Chapter 4 Empirical Results
4.1 Results of the U.S
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Chapter 4 Empirical Results
In this chapter, the relationship between REITs and direct real estate transaction price is examined by testing for the existence of cointegration relation and by estimating VECM. The occurrence of structural change and the order of integration of the variables are checked first. Then cointegration test is conducted. Finally, Granger causality is examined based on the estimated VAR model or VECM.
4.1 Results of the U.S.
4.1.1 Structural Change
In performing unit root tests, special care must be taken if it is suspected that structural change has occurred. When there are structural breaks, the unit root test statistics are biased toward the non-rejection of a unit (Enders, 2004). In order to avoid the results of following examination be deviated, we should identify whether the series has structural change during the sample period. This study applies the Cumulative Sum of the recursive residuals test (CUSUM test) proposed by Brown, Durbin and Evans in 1975.
The results shown in Figure 4-1 and Figure 4-2 are obtained from the CUSUM of forward recursive residuals. It is apparent from Figure 4-1 and Figure4-2 that both the W (CUSUM quantity) of NAREIT and TBI do not exceed the critical value at the 5% significance level (dashed line). The result suggests that there is no structural change significantly in the NAREIT and TBI series during the study period. Therefore, it is appropriate to use the original series to conduct the following tests, and the results would not be distorted.
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Figure 4-1 Result of CUSUM Test for NAREIT
Figure 4-2 Result of CUSUM Test for TBI -30
-20 -10 0 10 20 30
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010
CUSUM 5% Significance
-30 -20 -10 0 10 20 30
1992 1994 1996 1998 2000 2002 2004 2006 2008 2010
CUSUM 5% Significance
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4.1.2 Unit Roots Test
In determining the possible cointegration relationships, the second step is to examine whether the time series of variables contain unit roots. Unit root tests provide basis for assessing whether a time series is non-stationary and integrated of a particular order. In the presence of non-stationary variables, there might be spurious regression (Granger and Newbold, 1974). 11 We thus employ Augmented Dickey-Fuller (ADF) (Dickey and Fuller, 1981) and Phillips-Perron (PP) (Phillips and Perron, 1988) tests to examine the existence of unit roots.
Table 4-1 reports the results of unit root tests for the NAREIT and TBI series by using ADF and PP tests. Both ADF and PP tests suggest that the null hypothesis of a unit root cannot be rejected for the level of each series, i.e., these time series are not stationary. However, the ADF and PP tests reject the null hypothesis for the series which take first difference, becoming stationary series. Hence, the results indicate that the NAREIT and TBI series are integrated of order one, and denoted as I(1) series.
Table 4-1 Test for Unit Roots on NAREIT and TBI
ADF test PP test
Level 1st difference Level 1st difference
NAREIT -2.6773 -6.0396 *** -2.0586 -6.1096 ***
TBI -2.5401 -6.6199 *** -2.1042 -8.8425 ***
Note: 1. The null hypothesis is that the series has a unit root.
2. *** denotes significance at the 1% level.
4.1.3 Cointegration Test
Since the existence of cointegration between REITs and direct real estate market would have important implications regarding portfolio diversification, we intend to detect whether the long-run equilibrium relationship exists between these two markets by employing cointegration test proposed by Johansen (1988). If there is a cointegration between I(1) variables, we could observe the short-term dynamics of variables by estimating VECM. If there is no cointegration, however, we should
11 A spurious regression has a high R2 and t-statistics that appear to be significant, but the results are without any economic meaning. The regression output looks good because the least-squares estimates are not consistent and the customary tests of statistical inference do not hold.
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examine the interrelation between them by using VAR model in first difference.
The results of Johansen cointegration test can be sensitive to the lag length.
Hence, it is essential to estimate a vector autoregression using the undifferenced data, and perform the same lag-length tests as in a traditional VAR. In this study, the optimal lag length is selected based on the Akaike information criterion (AIC) and the likelihood ratio (LR) test statistic recommended by Sims (1980).12 As shown in Table 4-2, the second lag is appropriate for the equations in the VAR model. We then consider the lag length selected by the VAR model to conduct cointegration test.
Table 4-2 VAR Lag Length Selection
Note: * denotes the lag order selected by Akaike Information Criterion (AIC) and likelihood ratio test statistic (LR).
According to the trace and maximum eigenvalue tests, the null hypothesis of no cointegrating vector (r=0) can be rejected at the 5% significance level, which is reported in Table 4-3. The results of cointegration test indicate that NAREIT are cointegrated with TBI in the sample period. In other words, the long-run equilibrium relationship exists between the NAREIT and TBI indices. As expected, it appears that there is a long-term price co-movement between these two series. This finding is not only consistent with the long-run relationship between NAREIT and TBI as we conjectured from Figure 3-1, but also in line with the recent findings by Oikarinen et al. (2011).
Since the REITs and direct real estate indices are cointegrated, it implies that there exists a common real estate factor driving the REITs and direct real estate
12 This type of likelihood ratio test is applicable to any type of cross-equation restriction. Let ΣE and Σ$
be the variance/covariance matrices of the unrestricted and restricted systems, respectively. If the equations of the unrestricted model contain different regressors, let c denote the maximum number of regressors contained in the longest equation. Sims’ recommendation is to compare the test statistic
(T − c)(log|Σ$| − log|ΣE|)
to the χdistribution with degrees of freedom equal to the number of restrictions in the system.
Note: T = number of observations; c = number of parameters in the unrestricted system;
log|Σ| = natural logarithm of the determinant of Σ
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markets in the long run. In addition, the diversification properties of these two assets are likely to be similar over the long horizon. It appears that REITs and direct real estate are substitutable assets in a portfolio of long term. These economic implications of the cointegration results could provide investors to determine the investment portfolio adjustment.
Table 4-3 Test Statistics for the Cointegration between NAREIT and TBI
Null hypothesis：
Note: ** denotes that the null hypothesis of no cointegration can be rejected at the 5% significant level.
4.1.4 Vector Error Correction Model
As discussed, there is a cointegration relationship between REITs and direct real estate. It is useful to detect the linkage and causality between two cointegrated variables by VECM. This model allows us to investigate the variables’ long-run speed of adjustments of deviation from their equilibrium value in the previous period as well as their short-term dynamic relationship.
Table 4-4 shows that the current NAREIT is affected by the first lag of NAREIT.
On the other hand, the current TBI are affected by the first and second lag of NAREIT and the first lag of TBI. The results suggest that the movements in TBI lag NAREIT performance by two quarters.
In terms of speed adjustment parameters, we are concerned about the sign and significance of coefficient. In Table 4-4, the signs of regression coefficients of error terms, denoted as “CointEq1”, are negative for the NAREIT variable and positive for the TBI variable, respectively. It suggests that NAREIT would decrease while TBI would increase in response to a positive deviation from long-run equilibrium. The
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error correction coefficient of TBI is significant at the 1% level. It implies that the adjustment of TBI will be about 16% of the deviation of ∆TBI from its long-run equilibrium value, which is highly sluggish.
The results indicate that only the TBI series adjusts towards the long-term equilibrium relationship with the NAREIT series. It is possible that the REITs market is more efficient than the direct real estate market. In other words, the information about the real estate fundamentals is reflected more rapidly in REIT price than in direct real estate transaction price.
Table 4-4 VECM Analysis on NAREIT and TBI
Variables ∆NAREIT ∆TBI
Coefficient t-statistic Coefficient t-statistic
CointEq1 -0.0666 -0.6865 0.1574 *** 2.7529
∆NAREIT(-1) 0.4384 *** 3.3402 0.1411 ** 1.8239
∆NAREIT(-2) -0.1517 -1.0957 0.1784 ** 2.1862
∆TBI(-1) 0.1094 0.5941 -0.2431 ** -2.2399
∆TBI(-2) 0.0350 0.1856 0.1190 1.0693
Note: ***and ** denote significance at the 1% and 5% level, respectively.
4.1.5 Granger Causality Test
Since there is a cointegration relationship between REITs and direct real estate markets, we employ Granger causality test which considers the error correction term to examine the existence of lead-lag relations. In Table 4-5, the result rejects the null hypothesis that NAREIT does not Granger cause TBI at the 1% significant level. As expected and in line with the recent findings by Oikarinen et al. (2011), changes in NAREIT appear to lead movements in TBI without feedback from TBI to NAREIT after 1990. It suggests that NAREIT performance can be employed to predict future movements in the TBI series due to better informational efficiency in the REITs market.
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Table 4-5 Granger Causality Test Results
Independent Variable Dependent Variable
NAREIT TBI
NAREIT — 0.0139 ***
TBI 0.8293 —
Note: 1. The table shows the p-values of the Granger causality tests.
2. The null hypothesis is that of no Granger causality.
3. *** denotes significance at the 1% level.
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