exhibit unit roots and are highly persistent. The fractional bivariate cointegration tests (see Marinucci and Robinson, 2001) suggest that there exist bivariate fractional cointegrating relationships between the exchange rate of the Tanzanian shilling and those of the other EAC countries, and also between the exchange rates of the Rwandan franc, the Burundian franc and the Ugandan shilling. The FCVAR results (see Johansen and Nielsen, 2012) imply the existence of a single cointegrating relationship between the exchange rates of the EAC countries. On the whole, there is evidence in favour of G-PPP. In addition, there appears to be a high degree of business cycle synchronization between these economies. On both grounds, one can argue that a monetary union should be feasible.


Introduction
This paper aims to assess the prospects for a monetary union in the East African Community (EAC), a group of six countries intending to achieve a common monetary policy and currency by 2024, by considering some of the conditions for an Optimal Currency Area (OCA). More specifically, it applies fractional cointegration methods to test whether Generalized Purchasing Power Parity (G-PPP) holds in the EAC. In addition, it examines business cycle synchronisation by using the Hodrick-Prescott (HP) filter to decompose GDP into trend and cyclical components and measure the degree of correlation between the latter in this set of countries. Because South Sudan joined the EAC only in April 2016, and therefore very few observations are available for this country, the analysis focuses on the other five members of the union only.
Unlike earlier studies on the EAC based on the classical I(0)/I(1) dichotomy (see, e.g., Buigut and Valev, 2005;Mafusire and Brixiova, 2013;Yabara, 2014), we adopt a fractional cointegration framework that allows for long memory in the residuals of the cointegrating relationship, and therefore for a slow dynamic adjustment towards the long-run equilibrium. Long-memory models have already been estimated in various papers testing for Purchasing Power Parity (PPP). For instance, Kaen and Koveos (1982) found evidence of long memory during the flexible exchange rate period (1973)(1974)(1975)(1976)(1977)(1978)(1979), and Cheung (1993) during the managed floating regime. Baum et al. (1999) estimated ARFIMA models for real exchange rates in the post-Bretton Woods era and found no evidence to support long-run PPP. Diebold et al. (1991) and Baillie and Bollerslev (1994) reported fractional cointegration with non-stationary but mean- More recent studies have employed fractional integration and cointegration to analyse OCAs (see, e.g., De Truchis and Kedadd, 2014 for the case of the ASEAN economies). In the present paper we carry out for the first time this type of analysis for the EAC and employ, among others, the recently introduced Fractionally Cointegrated VAR (FCVAR) approach proposed by Johansen and Nielsen (2012).
The structure of the paper is as follows: Section 2 provides some background information about the East African Community; Section 3 explains the relevance of Generalized Purchasing Power Parity for Optimal Currency Areas; Section 4 outlines the fractional integration and cointegration methods used; Section 5 presents the empirical results, and Section 6 offers some concluding remarks.

The East African Community
The non-negligible risk of failure, and therefore it is essential to ensure that the requirements for a successful EAMU are met.

Generalized Purchasing Power Parity and Optimal Currency Areas
Generalized Purchasing Power Parity (G-PPP) for m countries in a world of n countries requires that there exists a long-run equilibrium cointegration relationship between their m-1 bilateral real rates. When G-PPP holds, the real exchange rate between two countries can be expressed as a weighted average of the other real rates in the currency area. These weights reflect not only trade linkages, but also technology transfers, immigration and financial flows.
G-PPP can be interpreted in terms of an Optimum Currency Area (OCA), that is, a group of regions or countries with economies closely linked by trade in goods and services and by factor mobility for which it is ideal to adopt a single currency or a group of currencies pegged to each other and fluctuating together vis-à-vis other currencies.
According to Mundell (1961), under the assumption of short-run rigidity of prices and wages and no factor mobility, a group of economies can be considered an OCA if they experience the same types of real disturbances. The volume of intra-regional trade among members is also important: in the Heckscher-Ohlin model, if two countries are major trading partners then there will be some degree of factor price equalization. Thus, within a currency area with sufficiently linked economies, the real exchange rates will share a common stochastic trend; this implies that there should be at least one cointegrating relationship between them (see Enders and Hurn, 1994

Methodology
Until the 1980s non-stationary economic and financial time series were usually modelled assuming a deterministic function of time and stationary I(0) residuals from the regression model. After the seminal work of Nelson and Plosser (1982), the consensus became that the non-stationary element of most series is stochastic, and I(1) models with unit roots were normally specified. However, the I(0)/I(1) dichotomy is a rather restrictive assumption, since the differencing parameter required to obtain stationarity is not necessarily an integer but could be any real value as in the case of fractionally integrated or I(d) processes belonging to the long-memory category.
Long memory implies that observations which are far apart in time are highly correlated, and this property can be captured in a fractional integration framework. A fractionally integrated, or I(d) model, , can be expressed in the following form: (1) where d can be any real value, L is the lag-operator (Lx t = x t-1 ) and u t is I(0), defined as a covariance stationary process with a spectral density function that is positive and finite at the zero frequency. The polynomial in equation (1) can be expressed in terms of its binomial expansion, such that, for all real , and thus In this context, plays a crucial role since it indicates the degree of dependence of the time series. The higher the value of is, the higher the level of association between the observations will be. Specifically, if d = 0, x t = u t , x t is said to be characterized by "short memory" or I(0), and autocorrelation (AR) is of a "weak" form, with the autocorrelation coefficients decaying exponentially. If d > 0, x t is said to exhibit "long memory", so called because of the strong association between observations that are distant in time. If d belongs to the interval (0, 0.5) then x t is still covariance stationary, while d ≥ 0.5 implies non-stationarity. Finally, if d < 1, the series is mean-reverting, i.e. the effects of external shocks disappear in the long run, in contrast to the case of d ≥ 1, when they persist indefinitely.
There are several methods for estimating and testing the fractional differencing parameter d. Some of them are parametric while others are semi-parametric and can be specified in the time or in the frequency domain. In this paper we use a Whittle estimator of d in the frequency domain (Dahlhaus, 1989) along with a testing procedure based on the Lagrange Multiplier (LM) principle that also uses the Whittle function but in the frequency domain. We test the null hypothesis: (2) for any real value d o , in a model given by the equation (1), where x t is the errors in a regression model of the form: ( 3) where y t is the observed time series, β is a (kx1) vector of unknown coefficients and z t is a set of deterministic terms that might include an intercept (i.e., z t = 1), an intercept with a linear time trend (z t = (1, t) T ), or any other type of deterministic processes. The LM test of Robinson (1994) is robust to a certain degree of conditional heteroscedasticity and is the most efficient method in the Pitman sense against local departures from the null (see Robinson, 1994).  (2008) and further expanded by Nielsen (2010, 2012). This is a generalization of Johansen´s (1996) Cointegrated Vector AutoRegressive (CVAR) model which allows for fractional processes of order d with cointegrating order d-b. Consider first the well-known, nonfractional, CVAR model. Let y t , t = 1, 2, …, T be a p-dimensional I(1) time series. The CVAR model is specified as (4) The simplest way to derive the FCVAR model is to replace the difference and lag operators and in (5) with their fractional counterparts, and , respectively. We then obtain (5) which is applied to such that (6) where is p-dimensional independent and identically distributed with mean zero and covariance matrix . The parameters have the usual interpretations from the CVAR model. Thus, α and β are matrices, where . The columns of are the cointegrating relationships in the system, that is to say the long-run equilibria. The parameters Γ i govern the short-run behaviour of the variables, and the coefficients in α represent the speed of adjustment towards equilibrium for each of the variables. The FCVAR model permits simultaneous modelling of the long-run equilibria, the adjustment responses to deviations from them and the short-run dynamics of the system. Nielsen and Morin (2016) provide Matlab computer programmes for the estimators and test statistics.

Empirical Results
We employ monthly data on real exchange rates from 1990 up to 2015 obtained from the IMF's International Financial Statistics. These series are shown in Figure 1, and appear to behave rather similarly, all of them exhibiting an upward trend. Standard unit root tests suggest that none of them is characterized by I(0) stationarity (see Table 1).
[Insert Table 1 about here]  Tables 2 and 3 about here] Table 3 shows the bivariate fractional cointegration test results. In 6 out of 10 cases the null of fractional cointegration cannot be rejected. The exchange rate of the Tanzanian shilling is cointegrated with all the other exchange rates, while that of the Rwandan franc is cointegrated with those of the Burundian franc and the Ugandan shilling. By contrast, the Kenyan Shilling does not appear to be linked to the other currencies in the region. On the whole, the evidence concerning G-PPP is not conclusive.

[Insert Tables 4 and 5 about here]
Next, we estimate the FCVAR model. The null of one fractional cointegration relationship cannot be rejected (see Table 4), which suggests that G-PPP holds. The resulting VECM specification is the following: The estimated coefficients imply that external shocks have opposite effects in the case of the former British territories compared to Burundi and Rwanda.
Finally, we analyse business cycle synchronization in the EAC. Specifically, we apply the Hodrick-Prescott method to decompose GDP into trend and cyclical components using annual data from the Pennworld [Insert Figure 2 and Table 5 about here] The results are shown in Figure 2. In all cases there is an upward trend. However, only Uganda appears to have experienced continuous growth, whilst the other countries have also gone through periods characterised by declines in GDP growth: in Ruanda this occurred following the genocide of the early 1990s; in Tanzania, after a period of buoyant growth driven by public investment in all sectors of the economy, poverty reemerged at the beginning of the 90s; in both Kenya and Burundi the 1990s were a period of slow growth. Table 6 reports the correlations between the cyclical components for the five EAC countries analysed. Most of them are high and positive, which represents evidence in favour of the feasibility of a monetary union.

Conclusions
This paper examines real exchange rate linkages and business cycle synchronization in the EAC with the aim of assessing whether or not this set of countries is likely to be able to create a successful monetary union. The univariate fractional integration analysis shows that the individual series exhibit unit roots and are highly persistent. The Franc Burundian ε µ υ fractional bivariate cointegration tests (see Marinucci and Robinson, 2001) suggest that there exist bivariate fractional cointegrating relationships between the exchange rate of the Tanzanian shilling and those of the other EAC countries, and also between the exchange rates of the Rwandan franc, the Burundian franc and the Ugandan shilling.
The FCVAR results (see Johansen and Nielsen, 2012) imply the existence of a single cointegrating relationship between the exchange rates of the EAC countries. On the whole, there is evidence in favour of G-PPP. In addition, there appears to be a high degree of business cycle synchronization between these economies. On both grounds, one can argue that a monetary union should be feasible. Differences in exchange rate behaviour still exist between the former British colonies relative to Burundi and Ruanda, but on the whole the EAC might qualify as an OCA. A similar approach could be used to analyse the feasibility of other currency unions in Africa such as the South African Development Community or the West African Monetary Zone.
It should be stressed, however, that a successful union also requires fiscal convergence. At present there is no evidence that this has been achieved. The EAC countries are heavily dependent on external aid flows to combat fiscal imbalances; a measure of the fiscal deficit inclusive of foreign aid would be more informative about the state of their public finances with a view to forming a monetary union. It would also be useful for the EAC countries to agree on surveillance and the enforcement mechanisms for convergence criteria. A possibility would be to give an appropriate mandate to the EAC Secretariat. Despite being heterogeneous economies, these countries have been kept together by their common historical ties to the Francophone world. The existence of equivalent ties could also facilitate the creation of a union between the members of the EAC. Pegging the new EAC common currency to an international currency with a strong historical link such as the British pound could be an appropriate starting point.     The first two values refer to the test statistics for H x and H y respectively using the Hausman test of Marinucci and Robinson (2001). The third value is the estimated value of d * . χ 1 2 (5%) = 3.84. In bold and with an asterisk, those cases where we reject the null hypothesis of no cointegration at the 5% level.