Results of Cointegration Test

Chapter 4 Empirical Results

4.2 Results of Cointegration Test

In order to explore the long-run relationship between T-REITs and other variables, this study applies cointegration test to determine whether the long-run equilibrium relationship exists between T-REITs and macroeconomy as well as T-REITs and commercial real estate market. If cointegration exists in the variables, we can directly use the standard value to do the VECM estimation. However, if the variables are not cointegrated, we will apply the VAR approach to test the stationary series at first-order differential. This study applies the Trace test and Maximum Eigenvalue proposed by Johansen to examine the cointegration relationship. The Johansen cointegration test is based on the VAR approach, so the lag order of an unrestricted VAR must be determined in the first place in order to avoid the individual lag impact of inconsistencies affecting the final determination of cointegration. In this study, we use AIC and LR values to select the optimal lag order. The results can be seen from table 4-2.

Table 4-2 The Optimal Lag Order

T-REITs and Stock Price Index T-REITs and Inflation Rate

Lag LR AIC Lag LR AIC

0 NA -3.493597 0 NA 1.661338

1 137.451 -6.827504 1 109.68 -0.960493

2 19.39852 -7.161313 2 23.59547* -1.407732*

3 2.131034 -7.031723 3 0.166688 -1.222019

4 16.42720* -7.339041* 4 8.7205 -1.2958

T-REITs and Interest Rate T-REITs and Commercial Rent

Lag LR AIC Lag LR AIC

0 NA -2.341604 0 NA -5.814883

1 138.5813 -5.704494 1 226.4817 -11.43163

2 17.68494* -5.991989* 2 38.93902 -12.29356

3 3.534391 -5.902495 3 1.518963 -12.14648

4 5.433225 -5.876662 4 17.76841* -12.49444*

T-REITs and Commercial Price

Lag LR AIC Lag LR AIC

0 NA -3.512245 3 8.502966 -5.073092

1 57.68971 -4.800992 4 11.64293* -5.235432*

2 15.17407 -5.020626

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After selecting the optimal lag order, we can carry out the Johansen cointegration test, and the results are listed in table 4-3. The results of cointegration between T-REITs and stock price index can’t reject the null hypothesis of r=0 under the Trace test, but it can be rejected under Maximum Eigenvalue test, meaning that T-REITs and stock price index are cointegrated. The results of cointegration between T-REITs and commercial rent as well as T-REITs and commercial price indicate that the cointegration relationships do exist between the variables at the 5% significant level, ,meaning the variables have long-run relationship. However, the statistic values of Trace test and Maximum Eigenvalue imply that the cointegration relationships do not exist between T-REITs and inflation rate or T-REITs and interest rate at the 5%

significant level, indicating that according to Johansen cointegration test, T-REITs and inflation rate as well as T-REITs and interest rate are not cointegrated.

Therefore, the discussion of long-run equilibrium relationship among T-REITs, macroeconomic and commercial real estate market shows that the equilibrium relationship exists only in T-REITs and the stock price index, T-REITs and commercial rents, as well as T-REITs and commercial price, meaning there is a long-run stability movement between T-REITs and those three variables. Interestingly, the result in this study suggests that T-REITs and stock price index are cointegrated, which is contrary to other relevant domestic results. The possible answer may be that the previous study period only contains the first two to three years information of T-REITs, so the cointegration results were not significant. In this study, we obtain four years information, so the long-run relationship becomes significant.