ECON 712, Fall 2017 Financial Markets and Business Cycles Guillermo Ordoñez University of Pennsylvania and NBER September 17, 2017
Introduction Credit frictions amplification & persistence of shocks Two roles for capital - Factor of production - Collateral for loans Negative productivity shock - Reduces output; reduces value of collateral - Reduces borrowing, which reduces output further - Multiplier effects amplifies losses
Mechanism Summary credit cycles 213 Fig. 1
Agents Farmers. measure 1 Gatherers, measure m E t s=0 E t s=0 β s x t+s β s x t+s Farmers more impatient (β < β ) (will imply that Farmers are the borrowers in equilibrium) Both use land k t to produce fruit Value of land k t q t used as collateral
Farmers Farmers production function for fruit y t+1 = (a + c)k t ak t = sellable fruit ck t = bruised fruit which must be consumed Investment happens at a rate R = 1 β, then a + c = x + a x β Assumption a + c > a β (farmers do not want to consume more than ck t, then sell ak t )
Farmers (constrained) Can borrow b t at rate R Borrowing Constraint (from inalienability of farmers human capital) Rb t q t+1 k t Farmers flow of funds constraint (a + c)k t 1 + b t + q t k t 1 = x t + Rb t 1 + q t k t x t is consumption of fruit
Gatherers (unconstrained) They do not have specific skills to threat not paying. Gatherers production function for fruit y t+1 = G(k t) G( ) has decreasing returns to scale Gatherers budget constraint G(k t 1) + b t + q t k t 1 = x t + Rb t 1 + q t k t x t is consumption of fruit
Equilibrium Sequences of land prices, allocations of land, debt, consumption for farmers and gatherers {q t, k t, k t, b t, b t, x t, x t} such that everyone s optimizing and markets clearing. No uncertainty: perfect foresight
Equilibrium Results: Farmers Farmers always borrow the maximum and invest in land b t = q t+1 k t /R and x t = ck t 1 From the budget constraint, farmers land holdings are k t = 1 q t q t+1 /R [(a + q t)k t 1 Rb t 1 ] }{{} net worth u t q t q t+1 /R = down payment Farmers spend entire net worth on difference between price of new land q t and amount against which they can borrow against each unit of land q t+1 /R
Farmers in the Aggregate Farmer aggregate landholding & borrowing K t = 1 u t [(a + q t )K t 1 RB t 1 ] B t = 1 R q t+1k t Note: higher q t, q t+1 farmers demand more k t - can borrow more when q t+1 k t (collateral) values higher - net worth higher when q t higher
Equilibrium Results: Gatherers Gatherer s demand for land. G (k t)/r = u t = q t (q t+1 /R) }{{} user cost Equalize the marginal product of land (G (k t)) with its opportunity cost (Rq t q t+1 ).
Market Clearing Land market resource constraint mk t + K t = K Land market clearing u t = q t q t+1 /R = G 1 m ( K K t ) /R }{{} k Note u t is decreasing in k t (increasing in K t ). Note also Gatherers are not constrained, then R = 1 β (first Assump) ASS: No bubbles in land price: lim s E t (R s q t+s ) = 0
Steady State u = (1 1/R)q = a ( ) 1 u = G m ( K K ) /R (R 1)B = ak Assumption 1: Ra = G ( 1 m ( K K ) ) < a β < a + c. Inefficient allocation because of collateral constraint.
Steady State credit cycles 223
One-time Productivity Shock with Credit Constraints Say y t+1 = (1 + )(a + c)k t Period of shock (period t) u(k t )K t = (a + a)k + q t K RB }{{} q K = u(k t )K t = (a + a + q t q )K Subsequent periods (periods t + s, s = 1, 2,...) u(k t+s )K t+s = ak t+s 1 + q t+s K t+s 1 RB t+s 1 }{{} =0
One-time Productivity Shock with Credit Constraints Log-linearize around steady state Define for variable X t the proportional change from steady state ˆX t = X t X X Period of shock (period t) (1 + 1/η) ˆK t = + R R 1 ˆq t Subsequent periods (periods t + s, s = 1, 2,...) (1 + 1/η) ˆK t+s = ˆK t+s 1 where η denotes elasticity of land supply of gatherers to user cost
Response of Land Price & Land Holdings Land price response ˆq t = 1 η Overall land holding response ˆK t = 1 1 + 1 (1 + R 1 R 1 η ) η }{{} >1
Response of Land Price & Land Holdings Land price response ˆq t = 1 η Overall land holding response ˆK t = 1 1 + 1 (1 + R 1 R 1 η ) η }{{} >1 Say η = 1, R = 1.05 ˆK t 11
Static Response of Land Price & Land Holdings Land price response ˆq t qt+1=q = 1 η R 1 R }{{} <1 Overall land holding response ˆK t qt+1=q =
Response of Output & Productivity Ŷ t+s = a + c Ra a + c }{{} (a + c)k Y }{{} Productivity diff. Farmers share ˆK t+s 1
Response to Shock 238 journal of political economy Fig. 3
Net Worth Shock One time reduction in debt obligations Increases net worth Farmer increases leverage, production Another view of Bernanke-Paulson policies?
One-time Productivity Shock at First-Best Steady State Say y t+1 = (1 + )(a + c)k t Output rises by Net worth rises But prices q 0 unaffected; land k 0 unaffected No change to future variables Prices and production do not depend on changes in net worth. Fluctuations are magnified and prolonged by collateral constraints.
Conclusions Firms productive capital also used as collateral Amplification and persistency of real shocks through lower collateral value of capital Real effects of lower asset values and financial frictions.
Critiques/Comments Kocherlakota (QR, 2000): Quantitative importance likely to be small if land & capital share less than 0.4 Andres Arias (WP, 2005): Calibrated RBC model with KM credit constraints deliver small amplification effects Does this work through investment wedge? or TFP, or both? Real effects of housing/stock bubbles
Bernanke and Gertler, AER 89 Financial Accelerator Model Bernanke and Gertler (1989). Costly state verification in a Real Business Cycle model. Debt-Deflation meets Real Business Cycle. Main idea. The borrowers net worth determines their solvency and risk of default. Net worth affects agency problems and the intermediation cost. Net worth is procyclical. In recessions the costs of intermediation increase, reduce the net return of investment and depress investment, magnifying the recession.
Bernanke and Gertler, AER 89 Model Main elements. Two period lived agents. Overlapping generations. Two types of agents: Entrepreneurs: A fraction η of agents. Each has a single project with cost, ω U[0, 1] to produce capital. Investors. Monitoring cost γ. Two goods: Output: Can be consumed, stored or invested. Capital. Fully depreciated in one period. Production functions: y t = θ tf (k t) k t+1 = κi t, where κ = πκ L + (1 π)κ H (the output is non-observable to investors).
Bernanke and Gertler, AER 89 Model Main elements. Preferences Entrepreneurs: E t(ct+1 e ) Investors. U(c y t ) + βet(co t+1 ) Labor income at wage w t. Average savings Entrepreneurs: St e = wtle Investors: S t = w tl cy (r), where cy is the optimal consumption when young and r is the storage rate of return.
Bernanke and Gertler, AER 89 Perfect Information The Case of γ = 0. Denote q t price of capital in terms of output. Expected gross return of a project: E t(q t+1)κ Cost of a project: rx(ω) Then ω is defined by E t(q t+1)κ rx(ω) = 0. Then k t+1 = κωη Supply of capital and Demand from output. SS curve: E t (q t+1 ) = rx ( kt+1 ) κη κ DD curve: E t (q t+1 ) = E t (θ t+1 )f (k t+1 )
Bernanke and Gertler, AER 89 Perfect Information Investment is constant and production (the consumption and inventories) move with productivity shocks. E(q t+1 ) DD SS k t+1
Bernanke and Gertler, AER 89 Asymmetric Information The Case of γ > 0. Consider entrepreneurs who require to borrow x(ω) > S e Full collateralization. The entrepreneur can pay even when the worst outcome κ L occurs. E t(q t+1)κ L r(x(ω) S e ) Incomplete collateralization. Monitoring problem because entrepreneurs are tempted to lie and say they produced κ L E t(q t+1)κ L < r(x(ω) S e )
Bernanke and Gertler, AER 89 Asymmetric Information Costly State Verification Contract If entrepreneurs report κ H, R = E t(q t+1)κ H Ct+1. e If entrepreneurs report κ L, they pay E t(q t+1)κ L and get monitored with probability p. If entrepreneur told the truth, the lender gets nothing extra. If the entrepreneur lied, the lender gets E t(q t+1)(κ H κ L ). Entrepreneurs tell the truth in good states. E t(q t+1)κ H R (1 p)e t(q t+1)(κ H κ L ) C e t+1 (1 p)e t(q t+1)(κ H κ L )
Bernanke and Gertler, AER 89 Asymmetric Information Costly State Verification Contract If entrepreneurs report κ H, R = E t(q t+1)κ H Ct+1. e If entrepreneurs report κ L, they pay E t(q t+1)κ L and get monitored with probability p. If entrepreneur told the truth, the lender gets nothing extra. If the entrepreneur lied, the lender gets E t(q t+1)(κ H κ L ). Lenders prefer to lend than to store at rate r r(x(ω) S e ) (1 π)r + πe t(q t+1)κ L πpe t(q t+1)γ r(x(ω) S e ) (1 π)[e t(q t+1)κ H C e t+1] + πe t(q t+1)[κ L pγ]
Bernanke and Gertler, AER 89 Asymmetric Information The two constraints bind. Optimal monitoring probability p is p = r(x(ω) S e ) E t (q t+1 )κ L E t (q t+1 )[(1 π)(κ H κ L ) πγ] and consumption of the entrepreneur in good states is, C e t+1 (1 p )E t (q t+1 )(κ H κ L )
Bernanke and Gertler, AER 89 Asymmetric Information What projects SHOULD be financed (efficiency) E t (q t+1 )κ rx(ω) What projects ARE financed. The fully collateralized: E t(q t+1)κ L r(x(ω) S e ) Partially collateralized if E t(q t+1)(κ p γ) rx(ω)
Bernanke and Gertler, AER 89 Asymmetric Information Cyclical movements in S e affects investment, no longer constant. Can you see how? E Profits E t (q t+1 )[κ p(ω, S e )γ] r E t (q t+1 )κ L + S e r E t (q t+1 )κ r ω
Bernanke and Gertler, AER 89 Asymmetric Information Now investment depend on a current variable, which is the net worth of entrepreneurs that affect agency costs. E(q t+1 ) DD SS (γ > 0) SS k t+1
Bernanke and Gertler, AER 89 Shocks Where exogenous movements in S e come from? Redistribution of endowment from entrepreneurs to lenders. Debt-deflation story in which a combination of unindexed contracts and deflation redistributes wealth from debtors to creditors.
Bernanke and Gertler, AER 89 Implications Financial frictions do not generate business cycles. Financial frictions do amplify business cycles. The financial accelerator effect is nonlinear and asymmetric over time. Financial instability has asymmetric effects across borrowers and lenders. How long a recession lasts depend on the flexibility of agent to reevaluate the default risk. Monetary policy that reduces interest rates may be irrelevant if there is a pessimism trap.
Bernanke and Gertler, AER 89 Critiques If investment is not sensitive to interest rates, it may be even less sensitive to intermediation costs. Quantity constraints (no credit) seem more relevant than price constraints (always a price at which credit is available).
Bernanke and Gertler, AER 89 Quantitative Implications Carlstrom and Fuerst (AER, 1997) Calibration analysis of Bernanke and Gertler. They replicate the hump-shaped response of output, i.e., it generates some propagation dynamics that are absent in the technology shock. Households delay their investment decisions until agency costs are at their lowest, several periods after the shock. Agency costs fall over time because the productivity shock increases the return to internal funds, which in turn distributes wealth from households to entrepreneurs. Ordonez (JPE, 2013). Asymmetric Effects of Financial Frictions.