Laetitia Lepetit
email: laetitia.lepetit@unilim.fr

Clovis Rugemintwari
email: clo-vis.rugemintwari@unilim.fr

Frank Strobel
email: f.strobel@bham.ac.uk

Monetary, …nancial and …scal stability in the East African Community: ready for a monetary union?

Keywords: monetary union, East African Community, …nancial stability, real option JEL Classi…cation: E58, F33, O55

research documents, whether they are published or not. The documents may come

Introduction

The East African Community (EAC), currently consisting of Burundi, Kenya, Rwanda, Tanzania and Uganda, has been engaged in an ambitious integration process since its o¢ cial relaunch in 2000. A customs union was set up in 2005 which became fully operational in 2010, a common market project was initiated in 2010 which is scheduled to be completed by 2015, and the EAC member countries are also in the process of further moving towards establishing a monetary union as well. Negotiations of monetary union protocols were initiated in January 2011 (EAC 2011) and are currently anticipated to be concluded by the end of 2012, making way for discussions of suitable roadmaps for a possible transition to a single currency in the region (Rusuhuzwa & Masson 2012). Our paper aims to contribute to this debate by highlighting several important issues that have not been previously focussed on in the academic literature on the subject.

While there is a fair number of studies examining the feasibility or desirability of monetary unions in Africa more generally (see e.g. Debrun et al. 2011 for a survey), the literature focussing on the EAC in particular is relatively small for the time being. Most of the research focussing on the EAC examines the potential for a monetary union in the light of the Optimal Currency Area (OCA) approach which has its origins in the seminal work of Mundell (1961), McKinnon (1963) and Kenen (1969). Mkenda (2001), using data for varying periods up to 1998, examines the three original EAC member countries, Kenya, Uganda and Tanzania, and …nds some support that they constitute an OCA. Buigut & Valev (2005), on the other hand, consider this question for all …ve current EAC member countries using data for the period 1970-2001, with results that are rather unsupportive of these countries forming an OCA. In a similar spirit, Buigut (2011) focusses on the state of convergence across several macro measures over the period 1997-2008 for the …ve EAC members, whereas Kishor & Ssozi (2011) examine their degree of business cycle synchronization over the period 1970-2007; both similarly conclude that the evidence for these countries representing an OCA is weak.

A di¤erent methodological approach is pursued in the related but complimentary papers of Buigut & Valev (2009) and Debrun et al. (2011). They aim to model potential bene…ts as well as costs associated with a monetary union by focussing on the reduction in in ‡ation bias (in a Barro & Gordon 1983b sense) achievable through being in a monetary union. Calibrating their model, which allows for random supply shocks to output and stochastic preferences for output stimulation, to EAC data for the period 1990-2004, Buigut & Valev (2009) …nd that Uganda and Tanzania would bene…t from a monetary union whereas the other countries would lose from it. Debrun et al. (2011), whose model allows for the setting of tax and seigniorage revenues to achieve optimal productive expenditure and its interaction with stabilizing monetary policy reactions to shocks, …nd using data covering the period 1990-2008 that Burundi and Kenya would bene…t most from a monetary union in the EAC, whereas Tanzania would lose from joining it.

The methodological approach used in the present paper to assess whether the EAC is "ready" for a monetary union is related to the previous two papers, in that it builds on work in Strobel (2005, 2007) which also examine countries' willingness to join a monetary union when a time inconsistency problem in monetary policymaking causes an in ‡ation bias to persist, but stress the importance of taking the real option associated with such monetary regime changes into account. The papers argue that, when the future evolution of policymakers'in ‡ation preferences is uncertain in such a context, countries might …nd it bene…cial to hold back on joining a wider monetary union due to their reluctance to commit to a largely irreversible decision that might later prove less advantageous than initially thought. This value of waiting, stemming from the real options nature of the decision problem, is well-known from the literature on irreversible investment under uncertainty, can generally be substantial and needs to be properly accounted for. 1 In order to highlight the importance of the role of uncertainty in policymakers' decision making in this respect, we develop a stylized model of policymakers'decision problem that allows for the stochastic nature of three key areas of relevance in the decision of whether or not to join a monetary union: monetary, …nancial and …scal stability. In addition to the monetary stability aspect that has so far been center stage in this context, the recent developments in the euro zone have provided ample proof that both …nancial and …scal stability aspects can also have a tremendous impact on the functioning and even viability of a monetary union, even if no prior informal arrangements or even explicit institutional structures regarding the sharing of …nancial and …scal risk exist in the region constituting the monetary union. Deriving the trigger values of monetary, …nancial and …scal stability measures which determine whether or not policymakers …nd it bene…cial to exercise the real option of engaging in the monetary union, we show that when policymakers properly account for the uncertainty regarding the evolution of the monetary, …nancial and …scal stability measures considered, they might prove quite reluctant to go ahead with participation in a monetary union unless compensated for by potential other factors (such as institutional improvements or more transactional bene…ts), as the net bene…ts derived from being in the monetary union might later prove less advantageous than initially thought.

We then calibrate our model for the EAC, using annual data for the period 2003 to 2010, for various proxies of our respective monetary, …nancial and …scal stability measures. Two key results emerge from our calibrations: …rstly, the choice of proxies we consider for our monetary, …nancial and …scal stability measures matters for whether or not policymakers …nd joining a monetary union bene…cial for their particular country. Secondly, and more importantly, however, allowing for the impact of uncertainty surrounding the evolution of these measures of monetary, …nancial and …scal stability generally makes policymakers signi…cantly less eager to engage in a mone-tary union, unless compensated for by su¢ cient degrees of other bene…ts, such as of a transactional nature, or more importantly in our view, institutional improvements over existing national arrangements. When policymakers properly allow for the role of uncertainty in this context, we conclude that none of the countries wants to engage in a monetary union based on either monetary or …nancial stability considerations unless compensated for by signi…cant relative levels of additional bene…ts, requiring in our view credible and robust institutional arrangements at the monetary union level assuring substantial improvements in monetary and …nancial stability. When looking at the …scal stability aspect, all countries except possibly Rwanda would be reluctant to join the monetary union from this perspective when uncertainty is taken into account, unless compensated for by a su¢ cient relative degree of additional bene…ts, again asking for a sound institutional structure assuring …scal stability in the monetary union.

Section 2 now provides some background for the EAC countries; Section 3 develops our model; Section 4 describes our calibration approach; Section 5 presents and discusses our results; and Section 6 concludes the paper.

Political, economic and institutional background

The roots of the East African Community (EAC) go back to the colonial period when a customs union between Kenya and Uganda was signed in 1917, which was later joined by Tanzania (called at that time Tanganyika) in 1927. The …rst treaty establishing the EAC was signed in 1967; however, it collapsed a decade later in 1977 and was o¢ cially dissolved in 1983. Several reasons for the collapse of the old EAC have been put forward (Mugomba 1978, Hazlewood 1979). Firstly, there was a sentiment that the common market was more bene…cial to Kenya than to Tanzania and Uganda. This can be explained by di¤erences in the level of industrialization, with a more developed industrial sector in Kenya than in the two other countries. Secondly, Kenya, Tanzania and Uganda had important ideological and domestic political di¤erences. Kenya was committed to capitalism, but internal political tensions and corruption had led to economic stagnation. On the other hand, Tanzania and Uganda pursued forms of African socialism (Ujamaa in Tanzania and Common Man's Charter in Uganda).

The region went through several political and economic shocks after the collapse of the initial EAC. However, the three countries have lately followed broadly similar policies by adopting capitalism, without any central economic coordination. In 1999, the three original partner states Kenya, Uganda and Tanzania rati…ed the treaty reviving the EAC, which came into force in July 2000. 2 In July 2007, two more countries, Burundi and Rwanda became o¢ cially full members of the EAC, giving it its current shape of …ve partner states. The integration process of the EAC is embedded in Article 5(2) of its Treaty, stipulating that the "Partner States undertake to establish among themselves [...] a Customs Union, a Common Market, subsequently a Monetary Union and ultimately a Political Federation". The …rst of these four steps has been completed: the customs union was signed in March 2004, was launched in 2005 and became fully operational in 2010. The common market project was initiated in 2010 and is scheduled to be completed by 2015; the completion of these …rst two steps will allow the free movement of goods, labour, services and capital among the …ve member countries. The next step in this integration process is the move towards a monetary union, with negotiations of monetary union protocols having started in January 2011 which are currently anticipated to be concluded by the end of 2012. 3 Before looking more closely at the decision of individual EAC member countries of whether joining a monetary union based on monetary, …nancial and …scal stability considerations may be bene…cial, it is helpful to look at some more general indicators of the economic structure, the development of the …nancial system and the institutional environment of these countries.

All EAC countries have pursued programs to restructure their economies over the last two decades, with the help of the International Monetary Fund and the World Bank. Uganda and Rwanda were the most successful reformers (public sector reforms, trade liberalization, market and price reforms) leading to an economic expansion. These two countries display the highest average GDP growth rate in the EAC over the period 2000-2010 (see Table 1) accompanied by an increase of GDP per capita of 58% for Rwanda and 47% for Uganda (see Figure 1). This means that those two countries may ultimately catch up with Kenya which has the highest GDP per capita. Uganda and Rwanda have also had success in reducing their in ‡ation rates to comparatively low levels of 2.3% and 4%, respectively, in 2010 (see Table 1). They furthermore, together with Tanzania, have the lowest budget de…cit and domestic public debt (as percentage of GDP) on average over the last decade (see Table 2).

Kenya has been a¤ected by government mismanagement, counterproductive economic policies and corruption for decades (Heritage Foundation 2012). Political pressures lead to several breakdowns of …scal and monetary discipline, and Kenya has on average the highest domestic public debt to GDP ratio and a high in ‡ation rate over the period 2000-2010. Tanzania, a historically state-led economy, made progress in fostering growth over the past decade with a GDP per capita in 2010 close to Kenya's (see Table 1 and Figure 1), through implementing a large program of reforms to become more market-based. Amongst the EAC countries, Burundi is the least performing one with a GDP per capita 25% of the ones of Kenya and Tanzania, and 35% of those of Uganda and Rwanda. According to Heritage Foundation (2012), the repressive policy environment in Burundi makes it di¢ cult for the private sector to create employment and sustained economic growth. Despite these di¤erences, the EAC countries are fairly similar when looking at the sectoral composition of GDP (see Table 1). All are heavily dependent on agriculture, with exports being largely resource-based.

World Development Indicators on government e¤ectiveness, control of corruption, political stability, rule of law and regulatory quality further show that there are strong disparities in terms of institutional environment between EAC countries (see Figures 2 to 6). Such di¤erences can possibly go a long way towards explaining the di¤erent economic performances observed. Rwanda shows the highest degree of improvement over the last decade in terms of quality of public services, credibility of government policies, control of corruption and con…dence in the rules of society.

Important di¤erences across the EAC can furthermore be observed regarding the size and the development of the …nancial sector. While EAC …nancial systems are all concentrated in commercial banking and very small in relation to the economy, the level of development of capital markets varies greatly. Kenya has a relatively well-developed …nancial sector, Tanzania and Uganda have small stock exchanges and Burundi and Rwanda do not have a stock market at all (see Table 3). The market capitalization of the 55 listed Kenyan companies stands at about 35% of GDP, whereas that of the 11 Tanzanian and the 8 Ugandan ones is about 27% and 5.5%, respectively. The development of the securities market in the EAC countries is constrained by the small number of private …rms with the capacity to raise funds through the capital markets. Similarly, the demand for …nancial products is also relatively low.

The …nancial system of all EAC countries is dominated by banks. Large reforms have been implemented during the last two decades in order to liberalize the banking system, privatize state-owned banks and restructure loss making banks characterized by a high level of non performing loans (Cihak & Podpiera 2005, UN Economic Commission for Africa 2008). The expected positive e¤ects from liberalization in terms of savings mobilization and credit allocation were slow to emerge, but one can observe over the last …ve years a sharp acceleration in the domestic credit provided by the banking sector relative to GDP, apart from for Rwanda (see Figure 7). These reforms notwithstanding, EAC countries have overall a low level of …nancial intermediation and access to …nance is a critical issue. As shown in Table 3, less than 30% of the population in Rwanda, Tanzania and Uganda have access to the formal …nancial system, whereas more than 50% of the population in Rwanda and Tanzania are completely excluded from access to …nancial services. In Kenya, the development of mobile banking has however increased the proportion of the population that has access to the formal banking sector to 40%. Furthermore, bank deposits as a percentage of GDP are less than 35% for Burundi, Tanzania, Uganda and Rwanda and just above 50% for Kenya, well below the levels of some other African countries (e.g. 70% in South Africa).

This high level of …nancial exclusion could be explained by the small number of banks which operate in the EAC (see Table 3), as well as by the lack of competition between these banks. Sanya & Gaertner (2012) show that despite the lack of formal regulatory barriers to entry, there are structural factors that enable some banks to bene…t from a degree of monopoly power. More than two decades after reforms were started, the spread between lending and deposit rates is still high (above 8%, see Table 3), re ‡ecting this lack of competition. The banking system in Uganda shows the highest bank spread, but it is also the most robust one with the highest return on assets on average over the period 2003-2010, the highest capital adequacy and equity ratios, the lowest non performing loans to gross loans ratio and a relatively high value of the aggregate Z-score,4 re ‡ecting a relatively low level of aggregate bank insolvency risk (see Table 4). The banking system in Kenya, which is by far the most developed in the EAC, also displays good performance with a strong decrease in the non performing loans ratio over the period 2003-2010 and the highest aggregate Z-score, i.e. the lowest degree of aggregate bank insolvency risk. The banking systems in Burundi and Rwanda, on the other hand, are the smallest in the EAC and have a relatively high level of non performing loans. Lastly, there are also important di¤erences in banking regulation across the EAC as shown in Table 5: there is no explicit deposit insurance system in Burundi and Rwanda, and there is no harmonization on activity restrictions and capital adequacy requirements throughout.

Overall, despite tremendous improvements in economic fundamentals in the EAC countries in the last decade, we still observe a substantial degree of divergence in these, supplemented with even stronger di¤erences in the institutional environment in place in these countries.

[Insert Tables 1-5 andFigures 1-8] 3 Policymakers'stylized decision problem As our …rst step towards examining prospects for a monetary union in the EAC, we now develop a stylized model of policymakers' decision problem regarding whether or not to join a monetary union that allows for the uncertainty arising in three key areas of importance in this context. Policymakers are assumed to be concerned with monetary (m), …nancial (f ) as well as …scal (g) stability, in their own countries (c) or the monetary union (u) if they decide to participate in it. They face instantaneous bene…t rates sit = sit , where s = m; f; g and i = c; u, that are concave, with concavity parameter 0 < 1, in monetary, …nancial and …scal stability measures mit ; f it ; git 0 which are stochastic and follow geometric Brownian motions5

d sit = si sit dz sit ; s = m; f; g ; i = c; u (1)
where si > 0, dz sit = " sit p dt are increments of Wiener processes with " sit NID(0; 1), and E t (dz sct dz sut ) = s dt with s the coe¢ cient of correlation between the processes z sit (and 1 s < 1). The expected present discounted value of bene…ts associated with monetary, …nancial or …scal stability is then6

B sit = E t Z 1 t si e ( t) d = sit 1 2 2 si ( 1) ; s = m; f; g (2)
where > 0 is the (possibly subjective) discount rate, and

1 2 2 si ( 1) > 0 represents a natural convergence condition.
The decision of a country c on whether or not to participate in the monetary union u, on monetary, …nancial or …scal stability grounds, [START_REF] Strobel | Bank insolvency risk and di¤erent approaches to aggregate Z-score measures: A note[END_REF] then involves solving the Bellman equation for the optimal stopping problem8

F (B su ; B sc ) = max (1 + s ) B su B sc ; 1 dt E[dF (B su ; B sc )] ; s = m; f; g
(3) where F (B su ; B sc ) is the value to country c of the option of participating in the monetary union u, and (1 + s ) B su B sc is the expected discounted bene…t from improved monetary, …nancial or …scal stability of such a participation, with all potential other bene…ts9 captured by the proportionality factor s 0. Note that this implicitly assumes that participating in a monetary union is an irreversible process, so that the costs of possibly later leaving it, both reputational and institutional, are considered prohibitively high. 10 We can then obtain Proposition 1 Country c will want to exercise the option of participating in the monetary union u, on monetary (m), …nancial (f ) or …scal (g) stability grounds, if

su sc su sc = + s 1 2 2 su ( 1) (1 + s ) ( + s 1) 1 2 2 sc ( 1) ! 1 ; s = m; f; g
where + s is the positive root 11 of the characteristic equation

2 su 2 s su sc + 2 sc 2 2 s 2 ( 2 sc s su sc ) + 2 su 2 sc s + 2 sc ( 1) 2 = 0 ; s = m; f; g
and not exercise it otherwise.

Proof. See the Appendix.

Country c thus perceives exercise of the option of participating in the monetary union u, on monetary, …nancial or …scal stability grounds, as desirable only when the current value of relative monetary, …nancial or …scal stability measure su = sc is greater than (or equal to) its derived trigger value su = sc ; intuitively, the lower a country's monetary, …nancial or …scal stability relative to the potential monetary union's, the more it stands to gain from participating in that union. While su = sc < su = sc applies, on the other hand, country c strictly prefers to leave the option of participating in the monetary union u unexercised and remains outside it for the time being.

Figures 9-11 numerically illustrate the economic relevance of these results, graphing the trigger values u = c derived in Proposition 1 for di¤erent parameter combinations of standard deviations i , correlation coe¢ cients for as well, albeit at nontrivial analytical cost. Qualitatively, however, results would be very similar to the benchmark case considered here as long as the costs associated with later leaving the monetary union are su¢ ciently high, a scenario vividly illustrated by the Eurozone crisis debate of 2012.

11 While + s can be derived analytically, it is rather unwieldy and not too insightful for our purposes here.

, discount rates , concavity parameters and the proportionality factor . 12 We observe from the nontrivial magnitudes of trigger values arising that when policymakers properly account for the uncertainty surrounding the future evolution of the monetary, …nancial and …scal stability measures considered, they might prove quite reluctant to go ahead with participation in a monetary union unless compensated for by potential other bene…ts (captured by the proportionality factor ), as the associated bene…ts and costs might later prove less advantageous than initially thought. [Insert Figures 9-11] 4 Calibration approach To calibrate our model for the EAC, we use annual data from the EAC Statistics database13 as our main source of data. As this data is harmonized for the …ve EAC member countries, data discrepancies that might stem from di¤erences in de…nitions or calculations across di¤erent sources are reduced. The period over which our calibration is carried out is driven by data availability, and covers the period 2003 to 2010. Some missing data (for 2003 and 2004 for Tanzania and for 2009 for Uganda in particular) was completed from central bank reports. Our data was furthermore checked against two other data sources, International Financial Statistics (IFS) and World Development Indicators (WDI), turning out broadly comparable (with the exception of Kenya, where the in ‡ation rate reported in the EAC database was comparatively lower for 2006-2009).

We consider various proxies for our monetary, …nancial and …scal stability measures. We proxy the monetary stability measure m by two indicators: the inverse of the (realized) in ‡ation rate given by the consumer price index (CPI), and the inverse of the public domestic debt to GDP ratio. These measures aim to capture the potential in ‡ation bias resulting when governments try to stimulate output in the short run (the expectational Phillips curve argument) or to reduce the real value of outstanding public (domestic) debt (the governmental revenue motive). 14 We …nd non-trivial ranges of the standard deviations mc used in our calibrations that go from 0.09 to 1.01, and correlation coe¢ cients m that range between -0.07 and 0.97.

We also consider two proxies for our …nancial stability measure f : the inverse of the bank nonperforming loans to gross loans ratio, one of the traditional …nancial soundness indicators used by the International Monetary Fund (IMF), and aggregate Z-score measures re ‡ecting the overall insolvency risk faced by a country's banking sector. 15 Using aggregate country data for the banking sector, we construct these aggregate Z-score measures as Z = ROA + EQ_TA = ROA where ROA and EQ_TA are three year rolling means of the return on assets and the equity to total assets ratio, and ROA is the three year rolling standard deviation of the return on assets. 16 We observe values of the standard deviations f c used in our calibrations that range from 0.11 to 0.89, and correlation coe¢ cients f that lie between -0.38 and 0.99.

Lastly, we use the two following proxies for our …scal stability measure g : the inverse of the budget de…cit (including all grants) to GDP ratio, and the inverse of the budget de…cit (excluding all grants) to GDP ratio. The distinction between the two is relevant as we note from Table 2 that the government …nances of Burundi and Rwanda, in particular, are strongly dependent on grants. As the level and continuity of such grants can be unpredictable, the measure excluding all grants is more "structural" in a sense than the one including them. We …nd values of the standard deviations gc used in our calibrations that go from 0.08 to 0.22, and correlation coe¢ cients g that range between -0.08 and 0.88.

The potential monetary union's monetary, …nancial and …scal stability measures su are then constructed as the arithmetic means of the constituent countries'proxied values, weighted by domestic credit provided by the banking sector for the …nancial stability proxies, and (constant) GDP for the monetary and …scal stability proxies (these were retrieved from WDI). For the monetary stability measures, this mimics a bargaining outcome over the union's monetary policy where individual member countries' votes re ‡ect their relative size in the union. For the …nancial and …scal stability measures, on the other hand, this approximates …nancial and …scal risk sharing arrangements implicitly (or even explicitly) associated with the monetary union, again allowing for individual member countries'respective size.

In order to then compute the proxied trigger values of relative monetary, …nancial and …scal stability measures su = sc given by Proposition 1, we derive the standard unbiased estimates17 of si and s by calculating the standard deviations and correlation coe¢ cients for the respective transformed series ln ( t = t 1 ) for each of our proxies. In line with discount rates applied by the World Bank and African Development Bank, we assume a (social) discount rate of = 12% (see e.g. Harrison 2010), consistent with a substantial amount of myopia attached to policymaker's decision making. 18 We furthermore set the concavity parameter in policymaker's bene…t functions at = 0:5, re ‡ecting the plausible assumption that the bene…ts policymakers derive from increased monetary, …nancial or …scal stability exhibit diminishing marginal returns. 19 An interesting benchmark case in our calibrations is going to be the decision problem for a policymaker that ignores the importance of uncertainty in their decision making process: it is straightforward to see that the trigger value corresponding to the one given in Proposition 1 would then simply be su = sc = 1 in this case.

Results and discussion

We present the results from our calibrations in Tables 678, examining policymakers'willingness to participate in a monetary union on monetary, …nancial and …scal stability grounds, respectively. Our analysis is carried out …rst considering a monetary union consisting of all …ve current member countries of the EAC; we then alternatively examine whether the results di¤er when we restrict the analysis to the three original member countries that may have deeper ties by comparison. This will allow us to determine whether the addition of Burundi and Rwanda in 2007 to the EAC made the move towards a monetary union more di¢ cult to achieve or not. In each case, we examine whether countries would be willing to participate in a given monetary union under two scenarios: …rstly, where policymakers abstract from the role of uncertainty, 20 and then, secondly, where they do properly account for the importance of uncertainty in the decision problem they face, in line with Proposition 1. By comparing the respective trigger values su = sc with the actual values su = sc of each criterion/proxy in the year 2010 (our reference period), we then explicitly answer the question whether each country would currently …nd participating in the given monetary union advantageous or not. Where they would prefer to stay outside a given monetary union for the time being, we further calculate the minimum level of relative other bene…ts s associated with being in a monetary union that would nevertheless make it worthwhile for them to participate in the monetary union after all. 21 The results from our calibration considering countries'willingness to par-

= sc = + s 1 2 2 su ( 1) = (1 + s ) ( + s 1) 1 2 2 sc ( 1)
1 from Proposition 1, or s = sc = su 1 for the certainty case.

ticipate in a monetary union on monetary stability grounds are presented in Table 6. When policymakers ignore the role of uncertainty in the decision of whether or not to join a monetary union consisting of all EAC countries, we observe that for Proxy 1 (inverse of realized in ‡ation) Burundi and Tanzania, and for Proxy 2 (inverse of public domestic debt to GDP) additionally Kenya, are in favor of entering into such a union. The other countries are only willing to go ahead with such a move when the other bene…ts associated with a monetary union are of a su¢ cient magnitude, as expressed by the level of . Considering Proxy 1, Rwanda is the most reluctant (has the highest level of ), whereas for Proxy 2 this place is taken by Uganda. This is in line with our observation in Section 2 that both Rwanda and Uganda had substantial success in reforming their economies in the last decade. When policymakers do properly account for the role of uncertainty in this decision problem, by allowing for the value of the real option introduced by the uncertainty surrounding the bene…ts from a potential monetary union (driven by the variability in our monetary stability measures observed in Tables 1 and2), only Burundi and Kenya, and that exclusively for Proxy 2, still want to go ahead with the monetary union. The other three countries for Proxy 2, and all …ve EAC member countries when focussing on Proxy 1, would now be reluctant to join, with the countries requiring the highest, and now substantially larger, relative levels of other compensating bene…ts from such a monetary union still being Rwanda when considering Proxy 1, and Uganda when focussing on Proxy 2. Interestingly, we can further note that considering only a monetary union consisting of the original EAC member countries Kenya, Tanzania and Uganda does not change those countries'incentives to join such a narrower monetary union compared to the larger …ve country union, irrespective of whether policymakers properly account for the role of uncertainty in their decision making or not.

The importance of allowing for the role of uncertainty in policymakers' decision making also shows when we examine countries'willingness to par-ticipate in a monetary union based on …nancial stability motives, the results of which are presented in Table 7. When uncertainty is abstracted from, almost all countries …nd participation in a monetary union consisting of all …ve EAC countries bene…cial, with the exception of Uganda when considering Proxy 1 (inverse of nonperforming loans to gross loans), and Kenya when examining Proxy 2 (aggregate Z-score). Again this is consistent with our discussion in Section 2 which showed that Kenya and Uganda have the most robust banking systems amongst the group of EAC countries. When uncertainty regarding the evolution of our …nancial stability measures (see Table 4) is properly accounted for in policymakers'decision problem, Kenya also loses interest in joining the monetary union based on Proxy 1, with Uganda becoming even more strongly opposed to such a move (as shown by its high level of ). When considering Proxy 2, however, none of the countries want to move towards the monetary union unless su¢ ciently compensated by the respective relative other bene…ts associated with it, with Uganda again being the most demanding in this sense (having the highest level ), followed closely by Tanzania. Similarly to the results obtained for the monetary stability criteria above, countries' incentives of joining a narrower monetary union consisting of only the original EAC member countries are unchanged compared to those associated with joining the larger one, again irrespective of whether uncertainty is allowed for in policymakers decision making or not.

A further illustration of how important the consideration of uncertainty is in this context is given when we lastly examine countries' willingness to participate in a monetary union on …scal stability grounds (Table 8). Results for the no uncertainty case are somewhat mixed, providing an exactly opposing picture of whether or not countries want to join the monetary union consisting of all …ve EAC member countries depending on whether Proxy 1 (inverse of budget de…cit inc. grants to GDP), or Proxy 2 (inverse of budget de…cit excl. grants to GDP) is used. This stresses, in a sense, the importance of being careful as to which measure to use in this context; as the latter one clearly gives a more "structural" picture of a country's …scal position, we would favor concentrating on the second one. On this basis, Kenya and Uganda would be opposed to the monetary union on …scal stability grounds, with the other countries …nding it bene…cial. These results change dramatically, though, once we consider that policymakers do allow for the role of uncertainty in the …scal stability measures (see Table 2), in that no country wants to join the wider monetary union when considering Proxy 1 in this case. Only Rwanda …nds the move towards the monetary union bene-…cial when focussing on Proxy 2, with the remaining countries opposed and Uganda again showing the highest level of reticence in this scenario. As for the previous two stability motives considered, countries'decisions of whether or not to join the monetary union are unchanged when only concentrating on the three original EAC member countries, again whether uncertainty is properly accounted for or not.

Overall, we take away two key results from our calibrations: …rstly, the choice of proxy for our monetary, …nancial and …scal stability measures is not innocuous and does matter; secondly, and more importantly, allowing for the role of uncertainty in measures of monetary, …nancial and …scal stability generally makes policymakers' signi…cantly less eager to engage in a monetary union unless compensated for by su¢ cient degrees of other ben-e…ts, such as transactional bene…ts or, more importantly in our view, institutional improvements. Looking at the monetary stability aspect of our calibrations, and focussing on the arguably more solid, as direct, measure of (realized) in ‡ation, none of the countries wants to engage in a monetary union in the uncertainty scenario unless compensated for by signi…cant relative levels of additional bene…ts ranging between 0.52 (for Tanzania) and 2.16 (for Rwanda). Given the evident current political will to move ahead with a monetary union in the EAC, this in our view calls for a suf-…ciently robust, credible institutional structure assuring monetary stability in the monetary union beyond what individual central banks are able to achieve at the moment. Turning to the …nancial stability aspect of the question, and concentrating on the aggregate Z-score measure which arguably is more robust than the one relying on often more unreliable non performing loans data, we observe a similar picture: all countries are unwilling to engage in the monetary union when uncertainty is taken into account, unless compensated for by substantial relative levels of additional bene…ts in the range of 0.43 (for Rwanda) and 2.78 (for Uganda). Again, this calls for considerable improvements in the institutional arrangements regarding …nancial stability in the monetary union area, and given the euro zone countries' recent experience, preferably in a formalized arrangement that is set out right from the start of the monetary union, rather than as more informal ad hoc structures. Lastly, a similar picture again evolves when looking at the …scal stability aspect examined, where we prefer to focus on the budget de…cit (excl. grants) measure as the one most closely re ‡ecting the underlying, structural …scal position in a country. All countries except possibly Rwanda would be reluctant to join the monetary union from a …scal stability perspective when uncertainty is taken into account, unless compensated for by relative levels of additional bene…ts ranging from 0.02 (for Burundi) and 0.26 (for Uganda). Compared to the monetary and …nancial criteria, these additional required relative bene…ts are fairly small, suggesting that a reasonable amount of credible institutional structure assuring …scal stability in the monetary union area should su¢ ce to satisfy all potential member countries in this respect.

[Insert Tables 678]

Conclusion

Our paper aims to contribute to the ongoing academic debate accompanying the current political drive towards the establishment of a monetary union in the East African Community (EAC). Rather than focus more narrowly on the discussion of convergence issues for di¤erent sets of economic criteria, we use a somewhat di¤erent approach that particularly highlights the importance of the role of uncertainty in policymakers'decision making in this context.

To this end, we develop a stylized model of policymakers'decision problem that allows for the stochastic nature of monetary, …nancial and …scal stability as three key areas of relevance for the decision to join a monetary union. In addition to the more common monetary stability aspect, the recent upheaval in the euro zone motivates us to also focus on …nancial and …scal stability in this context. By characterizing the real option implicit in a policymaker's decision of whether or not to join the monetary union, we derive the trigger values of monetary, …nancial and …scal stability measures which drive whether or not policymakers …nd it bene…cial to engage in the monetary union at the moment. We can show that when policymakers properly account for the uncertainty regarding the evolution of these monetary, …nancial and …scal stability measures, they might show a substantial degree of reluctance to participate in the monetary union unless compensated for by potential other factors, such as institutional improvements or more standard transactional bene…ts.

Calibrating our model for the EAC using annual data for the period 2003 to 2010, for various proxies of our respective monetary, …nancial and …scal stability measures, we then conclude that when policymakers properly allow for the uncertainty surrounding the evolution of these measures, none of the countries wants to engage in a monetary union based on either monetary or …nancial stability grounds, and only Rwanda might want to engage in it on …scal stability grounds, unless compensated for by signi…cant relative levels of additional bene…ts associated with being in the monetary union. Particularly in the context of the current dramatic euro zone experience, this highlights the importance of agreeing and setting up, from the very start, credible and robust institutional arrangements at the monetary union level assuring substantial improvements in monetary, …nancial and …scal stability for the countries participating in the monetary union. In our mind this is a key lesson: as we saw in the European case, when the political will to form a monetary union is there, economists'views on whether or not a region forms an optimum currency area are easily swept aside. Our results, supported by the experience of the recent turmoil in the euro zone, suggest that the key to a viable and sustainable monetary union may lie in good institutional foundations, not only supporting monetary stability as such, but also assuring wider …nancial and …scal stability as well.

A Appendix

Proof. (Proposition 1) For country c, not participating in the monetary union u for a further instant dt is optimal in the continuation region of the optimal stopping problem eq. ( 3), giving the relevant Bellman equation as

F (B su ; B sc ) = 1 dt E t [dF (B su ; B sc )] ; s = m; f; g (4)
Applying Ito's Lemma to eq. ( 4) and noting that the value function F (B su ; B sc ) should be homogeneous of degree 1,22 so that F (B su ; B sc ) = B sc f ( s ) where s B su =B sc , we obtain

2 su 2 s su sc + 2 sc 2 2 s f 00 ( s ) + 2 su 2 sc ( 1) s f 0 ( s ) + 2 sc ( 1)f ( s ) 2 f ( s ) = 0 ; s = m; f; g (5)
as the di¤erential equation that characterizes the evolution of f ( s ) in that region.

We solve eq. ( 5) by standard methods, using the value-matching and smooth-pasting conditions f ( s ) = (1 + s ) s 1 and @f ( s )=@ s = (1 + s ) and the boundary condition 23 f (0) = 0 ; we thereby obtain s = ; s = m; f; g is the trigger value of relative monetary, …nancial or …scal stability measures su = sc separating the region in ( su ; sc ) space where country c's option of participating in the monetary union u remains unexercised (i.e. for su = sc < su = sc ) from the one where immediate exercise of that option is perceived as optimal (i.e. for su = sc su = sc ). 23 The geometric Brownian motion s has an absorbing barrier at zero.

  0 ; s = m; f; g as the critical (trigger) value s . From the de…nition of s it follows that su = sc =

Figure 1 :

 1 Figure 1: EAC GDP per capita (constant 2000 US$)

Figure 3 :

 3 Figure 3: EAC control of corruption

Figure 4 :Figure 5 :

 45 Figure 4: EAC political stability and absence of violence/terrorism

Figure 6 :

 6 Figure 6: EAC regulatory quality

Figure 7 :

 7 Figure 7: EAC money and quasi money (M2) as % of GDP

Figure 8 :

 8 Figure 8: EAC domestic credit provided by banking sector as % of GDP

Figure 9 :

 9 Figure 9: Trigger value u = c (for = 0:5; = 0:12; = 0:5; = 0)

Table 3 :

 3 EAC financial development (2010)

		Burundi	Kenya	Rwanda	Tanzania	Uganda
	Access to financial services (%)
	Formal	na	40	21	17	28
	Informal	na	27	26	27	42
	Excluded entirely	na	33	52	56	30
	Number of commercial banks
	Domestic banks	7	31	9	17	8
	Foreign banks	0	12	3	16	14
	Bank deposits (% of GDP)
		34	51	18	29	23
	Interest rate spread (lending -deposit rate)
		na	9.81	7.98	7.98	12.48
	Market capitalization (% of GDP)
		-	35.17	-	5.51	23.69
	Listed domestic companies, total
		-	55	-	11	8

Sources: World Bank (2012): World Development Indicators (Edition: April 2012); Finscope (2010); Central banks.

See e.g.McDonald/Siegel (1986) and[START_REF] Dixit | Investment under Uncertainty[END_REF].

The treaty laying down the foundations of the current EAC can be found at <http://www.eac.int/treaty/index.php>.

As for a political federation, preparations are at early stages and no precise timetable has yet been given.

See Section 4 for details of this measure.

[START_REF] Strobel | Financial fragility and crisis union in the Asia-Paci…c Region[END_REF] uses a related but less general framework limited to strictly linear bene…t/loss functions.

See e.g.Dixit (1993, eq. (2.7)).

As the relative bene…ts associated with monetary, …nancial and …scal stability are far from straightforward to quantify jointly, we consider these decision problems separately.

We drop time subscripts for ease of notation.

These could e.g. be of a transactional nature or relate to institutional improvements; for a survey see DeGrauwe (2012, ch. 3).

The option of possible future monetary disintegration could in principle be allowed

These are consistent with Section 4's calibration.

This is available at <http://www.eac.int/statistics/index.php>.

See e.g.Barro & Gordon (1983a) and[START_REF] Barro | In ‡ationary …nance under discretion and rules[END_REF], respectively.

For a survey of di¤erent approaches to constructing such aggregate Z-score measures, see[START_REF] Strobel | Bank insolvency risk and di¤erent approaches to aggregate Z-score measures: A note[END_REF].

We also considered an alternative way of computing the Z-score measure, given by Z = ROE + 100 = ROE , where ROE is the return on equity (in percent), with similar results.

See e.g.Ingersoll (1987, p. 358).

See e.g.Strobel (2007, fn. 16); we also used alternative discount rates of 10 and 11%, with similar results.

We also used = 1 in our calibrations, with similar results.

This adopts the solution strategy inDixit & Pindyck (1994, p. 210).

Acknowledgments

Parts of this study were completed while Clovis Rugemintwari was a visiting researcher in the Department of Economics at University of Birmingham. We are grateful for very helpful comments by Sugata Ghosh, Alex Mandilaras, Alain Sauviat and the participants at the Seventh Annual CEDI Conference at Brunel University; the usual disclaimer applies.

) and the minimum level of relative other benefits   associated with being in a monetary union that makes joining the monetary union worthwhile are derived from Proposition 1, assuming discount rate =12% and concavity factor =0.5. ) and the minimum level of relative other benefits   associated with being in a monetary union that makes joining the monetary union worthwhile are derived from Proposition 1, assuming discount rate =12% and concavity factor =0.5.