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山东大学
硕士学位论文
两部门内生增长模型里的多重均衡问题：一个文献综述
姓名：蔡宇
申请学位级别：硕士
专业：西方经济学
指导教师：叶海云
20090521
IIJ东大学硕士学位论文
量皇量曹舅量,,． 一m—m m— g -p!
中文摘要
人类社会发展到21世纪，科技、文化、经济和生活水平进入了前所未有的
崭新阶段。几千年的文明发展使人类积累了巨大的财富，然而与此同时我们也看
到当今不同国家和地区的经济总量以及发展速度极不平衡。如何解释这些国家和
地区经济发展水平的差异是现代经济增长理论研究的重要主题。
以索罗为代表的经济学家认为，在新古典生产函数和效用函数假设条件下，
经济系统仅存在一个鞍点稳态，在稳态点的附近存在唯一的一条平衡增长路径，
即确定性的增长路径，收敛到该稳态点。从而说明不同国家或者地区，只要具有
相同的初始禀赋和文化特征，它们最终都会趋于相同的经济均衡点。这显然不能
完全解释当今出现的各类经济现象(如韩国和菲律宾)。
经济增长的不确定性理论是基于经济增长的“复杂性’’来解释不同国家或地
区的增长差异。经济系统是一个非线性的、不确定的、演化着的复杂系统。经济
增长过程定量上具有多输入(例如劳力、资本、技术和资源等)和多输出(例如
产品、消费等)，定性上表现为非线性、外部扰动、内在结构及参数的不确定性，
这些复杂性特征决定了经济增长具有内生的不稳定性——可能并不只有一个稳
态，而是多个稳态，那么经济增长就具有多重平衡增长路径：不同国家或地区在
发展过程中可以趋于不同的平衡增长路径，从而呈现增长的差异；或者经济系统
只有一个稳态，但它是局部稳定的，那么经济增长存在均衡路径的连续统或多重
均衡增长路径：经济在收敛过程中可能会沿着不同的路径趋于这唯一的稳态；又
有可能稳态是中心点，这样会出现循环的增长路径。相对于唯一、确定的增长路
径，我们称这些情形下的经济增长具有不确定性。
本文的主要目的是跟踪字泽一卢卡斯框架下两部门内生增长模型里的过渡
动态学的最新发展情况，以及探讨不确定性(即多重均衡)与其主要生成因素之
间的内在联系。
全文的结构安排如下：
第一章为引言部分，主要介绍不确定性理论产生的现实及理论背景。文章首
先描述一个具有代表性的经济现象，指出新古典经济增长理论不能给出合理的解
释。卢卡斯(1988)在宇泽(1965)两部门增长模型的基础上引入人力资本外部
性，并尝试对该现象进行解释，但他没有研究从非均衡状态到稳态点(平稳增长
路径)的动态过渡问题。在此基础上引出不确定性的概念，并探讨生成不确定性
的主要因素。
第二章到第四章是文章的主体部分，分别就生成不确定性的三种主要因素进
行深入分析。其中：
第二章探讨外部性对生成不确定性的影响，分为三小节。前两节从生产的角
lII东大学硕士学位论文
度进行探讨，根据对外部性强度的不同要求而将其分为两个阶段：第一阶段的研
究依赖于很强的外部性(需要很高的增回报)，并对偏好结构比较大的限制(消
费的跨期替代弹性需要足够高)。随着越来越多的学者证明现实(美国)经济中
仅存在微弱的规模报酬递增，对不确定性的研究进入到第二阶段。在这一阶段中，
经济学者通过将一部门模型拓展到多部门模型并引入特定部门的外部性，发现不
确定性的产生对外部性的依赖大大降低，但对偏好结构仍有较大的限制。因此在
该章的最后一节我们从效用函数出发来对不确定性进行探讨，指出将休闲引入效
用函数(亦即内生化劳动)后，不确定性的产生同样只需要很弱(如果有的话)
的外部性条件。
第三章探讨扭曲性财政政策对生成不确定性的影响。指出当政府对不同生产
投入要素(劳动，资本等)采取不同的的税收(或补贴)政策时，会造成不同部
门(投资，消费等)之间要素强度的扭曲，从而产生不确定性。
第四章探讨不完全竞争对生成不确定性的影响。这方面的研究主要由加利
(Gali)等人进行，他们指出在不完全竞争(垄断竞争)模型中引入可变的成本
加成(variable markup)后，经济系统会产生不确定性，即使在没有增回报的情
况下也是如此。
在第五章中我们将分析从封闭经济拓展到小型开放经济，这样做是因为随着
全球经济一体化的发展，越来越多的经济学者开始从开放经济的视角来研究不确
定性问题，并提出了很多令人耳目一新的观点。本章试图对他们的研究成果做一
个概括和总结。
最后总结全文并探讨了研究不确定性问题的常用分析方法。
关键字：经济增长不确定性外部性扭曲性财政政策不完全竞争
【IJ东大学硕士学位论文
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Abstract
W11y does one economy grow faster than another?This remains one
of the key questions of economic science，in large part because of the
hope that an understanding of the causes of growth will point to policies
which will enable countries to achieve faster growth and therefore higher
standards of living．
It seems very natural to begin the search for all explanation of why
growth rates differ by looking for differences across countries in those
fundamental economic attributes which might be expected to contribute
to higher growth．For example，countries with higher growth rates may
save more．Or,such countries may have access to superior technology．Or
perhaps citizens of higher growth countries simply work harder．
This list of fundamental economic attributes could be expanded．but
recently a number of studies have called this‘‘fundamentalist’’approach
into question．In a variety of models of growth，there are empirically
reasonable parameter values at which economic growth is indeterminate．
That is to say,for given preference，given technology,and a given initial
capital stock，the future equilibrium growth path of the economy is not
unique，indeed iS not even locally unique．This means that two
‘‘fundamentally'’identical economies could evolve along quite different
growth path．
The main purpose of my dissertation is to trace the latest
development of transitional dynamics in two-sector models of
endogenous growth under the Uzawa-Lucas framework，and to explore
the immanent relationship between indeterminacy(that is，multiple
equilibria)and the factors such as increasing returns to scale in
technology,production extemality, incomplete competition， and
distortionary fiscal—policy,etc．(Benhabib and Farmer(1 999)did an
excellent，though not extensive enough，survey on this topic)
The Paper‘ ganized follows．From一2 char4heP er is organized as follows From chaoter to chapter 4 I Ri。ve ap ． 1
an elaborate analysis of the three sources that generate indeterminacy in
growth model and are most frequently explored and argued by
economists today：Externality,distortionary fiscal policy,incomplete
competition．All models considered in the first three chapters are closed
山东大学硕士学位论文
economy,therefore in chapter 5 I extend our analysis into small open
economy．Then I conclude the paper and give a brief review about the
tools that ar e widely used in economic researching fields，especially
sunspots and indeterminacy．
Key words：Economic Growth；Indeterminacy；Externality；Distortionary
Fiscal Policy；Imperfect Competition
原创性声明
本人郑重声明：所呈交的学位论文，是本人在导师的指导下，独
立进行研究所取得的成果。除文中已经注明引用的内容外，本论文不
包含任何其他个人或集体已经发表或撰写过的科研成果。对本文的研
究作出重要贡献的个人和集体，均已在文中以明确方式标明。本声明
的法律责任由本人承担。论文作者签名：鳕日期：
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和电子版，允许论文被查阅和借阅；本人授权山东大学可以将本学位
论文的全部或部分内容编入有关数据库进行检索，可以采用影印、缩
印或其他复制手段保存论文和汇编本学位论文。
(保密论文在解密后应遵守此规定)
论文作者签名： 导师签名：塔坐亟L一日期： 迎。≥弓
山东大学硕士学位论文
Chapter I Introduction
Despite the explosion of research in modem growth theory,many
important questions remain unsettled．Among them is how to explain the
different levels and growth rates in income across countries．In 1 960．The
Philippine and South Korea had about the same standard of living，as
measured by their per capita GDPs of about$640 U．S．1975．The two
countries were similar in many other respects．There were 28 million
people in the Philippines and 25 million in Korea，with slightly over half
of both populations of working age．Twenty seven percent of Filippino’S
lived in Manila，28 percent of South Koreans in Seoul．In both countries．
all boys of primary school age were in school，and almost all girls，but
only about a quarter of secondary school age were in sch001．Only 5
percent of Koreans in their early twenties were in college，as compared to
1 3 percent in the Philippines．Twenty six percent of Philippine GDP was
generated in agriculture，and 28 percent in industry．In Korea，the
comparable numbers were 3 7 and 20 percent．Ninety six percent of
Philippine merchandise exports consisted of primary commodities and 4
percent of manufactured goods．In Korea，primary commodities made up
86 percent of exports，and manufactured goods 1 4(of which 8 were
textiles)
From 1 960 to 1 988，GDP per capita in the Philippines grew at about
1．8 percent per year'about the average for per capita incomes in the
world as a whole．In Korea，over the same period，per capita income grew
6．2 percent per year,a rate consistent with the doubling of living standards
every 11 years．Korean incomes are now similar to Mexican，Portuguese，or
Yugoslavian，about three times incomes in the Philippines，and about one
third of incomes in the United States．1
Why does this phenomenon happen?According to the neoclassical
model，given identical preferences and technologies，two economies that
start out with different per capita output levels should converge over time
in terms of that variable(seefigure below)．This，obviously,contradicts
the realistic economy we presented above．
1 This example is excerpted from Lucas(1993)
山东大学硕士学位论文
【：
K’
K
Lucas(1 988)argued that one—sector neoclassical growth models fail
to account for the wide variation in observed cross—country growth rates
because they do not endogenize the accumulation of labor augmenting
technology．Building on earlier work by Uzawa，he studied the
steady-state growth properties of a model that included an extra sector
producing human capital．He proposed that beyond the direct role of
human capital in the production of final goods，higher levels of education，
or increased investment in research and development，generate indirect
improvements in the overall efficiency of production．external economies
not captured at the level of the individual worker or fn'm．He developed
this idea in his“Human capital and growth"model．
Lucas concluded that although the growth rates in different countries
tend to converge to each other in the long run，their income levels can be
permanently different．The country that has greater initial endowments of
physical and human capital will be permanently richer than the one with
lower initial endowments(seefigure below)．However,he admited that this
last statement iS only a conjecture because he has never worked out the
transitional dynamics of the model．
2
⋯东大学硕士学位论文
Z-
(e州+入¨K)
【e州h) g-
Recent research in literature on indeterminacy uses endogenous
growth models with indeterminate equilibria to give a potential
explanation for different income levels and growth rates of countries that
start out with similar endowments and wealth levels．This stands as an
alternative to theories that rely on exclusively on fundamentals and／or
initial conditions．
By indeterminacy we mean that from the same initial condition there
exist an infinite number of equilibria．all of which converge to a common
steady state．This allows for the existence of sunspot equilibria．that
is，equilibrium allocation infuenced by purely extrinsic unrelated to the
economy’S fundamentals，see，e．g．，Cass and Shell(1 983)；Woodford(1 986)．
In tum，such sunspot equlibria provide a modem interpretation of
Keynes’S hypothesis that economic fluctuations are driven by the‘‘animal
spirits”of businessmen．
The implications of the continuum of equilibria are as follows．TwO
identically endowed economies with identical initial conditions may
consume and allocate labor between the production of human and
physical capital at completely different rates．Only in the long l'un will
those economies converge to the same growth rate，but not to the same
level of output and human and physical capital．Therefore it is possible to
view cultural and non．economic factors in such models not as affecting
3
fundamentals 1ike technology or preferences，but simply as selection
devices for equilibria which differ on the transition paths．
There are five sources which can generate 1ndeterminacy ln
macroeconomics：(1)incomplete participation in insurance markets as in
the overlapping generations model，(2)incomplete markets due to
transaction costs or asymmetric information，(3)increasing returns to
scale in the technology,(4)market imperfections associated with fixed
costs，entry costs or external effects，and(5)the use of money as a
medium of exchange．2
In this paper'I restrict my analysis to the infinite lived representative
consumer framework，and won’t touch upon the literature that deals with
indeterminacy in finite markets with incomplete participation，nor the
literature dealing with money and indeterminacy(there iS no existence of
money in growth theory)．I do SO f．or the sake of analytical tractability and
because I intend to，just as Benhabib and Farmer(1 995)proposed，show
the fact that．far from being restricted to‘'exotic”model economies，
indeterminacy is a property that is latent in many of the growth models
macroeconomists are familiar with．
2 PIe躐refer to Jess Benhabib and Roger Farmer(1 999)for details．
4
IJI东大学硕士学位论文
Chapter 2 Externality,Increasing Returns and
Indeterminacy
Growth models with externalities are very important components of
New研owth Theory．Arrow(1962)was the first endogenous growth
model by assuming the proliferation of technology in aggregate economy．
Following his pioneering work，representative growth models with
externalities included Romer(1986)(the spill-over of knowledge)and
Lucas(1 988)(the spill．over of human capital)．In these models the
production shows increasing returns to scale because of externalities．
After that，many macroeconomists try to explore the indeterminacy in
growth models with the assistance of research methods used by these
authors．Their researches can be divided into two periods．In the first
period，externalities required to generate indeterminacy is relatively
strong(high increasing returns to scale)and the intertemporal elasticity of
subIstitution of consumption should be high enough．In the second period，
however,it only needs mild enough or even no externalities at all in order
to generate indeterminacy．Let’S elaborate on them respectively．
Section 2．1 The First Period
Chamley(1 993)analyzes the dynamics of general equilibrium
models with externalities in human capital accumulation which extends
that of Uzawa．Lucas．A key assumption of his paper is the substitution of
time between activities of‘‘learning’’(human capital accumulation)and
‘'doing”(production of physical goods)．He shows that local stability
Occurs with externalities when the intertemporal elasticity of substitution
is not too large，and when there are positive exte：rnalities in learmng，a
large intertemporal elasticity of substitution makes the model unstable or
generates a continuum of dyna血cs path．
Chamley also studied the impact of endowments in physical and
human capital on the level of output in the short and the long term．In
general，a positive shock on physical capital has two opposite enects on
human capitalinvestment：it increases the opportunity cost of investment
in human capital．but it reduces the profitability of investment in physical
capital compared to that of human capital．The dynamic properties of his
5
山东大学硕士学位论文
model imply that a negative correlation between output level and growth
rate cannot be interpreted as evidence against a structure of endogenous
growth．
When there is a continuum of paths，the equilibrium is obviously not
determinate．It is remarkable that a higher degree of intertemporal
substitution(a higher value of 1／tr)makes the model less stable in the
presence of externalities．This property is the opposite of what is found in
models with no externalities．The indeterminacy arises here because of
self-fulfilling expectations：a large investment in human capital by all
individuals today increases the future wage rate relative to its value today,
and has therefore a positive incentive effect on investment in human
capital for each individual．
Boldrin and Rustichini(1 994)studies the indeterminacy of equilibria
in infinite horizon capital accumulation models with technological
externalities．Their investigation encompasses of models with bounded
and unbounded accumulation paths，and models with one and two sectors
of production．They find that equilibria are locally unique in one—sector
economies．However,they demonstrates that in economies with two
sectors of production it is easy to construct examples where a positive
external effect induces a two-dimensional manifold of equilibria
converging to the same steady state(in the bound case)or to the same
constant growth rate(in the unbounded case)．
Benhabib and Perli(1 994)characterizes the regions of the parameter
space that give rise to unique equilibrium as well as the regions that yield
a continuum of equilibria with positive growth rates．They demonstrates
that when there are no human capital externalities，the model exhibits a
unique growth equilibrium，a result which is very much in line with the
finding of Caballe and Santos(1 993)．However,when modest and
realistic externalities are introduced，multiple equilibria are easily found．
They prove that a continuum of equilibria with positive growth rates
exists provided that the discount factor is larger than 8(a parameter
relevant to the growth of human capital)andais sufficiently low(in other
words，the intertemporal substitution rate of consumption is high enough)．
They then extend the model to allow for labor supply to be endogenous，
6
lJI东大学硕士学位论文
and find that a continuum of equilibria may exist even when the utility of
consumption is logarithmic(i．e．tr=1)，provided the marginal utility of
leisure iS not too strong diminishing．
Xie(1 994)presents a demiled analysis of transitional dynamics in
the presence of indeterminacy by setting specific conditions on parameter
values involved in the Lucas model，e．g．the inverse of the intertemporal
rate of substitution being equal to the(physical)capital income share，
expressed in Lucas’S notations，it is simply：a=p．With this restriction
imposed，the whole dynamics becomes transparent．His findings can be
summarized as follows：
(a)When parameter 7'in Lucas’S specification that captures the external
effects of human capital in goods production is larger than
parameterfl，then．
1．Not only there exist a continuum of balanced growth paths as noted by
Lucas，but there exist also a continuum of equilibrium paths starting
from the same initial endowments of physical capital and human
capital．These equilibrium paths can be indexed by玑，the fraction of
non．1eisure time that iS devoted to goods production at time zero．
2．A country that has lower endowments of physical capital and human
capital can overtake a country that has great endowments，provided
that the former devotes considerably smaller initial fraction of
non—leisure time in goods production than the latter．
(b)When7<户，then
1．For each economy,there is a unique equilibrium path that converges to
a balanced growth path．
2．No overtaking can happen．
What seems interesting iS that Xie also considers the welfare effects
due to variance in玑．he demonstrates that among a11 the equilibrium
paths starting from(R，％)and indexed by{‰：‰∈(o，1】}，the one
associated with a loweru0 always gives a better lifetime welfare．
Before concluding his paper,he presents both normative and positive
implications of his finding：the former urges that a government should do
whatever iS necessary to improve the return to human capital，which
would induce people to spend more time in schooling and raise the
7
山东大学硕士学位论文
productivity of physical capital and of labor,and ultimately,improve the
society’S welfare；the latter argues that it is no wonder we don’t observe a
clear convergence among the economies in the world and it is
understandable that some countries have had a great performance due to
growth enhancing policies，while others have lagged behind permanently
due to short．sighted behavior．
Section 2．2 The Second Period
The increasing retums models discussed above were stimulated by
the empirical papers of Robert Hall(1 98 8，1 990)who found evidence of
a high degree of increasing retums to scale in U．S．data．However,
subsequent studies suggest that Hall’S estimates were too large，see，e．g．，
Basu et a1．(1 995，1 997)；Burnside(1 996)；Harrison(2003)，among
others．
Basu and Femald(1 995)argues that the earlier work ignores the
share of intermediate goods in computing the Solow residual．Using data
that correct this problem，they estimate the degree of returns to scale in
individualindustries to be of the order of 1．03．much lower than the values
of 1．5 or more that are required for indeterminacy in single sector models．
Burnside(1 996)studies the properties of production function
regressions prevalent in the literature on market structure，returns to scale，
and external effects．The main findings of his paper are：
1．Cross-industry restrictions on the parameters of these regressions
are rejected stongly．The restrictions lend considerable precision to
parameter estimates and lead to sharp inferences about the nature of
manufacturing industries in the U．S．However,the sharpness of these
inferences iS found to be unwarranted when the restriction iS relaxed．
Furthermore，in value—added regressions the restriction seems to induce an
upward bias in the estimated degree of returns to scale．
2．Correcting measures of input for cyclical changes in the
utilization of capital has a significant impact on estimates of returns to
scale and external effects．Most of the evidence suggests that．once this
correction iS made，returns to scale are constant or slightly
decreasingk，while external effects are negligible，in the typical
8
ffJ东大学硕士学位论文
鼍毫寡暮鼍皇量曼曼鲁曼曼鼍毫曼曼曼皇皇曼曼鼍曼= I
=il II I=-舅
manufacturing industry．
3．Separate identification of intemal returns to scale and external
effects parameters iS extremely difficult using standard instruments．Some
of the instrument sets considered simply do not fit the data very well．
Others fit the two right·-hand··side variables individually,but appear to
identify aggregate business cycle components of both．As a result，the
second and third—stage regressions are i11-conditioned．This iS offered as
an explanation of the lack of robustness of the point estimates in external
effects regressions across different instrument sets．
A typical(roughly)two—digit industry in the United States appears
to have constant or slightly decreasing returns to scale．Three puzzles
emerge，however．First，estimates often rise at higher levels or
aggregation．Second，apparent decreasing returns contradicts evidence of
only small economic profits．Third，estimares with value added di仃er
substantially from those with gross output．A representative．firm
paradigm cannot explain these puzzles，but a simple story of aggregation
invalidate the common use of demand．side instruments．Basu．et a1．(1 9971
provides new empirical evidence on the importance of deviation from
constant returns and perfect competition．Using data on 34 industries that
together constitute the U．S．private business economy,including 2 1
roughly two-digit manufacturing industries，we conclude that a typical
industry has roughly constant returns to scale，implying at most small
markups of price over marginal cost．This finding contrasts with those of
Hall(1 990)，for example，whose estimates suggest large increasing
returns．However,they find substantial heterogeneity across sectors．
which turns out to have cyclical implications：neither industries nor
aggregates behave as though they were single firms．On both empirical
and theoretical grounds，heterogeneity in production appears important
for macroeconomics．Although estimates of returns to scale vary widely
across relatively disaggregated industries，the average industry appears to
produce with constant or even decreasing returns．Take literally,apparent
widespread decreasing，returns contradicts empirical evidence of small
economic profits．These industry results also contrast sharply with
aggregate results at the level of manufacturing and the private business
9
III东大学硕士学位论文
economy,which show large increasing retums．A representative—finn
framework，used in many recent macro models，cannot easily explain
these findings．Another popular explanation for procyclical productivity
---unobserved changes in factor utilization--also cannot explain these
findings since variable utilization explains apparent industry increasing
returns rather than apparent decreasing returns．
Harrsion(2003)contributes to this literature by estimating returns
to scale for the consumption and investment sectors．allowing for the
existence of sector-specific externaI effects．A main result of the Paper is
the finding of statistically significant external effects for the investment
sector,a result which stands in sharp contrast to that of previous work．
The author argue that such work has misspecified the production function
by restricting both internal and external returns to scale to be the same
across sectors of the economy．
Her results can be summarized as follows．For consumption，
estimates indicate that there may be an externality in production．but that
internal returns may be decreasing as opposed to constant，even when the
externality is left out of the equation．These results are qualitatively
consistent with recent evidence on returns to scale for nondurable goods．
For investment find evidence of a statistically significant externality and
constant to increasing internal returns．The finding that sector-specific
external effects can be economically and statistically important iS a main
result of the Paper．It iS also worthwhile to note that these results have
implications for recent theoretical work．in which a minimum level of
increasing returns to scale is needed for indeterminacy．
The impetus from this new empirical work led to a further burst of
theoretical activity that studied alternative routes to indeterminacy．
Jess Benhabib and Roger Farmer(1 996)argues that，with the
introduction of sector-specific externalities’，the magnitude of increasing
returns to scale could be much lowered．from more than 1．5 to rough
1．07．and for externalities mild enough SO that labor demand curves are
down—sloping，contrary to some earlier literature on indeterminacies．4jess
3
By sector-specific externalities they mean the externalities where the output of the consumption
and investment sectors has extemaI effectS on the OUtput of fmm witllin their own sector．
4
See Jess Benhabib and Roger Farmer(1 994)and Roger Farmer and Guo Jing—Tang(1 994)．In
lO
山东大学硕士学位论文
Benhabib and Kazuo Nishimura(1998)goes farther,they show that
indeterminacy can easily occur in standard two—sector growth models
with constant social returns，decreasing private retums，small or
negligible external effects and standard parameter values that are
typically used in the literature on business cycles，only if the utility of
consumption is equal or close to linear．In other words．the condition of
increasing returns to scale may not be needed at all for indeterminacy to
arise in a plausible manner．
Jess Benhabib and Kazuo Nishimura(1 999)give a theoretical
characterization of the size of extemal effects required for indeterminacy
in multisector models with constant social returns，and decreasing private
returns．Their characterization makes clear that there is a large class of
constant returns to scale economies，with standard Cobb．Douglas
production technologies and linear utility functions，which when
perturbed to incorporate external effects．exhibit indeterminacy or
multiple equilbiria．The perturbations that introduce external effects are
constrained to maintain constant returns to scale at the social level．and
therefore imply that there are decreasing returns to scale from the private
perspective．For a large class of constant returns Cobb—Douglas
technologies。the authors provide a method to construct indeterminate
economies by such perturbations，and characterize the magnitude of the
external effects that veiled multiple equilibria in terms of the parameters
of the unperturbed economy．They show that it’S very easy to construct
large and plausible classes of economies that exhibit indeterminacy with
constant returns to scale，and with external effects that are arbitrarily
small．They also provide several examples of such economies．both with
linear and non．1inear(109arithmic)utility functions．
Jess Benhabib，Meng Qinglai and Kazuo Nishimura(2000)argue
that in multisector models indeterminacy can arise as a type of
coordination problem，even without increasing returns，if there is a small
wedge between private and social returns．In simple one．sector models
increasing returns．sustatined in a market context by external effects or
monopolistic competition，can create a coordination problem．In such a
Jess Benhabib and Roger Farmer(1 994)，the magnitude of increasing returns to scale is SO high
that the demand curve of labor should slope up more steeply than the curve of labor supply．
11
山东大学硕士学位论文
setting，if all agents were to simultaneously increase their investment in an
asset above the level associated with the initial equilbirium．the rate of
return on that asset would tend to increase，justifying the higher level of
investment．In a multisector model however,the rates of return and
marginal products depend not only on the stocks of assets，but also on the
composition of output across sectors．The rate of retum on an asset can
increase with the stock of the asset even in the absence of increasing
returns．For example．consider a two．sector model with a pure
consumption and a pure capital good．Increasing the relative price and
hence the output of the capital good by moving along the production
possibility frontier will increase the marginal product of the capital good
if it iS relatively more capital intensive．Ⅵmen combined with market
distortions and external effects．the consequent rise in the stock of capital
may not be enough to offset the initial increase of its marginal product．
Both the stock and the marginal product of the capital good would rise
simultaneously,mimicking the effect of increasing returns in the
one—sector model．It is therefore possible to have constant aggregate
returns in all sectors at the social level．and still to obtain indeterminacy
with minor or even negligible external effects in some of the sectors．
Harrison and Weder(2000)present a two sector dynamic general
equilibrium model with both sector-specific and aggregate externalities．
They demonstrate that it iS the presence of these externalities．and
specifically of those that come from the production of the investment
good，that can lead to indeterminacy of equilibria．They also find that
including aggregate effects does not reduce the overall level of returns to
scale needed for indeterminacy．Instead．it simply allows for a trade．Ofr
between the two types of spillovers．
Harrison(200 1 1 presents a discrete time version of the Benhabib and
Farmer(1 996)two sector model．She relaxes their restriction that the two
sectors experience the same size externality and uses a more general
constant relative risk aversion form，instead of the logarithmic utility
function used in Benhabib and Farmer model． She finds that
indeterminacy results with a certain，minimum value of the externality in
the investment sector,even with no extemality in the consumption sector；
12
山东大学硕士学位论文
in addition．when there iS an externality in the consumption sector,the
size of the externality in the investment sector needed for indeterminacy
depends on this parameter and on the curvature ofthe utility function．
Harrison and Weder(2002)offers further inquiry into sources for
indeterminacy in general equilibrium．They find that in the one-sector
model it is primarily the extemalities associated with labor that generate
the result．Matters are difrerent in the two．sector model．however．
Indeterminacy can be ultimately traced back to the extemal effects from
capital in the investment sector．It is these externalities that set in motion
the countercyclical pricing sequence that constitutes indeterminacy in the
two．sector model．
Section 2．3 Preference Structure and Indeterminacy
An the models considered in former sectors assume that the utility
function is additively separable between consumption and leisure．The
drawback of such an assumption is that it implies the intertemporal
elasticity of substitution in consumption must equal one，which greatly
limits these models’power in explaining various economic phenomena．
The advantage of including leisure as an extra choice variable in the
model is that it makes the supply of labor endogenous．Due to this
flexibility in the labor supply the dynamics of the model change
significantly．
It has been well known that in monetary dynamic models if the
representative household has a utility function that is not additively
separable between consumption and real money balances．there could
exist multiple equilibria converging to the steady state：see，for example，
Obstfeld(1 984)and Matsuyanma(1 99 1)．In the representative agent
models without money,however,the relation between preference
structure and indeterminacy of equilibrium has not been fully investigated，
and therefore indeterminacy stems from production technology alone．In
this subsection．we explore the relationship between indeterminacy and
leisure．dependent utility．As before．we focus on two．sector models．)
5 For papers dealing with indeterminacy in one．sector models with leisure-dependent utility,
please see Alessandra Pelloni and Robert Waldmann(1 998)；Paul A．de Hek(1 998，1 999)；Rosalind
L．Bennett and Roger Farmer(2000)，among others．Bennett and Farmer(2000)introduce a
13
lII东大学硕士学位论文
Regarding transitional dynamics，a higher proportion of
physical(or human)capital may effect the time devoted to education，and
thus may induce changes in the accumulation of human capital．Since the
level of human capital varies the value of the marginal productivities，a
change in physical capital may move the economy to a different
steady—state path．Indeed，making an appropriate renormalization of the
variables，an increment in physical capital from a given steady—state
solution can lead to the following three situations：(a)the normal case，the
level of human capital goes up and the economy converges to a higher
steady state；(b)the exogenous growth case，the level of human capital
remains constant and the economy converges back to the initial steady
state；(c)the paradox&al case，the level of human capital goes down and
the economy converges to a lower steady state．A sudden increase in
physical capital makes labor more productive，raising thereby the
opportunity cost of going to school，and discouraging thus the
accumulation of human capital．This negative effect is determined by the
elasticity of the marginal productivity of labor with respect to capital．
Also，a sudden increase in physical capital raises future wages and lowers
the rate of growth in consumption，fostering thus human capital
accumulation．This positive effect is inversely related to the intertemporal
elasticity of substitution：Human capital investment will be less attractive
in economies where agents are more willing to intertemporally substitute
consumption．Ladron-de—Guevara et al(1 997)find that leisure has a
noticeable effect on the transitional dynamics to a given balanced path．If
leisure activities are present，an increment in physical capital in the
economy from a certain steady state induces an increase in both
consumption and leisure．Agents find now more costly to spend time in
the educational sector．As a consequence，the paradoxical case gains more
plausibility．
The multiplicity of steady states implies that a different composition
of physical and human capital across countries not only has temporary
non-separable utility function into the model of Benhabib and Farmer(1 994)and demonstrate that
a small degree of increasing returns would be enough for indeterminacy to hold．Pelloni and
Waldmann(1 998)，on the other hand，examine the role of non-separable utility in the olle sector
endogenous growth model developed by Romer(1 986)．They show that indeterminacy Can be
observed in a simple AK framework if there ale sufficiently strong increasing returns．
14
IJJ东大学硕士学位论文
effects on growth，but may lead to increasing differences over time in
income per capita．Without resorting to extemality-type arguments they
show that a country with a higher ratio of human capital may prefer to
consume less，grow faster,and devote less proportion of time to leisure
activities．This observation also agrees with some facts in the labor
market where one can find that the most qualified people accumulate
even more human capital over their professional careers，and devote a
smaller fraction of their available time to leisure activities．
Then in 1 999 they again analyses the equilibrium dynamics of all
endogenous growth model with physical and human capital in which
leisure enters the utility function．(please refer to Ladron．de．Guevara et
口J『(1 999))．Under the assumption that education has no effect on the
quality of leisure，they show that the inclusion of leisure introduces a
potential source of non．convexities in the optimization problem and lcads
to the possible existence of multiple balanced growth paths．
At the same time，Mino shows that non．separability of utility function
may produce indeterminacy of equilibrium in the representative agent
models with labor leisure choice．By using a two．sector model of
endogenous growth he demonstrates that if the utility function iS not
additively separable between consumption and leisure，indeterminacy
may emerge even in the absence of external increasing returns．(see，Mino
1999)
15
IIJ东大学硕士学位论文
Chapter 3 Distortionary Fiscal Policy and Indeterminacy
Recently,there is an increasing amount of literature on growth and
fiscal policy studying the effects of factor taxes on both the
macroeconomic stability and the economic growth rate．This literature
shows that factor taxes may affect the macroeconomic stability by means
of changing the stability properties of the equilibrium．For example，
Schimitt．Grohe and Uribe(1 997)embed a balanced．budget rule into the
neoclassical growth model and assume that the fiscal authority finance its
expenditures with distortionary income taxes．They show that under this
type of policy the equilibrium exhibit local indeterminacy．o Thus in this
subsection we concentrate on the effects of distortionary fiscal policy in
generating indeterminacy,we begin with Bond，Wang and Yip(1996)，an
extensive form of Lucas(1 988)．
Bond et al(1 996)analyzes a two-sector model of endogenous growth，
consisting of a goods sector and an education sector,in which each sector
produces the respective type of capital(i．e．，physical or human)under
conditions of constant retums to scale．By drawing on techniques from
international trade theory(namely Stolper-Samuelson theorem and
Rybczynski theorem7)，with an intertemporal no—arbitrage condition，5
they obtain conditions under which there exists a unique balanced growth
equilibrium with a positive common growth rate，and highlight the role
played by the relative factor intensities of the two production sectors in
determining the transitional dynamics of the system．
They consider three types of factor taxes in their model：taxes on
physical capital，taxes on human capital in the goods sector,and subsidies
to human capital in the education sector,and show that each type of
o
However'Guo and Harrison(2004)prove that indeterminacy generating in Schimia-Grohe et al
(1 997)disappears if the government finances endogenous pubfic spending and transfers with缸cd
income tax rates．
h‘Stolper-Samuelson theorem”means an increase in the price of one sector’S output lcads to a
more than proportional increase in the price of the factor used intensively in that
sector；“Rybczynski theorem"’means an increase in the quantity of a factor lcads to a mote than
proportional expansion of the output of the good that uses that factor intensively．As we will see
later,these two theorems have great power in interpreting the effects of distortionary tax On the
dynamic properties of the model．For an elaborate illustration of these theotems。please refer tO the
Chapter l 5 of MWG：“Microeconomic Theory”，Oxford Press．
5 This requires all equality between the net rates of return on physical and human capiml．
16
置鼍喜皇曼量孽鼍皇曼曼量皇-=I：I I；II鲁J鼍东皇大皇学舅硕孽士毫学皇皇位皇论曼文鼍皇皇皇量鼍皇窖曼鼍皇量曼曼鼍皇舅曼詈葛
factor tax will reduce the rate of growth while the subsidy will increase it，
regardless of the sectoral factor intensities．More importantly,they prove
that instability or indeterminacy can emerge when factor taxes are too
distortionary．
Mino(1 996)investigates a two—sector model of endogenous growth
with capital income taxation．In his model，one sector produces final
goods and the other produces new capital．Both sectors produce by using
human capital as well嬲physical capital under constant returns to scale
technologies．The central concern of his paper iS to present dynamic
analysis of a two—sector endogenous growth model with constant rctums
to scale technologies．He first discusses the uniqueness and stability of
the perfect．foresight competitive equilibrium path．It shows that the
dynamic behavior of the equilibrium path depends heavily upon factor
intensity conditions．In particular,if the technology employed in the new
human capital sectors iS more physical．capital intensive than that in the
final goods production sector,then the rental ratio of two types of capital
and the relative price outputs stay constant even out of the steady state．In
this case，the dynamic behavior of the economy iS quite simple and the
author shows that the equilibrium path of the economy is globally unique
and stable．On the other hand，if the final goods sector uses morg
physical-capital intensive technology
production sector,both the rental ratio
than the new human capital
as well as the relative price will
change during the transition process．It also shows in his Paper that a
unique and stable perfect—foresight equilibrium path exists at least around
the steadY．growth equilibrium under mild restrictions．
Mino also anayzes the effects of a change in taxation bcIth in and out
of a steady．growth equilibrium．It iS shown that the effects of capital
taxation also hinge on the factor intensity．For example，a rise in the rate
of tax always depresses the long．term rate of economic growth．Its initial
impact on the growth rate of consumption and the rate of human capital
accumulation may be different，however’depending on whether or not the
new human capital production sector iS more physical capital intensive．
Therefore．policy impacts on the transitional dynamics are also quite
sensitive to the factor intensity conditions．
fJf东大学硕士学位论文
The introduction of sector-specific externalities into Bond et al
(1 996)was also done by Mino(200 1)．He analyzes a two．sector model of
endogenous growth with sector-specific externalities in which both final
good and new human capital production sectors employ human as well as
physical capital．It shows that the presence of small degree of
externalities may yield indeterminacy even without assuming social
Increasing returns．In particular,Mino demonstrates that a small
divergence between private and social factor intensity conditions
generates indeterminacy of equilibrium rather easily even under constant
returns．
Many economists are interested in studying the relationship between
economic growth and public services．Under the assumption that the
production function displays socially constant returns to scale，they argue
that public services，especially infrastructure services，are essential for
persistent growth．This policy implication has often been proposed to
developing countries which face serious problems of scarcity of public
goods，in particular infrastructure．However，Zhang(2000)casts off the
above standard assumption and consider the government expenditures
serve as a source of utility and all input to production．He shows that，
under rather general functional forms of utility and production，the model
can generate many interesting dynamics．With mild increasing returns，
not only does an indeterminacy steady state take place，but also there
exist divergent perfect foresight paths in expanding oscillations and
economic cycles，two possibilities which are relatively unknown in the
existing literature．
Specifically,there are three distinct cases when increasing returns are
mild．This first one involves in that the elasticity parameter of utility to
government spending is sufficiently large．Zhang finds that the system
gives rise to a unique interior equilibrium which turns out to be a sink，
and thus it yields a continuum of equilibrium paths converging to the
stationary point．The second case concerns a moderate elasticity．It iS
shown that the interior equilibrium iS a source．Taking into account two
terminal points，and immediate question arises as to which state the
economy actually gets established．The nature of this question entails one
18
III东大学硕士学位论文
m．．m．．m．．m．．mm___⋯L m m_m．m鼍皇量皇寡曼鼍皇量寰
to carry out an analysis of the global perfect foresight dynamics．The
information on the local dynamics iS not enough，because the existence of
a unique perfect foresight path in a neighborhood of a stationary state
does not necessary rule out the existence of other perfect foresight paths
in the large．Global dynamics also bring the possibility of a meaningful
and thorough understanding of the history versus expectmions distinction，
an issue known in other fields of economics：industrial organization，
international trade，etc．Making use of the global dynamics technique，it is
possible to determine precisely under what circumstances history maaers
and when expectations may be decisive．
An interesting case in Zhang’s paper is that when the elasticity
parameter is equal to a critical value，economic cycles emerge．The
existence of cycles is established using the Hopf bifurcation theorem，and
a detailed description of the limit cycle，including its explicit expression，
bifurcated period and stability conditions is presented in his paper．Since
the ultimate reason for studying nonlinear cycles is to develop an
endogenous theory of the business cycle that can compete with the
dominant linear stochastic paradigm,his finding is useful in that it
provides yet another mechanism for economic systems to generate
periodic equilibria endogenously．On the other hand，when interesting
returns are very strong，the local stability of the interior equilibrium
changes entirely because it becomes a saddle point．Given an initial
condition，there exists a unique equilibrium path which converges
monotonically to the stationary state．
Raurich(200 1)analyzes the dynamic behavior of a two·sector
model of endogenous growth with unproductive government spending．
The author proves that the subspace of the parameter space where the
equilibrium exhibits indeterminacy is larger,the larger the fraction of
government expenditures is，the more patient consumers are，and the
more consumers are willing to substitute consumption intertemporally,
and with the introduction of unproductive government spending，
indeterminacy becomes a plausible property of the dynamic equilibrium
in a two—sector growth model with factor taxes as the only market
imperfection．
19
llI东大学硕士学位论文
Guo and Harrison(200 1)explore the interrelations between income
tax policies and stability of equilibria in an infinite—horizon representative
agent model with two production sectors，consumption and investment．
They find that，when the economy exhibit no or low investment
externalities，a regressive tax policy can lead to aggregate instability by
causing belief-driven fluctuations，moreover，depending on the size of
investment externalities and the slope parameter of the tax schedule，the
economy exhibits various types of endogenous fluctuations，including
Hopf or saddle-node bifurcations and stochastic sunspot equilibria．On
the other hand，when the size of investment externalities is sufficiently
strong，regressive taxes Call ensure saddle path stability in such a
framework．
Ben·-Gad(2003)investigates the dynamic behavior of two--sector
models of endogenous growth with sector-specific external effects，and
govemment expenditure financed by distortionary taxation．He proves
that when this type of external effect is combined with a sufficient degree
of capital taxation in a Uzawa-Lucas endogenous growth model，continua
of equilibria will emerge in the region of the balanced growth paths．By
contrast，indeterminacy is not possible when either sector-specific
external effects or factor taxation are added the modelin isolation．In the
second part of the papeL the author demonstrates that if labor supply is
endogenous，then indeterminacy can be consistent with much lower
degrees of increasing returns to scale．Moreover,certain types of fiscal
policy will be associated with multiple balanced growth paths and the
existence of a poverty trap．
In the context of multisector endogenous growth models，the
indeterminacy issue has mostly been discussed in the context of a
framework in which human capital is the engine of persistent growth．
However'existing empirical studies reveal the importance of public
sector in pushing an economy’S growth，especially at its early stage of
development．Therefore．it would be useful to clarify the dynamic
properties of a multisector endogenous growth model in which
govemment expenditure on a public intermediate good is the source
persistent growth．This is the main purpose of Hu Yunfang，et，al(2007)．
TheY extend Barro(1 990)into two sectors，and find that an indeterminate
BGP exists under a factor-intensity ranking such that the investment good
is more capital．intensive than the eonsurnption good，in contrast to the
existing multi．sector endogenous growth models in which human capital
accumulation is the engine of persistent growth．
山东大学硕士学位论文
Chapter 4 Imperfect Competition and Indeterminacy
In an imperfectly competitive environment，investment decisions
are affected by what firms correctly perceive as demand constraint：
when considering whether to investment in an additional unit of capital
any individual firm takes into account the price reduction that will be
necessary in order to sell the marginal product．Those considerations are
absent in the perfectly competitive environment assumed in the majority
of growth models found in the literature．
Markup variations brought about by changing demand conditions
can have a significant impact on the growth dynamics of imperfectly
competitive economies：they can generate multiple steady states，as well
as multiple equilibrium paths for given initial conditions．
In their 1 993 paper,Gali and Zilibotti develop a dynamic general
equilibrium model of capital accumulation with increasing returns and
imperfect competition．The model is characterized by a continuum of
industries，and Counot competition with free entry and exit within each
industry．Given a constant marginal product of capital at the firm level，
such a framework generates an equilibrium interest rate schedule which
is increasing in the aggregate capital stock．The latter feature implies the
existence of two steady states，one of which is always unstable，while
the other is characterized by an autarky allocation with zero capital．
Most interestingly,the model has been shown to yield，for plausible
parameter values and for some range of initial conditions，multiple
equilibrium paths，some of which drive the economy to the autarky state．
While some other converges to the asymptotic balanced growth path．
For some parameter values the possibility of a‘'poverty trap’’emerges：
for levels of the initial aggregate capital stock below a certain threshold，
the equilibrium is unique and converges to the autarky,zero capital state．
(See thefigures below)
The below figure(Figure 2 in Gali’S paper)portrays the
equilibrium paths of our calibrated economy,drawn as solid lines with
arrows．We can distinguish three relevant regions for the initial capital
stock K(O)．If K(O)∈【0，a)the equilibrium is unique and converges to
f|J东大学硕士学位论文
50
O
[厂戈
L—一：
R3urc 2 ： ‘z 1
the autarky steady state．Along that equilibrium path consumers eat up
their endowment 10 and part of their capital holdings．and end up
consuming缈only Any economy whose initial capital stock is dn
region is effectively in a‘'poverty trap’’：the low capital stock is not
sufficient to support the minimum number of firms that would be
required to make the demand elasticity(and，thus，the return to
investment)high enough to support further capital accumulation and
entry．IfK(O)∈(6，+一)the equilibrium iS also unique．but in this case it
involves unbounded capital accumulation and convergence to一一an
asymptotic path in which consumption，capital，and output all grow at a
2 percent annual rate．Intuitively,the high initial capital stock
guarantees a high degree of competition，a high demand elasticity and，
consequently,a return to investment that is sufficient to support further
capital accumulation，which will in turn increase the return to
lnvestment even further,reinforcing the growth process．As is evident in
Figure 2，multiple equilibrium paths coexist wheneverK(0)∈[口，6】．Each
path iS characterized by perfect foresight，i．e．is fully consistent with
agents’initial expectations．Furthermore．some of those paths converge
to the asymptonic balanced growth path，while some lead the economy
Into the poverty trap region．Thus if agents anticipate that the economy
as a whole will follow the trajectory converging to the asymptonic
balanced growth path，the expectation of higher future returns to
IIJ东大学硕士学位论文
investment makes it optimal for any individual agent to make
investment decisions that are consistent，in the aggregate，with the
foreseen trajectory．Alternatively,if agents are pessimistic and come to
believe that the economy will eventually experience negative savings
which will take it to the‘'poverty trap”region，their anticipation of low
future invest returns resulting from the decline in competition will affect
their savings decision in a self-fulfilling fashion．Ⅵmether the economy
converges to the path with unbounded growth or to the‘‘autarky'’state
depends on which of those equilibrium paths iS actually chosen．In other
words，the initial conditions are not enough in that case to pin down the
outcome that will be observed，and the latter can differ for economies
that have identicalinitial conditions．
Figure 3 and 4 illustrate some of the qualitative changes in the
equilibrium dynamics that are brought about by a sufficiently large
increase or decrease in the intertemporal elasticity of substitutiona，while
keeping the remaining parameters at their benchmark settings．
1CO
SO
O
f÷ jj厂
乙戈
k。
I ● 一一
一一÷一一一
石yre。3： F=2-z
In figure 3(仃=2．2)．As in the previous figure，there exist a threshold
level色such that ifK(O)∈(6，佃)the equilibrium is unique and converges
asymptotically to the balanced growth path．In contrast，now there is no
minimum capital stock necessary for atl equilibrium path with unbounded
山东大学硕士学位论文
growth to exist；in other words，no matter how low an economy’S initial
capital stock is，it can always‘'hope’’to take off and enjoy unlimited
growth subsequently．The economy may be poor,but not because it is in a
poverty trap．
：苎O
lOe
0
：I
‘I —∥ I 艺夕
I
I
’I
——一
l ．一一／
l 一
-／
Fiqure
、J f=0．2 F
)曲
Figure 4 shows the equilibrium paths consistent with tr=0．25．As
comparison of figure 2 and t makes clear,a reduction in consumer’S
willingness to substitute intertemporally shrink the size of the
interval K(0)of values for which there exist a multiplicity of equilibria．In
the case portrayed，that interval iS already hard to see．and would
eventually vanish for a low enough仃
Gali(1 994)develops a dynamic general equilibrium model with
monopolistically competitive firms and endogenous markups and show
the possibility of equilibria with persistent fluctuations driven by
self-fulfilling revisions of expectations．For some parameter values such
fluctuations are characterized by time series properties similar to those
observed in U．S postwar business cycles．In contrast with the existing
literature Gali’S results do not rely on the presence of increasing returns
or nominal rigidities．A key ingredient of the model iS the link between
markups and the composition of aggregate demand．For some plausible
parameter values，sunspot equilibria show to exist and to be
characterized by time series properties for di fferent aggregate variables
which qualitatively match those observed in actual business cycles．
山东大学硕士学位论文
Gali(1 995)analyze the implications for the dynamics of capital
accumulations of endogenous markups，in an environment in which the
intensity of competition increases with economic development and the
associated range of products available．The main point of his paper Call
be summarized嬲follows：
The presence of market power drives a wedge between the
marginal product capital and the return to investment，which is
immediately apparent when looking at the first order condition for profit
maximization of an imperfectly competitive firm：
，．=燃(1一吉)一万
Where，．is the interest rate，MPK is the marginal product of capital，孝
is the price elasticity of demand，and万is the depreciation rate．(1 1孑)
is the marginal revenue．The(implicit)optimal markup is given by
∥=(1一百1)一．Notice that肋Ⅸ(1 l；)corresponds to the marginal revenue
product?of capital(MRPK)．The：intuition for the presence of孝in the
expression for the interest rate is straightforward：when considering
whether to employ an additional unit of capital(at a given rental cost
，．+万)，any individual firm must take into account the price reduction that
is necessary in order to sell the additional output．The size of the price
reduction(and thus the wedge between MRPK and MPK)will be greater
the lower is the perceived price-elasticity of demand(and，thus，the higher
is the optimal markupg)
Suppose now that the structure of the economy is such that the
price—elaSticity of demand is positively related to the aggregate capital
stock(or,equivalently,the size of markups decreaSes with the capital
stock)．In that caSe，MRPK and，嬲a result，the real interest rate may no
longer be decreasing in the capital stock,even in the presence of a
diminishing MPK．That feature raises the possibility of multiple steady
states and，most interestingly,multiple equilibrium paths converging to
different steady states，for given initial conditions．
The key assumption of Gali’S model is embedded in the technology
used to produce final goods，which implies that the substitutability
among intermediate goods is increaSing in the number of intermediate
山东大学硕士学位论文
goods used．That feature is responsible for the negative link between
optimal markups and the number of firms in that sector at any point in
time is positively related to the level of aggregate demand and output
and，consequently,to the aggregate capital stock．
The intuition for the possible positive relationship between the
interest rate and the capital stock can be summarized as follows：nil
increase in the stock of capital raises output，aggregate demand，and the
sales and profits of each incumbent firm．The latter effect leads to entry
of new firms and，consequently,more competition and lower markups．
If the previous effect is strong enough it might more than offset the
decline in the marginal product of capital，thus leading to all increase in
the interest rate．
The presence of a non monotonic interest rate schedule is shown to
be a potential source of multiple steady states．High capital，high
income steady states are associated with a larger number of firms，4
greater variety of intermediate goods，and lower markups than low
capital，low income steady states．
The existence of multiple steady states will generally(though not
always)imply the existence of multiple(off-steady state)equilibrium
paths for a range of initial conditions．Needless to say,the emergence o，f
such multiplicity can also be found in other recent papers．Most existing
models，however,are characterized by either price taking behavior or
constant markups，and rely on a different mechanism to generate
multiple equilibria．More specifically,the example found in the
literature typically embedded some form of external increasing returns
in production or pecuniary externalities as the basic source of the
complementarity between private and aggregate investment that
underlies the multiplicity of equilibrium outcomes．In contrast，in Gali’S
model the possibility of increasing returns to investment(necessary for
multiple equilibria)is purely a consequence of the effect of entry on
equilibrium markups．
Then in his 1 996 paper,Gali depicts two types of qualitative global
equilibrium dynamics，these types emerge in the presence of three
stationary equilibrium and which are illustrative of the qualitative
【IJ东大学硕士学位论文
implications of such multiplicity for off-steady state equilibrium paths．
C
畸h Ic：I k K 良k
Figure 2
Tlle figure above(Figure 2 in Gali’S paper)displays the equilibrium
dynamics for an economy with an unstable middle stationary
equilibrium(with lOW intertemporal substitution)．Two of the
trajectories departing from(七宰，，c木。)coincide with two branches of the
stable manifolds of(七木，，c木，)and(七气，c气)，denoted respectively
by e‘and W．TIle solid lines with arrows depict trajectories that satisfy
all the equilibrium conditions．As the figure makes clear,the
equilibrium set depends on the size of the initial capital stock relative to
the benchmarks毛and七2．The latter are defined by the projections
onto the k axis of the leflmost point of眸and the rightmost point
of彬5，respectively．If七(0)∈(0，墨)the equilibrium is unique，and
converges monotonically to the low stationary equilibrium(七气，c枣A If
k(0)e(乞，k)the equilibrium is also unique but it converges now to
(睇，‘)instead．Most interestingly,if七(o)∈【ki，如】there exist multiple
trajectories that satisfy all the equilibrium conditions．Some of those
paths lead to(七宰，，c木，)whereas others converge to(《，‘)．Thus，whether
the economy converges to the high or the low stationary equilibrium
depends on the selected path．That selection much be consistent with
．味．钿
．q
山东大学硕士学位论文
agents’(self-fulfilling)expectations嬲of t=O Oil the future path of the
economy．In contrast with the neoclassical model，knowledge of the
initial capital stock and the set of equilibrium conditions is no longer
SHmcient to pin down the equilibrium outcome．
The figure below displays the phase portrait of an economy with a
stable middle stationary equilibrium,a feature associated with a
relatively low value 7(i．e．，high intertemporal substitution)．For any
given initial capital stock七(o)∈(o，k)there are three types of trajectories
consistent with perfect foresight equilibrium．In the first type，the
consumption level chosen as of t----O iS the highest consistent with
equilibrium(givenk(O))and the one that puts the economy exactly on
彬5，implying subsequent convergence to the lOW stationary equilibrium．
In the second type，agents choose the lowest possible consumption level
compatible with equilibrium(given k(O))，i．e．，the one on形h’；in that case
the economy converges to the higlI stationary equilibrium．In addition to
the previous trajectories，there exists a continuum of trajectories
between形。and啄，represented by the shaded area．Each of those
trajectories satisfies all the equilibrium conditions．eventually
converging to the(stable)stationary equilibrium(拈。，c宰。)．
C
k
29
．‰．～
．q
山东大学硕士学位论文
Chapter 5 Indeterminacy in Small Open Economy
Most models in the indeterminacy literature are closed economy．This
has made it hard to satisfy the conditions necessary for generating
indeterminacy．One issue has to do with technology．Ⅵmile early models
relied on large increasing returns or large external effects to generate
indeterminacy,recent theoretical work，in particular in multisector models，
demonstrates that only small market imperfections are required．The other
issue has to do with preferences．These closed．economy models also
require restrictions on the curvature on the utility function to generate
indeterminacy when the intertemporal elasticity of substitution in
consumption is high—indeed，in some cases，the utility function has to be
linear or close-to-linear in consumption．In short，there exists a tradeoff
between the size of market imperfections and the magnitude of
intertmeporal elasticity of substitution needed for indeterminacy．
In this subsection we focus on the literature dealing with
indeterminacy in small open economy and investigate how and when
indeterminacy can Occur．Our central conclusion is that in a small open
economy,the conditions for indeterminacy can be satisfied more easily
than in a closed economy．Specifically,in a two-sector small open
economy with perfect access to world bond market，indeterminacy can
OCCur under very small or even negligible market imperfections．
Intuitively,allowing for perfect access to world bond market leads to
perfect capital mobility,this implies that agents are able to smooth
consumption perfectly．This induces all economy with open capital
markets to behave like a closed economy with linear preferences thereby
increasing the possibility of equilibrium indeterminacy．
Amartya Lahiri(200 1)is the first paper to study indeterminacy in
open economy．The author presents a simple model of human capital
driven endogenous growth which，in general，exhibits an indeterminacy
of equilibrium growth paths．The first result of interest iS that reasonable
restrictions on preferences are sufficient to rule out the possibility of
equilibrium indeterminacy in a closed economy．It iS then demonstrated
that for a small open economy with perfect capital mobility,the
possibility of equilibrium indeterminacy in a closed economy．It is then
Il J东大学硕士学位论文
demonstrated that for a small open economy with perfect capital mobility,
the possibility of equilibrium indeterminacy is much greater．In particular,
simple restriction on preferences are no longer sufficient to role out the
indeterminacy of growth paths．
Lahiri also provides an interesting contrast to the results obtained in
a related paper by Boyd and Smith(1997)．Using an overlapping
generations model with a neoclassical technology，they show that under
credit market imperfections capital mobility across countries can give rise
to multiple steady states and equilibrium cycles．Moreover,the
asymmetric steady states are characterized by perverse capital flows from
the poorer to the richer country．Their results are complementary to the
results of Lahiri’S paper in that both suggest reasons for caution regarding
intemational in the absence of any credit manet imperfections could
open the door to extrinsic uncertainty and，hence，output volatility,Boyd
and Smith show that financial flows in the presence of credit market
frictions could lcad to cyclical fluctuations and pen，eme capital flows．
The role played by capital mobility in rationalizing equilibrium
indeterminacy can be understood by noting that under closed capital
markets the output and consumption profiles are identical since one
cannot borrow or lend．Since the schooling choice today implies an
intertemporal substitution of output and consumption，private agents also
have to incorporate the utility cost of this substitution into their
decision．Perfect capital mobility,on the other hand，implies that agents are
able to smooth consumption perfectly．Complete consumption smoothing
implies that the intertemporal substitution of output has no utility costs
making current and future output perfect substitutes．Hence，the dynamics
of the economy resemble those of a closed economy with linear utility
and many more paths can be rationalized．However,it iS important to note
that openness of capital markets by itself is not good enough to generate
indeterminacy．The primary message of the paper is that if the model
permits indeterminacy then open capital markets will increase the range
of parameter values for which indeterminacy may occur．
It should be noted that while models exhibiting equilibrium
indeterminacy could be interpreted as providing a rationalization for the
lIJ东大学硕士学位论文
cross-country evidence on growth，the focus on the issue in Lahiri’S paper
is also reflective of a desire to study and understand the dynamic
implications of financial market integration．Moreover,the result of his
paper also raise potentially interesting and important questions
regarding the emergence of sophisticated and more complete financial
markets and their dynamics implications．This is an area of potentially
fruitful future work．
Weder then presents a small open economy version of the Benhabib
and Farmer(1 996)two-sector optimal growth model with production
externalities(see Mark Weder 200 1)．The intent of his paper is to develop
a two sector open economy model with externalities in production．It
shows that indeterminacy is obtained not only at lower retums to scale
than in the closed economy case but also at insignificant levels．This
aspect of the model is of importance since recent empirical work has
demonstrated that aggregate scale economies are close to constant．
Moreover,these estimates have pointed to values that are too low to give
a number of existing indeterminacy models a sufficient empirical
foundation
The reason for indeterminacy in Weder’S model is that perfect capital
markets allow the smoothing of consumption via intemational lending
and borrowing at a constant world interest rate．Accordingly,the implied
irrelevance of utility curvature makes it easier to construct alternative
investment paths-the need to curtail consumption as a consequence of
investment bunching disappears．Indeterminacy still arises from a correct
path of prices in the presence of externalities however these can be
minimalin size．Unlike the closed economy variant，the desire to smooth
consumption must not be offset by a sufficient amount of increasing
retuI llS．
The assumption of a constant external interest rate Can be justified as
long as the country is small compared to the world market．However,
there are many situations where the rate of interest does depend on the
amount of debt．So Weder also consider an open economy which faces an
imperfect capital market and it is shown that the qualitative results on
indeterminacy remain basically unaffected by this extension．
32
III东大学硕士学位论文
Nishimura and Shimomura(2002)shows that indeterminacy arises if
the ranking of private and social factor intensities among sector satisfies
certain conditions and if the rate of time preference is an increasing
function of the level of consumption．Specifically,their paper makes three
contributions to the literature on indeterminacy and to that on endogenous
time preference：
First，while Benhabib et a1．assumed socially constant but privately
decreasing returns，they show that indeterminacy can arise even under
both socially and privately constant returns，if a part of the assumed
externalities is negative．This result implies that indeterminacy is
compatible with the standard free entry and exit condition：We do not
need to assume any type of market imperfection or regulation that fixes
the number of firms．
Second，based on the main result，they prove that under the same
ranking of factor intensities as above，the steady state is saddlepoint’
stable if the rate of discount is decreasing in the level of consumption．’’
Third，while Benhabib and Nishimura(1998)specify production
functions as Cobb-Douglas，the main result of Nishimura et a1．(2002)
implies that，in a small open economy,the specification is not necessary
for indeterminacy． 、
Meng Qinglai(2003)introduces a two-·sector open··economy
endogenous growth model with traded and nontraded capital and with
production externalities，he shows that externalities are not necessary to
obtain the indeterminacy result，other distortions like factor taxations that
introduce a wedge between private and social returns have the same
effects．In particular,if the production functions are standard constant
retums to scale without externalities but the government implements
asymmetric tax policies across sectors，indeterminacy remains likely．His
finding can be exactly summarized as the following two propositions：
Proposition 1．In the two—sector open economy of endogenous伊owth
with production externalities，if the traded sector is relatively intensive in
traded capital from social perspective(a>∥)and relatively intensive in
nontraded capital from private perspective(属q一届％>o)，then the steady
state for prices P and q is indeterminate in the sense that there are a
33
山东大学硕士学位论文
continuum of initial values of prices，and there exist a continuum of
growth rates of output，consumption and capital stocks that converge
respectively to their steady—state growth paths．
Proposition 2．In the two-sector open economy of endogenous growth
with CRS technologies and factor taxations，if the traded sector is
relatively intensive in traded capital from social perspectiVe(口>∥)and
relatively intensive in nontraded capital from private perspective
c南鲁>高鲁mn帆tea们tate ror prices p觚⋯s
indeterminate in the sense that there ar e a continuum of initial values of
prices，and there exist a continuum of growth rates of output，
consumption and capital stocks that converge respectively to their
steady-state growth paths．
Meng and Velasco(2004)consider a two-sector small open
economy with production externalities．With the assumption that the
consumption good is traded and the capital good is nontraded，they prove
that for the small open economy facing a perfect world bond market，
indeterminacy can occur regardless of the degree of intertemporal
substitution in consumption，only a technological condition on the
sectoral factor intensities iS required．They then extend the model in two
directions：the first extension shows that including traded capital does not
alter the main result，and that a similar condition on the sectoral factor
intensities iS all that iS needed for indeterminacy；In the second extension，
they demonstrate that externalities are not necessary to obtain the
indeterminacy result，other market distortions like factor taxation have the
same effect．
The work of extending Lucas’S two．sector model of endogenous
growth into two countries was done by Farmer and Lahiri(2005)．They
study the competitive equilibria of a two-country endogenous growth
model in which the source of growth is the linearity of technology in
山东大学硕士学位论文
reproducible．They show that in a model with no externalities there iS a
unique equilibrium，then introduce an externality to human capital and
find that the model has multiple equilibria that can be Pareto ranked．
Their model with externalities has three types of equilibria．First，there is
a symmetric equilibrium in which both countries invest and growt at the
same rate．Second，there are two asymmetric equilibria in which one of
the two countries shuts down its human capital sector completely and．
hence，doesn’t grow at a11．Third，there is a continuum of switching
equilibria in which all asymmetric equilibrium prevails for a finite length
of time followed by a switch to the symmetric equilibrium．Crucially,the
existence of multiple equilibria in the model does not depend on the size
of the production externality,an arbitrarily small externality is SUmcient
to guarantee the existence of multiple equilibria．Farmer and Lahifi’S
work Was closely related to the previous papers dealing with externalities
but the mechanism by which indeterminacy OCCUrs is very different：It
relies critically on the assumption that there are two alternative
geographical locations in which a common traded good may be produced．
Recently most static／dynamic trade theories deal with a trading
world in which markets are subject to imperfect competition，government
intervention．and／or externalities．However,Nishimura and Shimomura
(2006)shows that even if we assume there iS no those market．failure．
dynamic trade models could be Pareto．suboptimal．This seemingly
surprising result is based on the premise that international borrowings and
lendings are not allowed in the two．country model．which contrasts well
with the Bewley．Yano model in which each consumer’S utility
optimization iS subject to her wealth constraint alone．Therefore，this
difference between the Bewley．Yano model and Nishimura et a1．(2006)
model makes it possible that dynamic equilibrium paths of the latter
．model are not generally Pareto—optimal and it cannot be aggregated to a
single—consumer world economy．
The Hecksher-Ohlin(H．O)model has been a fundamental general
equilibrium framework in trade theory for a long time．Doi，et，al(2007)
develop a dynamic H．O trade model of intemational trade and
endogenous growth to discuss what j ointly determines the long—ran
35
山东大学硕士学位论文
paUem of international trade and the long-run growth rate．They also
examine the main trade propositions in the static H．O model，i．e．the
factor-price equalization theorem，the Stolper-Samuelson theorem，the
Rybczynski theorem，the Heckscher-Ohlin theorem and the law of
comparative advantage，and find that while the first three trade theorems
basically hold，the last two theorems need to be modified．
In the second part of paper,they explore the relationship between
growth rate and trade volume among balanced growth paths in the
continuum，they find that under certain conditions concerning social and
private rankings of factor intensities between production sectors，the
higher is the growth rate，the smaller is the volume of international trade
among balanced growth paths in the continuum．
36
山东大学硕士学位论文
Concluding Remarks
In this paper we have overviewed some recent two—sector models of
growth that are capable of generating multiple equilibria for given initial
conditions．Those models offer a potential explanation for differences in
income levels across economies which stands as an alternative to theories
that rely exclusively on differences in fundamentals and／or initial
conditions．
A common theme in all the models with multiple equilibria that we
have considered is the presence of some market imperfection，including
productive externalities，market power,etc．This is not surprising for in
their absence equilibrium allocations would be e伍cient．and would
correspond to the unique solution of the social planner’S problem．On the
other hand，the introduction of certain market imperfections makes it
possible for private returns to the accumulation of some productive asset
to be positively related to the aggregate stock of that one pair of
expectations／outcomes that are consistent with individual optimization，
market clearing，and rational expectations，i．e．，more than one
equilibrium．
While other explanations are possible，the evidence SO far suggests
that we should take seriously the possibility that the differences in
economic performance among countries with similar endowments may be
partly the result of self-fulfilling expectations coordinated on different
equilibrium paths．
According to Xie(1994)，there are four different ways to study
transitional dynamics in endogenous growth models：phase diagram
approach(e．g．Romer(1 986))，local stability analysis(e．g．Benhabib and
Perli(1 994))，numerical methods(Mulligan and Sala-i—Martin(1 993))，
and explicit dynamics method he uses in his paper．
Among the four approaches，phase diagram approach puts the least
restriction on the function forms of preferences and technology．Often，
the restrictions only require the first and second derivatives of the utility
and production functions to have desired signs and limiting behavior．
Local stability analysis sometimes requires further specifications of the
functional forms．Numerical methods definitely need the functional forms
37
IlI东大学硕士学位论文
to be explicit．Usually,the specification iS identified with a set ot
parameters such as the intertemporal rate of substitution，the rate of time
preference，the capital income share，etc．The explicit dyllamics method
needs to put some further restrictions on the set of parameters in order to
reduce the optimization problems to a set of differential equations with
initial constraints only,which are easy to compute．
Here 1 would like to discuss the technical tools we employ in doing
academic research in macroeconomics，especially sunspots and
indeterminacy．I do this for the sake of showing you what I have learned
and reminding myself of the tools that I have not grasped and need to
study hard on in the near future．I illustrate my argument from three
aspects：English proficiency；mathematical ability；computer skills．
The first and most fundamental ability in doing economic research is
one’S English proficiency．As is well known，almost all the top economics
journals are written in English，e．g．Journal ofPolitical Economy(Which
is my favorite journal)；American Economic Review；Quarterly Journal
of Economics and Econometrica(one of the most tedious joumals)，etc．
moreover,a great part of universities that have global reputation are
located in English speaking countries and regions，such as USA，Canada，
Hong Kong and SO on．
Second，in order to leam economics well，we should study a certain
amount of mathematical tools，such as mathematical analysis,advanced
algebra,real analysis andfunctional analysis．As to specific research
field like sunspots and indeterminacy,we need learn the ordinary
differential equation and more profound courses like dynamic systems
and bifurcation theory as well．In addition，there are also two tools，
namely dynamic optimization and dynamic programming，which are
frequently used by macroeconomists to induce FOC(first order
conditions)in optimization problems．
Last，and most likely to be omitted by many students in mainland
China，iS the computer skills．As mentioned by Xie(1 994)，numerical
methods have been becoming increasingly important in calibrating
abstract models to actual economy,and testing the plausibility of
hypotheses and parameters through numerical simulation．There is a
置皇曼曼寰- IIJ东大学硕士学位论文i
．m m．i皇曼曼鼍曼曼鼍皇曼鲁
variety of software doing such works，such as Matlab，Mathematica．
One should note that these skills are only necessary but not SU师cient
conditions for one to become a successful researcher in economics．many
other skills such as firm understand of the economic theory and proficient
in manipulating statistic and econometric software(namely,say,SPSS，
Eviews，SAS，STATA，etc．)al e also very important tools in doing
economic research．
39
⋯东大学硕士学位论文
Reference
Arrow,Kenneth J．,(1 962)．“The economic implications of learning by doing",Review
of Economic Studies，29，1 55一l 73．
Barro，R．J．，(1 990)．"Government spending in simple model of endogenous
growth",Journal ofPolitical Economy98．103．125．
Basu，S．and Femald，J．G．，(1 995)．‘'Are apparent productive spillovers a figment of
specification error?”，Journal of Monetary Economics，36，1 65-1 88．
Basu，S．and Femald，J．G．，(1 997)．“Returns to scale in U．S．production：estimates and
implications”，Journal ofPolitical Economy 105，249．283．
Ben—Gad，Michael．，但003)．"Fiscal Policy and Indeterminacy in Models of Endogenous
Growth”，Journal of Economic Theory,1 08，322．344．
Benhabib，Jess．and Farmer,Roger E．，(1994)．"Indeterminacy and increasing
returns",Journal of Economic Theory,63．1 9．46．
Benhabib，Jess．and Perli，R．，(1994)．“Uniquenes and indeterminacy：transitional
dynamics in a model of endogenous growth",Journal of Economic
Theory,63．1l 3．1 42．
Benhabib，Jess．and Gali，Jordi．，(1995)．“On growth and indeterminacy：some theory and
evidence”．Camegie-Rochester Conference Series on Public Policy，43，163．21 1．
Benhabib，Jess．and Farmer,Roger E．，(1 996)o'GIndeterminacy and sector-specific
externalities”，Journal of Monetary Economics，37，42 l—443．
Benhabib，Jess．and Nishimura，Kazuo．。(1 998)．"indeterminacy and sunspots with
constant returns”，Journal of Economic Theory，8 l，58—96．
Benhabib，Jess．and Farmer,Roger E．，(1 999)．66Indeterminacy and sunspots in
macroeconomics”,Handbook ofMacroeconomics，John Taylor and Micheal Wbodford．
eds．．North Holland．
Benhabib，Jess and Nishimura，Kazuo．，(1 999)01'Indeterminacy arising in multi．sector
economies”，Japanese Economic Review,50，485．506．
Benhabib，Jess．Nishimura，Kazuo．and Q．Meng．，(2000)．"Indeterminacy under constant
returns to scale in multisector economics”，Econometrica，68，l 54 1．1 548．
Bennett，Rosalind L．and Farmer,Roger E．，(2000)．"Indeterminacy with non．separable
utility",Journal ofEconomic Theory,93．118．143．
Boldrin，Michele．and Rustichini，Aldo．，(1 994)．"Growth and indeterminacy in dynamic
models with externalities”，Econometrica，62，323．342．
Bond，Eric．Ping，Wang．and Chong K．Yip．，(1 996)，“A general two-sector model of
endogenous growth with human capital and physical capital：balanced growth and
transitional dynamics"．Journal ofEconomic Theory,68．149．173．
Boyd，J．，and Smith，B．，(1 997)．"Capital market imperfections，international credit
markets，and nonconvergence",Joumal of Economic Theory,73，335．364．
Burnside，C．，(1 996)．"Production function regressions， returns to scale and
externalities",Journal ofMonetary Economics，37，177．201．
Caballe，Jordi．and Santos，Manuel S．，(1 993)．“on endogenous growth with physical and
human capital",Journal of Political Economy,l 0 1．1 042．1 067．
Cass，David．and Shell，Karl．，(1 98311．‘‘Do sunspots matter?”，Journal of Political
IlJ东大学硕士学位论文|曼曼曼皇曼曼皇曼i i m, !量皇曼皇曼鼍寡曼皇曼皇曼量鼍曼皇曼量毫寡皇皇皇皇曼鼍皇寡鼍曼曼量鲁皇皇皇鲁量量曼量鼍曼皇曼鲁曼
Economy,91，193-227
Chamley,Christophe．，(1 993)．"Externalities and dynamics in models of learning or
doing”．Intemational Economic Review,34，583—6 1 0．
De Hek，P．A．，(1998)．"An aggregative model of capital accumulation with
leisure．dependent utility",Journal of Economic Dynamics and Control，23，255．276．
De Hek，P．A．，(1 999)．“Endogenous technological change with leisure-dependent
utility'’，Economic Theory,14，669—684．
Doi，Junko．,Nishimura，Kazuo．and Shimomura，Koji．，(2007)．"A two—country dynamic
model of international trade and endogenous growth：Multiple balanced growth paths
and stability",Journal ofMathematic Economics，43，390-419．
Farmer,Roger E．and Guo，Jingtang．，(1994)．“Real business cycles and the animal spirit
hypothesis",Journal ofEconomic Theory,63，42—73．
Farmer,Roger E．and Lahiri，Amartya．，(2005)．"A two—country model of endogenous
growth",Review of Economic Dynamics，8，68-88．
Gali，Jordi．，and Zilibotti，Fabrizio．，(1993)．"Endogenous growth and poverty traps in a
Cournotian model",working paper．
Gali，Jordi．，(1 994)．"Monopolistic competition，business cycles，and the composition of
aggregate demand”．Journal of Economic Theory,63，73—96．
Gali，Jordi．，(1 995)．"Product diversity，endogenous markups，and development
traps",Journal of Monetary Economics，36，39—63．
Gali，Jordi．，(1 996)．“Multiple equilibria in a growth model with monopolistic
competition'’，Economic Theory 8,25 1-266． 一
Guo，Jingtang and Harrison，Sharon G，(200 1)．“Indeterminacy with capital utilization
and sector-specific externalities”，Economic Letters，72，355—360．
Guo，Jingtang and Hamson，Sharon G，(200 1)．“Ta)【policy and stability in a model with
sector-specific externalities",Review of Economic Dynamics，4，75．89．
Guo，Jingtang and Harrison，Sharon G，(2004)．“Balanced-budget rules and
macroeconomie(111)stability'’，Joumal ofEconomic Theory,1 19，357．363．
Hall，Robert E．，(1 988)．"The relation between price and marginal cost in US industry'’，
Journal of Political Economy,96，92 1—948．
Hall，Robert E．，(1 990)．"invariance properties of Solow’S productivity residual”，In
Peter Diamond，ed．，Growth,Productivity,Unemployment,71-1 12．Cambridge：MIT
Press．
Harrison,Sharon G．(2001)．"hdeterminacy in a model with sector-specific
externalities”．Journal of Economic Dynamics and Control，25，747-764．
Harrison，Sharon G，(2003)．"Returns to scale and externalities in the consumption and
investment sectors”，Review of Economic Dynamics，6，963—976．
Harrison,Sharon G and Weder,Mark．．(2000)I．"Indeterminacy in a model with
aggregate and sector-specific externalities,Ecnomies Letters，69，1 73·1 79．
Hamson，Sharon G and Weder,Mark．，(2002)．“Tracing externalities as sources of
indeterminacy'’．Joumal of Economic Dynamics and Control，26，85 l-867．
Hu，Yunfang．，Ohdoi，Ryoji．，and Shimomura，Koji．，(2008)．“Indeterminacy in a
two-sector endogenous growth model with productive government spending",Journal
of Macroeconomics，30，ll 04．1l 23．
41
II I东大学硕士学位论文
Jones，Larry E．and Manuelli，Rodolfo E．，(1997)．"Endogenous growth theory：An
introduction”，JournaI of Economic Dynamics and Control，2 l，1．22．
Ladron—de-Guevara，A．，Ortigueira，and S．，Santos，M．S．，(1997)．"Equilibrium dynamics
in two-sector models of endogenous growth”,Joumal of Economic Dynamics and
Control，2l，115．143．
Ladron—de-Guevara，A．，Ortigueira，and S．，Santos，M．S．，(1 999)．‘‘A two—sector model of
endogenous growth with leisure",Review of Economic Studies，66，609．63 1．
Lahiri，Amartya．，(200 1)．"Growth and equilibrium indeterminacy：the role of capital
mobility'’，Economic Theory,7。l 97．208．
Lucas，Robert E．，(1 988)1．‘‘oIl the mechanics of economic development'’，Journal of
Monetary Economy,22，3．42．
Lucas，Robert E．，(199311．"Making a miracle”，Eeonometrica，61，251-272．
Matsuyanma，K．，(1 99 1)．‘'Endogenous price fluctious in粕optimizing model of a
monetary econom：’，Econometrica，62，323-342．
Meng，Qinglai．，(2003)“multiple transitional growth paths in endogenous growing open
economies”，Journal of Economic Theory,l 08，365．376．
Meng，Qinglai．and V弓lasco，Andres．，(2004)．“Market imperfections and the instability
of open economy'',Joumal of International Economies，64，503—5 1 9．
Mino，Kazuo．，(1 996)．‘'Analysis of a two-sector model of endogenous growth with
capital income taxation",Intemational Economic Review,37．227．25 1．
Mino，Ka殂lO．，(1 999)．"Non．separable utility function and indeterminacy of
equilibirium in a model with human capital",Economics Letters，62，3 11．3 l 7．
Mino，Kazuo．，(200 1)I．"Indeterminacy and endogenous growth with soeial constant
returns”，Journal ofEconomic Theory,97，203-222．
Mulligan，Casey B．and Sala-i—Martin，Xavier．，(1 993)1．"Transitional dynamics in
two-sector models of endogenous growth"．Quarterly Joumal of Economics，
1 08，739—773．
Nishimura，Kazuo．，and Shimomura，Koji．，(2002a)．"Indeterminacy in a dynamic small
open economy",Journal of Economic Dynamics&Control。27，27 1．28 1．
Nishimura，Kazuo．，and Shimomura，Koji．，(2002a)．“Trade and Indeterminacy in a
Dynamic General Equilibrium Model",Journal of Economic Theory,105．244．260．
Nishimura，Kazuo．，and Shimomura，Koji．，(2006)．“Indeterminacy in a dynamic
two．country model”，Economic Theory,29，307—324．
Obstfeld，M．，(1 984)．"Multiple stable equilibrium in an optimizing perfect foresight
model”。Econometrica，52，223．228．
Pelloni，Alessandra．and Waldmann，Robert．，(1 998)．“Stability properties of a growth
model”．Economics Letters，6 1，55．60．
Raurich，Xavier．，(200 1)．"Indeterminacy and government spending in a two—sector
modeI of endogenous growth",Review of Economic Dynamics，4．2 1 0．229．
Romer,Paul M．，(1 986)．"Increasing Fetunls and long-run growth’'’Journal of Political
Economy,94，1 002-1 037．
Schmitt·Grohe，Stephanie．and Uribe，Martin．，(1 997)．"Balanced—budget rules，
distortionary taxes，and aggregate instability'’，Journal of Political Economy'
105．976．1000．
42
LJI东大学硕士学位论文
Uzawa，Hirofumi．，(1 965)．"Optimum technical change in锄aggregative model of
economic growth”．International Economic Review,6，l 8-3 1．
Weder,Mark．，(2001)1．"Indeterminacy in the small open economy ramsey growth
model”．Joumal of Economic Theory,98，339．356．
Xie，Danyang．，(1994)．"Divergence in economic performance：transitional dynamics
with multiple equilibria'’，Journal ofEconomic Theory,63，97．112．
Zhang Jtmxi．，(2000)1．"Public services，increasing returns，and equilibrium dynamics”，
Joumal of Economic Dynamics&Control，24，227—246．
43
山东大学硕士学位论文
Acknowledgements
Time flies，three years have passed since the first day I came to
Shanda’S beautiful campus．Here I not only got the chance to learn the
most sophisticated economic knowledge in the world，but made friends
with many excellent classmates and schoolmates．and most importantly,I
had the honor to recognize and communicate with a variety of
knowledgeable and prestigious professors and teachers．The friendship
with them will remain as the most precious wealth in my rest life．
I gratefully thank my advisor,associate professor Ye Haiyun，for his
kind and meticulous care about both my study and life．He iS the first
person who led me into the palace of economic research．Because of him
in the past three years，I have grown from an unenlightened child in
economics into an educated adult who know the beauty and poetry of
economics．Though I am still not proficient in manipulating analyzing
tools and penetrating the economic rules of the realistic society by now,1
will keep his words and instructions in my deep heart and move forward
bravely on the road leading to light and truth．
I also would like to say thanks to our Center’S boss，Huang
Shaoan，and respected professor Wang Jinli，for their kind-hearted help
and instructions during my study here．Their kindness and wisdom has
left a deep impression on me and will definitely continue to influence my
thought and deeds in the future．
At the same time，teacher Zhao Yanping，Shi Ying，Li Zenggang，Xie
Zhiping，Chen Kunting，Zhang Weiguo；friend Shi Xinguo，Zhao Xia，Shi
Zhensheng，Teng Fei，Han Peng，and many other teachers and friends not
mentioned，I thank all ofyou!
Above all，I thank my beloved mother,for her giving of my life，for
her selfless care in the past twenty five years!It is beyond the words for
me to express my gratitude for her．Only by hard working and living a
happy and healthy life can I feel a little relieved in reciprocating her．