Incorporate Financial Frictions into a Business Cycle Model Business - PowerPoint PPT Presentation

Incorporate Financial Frictions into a Business Cycle Model Business Cycle Model • General idea: – Standard model assumes borrowers and lenders are the same people..no conflict of interest – Financial friction models suppose borrowers and lenders are different people, with conflicting lenders are different people, with conflicting interests – Financial frictions: features of the relationship between borrowers and lenders adopted to mitigate conflict of interest mitigate conflict of interest.

Standard Model consumption Firms Firms Investment goods Investment goods Rent capital Supply labor Households Backyard capital accumulation: K t  1   1 −   K t  G  I t , I t − 1     t , t 1  y p t  1 t   1 −   P k ′ , t  1 k r t  1 u c , t   E t u c , t  1 P k ′ , t Savers and investors are the same: NO FRICTIONS!

Frictions in Financing of Physical Capital Money Savers Investors (‘entrepreneurs’) Have money, but y, no ideas Have ideas, but not enough money.

Frictions in Financing of Physical Capital Money Savers Investors (‘entrepreneurs’) Have money, but y, no ideas Problem: ‘stuff’ happens. Incentive of entrepreneurs to under ‐ report earnings

A Very Simple Two ‐ Period Model to Get at the Basic Idea h d • Bernanke Gertler and Gilchrist 1999 The Bernanke, Gertler and Gilchrist, 1999, The financial accelerator in a quantitative business cycle framework, in: Taylor, J.B., Woodford, M. y , y , , , (Eds.), Handbook of Macroeconomics, Vol. 1C. North Holland, Amsterdam, pp. 1341 ‐ 1393. • Also, Christiano, Motto, Rostagno, 2003, The Also, Christiano, Motto, Rostagno, 2003, The Great Depression and the Friedman ‐ Schwartz Hypothesis. yp

• Period 1 Period 1 – No uncertainty – Households face leisure ‐ work choice and buy Households face leisure work choice and buy bonds from a bank, with state ‐ non contingent interest. – Entrepreneurs own equal share of capital, k , in first period, and apply income and loans from bank to buy capital for use in period 2 Experience bank to buy capital for use in period 2. Experience an idiosyncratic productivity shock. • Period 2 Period 2 – Aggregate uncertainty – Entrepreneurs pay back loans from banks, which Entrepreneurs pay back loans from banks, which repay households.

Households • Household preferences H h ld f U  c , l    U  c h , l h    1 −   U  c l , l l  . • Budget constraints c  B ≤ wl , c  B ≤ wl c h ≤ w h l h  RB , c l ≤ w l l l  RB c ≤ w l  RB . • Euler equations: h l U c  w , − U l h  w h , − U l − U l l  w l U c U c h l 1    U c U c   1 −   U c R , U c

Goods ‐ producing firms • Technology: y  F  k , l  y y h  F h  K , l h  y l  F l  K , l l  , • Competition ensures: w  F l  k , l  , w h  F l h  K , l h  , w l  F l l  K , l l  l  K , l l  , r  F k  k , l  , r h  F k h  K , l h  , r l  F k h l h h l l

Entrepreneurs • In period 1, each owns equal share of capital stock, k • Net worth at end of period, N=rk (100% k p , ( depreciation) • Entrepreneurs borrow K ‐ N from banks at end of period 1 and banks get the money by of period 1, and banks get the money by issuing bonds, B , to households.

Idiosyncratic uncertainty • After purchasing K , entrepreneurs experience idiosyncratic shock: idiosyncratic shock: K →  K ,  ~ F    , E   1. • Standard debt contract ̄ h → pay     ̄ h r h K to bank ̄ h → pay  r h K to bank, bank pays  r h K in monitoring costs   

Standard Debt Contract, cnt’d Standard Debt Contract, cnt d ̄ l → pay     ̄ l r l K to bank ̄ l → pay  r l K to bank, bank pays  r l K in monitoring costs    • Parameters of Standard Debt Contract: ̄ l and K  ̄ h , 

Determination of Parameters of Standard Debt Contract d d b • Expected utility of entrepreneur at start of Expected utility of entrepreneur at start of contract: share of gross entrepreneurial earnings in state h kept by entrepreneur   1 − Γ h   r h K   1 −   1 − Γ l  r l K , share of gross earnings of entrepreneur taken by bank  ̄ h    ̄ h   0  dF        Γ h Γ  dF      ̄ h dF    dF     ̄ l   ̄ l  Γ l      dF        dF       ̄ l 0

Contract • Competition among banks ensures zero profits C titi b k fit for the banks. – Zero profit condition represents a ‘menu’ of f ‘ ’ f contracts, with different interest rates and loan amounts amounts. • Contract which trades in equilibrium is the C t t hi h t d i ilib i i th one entrepreneurs most prefer. ̄  s  , K   1 − Γ h  r h K   1 −   1 − Γ l  r l K max  ̄  s   f    d  .  ̄  s       h  Γ h −  G h  r h K −  K − N  R  G      f      Γ  G  r K  K N  R  0 0   l  Γ l −  G l  r l K −  K − N  R  ,

Characterizing Equilibrium Contract • First order condition for K ( K ‐ N is loan amount) amount)   1 − Γ h  r h   1 −   1 − Γ l  r l   h  Γ h −  G h  r h − R    l  Γ l −  G l  r l − R  ̄ h and  • First order condition for :  ̄ l  Γ ′ h  h  Γ ′ h −  G ′ h Γ ′ h G ′ h Γ ′ l   l   1 −   1 − Γ l   1   1 . Γ ′ l −  G ′ l

Equations Characterizing Contract: q g • Optimality:   1 − Γ h  r h   1 −   1 − Γ l  r l  1 −   1 − Γ ′ l  Γ ′ h −  G ′ h  Γ h −  G h  r h − R    1   1 Γ   Γ ′ h Γ ′ h  Γ l −  G l  r l − R   Γ ′ l −  G ′ l • Competition (i.e., zero profits)  Γ h −  G h  r h K   K − N  R  Γ l −  G l  r l K   K − N  R .  Γ  G  r K  K N  R .

Equilibrium • Three equations for loan contract (optimality and competition) and competition) • Resource constraints: c  K ≤ F  k , l  household consumption resources used in monitoring entrepreneur consumption    G   ̄ h  r h K   1 − Γ h  r h K ≤ F  K , l h  c h c l   G   ̄ l  r l K   1 − Γ l  r l K ≤ F  K , l l  • Household and firm first order conditions: h h l l U c  F l  k , l  , − U l h  K , l h  , − U l − U l h  F l l  F l l  K , l l  U c U c U h U l 1    U c U c   1 −   U c R , U c

Equilibrium Equilibrium • Ten equations in 10 unknowns: Ten equations in 10 unknowns: l , l h , l l , c , c h , c l , K ,  ̄ h ,  ̄ l , R

Incorporating BGG Financial Friction into a Monetary Model d l

V t  1  real earnings on capital (rent plus capital gains) t − nominal rate of interest t − 1 i l t f i t t real debt to banks t − 1  t e    1 −   W t  1 Net Worth t  1    V t  1  W t  1 e

Prediction of financial friction model: Prediction of financial friction model: • Shocks that drive output and price in the same Shocks that drive output and price in the same direction (‘demand’) accelerated by financial frictions. – Fisher and earnings effects reinforce each other. • Shocks that drive output and price in opposite directions (‘supply’) not much affected by ( pp y ) y financial frictions. – Fisher and earnings effects cancel each other.

Model with Financial Frictions Firms L K Labor Labor I market C Capital Entrepreneurs Producers Producers household

Model with Financial Frictions Firms Labor Labor market Capital K’ Entrepreneurs Producers Producers Loans banks household

The equations of the financial friction model d l • Net addition of two equations to consensus model: model: – Subtract the household intertemporal equation for capital. – Add three equations pertaining to the entrepreneurs Add three equations pertaining to the entrepreneurs

Three equations pertaining to entrepreneur • Law of motion of net worth a o ot o o et o t • Zero ‐ profit conditions of banks p revenues from non-bankrupt entrepreneurs  quantity of non-bankrupt entrepreneurs  receipts from bankrupt entrepreneurs net of bankruptcy costs  receipts from bankrupt entrepreneurs net of bankruptcy costs  payment obligations on bank debt to households • Optimality condition associated with entrepreneur’s choice of contract.

Empirical Analysis of Financial Friction Model d l • Christiano ‐ Motto ‐ Rostagno (2008), based on Ch i i (2008) b d Bernanke ‐ Gertler ‐ Gilchrist (1999) model of fi financial frictions. i l f i i