Identification Strategy of Supply and Demand Shocks

Before we discover the incidences of supply and demand shocks, we need to specify the identifying assumptions in the SVAR model. Thus, the study follows the identification scheme of Bayoumi and Eichengreen (1992; 1994), with some extension in variables in order to identify the different types of shocks affecting East African Community.

Therefore, in line with the OCA predictions, we used a four-variable SVAR model to examine the underlying shocks affecting the EAC region. The variables used were global real GDP (y*), country specific real GDP (y), real exchange rate (e) and domestic price level (p). Therefore, we can write the structural model as follows:

4.13

4.14

4.15

4.16

Where ; comprising of global real GDP (y*), country specif real GDP (y), real exchange rate (e) and domestic price level (p), which are all expressed in log difference form. The matrix Ai is a 4x4 matrix that represent the impulse responses of endogenous variables to structural shocks.

, comprising of external global supply shock ( ), country specific supply shock ( ), country specific demand shock ( ) and country specific monetary shock ( ) respectively, which are assumed to be serially uncorrelated, and are orthonormal.

To identify the structural shocks, we impose the following long run restrictions: i) global GDP is considered to evolve exogenously so that country specific supply, country specific demand and country specific monetary shock do not affect world real GDP in the long run. Thus, our restrictions would A12 = A13 = A14 = 0. ii) In the long run country specific real GDP is affected exclusively by supply shocks, thus, the restriction equation would be A23 = A24 = 0. ii) Monetary shocks do not have effects on real exchange rates in the long run.

These restrictions can be rewritten in the following matrix form:

Given the above restrictions, the structural shocks can be recovered as linear combinations of reduced-form innovations and they are serially uncorrelated and orthonormal. In places relevant, we compared the identified East African shocks to the existing monetary unions such as European Monetary Union, Gulf Co-operation Council GCC and some other monetary unions.

AD

E

D’’

D’

Short run

Aggregate Supply Long run

Aggregate Supply

Y Y ^’ Production

E

S’

S”

AD Price

r

Prices r

Production Y Y ^’ Y ^’’

Long run

Aggregate Supply Short run

Aggregate Supply Short run Aggregate Supply’

Short run Aggregate Supply Long run

Aggregate Supply

Production

Figure 4-3: The aggregate supply and aggregate demand model AD

E P

Y Price

r

AD^’

A Demand Shock A Supply Shock

The Model

4.2.3 Impulse Response Function Test

Impulse response function (IMF) is a device that helps us learn the dynamic properties of vector autoregressions of interest to forecasters. This test determines the responsiveness of the dependent variables in the SVAR to the corresponding shocks of each variable. In other words, a unit shock is applied to the error for every variable in the equation to identify the effect of shocks upon SVAR over time. Therefore, if there are k variables in a system, a total of k² impulse responses could be generated. The way that this is achieved in practice is by expressing the SVAR model as a vector autoregressive model. When SVAR models are stable, the shock should gradually decapitate (Brooks, 2008).

Let us assume that Y_t is a k-dimensional vector series created by

where is the moving average coefficients that calculates the impulse response. More specifically, stand for the response of variable j to unit impulse in variable k occurring i-th period ago. Interpretation of the IRF is straightforward, if the innovations are contemporaneously uncorrelated. The i-th innovation is simply a shock to the i-th endogenous variable . Innovations are usually correlated, and may be viewed as having a common component which cannot be associated with a specific variable (Saatcioglu & Korap, 2006). Impulse response function analysies are used to evaluate the usefulness and effectiveness of a policy change (Lin, 2006).

4.2.4 Variance Decomposition Test

Variance Decomposition analysis is used to identify the contribution of each shock in explaining variations of the other variables in the Structural Vector Auto-Regression models. Variance decomposition analysis provides a somewhat different means for explaining the dynamics of a SVAR model. This test exhibits the proportion of movements in the dependent variables that are due to their ‗own‘ shocks, versus shocks to the other variables. A shock to the i th variable will directly explain the effect of variable that would be transmitted to all of the other explanatory variables in the system through the dynamic structure of the VAR.

The variance decomposition analysis provides information on how much of the h-step-ahead forecast error variance for each given variable is explained by the innovations to each explanatory variable for h = 1, 2 ... In practical, most of the time it is customary to observe that own series shocks explain most of the forecast error variance of the series in a SVAR. To a certain extent, variance decompositions and impulse response functions provide similar information but they do so in slightly different ways (Mitze, 2011).

The variance decomposition test presents a table format that displays separate variance decomposition for each explanatory variable. The 1st column, labelled ―period‖ refers to the h-step-ahead forecast error variance of the variable i-th (in this case, we reported i until the 20^th). The second column, labelled ―S.E.‖, provides information on the forecast error of the variable at a given h-step-ahead forecast horizon. The forecast error is the variation in the current and future values of the shocks to the explanatory variable in the system (SVAR). The remaining columns show the percentage of the forecast variance due to each innovation, with each row adding up to 100 (QMS, 2004).

4.2.5 Merits of the Adaptation of the Current Method

Over the last three decades, Structural Vector Autoregressive (SVAR) models have become an important research tool that is widely used in the applied macroeconomic analysis as well as monetary union analysis. SVARs provide fruitful insights on the interrelations between macroeconomic variables. The main importance of SVAR as opposed to the traditional VAR is that in structural vector auto regressions (SVARs),

‗theoretical‘ restrictions are imposed to identify the underlying shocks. As discussed in earlier sections, the OCA theory has pointed out the importance of similarity in demand and supply shocks for members of a monetary union. Structural Vector Auto regression model is used to extract the underlying demand and supply shocks among East African economies. In this respect, SVAR would give a clear understanding on whether or not future members of a currency union are able to form a monetary union.

There are several key methodologies for testing the feasibility of monetary union in a region, and among the popular methods are the following: (i) Analysis of macroeconomic economic shocks effecting a region using SVAR (Structural Vector Autoregression), (ii) Analysis of synchronization of business cycle, (iii) G-PPP (Generalized Purchasing Power Parity) Analysis, (iv) Trade Effects (Gravity Model), and (v) DSGE (Dynamic stochastic general equilibrium modelling) etc. Some of the above mentioned techniques for analyzing a monetary union have drawbacks and do not provide a clear conclusion of whether a successful monetary union is feasible. For example, one critique of the Generalized-PPP model is that movements in the macroeconomic variables do not distinguish disturbances from responses (S. K. Buigut

& Valev, 2005b). As for the Gravity model, the critique is that the theoretical justifications of the model are subject to some dispute (Adams, 2005).

Drawing from the OCA theory and the experience of the European Monetary Union,

―symmetry of shocks – SVAR‖ and ―synchronization of business cycle‖ are among the popular methods to analyse the suitability of a monetary union in a region. Over the past decade, there has been significant progress in the specification and estimation of the contemporary macroeconomic analysis. The progress in econometrics, statistics and computer technology spurred the introduction of dynamic stochastic general equilibrium modelling (DSGE) which seems to be a relatively attractive methodology and has been used in different fields (Tovar, C. E. 2009). However, DSGE analysis is a highly complicated process, since it is reliant on detailed economic data which makes it currently unsuitable to be applied in Africa where such data is scarce (K.A. Sheikh et al., 2011). Thus, the research on DSGE models can be addressed in future studies.

The Structural Vector Auto regression model (SVAR) is a method that is widely used to determine whether future members of a monetary union can form an Optimum Currency Area. This method assesses the similarities of a broad range of OCA properties⁴ available in a geographical domain; it finds out subsets of groups that have similar characteristics which might make it more appropriate for them to have a common currency (Alturki, 2007). This method can assess the degree of symmetry of shocks and the speed at which the economies adjust to the shocks.

4.2.6 Constraints of Adopting the Current Method

Despite the importance and dominance of structural vector autoregressive (SVAR) models in the research arena, they are still subject to some constraints and shortcomings. The following are major limitations of the SVAR that are available in the literature: