5.7.1.3 Co-integration Long Run Estimates
The Co-integration equation is estimated in the following, representing the long run (level) parameters; The Univariate Co-integration test suggests that even though the variables are significantly affecting the exchange rate, still there is no evidence for the presence of co-integration even at 10% level hence there is no long run equilibrium relationship between these variables. The problem of non existing equilibrium and Bond Rate of Pakistan having wrong expected signs may due to of two reasons, one is the presence of boundary line I variable that could be considered I and another case might be the issue of endogeniety as in long run all variables may affect with each other.
As this linear combination of the variables (i.e. residuals), are found to be non-stationary hence an Error Correction Model cannot be constructed to see the short run deviations around this long run path The gap between the Actual and the Estimated Exchange Rate that this Long Run Estimate Equation predicts move together seen in figure 10, accept for the year 2001 and 2002 where the model is suggesting the Actual Exchange Rate to be Overvalued, but this results are expected to be misleading and spurious because of the lack of converging ability of this linear combination.
5.8 Multivariate Analysis
For the multivariate analysis following vector is used x = [S, P, P*, i, i*]
In this vector form the long run equilibrium can be written at minimum of k number of ways, and all the valid equilibriums will be statistically different from each other that cannot be transformed into one form or the other. So out of five possible equilibriums, rank method will be applied to find the number of significant equilibriums. The rank test checked using several lag structures, the hypothesis revealed that there in one linear combination among all these variables this will show properties of convergence and hence called as long run equilibrium path. Now a Vector Error Correction Model will be estimated below with given specification of lags that washed away the autocorrelation among residuals and the rank (Long Run Equation) suggested by the Trace test.
Figure 9. Actual vs ECM estimated exchange rate
Table 10. Long run estimate equation
Engle-Granger 1^{st}-step regression | |||||
Dependent variable | Intercept | Parameters | |||
Pt-1 | ^ * Pt-1 | it-1 | *it-1 | ||
St | 3.11 | 1.03 (0.09) | -0.73 (0.27) | -0.10 (0.103) | –.13 (0.051) |
Standard Errors in Parenthesis. All parameters significant at 1.4% | |||||
Engle-Granger test regression | |||||
Dependent Variable | Parameter | Test statistic | Critical Values | ||
Residual _{t-1} | Z(t) | 1% | 5% | 10% | |
A Residuals | -0.04 (0.02) | -2.25 | -4.73 | -4.15 | -3.85 |
5.7.1.3 Co-integration Long Run Estimates The Co-integration equation is estimated in the following, representing the long run (level) parameters; The Univariate Co-integration test suggests that even though the variables are significantly affecting the exchange rate, still there is no evidence for the presence of co-integration even at 10% level hence there is no long run equilibrium relationship between these variables. The problem of non existing equilibrium and Bond Rate of Pakistan having wrong expected signs may due to of two reasons, one is the presence of boundary line I variable that could be considered I and another case might be the issue of endogeniety as in long run all variables may affect with each other. As this linear combination of the