Monetary Economics Financial Markets and the Business Cycle: The Bernanke and Gertler Model Nicola Viegi September 2010 Monetary Economics () Lecture 7 September 2010 1 / 35
Introduction Conventional Model with Perfect Capital Markets: Arbitrage between return to capital and riskless rate makes the nancial structure irrelevant E t βλ t,t+1 R kt+1 = E t βλ t,t+1 R t+1 Where Λ t,t+1 is the household stichastic discount factor With capital market frictions: 1 External nance premium =) E t βλ t,t+1 R kt+1 > E t βλ t,t+1 R t+1 2 Premium depends inversely on borrower balance sheets 3 If borrower balance sheets move procyclically, external nance premium move countercyclically: =)feedback betweeen nancial and real sectors (" nancial accelerator,") =)disturbances originating in the nancial sector can have real e ects. Monetary Economics () Lecture 7 September 2010 2 / 35
Bernanke Gertler (1989) Agency Cost Model Real Business Cycle with Financial frictions 1 Focus on Borrower Net Worth 2 Asymmetric Information Between Borrower and Lender introduces "deadweight losses" (agency cost) 3 Agency cost referers to the cost necessary to overcome asymmetric information contraint 4 Greater the net worth (inside nance) lower the external nance premium 5 Finance accelarator due to procyclicality of net worth Monetary Economics () Lecture 7 September 2010 3 / 35
Bernanke Gertler (1989) Agency Cost Model Real Business Cycle with Financial frictions 1 Focus on Borrower Net Worth 2 Asymmetric Information Between Borrower and Lender introduces "deadweight losses" (agency cost) 3 Greater the net worth (inside nance) lower the external nance premium 4 Finance accelarator due to procyclicality of net worth Monetary Economics () Lecture 7 September 2010 4 / 35
Bernanke Gertler Gilchrist Accelarator Model Dynamic General Equilibirum Framework with: 1 Money 2 Imperfect Competition 3 Nominal Price Rigidities (Calvo staggered price setting.) 4 Financial Accelerator as in Bernanke/Gertler(1989), featuring asset price mechanism as in Kiyotaki and Moore (1997) Monetary Economics () Lecture 7 September 2010 5 / 35
Sectors 1 Households 2 Business Sector 1 entrepreneur/ rms 2 capital producers 3 retailers (Monopolistic competition and sticky prices) 3 Central Bank Monetary Economics () Lecture 7 September 2010 6 / 35
Household Objective max E t Subject to β log i Mt+i (C t+i ) + a m log i=0 +i 1 a n L 1+γ n t+i 1 + γ n C t + B t + M t Assume Cashless Limit (a m! 0) = W t L t + Π T t + M t 1 + (1 + i t ) B t 1 Monetary Economics () Lecture 7 September 2010 7 / 35
Decision Rules (Standard) Labour Supply Consumption and Savings W t 1 = a n L γ n 1 t / 1 + γ n C t 1 C t = E t (1 + i t ) β 1 +1 C t+1 Monetary Economics () Lecture 7 September 2010 8 / 35
Entrepreneurs/Firms Produce wholesale output (with price P w ) Competitive, risk neutral, face capital market frictions. i.i.d survival probability θ : The expected horizon is accordingly 1 1 θ. 1 θ enter to replace exiting entrpreneurs (overlapping generation of rms). Monetary Economics () Lecture 7 September 2010 9 / 35
Production Technology and Labour Demand Production Technology Labour Demand Y t = A t K α t L 1 W t Yt = (1 α) P wt L t t α Monetary Economics () Lecture 7 September 2010 10 / 35
Capital Producers Capital Producers are competitive. They produce new capital and sell at the price Q t Evolution of Capital (with adjustment cost) It K t+1 = Φ K t + (1 K t δ) K t Φ 0 > 0, Φ 00 < 0, Φ I K = I K Optimal Choice of Investment E t 1 ( Q t ) 1 Φ 0 It K t Q is increasing in Investment - as in Tobin Q theory Monetary Economics () Lecture 7 September 2010 11 / 35
Capital Demand (1) Gross Return to Capital ( Pwt P E t fr kt+1 g = E t α Y ) t+1 K t+1 + (1 δ) Q t+1 t Q t Where Q t is the price of capital and δ the depreciation rate Opportunity Cost E t (1 + i) P t+1 Monetary Economics () Lecture 7 September 2010 12 / 35
Capital Demand (2) Under perfect capital markets, capital demand given by: E t fr kt+1 g = E t (1 + i) P t+1 With imperfect capital markets: E t fr kt+1 g > E t (1 + i) +1 Monetary Economics () Lecture 7 September 2010 13 / 35
Capital Demand (3) The nance of capital is divided between net worth and debt Q t K t+1 = N t + B t Monetary Economics () Lecture 7 September 2010 14 / 35
Costly State Veri cation costly state veri cation and limited liability one period contracts payouts based only on rm-speci c contingencies =): 1 Debt with costly default is optimal (risk of default on lender) 2 Agency costs of external nance (expected default costs) 3 Collateral reduces expected default costs Monetary Economics () Lecture 7 September 2010 15 / 35
Optimal Choice of Capital (1) 0 Q t K t+1 = v @ E t fr kt+1 g E t n(1 + i) +1 1 o A N t Monetary Economics () Lecture 7 September 2010 16 / 35
Optimal Choice of Capital (2) Aggregate Demand of Capital Where and E t fr kt+1 g = (1 χ t ) E t (1 + i) P t+1 Qt K t+1 χ t = χ N t χ 0 () > 0, χ (0) = 0, χ ( ) = Monetary Economics () Lecture 7 September 2010 17 / 35
Evolution of Net Worth N t = θv t + (1 θ) D Where with V t = (1 m t ) R kt Q t 1 K t (1 + i t 1 ) P t 1 ( Pwt P R kt = E t α Y ) t K t + (1 δ) Q t t Q t 1 Bt 1 m t = µg (ω t 1) Monetary Economics () Lecture 7 September 2010 18 / 35
Evolution of Net Worth Main Sources of Net Worth Fluctutions Unexpected movements in Q t and Irving Fisher s debt-de ation hypothesis: unanticipated declines in price level raise real debt burdens. Monetary Economics () Lecture 7 September 2010 19 / 35
The Role of Leverage Given we have Q t 1 K t = N t 1 + B t 1 1 V t = [(1 m t ) R kt R t ] φ t 1 + R t N t 1 where φ t 1 = Q t 1K t N t R t = (1 + i t 1 ) 1 The sensitivity of net worth to unanticipated returns is increasing in the leverage ratio φ t 1 Monetary Economics () Lecture 7 September 2010 20 / 35
Retailers Buy wholesale output and sell as di erentiated product Set prices on a staggered basis as in Calvo (1983) 1 µ Pw t λ E t Pt+1 β π t = λ(p wt p t ) + βe t π t+1 Note:p t p wt is the log price markup. Monetary Economics () Lecture 7 September 2010 21 / 35
Resource Constraint Let C e t be the entrepreneurial consumption and M t be the total monitoring costs with Y t = C t + C e t + I t + G t + M t C e t = (1 φ) (V t D) M t = m t R t Q t 1 K t Monetary Economics () Lecture 7 September 2010 22 / 35
Monetary and Fiscal Policy Monetary Rule i t = ρi t 1 + (1 ρ n )(γ π π t + γ y y t ) + ɛ rn t i t = r t+1 E π t+1 i t = ρi t 1 + (1 ρ n )(γ π π t + γ y y t + γ q q t ) Fiscal Policy Gov t spending exoxgenous and nance by lum sum taxes. Monetary Economics () Lecture 7 September 2010 23 / 35
Investment, Finance and Monetary Policy in BGG where E t R kt+1 = 1 + χ I t = φ (Q t ) K t Qt K t+1 N t (1 + i) P t +1 ( Pwt P E t R kt+1 = E t α Y ) t+1 K t+1 + (1 δ) Q t+1 t Q t Monetary Economics () Lecture 7 September 2010 24 / 35
Investment, Finance and Monetary Policy in BGG Notice N t = θ (1 m t ) R kt Q t 1 K t (1 + i t 1 ) P t 1 Thus: Bt 1 + (1 θ) D Positive feedback between asset prices and investment ( nancial accelerator) Strength depends positively on leverage ratio ratio Q t K t+1 N t Monetary Policy has additional impact via balance sheets Monetary Economics () Lecture 7 September 2010 25 / 35
Log Linear Model Aggregate Demand y t = C Y c t + G Y g t + I Y i t + C e Y ce t (1) c t = σr t+1 + E t c t+1 (2) c e t = n t+1 (3) r k t+1 r t+1 = v[n t+1 (q t + k t+1 )] (4) r k t+1 = (1 ɛ)(y t+1 x t+1 k t+1 ) + υq t+1 q t (5) q t+1 = φ(in t k t ) (6) Monetary Economics () Lecture 7 September 2010 26 / 35
Log Linear Model Aggregate Supply y t = a t + αk t 1 + (1 α)h t (7) h t = η h 1 + η h (y t x t c t ) (8) π t = λx t + βe t π t+1 (9) Monetary Economics () Lecture 7 September 2010 27 / 35
Log Linear Model Evolution of State Variables k t = δi t + (1 δ)k t 1 (10) n t = γrk N (r k t r t ) + r t + n t 1 (11) Monetary Economics () Lecture 7 September 2010 28 / 35
Log Linear Model Monetary Policy and shock Processes r t = r n t π t (12) r n t = ρr n t 1 + (1 ρ n )(ν b π t 1 ) + e n t, e n t ~N(0, σ 2 n) (13) a t = ρ a a t 1 + e a t, e a t ~N(0, σ 2 a) (14) g t = ρ g g t 1 + e g t, e g t ~N(0, σ 2 g ) (15) Monetary Economics () Lecture 7 September 2010 29 / 35
Calibrating Financial Sector Parameters Choose (i) survival probability θ, (ii) monitoring costs µ, and (iii) the moments of the idiosyncratic shock to match evidence on: 1 Steady state external nance premium:r k /R.. 2 Steady state leverage ration QK /N 3 Annual business failure rate Monetary Economics () Lecture 7 September 2010 30 / 35
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Conclusion Dynamic General Equlibrium Model with nancial frictions Can we use this model to evaluate if monetary policy should target asset prices? Is this model useful in understanding the causes (not the propagation) of crisis? Next time - Monetary Policy and Asset Prices Monetary Economics () Lecture 7 September 2010 35 / 35