A Dynamic Network Model of the Unsecured Interbank Lending Market 1

Transcription

1 A Dynamic Network Model of the Unsecured Interbank Lending Market 1 Francisco Blasques a Falk Bräuning b Iman van Lelyveld a,c a VU University Amsterdam b Federal Reserve Bank of Boston c De Nederlandsche Bank The Role of Liquidity in the Financial System Atlanta, November 19th, The views expressed in this presentation do not necessarily represent those of the Federal Reserve Bank of Boston, the Federal Reserve System, De Nederlandsche Bank, or the Eurosystem. 1 / 29

2 This Paper in a Nutshell Model of formation of interbank lending relationships, implications for credit availability and conditions (interest rates and volumes) 2 / 29

3 This Paper in a Nutshell Model of formation of interbank lending relationships, implications for credit availability and conditions (interest rates and volumes) Role of credit risk uncertainty and peer monitoring in OTC market 2 / 29

4 This Paper in a Nutshell Model of formation of interbank lending relationships, implications for credit availability and conditions (interest rates and volumes) Role of credit risk uncertainty and peer monitoring in OTC market Parameter estimation using Dutch interbank loan-level data / 29

5 This Paper in a Nutshell Model of formation of interbank lending relationships, implications for credit availability and conditions (interest rates and volumes) Role of credit risk uncertainty and peer monitoring in OTC market Parameter estimation using Dutch interbank loan-level data Model analysis: network structure, dynamic behavior and monetary policy 2 / 29

6 Table of Contents 1. Motivation 2. Model 3. Estimation 4. Results 3 / 29

7 Dutch Interbank Market during Crisis Before Lehman 08/2008 Figure : Nodes: banks; links: ON loans; big green node: central bank; small green nodes: banks only relying on central bank; pink nodes: banks without use of central bank facilities, see Video 3 Heijmans et al. (2014) 4 / 29

8 Dutch Interbank Market during Crisis Before Lehman 08/2008 After Lehman 12/2008 Figure : Nodes: banks; links: ON loans; big green node: central bank; small green nodes: banks only relying on central bank; pink nodes: banks without use of central bank facilities, see Video 3 Heijmans et al. (2014) 4 / 29

9 Dutch Interbank Market during Crisis Before Lehman 08/2008 After Lehman 12/2008 After 3-yr LTRO 12/2011 Figure : Nodes: banks; links: ON loans; big green node: central bank; small green nodes: banks only relying on central bank; pink nodes: banks without use of central bank facilities, see Video 3 Heijmans et al. (2014) 4 / 29

10 Relevance of Private Information Why should central banks not resume the role of central counterparty for money market transactions also in normal times (i.e. non-crisis times)? 5 / 29

11 Relevance of Private Information Why should central banks not resume the role of central counterparty for money market transactions also in normal times (i.e. non-crisis times)? Efficiency of liquidity allocations, Rochet & Tirole (1996) Specifically, in the unsecured money markets, where loans are uncollateralised, interbank lenders are directly exposed to losses if the interbank loan is not repaid. This gives lenders incentives to collect information about borrowers and to monitor them [...]. Therefore, unsecured money markets play a key peer monitoring role. from speech by Benoît Cœuré (ECB Executive Board), June / 29

12 Relevance of Private Information Why should central banks not resume the role of central counterparty for money market transactions also in normal times (i.e. non-crisis times)? Efficiency of liquidity allocations, Rochet & Tirole (1996) Specifically, in the unsecured money markets, where loans are uncollateralised, interbank lenders are directly exposed to losses if the interbank loan is not repaid. This gives lenders incentives to collect information about borrowers and to monitor them [...]. Therefore, unsecured money markets play a key peer monitoring role. from speech by Benoît Cœuré (ECB Executive Board), June 2012 Key issue: Role of credit risk uncertainty, peer monitoring and private information in the interbank market? In OTC market we need to consider uncertainty as bank-to-bank specific problem! 5 / 29

13 Preview of Main Results Network model of credit risk uncertainty and peer monitoring explains two stylized facts of decentralized interbank lending markets Sparse core-periphery structure of lending network Stable long-term trading relationships, relationship lending 6 / 29

14 Preview of Main Results Network model of credit risk uncertainty and peer monitoring explains two stylized facts of decentralized interbank lending markets Sparse core-periphery structure of lending network Stable long-term trading relationships, relationship lending Estimated model generates dynamic amplification mechanism of shocks due to interrelation between directed search and peer monitoring Shocks to credit risk uncertainty lead to extended period of market turmoil Trading more concentrated towards bank pairs with strong relations 6 / 29

15 Preview of Main Results Network model of credit risk uncertainty and peer monitoring explains two stylized facts of decentralized interbank lending markets Sparse core-periphery structure of lending network Stable long-term trading relationships, relationship lending Estimated model generates dynamic amplification mechanism of shocks due to interrelation between directed search and peer monitoring Shocks to credit risk uncertainty lead to extended period of market turmoil Trading more concentrated towards bank pairs with strong relations Monetary policy implication for size of interest rate corridor wider corridor increases interbank lending (direct effect on outside options) indirect multiplier effect through changes in monitoring and search 6 / 29

16 Table of Contents 1. Motivation 2. Model 3. Estimation 4. Results 7 / 29

17 A Model of Bilateral Link Formation Bank 1 Bank 3 Bank 4 Bank 5 Bank 2 Bank N Bank i Bank j 8 / 29

18 A Model of Bilateral Link Formation Bank 1 Bank 5 Bank 3 Bank 4 Bank 2 Bank N Liq shock ζ i,t (> 0) Bank i Bank j Liq shock ζ j,t (< 0) 8 / 29

19 A Model of Bilateral Link Formation Bank 1 Bank 5 Bank 3 Bank 4 Bank 2 Bank N Liq shock ζ i,t (> 0) Bank i Bank j Liq shock ζ j,t (< 0) Central Bank standing facilities r > r 8 / 29

20 A Model of Bilateral Link Formation Bank 1 Bank 5 Bank 3 Bank 4 Bank 2 Bank N Liq shock ζ i,t (> 0) Bank i loan y i,j,t, r i,j,t Bank j Liq shock ζ j,t (< 0) Central Bank standing facilities r > r 8 / 29

21 A Model of Bilateral Link Formation Bank 1 Bank 5 Bank 3 Bank 4 Bank 2 Bank N Search frictions Liq shock ζ i,t (> 0) Bank i loan CR uncertainty y i,j,t, r i,j,t Bank j Liq shock ζ j,t (< 0) Central Bank standing facilities r > r 8 / 29

22 A Model of Bilateral Link Formation Bank 1 Bank 5 Bank 3 Bank 4 Bank 2 monitoring m i,j,t Bank N Liq shock ζ i,t (> 0) Bank i loan y i,j,t, r i,j,t Bank j Liq shock ζ j,t (< 0) Central Bank standing facilities r > r 8 / 29

23 A Model of Bilateral Link Formation Bank 1 Bank 5 Bank 3 Bank 4 Bank 2 monitoring m i,j,t Bank N Liq shock ζ i,t (> 0) Bank i loan y i,j,t, r i,j,t Bank j Liq shock ζ j,t (< 0) search s i,j,t Central Bank standing facilities r > r 8 / 29

24 A Model of Bilateral Link Formation Bank 1 Bank 5 Bank 3 Bank 4 Bank 2 monitoring m i,j,t Bank N Liq shock ζ i,t (> 0) Bank i loan y i,j,t, r i,j,t Bank j Liq shock ζ j,t (< 0) search s i,j,t Central Bank standing facilities r > r 8 / 29

25 Model Perspective Model focuses on formation of bilateral lending relationships under credit risk uncertainty and search frictions peer monitoring and directed search Model does not take into account for: endogenous true riskiness (unrelated to uncertainty, liquidity shocks, monitoring) other assets/liabilities (treasury perspective) serial correlation in liquidity shocks, common factors other monetary policy instruments than standing facilities (MROs, LTROs) liquidity hoarding for precautionary reasons bank heterogeneity other than in liquidity shocks (default risk, bargaining power) 9 / 29

26 Liquidity Shocks Banks are hit by exogenous liquidity shocks ζ i,t ζ i,t iid N (µζi, σ 2 ζ i ) where µ ζi N (µ µ, σ 2 µ) and log σ ζi N (µ σ, σ 2 σ) and correlation parameter ρ ζ := corr(µ ζi, log σ ζi ) Heterogeneity related to scale of bank s business (σ ζi ) and structural liquidity deficit or surplus (µ ζi ) 10 / 29

27 Credit Risk Uncertainty and Peer Monitoring Perceived financial distress: z i,j,t = z j,t + e i,j,t z j,t (0, σ 2 ) is true financial distress of j, true PD: P(z j,t > ɛ) e i,j,t (0, σ 2 i,j,t ) is independent perception error 11 / 29

28 Credit Risk Uncertainty and Peer Monitoring Perceived financial distress: z i,j,t = z j,t + e i,j,t z j,t (0, σ 2 ) is true financial distress of j, true PD: P(z j,t > ɛ) e i,j,t (0, σ 2 i,j,t ) is independent perception error Perceived probability of default P(z i,j,t > ɛ) σ2 + σ 2 i,j,t σ 2 + σ 2 i,j,t + ɛ2 =: P i,j,t 11 / 29

29 Credit Risk Uncertainty and Peer Monitoring Perceived financial distress: z i,j,t = z j,t + e i,j,t z j,t (0, σ 2 ) is true financial distress of j, true PD: P(z j,t > ɛ) e i,j,t (0, σ 2 i,j,t ) is independent perception error Perceived probability of default P(z i,j,t > ɛ) σ2 + σ 2 i,j,t σ 2 + σ 2 i,j,t + ɛ2 =: P i,j,t Evolution of σ i,j,t 2 (credit risk uncertainty) log σ 2 i,j,t+1 = ασ + γσ log σ2 i,j,t βσm i,j,t + u i,j,t, u i,j,t N (0, σ 2 u ) where m i,j,t is bank-to-bank monitoring expenditure 11 / 29

30 Link Formation, Interest Rates and Loan Volumes B i,j,t Bernoulli(λ i,j,t ) indicates link between bank i and j at time t with λ i,j,t = exp( β λ (s j,i,t α λ )) where s j,i,t is bank-to-bank search expenditure 12 / 29

31 Link Formation, Interest Rates and Loan Volumes B i,j,t Bernoulli(λ i,j,t ) indicates link between bank i and j at time t with λ i,j,t = exp( β λ (s j,i,t α λ )) where s j,i,t is bank-to-bank search expenditure If B i,j,t = 1, bilateral Nash bargaining about rates P i,j,t r i,j,t = θr + (1 θ) 1 P i,j,t where θ is bargaining power of lender, with r = r > r = 0 details 12 / 29

32 Link Formation, Interest Rates and Loan Volumes B i,j,t Bernoulli(λ i,j,t ) indicates link between bank i and j at time t with λ i,j,t = exp( β λ (s j,i,t α λ )) where s j,i,t is bank-to-bank search expenditure If B i,j,t = 1, bilateral Nash bargaining about rates P i,j,t r i,j,t = θr + (1 θ) 1 P i,j,t where θ is bargaining power of lender, with r = r > r = 0 details If r i,j,t [0, r], loan granted (l i,j,t = 1) with exogenous volume y i,j,t = min{ζ i,t, ζ j,t }I(ζ i,t 0)I(ζ j,t 0), where ζ i,t and ζ j,t are liquidity shocks specific to each transaction 12 / 29

33 Dynamic Optimization Problem Dynamic optimization problem of each bank i: ( 1 ) s t N max E t (l {m i,j,t,s i,j,t } 1 + r d i,j,t R i,j,ty i,j,t + l j,i,t(r r j,i,t)y j,i,t m i,j,t s i,j,t) s=t j=1 s.t. constraints; where R i,j,t = (1 P i,j,t)r i,j,t P i,j,t, no default occurs! 13 / 29

34 Dynamic Optimization Problem Dynamic optimization problem of each bank i: ( 1 ) s t N max E t (l {m i,j,t,s i,j,t } 1 + r d i,j,t R i,j,ty i,j,t + l j,i,t(r r j,i,t)y j,i,t m i,j,t s i,j,t) s=t j=1 s.t. constraints; where R i,j,t = (1 P i,j,t)r i,j,t P i,j,t, no default occurs! Linearized policy function for optimal monitoring m i,j,t = a + b σ 2 i,j,t + cet σ2 i,j,t+1 + dety i,j,t+1 + ee tb i,j,t+1 Non-linear policy function for optimal search s i,j,t = h(e t(r r j,i,t )y j,i,t ) h( ) 0 13 / 29

35 Dynamic Optimization Problem Dynamic optimization problem of each bank i: ( 1 ) s t N max E t (l {m i,j,t,s i,j,t } 1 + r d i,j,t R i,j,ty i,j,t + l j,i,t(r r j,i,t)y j,i,t m i,j,t s i,j,t) s=t j=1 s.t. constraints; where R i,j,t = (1 P i,j,t)r i,j,t P i,j,t, no default occurs! Linearized policy function for optimal monitoring m i,j,t = a + b σ 2 i,j,t + cet σ2 i,j,t+1 + dety i,j,t+1 + ee tb i,j,t+1 Non-linear policy function for optimal search s i,j,t = h(e t(r r j,i,t )y j,i,t ) h( ) 0 Adaptive expectations of x i,j,t using exponentially weighted moving average E tx i,j,t+1 =: xi,j,t = (1 λx )xi,j,t 1 + λx B i,j,tx i,j,t 13 / 29

36 Table of Contents 1. Motivation 2. Model 3. Estimation 4. Results 14 / 29

37 Data Characterization Using Network Statistics Observed variables are l i,j,t (link/loan indicator), y i,j,t (volumes) and r i,j,t (spreads), for unsecured overnight loans between N = 50 Dutch banks from to (T = 810) At each t, we compute statistics of trading network implied by {l i,j,t }, with link weights {y i,j,t }, {r i,j,t } to characterize network topology Statistic Density Reciprocity Stability Degree Centrality Clustering Corr(l i,j,t, #l i,j,t 1 rw ) Corr(r i,j,t, #l i,j,t 1 rw ) Interpretation Fraction of existing trading relations (links) relative to all potential relations Fraction of reciprocal relationships among all existing trading relationships Fraction of relationships that did not change as compared to previous network In- and out-degree of node: number of different lenders/borrowers per bank cross-sectional degree distribution How close are a node s neighbors are to being a clique (complete network) average distribution as global measure Stability of bilateral trading relationship Price impact of intensity of bilateral relationship (relationship lending) From dynamic lending network we obtain sequences of network statistics 15 / 29

38 Indirect Inference Estimator of Network Model Idea: characterize data X by vector of auxiliary statistics β in a way that identifies structural parameters θ, then simulate s = 1,..., S different datasets X s and choose ˆθ as ˆθ := argmin ˆβ(X) 1 θ Θ S S ˆβ(X s(θ)). s=1 Indirect inference estimator ˆθ is consistent and asymptotically normal, see Gouriéroux et al. (1993) Moments of sequence of network statistics and moments of bilateral volumes and spreads as auxiliary statistics, see Blasques and Bräuning (2014) details 16 / 29

39 Table of Contents 1. Motivation 2. Model 3. Estimation 4. Results 17 / 29

40 Observed and Simulated Lending Network (a) Observed network (b) Simulated network (under ˆθ T ) Figure : Interbank network during one week. Nodes are scaled according to total trading volume. 18 / 29

41 Comparison of Auxiliary Statistics Observed Simulated Auxiliary statistic (mean) ˆβ T β TS (ˆθ T ) Density Reciprocity Avg clustering Stability details 19 / 29

42 Comparison of Auxiliary Statistics Observed Simulated Auxiliary statistic (mean) ˆβ T β TS (ˆθ T ) Density Reciprocity Avg clustering Stability Corr(l i,j,t, #li,j,t 1 rw ) Corr(r i,j,t, #li,j,t 1 rw ) details 19 / 29

43 Comparison of Auxiliary Statistics Observed Simulated Auxiliary statistic (mean) ˆβ T β TS (ˆθ T ) Density Reciprocity Avg clustering Stability Corr(l i,j,t, #li,j,t 1 rw ) Corr(r i,j,t, #li,j,t 1 rw ) Avg log volume Std log volume Avg spread Std spread details 19 / 29

44 Simulated Degree Distributions Relative frequency Relative frequency Out degree In degree (a) Out-degree (# borrowers) (b) In-degree (# lenders) Observed Simulated Auxiliary statistic (mean) ˆβT βts (ˆθ T ) Avg degree Std outdegree Skew outdegree Std indegree Skew indegree / 29

45 Parameter Estimates: What Drives the Lending Patterns? 16 structural parameters estimated, 8 calibrated (not identified) details Some key results: Economic hypothesis H 0 ˆθ reject at 1% Monitoring has no effect on information β σ = Yes Search has no effect on link probability β λ = Yes No liquidity shock heterogeneity in mean σ µ = Yes No liquidity shock heterogeneity in variance σ σ = Yes Linear policy rule for monitoring: CR Uncertainty Link Volume Variable σ i,j,t E t σ i,j,t+1 E tb i,j,t+1 E ty i,j,t+1 Coefficient Persistent expectations about bilateral link probabilities (λ B = 0.93) and volumes (λ y = 0.85), less for spreads (λ r = 0.41) 21 / 29

46 Heterogeneous Liquidity Shock Distributions 35 x σζi µζi Figure : Joint distribution of mean and standard deviation parameter ζ i,t N (µ ζi, σ 2 ζ i ) where ) (( ) ( µµ σ 2 )) N, µ ρσ σσ µ log σ ζi µ σ ρσ σσ µ ( µζi σ 2 σ 22 / 29

47 Heterogeneous Liquidity Shocks and Trading Relationships σζi µ ζi ζ i,t N (µ ζi, σ 2 ζ i ) where ) (( ) ( µµ σ 2 )) N, µ ρσ σσ µ log σ ζi µ σ ρσ σσ µ ( µζi σ 2 σ 23 / 29

48 Role of Peer Monitoring on Lending Structure Comparison with no monitoring calibration ˆθ A, where β σ = 0, and all other parameters fixed at estimated values ˆθ U And comparison with restricted estimates ˆθ R, where β σ = 0, and all other parameters re-estimated Restricted Unrestricted Calibrated Estimation Estimation Observed Auxiliary statistic (mean) β TS (ˆθ A ) β TS (ˆθ R ) β TS (ˆθ U ) ˆβ T Corr(l i,j,t, l rw i,j,t 1 ) Corr(r i,j,t, l rw i,j,t 1 ) Skew outdegree Skew indegree / 29

49 Dynamic Network Responses to Credit Risk Uncertainty Shock Density 6.56 Total volume Stability Reciprocity Skewness outdegree Skewness indegree Figure : Simulated network responses to common shock to credit risk uncertainty 25 / 29

50 Responses of Monitoring and Search 5.6 Mean monitoring 1.6 Mean search Figure : Amplification mechanism due to feedback between monitoring and search 26 / 29

51 Monetary Policy Analysis: Changes in Interest Rate Corridor Density Reciprocity Stability Total volume Mean log volume Std spread Figure : Responses of lending network structure / 29

52 Monetary Policy Analysis: The Multiplier Effect of Monitoring Mean monitor Mean search Changes in lending network are driven by two effects Direct effect on interbank lending activity by altering outside options Indirect multiplier effect through changes in monitoring and search efforts 28 / 29

53 Conclusion We introduce and estimate structural interbank network model where banks monitor and search counterparties for bilateral bargaining in OTC market CR uncertainty and monitoring are key driver of sparse core-periphery structure trading network and existence of relationship lending Dynamic analysis reveals importance of monitoring and search as driver behind prolonged market inactivity after shock to uncertainty Changes in discount window lead to direct effect on interbank lending and indirect multiplier effect through altered monitoring and search efforts 29 / 29

54 A Dynamic Network Model of the Unsecured Interbank Lending Market 1 Francisco Blasques a Falk Bräuning b Iman van Lelyveld a,c a VU University Amsterdam b Federal Reserve Bank of Boston c De Nederlandsche Bank The Role of Liquidity in the Financial System Atlanta, November 19th, The views expressed in this presentation do not necessarily represent those of the Federal Reserve Bank of Boston, the Federal Reserve System, De Nederlandsche Bank, or the Eurosystem. 30 / 29

55 Details of Bilateral Interest Rate Bargaining For bank i, lending funds to bank j at time t is a risky investment { r ijt w.p. 1 P i,j,t R i,j,t = 1 w.p. P i,j,t. with expected return (expectation under perceived probability measure) R i,j,t = E tr i,j,t = (1 P i,j,t )r i,j,t P i,j,t. For borrowing bank j cost of borrowing are simply r i,j,t Bilateral Nash bargaining solution then satisfies Back to Bargaining r i,j,t arg max ((1 P i,j,t )r P i,j,t r) θ (r r) 1 θ. r 30 / 29

56 Details of Indirect Inference Estimation We use quadratic form with diagonal weight matrix (equal unit weights, except density and RL measures which are set to 10 and 50), S = 24 simulated networks with each T = 3000, burning 1000 periods The reduced form can be written as a nonlinear Markov autoregressive process, X t = G θ (X t 1, e t) Restrict parameter space Θ to ensure model identification and stability; contraction condition to ensure stability of dynamic network E log sup G θ (x, e t) < 0 x where G θ denotes the Jacobian of G θ and is a norm. Lyapunov stability of the dynamic stochastic network model Parameter vector initial point: θ 0 estimated point: ˆθ T Lyapunov exponent Back to Estimation 30 / 29

57 Details of Auxiliary Statistics Table : Auxiliary network statistics. The table reports the values of the observed auxiliary statistics ˆβ T used in the indirect inference estimation along with the HAC robust standard errors. The simulated average of the auxiliary statistics β TS for S = 24 paths is shown for the estimated parameter vector ˆθ T and the alternative calibration θa (model without monitoring). The observed statistics are computed on a sample of daily frequency from 18 February 2008 to 28 April 2011 of size T = 810. Simulated Observed Calibrated Estimated Auxiliary statistic βts (θa) βts ( ˆθ T ) ˆβT ste( ˆβ T ) Density (mean) a Reciprocity (mean) Stability (mean) Avg clustering (mean) Avg degree (mean) Std outdegree (mean) Skew outdegree (mean) Std indegree (mean) Skew indegree (mean) Corr(r i,j,t, l i,j,t 1 rw ) (mean) Corr(l i,j,t, l i,j,t 1 rw ) (mean) Avg log volume (mean) Std log volume (mean) Skew log volume (mean) Avg interest rates (mean) Std interest rates (mean) Skew interest rates (mean) Corr(density,stability) Corr(density,rates) Autocorr(density) Autocorr(avg volume) Autocorr(avg rate) Objective function value Euclidean norm ˆβ T β TS Sup norm ˆβ T β TS a Not included in vector of auxiliary statistics as proportional to average degree. Back to Auxiliary Statistics 30 / 29

58 Back to Parameter Estimates 30 / 29 Details of Parameter Estimates Table : Estimated parameter values. The table reports the estimated structural parameters (ˆθ T ) and corresponding standard errors and 90% confidence bounds. The parameter θa represents an calibrated model parametrization without monitoring (β φ,1 = 0). For calibrated parameters no standard errors and confidence bounds are reported. The indirect inference estimator is based on S = 24 simulated network sequences of length T = Note also that σ µ = log(σµ). Structural parameters Calibrated Estimated St.Errors 90% Bounds θa ˆθ T ste( ˆθ T ) LB UB Added information α φ β φ, β φ, Perception error variance ασ βσ γσ δσ Search technology α λ β λ Liquidity shocks µµ σµ µσ σσ ρ ζ Expectations λ y λ B λ r λ σ Bargaining lender θ CB corridor width r Default threshold ɛ Financial distress σ Discount rate r d Scale logistic β I