CrossCountry Spillovers in East Africa: A Global Vector Autoregressive Analysis
Daniel Njoora^{1}, Olusanya E. Olubusoye^{2}, Patrick Weke^{3}
^{1}Pan African University, Institute of basic Sciences, Technology and Innovation, Department of Mathematics, Nairobi, Kenya
^{2}University of Ibadan, Department of statistics, Ibadan, Nigeria
^{3}University of Nairobi, School of Mathematics, Nairobi, Kenya
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To cite this article:
Daniel Njoora, Olusanya E. Olubusoye, Patrick Weke. CrossCountry Spillovers in East Africa: A Global Vector Autoregressive Analysis. American Journal of Theoretical and Applied Statistics. Vol. 4, No. 3, 2015, pp. 125137. doi: 10.11648/j.ajtas.20150403.18
Abstract: The recent financial crisis raises important issues about transmission of financial shocks across borders. This paper uses the global vector autoregressive model as developed in Dees, di Mauro, Pesaran and Smith (2007) to study crosscountry interlinkages among East African countries. The paper uses trade weights to capture the importance of the foreign variables. Results reveal that there is no evidence of strong international linkages across countries in East Africa. Results also reveal that the variable in which a shock is simulated is the main channel through whichin the shortrunshocks are transmitted, while the contribution of other variables becomes more important over longer horizons.
Keywords: Global VAR, Linkages, VARY*, Spillovers, Linkages
1. Introduction
East African economies have undergone remarkable changes over the past ten years. Crossborder ownership of assets and investment has increased, revealing important benefits and new risks associated with integration. The financial and economic interlinkages between East African countries have increased significantly over the past years. The formation of the East Africa Community (EAC) has been one of the major drivers of closer East Africa integration. Moreover, the number of countries in the EAC has increased from 3 to 5 after Rwanda and Burundi joined the organization.
Trade between East African countries has increased rapidly: for instance, in 2010, the EAC launched its own common market for goods, labor and capital within the region with the goal of creating a common currency and eventually a full political federation. In 2013, a protocol was signed outlining the member states’ plans for launching a monetary union within 10 years. Despite challenges on these establishments, this is a clear indication that trade and financial interactions have increased among these countries.
Much as trade has gained an increase, financial integration has also proceeded apace. Banks across East Africa have gained a dominant position in the banking systems in most countries. The share of foreign banks in terms of assets of local banking systems has increased rapidly over the last decade. As a result, these banks have become the main source of capital in terms of funding and foreign direct investment (FDI) for private investors in these countries.
For these countries, these closer linkages bring clear benefits but also carry risks. Trade links and financial capital inflows from more developed countries in this region like Kenya make it possible for other countries to boost their potential growth faster than they otherwise could achieve. As the countries rely on each other for capital and trade, economic slowdowns and financial market turmoil in any of these countries spill over across other countries. For instance, when Kenya experienced the postelection violence in 20072008, this triggered a sudden stop of trade flows in the region, which contributed to a deep crisis in addition to the global financial crisis.
In this paper, we attempt to explore the crosscountry linkages between East Africa countries using the GVAR framework. The main motivation of the paper is that our study has a very major difference in country coverage and the key variables studied compared to similar regional studies. As explained later in the paper, a key step of GVAR analysis is to construct, for domestic variables of each country in the system corresponding foreign variables, usually a weighted average of corresponding variables of its partners. For example, if the variable of interest is inflation rates, then its corresponding foreign variable (foreign inflation) is constructed as a weighted average of the inflation of its partners. The weighting scheme usually reflects the strength of economic ties of a particular country with its foreign partners.
In existing literatures, the selection of weights often varies. In this work we follow the literature of Pesaran et al. (2004), DdPS (2007), Feldkircher and Korhonen (2012) whereby we use weights based on trade flows. Other works use geographical distance based weights, Vansteenkiste (2007) whereas Galesi and Sgherri (2009) adopt weights based on bank lending data across countries.
In the paper, we focus on comovements between our variables of interest. The objective is to show how simulated shocks are propagated across the countries. The variables in our model are inflation rates, interest rates and exchange rates. We follow the bulk of existing literature in including oil prices as a global variable. The country sample includes all countries across East Africa, that is, Kenya, Uganda, Tanzania, Rwanda and Burundi. The model has yielded interesting results in that there is no evidence of strong international linkages across countries in East Africa. Results also reveal that the variable in which a shock is simulated is the main channel through whichin the shortrunshocks are transmitted, while the contribution of other variables becomes more important over longer horizons.
The rest of the paper is structured as follows: section 2 describes the analytical basis of the global VAR framework and the data used in the analysis. Section 3 presents estimation results. Section four analyses countryspecific global shocks by using GIRFs and GFEVD from the GVAR model. Conclusion is included in section 5.
2. The GVAR Model (20002013)
2.1. Structure of the Model
In order to capture the importance of crosscountry spillovers among countries, we build a GVAR model, following Pesaran, Schuermann and Weiner (2004) and DdPS (2007). The GVAR model is a crosscountry framework which allows the investigation of interdependencies among countries. It is generally composed of several country economies modeled by corresponding vector autoregressive (VAR) models. Each country model is linked with others by including foreignspecific variables. In this way, each country is potentially affected by developments in other countries, thus the need to use a global macroeconometric modeling approach in the analysis of regional propagation of shocks.
In our paper, foreignspecific variables are constructed using trade weights, hence indicating the importance of each country’s trade partner. By using trade weights, we follow the works of Pesaran et al. (2004) and DdPS (2007) who employ trade weights based on crosscountry trade flows. We deviate from the fact that in the original GVAR modeling technique, financial weights are used to capture the foreign variables. Other literature employ financial weights, for instance Galesi and Sgherri (2009), Vansteenkiste (2007) uses weights based on geographical distances among regions whereas Hiebert and Vansteenkiste (2007) adopt weights based on sectoral inputoutput tables across industries.
Our GVAR model covers 5 countries in East Africa. Since all countries are modeled individually, the GVAR model is composed by 5 VARY*, that is, VAR models augmented by weakly exogeneousI (1) foreign variables. Countries included in the analysis are Kenya, Uganda, Tanzania, Rwanda and Burundi. In each country VARY* model, country specific variables are related to deterministic variablessuch as time trendand a set of countryspecific foreign variables, calculated as weighted variables of the corresponding countryspecific variables for the remaining countries.
Each country will be modeled as a VARY* model as shown below
(1)
Where
is a vector of country specific domestic variables
is the vector of foreign variables specific to country
is a matrix of coefficients associated to lagged domestic variables
is a matrices of coefficients related to contemporaneous foreign variables
is a matrices of coefficients related to the lagged foreign variables
is a vector of fixed intercepts
is a vector of coefficients of the deterministic time trend
is a vector of country specific shocks assumed to be serially uncorrelated with a zero mean and a nonsingular covariance matrix. Specifically .
Moreover, a crosscountry correlation among the idiosyncratic shocks is allowed. In particular it is assumed that
Therefore, by construction, the GVAR model allows for interactions among the different economies through two channels: (a) the contemporaneous interrelation of domestic variables, , with foreignspecific variables, , and with their lagged values; (b) the contemporaneous dependence of shocks in country on the shocks in country , as described by the crosscountry covariances, , where .
The domestic variables included in the countryspecific models are the following: inflation rates, interest rates and exchange rates. Oil prices enter the model as a global variable.
The foreign variables are specific to each country and represent the influence of trade partners for a given country. These are calculated as weighted averages of the corresponding variables for that country. Specifically the set of foreignspecific variables for country , , is given by:
Where
and .
The weights, for , capture the importance of country for country . They are based on crosscountry trade flows.
The domestic variables and foreign variables are grouped as
(2)
Each country model in (1) is then written as
(3)
where it is assumed that for ease of computation
In equation (3)
(4)
And the coefficient matrices are all of size . Equation (3) can be treated like a VAR (p) model by multiplying throughout by .
To examine the endogeneity of the foreign variable , we need to solve the entire (global) model. Stacking over the countries model can be written as
(5)
Where
The solution of the stacked model is obtained as
(6)
Provided the innovations are independent in the time dimension, the endogeneity of the regressors follows from
(7)
Pesaran et al. (2002) assume that the weight matrices are diagonal with
and that , as
However, this implies that asymptotically the foreign variables have no explanatory power in the model. Asymptotic properties of such model should not be used as small sample guidance for our estimators if we actually expect some degree of cross sectional dependence in our model.
The assumption , where the constant does not depend on the sample size N. This is clearly a weaker assumption but it turns out to be powerful enough to allow us derive asymptotic properties of our model.
We can also build a simple version of our GVAR model from each country models represented by equation (1) as follows.
We collect all the domestic variables of all the countries to create the global vector
(8)
Which is a vector containing all endogeneous variables, where . Following the step that gives rise to equation (1) and the one above, we obtain the identity
(9)
For is a countryspecific link matrix of dimensions constructed on the basis of trade weights. This identity allows writing each country model in terms of the global vector in (8). By substituting (9) in (1), we obtain
(10)
The individual country models are then stacked, yielding the model for all the variables in the global model to obtain
(11)
Where
,
Premultiplying equation (11) by yields an autoregressive representation of the GVAR (p) model shown below
(12)
Where
Equation (12) can be treated like any other VAR equation of order p.
2.2. Properties of the Data Series
Our data set includes 5 countries from East Africa. The sample period spans, on a quarterly basis, from 2000Q1 to 2013Q3. For each country we consider the following variables: inflation rates, exchange rates and interest rates obtained from the national authorities of the respective countries.
The countryspecific foreign variables are constructed using trade weights. In particular, the trade of country with country is considered to be the total exports and imports from the period 20042011.
We investigate the order of integration of each variable under study by means of formal unit root tests. We discuss the ADF unit root tstatistics as well as those based on weighted symmetric estimation of ADF type regressions introduced by Park and Fuller (1995). The latter tests denoted by Ws, exploit the time reversibility of stationary autoregressive processes in order to increase their power performance. Leybourne, Kim and Newbold (2005) and Pantula, Gonzalez, Farias and Fuller (1995) provide evidence of superior performance of the weighted symmetric test statistic compared to the standard ADF test or the GLSADF test proposed by Elliot et al. (1996). The lag length employed in the ADF and Ws unit root tests has been selected by the Akaike Information Criterion (AIC). Results of the ADF and WS statistics are provided for the level, first differences and second differences of all the country specific domestic and foreign variables as well as global variables. When testing the levels, two types of regressions have been computed: one including both an intercept and a trend, and another including an intercept only. When testing first and second differences, only the intercept is included. Asymptotic 5% critical values for both statistics have been employed. The results are reported in tables 2, 3 and 4. The 95% critical values are indicated in the third column for regressions with and with no trend. The unit root hypothesis at the 5% level of significance is not rejected for all domestic, foreign and the global variables.
country  rwanda  kenya  uganda  tanzania  burundi 
rwanda  0  0.0983761  0.1196532  0.0532244  0.1072535 
kenya  0.442186  0  0.7372607  0.7488049  0.2510997 
uganda  0.3773395  0.517266  0  0.150186  0.4867709 
tanzania  0.1112848  0.3483198  0.099574  0  0.1548759 
burundi  0.0691896  0.036038  0.0435121  0.0477847  0 
Domestic Variables  Statistic  Critical Value  rwanda  kenya  uganda  tanzania  burundi 
inf (with trend)  ADF  3.45  5.4171  4.1712  3.9697  6.3820  4.8858 
inf (with trend)  WS  3.24  5.7648  4.4711  5.0028  6.6417  5.1293 
inf (no trend)  ADF  2.89  5.4186  4.2241  3.5906  6.3971  4.9299 
inf (no trend)  WS  2.55  5.7941  4.5176  4.5980  6.6598  5.1691 
Dinf  ADF  2.89  5.8135  6.7319  6.8172  6.7142  8.5082 
Dinf  WS  2.55  6.1495  7.0027  3.4995  7.0892  8.7924 
DDinf  ADF  2.89  6.2798  6.2581  4.0608  8.0522  6.6873 
DDinf  WS  2.55  6.6166  6.6947  4.3282  8.3351  7.1333 
exc (with trend)  ADF  3.45  3.6331  6.0477  5.1100  5.9118  4.4346 
exc (with trend)  WS  3.24  2.3780  6.1804  4.7805  6.0616  4.4125 
exc (no trend)  ADF  2.89  4.1532  6.0651  5.0802  5.8028  4.4635 
exc (no trend)  WS  2.55  2.1383  6.2273  4.8339  6.0020  4.2994 
Dexc  ADF  2.89  5.6601  6.9817  7.3188  5.5866  6.6787 
Dexc  WS  2.55  5.5670  7.3460  7.6653  5.4044  5.7036 
DDexc  ADF  2.89  7.1903  7.2466  7.5913  7.2045  8.0991 
DDexc  WS  2.55  7.2784  7.7113  7.9295  7.5641  8.8900 
int (with trend)  ADF  3.45  6.7020  4.5298  5.0533  5.7577  5.7907 
int (with trend)  WS  3.24  6.3029  4.5884  4.9363  5.4614  5.9809 
int (no trend)  ADF  2.89  6.4890  4.4180  4.8196  5.1851  5.8335 
int (no trend)  WS  2.55  6.5372  4.2741  4.9275  5.1624  5.9970 
Dint  ADF  2.89  9.7974  7.4423  6.0772  6.5831  7.5631 
Dint  WS  2.55  6.4099  7.5136  5.8732  6.4763  8.0331 
DDint  ADF  2.89  10.363  5.9243  7.0431  9.9380  10.8254 
DDint  WS  2.55  7.7119  6.0285  6.9330  9.8297  11.3713 
Foreign variable  Statistic  Critical value  rwanda  kenya  uganda  tanzania  burundi 
infs (trend)  ADF  3.45  3.9697  3.9697  3.7402  3.9697  3.9697 
infs (trend)  WS  3.24  5.0028  5.0028  3.9677  5.0028  5.0028 
infs (no trend)  ADF  2.89  3.5906  3.5906  3.7612  3.5906  3.5906 
infs (no trend)  WS  2.55  4.5980  4.5980  3.9956  4.5980  4.5980 
Dinfs  ADF  2.89  6.8172  6.8172  6.7574  6.8172  6.8172 
Dinfs  WS  2.55  3.4995  3.4995  7.0235  3.4995  3.4995 
DDinf  ADF  2.89  4.0608  4.0608  6.2533  4.0608  4.0608 
DDinf  WS  2.55  4.3282  4.3282  6.9302  4.3282  4.3282 
excs (trend)  ADF  3.45  5.2984  4.4104  5.7549  5.8798  5.0718 
excs (trend)  WS  3.24  5.3574  4.5269  5.8358  5.9334  5.1650 
excs (no trend)  ADF  2.89  5.3364  4.4483  5.8081  5.9114  5.1213 
excs (no trend)  WS  2.55  5.4098  4.5199  5.8917  5.9900  5.2099 
Dexcs  ADF  2.89  7.4421  6.2559  6.7551  7.3853  6.9980 
Dexcs  WS  2.55  7.8599  6.6718  7.1413  7.7658  7.4242 
DDexc  ADF  2.89  7.4314  6.7954  7.0989  7.3335  7.1169 
DDexc  WS  2.55  7.8816  7.0697  7.5909  7.8271  7.5565 
ints (trend)  ADF  3.45  3.4725  5.11  4.3480  4.0247  3.5720 
ints (trend)  WS  3.24  3.6872  4.6388  4.5056  4.1784  3.7095 
ints (no trend)  ADF  2.89  3.2560  4.8700  4.1904  3.9158  3.2296 
ints (no trend)  WS  2.55  3.4911  4.6134  4.1787  3.9041  3.4706 
Dints  ADF  2.89  6.7967  5.8527  7.8125  7.0893  6.9757 
Dints  WS  2.55  6.9505  5.2322  7.9063  7.1888  7.1028 
DDint  ADF  2.89  8.6701  7.4101  7.9962  6.5924  6.7629 
DDint  WS  2.55  8.6134  6.5496  8.3707  7.0019  6.8185 
Global Variables  Test  Critical Value  Statistic 
poil (with trend)  ADF  3.45  5.2370335 
poil (with trend)  WS  3.24  5.4398825 
poil (no trend)  ADF  2.89  5.0521658 
poil (no trend)  WS  2.55  5.2925515 
Dpoil  ADF  2.89  6.8166702 
Dpoil  WS  2.55  7.1716318 
DDpoil  ADF  2.89  6.4942482 
Dpoil  WS  2.55  6.9426192 
3. Estimation
3.1. Conditions for the GVAR Estimation
Given the considerable dimension of the GVAR model with respect to a traditional VAR model, it is not possible to estimate the global model using the traditional procedure. This is because it would involve the estimation of a number of parameters greater than the number of available observations. This shortcoming is solved by having an estimation procedure based on a countrybycountry estimation, rather than a full system estimation, given the weak exogeneity of the foreignspecific variables. The weights used for the construction of the foreign variables are computed rather than estimated. In doing so, the estimation procedure reduces considerably the number of unrestricted parameters to be estimated.
Pesaran et al. (2004) in Galesi and Sgheri (2009) indicate three further requirements as sufficient conditions for the validity of the GVAR methodology:
1. The global model must be dynamically stable. Specifically the Eigen values of the F matrix in (12) must be either on or inside the unit circle.
2. The weights must be relatively small, such that as , for .
3. The crossdependence of the idiosyncratic shocks must be sufficiently small, so that , as , for all Where is the covariance of the variable in country with the variable in country .
All the three requirements are met in our GVAR model. First the model is dynamically stable: the moduli of the Eigen values of the F matrix in 13 are all on or within the unit circle. Specifically, 3 Eigen values lie on the unit circle as reported while the rest lie inside the unit circle as reported in table 12.
Majority of the weights are ‘granular’ for each country, that is, they are not too close to one. The largest weights are observed for Kenya towards Uganda and Tanzania with 0.7372607 and 0.74880049 respectively.
Lastly, the idiosyncratic shocks are weakly correlated. Among the variables in levels, exchange rates appears to be the most correlated, with a maximum of 0.275157 for Uganda and a minimum of 0.092029 for Burundi. Moreover, with respect to variables in differences, we observe a fall in the degree of correlation. The VECMY residuals are obtained from the estimation of each VECMY* model, containing both the domestic and foreign variables. The VECMY residuals are generally weakly correlated and in some cases negatively weakly correlated for all the variables under study. This is a clear indication that the inclusion of the foreign variables in the country model estimation cleans the common factor among the variables, thereby yielding weakly correlated residuals. In this way, this condition allows us to simulate shocks which are mainly countryspecific.
3.2. Estimation of the CountrySpecific Models
Given that the variables under study have a unit root, we individually estimate each countryVARY* model in its vector error correcting form, Johansen (1992).The rank of the cointegrating space for each country is computed using Johansen’s trace and maximal eigen value statistics as set out in Pesaran, Shin and Smith (2000) for models with weakly exogeneous I(1) regressors. The final selection of the rank orders is determined by the trace statistic, which in small samples is known to have better power properties than the maximal Eigen value statistic. The results are reported in tables 58. In cases where cointegration is found, each countryVARY* model is estimated under its vector errorcorrecting (VECMY*) form.
Country  Rwanda  Kenya  Uganda  Tanzania  Burundi 
Number of endogeneous variables  3  4  3  3  3 
Number of foreign variables  4  3  4  4  4 
 72.2582  69.5551  55.0400  51.3710  59.8783 
 59.7675  47.1868  34.5418  32.7366  21.1041 
 27.9424  22.0356  14.3360  19.4847  16.1002 
 20.2550 
Country  rwanda  kenya  uganda  tanzania  burundi 
Number of endogenous variables  3  4  3  3  3 
Number of foreign (star) variables  4  3  4  4  4 
 159.9681  159.0324  103.9178  103.5922617  97.08264 
 87.70989  89.47732  48.87775  52.22128167  37.20437 
 27.94238  42.29056  14.33595  19.48465381  16.10018 
 20.25498 
Country  rwanda  kenya  uganda  tanzania  burundi 
Number of endogenous variables  3  4  3  3  3 
Number of foreign (star) variables  4  3  4  4  4 
 71.56  91.81  71.56  71.56  71.56 
 45.9  64.54  45.9  45.9  45.9 
 23.63  41.03  23.63  23.63  23.63 
 20.98 
country  number of cointegrating relations 
rwanda 

kenya 

uganda 

tanzania 

burundi 

3.3. Weak Exogeneity Tests
The main assumption underlying the estimation of the individual country VARY* models is the weak exogeneity of the foreign variables. This assumption is compatible with a certain degree of weak dependence across as discussed in Pesaran, Schuermann and Weiner (2004). A formal test of this assumption for the country specific foreign variables and the observed global variables is carried out as described in Johansen (1992) and Harbo, Johansen, Nielsen and Rahbek (1998). Testing for weak exogeneity involves the marginal model of the foreign variables.
The weak exogeneity test in this work contains the F statistics for testing the weak exogeneity of the foreign variables. The test statistics have been generated with the critical values at 5% level of significance and the given degrees of freedom as shown in table 9. The weak exogeneity assumption is not rejected for most of the foreign variables, despite some exceptions. In particular, the assumption is rejected at the 5% significance level for Kenyan inflation. Therefore, given that only 1 out of 19 foreign variables fail to satisfy the weak exogeneity assumption, we consider these outcomes as acceptable, thereby justifying the estimation procedure of each country model in the GVAR.
Country  F test  Fcrit_0.05  infs  excs  ints  poil 
Rwanda  F(3,6)  4.7571  
Kenya  F(3,18)  3.1599  5.9758  4.5338  0.6712  
Uganda  F(2,7)  4.7374  
Tanzania  F(2,33)  3.2849  0.1098  0.7379  1.2047  0.7937 
Burundi  F(1,20)  4.3512  0.2617  3.2293  4.7369  0.1106 
3.4. Impact Elasticities
The contemporaneous effects of foreign variables on their domestic counterparts are provided together with tratios computed based on standard, as well as White and NeweyWest adjusted variance matrices. These contemporaneous effects are given by the estimated coefficients on the contemporaneous foreign variables and can be interpreted as impact elasticities between domestic and foreign variables. They are particularly informative as regards the international linkages between the domestic and foreign variables. High elasticities between domestic and foreign variables imply strong comovements between the two. In addition to these coefficient estimates, standard errors and tvalues are also calculated. White’s heteroskedasticity robust and NeweyWest heteroskedasticity and autocorrelation consistent standard errors as well as the corresponding tvalues are also computed. The results are listed in table 10. The results in the table above indicate that, the impact elasticities of all the variables are statistically significant for all the countries. All the values are positive but lower than one. For a given country, impact elasticities lower than one indicate that the domestic variables do not overreact to a variation in the foreign variable of its trade partners, while an impact elasticity greater than one indicate that the domestic variables overreacts to a variation in the foreign variables of the corresponding trade partners. Moreover, these findings give us already some insights with respect to the dynamics of the GIRFs: there is no evidence of strong international linkages across countries.
inf  exc  int  
RWANDA  Coefficient  4.351x109  0.003841  0.0939  
RWANDA  Standard error  2.943 x109  0.032030  0.1419  
RWANDA  tRatio  1.4786474  0.119930  0.6618  
RWANDA  White's Adjusted SE  8.013x1010  0.029187  0.1516  
RWANDA  tRatio  5.4303699  0.131615  0.6194  
RWANDA  NeweyWest's Adjusted SE  7.73 x1010  0.026376  0.1467  
RWANDA  tRatio  5.6264517  0.145642  0.6403  
KENYA  Coefficient  6.76 x1010  0.8312  0.5008  
KENYA  Standard error  8.95 x1010  0.1945  0.2975  
KENYA  tRatio  0.755774  4.2737  1.6835  
KENYA  White's Adjusted SE  5.44 x1010  0.2737  0.2851  
KENYA  tRatio  1.2439378  3.0365  1.7566  
KENYA  NeweyWest's Adjusted SE  4.67 x1010  0.2995  0.2848  
KENYA  tRatio  1.4472997  2.7755  1.7582  
UGANDA  Coefficient  22100185  0.9492  0.0659  
UGANDA  Standard error  44139876  0.1379  0.1725  
UGANDA  tRatio  0.5006853  6.8822  0.3821  
UGANDA  White's Adjusted SE  27955489  0.1438  0.1406  
UGANDA  tRatio  0.7905491  6.5998  0.4689  
UGANDA  NeweyWest's Adjusted SE  29982063  0.1279  0.1373  
UGANDA  tRatio  0.7371136  7.4219  0.4803  
TANZANIA  Coefficient  1.197x108  0.0552  0.0996  
TANZANIA  Standard error  1.156 x108  0.0843  0.1318  
TANZANIA  tRatio  1.0353234  0.6544  0.7558  
TANZANIA  White's Adjusted SE  8.435x109  0.0632  0.1128  
TANZANIA  tRatio  1.4186784  0.8723  0.8828  
TANZANIA  NeweyWest's Adjusted SE  8.455 x109  0.0499  0.0849  
TANZANIA  tRatio  1.4153838  1.1054  1.1733  
BURUNDI  Coefficient  3.069 x109  0.0716  0.2428  
BURUNDI  Standard error  3.869 x109  0.0901  0.2808  
BURUNDI  tRatio  0.7933594  0.7942  0.8646  
BURUNDI  White's Adjusted SE  7.026x1010  0.0726  0.2691  
BURUNDI  tRatio  4.3679583  0.9858  0.9023  
BURUNDI  NeweyWest's Adjusted SE  7.23 x1010  0.0533  0.2652  
BURUNDI  tRatio  4.2428634  1.3419  0.9156  
4. Dynamic Analysis
Impulse responses refer to the time profile of the effects of variable specific shocks or identified shocks (such as monetary policy or technology shocks, identified using a suitable economic theory) on the future states of a dynamical system and thus, on all the variables in the model. In this work different types of shocks are simulated. For instance, we simulate a negative global shock to a domestic variable, a shock to a global variable and a shock to domestic variables.
4.1. Generalized Impulse Response Functions
The impulse responses of shocks to specific variables considered for the GVAR model are the Generalized Impulse Response ResponseFuctions (GIRFS), introduced in Koop et al. (1996) and adapted to VAR models in Pesaran and Shin (1998).
This relatively new approach differs in a number of ways from traditional Orthogonalized Impulse Responses (OIRs) in Sims (1980). First, it does not orthogonalize the residuals of the system, as it takes into account the historical correlations among the variables, summarized by the estimated variancecovariance matrix. For this reason, it does not require any a priori economicbased restrictions and its outcome is invariant to the ordering of the variables in the model. Second, since the shocks are not identified, the GIRFs cannot provide information about the causal relationships among the variables. This shortcoming limits the potential; applications of the GIRFs, especially for purposes of policy simulation. Nonetheless, GIRFs have a comparative advantage with respect to the traditional OIRs in the context of multicountry frameworks such as the GVAR model, Galesi and Sgherri (2009). Infact, they can provide interesting insights on how shocks internationally propagate, by unveiling potential linkages among different national economies. In addition, it is actually a difficult task to employ traditional OIRs in a GVAR, since there is no reasonable way to order the countries in the model.
In our application, we analyze the dynamic properties of our GVAR model by simulating either a positive or a negative standard error shock to each country’s variable. The scope of this simulation is to determine the degree of intercountry financial spillovers: in other words, we seek to analyze how each country responds to a specific shock.
For instance, the GIRFs associated to one standard error negative shock to Kenyan inflation on its partners’ inflation are plotted in figure 2 below. For each region, the charts show the dynamic response of each variable over a time horizon of 10 years which has been used as our forecast horizon.
The graphs in figure 1 indicate that Uganda and Tanzania have a significant response to a one standard error (s.e.) negative shock to Kenyan inflation as compared to Rwanda and Burundi. Rwanda and Burundi are only responding in the shortrun.
The graphs in figure 2, show the responses associated with exchange rates to one s.e shock to Kenyan inflation.The graphs indicate that there are strong fluctuations in GIRFs for Kenya, Uganda, Tanzania and Burundi in the shortrun but the trend stabilizes after 3 years. In the case of Rwanda, there are strong fluctuations for the first 3 years and a monotonic decrease in exchange rates’ GIRFs in the longrun.
The graphs in figure 3 indicate that there are strong fluctuations in interest rates for the first three years but the trend stabilizes in the longrun. Moreover, there is a notable response that is observed for Kenya. The associated GIRFs monotonically decrease over the first year i.e. first four quarters but the trend thereafter is similar to the other countries.
Another form of shock simulated is a global shock to inflation. The results are represented in the graphs in figures 4, 5, 6 and 7 for the stated variables. The GIRFs for Kenyan inflation decreases for two years then stabilizes, while that of the other countries in the study keeps fluctuating for 2 years and then stabilizes. For the case of exchange rates, there is a striking fluctuation in the GIRFs for all countries as shown in the graphs above. A similar trend is observed for the response in interest rates as shown in figure 6. Other types of shocks simulated show similar trends to the ones discussed above, that is, sharp fluctuations in the shortrunmostly 2 to 4 years and then stabilization in the longrun.
4.2. Generalized Forecast Error Variance Decompositions
Traditionally the forecast error variance decomposition of a VAR model is performed on a set of orthogonalised shocks, whereby the contribution of the orthogonalised innovation to the mean square error of the nstep ahead forecast of the model is calculated. In the case of the GVAR, the shocks across countries, that is for , are not orthogonal. In fact, there is evidence that on average, the shocks across countries are positively correlated, Smith and Galesi (2011). The standard application of the orthogonalised FEVD to the GVAR model is therefore not valid.
Results of the GFEVDs are reported in table 13.Following a shock to the Kenyan exchange rates, we observe that among the Kenyan variables, exchange rates explain most of the forecast error variance in the short run. However, the relative contribution of exchange rates decreases over time, while the opposite is for the other Kenyan and nonKenyan variables. Hence, we observe that if a shock is simulated, the variable which explains most of the variance of the shock in the shortterm is the variable in which that shock is injected. On the contrary, in the longer term, the other domestic variables gain increasing relevance.
From a global perspective, we generally observe the same dynamic behavior just highlighted in the Kenyan case: the variable in which the shock is injected explains most of the forecast error variance for all countries over the short run; its relative importance decreases over time, while the opposite is observed for the rest of the variables.
Variable  Country  Levels  First differences  VECMY residuals 
inf  RWANDA  0.229627  0.137225  0.143227367 
inf  KENYA  0.142006  0.044708174  0.065463145 
inf  UGANDA  0.146446  0.196894237  0.047937892 
inf  TANZANIA  0.076313  0.005831563  0.027205082 
inf  BURUNDI  0.238314  0.2148156  0.171931019 
exc  RWANDA  0.156425  0.05939349  0.046309577 
exc  KENYA  0.217059  0.198115649  0.204706288 
exc  UGANDA  0.275157  0.236599354  0.038302568 
exc  TANZANIA  0.127288  0.081996551  0.00354272 
exc  BURUNDI  0.092029  0.110613956  0.031487735 
int  RWANDA  0.00857  0.026386876  0.001810624 
int  KENYA  0.00796  0.029611946  0.115923104 
int  UGANDA  0.03486  0.04330711  0.008430689 
int  TANZANIA  0.020174  0.046061863  0.031504121 
int  BURUNDI  0.012512  0.024029082  0.038705345 
Eigenvalues of the GVAR Model in Descending Order  Corresponding Moduli 
1.02981416203722 +0.00000000000000i  1.029814162 
1.00000000000000 0.00000000000001i  1 
1.00000000000000 +0.00000000000001i  1 
0.73825198141311 0.00000000000000i  0.738251981 
0.41446466318635 0.07890768783217i  0.652142445 
0.41446466318635 +0.07890768783217i  0.652142445 
0.15171280897435 +0.14459097421581i  0.493157551 
0.15171280897435 0.14459097421581i  0.421909209 
0.03466968718702 0.40465695338521i  0.421909209 
0.03466968718702 +0.40465695338521i  0.406139431 
0.00969975457916 +0.00000000000000i  0.406139431 
0  0.358265217 
0  0.209578926 
0  0.209578926 
0  0.171419581 
0  0.104784157 
0  0.104784157 
0  0.020272797 
0  0.009699755 
0  0 
0  0 
0  0 
0  0 
0  0 
0.02027279690868 0.00000000000000i  0 
0.10463456254011 0.00559714000765i  0 
0.10463456254011 +0.00559714000765i  0 
0.17141958056471 +0.00000000000000i  0 
0.22349000598944 0.61265160196674i  0 
0.22349000598944 +0.61265160196674i  0 
0.35826521686838 +0.00000000000000i  0 
0.49315755115142 +0.00000000000000i  0 
Quarter  0  5  10  15  20  25  30  35  40  
Kenya  Inf  0.017  0.108  0.128  0.141  0.160  0.177  0.0194  0.209  0.223 
Kenya  Exc  0.577  0.304  0.254  0.238  0.228  0.219  0.210  0.203  0.196 
Kenya  Int  0.001  0.126  0.108  0.101  0.097  0.093  0.090  0.087  0.084 
Rwanda  Inf  0.010  0.013  0.013  0.013  0.014  0.014  0.015  0.015  0.016 
Rwanda  Exc  0.012  0.010  0.009  0.009  0.009  0.009  0.008  0.008  0.008 
Rwanda  Int  0.002  0.017  0.019  0.018  0.018  0.018  0.018  0.018  0.018 
Uganda  Inf  0.001  0.004  0.028  0.029  0.029  0.029  0.029  0.030  0.030 
Uganda  Exc  0.050  0.090  0.093  0.087  0.084  0.082  0.079  0.077  0.075 
Uganda  Int  0.011  0.029  0.030  0.048  0.049  0.056  0.059  0.063  0.067 
Tanzania  Inf  0.009  0.031  0.031  0.029  0.029  0.028  0.027  0.027  0.026 
Tanzania  Exc  0.020  0.080  0.065  0.062  0.062  0.062  0.061  0.060  0.060 
Tanzania  Int  0.005  0.011  0.012  0.014  0.013  0.014  0.014  0.014  0.014 
Burundi  Inf  0.005  0.005  0.006  0.006  0.006  0.006  0.006  0.005  0.005 
Burundi  Exc  0.007  0.014  0.014  0.014  0.015  0.015  0.016  0.016  0.016 
Burundi  int  0.001  0.010  0.010  0.011  0.013  0.014  0.015  0.016  0.017 
a) Kenya inflation
b) Rwanda inflation
c) Uganda inflation
d) Tanzania inflation
e) Burundi inflation
a) Kenya exchange rates
b) Rwanda exchange rates
c) Uganda exchange rates
d) Tanzania exchange rates
e) Burundi exchange rate
a) Kenya interest rates
b) Rwanda interest rates
c) Uganda interest rates
d) Tanzania interest rates
e) Burundi interest rates
a) Kenya inflation
b) Rwanda inflation
c) Uganda inflation
d) Tanzania inflation
e) Burundi inflation
a) Kenya exchange rates
b) Rwanda exchange rates
c) Uganda exchange rates
d) Tanzania exchange rates
e) Burundi exchange rates
a) Kenya interest rates
b) Rwanda interest rates
c) Uganda interest rates
d) Tanzania interest rates
e) Burundi interest rates
References