"Leverage Stacks and the Financial System" by John H. Moore Background reading

Melania Nica, LSE, October 2011

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Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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John Moore’s paper (few ideas)

Occam’s razor: "Numquam ponenda est pluralitas sine necessitate" (in Latin) "Plurality must never be posited without necessity" (in English)

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Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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John Moore’s paper (few ideas)

The current …nancial system is built on many levels of …nancial intermediation: Lenders (households) - bank - bank - borrowers (entrepreneurs) No …nancial intermediation: lender’s loan is secured against the underlying investment project of the borrower; Financial intermediation: lender’s loan to bank is secured against bank’s loan to the next bank which is secured against bank’s loan to borrower

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Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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John Moore’s paper (few ideas) Questions: Why do we see this type of …nancial stacking or why banks hold gross positions (banks lend and borrow from each other)? Do gross positions create systemic risks?

Important points: Lead banks versus non-lead banks (banks with outside option of lending to entrepreneurs or not) Roll over: a bank issues inside bonds (borrows) usually against current holding of outside assets (inside borrowing has a shorter maturity than outside lending) Both non-lead and lead banks do roll over Problem with non-lead banks doing roll over.(they are both borrowers and lending in the interbank market): if bank’s value of inside borrowing decreases, banks value of inside lending decreases by a higher percentage: bank net lending decreases Background reading ()

Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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Related Papers

"Financial Intermediation and Credit Policy in Business Cycle Analysis" by Gertler and Kiyotaki (GK 2010) "Financial Crises, Bank Risk Exposure and Government Financial Policy" by Gertler, Kiyotaki and Queralto (GKQ 2011)

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Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GK 2010 Environment Continuum of …rms located on a continuum of islands Production technology: Yt = At Ktα L1t

α

with α 2 (0, 1)

Labour perfectly mobile across islands. Capital not mobile. Investment opportunities arrive randomly to a fraction π i of islands Law of motion of capital: 1 0 B Kt + 1 = ψ t + 1 @ ψ t +1

It + π i (1 {z |

δ ) Kt }

capital accumulated by investing on islands

|

1

π i (1 {z

δ ) Kt }

C A+

remaining capital on non-inv.islands after δ

ψt +1 is a shock to the quality of capital Background reading ()

Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GK 2010

Aggregate output is divided between household consumption, investment and government consumption: Yt = Ct + 1 + f

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It It

It

+ Gt

1

Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GK 2010 Households Representative household with a continuum of members f bankers

(1 f ) workers there is turnover between bankers and workers with probability (1 σ) a banker exists next period - 1 1 σ survival time; to keep the numbers constant, each period (1 σ) f workers randomly become bankers each banker manages a …nancial intermediary (a bank) households do not hold capital directly but invest in banks (other than the one they own)

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Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GK 2010

∞

max Et

∑ βi

ln (Ct +i

γCt +i

1)

i =0

χ 1 +ε L 1 + ε t +i

s.t. Ct = Wt Lt + Πt

Tt + Rt Dht

Dht +1

Πt net funds transferred to households (pro…ts) from …rms and banks Πt is net of transfers to new bankers (small constant which represents start-up funds to new bankers) Dht quantity of riskless debt held Rt return on riskless debt from t 1 to t Tt taxes

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Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GK 2010

FOC: Et uCt Wt Et Λt,t

1 Rt +1

Λt,t

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1

= χ = 1 = β

uCt +1 uCt

Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GK 2010 Non-Financial Firms Goods Producers O¤er wage: Wt = ( 1

α)

Yt Lt

Gross pro…t per unit of capital: Zt =

Yt

Wt Lt = αAt Kt

Lt Kt

A good producer with opportunity to invest obtains funds from an intermediary by issuing securities at price Qti .These securities are state-contingent claims to future returns on investment: ψt +1 Zt +1 , (1 Background reading ()

δ) ψt +1 ψt +2 Zt +2 , (1

δ)2 ψt +1 ψt +2 ψt +3 Zt +3,...

Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GK 2010

Capital goods producers Sell new capital to …rms at price Qti ∞

max Et

∑ Λt,τ

τ =t

Q ti

= 1+f

Iτ Iτ +1

Background reading ()

+

Iτ Iτ +1

f0

Qτi Iτ

Iτ Iτ +1

1+f

Iτ Iτ +1

Et Λt,t +1

Iτ

Iτ Iτ +1

2

f0

Iτ Iτ +1

Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GK 2010

Banks Retail Financial Market: At the beginning of the period household deposit dt at rate Rt +1 . After the retail market closes, investment opportunity arrive to each island. Wholesale Market - interbank market where banks borrow and lend from each other Banks on islands with investment opportunities will borrow funds from banks located on islands with no investment opportunities.

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Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GK 2010

Banks After learning about lending opportunities a bank decides the volume of loans sth to make to non …nancial …rms and the volume of the interbank borrowing bth ; h = i, n either investing or non investing island. Value of the bank (expected present value of future dividends): ∞

Vt = max Et

∑ (1

σ ) σi

1

Λt,t +i nth+i

i =1

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Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GK 2010

such that: 1. Flow of funds constraint for an individual bank: Qth sth = nth + bth + dt which means the value of loans funded within a given period must be equal to the sum of the bank net worth, its borrowings on the interbank market and deposits. Net worth h i nth = Zt + (1 δ) Qth ψt st 1 Rbt bt 1 Rt dt 1

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Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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2. Bank does not divert funds (incentive constraint) must hold. Vt (st , bt , dt )

θ Qth sth

ωbth

where: θ proportion of funds divertable by the banker to his family ω :relative e¢ ciency of the inter bank market: ω = 1 banks cannot divert assets …nanced by borrowing from other banks or no frictions on the interbank market; Creditors recognize the incentive of bankers to divert funds; so they will lend them money only if they do not steal them

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Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GK 2010

Bellman equation

Vt

1

( st

1 , bt 1 , dt 1 )

= Et

1 Λt 1,t

∑

πh

h =i ,n

(1

σ) nth + σ max max Vt (st , bt , dt ) dt

sth ,b th

Equilibrium: Market clearing in market for securities and the labor market. Total securities issued in investing and non investing islands correspond by the total capital acquired.

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Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GK 2010 Results: ω = 1 frictionless interbank market RBC framework with habit formation and investment adjustment costs ω = 0 - imperfect interbank market A negative quality shock directly arrises which reduces the value of bank net worth As a result: because banks are leveraged, the e¤ect of decline in asset values of the bank is enhanced by a factor equal to the leverage ratio. borrowing constraint kicks in: banks are forced to reduce assets holdings (st ).. the sale of assets reduces the market price of capital. a contraction in asset prices, reduces the investment level and as a result also the …nal output employment drops. Background reading ()

Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GKQ 2011 Di¤erent than GK 2010 by the fact that banks can issue outside equity and short term debt. Allow for the existence of intermediaries that have di¤erent risky balance structures. Households ∞

max Et

∑ βi

ln (Ct +i

γCt +i

1)

i =0

χ 1 +ε L 1 + ε t +i

s.t. Ct + Dht + qt e¯t = Wt Lt + Πt

Tt + Rt Dht

1

+ [Zt + (1

δ) qt ] ψt e¯t

1

qt price of equity; e¯t outside equity Non Financial Firms The same Background reading ()

Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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GKQ 2011 Banks Flow of funds constraint for an individual bank Qt st = nt + qt et + dt Net worth: nt = Rkt Qt

1 st 1

Ret qt

1 et 1

Rt dt

1

The incentive compatibility constraint takes into account the fact that it is easier to divert money from equity than from short debt; Dividend payments are tied to the performance of bank assets which is di¢ cult for outsider to monitor. Results: the severity of the crises depends on the riskiness of banks’ balance sheets which is endogenous.

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Melania Nica, LSE, October 2011 "Leverage Stacks and the Financial System" by John H. Moore

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