The Credit Channel of Monetary Policy I

The Credit Channel of Monetary Policy I Ragna Alstadheim Norges Bank March 11th 2010 (Norges Bank) ECON4325 03/10 1 / 41

Introduction Chapter 7, Walsh is available on 12th oor. Web sites of the Fed and Bank of England worthwile to look at: http://www.federalreserve.gov/ and http://www.bankofengland.co.uk/ Informative speeches, for example: http://www.federalreserve.gov/newsevents/speech/bernanke20091207a.h (Norges Bank) ECON4325 03/10 2 / 41

The credit channel: motivation The great depression: nancial channels worsened situation. Financial system under stress more recently Does the health of the nancial system, and degree of leverage, a ect how the economy and policy works? Yes! Standard: Sticky prices make nominal interest rate changes become real interest rate changes and exchange rate changes become real exchange rate changes in the short run Standard: Only two types of capital: Money and Bonds, no modelling of nancial intermediation IS-LM or NK model not useful to analyze nancial stress (Norges Bank) ECON4325 03/10 3 / 41

What is the credit channel? Traditional: Banks special, they transform short term deposits into long term lending. Historically, reserve requirements/quantitative measures. Availability of bank funding linked to monetary policy? Focus here: Financial accelerator, including broader credit channel "external nance premium", Collateral and balance sheets important. Changing availability of collateral/own funds may amplify swings in economic acitivity (Norges Bank) ECON4325 03/10 4 / 41

Plan for presentation Micro-structure of nancial markets: Principal-agent problem Micro-structure e ects in partial equilibrium model Macro model with nancial sector and role for monetary policy Next week: unconventional measures implemented by central banks to help nancial market functioning (Norges Bank) ECON4325 03/10 5 / 41

Principal-agent problems in credit markets Perfect markets: Modigliani and Miller theorem states that nancing irrelevant to value of rm Market imperfections: funding structure matters Lender/supplier of capital is principal, borrower is agent. Di erent types of funding: Own funds/withheld earnings (no "agency costs") Bank loans (nominal return known, highest priority, loss if default/bankruptcy) Bonds (higher return than on loans, some more downside than loans) Shares (highest risk, lowest priority, involves monitoring of rm&in uence) Here: study market for loans (Norges Bank) ECON4325 03/10 6 / 41

Principal-agent problems in credit markets Two types of agency problem may make external funding more expensive: Moral hazard (hidden action by agent) Adverse selection (hidden information about agent) If perfect information: loan contract could be tailor made to each project or borrower. (Norges Bank) ECON4325 03/10 7 / 41

Moral hazard Example Suppose borrower can invest in project A or project B. B is more risky. Payo : R a < R b, but probability p a > p b.with probability (1 p a ) and (1 p b ), payo is 0 for both projects. If so, lender gets collateral C. If project is pro table, lender gets return (1 + r l )B. Pro t to borrower: E π A = p a [R a (1 + r l )B] (1 p a )C, E π B = p b [R b (1 + r l )B] (1 p b )C The interest rate that gives equal expected pro t for the two projects is characterized by: (1 + rl )B C = pa R a p b R b p a p b (Norges Bank) ECON4325 03/10 8 / 41

Moral hazard Interest rate above this rate=> project B is preferred by borrower=> expected pro t to lender is p b (1 + r H l )B + (1 p b )C Interest rate below this rate=>project A is preferred by borrower=> expected pro t to lender is Since in borderline case (r = r l ) p b (1 + r l )B + (1 p a (1 + r L l )B + (1 p a )C p b )C < p a (1 + r l )B + (1 p a )C Lender will make sure r l is (marginally below) r l.if higher interest rate: con ict of interest between borrower and lender. Lender will negotiate mechanism, or loan contract, that takes into account borrower s incentives. May negotiate collateral, lending rate, size of loan. (Norges Bank) ECON4325 03/10 9 / 41

Financial accelerator - example with no uncollateralized lending Example Two periods, 0 and 1. Entrepreneur uses inputs from period 0 to produce in period 1. Fixed input K, variable input x 1.Market price of K at end of period is q 1 per unit. Output period 1: a 1 f (x 1 ). Gross cash ow from previous production a 0 f (x 0 ). Entrepreneur maximizes period 1 output net of debt, a 1 f (x 1 ) r 1 b 1, subject to accounting identity Unconstrained optimal value of x 1: x 1 = a 0 f (x 0 ) + b 1 r 0 b 0 (1) Max (a 1f (x 1 ) x1,b1 r 1 b 1 ) = Max b1 [a 1f (a 0 f (x 0 ) + b 1 r 0 b 0 ) r 1 b 1 ] implies x 1 = x 1 such that a 1f 0 (x 1 ) = r 1 (Norges Bank) ECON4325 03/10 10 / 41

Example of nancial accelerator cont But borrowing is subject to constraint (no unsecured borrowing), because lender does not trust borrower.. Which implies If constraint binding, x 1 is suboptimal: b 1 (q 1 /r 1 )K (2) x 1 a 0 f (x 0 ) + (q 1 /r 1 )K r 0 b 0 (3) x 1 < x 1 ) a 1 f 0 (x 1 ) > r 1 (f () is concave) ) Shadow price for internal funding = a 1 f 0 (x 1 ), higher than r 1, re ects "agency costs". (Norges Bank) ECON4325 03/10 11 / 41

E ects of monetary policy in nancial accelerator model: (Norges Bank) ECON4325 03/10 12 / 41

Example of nancial accelerator cont. Conclusions from example: Internal funds special value Agency premium a 1 f 0 (x 1 ) r 1 increases when a 0 f (x 0 ) # or (q 1 /r 1 )K # or r 0 b 0 " because "no unsecured borrowing constraint" more binding Higher agency premium reduces spending x 1 and production f (x 1 ) Financial accelerator: uctuations in borrowers net worth lead to uctuations in real activity Negative demand shock reduces net worth =>downturn ampli ed by collateral-e ects (Norges Bank) ECON4325 03/10 13 / 41

Financial accelerator model central in discussion of nancial crisis De nition of nancial crisis: collateral constraint suddenly binding (Christiano, Rust, Roldos (2002)): Monetary Policy in a Financial Crisis, NBER WP9005 Variants of the premium in many modern models of credit channel (Norges Bank) ECON4325 03/10 14 / 41

Model with less extreme collateral assumption (Norges Bank) ECON4325 03/10 15 / 41

Simple model illustrates: External nance more expensive than internal nance Premium on external nance varies inversely with borrower s net worth External shock that also reduses net worth of borrowers is ampli ed via nancial accellerator High leverage may make economy more volatile, and imply ight to quality Saw this in interbank market in fall of 2008 (Norges Bank) ECON4325 03/10 16 / 41

"The Financial Accelerator in a quantitative business cycle framework", Ben S. Bernanke, Mark Gertler and Simon Gilchrist, Handbook of Macroeconomics, Vol. 1, 1999 (eds: J. B. Taylor and M. Woodford) http://www.federalreserve.gov/ - look at minutes from FOMC meetings (Norges Bank) ECON4325 03/10 17 / 41

Bernanke, Gertler and Gilchrist (BGG) (1999) Three types of agents: Households, Entrepreneurs and Retailers Closed economy, need heterogenous agents to get gross borrowing/lending Entrepreneurs borrow from households (via zero-cost nancial intermediation), "die" with a certain probability, risk neutral. Retailers act as "aggregator": buy intermediate goods from entrepreneurs, make diversi ed nal output, motivates monopolistic competition/enables sticky prices. Look closely at partial equilibrium capital demand. Rest is more conventional. (Norges Bank) ECON4325 03/10 18 / 41

Costly state veri cation (CSV) Information problem (moral hazard and adverse selection) gone if lender can see distribution of borrowers return perfectly: F (R, θ) If type of borrower (θ) can be seen, lender can make contract contingent on θ, so that more risky borrowers are charged higher interest rate, less risky borrowers charged lower interest rate (avoid adverse selection/credit rationing) If type of project that is chosen (θ) can be seen, lender can make contract contingent on type of project (avoid moral hazard/credit rationing) Here: assume realized return R can be checked at a cost, ex post. Will check return in order to get as much as possible in case of bankruptcy. If no bankruptcy, lender receives contracted return. If bankruptcy, part of return on project goes to cover "monitoring costs" or "bankruptcy cost". (Norges Bank) ECON4325 03/10 19 / 41

CSV (cont.) Entrepreneur works, and borrows or uses internal funds to nance capital. One period loan contract. Not collateral, but lender checks return at a cost. Entrepreneur buys capital in period t, for use in period t + 1, denoted K t+1. The price in period t is Q t. Can nance with net worth going into period t + 1, N t+1, or borrowing: B j t+1 = Q tk j t+1 N j t+1 Return to capital for entrepreneur j is ω j Rt+1 k.investment decision made before ω known. E (ω j ) = 1,i.i.d across time and across rms, c.d.f is F (ω). For lender, ω is observable only at a cost µω j R k t+1 Q tk t+1. E (Rt+1 k ) gross return to capital is determined in equilbrium. In partial equilibrium: assume constant. (Norges Bank) ECON4325 03/10 20 / 41

CSV (cont.) Notation of Bernanke, Gertler, Gilchrist: Loan rate Z j t+1 paid by entrepreneur j to lender in period t + 1. To borrower: π(ω j Rt+1, k Z j t+1 ) = max[ωj Rt+1Q k t K j t+1 Z j t+1 Bj t+1 ; 0] To lender ρ(ω j Rt+1, k Z j t+1 ) = min[(1 µ)(ω j Rt+1Q k t K j t+1 ; Z j t+1 Bj t+1 ] (Norges Bank) ECON4325 03/10 21 / 41

Contract gives lender zero pro t in equilibrium De ne the critical ω j = ω j and Z j t+1 covers gross borrowing costs: where aggregate return exactly ω j : ω j R k t+1q t K j t+1 = Z j t+1 Bj t+1 =>F ( ω j ) is probability of default. For which ω j and Z j t+1 return equal to the risk-fre return on capital? Condition: is lenders [1 F (ω j )]Z j t+1 Bj t+1 + (1 µ) Z ω j 0 ωr k t+1q t K j t+1 df (ω) = R t+1b j t+1 (3.4) (Norges Bank) ECON4325 03/10 22 / 41

Substitute in expression for Z j t+1 Bj t+1 and for and forb j t+1 = Q tk j t+1 N j t+1, into previous equation and get condition only in terms of ω j. Zero pro t condition is now: ( ) [1 F (ω j )]ω j + (1 µ) Z ω j 0 ωdf (ω) R t+1 (Q t K j t+1 N j t+1 ) R k t+1q t K j t+1 = (3.5) Note that as ω j increases to an upper limit, as default probability F (ω j ) goes to one, and lender must pay default cost with certainty. Assume R t+1 low enough to make LHS increasing in ω j in equilibrium (Norges Bank) ECON4325 03/10 23 / 41

Optimal contract (cont.) Expected payo from loan contract concave and increasing in ω j for values below maximum ω j ; d(lhs) dω j = [1 F (ω j )] µ ω j df ( ω j ) R k t+1q t K j t+1 > 0 Two e ects of ω j ": non-default payo " but also probability of default " In equilibrium, ω j depends on demand for capital, assume no credit rationing/ceiling on ω j in equilibrium. Optimal ω j also depends on R k t+1 : Each realized Rk t+1, goes with one ωj. Borrower risk-neutral. (Norges Bank) ECON4325 03/10 24 / 41

Behavior of borrower Borrower is willing to agree to contract with ω j depending on realization of Rt+1 k (risk neutral). Cares about: Z E ωrt+1q k t K j ω j t+1 df (ω) (1 F (ωj ))ω j Rt+1Q k t K j t+1 (3.6) From 3.5 (zero pro t condition) we know, for each R k t+1, [1 F (ω j )]ω j R k t+1q t K j t+1 = Z ω j R t+1 (Q t K j t+1 N j t+1 ) (1 µ) ωdf (ω)rt+1q k t K j t+1 Plug this into (3.6), multiply by E (Rt+1 k ) and divide by Ut+1 rk R t+1 k E (Rt+1 k ) => The equilibrium relationship between R k and capital (K t+1 ) purchased is found as (Norges Bank) ECON4325 03/10 25 / 41 0

Demand for capital max 8 < E : [1 µ ω j Z 0 ωdf (ω)]u rk t+1 9 = ; E (Rκ t+1)q t K j t+1 R t+1 (Q t K j t+1 N j t+1 ) with respect to K t, and ω j (given Rt+1 k ), subject to a set of constraints for each Rt+1 k ( ) [1 F (ω j )]ω j + (1 µ) Z ω j 0 ωdf (ω) R t+1 (Q t K j t+1 N j t+1 ) R k t+1q t K j t+1 = (3.5) Exogenous: Price of capital, net worth brought in, aggregate risk-free return R t+1, and distribution of risk. (Norges Bank) ECON4325 03/10 26 / 41

Partial equilibrium in capital market De ne the return to capital: Entrepreneur investing only if s t 1 s t E fr k t+1/r t+1 g Solving max-problem gives rst order optimality condition: Q t K j t+1 = ψ(s t)n j t+1 (3.8) In equilibrium, capital stock depends positively on net worth. ψ(1) = 1 means that with E fr k t+1 /R t+1g = 1, entrepreneurs will not borrow to invest. (Norges Bank) ECON4325 03/10 27 / 41

Partial equilibrium in capital market (cont) ψ 0 () > 0 means that increased return to capital reduces default probability and allows the rm to take on more debt. But size of rm cannot grow without limits: default costs rise as leverage rate increases. In model last time: ψ(s t ) = 1, could only nance using full collateral or internal funds. Here: aggregate over rms to get total demand for capital. Linear relationship (CRS)=>adding net worth gives total demand for capital. (Norges Bank) ECON4325 03/10 28 / 41

Invert (3.8) to get expected excess return - the external nance premium, or supply of funds - as function of net worth: E (Rt+1 k ) = s( Nj t+1 R t+1 Q t K j ), s 0 () < 0 t+1 Expresses inverse relationship between external nance premium and amount of investment nanced by own funds: (Norges Bank) ECON4325 03/10 29 / 41

General equilibrium - the entrepreneurial sector Shifts in net worth N j t+1 shifts capital demand. Countercyclical: Low net worth in recession=>high external nance premium and low capital demand in recession. Same logic for consumers. Entrepreneurs purchase capital each period for use next period. Idea: Use capital adjustment cost to get variable price of capital and hence variable N t+1. Entrepreneurs hire workers, combine with K t, CRS means aggregation easy, Y t = A t Kt α L 1 α t (Norges Bank) ECON4325 03/10 30 / 41

Adjustment costs in capital stock : => K t+1 = Φ( I t K t )K t + (1 Q t = [Φ 0 ( I t K t )] 1 δ)k t Entrepreneurs sell output to retailers. X t markup of retail goods over wholesale goods produced by entrepreneurs. Rent paid to unit of capital in t + 1 1 X t+1 αy t+1 K t+1 Gross return to capital (including price change) E fr k t+1g = f 1 X t+1 αy t+1 K t+1 + Q t+1 (1 δ) g Q t (Norges Bank) ECON4325 03/10 31 / 41

Aggregate capital market equations/demand side: Three main equations new in this paper: E (Rt+1 k ) = s( Nj t+1 R t+1 Q t K j ), s 0 () < 0 (4.5) t+1 E fr k t+1g = f 1 X t+1 αy t+1 K t+1 + Q t+1 (1 δ) Q t g (4.4) Q t = [Φ 0 ( I t K t )] 1 (4.3) Log-linearize these to get (4.17)-(4.19) in paper, supply of external funds, marginal product of capital and link between asset prices and investment. (Norges Bank) ECON4325 03/10 32 / 41

Supply side Labour input: L t = H Ω t (H e t ) 1 Ω V t =entrepreneural equity, Wt e = entrepreneural wage, ω t is state contingent value of ω set in period 1. Aggregate net worth at end of period 1: N t+1 = γv t + Wt e Only share γ of entrepreneurs from t 1 still active in period t. (and Ct e = (1 γ)v t ) " V t = Rt k Q t 1 K t R t + µ R # ω t ωr 0 t k Q t 1 K t df (ω) (Q t 1 K t N t 1 ) Q t 1 K t N t 1 External nance premium re ected in µ R ωt 0 ωr k t Q t 1 K t df (ω) Q t 1 K t N t 1, which is ratio of default costs to quantity borrowed. (Norges Bank) ECON4325 03/10 33 / 41

The dynamics of net worth Demand for labour: From rst order conditions in entrepreneurs pro t-max problem (perfect competition, zero pro ts) (1 α)ω Y t H t = X t W t (4.11) (1 α)(1 Ω) Y t H e t = X t W e t (4.12) (Norges Bank) ECON4325 03/10 34 / 41

Combine Y t = A t K α t L 1 t α, N t+1 = γv t + W e t, and (1 α)(1 Ω) Y t H e t = X t W e t with " V t = Rt k Q t 1 K t R t + µ R # ω t ωr 0 t k Q t 1 K t df (ω) (Q t 1 K t N t 1 ) Q t 1 K t N t 1 to get N t+1 = γ[rt k Q t 1 K t R t + µ R! ω t ωr 0 t k Q t 1 K t df (ω) (Q t 1 K t N t Q t 1 K t N t 1 +(1 α)(1 Ω)A t Kt α (1 α)ω H t (Norges Bank) ECON4325 03/10 35 / 41

Have now determined variation in net worth N t, and we know how net worth in uences cost of capital from E (Rt+1 k ) = s( Nj t+1 R t+1 Q t K j ) t+1 Now, need to determine variables kept exogenous so far: Relative price of wholesale goods 1 X t, R t, and household real wage W t. Need household, retail and government sector. (Norges Bank) ECON4325 03/10 36 / 41

General equilibrium, complete model: Households maximize utility over consumption, leisure and money Retailers monopolistic competition, calvo price setting Households and entrepreneurs buy nal goods from retailers, for consumption and investment. Households own retailers and get their pro ts. Two state variables: net worth and capital Monetary policy rule: r t = ρr n t 1 + ςπ t 1 + ε rn t (Norges Bank) ECON4325 03/10 37 / 41

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