International Economic Integration and

Commercial Real Estate Performance

(Preliminary and Incomplete)

Ashok Deo Bardhan, Robert H. Edelstein and Charles Ka Yui Leung∗

March 31, 2005

Abstract

Has globalization and increasing economic-financial integration affected

∗Correspondence: Edelstein, F 602, Hass School of Business, University of Califor-nia, Berkeley, CA 94720-6105, USA; (Phone) 510-643-6105; (Fax) 510-643-7357; (Email)edelstei@haas.berkeley.edu; Bardhan, bardhan@haas.berkeley.edu; Leung, Department ofEconomics, Chinese University of Hong Kong, Shatin, Hong Kong; (Phone) 852-2609-8194;(Fax) 852-2603-5805; (E-mail) charlesl@cuhk.edu.hk.

1

commercial real estate in cities around the world? We attempt to answer this

question by developing a model of a small open economy which can import

investment goods and where commercial capital stock is an input in produc-

tion. In this model increased openness has a positive impact on commercial

real estate prices, because of the low supply elasticity and non-tradable na-

ture of real estate. We test this implication using a set of multi-factor models

for annual data for 40 cities in 40 different countries and estimate the impact

of a country’s economic openness, foreign investment flows and other mea-

sures of globalization of national economies on the price of commercial real

estate (office), after controlling for the effects of domestic macro-economic,

and local, geographic and city-wide variables.

Keywords: globalization, economic openness, international financial mar-

kets, real estate returns, international financial integration

JEL Classification Number: F36, F21, G15

2

1 Introduction and Motivation

Real estate markets have been undergoing rapid change over the last three

decades. The foci of the markets have evolved from local to national and

now to international with concomitant hallmarks of increased securitization,

financial depth and sophistication. The development of these markets and

property-related firms has become transnational for several reasons; some

are servicing multinational corporations, i.e. for the purposes of exporting

expertise, such as that of US real estate firms which usually gain an entry

into other countries by accompanying US MNCs and catering to their real

estate needs (e.g., Hines); and for investment, both portfolio investment in

foreign publicly traded real estate firms as well as foreign direct investment

in real estate (e.g., AMB and Prologis in logistics real estate).

The globalization of commercial real estate raises interesting questions

for academic research. By and large, the academic international trade and

urban real estate economics literatures co-exist in virtually isolated arenas,

with rare contact, connectivity or cross-fertilization. Notable exceptions are

Henderson (1982) and the emerging literature on the "new economic geogra-

phy," which examines the interplay between cities, urban agglomerations and

international trade (Fujita, Krugman and Venables, 2001). As observed by

3

Bardhan, Edelstein and Leung (2004), the interaction of globalization, for-

eign trade, investment and portfolio flows with real estate markets exposes

an entirely new area of hitherto uncharted territory in economics — i.e. the

intertwining of international trade, financial economics, urban economics and

real estate economics.

In product and services markets, the development of free trade treaties

and the expansion of the World Trade Organization have promoted interna-

tional trade and investment flows, and have caused structural shifts for the

demand of various inputs, including real estate, in cities around the world.

In the financial markets, burgeoning real estate securitization and the chang-

ing real estate financial systems have generated intense international investor

participation. Investors, seeking improved portfolio allocation - diversifica-

tion and increased returns, have a demonstrated penchant for investing in

blossoming real estate markets.

Globalization may affect real estate through two related transmission

mechanisms in which rising integrated international economic activity may

raise the quasi-rents to the real estate sector. The first transmission mech-

anism operates through the supply elasticity for real properties. When in-

creased economic openness engenders higher productivity and output, there

4

will be an increased derived demand for real estate, combined with an in-

herently low elasticity of supply for “local” non-tradable real estate, and,

therefore, a disproportionate increase in real estate rents and prices, vis-s-vis

tradable goods.1 That is, since the supply of local real estate is relatively

fixed in both the short run and long run, the increase in derived demand for

real estate, brought about by increasing prosperity via openness and glob-

alization, ceteris paribus, will raise the real rents and asset prices of real

estate. The second, and a related transmission mechanism, predicated upon

the Balassa-Samuelson hypothesis, implies that increasing international trade

leads to an asymmetric increase in the country’s productivity of traded goods

vis-a-vis non-traded goods, leading to an increase in the relative price of the

latter. Higher productivity growth in the traded goods sector, engendered by

knowledge spill-over and country specialization because of globalization, will

bid up wages in that sector. Assuming that labor within a country is mobile

across the traded goods and non-traded goods sectors, wages in the entire

economy will rise eventually, thus connecting this mechanism to the previous

one. Since real estate is considered to be one of main non-traded goods in

every economy, the relative prices of real estate will rise as a consequence of

1Non-tradable goods and assets are those that are not exportable or importable, andare essentially domestically produced and consumed.

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globalization and increasing international trade.

i) Real Causes of Property Demand: As examples, market opportunities,

access to low-cost labor and economies of scale may cause expansion across

global regions. At present, Multinational companies are in the throes of a

massive expansion of their operations in foreign countries, particularly in

emerging markets. As their direct investment abroad and trade ties grow,

these firms often need to scrounge around for office space, industrial sites, and

suitable expatriate housing, augmenting real estate demand over and above

that brought about by the general increase in prosperity and globalization.2

ii) Diversification: International diversification is now widely practiced

for stock and bond portfolios. Portfolio investment in foreign real estate

markets, through investments in publicly traded real estate firms, real estate

mutual funds is another method for diversifying holdings. Cross-country di-

versification is attractive because the correlations among regional property

share markets are lower than those among the property share markets aggre-

gated by use sector. This implies that property markets are more strongly

2Many full service real estate firms have major corporate clients and tend to followthe latter in their geographical expansion. Also, for example, CB/Madison of Los Angelesand Cushman and Wakefield have teamed up with Ford Motor Land Services, a Ford sub-sidiary, to provide global real estate services for the parent Ford company’s internationaloperations.

6

segmented by regions rather than by sectors. This would be an additional

factor in favor of international diversification in real estate rather than single

market region diversification across property uses.

iii) Potential Returns of FDI: The nature of real estate markets, immobil-

ity, illiquidity and "lumpiness", create opportunities for good returns on in-

vestment; particularly in the Asia-Pacific region where the enormous backlog

in real estate development is related to rent-up and anticipated growth. This

acts as a pull-factor for foreign direct investment into real estate. Although

large pension funds and insurance companies account for most cross country

investments in overseas real estate, mostly in the for portfolio diversification,

private funds, real estate investment trusts, and individual entrepreneurs are

seeking increasingly physical investment in international real estate markets.

1.1 A Selective Literature Review

We provide a selective review of three (not fully recognized interwoven)

strands of literature: a) international real estate investment and diversifica-

tion, b) the interaction of openness and non-tradables, and c) urban growth

economics.

A few pioneering efforts focus on international real estate diversification,

7

examining mean-variance portfolio performance; the collective findings are

varied. Eichholtz (1995) studies the covariance structure of international

property share returns, using monthly property company returns from differ-

ent countries from 1973-1993. He finds that the international property rates

of return covariances are unstable, which may limit their usefulness in stan-

dard portfolio allocation models. Goetzmann and Wachter (1996) perform

a mean-variance analysis for a sample of international office markets. By

examining cross-sectional behavior of the global office market, they identify

three clusters of office markets that tend to “move together”. “Clustering” of

commercial property markets may impair investor ability to diversify across

international markets.

Balassa (1964) and Samuelson (1964) contend that purchasing power par-

ity would not hold in the long run because of differential rates of productivity

growth in the traded goods sector across countries; this is due to the fact that

greater openness in some sectors leads to higher productivity, due to greater

competition, market learning effects etc., and that in turn would raise wages

and the relative prices of non-tradable goods and services. The strand of

literature based on this line of reasoning involves the relationship between

real exchange rates, international purchasing power and economic openness,

8

usually with both traded and non-traded sectors viewed as aggregate goods

and services. Using 1970-1985 sectoral data for the OECD countries, De Gre-

gorio et al (1994) show that inflation in non-tradable goods exceeds inflation

in tradables. Their contention is that growth in total factor productivity in

the tradable goods sector and a demand shift in favor of non-tradables are

the major determinants of the differential price rise. In an alternative yet re-

lated tack, DeLoach et al (2001) provide evidence of a statistically significant,

long-run, positive relationship between the relative price of non-tradables and

real output, consistent with the notion of relative productivity increases in

the tradable sector, hypothesized by Balassa and Samuelson. That is, in-

creases in productivity in the traded goods sector due to increased global

economic integration lead to a traded-goods sector led growth in output, and

a concomitant rise in relative prices of non-tradables.

Urban economics literature provides a series of inter-related insights that

are useful for our analysis. The seminal paper of Alonso (1971) explores the

costs and benefits associated with urban size and its impact on housing prices.

In essence, larger urban areas lead to higher real estate prices and rents

because of transportation frictions. The research of Isard (1956) and Anas,

Arnott and Small (1998) sheds light on a related subject area, the interplay

9

between the dynamics of evolving urban structure and economic forces. The

work of Ades and Glaeser (1995) and Krugman and Livas-Elizondo (1996)

is also of some relevance here. These last two studies are among a handful

of more recent papers that link urban economics, international economics

and trade policy. The former, an empirical work, includes case studies, and

avers that high tariffs and low levels of international trade (i.e., countries

with a low level of economic openness) increase the degree of concentration

of a nation’s population in the largest city, a matter of some importance to

us since our sample contains the largest cities of the respective countries.

The latter paper, a theoretical model, explains why the “..giant third world

metropolis is an unintended by-product of import-substitution policies and

will tend to shrink as developing countries liberalize. . . .” Presumably, strong

forward and backward domestic economic linkages arise in a small market,

leading to this kind of agglomeration; increasing openness would increase

market size and weaken these linkages, and hence be the raison d’etre for

size clustering.

However, to the best of our knowledge, prior research has not focused

upon real estate pricing and its simultaneous relationship to both domestic

urban and international economic and financial variables, despite the fact

10

that real estate is the major asset component of the non-tradable sector.3

In the next section we present our model, which is an extension of the

otherwise standard small open economy model presented in Grossman and

Helpman (1991), Rebelo (1991), Easterly, King, Levine and Rebelo (1993).

We introduce commercial property in the model, as in Kan et. al. (2004).

We differ from the previous efforts by allowing the trade in investment goods

(or intermediate products, which will be used interchangeably) to drive the

property market. While the economy can always import capital goods or in-

termediate products to match up with a favorable shock or increased demand

due to higher incomes etc., it takes time to adjust the commercial property

stock due to its inelastic supply, which for our purposes can be attribut-

able to its unimportability. Thus, the relative price of commercial property

will tend to increase. Allowing for foreign direct investment only strength-

ens this channel because foreign investors can only bring capital goods or

3Connected to our approach above is also, a) the unexplored issue of whether there isunderinvestment in fixed assets as an economy opens up, since it becomes more expensive.This could connect the real estate literature to a growing, influential strand in macro-economics literature on cross-country studies of investment, except that everybody elselooks at the “other” investment, i.e. equipment and machinery; and b) the CrosslistingIssue: There is some literature on ADRs (American Depository Receipts) and crosslistingof securities, but there is little systematic study that simultaneously accounts for countryand currency risks, as well as the tradability of sectors, products and inputs of firms thatare crosslisted. In short a study of ADRs of global real estate firms has not been done tothe best of our knowledge.

11

financial resource into the country, but not the commercial property directly,

again the non-tradable nature of real estate steps in. Since capital and com-

mercial property are complements in production, more capital injecting into

the country would only intensify the competition for the usage/ownership of

commercial property. Thus, again it is intuitive to expect that, other things

being equal, the price for commercial property would increase.

2 A Suggestive Model

In this section, we develop a suggestive theoretical model that enables us to

demonstrate that higher openness, in terms of trade in intermediate products,

and a higher willingness to import foreign technology, determines commercial

property rents. A merit of our model is simple yet in line with the macro-

real-estate literature.

We now present a schematic model, that (1) embeds these insights in a

dynamic general equilibrium, where the amount of imported capital goods,

and the commercial property, instead of being fixed, as in some static models,

will be endogenously determined; the labor supply and the intertemporal sav-

ing/investment decisions will be simultaneously optimized, and (2) leads us

12

to an estimation procedure for metropolitan rents as a function of openness,

as well as providing appropriate control variables.

As we have mentioned earlier, our model is an extension of the otherwise

standard small open economy model presented in Grossman and Helpman

(1991), Rebelo (1991), Easterly, King, Levine and Rebelo (1993) (EKLR

hereafter), and later extended by Leung (2001). This family of models em-

phasize the role of intermediate goods trade, as confirmed by many empirical

studies.4 Since the model is somehow standard in the literature, the descrip-

tion will be brief.

Now we provide a formal description of the model. Time is discrete in this

model and the horizon is infinite. The “small open economy” is populated

by a continuum of infinite-lived agents. The population is N , which is fixed

over time. In each period t, t = 1, 2, 3,..., the representative agent derives

utility u(Ct) from non-durable consumption goods Ct . Previous work such

as Kan et. al. (2004) shows that introducing endogenous labor-leisure choice

4Economists have long recognized that in practice, most of the international trade areintermediate goods trade. The literature is too large to be reviewed here. See Jones (2000)and the reference therein. For the empirical significance of the FDI, see Feenstra (2004)for a textbook treatment.

13

would not alter the qualitative result. For simplicity, it is assumed that

u(Ct, Lt) = lnCt. (1)

The representative agent is assumed to maximize the life time utilityP∞

t=0 βtu(Ct)

, participate in the production of consumption goods Ct, and commercial

property Ft. β is the time discount factor, 0 < β < 1.5

At period t, the representative agent combines different intermediate

goods i, i ∈ [0, At] and the service provided by commercial property to pro-

duce final output

Yt ≡∙Z At

0

(Xt(i))1−α di

¸(Ft)

α , (2)

where 0 < α < 1, and Xt(i) is the amount of intermediate goods i purchased

from the world market at period t. It is easy to see that it is a constant

return to scale production function, which is what empirical studies confirm

in general.6 Notice here that At represents the range of intermediate goods

this small open economy is able to employ in production, and as it will

become clear, it also represents the “level of the technology”. Final output

5See Stokey, Lucas and Prescott (1989, esp. chapter 3) for more discussion on the roleof the time discount factor.

6For instance, see Burnside, Eichenbaum and Rebelo (1995).

14

can be consumed ct, or to be used to purchase commercial property directly

from the market Fmt at unit price Qt, or to invest in adopting new technology

(At+1−At) at unit cost 1/BA, with the rest be used to pay for the intermediate

goods imported from foreign countries (including tariff)R At

0ΓtPt(i)Xt(i)di.

Γt represents the tax factor, Γt = (1 + τ t), where τ t is the tariff rate at

time t. Here, τ t represents not only the official rate of tariff, but also the

transportation cost, quota, and any administrative or transaction cost that

particularly involved in cross-country transactions. Empirical studies have

confirmed that crossing a national border by itself is like adding a significant

amount of miles in transportation, and can therefore create a deviation of

the Law of One Price.7 Here we simply capture all these in the variable τ t.

Clearly, if all these costs are zero, then τ t = 0 and Γt = 1.

Notice that in this economy, adopting new technology is the only mean

to sustain the economic growth.8 Since the new technology is embodied

in “new” intermediate goods, the representative agent needs to expand the

scope of intermediate goods imported from aboard. There is a once-and-

for-all “set up” cost (or “fixed cost”) to operate with the new intermediate

goods, which is equal to 1/BA unit of final output. Notice that, in principle,

7For instance, see Engel and Roger (1996, 2001).8The rate of return of any particular intermediate goods is diminishing (α1 < 1).

15

BA captures not only the physical cost to adopt new technology, but also

the change in organizational form in order to maximize the efficiency of the

usage of new technology, as well as the administrative cost to go through the

domestic as well as foreign government to legalize the technological adoption.

A higher value of BA is associated with a lower cost of technological adoption.

Thus, under this formulation, the “degree of openness” is captured by two

parameters: the tax factor Γt and the adoption factor BA. Notice also that

At+1 does not affect the output at time t.

For simplificty, we assume that the supply of commercial property is fixed,

and that the agent can only accumulate property through purchasing from

the market,9

Ft+1 = Ft + Fmt . (3)

Now, the representative agent is assumed to maximize the expected value

of the discounted sum of utility, E0P∞

t=0 βtu(Ct). The dynamic optimiza-

tion problem of the representative agent can be represented by the following

Bellman equation:

9It is possible to allowing for endogenous yet sluggish adjustment in commercial prop-erty, as shown in closed economy model such as Kan et. al. (2004).

16

V (At, Ft) = max .u(Ct) + βV (At+1, Ft+1) (4)

s.t. Yt ≥ QtFmt +

(At+1 −At)

BA+

Z At

0

ΓtPt(i)Xt(i)di+ Ct, (5)

and equation (2), (3) hold.

Notice that the intermediate goods are imported and then “used up” in

the production process within the same period. Therefore, the maximization

problem can be broken into two parts. First, the agent needs to decide the

amount of intermediate goods i to purchase, Xt(i), i ∈ [0, At]. The second

step is to optimize over other variables. Following Grossman and Helpman

(1991), EKLR, the symmetry assumption is imposed, Pt(i) = P, ∀t,∀i. And

the tariff rate is assumed to be constant over time, Γt = Γ. This assumption,

though not necesary for the results, enables us to dramatically simplify the

problem and to present the intuition more transparently. The appendix

shows that (5) can be simplified as

AtRFt ≥ QtFmt +

(At+1 −At)

BA+ Ct, (6)

whereR is a complicated function of parameter and price, R =£α1(1− α1)

(1−α1)/α1¤·

17

(ΓP )−(1−α1)/α1 , and the term AtRFt is the aggregate output net of the pay-

ment of imported intermediate goods, which is in a sense the “net output”

of this economy, Y nt . Now we maximize (4) subject to (6) and (3). To solve

the model, we need to impose an additional market clearing condition. For

simplicity, we assume that the total stock of commercial do not increase nor

decrease,

Ft+1 = Ft ≡ F. (7)

Clearly, it is equivalent to imposing the zero-net-trade condition in Lucas

(1978), that Fmt = 0. The following proposition is proved in the appendix:

Proposition 1 Along the balanced growth path, the economy grows at a fac-

tor g, where

g = At+1/At = Ct+1/Ct = β (BARF + 1) , (8)

and the commercial property price is proportional to the technology,

Qt =β

1− β·RAt. (9)

From now on, we will focus on the commercial property price. First, we

will rewriting our variables in log form, ct = lnCt, qt = lnQt, etc. We can

18

then have the following proposition. (again, see the appendix for details)

Proposition 2 The (log) equilibrium price of commercial property can be

written as a function of the tax, the price of the intermediate goods, and the

technology of the country,

qt = θq + at −(1− α1)

α1τ − (1− α1)

α1p, (10)

for some constants θq.

The result is intuitive. A higher level of technology means a higher de-

mand for commercial property, and hence a higher level of commercial prop-

erty price. A higher level of tax or intermediate goods price would discourage

the importation of foreign goods, which would translate into a lower demand

for commercial property. However, if we want to do cross-country compari-

son with (10), this formula may not be as informative as it seems. The (log)

technology at is not directly observable. Hence, we will need to use different

kinds of proxies for that. Furthermore, since the technology and the com-

mercial property price are growing over time, (and their log values), both left

hand side and right hand side of (10) contains non-stationary terms. Thus,

we will need some sort of de-trending, which is the focus of the following

19

proposition:

Proposition 3 The (log) commercial property stock price can be described

by the following difference equation:

qt = θq −(1− α1)

α1τ − (1− α1)

α1p+ t ln g + lnA0, (11)

where A0 is the initial technology level, and g is the growth factor.

Notice that ln g is a non-linear function of several variables, including

the stock of commercial property stock F , the cost of technological adoption

BA, and the marginal return of an additional variety of intermediate goods

R. it should be beared in mind that R itself is a function of the tax factor

Γ and the imported price P . Thus, in reduced form, (10) actually implies

a potentially very non-linear relationship between the "degree of openness",

some initial condition, and the level of stock.

(to be added)

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3 Data and Empirical Results

3.1 Data Description

We have assembled data for 40 cities in 33 countries, for office property rents,

prices, local wages, openness, city population, city business activity, foreign

direct investment as well as other related macro-economic variables. The

data employed in our study have been collected from a variety of sources, as

follows:

a) Global metropolitan office rents and prices: We have acquired these

proprietary data from CB Richard Ellis, Frank Knight and Cushman and

Wakefield.

b) Urban Wages and Services Price: The United Bank of Switzerland

(UBS) research group has created a unique international database containing

international comparisons of purchasing power. These data were designed

for the multinational corporations the business executive community who

require the data about the cost of living for salary adjustments and other

compensation. The UBS publication, entitled "Prices and Earnings Around

the Globe, 2000", contains data for wages and some other variables for our 40

major world cities, on five continents, and is generated from comprehensive

21

surveys. Great effort and care has been taken, including qualitative and

other adjustments, to ensure accuracy of the data. The data are in nominal

US dollars.

c) Gross Domestic Product and Gross Domestic Product per capita:

These data are obtained from the World Development Indicators database

of the World Bank at http://devdata.worldbank.org/data-query. These data

are in nominal US dollars.

d) City area and population: These data are available from various

sources on the World Wide Web, including http://www.citypopulation.de,

as well as the United Nations statistical database. The coastal attributes of

cities were elicited from http://www.worldatlas.com.

e) Openness: We use the standard openness indices maintained by the

National Bureau of Economic Research (NBER). This measure is calculated

as the ratio of exports plus imports to the Gross Domestic Product.

f) Foreign Direct Investment: This information is available from the In-

ternational Financial Statistics Database of the IMF, as well as the World

Bank.

g) Business Formation: We are attempting to get variables on business

formation, as well as a proxy for finance, insurance, real estate employment

22

growth variable for the cities in our sample. We are also looking at alternative

occupational data as a proxy for office demand.

h) The interest rate spread: We have obtained this variable from the

Global Financial Database. The spread measured by the difference of a coun-

try’s short (3-month) and long (10-year) term interest rates, a well-recognized

standard measure of credit cost and availability, affects real estate market

supply since, ceteris paribus, profitability of developers depends critically on

cost and availability of borrowed funds.

3.2 Empirical Results

We plan to estimate a pooled equation of the following type, based on our

earlier work on globalization and residential rents:

Commercial rents/prices = α + β1·(wages) + β2·(business activity

proxies) + β3·(interest spread) + β4·(GDP) + β5·(city density) + β6·(FDI

or openness)

In addition, we shall determine the effects of the share of city population

in country population, GDP per capita, employment data etc. The only

data lacunae at present are panel data for the dependent variable, and some

proxies for business formation and business activity.

23

(to be ADDED)

4 Concluding Remarks

[preliminary — subject to change]

This paper opens an untapped area for potential research that should

integrate international economics and urban/real estate economics, and of the

interplay of tradeables and non-tradables. The growing, more extensive and

improved international macro and real estate information for pooled time-

series and cross-sectional data are keys for the exploration of the relationship

between international openness and commercial property market.

24

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30

Appendix(Note for the editors: In case it is decided that the appendix need not

be published, it will be available upon request)

A Proofs

A.1 Proof of (6) (Simplification of the original maxi-mization problem)

Here follows EKLR to break the original maximization problem into twostages. Given the prices of the intermediate goods, the first step is to computethe optimal amount of import. It will determine the amount of “net output”,the total production net of the payment of imports. The second step is tochoose the amount of consumption goods, household capital goods and theoptimal level of technological adoption for the given amount of net output.Differentiating with respect to Xt(i) gives the following first order condi-

tion,

(1− α1) (Ft)α (Xt(i))

−α1 = ΓtPt(i), (12)

which implicitly define the “demand function” of each Xt(i). Equation (12)says that the demand of (imported) intermediate goods i, Xt(i), is determinedby the equalization of its marginal product and after-tax price, Γt ·Pt(i). Nowwe define the net output Y n

t as the aggregate output net of cost of inter-

mediate goods, Y nt ≡

hR At

0(Xt(i))

1−α dii(Ft)

α −R At

0ΓtPt(i)Xt(i)di. Since

Pt(i) = Pt, Γt = Γ (assumed in the text) it is clear that

Xt(i) ≡ Xt = Ft

µ(1− α1)

ΓP

¶1/α1, (13)

31

∀t,∀i. Thus,

Yt =

∙Z At

0

(Xt(i))1−α di

¸(Ft)

α

= At (1− α)(1−α)/α Ft (ΓP )−(1−α)/α

and hence Y nt = At ·R · Ft, (14)

where Rt is in a sense the marginal product of an additional intermediategoods, conditioning on the amount of commercial property stock,

R =£α1(1− α1)

(1−α1)/α1¤· (ΓP )−(1−α1)/α1, (15)

and equation (5) can hence be re-written as (6).

A.2 Proof of (8)

To prove (8), we need to derive the first order conditions of the representativeagent. Let λ1t, λ2t be the Lagrangian multipliers of the constraints (6) and(3) respectively. The first order conditions are standard:

λ1t = (Ct)−1 , (16)

λ1tBA

= βλ1,t+1

µRF +

1

BA

¶, (17)

λ2t = β [λ2,t+1 + λ1,t+1At+1R] , (18)

Qt = λ2t/λ1t. (19)

Note that we can combine (16) and (17) and get

Ct+1

Ct= β (1 +BARF ) .

Now we follow the appraoch by Ljungqvist and Sargent (2000), whichis to simply state our conjecture, and then we will verify that it is indeedconsistent with all other equations of the model.

32

Conjecture 4 The consumption and the technology grows at the same rate,

Ct+1

Ct=

At+1

At. (20)

With (20), we substitute (7) into (6), we get

Ct = At

∙RF − g − 1

BA

¸. (21)

Notice that everything in the [.] is invariant over time, and hence we candeduce (20) from (21). For future reference, we also combine (21) with (16)and obtain

λ1tAt =

∙RF − g − 1

BA

¸−1, (22)

and we notice that the right hand side is indeed a constant.Now we want to solve for (18). With (22), (18) is simply

λ2t = β

"λ2,t+1 +R

∙RF − g − 1

BA

¸−1#,

Following Lucas (1978), we impose further the no-bubble condition

limt→∞

(β)t λ2t = 0,

(18) can be simplified as

λ2t =βR

1− β

∙RF − g − 1

BA

¸−1. (23)

Now we are ready to obtain an expression for commercial property price.Combining (22), (23) with (19), we get

Qt =β

1− β·RAt,

which is clearly (9).

33

A.3 Proof of (10)

We start with (9). Taking log on both sides, we have

qt = ln

µβ

1− β

¶+ r + at

where

r = lnR

= ln¡£α1(1− α1)

(1−α1)/α1¤· (TP )−(1−α1)/α1

¢= ln

£α1(1− α1)

(1−α1)/α1¤− (1− α1)

α1τ − (1− α1)

α1p,

with τ = lnΓ, p = lnP . Thus,

qt = θq + at −(1− α1)

α1τ − (1− α1)

α1p,

where θq = ln³

β1−β

´+ ln

£α1(1− α1)

(1−α1)/α1¤.

A.4 Proof of (11)

Recall (10) that the only non-stationary term on the right hand side is at.By (8),

at = lnAt

= ln (gAt−1)

= ln g + lnAt−1

= ...

= t ln g + lnA0,

34

where

ln g

= ln (β (1 +BARF ))

= lnβ + ln (1 +BARF ) ,

which has no closed form solution ready for further analysis.

35