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The Macroeconmic Consequences of Financial Imperfections

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### The Macroeconmic Consequences of Financial Imperfections

指導老師： 黃介良 博士

分組組員：695515058 陳誌原

695515046 林宏彥

695515025 胡竣盛

694515006 彭鈺珺

Introduce

- The discussion so far has focused on the microeconomic approach to banking
- The macroeconomic implications of the same financial imperfections have been used to explain the role of banks and financial intermediaries

Con.

- The transmission channels of monetary policy
- The fragility of the financial system
- The existence of financial cycles
- The real effects of financial intermediation
- The impact of financial intermediation on growth

Historical perpective

- Fisher(1933) argued that the severity of the economic downturn during the Great Depression resulted from the poor performance of financial markers.
- Gurley-Shaw(1955) argued that financial intermediaries play a critical role in the savers and borrowers.

Con.

- Friedman and Schwartz(1963) argued that money supply was the key financial aggregate gained wide support
- Bernanke(1983) argued that the collapse of the financial system was the important factor to expain the Depression

Credit view

- In response to Friedman and Schwartz’s “money view”, the alternative position was to emphasize the “credit view”
- The stock of money is less important than the financial capacity, defined as the aggregate volume of credit that lenders grant to borrowers

The money channel

- IS/LM model:

two assets(money D and bonds B),

four types of agents:households, firms

banks, gobernment

- LM: R=αDh(y,rB) …(6.6)

IS:I(rB)+G=S(y,rB) …(6.7)

LM

LM’

rB*

rB**

IS

y

Y*

Y**

IS/LM model- The effect of monetary policy: increase R or decrease Bg(liquidity injection), y increase, rB decreases.

The implicit assumptions

- A1: prices do not adjust instantaneously to offset changes in the quantity of money
- A2: the Central Bank can directly influence the nominal quantity of money by adjusting reserves
- A3: Loans and bonds are perfect substitutes for the borrowers

Credit view~Bernanke&Blinder(1998)

- Add loans
- LM: R=αDh(y,rB) …(6.6)
- IS CC curve

I(rB, Φ(rB,R))+G=S(y,rB) …(6.14)

LM

LM’

rB**=rB*

rB**

CC”

CC’

CC

y

Y*

Y**

Y**

Adjusted IS/LM modelEffect:

- the quantity of money increases (LM shifts downward)
- The volume of credit increases (cc shifts upward)

The implicit assumptions

- A1: prices do not adjust instantaneously to offset changes in the quantity of money
- A2: the Central Bank can directly influence the volume of credit by adjusting reserves
- A3: Loans and bonds are imperfect substitutes for the borrowers

The Fragility of the Financial System

- Financial Collapse Due to Adverse Selection—simpler model of Mankiw(1986)
- Financial Fragility and Economic Performance—Bernanke and Gertler(1990)

The Fragility of the Financial System

- Mankiw model :
- Because of adverse selection , the credit market may collapse after a small increase in the money market rate
- Bernanke and Gertler Model :
- Because of moral hazard , the general financial conditions (credit worthiness of borrowers , or banks’ solvency) can affect macroeconomic performance

Financial Collapse Due to Adverse SelectionMankiw Model(1986)

- Risk neutral borrowers
- (X,p) –parameterized in their investment project
- Each project costs $1
- Return is X/p with probability p (success) and zero with probability 1-p (failure)
- X : expected return on the project
- Risk neutral banks
- Repayment is R in case of success and zero in case of failure
- (X,p) is private information of the borrower ,R cannot be conditioned on it
- pR: expected return on the project
- Results : bankers are confronted with adverse selection
- →the firms that apply for credit are the more risky ones

Mankiw Model

- A Firm apply for credit when X-pR >U0 =0
- X-pR :expected gain of a firm
- U0 :reservation utility (assume U0 =0)
- Π(R) :average probability of repayment (decreasing function of R)
- Π(R)=E[ p | p<X/R]
- Π(0)=E[p] and lim Π(R)=0
- r : money market or interbank rate (assume to be exogenous)
- Equilibrium condition on the credit market :
- Π(R)R = 1+ r

R →+∞

Probability of Repayment

ΠR=1+r2

E[p]

ΠR=1+rc

C

A

ΠR=1+r1

B

R

Nominal Interest

Equilibria of the credit Market

Financial Fragility and Economic PerformanceThe Model of Bernanke and Gertler(1990)

- Assumptions:
- Two period (t=1,2)
- Infinite number of agents (entrepreneurs in proportion μ or households in proportion 1-μ)
- All agents are risk neutral and have access to a riskless (storage) technology :1 unit of the good at t=1 becomes (1+ r) units at t=2
- Initial endowment is normalized 1 unit of the good
- Entrepreneurs (we) is less than one (we<1 and E(w)=we)
- Entrepreneur owns a risky technology :1 unit of the good at t=1 becomes X units (at t=2) with probability p ,and 0 with probanility(1-p)
- p is unknown ,entrepreneur costs C to 「screen」it
- Entrepreneur decides to undertake the project if p is large enough

T he Model of Bernanke and Gertler(con.)

- h(p): the density function of p on [0,1]
- H(p): cumulative distribution
- A(p0)=E[p|p≧p0](average success probability conditionally on p ≧p0)
- Projects with a positive expected excess return will be undertaken (pX>1+r)
- p*=(1+r) / X (cutoff probability under which projects are not financed)
- Option value:
- Not to screen profit is max( E(p)X ,1+r )
- (we assume E(p)X<1+r ,so the firms would use the storage technology)
- To screen profit is maxEp[ max pX , (1+r) ]
- Option value =V=E[max(pX-1-r,0)]
- Screening will take place when C<V= Ep[ max(0, pX-1-r) ]

{

success

Lender gets R

Entrepreneur gets (X-R)

screening

Contract signed,(1-w) is lent ,project is financed

w≧wc

Failure

{

Both lender

And entrepreneur get 0

W<wc

No screening

Introducing Credit Constrants and Limited Liability- Assume entrepreneurs cannot self-finance (w<1) ,they have to found the remaining part (1-w) and sign with the lender a contract specifying the repayment R in case of success , no repayment in case of failure .
- The contract is signed after screening takes place after the borrower observes p , but the borrowers cannot credibly communicate the value of p

Con.

- p^(w) : the minimum cutoff probability required by the
- entrepreneur to implement the project
- The equilibrium contract will be determined by
- (X-R(w))p^(w) = (1+r)w (6.26)
- Zero profit condition for lenders :
- A(p^(w))R(w) = (1+r)(1-w) (6.27)
- The option value of the screening technology becomes
- V(w)=Ep[max(0,p(X-R(w))-(1+r)w)]
- =∫p^(w) (p(X-R(w))-(1+ r)w)h(p)dp
- V(w)= Ep[(pX-(1+r)) ∥p>p^(w)]
- = ∫p^(w) (pX-(1+r))h(p)dp (6.28)

1

R(w) = [(1+r)(1-w)]/p^(W)

1

Results 6.3The consequences of moral hazard and limited liability

- 1.Overinvestment
- p^(w) ≦p*=(1+r)/X
- 2.Invest in the storage technology when w<wc wc is defined implicitly by V(wc)=C
- 3.r(w)=R(w)/(1-w) is a decreasing function of w

def

Proof

- 1.When w=1 R(1)=0 p^(1)=p* by(6.27&6.26)
- p^(w) ≦p^(1)=p*=(1+r)/X →p^(w)X-1-r<0
- 2.dV/dw=-h(p^(w))(p^(w)X-1-r)(dp^/dw)>0 (by6.28)
- V(1)=V>C by assumption
- E(p)R(w)/(1-w) ≧1+r (lender benefit but borrower loss)
- 3.R(w)/(1-w) =r(w) =(1+r)/A(p^(w)) (by 6.27)
- PS: dp^/dw >0

def

>0

>0

p^(w) is a nondecreasing function of w- By (dw 6.26&6.27)
- [X-R(w)](dp^/dw)-(dR/dw)p^=1+r…….(1)
- A’(p^)R(dp^/dw)+A(p^)(dR/dw)=-1-r…(2)
- (1)*A(p^)+(2)*p^ we get
- {A(p^)[X-R(w)]+ p^A’(p^)R} (dp^/dw) =(1+r)[A(p^)-p^]
- Therefore dp^/dw >0 and the proof is complete

Macroeconomic Implications

- F(w) : the distribution function of the firm’s wealth
- f(w) :associated density [w0 , w1]
- w0 <wc< w1
- Firm’s expected output :
- q(w)=rw if w<wc
- =rw+V(w)-C if w>wc

Macroeconomic Implications(con.)

- Aggregate economic variables(per capita)
- I=μ∫wc (1-H(p^(w)))dF(w)
- S=μ∫wc (1-w)(1-H(p^(w)))dF(w)
- q=r+ μ∫wc(V(w)-C)dF(w)
- Compared with their first-best levels
- I*=μ(1-H(p*))
- S*= μ(1-we)(1-H(p*))
- q*=r+μ(V-C)

w1

w1

w1

Conclusion

1.Global performance (output q and investment I)of this economic does not depend only on the fundamentals of investment (i.e.,p*,μ,V and C) but also on the financial situation of firms (i.e. firm’s initial wealth distribution, w)

2.When firm have low wealth (i.e.F(wc) is close to one or wc close to w1)

investment and output will be low even if the the fundamentals are good .This situation is described by Bernanke and Gertler as “financial fragility”

3.If there is a shock on the distribution of w such that w1 falls below wc , a collapse of investment will occur as a result of the poor financial condition of firms

Policy Implications

- 1.The types of agents are not observable:
- A tax on successful investment projects (used to subsidize households) will be welfare improving →to make entrepreneur not to invest too much (p^(w)<p*)
- 2.The types of agents are observable:
- Subsidizing entrepreneurs by taxing households will be welfare improving

Financial Cycles and Fluctuations

- Explore the possible explanation of business cycles and economic fluctuations that can be attributed to financial constraints or imperfections
- Bankruptcy Constraints，Farmer(1984)
- Credit Cycles，Kiyotaki and moore(1995)

Bankruptcy Constraints

Yt=(1+st)min(kt,lt)-δktlt

- Yt：net production at period Pt
- St：productivity shock st=>[0，1]
- Kt：capital
- lt：lt={0，1} labor supply
- δ：depreciation of capital

Bankruptcy Constraints

Optimal Contracts

- Without asymmetric information

1+st≥ δ,active；inactive w

- Asymmetric information

R,active；inactive 0

- Nominal interest factor influences the probability of repayment：

Π(R)=Proba{yt ≥R}=proba{st ≥δ+r-1}

Yt=(1+st)min(kt,lt)-δktlt

δ

Bankruptcy ConstraintsMacroeconomic Equilibrium

Without bankruptcy constraint

- Y*=K[∫ (1+s-δ)h(s)ds]

Bankruptcy constraint

- Y(R)= K[∫ (1+s-δ-R)h(s)ds]
- Productivity shocks will affect tomorrow’s interest rates

1

δ+R

Credit Cycles

bt≦(Ktqt+1)/(1+r)

- bt：the amount of loan
- Kt：the amount of land
- qt：price of land during period t
- r： riskless rate

ht=m(At+h0)

- ht：rental rate
- At：real estate used for production
- Linear specification for this inverse demand function

Credit Cycles

At=λ[(Aqt+1)/(1+r)]

- (Aqt+1)/(1+r)：the total amount that firm arealbe to borrow

qt+1+(X-(1+r))qt+1/(1+r)+ht(1-(λqt+1)/(1+r)

=(1+r)qt

- No-arbitrage condition yidlds

qt=a(qt+1)2+bqt+1+c def= ψ(qt+1)

金融中介機構之實際作用(1)

- 公司為投資尋求外部融資，但存在道德問題；公司管理人會選擇低成功率PL，因其帶來收益比高成功機率PH高。

私人收益 B＞b + C 銀行監督成本

Review CH2 :Holmstrom-Tirole model

Holmstrom-Tirole(1994) model

銀行融資：

- PH*(R-Ru-Rm)≧PL*（R-Ru-Rm)+b
- Ru+Rm ≦R-b/∆p

加入監督成本C

- PHRm-C≧PLRm
- Rm≧ C/∆p

直接融資成本小於銀行融資

- 令Rm= C/∆p 則 PHRm/ß=PHC/ß∆p，Iu=PHRu/ρ
- Ru≦R-(b+C)/∆p 則Iu≦PH/ρ〔R-(b+C)/ ∆p〕
- 融資條件
- A+Iu+Im≧I
- A(ß,ρ)=I-Im(ß)-PH/ρ*[R-(b+C)/∆p]

金融中介機構之實際作用(2)

公司若有足夠現金資產在沒有銀行監督下即可解決道德問題

- A≧Ã(ρ)=I- PH/ρ(R-B/ΔP) 6.41

R：貸款成功的報酬

ρ：金融市場的投資報酬（1+r）

ΔP：PH-PL

金融中介機構之實際作用(3)

公司資產不夠，部分資金由銀行借貸Im

- A(ß,ρ) ≦ A ≦Ã(ρ)

ß ：銀行貸款的投資報酬

- A(ß,ρ)=I-Im(ß)-PH/ρ*[R-(b+C)/(PH-PL)]

公式6.42

Im(ß)= PH*C / ß*(PH-PL )

銀行資本市場均等式

- Km=[G(Ã(ρ))-G( A(ß,ρ)]* Im(ß)

G()：公司資產分布函數

Im (ß)：貸款中銀行用自有資產融資比

ρ：金融市場的投資報酬（1+r）

- 決定於金融市場之均衡條件

儲蓄供給S（ρ）=資金需求D(ß,ρ,C）

金融衝擊類型

Holmostrom-Tirole考慮3種類型

ρ金融市場均衡回報，ß銀行貸款均衡回報

- 信用萎縮

(銀行業資本Km↓) ρ↓，ß↑

- 抵押值縮減

（廠商資產↓） ρ↓，ß↓

- 儲蓄緊縮

（儲蓄函數S下移） ρ↑，ß↓

經濟成長V.S金融發展及結構之研究(1)

- Schumpeter （1911）強調銀行體系在經濟成長的重要性。
- Goldsmith(1969), McKinnon(1973)以及Shaw(1973)曾提出金融體系在經濟成長中扮演重要角色。
- Greenwood與Jovanovic(1990), Bencivenga，以及Smith(1991), 闡述金融機構刺激經濟成長。
- Boyd與Prescott（1986）金融機構功能為篩選，回報夠高就可使投資實現。

經濟成長VS金融發展及結構之研究(2)

- Bencivenga與Smith、Diamond與Dyvig(1983)金融中介機構促進儲蓄向生產性投資分配，及降低投資項目不必要的流動性資產，提高效率及促進經濟成長。
- Sussman與Zeira(1995)經濟發展與金融發展反向效應。
- King 及 Levine (1993)實證研究方面使用跨國的資料去分析經濟成長與金融發展之間的關係。分析結果顯示金融指標的變動範圍和經濟成長呈強烈地正向關係。

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