CREDIT SEARCH AND CREDIT CYCLES Feng Dong Pengfei Wang Yi Wen Shanghai Jiao Tong U Hong Kong U Science and Tech STL Fed & Tsinghua U May 215 The usual disclaim applies.
Motivation The supply and demand are not always well aligned and matched in our real life. labor, finance, monetary, etc. credit. Data pattern: excess reserve-to-deposit ratio interest spread Data Data Austrian school and many others: credit supply and financial intermediation plays a critical role in generating and amplifying the business cycle.
Preview This paper provides a framework to rationalize the Austrian theory and the observed credit cycles. We develop a search-based theory of credit allocation. Credit search can lead to endogenous increasing returns to scale and variable capital utilization, even in a model with constant returns to scale production technology and matching functions. a micro-foundation for the indeterminacy literature of Benhabib and Farmer (1994) and Wen (1998). Literature Review
Intuition Prevalence of and the essential role played by intermediation. people carry money but no investment opportunity. investors carry investment projects but no money. Intuition: Amplification. Propagation. Sunspot.
Setup Continuous time; infinite horizon. Players: a representative household (HH). unit measure of workers/depositors. a representative and perfectly competitive bank (FI). unit measure of loan officers. intermediation between HH and firms. firms. free entry into credit market by paying a fixed cost.
Household and Deposit Search (I) The constrained optimization by HH: subject to { [ ]} + maxe e ρt log(c t ) ψ N1+ξ t 1 + ξ C t + Ṡ t = W t N t + er d t S t δ (e)s t + (profits from banks and firms) t e [,1]: the proportion of savings transferred to deposit, δ (e): the convex depreciation function w.r.t. e.
Household and Deposit Search (II) We use household s deposit search to rationalize δ (e). Denote x as the search effort by household such that cost: δ = φ H x t, benefit: e t part of savings successfully transferred to deposit, e(x t ) = M H (x t H,B), H,B: measure of household and bank officers, e is concave in x and thus δ is convex in e.
Bank, Firms and Loan Search (I) Matching between loan officers and firms: q M (B,V) V u M (B,V) B Banks are fully competitive: = M (θ,1), ( 1, 1 θ = M ). R d t = u t R l t Given matched, the total surplus is S t = e t S t. { } Π t = max A t S t α n 1 α t W t n t π t S t. n t
Bank, Firms and Loan Search (II) Bargaining: (η, 1 η), firm vs bank. R l t = (1 η)π t. Firm s free entry condition into the credit market: φ t = q t ηπ t = q t ηπ t S t. Aggregate profit to the household: profit t = ( R d t + u t R l t) S t + ( φ t + q t ηπ t )V t =. }{{}}{{} profit from banks profit from firms
Equilibrium (I) Given (e t,u t,a t,s t,n t ), Feedback: Y t = A t (e t u t S t ) α N 1 α t. If M H (xh,b) = γ H (x t H) ε H B 1 ε H, then e t If M (B,V) = γb 1 ε V ε, then ( Yt S t ) εh. u t Y ε t.
Derivation on e: Equilibrium (II) ( δ (e) = R d = ur l = u(1 η)π = u(1 η) α Y ), u S S = es. Derivation on u: ( ) B V = = 1 ( ) 1 u ε θ θ = γ [ ( )] Y φ = qηπ S = qη α S = αηy Vq S V.
Equilibrium (III) In equilibrium, Y t A τ t S α s t N α n t. where τ = 1 1 α(ε+ε H ), α s = α (1 ε H )τ, α n = (1 α)τ. Increasing return to scale: indeterminacy region: α s + α n = 1 αε H 1 α (ε + ε H ) > 1. Sunspot Condition Sunspot Figure dual search is indispensable to sustain sunspot.
Welfare (I) Under what condition does η maximize the HH s welfare, i.e., Given (S t,n t ), { [ ]} + Ω maxe e ρt log(c t ) ψ N1+ξ t. 1 + ξ η = argmax η [,1] ( ) Y DE t Yt SP = ε. ε + ε H Unlike the standard labor search, capital and labor supply is endogenous here. ( ) in steady state, argmax Ω DE ε Ω η [,1] SP ε+ε H in general.
Welfare (II) -1-12 Welfare -14-16 -18 Welfare Classic Hosios Condition: = Modified Hosios Condition: = /( + H ) Calibrated Optimal -2.2.4.6.8 1 : Bargaining Power of Firm
Calibration Table 1. Calibration Parameter Value Description ρ.1 Discount factor (quarterly) A 1 Normalized aggregate productivity α.33 Capital income share ψ 1.75 Coefficient of labor disutility ξ.2 Inverse Frisch elasticity of labor supply ε H.82 Matching elasticity in 1st Stage Search δ.4 Depreciation rate η.187 Firm s bargaining power φ.86 Vacancy cost to search for credit. γ.797 Matching efficiency in 2nd stage search ε.729 Matching elasticity in 2nd stage search
Comparative Statics: Productivity Shock.5.4 Credit Search Standard RBC 1 95 Credit Search Standard RBC 6 Credit Search Standard RBC.3 9 5 log(output).2.1 -.1 Utilization Rate (%) 85 8 75 7 65 Interest Spread (%) 4 3 2 -.2 6 1 -.3 55 -.4 -.1.1 5 -.1.1 log(tfp) -.1.1
Comparative Statics: Credit Shock log(output).25.2.15.1.5 -.5 Utilization Rate (%) 85 8 75 7 65 6 55 Interest Spread (%) 5.5 5 4.5 4 3.5 3 2.5 2 1.5 -.1.7.8.9 5.7.8.9 : credit matching efficiency 1.7.8.9
Impulse Response: Productivity Shock 1 Output (%) 5-5 -1 5 1 15 2 25 3 35 4 45 5 55 6 5 Utilization (%) -5 5 1 15 2 25 3 35 4 45 5 55 6.5 Spread (%) -.5 5 1 15 2 25 3 35 4 45 5 55 6
Impulse Response: Credit Shock 5 Output (%) -5 5 1 15 2 25 3 35 4 45 5 55 6 Utilization (%) 2-2 5 1 15 2 25 3 35 4 45 5 55 6 Spread (%).2.1 -.1 -.2 5 1 15 2 25 3 35 4 45 5 55 6
Impulse Response: Sunspot Shock 4 Output (%) 2-2 5 1 15 2 25 3 35 4 45 5 55 6 2 Utilization (%) 1-1 5 1 15 2 25 3 35 4 45 5 55 6.2 Spread (%).1 -.1 -.2 5 1 15 2 25 3 35 4 45 5 55 6
Impulse Response A-shock, γ-shock and sunspot shock all imply: procyclical credit utilization. countercyclical interest spread.
Credit Chains Household (ee 11 tt, RR 11 tt ) FI-(j-1) (ee jj tt, RR jj tt ) FI-2...... FI-J Fin-Intermediary-1 FI-j Firms (ee tt 22, RR tt 22 ) (uu tt, RR tt ll ) The baseline is a special case with J = 1. Amplification, propagation and the possibility of sunspot increases with J.
Long-Term Credit Relationship A strong assumption made so far. credit relationship always terminates by the end of each period. purely for analytical illustration. We relax this assumption to build a fully fledged DSGE model, and do more serous quantitative work to address government policy like liquidity injection, etc. to model banking heterogeneity, inter-banking lending, and macro-prudential policy, etc.
Takeaway Supply and demand do not necessarily equal to each other in real life. not only true for labor, but also for credit markets. Motivated by the regulated data pattern, we develop a model to show how demand and supply fails to equal each other by using credit search. to show credit supply and financial intermediation plays a critical role in generating and amplifying the business cycle.
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Data: Excess Reserve 5 4 3 2 GDP growth rate 1 1 2 Excess reserve ratio 3 Return
Data: Interest Spread 8 7 6 5 4 3 2 1 1 2 3 Interest Spread GDP growth rate Return
An Incomplete Sample of Literature Self-fulfilling Business Cycles sunspot: Cass and Shell (1983), etc. production externality and indeterminacy: Benhabib and Farmer (1994) and Wen (1998), etc. credit market frictions: Gertler and Kiyotaki (214), Azariadis, Kaas and Wen (214), and Benhabib, Dong and Wang (214), etc. Search Frictions in Business Cycles labor: Merz (1995), Andolfatto (1996), Shimer (25), etc. credit: Den Haan, Ramey and Waston (23), Wasmer and Weil (24), Petrosky-Nadeau and Wasmer (213), etc. Empirics on Credit Allocation Contessi, DiCecio and Francis (215), etc. Return
Indeterminacy Analysis (I) Return We have [ ṡt ċ t ] [ ŝt = J ĉ t Indeterminacy emerges, i.e., Trace(J) <, and Det(J) > if and only if ( )( ) 1 α + ξ ε H + ε > > 1. α 1 + ξ ],
Indeterminacy Analysis (II) α + ξ α(1 + ξ) ε 1 Indeterminacy O 1 ε H α + ξ α(1 + ξ) Return