WP-2017-006

Center for Advanced Economic Study Fukuoka University

(CAES) 8-19-1 Nanakuma, Jonan-ku, Fukuoka,

JAPAN 814-0180 +81-92-871-6631

Junmin Wan

Faculty of Economics, Fukuoka University, Japan

Bubble Premium, Bubble Prevention, and Bubble Landing

CAES Working Paper Series

Bubble Premium, Bubble Prevention, and Bubble Landing1

Junmin Wan2

Faculty of Economics, Fukuoka University

October 25, 2017

1 This research was partially supported by the China Natural Science Foundation - Peking University Data Center for Management

Science (Research grant 2016KEY05), and the JSPS KAKENHI Grant (#16K03764). The author gratefully acknowledges the

support of these funds.

2 The author thanks Masahiro Abiru, Takao Fujimoto, Takashi Kamihigashi, Koji Kitamura, Takamitsu Kurita, Shi Li, Federica

Liberini, Chuliang Luo, Hiroshi Morita, Ko Nishihara, Masao Ogaki, Kazuo Ogawa, Masaya Sakuragawa, Kar-yiu Wong, Ping

Zhang, and the participants for their beneficial comments and encouragements when the paper was presented at universities,

including Aoyama Gakuin, Central University of Economics and Finance, Dalian University of Technology, Università della

Svizzera italiana, Henan, Kyushu, Nanchang, Nankai, Peking, Peking Normal, South West University of Economics and Finance,

Tsukuba, Zhejiang, and the Institute of Economics of China Academy of Social Science. The author is deeply indebted to Carl R.

Chen (the editor) and an anonymous referee for constructive comments. Any remaining errors here are the author’s responsibility.

Correspondence: Nanakuma 8-19-1, Jounan Ward, Fukuoka City, Fukuoka 8140180, Japan; (e-mail) wan@econ.fukuoka-u.ac.jp;

(tel) +81-92-871-6631(ext.4208); (fax) +81-92-864-2904.

The revised version entitled ``Prevention and Landing of Bubble’’ is forthcoming in International Review of Economics and Finance.

http://www.sciencedirect.com/science/article/pii/S105905601730816X

Highlights

1. Rational bubble term grows faster than the risk-free asset because bubble premium is required by a risk-neutral investor.

2. By replacing conventional assumptions on the satisfaction of the transversality

condition with introducing capital gains taxes, transaction or property taxes, rebate

options, and fixed periods of asset usage, a rational bubble has been shown to be

preventable.

3. For an existing bubble, hard，soft and medium landings have been shown to be

possible via tax tools.

4. Japan, the United States, and Greece experienced real estate bubbles and hard

landings, while Taiwan ended its real estate bubble in the 1980s with a soft landing.

Abstract

Rational bubble term grows faster than the risk-free asset because bubble

premium is required by a risk-neutral investor. By replacing assumptions on the

satisfaction of the transversality condition with introducing capital gains taxes,

transaction or property taxes, rebate options, and fixed periods of asset usage, rational

bubble is shown to be preventable. For an existing bubble, hard- and soft-landings are

shown to be possible. Hard landing is defined by a bubble which crashes via financial or

tax tools, while soft landing is defined as an increasing bubble reaching some stable

value via taxes. Japan, U.S., and Greece experienced real estate bubbles and hard

landings, while Taiwan ended its real estate bubble in the 1980s with a soft landing.

JEL classification: D46, D82, D84, G18

Keywords: Bubble premium, Bubble prevention, Hard landing, Soft landing, Tax

1 Introduction

The global economy is unstable and faces uncertainty because major countries,

such as the United States, have undergone financial and economic crises. Stiglitz (2009)

and Rogoff (2010) have argued that the current economic system, especially the regulation

of capital markets, “contributes” substantially to economic crises. The bubble and

subsequent crash of the asset market, especially the housing market, were the major cause

of these crises. There have been similar bubble-crash crises in different countries at

different times, but until now, we have had little idea of how to solve this problem. This

prompted Wan (2012, 2014a, b) to state that the bubble effect would be a “cancer” of the

market economy and that we need to develop some “medicine” to treat it. In this paper, we

will propose appropriate tools and taxation on asset trading as preventative “medicine.”

If we do not find a solution, to prevent the occurrence of bubbles, the result will be

repeated instances of bubble and crash, and economies will face recession. This could result

in significant damage if recession persists in the long run after a crash. Ogawa and Wan

(2007) and Ogawa (2009) pointed out that a crash in the asset market, especially in the

housing market, was the main cause of Japan's lost decade, even though the economy had

been booming from huge capital gains in the bubble era (Horioka, 1996). In the Japanese

case, we tend to think “what should have been done after a bubble crash, and why did the

bubble occur in the 1980s?” (Wan, 2004, 2014a). The answer to the former question is that

a reduction of debt among households, firms, and banks is necessary for economic recovery

(Ogawa, 2009). Wan (2014b) noted that the most important reason for the bubble of the

1980s was that the Japanese government gave up the “real demand principle” in the asset

1

market by accepting “financial freedom” and “global standards in the financial market” to

permit “speculative transactions.” Wan (2014b) further argued that the main difference in

market-oriented economic thought between the East and the West would come from

different views on “speculative transactions.” For example, it is considered common sense

in China that speculative trading is not only a type of “unfair exchange,” but can also be a

criminal action, at least ex post.1

There is abundance literature from China, dating back thousands of years, on the

idea of anti-speculation. “If there is speculation in goods by private traders, the prince's

plans will fail and the people will lose their livelihood. Therefore, those who were skillful

in ruling the empire also extended their control to things other than the two chief targets for

speculation (Guan, BC645, p. 405).” In present-day China, there are price bureaus in both

central and local governments, and the main objective of these bureaus is to prevent

speculation. However, there have been opposing views on speculation in other countries.

For example, speculation has been considered a scheme of natural selection to stabilize the

trading price, as argued by Friedman (1953), though De Long et al. (2001) and Yan (2008)

doubt this hypothesis.

A speculative trade has been defined as one having expectations of capital gains

from resale of an asset. The rational bubble is caused by speculative trade and is

mathematically equivalent to relaxation of the transversality condition.2 There are two

1 The concept of “fair exchange” was mentioned by Aristotle in ancient Greece (Trever, 1916; Monroe, 1924) and can also be found in ancient India (Joshi, 1928), although no record could be found in ancient Egypt. This is the reason barter systems were used. See Yoshimura (2005) for details. The "unfair exchange" or "unfair trade" of labor was analyzed byMarx(1867). 2 Ikeda and Shibata (1992) deal with the issue of fundamentals-dependent bubbles in stock prices.

2

main opposing views on rational bubbles among economists. Many researchers believe that

rational bubbles may act as Pareto improvements in a dynamic inefficient economy as

argued by Diamond (1965), while the other ones argue that a bubble hurts an economy

(Bernanke, 2009; Hirano et al. 2015; Miao et al 2015; Stiglitz, 2009). In our view on

bubbles, however, as the bubble equilibrium in Diamond (1965) is established by the

rational expectation of all economic agents, its stability would be difficult to guarantee

because the belief that future generations may change with time. Thus, it may be difficult to

emulate the old generation. Apart from rational bubbles, literature about speculation and

overconfidence offer some insight for understanding the bubble issue (Shiller 1981;

Scheinkman and Xiong 2003; Xiong and Yu 2011). Xiong (2013) recently performed a

survey on bubbles, crises, and heterogeneous beliefs. The bubble in this framework would

also be considered a type of premium of market incompleteness or incorrect belief. Hence,

this type of bubble would be essentially different from the rational bubble.

Additionally, as pointed out by Wan (2012, 2014a), one result of the occurrence of

a bubble and a crash is the redistribution of wealth among asset traders with ex post

unfairness; the trade of bubble assets is a type of zero-sum game that has a negative

externality and long-term recession problems after the bubble bursts (i.e., the “Occupy Wall

Street” movement). Thus, the government is responsible for stopping speculative

transactions and, at the same time, for inducing private traders’ expectations, not of capital

gains, but of income gains from asset trading. This is because the income gain or dividend

is the added value of the asset and thus components of gross domestic product, whereas the

zero-sum type of capital gains is not.

3

It is difficult for government to recognize speculators and to distinguish “real

demand” based on fundamentals in the asset trading market. Traders themselves could

know their own intent, but how can a government distinguish speculative traders from

fundamental ones? This is a typical example of information asymmetry between private

traders and government. For the purpose of examining anti-speculation, we consider that

governments use capital gains tax, a form of taxation used in many countries, to identify

speculation and to monitor it. Burman (1999) identified the popularity of the capital gains

tax in major countries. For example, the maximum tax rates of long-term capital gains in

Australia, Canada, France, Italy, Japan, Sweden, the United Kingdom, and the United

States in 1998 were 48.5%, 23.5%, 26.0%, 12.5%, 20.0%, 30.0%, 40.0%, and 20.0%,

respectively (Burman, 1999, p. 29).3 Even with these tax rates, significant asset bubbles

occurred and crashed in Japan and the United States. Our analysis finds that the reason for

these occurrences is that capital gains tax rates were too low.4

When bubbles occur, what should be done to prevent a crash? Wan (2012, 2014b)

suggested the following steps: first, government should control the asset price at some

stable value for some time; second, government should gradually raise the consumer price

index. If these policies succeed, a bubble economy will have a soft landing. However, even

if this soft-landing policy succeeds, a huge redistribution of national wealth will have

occurred because those agents with substantial bank holdings will have incurred significant

losses as a result of the new consumer price index. Compensation for losses will therefore

3 We do not support the idea of an indirect taxation problem as proposed by Frank P. Ramsey in 1927 and Fujimoto and Wan (2009). 4 Lei, Noussair and Plott (2001, 2002) report that neither no-resale constraints nor a 53.4% capital gains tax rate could stop the occurrence of a bubble in the experiment.

4

be necessary. The government must subsidize real wealth losses using tax revenue and

seigniorage. These related policies are difficult to enact, but may be the only way to solve

housing bubble issues in many big cities, such as Beijing and Shanghai.5 Dreger and

Zhang (2010), Ueda (2011), and Wan (2015a, b, forthcoming) have argued that we can

anticipate the extent of a housing market bubble in urban China. If China fails to do this, a

crisis similar to that experienced in Japan and the United States could occur in the near

future.

The asset bubble might also cause excessive domestic saving and consumption

shortage issues. Wan (2011b, 2016) proposed that the speculative saving motive could be

measured based on the degree of distortion in financial intermediate markets and the

leverage ratio. He showed that these factors had a significant impact on saving and could

provide an explanation for why China saves so much compared with the United States.

Wan’s (2015a) provincial panel data from 1995 to 2010 and individual data from China

supported the speculative saving hypothesis. After controlling for life cycle and other

related factors, Wan (2015a) found that bubbly housing prices and loan interest payments,

especially those in urban sectors, significantly increased the saving rate in cities and the

nation as a whole. Therefore, an anti-speculation policy could contribute to solving

domestic excess saving and consumption shortage issues as well as the problem of global

imbalance.

The soft landing policy is a method to address a bubble before a crash. However,

“the best solution is the prevention of bubbles arising in the first place” (Wan, 2004,

5 Also see Dreger and Zhang (2010), Ueda (2011) and Xiong and Yu (2011) for details on bubbles in present-day China.

5

2014b).6 There are ways to prevent the occurrence of the rational bubble in asset trading,

but this requires examining and refuting some existing assumptions. First, a strictly positive

capital gains tax can induce “real demand” to exclude the rational bubble ex ante and ex

post. This does not distort the asset price based on fundamentals, even in the case that the

information on fundamentals is renewed. Second, a transaction tax by Tobin's proposal is

not a perfect solution in a market-oriented economy because it distorts the fundamental

value of assets. Third, a dividend tax cannot exclude a bubble. Fourth, a rebate option can

exclude a bubble. Finally, fixed-period land-use rights without taxation and rebate option

can prevent a bubble in the land market.

For the land bubble, considered a result of market failure, the government has

three kinds of policies, which we will call hard landing, soft landing, and medium landing.

Hard landing is when the government chooses financial or tax tools to make the bubble

crash, but the land market value after the crash may be lower than that of fundamentals.

Thus, a hard landing is considered a secondary governmental failure. Soft landing is when

the government chooses a land value added tax or a capital gains tax to make the increasing

bubble remain at a constant value. Medium landing is when tax tools (not financial tools),

such as capital gains tax and land value tax, are used to maintain the increasing bubble at a

constant value, and then the land market value ex post can be equal to that of the

fundamentals without a bubble and taxes. Based on historical facts, Japan, the United

States, and Greece experienced serious land bubbles and then their bubbly economies

landed hard. However, Taiwan made the land bubble in the 1980s land softly. Our findings

6 Bernanke (2009) also mentioned the problem of bubble prevention.

6

here would be an important reference, especially for solving serious land and housing

bubble issues in some large cities of contemporary Mainland China.

This paper is largely different from Wan (2014b) and would be a more general

analysis. Fundamental term and bubble term grow at the same rate in Wan (2014b), while

bubble term grows faster here because bubble premium is introduced. A bubble investor

borrows money from financial institutions; thus, this setting would accelerate the degree of

speculation by financial leverage and it would be closer to the real world. Wan (2014b)

would be a special case of this framework. Furthermore, the analysis of unlimited liability,

endogenous interest rates, rebate option, and the recent bubbly price at country level,

including Greece, Japan, and the United States, and at the city level, including Beijing,

Shanghai, and Taipei, did not appear in Wan (2014b), but are newly added here.

This paper below is organized as follows: Section 2 presents the basic model of a

rational bubble; Section 3 presents some ways to prevent a rational bubble within the

framework of private ownership; Section 4 provides a solution in the context of mixed

ownership; Section 5 shows polices for hard landing, soft landing, and medium landing of

rational bubble, as well as some historical facts on hard landing policies from Japan, the

United States, and Greece, and soft landing policy from Taiwan. Section 6 presents

concluding remarks, discusses policy implications, and identifies issues for future research.

2 The Bubble

2.1 Rational Bubble

Blanchard and Watson (1982) outlined the basic framework of a rational bubble.

7

Assume there are two assets in an economy, one safe and the other risky, like land. The

market is assumed to have no opportunity for arbitrage, with private ownership of the assets

established. The investor or asset owner considers the following risky asset-trading

problem:

r : the interest rate of a risk-free asset;

td : the dividend of the risky asset at time t ;

tp : the market price of the risky asset at time t .

We further assume that r is consistently positive over the time horizon. A risk-

neutral investor is assumed to freely choose to invest in a risk-free or risky asset. The

source of the risk is uniquely from the infinite time horizon, and we consider it as a type of

“certain uncertainty.” This risk uncertain because we do not know when the ending point

of the time horizon will be reached, and we say it is “certain” because this type of

uncertainty is well known to every investor. Under the no-arbitrage condition, the following

equation should be satisfied in partial equilibrium for an agent with a finite time life span,7

t

ttt

pdpEr ][1 11 ++ +

=+ , (1)

where tE is the expectation operator at time t . The forward-looking solution of tp in

the Equation (1) is,

7 If the investor has a limited life span and the maturity of the asset, such as land, is infinite, he or she must consider reselling the asset when initiating the purchase. It can be considered one of the resources necessary for resale. It is equivalent to the bubble setting offered by Harrison and Kreps (1978) and Tirole (1985).

8

+

+

+

= +

=

+∑ TTt

t

T

jj

jttt r

pEr

dEp

)1()1(1

, (2)

where ),1[ ∞∈T , and when ∞→T , the result is,

+

+

+

= +

∞→

∞

=

+∑ TTt

Tt

jj

jttt r

pEr

dEp

)1()1(1

. (3)

The first and second terms on the right-hand side of Equation (3) are the fundamental

values of income gain and the bubble term of the risky asset, respectively. The bubble term

is also called a transversality condition, and a rational bubble occurs if and only if

0)1(

>

++

∞→T

Tt

T rp

tE . (4)

In the literature, such as Miller and Modigliani (1961) or Montrucchio (2004), the above

condition was assumed to be satisfied to exclude the rational bubble,

0)1(

=

++

∞→T

Tt

T rp

tE . (5)

Equation (5) shows no rational bubble by assumption. For simplicity, if we assume that,

][][1 jttt dEdE

t +=+

for any ),1[ ∞∈j , then the Equation (3) becomes,

+

+

= +

∞→

+T

Tt

Tt

ttt r

pEr

dEp)1(

1 . (6)

Some cases satisfy or violate Equation (5). We assume the growth rate of

expectation for Ttp + is bg , where bg expresses speculative aspects of the investor,

which are independent from dividend d . The speculative investor believes that the asset

will be bought by a new speculator, even though the bubble term is common knowledge for

9

all investors. Phillips et al. (2015a, b) developed an empirical method of detecting an

explosive bubble, and serious housing bubbles in large cities in China were determined via

a similar method in Wan (2015a, b). This empirical method would, theoretically, be

expected to measure the size of bg . We then have,

TbTt gp )1( +=+ , (7)

where,

0)1(

→

++

∞→T

Tt

T rp

tE , for rgb < , (8)

1)1(

=

++

∞→T

Tt

T rp

tE , for rgb = , (9)

∞→

++

∞→T

Tt

T rp

tE )1(, for rgb > , (10)

and Equations (8), (9), and (10) show conditions of no bubble, concurrent or coexisting

bubbles (Kamihigashi 2010), and explosive bubble, respectively. For the explosive bubble

expressed by Equation (10) and in Wan (2014), the growth rate of bubble, bg , is higher

than the interest rate, r ; then, the discounted value of bubble becomes infinity. However,

this situation rules out the no-arbitrage condition from Equation (1). Furthermore, for an

investor, if the growth rate of bubble is equal to that of risk-free asset, what is the incentive

for an investor to purchase a risky bubble that may crash? We will analyze this issue in the

following subsection.

2.2 Bubble Premium

10

For the trading of a risky asset, it is a conventional approach to assume that the

investor is a risk averter; for example, a consumer always asks for risk premium in a

consumption-based asset pricing model (Merton, 1973, Poterba and Summers, 1986).

However, it is unnatural to assume that a risk-averter would actively buy a bubbly asset that

may crash at any time. Here we turn to focus on the essential difference between a risk-free

asset and a bubbly asset in a market with financial friction. An investor obtains cash flow of

interest rate, r , at every period when holding a safety asset, but there is dividend sequence

d at every period when holding a bubbly asset, and the cash flow of a pure bubbly asset is

zero before it is sold. Further suppose that the investor needs to borrow from a lender such

as bank to finance the payment tp , then the bank has to assess the risk of repayment. The

major risk would be the credit risk when the investor cannot pay back the loan because of

the asset price crash; hence, the bank requires collateral. Suppose the investor has no other

assets for collateral; then, the risk asset is also used as collateral.8

The first work of the bank would be to evaluate the value of collateral. Assume the

bank must hold the collateral forever when the investor defaults; then, the value of

collateral is the summation of discounted dividend sequence d , which is equal to the ratio

of d to r . The bank also knows the default risk associated with the size of the loan

and the value of collateral (Furstenberg 1969; Brunnermerier and Pedersen 2009). The loss

given default (LGD) is the loan balance tp net of the ratio of d to r divided by tp , 1-

8 The subsequent content is to answer the referee’s question. The author is deeply indebted to the referee’s constructive comment.

11

( d / r )/ tp = ( tp - d / r )/ tp . The credit risk increases with LGD;9 thus, the bank asks for

credit spread or premium to cover the LGD (Barro 1976; BIS 2004; Benmelech and

Bergman 2009; Niinimäki 2009; Berger et al. 2016). Hence, the investor is required to pay

a premium corresponding to the LGD with a positive coefficient γ, which measures the

elasticity of premium to the purchase of bubbly asset.10

The no-arbitrage condition is re-written as,

−−

+=+ +++

t

ttt

t

ttt

prdpE

pdpEr /][1 111 γ . (11)

If ][][1 jttt dEdE

t +=+

for any ),1[ ∞∈j , then the forward-looking solution of the Equation

(11) becomes,

++

+

= +

∞→

+T

Tt

Tt

ttt r

pEr

dEp)1(

1

γ, (12)

and the condition of no bubble in Equation (11) becomes,

0)1(

=

+++

∞→T

Tt

T rp

tEγ

. (13)

The fundamental value of Equation (12) is the same as the one of Equation (6). The

premium parameter γ has impact on the bubble term, but not the fundamental term. It

implies the investor would ask for a premium for purchasing a bubble. This premium can

also be called bubble premium.11 Then we have,

9 If the down payment ratio is set to be LGD, the credit risk will decrease to zero. Hence, appropriate down payment may raise the stability of banking sector. 10 This bubble premium would be a mixture of credit risk and external finance premium in Bernanke et al. (1999) and Graeve (2008). In reality, down payment is always required; then, γ would be adjusted by ratio of external finance which is equal to unity net of ratio of down payment. 11 The bubble premium could also be from probability of crash of stochastic bubble in a frictionless market described in

12

0)1(

→

+++

∞→T

Tt

T rp

tEγ

, for γ+< rgb , (14)

1)1(

=

+++

∞→T

Tt

T rp

tEγ

, for γ+= rgb , (15)

∞→

+++

∞→T

Tt

T rp

tE )1( γ, for γ+> rgb . (16)

Equations (14), (15), and (16) show new conditions of no bubble, concurrent or coexisting

bubbles, and explosive bubble, respectively. Noticeably, the growth rate of bubble term is

higher than that of risk-free asset, and the ratio of the former to the latter increases with

time. Thus, the portion of bubble term increases with time when bubble occurs, while in the

standard bubble model in the last subsection or in the model with a risk-averter who asks

for risk premium (Wan 2011a), this portion is unchanged. This setting would give a

plausible explanation of why bubble grows obviously faster than interest rate in Figures 1

and 2 at the country and city level.

Easy and cheap money with lower bubble premium or lower interest rate tends to

satisfy bubble condition of Equation (16). The external finance premium decreased from

Fama (1970). For example, if the bubble remains with positive probability 10 <<π and bursts with probability π−1 in each period, the no-arbitrage condition will be re-written as,

t

tttttt

prdEpEdEr ]/[)1(][][1 111 +++ −++

=+ππ

. If ][][

1 jttt dEdEt +=+

for any

),1[ ∞∈j ; then, the forward-looking solution will become,

+

+

= +

∞→

+T

Tt

Tt

ttt r

pE

rd

Ep)]/)1[(

1

π

, and it will be similar to the form of the

Equation (12). We obtain γπ ++=+ rr 1/)1( if ππγ −

+=1)1( r

. Even without external finance premium, we can show that the growth rate of bubble term increases faster than that of risk-free asset in a stochastic bubble model. Hence, the external finance premium would be unnecessary. Bubble premium is jointly determined by the external finance premium and the credit risk premium. The improvement of market efficiency decreases the external finance premium but increases the credit risk premium (CRP), and the later presumably dominates the former. Hence, the more efficient market would have higher bubble premium. Presumably, the bubble premium γ is a mixture of external finance premium (EFP) and CRP, and it is expressed by, γ= EFP*CRP + CRP=(EFP +1) CRP. The market efficiency is expressed by ε , where higher ε indicates higher efficiency. EFP decreases with ε , while CRP increases with ε . If we assume that ,0)1( >++ ∂

∂∂

εεCRPEFP EFPCRP γ will increase with ε . That is, a more efficient market may have higher bubble premium.

13

2.2% in 2000 to 0.8% in 2004 in the United States (Graeve 2008), and decreased from 2.4%

in 2000 to 1.7% in 2006 in euro economies (Gelain 2010); then, these areas experienced

housing bubbles in the same period. The interest rate, which decreased from 7.25% in 1980

to 2.4% in 1987, caused a serious real estate bubble in the 1980s in Japan (Ogawa 2009).

The LGD would be necessary for bubble premium. Assume that the investor and the

bank are the same agent (in other words, the bank is the investor); then, the external finance

premium becomes zero. The risk of bubble crash still remains; thus, the bank also requires

bubble premium to cover the LGD. Risk from bubble crash would be more important than

external finance premium, though the external finance premium may amplify the risk

premium from bubble crash.

The bubble premium would be mainly from the LGD, 1/)/(0 ≤−=≤ prdpLGD ,

though it is also from the external finance premium. For an efficient market LGD should be

0, while it would equal 1 in an extremely inefficient market. Hence, bubble would not occur

if the bubble premium is sufficiently high. LGD, here, could also be considered as a

measurement of market efficiency.12 Therefore, we would not be puzzled by that less

efficient market having lower bubble premium γ, and that no-bubble condition of Equation

(14) is easily violated.

The investor here is assumed to borrow from a lender, such as a bank, to finance

the bubble investment. He or she would change the belief or could not borrow enough

money when a new regulation of lending volume is levied on banks; thus, the bubble would

12 For example, market efficiency (ME) can be defined as 1/)/(10 ≤=−=≤ prdLGDME , then a more efficient market would have higher ME.

14

suddenly burst, and then, accordingly, a banking crisis would occur (Roy and Kemme

2012). This is just as in Japan’s case in the 1990s because Japan set the upper bound of

bank lending related to land purchase and raised the interest rate before the land bubble

burst (Ogawa, 2009).

It is found in the literature that financial policies, such as changes of interest rate,

reserve ratio, and lending volume regulation have significant impacts on not only the asset,

such as land market, but also on the whole macro economy (Ogawa, 2009); therefore, the

radical intervention of financial tools would not be preferable. We only think of the impacts

of tax policies on the asset bubble in the following sections in line with proposals by

Stiglitz (1989).

3 Preventing a Bubble under Private Ownership

3.1 Taxation

3.1.1 Capital Gains Tax

We introduce a mechanism to satisfy the transversality condition at ∞→T

without the assumption in Equation (13). We first consider a capital gains tax with rate

]1,( r−∈κ in Equation (11); then, examine how the tax would exclude the bubble term. We

also investigate the impact of this tax on the fundamental term. This creates a new no-

arbitrage condition faced with a capital gains tax,13

13 We do not consider the negative bubble case. The negative capital gains tax means a subsidy from the government.

15

t

ttttttttt

pppErdpEdpEr ][]/[][1 1111 −−−−+

=+ ++++ κγ . (17)

By solving for tp we obtain,

−++

−+

−++

+−= +

∞→

∞

=

+−

∑ TTt

T

Tt

jj

jtj

tt rpE

rrd

Ep)1(

)1()1(

)/1()1(

1

1

κγκ

κγγκ

. (18)

Proposition 1:

A capital gains tax with rate

+−∈ 1,)(

b

b

grg γκ excludes the rational bubble

without the assumption of the transversality condition, and 1→κ for γ+>> rgb .

Proof:

0)1()1)(1(

)1()1(

→

−+++−

=

−++

−∞→

+

∞→

Tb

TtT

TtT

Tt r

gEr

pEκγ

κκγ

κ,

for

+−∈ 1,)(

b

b

grg γκ , then 1

1)1)(1(<

−+++−κγ

κr

gb . Q.E.D.

Property 1:

For the special case ][][1 jttt dEdE

t +=+

, for any ),1[ ∞∈j , the capital gains tax does

not distort the fundamental value.

Proof:

If ][][1 jttt dEdE

t +=+

for any ),1[ ∞∈j ; then, Equation (18) becomes

16

−++

−+

= +

∞→

+T

TtT

Tt

ttt r

pEr

dEp)1(

)1(1

κγκ , (19)

and the first term of the right-hand side of Equation (19) is the same as that of Equation (6).

Q.E.D.

Therefore, without the assumption of satisfaction of the transversality condition,

we can introduce a strictly positive capital gains tax that excludes the rational bubble.

Furthermore, this strictly positive tax does not distort the fundamental value of a risky asset

for the special case ][][1 jttt dEdE

t +=+

for any ),1[ ∞∈j . The intuition of no distortion

here is that the discounted value for any ),1[ ∞∈j is constant over time; thus, the

capital gains should only be from the bubble term.

The Arrival of New Information on Future Dividend Payments

Next, we consider the case where the new information on future dividend

payments arrives. We assume that an investor buys a risky asset at the following price,

][][1 jttt dEdE

t +=+

for any ),1[ ∞∈j ,

= +

rdEp t

tt1 , while 0

)1()1(

=

−++

− +

∞→T

TtT

Tt r

pEκγ

κ for 1=κ .

When the information on future dividend payments from the asset is renewed,

][][][][11

''jtttjttt dEdEdEdE

tt ++ =>=++ . For any ),1[ ∞∈j , the market price will be

,1'

'

= +

rdEp t

tt (20)

17

where

=>

= ++

rdEp

rdEp t

ttt

tt11

'' . (21)

Proposition 2:

Assume the arrival of new information on future dividend payments is perfectly

realized and the realized dividends are equal to those observed ex post by the government: a

100% capital tax rate ex ante with payback ex post, the same amount as the capital gains

from the government to the investor, excludes the bubble and does not distort the market

price of the risky asset.

Proof:

For a 100% capital gains tax rate, the amount of capital gains tax ex ante will be

−=− ++

rddEpp tt

ttt11

'' . (22)

For the investor, the value of the risky asset becomes,

==−+ +

rdEpppp t

ttttt1

''' )( , (23)

which is exactly equal to Equation (20). Q.E.D.

3.1.2 Transaction Tax

As proposed by Tobin (1974), we consider a transaction tax with a rate ( )1,r−∈τ

18

in Equation (11),14 and obtained a new no-arbitrage condition,15

t

tttttttt

ppErdpEdpEr ][]/[][1 1111 ++++ −−−+

=+τγ . (24)

It is equivalent to the land value tax or asset holding tax or property tax when it is assumed

that the asset owner trades the asset at every period. By solving for tp we obtain,

++

−+

++

+−= +

∞→

∞

=

+−

∑ TTt

T

Tt

jj

jtj

tt rpE

rrd

Ep)1(

)1()1(

)/1()1(

1

1

γτ

γγτ

, (25)

and for ][][1 jttt dEdE

t +=+

for any ),1[ ∞∈j , the market price will be

++

−+

++

+= +

∞→

+TTt

T

Tt

ttt r

pEr

rdEp)1(

)1()/1(1

γτ

τγγ . (26)

Proposition 3:

To exclude the rational bubble, a transaction tax with the rate

+

+−∈ 1,

1)(

b

b

grg γ

τ

is necessary, and any strictly positive transaction or property tax distorts the fundamental

value of the asset, even for the special case ][][1 jttt dEdE

t +=+

for any ),1[ ∞∈j .

Proof:

14 If a strict 100% transaction tax rate were levied on asset trading, there would not be any asset sellers. It means that a market economy

would be excluded. Therefore, the transaction tax rate should be lower than 100%. The negative transaction tax means a subsidy from the

government.

15 If the speculative trader trades the asset ),1[ ∞∈z times at the same expected price within one period, the arbitrage condition

will be t

tttttttt

ppEzrdpEdpEr ][]/[][1 11111 +++++ −−−+

=+τγ , where z here expresses the degree of speculation.

19

For the second term of the right-hand side of Equation (26), if

0)1(

)1)(1()1(

)1(→

+++−

=

++

−∞→

+

∞→

Tb

TtT

TtT

Tt r

gEr

pEγ

τγ

τ, for

+

+−∈ 1,

1)(

b

b

grg γ

τ ,

then 11

)1)(1(<

+++−γ

τr

gb . For the first term of the right-hand side of Equation (26),

<

++

=

++

+ ++

)/()/1( 11

τγττγγ

rrdE

rrdE t

tt

t

+

rdE t

t1 for )1,0(∈τ . (27)

Q.E.D.

If a strictly positive transaction or property tax rate is levied on asset trading, the

fundamental value of the asset will be distorted. Hence, Tobin's proposal would not be the

best instrument to eliminate a rational bubble. However, to exclude the same-sized bubble

( bg ), the transaction or property tax rate can be strictly lower than the capital gains tax rate

because b

b

b

b

grg

grg )(

1)( γγ +−<

++− . Therefore, for an economy with politically opposite

taxpayer power, the transaction or property tax would be more easily distributed than a

capital gains tax.

According to Torello (2011), “the EU commission has made a proposal for a tax on

financial transactions globally. It would tax exchanges of shares and bonds at a rate of

0.1%, while the rate for derivative contracts would be 0.01%. Even though the U.S. and

Canada have opposed the idea, all 27 EU countries would have to support the proposal.”

Our analysis finds that even though this idea could prevent a bubble in asset trading, it

would distort fundamental price.

20

This tax does not require a very high rate to exclude bubble based on the above

proposition. Japan introduced a new law entitled Land Value Tax Law at the rate of 0.15%

on May 2, 1991 and enforced it in 1992. The land bubble burst in midyear of 1992; thus,

this tax may have significant impact on the burst.

3.1.3 Mixed Taxation

Next, we introduce a capital gains tax with rate ]1,( r−∈κ and a transaction tax

or property tax with rate )1,( r−∈τ in Equation (11), and obtained a new arbitrage

condition,

t

ttttttttttt

ppEppErdpEdpEr ][][]/[][1 11111 +++++ −−−−−+

=+τκγ

. (28)

By solving for tp we obtain,

−++

−−+

−++

+−−= +

∞→

∞

=

+−

∑ TTt

T

Tt

jj

jtj

tt rpE

rrd

Ep)1(

)1()1(

)/1()1(

1

1

κγτκ

κγγτκ

. (29)

For ][][1 jttt dEdE

t +=+

for any ),1[ ∞∈j , the market price will be

−++

−−+

++

+= +

∞→

+TTt

T

Tt

ttt r

pEr

rdEp)1(

)1()/1(1

κγτκ

τγγ . (30)

Proposition 4:

To exclude the rational bubble, the sum of a capital gains tax rate and a transaction

21

or property tax rate requires

+

++−∈+ 1,

1)(

b

b

grg κγ

τκ . Any strictly positive transaction or

property tax distorts the fundamental term of the asset price even for the special case

][][1 jttt dEdE

t +=+

for any ),1[ ∞∈j .

Proof:

The second term on the right-hand side of Equation (30) is,

−++

−− +

∞→TTt

T

Tt r

pE)1(

)1(κγ

τκ = 0. (31)

For

+

++−∈+ 1,

1)(

b

b

grg κγ

τκ , and for the special case 1=+τκ , the first term on the right-

hand side of Equation (30) is,

<

++

=

++

+ ++

)/()/1( 11

τγττγγ

rrdE

rrdE t

tt

t

+

rdE t

t1 for )1,0(∈τ . (32)

Q.E.D.

The implication of Proposition 4 is that a strictly positive capital gains tax rate and

a 0% transaction or property tax rate would be preferable for the special case with constant

dividend payments over time.

3.1.4 Endogenous Interest Rate and Tax on Dividends

We introduce an endogenous interest rate ))(( 1+= tt pErr , depending on the

market price of the risky asset. This is because the financial policy maker may adjust the

interest rate for macroprudential and counter cycle requirements of the economy, as argued

22

by Hanson et al. (2011). Assume that a dividend tax with rate ]1,0[∈δ and a capital gains

tax with rate ]1 (-r,∈κ are levied simultaneously in Equation (11), and we obtain a new

no-arbitrage condition,

t

ttttttttttttttt p

ppEdEpErdpEdpEpEr )(][))]((/[)())((1 1111111

−−−−−+=+ ++++++

+

κδγ.

(33)

By solving for tp we obtain,

−++

−+

−++

+−−=

+++

+

∞→

∞

= +−+

+−++−

∑ TTtTt

TtT

Tt

jj

jtjt

jtjtjtj

tt pErpE

pErpErd

Ep]))((1[

)1(]))((1[

))]((/1[)1(

11 1

11

κγκ

κγγδκ

.

(34)

Proposition 5:

Any strictly positive dividend tax cannot eliminate rational bubble, but does distort

the fundamental price. To exclude the rational bubble, if the bubble term is excluded by a

100% capital gains tax rate, the fundamental term of the asset price for the case

][][1 jttt dEdE

t +=+

for any ),1[ ∞∈j can have a solution.

Proof:

The second term on the right-hand side of Equation (34) is,

0]))((1[

)1(

1

=

−++

−

+++

+

∞→T

TtTt

TtT

Tt pEr

pEκγ

κ , (35)

23

for 1=κ , when [ ] 0)((1 1 >−++ ++∞→

kpErE TttT

t γ is assumed. The first term on the right-

hand side of Equation (34) is,

<

+−

=

+

+− ++

rdrrE

rdrE t

tt

t11 )]/(1[)/1( γδ

γγδ

+

rdE t

t1 for )1,0(∈τ , (36)

if ))(())(( 11 jtjttt pErpErr +−++ == under )()( 11 jtjttt pEpE +−++ = for any ),1[ ∞∈j .

Q.E.D.

3.1.5 The Speculative Trading Price and the Degree of Liability

We next analyze the effect of the degree of liability on the speculative spot trading

price without any tax. Assuming that a speculative trader knows the fundamental asset

value of a risky asset is fp and has an expectation on price ][ 1+tt pE , the price that a

trader is willing to pay is tp . The speculative trader has the following object function,

0)()( 1 ≥−+−= + tftttp

pplppEt

σ (37)

s.t. tt cp ≤ , (38)

],1,0[∈l (39)

when the expected profit is denoted by σ , the amount of cash holdings is expressed by

tc , and the degree of liability is expressed by l (redemption of loss, 1=l represents

unlimited liability).

Proposition 6:

24

A higher degree of liability lowers the price that a speculative trader is willing to

pay, and the price that trader is willing to pay will be higher than the fundamental price

even under conditions of unlimited liability.

Proof:

Assuming ft npp = where ),,1[ ∞∈n we obtain a solution for tp ,

)()1( 1+−+

= ttt pElnn

np for ttt cpElnn

n<

−+ + )()1( 1 , (40)

tc= for ttt cpElnn

n≥

−+ + )()1( 1 . (41)

And for 1=l ,

)(12 1+−

= ttt pEnnp for ttt cpE

nn

<− + )(

12 1 , (42)

tc= for ttt cpEnn

≥− + )(

12 1 . (43)

Q.E.D.

Figure 3 shows that a different degree of liability results in a different ceiling

price, and the curves OAC and OBD kink under the same expectation ][ 1+tt pE . Thus, the

capital gains tax proposed in the preceding subsection is needed to exclude the type of

bubble caused by speculative trading.

3.2 Rebate Option

Resale option theories of bubbles were analyzed by Harrison and Kreps (1978) and

Scheinkman and Xiong (2003). In this setting, there would be no bubble without resale. In

25

line with this idea, we consider the possible effect of a rebate option on the rational bubble.

Assume the seller knows the asset price tp has two components, the fundamental term

fp , and the other the bubble term b . Then the asking price is,

(44)

Also assume the seller must provide a rebate option to the buyer where the buyer may

rebate the asset at trading price tp when the asset price bubble bursts.

Proposition 7:

The rebate option excludes the bubble if a seller’s loss is strictly larger than the

option value.

Proof:

If the bubble bursts, and the asset price drops to fundamental term fp , then the

buyer will exercise the option. The option value ο will be,

bpbppp ffft =−+=−= )(ο . (45)

The seller’s expected pure profit σ will be,

µοσ −−= )(max ftp

ppt

(46)

bpbp ff µ−−+= )(

bb µ−=

b)1( µ−= (47)

.bpp ft +=

26

1,0 >≤ µfor . (48)

For the seller, if and only if tp is set to fp , the option value ο decreases to zero and the

seller obtains the maximum expected pure profit. In this case, the assumption 1>µ

would be plausible because the bubble occurrence and its collapse is not a pure zero-sum,

but a strictly negative social gain. The intuition of 1>µ would also be that the seller

may pay a part of the transaction cost of the exercise of the rebate option. This social loss

resulting from a bubble should be borne by both seller and buyer. Q.E.D.

4 Preventing a Bubble under Mixed Ownership

The “certain uncertainty” in the preceding section tells us that the infinite horizon

of the risky asset is the intrinsic source of a rational bubble. In this section we consider

whether mixed ownership of a risky asset, such as land, without the use of taxation or the

rebate option presented in a framework of private ownership, can exclude a rational bubble.

Assume the government initially owns all land and then divides it into ω parts, where

ω is some fixed value ( ∞<<ω0 ). The square measure of each part is equal to ω/1 . For

each period, the government puts one part of land into the market with T ( ∞<< T0 )

period of land-use rights. We then obtain the following proposition:

Proposition 7:

The fixed period of land-use rights prevents a rational bubble in the land market.

Proof:

27

The price of the fixed period of land-use rights is,

+

= ∑=

+T

jj

jttt r

dEp

1 )1(. (49)

The bubble term in Equations (3) and (11) converges to zero because the land at the time T

no longer has any right of use. ∑=

+

−=+

=T

jTjt r

drr

dp1 )1(

11)1(

, and rdp

rd

t <≤+1

when

ddEdE jttt t== ++

][][1

for any ),1[ ∞∈j . Q.E.D.

The intuition of this institution of land is to eliminate the “certain uncertainty” by

eliminating the infinite horizon of land-use rights. The idea not only excludes the bubble

effect, but also reduces the social cost of tax evasion and then supports the sustainability of

a fiscal budget. This concept is also consistent with those arguments on land by Walras

(1860), George (1879), and Sun (1922).16 Chao and Chen (2006) argue that the history of

land institution in China has been characterized by the evolution of a trend toward

“division,” which includes the division of land square and the division of property rights.

The idea here has been practiced in Hong Kong and Mainland China. Hong Kong had been

a colony of the United Kingdom, and the United Kingdom borrowed 150 years of land-use

rights from the Ching Dynasty; thus, 75 years—half of 150 years—of land-use rights had

been bought from the colonial government. When Mainland China switched the planned

economy to a market-oriented one, the pure public ownership of land in the socialist era

switched to a fixed term of land-use rights by selling 40 and 70 years of land-use rights to

corporate firms and households, respectively, based on the Hong Kong experience. The

16 See Bürgenmeier (1994) and Trescott (1994) for details.

28

fixed periods of land-use rights can be traded again in the market with different maturity

such as 1, 2, ..., 70 years.

The government nominally owns all lands, and private firms and households

purchase use rights for a fixed period such as 40 or 70 years from the government.

Theoretically, this land institution could also be considered as a type of private ownership,

because in every period private firms or households really and actually use land ad

infinitum. Therefore, from the viewpoint of preventing a land price bubble, this institution

would be expected to continue. It might also be a type of share economy.

5 Hard, Soft and Medium Landing of Bubble

5.1 Hard Landing

Assume there is a bubble in the land market and ][][1 jttt dEdE

t +=+

for any

),1[ ∞∈j , in other words γ+> rgb in Equation (16), according to Proposition 1, the

government can choose capital gains tax with rate

+−∈ 1,)(

b

b

grg γκ to exclude the

bubble; then, the land price is reduced to

= +

rdEp t

tt1 . The government can also choose

transaction or land value tax with the rate

+

+−∈ 1,

1)(

b

b

grg γτ , according to Proposition 3,

to exclude the bubble, then the land price reduces to

++

τrdE t

t1 .

29

Proposition 8:

A bubble will land hard or burst after the government introduces capital gains tax

with rate

+−∈ 1,)(

b

b

grg γκ or transaction or land value tax with the rate

+

+−∈ 1,

1)(

b

b

grg γτ , and the land price after the transaction or land value tax is lower than

that after capital gains tax.

Proof:

++

τrdE t

t1 <

+

rdE t

t1 . Q.E.D.

The land is always used as a borrower’s collateral to a lender; thus, the hard

landing of a bubble will deteriorate the balance sheet of the borrower. From this view of

point, the capital gains tax would be better than transaction or land value taxes.

5.2 Soft and Medium Landing

Assume there is a bubble in the land market and ][][1 jttt dEdE

t +=+

for any

),1[ ∞∈j , in other words γ+> rgb in the Equation (16), the government can choose

capital gains tax with rate b

b

grg )( γ

κ+−

= to make the Equation (15) after tax to be

satisfied; then, there is a concurrent or coexisting bubble in the land market and the land

price after tax will be kept constant at brdpt += . The government can also introduce a

30

transaction tax or land value tax with the rate b

b

grg

++−

=1

)( γτ to make Equation (15) after

tax to be satisfied; then, there is also a concurrent or coexisting bubble and the land price

after tax will be constant at br

dpt ++

=τ

.

Proposition 9:

The bubble will land softly or not burst after the government introduces a capital

gains tax with the rate b

b

grg )( γ

κ+−

= or transaction or land value taxes with the rate

b

b

grg

++−

=1

)( γτ . The land price after capital gains tax is distorted because it is higher than its

fundamental value, while the land price after the transaction or land value tax may not be

distorted because land price may be just its fundamental value. This case is also called

medium landing.

Proof:

For the case with capital gains tax at the rateb

b

grg )( γ

κ+−

= , the price after tax will

be brdpt += . The fundamental value of the land is

rd , b

rdpt += >

rd . For a case with

transaction or land value tax rate b

b

grg

++−

=1

)( γτ , the price after tax will be

brggrgr

rdb

rdp

bb

bt +

−+

+=+

+=

γτ=

rd for

−+−−

=γγ

rggrg

rdb

bb

b . Q.E.D.

When bubble occurs, it would increase with time. Thus, it is important for the

31

policy maker to seek the timing of the medium landing.

5.2 Historical Facts

We know that many developed countries, such as Japan, the United States, and

Greece, experienced land and housing bubbles and hard landings of said bubbles. Figure 1

shows the changes of real estate prices in the past decades based on statistical data from the

Japan Institute of Real Estate, the U.S. Census Bureau, and the Bank of Greece. Figure 2

also shows the changes of real estate prices in the past decades based on statistical data

from Taipei, Beijing, and Shanghai. From this figure, it is easy to see that Taiwan

experienced a sharp rise of housing price within the same period of Japan’s bubble, and it is

pointed out that 47% to 54% of Taipei’s housing prices were from bubble, according to

Chang et al. (2009). However, unlike the Japan bubble burst, the housing price had seen

almost no big changes since the 1990s. Here we would consider Taiwan’s case as a success

of soft landing of housing bubble. Also from this figure, the housing prices in Beijing and

Shanghai had a much sharper rise than that of Taipei; thus, we can easily infer that these

two cities had a much more significant bubble than Taipei. Wan (2015a, b) reports that

these big cities in Mainland China have been experiencing an explosive housing bubble. If

the housing prices now sharply fall as Japan’s did, it means that Mainland China would

experience a big financial crisis and a big economic slow down. Thus, the case and the

related policies in Taiwan would be good lesson for current Mainland China to make the

housing bubble a soft landing.

32

6 Conclusions and Policy Implications

This paper has shown that the rational bubble term may grow faster than the risk-

free asset by introducing bubble premium. The paper has also presented several

mechanisms for preventing the occurrence of a rational bubble in asset trading. First, this

research found a strictly positive capital gains tax can exclude the rational bubble ex ante

and ex post. In a special case, this approach does not distort the asset price based on

fundamentals, even when information on fundamentals is renewed. Second, we have shown

that a transaction tax for the capital market, as proposed by Tobin, can exclude “speculative

demand” and, therefore, exclude a rational bubble, but that it distorts asset price based on

fundamentals, making this type of taxation solution inappropriate for a market-oriented

economy. Third, we have shown that a dividend tax cannot exclude a bubble, but that,

fourth, a rebate option can exclude the bubble. Finally, we have shown that a fixed period

of land-use rights can prevent the rational bubble in the land market.

This paper also shows that for the land bubble to be considered a result of market

failure, the government has three kinds of policies called hard landing, soft landing, and

medium landing. Hard landing is when the government chooses financial or tax tools to

make the bubble crash, but the land market value after crash may be lower than that of

fundamentals; thus, hard landing is considered as the secondary governmental failure. Soft

landing is when the government chooses land value added tax or capital gains tax to make

the increasing bubble a constant value. Medium landing is not a financial but a tax tool, just

as capital gains tax and land value tax are used to make the increasing bubble a stable

value, and then the land market value ex post can be equal to that of fundamentals without

33

bubble or tax. Based on the historical facts, Japan, the United States, and Greece

experienced serious land bubbles and then made the bubbly economies have a hard landing.

However, Taiwan made the land bubble in the 1980s a soft landing. Our findings here

would be an important reference, especially for solving the serious land and housing bubble

issues in some large cities of current mainland China.

The results presented here also carry policy implications for the current global

economy, especially for solutions that would assure fair exchange among economic agents

ex ante and ex post, and could help avoid economic crises caused by cycles of bubble and

crash. This, in turn, would contribute to the stability and efficiency of the social economy.

In the real world, markets have many imperfections. Thus, the government must provide

some appropriate intervention to foster complementary functionality. For example, because

of limited liability, bankers can be incentivized to engage in speculative trading through the

expectation of huge capital gains. It would therefore be appropriate for the government to

use the proposals presented herein as a macroprudential policy to curtail this type of

morally hazardous behavior.17

In reality, the reason for bubble occurrence would be a mix in heterogeneous

believes, market frictions, and speculative trading motives. The bubble premium would

speed up bubble growth. The most important reason would be speculative trading motive,

because without trading the bubble, the redistribution of wealth could not be realized ex

post. Therefore, policy makers had better guide investors to have correct beliefs on return

of risky asset; try to make a frictionless market, ex ante, via tax policies presented in this

17 See Hanson et al. (2011) for the details on macroprudential and financial regulation.

34

paper in the long run; and perform an appropriate bailout policy after the bubble bursts.

The limitation of the analysis in this paper is as follows. First, some results were

obtained from only the partial equilibrium framework.18 In the real world, the

fundamentals, such as the interest rate and dividend, would be affected by the tax policies

in a general equilibrium model. Next, taxation would always be accompanied by distortion,

but these aspects were not sufficiently captured. Furthermore, tax is always difficult to

assure Pareto improvement; thus, it would be very politically sensitive anywhere, at any

time. When and how to introduce a new tax would be a crucial issue, but it has not been

discussed. Therefore, the main results here should be understood with some related

cautions.

Consequently, this research has also raised some issues for future research. It

would be useful to test the present proposal via an experimental approach. Such an

experiment could be easily implemented and would provide important information for

governments considering real applications in the capital market. A second research effort

should investigate how investors establish the fundamental value of different currency

assets with flexible exchange rates. This would be a more challenging task because

determining the fundamental exchange value of currency is difficult. The third issue raised

by the proposed model is that a heavy capital gains tax could incentivize investors to

conduct underground trading, evade taxation, and lock-in the supply of assets. This is an

example of a problem that would need to be addressed with implementation of the proposed

18 The policies such as bailout or tax are analyzed in a dynamic general equilibrium model where asset bubble occurs by market imperfection. See Hirano et al. (2015) and Miao et al. (2015) for the details.

35

model, simultaneously. The fourth issue raised is that the proposed solutions would incur

some new costs, such as making a new law. A cost-benefit analysis of the proposed model

will be necessary before application. Finally, it is important to note that the proposed tools

should be in, not a partial, but a general equilibrium framework.

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Bernanke, Ben (2009) On Bubble Prevention. The Wall Street Journal, U.S. NEWS,

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Figure 1: Bubbles in Japan, U.S., Greece (1997=100)

Japan U.S. Greece

Source: Data from Japan Real Estate Institute, Census Bureau of U.S., and Bank of Greece

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Source: Data from Real Estate Statistical Yearbook of China, The Statistical Yearbook of Taipei City

Figure 2: Bubbles in Taipei, Beijing and Shanghai (1997=100)

Taipei Beijing Shanghai

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Figure 3: The price speculative traders are willing to pay and limited liability

tp

O Source: Drawn by the author

A

B

C

D

ct

ceiling price

ceiling price

47