THE DYNAMICS OF
REAL ESTATE RETURNS
IN THE EUROPEAN
MARKET
Are listed real estate returns ahead of direct real
estate returns?
Reinier Stuyt 10807748 Economie en Bedrijfskunde Financiering & Organisatie Supervised by P. van Gool 26-06-2018
Abstract
This thesis investigates the dynamics of the returns of listed and
direct real estate in Europe during the years 2006 till 2018. The
research question of this thesis; Are REITs returns ahead of direct
real estate returns? After testing and comparing five econometric
measures, a final test for Granger causality will be carried out. This
test turns out to be significant with a p-value of 0.008. This result
confirms the predictions made in the second part of the thesis; the
lagged REITs returns help explain the current returns of direct real
estate.
1
Statement of Originality
This document is written by Reinier Stuyt who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
2 TABLE OF CONTENTS
1. Introduction. ... 3
2. Literature Review ... 5
3. Data and methodology ... 9
3.1 Description of data ... 9
3.2 Research methodology and models ... 11
3.2.1 Ordinairy Least Squares ... 11
3.2.2 Pearson correlation coefficient ... 12
3.2.3 Chow-test ... 12
3.2.4 Augmented Dickey Fuller test ... 12
3.2.5 Vector auto regression ... 12
3.2.6 Granger causality test ... 13
4. Test results ... 14
4.1.1 Results ordinary least squares regression ... 14
4.1.2 Pearson correlation results ... 15
4.1.3 Chow test results ... 16
4.1.4 Augmented Dickey Fuller test results ... 17
4.1.5 Vector auto regression results ... 19
4.1.6 Granger causality test results ... 21
5. Conclusion and discussion... 23
5.1 Conclusion ... 23
5.2 Discussion ... 25
6. References ... 26
7. APPENDIX ... 28
7.2 short overview return data used ... 28
2.1 Full regression output table OLS 1 ... 29
7.2.2 Full regression output table OLS 2 ... 30
7.2.3. full regression output second OLS regressoion chow test ... 31
7.2.4 full one lag vector auto regression output table ... 31
3 1. INTRODUCTION.
Investing can be done through countless different channels. Three big traditional channels of investing are Stocks, Bonds and Real estate. Stocks and bonds are small liquid investments which make them affordable for most individuals. Real estate on the other hand, is not liquid at all and can be bought only with bigger investments. This made investing in real estate only possible to a small wealthy group of individuals until 1960. ‘’ On Sept. 14, 1960 President Dwight D. Eisenhower signed legislation that created a new approach to income-producing real estate investment – a manner in which the best attributes of real estate and stock-based investment are combined’’(‘’History of REITs’’, n.d.). This involves investing in listed property shares(included listed and public real estate). ‘’REITs, for the first time, brought the benefits of commercial real estate investment to all investors – benefits that previously had been available only through large financial intermediaries and to wealthy
individuals.’’(‘’History of REITs’’, n.d.).
The favorable risk-return ratio and the presumed relatively low correlation to other assets like stocks and bonds have contributed to today's popularity of these listed real estate funds. REITs are reputed to have low correlations with bonds and are therefore seen as a good option to diversify a mixed asset portfolio. But if you look at the existing academic literature, the findings concerning the correlation with bonds, stocks and even direct real estate are quite diverse. It is still debated to what extent the real estate factor influences the return of shares ofreal estate investment trusts.
Since the existence of real estate investment trusts the new role of these so called REITs have attracted lots of academic attention. Essentially both, direct real estate and listed (public) real estate, have the same underlying assets, namely properties. From this point of perspective, it is only reasonable to expect both direct and listed (indirect) real estate to show somewhat similar return patterns. The first research done on the returns of REITs sometimes displayed quite the opposite and the expected similar yield behavior is debated ever since (Giliberto, 1990; Seck, 1996). In the early 90s academics discovered diverse results which made it hard to decide whether REITs were a new type of real estate asset or just another kind of stock. In this thesis, listed real estate will be represented by Real Estate Investment Trusts, from now on REITs. In prior research listed real estate is also referred to as indirect or public real estate, direct real estate could be named private or ‘unsecuritized’ real estate. Also rate of return and yield will be used interchangeably.
Boundry et al. (2012) proved in a study that a long-term relationship between the returns of direct and listed real estate exists in the United States real estate market. Other research proves that the return of REITs was mainly determined by stock and bond factors and the role played by a direct real estate factor was only limited (Giliberto, 1990; Seck, 1996; Clayton and MacKinnon, 2003; Ling and Naranjo, 2003). With the maturing of the REIT market and more historical data becoming available, some new interesting hypotheses concerning the relationship between direct and listed real estate have been researched. The field of research has expanded and not only focuses on the factors influencing REIT returns anymore. The speed of processing new information affecting returns in the real estate market is one of those new research areas. Although having the same underlying assets, the listed real estate market
4 is presumed to be much more liquid and therefore it should be able to reflect new information a lot faster than the rigid direct real estate market. According to Ling and Naranjo (2015) the lagged REITs returns can help forecast returns of the direct real estate market. Ling and Naranjo (2015) have studied this phenomenon in the United States real estate market, where most of the research concerning REITs is done. This is simply the case because of the better availability of historical data in the area. Yunus et al. (2012) have studied the dynamic
interactions between private and public real estate markets in The Netherlands, Australia, The United Kingdom and the United States. Yunus et al. found the existence of a lag-lead
relationship where the lagged public returns have a forecasting power over the direct real estate returns.
The relation between listed and direct real estate as a whole is a topic requesting more research. Since the biggest share of the existing research focuses on the United States, especially the European REITs market is understudied. The data used in this thesis is not easily accessed. The benchmark indices used for direct and listed real estate, which will be extensively introduced in section 3.2, are not provided by subscriptions of the University of Amsterdam. Due to the help of P. Van Gool, The Amsterdam School of Real Estate and the circumstance that I am an employee of CBRE Amsterdam made it possible to use these rare indices. This thesis will also contribute to existing literature by investigating the relationship between REITs and direct real estate in Europe. The dynamics of real estate returns and information transmission in the different real estate markets have never been researched in Europe as a whole. In particular, this thesis is intended to examine if there is a Granger cause-effect relationship between REIT returns and direct real estate returns (Granger, 1969). This Granger causality test can eventually answer the research question of this thesis; Are returns of REITs ahead of direct property returns?
The second paragraph of this thesis will be a literature review. This part will parallel and contemplate the different findings in prior research. This will not only contribute to better understanding the return dynamics of direct and listed real estate but it will also reveal understudied territory of the lag-lead relationship between the returns REITs and direct real estate. After the literature review the data and methodology will be elaborated. Not only the specifics and editing of the data but also all econometric measures will be described in detail. Subsequently the results of the empirical test will be displayed and explained. Further to this a conclusion will be drawn and finally suggestions for further research in this field will be discussed.
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2. LITERATURE REVIEW
Since the existence of real estate investment trusts, researchers and academics have tried to discover the true identity of these in short called REITs. In the beginning of REITs it was even debated whether it was a new way of investing in real estate asset class at all. The early REITs studies in the United States tried to find a connection between direct property and the listed REITs.
In prior literature one of the most important factors determining the outcome in REITs returns research is the measure of the direct real estate returns. In short there can be two ways of measuring the returns of direct real estate, namely appraisal-based and transaction based. The data of appraisal-based direct real estate is more widely available and less difficult to access but brings along the following complication; appraisal-based returns are based on a number of factors, for example a weighted average of current and historical returns, the current returns and costs and the fair market value. Not all factors influencing the real estate asset can be included in the appraisal. This makes the Appraisal based returns show less volatile than the real underlying transactions of the assets and therefore these returns have a more ‘’smoothed’’ appearance. Edelstein and Quan (2006) explain in their paper why this smoothing causes an underestimation or downward bias in the returns. Edelstein and Quan proved this by using data from the appraisal and later compare this with the corresponding transaction. Diery Seck ran a vector auto regression to discover the substitutability of direct and listed real estate in the United States. Seck also discovered that an increase in the level of economic activity increases the ability to forecast the price of appraisal-based real estate assets (Seck, 1996).
Clayton and MacKinnon have published one of the most referenced papers concerning the returns of REITs. They wanted to study the relation between REITs, direct real estate and equity in the United States. In their study they compose a variance decomposition which contains small cap stock, large cap stock, bonds and direct real estate. Respectively
represented by the Russel2000, S&P 500, UNITED STATES 10-year government bond and the NCREIF index. For the REITs they used the NAREIT index for the United States. Clayton and MacKinnon were also developing a theory that there were major changes in the behavior of REIT returns after the REIT-boom which started in 1992. Clayton and
MacKinnon looked at the REITs altogether but they also distinguished between four categories of different real estate i.e. apartment, industrial, office and retail. Due to their extensive research they discovered some new and interesting things. When Clayton and MacKinnon divided their whole sample period into sub-periods they found a shift in the explanation of variance in REIT returns. In the early 1980s REIT returns were mainly determined by large cap stock returns but this shifted in the early 1990s when they exposed small capital equity and real estate factors became more and more significant. As their sample period matured, a decrease of the volatility explained by equity took place. In the latest sub-period of their research, 1993-1998, they discovered small cap REITs to behave more like direct real estate than large cap REITs (Clayton, MacKinnon 2003).
Where previous research in the United States real estate market has mainly been done using appraisal-based indices for direct real estate, for instance the NCREIF index, Boundry et al. choose a different path. In their cointegration test, they prefered to use transaction based
6 historical data instead of appraisal based. Using the MIT TBI index from 1994-2012, they could test their cointegration framework on both the aggregate and the sub-index levels (apartment, office, industrial and retail). On both sector level and total level results prove a robust long-term relationship between the returns of REITs and direct real estate (Boundry et al., 2012).
In his paper Giliberto (1990) is researching EREITs (equity real estate investment trusts) in the United States by using an OLS regression. This regression results prove there exists correlation between the returns of the EREITs and both financial assets and real estate
returns. Furthermore, Giliberto finds that the lagged values of EREITs help explain variations in direct real estate return residuals using a Granger causality test (Giliberto 1990).
Until 1993 most studies concerning REITs have focused on the standard deviation and the mean of returns. Myer and Webb added some new dimensions to the REITs returns research such as normality tests, skewness and kurtosis. Just as Giliberto (1990) Myer and Webb research the REITs in the United States, and they describe their findings as an extension of the results Giliberto published earlier. In their search to find new prove in the field of the intertemporal relation between REITs and direct real estate, they perform a number of Granger causality tests and a vector auto regression. Myer and Webb find differences between intertemporal and distributional REITs and direct real estate returns. Intertemporal, using the Granger causality, the returns of REITs show a lag-lead relationship with direct real estate returns. When normal time series are taken into account, REITs returns show stronger relationships with normal stock than they do with direct real estate. Remarkably these results where uniform for different REITs indices but not when looked at different individual REITs (Myer Webb, 1993).
Europe is not the only area where REITs return behavior is understudied compared to the United States. For a long time Asia and Europe had the same problem; which was the lack of a uniform historical data. In 1997 Ong was one of the first to perform research similar to the research which had been done multiple times in the United States. By means of a
cointegration test, Ong discovered in Singapore no long-term contemporaneous relationship between REITs and direct real estate returns proved to be significant.
In 2000 Tuluca et al. proved the price indices of their five assets to be nonstationary and cointegrated in the United States. These five assets (bonds, T-bills, stocks and both listed and direct real estate) were also tested with a Granger causality framework and vector-auto regression tests, both restricted and unrestricted, respectively VECM and VAR. Tuluca et al. proved VECM improves the prediction on private real estate returns compared to VAR which is mainly been used in REITs studies. With this new finding they question the reliability of prior research on dynamics between direct and listed real estate returns. Tuluca et al. argue the long-term relationship between the two real estate markets establish a ‘’feedback’’. Which in a sense means both variables influence each other and this causes them to get caught in a negative or positive cycle (Chernobail, Hossain, 2012). The final conclusion excludes this feedback mechanism because the markets do not influence each other’s returns simultaneously, the ‘’private’’ real estate leads the ‘’public’’ real estate market according Tuluca et al. 2000. The paper published by Tuluca et al. proves the opposite of later published studies by Boundry et al (2012) and Yunus et al, 2012).
7 Focusing less on the characteristics of real estate returns, Ciochetti et al. research another interesting field in REITs research; what do investors prefer? In 2002 a relatively new regression in the research of REITs returns is used, the multivariate Tobit regression. In line with the results of their regression, Ciochetti et al. argue that institutional investors prefer more the liquid REITs over direct real estate (Ciochetti et al. 2002). The results found by Pagliari et al. are conflicting with those of Ciochetti. Pagliari opposed large real estate
investors would favor direct real estate, where small real estate investors preferred the smaller and more liquid listed real estate investments (Pagliari et al., 2005).
The paper that comes closest to the intentions of this bachelor thesis is the research paper published by Yunus et al. in 2012. This paper does not only attempts to evaluate the long-run relationships and short-run similarities between listed and direct real estate in the United States, but it also evaluates this phenomenon in the UK, Australia and The
Netherlands. Before the Granger causality test, a unit root test is performed to check whether the variables are characterized as non-stationary. A significant long-term relationship for all four countries is found. Yunus et al. conclude this makes it impossible to diversify a portfolio in the long-term with both listed and direct real estate, because both assets are substitutable in the long-term. Not only is the lag-lead relationship established in all four countries but
interestingly also a short term causal relationship was found. This last finding is not in line with some early research done in the United States (Giliberto 1990; Myer Webb 1993; Seck 1996).
Another recent paper published in 2012 by Hoesli et al. examined whether the returns of listed real estate are better reflected by stocks or by the underlying direct real estate. This paper compares the differences between the real estate markets of the United States, The UK and Australia and focuses on sector level data to discover potential undiscovered
relationships both short and long-term. The VECM used, does not only include stocks and real estate but also more general variables which are expected to influence returns like GDP and inflation rate. Both the variance decomposition and the impulse responses strongly suggest the listed REITs are more closely related to direct real estate than to stocks. The conclusion of Hoesli et al. is not new or shocking; no portfolio diversification is possible in the long-term because of the substitutability of listed and direct real estate in the long-term . Though the paper was a contribution to existing literature because it contained an event, the financial crisis, and new empirical research regarding Australia and The United Kingdom (Hoesli et al, 2012).
Ling and Naranjo published multiple papers in the quest for understanding dynamics between direct and listed real estate returns in the United States. In one of their later papers published in 2015 they draw firm conclusions. In a research period between 1994 and 2012 and they tested on both aggregate and sector specific level. Ling and Naranjo discovered REITs outperform their private benchmark by 0.49 basis points annualized. Using a baseline vector auto regression they conclude REITs do not use different or new real-estate specific information. According to Ling and Naranjo the results of the regression prove REITs react faster to the same information than their direct benchmark because REITs are more liquid. The final conclusion of this paper says that in the United States REITs are a fundamental information transmission channel regarding direct real estate when asset pricing variables are omitted (Ling and Naranjo, 2015).
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The conclusion from the literature above is mixed. Different models and datasets have resulted in diverging conclusions of the various studies and papers concerning the dynamics of REITs returns. There seems to emerge a fragmentation between results of early research done before 2000 and the later research. The latter keeps finding long-term relationships between listed and direct real estate and therefore conclude no portfolio diversification is possible in the long run (Boundry et al.,2012; Hoesli et al., 2012; Ling and Naranjo, 2015; Yunus et al., 2012). The first researchers of this topic found no significant relationship between listed and direct real estate returns (Giliberto, 1990; Myer and Webb, 1993; Seck, 1996). The diverging results and conclusions in the United States make this research field in Europe even more interesting and necessary.
9 3. DATA AND METHODOLOGY
In this third section the choice of the variables in the model and the indices chosen to represent them will be described. Thereafter the hypotheses and the corresponding tests will be described. The choice of the tests and the econometric intuition behind these tests will be discussed briefly. The description of the mathematical intuition of the models will be kept as short as possible, since this is not the main focus of this thesis.
3.1 DESCRIPTION OF DATA
The total returns of listed real estate will be proxied by the total returns of the FTSE EPRA/NAREIT Eurozone index. The index was launched in January 2005 and counts 103 constituents in January the first 2018. The Index is calculated real-time and end of day. The countries represented by the index are; Austria, Belgium, Finland, France, Greece, Ireland, Germany, Italy, The Netherlands, Norway, Sweden, Switzerland, Poland, Portugal and Spain. The returns are processed from daily to monthly, and both REITs and the data was cleared for constituents where data was not available for the full period of the research fourth quarter of 2006 till first quarter of 2018. This data was handed to me by CBRE, since the University of Amsterdam has no subscription to this database. The largest part of cleaning the data was already done by CBRE, which was very convenient.
This thesis planned to use the MSCI IPD Europe property index to get direct real estate returns. This benchmark index mainly used in other research papers mentioned in the literature review when the European real estate return dynamics are researched.
Unfortunately the University of Amsterdam has no subscription to this database anymore and both CBRE and the ASRE were also unable to provide the MSCI databases needed for this research. I found another direct real estate return benchmark index, provided by Real Capital Analytics. This index was lacking a few characteristics compared to the MSCI IPD; the returns were only available quarterly, the index data was only available from 2006 and the returns were not available on sector level. On the other hand this index was transaction based instead of the appraisal based MSCI. This automatically released my thesis from the
‘’smoothed’’ returns and the bias that comes with it. All transactions in the RCA Index are at least equal to 2,5 million Euro.
The large cap stock index used in this research is the Standard & Poor’s 350, which includes the returns of the 350 biggest European stocks. The small cap stock index was also a S&P index, namely the S&P SMALL CAP EUROZONE. Regrettably, the last index does not include the United Kingdom, which is included in all the other indices used in this thesis. It is important to distinguish between large and small cap stock because both react differently to market information and prior literature (Clayton and MacKinnon 2003) has shown it is possible that listed real estate shows significantly more correlation with one of the two. The S&P 350 has 365 constituents today but after clearing the data only 261 constituents could be used efficiently. The same data clearing process resulted in 301 constituents from the original 454 in the S&P SMALL CAP EUROZONE index. The bond index is provided by the OECD and is an aggregate of all the yields of 10-year government bonds from the OECD countries. No clearing of data has taken place concerning the bond index since the list of constituents
10 was not provided by the OECD. Below a line graph of all the percentage of changes in
returns from all the variables that have been plotted.
-.4 -.2 0 .2 .4 % to ta l r et ur n 1/1/2006 1/1/2008 1/1/2010 1/1/2012 1/1/2014 1/1/2016 1/1/2018 Date REIT DIRECT LARGE SMALL BOND -.3 -.2 -.1 0 .1 .2 % to ta l r et ur n 1/1/2006 1/1/2008 1/1/2010 1/1/2012 1/1/2014 1/1/2016 1/1/2018 Date REIT DIRECT
11 As mentioned above, the focus of was set on a 20-years monthly data, separated by sector level. Especially the monthly data was important since the relationship between lagged values becomes harder to find when periods become larger. Both benchmark indices for real estate, the RCA and the FTSE EPRA/NAREIT are problematic acquire. Due to CBRE I managed to access these two indices. Especially the RCA EUROPE index, which I have not come across in prior research, will contribute to the existing research done on the dynamics of real estate returns.
3.2 RESEARCH METHODOLOGY AND MODELS
A short explanation of the econometric tests and models will be provided in this section as well as the accompanying null hypotheses of the tests. Subsequently an expectation of the outcome will be introduced without going into too much detail on the mathematical aspect of the tests and models. In this thesis six econometrical test will be carried out,
respectively an OLS regression, a test for Pearson correlation, the Chow-test, the Augmented Dickey Fuller test, the Vector auto regression and a Granger causality test. The research period of this thesis is 12,5 years, and starts in the last quarter of 2006 and ends in the first quarter of 2018.
3.2.1 ORDINAIRY LEAST SQUARES
The goal of this regression is to see if the total returns of REITs are indeed influenced by their underlying assets; properties. Before testing whether the lagged returns of REITs ‘’Granger cause’’ returns of direct real estate, it is important to establish that REITs returns are influenced by real estate market information at all. The regression will control for normal asset pricing factors like stocks and bonds. If the returns of direct real estate play a significant role in the returns of REITs the assumption that REITs are indeed a form of real estate
investment and not just another stock can be verified. In this regression, the dependent variable will be the return of REITs, the FTSE EPRA/NAREIT EUROPE. The independent variable will be the total return on direct real estate, in this case the returns of the RCA EUROPE index. To control for other asset factors, control variables for small cap stocks, large cap stocks and bonds will be introduced in the model, respectively the S&P SMALL CAP EUROZONE, S&P 350 and the European 10-year government bond index.
Respectively these variables will be displayed as REIT, DIRECT, LARGE, SMALL, BOND and a constant; 𝜷𝜷𝜷𝜷 . The null hypotheses of this test is the following;
H0: When controlled for asset pricing factors like stocks and bonds, the real estate factor, represented by DIRECT, plays no significant role in explaining the returns of REIT. The OLS equation equates;
12
3.2.2 PEARSON CORRELATION COEFFICIENT
The Pearson correlation coefficient gives clear insight into the correlations between all of the variables used in regression 3.2.1. The Pearson correlation coefficient does not belong to a test or any hypotheses. This measure is calculated by dividing the covariance of two variables by the multiplied standard errors of the 2 variables. The Pearson correlation coefficient is always a value between -1 and 1. When dealing with more than two variables a correlation matrix is a convenient way of displaying the correlations in the model. This correlation matrix will give insight in the relations between the variables used in the model and they may or may not move together.
3.2.3 CHOW-TEST
With the Chow-test a regression can be tested for a structural break. This means that when the data points of the squared residuals change significantly during the period and one line could not be the best fit for the regression. A structural break in the dataset could be caused by events or shocks. This could influence the behavior of the returns so much that it makes more sense to draw a second or third regression line from a certain ‘’breakpoint’’ in the time series.
H01: There exists no structural breakpoint, the best fitting line through the data is the regression line from 3.2.1
3.2.4 AUGMENTED DICKEY FULLER TEST
Before carrying out the VAR and the Granger causality test, a test for the stationarity of the time series data needs to be performed. When data is non-stationary, there exists a unit root. When there is no unit root, and the data is stationary, the shape of the data does not change when a shift in time takes place. This unit root can cause unpredictable outcome when doing tests like vector auto regression or Granger causality. Although the augmented Dickey Fuller test is known to have ‘’Type I errors’’, it can handle more complex regressions than the normal Dickey Fuller test. The outcome of the augmented Dickey Fuller test is always negative. The lags should be chosen so they are significant which can be done by trial or using the AIC or HQIC test statistic (Akaike, 1974).
H02: there exists a unit root/non-stationarity in the multivariate time series data.
3.2.5 VECTOR AUTO REGRESSION
Before one can carry out a vector auto regression it is required for the data to be stationary. If the data are non-stationary the regression results are unpredictable and there is a high chance on what is called ’’a spurious regression’’ (Granger and Newbold, 1974). Thus, the rejection of the null hypothesis in section 3.2.4 is necessary to proceed the VAR of this research. If the data turn out to be non-stationary, other options like taking the first difference of the returns and performing a Johansen cointegration test and afterwards a vector error corrected model (VECM)(Boundry et al., 2012), can be used as an escape route to get to our final Granger causality test, but for now we assume data will be stationary (Johansen, 1991).
13 The vector auto regression, from now on VAR, is a multivariate time series regression for the interdependencies of multivariate time series.
The autoregressive part is the fact that all of the outcome from the variables are based on its own lagged values and the lagged values of the other variables in the model. Accordingly, all variables in the VAR model have their own explaining equation containing a component of their own lagged values, a different component for every other variable it’s lagged values and an error term. The VAR can be interpreted much like the OLS regression. The major
difference between the two is the fact VAR can have multiple dependent variables. This is because all variables ‘’enter’’ the VAR model in the same way. The opposite happens with OLS were al variables enter the model in a different way, because each variable has their own individual characteristic, either as the one dependent or as an independent variable.
H03: The lag number values explaining REIT = zero
3.2.6 GRANGER CAUSALITY TEST
This final test has the ability to test if the lagged values of one variable ‘’Granger cause” the other variable. What is also interesting about the Granger causality is the fact that it automatically displays the model the other way around. We can also see the significance and the explaining power of the lagged direct real estate values on listed real estate returns. At first it might seem confusing that ‘lagged’ values prove if some variable is ‘leading’. Therefore it is even more important to understand the lagged values are the values belonging to the variable which is presumed to be leading. Very important to distinguish is the
difference between Granger causality and real causality. A Granger cause will not
automatically imply there exists causality between the times series. Real causality requires theoretical motivation.
H04: The lagged returns of REIT do not Granger cause the returns of the DIRECT. .
14 4. TEST RESULTS
4.1.1 RESULTS ORDINARY LEAST SQUARES REGRESSION
The results of the OLS regression can be found in the accompanying table. The R-squared of this regression is 0.4552. This implies that 45.52 % of the squared residuals of the total returns of the FTSE EPRA/NAREIT EUROPE, in the regression called REIT, can be explained by the total returns of direct real estate, large cap stocks, small cap stocks and bonds.
𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹 = 𝜷𝜷𝜷𝜷 + 𝑫𝑫𝑹𝑹𝑹𝑹𝑹𝑹𝑫𝑫𝑹𝑹 ∗ 𝜷𝜷𝜷𝜷 + 𝑳𝑳𝑳𝑳𝑹𝑹𝑳𝑳𝑹𝑹 ∗ 𝜷𝜷𝜷𝜷 + 𝑺𝑺𝑺𝑺𝑳𝑳𝑳𝑳𝑳𝑳 ∗ 𝜷𝜷𝜷𝜷 + 𝑩𝑩𝑩𝑩𝑩𝑩𝑫𝑫 ∗ 𝑩𝑩𝑩𝑩 + 𝜺𝜺 We see that DIRECT is very significant because the p-value is below 0.01 or 1%. Remarkably all other asset pricing variables come out insignificant when alpha is smaller than 0.05 or 5% is chosen. This is not in line with prior research done in the United States (Ling and Naranjo 2003) (Boundry et al. 2012). Bonds are significant when alpha is set at 10%. At first sight this is in line with the research done in the United States by Clayton and MacKinnon in 2003, who discovered that REITs returns behaved much like bond returns, but the time window of these findings apply in the years before the REIT boom 1992. Although it is not really clear why stocks are so insignificant, for the main focus of this research the results are satisfying. The fact that DIRECT is very significant means the returns of listed real estate are indeed influenced by the underlying assets; direct real estate when controlled for normal asset pricing factors like stocks and bonds. The first null hypotheses posed in 3.2.1 can be rejected.
H0: When controlled for asset pricing factors like stocks and bonds, the real estate factor, represented by DIRECT, plays no significant role in explaining the returns of REIT.
𝑹𝑹𝑹𝑹𝑹𝑹𝑹𝑹 = −𝜷𝜷. 𝜷𝜷𝜷𝜷𝟎𝟎𝜷𝜷 + 𝑫𝑫𝑹𝑹𝑹𝑹𝑹𝑹𝑫𝑫𝑹𝑹 ∗ 𝜷𝜷. 𝟖𝟖𝟖𝟖𝜷𝜷𝟖𝟖 + 𝑳𝑳𝑳𝑳𝑹𝑹𝑳𝑳𝑹𝑹 ∗ −𝜷𝜷. 𝜷𝜷𝑩𝑩𝜷𝜷𝟎𝟎 + 𝑺𝑺𝑺𝑺𝑳𝑳𝑳𝑳𝑳𝑳 ∗ 𝜷𝜷. 𝜷𝜷𝟑𝟑𝜷𝜷𝜷𝜷 + 𝑩𝑩𝑩𝑩𝑩𝑩𝑫𝑫 ∗ −𝜷𝜷. 𝜷𝜷𝜷𝜷𝜷𝜷𝟖𝟖 + 𝜺𝜺 VARIABLES REIT DIRECT 1.8939*** (0.6234) LARGE -0.1425 (0.3425) SMALL 0.3603 (0.2745) BOND -0.1228* (0.0674) Constant -0.0151 (0.0114) Observations 45 R-squared 0.4552
Standard errors in parentheses *** p<0.01, * p<0.1
15
4.1.2 PEARSON CORRELATION RESULTS
The correlation matrix below does not show very shocking results. When REITs returns increase by 1%, the returns of direct real estate move up by 0.6057 * 1%. Other results like the correlation of 0.9259 between LARGE and SMALL confirm the suitability of the data used in the model. This very high correlation is easily explained by the fact that both assets are stocks and even though different in size their returns movements are much alike. The matrix also displays a negative correlation between bonds and both the listed and the direct real estate assets. It is known for REITs to be negatively related to interest rates, which are represented by of government bonds. When approaching the correlations that way, it is strange for the LARGE and SMALL stock components to be positively correlated with the interest rates/ bonds component. The important factor in this correlation matrix is the fact that all the returns could be cointegrated with each other.
. correlate REIT DIRECT LARGE SMALL BOND (obs=45)
variables REIT DIRECT LARGE SMALL BOND
REIT 1.0000
DIRECT 0.6057 1.0000
LARGE 0.4678 0.5131 1.0000 SMALL 0.5008 0.5375 0.9259 1.0000
BOND -0.1890 -0.0630 0.0830 0.1680 1.0000
Cointegration can be best described with the help of graphs. Shortly put, cointegration happens when 2 variables are not correlated, but they do move in the same direction. Because both variables are, for instance, increasing over time they will show some correlation even though the returns might be independent. This problem happens when the variables are non-stationary, which means the shape of the variables graphed changes when the time frame is shifted. Later on in section 4.2.4 a test for stationarity will be carried out to see if we indeed have to deal with cointegration tests because of r non-stationary variables.
16
4.1.3 CHOW TEST RESULTS
In prior literature of Clayton and MacKinnon in 2003, a structural break was found. What they called ‘’the REIT boom’’, in 1992, had so much influence on the behavior of REITs returns that the pattern of the regression was no longer the best fit. In their research they found a breakpoint in the regression using the Chow test. Subsequently they divided their sample period in multiple periods and performed OLS regressions per period. These new regressions were compared and significant differences were explained. The time frame used in this thesis does not include the REIT boom in 1992 but it does include another event. The reason the Chow test is included in this research is the presence of the financial crisis, which started around 2008. The outcome of the Chow test is displayed in the table below. Test for a structural break: Unknown break date
Number of obs = 45
Full sample: 2 - 46 Trimmed sample: 9 - 40 Estimated break date: 11 Ho: No structural break
Test Statistic p-value swald 23.6243 0.0063
Exogenous variables: DIRECT LARGE SMALL BOND Coefficients included in test: DIRECT LARGE SMALL BOND _cons
As expected the Chow test does find a structural breakpoint in the sample data in the second quarter of 2009. As shown in the graph below the returns stabilize compared to the period before. On the contrary of the research of Clayton and MacKinnon, the breakpoint is not in the middle of the sample. This makes it superfluous to perform two new regressions, since the first regression would only include 10 observations. Although the sample size of the full sample period, which is 45 observations, is already low, a second OLS regression is carried out on the sample period after the structural breakpoint. Because the fit of the model
decreased with the new regression and the research cannot afford to lose observations, this research will continue with the full sample size. The graph below exhibits the structural breaking point in the percentage change total returns of REIT in the first OLS regression. REIT is chosen because it makes the structural breakpoint best visible.
17
4.1.4 AUGMENTED DICKEY FULLER TEST RESULTS
The importance of the augmented Dickey Fuller test is enormous in this research. As mentioned earlier, when data is non-stationery the regression results will be spurious and therefore they will not have any meaning. The augmented Dickey Fuller results are all negative as was predicted in section 3.2.4. The number of lags for which we tested could be found for instance by looking at the AIC or HQIC statistics. For this research a lag of one unit meaning 1 quarter is used. As declared earlier, the intention of this thesis was to use monthly data instead of quarterly data, and one of the reasons behind this choice was the fact that more precise research regarding lagged periods could be carried out. As shown below in the results, all variables but DIRECT came out significant with an alpha of 0.01 or 1%. DIRECT is highly significant when an alpha of 0.05 or 5% is used. Also note the change in the number of observations due to the fact that all observations shifted 1 row downwards. The results show de data used are stationary. With this evidence we can reject the possible
assumption of cointegration made in section 3.2.2., where cointegration could be playing a part in the Pearson correlation coefficients found. This result also permit us to proceed our econometrical path towards the VAR model and the end test, the Granger causality test. . dfuller REIT, noconstant lags(1)
Augmented Dickey-Fuller test for unit root Number of obs = 43 --- Interpolated Dickey-Fuller ---
Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value
-.3 -.2 -.1 0 .1 .2 % to ta l r et ur n 1/1/2006 1/1/2008 1/1/2010 1/1/2012 1/1/2014 1/1/2016 1/1/2018 Date
18 Z(t) -4.189 -2.631 -1.950 -1.607
. dfuller DIRECT, noconstant lags(1)
Augmented Dickey-Fuller test for unit root Number of obs = 43 --- Interpolated Dickey-Fuller ---
Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value Z(t) -2.569 -2.631 -1.950 -1.607 . dfuller LARGE , noconstant lags(1)
Augmented Dickey-Fuller test for unit root Number of obs = 43 --- Interpolated Dickey-Fuller ---
Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value Z(t) -4.319 -2.631 -1.950 -1.607 . dfuller SMALL , noconstant lags(1)
Augmented Dickey-Fuller test for unit root Number of obs = 43 --- Interpolated Dickey-Fuller ---
Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value Z(t) -4.532 -2.631 -1.950 -1.607 . dfuller BOND , noconstant lags(1)
Augmented Dickey-Fuller test for unit root Number of obs = 43 --- Interpolated Dickey-Fuller ---
Test 1% Critical 5% Critical 10% Critical Statistic Value Value Value Z(t) -5.294 -2.631 -1.950 -1.607
19
4.1.5 VECTOR AUTO REGRESSION RESULTS
The results of the vector auto regression may seem difficult to interpret at first sight. The full table of output is provided in the appendix, in this section we will only show what is relevant to this research. The idea of the VAR model is a test which displays the lagged values of which variables are significant in explaining the dependent variable. Remember that in the VAR model every variable is a dependent variable, and this is why the table shows so many statistics. For this thesis only listed and direct real estate, represented respectively by REIT and DIRECT, are important. The table in the appendix shows a dependent variable. Then it shows coefficients, standard errors and test statistics of all lagged values from 1 quarter of all other variables in the model. The test statistic can be obtained by dividing the coefficient by the standard error. The test statistic tells us how much of the lagged value in question is explaining about the dependent variable.
The null hypotheses stated the lag of REIT equals zero, meaning no lagged values of any variable have significant explaining power in the REIT. The largest difference between the OLS regression and the VAR, is the way the variables enter the model. As stated in section 3.2.6 the VAR model has multiple dependent variables, because all variables in the model are dependent on one another. And with this absence of independent variables the interpretation of results becomes different from OLS results. When there are no proves for cointegration, the VAR can only be used on long-term relationships. (Johansen, 1991).
On the left side of the table we see all the lagged values and on the top columns of the table we see the dependent variables. Several lagged values appear to be significant in
explaining the dependent variables and it is difficult to draw a conclusion from this big pile of numbers.
(1) (2) (3) (4) (5)
VARIABLES REIT DIRECT LARGE SMALL BOND
L.REIT 0.3420** 0.0216 1.0034*** 1.1728*** 0.0131 (0.1651) (0.0177) (0.1328) (0.1595) (0.4133) L2.REIT -0.5147** 0.0017 -0.1152 -0.1821 0.8464* (0.2051) (0.0219) (0.1650) (0.1982) (0.5135) L3.REIT -0.2376 0.0072 0.2305 0.1435 -0.4109 (0.2216) (0.0237) (0.1781) (0.2140) (0.5546) L.DIRECT 4.8116*** 1.4002*** 1.6286 3.4530** -7.4139* (1.5749) (0.1685) (1.2663) (1.5212) (3.9420) L2.DIRECT -2.1988 -0.5858** -3.5554 -5.8211** 4.8844 (2.7658) (0.2959) (2.2240) (2.6716) (6.9231) L3.DIRECT -0.3913 0.1310 2.3133* 3.1451** 0.5569 (1.5335) (0.1640) (1.2330) (1.4812) (3.8384)
20 L.LARGE 0.5385* -0.0269 0.1373 0.4061 -0.1463 (0.2990) (0.0320) (0.2404) (0.2888) (0.7485) L2.LARGE 0.7789*** 0.0360 -0.4270* -0.5344* -0.5444 (0.2942) (0.0315) (0.2366) (0.2842) (0.7364) L3.LARGE -0.3252 -0.0494 -0.3266 -0.3923 0.9371 (0.3159) (0.0338) (0.2540) (0.3051) (0.7907) L.SMALL -0.4135 -0.0044 -0.2956 -0.4308* 0.3338 (0.2607) (0.0279) (0.2096) (0.2518) (0.6526) L2.SMALL -0.3326 -0.0405 0.1610 0.1978 -0.1765 (0.2378) (0.0254) (0.1912) (0.2297) (0.5952) L3.SMALL 0.2639 0.0250 0.1249 0.2438 -0.4150 (0.2491) (0.0267) (0.2003) (0.2407) (0.6236) L.BOND 0.0624 -0.0006 0.1181** 0.1630** 0.2305 (0.0737) (0.0079) (0.0593) (0.0712) (0.1845) L2.BOND -0.1250* 0.0048 -0.0312 -0.0166 -0.1525 (0.0662) (0.0071) (0.0532) (0.0639) (0.1657) L3.BOND -0.0252 0.0011 0.1057** 0.1302** -0.0955 (0.0656) (0.0070) (0.0528) (0.0634) (0.1643) Constant -0.0065 0.0016 0.0124 0.0169* -0.0051 (0.0104) (0.0011) (0.0084) (0.0101) (0.0261) Observations 42 42 42 42 42
Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
This thesis is mainly interested in the explaining power of the lagged REITs returns of one quarter. The data is formatted quarterly, which is already a long period to test for the effect of faster information transmission. In theory, every extra lag included in the model stands for three extra months that the direct real estate market is behind on the listed real estate market. For the quality of this research from now on the VAR and Granger causality test will be carried out with only one lag period. An additional benefit of this assumption is the following tables appear more clear.
(1) (2) (3) (4) (5)
VARIABLES REIT DIRECT LARGE SMALL BOND
L.REIT 0.532*** 0.049*** 0.810*** 1.032*** 0.073 (0.167) (0.018) (0.117) (0.149) (0.353)
21 (0.730) (0.080) (0.511) (0.652) (1.544) L.LARGE 0.280 -0.009 0.157 0.458 0.467 (0.363) (0.040) (0.254) (0.324) (0.767) L.SMALL -0.446 -0.019 -0.362* -0.591** 0.121 (0.296) (0.032) (0.207) (0.264) (0.626) L.BOND 0.094 0.005 0.124** 0.167** 0.045 (0.075) (0.008) (0.053) (0.067) (0.159) Constant 0.002 0.001 0.013 0.021* -0.006 (0.012) (0.001) (0.009) (0.011) (0.026) Observations 44 44 44 44 44
Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
Still several lagged values appear to be significant in explaining the dependent variables and it airs unclear. This is why in the next section, the Granger causality test will summarize the VAR model table. Since the data is found to be stationary, no Johansen test for cointegration is performed and therefor only long-term relations can be discovered using this VAR.
4.1.6 GRANGER CAUSALITY TEST RESULTS
The results of this Granger causality test will eventually answer the research question posed in the introduction of this thesis; Are REITs returns ahead of direct real estate returns? The number of lags in this research is set at one, because this gave the highest significance and it makes the most sense when looking at the theoretical aspect of this study. The information shocks could be transmitted faster in the more liquid listed real estate market. But the direct real estate market does not wait half a year to respond to the same information. As mentioned multiple times, three months lag time, or one unit, is already longer than planned to test at the beginning of this research. The table should be interpreted in the following manner: The column ‘’excluded’’ is the column with the lagged returns of the variable it represents. This implies that the first row of results tells us the lagged values of DIRECT do not significantly Granger cause the returns of REIT at an alpha of 0.1 or 10%, since the p-value of this statistic is 0.193 or 19,3%. If we summarize the first five rows of the test we can conclude that none of the variables DIRECT , LARGE, SMALL and BOND Granger cause REIT at an alpha of 0.1 or 10%. This is in line with the predictions and makes sense when you translate the numbers in economic intuition). There is no reason for any of the independent variables returns to be three months ahead of REITs returns. The information transmission of neither stocks nor bonds is faster than REITs, assuming they do not use other information than the REITs do.
22 When we look at the latter 5 rows, displaying the Granger causality of REIT,
LARGE, SMALL and BOND on DIRECT were see very satisfying results. The sixth row tells us the lagged returns of listed real estate Granger cause the returns of direct real estate when the alpha is set at 0.01 or 1% since the p-value of the test statistic is 0.008. This result is in line with the predictions made in the second section of this thesis and the findings in prior literature (Boundry et al.,2012; Hoesli et al., 2012; Ling and Naranjo, 2015; Yunus et al., 2012). All other variables do not Granger cause the returns of direct real estate which makes the significance of REIT only stronger.
Granger causality Wald tests Equation Excluded chi2 df Prob > chi2
REIT DIRECT 1.694 1 0.193 REIT LARGE 0.59437 1 0.441 REIT SMALL 2.2692 1 0.132 REIT BOND 1.5573 1 0.212 REIT ALL 4.885 4 0.299 DIRECT REIT 7.0361 1 0.008 DIRECT LARGE 0.0486 1 0.826 DIRECT SMALL 0.32704 1 0.567 DIRECT BOND 0.34949 1 0.554 DIRECT ALL 8.0758 4 0.089
23 5. CONCLUSION AND DISCUSSION
5.1 CONCLUSION
In this section all previous results will be summarized and interpreted. As mentioned in the literature review, the research regarding the dynamics of listed and direct real estate returns is understudied, especially in Europe. In this thesis the biggest challenge of the whole process was acquiring the suitable data for real estate returns in Europe, both direct and listed. Chances are high this must be one of the major reasons so little research has been done in this field in Europe.
The results of the first OLS regression in section 3.2.1 proved REITs are indeed a type of real estate investment and not some kind of stock. This finding was important,
because if REITs was not a more liquid type of real estate investment, it would be impossible to drawn sensible conclusions about the lag-lead relationship of direct and listed real estate. H0: When controlled for asset pricing factors like stocks and bonds, the real estate factor, represented by DIRECT, plays no significant role in explaining the returns of REIT.
The Chow test for structural breaks uncovered similarities between this research and one of the most referenced studies published by Clayton and MacKinnon in 2003. Just as their REIT boom event, the event in this study, the financial crisis, caused a structural breakpoint in the data. Unfortunately, we also need to conclude that the lack of observations made it impossible to draw other firm conclusions except the fact that a breakpoint exists. H01: There exists no structural breakpoint, the best fitting line through the data is the regression line posed in section 3.2.1.
The fact that the data series used in this research proved to be stationary prevented a lot of extra econometrical sidesteps.
H02: There exists a unit root/non-stationarity in the multivariate time series data.
The vector auto regression is not an easy concept to understand. Since it was widely used in the academic literature in this field it was almost an obligation to carry out a VAR in this research. Although I could have also published the Granger causality test results right away, I feel it is a real contribution to the research to display and explain the VAR model. Even though it took time and effort to understand and interpret the VAR, in the end this made me better understand what was actually happening with the data.
H03: The lag number values explaining REIT = zero
The Granger causality test results proved what was predicted in earlier sections of the thesis. It is satisfying the test results are in line with the latest papers and studies published on this matter. (Boundry et al.,2012; Hoesli et al., 2012; Ling and Naranjo, 2015; Yunus et al., 2012). It is interesting to think what would have been the outcome of this research when the
24 data was monthly. Maybe the exact matching conclusion was drawn, but maybe a two or one month lag would be an even better Granger causality measure.
H04: The lagged values of REIT do not Granger cause the returns of the DIRECT
Even though the data was not monthly but quarterly and not indexed by sector level, the predicted leading returns of listed real estate were visible. As multiple studies in the United States real estate market already proved, the information transmission is faster in more liquid markets like the listed real estate market compared to the direct real estate market. This faster transmission of information results in the returns of REITs reacting to this information before the returns of direct real estate do. After all, tests carried out in this research we can now conclude the same is true for Europe. As an additional prove of the findings in this research, the lagged returns of REIT were regressed against DIRECT, LARGE, SMALL and BOND. The R-squared of this model, better known as ‘’ the fit of the model’’ describes the percentage squared residuals explained by the model, improved from 0.4552 to 0.647.
Although the quality and frequency of the data used in this study might not be as hoped for, to my knowing I am still the first to research the return dynamics and lag-lead relationship of real estate returns in Europe as a whole.
VARIABLES REIT_01 DIRECT 1.618*** (0.521) LARGE 0.261 (0.280) SMALL 0.282 (0.224) BOND -0.024 (0.055) Constant -0.013 (0.009) Observations 44 R-squared 0.647
Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1
25 5.2 DISCUSSION
In this final section the possible improvements of this paper and suggestions for further research in this particular field will be addressed. One of the reasons why the European real estate market is understudied leads to the unavailability of uniformly distributed historical return data for both listed and direct real estate. Compared to the NCREIF index in the United States the FTSE EPRA/NAREIT database is of lesser quality. The MSCI IPD indices are outperforming the RCA index used in this study in multiple ways. The data is provided more frequently, by sector and goes back a lot longer than 2006. If better data was available for Europe, the academic research could catch up with the United States. It would be at least to say interesting to compare the econometrical measures used in this thesis between different sectors and different countries. If more observations were at hand, topics like the Chow test for structural breakpoints could be elaborated much more. For this research it might be too much, but the econometrics behind the used models could be explained in more detail. This will eventually contribute to a better understanding of the tables and graphs used along this paper.
26 6. REFERENCES
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28 7. APPENDIX
29
2.1 FULL REGRESSION OUTPUT TABLE OLS 1
regress REIT DIRECT LARGE SMALL BOND
Source SS df MS Number of obs = 45
F(4, 40) = 8.36
30 Residual .201433996 40 .00503585 R-squared = 0.4552
Adj R-squared = 0.4008
Total .369760476 44 .008403647 Root MSE = 0.07096 REIT Coef. Std. Err. t P>t [95% Conf. Interval] DIRECT 1.893935 .6233609 3.04 0.004 .6340755 3.153794 LARGE -.1424549 3424829 -0.42 0.680 -.8346386 0.549729 SMALL .3603378 .2745098 1.31 0.197 -.1944673 0.915143 BOND -.1227987 .067444 -1.82 0.076 -.2591081 0.013511 _cons -.0151484 0114126 -1.33 0.192 -.0382142 0.007917
7.2.2 FULL REGRESSION OUTPUT TABLE OLS 2
Source SS df MS Number of obs = 44 F(4, 39) = 17.91 Model 0.239391 4 .059847662 Prob > F = 0 Residual 0.130332 39 .00334185 R-squared = 0.6475 Adj R-squared = 0.6113 Total 0.369723 43 .008598204 Root MSE = 0.05781 REIT_01 Coef. Std. Err. t P>t [95% Conf. Interval] DIRECT 1.617649 0.521232 3.10 0.004 .5633582 2.67194 LARGE 0.260662 0.280097 0.93 0.358 -.3058882 0.827211 SMALL 0.281654 0.224208 1.26 0.217 -.1718491 0.735157 BOND -0.02448 0.055066 -0.44 0.659 -.135858 0.086906 _cons -0.01338 0.009308 -1.44 0.158 -.032211 0.005444
31
7.2.3. FULL REGRESSION OUTPUT SECOND OLS REGRESSOION CHOW TEST
. regress REIT DIRECT LARGE SMALL BOND if d2==1
Source SS df MS Number of obs = 35
F(4, 30) = 2.77
Model .034768737 4 .008692184 Prob > F = 0.0453 Residual .094179931 30 .003139331 R-squared
= 0.2696
Adj R-squared = 0.1723
Total .128948667 34 .003792608 Root MSE = 0.05603
REIT Coef. Std. Err. t P>t [95% Conf. Interval]
DIRECT .0043012 .8966788 0.00 0.996 -1.835564 1.826961 LARGE .0782082 .3039299 0.26 0.799 -.5424996 0.698916 SMALL .2218593 .2307092 0.96 0.344 -.2493118 0.69303 BOND -.1593427 .0692708 -2.30 0.029 -.3008127 -0.01787 _cons .0155509 .0161419 0.96 0.343 -.0174153 0.048517
7.2.4 FULL ONE LAG VECTOR AUTO REGRESSION OUTPUT TABLE
Vector autoregression
Sample: 3 - 46 Number of obs = 44 Log likelihood =
390.9478 AIC = -16.4067
FPE = 5.20e-14 HQIC = -15.9556 Det(Sigma_ml) =
1.32e-14 SBIC = -15.1902
Equation Parms RMSE R-sq chi2 P>chi2
REIT 6 0.081137 0.3068 19.47486 0.0016 DIRECT 6 0.008876 0.8307 215.9253 0 LARGE 6 0.058531 0.5803 60.84489 0 SMALL 6 0.074409 0.5922 63.8897 0 BOND 6 0.129996 0.173 9.205411 0.1011
Coef. Std. Err. z P>z [95% Conf. Interval]
32 REIT REIT L1. .509464 0.165457 3.08 0.002 0.185174 0.833754 DIRECT L1. 1.000754 0.739713 1.35 0.176 0.449056 2.450565 LARGE L1. .2567472 0.364148 0.71 0.481 0.456969 0.970464 SMALL L1. -.4200466 0.297308 -1.41 0.158 1.002759 0.162666 BOND L1. .0930645 0.09506 0.98 0.328 -0.09325 0.279378 _cons .002647 0.012736 0.21 0.835 0.022315 0.027609 DIRECT REIT L1. .0448533 0.0181 2.48 0.013 0.009377 0.080329 DIRECT L1. .80613 0.080922 9.96 0 0.647527 0.964733 LARGE L1. -.0145536 0.039836 -0.37 0.715 0.092631 0.063524 SMALL L1. -.0108645 0.032524 -0.33 0.738 0.074611 0.052882 BOND L1. -.0019536 0.010399 -0.19 0.851 0.022336 0.018428 _cons .0008374 0.001393 0.6 0.548 0.001893 0.003568 LARGE REIT L1. .7710115 0.119358 6.46 0 0.537073 1.00495 DIRECT L1. .3616465 0.533618 0.68 0.498 0.684225 1.407518 LARGE L1. .1102519 0.262691 0.42 0.675 0.404613 0.625116
33 SMALL L1. -.3049771 0.214473 -1.42 0.155 -0.72534 0.115383 BOND L1. .0990327 0.068575 1.44 0.149 0.035371 0.233437 _cons .0129062 0.009188 1.4 0.16 -0.0051 0.030913 SMALL REIT L1. .9867025 0.151736 6.5 0 0.689306 1.284099 DIRECT L1. .4054881 0.678367 0.6 0.55 0.924087 1.735063 LARGE L1. .4067669 0.333948 1.22 0.223 0.24776 1.061294 SMALL L1. -.5301435 0.272651 -1.94 0.052 -1.06453 0.004243 BOND L1. .1504283 0.087176 1.73 0.084 -0.02043 0.321291 _cons .0210704 0.01168 1.8 0.071 0.001821 0.043962 BOND REIT L1. .0601502 0.26509 0.23 0.82 0.459417 0.579717 DIRECT L1. -2.732743 1.185143 -2.31 0.021 -5.05558 -0.40991 LARGE L1. .066726 0.583425 0.11 0.909 1.076766 1.210218 SMALL L1. .4814038 0.476336 1.01 0.312 0.452198 1.415006 BOND L1. .0142082 0.152301 0.09 0.926 0.284297 0.312713 _cons -.0179276 0.020405 -0.88 0.38 0.057921 0.022066
34
7.2.5 FULL THREE LAGS VECTOR AUTO REGRESSION OUTPUT TABLE
Vector autoregression
Sample: 5 - 46 Number of obs = 42 Log likelihood =
413.3929 AIC = -15.8759
FPE = 1.07e-13 HQIC = -14.6627 Det(Sigma_ml) =
1.94e-15 SBIC = -12.566
Equation Parms RMSE R-sq chi2 P>chi2
REIT 16 0.068881 0.6333 72.52327 0 DIRECT 16 0.007368 0.9184 472.8495 0 LARGE 16 0.055386 0.7401 119.5979 0 SMALL 16 0.066534 0.7749 144.6025 0 BOND 16 0.172414 0.3596 23.583 0.0725
Coef. Std. Err. z P>z [95% Conf. Interval]
REIT REIT L1. .3419894 0.165105 2.07 0.038 0.01839 0.665589 L2. -.5146795 0.205144 -2.51 0.012 0.916754 -0.1126 L3. -.2376462 0.221553 -1.07 0.283 0.671882 0.19659 DIRECT L1. 4.81162 1.574882 3.06 0.002 1.724908 7.898332 L2. -2.198844 2.765829 -0.8 0.427 -7.61977 3.222081 L3. -.3913342 1.533471 -0.26 0.799 3.396882 2.614214 LARGE L1. .5384887 0.299028 1.8 0.072 0.047595 1.124572 L2. .7788664 0.294195 2.65 0.008 0.202254 1.355479 L3. -.3252086 0.315889 -1.03 0.303 0.944339 0.293922 SMALL L1. -.4135147 0.260714 -1.59 0.113 0.924505 0.097475
35 L2. -.3325518 0.23778 -1.4 0.162 0.798593 0.133489 L3. .2638673 0.24914 1.06 0.29 0.224439 0.752173 BOND L1. .0624468 0.073716 0.85 0.397 0.082034 0.206927 L2. -.1249804 0.06619 -1.89 0.059 -0.25471 0.004749 L3. -.0252477 0.065646 -0.38 0.701 0.153911 0.103415 _cons -.0064657 0.010409 -0.62 0.534 0.026866 0.013935 DIRECT REIT L1. .0215771 0.017661 1.22 0.222 0.013038 0.056192 L2. .0017368 0.021944 0.08 0.937 0.041272 0.044746 L3. .0072338 0.023699 0.31 0.76 0.039216 0.053683 DIRECT L1. 1.400192 0.168462 8.31 0 1.070013 1.730372 L2. -.5858276 0.295856 -1.98 0.048 1.165694 -0.00596 L3. .1310473 0.164033 0.8 0.424 0.190451 0.452545 LARGE L1. -.0269349 0.031986 -0.84 0.4 0.089627 0.035757 L2. .0359716 0.03147 1.14 0.253 0.025708 0.097651 L3. -.0494355 0.03379 -1.46 0.143 0.115663 0.016792 SMALL L1. -.0044377 0.027888 -0.16 0.874 0.059097 0.050222 L2. -.0405297 0.025435 -1.59 0.111 0.090381 0.009322 L3. .0249588 0.02665 0.94 0.349 0.027274 0.077192 BOND L1. -.0006026 0.007885 -0.08 0.939 0.016057 0.014852 L2. .0047873 0.00708 0.68 0.499 0.00909 0.018664 L3. .0011475 0.007022 0.16 0.87 0.012615 0.01491 _cons .0015584 0.001113 1.4 0.162 0.000624 0.003741 LARGE REIT L1. 1.003358 0.132759 7.56 0 0.743156 1.26356 L2. -.1152282 0.164954 -0.7 0.485 0.438531 0.208075 L3. .2305427 0.178148 1.29 0.196 0.118621 0.579706 DIRECT
36 L1. 1.628592 1.266341 1.29 0.198 -0.85339 4.110575 L2. -3.555387 2.223966 -1.6 0.11 -7.91428 0.803505 L3. 2.313272 1.233043 1.88 0.061 0.103448 4.729993 LARGE L1. .1373306 0.240444 0.57 0.568 0.333931 0.608593 L2. -.4270455 0.236559 -1.81 0.071 0.890692 0.036601 L3. -.3266208 0.254002 -1.29 0.198 0.824455 0.171214 SMALL L1. -.2956357 0.209637 -1.41 0.158 0.706516 0.115244 L2. .1610208 0.191196 0.84 0.4 0.213716 0.535758 L3. .1249386 0.20033 0.62 0.533 0.267702 0.517579 BOND L1. .1181367 0.059274 1.99 0.046 0.001962 0.234311 L2. -.0311864 0.053222 -0.59 0.558 0.1355 0.073127 L3. .105709 0.052785 2 0.045 0.002253 0.209165 _cons .0124444 0.008369 1.49 0.137 0.003959 0.028848 SMALL REIT L1. 1.172833 0.159479 7.35 0 0.86026 1.485406 L2. -.1821242 0.198154 -0.92 0.358 0.570498 0.20625 L3. .1434982 0.214004 0.67 0.503 -0.27594 0.562937 DIRECT L1. 3.452956 1.521217 2.27 0.023 0.471425 6.434487 L2. -5.821091 2.671583 -2.18 0.029 -11.0573 -0.58489 L3. 3.145088 1.481218 2.12 0.034 0.241955 6.048221 LARGE L1. .4061249 0.288838 1.41 0.16 0.159988 0.972238 L2. -.5343551 0.284171 -1.88 0.06 1.091319 0.022609 L3. -.3922619 0.305125 -1.29 0.199 0.990296 0.205772 SMALL L1. -.4308238 0.25183 -1.71 0.087 0.924402 0.062754 L2. .197829 0.229678 0.86 0.389 0.252331 0.647989 L3. .243772 0.240651 1.01 0.311 0.227895 0.715439 BOND L1. .162993 0.071204 2.29 0.022 0.023436 0.30255 L2. -.0165714 0.063934 -0.26 0.795 0.14188 0.108738
37 L3. .1301811 0.063409 2.05 0.04 0.005903 0.25446 _cons .0168553 0.010054 1.68 0.094 0.00285 0.03656 BOND REIT L1. .0131164 0.413268 0.03 0.975 0.796875 0.823107 L2. .8464213 0.513489 1.65 0.099 0.159998 1.852841 L3. -.4109194 0.554562 -0.74 0.459 -1.49784 0.676002 DIRECT L1. -7.413941 3.942032 -1.88 0.06 15.14018 0.312299 L2. 4.884431 6.92305 0.71 0.48 8.684498 18.45336 L3. .5569481 3.838378 0.15 0.885 6.966135 8.080031 LARGE L1. -.1462782 0.748486 -0.2 0.845 1.613284 1.320727 L2. -.5444031 0.73639 -0.74 0.46 1.987702 0.898895 L3. .9370782 0.79069 1.19 0.236 0.612646 2.486803 SMALL L1. .3338183 0.652584 0.51 0.609 0.945223 1.61286 L2. -.176477 0.59518 -0.3 0.767 1.343007 0.990053 L3. -.415046 0.623614 -0.67 0.506 1.637307 0.807216 BOND L1. .2304631 0.184516 1.25 0.212 -0.13118 0.592107 L2. -.1525365 0.165677 -0.92 0.357 0.477258 0.172185 L3. -.0955293 0.164315 -0.58 0.561 0.417581 0.226522 _cons -.0051392 0.026053 -0.2 0.844 0.056202 0.045924
