THE DYNAMIC CONNECTEDNESS AMONG PROPERTY AND INFRASTRUCTURE MARKETS: EVIDENCE FROM M-GARCH APPROACHES

Abstract

This paper performs a formal investigation on the volatility connectedness, stability and potential breaks among global infrastructure and property markets. Global Infrastructure markets include utilities, industrials, energy, and Global Property markets contain property diversified, healthcare, industrials, office space, and residential. Unknown break tests, cumulative sum tests, granger causality test and the DCC-MGARCH model, the study provides the critical findings as follows: (1) the selected markets present a good stability through cumulative sum tests; however, there are still potential break dates detected via the potential unknown break tests in some of those markets and the Global Infrastructure Energy presents its earliest breaks compared to the other peer ones. (2) While the connectedness and systematic risk transmission among the sample markets are presented globally, the property markets show a stronger spill over effects compared to the infrastructure markets via the DCC-MGARCH pairwise correlation examinations. (3) the causality is well presented among both the infrastructure and property markets detected via the granger causality Wald tests. Our results imply the limitation in systematic risk diversification among the markets, especially within the property markets globally.

Full text

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THE DYNAMIC CONNECTEDNESS AMONG PROPERTY AND
INFRASTRUCTURE MARKETS: EVIDENCE FROM M-GARCH APPROACHES
HAI HONG TRINH and GRAHAM SQUIRES
Department of Property, School of Economics and Finance, Massey Business School, Massey
University, Private Bag 11 222 Palmerston North, 4442, New Zealand.
*This version is for 2021 PRRES Conference
ABSTRACT
This paper performs a formal investigation on the volatility connectedness, stability and
potential breaks among global infrastructure and property markets. Global Infrastructure
markets include utilities, industrials, energy, and Global Property markets contain property
diversified, healthcare, industrials, office space, and residential. Unknown break tests,
cumulative sum tests, granger causality test and the DCC-MGARCH model, the study provides
the critical findings as follows: (1) the selected markets present a good stability through
cumulative sum tests; however, there are still potential break dates detected via the potential
unknown break tests in some of those markets and the Global Infrastructure Energy presents
its earliest breaks compared to the other peer ones. (2) While the connectedness and systematic
risk transmission among the sample markets are presented globally, the property markets show
a stronger spill over effects compared to the infrastructure markets via the DCC-MGARCH
pairwise correlation examinations. (3) the causality is well presented among both the
infrastructure and property markets detected via the granger causality Wald tests. Our results
imply the limitation in systematic risk diversification among the markets, especially within the
property markets globally.
Keywords: connectedness, systematic risk, GARCH models, granger causality, structure
breaks.

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Highlights
. A formal analysis of systematic risk and spill-over effects among property and infrastructure
markets.
. Unknown break tests, cumulative sum tests, granger causality test and the DCC-MGARCH
models are employed.
. An overall stability is presented; however, there are potential break dates detected and the
Global Infrastructure Energy presents its earliest breaks.
. The property markets show stronger spill-over effects compared to the infrastructure markets.
. The causality is well presented among both the infrastructure and property markets via the
granger causality Wald tests.

3
1. Introduction
Since the Great Depression during the 1930s, the 2007-2009 Global Financial Crisis (GFC)
which was originally caused by the US subprime mortgage crisis had extreme widespread
effects. Right after the US financial crisis commenced, its effects have spilled over to other
financial markets generating severe downturn across the global markets. As a result, previous
studies increasingly detect the potential spillover effects between different financial markets.
Detecting the connectedness across market has generated crucial contributions to the literature,
Diebold and Yilmaz (2012) propose directional measurement to predict market volatility
spillovers; Teye, Knoppel, de Haan, and Elsinga (2017) reveal market forecasting related to
shocks; and Tsai (2018) provides the roots and consequences of ripple effects among markets
through their transaction trading volumes and prices.
Previous studies have detected the presence of connectedness across regional, national and
multinational housing markets. For the regional and national levels. Miao, Ramchander, and
Simpson (2011) document spatial connectedness among metropolitan markets in the US; Cook
and Watson (2015), Antonakakis, Chatziantoniou, Floros, and Gabauer (2018)and D. Zhang
and Fan (2019) examine the UK and China’s connectedness among their regional housing
markets, respectively. At multinational level, some studies reveal the international housing
markets’ connectedness such as among European securitized real estate markets (Liow, Zhou,
& Ye, 2015); in East Asia and Greater China (Kim & Park, 2016); among five public real estate
markets including the UK, the US, Hongkong, Japan and Singapore (Liow & Angela, 2017);
among G7 private real estate markets (Lee & Lee, 2018); and across 18 OECD-member
countries (Nguyen, Naeem, Balli, Balli, & Syed, 2021). Lee and Lee (2018) and Miao et al.
(2011) notice that the connectedness among housing markets reach its peak surrounding
financial market disruption periods.
The previous literature has underpinned the connectedness among residential property
(housing) markets, while the connectedness between different property markets and other
markets/asset classes still need more research works to fulfil. Especially in the context of
sustainable development, the role of infrastructure markets is undeniable given its important
nexus of economic productivity, poverty reduction and growth (World Bank, 2019). Prior
studies document important linkages between infrastructure and housing markets such as
infrastructure and housing supply (Stover, 1987); urban infrastructure, housing finance,
affordability and development (Bryant, 2017; Collier & Venables, 2016; Gallent et al., 2020;
Kim, 1997); airport, local, bicycle infrastructure and housing prices (Conrow, Mooney, &

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Wentz, 2020; Lipscomb, 2003), infrastructure for new housing (Kellett & Nunnington, 2019).
The strategy toward the long-term suitability and inclusive economic growth, the connectivity
among different markets is a requisite, this point once again stresses the extremely important
of infrastructure markets such as transportation, information technology (IT), energy,
electricity and the infrastructure systems as the whole to promote the integration and
transmission among different markets. Especially in the context of economic cooperation such
as the network of OECD-member countries for commercial, trade and many other economic
opportunities, leading to an increasing need for a higher level of cross-market connectedness.
Motivated by several unexplored works needed, this study shed first further light on the
efficiency among property and infrastructure markets through detecting their volatility
transmissions and structural break as an asset class. The study aims to answer the question
‘Does better diversification among different property and infrastructure markets help investors
to mitigate infrastructure-related risk? Particularly when considering up-front investments and
future cash flows/revenues to pay back their bulk investments in infrastructure projects. This
is particularly important to attract more investments in infrastructure financing that often
requires bulk up-front investments while there is no guarantee of future revenue streams for
investors (Squires, Javed, & Trinh, 2021). This is even more important when studies in the
field of infrastructure and property markets as an asset class still in their early stage with less
focus than other markets such as commodities (Balli, Naeem, Shahzad, & de Bruin, 2019;
Kang, McIver, & Yoon, 2017; D. Zhang & Broadstock, 2018), equity (Maghyereh, Awartani,
& Bouri, 2016), cryptocurrencies (Bouri, Vo, & Saeed, 2020; Canh, Wongchoti, Thanh, &
Thong, 2019; Ji, Bouri, Lau, & Roubaud, 2019), fixed income securities (Naeem, Nguyen,
Nepal, Ngo, & Taghizadeh–Hesary, 2021; Nguyen, Naeem, Balli, Balli, & Vo, 2021; Pham,
2021), housing and rental markets (Squires, Webber, Trinh, & Javed, 2021) and among other
markets (Demirer, Ferrer, & Shahzad, 2020; Le, Do, Nguyen, & Sensoy, 2021) in the recent
years.
Investigating the ten global infrastructure (global, utilities, industrials, energy) and property
markets (global, diversified, healthcare, industrials, office space, residential) for the period of
Q2/2011-Q1/2021 on a daily frequency basis through several time-frequency econometric
approaches, the study provides evidence that the unknown structural breaks are presented in
both the infrastructure and property markets with the earliest potential break date detected in
the infrastructure energy market, regardless their stability examined earlier. Systematic risk
spillover effects are positive and well detected specially within the property markets via the

5
findings of DCC-MGRACH approach. The correlations and granger causality are universally
presented from the lowest value of 0.59 for the pair of global property diversified and industrial
to the highest value of 1.01 for the pair of the global infrastructure in general and infrastructure
industrials market. Overall, our results imply the limited ability in systematic risk
diversification that might lead to potential asset bubbles, especially within the global property
markets.
The remaining parts of this paper are structured as follows. Section 2 presents the data selection
and Section 3 provides a detailed description of econometric settings. Section 4 presents
empirical findings and their discussions. Section 5 concludes the main findings, their insights
for policy implications, important contributions and suggests future studies needed.
2. Data
To detect the comprehensive detection of structural breaks as well as the spillover effects
among property and infrastructure markets, the study employs the main global property and
infrastructure markets. The study collects daily price index for each of global infrastructure
and property markets and then combine them to attain the longest time span including as many
as the key global markets. Through several filter and econometric adaptation steps, the final
dataset includes a total of nine global equity indices for both markets. The study data sample
is extracted from Thompson Reuters DataStream that includes (1) for property: S&P global
property index, S&P global property diversified, S&P global property healthcare, S&P global
property industrial, S&P global property office space, S&P global residential, S&P global
infrastructure utilities; (2) for infrastructure: S&P global infrastructure index, S&P global
infrastructure utilities, S&P global infrastructure industrial, and S&P global infrastructure
energy. Following the procedures proposed in the previous literature (Canh et al., 2019;
Dyhrberg, 2016), the study takes the natural logarithm and the first difference
1
of logged price
index for each of infrastructure and property indexes (see Appendix 1). The final period covers
from 6/8/2011 to 30/4/2021, approximately ten years for all sample indices.
3. Methodology
The study first detects the dynamics of property and infrastructure price indices by estimating
the unknown structural break date utilizing the exponential, mean and maximum of the tests’
average forecasted for each potential break day. The study assumes each S&P global equity
index for both markets is a function as below:
1
By taking the difference of the logged prices for each equity index, the study implements seasonal adjustment by subtracting the logged
prices of each equity index on day
!
of the current year t0 for its logged price on day
!
in the previous year t-1 before the other estimations.

6
!"#$%&'()&!* +", +#!"#$%&'()&!$# , -!
(1)
Where
.
present a given day
.
.
!"#$%&'()&!
indicates the first difference
2
of daily logged
prices of each S&P global equity index for either infrastructure or property markets.
+
is the
estimated coefficient and
-
presents the residual term. To test for a structural break with
unknown break day, we fit the model (1) and consider S&P equity indices as a function of their
first lag form and test the model to see whether coefficients are changed at a possible break
date. The break dates are detected to provide an initial perspective on the time span of structural
breaks. Those timespans of structural breaks are important to investigate the price behaviours
on those selected markets. Finally, the study estimates both the connectedness and volatility
among infrastructure and property markets by using the dynamic conditional correlation
multivariate DCC-MGARCH model invented by Engle (2002).the DCC-GARCH model
provides higher flexibility than the conditional correlation CCC-MGARCH model and also
more parsimonious than the Diagonal VECH multivariate DVECH-MGARCH model (Engle,
2002). the DCC-MGARCH can be presented as:
/!* 01!, 2!
2!* $ 3!
#/&4!$$
(2)
Where:
/!
presents the
5 6 7
vector of dependent variables;
0
is the
5 6 7
matrix of parameters;
1!
present the
7 6 8
array of control variables including the lags of
/!
;
3!
#/&
presents the Cholesky factor of the time-varying conditional covariance matrix
3!
; and
4!
indicates the
5 6 8
vector of normal, independent and distributed identical innovations.
4. Results and discussion
The findings of cumulative sum tests for parameter stability with nine property and
infrastructure markets indicate that the estimated coefficients are stable over time, presented in
Table 2 Panel A and visualization presented in Fig. 2. While the cumulative sum tests for in
2
As the starting points vary for different equity indices, hence the study chooses a common time span that covers for all sample selected
equity indices which is from 6/8/2011 to 30/4/2021.

7
each time-series indicate the stability (no structural break), we extend the study by examining
the structural break with unknown break date, presented in Panel B. Interestingly, the findings
are consistent with S&P global property industrials, property residential and infrastructure
utilities; however, there are potential estimated break date for the other series.
Table 2:
Panel A: Cumulative sum test for parameter stability
Index
Statistic
Test
1%
critical
value
5%
critical
value
10%
critical
value
Conclusion
S&P's Global Infrastructure
recursive
0.1067
1.143
0.9479
0.85
No structural break
S&P's Global Property
recursive
0.0739
1.143
0.9479
0.85
No structural break
S&P's Global Property Diversified
recursive
0.049
1.143
0.9479
0.85
No structural break
S&P's Global Property Health Care
recursive
0.0387
1.143
0.9479
0.85
No structural break
S&P's Global Property Industrial
recursive
0.0683
1.143
0.9479
0.85
No structural break
S&P's Global Property Office Space
recursive
0.0911
1.143
0.9479
0.85
No structural break
S&P's Global Property Residential
recursive
0.0882
1.143
0.9479
0.85
No structural break
S&P's Global Infrastructure Utilities
recursive
0.0988
1.143
0.9479
0.85
No structural break
S&P's Global Infrastructure Industrials
recursive
0.1154
1.143
0.9479
0.85
No structural break
Ho: No structural break
Panel B: Test for a structural break: Unknown break date
Index
Estimated break date
Swald test
statistics
p-value
Conclusions
S&P's Global Infrastructure
1549 [2017-05-15]
44.9205
0.0000
Break
S&P's Global Property
1725 [2018-01-16]
64.3903
0.0000
Break
S&P's Global Property Diversified
1725 [2018-01-16]
56.4162
0.0000
Break
S&P's Global Property Health Care
1692 [2017-11-30]
35.954
0.0000
Break
S&P's Global Property Industrial
1725 [2018-01-16]
3.4905
0.8125
No structural break
S&P's Global Property Office Space
1721 [2018-01-10]
29.4976
0.0000
Break
S&P's Global Property Residential
1692 [ 2017-11-30]
9.4575
0.1174
No structural break
S&P's Global Infrastructure Utilities
1526 [2017-04-12]
1.957
0.9921
No structural break
S&P's Global Infrastructure Industrials
1549 [2017-05-15]
54.3892
0.0000
Break
S&P's Global Infrastructure Energy
1258 [2016-04-01]
32.2723
0.0000
Break
Ho: No structural break
Additionally, while the property and infrastructure markets have systematic structural breaks,
the unknown break dates are changed among different markets (see Table 1 Panel B). For
instance, while S&P global property, property diversified, and property industrial present their
estimated break on the similar date of 1725, S&P global property health care and property

8
residential break on 1692. S&P's Global Infrastructure, infrastructure industrials and
infrastructure utilities break earlier on the dates of 1549 [2017-05-15] and 1526 [2017-04-12],
respectively. S&P's Global Infrastructure Energy breaks at the earliest on the date 1258. The
findings release that even the property and infrastructure markets show a parameter stability
through the cumulative sum tests (Table 2 Panel A) in overall, but there are still unknown break
dates estimated among the infrastructure and property markets. it is also critical to notify that
the S&P global infrastructure for energy breaks at the earliest followed by the other markets
showing their structural breaks later such as S&P's Global Infrastructure Industrials, property
office space, global infrastructure, property health care, property diversified and property
global markets.
Figure 1. S&P Global Infrastructure and Property Indices (in log form) ranging from
6/8/2011 to 4/30/2021.

9

10

11
Figure 2: Cumulative sum test for parameter stability
With the presence of estimate unknown structural break dates estimated earlier, we continue
our study by employing the DCC-MGRACH model invented by Engle (2002) to detect the
dynamic correlations of volatility among the selected markets.
Tables 3 and 4 provide the estimated findings of the DCC-MGRACH models among property
and infrastructure markets, respectively. For the property markets presented in Table 2, the
results show that almost the correlations between ARCH(1), GRACH(1) and ARCH have
positive signs and statistically significant at 10%, 5% and 1% levels (from 0.012 to 0.984)
which compose the GRACH (1,1)’s conditions (Nelson & Cao, 1992). The results indicate that
the higher the errors and their variances during the previous date are related to the higher
error variances on the current date. It is worth to note that since the coefficients of ARCH (1)
are higher than the values of GRACH (1) for the S&P property industrials and property office
space indicating that the current systematic risk today relies on its previous volatility more
significantly detected in those two markets compared to the other ones.
The estimated conditional quasi-correlations among the property and infrastructure markets are
reported in Panel B of Tables 3 and 4, respectively. The correlation among the six property
markets (Global property, property diversified, property health care, industrial, office space
and residential) are positive and strong ranging from 0.589 (lowest value) to 0.953 (highest
value) and all the coefficients are statistically significant at 1% level. The results imply a very
strong correlations among the global property markets indicating that the higher the volatility
spillovers in the prices of those six property markets are related to the higher volatility
spillovers in the another one. This also suggests that the property market is not effectively
diversified. In other words, this market is not capable in its risk diversification. The results
further support to the unknown structural break dates estimated earlier that the property market
is exposed to bubble systematic risks. Conversely with the property markets, while the results

12
are consistent among the global infrastructure and infrastructure industrials only, the other
infrastructure markets show better capacity in risk diversification in themselves.
Table 3:
Panel A: Dynamic conditional correlation MGRACH model for property markets
Variables
Global
Property
Property
Diversified
Property
Health Care
Property
Industrial
Property
Office Space
Property
Residential
Cons
-0.0007
[0002]
-.0001
[.0024]
.0002
[.0027]
.0060
[.0061]
.0008
[.0022]
.0064
[.0039]
ARCH
L1.
0.0826***
[0.0057]
.1066***
[.0115]
.0126***
[.0024]
.0212*
[.0082]
.0189**
[.0060]
-.055***
[.0042]
GARCH
L1.
.2185***
[.0460]
.5141***
[.0432]
.9844***
[.0032]
-.7812***
[.0449]
-.7985***
[.0656]
.1774*
[.0765]
Cons ARCH
.01716***
[.0011]
.0099***
[.0010]
.00009*
[.00003]
.2538***
[.0095]
.0377***
[.0017]
.0510***
[.0047]
N
2,582
2,582
2,582
2,582
2,582
2,582
Log likelihood
17059.51
Lambda1
.0152***
[.0008]
Lambda2
.9740***
[.0015]
*, **, and *** indicate the significance level at 10%, 5% and 1%, respectively. Standard errors are presented in the parentheses
Table 3:
Panel B: the estimated conditional quasi-correlation in DCC-MGARCH model
Global Property
Property
Diversified
Property
Health Care
Property
Industrial
Property Office
Space
Property Diversified
.9255***
[.0064]
Property Health Care
.8249***
[.0155]
.7605***
[.0205]
Property Industrial
.7687***
[.0187]
.5891***
[.0291]
.4975***
[.0353]
Property Office Space
.9536***
[.0045]
.8829***
[.0104]
.8486***
[.0132]
.6067***
[.0290]
Property Residential
.8701***
[.0108]
.6737***
[.0236]
.5971***
[.0296]
.9407***
[.0052]
.7688***
[.0185]

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*, **, and *** indicate the significance level at 10%, 5% and 1%, respectively. Standard errors are presented in the parentheses
Table 4:
Panel A: Dynamic conditional correlation MGRACH model for infrastructure markets
Variables
Global
infrastructure
Infrastructure
Utilities
Infrastructure
Industrials
Infrastructure
Energy
Cons
-.0009
[.0026]
.0002
[.0026]
-.0017
[.0036]
-.0020
[.0046]
ARCH
L1.
.0097***
[.0015]
.0037
[.0021]
.0040***
[.0010]
-.0128***
[.0040]
GARCH
L1.
-.7004
[.0486]
.9371***
[.0340]
.9586***
[.0138]
.1210
[.1588]
Cons ARCH
.0337***
[.0010]
.0010
[.0005]
.0014**
[.0005]
.0505***
[.0090]
N
2,582
2,582
2,582
2,582
Log likelihood
12120.41
Lambda1
.0027***
[.0004]
Lambda2
.9967***
[.0001]
*, **, and *** indicate the significance level at 10%, 5% and 1%, respectively. Standard errors are presented in the parentheses
Table 4:
Panel B: the estimated conditional quasi-correlation in DCC-MGARCH model
Variables
Global
infrastructure
Infrastructure
Utilities
Infrastructure
Industrials
Infrastructure Utilities
.3961
[.4025]
Infrastructure Industrials
1.0166***
[.0922]
.2859
[.3908]
Infrastructure Energy
-.0214
[.4324]
-1.2915
[1.2534]
.2597
[.]
*, **, and *** indicate the significance level at 10%, 5% and 1%, respectively. Standard errors are presented in the parentheses
The findings shed further the light to the literature on the connectedness among different asset
classes including commodities (Balli et al., 2019; Kang et al., 2017; D. Zhang & Broadstock,

14
2018), equity (Maghyereh et al., 2016), cryptocurrencies (Bouri et al., 2020; Canh et al., 2019;
Ji et al., 2019), fixed income securities (Naeem et al., 2021; Nguyen, Naeem, Balli, Balli, &
Vo, 2021; Pham, 2021), among other markets (Demirer et al., 2020; Le et al., 2021) and
particularly among housing and rental markets (Antonakakis et al., 2018; Nguyen, Naeem,
Balli, Balli, & Syed, 2021; D. Zhang & Fan, 2019; D. Y. Zhang, Hu, & Ji, 2020) in the recent
years. Additionally, while the systematic spillover effects among several popular markets have
been detected recently, the study provides early findings on the dynamic spillover effects
among infrastructure markets as an asset class contributing the previous studies (Andonov,
Kräussl, & Rauh, 2018; Regan, 2005; Regele, 2018).
In the subject of investment portfolio diversification, the study further contributes to the field
by showing the spillover effects of systematic risk among the property and infrastructure
markets. Hence, investors would acquire their portfolio diversification by investing in different
property markets with the inclusion of infrastructure as an alternative asset class to mitigate
systematic risk. The study formally provides empirical evidence that it is in the context of the
global major property and infrastructure markets. In the empirical procedure, the study also
releases the decent characteristics and dynamic correlations among the selected market as an
asset class. The most recent related papers related to our study is Nguyen, Naeem, Balli, Balli,
and Syed (2021) and Squires, Webber, et al. (2021) disclosing the transmission between the
oil price (WTI), housing and rental markets at the multinational and national context,
respectively. We extend their research works by using the different major property markets
including property global, property office space, property health care, property industrial,
property office space and property residential.
5. Conclusion
Property markets including both residential and real estate have continuously attracted the
focus of international scholars, especially their transmissions from/to other markets in the
world. While scholars’ attention to property has been channelled mainly on residential using
the Residential Housing Price Indices (RPPI) and somehow missed the important presence of
infrastructure markets as an asset class providing the most daily fundamental but essential to
people’s lives. Motivated by those reasons, the study contributes to the literature through
investigating the efficiency of the property and infrastructure markets with their parameter
stability, structural unknown break dates and systematic risk spillover effects. Additionally,
this study considers for a range of several sub-markets for the global infrastructure and property

15
markets in its empirical examinations rather than only focuses on ‘residential’ (housing) market
in the most previous literature.
The study first releases that those markets presence a good presence of parameter stability in
their prices (in log form). However, there are still unknown structural breaks estimated in the
selected market and the break dates differ among different markets. Specifically, the S&P
global infrastructure energy breaks at the earliest followed by the other peer markets, while the
S&P office space breaks at the latest. Additionally, the study unveils a strong correlation among
the major property markets, while the infrastructure markets also show their connectedness but
at a lower degree. Finally, the systematic spillovers between the major global property and
infrastructure markets are detected through the results of DCC-MGARCH approach. The
results are positive and significant among those markets with the estimated coefficients of
ARCH (1) and GRACH (1) but there are still uncommon inverse estimated coefficients such
as the global property industrial, property office space, and infrastructure energy. The results
indicate that while almost the sample markets are lack of diversification capacity, the markets
with the inverse detection results show a better diversification capacity to mitigate the
systematic risk.
Lastly, this study shed first light on the connectedness and spillover effects among
infrastructure and property markets because it is critical to note that previous studies in the
recent years mainly focus on the property residential markets when studying ‘housing’ markets
that unintendedly misses the other important property markets and their functions.
Additionally, infrastructure as an alternative asset class and its spillover effects have not been
investigated or focused on significantly.

16
Appendix
Table A1: Descriptive statistics
Name
Time span, frequency
Market
N
Mean
Min
Max
St. Dev
S&P's Global Infrastructure
11/16/2001 - 4/30/2021, Daily
Global
2583
7.7519
7.4096
7.9693
0.1050
S&P's Global Property
6/30/1989 - 4/30/2021, Daily
Global
2583
5.2021
4.8124
5.4056
0.1115
S&P's Global Property Diversified
6/8/2011 - 4/30/2021, Daily
Global
2583
5.2450
4.8873
5.4443
0.1052
S&P's Global Property Health Care
6/8/2011 - 4/30/2021, Daily
Global
2583
4.9269
4.3438
5.1809
0.1109
S&P's Global Property Industrial
6/8/2011 - 4/30/2021, Daily
Global
2583
4.8727
4.2384
5.5330
0.2889
S&P's Global Property Office Space
6/8/2011 - 4/30/2021, Daily
Global
2583
5.1121
4.7774
5.3708
0.1091
S&P's Global Property Residential
6/8/2011 - 4/30/2021, Daily
Global
2583
5.4866
5.0180
5.8635
0.2048
S&P's Global Infrastructure Utilities
2/27/2009 - 4/30/2021, Daily
Global
2583
4.2530
4.0671
4.5392
0.1017
S&P's Global Infrastructure Industrial
2/27/2009 - 4/30/2021, Daily
Global
2583
4.6447
4.1971
4.9545
0.1645
S&P's Global Infrastructure Energy
2/27/2009 - 4/30/2021, Daily
Global
2583
4.9325
4.1951
5.3655
0.1823
Note: The data are extracted from Thompson Reuter DataStream.

17
Table A2: Granger causality Wald tests
Equation
Excluded
chi2
df
Prob > chi2
S&P Global Infrastructure granger to
S&P Global Infrastructure
S&P Global Property
32.898***
2.000
0.000
S&P Global Infrastructure
S&P Global Property Diversified
25.578***
2.000
0.000
S&P Global Infrastructure
S&P Global Property Healthcare
10.744**
2.000
0.005
S&P Global Infrastructure
S&P Global Property Industrials
73.969***
2.000
0.000
S&P Global Infrastructure
S&P Global Property Office Space
83.687***
2.000
0.000
S&P Global Infrastructure
S&P Global Property Residential
35.532***
2.000
0.000
S&P Global Infrastructure
S&P Global Infrastructure Utilities
329.17***
2.000
0.000
S&P Global Infrastructure
S&P Global Infrastructure Industrials
265.83***
2.000
0.000
S&P Global Infrastructure
S&P Global Infrastructure Energy
265.69***
2.000
0.000
S&P Global Infrastructure
ALL
2152.9***
18.000
0.000
S&P Global Property granger to
S&P Global Property
S&P Global Infrastructure
265.02***
2.000
0.000
S&P Global Property
S&P Global Property Diversified
1.422
2.000
0.491
S&P Global Property
S&P Global Property Healthcare
44.388***
2.000
0.000
S&P Global Property
S&P Global Property Industrial
125.19***
2.000
0.000
S&P Global Property
S&P Global Property Office Space
25.81***
2.000
0.000
S&P Global Property
S&P Global Property Residential
10.132**
2.000
0.006
S&P Global Property
S&P Global Infrastructure Utilities
318.26***
2.000
0.000
S&P Global Property
S&P Global Infrastructure Industrials
265.06***
2.000
0.000
S&P Global Property
S&P Global Infrastructure Energy
232.08***
2.000
0.000
S&P Global Property
ALL
2425.6***
18.000
0.000
S&P Global Infrastructure Diversified granger to
S&P Global Infrastructure Diversified
S&P Global Infrastructure
204.55***
2.000
0.000
S&P Global Infrastructure Diversified
S&P Global Property
24.91***
2.000
0.000
S&P Global Infrastructure Diversified
S&P Global Property Healthcare
21.046***
2.000
0.000

18
S&P Global Infrastructure Diversified
S&P Global Property Industrial
55.056***
2.000
0.000
S&P Global Infrastructure Diversified
S&P Global Property Office Space
6.9214*
2.000
0.031
S&P Global Infrastructure Diversified
S&P Global Property Residential
28.107***
2.000
0.000
S&P Global Infrastructure Diversified
S&P Global Infrastructure Utilities
261.01***
2.000
0.000
S&P Global Infrastructure Diversified
S&P Global Infrastructure Industrials
206.12***
2.000
0.000
S&P Global Infrastructure Diversified
S&P Global Infrastructure Energy
181.17***
2.000
0.000
S&P Global Infrastructure Diversified
ALL
1644.7***
18.000
0.000
S&P Global Property Healthcare granger to
S&P Global Property Healthcare
S&P Global Infrastructure
39.625***
2.000
0.000
S&P Global Property Healthcare
S&P Global Property
50.114***
2.000
0.000
S&P Global Property Healthcare
S&P Global Property Diversified
95.335***
2.000
0.000
S&P Global Property Healthcare
S&P Global Property Industrial
48.736***
2.000
0.000
S&P Global Property Healthcare
S&P Global Property Office Space
6.5324*
2.000
0.038
S&P Global Property Healthcare
S&P Global Property Residential
45.023***
2.000
0.000
S&P Global Property Healthcare
S&P Global Infrastructure Utilities
48.729***
2.000
0.000
S&P Global Property Healthcare
S&P Global infrastructure Industrials
48.8***
2.000
0.000
S&P Global Property Healthcare
S&P Global Infrastructure Energy
27.131***
2.000
0.000
S&P Global Property Healthcare
ALL
810.31***
18.000
0.000
S&P Global Property Industrial granger to
S&P Global Property Industrial
S&P Global Infrastructure
212.03***
2.000
0.000
S&P Global Property Industrial
S&P Global Property
93.234***
2.000
0.000
S&P Global Property Industrial
S&P Global Property Diversified
151.53***
2.000
0.000
S&P Global Property Industrial
S&P Global Property Healthcare
2.9916
2.000
0.224
S&P Global Property Industrial
S&P Global Property Office Space
140.69***
2.000
0.000
S&P Global Property Industrial
S&P Global Property Residential
23.273***
2.000
0.000
S&P Global Property Industrial
S&P Global Infrastructure Utilities
250.49***
2.000
0.000
S&P Global Property Industrial
S&P Global Infrastructure Industrials
208.41***
2.000
0.000
S&P Global Property Industrial
S&P Global Infrastructure Energy
206.2***
2.000
0.000

19
S&P Global Property Industrial
ALL
2811.5***
18.000
0.000
S&P Global Property Office Space granger to
S&P Global Property Office Space
S&P Global Infrastructure
150.46***
2.000
0.000
S&P Global Property Office Space
S&P Global Property
72.305***
2.000
0.000
S&P Global Property Office Space
S&P Global Property Diversified
7.6589*
2.000
0.022
S&P Global Property Office Space
S&P Global Property Healthcare
99.302***
2.000
0.000
S&P Global Property Office Space
S&P Global Property Industrial
103.72***
2.000
0.000
S&P Global Property Office Space
S&P Global Property Residential
15.562***
2.000
0.000
S&P Global Property Office Space
S&P Global Infrastructure Utilities
190.24***
2.000
0.000
S&P Global Property Office Space
S&P Global Infrastructure Industrials
150.05***
2.000
0.000
S&P Global Property Office Space
S&P Global Infrastructure Energy
134.67***
2.000
0.000
S&P Global Property Office Space
ALL
2405.6***
18.000
0.000
S&P Global Property Residential granger to
S&P Global Property Residential
S&P Global Infrastructure
277.21***
2.000
0.000
S&P Global Property Residential
S&P Global Property
49.342***
2.000
0.000
S&P Global Property Residential
S&P Global Property Diversified
44.906***
2.000
0.000
S&P Global Property Residential
S&P Global Property Healthcare
37.734***
2.000
0.000
S&P Global Property Residential
S&P Global Property Industrial
187.82***
2.000
0.000
S&P Global Property Residential
S&P Global Property Office Space
124.07***
2.000
0.000
S&P Global Property Residential
S&P Global Infrastructure Utilities
321.59***
2.000
0.000
S&P Global Property Residential
S&P Global Infrastructure Industrials
264.29***
2.000
0.000
S&P Global Property Residential
S&P Global Infrastructure Energy
255.58***
2.000
0.000
S&P Global Property Residential
ALL
3687.2***
18.000
0.000
S&P Global Infrastructure Utilities granger to
S&P Global Infrastructure Utilities
S&P Global Infrastructure
111.27***
2.000
0.000
S&P Global Infrastructure Utilities
S&P Global Property
101.6***
2.000
0.000
S&P Global Infrastructure Utilities
S&P Global Property Diversified
134.24***
2.000
0.000
S&P Global Infrastructure Utilities
S&P Global Property Healthcare
8.8101*
2.000
0.012

20
S&P Global Infrastructure Utilities
S&P Global Property Industrial
62.611***
2.000
0.000
S&P Global Infrastructure Utilities
S&P Global Property Office Space
225.19***
2.000
0.000
S&P Global Infrastructure Utilities
S&P Global Property Residential
6.582*
2.000
0.037
S&P Global Infrastructure Utilities
S&P Global Infrastructure Industrials
112.92***
2.000
0.000
S&P Global Infrastructure Utilities
S&P Global Infrastructure Energy
111.73***
2.000
0.000
S&P Global Infrastructure Utilities
ALL
2139***
18.000
0.000
S&P Global infrastructure Industrials granger to
S&P Global infrastructure Industrials
S&P Global Infrastructure
395.99***
2.000
0.000
S&P Global infrastructure Industrials
S&P Global Property
71.703***
2.000
0.000
S&P Global infrastructure Industrials
S&P Global Property Diversified
11.947**
2.000
0.003
S&P Global infrastructure Industrials
S&P Global Property Healthcare
23.747***
2.000
0.000
S&P Global infrastructure Industrials
S&P Global Property Industrial
110.6***
2.000
0.000
S&P Global infrastructure Industrials
S&P Global Property Office Space
51.426***
2.000
0.000
S&P Global infrastructure Industrials
S&P Global Property Residential
83.103***
2.000
0.000
S&P Global infrastructure Industrials
S&P Global infrastructure Utilities
463.14***
2.000
0.000
S&P Global infrastructure Industrials
S&P Global Infrastructure Energy
372.1***
2.000
0.000
S&P Global infrastructure Industrials
ALL
3060.2***
18.000
0.000
S&P Global Infrastructure Energy granger to
S&P Global Infrastructure Energy
S&P Global Infrastructure
9.3457**
2.000
0.009
S&P Global Infrastructure Energy
S&P Global Property
9.715**
2.000
0.008
S&P Global Infrastructure Energy
S&P Global Property Diversified
61.817***
2.000
0.000
S&P Global Infrastructure Energy
S&P Global Property Healthcare
0.46451
2.000
0.793
S&P Global Infrastructure Energy
S&P Global Property Industrial
18.542***
2.000
0.000
S&P Global Infrastructure Energy
S&P Global Property Office Space
21.365***
2.000
0.000
S&P Global Infrastructure Energy
S&P Global Property Residential
109.18***
2.000
0.000
S&P Global Infrastructure Energy
S&P Global infrastructure Industrials
17.016***
2.000
0.000
S&P Global Infrastructure Energy
S&P Global infrastructure Utilities
3.1142
2.000
0.211
S&P Global Infrastructure Energy
ALL
2312.4***
18.000
0.000

21
* p < 0.05, ** p < 0.01, *** p < 0.001

22
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