Advanced Macroeconomics I ECON 525a - Fall 2009 Yale University

Transcription

1 Advanced Macroeconomics I ECON 525a - Fall 2009 Yale University Week 4

2 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

3 Mechanism Summary credit cycles 213 Fig. 1

4 Agents Farmers. measure 1 Gathers, 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

5 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 Assume c > a( 1 β 1) (in equilibrium farmer wants to consume ck t and sell ak t )

6 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

7 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

8 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

9 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 Implied optimal land holdings 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

10 Equilibrium Results: Gatherers Gatherer s demand for land G (k t)/r = u t = q t (q t+1 /R) }{{} user cost

11 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

12 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 No bubbles in land price: lim s E t (R s q t+s ) = 0

13 Steady State u = (1 1/R)q = a ( ) 1 u = G m ( K K ) /R (R 1)B = ak

14 Steady State credit cycles 223

15 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 + q t q )K Subsequent periods (periods t + s, s = 1, 2,...) u(k t )K t = (a + a + q t q )K

16 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

17 Response of Land Price & Land Holdings Land price response ˆq t = 1 η Overall land holding response ˆK t = (1 + R 1 R 1 η ) η }{{} >1

18 Response of Land Price & Land Holdings Land price response ˆq t = 1 η Overall land holding response ˆK t = (1 + R 1 R 1 η ) η }{{} >1 Say η = 1, R = 1.05 ˆK t 11

19 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 =

20 Response of Output & Productivity Ŷ t+s = a + c Ra a + c }{{} (a + c)k Y }{{} Productivity diff. Farmers share ˆK t+s 1

21 Net Worth Shock One time reduction in debt obligations Increases net worth Farmer increases leverage, production Another view of Bernanke-Paulson policies?

22 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

23 Conclusions Firms productive capital also used as collateral Amplification of real shocks through lower collateral value of capital Real effects of lower asset values

24 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