Determinants of rent and yield correlations across European office markets : a panel approach

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Mas

t

er thesis

Determinants of Rent and Yield Correlations Across

European Office Markets:

A Panel Approach

1994 2016

University of Amsterdam - Amsterdam Business School

MSc Finance - Real Estate Finance

August 2017

BSc. B.A.J. (Bas) Hilgers 11223197 Supervisor dr. M.A.J. (Marcel) Theebe

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STATEMENT OF ORIGINALITY

This document is written by Student Bas Hilgers 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.

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ACKNOWLEDGEMENT

I would first like to thank my thesis advisor dr. Marcel Theebe of the Amsterdam Business School at the University of Amsterdam and director of research analytics at CBRE Global Investors. His extensive knowledge of both theories from the academic world and practical application of it to international real estate market research has helped me a lot in specifying my research and providing the necessary information to steer me in the right direction. Despite his busy schedule, he never failed to provide extensive feedback to all of my questions whenever I needed it. In addition, I would like to extent my gratitude to Ralph van Polanen-Petel RT CFA and MSc Matthijs Schriek RT of Cushman & Wakefield for their input and providing me the time to work on my thesis during my internship.

Furthermore, I want to highlight the support of four books in writing this thesis. Firstly, ‘Real Estate Modelling and Forecasting’ by Brooks & Tsolacos (2010) has provided the necessary background for modelling cross-sectional and time-series and theory about forecasting, supported by real estate specific examples. Secondly, ‘Introduction to Time Series Using Stata’ by Becketti

(2013) has been a useful guide to basic regression and forecasting techniques in STATA. Thirdly, ‘Panal data a practical guide’ by Longhi & Nandi (2015) has provided additional insights into how to apply and test panel specifications in STATA. Lastly, ‘Introduction to Econometrics’ by Stocks & Watson (2015) presented the necessary econometric foundation.

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ABSTRACT

This thesis investigates whether, how, and why the rent and yield correlation structure across European office markets change over time. We hypothesize that if two markets show greater cointegration in various aspects of their economy and real estate related factors, rent and yield comovements are higher. This finds its basis in either factors that identify the dependency of one market on another, commonalities in the factors that influence the underlying cash flows or certain events that cause shifts in the correlation structure. To test this, we propose a theoretical model that allows us to identify significant determinants from a list of seventeen variables provided by previous literature. The model is employed to yearly nominal-, real- and yield growth correlations obtained from Cushman & Wakefield of fifty office markets across nineteen countries, from 1994 through 2016. A panel specification allows us to to control for time- and entity fixed effects while at the same time significantly increase our number of observations in a relatively thin market that is the commercial real estate sector. We find a plentitude of variables that are significant in explaining comovements and it thus becomes important to only include those factors that are particularly useful for modelling the changes in rents and yield movements. Our contribution is positive in this direction.

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BIBLIOGRAPHY ... 45 Appendix A Length Zero-Growth Periods Dependent Variable ... 48 Appendix B Formulas Trilemma Indices ... 49 Appendix C Background Information Variable List ... 50 Appendix D Correlation Between Variables ... 53 Appendix E Case Study Amsterdam – Frankfurt ... 54 Appendix F Results Nominal Rent Growth ... 57 Appendix G Submarket and Subregion Specification ... 60 Appendix H Transformation Dependent Variable ... 61 Appendix I Forecasting Evaluation Formulas ... 62

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1. INTRODUCTION

The real estate sector has seen an exceptional increase of cross-border investment over the last decades. Until the mid-90’s cross-border investments were virtually nonexistent with national property markets mainly locally oriented whereas nowadays we see that over forty percent of capital targeting the EMEA alone comes from outside their respective regions (Cushman & Wakefield,

2016). The rationale behind this movement is mainly rooted in the view of increased diversification benefits – that is, as the performance of a real asset are interconnected with the economic fundamentals, investor who diversify their portfolio globally are subjected to more differentiated underlying driving forces and thus reduce their idiosyncratic risk. Hence, reduced correlations between markets equals increased diversification benefits. This rationale seems to be especially relevant for real estate investors since real assets are closely related to the underlying fundamentals as a large body of literature has shown. For example, D'Arcy et al. (1997) and De Wit & van Dijk

(2003) both find similar economic factors that significantly impact rents and yields across markets. Nevertheless, obtaining a well diversified portfolio through international diversification is getting more difficult as global market are increasingly cointegrated. The combination of interdependent determinants and more similarities among investors effectively means that global real estate investors gain little from international diversification, and may in fact even be increasing their risk if the correlations between these markets are not well understood.

This thesis therefore focuses on modeling the movements in the rent and yield correlation structure between European office markets to identify significant determinants in order to better understand the nature and extent of cross-border integration1_{. Few studies (for example}_Jackson et al., 2008; Srivatsa & Lee, 2012) have shown how similarities in both the underlying economic environment of two markets as well as investment behavior significantly contribute to their commonality. However, to our knowledge this thesis is a first attempt to model the correlation structure of rent and yield growth across a large panel dataset to specifically identify factors that have a systematic effect and therefore focusses more on the why markets are integrated. Such understanding could provide investors with additional information about potential drivers behind diversification benefits which could help to analyse different scenarios – for example, to what extent would a relative growth of inflation influence the correlation structure or would new trade

1_{Throughout this thesis the term correlation structure refers to the time-varying correlations in yearly rent}

and yield growth between all bivariate market pairs obtained with the Pearson correlation coefficient over a 5-year rolling estimation window. We focus on the integration among real estate markets and its definition is therefore closely related with the terms interdependencies and co-movements. Of course, a different view is based on the law of one price but is excluded from their definition.

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agreements that opens up borders for foreign capital flows influence the interdependencies between office market performance.

We hypothesize that greater integration among variables related to the rent and/or yield growth across office markets result in greater comovements in their performance. Accordingly, greater divergence in the economic and other real estate related factors across markets is negatively related to this correlation structure. A distinction can be made between three broad categories through which markets are interlinked. First, the extent to which markets are dependent on one another such as Trade between countries and Monetary Independence. Second, similarities in factors that influence the cashflow model and in result the performance of the office sector such as the Inflation and Interest rate. Third, specific events that cause shifts from these systematic effects such as Financial crises and the establishment of the European Monetary Union.

We employ yearly rent a yield data obtained from Cushman & Wakefield from 1994 through 2016 to construct a five-year rolling window estimation of the correlation structure. The final sample consists of fifty market with a time series of 23 years amounting to more than 23 thousand observations. Drawing on the existing literature about the drivers of rent and yield growth across international markets and research on co-movements in the securitized real estate markets, we formulate a set of potential explanatory variables of the correlation structure to develop our theoretical model. The panel model specification seems to be naturally appropriate since it allows us to control for common international sources of comovement across market and over time that would otherwise cause omitted variable bias. The model is used to obtain out-of-sample forecasts of the correlation structure to evaluate its one-step-ahead forecasting ability that lets investors analyse different future scenarios.

This thesis proceeds as follows. Chapter 2 provides theory background of international real estate market integration with potential drivers of the co-movements. Chapter 3 specifies the data of the sample including the interpretation and expectation of the determinants and presents the usual descriptive statistics. Chapter 4 discusses the empirical methodology used to estimate the correlation structure, a list of explanatory variables and the steps towards the final econometric specification. Chapter 5 discusses the empirical findings of the panel regression, diagnostic tests and results per submarket and subregion. Further robustness checks are found in Chapter 6 in addition to the out-of-sample-forecasts evaluation of the model while the Final Chapter concludes this thesis.

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2. LITERATURE REVIEW

With a seemingly ever-increasing amount of cross-border investments, the amount of papers that investigate the dynamics and determinants of the comovements between international markets are filling gaps in the literature at a staggering pace. Nevertheless, most papers in real estate have focused on the securitized market while the private sector remains relatively under-highlighted. This is in part due to the absence of long-term quality data series and the lack of consistency across global property datasets which makes contributions such as this thesis particularly valuable.

This chapter reviews the main literature and theories regarding the commonalities and links between international real estate markets and is divided into two categories. Paragraph 2.1

establishes an overview of literature about the integration of international real estate markets and mainly focuses on how they are integrated, including reasons for shifts in relationship. Paragraph 2.2 establishes a theoretical background about common determinants of international rents and yields across markets and over time, plus potential drivers found behind comovements of the broader securitized markets to obtain some prior information why real estate markets could be integrated.

2.1 International Real Estate Market Integration and Convergence

Many of the early papers have focused on the existence of cointegration between international markets. Eichholtz et al. (1998) were the first to find evidence of a common factor within the global real estate markets. Through monthly data from Global Property Research over the period 1984 - 1996 they found significant evidence of continental factors that influence the real estate returns with in particular the European market that showed signs of growing integration at the beginning of the 90’s. In a follow-up study by Brounen & Huisman(2007) over the period 1997-2007 we see that six European countries had become less dependent on a continental factor namely, Austria; Belgium; the Netherlands; Spain; Switzerland and the UK while France; Germany; Italy and Sweden became more dependent. This clearly shows that the extent of convergence is time-varying and could even diverge at times. Any study that does not account for this fact in their conclusion fail to convince.

After the widespread acceptance of possible time-varying cointegration among markets, the focus of the academic world shifted towards investigating the causes behind increased this integration. A Series of papers looked specifically at securitized real estate sectors and the convergence of real estate in relation to the establishment of the European (Monetary) Union (EMU). Lizieri et al. (2003) used four different approaches - among which a five-year rolling window correlation approach similar to this thesis - to examine the extent to which shifts in economic behaviour due to the establishment of the EMU influenced the performance of

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publicly-traded commercial real estate companies. They conclude through found convergence in inflation and bond yield that the “dispersion of performance is higher, correlations are lower and the cointegration of economic factors have much lower explanatory power, while lead-lag relationships are stronger than the wider stock market”. The authors link the less and slower integration to the relatively small size of the real estate securities market and its local nature. Grissom & Colin(2003) and McAllister & Lizieri(2006) add that there is increasing integration in core Eurozone countries relative to non-core (non)-Eurozone countries which they both link to the differences in Marco-economic drivers. In addition, McAllister & Lizieri (2006) highlight that the inclusion of a (European) stock factor adds explanatory power to models of integration. Similarly, Lee(2009) shows that the UK real estate markets behaves differently from other European developed markets shifts between convergence with the US and European market, while Yang et al. (2005) find that the larger EMU countries show greater integration than smaller ones and that the integration among non-euro currency countries exhibited little change after the establishment of the UME. This shows that in addition to the time-period studied, also the markets included in studies impact the findings about the extent of integration.

A large body of literature has looked specifically at periods of high volatility and crises to investigate the effects of such events on the convergence between markets. Joyeux & Milunovich

(2015) for example investigated price bubbles in REIT markets and measured the degree of convergence toward a common trend during those times. They found that convergence indeed occurs during periods of financial distress and market exuberance. In addition, they highlight that the use of a rolling window approach does well to address changing comovements over time. Liow

(2012) found similar results in his extensive study on co-movement and correlations across Asian Securitized Real Estate. Real estate stock volatilities, covariance and correlations at local, regional and global levels increased during both the global financial crisis and the period before, with the implication that benefits of portfolio diversification are not uniform over time. He highlights the need for a better understanding about changes in the correlations structure within the international portfolio asset literature and its drivers.

But also the extent of cointegration or degree of convergence in the context of the similarities and differences between market characteristics has been widely investigated in recent years. Brooks & Tsolacos (2008) investigated the long-run relationships between markets and found that they adjust at different paces from their disequilibrium paths. Furthermore, they highlight that degree of integration to some extent is reflected by the difference economic and financial linkages and that diversification benefits are only achievable in the short-run. Jackson et al. (2008) use quarterly total returns and prime rental data of the key office districts in New York and London over the period 1988 through 2004 to investigate the cointegration between these markets in more detail than had been done before. They found that there is a causal link that originates mainly from the total returns and to a lesser extent from the rental values. It is therefore inferred that this is the

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effect of investment behavior towards the largest and most liquid markets rather than common economic drivers. Nevertheless, they do highlight that some of the evidence indicates that fundamental economic factors do play a role. It is these underlying forces of the rental data that

Suran(2013) further investigates. She applies Principal Component Analysis to the rents of both smaller, regional markets and established financial sectors across Europe, North America and Asia-Pacific to confirm that the changes in office rents are indeed driven by a common underlying (global) factor that is fairly stable over time. While several markets also seem to be driven by more regional factors. During the Global Financial Crisis, they found that rental changes did become less integrated. That is, even though most markets showed declines, many remained relatively unscratched which contrasts previous findings about returns.

Similarly, Srivatsa & Lee(2012) tested the extent of convergence of European office markets using property-level data from seven key centers during the period 1982 through 2009. They do look at both yield and rental growth data to specifically distinguish the influences from global capital markets. Beta-convergence and sigma-convergence tests are used to show not only the degree but also the speed of convergence between prime office markets. In contrast to McAllister

(2008), they do find some evidence of increasing convergence, especially after the introduction of a single currency in 1999. This convergence is mainly visible in yields and lesser in the rents which supports the inference of Jackson et al. (2008) that it is more caused by investment behavior through the capital markets and increases in cross-border real estate investments. Worzala & Bernasek (1996) analyze in detail the descriptive statistics of real-estate specific, financial, fiscal policy and indicators of economic conditions between countries and over time in search of signs of the predicted convergence between markets. The results suggest that convergence across the European Community is likely to continue in the future if the trend of economic integration is extended. Nevertheless, this process is expected to be slow due to various barriers and large differences are expected to remain. The paper of Haran et al. (2016) is unique in that it looks at market dynamics and cointegration of emerging real estate markets also included in this thesis - namely, Czech Republic, Hungary and Poland - in the wake of the 2007-2008 global financial crises. They find a lack of uniformity across these markets that might indicate that cross-border investments in these countries can still serve as a viable diversification strategy. It implies that these markets show different behavior and is worth investigating.

Alternatively, many other papers have looked at a range of different aspects of office market integration. For example, Lizieri & Pain (2014) set out a framework without to their saying complicated econometric analysis to unravel linkages between economic developments, office investment performances, and financial crises. First, Principal Component Analysis on twenty-seven European cities return clearly distinguishes common drivers among returns. Second, Regression analysis highlight that the commonalities among major financial centers are larger and more volatile than secondary markets. Regional investment does not show a lead-lag relationship

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in the performance of the office sector. They also highlight the importance of additional researchers in linkages between international real estate markets in relation to economic and financial activity. Stevenson et al. (2014) assess the degree of synchronization across the cycles of twenty global office markets and they find through the use of a concordance measure significance similarities among a large number of market pairs. Furthermore, they highlight that cross-border investment are often focused on a few key markets and that through such concordance diversification benefits may not be achieved. Continuing on these market interdependencies of office markets, Liow & Schindler (2017) focus on cross-market volatility spillover measurements of sixteen major European office markets over the period 2003 through 2013. They find that volatility spillovers are important and time-varying across the leading office markets, with cross-market volatility interaction being bi-directional and of relative endogenous nature for many markets. Furthermore, the London office market is the “volatility leader” and has a significant influence on most markets. Lastly, the volatility spillovers between business cycle fluctuations and asset market cycle volatilities are linked across some European economies.

In summary, the empirical literature on cointegration and convergence of real estate markets to date has provided us with several stylized facts. First, the degree cointegration between markets is time-varying and has in general increased over time. Second, different markets show different degrees of cointegration. Third, even though commercial real estate has been found to be less integrated than its wider stock market, economic drivers and investment behavior in the capital markets still provide significant explanatory power in terms of their commonalities. Forth, the conversion rate is influenced by policy regimes such as the establishment of the EMU through for example economic integration. Nevertheless, this process has been slow and due to various barriers large differences are expected to remain. Lastly, comovements between markets tends to coincide during periods of crisis and market exuberance and many have therefore inferred that diversification benefits tend to fail at the times one needs it the most. The need for a better understanding of the correlation dynamics between markets is often promoted.

2.2 Drivers of the Cross-Market Correlation Structure

As we have seen, the literature to date has provided a wide range insights into how real estate markets are integrated, but relatively few studies have investigated in detail why different markets are integrated, especially in terms of the performance of private real estate markets. Theories and findings from the broader equity market may provide some priori.

Bracker & Koch (1999) analyze in depth whether, how and why the correlation structure across cross-border equity markets co-move. Through their theoretical model, they find that global stock market volatility and a nonlinear trend have a positively function on comovements, while the terms structure differential, real interest rate differential, the exchange rate volatility and the return on the world market index have a negative effect. This thesis uses the same framework as the one

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proposed in this study to evaluate the theoretical model in an out-of-sample forecasts. Pretorius

(2002) looks specifically at the interdependencies of emerging markets also included in this thesis. She finds that interdependence among emerging stock markets could be explained significantly by their fundamentals and further infers that the found stock market comovements can divided into three broad categories, namely: economic integration, contagion effects, specific industrial similarities; with contagion effects referring to co-movement of markets not by the fundamentals.

Wälti (2011) on the other hand focuses on fifteen developed European economies to further investigate their stock market comovements and the effects of monetary integration over the period 1995 trough 2006 and find that both higher bilateral trade and monetary integration have led to increases in the correlation structure.

This direction of study with explicitly reflecting the cointegration and interdependencies of fundamental economic drivers on the correlation structure have also recently been picked up by international securitized real estate market research. Liu et al. (2012) are one of the first to investigate in-depth a range of underlying determinants of the co-movement in public real estate. Using a DCC-GARCH approach applied to REIT indices of the USA and Hong Kong, Japan and Singapore, time-varying correlations between 2001-2011 are estimated and regressed onto a set of four economic (unemployment, wages, inflation and GDP) and seven financial factors (share market, risk-free rate, term spread, credit spread, exchange rate, global volatility and global volume). They find significant time variation between REIT return co-movements; with higher correlations related to increases in the interaction of national inflation rates and higher global equity market uncertainty. They also find that REIT correlations decrease with rises in global equity market volume and US default risk premium. No substantial differences in results are present when switching from the US dollar to local currency denominated returns in this study.

Perhaps the study closest to ours is that of Liow et al. (2015) about correlation changes in international securitized real estate markets. They recognize the gap in the literature on the identification of significant drivers of cross-border correlations for the real estate sector and make a significant contribution towards filling it. Through their panel regression specification, they investigating quarterly averaged realized correlations - with unconditional and conditional correlations as robustness checks - between eight global real estate securities market over the period 1995 to 2012. Specifically, they attempt to address all three broad categories defined by Pretorius

(2002) by not only looking at general economic factors like previous studies, but also including industry specific real estate factors (on top of the additional volatility spillover and policy regime study). The real estate factors included are: return on the direct real estate market pairs, pairwise market size and volatility differentials, the influence of the existence of REITs, as well as a set of control variables were all found to be significant over most specifications with the expected sign and significant explanatory power, so they advise that these should be included in correlation structure modelling of real estate. The control variables included were: the absolute differentials

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between markets of the gross domestic product growth, inflation differential, term structure premium differential, real interest rate differential, percent change in the monetary aggregate and bilateral exchange rate, the variability in exchange rate, the bilateral trade openness, total stock market returns, stock market integration measured by its correlation and regional effects based on continents, institutional quality differential measured as the simple average of six main indicators from the World Bank governance and lastly dummies for crisis periods and to account for non-linear trends in the series.

Similarly, Stevenson (2016) examines conditional correlations across listed real estate sectors in combination to their respective global stock market from 1973 to 2014, but uses a different model specification and alternative explanatory variables than the previous studies mentioned. The empirical results show that both trade openness as well as two alternative measurements (trade in services and net foreign direct investment) are significant. In addition, where Wälti (2011) only used a monetary independence measure in their model, Stevenson (2016) also include Financial Openness and Exchange Rate Stability to form the complete trilemma index as they quote that “it is important to consider all three in any empirical analysis given the importance of the interaction between the three variables”. These variables were also found to be positive significant with minor exceptions in some of the model specifications. Furthermore, he highlights the significance of related market interdependencies on the correlation structure and the performance in real estate.

Relatively few literature however investigate the correlation structure between international direct real estate markets and the ones that do only seem scratch the surface of theory and methods devoted to broader equity market research. Goetzmann & Wachter (2001) and Quan & Titman

(1999) looked at office rents, values and returns to find that correlation between their respective markets arise more from their economic fundamentals rather that expectations about future growth.

Quan & Titman (1999) further show that due to their large dataset and inclusion of lags the rental rates were found to be highly correlated with GDP growth and also inflation seem to be important, while interest-rates are insignificant in contrast to previous studies. Case et al. (2000) also found that cross-border correlations of real estate are in part due to common exposure to fluctuations in the global economy and link global GDP as its main driver. De Wit & van Dijk (2003) find that GDP, inflation, unemployment, vacancy rate, and the available stock have and significant effect on rents, capital appraisals and total returns across global office markets. Tyrrell & Jowett(2008) on the other hand used the nominal GDP in their more practical applicable approach to derive estimates of correlations for global real estate markets and, while noting the large margins of error, find results which are “sufficiently robust” to use as input to real-word investment strategies.

In summary, although the literature on the determinants of co-movements between private real estate markets is still relatively thin, a broader equity market review provides some priori information about factors that potentially influence interdependencies between office market performance. Many have highlighted the importance of distinguishing the most important

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significant variables from the plentitude that could be chosen. We have seen that various theoretical models have found a wide range of variables that significantly explain the correlation structure between markets. An overview of significant variables found are divided into the three broad categories defined by Pretorius (2002): Economic integration with fundamental factors (real GDP, unemployment rate, inflation, interest rate, term structure premium) are found to significantly influence the extent of integration among markets and have theoretical basis to influence the cashflows of direct real estate. Other potential factors (money supply, trade openness, foreign direct investment) are less often used and their impact on real estate remains relatively unknown, thus are worth investigating. The trilemma index (exchange rate stability, monetary independence, capital openness) proxies’ various policies in place within markets and if investigated should all three be included. The Industry specific similarities are reflected by some real estate related factors (REITs structure and global market performance) while contagion effects are excluded from this study and could be addressed in further research.

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3. DATA AND DESCRIPTIVE STATISTICS

Commercial real estate (CRE) is often characterized by various types of heterogeneity making the study of real estate pricing uniquely challenging, especially in a cross-border setting. Nevertheless in recent years, major steps have been taken in terms of the availability and quality of data that enable us to test new theories and hypotheses and in result we see more and more articles appear in major journals filling up the gaps. Still, the literature about private commercial real estate investments remain relatively lean, which makes contributions like this thesis to the body of literature all the more valuable. This chapter describes the data used in two parts. Paragraph 3.1

describes the dependent variables consisting of rent and yield data in more detail where Paragraph 3.2 elaborates the explanatory variables and their usual descriptive statistics.

3.1 Rent and Yield Correlations

The office market data used to generate pairwise market correlations were provided by Cushman & Wakefield (C&W). Cushman & Wakefield is a leading commercial real estate advisory company that has offices in many countries around the world through which it collects data for its database that are published quarterly on their corporate website. Reflecting the aim of this thesis, both rent and yield, the two components that make produce the value of the building, are employed in each stage of the analysis. Using data from a single source like C&W increases consistency in the calculation methodology and thus provides a suitable way for handling data issues2_.

The rents recorded by C&W are based on professional valuations of the rent that would in the absence of special circumstances be achieved for high quality space in the CBD and is based on market transaction informaton. All values are denoted in local currencies which are used in this ‘raw’ form for the correlation structure to avoid any impact from exchange rate volatility. Both nominal and real rents that are deflated by the CPI index are tested and compared throughout the analysis. The yields recorded C&W denote the performance of real estate asset for the investment market segment and reflect the prime yields. A full overview of markets included can be found in

Appendix A.

2_{The international setting of this thesis causes problems with differences in law and reporting of rents and yields}

across countries. Furthermore, valuation processes may themselves be different which has an impact on the smoothness and volatility of real estate data. Nevertheless, this study assumes all markets to be comparable.

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Correlation Estimates

We estimate the correlation of both the rent and yield growth between fifty European office markets across nineteen countries, equaling 50x49/2 = 1,225 bivariate pairs3_{. The method used is}

the Pearson Correlation Coefficient that is discussed in more detail in Paragraph 4.1. The study covers the period 1994 through 2016 to which a rolling estimation window of five-years is applied with a stepsize of one year. This results in nineteen observations per market pair. The correlation values are reported at the current year of the window estimate and thus are backward looking only (historic correlations). The selection of markets is based on the data that was available during this time range. Additionally, markets with low variation in either their rents or yields were excluded from the sample (see Appendix A). Still, a handful of observations had zero-growth over the estimation window that are automatically dropped from the sample. This results in a strongly-balanced panel dataset in terms of the dependent variable of 23,275 unique observations for real rent growth correlations and 23,079 for yield- and nominal rent growth.

To provide an indication of changing correlation dynamics of rent and yield growth, Table 1

displays the descriptive statistics of these dependent variables. A number of issues become apparent. First, we see that in total the yield correlations are in general higher than their rents. This seems to be in line with previous findings (e.g. Jackson et al., 2008; Srivatsa & Lee, 2012) that rents are more dependent on local factors while yields are determined trough the broader capital markets. Second, the yield correlations seem to be slightly higher that to that of securitized real estate markets return correlation [e.g., Liow et al. (2015, p. 560)] who find an average correlation around 0.35 over a comparable timespan4_{. Third, there seems to be a slightly upward trend in the}

correlation structure of yield growth that may reflect increased cointegration between markets. The real rents on the other hand seem to remain relatively level. Fourth, we see that the correlations vary significantly throughout the estimation period and similarly to the findings of Lee (1998), there does not seem to inter-temporal stability among correlations. Low correlation between markets in one period can quickly disappear in a subsequent one, threatening potential diversification benefits. Still as Eichholtz (1996) conclude for securitized real estate; correlations coefficients measure to some extent the integration between markets that likely show more stability over time than for example the variances in returns. A similar rationale could therefore also hold in this thesis and could indicate some degree predictability.

3_{Some countries have more information available on their markets. On the one hand, including more market for}

a country could be argued to over represent the effects of some countries, while on the other and could also be seen as some kind of natural weight towards those countries importance for determining growth across Europe. Therefore, included as reported.

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Table 1 ◼ Descriptive Statistics Correlation Structure real RENTS and YIELDS

This table reports the summary statistics of the average correlation coefficients between 50 markets obtained trough the Pearson correlation measure. The sample selection overview is provided in Appendix A and is described in Paragraph 4.1. The yearly rent and yield data are obtained from Cushman & Wakefield over the sample period 1994-2016. Correlation is measured over these data with a 5-year rolling estimation window of yearly yield and rent growth. ‘Average’ is measured as arithmetic mean over all observations.

Average 1994-1998 1999-2003 2003-2007 2007-2011 2012-2016

Panel A: real RENT growth correlations

N 23,275 1,225 1,225 1,225 1,225 1,225

Mean 0.21 0.22 0.20 0.27 0.44 0.18

Std.Dev. 0.50 0.51 0.52 0.46 0.41 0.50

Min. -1.00 -0.99 -0.99 -0.97 -0.89 -1.00

Max. 1.00 1.00 1.00 0.75 0.89 1.00

Panel B: YIELD growth correlations

N 23,079 1,176 1,225 1,225 1,225 1,225

Mean 0.38 0.14 0.18 0.41 0.57 0.33

Std.Dev. 0.46 0.50 0.49 0.40 0.36 0.42

Min. -1.00 -1.00 -0.98 -0.93 -0.89 -0.95

Max. 1.00 1.00 1.00 1.00 1.00 1.00

Figure 1 ◼ Office Market Correlation Structure RENT and YIELD growth

The graphs show the average correlation between 1,225 market pairs per year over 1994-2016. In addition, the 5-95 percent interval per year are shown per year.

Average real RENT growth correlation

Average YIELD growth correlation

Lastly. correlations clearly seem to be higher during periods of financial distress and market exuberance while the standard deviations drop slightly. This highlights the importance of a better understanding of the driving forces behind the correlation to obtain the necessary diversification benefits in times investors need it the most. The minimum and maximum correlations are in general at -1 and +1 at any point in time. When we however windsorize the data as shown in the graphs it clearly shows that the maximum consistently remains at +1, but the minimum correlation shifts up before and during the global financial crisis. A further empirical analysis and interpretation of the differences in the correlation structure between markets and over time will be our modest contribution to the international real estate literature.

-1 -.5 0 .5 1 2000 2005 2010 2015 -1 -.5 0 .5 1 2000 2005 2010 2015

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3.2 Explanatory Variables

The theoretical background submits numerous aforementioned determinants that possibly affect the correlation structure between real estate markets. Table 2 summarizes the usual descriptive statistics of the variables used in this thesis, mainly to indicate data used per country, to spot outliers or faults and for possible reproductive purposes. Liow et al. (2015) provided us most variables to included in our model, but also Bracker & Koch (1999), Liu et al. (2012) and

Stevenson (2016) provided input. The data are primarily obtained from Thomson Reuters DataStream. The exception are the Trilemma indices which are obtained from Aizenman et al.

(2013). Appendix C provides a more detailed description of our data sample including the time range the data were available for each county and the source the data was obtained from.

A couple of things are noteworthy. First, the data is denoted in the forms used to measure the degree of integration between bivariate market pairs taken as either the correlation or the absolute difference. Second, some observations are missing as shown in the third column, especially in early years for developing markets. The panel data specification automatically drops these missing observations out of the sample. Lastly, the interest rate growth and term structure premium growth appear to be rarely high but is the effect of the rates close to zero. For example, the 3-month interbank interest rate for Spain decreased from 0.07 to -0.31 which equals a shift of -4,528.57. No unexpected outliers are noticeable in the data, hence is assumed to be usable as the basic inputs four our theoretical model.

The set of variables can be grouped into four broad categories: Fundamental Macro-Economic, Potential Macro-Macro-Economic, Financial and Real Estate Variables. The data are briefly described below, including their theoretical basis plus the expected impact on the correlation structure. All metrics are obtained at country level.

Fundamental Macro-Economic Variables

Greater convergence in the performance of two economies is expected to be reflected in the rents and yields by more similar growth; implying positive coefficients in terms of lower absolute differential between explanatory variables, or alternatively higher correlations. Gross Domestic Product (GDP) is an often-used performance indicator which serves as a proxy for the growth of the economy. During periods of high economic growth there is confidence within the economy that stimulates demand for products, services, and consequently for commercial real estate. The real GDP is modelled to allow for comparison of purchasing power over time. Alternatively, the Unemployment rate might be a better proxy for rent and yield comovements since employment is proven to be highly correlated with the demand for office space. To account for structural differences in economies and stationary properties, these variables are modelled in terms of growth. Both series are captured with a five-year rolling historic growth correlation window.

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Table 2 ◼ Summary Statistics Explanatory Variables - 2016

This table shows the usual summary statistics of variables used in the theoretical model for the sample of 50 markets (19 countries) for the year 2016. The data are primarily from the Thomson Reuters DataStream with the exception of the Trilemma Indices which are from the website of Aizenmann (2013) All variables are on country level. The second column denotes the used as input to measure the degree of cointegration between markets. The count (N) are the total number of observations in the dataset, while the other statistics are the average of the and only the 19 countries included. Appendix C provides a more detailed overview of the variables including data sources and missing sources.

Variable N Mean Std.Dev. Min. Max. Median

Real GDP growth %yoy 24,500 1.87 1.13 0.01 5.21 1.48 Unemployment rate growth %yoy 24,500 -6.72 8.71 -24.14 11.87 -4.56 Inflation growth (CPI) %yoy 24,500 1.19 0.67 -0.01 3.46 1.03 Interest rate growth %yoy 24,427 -130.68 1060.78 -4528.57 251.68 143.51 Term structure growth %yoy 24,500 -15.49 56.35 -67.24 174.67 -31.22 Money aggregate growth %yoy 23,753 6.10 5.95 -7.21 22.08 5.61 Trade openness Per GDP 24,500 1.03 0.48 0.57 2.17 0.84 Foreign direct investment Per GDP 24,464 3.21 7.50 -7.27 26.92 2.12 Exchange rate stability index 24,500 0.71 0.33 0.27 1.00 0.97 Monetary independence index 24,500 0.18 0.22 0.00 0.55 0.05 Financial openness index 24,500 0.97 0.11 0.54 1.00 1.00 Institutional quality index 24,500 3.21 7.50 -7.27 26.92 2.12

The change in Inflation is used to captures short-term adjustments in prices and is based on the growth over the last year at year-end. If Inflation converge/diverge, it forces performance of the office sector in the same/different direction. Similarly, more commonalities in interest rate growth could influence discount rates that in turn influence valuations. In addition, the Term structure premium is included since real estate is in general a long-term investment. The metric measures the premium demanded for long term investments in a country. Again, the five-year rolling correlations are used in the model to capture the extent of cointegration between the variables. The absolute differences of the yearly averages between markets are used as a robustness check for the correlation measure and vice versa.

Other Macro-Economic Variables

The second set of variables include other macro-economic variables that may directly influence rent and/or yield correlations that are rarer in literature. First, Money supply can impact returns and integration between markets due to “implications for portfolio selection or increased inflation uncertainty” (Bodurtha et al., 1989). The metric depicts the quantity of money in the economy and is measured by the correlations between the growth in the most liquid proportions (M1). Second, Trade openness is used as a proxy of potential economic policies that either restrict or invite trade between countries. Similarly to Stevenson (2016), trade openness is measured per country by (imports+ exports)/GDP. Data are obtained from the World Bank. Alternatively, Net Direct Investments can be viewed as a proxy for real asset foreign capital flows and might be closer relate to real asset nature of commercial real estate. This metric is also measured as its ratio over GDP and the cross-market integration is also captured by rolling correlations.

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Trilemma Index Variables

The three Trilemma Indices (Exchange Rate Stability, Monetary Independence and Financial Openness) are an often-used hypothesis in international finance and refers to that countries cannot obtain all three aims at one point in time (Aizenman et al., 2013). Policies may benefit to accomplish one or two measures, but will have a negative affect on the other one(s). It is therefore stated that including less than all three measures in empirical analysis fails to capture the complete picture of a countries’ policy aim. In this thesis, it is used to reflect the extent a markets’ achievement at a certain point in time and captures events like the adaptation to the Euro or restrictions on (foreign) capital. A smaller absolute differential between two countries is assumed to be related to relative focus on and achievement of similar policy goals and countries are more dependent on one another.

Appendix B provides the description of the the metrics and their measurements.

The first Trilemma Index Variable is Exchange Rate Stability. This is based on the annual standard deviation of monthly exchange rates. Besides capturing the effects of a single currency for the sample, a smaller absolute differential between countries might be related to a more similar demand from foreign investors due to a similar risk in the stability of exchange rate movements. The second measure, Monetary Independence, is measured as the correlation between monthly interest rate. This measure thus reflects as similar metric as the three-month interbank variable and should be interpreted with caution. Lastly, Financial Openness, also known as capital openness, is describes as the extent and intensity of openness in capital account transactions. Greater similarities are expected to be reflected in higher cointegration between a markets’ performance

Real Estate and Other Variables

The last set of variables contains variables that relate directly to the real estate sector or the broader stock market. First, REITs are a unique feature of securitized real estate markets and have been established at different points in time across countries. Accordingly, it might well be that two markets are more interdependent due to the co-existence of REIT influence and correlations of the performance of office sector higher. Second, correlations in the broader equity market have been found to increase during times of high volatility or fall during periods of high return. Investors could demand more return for their risk during such times or vice versa. Hence, a Global Stock Market Return and Volatility measure has been included to investigate of a similar rationale holds for rent and/or yield growth correlations. Lastly, Institutional Quality may reflect the attractiveness of an economy for foreign capital flows in the economy and commonality is associate with more similar interdependencies between markets.

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4. METHODOLOGY

In this thesis, we aim to explore the correlation structure between market pairs by examining the role of key macro-economic, financial and real estate factors in order to answer whether, how, and why the rent and yield growth correlations vary in intensity across European office markets and over time. The use of a panel specification allows us to simultaneously address both the cross-sectional and time-varying differences. Furthermore, it allows us to test on a relatively large number of observations in a relatively thin market that is the commercial real estate sector. Paragraph 4.1

denotes the empirical estimation of the dependent variables. Paragraph 4.2 discusses the estimation methods of the explanatory variable and the way the data are modelled and Paragraph 4.3 presents the theoretical model of the correlation structure, including information on the diagnostic tests and robustness checks.

4.1 Correlation Estimates

To capture the interdependencies between markets, a large variety of measurements can be applied. Extensive models have been developed to account for all kinds of scenarios, however, it is often mentioned that the simplest models do not perform any worse, especially with low frequency data like the yearly rent and yield growth used in this thesis. In addition, the interpretation is often more straightforward as it is the actual realized correlations that are reported and can be applied to measure short-time comovements. These are few of the reasons why the Pearson correlation coefficient is still often-used in theory and practice, and exactly the reason why the comovements between rents and yields in this study are measured through this method.

The Pearson correlation coefficient is a metric that measures the linear correlation between two markets and returns a value between the range -1 and +1, with -1 as perfect opposite and +1 as identical movements in growth. This thesis applies a rolling correlation window of five year with a step size of one year - that is, a four-year overlap. This length minimizes the number of missing values due to zero-growth periods while at the same time capture enough short- to medium movements in the correlation structure to explain changes in cointegration over time. That is, when there is no growth over the estimation period, the Pearson method cannot generate values as it then divides through zero. Section 4.1 and Appendix A provide further details about the variations in the dependent data and support our sample choice. The bivariate correlations between markets are measured as follow:

ρ_{𝑥𝑦,𝑡}= 𝑥𝑡− 𝑥 𝑦𝑡− 𝑦 𝑇 𝑡=−5 𝑥_𝑡− 𝑥 2 𝑇 𝑡=−5 𝑇𝑡=−5 𝑦𝑡− 𝑦 2 (1)

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where t denotes the quarter within the estimation window. The markets concerned are denoted by the letters x and y with 𝑥 and 𝑦 as the average of the five-year rolling estimation window. We computed the Pearson correlation coefficients (𝜌xy,t) between 1994 and 2016 for all markets that

had data available over the period, resulting in a sample of 1,225 bivariate office market pairs. Cushman & Wakefield reports rents and yields on a quarterly basis, but the decision has been made to use end-of-the year numbers only. The year-on-year growth rates have in general a higher correlation as not all markets show the same growth in exactly the same quarter even though they experience more similar growth over the full year, and therefore suit the aim of or thesis better. The correlation values are denoted at the current year of the window estimate and thus are backward looking only.

Alternatively, many studies on cross-border dependence research use the multivariate DCC-GARCH(1,1) models of Engle (2002) to extract conditional correlations. This model is preferred by most literature studying the interlinkages between securitized real estate markets – for example,

Liu et al. (2012); Liow et al. (2015) and Stevenson (2016). Most often it is used for financial time series with high frequency data to account for periods of relatively low and high volatility to be grouped together and is not constant over time. The model can also be applied to lower frequency data as shown in Liow (2010), who applies GARCH to international quarterly private real estate return series. Nevertheless, due to low variations in our data the rolling correlation coefficients on a GARCH approach cannot consistently be generated and is thus excluded from our study. Further studies might benefit of including this approach.

4.2 Explanatory Variables

As concluded in the literature review, from a macroeconomic perspective, the degree of integration between office markets can be divided into three broad categories. First, the extent to which two markets are tied together could influence rent and yield comovements. In other words, how one market is interdependent on another. For example, similar trade restrictions or investments from abroad could sign a similar degree influence of foreign markets which might result in stronger comovements. Second, based on the cashflow model underlying the performance of office markets, similar movements in their fundamentals is expected to influence the performance in a similar way. Third, certain unique events cause shifts in the correlation structure that deviate from the above more systematic trends, such as financial crises or the establishment of the European Monetary Union.

In general, we see that if there is greater divergence in the macroeconomic behaviour and other real estate related factors across markets and over time, the absolute differential between these markets is then expected to be negatively related to the correlation structure of rent- and yield growth. In other words, if the correlation between these determinants is low, then the correlation in rent and yield is expected to be low. Accordingly, smaller divergence and thus higher

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comovements in economic behaviour should lead to greater correlation among their respective office market performance.

However, there does not seem to be widespread agreement about a one correct way to measure this. Most literature makes use of average absolute differentials between variables to capture similarities or differences, but due to the use of an estimation window of five-year the data with high volatility would miss a lot of information in between estimates by ‘averaging out’ the effect of large versus small or opposite movements, although this effect is somewhat eased by the use of rolling averages and the large panel data to increase number of observations. The relatively lengthy estimation window on the other hand provides us the unique chance to measure correlations not possible in previous studies due to the frequency macroeconomic data is reported. Therefore, similar to the dependent variable, a five-year rolling estimation window is used to capture the comovements of variables included in the model. The only exceptions are variables that are ratios. For these values the absolute difference of the five-year geometric average is used to capture market similarities that is analysed to be more representative for the way pairwise markets depend on one another.

Unit-Root

Before determining the correlations between markets and implementing, both the explanatory and dependent variables are tested for stationarity using three panel unit-root tests, namely: Harris & Tzavalis (1999), Breitung (2000) and Choi (2001) Fisher ADF tests. All three have the null that panels contain a unit root, but differ in their alternative hypothesize whether all, some or at least one panel is stationary. The models are tested in both their levels and first differences, and by including a trend and excluding the constant. In addition, for the ADF test, one lag has been included as a rule of thumb for the yearly data used to eliminate potential serial correlation.

The rationale behind the need of stationary in time series analysis is as follows. If trending (also known as having a unit root or being non-stationary) while data are employed in their raw forms without being transformed appropriately, a number of undesirable consequences can arise. Besides that any inferences from the sample to the population are likely to be invalid, the problem of spurious regression arises. In other words, if the two variables are trending over time, the statistical techniques that we employ to determine whether there is a relationship between two series may indicate that the series are associated when in fact they are not. This situation can be avoided by always ensuring that the time series employed for analysis are not trending (i.e. that they are stationary).

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4.3 Panel Regression Model

In line with the aim of this thesis to provide improved understanding regarding the evolution of office market integration over the last two-and-a-half decades, we undertake a panel data analysis to assess quantitatively whether and to which extent each of the proposed explanatory factors are able to explain the correlations between rent and yield growth of European office markets. This method constrains the regression parameters to be the same for all pair-wise correlations and furthermore assumes that the error terms are independent, both over time and in the cross-section. In Chapter 5Equation (2) is tested both stepwise per category as well as the pooled set of variables.

Regression Model

Guided by the theoretical background of the literature review that provides a priori about relevant variables and the signs of their coefficients, a list of explanatory variables has been composed that in theory or assumption is related to the correlations in either rents or yields. For clarity, the variables are categorized into fundamental macro-economic, potential economic, trilemma indices and other real estate related factors. Given the significant results of Liu et al.

(2012), Liow et al. (2015), Stevenson (2016) and others, it is clear that a similar set of variables is significant in explaining level of integration of securitized real estate markets and thus also potentially similarly related to the private real estate market as explained in the literature review.

Table 3 provides the list of selected seventeen factors, their measurement proxy and the expected signs of coefficients. Our pooled theoretical panel regression model is defined as follows:

ρ_{𝑥𝑦,𝑡}= 𝛽0 + 𝛽1 corr(∆GDPx, ∆GDPy)t + 𝛽2 corr(∆UNEMx, ∆UNEMy)t

+ 𝛽3 corr(∆INFx, ∆INFy)t + 𝛽4 corr(∆INTx, ∆INTy)t

+ 𝛽5 corr(∆TERMx, ∆TERMy)t + 𝛽6 corr(∆MSx, ∆MSy)t

+ 𝛽7 |TRADEx – TRADEy|t + 𝛽8 |FDIx – FDIy|t

+ 𝛽9 |ERSx – ERSy|t + 𝛽10 |MIx – MIy|t

+ 𝛽11 |KAOPENx – KAOPENy|t + 𝛽12 |ISx – ISy|t

+ 𝛽13 STRETt +𝛽14 STVOLt +

+ 𝛽15 dREITxy,t +𝛽16 dEUxy,t + 𝛽17 lnTRENDt

+ dYEAR + axy,t + 𝜀xy,t

where dYEAR captures the time-fixed effects, axy,t the market-fixed effects and 𝜀xy,t denotes

the noise remaining. The model includes entity-fixed effects to control for omitted variables that differ between country-pairs but are constant over time. In addition, there are unobserved variables that are constant between markets but that vary over time as shown from residual analysis. Hence, we include year-fixed effects to solve for this type of omitted variable bias by including a year dummy. Although some trends seem to remain in residuals of some panels, the inclusion of incidental trends do not fix this and are thus excluded from the empirical model.

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Table 3 ◼ Explanatory Variables Theoretical Model

This table provides an overview of the variables used in the pooled theoretical model. The first column denotes the familiar variable names and the second column the formula denotation. The third column provides additional information about the type of metric used, the estimation period and the frequency of the data. The last column provides the expected effect of the variable on the correlation structure based on economic theory. Appendix C provides a more detailed overview of the variables including data sources and missing data.

Variable Notation Measured by Sign

Fundamental Economic Factors

Gross Domestic Product ∆GDPxy,t Real GDP growth correlation between

economies during years t-5 to t. + Unemployment Rate ∆UNEMPxy,t UNEMP growth correlation between economies

over years t-5 to t. Based on percentage of total labour force.

+

Inflation ∆INFxy,t INF growth correlation between economies over

years t-5 to t. Based on the CPI.

+ Interest Rate ∆INTxy,t INT rate correlation between markets over years

t-5 to t. Based on three-month interbank rate.

+ Term Structure Premium ∆TERMxy,t TERM correlation between economies over years

t-5 to t. Based on 10-year difference in

government bonds.

+

Potential Economic Factors

Monetary Aggregate ∆MSxy,t MS growth correlation between economies over

year years t-5 to t. Based on M1. + Trade Openness Tradexy,t Absolute TRADE differential between

economies of the geometric average of years

t-5 to t. Measured as (import+export)/GDP.

−

Foreign Direct Investment FDIxy,t Absolute FDI differential between economies of

the geometric average of years t-5 to t. Based on current net inflow over GDP.

−

Trilemma Index Factors

Exchange Rate Stability ERSxy,t Absolute ERS differential between economies as

geometric average of years t-5 to t. − Monetary Independence MIxy,t Absolute MI differential between economies as

geometric average of years t-5 to t. − Financial Openness KAOPENxy,t Absolute KAOPEN differential between

economies as geometric average years t-5 to t. −

Real Estate and Other Factors

Institutional Quality ISxy,t Absolute IS index differential between

economies during years t-5 to t. Measured as simple average of six metrics as provided by WDI.

−

Global Stock Market Return STRETt Average global stock market RET growth during

years t-5 to t. Based on MSCI global index. − Global Stock Market Volatility STVOLt Average global stock market VOL during years t-5

to t. Based on MSCI global index. + Co-existence REIT Influence dREITxy,t Dummy equals 1 if both markets have REIT

structure during more than of of the estimation window; 0 otherwise

+

Co-existence EU Members dEUxy,t Dummy equals 1 if both markets are EU

member states during more than of of the estimation window; 0 otherwise

+

Non-Linear Trend LNTRENTt Non-linear trend that account for increased

correlation developments. Measured as ln(t)

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Hausman Test

The Hausman test is a statistical test that allows us to see whether the random-effect model is appropriate to use or that the data requires a fixed-effect model. The Hausman test (1978) statistic is denoted as follows:

𝐻 = 𝑁(𝑏_𝑓𝑒+ 𝑏_𝑟𝑒)′ 𝑉𝐴𝑅(𝑏_𝑓𝑒+ 𝑏_𝑟𝑒)−1_(𝑏

𝑓𝑒− 𝑏𝑟𝑒)

where N are the total number of observations, bfe is estimates of a fixed-effect model and bre is

estimates of a random-effect model. The Hausman statistic has a !2_{distribution with k degrees of}

freedom. Under the null hypothesis (H0), bre is consistent but bfe is inconsistent. So if H0 is accepted,

the random-effect model is more suitable to use. If the H0 is rejected, the fixed-effect model with

time varying intercept is the preferred model.

The Hauseman test on the baseline regression model of this thesis rejects the H0 in favor of

the fixed-effect model with time-varying intercepts5_{. This is a similar approach to that adopted by} Wälti (2011) and has the advantage that it controls for common international shocks in the correlations during periods of financial crises, which would otherwise be difficult to model due to the five year estimation window.

Autocorrelated Disturbances

Due to the nature of our theoretical model specification (Equation 2) with differences in the frequencies of observed data plus the use of a rolling window estimate of both the dependent and explanatory variables, the model is expected to suffer from autocorrelations within the panels. In other words, a random variable might be correlated with its past and future values and consequently, the error term in the regression might show autocorrelation. This violates the classical assumption that the error terms are independent and least-squares estimates of the regression coefficient are ineffective while hypothesis tests are affected. By making use of robust standard errors per bivariate market pair these effects are treated. Since we are dealing with a micro-panel data set (characterized by a large number of markets relative to the number of years) clustering standard errors is often mentioned to provide enough support in the fixed effect specification to deal with autocorrelation. However, as a robustness check, the Feasible Generalized Least Squares (FGLS) is used as an alternative empirical model to control for autocorrelation among error terms. However, it does not treat the case of correlations between variables and the error term. Therefore, also the Generalized Methods Moments (GMM) model of Arellano-Bonds (1991) is used to test for possible model misspecification

5_{For the Hauseman test, the assumption of possible heteroscedasticity or clustered errors is loosened since}

clustering standard errors is not allowed in the Hausman function

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Out of Sample Forecasts

The final theoretical model is evaluated trough its ability to generate out-of-sample forecasts of the correlation structure for both rent and yields. Following Bracker and Koch (1999), Pretorius

(2002), Liow et al. (2015) and others, we test the out-of-sample forecasting ability of the correlation structure of our model and compare it with three other forecasting models that do not depend on economic specifications – that is: no change, historical average model and the ARIMA model. Briefly: the no change model uses the current values for the one-step-ahead forecast. The historical

average specification uses the average one-step forecast correlation over previous three years. The

third model develops an individual ARIMA specification to forecast the fitted values one-step ahead. Similarly, the fitted values of our theoretical model are employed to forecast the one-step-ahead correlations. Besides that the performance of our theoretical model in terms of their forecasting ability in comparison to other atheoretical models provides additional information on the explanatory power of the model, results also show whether it possibly to analyse different scenarios by predicting the effect of certain changes between economic variables on the correlation between rents or yields. For example, to what extent would the correlation structure between a market pair change if a country would adopt the Euro, or what would happen to the correlation structure if the interest rates in one market rises relative to the other market. Important to note is that some prediction about the the explanatory variables have to be made.