Incorporate Financial Frictions into a

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1 Incorporate Financial Frictions into a 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 aredifferent people, with conflicting interests Financial frictions: features of the relationship between borrowers and lenders adopted to mitigate conflict of interest.

2 Standard Model consumption Firms Investment goods Supply labor Rent capital Households Backyard capital accumulation: K t 1 1 K t G I t,i t 1 1 k r u c,t E t u t 1 c,t 1 1 P k,t 1 P k,t Savers and investors are the same: NO FRICTIONS!

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

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

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

6 Period 1 No uncertainty 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 an idiosyncratic productivity shock. Period 2 Aggregate uncertainty Entrepreneurs pay back loans from banks, which repay households.

7 Households Household preferences U c,l U c h,l h 1 U c l,l l. Budget constraints Euler equations: U l U c c B wl, c h w h l h RB, c l w l l l RB. w, U h l h U c 1 U c h U c w h, U l l l U c 1 U c l U c R, w l

8 Technology: Goods producing firms y F k,l 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 r F k k,l, r h F h k K,l h, r l F l k K,l l,

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

10 Idiosyncratic uncertainty After purchasing K, entrepreneurs experience idiosyncratic shock: K K, ~F, E 1. Standard debt contract h pay hr h K to bank h pay r h K to bank, bank pays r h K in monitoring costs

11 Standard Debt Contract, cnt d l pay lr l K to bank l pay r l K to bank, bank pays r l K in monitoring costs Parameters of Standard Debt Contract: h, l and K

12 Determination of Parameters of Standard ddebt Contract 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 Γ h Γ 0 df h df h df h df Γ l l df l df 0 l

13 Contract Competition among banks ensures zero profits for the banks. Zero profit condition represents a menu of contracts, with different interest rates and loan amounts. Contract twhich h trades in equilibrium i is the one entrepreneurs most prefer. max 1 s,k Γh r h K 1 1 Γ l r l K h Γ h G h r h K K N R l Γ l G l r l K K N R, s G s f d. 0

14 Characterizing Equilibrium Contract First order condition for K (K N is loan 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 First order condition for h and l : h Γ h Γ h G G h 1 1 Γ l l 1 1 Γ l Γ l G l.

15 Equations Characterizing Contract: Optimality: 1 Γ h r h 1 1 Γ l r l Γ h Γ h Γ h G h Γh G h r h R 1 1 Γ l Γ l G l Γ l G l r l R 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.

16 Equilibrium Three equations for loan contract (optimality and competition) Resource constraints: household consumption c h resources used in monitoring G h r h K entrepreneur consumption 1 Γ h r h K c K F k,l F K,l h c l G l r l K 1 Γ l r l K F K,l l Household and firm first order conditions: U l U c F l k,l, U l U h U c 1 U c h U c h F l h K,l h, U l U l 1 U c R, U c l U c l F l l K,l l

17 Equilibrium Ten equations in 10 unknowns: l,l h,l l,c,c h,c l,k, h, l,r

18 Incorporating BGG Financial Friction into a Monetary Model dl

19 V t 1 real earnings on capital (rent plus capital gains) t i l t f it t nominal rateof interest t 1 t real debt to banks t 1 e Net Worth t 1 V t 1 W t 1 e 1 W t 1

20 Prediction of financial friction model: 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 ) ppy not much affected by financial frictions. Fisher and earnings effects cancel each other.

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

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

23 The equations of the financial friction model dl Net addition of two equations to consensus model: Subtract the household intertemporal equation for capital. Addthreeequationspertaining equations to theentrepreneurs entrepreneurs

24 Three equations pertaining to entrepreneur Law of motion o of net worth ot Zero profit conditions of banks revenues from non-bankrupt entrepreneurs quantity of non-bankrupt entrepreneurs receipts from bankrupt entrepreneurs net of bankruptcy costs payment obligations on bank debt to households Optimality condition associated with entrepreneur s choice of contract.

25 Empirical Analysis of Financial Friction Model dl Christiano Motto Rostagno i (2008), based on Bernanke Gertler Gilchrist (1999) model of financial i fi frictions. i

26 Risk Shock and News Assume iid i i t i ti t t 1 t 1 iid, univariate innovation to t ut Agents have advance information i about pieces of u t u t t t 1... t 8 i t i i ~iid, E t i 2 2 i i t i ~piece of u t observed at time t i

27 Estimation EA and US data covering 1985Q1 2007Q2 Δ log N t 1 P t X t t log per capita hours t per capita credit t P t Δ log p p t Δ log per capita GDP t Δ log Wt P t Δ log per capita I t Δ log Δ log per capita M1t P t per capita M3t P t Δ log per capita consumption t Et ExternalFinance Premium t R t long R t e R t e Δ logp I,t Δ logreal oil price t, Δ log per capita Bank Reserves t P t Standard Bayesian methods We remove sample means from data and set steady state of X to zero in estimation.

28 Summary of Empirical Results With Risk shocks: Financial i Fiti Frictions important source of fluctuations. news on the risk shock important The Fisher debt deflation channel lhas a substantial impact on propagation. Money demand dand mechanism of producing inside id money: relatively unimportant as a source of shocks modest contribution to forecast ability Model accounts or substantial fraction of fluctuations in term structure. Out of Sample RMSEs of the model perform well compared with BVAR and simpler models.

29 Risk Shocks are Important Actual data versus what actual data would have been if there were only risk Shocks: Note: (1) as suggested by the picture, risk shocks are relatively important at the lower frequencies (2) We find that they are the single most important source of low frequency fluctuation in the EA, and a close second (after permanent tech shocks) in the US

30 Table: Variance Decomposition, HP filtered data, EA shock output consumption investment hours inflation labor productivity interest rate f x b Markup Banking tech Capital tech Money demand Government g Permanent tech z Gamma shock Temporary tech Monetary policy Risk, contemp policy Signals on risk ik signal Risk and signals Discount rate Marginal eff of I and signal c i Price of oil oil Long rate error long measurement error inflation target all shocks x

31 Table: Variance Decomposition, HP filtered data, EA shock output consumption investment hours inflation labor productivity interest rate f x b g z policy and signal c i oil long measurement error inflation target all shocks It s the signal signals! x

32 Markup Banking tech Capital tech Money demand Government Permanent tech Table: Variance Decomposition, HP filtered data, EA x shock stock market credit spread term structure real M1 real M3 f x b g z Gamma shock Temporary tech Monetary policy policy Risk, contemp Signals on risk Risk and signals Discount rate signal and signal c Marginal eff of I i Price of oil oil Error in long rate long measurement error inflation target all shocks

33 Markup Banking tech Capital tech Money demand Government Permanent tech Table: Variance Decomposition, HP filtered data, EA x shock stock market credit spread term structure real M1 real M3 f x b g z Gamma shock Temporary tech Monetary policy policy Risk, contemp Signals on risk Risk and signals Discount rate signal and signal c Marginal eff of I i Price of oil oil Error in long rate Signal matters! long measurement error inflation target all shocks

34 Importance of Risk Signals News Specification on Risk and Marginal Likelihood (EA data) p t 1 t 1 t 0 t 1 t 2... t p p log, marginal likelihood odds ( exp(difference in log likelihood from baseline)) 8 (baseline)

35 Why is Risk Shock so Important? According to the model, external finance premium is primarily risk shock. To look kfor evidence that risk ikmight ihbe important, look at dynamics of external finance premium and gdp. E lfi i i i l di External finance premium is a negative leading indicator

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37 Why is Risk Shock so Important?: A second reason Our data set includes the stock market Output, stock market, investment allprocyclical (surge together in late 1990s) This is predicted by risk shock.

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40 Impact of Financial Frictions on Propagation Effects of monetary shocks on gdp amplified by BGG financial frictions because P and Y go in same direction. Effects of technology shocks on gdp mitigated by BGG financial i frictions fiti because P and Y go in opposite directions.

41 Baseline model with no Fisher Effect Baseline model Blue line: baseline model with no financial frictions

42 Out of Sample RMSEs There is not a loss of forecasting power with the additional complications of the model. The model does well on everything, except the risk ikpremium.

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44 Models with Financial Frictions Can be Used to Address Important Policy Questions When there is an increase in risk spreads, how should monetary policy respond? How should monetary policy react to credit variables and the stock market? Does monetary policy cause excess asset price volatility? Taylor: deviations from Taylor rule may cause asset price volatility Christiano Ilut Motto Rostagno: Taylor rule may cause asset price volatility

45 How Should Policy Respond to the Risk Spread? Taylor s recommendation: R t e t y t Risky rate t Risk free rate t 1 Evaluate this proposal by comparing performance of economy with 1 and against Ramsey optimal benchmark. 0

46 Get a recession, just like in earlier graph

47 Taylor suggestion creates a boom Is it too much?

48 Taylor s suggestion overstimulates

49 Conclusion of Empirical Analysis with Financial i Fi Frictionsi Incorporating financial frictions changes inference about the sources of shocks and of propagation p risk shock. Fisher debt deflation Opens a range of interesting questions that can be addressed