Modelling Bahrain´s Economy A Vector Autoregression (VAR) Approach

Modelling Bahrain´s Economy A Vector Autoregression (VAR) Approach 1 MODELLING BAHRAIN’S ECONOMY A VECTOR AUTOREGRESSION (VAR) APPROACH RIZWAN TAHIR AHMED ABDUL GHANI ABSTRACT: The last decade or so has witnessed a significant growth in research studies applying Vector Autoregression (VAR) technique for macroeconomic modelling. A VAR technique pioneered by Sims and popularized by researchers such as Litterman and Doan is useful particularly when knowledge about “true” structural relations is absent. This study represents the first attempt to apply such a technique to Bahraini yearly data (1971 – 2002) for five key macroeconomic variables. The results of the study indicated that all key macroeconomic variables are interlinked and influence each other. Oil exports is pure exogenous and is unaffected by any other macroeconomic variable. There is an evidence of bi-directional money-income causality and uni-directional causality from Government expenditure to CPI.. Impulse response and variance decomposition analysis suggest that fiscal policy is relatively more effective in short-run and monetary policy is more effective in the long run. Both oil exports and money are the sources of variation in GDP in the long-run and Government expenditures is the source of variation in the short-run. The result also suggests that money and oil exports are the important sources of variations in CPI in the long-run and Government expenditures is important source in the short-run. Inflation is found to be a fiscal phenomenon in the short-run but monetary phenomenon in the long-run. This result supports the view of monetarists. KEYWORDS: VAR MODELLING, MACROECONOMIC POLICIES, OIL EXPORTS, BAHRAIN 1 2 1. INTRODUCTION Being pioneer of oil producer in the Arabian Gulf region, Bahrain witnessed the prospects of potential economic prosperity in 1932 with the discovery of oil. Although oil exports contributed significantly in achieving higher levels of GDP over past few decades, its volatile nature (because of oil prices) and gradually decreasing share in GDP provided a challenge of maintaining higher levels of GDP. As a result, export base was diversified to non-oil products like Petrochemicals and Aluminium whose share in GDP has gradually increased. Inspite of diversifying sources of GDP, the rates of real GDP growth have showed wide fluctuations of more than 8 percent to negative 2 percent, over the period of last ten to fifteen years. In order to analyze the sources of fluctuations in GDP growth, a standard complete structural macro model is probably desirable. However, such a model is derived on the basis of economic theory. Thereby two major problems arise: the theory must be exact enough to identify the endogenous and exogenous variables and the functional form connecting them. The second problem concerns the identification problem of recovering structural parameters from estimated reduced form. Out of these problems another class of nonstructural models: Vector autoregressive (VAR models) have been evolved, pioneered by Sims (1980) and popularized by researchers such as Litterman (1984) and Doan(1984). VAR model does not require any explicit economic theory to estimate a model. It uses only the observed time series properties of the data to forecast economic variables. The VAR models have many applications (see Cooley and Leory, 1985). They are used to determine how each endogenous variable responds over time to a shock in that variable and in every other endogenous variable. VAR models are useful for analysis of the effect of alternative monetary or fiscal policies (Sims, 1982). The VAR models also provide a 2 3 straightforward way of predicting the values of set of economic variables at any given point in time. Our study represents the first attempt to apply such an approach in the case of Bahrain. In this paper, we develop and estimate an annual macroeconometric model for the economy of Bahrain over the period 1971 to 2002 using VAR technique proposed by Litterman (1984) and Sims (1980, 1982 & 1986). The main focus of this study is to analyze empirically the strength of short-run and long-run impacts of anticipated and unanticipated macroeconomic policies and oil exports shock (or innovations) on Bahrain’s macroeconomy. The paper is divided into five parts. VAR approach is outlined next, followed by a discussion on the data used to estimate the model. The next part discusses the empirical results, concluding with the summary and conclusions. i2. THE VAR METHODOLOGY The methodology of the VAR is briefly described here. A k-equation VAR can be represented in a matrix form as follows: A(L)Y= A + U (1) t t and 2nA(L) = I – HL – HL - …..HL (2) 112k Y is an kx1 vector of variables, A is an kx1 vector of constants, and U is an kx1 vector tt of random variables. Equation (2) is an kxk matrix of normalized polynomial in lag moperator L (L Y=Y) with the first entry of each polynomial on A’s being unity. tt-1 3 4 Since the right-hand side of the equations in the system contains only the predetermined variables, the error terms are assumed to be serially uncorrelated with constant variance and zero mean. Hence, each equation in the system can be estimated using OLS. Moreover, OLS estimates are consistent and asymptotically efficient. Even though the error terms are correlated across equations, Seemingly Unrelated Regression (SUR) do not add to the efficiency of the estimation procedure since all regressions have identical right-hand-side variables. However, before estimating the model, the lag length must be chosen. If L is the lag length, number of coefficients to be estimated is k(kL + c), where c is the number of constants. The VAR model presented above indicates that the current innovations (U) t are unanticipated but becomes part of the information set in the next period. The implication is that the anticipated impact of a variable is captured in the coefficients of lagged polynomials while the residuals capture unforeseen contemporaneously events. A joint F-test on the lagged polynomials provides information regarding the impact of the anticipated portion of the right-hand side variables. The impact of the unanticipated policy shocks (i.e. the policy variables such as changes in money supply and government expenditures) on other economic variables can be analyzed by employing the “impulse response functions” (IRFs) and “variance decompositions” (VDCs) that are obtained from a moving average representation of the VAR model given below[equations (3) & (4)]: Y = Constant + H(L)U (3) t and H(L) = I + HL + HL + ….. (4) 12 where H is the coefficient matrix of the moving average representation, which can be obtained by successive substitution in equations (1) and (2). The elements of the H matrix trace the response over time of a variable i due to a unit shock given to a variable j. The impulse response functions make it possible to analyze the dynamic behavior of the target variables due to unanticipated shocks in the policy variables. Variance 4 5 decompositions show the portion of variance in the prediction for each variable in the system that is attributable to its own innovations and to shocks to other variables in the system. 3. DATA ANALYSIS The data for the study is obtained from various publications of Government of Bahrain. Because of the unavailability of quarterly data, the model is estimated using yearly data from 1971 to 2002. The variables included in the VAR model are gross domestic product (GDP), consumer price index (CPI), government expenditures (GEXP), value of oil exports (XOIL) and money supply (M1). The objective here is to study the dynamics of the variables or the inter-relationship between these key macroeconomic variables, in particular, the influence of policy variables, such as Government expenditures or money stock and oil exports on economic activities. All the variables are in logarithms. It is important to note that in order to capture the finer details of the economy, a larger model with more variables would be desirable. However, with VAR models, one runs into serious degrees of freedom problems when the variables are many, especially with yearly data. For example, with 5 variables (k = 5) and 2 lags (L = 2), one would need to estimate 10 (kL) parameters (excluding the intercept) for each equation. Also, if the number of lags is increased by one, then with the same model, the estimated parameters increase to 15. Unit root and cointegration tests As a pre-requisite certain properties of the variables in the model must be checked in order to determine the appropriate specification for VAR estimation. The order of integration for each variable is determined using Augmented Dickey and Fuller (1979) and Phillips and Perron (1988) tests. The results of these tests are reported in table I. With the exception of ADF test with constant for GDP & CPI and with constant ant trend for CPI and PP test with constant for GDP, CPI & GEXP, all other ADP and PP tests for variables in log levels indicate that they are non-stationary. When first differenced in log, 5 6 we find the evidence that the variables are stationary. ADF test with constant & trend and PP test with constant indicate the presence of two unit roots in CPI and GEXP. Since the results, overall, tend to suggest non-stationarity in log levels of the variables but stationarity in their log first differences, we proceed by contending that the variables belong to the I(1) process. TABLE I TESTS FOR UNIT ROOTS ADF PP No Constant Constant No Constant Constant & constant & trend constant trend Variables & no trend & no trend Log Levels 111.397471 -5.034180 -2.104510 1.772711 -4.169035 -2.870965 GDP 1110.250873 -8.196264 -7.682655 1.594314 -5.416856 -2.304288 CPI 11.381006 1.070895 -1.185481 1.611615 -5.059701 -3.363113 GEXP 0.673281 -3.085783 -2.674549 0.692473 -3.183007 -2.727758 XOIL 1.684001 -1.543266 -2.491304 2.624443 -1.835356 -2.068293 M1 Log first differences ********-2.867525 -3.539993 -4.451694 -2.771254 -3.660785 -4.603926 GDP **2***2**-6.051877 -5.121595 -2.707843 -1.697754 -2.184407 -4.048458 CPI ****2 **2***-2.784017 -2.608528 -1.431355-2.072438 -2.608528 -3.297932 GEXP ******-5.472073 -5.537618 -5.854153 -5.472099 -5.537852 -5.905655 XOIL *********** **8-2.518638 -3.252550 -3.233277 -2.460782 -3.255888-3.182406 M1 Notes: 1 reject null hypothesis (series has no unit root) 2 cannot reject null hypothesis (series has a unit root) * reject null hypothesis (unit root) at 1 percent level; ** reject null hypothesis (unit root) at 5 percent level; *** reject null hypothesis (unit root) at 10 percent level; 6 7 TABLE II MacKinnon(1996) CRITICAL VALUES FOR ADF & PP UNIT ROOT TESTS ADF PP No Constant Constant No Constant Constant & constant & trend constant trend Level of & no trend & no trend significance Log Levels -2.644302 -3.670170 -4.356068 -2.641672 -3.661661 -4.284580 1 percent -1.952473 -2.963972 -3.595026 -1.952066 -2.960411 -3.562882 5 percent -1.610211 -2.621007 -3.233456 -1.610400 -2.619160 -3.215267 10 percent Log first differences -2.644302 -3.670170 -4.296729 -2.644302 -3.670170 -4.296729 1 percent -1.952473 -2.963972 -3.56879 -1.952473 -2.963972 -3.568379 5 percent -1.610211 -2.621007 -3.218382 -1.610211 -2.621007 -3.218382 10 percent Since the five variables are noted to be I(1), there exists the possibility that they share a long-run equilibrium relationship, as was pointed out by Engle and Granger (1987). To iitest this, we used Eviews which implements VAR-based cointegration tests using the methodology developed in Johansen (1991, 1995). In formulating the dynamic model for the test, the question of whether an intercept and trend should enter the short- and/or long-run model is raised (Harris, 1995, p.95). We used all five deterministic trend iiimodels considered by Johansen (1995, pp. 80,84). The number of cointegrating relations from all five models, on the basis of trace statistics and the maximal eigenvalue statistics using critical values from Osterwald-Lenum (1992) at 5 percent level, are summarized in table III. 7 8 TABLE III SELECTED NUMBER OF COINTEGRATING RELATIONS BY MODEL TEST TYPE MODEL 1 MODEL 2 MODEL 3 MODEL 4 MODEL 5 TRACE 4 4 2 3 3 MAXIMUM EIGENVALUE 2 2 2 3 3 Notes: the selection of cointegrating relations is based on .05 level critical values from Osterwald-Lenum (1992) There is an evidence of minimum two and maximum four cointegrating relations. Generally, there are two different ways of specifying a VAR when the time series under study are cointegrated - an unrestricted VAR in levels or a VECM. Which specification is more appropriate remains debatable. While the VECM conveniently combines the long-run behavior of the variables and their short-run relations and thus can better reflect the relationship among the variables, there is no guarantee that imposing restriction of cointegration can be a reliable basis for making structural inferences (Faust and Leeper, 1997). Moreover, current finding is still unclear on whether the VECM outperforms the unrestricted VAR at all forecasting horizons. Naka and Tufte (1997) found that the two methods have comparable performance at short horizons. The support for the use of the unrestricted VAR can also be found in Clements and Hendry (1995), Engle and Yoo (1987) and Hoffman and Rasche (1996). Accordingly, with low computational burden required by the VAR in levels, we implement the VAR using the variables in levels. 4. VAR MODEL ESTIMATION AND EMPIRICAL RESULTS In specifying a VAR model, number of lags to be included can not be determined arbitrarily. Various criteria are available to choose proper lag length for the VAR model. 8 9 We used five criteria, as discussed in Lutkepohl (1991, section 4.3) in deciding the lag length for our model. The results from all criteria are summarized in table IV. All the criteria indicated a maximum lag length equal to four. We estimated our five variable VAR with a lag length of four. But one of the diagnostic views, inverse roots of the characteristic AR polynomials, indicated our estimated model to be unstable because one of the roots turned out to be greater than one. In order for VAR model to be stable (stationary), all the roots should have a modulus less than one and lie inside the unit circle. If the VAR is not stable, certain results (such as impulse response standard errors) are not valid (Lutkepohl, 1991). The model became stable by reducing the lag length to three. Although, all criteria to choose lag length suggested optimal lag length to be four, we proceeded with a lag length of three to keep our estimated model stable. TABLE NO IV TESTS FOR MODEL LAG LENGTH Lag LogL LR FPE AIC SC HQ 0 50.98231 NA 2.58e-08 -3.284451 -3.046557 -3.211724 1 168.0080 183.8975 3.73e-11 -9.857715 -8.430353 -9.421356 2 195.9217 33.89520 3.66e-11 -10.06584 -7.449006 -9.265845 3 226.3454 26.07748 4.34e-11 -10.45324 -6.646946 -9.289622 4 309.4555 41.55502* 2.91e-12* -14.60396* -9.608196* -13.07671* Notes: * indicates lag order selected by the criterion LR: sequential modified LR test statistic (each test at 5% level) FPE: Final prediction error AIC: Akaike information criterion SC: Schwarz information criterion HQ: Hannan-Quinn information criterion 9 10 VAR Granger causality and block exogeneity VAR model can be used to test Granger causality among the variables of the model and also that an endogenous variable can be treated as exogenous. We used chi-square (Wald) statistics for the joint significance of each of the other lagged endogenous variables in each equation of the model & also for joint significance of ALL other lagged endogenous variables in each equation of the model. The results are reported in table V. TABLE V VAR GRANGER CAUSALITY/BLOCK EXOGENEITY (CHI-SQUARE-WALD TESTS) EXCLUDED VARIABLES BLOCK EXOGENEITY ALL VARIABLES DEP. GEXP M1 XOIL CPI GDP TOGETHER VARIABLE 1 2 3 4 5 6 *** * GEXP 7.70560.6060 5.8791 2.0464 56.40362 (O.0525) (0.8951) (0.1176) (0.5628) (0.0000) (ROW 1) **M1 3.5252 0.64638 5.0903 13.645 33.26219 (0.3175) (0.8857) (0.1653) (0.0034) (0.0009) (ROW 2) XOIL 0.6156 1.3927 1.7682 0.7554 9.745599 (0.8928) (0.7072) (0.6219) (0.8601) (0.6383) (ROW 3) ***CPI 8.3360 2.0178 2.8448 5.3024 15.52247 (0.0396) (0.5687) (0.4162) (0.1509) (0.2141) (ROW 4) ****GDP 1.3912 6.5353 3.1127 1.9827 38.56084 (0.7076) (0.0883) (0.3746) (0.5760) (0.0001) (ROW 5) NOTES: The values in each box represents chi-square (wald) statistics for the joint significance of each other lagged endogenous variables in that equation. The statistics in the last column is the chi-square statistics for joint significance of all other lagged endogenous variables in the equation. The critical values (for individual excluded variables) with 3 df at 1,5& 10 percent are 11.3449, 7.81473, & 6.25139 respectively. The critical values (for all excluded variables) with 12 df at 1,5& 10 percent are 26.2170, 21.0261, & 18.5494 respectively. * , significant at 1 percent, **, significant at 5 percent & ***, significant at 10 percent 10 11 A chi-square test statistics of 13.645, in row 1 and column 5 represents the hypothesis that lagged coefficients of GDP in the regression equation of M1 being equal to zero. The test results for XOIL equation indicates that null hypothesis can not be rejected for individual lagged coefficient as well as block of all coefficients. This suggests that XOIL is not influenced by any of the variables in the model and that it can be treated as pure exogenous. XOIL equation is the only exception as far as the block exogeneity is concerned. The null hypothesis of block exogeneity is rejected for all other equations indicates that all variables (with the exception of XOIL) are jointly influenced by the each other and can not be treated as pure exogenous. There is also an evidence of bi-directional causality between GDP and M1. Both money and income are influenced by each other. The results further suggest uni-directional causality from monetary policy variable (M1) to fiscal policy variable (GEXP) and uni-directional causality from fiscal policy variable (GEXP) to inflation variable (CPI). The dynamic responses The results of table V, enabled us to analyze the impact of anticipated policies. They do not give us clear understanding of the dynamic behavior of the model. The impulse response functions provide information to analyze the dynamic behavior of a variable due to a random shock or innovation in other variables. The impulse response traces the effect on current and future values of the endogenous variables of one standard deviation shock to the variables. To identify orthogonalized innovations in each of the variables and the dynamic responses to such innovations, variance-covariance matrix of the VAR was factorized using Choleski decomposition method suggested by Doan (1989). This method imposes an ordering of the variables in the VAR and attributes all of the effect of any common component to the variable that comes first in the VAR system. The responses can change dramatically if ordering of the variables in the VAR system is changed. We tried several orderings keeping most endogenous variable last and most exogenous first. Although, the results were marginally sensitive to the ordering but general findings were similar in each case. The results reported here are based on ordering of the variables as: 11 12 XOIL,GEXP,M1,CPI & GDP. As Runkle (1987) pointed out that impulse response functions or variance decompositions without confidence intervals (standard error bands) is akin to reporting regression coefficients without t-statistics. Therefore, we obtained the error bands for impulse responses by using a Monte Carlo simulation procedure with 1,000 replications. Figure 1 illustrates the dynamic response of the target variables (GDP & CPI) to a one standard deviation shock in the oil exports (XOIL). Figure 2 illustrates the dynamic response of the target variables (GDP & CPI) to a one standard deviation shock in fiscal policy variable (GEXP) and figure 3 illustrates the dynamic response of the target variables (GDP & CPI) to a one standard deviation shock in monetary policy variable (M1). A shock to oil exports has a consistently negative effect on country’s gross domestic product which is small in short-run but becomes relatively larger in long-run. A shock to fiscal policy variable (GEXP) and monetary policy variable (M1), on the other hand, have a consistently positive but moderate effect on gross domestic product. It is noticeable that fiscal policy seems to be relatively more effective in short-run and monetary policy seems to relatively more effective in long-run. The response of CPI to a shock in two policy variables and oil exports is different than GDP. The effect of policy variables on CPI is initially negative but becomes positive in long-run. GEXP create negative effect for a longer period than M1. The effect of oil exports has opposite effect on CPI which is positive in short-run but negative in long-run. 12 13 FIGURE 1 IMPULSE RESPONSES OF GDP & CPI TO ONE STANDARD DEVIATION SHOCK OF XOIL Response to Cholesky One S.D. Innovations ? 2 S.E. .1 Response of LOG(GDP) to LOG(XOIL).0 -.1 -.2 -.3 12345678910 .04 Response of LOG(CPI) to LOG(XOIL).02 .00 -.02 -.04 -.06 -.08 12345678910 13 14 FIGURE 2 IMPULSE RESPONSES OF GDP & CPI TO ONE STANDARD DEVIATION SHOCK OF GEXP Response to Cholesky One S.D. Innovations ? 2 S.E. .20 Response of LOG(GDP) to LOG(GEXP) .15 .10 .05 .00 -.05 -.10 -.15 12345678910.05 Response of LOG(CPI) to LOG(GEXP).04 .03 .02 .01 .00 -.01 -.02 -.03 -.04 12345678910 14 15 FIGURE 3 IMPULSE RESPONSES OF GDP & CPI TO ONE STANDARD DEVIATION SHOCK OF M1 Response to Cholesky One S.D. Innovations ? 2 S.E. .4 Response of LOG(GDP) to LOG(M1).3 .2 .1 .0 -.1 -.2 12345678910 .08 Response of LOG(CPI) to LOG(M1).06 .04 .02 .00 -.02 -.04 12345678910 15 16 Variance decompositions The impulse response functions illustrate the qualitative response of the variables (GDP & CPI) in the system to shocks to XOIL, GEXP & M1. To indicate the relative importance of these shocks require a variance decomposition. In order to achieve this, consider the n-step ahead forecast of a variable based on information at time t. The variance of the error associated with such a forecast can be attributed to unforecastable shocks (or innovations) to each of the variables comprising the system that occur between t +1 to t + n. Table VI reports the variance decompositions of the forecast errors for each variable in the model at horizons up to nine years. The results of the variance decompositions seem to be consistent with impulse responses. Variance decomposition for GDP: A shock to XOIL accounts for only 3 percent variation in the first year which gradually increases to 33 percent in the ninth year. A shock to GEXP accounts for 22 percent variation in first year and decreases to 12.5 percent in the ninth year. A shock to M1 accounts for 12 percent variation in first year and increases to thth40 percent in the 7 year before declining to 37 percent in the 9 year. The indication of these results is that fiscal policy is relatively more effective in short-run and monetary policy is more effective in the long run. Both oil exports and money are the sources of variation in GDP in the long-run and Government expenditures is the source of variation in the short-run. Variance decomposition for CPI: A shock to XOIL is insignificant in the first year but contributes moderately in the variation of CPI in later years. A shock to GEXP accounts for almost 41 percent variation in the first year and gradually decreases to 20 percent in ththe 9 year. A shock to M1 accounts for larger variations in the long run, 37 percent in ththe 9 year. The results indicate that money and oil exports are the important sources of variations in CPI in the long-run and Government expenditures is important source in the short-run. The results also indicate that inflation is a monetary phenomenon in the long-run. 16 17 TABLE VI VARIANCE DECOMPOSITIONS PROPORTION OF VARIANCE EXPLAINED BY SHOCKS VARIANCE PERIOD S.E. XOIL GEXP M1 CPI GDP DECOMPOSITION XOIL 1 0.3238 100.00 0.0000 0.0000 0.0000 0.0000 3 0.3966 87.325 7.4898 4.0885 0.6579 0.4385 5 0.4513 81.932 7.8965 5.1266 2.9431 2.1007 7 0.4772 73.615 8.3898 7.4076 3.2830 7.3034 9 0.4955 70.867 8.7462 8.4099 3.0621 8.9144 GEXP 1 0.0726 4.2148 95.785 0.0000 0.0000 0.0000 3 0.1346 6.3985 41.145 28.560 3.1611 11.475 5 0.1762 13.400 24.028 40.735 8.2925 13.543 7 0.2078 14.921 23.972 43.057 6.3058 11.742 9 0.2598 18.118 22.856 41.737 4.3062 12.981 M1 1 0.0767 1.4157 17.556 81.027 0.0000 0.0000 3 0.2025 4.9186 15.609 57.987 0.6918 20.792 5 0.2416 13.142 12.690 53.005 1.0331 20.128 7 0.2924 19.328 14.574 48.468 0.7437 16.885 9 0.3418 26.334 12.987 43.791 0.7004 16.185 CPI 1 0.0321 0.8687 40.819 0.2029 58.109 0.0000 3 0.0479 15.817 21.537 6.5949 45.513 10.536 5 0.0627 18.017 18.311 27.480 26.944 9.2461 7 0.0773 12.401 22.228 34.190 18.478 12.701 9 0.0919 14.331 20.000 36.638 13.115 15.914 GDP 1 0.0880 3.0800 22.239 11.916 19.328 43.436 3 0.1471 12.695 10.777 39.630 11.490 25.405 5 0.2279 19.538 12.440 43.800 5.3068 18.913 7 0.3048 25.864 13.783 40.409 2.9808 16.961 9 0.3605 33.120 12.548 36.958 2.3453 15.027 17 18 5. SUMMARY AND CONCLUSION The last decade or so has witnessed a significant growth in research studies applying Vector Autoregression (VAR) technique for macroeconomic modelling. A VAR technique pioneered by Sims and popularized by researchers such as Litterman and Doan is useful particularly when knowledge about “true” structural relations is absent. This study represents the first attempt to apply such a technique to Bahraini data for five key macroeconomic variables. The results of the study indicated that all key macroeconomic variables are interlinked and influence each other. Oil exports is pure exogenous and is unaffected by any other macroeconomic variable. There is an evidence of bi-directional money-income causality and uni-directional causality from Government expenditure to CPI. Impulse response and variance decomposition analysis suggest that fiscal policy is relatively more effective in short-run and monetary policy is more effective in the long run. Both oil exports and money are the sources of variation in GDP in the long-run and Government expenditures is the source of variation in the short-run. The result also suggests that money and oil exports are the important sources of variations in CPI in the long-run and Government expenditures is important source in the short-run. Inflation is found to be a fiscal phenomenon in the short-run but monetary phenomenon in the long-run. This result support the view of monetarists. 18 19 i Follows standard text book description of VAR methodology ii Econometric software Eviews (version 5) is used for all tests and estimation in this paper. iii Johansen (1992c) suggests the need to test the joint hypothesis of both the rank order and the deterministic components, based on the so-called Pantula principle. That is, all models are estimated and the results are presented from the most restrictive alternative (i.e., r = 0 and model 1) through to the least restrictive alternative (i.e., r = n – 1 and model 4). The test procedure is then to move through from the most restrictive model and at each stage to compare the trace (or max eigenvalue) test statistic to its critical value and only stop the first time the null hypothesis is not rejected. References Cooly, T.F. and Leroy, S.F. (1985), “Atheoretical Macroeconomics: a critique”, Journal of Monetary Economics, pp. 221-54 Dickey, D.A. and Fuller, W.A. (1979), “Distribution of the Estimators for Autoregressive Time Series with Unit Root”, Journal of the American Statistical Association, June, pp. 427-31 Doan T.,R. Litterman and C. Sims (1984), “Forecasting and Conditional Projection using Realistic Prior Distribution”, Economic Review, 3, 1-100 Doan, T. (1989), “Rats user’s manual”, version 4 Engle, R.E. and Granger, C.W.J. (1987), “Cointegration and Error-Correction: Representation, Estimation, and Testing”, Econometrica, V Ol. 55, pp. 251-76 Engle, R.F. and Yoo, B.S. (1987), “Forecasting and Testing in Co-integrated Systems”, Journal of Econometrics, vol. 35 no. 1, pp. 143-59 EViews, (2004), “user’s guide” version 5, QMS Faust, J. and Leeper, E. (1997), “When Do Long-Run Identifying Restrictions give Reliable Results”, Journal of Business and Economic Statistics, vol. 15 no. 3, pp. 345-53 Haris, R. (1995), “Cointegration Analysis in Econometric Modeling”, Prentice Hall Hoffman, D.L.and Rasche, R.H. (1996), “Assessing Forecast Performance in a Cointegrated System”, Journal of Applied Econometrics, vol. 11 no. 5, pp. 495-517 Johansen, S. (1991), “Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregression Models”, Econometrica, 59, pp. 1551-1580 Johansen, S. (1995), “Liklihood-Based Inference in Cointegrated Vector Autoregressive Models”, Oxford University Press 19 20 Litterman, R. (1984), “Forecasting and Policy Analysis with Baysian Vector Autoregression Models”, Federal Reserve Bank of Minneapolis Quarterly review, fall, 30-41 Lukepohl, Helmut (1991), “Introduction to Multiple Time Series Analysis”, New york: Springer-Verlag Naka, A. and Tufte, D. (1997), “Examining Impulse Response Functions in Cointegrated Systems”, Applied Economics, vol. 29 no. 12, pp. 1593-603 Osterwald-Lenum, M. (1992), “A Note with Quantiles of the Asymptotic Distribution of the Maximum Likelihood Cointegration Rank Test Statistics”, Oxford Bulletin of Economics and Statistics, vol. 54, pp. 461-72 Phillips, P. and Perron, P. (1988), “Testing for a Unit Root in Time Series Regression”, Biometrica, Vol. 75, pp. 335-46 Runkle, D.E. (1987), “Vector Autoregression and Reality”, Journal of Business and vol. 5, pp. 437-42 Economic Statistics, Sims, C.A. (1980), “Macroeconomics and Reality”, Econometrica, Vol. 48, pp. 1-48 Sims, C.A. (1982), “Policy Analysis with Econometric Models”, Brookings Papers on Economic Activity, Vol. 1, pp.107-52 Sims, C.A. (1986), “Are Forecasting Models Usable for Policy Analysis?”, Federal Reserve Bank of Minneapolis Quarterly review, winter, 2-16 (1991), “30 years of Economic and Social Development in the State of Bahrain”, Ministry of Finance and National Economy, State of Bahrain (1998), “Human Development Report: State of Bahrain”, Achievements and Challenges of Human Development, UNDP 20