貨幣、匯率與動態均衡之學術前沿研究-總計畫(II)Frontier Research on Money,Exchange Rates and Dynamic Equilibrium

I. COVER

Program for Promoting Academic Excellence of Universities（Phase II）

Midterm Report

Title of Proposal (Chinese)：

貨幣、匯率與動態均衡之學術前沿研究

Title of Proposal (English)：

Frontier Research on Money, Exchange Rates and Dynamic Equilibrium

96-2752-H-110-001-PAE

Overall Duration: Month 04 Year 2006 - Month 03 Year 2010 Report Duration: Month 04 Year 2007 - Month 03 Year 2008

National Sun Yat-sen University

01/31/08

II.(FORM1) BASIC INFORMATION OF THE PROGRAM/Sub-project

Program Title: Frontier Research on Money, Exchange Rates and Dynamic Equilibrium

貨幣、匯率與動態均衡之學術前沿研究—總計畫 (1/4)

Serial No.: 96-2752-H-110-001-PAE Affiliation

Institute of Economics, National Sun Yat-sen University

Name Wu, Jyh-Lin 吳致寧 Name 吳若緯

Tel: 07-5255501 ext 5616 Tel: 05-2720411 ext 34117

Fax: 07-5255611 Fax: 07-5255611 Prin ci pa l In vestig ato r

E-mail [email protected] Pro

gram C oor di nat or E-mail [email protected] Expenditures1 _{(in NT$1,000) Manpower}2_{:Full time/Part time(Person-Months)}

Projected Actual Projected Actual

FY 95 10736 6829.233 30 34

FY 96 10723 6662.58 30 32

FY 97 11022 -- 30 -

FY 98 11506 -- 30 -

Overall

Serial No. Project Title Principal

Investigator Title Affiliation Main Project

NSC96-2752-H-110-0 01-PAE

Frontier Research on Money, Exchange Rates and Dynamic Equilibrium

貨 幣 、 匯 率 與 動 態 均 衡 之 學 術 前 沿 研 究 Jyh-Lin Wu 吳致寧 Professor 教授 Institute of Economics, National Sun Yat-sen University 中 山 大 學 經 濟 研 究 所 Sub-Project 1 NSC96-2752-H-001-0 02-PAE

Money and endogenous growth in an open economy

開放經濟的貨幣與內生成長 Lai, Ching-chon 賴景昌 Research Fellow 研究員 Institute of Economics, Academia Sinica 中 央 研 究 院 經 濟 研 究所 Sub-Project 2 NSC96-2752-H-001-0 03-PAE

Endogenous fluctuations in multi-sector models

多部門模型內生經濟波動 Chen, Been-Lon 陳明郎 Research Fellow 研究員 Institute of Economics, Academia Sinica 中 央 研 究 院 經 濟 研 究所 Sub-Project 3 NSC96-2752-H-001-0 04-PAE

Identifying the effects of monetary policy in a small open economy with active foreign exchange intervention 貨幣政策效果的認定：小型開放經濟與外匯干預 Wang, Hung-Jen 王泓仁 Research Fellow 研究員 Institute of Economics, Academia Sinica 中 央 研 究 院 經 濟 研 究所 Sub-Project 4 NSC96-2752-H-001-0 05-PAE

Equilibrium dynamics, (in)determinacy, and monetary rules in an endogenous growth model of money and banking

均衡動態，非唯一性與貨幣法則：ㄧ個貨幣與銀行的 內生成長模型 Chang, Juin-jen 張俊仁 Associate Research Fellow 副研究員 Institute of Economics, Academia Sinica 中 央 研 究 院 經 濟 研 究所 Sub-Project 5 NSC96-2752-H-001-0 06-PAE

Liquidity and interest rates in a search model with multiple assets 具多元資產之搜尋模型中的流動性與利率 Li, Yiting 李怡庭 Professor 教授 Department of Economics, National Taiwan University 台灣大學經濟系

NSC96-2752-H-001-0 07-PAE 副教授 Taiwan University 台灣大學經濟系 Sub-Project 7 NSC96-2752-H-001-0 08-PAE

Understanding exchange rate predictability: the role of estimation risk.

匯率預測:估計風險之角色

Kuo, Biing- hen S

郭炳伸 Profess r o 教授 Department of International Trade, National Chengchi University 政治大學國貿系 Sub-Project 8 NSC96-2752-H-001-0 09-PAE

Inflation targeting, growth and the pattern of trade

通貨膨脹指標、 經濟成長與貿易型態 Chang, Wen-Ya 張文雅 Distinguished Professor 講座教授 Department of Economics, Fu-Jen Catholic University 輔仁大學經濟系 Sub-Project 9 NSC96-2752-H-001-0 010-PAE

Exchange rate dynamics under central bank intervention 央行干預下之匯率動態相關研究 Lee, Hsu-Yun 李秀雲 Profess r o 教授 Department of Economics, National Chung Cheng University 中正大學經濟系 Sub-Project 10 NSC96-2752-H-110-0 02-PAE

A revisit to the purchasing power parity puzzle and the linkage between uncertainties and exchange rates: Evidence from a non-linear approach

再探購買力平價謎題及匯率與不確定性間之關聯：非 線性分析之實證研究 Jyh-Lin Wu 吳致寧 Professor 教授 Institute of Economics, National Sun Yat-sen University 中 山 大 學 經 濟 研 究 所

Notes: 1,2 _{Please explain large differences between projected and actual figures.}

III.(FORM 2)LIST OF WORKS,EXPENDITURES,MANPOWER, AND MATCHING SUPPORTS FROM THE PARTICIPATING INSTITUTES（REALITY）.

Serial No.: 96-2752-H-110-001-PAE Program/Sub-project Title: Program Title: Frontier Research on Money, Exchange Rates and Dynamic Equilibrium 貨 幣 、 匯 率 與 動 態 均 衡 之 學 術 前 沿 研 究 —總 計 畫 (1/4)

Expenditures (in NT$1,000) Manpower (person-month) Research Item (Include sub projects) Major tasks and objectives Salary Seminar/ Conference-re lated expenses Project- related expenses Cost for Hardware & Software Total Principal Investigators Consultants Research/ Teaching Personnel Supporting Staff Total

Matching Supports from the Participating Institutes (in English & Chinese)

Main project Cordinating, integrating, supervising and monitoring the progress of the overall project 540 116 88 237 981 1 0 1 0 2 Sub-project 1 Develop a monetary endogenous growth model for an open economy, and use it to examine the consequence of adjusting 637 80 101.6 49 867.6 1 0 2 1 4

the targeting rate of various monetary policy rules on the balanced growth rate. Sub-project 2 Find mechanisms leading to endogenous fluctuations using multi-sector models 233.5 104.668 90.432 68.05 496.65 1 0 0 2 3 Sub-project 3 examine why the effect of monetary policy on output is often found to be minor and insignificant in Taiwan. 284 0 2.8 25 311.8 1 0 1 0 2 Sub-project 4 Analyzing 438 0 16.5 30 484.5 1 0 1 0 2

the effects of CAR on the banking sector and the impacts of CAR on the bank lending channel. Sub-project 5 Studying Liquidity and Interest Rates in a Search Model with Multiple Assets 236.274 0 3.981 0 240.255 1 0 3 0 4 Sub-project 6 Investigating the dynamic interactions among the internal fund positions of entrepreneur s, the monitoring activities of financial intermediari es and business cycles. 335 66 42 15 458 1 0 2 0 3

Sub-project 7 Developing a reliable inference procedure for the predictabilit y both in-sample and out-of-sampl e by appropriatel y controlling the estimation risk. 516 148 0 0 664 1 0 2 0 3 Sub-project 8 Examining the effects of inflation targeting on the economy’s long-run growth rate. 629.15 0 159.097 35 823.247 1 0 2 0 3 Sub-project 9 Modeling official intervention as an 518.760 0 65.755 16.913 601.428 1 0 1 0 2

endogenousl y decided variable through optimizing a government’ s objective function. Sub-project 10 Dissecting the purchasing power parity puzzle based on a nonlinear TAR model 528 80 126.1 0 734.1 1 0 3 0 4 SUM 4895.684 594.668 696.265 475.963 6662.58 11 0 18 3 32

LISTING TOTAL DOMESTIC INTERNATIONAL SIGNIFICANT1 CITATIONS2 TECHNOLOGY TRANSFER JOURNALS 3 3 CONFERENCES 20 20 PUBLISHED ARTICLES TECHNOLOGY REPORTS PENDING - PATENTS GRANTED - COPYRIGHTED INVENTIONS ITEM

ITEM 2 2

WORKSHOPS/CONFERENCES3

PARTICIPANTS 100 100

HOURS TRAINING COURSES

（WORKSHOPS/CONFERENCES） PARTICIPANTS

HONORS/AWARDS4

KEYNOTES GIVEN BY PIS PERSONAL ACHIEVEMENTS

EDITOR FOR JOURNALS

ITEM

LICENSING FEE TECHNOLOGY TRANSFERS

ROYALTY INDUSTRY STANDARDS5 ITEM

ITEM - - -

TECHNOLOGICAL SERVICES6

SERVICE FEE - - - 1 _{Indicate the number of items that are significant. The criterion for “significant” is defined by the PIs of the program. For example, it may refer to Top journals (i.e., those with impact factors in the upper 15%) in the area of research, or}

conferences that are very selective in accepting submitted papers (i.e., at an acceptance rate no greater than 30%). Please specify the criteria in Appendix IV.

IV.(FORM 3)STATISTICS ON RESEARCH OUTCOME OF THIS PROGRAM/Sub-project

2 _{Indicate the number of citations. The criterion for “citations” refers to citations by other research teams, i.e., exclude self-citations.} 3 _{Refers to the workshop and conferences hosted by the program.}

4 _{Includes Laureate of Nobel Prize, Member of Academia Sinica or equivalent, fellow of major international academic societies, etc.} 5 _{Refers to industry standards approved by national or international standardization parties that are proposed by PIs of the program.}

V.(FORM4) EXECUTIVE SUMMARY ON RESEARCH OUTCOMES OF THIS PROGRAM/Sub-project

(Please state the followings concisely and clearly)

1. General Description of the Program: Including Objectives of the Program

Ever since the seminal works of Romer (1986) and Lucas (1988), endogenous growth has been a mainstream research of macroeconomic theory. This analytical framework has led numerous studies in both closed and open economies (Barro, 1990; Rebelo, 1991; Marquis and Reffett, 1991; and Bond, et al. 1996). There is, however, an unexplored garden in a monetary endogenous growth model of the open economy. Money and exchange rate dynamics in an endogenous growth setting are certainly worth conducting. In addition, endogenous fluctuations without changes in fundamentals are also emphasized in the literature (Benhabib and Farmer, 1999). On the other hand, in an influential series of papers, Meese and Rogoff (1983a, 1983b, 1988) pointed out the poor out-predicting performance of structural models relative to random walks, stimulating a strand of articles in discussing exchange rate predictability. There are several unsettled issues on this topic such as how to consider the uncertainties of fundamentals and how to control for the high persistence of fundamentals in estimation. In addition, the effect of monetary shocks under active intervention in foreign exchange markets is also an interesting topic in literature. How to classified exchange rate regimes? How to appropriately specify the reaction function of the central bank? How nominal exchange rate dynamics differ between the case with and without active interventions in foreign exchange market?

The purpose of this integrated research project is to examine the relationship among money, exchange rates, and dynamic equilibrium from both a theoretical perspective and empirical viewpoint. The project will address endogenous fluctuations driven by fundamentals and those driven by belief from a growth perspective and investigate empirically the linkage between exchange rates and fundamentals. We expect to contribute to existing literature by enriching our understanding on the fluctuation of macro variables. In addition, our empirical findings will provide new insights for exchange-rate dynamics and the effects of monetary policy in Taiwan. The important topics of this project include the following. The main project and sub-projects aim at some of the most important issues to date.

The objectives of the main project are four-fold. First, it coordinates and integrates the contents of the sub-projects. Second, it supervises and monitors the progress of the overall project. Third, it provides different econometric software as well as a database for empirical research, and provides training programs for research assistants and other participants. Finally, it organizes annual workshops or conferences to share our findings or discuss encountered problems with other participants.

To achieve these objectives, there will have coordinating meetings during the research period. The project will provide several analytical and econometric softwares, such as GAUSS 6.0 and its application modules, RATS, Stata, Eviews, Mathematica. It will also purchase AREMOS database to facilitate the progress of sub-projects. The database will be installed in the library of National Sun Yat-sen and National Chung-Cheng universities. Finally, the main project will hold international conferences and workshops to share research findings with other scholars, and these conferences and workshops will be open to students,

researchers, and academic scholars. Therefore, it also provides a bridge for communicating research ideas and exchanging research methods. Research papers generated from the projects will be submitted to distinguished journals for possible publication.

2. Breakthroughs and Major Achievements

One of the major purposes of this project is to publish project papers on 5 top leading journals in economics and 12 top journals in the fields of international economics, macro-economic dynamics and money and banking. The 5 top leading journals and 12 top field journals are defined in the following section. During the first year, our team members have published three papers in top field journals. In the second year, the team members produce 10 working papers, which are expected to be published in top leading journals in the next few years. The major achievements of each sub-project are briefly described as follows:

The purpose of the first sub-project is to develop a monetary endogenous growth model with the Benhabib-Farmer production externalities for an open economy, and then uses it to investigate the possibility of indeterminacy. Several interesting findings are observed. First, when capital is internationally mobile and investment does not involve adjustment costs, the monetary equilibrium is locally determinate regardless of the strength of productive externalities and the extent of capital mobility. This result obviously stands in sharp contrast to those in the existing studies that deal with belief-driven fluctuations in an open economy, e.g., Benhabib and Farmer (1996), Guo (1998), and Wen (1998). Second, in the presence of investment adjustment costs the monetary equilibrium may exhibit indeterminacy when the aggregate increasing returns-to-scale in production is sufficiently strong. Third, when capital is imperfectly mobile, the private rate of return on foreign debts will be lower than its social rate. This leads the household to borrow too much foreign debts compared to the optimum. So, the second-best nominal money growth rate that exceeds the rate associated with the Freidman rule should be applied to correct the unduly high level of foreign debts. Fourth, if capital is perfectly mobile and the representative household accumulates physical capital without involving adjustment costs, then the representative household accumulates its physical capital without involving any externality, and the private rate of return on capital investment is the same as its social rate. As a consequence, optimal nominal money growth rate is maintained at the rate that is conformable to the Friedman rule.

The objective of the second sub-project is to find mechanisms leading to endogenous fluctuations using multi-sector models Two findings are as follows. First, local indeterminacy results based on differential factor taxation and sector-specific externality are fragile in models with productive public goods. Second, a congestion effect in the use of public goods is possible to generate local indeterminacy.

The purpose of the third sub-project is to examine why the effect of monetary policy on output is often found to be minor and insignificant in Taiwan. A structural VAR (SVAR) model that takes into account the inter-relationships between monetary policy, exchange rate policy, and foreign exchange interventions is applied to examine the effect of monetary policy. Empiricalresults indicate that when the predicted policy rate is used as the measure of monetary policy, the impulse response of output is large and significant, and the dynamic is also plausible. The policy’s effects on other variables are also quite reasonable.

In the fourth sub-project, we focus on a careful treatment of the bank’s balance sheet components and the implications thereof for bank lending and monetary policy. We not only analyze the effects of capital adequacy requirement (CAR) on the banking sector, but also investigate the possible impacts of CAR on the bank lending channel, i.e., the channel of interaction between bank lending and the real sector. Several interestinf findings are observed. First, if the capital adequacy ratio is high (low) initially, increasing the capital adequacy ratio of bank will decrease (increase) steady-state capital and loan, but increase (decrease) interest spread. Second, while a lower target rate of interest rate will result in a higher capital and loan, it will decrease result in interest spread. Of importance, the effectiveness of interest rate policy will be weakened when capital adequacy ratio of bank is high. Third, an increase in the reserve required ratio will decrease capital and loan but increase interest spread. Similarly, the effectiveness of reserve requirement policy will be weakened when capital adequacy ratio of bank is high. Fourth, while a higher bank efficacy will result in a higher capital and loan, it will decrease interest spread.

The aim of the fifth sub-project is to discusses an equilibrium where checks are used only in big transactions while cash is used in all transactions. Higher inflation or lower reserve requirements raise the deposit interest rate, lower the currency deposit ratio and thereby increase the money multiplier and money supply. However, both policies have differential impacts on the terms of trade in transactions using different means of payment. During high inflation, individuals economize on the holding of nominal assets and use checks more often, implying higher liquidity of M1. This increase in liquidity is individuals' optimal response to inflation. We also provide a micro foundation for the precautionary demand for money.

The aim of the sixth sub-project is to to bridge the gap between existing theoretical works that establish the credit multiplier mechanism and recent empirical evidence on bank credit decisions. In the model we demonstrate that by way of the dynamic interactions among the internal fund positions of entrepreneurs, monitoring activities of intermediaries, and business cycles, both the credit multiplier mechanism and the credit reversal mechanism can arise. Contrary to the credit multiplier view suggesting that credit market imperfections hit economic activity harder in recessions, the existence of the credit reversal mechanism implies that credit market imperfections may have an equally profound effect on the aggregate economy during booming times.

The primary goal of the seventh sub-project is in a pursuit of a more reliable inference procedure for the predictability both in-sample and out-of-sample by appropriately controlling the estimation risk. Two major conclusions emerging from the research can be summarized: 1) the magnitude of the estimation risks is so high that the exchange rate predictability can be masked even when it exists in the data; 2) The information about exchange rate movements from cross-section is valuable in the ways that it can reduce the estimation risk and thus improve the testing power for predictability, if it could be exploited effectively as the averaging estimator does.

In the eighth sub-project, we develop an endogenous growth model of a cash-in-advance small-open economy with flexible exchange rates in which there exist both the motive of status seeking and endogenous leisure-labor discretion and investigate the effects of inflation targeting on the economy’s long-run growth rate. In addition, we also present whether the theoretical results

are consistent with those in the existing closed-economy literature on money and growth and empirical evidence on the effect of inflation on output growth. Several important findings are summarized as follows. First, when there is endogenous leisure-labor choice and/or exists the motive of status seeking, a cash-in-advance small open economy with a perfect world capital market exhibits common growth in a non-degenerate balanced-growth path equilibrium. Second, when the motive of status seeking is present and there is an inelastic labor supply, the economy’s balanced growth rate is immune from inflation targeting if only consumption is liquidity constrained, and an increase in the rate of inflation targeting reduces the balanced growth rate if all consumption and a fraction of investment are liquidity constrained. Third, when both the motive of status seeking and endogenous leisure-labor discretion are present, the economy’s balanced growth rate is inversely related to the rate of inflation targeting even if only consumption is liquidity constrained and the negative relationship between the rate of inflation targeting and the balanced growth rate in the case that investment is also liquidity constrained is more pronounced than in the former case. Fourth, when there is endogenous leisure-labor choice and the motive of status seeking is absent, money super neutrality in the growth rate sense is valid regardless of whether or not investment expenditure is liquidity constrained.

The purpose of the ninth sub-project is to model official intervention as an endogenously decided variable through optimizing a government’s objective function. In this article we give two examples of which government has an exchange rate target consistent with the random walk fundamentals and show the difference between the level of the exchange rate under a managed floating without intervention and the rate’s level under a pure floating exchange rate one. However, they do share the same conditional variance. Because the conditional variance of the exchange rates under managed floating is a weighted average of exchange rates with and without intervention, it is lower than that under a pure floating regime given government’s concern about exchange rate targets. The firmer the government applies its attitude toward targeting the exchange rates, the more stable the rates are under a managed floating regime.

The purpose of sub-project ten is to re-investigate issues in purchasing power parity (PPP) convergence using a threshold vector error-correction model with deutschmark-based exchange rates. We find that the half-life of real exchange rates is less than two and a half years, that PPP convergence is attributed to nominal exchange rate adjustment for most countries, and that the half-life of nominal exchange rates is close to that of real rates and is longer than that of prices in general. Our findings are consistent with those of Cheung et al. (2004, Journal of International Economics 64, 135-150) except that our estimated half lives of real and nominal exchange rates are much shorter than theirs. These findings are important since they explain the PPP puzzle and indicate the significance of a nonlinear model in examining the engine of PPP convergence.

3. Categorized Summary of Research Outcomes. The criteria for top conferences and journals should be given and introduced briefly in the beginning of this section. In each research area, please give a brief summary on the research outcomes associated with the area. Note that the summaries should be consistent with the statistics given in Form3. Please list and number each research

outcomes in sorted order in Appendix II, and list all the publications in top conferences and journals in Appendix III.

One of the major purposes of this project is to publish project papers on 5 top leading journals in economics and 12 top journals in the fields of international economics, macro-economic dynamics and money and banking. The 5 top leading journals are American Economic Review, Econometrica, Quarterly Journal of Economics, Journal of Economic Theory and Journal of Political Economics. The 12 top field journals include Journal of Monetary Economics, Journal of International Economics, Journal of Economic Dynamics and Control, International Economic Review, Journal of Money, Credit and Banking, Journal of Econometrics, Journal of Applied Econometrics, Journal of Business and Economic Statistics, Review of Economics and Statistics, Economic Inquiry, Journal of International Money and Finance, and Southern Economic Journal.

Sub-project #1 (In)determinacy, Increasing Returns, and the Optimality of the Friedman Rule in an Endogenously Growing Open Economy

Background

The issue of local indeterminacy or belief-driven fluctuations driven by production externalities has been studied extensively in the field of macroeconomics. A very robust condition necessary for local indeterminacy to arise, proposed by Benhabib and Farmer (1994), is that in a one-sector growth model increasing returns to scale in production should be sufficiently large. Up till now, most successive studies, e.g., Benhabib and Farmer (1996), Guo (1998), and Wen (1998), confine their analysis to a real (non-monetary) economy in a closed-economy framework.

Lahiri (2001) first sets up a human-capital-driven endogenous growth model in a small open economy model embodying perfect capital mobility, and finds that the possibility of indeterminacy tends to be much greater. Weder (2001) then extends the two-sector growth model with production externality developed by Benahbib and Farmer (1996) to a small open economy. His analysis shows that indeterminacy is considerably easier to establish in an open economy with perfect capital mobility than in a closed economy. By incorporating endogenous labor supply behavior, Meng and Valasco (2003) find that indeterminacy can occur with small production externalities in an open economy with perfect capital mobility. A common feature of these studies is that they confine their model setting to real (non-monetary) perspectives. More specifically, these studies unanimously downplay the role of money, and only deal with the economy of the exchanges between export goods and import goods, and of the movement of physical capital rather than financial capital.

This paper develops a monetary endogenous growth model with the Benhabib-Farmer production externalities for an open economy, and then uses it to investigate the possibility of indeterminacy. Moreover, this paper intends to examine how the monetary authority will set its optimal anchor of the money growth rate from the viewpoint of welfare maximization.

The Theoretical Model

z Firms

firm. Suppose that output is produced using capital and labor as inputs. Following Benhabib and Farmer (1994) and Farmer and Guo (1994), each firm produces output

y k n

y

according to the following Cobb-Douglas production function:

α α_k Xn

y= 1− _{; 0<}

_α

_{≤1, (1a)}

where X stands for productive externalities that are treated as given by the individual firm.

In line with Benhabib and Farmer (1994) and Farmer and Guo (1994), productive externalities are assumed to take the following form: α η α − − =_n(1 ) _k1 X ;

η

≥0, (1b)

where

η

denotes the relative externality between labor and physical capital. The economy-wide average level of labor services

n and physical capital k represents production externalities given to the individual firm, due to a “learning by doing” mechanism proposed by Romer (1986).

z Households

The economy is populated by a large number of identical and infinitely-lived households. For simplicity, population is normalized to unity. The household derives utility from consumption and incurs disutility from working ; its lifetime utility can be expressed as:

c n 0 ; 1 1 ) ln( 1 0 > ⎥ ⎦ ⎤ ⎢ ⎣ ⎡ + − − + − ∞

∫

ψ

ε

ψ

n ε _e ρ _dt c t _{, (2a)}

where,

ε

(>0) represents the inverse of the intertemporal elasticity of substitution in labor supply and

ρ

(>0) is the constant rate of time preference.

For analytical simplicity, suppose that consumption purchases are the only activity that entails transactions costs. Let denote the total real resource costs required to facilitate transactions,

S M denote nominal money balances, P denote the price level, denote real money balances, denote the unit transaction cost in consumption purchases. Then, total transaction costs can be expressed as follows:

) / ( M P m =

s

S sc S = . (2b)

In line with Zhang (2000) and Itaya and Mino (2003), the unit transaction cost is assumed to be strictly increasing and convex in the ratio between consumption and real money balances . To reflect this property, we specify that takes the following function form:

s

/ m c

s

β ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Φ = ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ m c m c s , 0<Φ<1 and 0<

β

<1. (2c)

The representative household accumulates physical capital involving adjustment costs (installation costs) with the quadratic convex function. In line with Hayashi (1982), Abel and Blanchard (1983), and Turnovsky (1996), the adjustment cost function is specified

as: ); 2 1 ( ) , ( k I h I k I = + Ω h≥0, (2d)

where

I

denotes the level of investment, and is a constant parameter of adjustment costs, denoting the sensitivity of the adjustment costs. Adjustment costs depending upon investment relative to capital stock can be justified by learning-by-doing in the installation process. As stressed by Feichtinger et al. (2001, p. 255), “if capital stock is large, a lot of machines have been installed in the past so that this firm has a lot of experience, implying that it is more efficient in installing new machines.”

h

Let

δ

denote the capital depreciation rate. The representative household faces the physical capital accumulation constraint:

k I

k&= −

δ

. (2e)

At each instant of time, the representative household is bound by a flow constraint linking wealth accumulation to any difference between its gross income and its expenditure. Let D denote holdings of foreign debt measured in terms of foreign-currency, E

denote the nominal exchange rate, and denote foreign debt measured in terms of domestic output. In addition, the household has access to nominal government bonds B that pay the nominal interest rate R. Let denote real government bonds. Then, the household’s flow budget constraint is given by:

) / ( ED P d = ) / ( B P b = m d R b R wn k d b m+ _&− _&=

γ

+ +( −

π

) −( *+

ε

−

π

) −

π

& c m c ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎣ ⎡ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ Φ + − β 1 ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + − k hI I 2 1 , (2f)

where

γ

, w,

ε

, R*, and

π

denote the capital rental rate, the wage rate, the depreciation rate of the domestic currency, the world nominal interest rate on foreign debt, and the domestic inflation rate, respectively.

Imperfect capital mobility

In line with the setup proposed by Turnovsky (1997), Eicher et al. (2000), and Weder (2001), the domestic economy faces an upward-sloping curve for debt when borrowing from abroad. To be more specific, to reflect the extent of default risk in association with foreign debts, the borrowing rate charged from foreign country on debts is specified to be positively related to the debt-capital ratio: ) ( 1 0 * k d R =

ϕ

+

ϕ

,

ϕ

₀ >0,

ϕ

₁≥0, (3)

where

ϕ

₀ is the exogenous component of world interest rate and

ϕ

₁ reflects the borrowing premium associated with default risk. The coefficient

ϕ

₁ in equation (3) can be interpreted as the degree of capital mobility. In equation (3) R*=

ϕ

₀ holds if

0

1 =

ϕ

, implying that the domestic economy can borrow from the foreign economy as much as it would like to borrow. This reflects the fact that capital is perfectly mobile. However, in equation (3) _R* ₌

_ϕ

_{0 +}

_ϕ

₁(_d/_k) holds if ₀

1>

ϕ

, implying that the domestic economy can not borrow from the foreign economy as much as it would like to borrow. This corresponds to the

situation where capital is imperfectly mobile.

Main Findings

Based on our model, several main findings emerge from the analysis. First, when capital is internationally mobile and investment does not involve adjustment costs, the monetary equilibrium is locally determinate regardless of the strength of productive externalities and the extent of capital mobility. This result obviously stands in sharp contrast to those in the existing studies that deal with belief-driven fluctuations in an open economy, e.g., Benhabib and Farmer (1996), Guo (1998), and Wen (1998). Second, in the presence of investment adjustment costs the monetary equilibrium may exhibit indeterminacy when the aggregate increasing returns-to-scale in production is sufficiently strong. Third, when capital is imperfectly mobile, the private rate of return on foreign debts will be lower than its social rate. This leads the household to borrow too much foreign debts compared to the optimum. So, the second-best nominal money growth rate that exceeds the rate associated with the Freidman rule should be applied to correct the unduly high level of foreign debts. Fourth, if capital is perfectly mobile and the representative household accumulates physical capital without involving adjustment costs, then the representative household accumulates its physical capital without involving any externality, and the private rate of return on capital investment is the same as its social rate. As a consequence, optimal nominal money growth rate is maintained at the rate that is conformable to the Friedman rule.

Sub-project #2.Endogenous Fluctuations in Multi-sector Models Background

Models of economic growth with indeterminate paths offer an explanation concerning why we often observe diverse growth performances among countries with similar economic environments. Equilibrium indeterminacy in existing two-sector, human-capital based growth models emerges based upon two mechanisms. One of the mechanisms is differential factor tax rates, initiated in Bond, Wang and Yip (1996) and followed by Raurich (2001). The other mechanism is sector-specific externalities, pioneered in Benhabib and Farmer (1996) in an exogenous growth model and followed by Benhabib, Meng and Nishimura (2000), and Mino (2001) in endogenous growth models. Ben-Gad (2003) combined the two mechanisms. This report conducts two things. First, we argue that once productive public goods are considered, the two existing mechanisms are not robust in creating local indeterminacy. Then, we take into account congestion in public services so a two-sector model with the two existing mechanisms can generate local indeterminacy.

Our research is motivated as follows. In the existing models with sector-specific externalities or distorted factor taxes, there is either no government spending, or if the government spending is taken into account, only consumptive public spending and government transfers are considered. Recently, a number of authors have documented positive impact of public expenditure upon the productivity of private capital. When there is productive public spending, the production technology is externally enhanced by the public goods. Productive public goods as an engine of economic growth have received much attention in endogenous growth models. In particular, a number of studies in this line of modeling strategy have obtained local indeterminacy. It is thus important

to determine whether or not differential factor tax rates and sector-specific externalities create local indeterminacy in models with productive public goods.

However, as we will find, the two existing mechanisms no longer create local indeterminacy in a two-sector growth model with productive public goods, unless the difference in the factor tax rates and the gap in the sector-specific externalities are implausibly large. Intuitively, productive public goods introduce the effects of intersectoral externalities. They offset the effects of the two existing mechanisms that would have otherwise reversed the factor intensity from social viewpoint from the factor intensity from the private viewpoint. As a consequence, the two existing mechanisms are not robust in the establishment of local indeterminacy in models with productive public goods.

This paper then introduces the congestion effect in the use of public goods, an effect offsetting the effect from public spending, to salvage the two existing mechanisms. Congestion is a prevalent experience in the use of public services such as irrigation systems, highways, harbor, airports and other facilities. Such an effect has received much attention in public and spatial economics (e.g., Starrett, 1998; Edwards, 1990). The congestion effect has recently been taken into account extensively in endogenous growth models (e.g., Barro and Sala-i-Martin, 1992; Fisher and Turnovsky, 1996; Glomm and Ravikumar, 1997).

With a congestion effect in the use of public goods, we find that local indeterminacy arises. Intuition suggests that under constant returns, the congestion effect reduces an otherwise strong intersectoral external effect due to the marginal contribution of public goods services and increases the marginal contribution of aggregate physical as well as human capital. This thus makes marginal social products to deviate from the marginal private products. The otherwise negative sloping relative marginal products of labor between the good and the human capital sectors is now positive sloping. As a result, a higher expected price in the sector that is more capital intensive reduces, rather than increases, the fractions of capital and labor allocated to that sector, thereby making the expectations about the higher price self-fulfilling.

The Model

The model is based upon Lucas (1988), Rebelo (1991), Bond, et al. (1996) and Ben-Gad (2003) and is general enough to include both the features of the sector-specific externalities and the distortionary factor taxation in existing literature. The economy consists of a continuum of representative consumers/producers with two sectors, referred to as the goods sector, Y, and the education sector, X. Human and physical capital both are used in the two sectors, with their productivity enhanced by public good services a la Barro (1990).

More specifically, we assume both sectors are of constant returns to scale and, for simplicity, of the following parametric forms:

( ) ( ) ( ) , (0) 0, (0) 0,

Y = A vk α uh β uH G Kε %γ > H > given (1)

[(1 ) ] [(1 ) ] [(1 ) ] ,

X =B −v k η −u hθ −u H Gξ %δ ₍₂₎

capital, h), allocated to the goods sector. Parameters A>0 and B>0 are productivity coefficients; 0<α<1 (0<η<1) and 0<β<1 (0<θ<1) are the shares of physical and human capital in the goods (education) sector. Moreover, both sectors are subject to sector-specific externalities, with the productivity in each sector enhanced by the average amount of aggregate human capital (denoted as H) employed in each sector, and the contribution of externality in the goods (education) sector being ε>0 (ξ>0). Finally, the public services, , affect both sectors, with parameter γ (δ) representing the degree to which the public services enhance the productivity in the goods (education) sector.

G%

Let us comment on the sector-specific externalities generated only by human capital. In general, physical and/or human capital may create sector-specific externalities (e.g., Benhabib, et al. 2000; Mino, 2001). The appearance of only one source of sector-specific externalities in the basic model is to maintain the insights in the existing models with sector-specific externalities while making the model as simple as possible in order to be easily tractable. In Appendix 4 we have considered sector-specific externalities of both physical capital and human capital in the technology. As the Appendix shows, the dynamic equilibrium system is exactly the same as the model using the technology in (1) and (2). As a result, the model with two sources of sector-specific externalities is more complicated, but the main results are expected to be the same as those in the model with once source of sector-specific externalities. We thus present in the text the model with once source of sector-specific externalities in order to keep the model simple while leaving the model with two sources of sector-specific externalities in the Appendix for references.

There is a congestion effect in that the amount of public goods services received by the representative agent in (1)-(2) may be less than the actual amount of public spending, G, with the perceived amount decreasing in the aggregate activity. Specifically, we assume that public services received by the representative agent are as follows

1 1

( ) ( )_{K H}

G G%= ⋅ ψ ζ , (3)

in which K is aggregate physical capital, and ψ indicates the degree of congestion due to the aggregate use of physical capital and ζ the degree of congestion due to the aggregate use of human capital. If ψ=ζ=0, the public service is non-rival and non-excludable and is therefore a pure public good.

The following parameter restrictions are imposed for the technologies.

Assumption 1 (i)

α

−

γψ

>0,

β ε γζ

+ − >0,

η

−

δψ

>0,and

θ ξ δζ

+ − >0;

(ii)

α β ε γ ψ ζ

+ + − ( + ) 1= −

γ

and

η θ ξ δ ψ ζ

+ + − ( + ) 1= −

δ

(iii) 0 ≤ ψ+ζ ≤ min(1+ε/γ, 1+ζ/δ)

While Assumption (i) assures that physical and human capital are both productive in each sector, Assumption (ii) requires socially constant returns to scale with respect to K and H in order to guarantee the existence of a BGP with a perpetual growth rate. Finally, in Assumption (iii) the restriction ψ≤0.5, so the aggregate congestion effect in (3) being less than 100%, ensures the

dominance of the positive effects over the congestion effects in the public services and thus avoids private increasing returns to scale.

The motions of the two kinds of capital stock are:

k (1 _k) (1 _l) ,

k&= −

τ

rvk+ −

τ

wuh+ − −

π

C

ς

(4)

,

h X&= −

ς

h (5)

where C denotes consumption, r and w are unit rewards to physical capital and to labor/human capital, respectively, π is the profits distributed to the household, and τk∈(-1, 1) and τl∈(-1, 1) are the tax/subsidy rates on capital and human capital. For simplicity, we assume the depreciation rates of physical capital and human capital are the same and denoted as ς. Assuming different rates of depreciation for physical and human capital, respectively, gains no extra insights except for the cost of tedious algebra. The taxation scheme implicitly assumes that the education output is not a market good and thus, is not subject to taxation, an assumption in line with Ben-Gad (2003). Note that the flow budget and the non-market education output imply the definition of distributed profits:

π

= −Y rvK wuH− .

The representative agent is assumed to possess the following lifetime utility, with a constant, intertemporal elasticity of substitution consistent with a perpetual growth framework:

1₁ 1 0 , C t U =

_∫

∞e−ρ −₋σ_σ− dt , (6)

in which ρ>0 is the instantaneous time-preference rate, and σ is the reciprocal of the intertemporal elasticity of substitution. Finally, the government budget satisfies:

G T= ≡

τ

_lwuH+

τ

_krvK=(

ατ

_k+

βτ

_l)Y ≡gY (7) where g≡τkα+τlβ denotes the share of government spending in output in the goods sector.

Findings

Two findings are as follows. First, local indeterminacy results based on differential factor taxation and sector-specific externality are fragile in models with productive public goods. Second, a congestion effect in the use of public goods is possible to generate local indeterminacy.

Sub-project#3 Identifying the Effects of Monetary Policy in Taiwan: 3.1 Introduction

In the literature, the VAR model is widely adopted in studying monetary policy, and the results are usually satisfactory for data from major industrial countries. When applying the same methodology to the data of Taiwan, however, the results are less encouraging. In particular, the policy’s effect on output is often shown to be minor and insignificant.

Choleski approach of VAR, which is commonly used in the literature, may make some sense for large and relatively closed economies but is likely to be problematic for small open economies. In addition to the alternative estimation approach, in this paper we propose the hypothesis that the monetary authority’s engagement in foreign exchange interventions may also contribute to the seemingly inconsequential monetary policy in Taiwan.

There are two reasons why the intervention may hinder the identification of monetary policy effect. Firstly, a not-fully sterilized intervention could move the volume and the interest rate of the domestic market, adding noises to the market-based measure of monetary policy. The second reason of why foreign exchange interventions may hinder the monetary policy estimation is because the intervention may weaken the exchange rate channel of monetary policy particularly when the goals of CBC’s exchange rate policy and monetary policy are not aligned. When this happens, foreign exchange interventions may clog the exchange rate channel of the monetary transmission mechanism, making the estimated monetary policy effect appears minor. In the extreme case of a fixed exchange rate regime, the monetary policy is essentially non-operative.

In this study, we seek to improve the estimation of Taiwan’s monetary policy effect by addressing the above issues. We use a regression method to extract information of monetary policy from the overnight rate and construct a better measure of monetary policy. We provide evidence that the newly constructed monetary policy variable is not influenced by CBC’s intervention actions. We then setup a SVAR model in which variables measuring monetary policy, exchange rate policy, and foreign exchange interventions are included. Instead of relying on the recursive Choleski approach to identify model parameters, we adopted a structural approach that imposes restrictions on the variables’ contemporaneous relationships. After the model is estimated, we then investigate by counterfactual simulations whether effects of monetary policy become more prominent in the absence of foreign exchange interventions.

3.2 The Model

The commonly used overnight rate may be a noisy measure of monetary policy because changes of the rate may be influenced by market factors including unsterilized foreign exchange interventions. Romer and Romer (1993) proposed a narrative approach to construct a monetary policy index (MPI) based on minutes of Fed’s meetings. Shen and Chen (1996) followed the approach and constructed the MPI for Taiwan. The index is categorical, taking a value of 1 for easy money and -1 for tight money, for instance. However, the categorical feature of the index makes it difficult to use in a VAR model where the monetary policy variable is endogenous in the system and appears as a dependent variable in one of the equations.

The discount rate (DR) is also used to measure the stance of monetary policy. Unlike the overnight rate, the discount rate is set by the monetary authority and is not under direct influence of market conditions. On the other hand, the discount rate is often symbolic in nature and serves as a declaration of the monetary authority’s long term policy goals. The result is a slow-moving interest rate which is not able to reveal the actual conduct of the monetary policy at a higher frequency. Although neither MPI nor DR is an ideal measure of monetary policy in a regression analysis, their close approximation to the policy is valuable in assisting the policy identification. Here we propose a simple regression method which uses MPI and DR to extract policy information from

the overnight rate.2 The regression model is constructed as the following: ORt = b1 + b2 MPIt + b3 DRt + et.

We estimate this equation and obtain the predicted policy rate which is the part of ORt that correlates with MPIt and DRt. Given that MPIt and DRt contain information directly related to monetary policy, the predicted value can be interpreted as the component of ORt that is most relevant to policy actions. In this way, movements of ORt that are not related to policy are purged off the measure of monetary policy.

}

We consider a SVAR model with monthly-frequency data in the period between April, 1989 and June, 2006. The foreign exchange rate was tightly controlled by the CBC in Taiwan prior to April, 1989, and therefore we do not consider sample periods prior to that. The model contains five endogenous variables:

{Y P R ER FX

, , ,

,

. Definitions of the variables are explained below. is the NTD/USD exchange rate. is the annual growth rate of CBC’s net foreign assets (after purging off effects o

ER

FX

f

exchange rate fluctuations). Following Wang (2005), is used in measuring CBC’s foreign exchange interventions. When CBC intends to exert downward pressure on the currency value, for example, it sells local currencies and accumulates foreign assets.

FX

R

is the overnight interbank loan rate which we use to measure CBC’s stance of monetary policy. We choose to use the interest rate instead of the money aggregate to measure the policy, and the reason is because movements of money aggregates (such as M2) are found to be inconsistent with economic fundamentals in recent years, and their are signs that CBC’s policy is lining toward interest rate targeting (Wang and Lee 2004).

Y

is the annual growth rate of Taiwan’s industrial production index. is the annual inflation rate based on the consumer price index. Figure 2 plots the data in their original units.

P

Trend and cyclical effects are removed from the variables before estimation; therefore, the model estimates the variables’ deviations from the long term trend. In studying Australian’s monetary policy effect, Dungey and Pagan (2000), among others, remove a deterministic linear trend from variables. Buckle et al. (2002) find that the same procedure does not work very well for New Zealand data and suggest the Hodrick-Prescott filter instead. In our paper, we remove trends and seasonal cyclicality from data using OLS regressions on the following variables: a time trend, a dummy of Asian financial crisis, the interaction of the time trend and the crisis dummy, twelve monthly dummies, and dummies of Chinese lunar new year. The Asian financial crisis dummy has the value equal to 1 from October 1997 to December 2002 and a value equal to 0 otherwise. The exogenous crisis has a substantial impact on the economy and we use the crisis dummy variable to capture the possible changes in the variables’ time trends during the period. As to the Chinese lunar new year dummies, Lin and Liu (2003) find that the holiday has significant effects on many of Taiwan’s economic variables. We follow their suggestion and use the method of Bell and Hillmer (1983) to great the corresponding holiday dummies to control for the holiday effect.

For a small open economy, foreign influences could not be ignored. We consider two of such exogenous foreign variables in this model: the annual growth rate of the U.S.industrial production index (Y∗) and the U.S.federal funds rate (

R

∗). The production index variable is adopted to approximate effects of international business cycles and foreign demands. The federal funds rate

measures the U.S.’s stance of monetary policy, and it is known that CBC routinely takes this rate into account in formulating monetary policy for the domestic economy. The two variables are filtered through a time trend and twelve monthly dummies before used in the estimation.

The empirical model is specified as follows:

and

[

_{t t}

]

_s

E

ε ε

=

D I

= .

The

B

_i is a

5

matrix containing coefficients of exogenous variables with lags. The first equation of Yt assumes that output adjustment is sluggish, therefore, output is not affected by contemporaneous changes in other variables. The second equation of price also emphasizes the sluggishness in the price adjustment. The third equation is CBC’s monetary policy function. The function assumes that information on current output and price is available to CBC when making the monetary policy, and it also allows foreign exchange intervention to affect interest rate if the intervention is not fully sterilized. The fourth equation assumes that the foreign exchange rate is affected by all the contemporaneous variables. The last equation is the CBC’s foreign exchange intervention function which is contemporaneously affected by the exchange rate.

2

×

i

We then ask what would happen to the effects of monetary policy if there is no foreign exchange intervention. The issue is investigated by counterfactual simulations based on previously estimated results. In the simulations, channels through which foreign exchange interventions affecting output and/or channels through which interventions responding to monetary policy shocks are shut down, and the resulting impulse responses are compared to those of the original model. The shut-down restriction amounts to setting some of the previously estimated coefficients to 0.

Ramey (1993) estimates a VAR model of the U.S.monetary policy, and she also uses counterfactual simulations to investigate the importance of the money channel and the credit channel in the monetary transmission mechanism. The importance is evaluated by shutting down one of the channels in the model and then comparing the resulting impulse responses to those obtained from the

original model. If the impulse responses show significant differences after the channel is closed, then the channel should hold importance for the monetary transmission mechanism. To shut down the transmission channel, Ramey’s method is to set selected elements of the estimated VAR matrixes to 0 to the effect that variables responsible for channeling the effect do not affect the rest of the variables in the model.

Our counterfactual simulations use strategies similar to that of Ramey (1993) but with some important differences. Firstly, we consider two different approaches in shutting down the channel of foreign exchange interventions. One of which imposes the restriction that is not affected by changes in the exchange rate, and the other approach imposes the restriction that changes in

do not affect the rest of the variables in the model. The latter approach is in line with the method of Ramey (1993). Secondly, unlike Ramey (1993), we provide confidence intervals via bootstrap techniques for the counterfactual impulse responses. The confidence intervals are particularly important to our study since the intervals allow us to assess statistical significance of the counterfactual impulse responses. The two simulation approaches are explained below.

FX

FX

Policy Reaction Function Method (PRFM)

This method simulates the no-intervention scenario by altering the the intervention policy reaction function which is the fifth equation in (7). In particular, the foreign exchange intervention is assumed to react to none of the variables in the model, thus effectively making the foreign exchange intervention function an auto-regressive form. To this end, the

[5 ]

,

j

elements of the estimated

ˆA

and

_A

ˆ

_k,

j

≤

4

and , are set to 0, and impulse responses are calculated based on the modified matrixes.

1,...

k

=

, p

Transmission Channel Method (TCM)

This method simulates the no-intervention scenario by shutting down the channel through which affects the economy. More specifically, changes in is assumed to have no impact on all the other varia

FX

FX

bles in the model. This is also the simulation

strategy adopted by Ramey (1993). The strategy is achieved by setting a value of 0 to all of the

[ 5]

i

,

elements of the estimated

ˆA

and

_A

ˆ

_k matrixes for

i

≤

4

and

k

= , , p

1 ...

, and impulse responses are calculated based on the modified matrix.

3.2 Findings

Estimation results provide evidence that the overnight rate is influenced by CBC’s foreign exchange interventions, which is likely to result from not-fully sterilized interventions. The constructed policy rate, on the other hand, is not influenced by the intervention actions. Using the constructed policy rate in the SVAR model, we are able to find significant monetary policy effects on output. For the hypothesis that the exchange rate channel of the monetary policy may be clogged by CBC’s interventions in the foreign exchange market, counterfactual simulations show that it is not likely to be the case in Taiwan. Shutting down the intervention channel in the model does not increase the estimated policy effects. The latter finding may indicate that the foreign

exchange policy and the monetary policy in Taiwan are always conducted in accordance, and therefore the intervention is done in a way that does not mitigate monetary policy’s transmission mechanism.

Sub-project #4 Capital Adequacy, the Bank Lending Channel, and Their Macroeconomic Implications 1. Introduction

Most of the finance literature has focused on bank-level analysis of portfolio risk, probability of failure, and the role of information asymmetries. Relatively little work sorts out monetary policy implications of capital adequacy requirements (CAR). However, it is important to address such an issue. First, it is generally agreed that bank capital is an important factor in bank asset and liability management and that its importance has likely increased since the implementation of the risk-based capital requirements of the 1988 Basle Accord. Second, taking into account capital adequacy regulations allows us to address the question what role bank lending plays in the monetary transmission in a world in which banks are increasingly able to issue non-reservable liabilities.

The existing papers discussing CAR confine the analysis into the framework of partial equilibrium. Therefore, they are not able to provide a complete picture concerning the implications of CAR. In addition, there have been many studies that investigate microeconomic implications of CAR, but, to our knowledge, there have been relatively few studies of its macroeconomic implications. Particularly, the modeling of these works seems to be ad hoc; although insightful, their works lack analytical foundation. The general equilibrium analysis undertaken through our model offers a new insight into the assessment of the effects of capital regulation that has never been considered before, at least in a formal setting.

The focus of this paper is not on the informational microfoundations that gives rise to the existence of banks, borrowers and the longer maturity of bank loans. Rather, the emphasis is on a careful treatment of the bank’s balance sheet components and the implications thereof for bank lending and monetary policy. We do not only analyze the effects of CAR on the banking sector, but also investigate the possible impacts of CAR on the bank lending channel, i.e., the channel of interaction between bank lending and the real sector.

2. The Model 2.1 Households

The economy is populated by a unit measure of identical, infinitely-lived households. Each household is endowed with one unit of labor; labor causes no disutility and working time is inelastically supplied for simplicity. Given a constant rate of time preference

ρ

(>0), the representative household, facing its budget constraint and the initial conditions, maximize the discounted sum of future instantaneous utilities by selecting optimally a consumption bundle C and a asset portfolio allocation between (real) bank deposits D, the stock of equities issued by banks and by firms , taking all prices and return rates of equities as given. Thus, the optimization problem can be expressed by:

B

∫

∞ _⋅ − 0 ln max C e ρtdt subject to , (1) TR C S p i S p i D r S p S p

D&+ _B&_B + _F &_F =( _D −

π

) + _{B B B} + _{F F F} − +

0 0 0_{, (0) , (0)} ) 0 ( D S_B S_B S_F S_F D = = =

where r_D is the deposit rate,

π

is the inflation rate, TR is a lump-sum transfer provided by the government, ( ) is the relative price of bank (firm) equity in terms of consumption good, ( ) is the return (dividend) rate on bank (firm) equality. The first order conditions will allow us to derive the following no-arbitrage condition:

B p p_F B i i_F B B B F F F D p p i p p i r −

π

= + & = + & . 2.2 Firms

The homogeneous good used in the economy are produced by competitive firms. Each firm has an identical production technology. The representative firm maximizes the shareholder value, i.e., the initial value of equality by investing physical capital K and purchasing investment projects provided by banks x. We highlight the role of financial instruments for a firm’s capital formation, namely converting effective bank loan services into productive capital. As argued by Vinala and Berges (1988), financial services play a crucial role in affecting real investment decisions by allowing firms to make better investment decisions through monitoring. Robinson (1969, ch. 4) illustrates that financial services have potentials to affect investment decisions by making available to firms cheaper external financing sources. In line with these arguments, the production function is given by: ) 0 ( F V x AK x K f( , )= ε , with x=

θ

⋅g(

χ

,L)=

θ

⋅

χ

σLv, 0< v

ε

, <1, 0<

ε

+v<1, and

σ

>1. (2)

The above equation indicates that effective bank loan services x increase with the parameter of banking efficacy

θ

and the amount of bank loans L, but decrease with the fraction of bad loans (1−

χ

). The individual firm’s capital can be converted from bank loans as “fractional substitutes” and treat the conversion coefficient

θ

as a measure of banking efficacy. A higher

θ

captures commercial banks’ provision of loan services in terms of market promotion and project evaluation. However, bank loans L cannot completely convert to the effective loan services which should be discounted by bad loans (it will be clear in next subsection). Therefore, we specify that x is decreasing in the fraction (1−

χ

). This specification reveals that loans are a risky investment for commercial banks. Since

χ

is lesser than one, we should further assume that

σ

>1.

The firm’s gross profit Π_F is defined by:

L x K f F = ( , )−(

δ

−

π

)

χ

Π =RE_F +Ω_F, (3)

where

δ

is the loan rate. The gross profit is either paid out as dividends Ω_F to stockholders or retained as earnings to finance further investment I, as shown by (3). A particular emphasis is that in addition to retained earning, firms can issue equality to households and borrow from banks in order to finance investment. Accordingly,

F

. (4) L S p RE I = _F + _F &_F +

χ

&

Now define the value of outstanding equalities to be:

. (5)

F F

F p S

V =

From (3) and (4), and the time derivative of (5), we have: , ) ( _{F F} F F F F F F F p S p S p S

V& = & + & = & + Ω −

γ

where the firm’s cash flow. By substituting the definition of the dividend rate and the household’s no-arbitrage condition into the above equation, we further obtain the following differential equation in terms of :

L I F F

χ

&

γ

=Π − + i_F =Ω_F/(p_FS_F) F V . (6) F F D F r V V& =( −

π

) −

γ

This implies is the rate at which the firm discounts its cash flow. By solving (6) for , the steady-state value of outstanding equalities is given by:

F V V_F ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ⋅ ⋅ =

∫

−

∫

∞

γ

τ

−

∫

−

τ

τ ξ π τ π d e e t V r d t F d r F D t D 0 0( ) ( ) ( ) ) ( . (7)

Given (7), the firm’s object is to choose investment (capital) and loan to maximize the initial value of equality . The optimization problem is:

) 0 ( F V max

[

δ

χ

]

τ

, (8) τ ξ π d e I L r x K f L V_{F D} rD d

∫

∞ − − − −

∫

− + − = 0 ) ( 0 ( , ) ( ) 0 ) 0 (

subject to _f(_K,_x)_=AKε(

_θχ

σ_Lv), _{K& =I−}

_η

_K, _K(0)=K0 and _L(0)=L0.

2.3 Banks

These is a continuum of banks with mass one, which take deposits D from households and make loans to firms. As mentioned above, in our model loans are a risky investment for banks; there is a fraction (1−

χ

) of outstanding loans L goes bad. By following Van den Heuvel (2005), we assume that these bad loans must be written off by banks. A legal requirement imposes a lower bound on the fraction of deposits banks hold, i.e., R≥

φ

D, where R is required reserve and

φ

is the corresponding rate of reserve requirements. Aside from reserve requirements R and the effective loans

χ

L, the bank also holds federal funds F (negotiable certificates of deposit) and physical capital as its assets. These assets are financed by debt instrument – deposit D and by equality capital,

B

K

B

V (= p_BS_B). In other words, the bank’s balance sheet is given by:

D V L F

R+ +

χ

= _B + . (9)

For simplicity, we abstract the bank’s capital from this model, K_B =0. Since the bank dose not need to invest capital, its retained earnings RE_B and the change of equality will be accumulated and, consequently, increase the market value of the bank’s