英语论文网

elationship between economic variables (Thomas, 1993). Johansen test is used to identify co –integrating identifies co-integrating relationship among the variables. Some authors (Cheung and Lai, 1993) point out that trace test gives better results and is more robust than maximum eigenvalue test for co-integration.

Co-integration of two or more time series suggests that there is long term, or equilibrium relationship between them and to avoid the risk of spurious regression. It can be assessed via unit root test on the residuals of the regression. Co-integration analysis is important because if two non-stationary variables are co-integrated, a VAR model in the first difference is misspecified due to the effect of a common tend. If co-integration relationship is identified, the model should include residuals from the vectors (lagged one period) in the dynamic Vector Error Correcting Mechanism (VECM) system.

4.7.1 Johansen co-Integration Tests

The Johansen trace tries to determine the number of co-integrating vectors among variables. Under the trace test, the null hypothesis that there are at most r co-integrating vectors(r=0) is tested against the alternative that (r≤ 0) where r equals the number of co-integrating vectors. For existence of co-integration there should beat least one co-integrating vector.

This method provides the maximum likelihood estimates of the long run co-integration relationships between variables. “The possibility to have multiple long run relationship is first investigated by Johansen and Juselius in 1990” (Kulendran and Witt, 2000).

With the help of E-View 6 software, the log –likelihood ratio statistic for statistics for determining the number (r) of long run relationship between variables can be determined. If the calculated value of the statistics is greater than the 95% critical value, the null of r =0, which indicates no relationship, is rejected against the alternative hypothesis. Rejection of null hypothesis shows that there is long-run relationship between variables.

In this stage, Johansen co-integration test is used to spot co-integrating relationship among the variables. The Johansen multivariate co-integrating structure, the following system is estimated:

Δzt = Π1 Δzt-1 + …+ Πk- 1 Δzt-k-1 + Пzt-1 + μ + ET: t =1, T (2)

Where Δ denote the first difference operator, z denotes vector of variables, εt —— niid (0, Σ), μ is a drift parameter, and Π is a (p x p) matrix of the form Π = αβ’, where α and β are both (p x r) matrices of full rank, with β containing the r co-integrating relationships and α carrying the equivalent adjustment coefficients in each of the r vectors. Johansen (1995) proposes two tests statistics to decide the co-integration rank.

4.8 Error Correction Model (ECM)

“Error Correction Model (ECM) is developed by Engle and Granger (1980), which means the reconciliation of the short run behavior of an economic variable with its long run behaviour” (Guajarati, p.730). Actually, it means the correction of error disturbances between disturbances between long –run and short run demand dynamics.

ECM can be estimated when YT and Xt are nonstationary, but co-integrating. One way to estimate the error correction model is to use least squares to estimate the co-integrating relationship y=β + β2 xt , and to then use the lagged residuals e t-1 =