Engle and Granger Two Stage Error Correction Model

The concept of cointegration will be analyzed with an error correction model (ECM). If Yt and Xt are

I(1) process we might estimate an ECM in first differences. The above unit root tests and the cointegration test results also imply that the dynamic modelling of stock prices and macroeconomic variables have a valid error correction representation. It is established that the dynamic structure of the variables can be investigated further by utilizing the error correction model (ECM) suggested by Engle and Granger (1987). Engel and Granger show that cointegration implies the existence of an error correction model of the variables involved. ECM integrates the short and long run information in the modelling process.

The Engle-Granger method has several limitations. First of all, it identifies only a single cointegrating relation, among what might be many such relations. This requires one of the variables, y1t to be identified as first among the variables in yt. This choice, which is usually

arbitrary, affects both test results and model estimation.

Another limitation of the Engle-Granger method is that it is a two-step procedure, with one regression to estimate the residual series, and another regression to test for a unit root. Errors in the first estimation are necessarily carried into the second estimation. The estimated,

rather than observed, residual series requires entirely new tables of critical values for standard unit root tests.

Finally, the Engle-Granger method estimates cointegrating relations independently of the VEC model in which they play a role. As a result, model estimation also becomes a two- step procedure. In particular, deterministic terms in the VEC model must be estimated conditionally, based on a predetermined estimate of the cointegrating vector.

However, the ECM model estimates provide important information about the short run relationship between stock return and macroeconomic variables while a negative and significant error correction term signifies the speed of adjustment to the long run equilibrium level. As an example, ECM model consider the following equation:

) 11 . 5 ( 1 1 1 1 0 t j t t h j j j t k j j t X Y U Y

Here Ytis the dependent variable (represents the log of the ASX200 index), and Xt represents

the independent variables (log of the macroeconomic variables listed in table 5.1). Ut is the

one-period lagged value of the estimated error of the cointegrating regression obtained from OLS estimation; this term is called the error correction term. And є_t is the error term. The principle behind this model is that there often exists a long run equilibrium relationship between economic variables. In the short run, however, there may be disequilibrium. With the error correction mechanism, a proportion of the disequilibrium is corrected in the next period. The error correction process is thus a means to reconcile short-run and long run behaviour. Therefore, in the error correction model, the right hand side contains the short-run dynamic coefficients (i.e., i, i) as well as the long-run coefficient (i.e., ). The absolute value of

Table 5.6. Specific Error Correction Model Estimate

Dependent Variable: Δ LNASX200

Variable Coefficient Std. Error t-Statistic Prob.

C 0.000478 0.007803 0.061297 0.9512 ΔLNRGDP 1.150000 0.564132 2.038529 0.0441 ΔLNLCI -0.792307 0.315500 -2.511274 0.0136 ΔLNNYSE 0.783311 0.074070 10.57529 0.0000 Ut(-1) -0.278955 0.070094 -3.979704 0.0001

R-squared 0.567187 Mean dependent var 0.020770 Adjusted R-squared 0.550378 S.D. dependent var 0.093281 S.E. of regression 0.062548 Akaike info criterion -2.660565 Sum squared resid 0.402966 Schwarz criterion -2.536392 Log likelihood 148.6705 Hannan-Quinn criter. -2.610217 F-statistic 33.74445 Durbin-Watson stat 1.884408 Prob(F-statistic) 0.000000

Note: All variables are in log form, Δ denotes first differences

Applying the above formula to proposed equation Eviews yielded the error correction model results in Table 5.6. Where, Ut is the error correction term which comes from the long run

cointegration equation (i.e. residual).

This specific error correction model is estimated using the following steps: Identified order of integration applying unit root tests12.

Identified the cointegration relationships using the Johanson‟s maximum likelihood technique.

Run a cointegration equation using OLS13.

Tested residual from this equation for unit roots using ADF, PP and the KPSS tests14.

If residual is stationary, stock market index and macroeconomic variables are cointegrated and there is a valid error correction model.

12 _{See Appendices A}

s Bs and Cs 13

Estimated the general error correction model15.

Dropped insignificant variables one by one, applied different combinations of variables and lags, obtained the specific error correction model16 given in table 5.6. These are the most common procedures in the literature. See for example Engle and Granger (1987), Kulendran (1996), Paseran et al (2000) and Kazi (2009).

Real GDP has positive sign as expected because higher GDP means higher demand for all goods and services therefore higher profit for the firms. And coefficient of real GDP is significant at 5 percent significance level. LCI has a negative relationship as expected and it is significant at 5 per cent level. This negative relationship can be attributed to effect of labour cost to firm‟s profitability. When labour cost goes up profit goes down, therefore, share prices go down. NYSE index has positive sign as expected and significant at 5 per cent level. The significance of NYSE implies the effect of overseas economic factors on the Australian stock market. However, this study found that CPI, 10 year bond yield, commodity price index and exchange rate (TWI) were not significant.

The error correction term is highly significant at 1 per cent level of significance and negative indicating the importance of long run relationship between stock market and the macroeconomic variables. It also implies that the system has a tendency to come back to their long run relationship. With the error correction mechanism a proportion of disequilibrium is corrected in the next period. The absolute value of the coefficient of error term ( ) decides how quickly the equilibrium is restored. Results in table 5.6 shows that 27 per cent of the divergence from the long run equilibrium is corrected in the next quarter.

The R2 means how much independent variables jointly can influence the dependent variable. The R2 value of 0.56 indicates that about 56 per cent of the variation in stock prices is explained by RGDP, LCI and NYSE. The remaining 44 per cent is explained by other

15

See appendix E.7

independent factors which are not here. In other words, 0.56 percent of fluctuations in AS200 index can be explained by RGDP, LCI and NYSE. The rest 44 percent fluctuation in ASX200 index can be explained by other variables or residuals.

F statistics talks about joint hypothesis of independent variables that means whether independent variables jointly can influence dependent variables or not. We can say from F statistics whether independent variables jointly can influence dependent variable.

The F value of 33.74 and corresponding probability value is statistically significant at 1 per cent level of significance. Here is p value is 0.000 percent which is less than 5 percent so RGDP, LCI and NYSE jointly can influence our dependent variable which is ASX200 index. This shows that the developed model is valid and that these three variables have an effect on the performance of the stock market in Australia.

The Durbin-Watson test for autocorrelation' is a statistic that indicates the likelihood that the deviation (error) values for the regression have a first-order autoregression component. The regression models assume that the error deviations are uncorrelated. Durbin- Watson statistics shows that the model does not have an autocorrelation problem (DW = 1.88).