National Sun Yat-sen University Institutional Repository:Item 987654321/29108

行政院國家科學委員會補助專題研究計畫成果報告

內生不確定性、投資與產業動態

ENDOGENOUS UNCERTAINTY, INVESTMENTS, AND INDUSTRY DYNAMICS

計畫類別：個別型計畫

計畫編號：NSC 89-2415-H-110-007

執行期限：89 年 8 月 1 日至 90 年 7 月 31 日

計畫主持人：Diana Hwei-An Tsai

*

執行單位：Graduate Institute of Economics, National Sun Yat-Sen

University

中 華 民 國 90 年 10 月 20 日

*

Correspondence to: Graduate Institute of Economics, National Sun Yat-Sen University, Kaohsiung, Taiwan; tel: +886-7-5252000 ext. 5619; fax: +886-7-5255611; e-mail: [email protected]

中文摘要

本研究目的在探討當產業面臨需求與

投 資 的 不 確 定 性 時 的 投 資 行 為 及 產 業 動

態，過去文獻研究產業動態模型的課題都基

於靜態預期，或純粹理性預期的架構，假設

經濟體對經濟結構有完全的認知，而在經濟

環境中的未知都是來自於外在的衝擊。本研

究建立一個創新的產業動態模型，含括內生

不確定性與異質預期的假設於金融部門與

實質部門，以探討金融部門的波動與實質部

門決策的互動，進而探討對產業動態的影

響。

近年來金融部門因其資產價格的波動

性 及 金 融 不 穩 定 事 件 造 成 高 度 的 社 會 成

本；亞洲金融風暴是個明顯的案例，且因其

資本投資的減緩，經濟活動及金融變數的波

動及金融機構的不穩定等因素，引起了大眾

對東南亞國家競爭力下降的高度注意。本文

研究金融部門的內生不確定性，投資人的異

質性合理信念及信念間相關造成市場的擴

大波動，並以異質性的合理信念來分析投機

行為、市場交易量和內生的價格波動程度；

在投資人、生產者、投機者的異質性合理信

念 及 信 念 間 相 關 對 產 業 動 態 所 造 成 的 影

響。本研究建立的產業動態模型，含括內生

不確定性與異質預期的假設，探討對產業動

態就其生產技術特性、產品市場的競爭、及

其所引發調整成本的影響。本文闡明投資不

確 定 性 及 差 異 信 念 預 期 對 產 業 動 態 的 影

響，及金融不穩定對產業動態的影響。

關 鍵 詞 ：內生不確定性、異質信念、信念

間相關性、合理信念均衡、投資不確定性、

產業動態模型

Abstract

The goal of this paper is to gain an understanding of the endogenous uncertainty and heterogeneous beliefs on investment behavior and industry dynamics. Previous researchers have looked at the issues of industry dynamic model with static expectation or purely rational expectation settings, developing industry dynamic models which assume economic agents know the true structure of the economy and all uncertainty in the economy consists of the exogenous shocks. This paper build ups a new industrial dynamic model with endogenous uncertainty and heterogeneous beliefs. The industry dynamic model with endogenous uncertainty and rational belief expectation built in this study is then used to explore the decisions to carry out real investments in relation to the volatility of the financial sectors.

Recent years have witnessed pronounced asset price fluctuations and costly episodes of financial fragility. The financial crisis in Asia is a prominent case and has raised a lot of concerns for declining competitiveness in the Asian Pacific countries for the following reasons: retarded capital investment; fluctuation in economic activities and financial variables; instability of financial institutions; etc. The paper shows how heterogeneous belief and correlation

among investor's beliefs amplify the effect of exogenous shocks in the financial sector. And we based on heterogeneous rational belief to analyze the speculative behavior, market transaction and endogenous price volatility. The paper then shows the interactions between the volatility of the financial and real sectors. The paper provides a new industrial dynamic model with endogenous uncertainty and heterogeneous beliefs and to investigate the impacts of financial instabilities on the industry dynamics. And the model is then applied to analyze how heterogeneous beliefs and correlation among investors, producers, and speculators would affect the industry dynamics. On the theoretical front, the paper illuminates the effects of investment uncertainty and rational belief expectations on industry dynamics.

JEL code: D8, L1

Keywords: Endogenous uncertainty,

Heterogeneous belief, Belief correlation,

Investment uncertainty, Industry dynamics

I. Introduction

Recent years have witnessed rapid financial sector liberalization, pronounced asset price fluctuations and costly episodes of financial fragility. The Asian Financial Crisis of 1997 is a prominent case and has raised a lot of concerns for declining competitiveness in the Asia Pacific countries for the following reasons: uncertainty in capital investment, fluctuation in economic activities and financial variables, instability of financial institutions, etc. To understand how sharp changes in financial factors might affect the

investment behavior, technological nature and adjustment effects for the industry facing demand and investment shocks, industry dynamic model need to consider stochastic investment behavior and also the impact of investment uncertainty on the associated adjustments. Also, projections and policy analyses related to financial instabilities require an understanding of the pattern of demand response over time. Finally, understanding the macroeconomic impact of changing financial variables requires an understanding of the response of real investment, which in turn requires a new industrial dynamic model.

This paper builds up a new industrial dynamic model with endogenous uncertainty and heterogeneous beliefs. The industry dynamic model with endogenous uncertainty and heterogeneous beliefs is used to explore the decisions to carry out real investments in relation to the volatility of the financial sectors. And the model is then applied to analyze how heterogeneous beliefs and correlation among investors, producers, and speculators would affect the industry dynamics.

This paper is different from the previous industry dynamic model in that we don't assume rational expectation. Under rational expectations economic agents are assumed to know the true structure of the economy and all uncertainty in the economy consists of only exogenous shocks. Instead, we assume the uncertainty is propagated within the economy (hence "endogenous") by the beliefs of investors and firms (based on rational beliefs expectation theory). The rational expectation regime, however, didn't account for endogenous uncertainty that could cause the market volatility (or financial instabilities), and further impact the nature and timing of investment

behavior and then on industry dynamics. Since there could be endogenous uncertainty involved in the investment behaviors and production decisions, the current industry dynamic models with state -of-the-art would not appropriately interpret industry dynamics.

The previous industry dynamic model started from the theoretical cost of adjustment discussions by Lucas (1967a, 1967b) and Treadway (1969, 1971, 1974). Several approaches to the formulation and estimation of dynamic factor demand systems, with the generality of the technology and the expectation formation process specifications and in terms of informational requirements, are surveyed into the following four categories. The literatures along the lines of Nadiri and Rosen (1969, 1973), Berndt, Fuss and Waverman (1979), Denny, Fuss and Waverman (1981), and Morrison and Berndt (1981) incorporate endogenous determination of dynamic adjustment structure but retains a static expectation assumption.

The second category of rational expectations models following the lead of Thomas Sargent and Robert Lucas, developed by Hansen and Sargent (1980, 1981) and Epstein and Yatchew (1985), assumes that the firm sets inputs according to a stochastic closed-loop feedback control policy. It is based on an explicit analytic solution of the firm's intertemporal optimization problem and is restricted to very simplifying assumptions on the deterministic economic structure in order rigorously to specify the complex stochastic structure implied by the rational expectations assumption. Expectations on the exogenous variables in the firm's decision process are based on an autoregressive model, and hence the model is less general since it allows only for first-order

changes of factor inputs in the representation of adjustment costs. For an empirical application of the method by Epstein and Yatchew, see, e.g. Nadiri and Prucha (1985) and Mohnen, Nadiri and Prucha (1986).

The third approach is due to Kennan (1979), Hansen (1982), Hansen and Singleton (1982) and has been implemented in Pindyck and Rotemberg (1983a, b). It also assumes that inputs are set according to a stochastic closed-loop feedback control policy. The model relies on an instrumental variable approach to ensure error-othogonality and hence "consistency" with the rational expectations assumption. It replaces all expectations on future variables by their observed values in those future periods and applies an instrumental variable estimation technique. So, an explicit specification of the process that generates the variables exogenous in the firm's decision process or specific assumptions concerning the planning horizon are not required. This procedure allows for a more complete structural specification but does not explicitly incorporate an expectation process. And it is generally not fully efficient, since it ignores information from the remaining Euler equations and, in case of an infinite planning horizon, from the transversality condition.

The fourth category literatures, including Prucha and Nadiri (1986), Nadiri and Prucha (1989, 1996, 1999), Luh and Stefanou (1991), Morrison (1986), Morrison and Siegel (1997, 1998), and Tsai (1999a), the model of dynamic factor demands embodies dynamic optimization and rational expectations as non-static expectation. The approach assumes a firm with a finite but shifting planning horizon sets its inputs according to a certainty equivalence feedback

control policy. Under this category, approximations to rational expectations and certainty equivalence are used explicitly to incorporate anticipatory behavior of firms into the structural model of dynamic factor demands, based on the an explicit dynamic optimization framework. The rational expectation regime, however, didn't account for endogenous uncertainty that could cause the market volatility (or financial instabilities), and further impact the nature and timing of investment behavior and then on industry dynamics. Since there could be endogenous uncertainty involved in the investment behavior, the current industry dynamic models with state-of-the-art would not appropriately interpret industry dynamics.

The purpose of this study is to formulate a new industrial dynamic model to allow for heterogeneous belief and investment uncertainties, and which is general enough to serve as a framework for empirical work. The model built in this study modifies dual representation of production model to consider state dependent investment behavior, endogenous uncertainty in the stochastic investment process, and institutional changes. We study industry dynamics under the assumption the heterogeneous beliefs of agents and firms are rational in the sense of Kurz (1994a, b). The model is formulated by specifying a stochastic demand function and a continuum of investors and producers. Holding Rational Belie fs about future prices, producers maximize expected profits. In a Rational Beliefs Model, agents and firms select diverse forecast functions but each one is rational in the sense that it is based on a theory which cannot be rejected by the data.

This paper studies industrial dynamic

framework incorporating investment uncertainty under rational beliefs expectation. The scope of this study includes the followings:

1. Study the endogenous uncertainty in the financial sector. How heterogeneous belief and correlation among investor's beliefs amplify the effect of exogenous shocks in the financial sector? Based on heterogeneous rational belief to analyze the speculative behavior, market transaction and endogenous price volatility.

2. Formulate the new industrial dynamic model under rational beliefs expectation (RBE) and rational expectations (REH). And further, this study represents a step towards a synthesis of the structural and stochastic approaches to industry dynamic modeling, with emphasis on both the theoretical foundations and empirical tractability.

3. Understand the investment behavior under heterogeneous belief. The firm's investment decision becomes an interesting dynamic problem, in which anticipations about the future economic environment affect current investment, when frictions prevent instantaneous and costless adjustment of the capital stock.

4. Investigate the impacts of uncertainty in financial variables on industry dynamics. To analyze how the volatility of the decisions to carry out real investments in relation to the volatility of the financial sector, industry dynamic model need to consider investment uncertainty and also the impact of investment uncertainty on the industry dynamics. The model then examines how rationality vs. uncertainty affecting the industry dynamics.

II. Model of Industry

Dynamics with

Heterogeneous Firms

under Different

Expectation and Risk

Factors

Assume cost function for t, t+1, t+2, …

(1)

C

_t

(

w

_t

),

C

_t+1

(

w

_t+1

),

C

_t+2

(

w

_t+2

),...

The objective function of the firms is to

optimize the present value of the stream of

the future expected costs (with discounted

factors different for each firm)

(2)

E

_Q

Σ

β

t

C

_t

(

w

_t

)

Suppose there are R firms in one

industry and the firms choose different

investment strategy in terms of different

expectation and different risk factors (risk

averse, risk neutral, or risk lover)

(3)

∑

R t t R t Q

u

C

w

E

β

(

(

))

Assume firms combine two variable

factors, labor (L) and material (M), and one

quasi- fixed factor, capital (K) to produce

single output, Y, for current sales. Besides,

we assume quasi- fixed factor becomes

productive with one period time lag. Then,

we could specify the firm’s technology by the

following generalized factor requirement

function:

(4)

M

_t,i

=

M

(

Y

_t,i

,L

_t,i

,K

_t−1,i

,

∆

K

_t,i

,T

_t

)

where

∆

K

_t

=

K

_t

−

K

_t−1

represents the

internal adjustment costs of capital in term of

foregone output due to changes of stocks of

capital and

T denotes an index of

_t

exogenous technical change.

Suppose the accumulation of capital is

followed the investment equation:

(5)

K

_t,i

=

I

_t,i

+

(

1

−

δ

_t

)K

_t−1,i

where

I

_t,i

is the gross investment of

i t

K

_,

and

δ is the exogenous depreciation

_t

rate of capital which is also common across

firms.

The cost of firm i at period t under

variable cost minimization is given by:

(6)

[

(

)

]

(

)

(

)

[

ti t t 1i

]

K t t i t i 1 t L t M t i t i 1 t t i t K t i t L t t i t i 1 t i t i t M t K 1 K q ,T K , K p p Y G K 1 K q L p ,T K , ,K L , Y M p , , , , , , , , , , , , , , , ) ( − − − ∧ − ∧ − − ⋅ + = − − ⋅ + ⋅ + ⋅ δ ∆ δ ∆

where

p is the wage rate of labor ,

_tL

M t

p

is the price of raw materials, and

q

_tK

denote the price of new investment of capital.

(

t t t

)

L t M t t

p

p

K

,

K

,T

Y

G

,

,

,

₋₁

∆

represents the

restricted variable costs. Besides, factor

market faced by the firm is assumed to be

perfectly competitive.

Suppose firms choose different

investment strategy in terms of different

expectation and different risk factors.

Investment risk postures are expressed by

risk aversion, risk neutral, or risk averse, and

it is proxied by the demand for insurance.

The risk preference is then proxied by the

following function:

(7)

k k k R

u

π

γ

γ

−

−

=

Ω

1

)

(

1

1

)

(

By substituting cost function (6) into (7),

(8)

τ τ γ δ ∆ γ Ω − = − − − + ∏ − − + − = ) ( )} ) ( ( ) , , ( { ) ( , , , , , , , s t s 1 i 1 t t i t K t i t i 1 t L t i t i k R i r 1 K 1 K q ,T K , K p Y G 1 1 u i k

where

γ denotes the risk preference level

_{k ,i}

of firm i and

0

≤

γ

_k

<

1

.

Assume firm i follow a closed- loop

feedback control policy in his input decision

process and his objective is to minimize the

present value of the expected value of future

cost stream: (with discount factors different

for each firm):

(9)

τ τ γ τ δ ∆ γ − = − − − ∞ = + ∏ − − + − ∑ ) ( )} ) ( ( ) , , ( { , , , , , , , s t s 1 i 1 t t i t K t i t i 1 t L t i t i k t Q r 1 K 1 K q ,T K , K p Y G 1 1 E i k

where

r represent the discount rate at

_s

period

τ .

Standard control theory implies that the

stochastic closed loop feedback control

solution that minimized (9), say

∞₌

∧

t i

K

τ

}

_τ

{

,

has to satisfy the following stochastic Euler

equations:

(10)

(

)

[

]

(

)

(

)

[

]

        + ∂ ∂ ⋅         − − + = + ⋅         + − ∂ ∂ − ∂ ∂ ⋅         − − + − + + + + + + + + + + + K i i i i K i 1 1 1 K 1 Q i 1 i 1 Q i i 1 Q i 1 1 i 1 K 1 i 1 Q q K G K 1 K q G r 1 1 q E K G E K G E K 1 K Eq G E i K i K τ τ τ γ τ τ τ τ τ τ τ τ τ τ τ τ γ τ τ τ τ τ ∆ δ δ ∆ δ , , , , , , , , , , , , , , ) (

for

τ

=

t

,

t

+

1

,...

and

i

=

1

,

2

,...,

R

..

We proxy the following function

(

)

(

)

[

]

i k 1 i 1 i K i i 1 L i i k _{q K 1 K} ,T K , K p Y G 1 1 , , , , , , , , , γ τ τ τ τ τ τ τ τ τ δ ∆ γ − − −           − − ⋅ + −

to be linear quadratic equations, so that we

can apply certainty equivalence property to

reslove Euler equations.

In this model, we then show the

following expected results:

1. Modelling investment, and forecast

investment function in industry dynamic

model. Demonstrate that the impact of

diverse beliefs on price volatility can be

decomposed into two components: (a)

The added price volatility that arises

when beliefs are heterogeneous yet

uncoorelated. In this case, the structure of

beliefs amplifies the effects of exogenous

shocks on prices to a level of volatility

greater than that predicted by classical

Rational Beliefs theory. (b) Still greater

excess volatility that arises when the

heterogeneous beliefs of the agents are

correlated in different ways. We set forth

different ways in which belief correlation

alone can amplify price volatility.

2. Explain why is there heterogeneity rises

for firm heterogeneity. Compare REE

equilibria and the RBE equilibria, the

difference in volatility is due solely to the

presence of the heterogeneous beliefs of

the agents. In this model, we show the

phenomeno n of amplification that the

structure of beliefs in the economy

amplifies the effects of the exogenous

shocks in the economy.

3. Model investment, production model

with firm heterogeneity in expectation

and risk factors.

III. Results

We have conducted the survey to collect

the data of risk factors and expectations for

firms. So far the company dataset are not

completed. This is still an on- going project.

We are eager to get advice, both with respect

to industry dynamic perspectives, and to

rather readily applicable methods for

measuring and interpreting the concepts

related to risk factors and expectations

discussed above. We will also welcome

suggestions for other measures that may be

incorporated in the study.

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