Interbank Market Turmoils and the Macroeconomy 1

Transcription

1 Interbank Market Turmoils and the Macroeconomy 1 Paweł Kopiec Narodowy Bank Polski 1 The views presented in this paper are those of the author, and should not be attributed to Narodowy Bank Polski.

2 Intro 1: LIBOR / T-bill spread

3 This paper: contributions Macroeconomic perspective on interbank market disruptions A tractable DSGE model where conventional (unconventional) monetary policy is implemented through banking sector (where NK is a special case) The macro consequences of non-conventional policy tools: interbank market guarantees

4 This paper: contributions Macroeconomic perspective on interbank market disruptions A tractable DSGE model where conventional (unconventional) monetary policy is implemented through banking sector (where NK is a special case) The macro consequences of non-conventional policy tools: interbank market guarantees

5 This paper: contributions Macroeconomic perspective on interbank market disruptions A tractable DSGE model where conventional (unconventional) monetary policy is implemented through banking sector (where NK is a special case) The macro consequences of non-conventional policy tools: interbank market guarantees

6 Literature Interbank market crises: Flannery (1996), Freixas and Jorge (28), Freixas et al. (211), Acharya and Skeie (211), Heider et al. (215), Afonso et al. (211) Macro models with interbank market: Gertler and Kiyotaki (21), Bianchi and Bigio (214) Models using the big family trick : Lucas (199), Shi (215), Cui and Radde (216), Negro et al. (217)

7 Roadmap 1 Model without counterparty risk 2 Relationship to the NK framework 3 Model with counterparty risk 4 Interbank market guarrantees

8 The model Building blocks: Real sector: New Keynesian framework, households - depositors, firms - loan takers Banking sector: a modified version of the model by Bianchi and Bigio (214) (R&R ECMA) - reserves traded in a frictional interbank market as in Afonso and Lagos (215)

9 The model Building blocks: Real sector: New Keynesian framework, households - depositors, firms - loan takers Banking sector: a modified version of the model by Bianchi and Bigio (214) (R&R ECMA) - reserves traded in a frictional interbank market as in Afonso and Lagos (215)

10 The model Building blocks: Real sector: New Keynesian framework, households - depositors, firms - loan takers Banking sector: a modified version of the model by Bianchi and Bigio (214) (R&R ECMA) - reserves traded in a frictional interbank market as in Afonso and Lagos (215)

11 Banking sector: no counterparty risk t - 1 t Timeline: Balance sheet decisions are made Banks are divided into separate units Units receive withdrawal shocks Trade in the interbank market takes place Units collect revenues and repay debt Consumption takes place Units are merged into one bank

12 Banks: no counterparty risk V (e t 1,A t 1 ) = max {{c t (δ )},l t 1,m t 1,d t 1,e t } { + 1 } u (c t (δ))dµ (δ) + β B EV (e t,a t ) l t 1 + m t 1 = e t 1 + d t 1 δ : c t (δ) + e t + Φ E (e t,ē t ) 1+i L,t 1 l t i ER,t 1 m t 1 1+i D,t 1 d t 1 ( ) + I {δ<δ t 1 } χ t + I {δ δt 1} χ+ t M ( m t 1,d t 1 i D,t 1,i L,t 1,δ )

13 Banks: no counterparty risk V (e t 1,A t 1 ) = max {{c t (δ )},l t 1,m t 1,d t 1,e t } { + 1 } u (c t (δ))dµ (δ) + β B EV (e t,a t ) l t 1 + m t 1 = e t 1 + d t 1 δ : c t (δ) + e t + Φ E (e t,ē t ) 1+i L,t 1 l t i ER,t 1 m t 1 1+i D,t 1 d t 1 ( ) + I {δ<δ t 1 } χ t + I {δ δt 1} χ+ t M ( m t 1,d t 1 i D,t 1,i L,t 1,δ )

14 Interbank market: no counterparty risk Surplus (deficit) of reserves: M ( m t 1,d t 1 i D,t 1,i L,t 1,δ ) m t i D,t i ER,t 1 δ d t 1 ψ (1 + δ) d t 1 Critical value δ satisfies: m t i D,t i ER,t 1 δ d t 1 ψ (1 + δ ) d t 1 = Aggregate deficit and surplus of reserves: δ ( t D t m t i ) D,t δ d t ψ (1 + δ) d t dµ (δ) i ER,t + ( S t m t i ) D,t δ d t ψ (1 + δ) d t dµ (δ) 1 + i ER,t Interbank market tightness: δ t θ FF,t = D t S t

15 Interbank market: no counterparty risk Surplus (deficit) of reserves: M ( m t 1,d t 1 i D,t 1,i L,t 1,δ ) m t i D,t i ER,t 1 δ d t 1 ψ (1 + δ) d t 1 Critical value δ satisfies: m t i D,t i ER,t 1 δ d t 1 ψ (1 + δ ) d t 1 = Aggregate deficit and surplus of reserves: δ ( t D t m t i ) D,t δ d t ψ (1 + δ) d t dµ (δ) i ER,t + ( S t m t i ) D,t δ d t ψ (1 + δ) d t dµ (δ) 1 + i ER,t Interbank market tightness: δ t θ FF,t = D t S t

16 Interbank market: no counterparty risk Surplus (deficit) of reserves: M ( m t 1,d t 1 i D,t 1,i L,t 1,δ ) m t i D,t i ER,t 1 δ d t 1 ψ (1 + δ) d t 1 Critical value δ satisfies: m t i D,t i ER,t 1 δ d t 1 ψ (1 + δ ) d t 1 = Aggregate deficit and surplus of reserves: δ ( t D t m t i ) D,t δ d t ψ (1 + δ) d t dµ (δ) i ER,t + ( S t m t i ) D,t δ d t ψ (1 + δ) d t dµ (δ) 1 + i ER,t Interbank market tightness: δ t θ FF,t = D t S t

17 Interbank market: no counterparty risk Surplus (deficit) of reserves: M ( m t 1,d t 1 i D,t 1,i L,t 1,δ ) m t i D,t i ER,t 1 δ d t 1 ψ (1 + δ) d t 1 Critical value δ satisfies: m t i D,t i ER,t 1 δ d t 1 ψ (1 + δ ) d t 1 = Aggregate deficit and surplus of reserves: δ ( t D t m t i ) D,t δ d t ψ (1 + δ) d t dµ (δ) i ER,t + ( S t m t i ) D,t δ d t ψ (1 + δ) d t dµ (δ) 1 + i ER,t Interbank market tightness: δ t θ FF,t = D t S t

18 Interbank market: no counterparty risk Fed funds rate (results from the Nash bargaining problem): i FF,t = i ER,t + i DW,t 2 Effective rates on loans in the market: χ t = ψ t 1 iff,t 1 i ER,t 1 + ( 1 ψt 1 ) i DW,t 1 i ER,t 1 χ + t = ψ + t 1 iff,t 1 i ER,t 1 Spread between rates i L and i D depends on interbank market conditions: P ( δ < δ ) ( ] ) t 1 Eδ u (c t (δ)) [ δt 1 + ψ (1 δ) δ < δt 1 χt i L,t 1 i D,t 1 = E δ (u (c t (δ))) P ( δ δ ) ( [ ] ) t 1 Eδ u (c t (δ)) δ t 1 + ψ (1 + δ) δ δt 1 χ t + + E δ (u (c t (δ)))

19 Interbank market: no counterparty risk Fed funds rate (results from the Nash bargaining problem): i FF,t = i ER,t + i DW,t 2 Effective rates on loans in the market: χ t = ψ t 1 iff,t 1 i ER,t 1 + ( 1 ψt 1 ) i DW,t 1 i ER,t 1 χ + t = ψ + t 1 iff,t 1 i ER,t 1 Spread between rates i L and i D depends on interbank market conditions: P ( δ < δ ) ( ] ) t 1 Eδ u (c t (δ)) [ δt 1 + ψ (1 δ) δ < δt 1 χt i L,t 1 i D,t 1 = E δ (u (c t (δ))) P ( δ δ ) ( [ ] ) t 1 Eδ u (c t (δ)) δ t 1 + ψ (1 + δ) δ δt 1 χ t + + E δ (u (c t (δ)))

20 Interbank market: no counterparty risk Fed funds rate (results from the Nash bargaining problem): i FF,t = i ER,t + i DW,t 2 Effective rates on loans in the market: χ t = ψ t 1 iff,t 1 i ER,t 1 + ( 1 ψt 1 ) i DW,t 1 i ER,t 1 χ + t = ψ + t 1 iff,t 1 i ER,t 1 Spread between rates i L and i D depends on interbank market conditions: P ( δ < δ ) ( ] ) t 1 Eδ u (c t (δ)) [ δt 1 + ψ (1 δ) δ < δt 1 χt i L,t 1 i D,t 1 = E δ (u (c t (δ))) P ( δ δ ) ( [ ] ) t 1 Eδ u (c t (δ)) δ t 1 + ψ (1 + δ) δ δt 1 χ t + + E δ (u (c t (δ)))

21 Households: no counterparty risk Bellman equation for household j [,1]: ) { )} W ( d j,t 1,A t = max u (c j,t ) v (n j,t ) + β H EW ( d j,t,a t+1 c j,t, d j,t subject to : ( c j,t + d j,t + τ t + φ w wj,t 2 2 w j,t 1 1) nt 1+i D,t 1 d j,t 1 + w j,t p t n j,t + π t ( ) γw wj,t n j,t = w t nt

22 Firms: no counterparty risk Bellman equation for firm i [,1]: { pi,t ( ) F i p i,t 1, l i,t 1,S t,a t = max y i,t 1 + i L,t 1 p i,t,l i,t,n i,t,y i,t p t ( ) pi,t p 2 ) i,t 1 y t + EΛ t F i (p } i,t, l i,t,s t+1,a t+1 l i,t 1 φ 2 p i,t 1 subject to : l i,t = w t n i,t y i,t = n ( i,t ) pi,t γ y i,t = p t yt

23 Government: no counterparty risk Government chooses: rates i FF, i DW, i FF, supply of reserves m and tax τ Budget constraint of consolidated government: 1 + i ER,t 1 m t 1 = m t + τ t + Φ E (e t,ē t ) + ( 1 ψt 1 ) i DW,t 1 i ER,t 1 Monetary policy rule: δ t 1 1 M (δ)dµ (δ) log(1 + i FF,t ) = (1 ρ m ) log(1 + i ss FF ) + ρ m log(1 + i FF,t 1 ) +(1 ρ m ) [ν Π ( Π ss ) + ν y (logy t logy ss )] + ε m Money supply rule: m t = ψ d t

24 Government: no counterparty risk Government chooses: rates i FF, i DW, i FF, supply of reserves m and tax τ Budget constraint of consolidated government: 1 + i ER,t 1 m t 1 = m t + τ t + Φ E (e t,ē t ) + ( 1 ψt 1 ) i DW,t 1 i ER,t 1 Monetary policy rule: δ t 1 1 M (δ)dµ (δ) log(1 + i FF,t ) = (1 ρ m ) log(1 + i ss FF ) + ρ m log(1 + i FF,t 1 ) +(1 ρ m ) [ν Π ( Π ss ) + ν y (logy t logy ss )] + ε m Money supply rule: m t = ψ d t

25 Government: no counterparty risk Government chooses: rates i FF, i DW, i FF, supply of reserves m and tax τ Budget constraint of consolidated government: 1 + i ER,t 1 m t 1 = m t + τ t + Φ E (e t,ē t ) + ( 1 ψt 1 ) i DW,t 1 i ER,t 1 Monetary policy rule: δ t 1 1 M (δ)dµ (δ) log(1 + i FF,t ) = (1 ρ m ) log(1 + i ss FF ) + ρ m log(1 + i FF,t 1 ) +(1 ρ m ) [ν Π ( Π ss ) + ν y (logy t logy ss )] + ε m Money supply rule: m t = ψ d t

26 Government: no counterparty risk Government chooses: rates i FF, i DW, i FF, supply of reserves m and tax τ Budget constraint of consolidated government: 1 + i ER,t 1 m t 1 = m t + τ t + Φ E (e t,ē t ) + ( 1 ψt 1 ) i DW,t 1 i ER,t 1 Monetary policy rule: δ t 1 1 M (δ)dµ (δ) log(1 + i FF,t ) = (1 ρ m ) log(1 + i ss FF ) + ρ m log(1 + i FF,t 1 ) +(1 ρ m ) [ν Π ( Π ss ) + ν y (logy t logy ss )] + ε m Money supply rule: m t = ψ d t

27 Relationship to the standard NK model Proposition Equilibrium prices and quantities converge to those associated with the standard New Keynesian model with price/wage adjustment costs as in Rotemberg (1982) and the cost channel as in Ravenna and Walsh (26) if: 1) Bank units get risk neutral: ρ 2) Matching frictions in the interbank market decay: α FF + 3) Policy requirements concerning reserves and bank equity are eliminated: ψ, ξ

28 Model with counterparty risk Proportion 1 S t 1 of bank units with deficit reserves suffers from defaults on corporate loans l t 1 in period t Banks learn the value of shock S t 1 before entering the interbank market in period t 1 Banks know the value of S t 1 but they do not know which bank units will be affected by the shock 1 S t 1 bank units default on interbank loans and deposits in period t Liquidation procedure: government guarantees deposit repayment (FDIC) government confiscates equity and guarantees dividends c to affected units liquidated units are provided with a fresh start (no reputational concerns) Interbank loans are not secured so lending banks generate losses

29 Model with counterparty risk Proportion 1 S t 1 of bank units with deficit reserves suffers from defaults on corporate loans l t 1 in period t Banks learn the value of shock S t 1 before entering the interbank market in period t 1 Banks know the value of S t 1 but they do not know which bank units will be affected by the shock 1 S t 1 bank units default on interbank loans and deposits in period t Liquidation procedure: government guarantees deposit repayment (FDIC) government confiscates equity and guarantees dividends c to affected units liquidated units are provided with a fresh start (no reputational concerns) Interbank loans are not secured so lending banks generate losses

30 Model with counterparty risk Proportion 1 S t 1 of bank units with deficit reserves suffers from defaults on corporate loans l t 1 in period t Banks learn the value of shock S t 1 before entering the interbank market in period t 1 Banks know the value of S t 1 but they do not know which bank units will be affected by the shock 1 S t 1 bank units default on interbank loans and deposits in period t Liquidation procedure: government guarantees deposit repayment (FDIC) government confiscates equity and guarantees dividends c to affected units liquidated units are provided with a fresh start (no reputational concerns) Interbank loans are not secured so lending banks generate losses

31 Model with counterparty risk Proportion 1 S t 1 of bank units with deficit reserves suffers from defaults on corporate loans l t 1 in period t Banks learn the value of shock S t 1 before entering the interbank market in period t 1 Banks know the value of S t 1 but they do not know which bank units will be affected by the shock 1 S t 1 bank units default on interbank loans and deposits in period t Liquidation procedure: government guarantees deposit repayment (FDIC) government confiscates equity and guarantees dividends c to affected units liquidated units are provided with a fresh start (no reputational concerns) Interbank loans are not secured so lending banks generate losses

32 Model with counterparty risk Proportion 1 S t 1 of bank units with deficit reserves suffers from defaults on corporate loans l t 1 in period t Banks learn the value of shock S t 1 before entering the interbank market in period t 1 Banks know the value of S t 1 but they do not know which bank units will be affected by the shock 1 S t 1 bank units default on interbank loans and deposits in period t Liquidation procedure: government guarantees deposit repayment (FDIC) government confiscates equity and guarantees dividends c to affected units liquidated units are provided with a fresh start (no reputational concerns) Interbank loans are not secured so lending banks generate losses

33 Model with counterparty risk Proportion 1 S t 1 of bank units with deficit reserves suffers from defaults on corporate loans l t 1 in period t Banks learn the value of shock S t 1 before entering the interbank market in period t 1 Banks know the value of S t 1 but they do not know which bank units will be affected by the shock 1 S t 1 bank units default on interbank loans and deposits in period t Liquidation procedure: government guarantees deposit repayment (FDIC) government confiscates equity and guarantees dividends c to affected units liquidated units are provided with a fresh start (no reputational concerns) Interbank loans are not secured so lending banks generate losses

34 Model with counterparty risk Bellman equation becomes: { + V (e t 1,S t 1,A t 1 ) = max u (c t (δ))dµ (δ) + S t 1 P ( δ δ ) t 1 x t δt 1 P ( δ < δt 1 ) δ } t 1 u (c t (δ))dµ (δ) + (1 S t 1 ) u (c) + β B EV (e t,s t,a t ) 1 l t 1 + m t 1 = S t 1 e t 1 + d t 1 δ : c t (δ) + e t + Φ E (e t,ē t ) 1+i L,t 1 l t i ER,t 1 m t 1 1+i D,t 1 ( + I {δ<δ t 1 } χ t + I {δ δt 1} χ+ t d t 1 ) (S t 1) M ( m t 1,d t 1 i D,t 1,i L,t 1,δ )

35 Model with counterparty risk Bellman equation becomes: { + V (e t 1,S t 1,A t 1 ) = max u (c t (δ))dµ (δ) + S t 1 P ( δ δ ) t 1 x t δt 1 P ( δ < δt 1 ) δ } t 1 u (c t (δ))dµ (δ) + (1 S t 1 ) u (c) + β B EV (e t,s t,a t ) 1 l t 1 + m t 1 = S t 1 e t 1 + d t 1 δ : c t (δ) + e t + Φ E (e t,ē t ) 1+i L,t 1 l t i ER,t 1 m t 1 1+i D,t 1 ( + I {δ<δ t 1 } χ t + I {δ δt 1} χ+ t d t 1 ) (S t 1) M ( m t 1,d t 1 i D,t 1,i L,t 1,δ )

36 Model with counterparty risk Interbank market rate becomes: The counterparty risk component {}}{ 1 S t i ER,t + i DW,t + S i FF,t = t P(δ δt ) 2 Effective return on surplus reserves: χ t + (S t 1) = S t 1 P ( δ δt 1 ) P ( δ < δt 1 ) ψ t 1 + iff,t 1 i ER,t 1 }{{} Probability that counterparty is safe/solvent + 1 S ( ) t 1 P ( δ < δt 1 ) ψ t }{{} Probability that counterparty is risky/insolvent

37 Model with counterparty risk Interbank market rate becomes: The counterparty risk component {}}{ 1 S t i ER,t + i DW,t + S i FF,t = t P(δ δt ) 2 Effective return on surplus reserves: χ t + (S t 1) = S t 1 P ( δ δt 1 ) P ( δ < δt 1 ) ψ t 1 + iff,t 1 i ER,t 1 }{{} Probability that counterparty is safe/solvent + 1 S ( ) t 1 P ( δ < δt 1 ) ψ t }{{} Probability that counterparty is risky/insolvent

38 Calibration Parameter Description Value Target α Parameter of matching technology M 68.9 Probabilities ψ + and ψ equal to.99 i DW Discount window rate.147 Annual discount window rate in 26 i ER Interest on reserves Annual rate on excess reserves in 26 ξ Capital requirement ratio.4 Assets to equity ratio of 4% ψ Reserve requirement.1 Reserve requirement equal to 1% δ Std. error of withdrawal shock.5 Evidence by Bianchi and Bigio (214) m Supply of reserves.32 Value of tightness θ FF = 1

39 Simulation: a decrease in S

40 Simulation: a decrease in S

41 Interbank market guarantees P (, 1) denotes the proportion of non-performing interbank loans that are guaranteed by government I choose P =.5 Interbank market rate becomes: i FF,t (P) = i ER,t + i DW,t + (1 P) (1 S t ) S t +P (1 S t ) P(δ δ t ) 2

42 Interbank market guarantees P (, 1) denotes the proportion of non-performing interbank loans that are guaranteed by government I choose P =.5 Interbank market rate becomes: i FF,t (P) = i ER,t + i DW,t + (1 P) (1 S t ) S t +P (1 S t ) P(δ δ t ) 2

43 Interbank market guarantees P (, 1) denotes the proportion of non-performing interbank loans that are guaranteed by government I choose P =.5 Interbank market rate becomes: i FF,t (P) = i ER,t + i DW,t + (1 P) (1 S t ) S t +P (1 S t ) P(δ δ t ) 2

44 Simulation: interbank market guarantees

45 Simulation: interbank market guarantees

46 Simulation: interbank market guarantees

47 Simulation: interbank market guarantees

48 Conclusions Technical contributions: a dynamic model of banking industry with interbank market conventional (unconventional) monetary policy can be studied model nests the standard NK framework Simulation and policy experiment: interbank market crisis caused by higher counterparty risk the role of interbank market guarrantees Future research: other types of policy interventions diabolic loops between sovereign debt and banking sector

49 References I Acharya, V. V. and Skeie, D. (211). A model of liquidity hoarding and term premia in inter-bank markets. Journal of Monetary Economics, 58(5): Afonso, G., Kovner, A., and Schoar, A. (211). Stressed, Not Frozen: The Federal Funds Market in the Financial Crisis. Journal of Finance, 66(4): Afonso, G. and Lagos, R. (215). Trade Dynamics in the Market for Federal Funds. Econometrica, 83: Bianchi, J. and Bigio, S. (214). Banks, Liquidity Management and Monetary Policy. NBER Working Papers 249, National Bureau of Economic Research, Inc. Cui, W. and Radde, S. (216). Money and Asset Liquidity in Frictional Capital Markets. American Economic Review, 16(5): Flannery, M. J. (1996). Financial Crises, Payment System Problems, and Discount Window Lending. Journal of Money, Credit and Banking, 28(4):

50 References II Freixas, X. and Jorge, J. (28). The Role of Interbank Markets in Monetary Policy: A Model with Rationing. Journal of Money, Credit and Banking, 4(6): Freixas, X., Martin, A., and Skeie, D. (211). Bank Liquidity, Interbank Markets, and Monetary Policy. Review of Financial Studies, 24(8): Gertler, M. and Kiyotaki, N. (21). Financial Intermediation and Credit Policy in Business Cycle Analysis. In Friedman, B. M. and Woodford, M., editors, Handbook of Monetary Economics, volume 3 of Handbook of Monetary Economics, chapter 11, pages Elsevier. Heider, F., Hoerova, M., and Holthausen, C. (215). Liquidity hoarding and interbank market rates: The role of counterparty risk. Journal of Financial Economics, 118(2): Lucas, R. J. (199). Liquidity and interest rates. Journal of Economic Theory, 5(2):

51 References III Negro, M. D., Eggertsson, G., Ferrero, A., and Kiyotaki, N. (217). The Great Escape? A Quantitative Evaluation of the Fed s Liquidity Facilities. American Economic Review, 17(3): Ravenna, F. and Walsh, C. E. (26). Optimal monetary policy with the cost channel. Journal of Monetary Economics, 53(2): Rotemberg, J. J. (1982). Sticky Prices in the United States. Journal of Political Economy, 9(6): Shi, S. (215). Liquidity, assets and business cycles. Journal of Monetary Economics, 7(C):

52 The End Thanks for your attention!