Discussion Paper No. 1030

MACRO ASPECTS OF HOUSINGCharles Ka Yui Leung
Joe Cho Yiu Ng

May 2018

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Macro Aspects of Housing
Charles Ka Yui LEUNG, Joe Cho Yiu NG, City University of Hong Kong
This version: May, 2018
Abstract
This paper aims to achieve two objectives. First, we demonstrate that with respect to business cycle
frequency (Burns and Mitchell, 1946), there was a general decrease in the association between
macroeconomic variables (MV) and housing market variables (HMV) following the global
financial crisis (GFC). However, there are macro-finance variables that exhibited a strong
association with the HMV following the GFC. For the medium-term business cycle frequency(Comin and Gertler, 2006), we find that while some correlations exhibit the same change as thebusiness cycle counterparts, others do not. These “new stylized facts” suggest that areconsideration and refinement of existing “macro-housing” theories would be appropriate. We
also provide a review of the recent literature, which may enhance our understanding of the evolving
macro-housing-finance linkage.

Keywords: stylized facts, macro-housing-finance linkage, Global Financial Crisis, business cycle
frequency, housing market variables
JEL Classification Numbers: E30, G10, R30
Acknowledgment:This draft is prepared for the Oxford Research Encyclopedia of Economics and Finance(http://economics.oxfordre.com/), edited by Jonathan Hamilton, to be published by Oxford
University Press. We thank all our (former and current) co-authors, colleagues, teachers,
conference discussants, and referees (whose identities are unknown to us) for all the comments,
especially (in alphabetical order) Nan-Kuang Chen, Bob Edelstein, Eric Hanushek, Yuichiro
Kawaguchi, Fred Kwan, Steve Malpezzi, Tim Riddiough, Jim Shilling, Chung Yi Tse, Ko Wang,
Ping Wang for sharing their many insights over the years and City University of Hong Kong for
financial support.

Macro Aspects of Housing
Contents
SectionPage

1. Introduction

2

2. Stylized facts

3

2.1. Business Cycle Frequency

3

2.2. Medium Cycle Frequency

13

2.3. A Summary

20

3. A Review of Selected Literatures

21

3.1. Bankruptcy and Mortgage Contracts

22

3.2. Search and Belief

28

3.3. Urban Development and Housing Market

35

3.4. Urban Policy and Human Capital38

4. Concluding Remarks

40

Appendix

42

Tables and Figures

43

Reference49

1

1. Introduction
As suggested by the title, this chapter attempts to provide an incomplete
overview of the research that highlights the macroeconomic aspects of the
housing market. 1 It is incomplete because the literature has been constantly
growing, especially following the global financial crisis (GFC), and hence isalmost impossible to review completely. Therefore, we would like to apologize
in advance as some insightful papers may not have been discussed in this chapter,
not because they are unimportant, but simply because they have been discussed
in detail elsewhere. For instance, there have been several similar attempts todiscuss the literature in special issues of academic journals, survey papers, andmonographs.2

According to Leung (2004), housing was not included in traditional
macroeconomics. However, on account of a few path-breaking papers, much haschanged. 3 While prior literature focuses on residential investment and how itinteracts with other macroeconomic variables such as business investment, grossdomestic product (GDP), and so on, extant literature quickly expands to cover
house price, transaction volume, vacancy, and so on.4 As one of the objectives ofthis paper is to provide a general overview of the related research, we re-examine
1
This paper focuses on housing. Related literature covers studies on land markets, which is beyond the scope of
this paper. See Davis and Palumbo (2008), Krainer et al. (2010), Leung and Chen (2006), Liu et al. (2013),
Ogawa et al. (1996), among others, and the references therein.
2
The list is growing constantly, and it is difficult to provide a “complete list” here. See Bostic and Ellen (2014),
Davis and Van Nieuwerburgh (2014), Hendershott et al. (2010), Ihlanfeldt and Mayock (2015), Jordà et al. (2016),
Malpezzi (2017a, b, c), McMillen (2011), Piazzesi and Schneider (2016), Sanders and Van Order (2011), among
others, and the references therein.
3
See Baxter (1996), Greenwood and Hercowitz (1991), Kiyotaki and Moore (1997), among others.
4
See Aoki et al. (2004), Chang (2000), Davis and Heathcote (2005), Iacoviello (2005), Iacoviello and Minetti(2008), Jin and Zeng (2004), Kan et al. (2004), Kwong and Leung (2000), Leung (1999, 2003, 2014), Leung andFeng (2005), Leung et al. (2002a, b), Lin et al. (2004), Ortalo-Magné and Rady (2006), Tse and Leung (2002),
among others, and the references therein.

2some “stylized facts” of how the macroeconomic variables (MV) on the one hand,and housing market variables (HMV), on the other hand, are correlated.
Hopefully, this will inspire new research on macro-housing. Again, for the sakeof inspiring new research, we then selectively review some of the recent literature.
In the final section, we conclude this paper.

2. Stylized Facts
2.1. Business Cycle Frequency
We first focus on the business cycle frequency. To establish some “stylized
facts” on the “macro aspects of housing,” we follow the approach of Cooley and
Prescott (1995), which provides some (unconditional) correlations between MV
and HMV in the United States, where most macroeconomic research is done.5
Clearly, studies on the macroeconomic aspects of housing have used data fromdifferent countries.6 Here, we use data from the United States because (1) they
are the most accessible, and (2) most “macroeconomic research” uses U.S. dataand hence our use of the same data will facilitate comparison. Our list of HMV
includes not only the price index (which is the focus of most research), but also
the number of new houses sold, the vacancy rate, and the residential investment.
Owing to the well-known debate on the potential bias with respect to appraisals,
we use the transaction-based house price index.7 Hence, we trade off the length5

For an introduction to the U.S. housing market, see Green and Malpezzi (2003), among others. For a comparisonof the U.S. mortgage system with that in other countries, see Green (2014), Green and Wachter (2005), Cho (2007,2009), among others.
6
The literature is too vast to be reviewed here. See Bardhan et al. (2004, 2008, 2012), Ben-Shafar et al. (2008),
Cesa‐Bianchi et al. (2015), Chang and Chen (2012), Chao and Yu (2015), Cheung et al. (2017), Edelstein and Kim(2004), Ho et al. (2008), Kawaguchi (2009), Kim (2012), Leung (2017), Leung and Chen (2017), Leung and
Quigley (2007), Leung and Tang (2012), Lum (2012), Malpezzi and Sa-Aadu (1996), Mera and Renaud (2000),
Seek et al. (2014), Seko et al. (2012), Tirtiroglu (2012), Tiwari (2001), among others, and the references therein.
7
The literature is too vast to be reviewed here. See Gau and Wang (1991), Geltner (1991), Geltner et al. (2003),
among others.

3

of the time series data for a less controversial interpretation of the results. Except
for a few variables such as the consumer price index (CPI) and federal funds rate(FFR), all of the other variables are represented in real terms.
Following Burns and Mitchell (1946) and most subsequent research on
business cycles, this section focuses on the “cyclical components,” i.e.,
components with periodicity between 6 and 32 quarters. As many of the variables
are non-stationary, moments (including correlations) are not well defined. The
variables need to be detrended, and we therefore use the following procedures.
First, we use the band-pass filter developed by Christiano and Fitzgerald (2003)
to extract the “cyclical components.” 8 Second, we not only report thosecorrelations, but also test whether they are statistically significant or not. Third,
we compare two sampling periods: (1) from 1991 to 2006, which will be referred
to as the pre-crisis sub-sample (PCSS), and (2) from 1991 to 2017Q3, which will
be referred to as the full sample (FS). Some authors argue that there has been a“structural change” following the GFC. We therefore compute the correlations inboth sampling periods and examine whether there are indeed some importantdifferences. There is one technical issue here. Forbes and Rigobon (2002)
demonstrate that if the volatility of a variable increases over time, the measured
correlation could be biased. We mitigate this concern by following Stock andWatson (2002) to first standardize the volatility of all variables, and then computethe correlations among different variables. We explain the details in the appendix.
8

See Baxter (1991, 1994), Canova (1998), among others, who show that “stylized facts” are not robust to different
filtering methods and the first-difference filter exaggerates the high-frequency components. Burnside (1998)
shows that “stylized facts” are indeed robust if one turns to the frequency domain. Cogley and Nason (1995), Kingand Rebelo (1993) show that the Hodrick-Prescott (HP) filter creates spurious serial correlations and distorts“stylized facts.” Baxter and King (1999) and Christiano and Fitzgerald (2003) show that the band-pass filter,
which builds on some results in the frequency domain, is statistically “superior” to the commonly used HP filter.
In the present context, the “full sample” includes the GFC, which could be a high-frequency event for some data
series, and at the same time a lasting event for other series. As we do not know a priori in which series the GFC
is short-lived, and in which it is a long-lasting event, it is natural to use the band-pass filter to ensure that thecorresponding periodicities of the components that we extract are precise.

4

Table 1 Panel A shows the correlations (contemporaneous, one-period-lead,and one-period-lag) among the housing market variables and the moreconventional macroeconomic variables. Table 1 Panel B shows the counterparts
among the housing market variables and the macro-finance variables. The idea is
to investigate whether some macroeconomic variables may be “leading” thehousing market variables, or vice versa.9(Table 1 about here)

Several observations are in order. First, most correlations are significant,suggesting that the (aggregate) housing market variables and the macroeconomic
variables are indeed closely related. In other words, the “macro-housing”
literature is justified. Second, while most correlations in the two sampling periods
are similar, there are cases with some noticeable differences. For instance, in the
PCSS, the real GDP, and vacancy rate of the for-sale housing were significantly
and negatively correlated. The unemployment rate and house prices were alsosignificantly and negatively correlated. The idea is simple. When the economy
receives a positive shock, firms hire more labor and people are more willing topurchase housing units, resulting in an increase in the aggregate output and adecrease in the unemployment rate. At the same time, the house prices increase
and the vacancy rate of the for-sale housing market decreases. However, for the
full-sample, such intuitive correlations disappear. Clearly, these are simple
correlations and they provide no proof of causality. Nevertheless, they suggest
perhaps that there is a change in the dynamics between the macroeconomy and9
Clearly, the treatment here is heuristic. For further treatment of the subject see Berge (2015), Camacho and PerezQuiros (2002), among others, and the references therein.

5the housing market, which may be related to the “jobless recovery” following the
GFC in the sense that the aggregate GDP rebounds much faster than the labormarket. Moreover, the slow recovery of the labor market also affects the recoveryof the housing market.10 This is discussed in depth later.
Another set of important correlations is related to the level of the CPI. Thisis clearly important because many undergraduate students were taught that the
CPI and inflation are at the core of macroeconomics.11 Moreover, the mandateof several central banks is tied to some sort of “price stability.” Therefore, we
believe that it is important to examine the correlations between the CPI on the
one hand, and the housing variables on the other hand. Table 1 Panel A shows that
before the GFC, the CPI was positively correlated to house prices. However, thestatistical significance disappears when we consider the full sample, suggestingthat the relationship between the CPI and house prices has also “weakened” after
the GFC. Moreover, the correlations between the CPI on the one hand and otherhousing variables on the other hand also tend to be insignificant, which isconsistent with the recent literature that suggests that the relationship between the
inflation rate and other macroeconomic variables may have changed after theGFC.12

The fourth row of Table 1 Panel A also shows that the real private nonresidential fixed investment had a strong positive correlation with real house price,
and a negative correlation with the for-sale housing vacancy rate in the PCSS.
This intuition is simple to explain. When the economy is booming, more
10

For a general discussion on recovery and labor markets, see Christiano et al. (2015, 2016), among others. For a
discussion on the slow recovery and the housing markets, see Garriga and Hedlund (2017), Hedlund (2016 a, b),
Luo (2017), among others, and the references therein.
11
For instance, see Hubbard and O’Brien (2014). See also Doepke and Schneider (2006), among others.
12
The literature is too vast to be reviewed here. See Del Negro et al. (2015), Gilchrist et al. (2017), Hall (2011),
King and Watson (2012), among others.

6

investment is made for non-residential fixed assets. At the same time, the demandfor housing increases and hence house prices increase and the vacancy rate
decreases, which explains the observed correlations. Conversely, once we include
the post-crisis years, the correlation between non-residential fixed investment andhouse prices weaken, and the correlation between the non-residential fixed
investment and the for-sale housing vacancy rate becomes insignificant. Similarly,
while non-residential fixed investment and residential investment are evidently
correlated, 13 the correlations seem to weaken after the GFC. In fact, thecorrelation between the prior period of non-residential investment and the current
period of residential investment was around 0.4 before the GFC. The same
correlation drops to about 0.15 and becomes statistically insignificant in the fullsample. Again, we observe a “weakening” of the link between the macroeconomy
and the housing market.

The same “weakening” may also be exhibited in consumption. The “wealtheffect of consumption” is being discussed even in undergraduate macroeconomic
textbooks. There is extensive literature on whether (and how) fluctuations inhousing wealth and stock market wealth affects consumption.14 Table 1 Panel A
displays many correlations between the aggregate private consumption on the one
hand, and the housing market variables on the other hand. The correlations
between consumption and house price ranged from 0.66 to 0.73 before the GFC.
However, when we consider the full sample, those correlations drop to between
0.41 and 0.58. The intuitive correlations between consumption and the vacancy
13

It has been studied extensively. See Greenwood and Hercowitz (1991), Chang (2000), Chen and Liao (2017),
among others, and the references therein.
14
The literature is too vast to be reviewed here. See Bostic et al. (2009), Calomiris et al. (2009), Carroll et al.
(2011), Case et al. (2005), Gerardi et al. (2018), Kaplan et al. (2016), Zhou and Carroll (2012), among others, andthe references therein.

7

rate are negative and statistically significant. When the economy booms, people
consume more and are simultaneously more willing to buy a house, and hence
the vacancy rate drops. However, those correlations become insignificant when
we consider the full sample. Again, it only adds to the evidence that thecorrelations between housing market variables and macroeconomic variables
weakened after the GFC.

Similarly, before the GFC, the correlations between the trade surplus andhouse prices were high, and were around -0.77.15 At the same time, the trade
surplus (in real terms) is positively related to the vacancy rate of for-sale housing.
The intuition here is also simple to explain. When the trade account has a surplus,
the capital account is in deficit, suggesting that there is an outflow of capital. Withan outflow of capital, it is natural to expect that house prices fall and the vacancy
rate of housing increases. 16 However, when the years following the GFC are
included, the correlations between trade surplus and house prices drop to between-0.30 and -0.48. The correlations between the trade surplus and the vacancy rateof for-sale housing are also significantly reduced, and some even become
statistically insignificant.
Table 1 Panel B shows the correlations between some “macro-finance”
variables on the one hand, and the housing market variables on the other hand.
We begin with the Federal Fund Rate (FFR), which is often considered as the“policy rate,” an indicator of the “tightness” of the monetary policy. The first row
presents the results for the nominal FFR and the second row presents thecounterpart for the real FFR, which is defined as the difference between the15

There are studies relating the housing market to international trade, both theoretically and empirically. See
Bardhan et al. (2004), Corrigan (2017), Leung (2001), Leung et al. (2013), among others.
16
See Aizenman and Jinjarak (2009), Tomura (2010), among others, and the references therein for related analysis.

8nominal FFR and the inflation rate (based on the CPI). Note that after the GFC,
the Federal Reserve cuts the nominal interest rate to almost zero and many authors
argue that the “zero lower bound” (ZLB) introduces distortions in both parameter
estimation as well as welfare cost. To formally study the ZLB, however, is a very
involved process.17 Therefore, we introduce the real FFR instead, which does nothave a ZLB for comparison. Comparing the first and second rows of Table 1 PanelB, it is evident that the results related to the nominal and real FFR are usuallysimilar, which is perhaps because the CPI inflation rate is dominated by highfrequency components. As the Christiano and Fitzgerald band-pass filter
accurately extracts only the business cycle components (i.e., components withperiodicity between 6 and 32 quarters), the impact of inflation on the FFR is
minimal. Clearly, the FFR is positively correlated to the real house price, and only
weakly correlated with other housing market variables. This may sound counterintuitive because a higher interest rate should discourage people from investing.
However, if we take the endogeneity of the FFR into consideration, the correlation
between the FFR and house prices can be understood better. Nakamura andSteinsson (2017) explain this well:18“…The Federal Reserve lowered interest rates aggressively in 2008 as
evidence mounted that the economy was heading for a severe downturn. Suppose
one sought to use this variation in monetary policy to estimate the effect ofmonetary policy on the economy by estimating an OLS regression of the change
in output on the change in interest rates. Doing this might lead one to conclude
that reductions in interest rates lead to decreases in output. Would this constituteconvincing evidence on the effects of monetary policy? Of course not. The reason
17

The literature is too vast to be reviewed here. See Gust et al. (2017), Hirose and Inoue (2016), Wu and Xia(2016), among others.
18
See Sims (2010, 2012), among others.

9the Fed was lowering interest rates was that other factors—such as rapidly fallinghome prices and their effects on the balance sheets of households, firms, andbanks—were negatively affecting the economy. In a simple OLS regression, theseother factors would confound the effects of the change in monetary policy. Thisapproach would, therefore, uncover not the pure effect of the interest rate
reduction, but rather, the combined effect of the interest rate reduction and theadverse macroeconomic factors that led the Fed to undertake it.”In the literature, therefore, researchers have used other interest rates, as
proxies of the credit market conditions, and examine the co-movements of thoseinterest rates and the housing market variables.19 Table 1 Panel B also shows how
these interest rates are related to housing market variables. For instance, clearly
the term spread, which is the difference between the long-term and short-term
interest rate, is negatively correlated with house prices and residential investment.
Interestingly, while the correlations between the macroeconomic variables on the
one hand and the housing market variables, on the other hand, weakened after the
GFC, the correlation between the term spread and the residential investment
became stronger. Furthermore, the correlations between the term spread and thenumber of new houses sold are either enforced or turning from statisticallyinsignificant to negatively significant.

The Treasury-EuroDollar rate (TED) spread is the difference between ameasure of the interbank interest rate and the risk-free rate. An increase in TED
is often interpreted as an increase in the cost of external funds for financial

19
The literature is too vast to be reviewed here. See Chang et al. (2010, 2011, 2012, 2013, 2016), Chen and Wang(2007, 2008), Jin et al. (2012), Malpezzi (2017a, c), Yavuz (2014), among others, and the references therein.

10intermediaries. Not surprisingly, it is not significantly related to either the house
price or the residential investment before the GFC. However, when we examine
the same correlation for the full sample, the TED spread is negatively correlatedwith both house prices and the residential investment. In fact, it seems to be“leading” both house prices and the residential investment. The correlations
between the TED spread and the number of new houses sold are also strengthened
after the GFC. Such changes may be related to two factors: (1) the manner inwhich the Federal Reserve Bank implements the monetary policy,20 and (2) the
adoption of the unconventional monetary policy (UMP) since the GFC. Recent
research confirms that the UMP impacts the financial institutions and theeconomy through different channels. 21 Table 1 Panel B simply confirms that
research in the context of the housing market.

The case for the external finance premium (EFP) is interesting. The EFP is
the difference between the prime bank lending rate and the 3-month Treasury-bill(T-bill) rate. An increase in EFP is often interpreted as an increase in the cost of
external funds for non-financial firms, and it has been used in many types ofresearch.22 Table 1 Panel B shows that its correlation with the house price isnegative. On the other hand, it had a positive and significant correlation with thevacancy rate before the GFC. The idea is that when the credit market is tight, it isdifficult for both firms and households to obtain credit. And when households
cannot obtain credit, many of them cannot purchase homes. Hence, both the EFP
and the vacancy rate of the for-sale housing increase, and the house prices
20

See Frost et al. (2015), Ihrig et al. (2015), among others.
The literature is too vast to be reviewed here. See Bhattarai and Neely (2016), Chodorow-Reich (2014), Gertler
and Karadi (2011), Gertler and Kiyotaki (2011), among others, and the references therein.
22
See Bernanke and Gertler (1995), Bernanke et al. (1999), among others. Jin et al. (2012) modify the frameworkof Bernanke et al. (1999) and study how the EFP and housing price can interact.
21

11

decrease. When we consider the full sample, i.e., when the GFC and thesubsequent years are taken into consideration, the correlations between the EFP
and the vacancy rate of for-sale housing weaken, and some even become
statistically insignificant. At the same time, the negative correlation between the
EFP and house prices is “strengthened” in the sense that it becomes more negative.

There is extensive literature on the co-movement between the housing market
and the stock market.23 Table 1 Panel B shows that the correlations between thehouse price and stock price (measured by the S&P 500 index) are indeed positiveand statistically significant, both before and after the GFC. There is a subtle
difference here. In the PCSS, the correlation between the lagged stock price of
one period and the house prices of the current period is larger than thecontemporaneous correlation, which in turn is larger than the correlation between
the stock price of one period ahead and the house prices of the current period,
suggesting that the stock price is somewhat leading the house price. As we
consider the full sample, i.e., including the years after the GFC, we find thereverse pattern, suggesting that the stock price is somewhat lagging the house
price. Clearly, a formal testing for leading versus a lagging relationship would
need more sophisticated tests and perhaps a longer time series. Nevertheless, thissuggests a possible change in the relationship between the stock and housing
markets. At the same time, as we compare the correlations between the stock priceon the one hand, and the other HMV on the other hand (including the number of
new houses sold, the vacancy rate of for-sale housing, and the private residential
fixed investment), we see a “general weakening” of the relationship. For instance,
23

The literature is too vast to be reviewed here. See Chang et al. (2012, 2013, 2016), Chu (2010), Davis and Martin(2009), Kwan et al. (2015), Leung (2007), Piazzesi et al. (2007), Quan and Titman (1999), among others, and thereferences therein.

12the relationship between the stock price and the number of new houses soldremain positive, but the numerical values drop in the full sample. Somecorrelations between the stock price and the housing vacancy rate turn fromnegative and significant to insignificant. The correlations between the stock priceand the residential investment remain positive but are numerically much smaller.
Clearly, it is pre-mature to conclude a “de-coupling” between the stock market
and housing market. At the same time, it seems important to examine whether
and how the relationship between the stock and housing market has changed after
the GFC.

2.2. Medium Cycle Frequency

Thus far, we have focused on business cycle frequency, which many
macroeconomic studies have also focused on. However, some authors proposethat we should focus on the “longer run.”24 Here, we follow Comin and Gertler(2006) to study components with periodicity between 32 and 80 quarters, which
we label as “medium-run components.” We are aware that our sampling period isrelatively short and hence the estimate of the medium cycles may not be as
accurate as it should be. Constrained by the unavailability of data, we can only
recognize the limitations and proceed nevertheless. To facilitate the comparison,
we repeat the exercise in the previous section with the “medium-run components.”
The results are reported in Table 2, which are identical to those in Table 1, exceptthat the correlations are now correlations among medium-run components rather
than cyclical components. As in the case of cyclical components, most24
See Drehmann et al. (2012), among others. Borio (2014, p.183) claims “the financial cycle has a much lower
frequency than the traditional business cycle…”

13correlations are statistically significant, suggesting that the macroeconomy andthe housing market are closely related in the medium run as well. At the sametime, we do observe some difference between the PCSS and the full sample, andfocus our discussion on those differences.

Given the structure, we begin with the first row in Table 2 Panel A, thecorrelations between the GDP on the one hand, and housing market variables on
the other hand. Interestingly, while the correlations between GDP and housing
market variables are weakened in the business cycle frequency, they arestrengthened in the medium-cycle frequency. For instance, the correlations
between the cyclical components of GDP and the vacancy rate of a for-salehousing turn from negative and significant to insignificant, while the mediumcycle counterparts turn from mostly insignificant to mostly negative andsignificant. Undoubtedly, this is a challenge for future research to construct atheoretical model to explain these changes.25

Such a challenge is not limited to the relationship between GDP and housing
market variables. As we study the second row of Table 2 Panel A, we find that thecorrelations between the medium-run components of the unemployment rate andhouse price are strengthened, while the counterparts in cyclical components are
weakened. Moreover, while the correlations between the cyclical component of
the unemployment rate and the number of new houses sold are mostly
insignificant, they are negative and significant in the medium-run component.
Furthermore, the correlations are strengthened after the GFC. While the25

Research efforts have been devoted to explaining the heterogeneous “stylized facts” across different frequencies.
See Pancrazi (2015), who show how a change in the persistence of the exogenous shocks can generate“heterogeneous great moderation,” among others.

14correlations between the cyclical components of the unemployment rate and thevacancy rate of for-sale housing are mostly negative in the full sample, thecounterparts in the medium-run components are mostly positive in the full sample,
which seems to be more intuitive. When the economy is hit by a bad shock, theunemployment rate increases and hence the demand for housing drops, which inturn leads to an increase in the vacancy rate of housing.

Note that there are also situations in which patterns in cyclical components
and medium-run components are consistent. For instance, the third row of Table
2 Panel A shows that the correlations between the medium-run components of
CPI and (real) house price are negative and significant, but the correlations are
obviously weakened in the full sample. This is in line with the finding in thecyclical component that the positive correlation between the two variables turnfrom positive and significant to mostly insignificant. In fact, the correlations
between the medium-run components of CPI and other housing market variables(the number of new houses sold, a vacancy rate of for-sale housing, and private
residential fixed investment) are dramatically weakened in the full sample. Thus,
it is in line with the idea that changes in nominal variables have limited long-run
impact on real variables.26
The case for private non-residential fixed investment also poses achallenge. It is well known that the non-residential fixed investment and theresidential counterparts are positively correlated with business cycle frequency.27
Table 2 Panel A reveals that in fact, the counterpart in medium-cycle frequency
is negatively correlated before the GFC. It, however, turns to be positive andClearly, the treatment here is heuristic. The literature on “money neutrality” is too large to be discussed here.
See King and Watson (1997), Vaona, A. (2015), among others, and the references therein.
27
See Baxter (1996), Chang (2000), Greenwood and Hercowitz (1991), among others, and the references therein.
26

15

significant in the full sample. Similarly, the correlations between the medium-run
components of the non-residential investment and house price are negative before
the GFC and become positive and significant in the full sample. This is in contrast
to the case of cyclical components, which remain positive and significant in the
PCSS and the full sample.

The correlations between the medium-run components of trade surplus andhousing prices somewhat differ from the cyclical component counterpart. In thecase of cyclical components, the correlations between the trade surplus are
reduced from the -0.76 to -0.78 range to the -0.30 to -0.48 range as we extend
from the PCSS to the full sample. In the case of medium-run components,
however, the correlations are always in between -0.90 and -0.99, suggesting thatin real terms, the international capital flow and house prices are more correlated
in the medium run than in the business cycle frequency. In fact, the correlations
between the trade surplus on the one hand, and the number of new houses soldand the private residential fixed investment, on the other hand, display a similar
degree of co-movements. Thus, even for a large country like the United States,
where net exports constitute around 10% of the GDP, international capital flows
are important for the housing market. Future research may further explore thisdimension.

Table 2 Panel B exhibits the correlations between the medium-run
components of the macro-finance variables on the one hand, and housing market
variables on the other hand. Its format closely follows that of Table 1 Panel A,
where the counterpart of the business cycle components is displayed. The firstrow shows the correlation between the nominal FFR and the housing market
16variables. Its “pattern” dramatically differs from the counterparts of the cyclicalcomponents. For instance, the correlations between the medium-run componentof the nominal FFR and the house price are statistically significant, yetnumerically small (in the range of 0.17 to 0.33 in the full sample). In contrast, inthe case of cyclical components, the correlations are in the range of 0.55 to 0.69,
and they are statistically significant. The correlations between the medium-run
components of the nominal FFR and the vacancy rate of for-sale housing are in
the range of 0.84 to 0.93 in the PCSS, and in the range of 0.57 to 0.70 in the fullsample. Although the correlations are “weakened,” they remain statisticallysignificant. On the other hand, the cyclical counterpart is mostly insignificant. At
the same time, the correlations between the medium-run components of thenominal FFR and private residential fixed investment become marginallysignificant or even insignificant in the full sample. The cyclical component
counterparts are also statistically significant at the 1% level and in the range of
0.33 to 0.60. In other words, the co-movements between the nominal FFR and the
housing market are very different in the business cycle frequency and in themedium cycles.

In the previous section, we have also shown in the business cycle frequency,
the correlations between nominal FFR and housing market variables, and thosebetween the real FFR and housing market variables are similar. In the medium
run, however, this is not always the case. For instance, the second row of the Table
2 Panel B shows that the correlations between the real FFR and real house priceare negative and significant before the GFC. When we consider the full sample,
those correlations become numerically small and statistically insignificant. The
counterpart in the business cycle frequency is always positive and significant,17whether in the PCSS or in the full sample. In other cases, the behavior of themedium-run components of nominal and real FFR seem to be similar. Both thenominal and real FFR are positively correlated with the vacancy rate of the forsale housing in the medium run, while almost un-correlated with the vacancy ratein the business cycle frequency. Both the nominal and real FFR are statisticallycorrelated with the number of new houses sold before the GFC in the medium run
and then become almost uncorrelated in the full sample, while they are typicallyuncorrelated with the number of new houses sold in the business cycle frequency.
As monetary research constitutes a significant part of the macroeconomic
research, accounting for these differences may be important for future modelingdevelopment.

The third row of the Table 2 Panel B shows how the term spread correlateswith the housing market variables. It is interesting to note that before the GFC,
the medium-run term spread is only weakly correlated with the house price in the
PCSS. It becomes statistically correlated with the house price in the full sample.
Yet the numerical values are somewhat small, in the range of -0.18 to -0.25, whichis in sharp contrast to the case of business cycle frequency. The correlations
between the cyclical components of term spread and house price are always
between -0.61 and -0.70, and they are statistically significant. The cyclicalcomponent of the term spread is also negatively correlated with the number of
new houses sold in the full sample, with correlations between -0.20 and -0.40. In
the medium run, however, the two variables are more or less uncorrelated.

Similarly, a dramatic difference is observed in the TED spread. The fourth
row of Table 2 Panel B clearly shows that the correlations between the medium18

run components of the TED spread and house price are negative and significant
before the GFC and become almost insignificant in the full sample. In the cyclicalcomponent counterpart, while the two variables are not correlated before the GFC,
they become negatively and significantly correlated in the full sample. Moreover,the medium-run components of the TED spread and the vacancy rate of the forsale housing are significantly correlated. The correlations range between 0.75 and
0.80, whether in the PCSS, or during the full sample. The cyclical components ofthe same pair of variables are almost uncorrelated.

While the relationships between the EFP and housing market variables are
similar in the business cycle frequency and in the medium-cycle frequency, therelationships between the stock price (measured by the S&P 500 index, in realterms) and housing market variables are very different in the two frequencies.
Recall from Table 1 Panel B that the cyclical components of the stock price andhouse price are positively (and significantly) correlated, both before the GFC andin the full sample. Table 2 Panel B, however, shows that the medium-cycle
components of the same pair of variables are negatively and significantly
correlated before the GFC, with correlations between -0.36 and -0.42. In the fullsample, the two asset prices become uncorrelated. Similarly, the cyclicalcomponents of the stock price and the number of new houses sold are positively
and significantly correlated, both before the GFC and in the full sample. However,
the medium-cycle components of the same pair of variables are negatively andsignificantly correlated before the GFC, with correlations between -0.23 and 0.27. In the full sample, the stock price and number of new houses sold become
positively correlated. The correlations are statistically significant, but
economically weak, in the range of 0.25 to 0.26. The cyclical components of the19stock price and private residential investment is positively and significantly
correlated, both before the GFC and in the full sample. The correlations are 0.55
or above. However, the medium-cycle components of the same pair of variables
are negatively and significantly correlated before the GFC, with correlations
between -0.31 and -0.33. In the full sample, the stock price and residential
investment become positively correlated. The correlations are statisticallysignificant, but economically weak, in the range of 0.22 to 0.23.

2.3. A Summary
Here we provide a quick summary. For the business cycle frequency (or“cyclical components,” i.e., components with periodicity between 6 and 32
quarters), while macroeconomic variables and housing market variables arecorrelated in many dimensions, we find that some “stylized facts” indeed change
after the GFC. More specifically, many intuitive correlations between MV on the
one hand and HMV, on the other hand, are weakened. At the same time, several
measures of interest rates have their correlations with HMV strengthened. Thesechanges may be important because we may have built theoretical models to
explain the “old stylized facts,” and this is how our “intuitions” are formed. The
revision of those stylized facts may be a call for refining some existing models ofmacro-housing. Hopefully, we can see more refined models that are consistent
with both the “stylized facts” for the period before the GFC, as well as the period
after. 28 For the medium-cycle frequency, some correlations follow changes
similar to their counterparts in business cycle frequency, while others are very28
See Benes et al. (2014), Del Negro et al. (2013, 2015), Funke et al. (2017), Guerrieri et al. (2015), among others,
for related efforts.

20

different. Apparently, existing models are relatively silent on these differences,which reinforces the call for more serious theoretical modeling efforts.

Now we qualify our results in the following ways. First, all of these
correlations are unconditional and bilateral. Although they are statisticallysignificant, they do not indicate the direction of causality. It is possible that thecorrelations are driven by some “third factor.” While some of the unconditionalcorrelations are insignificant, it is possible that the conditional counterpart ofthese correlations are significant, i.e., when some third variable is being held
constant. In addition, if some variables exhibit non-linear dynamics such as
regime-switching or contain a “bubble” component, the unconditionalcorrelations may not provide us with the full picture.29 Moreover, all of these
correlations are based on aggregate data. Recent research, on the other hand, tends
to use micro-data. In the next section, we will, therefore, review some of thoseworks.

3. A Review of Selected Literatures

Although recent years have witnessed a rapid growth in the macro-housing
literature, this section only provides a review of a subset of this literature. The
order and topics selected are somehow arbitrary. Our only objective is to provide
an (incomplete) review that will facilitate the exchange of ideas and perhaps
encourage even more research in this area.

29

The literature is too vast to be reviewed here. See Chang et al. (2011, 2012, 2013, 2016), Chen et al. (2006, 2010,2015), Chen and Leung (2008), Deng et al. (2017), Phillips et al. (2015a, b), Yiu et al. (2013), among others, andthe reference therein.

21

3.1. Bankruptcy and Mortgage Contract

In their Mayekawa Lecture presented at the Bank of Japan, Goodhart andTsomocos (2011) argue the following: “What is the main limitation of much
macroeconomic theory, among the failings pointed out by William R. White at
the 2010 Mayekawa Lectures? We argue that the main deficiency is a failure toincorporate the possibility of default, including that of banks, into the core of theanalysis….” Recent research efforts have indeed addressed such a concern. In
particular, authors have introduced heterogeneity in banks, firms, households, andtheir potential defaults in macroeconomics.30 In the context of macro-housing, it
is natural to consider mortgage default. It follows that one should first introduce
mortgage debt in macro models. Chambers et al. (2009a, b, c), among others,
propose overlapping generation models (OGM) with stochastic labor income andendogenous tenure choice (to rent or to own).31 They also compare different typesof mortgage contracts and study their implications in equilibrium. Their models
can match some stylized facts of the U.S. aggregate economy and the housing
market, including the homeownership rates across different age groups.
Iacoviello and Pavan (2013) study an OGM with aggregate shock and match somestylized facts of housing and mortgage debt over the business cycles.

Carlos Hatchondo et al. (2015), among others, go one step further bybuilding a model in which the house prices are characterized by a stochastic

30
The literature is too vast to be reviewed here. See Athreya et al. (2012, 2015, 2017), Chatterjee et al. (2007),
Corbae and D’Erasmo (2017), Gertler and Kiyotaki (2011), Gertler et al. (2015), Khan et al. (2014), Krueger etal. (2016), among others, and the references therein.
31
There are many related studies on mortgage contract and/or homeownership. See Amior and Halket (2014),
Anagnostopoulos et al. (2013), Fisher and Gervais (2011), Ghent (2012), Kydland et al. (2016), Luo (2017),
Ortalo-Magne and Prat (2014), Ríos-Rull and Sánchez-Marcos (2008), Sun and Tsang (2016), Yao (2018), among
others, and the references therein.

22

process and allow agents to default the mortgage loan. This step significantly
complicates the analysis. For instance, in the case of recourse mortgage, if aborrower fails to make the scheduled mortgage payment, the lender has the rightto seize the other liquid assets of the borrower. Hence, the saving decision isrelated to the default decision and hence the dynamic optimization problem
involves interacting continuous and discrete choices, and some conventional
methods of modeling mortgage contract may not be suitable in this context.32
Based on their structural model, they conduct counter-factual experiments andfind that combining recourse mortgage and a loan-to-value (LTV) ratio limit may
mitigate the sharp increase in the default rate after a sharp decline in house prices.
Corbae and Quintin (2015) study a model in which agents stochastically age overtime. The house price is also exogenous. The agents can choose a high or low
level of down payment on the mortgage contract. Based on their structural model,
they conclude that high-leverage loans originating before the financial crisis are
responsible for the high foreclosure rate following the crisis. Apparently, both
Carlos Hatchondo et al. (2015) and Corbae and Quintin (2015) point to the policy
recommendation that some minimum level of down payment may mitigate theseverity of the crisis. Mitman (2016) also builds a dynamic model with anexogenous house price process, an endogenous tenure choice, different ways of“filing bankruptcy” (Chapter 7 or Chapter 13), and foreclosure that may or may
not happen.33 He also exploits the cross-state difference in the default laws in his
modeling and calibration, and subsequently examines two policies, namely, theBankruptcy Abuse Prevention and Consumer Protection Act (BAPCPA), which
32

Some previous studies model a mortgage contract as a staggered contract, following Taylor (1980) and others
model a mortgage contract as a down payment constraint, following Kiyotaki and Moore (1997). There is related
literature on optimal mortgage contract design, which is typically partial equilibrium and theoretical in nature.
See Pikorski and Seru (2018), among others, for a review of that literature.
33
See Karsten et al. (2013), Lambertini et al. (2017), among others, for a related analysis.

23was imposed in 2005, and the Home Affordable Refinance Program (HARP),
which was imposed in 2009. He finds that the BAPCPA reform significantly
reduces the number of bankruptcy cases, and simultaneously leads to a significant
increase in foreclosures during the Great Recession. He also finds that the HARP
program enables households with high LTV to refinance their mortgages, thereby
leading to significant welfare gains to those households.34
Justiniano et al. (2013, 2015a, b, 2016), among others, argue that it may be
important to distinguish borrowing constraint from lending constraint. In theirmodels, borrowing constraint is the same as the collateral constraint imposed byKiyotaki and Moore (1997), as the value of debt cannot exceed the product of an
exogenously imposed parameterand the total value of the collateral. In thiscase, a “loosening” of a borrowing standard refers to an increase in the value of, capturing the idea that the same value of collateral can now “support” a larger
amount of borrowing at the individual level. The lending constraint, on the other
hand, refers to an upper bound on the total amount of mortgage lending thathouseholds can obtain. Justiniano et al. (2015a) show in their appendix B that thelending constraint is equivalent to a leverage constraint faced by financial
intermediaries. They find that it is indeed the lending constraint, rather than the
widely used borrowing constraint, that is more consistent with the four stylized
facts related to the Great Recession: (1) house prices rise dramatically between
2000 and 2006, (2) household mortgage debt also increases dramatically during
the same period, (3) mortgage debt and house price increase in parallel, and (4)real mortgage interest rates decline during that period. They illustrate theirmechanism with two types of agents and an endogenous house price.35 However,34
35

See also Kaplan and Violante (2014), among others, for a related analysis.
See Chatterjee and Eyigungor (2015), among others, for a related analysis.

24that series of models does not consider mortgage default and householdbankruptcy.

If both the default and endogenous house price dynamics are important for
our understanding of the housing market, it is natural to conjecture that combining
both features will produce a very robust analysis.36 It should be noted that evenwith the exogenous house price process, models with default and bankruptcy are
typically difficult to solve. Thus, introducing endogenous house prices makes thetask even more difficult. There are a few papers that have taken up this challenge.
For instance, Favilukis et al. (2017) consider an overlapping generation model inwhich agents are subject to both idiosyncratic and aggregate risks on the one handand have limited access of instruments that can diversify those risks on the otherhand. Thus, a distribution of (ex-post) heterogeneous households will be
generated even if the agents were identical ex-ante. However, the agents are also
heterogeneous ex-ante. In Favilukis et al.’s (2017) model, a small fraction of
agents receives a bequest from their parents and makes a bequest to their offspring.
At the same time, most agents start with little wealth when they start to work,
which creates a non-trivial wealth distribution in the model. In addition, there areparticipation costs for the equity market, transaction costs for the housing market,
and borrowing costs, which have important implications for asset markets. For
instance, when the economy is hit by an adverse aggregate shock, some agents
who have (relatively) lower levels of income and wealth may choose not toparticipate in asset markets, leaving the relatively rich to actively participate inthese markets. 37 If the aggregate shock turns favorable, then those who held

36
37

See Foote and Willen (2017), among others, for a related discussion.
This result is well known. See Dixit and Pindyck (1994), Stokey (2009), among others.

25assets during the downturn capture a bigger share of the capital gains. In otherwords, with positive asset market participation costs, the distributional dynamics
of income and wealth and the dynamics of asset prices can interact in a non-trivial
manner. In fact, the model can then simultaneously match some macro-stylized
facts, life-cycle age-income profiles, and asset returns reasonably well.

While credit market conditions and beliefs are often cited as the driving
forces behind the Great Recession, their relative importance is still not known.
Kaplan et al. (2017) address this question by building a dynamic generalequilibrium model with three different types of aggregate shocks. The first typeof shock is the traditional shock on aggregate labor productivity. The second typeof shock, which is significant, impacts a group of parameters that capture credit
market conditions, including the maximum LTV ratio at mortgage origination,
the maximum payment-to-income (PTI) level, mortgage origination cost, and soon. The third type of shock is related to a clever formulation of the aggregate
preference for housing. In their model,

a three-state Markov process,

∈

∗

,

evolves stochastically and follows,, where∗. Thus,the preference for housing in the periods are the same when the economy is in thestate of∗,. On the other hand, the two states differ in terms of the(conditional) probability of transferring to the state of, where a higher

preference weight is put on housing. Kaplan et al. (2017) therefore distinguish
the news shock or belief shock (which is a transition between

∗

∗

or

an actual preference shock (which is a transition between

and
and

) from).

There are other important assumptions in Kaplan et al. (2017). For instance,
they assume that renters cannot borrow as they do not have collateral. However,26

homeowners can use their houses as collateral and borrow through a home equity
line of credit (HELOC). HELOC is refinanced on a period-by-period basis andhence the amount of borrowing is affected by the time-varying house value. It isclearly very different from a mortgage loan, where the amount of borrowing isaffected by the house value during the origination period only. They carefully
calibrate their model to match both cross-sectional and time-series facts related
to the housing market. 38 In addition, they perform a series of counterfactual
experiments to disentangle different effects including (1) households belief inhousing demand remain fixed over time, (2) households believe that they
themselves will increase the demand for housing in the future, and at the sametime believe that others will not, (3) mortgage lenders believe that households
will increase their demand for housing in the future, while rental firms andhouseholds do not, (4) mortgage lenders are pessimistic about the chance ofhouseholds increasing their housing demands, while the rental firms andhouseholds are in fact subject to the belief shock, and so on. They find that it isindeed important to include the rental sector, and it is the belief shock rather thantaste shock (the actual change in preference parameters) that accounts for theobserved boom-bust dynamics. Contrary to some earlier studies, Kaplan et al.
(2017) find that the relaxation and subsequent tightening of the credit market
conditions are relatively minor in explaining the observed boom and bust in
consumption and house prices. In Kaplan et al. (2017), the belief change isexogenous. The authors study endogenous belief dynamics in an environment38

As a matter of fact, the “stylized facts” related to the Great Recession are evolving over time, as more data
become available and more research efforts are being devoted. See Agarwal et al. (2017), Foote et al. (2008, 2016),
Foote and Willen (2017), Gerardi et al. (2008, 2015a, b), Mian and Sufi (2015, 2016), Palmer (2015), among
others, and the references therein.

27

with informational frictions. We will discuss some of their contributions in thenext section.
3.2. Search and Belief.
The application of the search-and-bargaining theory in housing market
research has been widely recognized. For instance, according to the Nobel
Committee (2010), “…This year’s three Laureates have formulated a theoreticalframework for search markets. Peter Diamond has analyzed the foundations ofsearch markets. Dale Mortensen and Christopher Pissarides have expanded thetheory and have applied it to the labor market.… Search theory has been applied
to many other areas in addition to the labor market. This includes, in particular,
the housing market. The number of homes for sale varies over time, as does thetime it takes for a house to find a buyer and the parties to agree on the price.”
Clearly, it is impossible to even provide an exhaustive list of that literature.39
Instead, we focus on a few papers and highlight their insights on themacroeconomic aspects of the housing market.40

One of the results of Kaplan et al. (2017) is that belief shocks matter
considerably. In fact, the importance of beliefs has been discussed in the realestate literature, perhaps with different names. 41 The more recent literature

39

Wheaton (1990) may be the first paper that adopts a search-and-matching approach (SMA) in an equilibrium
model to study the house price and vacancy. SMA is then adopted by many authors, including Albrecht et al.
(2007), Bayer et al. (2011), Díaz and Jerez (2013), Halket and Pignatti Morano di Custoza (2015), Halket andVasudev (2014), Hort (2000), Huang et al. (2017), Krainer (2001), Head and Lloyd-Ellis (2012), Head et al. (2014,2018), Ngai and Tenrevro (2014), among others. The mathematical foundation of the search-and-matching models
has been studied by Duffie and Sun (2012), among others.
40
The related literature uses partial equilibrium search models to analyze the housing market. Again, the literature
is too vast to be reviewed here. See Anglin and Gao (2011), Arnott (1989), Deng et al. (2012), Leung et al. (2006),
Leung and Zhang (2011), Lin and Vendall (2007), Yavas (1992), among others, and the references therein.
41
The literature is too vast to be reviewed here. See Case and Shiller (1988, 2003), among others, and thereferences therein.

28embeds “beliefs” in a general equilibrium search model so that we canquantitatively study its impact. For instance, Piazzesi and Schneider (2009) showthat in a simple house search model, a small number of “optimistic” buyers in theeconomy can drive up housing prices because in a search environment, prices are
determined in a bilateral trade. Optimistic buyers, although a small fraction in theeconomy, can arise endogenously as a large fraction of “active traders,” and hence
are able to exert a large impact on the market price. The result is clearly in sharp
contrast with the results reported in Kaplan et al. (2017), where “belief shock”
needs to impact virtually all agents to generate a significant increase in housing
prices. While the setup of the two models are very different and hence not trivial
to compare, it is crucial to note that in Piazzesi and Schneider (2009), the housing
market is decentralized and subject to search frictions while in Kaplan et al.
(2017), the housing market is centralized and cleared in every period.

Burnside et al. (2016) also explore the possibility of a small number of“optimists” that would affect the whole market through “social dynamics,”
meaning that the “beliefs” of some economic agents could change when theymeet others with different beliefs in a stochastic manner. Thus, a model withheterogeneous expectation is needed. Guided by the psychology literature,
Burnside et al. (2016) assume that when two agents meet randomly, the agent
who has less uncertainty about the fundamental of the housing market, measured
by the entropy, would not be convinced by the agent who has more. However, theprobability that an agent with high uncertainty is a decreasing function of thedifference of the ratio of the uncertainty of the two agents that, other things being
equal, agents are more likely to be changed by people with relatively similar
beliefs than by people with very different beliefs.
29

Given these assumptions, the authors show that although initially there is
only a small fraction of “skeptical” and “optimistic” agents, and most of the
population is, therefore, “vulnerable,” i.e., they are the ones who are most likely
to change their beliefs, it is possible that the number of optimistic agents will rise
and then fall as long as this uncertainty is not resolved. In one of the cases they
consider, “skeptical” agents are the least likely to change, followed by the“optimistic” and “vulnerable” agents, who are most likely to change. Here, whenan optimistic agent meets a skeptical agent, it is possible for the optimistic agent
to be “converted” into a skeptical agent. However, when an optimistic agent
meets a vulnerable agent, the former will remain optimistic and the latter may be
converted into an optimistic agent. In a world of random matching, and the initialamount of skeptical and optimistic agents being equally small, the chance of an
optimistic agent of “converting” a vulnerable agent is much higher than the
chance of him/her being “converted” by a skeptical agent. Hence, the populationof optimistic agents is expected to grow. The population of skeptical agents willgrow as well because whether they meet an optimistic agent or a vulnerable agent,
they could “convert” them into skeptical agents. However, as the beliefs ofskeptical agents are so different from those of the vulnerable majority, the growthrate of skeptical agents is slower than that of optimistic agents within certain
parameter values. At some point, however, the relative population of optimistic
agents becomes so large that the chance for them of meeting skeptical agents ishigher than that of meeting vulnerable agents. The net growth of optimistic agents
then becomes negative.

30

The rise and subsequent fall of the proportion of optimistic agents also leads
to a boom-bust cycle of housing prices, as they, unlike the other types of agents,
believe that housing will deliver a higher value of utility in the future. Burnside
et al. (2016) demonstrate the basic mechanism with a simple model and then showthat the intuition carries to a model with 12 different types of agents, who may
differ in terms of their beliefs or their housing market participation. They calibrate
their models and match some facts of the housing market.

While the previously mentioned papers are based on a random search,
Hedlund (2016a, b) explores a model using a directed search.42 In particular,
Hedlund assumes that all transactions are intermediated by brokers. Hence,buyers buy from brokers and sellers sell to brokers. Modifying the “search
activities” enables the model to consider a more complicated form of mortgage
contracts than many search-theoretic models of housing.43 In Hedlund’s model,
the pace of amortization is flexible and hence borrowers can slow down the speedof repayment when needed. However, homeowners can extract home equity only
by paying off the original mortgage contract first and then originating a new
mortgage contract. 44 There are two issues to consider here. First, thehomeowners who need to extract home equity may not have enough liquid assets
to pay off the original mortgage contract. Second, even if they are willing toborrow, banks may not be willing to lend. In the model, banks need to pay forboth the mortgage origination cost (which functions like a “fixed cost”) as well
as serving cost to maintain a mortgage cost (which functions like a “variable42

It is beyond the scope of this paper to discuss the expanding literature on directed searching. See Wright et al.
(2017), among others, for a review of the literature.
43
See also Eerola and Maattanen (2018) and Head et al. (2018).
44
See Laufer (2018), among others, and the references therein for the effect of equity extraction on the subsequent
default probability.

31

cost”). Thus, banks may not want to originate a new mortgage contract in certain
situations.

Equipped with this setup and through careful calibration, Hedlund mimics
the stylized fact that leverage, selling price, and time-on-the-market (TOM) arecorrelated. 45 The intuition is straightforward. When a homeowner needs tosmooth out his/her consumption, he/she can either sell his/her liquid assets,
extract home equity, or simply sell his/her house. When the number of liquid
assets decreases, he/she may be tempted to extract the home equity. However, thebank may not want to originate a new mortgage contract for such needy
homeowners. In this case, the homeowner will be forced to sell his/her house.
Thus, homeowners with little liquid assets, so-called distressed owners, may beforced to launch a “fire sale.” However, those who are highly leveraged may noteven be able to do that because they do not have enough liquid assets to make up
the difference between the selling price and the outstanding mortgage loan.
Therefore, those distressed owners who are also highly leveraged will be forced
to post high selling prices. Undoubtedly, other things being equal, high selling
prices will lead to a longer TOM, which further increases the opportunity forforeclosure. Hedlund (2016a, b) articulates this intuition with a cleverly designed
directed search model of the housing market.

Thus far, we have seen two extreme forms of house searching, namely, either
completely random (such as the case of Piazzesi and Schneider, 2009; Burnside
et al. 2016) or completely directed (such as the case of Hedlund), in which no45

Prior research explains the correlation by using behavioral economics such as the preference of loss aversion(for instance, see Genesove and Mayer, 1997, 2001). Some recent research, however, has cast doubts on theimportance of loss aversion (for instance, see Easley and Yang, 2015 and Li et al. 2017).

32

seller sells to an end-user directly. While these models succeed with respect tomany dimensions, the fluctuations in terms of trading volume seem to have been
overlooked. For instance, in Figure 5 and 6 of Burnside et al. (2016), we noticethat the transaction volume (which is also the turnover rate, as the total supply of
housing stock is fixed in their model) can deviate up to 20% from the steady-statevalue. Some studies are relatively silent on the turnover rate. Figure 1 represents
the real house price and the turnover rate in the United States.46 To facilitatecomparison, we normalize both series to 100 at the beginning of the period. It isclear that turnover rate fluctuates significantly more than the house price. Even at
the aggregate level, the turnover rate at its peak can be double of its own trough.

(Figure 1 about here)

Some attribute the volatile turnover to “speculative activities.” Leung and
Tse (2017) consider an intermediate case by introducing the (endogenous)
participation of “flippers” (or “speculators,” or “investors,” which are usedinterchangeably in their work). In their model, a homeowner may receive a“separation shock” (as the “job separation shock” in the Mortensen-Pissarides
model), after which he/she can choose to sell the house to a flipper, which isimmediate, and move to a rental housing unit or become a buyer and search foranother for-sale housing unit. Alternatively, he/she can wait for a buyer to visit.
Hence, the model endogenizes the extent of intermediated trade in the housing

46
Our real housing price is defined as the nominal house price, which is the transaction-based house price index
from OFHEO (http://www.fhfa.gov) divided by the CPI from the Federal Reserve Bank at St. Louis. Transaction
is measured by the quarterly sales in single-family homes, apartment condos, and co-ops, normed by the stock ofsuch units. The sales data are from the Real Estate Outlook by the National Association of Realtors, complied by
Moody’s Analytics. The housing stock is defined as the sum of owner-occupied units and vacant for-sale-onlyunits. The data are from the Bureau of Census's CPS/HVS Series H-111 available at
http://www.census.gov/housing/hvs/data/histtabs.html.

33

market and embeds two extreme cases: (1) buyers and sellers meet randomly andno trade is intermediated, and (2) all trade is intermediated (as in the case of
Hedlund). In the model, flippers have the advantage of bargaining (i.e., may geta bigger share of the gains from trade than the households) and of inventory (i.e.,face a lower discount rate while waiting for buyers to come than the households).
Recall that selling a house to a flipper involves receiving a lower selling price but
a shorter waiting time (or, a shorter TOM). Thus, it is possible to observe pricedispersion in equilibrium if some mismatched households sell their houses toflippers while others sell to buyers directly. From the household perspective,
whether to use the flipper to facilitate trade depends on (1) the price differential
between selling to a flipper versus selling to an end-user and (2) the timedifferential between selling to a flipper (which is assumed to be zero in theirmodel) versus selling to an end-user. 47 From the perspective of the flipper,
however, whether a flipper is willing to “facilitate” a trade depends on whether
his/her share of gains from trade is large enough, and whether his/her discountrate is sufficiently different from the household. Leung and Tse (2017) show bothanalytically and quantitatively that multiple equilibria are possible, meaning thatfor given preferences and technologies, it is possible to have different prices inequilibrium, and each price is associated with a different share of flipper
participation. In their calibration, even without a change in “economic
fundamentals,” average house price can differ by up to 20%. Moreover, by fixing
the discount rate of households, the effect of a change in a flipper’s discount rate
can have a very non-linear effect on the equilibrium price. The intuition is very
simple to explain. Note that the participation of flippers is endogenous. With aslight increase in their discount rate, the participation rate of the flippers may
47

See Guren (2016), among others, for more discussion on this point.

34

change slightly as well. However, after reaching some critical values, theparticipation rate of flippers may dramatically drop, and the probability of buying
and selling will change as well. The resulting equilibrium will look very different.

There are unanswered questions in Leung and Tse (2017). If we can havemultiple equilibria in the housing market, we would want to know how
equilibrium is being selected. A natural way to do so is to introduce the formationand evolution of beliefs. Thus, a natural extension is to combine a search modelwith beliefs (such as Piazzesi and Schneider, 2009; Burnside et al. 2016) with an
explicit modeling of flippers (such as Leung and Tse, 2017) and examine both thetheoretical and empirical implications. There are many opportunities for future
research in this regard.

3.3. Urban Development and Housing Market

According to United Nations (2016) “Most people can agree that cities areplaces where large numbers of people live and work; they are hubs of government,commerce and transportation. But how best to define the geographical limits of acity is a matter of some debate. So far, no standardized international criteria exist
for determining the boundaries of a city and often multiple different boundary
definitions are available for any given city.” In the economics literature, muchhas been discussed on city formation, the interaction of spatial agglomeration andeconomic development, and related topics. 48 Here, we only highlight a few
papers, which may encourage more research in this area.
48

It is beyond the scope of this paper to review the literature. See Berliant (2010), Berliant et al. (2002), Berliant

35

Most macro-housing papers assume that there is only one housing market,
and abstract away the spatial and urban considerations.49 Wang and Xie (2014)
develop a two-sector growth model with explicit spatial considerations. Morespecifically, Wang and Xie assume that the city is a line segment and agents canchoose their preferred locations. Hence, housing prices can vary across locations(i.e., different “points” on the same line segment) in equilibrium. In their model,
housing depends on the amount of land as well as the physical structure. Whileland does not depreciate, the physical structure does depreciate over time. Hence,
agents need to invest in structure continuously and consequently to trade off theinvestment in structure (for “housing consumption”) versus investment inphysical capital (for goods production). They further deviate from the commonlyused specification in the macro-housing literature in that (1) they assume that
there is a positive amount of minimum structure, and (2) housing is a luxury goodin the sense that its income inelasticity differs from that of consumption goods.
As agents can reallocate themselves freely across locations, the prices must adjustin a way that the utility at each location is equalized. Their model can mimic somecross-sectional and time series stylized facts. In addition, they show that if instead(1) they assume homothetic preference (i.e., housing has the same income
elasticity as consumption goods), or (2) there is no minimum physical structure,then the model would generate counter-factual predictions. In other words, weneed to assume that (1) housing is a luxurious good and (2) there is a minimum
physical structure.

and Mori (2017), Berliant and Wang (2008), Berliant and Watanabe (2015), Bond et al. (2016), Duranton (2007),
Duranton and Puga (2004), Glaeser (2011), Kopecky and Suen (2010), Li (2017), Liao et al. (2017), Lucas andRossi-Hansberg (2002), Schiff (2015), Wang et al. (2017), among others, and the references therein.
49
There are a few exceptions. See Lin et al. (2004), Leung and Teo (2011), among others, and the references
therein.

36

Clearly, both of these assumptions deviate from the standard macro-housing
models. Wang and Xie (2014) need these assumptions to be consistent with thestylized facts while standard models do not because they impose two realistic
conditions on the model: (1) the amount of land supply increases with the distancefrom the Central Business District (CBD) and (2) other things being equal, agents
prefer to live closer to the CBD (Wang and Xie call this a “locational discount”).
Essentially, Wang and Xie seem to suggest that, if we were to account for bothcross-sectional and time series facts of housing, we need to reconsider the
standard macro-housing models.

Recently, Herkenhoff et al. (2017), among others, take the “spatial macrohousing models” (SMHM) to another level. It is well-known that land-use
regulations limit housing supply and affect house prices.50 Leung and Teo (2011)
built one of the first multi-regional, dynamic, general equilibrium models andshow that their model is qualitatively consistent with several stylized facts.
However, they do not provide a careful calibration of the regional level data.
Herkenhoff et al. (2017) aggregate the 48 states of the United States into 8 regions
and separately model them, thereby allowing parameters to differ across regions.
They find that if they could de-regulate California and New York back to their1980 level of regulation, the “gain” in consumption would be up to 5%, which isa very significant number.

50
The literature is too vast to be reviewed here. See Glaeser et al. (2005), Green et al. (2005), Saiz (2010), among
others, and the references therein.

37

While most macro-housing models focus on the U.S. case, there areimportant exceptions. For instance, there is much debate on whether (1) the
housing market in China is expanding too fast, (2) it could collapse soon, and (3)if it indeed collapses, it could exert negative externality on other markets andcountries.51 Garriga et al. (2017) contribute to the debate by building a dynamic
model with “rural” and “urban/city” areas. In their model, continuous
productivity growth in the manufacturing sector plays an important role because
it widens the productivity gap between the manufacturing and agricultural sectors.
It enables city workers to afford more expensive housing over time, and also
attracts rural workers, who can only work in the agricultural sector, into urban
areas. Both effects lead to a continuous increase in the relative price of housing.
The authors calibrate their model carefully and find that they can explain mostchanges in the housing market. Clearly, China is not the only developing country.
Therefore, there is much room for the application and extension of the studies inother developing housing markets.

3.4. Urban Policy and Human Capital

Recent research confirms that human capital is important to economic growth,and educational reform has the potential to significantly improve the economic
growth rate (e.g., Hanushek et al., 2017 a, b; Hanushek and Woessmann, 2015).
Research has also confirmed that early stage human capital formation (forinstance, before the age of 10, or even earlier) is crucial to later stage human51

The literature is too vast to be reviewed here. See Wu et al. (2012, 2016), Deng et al. (2017), Hsu et al. (2017),
Huang et al. (2015), Leung et al. (2011), Song and Xiong (2018), Yang and Chen (2014), Zhang et al. (2016),
Zheng and Saiz (2016), among others, and the references therein.

38

capital formation (e.g., Cunha and Heckman, 2007, 2008; Cunha et al. 2010;
Heckman, 2008). In the United States, the approach to providing local publicfinancing of primary and secondary schools naturally binds the local housing
market and the financing of pre-college education. Hanushek and Yilmaz (2011,
p.583) summarize it this way, “…In simplest terms, poverty, race and schoolingare very highly correlated with location…. The reliance on the local tax for a large
portion of school funding implies that the government grant system has animportant effect on both locational decisions and educational outcomes…
Education in the United States is provided by local school districts that operatewith considerable autonomy. Funding is provided by a combination of local, state,
and federal revenues with the level of spending and the performance of schools
varying significantly across school districts….” Thus, it is possible that somefamilies who can only afford less desirable neighborhoods raise their offspring in
those neighborhoods. In turn, the future development of these offspring may beconstrained and adversely affected, and hence result in cross-sectionalsegregation and intergenerational immobility. Benabou (1993, 1996a, b), Durlauf(1996), among others, explore such related theoretical possibilities. Empirically,
however, this seems to be controversial and many authors have contributed to thisliterature.52 Here, we only highlight a few contributions and hopefully encourageeven more research on this literature. For instance, Hanushek and Yilmaz (2007,2013) build a static general equilibrium model, which allows for endogenous
community choice (according to Tiebout) and spatial locational choice (according
to Alonso).53 They calibrate the model to match some stylized facts of the United
52

The literature is too vast to be reviewed here. See Bayer et al. (2007), Brasington and Haurin (2009), Epple andNechyba (2004), Nechyba (2006), Nguyen-Hoang and Yinger (2011), among others, and the references therein.
More recently, Chetty and Hendren (2017a, b) confirm with their large administrative dataset that theneighborhood that children grow up in does have an impact on subsequent economic outcomes.
53
In Hanushek and Yilmaz, neighborhoods are identical ex-ante. Other authors study the case whenneighborhoods are different ex-ante (for instance, downtown versus suburban). See de Bartolome and Ross

39

States. Based on the calibrated parameters, they point out that the manner inwhich education is financed matters. Hanushek et al. (2011) introduce private
schools in that framework and find that private schools can indeed improve thewelfare of all types of agents. Leung et al. (2012) consider public housing versus
housing vouchers in the Hanushek-Yilmaz model. They find that although there
are different forms of market imperfections in the model, the conventional
wisdom, namely, distributing cash is better than distributing public housing units,prevails. Hanushek and Yilmaz (2015) find that the zoning policy affects botheducation and the housing market. Bayer et al. (2016), however, estimate adynamic, partial equilibrium model. They assume that the per-period utility
function is somehow additively separable. Their dynamic estimates suggest thatsome prior estimates that are based on static demand functions of non-market
amenities may be significantly biased. Given all of these calibrations andestimations, one may still wonder whether, or under what conditions, an urban
policy (such as public housing or affordable housing policy) or an education
finance reform (such as school finance consolidation) would necessarily improve
the welfare and promote the accumulation of human capital and economic
growth.54 Clearly, much more work is needed in this area.

4. Concluding Remarks
To most households, housing is the most important form of asset holding thatthey can manage on their own (a retirement fund is clearly important as well but
is typically subject to different constraints before retirement). Recently, the(2003), among others, and the references therein.
54
For more discussion, see Disney and Luo (2017), Favilukis et al. (2018), among others, and the references therein.

40

importance of housing has been increasingly recognized in economics andfinance. This paper achieves two objectives. First, we re-examine the “stylized
facts” of macro-housing. With respect to the business cycle frequency, we findthat in many cases, the correlations between traditional MV and HMV have
weakened following the GFC. However, the correlations between macro-financevariables and HMV have strengthened following the GFC. In the medium-cycle
frequency, some correlations display the same change as in the business cycle
frequency while others do not. Therefore, we urge researchers to pay more
attention to the “stylized facts” in macro-housing research.

Our second objective is to review some of the literature. We highlight some
contributions from important topics: mortgage and bankruptcies, search andbeliefs, urban development and housing market, and urban policy and humancapital. We find that substantial progress has been made, and at the same time,
there remain open questions in these areas. Clearly, many important papers andresearch areas have been overlooked. We can only allow for such “recognition
deficit” for the moment and hope for a more elaborate survey in the future.

41

Appendix
Forbes and Rigobon (2002) show that with a change in variance over time, themeasured correlation may be biased. We therefore follow Stock and Watson(2002) to standardize the variance. Our procedure is given below.

Step one. We first use the Christiano-Fitzgerald filter to extract the businesscycle components in the PCSS. By construction, the extracted time series isstationary and hence moments are well defined. Letbe such a time series.

is denoted by by

The correspondence variance of. We then“standardize” the volatility of all variables. Now a new variable
defined. Hence,

/

/

is

1. We apply thisdata transformation to all variables and hence all variables have the samevolatility. We can then compute all of the needed correlations.

Step two. We repeat the same procedure on the full sample. Note that even forthe same variable, for instance GDP, the sampling period is now different

and hence the variance of the extracted series may also be different. A
potentially different transformed variable′

will be generated. We apply theprocedure to all variables and then re-compute all of the needed correlations.

Step three. We repeat both step one and step two, only this time we extract themedium-cycle components instead of the business cycle components. We
calculate and tabulate all of the needed correlations.

42

Table 1 Correlation between the cyclical component of housing and macro-variables (Panel A)
Housing variables

Real “purchase-only” houseat time t

price index

Macro-variables

New house sold

Vacancy rate of for-saleReal private residential fixed

housing

investment

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

2006Q4

2017Q3

2006Q4

2017Q3

2006Q4

2017Q3

2006Q4

2017Q3t-1

0.77***

0.57***

0.24*

0.14

-0.39***-0.03

0.65***

0.54***

t

0.78***

0.66***

0.42***

0.34***-0.44***-0.10

0.76***

0.68***

t+1

0.74***

0.69***

0.58***

0.51***-0.52***-0.16

0.83***

0.76***

Unemploymentt-1-0.67***-0.27***

0.18

0.27***-0.12-0.28***-0.29**

-0.12

rate

t

-0.76***-0.43***

-0.01

0.09

0.08

-0.20**-0.48***-0.32***

t+1-0.81***-0.59***

-0.21

-0.13

0.33***-0.09-0.64***-0.51***

t-1

0.18

-0.12

-0.47***-0.37***

0.39***

0.19**-0.22*-0.21**

t

0.30**

0.00-0.33***-0.24**

0.14

0.13

-0.05

-0.06

t+1

0.46***

0.19*

-0.18

-0.10

-0.07

0.06

0.13

0.11

Real private

t-1

0.71***

0.31***-0.04-0.22**

-0.03

0.18*

0.39***

0.15

Nonresidentialt

0.78***

0.45***

0.14

-0.04

-0.18

0.12

0.55***

0.33***

Fixed Investment

t+1

0.81***

0.58***

0.31**

0.16-0.38***

0.03

0.69***

0.51***

Real personal

t-1

0.66***

0.41***

0.02

0.06

-0.25**

0.02

0.45***

0.41***

consumptiont

0.72***

0.52***

0.20

0.22***-0.33***-0.03

0.60***

0.55***

expenditures

t+1

0.73***

0.58***

0.37***

0.37***-0.43***-0.08

0.70***

0.65***

Real trade

t-1-0.77***-0.30***

-0.17

-0.10

0.25**

0.00-0.58***-0.45***

surplust-0.78***-0.39***-0.34***-0.27***

0.47***

0.11-0.72***-0.59***

t+1-0.77***-0.48***-0.50***-0.44***

0.69***

0.23**-0.82***-0.69***

Real GDP

CPI

43

Table 1 Correlation between the cyclical component of housing and macro-variables (Panel B)
Housing variables

Real “purchase-only” houseat time t

price index

Macro-variables

New house sold

Vacancy rate of for-saleReal private residential fixed

housing

investment

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

2006Q4

2017Q3

2006Q4

2017Q3

2006Q4

2017Q3

2006Q4

2017Q3Nominal federal

t-1

0.54***

0.56***

0.02

0.06

0.15

0.23**

0.27**

0.33***

funds ratet

0.61***

0.64***

0.08

0.18*

0.01

0.08

0.38***

0.47***

t+1

0.64***

0.69***

0.17

0.29***

-0.19

-0.07

0.50***

0.59***

Real federal

t-1

0.48***

0.63***-0.28**-0.06

0.35***

0.23**

0.06

0.13

funds ratet

0.62***

0.65***

-0.16

0.01

0.22*

0.08

0.24*

0.22**

t+1

0.66***

0.55***

-0.03

0.06

0.01

-0.03

0.39***

0.30***

t-1-0.64***-0.62***-0.10-0.20**

-0.08

-0.07

-0.36***-0.44***

t-0.69***-0.64***-0.19-0.32***

0.15

0.11

-0.46***-0.55***

t+1-0.68***-0.61***-0.27**-0.40***

0.42***

0.28***-0.55***-0.65***

t-1

-0.11

-0.43***-0.39***-0.45***

-0.08

-0.01

-0.22*-0.37***

t-0.11-0.36***-0.33***-0.43***

-0.15

0.11

-0.19

-0.28***

t+1

-0.03

-0.21**-0.28-0.35***-0.12

0.21**-0.14-0.17*

External financet-1-0.38***-0.42***-0.33***-0.29***

0.34***-0.06-0.48***-0.45***

premiumt-0.30**-0.52***-0.37***-0.41***

0.47***

0.12-0.49***-0.49***

t+1

-0.21

-0.57***-0.44***-0.50***

0.65***

0.31***-0.49***-0.49***

S&P 500 index

t-1

0.74***

0.57***

0.43***

0.22**-0.49***-0.04

0.73***

0.55***(real terms)t0.70***

0.68***

0.55***

0.41***-0.80***-0.12

0.78***

0.66***

t+1

0.62***

0.74***

0.64***

0.55***-0.53***-0.20**

0.78***

0.72***

Term spread

TED spread

44

Notes:1.

Sources of data: “purchase-only” house price index: Federal Housing Finance Agency; vacancy rate of for-sale housing, and new house sold: U.S. Bureau of the Census;
private residential Fixed Investment, personal consumption expenditures, GDP and trade surplus: U.S. Bureau of Economic Analysis; CPI: U.S. Bureau of Labor Statistics;
term spread: Federal Reserve Bank of St. Louis; effective federal funds rate: Board of Governors of the Federal Reserve System; External finance premium: corporatebond spread (Baa-Aaa): Moody's.

2.

Term spread is the difference between 10-Year Treasury Constant Maturity and 3-Month Treasury Constant Maturity. TED spread is the difference between the Eurodollar
deposit rate and the T-bill rate (both are 3-month). External finance premium is the corporate bond spread (Baa-Aaa).

3.

All the variables are seasonal adjusted. Real variables are nominal variables are deflated by CPI.

4.

Cyclical components are obtained by using Christiano and Fitzgerald (2003) band pass filter. Ng and Perron (2001) unit root test indicates that all the variables are I(1)except the nominal effective federal funds rate and the external finance premium: corporate bond spread (Baa-Aaa) which are I(0).

45Table 2 Correlation between the medium cycle component of housing and macro-variables (Panel A)
Housing variables

Real “purchase-only” houseat time t

price index

Macro-variables

New house sold

Vacancy rate of for-saleReal private residential fixed

housing

investment

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

2006Q4

2017Q3

2006Q4

2017Q3

2006Q4

2017Q3

2006Q4

2017Q3t-1

0.57***

0.81***

0.61***

0.73***

-0.11

-0.14

0.62***

0.80***

t

0.58***

0.79***

0.65***

0.79***-0.16-0.24***

0.65***

0.83***

t+1

0.56***

0.75***

0.68***

0.83***-0.26**-0.34***

0.67***

0.85***

Unemploymentt-1-0.34***-0.69***-0.35***-0.67***

-0.12

0.14

-0.38***-0.72***

ratet-0.36***-0.67***-0.41***-0.72***-0.07

0.24***-0.43***-0.76***

t+1-0.35***-0.63***-0.45***-0.76***

0.01

0.33***-0.46***-0.77***

t-1-0.57***-0.29***-0.53***-0.24***

0.56***

0.25***-0.49***-0.20**

t-0.53***-0.26***-0.49***-0.20**

0.55***

0.22**-0.44***

-0.15

t+1

-0.50***-0.23**-0.46***-0.17*

0.58***

0.22**-0.40***-0.13

Real private

t-1-0.32***

0.21**-0.25**

0.26***

0.26**-0.05-0.27**

0.28***

Nonresidentialt-0.30**

0.20**-0.23*

0.29***

0.28**-0.09-0.24*

0.31***

Fixed Investment

t+1-0.30**

0.18*-0.21*

0.32***

0.30**-0.13-0.21*

0.33***

Real personal

t-1

0.72***

0.86***

0.80***

0.78***-0.38***-0.19**

0.78***

0.83***

consumptiont

0.70***

0.84***

0.81***

0.83***-0.42***-0.29***

0.78***

0.86***

expenditures

t+1

0.67***

0.80***

0.81***

0.86***-0.51***-0.38***

0.77***

0.88***

Real trade

t-1-0.99***-0.98***-0.94***-0.84***

0.39***

0.17*-0.96***-0.90***

surplust-0.97***-0.96***-0.95***-0.88***

0.46***

0.28***-0.96***-0.92***

t+1-0.95***-0.93***-0.96***-0.92***

0.59***

0.38***-0.95***-0.93***

Real GDP

CPI

Notes: Our definition of “medium cycles” follow Comin and Gertler (2006), which captures the components with periodicity between 32 and 80 quarters.

46

Table 2 Correlation between the medium cycle component of housing and macro-variables (Panel B)
Housing variables

Real “purchase-only” houseat time t

price index

Macro-variables

New house sold

Vacancy rate of for-saleReal private residential fixed

housing

investment

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

1991Q1-

2006Q4

2017Q3

2006Q4

2017Q3

2006Q4

2017Q3

2006Q4

2017Q3Nominal federal

t-1-0.26**

0.17*-0.49***-0.19**

0.93***

0.70***-0.34***-0.03

funds rate

t

-0.14

0.25***-0.37***-0.08

0.89***

0.64***-0.22*

0.08

t+1

-0.05

0.33***-0.28**

0.02

0.84***

0.57***

-0.12

0.18*

Real federal

t-1-0.47***

0-0.57***-0.27***

0.78***

0.63***-0.48***-0.15

funds ratet

-0.38***

0.07-0.48***-0.17*

0.78***

0.59***-0.38***

-0.05

t+1

-0.32***

0.14-0.41***-0.08

0.77***

0.54***-0.31**

0.04

t-1

0.27**-0.18*

0.31***

0-0.60***-0.42***

0.25**

-0.10

t

0.20

-0.22**

0.23*

-0.09

-0.58***-0.35***

0.17-0.18*

t+1

0.17-0.25***

0.17-0.16*-0.55***-0.30***

0.10-0.25***

t-1-0.45***-0.02-0.59***-0.43***

0.75***

0.80***-0.53***-0.30***

t-0.35***

0.08-0.51***-0.32***

0.79***

0.78***-0.42***-0.19*

t+1-0.31**

0.16*-0.43***-0.22**

0.79***

0.75***-0.34***-0.08

External financet-1-0.39***-0.48***-0.58***-0.68***

0.30**

0.38***-0.54***-0.65***

premiumt-0.35***-0.43***-0.58***-0.68***

0.36***

0.45***-0.53***-0.63***

t+1-0.32***-0.38***-0.58***-0.67***

0.44***

0.52***-0.52***-0.61***

S&P 500 index

t-1-0.36***

0.12-0.23*

0.25***-0.03-0.25***-0.31***

0.23**(real terms)t-0.39***

0.09-0.25**

0.26***

0.03-0.26***-0.32***

0.23**

t+1-0.42***

0.05-0.27**

0.25***

0.09-0.27***-0.33***

0.22**

Term spread

TED spread

Notes: Our definition of “medium cycles” follow Comin and Gertler (2006), which captures the components with periodicity between 32 and 80 quarters.

47

Normalized Real House Price48
Normalized Turnover rate

2010Q3

2010Q1

2009Q3

2009Q1

2008Q3

2008Q1

2007Q3

2007Q1

2006Q3

2006Q1

2005Q3

2005Q1

2004Q3

2004Q1

2003Q3

2003Q1

2002Q3

2002Q1

2001Q3

2001Q1

2000Q3

2000Q1

1999Q3

1999Q1

1998Q3

1998Q1

1997Q3

1997Q1

1996Q3

1996Q1

1995Q3

1995Q1

1994Q3

1994Q1

1993Q3

1993Q1

1992Q3

1992Q1

1991Q3

1991Q1Figure 1: USA House Price and Turnover Rate

210

190

170

150

130

110

90

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