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

1、20modelling bahrains economy a vector autoregression (var) approachrizwan tahirahmed abdul ghaniabstract: 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 pop

2、ularized 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 i

3、ndicated 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.

4、 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 o

5、f 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

6、the long-run. this result supports the view of monetarists.keywords: var modelling, macroeconomic policies, oil exports, bahrain1.introductionbeing pioneer of oil producer in the arabian gulf region, bahrain witnessed the prospects of potential economic prosperity in 1932 with the discovery of oil.

7、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 prod

8、ucts 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 sou

9、rces 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 functio

10、nal 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 popularize

11、d 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

12、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 straightforward way of pre

13、dicting 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 va

14、r 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 bahrains macroeconomy.the

15、 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.2.the var methodology follows standard text book description of var methodolog

16、ythe methodology of the var is briefly described here. a k-equation var can be represented in a matrix form as follows:a(l)yt = a + ut (1)and a(l) = i h1l1 h2l2 - .hkln (2)yt is an kx1 vector of variables, a is an kx1 vector of constants, and ut is an kx1 vector of random variables. equation (2) is

17、an kxk matrix of normalized polynomial in lag operator l (lm yt=yt-1) with the first entry of each polynomial on as being unity.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 va

18、riance 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 pr

19、ocedure 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 t

20、he current innovations (ut) 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

21、 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 a

22、nalyzed by employing the “impulse response functions” (irfs) and “variance decompositions” (vdcs) that are obtained from a moving average representation of the var model given belowequations (3) & (4):yt = constant + h(l)u (3)andh(l) = i + h1l + h2l + . (4)where h is the coefficient matrix of th

23、e 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 beha

24、vior of the target variables due to unanticipated shocks in the policy variables. variance 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

25、 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

26、 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

27、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

28、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 in

29、crease to 15.unit root and cointegration testsas 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)

30、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 indic

31、ate that they are non-stationary. when first differenced in log, 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

32、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 itests for unit rootsvariablesadfppno constant & no trend constantconstant & trendno constant & no trendconstantconstant & tren

33、dlog levelsgdp1.397471-5.0341801-2.1045101.772711-4.1690351-2.870965cpi0.250873-8.1962641-7.68265511.594314-5.4168561-2.304288gexp1.3810061.070895-1.1854811.611615-5.0597011-3.363113xoil0.673281-3.085783-2.6745490.692473-3.183007-2.727758m11.684001-1.543266-2.4913042.624443-1.835356-2.068293log firs

34、t differencesgdp-2.867525*-3.539993*-4.451694*-2.771254*-3.660785*-4.603926*cpi-6.051877*-5.121595*-2.7078432-1.697754*-2.1844072-4.048458*gexp-2.784017*-2.608528*-1.4313552-2.072438*-2.6085282-3.297932*xoil-5.472073*-5.537618*-5.854153*-5.472099*-5.537852*-5.905655*m1-2.518638*-3.252550*-3.233277*-

35、2.460782*-3.255888*-3.182406*8notes:1reject null hypothesis (series has no unit root)2cannot 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

36、level;table iimackinnon(1996) critical values for adf & pp unit root testslevel of significanceadfppno constant & no trend constantconstant & trendno constant & no trendconstantconstant & trendlog levels1 percent-2.644302-3.670170-4.356068-2.641672-3.661661-4.2845805 percent-1.95

37、2473-2.963972-3.595026-1.952066-2.960411-3.56288210 percent-1.610211-2.621007-3.233456-1.610400-2.619160-3.215267log first differences1 percent-2.644302-3.670170-4.296729-2.644302-3.670170-4.2967295 percent-1.952473-2.963972-3.56879-1.952473-2.963972-3.56837910 percent-1.610211-2.621007-3.218382-1.6

38、10211-2.621007-3.218382since 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 test this, we used eviews econometric software eviews (version 5) is used for all tests and estim

39、ation in this paper. 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

40、 used all five deterministic trend models 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 alter

41、native (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 firs

42、t time the null hypothesis is not rejected.referencescooly, t.f. and leroy, s.f. (1985), “atheoretical macroeconomics: a critique”, journal of monetary economics, pp. 221-54dickey, d.a. and fuller, w.a. (1979), “distribution of the estimators for autoregressive time series with unit root”, journal o

43、f the american statistical association, june, pp. 427-31doan t.,r. litterman and c. sims (1984), “forecasting and conditional projection using realistic prior distribution”, economic review, 3, 1-100doan, t. (1989), “rats users manual”, version 4engle, r.e. and granger, c.w.j. (1987), “cointegration

44、 and error-correction: representation, estimation, and testing”, econometrica, v ol. 55, pp. 251-76engle, r.f. and yoo, b.s. (1987), “forecasting and testing in co-integrated systems”, journal of econometrics, vol. 35 no. 1, pp. 143-59eviews, (2004), “users guide” version 5, qmsfaust, j. and leeper,

45、 e. (1997), “when do long-run identifying restrictions give reliable results”, journal of business and economic statistics, vol. 15 no. 3, pp. 345-53haris, r. (1995), “cointegration analysis in econometric modeling”, prentice hallhoffman, d.l.and rasche, r.h. (1996), “assessing forecast performance

46、in a cointegrated system”, journal of applied econometrics, vol. 11 no. 5, pp. 495-517johansen, s. (1991), “estimation and hypothesis testing of cointegration vectors in gaussian vector autoregression models”, econometrica, 59, pp. 1551-1580johansen, s. (1995), “liklihood-based inference in cointegr

47、ated vector autoregressive models”, oxford university presslitterman, r. (1984), “forecasting and policy analysis with baysian vector autoregression models”, federal reserve bank of minneapolis quarterly review, fall, 30-41lukepohl, helmut (1991), “introduction to multiple time series analysis”, new

48、 york: springer-verlagnaka, a. and tufte, d. (1997), “examining impulse response functions in cointegrated systems”, applied economics, vol. 29 no. 12, pp. 1593-603osterwald-lenum, m. (1992), “a note with quantiles of the asymptotic distribution of the maximum likelihood cointegration rank test stat

49、istics”, oxford bulletin of economics and statistics, vol. 54, pp. 461-72phillips, p. and perron, p. (1988), “testing for a unit root in time series regression”, biometrica, vol. 75, pp. 335-46runkle, d.e. (1987), “vector autoregression and reality”, journal of business and economic statistics, vol.

50、 5, pp. 437-42sims, c.a. (1980), “macroeconomics and reality”, econometrica, vol. 48, pp. 1-48sims, c.a. (1982), “policy analysis with econometric models”, brookings papers on economic activity, vol. 1, pp.107-52sims, c.a. (1986), “are forecasting models usable for policy analysis?”, federal reserve

51、 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 con

52、sidered 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. table iiiselected number of coi

53、ntegrating relations by modeltest typemodel 1model 2model 3model 4model 5trace44233maximum eigenvalue22233notes: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. gen

54、erally, 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

55、-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 outperfo

56、rms 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). a