Lecture 1. Financial Market Frictions and Real Activity: Basic Concepts

Transcription

1 Lecture 1 Financial Market Frictions and Real Activity: Basic Concepts Mark Gertler NYU June

2 First Some Background Motivation... 1

3 Old Macro Analyzes pre versus post 1984:Q4. 1

4 New Macro Analyzes pre versus post August 2007 Post August 2007: EndoftheGreatModeration Downturn Precipitated by Disruption of Financial Intermediation Unconventional Monetary Policy 2

5 0.04 Real GDP growth

6 18 16 core inflation federal funds rate

7 Figure 1: Selected Corporate Bond Spreads Basis points Quarterly NBER Q4. Peak Avg. Senior Unsecured Medium-Risk Long-Maturity Baa Note: The black line depicts the average credit spread for our sample of 5,269 senior unsecured corporate bonds; the red line depicts the average credit spread associated with very long maturity corporate bonds issued by firms with low to medium probability of default (see text for details); and the blue line depicts the standard Baa credit spread, measured relative to the 10-year Treasury yield. The shaded vertical bars denote NBER-dated recessions. 37

8 real GDP growth (right) lending standards (left)

9 New Macro (con t) However, existing quantitative models not adequate: Baseline models (Christiano/Eichenbaum/Evans, Smets/Wouters) have frictionless capital markets Models with financial frictions (Bernanke/Gertler/Gilchrist, Christiano/Motto/Rostagno need updating: Basic financial accelerator("adverse feedback loop") mechanism relevant, but Frictions only on non-financial firms; intermediaries typically just a veil. Only consider conventional monetary policy: 3

10 Objective Illustrate the following key concepts: 1. Asymmetric information and/or costly contract enforcement as foundations of financial market imperfections 2. Premium for external finance 3. Rationing vs. non-rationing equilibria 4. Balance sheets and the external finance premium 5. Idiosyncratic risk and the external finance premium. 2

11 Objective (con t) Illustrate with two simple models: 1. Costly State Verification Model (CSV) (Townsend, 1979) 2. Costly Enforcement Model 3

12 Basic Environment Two Periods: 0 and 1. Risk Neutral Entrepreneur: Has project that requires funding in 0 and pays off in 1. Competive Risk Neutral Lender: Has opportunity cost of funds R. 4

13 Basic Environment (con t) Project Finance: QK = N + B K Capital Input N Entrepreneurs s Net Worth (Equity Finance) B Debt Finance 5

14 Basic Environment (con t) Period 1 Payoff eωr k QK R k Average Gross Return on Capital eω Idiosyncratic Shock Entrepreneur takes eωr k as given, but K is a choice variable. 6

15 Basic Environment (con t) Idiosyncratic Shock Distribution: E{eω} =1 eω [ω, ω] H(ω) =prob(eω ω) h(ω) = dh dω 7

16 Perfect Information and Perfect Contract Enforcement Given E eωr k = R k, entrepreneurs operates if R k R where R is the opportunity cost. If R k >R,entrepreneur s demand for funds is infinite Competitive market forces R k = R in equilibrium. Miller-Modigliani theorem applies: Real Investment Decision is independent of financial structure Financial Structure is indeterminate 8

17 Private Information and Limited Liability Private Information: Only entrepreneurs can costlessly observe returns. Lenders must pay a cost equal to a fixed fraction μ of the realized return ωr k K. Interpretable as a bankruptcy cost. Limited Liability: Entrepreneurs minimum payoff bounded at zero. 9

18 Private Information and Limited Liability (con t) Implications: Entrepreneur has incentive to misreport returns. Financial structure matters to real investment decisions, due to expected bankruptcy costs. Financial structure determinate: Designed to reduce expected bankruptcy costs. 10

19 Entrepreneur s Optimization Problem: 1. Investment Decision (choice of K) 2. Financial contract: payment schedule baced on ω and decision to monitor 3. Constraint: Lender must receive opportunity cost in expectation. 11

20 Optimal Contract 1. Induce Truth-Telling (revelation principle) 2. Minimize Expected Monitoring Costs For any choice of Optimal Contract is Standard Debt: i.e, Debt with bankruptcy 12

21 Optimal Contract (con t) Let D face value of debt and ω the cutoff value of ω D = ω R k QK The contract then works as follows: If ω ω : Lender s payoff is D = ω R k QK; Borrower s payoff is (ω ω )R k QK If ω<ω, The borrower announces default and then the lender monitors. Lender s payoff is (1 φ)ωr k K; Borrower s payoff is 0. Observe that the deadweight bankruptcy cost is φωr k QK. 13

22 Intuition for Optimal Contract Optimal Contract (con t) 1. There is no incentive for the entrepreneur to lie: In non-default states the payment to lenders is fixed In default states there is monitoring. 2. Expected bankruptcy costs are minimized. By giving the lender everything in the default state, the non-default payment D is minimized. Given D = ω R k K, the bankruptcy probability H(ω ) is which is increasing in D. H(ω D )=H( R k QK ) 14

23 Optimal Contract (con t) Given the form of the optimal contract: Lender s expected gross payment: Z ω ω ω R k QKdH + with Γ(ω )= Z ω ω Z ω ωr kqkdh Γ(ω )R k QK ω ω dh + Z ω ω ωdh 15

24 Optimal Contract (con t) Γ(ω ) is increasing and concave: Γ 0 (ω )=[1 H(ω )] > 0 Γ 00 (ω )= h(ω ) < 0 16

25 Optimal Contract (con t) Lender s expected net payment with Z ω ω ω R k QKdH + Z ω ω (1 μ)ωr kqkdh =[Γ(ω ) μg(ω )]R k QK G(ω )= Z ω ω ωdh 17

26 Optimal Contract (con t) G(ω ) is increasing and convex, assuming ω h(ω ) is increasing G 0 (ω )=ω h(ω ) > 0 G 00 (ω ) > 0 18

27 Entrepreneur s Decision Problem Objective: subject to max ω,k, max{[1 Γ(ω )]R k QK RN, 0} [Γ(ω ) μg(ω )]R k QK = R(QK N) with λ constraint multiplier = shadow value of N 19

28 Entrepreneur s Decision Problem Combining equations: max ω,k, max{[r k R μg(ω )R k ]QK, 0} where μg(ω )R k expected default costs related to premium for external finance 20

29 Entrepreneur s Decision Problem (con t) F.O.N.C: ω λ =1+ μg 0 (ω ) Γ 0 (ω ) μg 0 (ω ) K R k λ {[1 Γ(ω )] + λ[γ(ω ) μg(ω )]} R =0 λ [Γ(ω ) μg(ω )]R k = R(1 N K ) 21

30 Entrepreneur s Decision Problem (con t) Three observations: 1. λ is increaing in ω (from top eq.) 2. ω increasing in R k /R.(from middle equation) 3. λ {[1 Γ(ω )]+λ[γ(ω ) μg(ω )]} > 1 isthepremiumforexternalfinance. (Note that the premium is increasing in ω ). 22

31 Non-Rationing vs. Rationing Solution Lender s voluntary participation constraint: [Γ(ω ) μg(ω )]R k = R(1 N QK ) The expected return on debt per unit capital (the left side)depends on ω Γ 0 (ω ) μg 0 (ω )=(1 H(ω )) μω h(ω ) which in genereal has an ambiguous sign. 23

32 Non-Rationing vs. Rationing Solution (con t) Non-Rationing Solution: Lender s expected return increasing in ω, i.e., Rationing Solution: Just the opposite Γ 0 (ω ) μg 0 (ω ) > 0 Γ 0 (ω ) μg 0 (ω ) 0 Under reasonable parametrizations, the non-rationing solution holds. 24

33 Rationing Equilibrium The following two equations determine ω and QK : Lender s voluntary participation constraint: [Γ(ω ) μg(ω )]R k = R(1 N QK ) Maximum feasible ω Γ 0 (ω ) μg 0 (ω )] = 0 Observe that QK varies proportionately with N and with R k /R. 25

34 Non-Rationing Equilibrium The following two equations determine ω and QK : Lender s voluntary participation constraint: Optimal Choice of Captial [Γ(ω ) μg(ω )]R k = R(1 N QK ) with R k χ(ω )R =0 χ(ω )= λ(ω ) {[1 Γ(ω )] + λ(ω )[Γ(ω ) μg(ω )]} > 1; χ0 (ω ) > 0 26

35 Non-Rationing Equilibrium (con t) Inverting the lender s voluntary participation constraint: QK N = 1 1 [Γ(ω ) μg(ω )]R k /R ω is increasing in R k /R from FONCs for ω and K. with QK N = φ(r k R ) φ 0 ( R k R ) > 0 27

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37 The Demand for Capital Capital demand QK = φ( R k R )N where φ( R k R ) is the optimal leverage ratio. φ( R k R ) does not depend on firm specific factors Can aggregate capital demand across entrepreneurs: QK = φ( R k R )N where N is aggregate net worth and K is aggregate capital demand. 28

38 Figure 2: Leverage Ratio Quarterly NBER Peak Ratio Q Note: The black line depicts the time-series of the cross-sectional averages of the leverage ratio for U.S. nonfinancial corporations. Leverage is defined as the ratio of the market-value of the firm s total assets (V ) to the market-value of the firm s common equity (E), where the market-value of the firm s total assets is calculated using the Merton-DD model (see text for details). The shaded vertical bars denote NBER-dated recessions

39 Balance Sheet Strength and the Spread Inverting yields with R k R = χ(qk N ) χ 0 ( QK N ) > 0 where χ is the gross spread. Thus, in the market equilibrium, the spread is inversely related to aggregate balance sheet strength. 29

40 Increasing Idiosyncratic Risk Let ξ be an index of the spread of the distribution of ω. Then consider a mean-preserving increasing in the spread. Under reasonable parametrizations: H(ω ) > 0 ξ i.e. everyting else equal, a mean-preserving spread increases the default probability H(ω ) h(ω ) > 0 i.e., the density at the default cutoff also goes up. 30

41 Increasing Idiosyncratic Risk (con t) Lender s voluntary participation constraint: with Γ(ω,ξ) ξ [Γ(ω,ξ) μg(ω,ξ)]r k = R(1 N QK ) < 0 and G(ω,ξ) ξ > 0. Optimal Choice of Captial with Γ(ω,ξ) ξ > 0. R k χ(ω,ξ)r =0 31

42 Increasing Idiosyncratic Risk (con t) QK N = φ(r k R,ξ) with φ( R k R,ξ) ξ < 0 Increasing idiosyncratic risks reduces capital demand by "tightening margins." 32

43 Costly Enforcement Model Same basic setup as in CSV model, except the financial market friction is motivated by costs of enforcing contracts as opposed to private information: Borrower may decide to renege on debt. Lender can only recover the fraction (1 λ) of the gross returnr k QK, with (1 λ)r k <R Borrowerisabletokeeptherest,:λR k QK 33

44 Costly Enforcement Model (con t) Value of the project V V = R k QK R(QK N) = (R k R)QK + RN Incentive Constraint: Binding Incentive Constraint: V λr k QK (R k R)QK + RN = λr k QK 34

45 Costly Enforcement Model (con t) 1 QK =[ 1 (1 λ)r k /R ]N QK = φ(r k /R)N with φ(r k/r) R k /R > 0 35

46 Costly Enforcement Model (con t) Advantages Less complicated but similar predictions to CSV model: 1. QK depends positively on N 2. φ(r k /R) is increasing in R k /R. 36

47 Costly Enforcement Model (con t) Disadvantages 1. No default 2. No credit spreads (as debt is riskless) 3. Can t analyze shifts in idiosyncratic risk. 4. Less obvious how to calibrate or estimate parameters. 37

48 Moving to General Equilbrium Need to endogenize: 1. The external finance premium R k /R 2. Net Worth N. 3. The price of capital Q 38

49 Moving to General Equilbrium (con t) Financial Accelerator = Procyclical Movements in N induce countercyclical movements in R k /R Unexpected movements in Q induce movements in N, leading to feedback between the real and financial sectors. FInancial Crisis SharpdropinN Tightening net worth constraint (i.e., capital demand shrinks for a given N.) 39