Jenifer Piesse

Bruce Allen Hearn

Price Integration between Europe and Regional Markets in Africa

Keywords: financial market integration, causality, sub-saharan Africa

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Introduction

There has been considerable development of financial markets in Africa since the end of the cold war in 1989 and the consequent restructuring of global capital flows. However, while several new stock exchanges have been established and existing ones restructured, the financial markets of Sub Saharan Africa (SSA) have not been successful in attracting significant amounts of global capital flows [START_REF] Kenny | Stock Markets in Africa: Emerging Lions or White Elephants?[END_REF]. Markets are often dominated by a few large shareholders (see Lavelle (2001) and [START_REF] Hearn | The limited role of small stock exchanges in economic development: A case study of Mozambique and Swaziland. Development Southern Africa[END_REF] for an extended discussion of these issues) and severe illiquidity inhibits any potential gains from risk diversification by international portfolio managers [START_REF] Hearn | Modelling size and illiquidity in West African equity markets. Working paper no. WP-EMG-12-2009, Emerging Markets Group Cass Business School Johansen S[END_REF]. In order to counter some of these issues a major policy initiative to integrate these markets has been launched by the major regional development institutions, such as the New Partnership for Africa's Development (NEPAD) and the Southern African Development Community (SADC).

There has also been considerable progress in improving the institutions and many African countries have adopted best practice corporate governance codes, harmonised their accounting systems, and are developing appropriate regulation together with effective enforcement. However, there remain significant differences due to a number of factors. There are widely varying levels of development and differences arising from the underlying legal origins of the market that influence national institutions, business culture and levels of investor protection afforded by the judiciary (La Porta et al, 2008). Markets have different trading hours and trading methods, for example, markets have adopted either open outcry, electronic continuous auction, or simple forms of call auction to execute transactions [START_REF] Kenny | Stock Markets in Africa: Emerging Lions or White Elephants?[END_REF]. Finally, there are different degrees of macroeconomic stability, such that some markets are attractive to overseas portfolio investors and provide reliable and efficient operations and national and regional payments systems and others do not. Consequently, equity market integration has only been successfully achieved between markets with a shared macroeconomic environment, for example, the Two prominent strands of literature define approaches to measuring financial market integration. The first is the use of asset pricing models, commonly variations of the Capital Asset Pricing model (CAPM) or the Arbitrage Pricing model (APT), which are used to measure premiums between assets and markets.

However, both are hindered by rigid assumptions that concern the joint hypothesis of market efficiency, which states that security prices contain all information available, and for weak form efficiency, that prices reflect information to the point where the marginal benefits of acting on information do not exceed the marginal costs. As a result of this joint-hypothesis, when pricing models produce unexpected results, it is difficult to apportion anomalous results due to hidden information [START_REF] Fama | Efficient Capital Markets: II[END_REF].

The second uses an extended form of correlation analysis and statistical cointegration methods.

These are either Vector Autoregressive Error Correction models (VECM), or Autoregressive Distributed Lag models (ARDL) to analyse long run relationships between variables. While there are several applications of these methods in developed country markets using index level data, such as [START_REF] Corhay | Common Stochastic Trends in European Stock Markets[END_REF], there are far fewer applications in developing countries. There are disadvantages to the use of index level data due to aggregation bias where only a few stock in the index account for much of the capitalization, activity and movement, a situation that is particularly prevalent in emerging markets. Consequently, empirical applications relate to valuation differences between closed-end country funds and American and Global Depository Receipts (ADR/GDR) and their underlying assets (Lamont and Thaler, 2003).

However, this is not appropriate in African markets as there are few liquid ADR or GDR instruments.

Furthermore, the only closed-end funds currently are restricted to Egypt or South Africa (Bloomberg LP, 2009).

This study extends Piesse and Hearn (2002) but concentrates specifically on the largest African markets in order to assess the importance of the regional hubs and the potential for integration with world markets, represented here by London and Paris. There is a risk of aggregation bias through the use of market indices as proxies for the underlying national markets, but this is unavoidable due to the lack of country funds and liquid ADR/ GDR noted above. Vector Autoregression (VAR), VECM and ARDL models are useful in interpreting both potential price integration and feedback effects between markets when there is evidence of integration. Harris et al (1995) used these methods to test the Law of One Price in the context of weak-form information efficient markets with prices incorporating all possible information, by focussing on the price history of one stock listed on three domestic exchanges in the US in a study that was free of any potential aggregation bias despite using indices. This study takes the same approach while facing considerably greater challenges. This section briefly contrasts the most important institutional differences between the markets used. An extended description of the market institutions across Africa is in [START_REF] Hearn | Integration and the Asymmetric Transmission of Volatility: A Study of Equity Markets in Sub Saharan Africa[END_REF].

Data

The legal origins of the legal and regulatory systems in Africa can largely be traced back to the influence of the former colonial powers, in particular the UK and France. South Africa, by virtue of its history, developed a distinctive Roman-Dutch legal code, although the commercial code is heavily influenced by English common law, a structure that is shared by Namibia. Table 1 shows the differences in legal origins between the sample markets and provides comparisons between corporate governance regimes and the minimum primary listings criteria. As seen in the table, these vary considerably in terms of capital base requirements and audited history. The differences in primary market regulation and information disclosure give an indication of the degree of asymmetric information faced by potential investors, a factor that discourages investment by raising transactions costs. In general, short sales are prohibited in all markets with the exception of South Africa, which has a well-capitalized brokerage industry and follows international standards including G30 1 compliance. The brokerage industry in most other markets is small and even in Egypt and Nigeria, where there are 141 and 219 licensed brokers respectively, it is highly concentrated with only a small group of firms precipitating order flow.

Table 1

Table 2 shows the market concentration profiles in terms of capitalization and traded value on both a market-wide and industry sector level. London and Paris clearly have the highest number of listed firms and also a fairly equal distribution in terms of traded value and capitalization across sectors.

However, in the African markets the profile is different. Value is concentrated in only a small number of stocks and this is centred on the local finance industries. For example, concentration of the local finance industry ranges from 59.74% of capitalization in Tunisia to 24.72% in Egypt, compared to London and Paris where the financial sector accounts for 17.80% and 15.14% respectively.

Table 2

The sample includes the major African markets that are central to the NEPAD policy of regional integration that is intended to be implemented through between regional hub markets, namely Egypt (North Africa), Kenya (East Africa), Nigeria (West Africa) and South Africa (Southern Africa). In 1 The Group of Thirty is the most influential body to encourage the standardization and improvement in global securities administration. Following a symposium in London in March 1989, the following recommendations were agreed: i) Brokers should match trades on day after deal date (T+1); ii) Trade confirmation on trade day plus 2 days (T+2); iii) Central Depository for safe keeping of shares; iv) Net basis settlement of cash and stock; v) Settlement takes place as delivery vs. payment or receipt vs. payment; vi) Settlement in same day funds; vii Settlement effected on trade date plus 3 days (T+3) 8; viii) Securities lending should be permitted; ix) International securities numbering system must be adopted (ISIN code). All are expressed in natural logarithms and differenced to produce the final adjusted returns series. Table 5 4

Econometric Methods

The study uses two unit root tests, Augmented Dickey Fuller (ADF) [START_REF] Dickey | Distribution of the Estimators for Autoregressive Time Series with a unit root[END_REF]) and the KPSS test [START_REF] Kwiatkowski | Testing the null hypothesis of stationarity against the alternate of a unit root: how sure are we that economic times series have a unit root?[END_REF], to investigate the presence of unit roots in all index time series. The second stage involves the triangulation of VAR methods (Johansen (1988); Johansen and Jusilius (1991))

and ARDL (Pesaran and Shin (1995)) to assess the level of cointegration between markets.

a) Testing for the presence of Unit Roots

The application of both the ADF and KPSS unit root tests should provide more robust evidence of the nonstationarity of the underlying index time series. Given the ADF test has a well known shortcoming of being unable to differentiate between a unit root and a weakly stationary series [START_REF] Evans | Efficiency tests of the UK financial futures markets and the impact of electronic trading systems[END_REF] and performs poorly in the presence of structural breaks, the additional KPSS test is used. This effectively overcomes the ADF tests lack of power to reject the null hypothesis of a unit root when testing a null hypothesis of stationarity.

A considerable literature has developed recently using the ADF test to elaborate on the presence of unit roots usually as a prelude to undertaking further study into the informational efficiency of market time series [START_REF] Evans | Efficiency tests of the UK financial futures markets and the impact of electronic trading systems[END_REF]

= + + + - + = - + = - ∑ ε ϕ ϕ δ ϕ α (1)
where y t is the time series, δ t is the deterministic trend and ά is the non-zero drift constant.

Correspondingly, the test for first differences, with a new null hypothesis is H 0 : ρ = 1 -φ = 0, is defined:

∑ = - - = + ∆ + - + = ∆ p i t i t t t n t y y t y 1 1 ,..., 1 , ε γ ρ ρδ α (2)
As time trends are a common feature of financial time series both ADF tests are performed both with and without a constant and deterministic trends, or the (1 -φ)δt term. The Schwartz Bayesian Criterion (SBC) is used to assess the appropriate lag length of models. The null of a unit root is accepted (rejected) if the ADF test statistics is less (more) than the critical value at the 1%, 5% and 10% level of significance.

The KPSS test offers an alternative approach to testing for unit roots in time series in the light of the failings of the standard ADF procedure. Questions regarding the false rejection of unit root hypotheses first arose through an application of standard [START_REF] Dickey | Distribution of the Estimators for Autoregressive Time Series with a unit root[END_REF] techniques to US economic time series (Nelson and Plosser, 1982). [START_REF] Dejong | Integration versus trend stationary in macroeconomic time series[END_REF] provided further support for the inability of the ADF tests to have sufficient power against stable autoregressive alternatives with roots near unity while [START_REF] Diebold | On the power of Dickey-Fuller tests against fractional alternatives[END_REF] provided evidence that they also performed poorly when applied to fractionally integrated time series. In contrast to the ADF test, the KPSS method sets the stationarity around a deterministic trend of the series as the null hypothesis and alternate hypothesis of nonstationarity (unit root). Following [START_REF] Evans | Efficiency tests of the UK financial futures markets and the impact of electronic trading systems[END_REF] the KPSS test statistic is calculated as follows:

( )

L S S T T t t u 2 1 2 2 ∑ = - = η (3)
where L is the lag parameter and S t is the cumulative sum of the residuals (e t ) from the regression of the series on a constant and a linear trend (t),

t t e t P + + = β α (4) T t e S t i i t ........ , 2 , 1 1 = = ∑ = (5) and ( ) ∑ ∑ ∑ = + = - - = -             + - + = L s T s t s t t T t t t e L S T e T L S 1 1 1 1 2 1 2 1 1 2 (6) b)
Cointegration using a Vector Autoregressive process

The Augmented Vector Autoregressive (AVAR) model from Johansen (1989[START_REF] Johansen | Estimation and Hypothesis testing of cointegrating vectors in Gaussian Vector Autoregressive Models[END_REF]

… = + Ψ + Φ + + = ∑ = - p i t i t i t u w z t a a z (7)
where z t is a m x 1 vector of jointly determined (endogenous) variables, t is a linear time trend, w t is a q x 1 vector of exogenous variables, and u t is an m x 1 vector of unobserved disturbances assumed to satisfy the assumptions of iid, homoskedasticity, serially uncorrelated, orthogonality, normality with strict adherence to a multivariate normal distribution and stability.

Cointegrating VAR models are underlined by the general vector error correction model (VECM)

defined ∏ ∑ - = - - + Ψ + ∆ Γ + - + = ∆ 1 1 1 1 0 p i ty t y i t iy t y y y t u w z z t a a y (8)
where

) ( ′ = t t t x y z
This model distinguishes between four categories of variables, namely:

1. y t which is an m y x 1 vector of jointly determined (or endogenous) I(1) variables 2. x t which is an m x x 1 vector of I(1) exogenous variables 3. w t which is a q x 1 vector of I(0) exogenous variables

Intercepts and deterministic linear trends

The implicit VAR model for the I(1) exogenous variables, x t , is given by

∑ - = - + Ψ + ∆ Γ + = ∆ 1 1 0 p i t t x i t ix x t v w x a x (9)
and assumes the x t 's are not themselves cointegrated. Although (9) does not explicitly contain a deterministic trend, the levels of x t will be trended due to the coefficients, a 0x .

Combining equations ( 8) and ( 9) results in following:

∏ ∑ - = - - + Ψ + ∆ Γ + - + = ∆ 1 1 1 1 0 p i t t i t i t t u w z z t a a z (10) where ) ( ′ = t ty t v u u , ) ( ′ = x y a a a 0 0 0 , ) ( ′ = 0 1 1 y a a ) ( 0 0 y Π = Π , ) ( ′ Γ Γ = Γ ix iy i , ) ( ′ Ψ Ψ = Ψ x y
which is a restricted vector error correction form of the original AVAR model (1). The intercept and the trend coefficients, a 0y and a 1y are m y x 1 vectors. Π y is the long-run multiplier matrix of order m y x m, where m = m x + m y , Γ 1y , Γ 2y , . . . ., Γ p-1,y are m y x m coefficient matrices capturing the short-run dynamic effects, and Ψ y is the m y x q matrix of coefficients on the I(0) exogenous variables. Under the assumption that rank (Π y ) = r, i.e. when there exists r cointegrating relations among the variables in z t , then

c) Granger-causality for cointegrating and non-cointegrating systems

Following [START_REF] Johansen | Estimation and Hypothesis testing of cointegrating vectors in Gaussian Vector Autoregressive Models[END_REF], Granger non-causality for a system of I(1) variables and a common cointegrating vector can be determined through the transformation of the original AVAR (7) into a bivariate VECM in expression (11(i) and 11(ii)) where each y it term is a sub-element of the z t variable in (7).

∑ ∑ = = - - - - + ∆ + ∆ + - + = ∆ k i k i t t i t i t t t y y y y y 1 1 1 1 2 2 1 1 1 1 2 1 1 0 1 ) ( ε α α γ α (11i) ∑ ∑ = = - - - - + ∆ + ∆ + - + = ∆ k i k i t t i t i t t t y y y y y 1 1 1 1 2 2 1 1 1 1 2 1 1 0 2 ) ( ε α α γ β (11ii) where the ) ( 1 2 1 1 - --t t
y y γ represents a drift error correction process for the entire system to re-stabilise following short term deviations from the long term cointegrating trend.

The corresponding measure of causality for an AVAR system of non-cointegrated variables is block Granger non-causality. The null hypothesis that coefficients of a subset of jointly determined variables in the AVAR are equal to zero is tested using the log-likelihood ratio statistic. Statistically it provides a measure of the ability of one set of lagged values of a variable to predict another set of lagged values of a second variable within the model. Assuming ' , where z 1t and z 2t are m 1 x 1 and m 2 x 1 subsets of z t , and m = m 1 + m 2 . The block decomposition is then given by equation ( 12):

      ′ ′ = t t t z z z 2 1 ,
∑ ∑ = = - - + Ψ + Φ + Φ + + = p i p i t t j t i j t i t u w z z a a z 1 1 1 1 , 2 12 , , 1 11 , 11 10 1 (12i) ∑ ∑ = = - - + Ψ + Φ + Φ + + = p i p i t t j t i j t i t u w z z a a z 1 1 2 2 , 2 22 , , 1 21 , 21 20 2 (12ii)
The hypothesis that the subset z 2t does not Granger-cause z 1t is defined (1995).

The benefits compared to VAR methods are that pre-testing series for unit roots is not necessary as a prerequisite for measuring cointegration. Following Pesaran and Shin (1995) the formal augmented ARDL model is defined

( ) ( ) ∑ = + + = k i t t it i t u w x p L y p L 1 ' , , δ β φ (13) where ( ) p p L L L p L φ φ φ φ - - - - = ... 1 , 2 2 1 and ( ) k i L L q L q i iqi i i i i i ,..., 2 , 1 ... , 2 1 1 = + + + + = β β β β β (14)
and where L is a lag operator such that

1 - = t t y LY
, and t w is an s x 1 vector of deterministic I(0) variables including the intercept term, dummy variables, time trends or exogenous I(1) variables with fixed lags, none of which are used in this study to avoid any risk of pre-testing bias from a priori knowledge of events.

ARDL models are estimated by first collecting OLS estimates of equation 13 for all possible values of p = 0, 1, 2,…,m; i q = 0, 1, 2, …, m; and i = 1, 2, …, k, that is, for a total of the (

)

1 1 + + k m different ARDL models.
The choice of one of the ( )

1 1 + + k m
estimated models was made using the SBC informational criteria.

The ECM that corresponds to the model selected can be obtained by rewriting equation 13 in terms of the lagged levels and the first differences of

∑ ∑∑ ∑ - = - = - - = - - + ∆ - - ∆ + ∆ + - = ∆ ^^1 1 1 1 1 , * * ' 1 1 0 1 , 1 p j k i q j t j t i ij j t t k i t i t t i u x y w x EC p y β φ δ β φ (15)
where the error correction term,

t EC , is defined ∑ = - - = k i t it i t t w x y EC 1 ' ψ θ (16)
where the long run coefficients for the response of t y to a unit change in it x are estimated by ( ) ( )

p iqi i i i i i i p q φ φ φ β β β ϕ β θ .... 1 .... , 1 , 1 ˆ2 1 1 0 - - - - + + + = = (17) F o r P e e r R e v i e w
11 and where p ˆ and i q ˆ, i = 1, 2, …, k are the selected estimated values of p and i q , i = 1, 2, …, k. Similarly, the long run coefficients associated with the deterministic/ exogenous variables with fixed lags are estimated by ( )

p k q q q p φ φ φ δ ψ .... 1 ,...., , , ˆ2 1 2 1 - - - - = (18)
and where ( )

k q q q p ,....
+ + + ∆ + ∆ + ∆ = ∆ ∑ ∑ = - = - 2 2 1 1 1 2 1 1 ' 1 δ δ β β δ (19)

≠ ≠ δ δ

The second stage is the estimation of parameters within ARDL model and the long run coefficients in ( 13), ( 15) and ( 16).

Models and Results

a) Unit Root tests

The results from the unit root tests are reported in Table 6. The null hypothesis of a unit root using the ADF test cannot be rejected for all series both with and without a deterministic trend at the 99% confidence level. Similar results were obtained from using the KPSS test (without a trend) with the null hypothesis of stationarity rejected at the 99% confidence level for all series except Namibia Local, Egypt and Tunisia where the confidence level was 95%. However, while the null hypothesis of stationarity could not be rejected for all series in first differences, the results for these three series proved ambiguous in rejecting the null hypothesis at the 95% confidence level. Similar results were obtained using the KPSS test (with trend) although equally ambiguous results were obtained for the series in first differences for Kenya, Egypt and Nigeria. The ambiguities are most likely caused by the presence of outliers in the series and overall the evidence would suggest the presence of a unit root in series levels.

Table 6 b) Bivariate tests of cointegration

Table 7 reports the Johansen trace statistics for the bivariate VAR models, as outlined in expression (10).

The VAR models constructed have each of the four regional hub market indices in addition to each of the other market indices in turn. The results indicate Nigeria has no cointegrating vectors, and thus there is no relationship with any other market while Egypt, Kenya and South Africa have only very few long term relationship with other series. The null hypothesis of no cointegrating vectors is rejected at the 95% confidence level in the VAR including Egypt and France and Tunisia. A similar rejection of the null hypothesis at the same confidence level is found for the system including South Africa and Namibia

Overall, and between Kenya and Morocco and Kenya and Tunisia. The evidence at this stage suggests that as expected there is very little price-integration amongst equity markets in Africa with only a few exceptions and these are between markets with shared institutions, such as South Africa and Namibia

Overall, and between France, Egypt and Tunisia. The results concerning Kenya and its long run relationship with Tunisia and Morocco are initially confusing owing to the heterogeneity in institutions, macroeconomic environments and legal regimes. However, a likely explanation is that the index returns generating process in Kenya is very similar to that in the two illiquid North African markets, which would cause the statistical measure of cointegration between markets to be apparent when these markets have no other obvious ties and thus the relationship is spurious. 13 lagged values of dependent variable that account for the short term system dynamics. The very small time trend included in the long run cointegrating vector is contemporaneous in being representative of various other factors affecting the price levels between the two indices such as exchange rate, institutional and macroeconomic differences. In the Egypt -Tunisia system the long term error correction model is statistically significant in explaining returns in both Tunisia and Egypt only with no lagged dependent variables in the expression for either. However, the size of the ECM coefficient in the expression explaining Egyptian returns is four times greater than that for Tunisia, indicating that Egypt is more affected by Tunisia than the inverse. The three markets have similar institutions, with legal regimes and institutions derived from French civil code law, while illiquidity is greatest in Tunisia, where trading is by call auction, followed by Egypt. A possible explanation for the direction of Granger non-causality from Tunisia to Egypt and from Egypt to France is the affects of illiquidity on the returns generating processes in all three markets.

The evidence for the relationship between South Africa and Namibia Overall returns shows that contrary to the earlier study by Piesse and Hearn (2002) Granger non-causality runs from South Africa to Namibia, supported by the statistical significance of the ECM term and the size and significance of the Fstatistic. The size of this long-run relationship has also increased in absolute terms, seen from the long run coefficients taken from the normalised cointegrating vector, as a 1% change in the levels of South Africa leads to a 0.8531% change in Namibia. It is notable that the contemporaneous time trend coefficient is considerably smaller in the long run cointegrating vector between these two markets than between either Egypt and either Tunisia or France indicating fewer external variables influencing price levels between these two markets. This provides further indication of the strength of common institutions and common macroeconomic environment between Namibia and South Africa.

Finally, the evidence for Granger non-causality in the case of the two relationships centred on Kenya is similar to that for those centred on Egypt where the affects of illiquidity on the returns generating process affected the direction of the relationships. The ECM in the Kenya -Morocco system is only significant in explaining Moroccan returns and not Kenyan. Similarly, the ECM in the Tunisia -Kenya relationship is only significant in explaining Kenyan returns as the dependent variable and not those of Tunisia. Given the considerable institutional differences the only commonality between all three markets is their small size, relative insignificance as a source of finance in contrast to their better developed banking sectors and severe illiquidity. Thus, the returns generating processes of all three indices and the degree of co-movement is a function of the degree of inactivity than any tangible homogeneity in institutional development.

Table 8 d) Augmented Autoregressive Distributed Lag (ARDL) Analysis

The results from the initial stage of the ARDL methodology to test the null hypothesis that all the coefficients in the long run error correction term of the ARDL model are statistically different from zero are in Table 9. Seven ARDL models had the null hypothesis rejected at the 99% confidence level inferring that series were both I(1) and cointegrated. These included cointegrating relationships between

Table 9

The results of the ARDL models, with optimal lag criteria given by the SBC informational criterion, are in Appendix 2. Generally the evidence from the ARDL methods supports the earlier VAR methodology.

In the case of Kenya, the long run cointegrating relationship between variable levels is significant in explaining the returns in the small and highly illiquid Namibian local market. Equally, the long run relationship between variable levels is significant in explaining the index returns in Morocco and also in Paris, which is interestingly. The directions of these relationships are likely explained by the severity of illiquidity affecting the returns generating processes of the markets in the ARDL system as opposed to

Conclusions and Policy Implications

This study has examined the extent of price-integration between the major markets in Africa and Paris and London using two cointegration methods, Vector Autoregression and Autoregressive Distributed Lag.

The study has been motivated by the recent NEPAD and SADC policy drives to integrate the equity markets and introduce common institutions in Africa within a phased approach of first integrating regional markets centred on the geographical hubs of Egypt (North), Kenya (East), Nigeria (West) and South Africa (Southern).

The evidence from both the VAR and ARDL methods reveals that African markets are generally price-segmented and only those with shared financial and economic institutions such as Namibia and South Africa and Egypt, Tunisia and France is there any evidence of price-integration. However, the effects of severe illiquidity and the low trading activity that does occur is highly concentrated and this causes ambiguous strong long term relationships to appear between markets, which is probably spurious. This is the most likely explanation of the strong statistical long term relationship between Tunisia, Kenya and Morocco with Granger non-causality running from the most illiquid market (Tunisia) to the least illiquid market (Morocco). The evidence from the block Granger non-causality that results from the non- (2) One lag used in all unrestricted VAR models.

(3) Chi-Square value (1 degree of freedom) for 99.90% confidence is 10.83, for 99% confidence is 6.64, and for 95% confidence is 3.84

  is included as this market already shares an integrated link with South Africa, Morocco and Tunisia because of their importance in the North African Maghreb region and Mauritius, due it its importance in SADC as a prominent offshore market. Very small and highly illiquid markets are excluded from the study. Nominal end-of-week closing price-index values are from the national stock exchanges for Tunisia, Namibia and Mauritius and for all other markets from Datastream. UK sterling exchange rates are from Datastream and background information on the markets is from Bloomberg, Standard & Poors Global Markets Factbook and national stock exchange websites. Details of domestic index construction and trading systems and times are in Table5. Trading times in all markets are largely synchronous, as countries are either one hour less or two hours more than the South African time zone. The index data are converted to their UK sterling equivalence, which assumes long term purchasing power parity between national currencies and sterling to reduce the effects macroeconomic uncertainty in a region of high inflation. While this largely mitigates currency fluctuation effects on returns it facilitates the study of price-integration from the viewpoint of a UK-based investor.

  and β and m y x m and m x r matrices, each with full column rank r. The stochastic trace statistics then determine the number of cointegrating vectors.

  of constant and time trend. The hypothesis to be tested using the non-standard distributed F-test is the null of non-existence of the long-run relationship defined :

  Kenya and Namibia Local, Morocco, and Paris, between Egypt and Morocco and Tunisia, and between Nigeria and both the markets in Namibia. A further nine F-statistics fell between the upper and lower critical value bands. In these cases reference is made to the earlier unit root tests. The relationships with values falling between the bands are between Kenya and Namibia Local, between South Africa and Nigeria, Mauritius, both Namibian markets, and Morocco, and finally between Egypt and Namibia Local and Paris.

  common institutions. The directions of the relationships in the ARDL models centred on South Africa are more intuitive with the long term relationship with Nigeria, Morocco, Mauritius, both Namibian markets being highly significant in explaining the returns of these other markets. In line with similar findings involving VAR methods the relationship is particularly strong between South Africa and both Namibian markets, where the direction of influence from South Africa.However, owing to the high level of dual listings this relationship with South Africa is most significant and has the adjusted R-squared of all the ARDL models. In the case of Egypt the long adjustment term is significant in explaining the returns of Namibia Local, Morocco and Paris but not the returns of Egypt itself. This is probably the result of a combination of genuine shared institutions, as with the case of Morocco and France following French civil code along with Egypt, but also of illiquidity, as in the Namibian local market. Finally, the relationships between Nigeria and the both Namibian markets show that Nigerian returns are influenced by the long run error correction term in the case of the Namibian Overall while the results for the Namibian local market are inconclusive as they are not statistically different from zero.

  (4) * indicates 95% confidence, ** indicates 99% confidence, † indicates 99.90% confidence

Table 3 Table 4

 34 provides details of the stocks that are included in the country indices. As expected, the stocks in the London and Paris indices, which form the FTSE 100 and CAC40, have the lowest percentage

	daily zero returns, 8.90% and 5.91% respectively, and the lowest bid-ask spreads, of 0.58% and 0.27%
	respectively. They also have the highest average trading activity and market capitalization indicating that
	there are large, actively traded and highly liquid. Egypt and South Africa have the next highest percentage
	daily zero returns, at 35.35% and 16.82%, while Morocco and Kenya have values of 46.67% and 48.56%,
	indicating a similar degree of liquidity markets. There are similar findings for the Bid-Ask spread in each
	case. The least liquid markets are Tunisia (73.80% daily zero returns), Nigeria (78.19% daily zero
	returns), and Mauritius (84.69% daily zero returns). Namibia is the most illiquid of all the markets. The
	percentage daily zero returns are 59.76% for the overall market, which is composed of largely primary
	listed South African stocks with a secondary Namibian listing, and 92.35% for the local market. These
	indicators of price-rigidity are also reflected in the bid-ask spreads, which at 25.59% and 27.13% for the
	overall and local markets are by far the highest in the sample. The evidence also suggests that firms are
	smaller than in other markets but more actively traded in terms of turnover than in Mauritius, Kenya,
	Tunisia and Nigeria, which is an indication of the highly skewed nature of these markets, as seen earlier in
	Table 2.

  There has been a considerable increase in the literature applying ARDL techniques in the study of long term relationships between series since the development of these methods in Pesaran and Shin

										F o
														r
															P
																		e e r
																		R e v i e w
						H	G		: 12 = Φ	0
	where	Φ	12	=	(	Φ	12 , 1	,	Φ	2	12 ,	,.......,	Φ	p	12 ,	)	. The standard F-test with a χ 2 distribution can be used to test the
	null hypothesis that all coefficients are jointly equal to zero.
	d)	Autoregressive distributed lag approach
																		10

  δdenotes the OLS estimate of δ for the selected ARDL model.ARDL estimation is in two stages. The first relates to testing the null hypothesis of whether all the coefficients of the long term forcing variables or error correction term in (16) are jointly equal to zero against an alternate hypothesis of their being jointly significantly different from zero. Following standard OLS estimation methods an F-test is used although with a non-standard distribution this is further categorized into bounds where critical values are inPesaran et al. (1996). The lack of necessity for testing the initial presence of unit roots in series is justified by the F-statistic being greater than the upper bound critical value, which infers all component series within ARDL model are I(1). Unit root testing is required

	, ˆ2 1 ,	,
				p				p
	y	t	w	t	i	y	t	i	i	y	t	i	y	t	y	t	u	t
				i				i

when values from the F-test fall between the upper and lower bands, while values falling below the lower band can be assumed to be I(0). The error correction version of ARDL (p,q) model for a two-component system, which is a modification of (

15

) is defined

Table 7 c) Granger non-Causality for cointegrating and non-cointegrating systems

 7

	Granger non-causality between component series of cointegrating VAR models is investigated using the
	Vector Error Correction Model (VECM) defined in expressions 11(i) and 11(ii). The results of the error
	correction models are in Appendix 1.

The results for the relationship between Egypt and France indicate that the Paris index is significant in affecting Egyptian returns in the short run while the long-run error correction model does not have a statistically significant role. Conversely, the long run cointegration relationship in the error correction model does have a small but statistically significant role in explaining French returns and the Page 13 of 36 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 8

 8 The size, significance and direction of most of the Granger non-causality relationships are expected given prior knowledge of the markets. South Africa and Nigeria have the fewest relationships when included in bivariate non-cointegrating VAR models with other index series. While the former is the largest and most liquid in Africa the latter is quite segmented with poor regulatory enforcement, a lack of information disclosure and confusion over the application of Nigerian or OECD accounting standards in auditing. Both of these markets have few relationships with the rest of the sample while Nigeria is Granger non-causally affected by London, Paris, Morocco and Mauritius, and South Africa Granger noncausally affects Egypt, Namibia Overall market and Mauritius. There are many more inter-relationships between Egypt and Kenya and the rest of the sample. Egypt Granger non-causally affects Nigeria and Mauritius while being affected by Namibia Overall, London and Paris. Kenya is Granger non-causally affected by South Africa, Egypt, London, Paris and Namibia Overall while having a mutually Granger non-causal relationship with Mauritius and Tunisia.

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reports the results for the block Granger non-causality, which investigates the statistical interdependencies between the lagged first differences of dependent variables in a non-cointegrating VAR

Table 1 . Summary of African primary and secondary market regulations

 1 Mauritius and Morocco while Kenya is affected by South Africa, Egypt, Namibia Overall. Both Nigerian and Kenya are both affected by and affecting Tunisia and Mauritian returns. Finally, as expected London and Paris exert short term block Granger non-causality on the returns in Kenya, Egypt and Nigeria.Overall these results indicate a general lack of long term price-integration across markets in Africa and suggest that any relationships that are found are due to shared institutions or with a common level of illiquidity that gives potentially misleading results. Thus, considerable improvement in both economic and financial institutions is necessary before markets can be formerly integrated.

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cointegrating VAR systems concerning the short term statistical dependencies between different markets lagged returns is largely in line with expectations. South African returns Granger non-cause the lagged returns of Egypt, Mauritius and Namibia Overall, while Egypt exerts short term influence on returns of Nigeria, Mauritius and Namibia Overall. In Nigeria, returns are Granger non-causally affected by both Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Page 20 of 36 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript F o r P e e r R e v i e w 2 Table 2 Market profiles, 2008

	Page 21 of 36			Submitted Manuscript
		Europe			North Africa		West Africa East Africa	Southern Africa
		London †	Paris †	Egypt	Tunisia	Morocco	Nigeria	Kenya	South Africa	Namibia
	Listed Firms	2,210	1,164	302	53	78	234	46	373	8
	Proportion market capitalisation to total (%)
	Top 1	7.72	9.29	7.43	12.51	27.55	8.40	21.02	8.31	55.55
	Top 5	30.35	27.51	29.64	43.56	57.81	27.08	63.67	30.36	99.12
	Top 10 Top 20 Proportion Turnover value to total (%) 46.12 60.95 Top 1 ----Top 5 ----Top 10 ----Top 20 ----Sector Concentration by Market Capitalization 43.86 61.13 ----------------Financials 17.80 15.14 Comm. 9.74 10.79 Basic Materials (Mining etc) 11.98 2.08 Consumer cyclical 4.90 5.91 Consumer non-cyclical 26.84 17.74 Diversified 0.37 2.89 F o r P e e r R e v i e w 43.58 65.23 74.29 44.38 59.69 88.20 88.88 64.33 11.50 9.69 19.42 9.00 36.81 38.19 58.92 36.45 55.31 61.98 78.00 52.66 78.67 86.51 92.01 69.59 24.72 57.38 42.04 59.74 18.22 0.31 27.55 1.37 14.63 3.89 3.37 0.53 5.00 12.16 2.55 2.81 6.59 8.92 4.35 17.79 1.57 12.51 7.39 1.57	78.79 94.31 20.44 56.73 74.76 95.78 46.90 0.96 1.63 4.73 26.95 0.08	45.44 62.31 12.74 42.19 59.67 76.28 28.11 14.09 23.86 6.52 6.63 4.27	100.00 ----46.77 100.00 100.00 ----70.45 ------------21.12 8.42
	Energy	19.08	11.68	1.03	0.38	1.46	10.41	4.41	9.50	----
	Industrial	4.21	13.67	18.86	4.45	9.93	5.35	14.33	5.58	----
	Technology	1.13	2.15	0.12	----	0.14	0.02	----	0.31	----
	Utilities	3.96	17.95	0.18	----	1.23	----	----	0.00	----
	Source: Compiled by authors from Bloomberg
	Notes: (1) * Refers to Central Market and Block Trading Market
	(2) † Refers to entire market including Main and AIMS for London
					3

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 3 . Summary of trading arrangements and stock price index construction

 3 : Compiled by authors from Datastream and respective national stock exchanges Notes: All trading hours quoted are in local time. Nigeria is -1 hours less than South Africa, Kenya and Mauritius are +1 and +2 hours ahead of South Africa.

							Page
	Market		Trading Hours	Trading Arrangement	Index	Details of Index Construction
	London					Shares Electronically Traded	FTSE100	Top 100 London stocks by market capitalization.
						System (SETS) system
	Paris					Euronext electronic platform	Paris CAC40	Top 40 Euronext-Paris stocks by market capitalization.
	South Africa		8-25 am -9-00 am: Pre-	JSE SETS Electronic Trading	FTSE/JSE Top	Top 40 stocks by market capitalization. Index is under
			Opening electronic call	system (SETS trading system has	40	effectively constant review in terms of potential corporate
			auction// 9-00 am -4-00	been in place at the London	actions and capital structure changes.
			pm: Cont. Trading// 4-00	Stock Exchange and replaced the
			pm -6-00 pm: Run-Off.	former JET system in 2002)
	Namibia		As South Africa		As South Africa	NSX All Share	Capital weighted average of all listed stocks with base
							period in 1992 at start of index -100.
							NSX	Local	As above but with universe made up from only local
							Market	primary listed stocks
	Egypt (Cairo and	Listed Securities Market:	Exchange based Automated	EFG-Hermes	Top 40 stocks in terms of liquidity and is market
	Alexandria Stock	11-30am -15-30pm	trading system CASE -The	Financial	capitalisation weighted.
	Exchange(CASE))				CASE Trading System, or CTS
	Morocco		9-00am -9-30am: Pre-	Delocalized Electronic quote	CFG 25	Recalculated at the end of each trading session with a stock
			Open// 9-30am -15-30pm:	driven trading system -NCS.	by stock weighting in accordance to market capitalization
			Cont. Trading// 15-30pm-
			16-00pm: Pre-Close
	Tunisia		9-00am to 10-00am: Pre-	Delocalized Electronic order	BVMT	Market Capitalization weighted index of all companies
			opening// 10-00am -11-	matching system.	Terminals	Tunindex	traded on exchange.
			30am Trading Session	installed remotely at local
						brokers.
	Nigeria	(Lagos	11-00am to 13-00pm	Exchange based Automated	NSE All Shares	Index formulated in January 1984. Only common stocks
	Floor)					Trading System (ATS). Each	Index	(ordinary shares) are included in the computation of the
						exchange in Nigeria has its own	index. The index is value-relative and is computed daily.
						automated system.
	Mauritius		9-00am -10-00am: Pre-	Delocalized Automated Trading	SEMDEX (All	The SEMDEX reflects capitalisation based on each listed
			Opening electronic call	system. Authorised terminals	Share)	stock that is weighted in accordance to its shares in the total
			auction// 10-00am -13-30	installed at individual brokerage	market. The index has a base date of 5 July 1989 with a
			pm:	Cont.	Trading//	houses	value of 100.
			Closing: 13-30pm
	Kenya		10-00am -12-00noon	Exchange based Automated	NSE All Share	Market Capitalization weighted and takes account of all
						Trading system.	lines of stock on market.

Source

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Table 4 . Descriptive statistics of market price index constituent stocks

 4

	Local currency values	UK£ equivalent

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Table 5 . Characteristics of weekly index closing returns (Log UK$ adjusted): January 1998 to June 2009

 5 Compiled by authors from Datastream and Bloomberg for Tunisia, Kenya and Nigeria. Notes: The null hypotheses for the mean, median, skewness, excess kurtosis are that they are all respectively zero

		London	Paris	South	Namibia	Namibia	Nigeria	Mauritius	Egypt	Morocco	Tunisia	Kenya
				Africa	(Overall)	(Local)
	Observations	595	595	595	595	595	595	595	595	595	595	595
	Mean	-0.00011	0.00027	0.00067	0.00031	-0.00038	0.00061	0.00059	0.00074	0.00073	0.00079	-0.00019
	Median	0.00071	0.00122	0.00168	0.00204	-0.00015	0.00018	0.00033	0.00147	0.00044	0.00076	-0.00057
	Std. Deviation	0.01157	0.01425	0.01745	0.02004	0.01442	0.01623	0.01057	0.01780	0.01137	0.00751	0.01950
	Skewness	-0.23306	-0.19314	-0.49986	-0.81738	-0.72001	-0.32220	-0.14851	-0.54379	-0.85596 0.50735	1.08766
	Kurtosis	7.74695	6.78367	6.45622	8.05036	8.20916	7.92383	6.74438	4.64954	9.94631	5.37297	65.52867
	Jarque-Bera Statistic	564.03	358.62	320.93	698.59	724.14	611.35	349.78	96.78	1,268.88	165.13	97,048.62
	Correlations
	London	100.00%
	Paris	85.20%	100.00%
	South Africa	65.06%	61.46%	100.00%
	Namibia (Overall)	53.99%	51.52%	87.15%	100.00%
	Namibia (Local)	14.52%	16.10%	37.13%	35.73%	100.00%
	Nigeria	1.96%	6.34%	1.38%	-0.47%	2.72%	100.00%
	Mauritius	12.65%	18.23%	6.94%	3.58%	5.97%	23.51%	100.00%
	Egypt	19.19%	20.66%	22.36%	19.53%	12.29%	8.42%	25.97%	100.00%
	Morocco	6.58%	16.55%	10.07%	6.09%	6.21%	10.15%	16.86%	19.22%	100.00%
	Tunisia	3.15%	13.07%	5.59%	4.59%	9.94%	10.83%	27.49%	22.48%	26.31%	100.00%
	Kenya	13.44%	11.70%	9.43%	10.55%	10.57%	10.53%	17.72%	16.90%	9.80%	19.61%	100.00%
	Source:

Table 6 . Unit Root tests

 6

	Variable	Level	First Difference	Level with trend	First Differences
					with trend
	Panel 1: Augmented Dickey-Fuller test
	y Kenya	-1.207419	-29.09890***	-1.672027	-29.09265***
	y Nigeria	-0.804020	-24.91325***	-1.924238	-24.89205***
	y South Africa	-0.986699	-25.12033***	-2.436170	-25.10129***
	y Namibia Overall	-1.368295	-25.00205***	-2.365877	-24.98157***
	y Namibia Local	-1.888937	-23.62267***	-1.045911	-23.99650***
	y Mauritius	-0.145805	-23.31767***	-1.592750	-23.33935***
	y Egypt	-0.020077	-22.48868***	-1.559794	-22.56845***
	y Morocco	0.198336	-23.97215***	-1.030731	-24.03165***
	y Tunisia	1.498168	-24.72299***	-0.370133	-24.89954***
	y UK	-1.537415	-27.52569***	-1.684841	-27.51759***
	y France	-2.191621	-27.17065***	-1.999675	-27.18757***
	Panel 2: KPSS test
	y Kenya	1.236805***	0.278226	0.579296***	0.213267***
	y Nigeria	2.844602***	0.174440	0.104950***	0.174685**
	y South Africa	2.682842***	0.061519	0.355391***	0.053798
	y Namibia Overall	2.311163***	0.071164	0.300367***	0.068472
	y Namibia Local	0.885437**	0.874173**	0.700976***	0.071031
	y Mauritius	2.335987***	0.259857	0.625454***	0.118314
	y Egypt	1.932951***	0.516802**	0.624614***	0.226263***
	y Morocco	1.920662***	0.414741*	0.755967***	0.125661*
	y Tunisia	2.189443***	0.623850**	0.671684***	0.101473
	y UK	0.470552**	0.113354	0.383805***	0.100980
	y France	0.532316**	0.163082	0.322241***	0.117908*
	Notes: (1) Test statistics reported in each case
	(2) KPSS refers to Kwiatkowski, Phillips, Schmidt, and Shin (1992) unit root test with null hypothesis
	of stationarity or no unit root
	(3) Augmented Dickey-Fuller unit root test has null hypothesis of unit root
	(4) *, **, *** indicates 90%, 95%, and 99% confidence level of rejection of null hypothesis

Page 25 of 36 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

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Table 7 . Bivariate VAR cointegration tests

 7

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Table 8 . Block Granger non-Causality

 8

		Causation	Kenya	South Africa	Egypt	Nigeria
	Kenya	----/----> < ----/----
	South Africa	----/----> < ----/----	15.1286 [0.00] † 0.1642 [0.68]
	Egypt	----/----> < ----/----	5.6997 [0.02] * 0.5215 [0.47]	0.5551E-3 [0.98] 37.6950 [0.00] †
	Nigeria	----/----> < ----/----	0.2998 [0.58] 1.0056 [0.32]	0.4978 [0.48] 1.1388 [0.28]	0.4599 [0.49] 10.8677 [0.01] †
	Mauritius	----/----> < ----/----	11.2616 [0.01] † 5.1645 [0.02] *	0.0315 [0.85] 16.5455 [0.00] †	0.0049 [0.94] 12.7633 [0.00] †	7.8981 [0.05] ** 3.7383 [0.05]
	Namibia	----/---->	15.7725 [0.00] †	1.7716 [0.18]	30.9967 [0.00] †	0.6371 [0.43]
	Overall	< ----/----	0.0046 [0.95]	11.0205 [0.01] †	0.0196 [0.89]	1.1579 [0.28]
	Namibia	----/---->	0.2868 [0.59]	3.0372 [0.08]	2.7693 [0.09]	3.0974 [0.08]
	Local	< ----/----	0.2209 [0.64]	2.1197 [0.14]	1.9527 [0.16]	0.1127 [0.74]
	Morocco	----/----> < ----/----	0.5310 [0.47] 1.3148 [0.25]	0.0128 [0.91] 0.9851 [0.32]	1.4126 [0.24] 0.2107 [0.65]	7.0017 [0.01] ** 2.8898 [0.09]
	Tunisia	----/----> < ----/----	6.4925 [0.01] * 5.3725 [0.02] *	0.1513 [0.69] 3.6064 [0.05]	0.9489 [0.33] 1.3663 [0.24]	1.9042 [0.17] 1.0568 [0.30]
	UK	----/----> < ----/----	11.6415 [0.01] † 0.0524 [0.82]	0.0377 [0.84] 2.4811 [0.11]	20.9125 [0.00] † 0.0736 [0.79]	11.6728 [0.01] † 1.5178 [0.22]
	France	----/----> < ----/----	15.7648 [0.00] † 0.4009 [0.53]	0.1210 [0.72] 0.8351 [0.36]	21.9848 [0.00] † 0.0764 [0.78]	6.4928 [0.01] * 1.5177 [0.22]
	Notes: (1) Figures in square parentheses are standard errors

Page 33 of 36 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  LB represents Lower Bound of F-statistic critical values, UB represents Upper Bound of F-statistic critical values. LB-UB represents a value falling between bands. Four lags were chosen in all cases for the differenced variables in equation 19. Mauritius -1.1157*y South Africa + 2.1441*Intercept F(3, 571) = 10.3481 [0.00] Adjusted R-Squared = 0.0449 Estimated Long-run coefficients using ARDL(1,2) error correction model (N=572) Dependent variable is

			Submitted Manuscript
	Kenya -France South Africa -Mauritius Namibia Overall -South Africa
			Dependent Variable is ∆y Kenya Dependent Variable is ∆y South Africa Dependent Variable is y Namibia Overall
	Regressor Regressor Regressor			Coefficient Coefficient Coefficient	Standard Errors (T-Ratio) Standard Errors (T-Ratio) Standard Errors (T-Ratio)
	∆ Mauritius			0.0026	0.0079 (0.33)
	∆ Intercept			0.0131	0.0153 (0.86)
	ECM(-1)			-0.0052	0.0075 (-0.69)
	ECM = y South Africa -0.49277*y Mauritius -2.5053*Intercept
	F(2, 572) = 0.38728 [0.68]
	Adjusted R-Squared = -0.0021395
	Estimated Long-run coefficients using ARDL(1,0) error correction model (N=572) Dependent variable is South
	Africa
	y Mauritius	->	1.6706 [0.19]	0.8549 [0.43] 0.4927	0.6208 [0.54] 0.9712 (0.51)
	Nigeria Intercept	< ----/----	0.4094 [0.66]	4.8603 [0.08] UB-LB 2.5053	0.5816 [0.56] 1.1954 (2.09)
	----/----> Mauritius -South Africa	1.2127 [0.29]	0.4558 [0.64]	0.2092 [0.81]	0.5954 [0.55]
	Mauritius Regressor Namibia Overall Namibia Local Morocco Tunisia UK France Notes: (1) † 99% Critical Value bound. < ----/----0.5607 [0.57] Dependent Variable is ∆y Mauritius 4.4477 [0.01] UB-LB ----/----> 2.2338 [0.11] 2.7954 [0.06] Coefficient < ----/----1.4794 [0.23] 3.6579 [0.03] UB-LB ----/----> 3.1993 [0.04] UB-LB 1.3814 [0.25] < ----/----6.4806 [0.02] † UB 3.4277 [0.03] UB-LB ----/----> 1.2134 [0.29] 0.5353 [0.59] < ----/----7.5632 [0.01] † UB 3.4840 [0.03] UB-LB ----/----> 1.9493 [0.14] 0.6932 [0.50] < ----/----2.7997 [0.06] 2.5222 [0.08] ----/----> 2.7269 [0.07] 1.1910 [0.31] < ----/----2.3456 [0.09] 1.1751 [0.31] ----/----> 1.9351 [0.15] 1.2063 [0.30] < ----/----5.8574 [0.03] † UB 2.6207 [0.07] o r P e e r F o r P e e r F o r P e e r F o r P e e r ∆ South Africa 0.0459 ∆ South Africa1 0.0911 ∆ Intercept -0.0288 ECM(-1) -0.0134 ECM = y Mauritius y South Africa 1.1157 Intercept -2.1441 South Africa -Namibia Overall F o r P e e r F o r P e e r (2) F R e v i 5.2908 [0.05] † 0.9868 [0.37] 0.6254 [0.54] Standard Errors (T-Ratio) 1.3537 [0.26] 5.6695 [0.04] † UB 2.3930 [0.09] 1.8332 [0.16] 1.1530 [0.32] 5.2839 [0.05] † UB 4.2622 [0.02] UB-LB 2.7888 [0.06] 0.1958 [0.82] 0.5476 [0.58] UB 2.0406 [0.13] 1.0022 [0.37] 0.5414 [0.58] 4.9997 [0.01] † UB 1.1853 [0.31] 2.9941 [0.05] 1.3826 [0.25] 0.9468 [0.39] 1.7702 [0.17] 3.1053 [0.05] UB-LB 2.4321 [0.09] 4.4247 [0.01] UB-LB 2.6953 [0.07] 0.0250 (1.84) 0.0253 (3.60) 0.0092 (-3.15) 0.0047 (-2.84) 0.2007 (5.56) 0.5894 (-3.64) e w R e v i e w R e v i e w R e v i e w Dependent Variable is ∆y South Africa Regressor Coefficient Standard Errors (T-Ratio) ∆ South Africa1 -0.1867 0.0421 (-4.43) ∆ Namibia Overall 0.7651 0.0178 (42.86) ∆ Namibia Overall1 0.1160 0.0363 (3.19) ∆ Intercept 0.0060 0.0139 (0.43) ECM(-1) -0.0026 0.0101 (-0.26) ECM = y South Africa -0.54156*y Namibia Overall -2.3190*Intercept F(4, 570) = 474.24 [0.00] Adjusted R-Squared = 0.7672 Estimated Long-run coefficients using ARDL(2,2) error correction model (N=570) Dependent variable is South Africa R e v i e w R e v i e w
	y Namibia Overall			0.5416	2.1480 (0.25)
	Intercept			2.3190	3.9290 (0.59)
				13 14 15

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Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript