Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Financial Frictions in DSGE Models Jiˇr´ı Polansk´y Brno, Faculty of Science November 8, 2011 Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Outline of the Talk 1 Brief Introduction to DSGE Models 2 Monetary Transmission Channels 3 Financial Frictions Modeling 4 Financial Accelerator Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator 1 Brief Introduction to DSGE Models 2 Monetary Transmission Channels 3 Financial Frictions Modeling 4 Financial Accelerator Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Brief Introduction to DSGE Models (i) DSGE models are powerful tools for macroeconomic analysis and practical forecasting. They eliminate logical inconsistencies (as other models). They are useful for explaining the behavior of an economy (initial conditions, forecasting). But they cannot anticipate shocks (ex-post forecasting errors). DSGE models have several advantages: Derivation from optimization problems (w.r.t. older Keynesian models). Based on economic theory (w.r.t. non-structural models like VARs). More-detailed story (w.r.t. gap models). Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Brief Introduction to DSGE Models (ii) Dynamic stochastic general equilibrium models. GE theory: describes the behavior of the whole economy (interaction of many markets - demands, supplies, prices, policies etc.) Stochastic: the model economy is hit by various shocks. Dynamic: the model shows the interactions among markets and variables over time. DSGE models are widely used today. Tools for macro research (laboratories). Tools for policymakers to conduct their policies. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Brief Introduction to DSGE Models (iii) Models derived from micro principles. Optimizations of various agents on basis of their tastes, preferences, production capacities etc. ⇒ Parameters of these models are structural (supported from economic theory). Non-structural models exploit reduced-form correlations in observed data (VAR, Box-Jenkins etc.). Model-consistent forward-looking rational expectations. But: some critics today for ”ideal rational world” (no learning, herding behavior, asymmetric information etc.). Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Building Blocks of DSGE Models Many agents (sectors) in the economy. Households, firms, central bank, government, bundlers etc. Private agents solve optimization problems. Households are maximizing utility. Firms are maximizing profits or minimizing costs. Policy agents are not optimizing ... (e.g. a ”prescribed” monetary policy rule). But sometimes optimal policy rules. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Features of Modern DSGE Models Apart from RBC features... Intertemporal optimization, rational expectations, ”tastes and technologies”. ...these models contain some features to fit the data. Real rigidities (habit formation, capital adjustment costs, imperfect substitutions between inputs etc.). Monopolistic competition, markups. Nominal rigidities. Features for country-specific data. Core models of central banks should be tailor-made. Sector-specific features (technologies). Credible monetary policy is important for the real activity. MP matters because of price and wage stickiness. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Some Current Issues of DSGE Models Financial frictions Models for monetary policy and financial stability. Fiscal policy Unemployment etc. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator 1 Brief Introduction to DSGE Models 2 Monetary Transmission Channels 3 Financial Frictions Modeling 4 Financial Accelerator Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Monetary Transmission Channels How MP instruments affect the real economic activity. Policy rate setting affects ⇒ short-term nominal rates and inflation expectations. ⇒ short-term real rates (prices are sticky in short-run) and lending rates (long-term and client rates). Usually two groups: Traditional (focused by majority of DSGE models). Asset price channels (focused by models with financial frictions). Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Traditional Channels (i) Real interest rate channel Nominal rigidities ⇒ nominal interest rate changes imply real interest rate changes ↓ real interest rate → ↑ investment Works also with nominal interest rate near the zero floor (money expansion raises expected inflation). Nominal interest rate channel Effects due to credit-debt structure of an economy. ↑ nominal interest rate → worsening the cash-flow of indebted agents. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Traditional Channels (ii) Exchange rate channels 1 Direct channel via import prices Depreciation → ↑ import prices → ↑ CPI. 2 Indirect channel via terms of trade Depreciation → ↓ relative price of domestic goods → ↑ net export. 3 Balance of payments Depreciation → worsening a financial position of net foreign liabilities holders (higher payments in domestic currency). Inflation expectations channel Public declaration of inflation target anchors inflation expectations → price- and wage-setting. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Asset Prices Channels Work through wealth effects, balance sheets positions, bank lending etc. Captured by financial frictions models. Asset prices determine the value against agents can borrow. Net worth (financial accelerator approach). Value of collateral (collateral constraints approach). Two main groups Balance sheets channels. Lending channels. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Balance Sheets Channels Net worth is one of banks’ indicators for extending loans. MP expansion → ↑ equity prices → ↑ firms’ net worth → ↑ bank loans. ↓ interest rate → bonds are less attractive relative to equities → ↑ equity prices. Monetary expansion → people have more money than demanded → ↑ equity purchases → ↑ equity prices. Unanticipated price level movements affect financial position of indebted agents. ↑ price level → ↓ value of firms’ liabilities in real terms → ↓ debt burden → ↑ net worth. Also for households’ expenditures ↑ asset prices → ↑ net worth → ↑ consumption. Also, higher housing value increases construction. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Bank Lending Channel Bank credit is important source of firms’ funding. Bank lending depend on net worth of borrowers. Banks monitor the financial situation of borrowers. Loans can be collateralized by net worth. ↑ policy rates → ↑ interbank and lending rates → ↓ volume of credit. Lending channel crucial for smaller firms as large firms have usually access to funding from stock and bond markets. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator 1 Brief Introduction to DSGE Models 2 Monetary Transmission Channels 3 Financial Frictions Modeling 4 Financial Accelerator Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Objectives of Financial Frictions Modeling Understanding interactions between real and financial sectors. Implementation for policy purposes. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Understanding Interactions between Real and Financial Sectors ”The deteriorating of credit market conditions is not simply a passive reflection of a declining real economy but is itself a major factor depressing the economic activity.” (Bernanke et al., 1999). Assessing the role of asset prices transmission channels. Amplification (acceleration) effects of shocks during financial crises. ”New types” of shocks during financial crises - riskiness, bubbles etc. Different behavior during financial crises - non-linearities due to significant shocks. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Implementation for Policy Purposes Satellite models vs. core models. Simulations for monetary policy and financial stability purposes (sensitivity scenarios, forecasting). Implementation into core models for countries where asset prices matter continually (e.g. New Zealand). During financial crises, the policymaking process is more complex and a central bank should ”have” appropriate tools for evaluating the current state of an economy and forecasting. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Approaches of Financial Frictions Modeling (i) Financial frictions modeling is not a new issue. Papers before the mid-2008-2009 crisis. After the crisis, the interest has intensified and turned to more practical questions. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Approaches of Financial Frictions Modeling (ii) 1 Financial accelerator (e.g. Bernanke et al., 1999). Costly state verification and default risk. 2 Collateral constraints (e.g. Kiyotaki and Moore, 1999; Iacoviello, 2005). Limited contracts enforcement and collateralized debt. 3 Banking sector modeling (e.g. Edwards and V´egh, 1997). Banking services as costly activities. (1),(2) - focus on ”essence” of asset prices channels (costly state verification, limited contracts enforcement) (3) - rather stylized description of stylized facts Some models combine assumptions → (probably) sometimes to large to control (black boxes) Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Incorporating Financial Frictions (i) Standard DSGE models Complete financial markets with perfect information for all agents. ⇒ Risk-averse representative household which trades only government (risk-free) bonds to smooth consumption. ⇒ No borrowing/lending among agents. ⇒ One interest rate (for risk-free bonds). Modigliani-Miller theorem holds The market value of a firm is independent of its capital structure and is given by capitalizing its expected return. The real economic activity is independent of the financial structure and it does not matter how a firm is financed. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Incorporating Financial Frictions (ii) Information asymmetries in financial markets. Motivates incorporation of financial frictions. Affect the behavior between borrowers and lenders. ⇒ Interactions between real and financial sectors matter as the Modigliani-Miller theorem does not hold. E.g. entrepreneurs have better knowledge about their projects than lenders. ⇒ Investors prefer projects where entrepreneurs are engaged in or provide sufficient collateral. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Incorporating Financial Frictions (iii) The introduction of borrowing/lending. Requires heterogenous agents with different preferences (FA and CC approaches). Costly banking assumption Financial accelerator Risk-averse households. Risk-neutral entrepreneurs (linear utility in consumption). Collateral constraints Patient households. Impatient households - (i) different value of the discount parameter and (ii) liquidity constrained. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Financial Accelerator BGG - (Bernanke, Gertler and Gilchrist 1999). Currently the most used approach. Focus on balance sheets effects. How an endogenous development in balance sheet positions of borrowers can significantly amplify (accelerate) shocks. Model for understanding the role of credit market frictions within business cycles. Accelerator can transform small shocks into significant fluctuations in real economic activity. Friction is placed on a non-financial side of the economy (entrepreneurs). Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Financial Accelerator - Mechanism Link between net worth of entrepreneurs and the external finance premium (EFP). EFP - the difference between external and internal costs of funds (alternatively, additional costs above a risk-free interest rate). EFP depends inversely on the borrowers’ net worth. Net worth of borrowers is procyclical (profits, asset prices etc.) ⇒ EFP varies endogenously and countercyclically within business cycles. E.g. if a shock lowers net worth ⇒ EFP will increase ⇒ lower internal funding (lower profits) and lower demand for external funding (higher EFP). Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Financial Accelerator - Sectors Risk-averse households. Risk-neutral entrepreneurs. Purchase capital from capital good producers at the beginning of t, rent it to firms, and sell it back at the end of t. Entrepreneurs’ net worth is not sufficient. ⇒ They must combine their net worth with bank lending. They cannot accumulate enough equity for internal financing. Capital goods producers. To simplify the model (households and entrepreneurs cannot store the capital). Bank (financial intermediary). Transfers deposits from households to entrepreneurs. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Financial Accelerator - Debt Contracts The costly state verification (CSV) assumption. Information asymmetry between borrowers and lenders. Entrepreneurs observe the realized return on capital costlessly. Bank must pay fixed monitoring costs to observe entrepreneurs’ returns. Given the possibility of default and monitoring costs, lenders charge the external finance premium over the riskless rate. EFP is increasing with the leverage ratio of entrepreneurs (debt to net worth). ⇒ Optimal (not collateralized) contracts where The positive EFP (and monitoring costs) limits tho borrowing. The bank receives the expected return which is equal to the opportunity cost of its funds (the riskless rate). Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Collateral Constraints Similar approach to the financial accelerator. Based on the limited contract enforcement assumption. Repayment is secured by restricting the amount of loans to borrowers’ collateral. Lender requires a collateral when extending a loan (a bank expects possible problems of repayments when entrepreneurs declare default and secures the loan). Lender does not need to care about the borrower’s willingness to pay since the loan is secured by debtor’s assets (lower moral hazard). ⇒ Some durable assets serve as (i) production factors and (ii) collateral for loans (capital, housing, land). Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Collateral Constraints - Mechanism (i) Supply of durable assets is limited ⇒ Variation of asset prices. ⇒ Investment expenditures are sensitive to the net worth of credit-constrained agents. The interaction between credit limits and assets prices. ⇒ Amplification of shocks. ⇒ Shocks are more persistent. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Collateral Constraints - Mechanism (ii) Acceleration for demand shocks (implying higher consumer and asset prices) Higher consumer prices → ↓ real value of debt obligations → ↑ net worth of indebted agents. Higher asset prices → ↑ possible collateral of credit-constrained agents (higher borrowing capacity). Higher consumption and investment further increase the borrowing capacity. ⇒ Given assumption that borrowers have higher propensity to spend than lenders, the demand shock amplifies responses of real variables relatively to the frictionless case. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Collateral Constraints - Mechanism (iii) Decelerator mechanism for supply shocks (shocks with negative correlation between output and inflation) A negative supply shock increases debtors’ net worth (for debt obligations in nominal terms). MP shock (higher interest rate) Standard real interest rate channel. Decrease of assets prices which leads to lower borrowing. Moreover, a deflation raises the cost of debt service. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Collateral Constraints - Sectors Patient households. Credit-constrained sectors. Impatient households. Lower discount parameter - they discount the future more heavily (with higher discount rate). (The more heavily discounting means that they demand higher returns from their investment to save instead of consuming today.) Net borrowers. Entrepreneurs - similar assumptions as impatient households. Note that credit-constrained agents are more productive comparing to unconstrained agents as they do not hold optimal level of assets for production purposes. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator FA and CC Models - Similarities Both stress the balance sheet channel. Mechanisms through the net worth and asset prices. No explicit need for the financial intermediary. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator FA and CC Models - Differences CC models assume the limited availability of funds: Loans must be collateralized by the net worth of debtors. FA models assume increasing EFP with no explicit upper bound. CC models assumes constant EFP (lending rate moves identically with the riskless rate). CC borrowers do not face idiosyncratic risks (no default). FA - the borrowers’ net wealth is influenced by current (and past) conditions. CC - the value of collateral also reflects expected future values via varying asset prices. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Banking Sector Modeling Banking sector does not have an important role in canonical financial accelerator and collateral constraints models. Frictions are on households’ or non-financial firms’ side. Bank transfers funds from depositors to lenders. Several approaches for the incorporation of the banking sector into DSGE models. Perfectly competitive banking sector. Monopolistic banking sector. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Costly Banking (i) The perfectly competitive representative bank collects deposits from households and extends loans to borrowers. Banking services must be costly activities for achieving non-trivial role in the model. In a model: A bank must use resources to produce deposits and loans. In reality: Managing assets and liabilities, monitoring creditors, maintaining building etc. The costs of banking services are increasing functions of volume of provided services. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Costly Banking (ii) The bank’s optimization problem results in first order conditions of the form RD t = Rt − fD(·) and RL t = Rt + fL(·). RL ≥ R as bank can always lend to the rest of the world at R. RD ≤ R as bank can always borrow from the rest of the world. Costless banking ⇒ Both functions are zero (zero costs and zero profits by perfect competition). Costly banking ⇒ Marginal costs of taking deposits and extending loans are positive ⇒ Time-varying deposit and lending spreads. Procyclical lending spread (higher demand for loans during booms). Costly banking stabilizes an economy (higher costs during booms which lowers the lending). Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Uncertainties of Financial Frictions (i) Financial sector and frictions cover a wide variety of mechanisms. Several frictions in a single model ⇒ hardly feasible and probably black box. Different initial assumptions of frictions. ⇒ Usually focus on a single friction (accelerator on firms, constraints on households etc.). No workhorse model. Various approaches (based on various assumptions) with different effects of FF for the real economic activity. Moreover, combinations of frictions imply strengthening or weakening of the former effects (e.g. adding banking sector into a FA model can stabilizes accelerator’s effects). Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Uncertainties of Financial Frictions (ii) Financial crises have serious consequences for the real economic activity. Their frequency is rare. Crises might have different behavior and effects. ⇒ Calibration uncertainties, regular using of the model more uncertain. Unavailability of some time series and seeking proxy variables. E.g. different housing indices with different correlation with business cycles. Short series for the Czech economy (lending rates etc). Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator 1 Brief Introduction to DSGE Models 2 Monetary Transmission Channels 3 Financial Frictions Modeling 4 Financial Accelerator Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator State Contingent Contracts (Bernanke et al., 1999) Risk-neutral entrepreneurs and risk-averse banks Banks run zero profits and simply transfer funds from households to entrepreneurs. Lending rates are adjusting ex post in response to aggregate shocks to compensate for the defaulted entrepreneurs and the monitoring costs. ⇒ different lending rates RL t+1 for each the next-period possible future aggregate return on capital RK t+1. The bank always receives RtLt in the t + 1 whatever RK t+1. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator State Non-Contingent Contracts (Beneˇs-Kumhof, 2011). Risk-neutral entrepreneurs and risk-neutral banks (banks also bear the risk of the contracts). Lending rate fixed ex ante. Banks run profits or looses. Bank capital needed. Or assumption that households receive profits and compensate for looses. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Entrepreneurs - Timing at t Entrepreneurs (who survived from t − 1) purchase physical capital combining internal funds (net worth) and external funds (borrowing). The amount of loans is chosen Lt = PK t Kt − Et Banks intermediate funds from households to entrepreneurs. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Entrepreneurs - Timing at t + 1 (i) The aggregate return on capital RK t+1 is observed which determines the application of an appropriate lending rate RL t+1. Each entrepreneur observes his own return on capital ωRK t+1PK t Kt affected by idiosyncratic productivity ω. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Entrepreneurs - Timing at t + 1 (ii) There is a cutoff productivity level which divides entrepreneurs into defaulting and surviving. Defaulting entrepreneurs with insufficient return: ωRK t+1PK t Kt < RL t+1Lt ⇒ ¯ω ≡ RL t+1Lt RK t+1PK t Kt Surviving entrepreneurs with sufficient return: Repay the loan to the financial intermediary and keep the difference as their net worth. Banks receive payments From defaulting: The bank pays the monitoring costs and receives (1 − µ)ωRK t+1PK t Kt. The entrepreneur receives nothing. From surviving: The bank receives RL t+1Lt = ¯ωRK t+1PK t Kt. Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Entrepreneurs - Aggregate Return on Capital (i) The aggregate return on capital is RK t+1PK t Kt ∞ 0 ωf(ω)dω where E(ω) ≡ ∞ 0 ωf(ω)dω = 1 Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Entrepreneurs - Aggregate Return on Capital (ii) The return of defaulting entrepreneurs RK t+1PK t Kt ¯ω 0 ωf(ω)dω = µRK t+1PK t Kt ¯ω 0 ωf(ω)dω Private loss in the model + (1 − µ)RK t+1PK t Kt ¯ω 0 ωf(ω)dω bank’s payoff The return of surviving entrepreneurs RK t+1PK t Kt ∞ ¯ω ωf(ω)dω = ¯ωRK t+1PK t Kt ∞ ¯ω f(ω)dω bank’s payoff + RK t+1PK t Kt ∞ ¯ω ωf(ω)dω − ¯ω ∞ ¯ω f(ω)dω entrepreneur’s payoff Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Entrepreneurs - Profit Maximization (i) The expected profit of entrepreneur is maximized max Kt,RL t+1 ERK t+1      RK t+1PK t Kt ag. return on K − RL t+1Lt ∞ ¯ω f(ω)dω payment from surv. to B − RK t+1PK t Kt ¯ω 0 ωf(ω)dω loss from def.      s.t. a continuum of banks’ constraints for each RK t+1 RL t+1Lt ∞ ¯ω f(ω)dω from surviving entr. + (1 − µ)RK t+1PK t Kt ¯ω 0 ωf(ω)dω from defaulting entr. less monitoring = RtLt where Lt = PK t Kt − Et and ¯ω ≡ RL t+1Lt RK t+1PK t Kt Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Entrepreneurs - Profit Maximization (ii) After substitution max Kt,¯ωt ERK t+1 RK t+1PK t Kt(1 − Γ(¯ω)) s.t. RK t+1PK t Kt[Γ(¯ω) − µG(¯ω)] = Rt(PK t Kt − Et) where the expected gross share of profits going to the lender is Γ(¯ω) ≡ ¯ω 0 ωf(ω)dω + ¯ω ∞ ¯ω f(ω)dω and the expected monitoring costs µG(¯ω) ≡ µ ¯ω 0 ωf(ω)dω Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Data (i) - Non-Performing Loans I/04 I/05 I/06 I/07 I/08 I/09 I/10 I/11 3 4 5 6 7 8 9 10 Uvery v selhani (podil na celku,nonfin) Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Data (ii) - Interest Rates I/04 I/05 I/06 I/07 I/08 I/09 I/10 I/11 0 2 4 6 8 10 12 14 16 RL − households RL − nonfin PRIBOR 3M Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Data (iii) - Spreads I/04 I/05 I/06 I/07 I/08 I/09 I/10 I/11 0 2 4 6 8 10 12 14 RL − households − R RL − nonfin − R Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Shocks in the Model Standard shocks. Specific shocks (fin.crises, bubbles, significant cycles). Focus on ”true exogenous” shocks (e.g. no direct shock to lending rate but shock which increases the lending rate). One of model’s objectives. E.g. higher riskiness during crises (temporarily increased standard deviation of the log-normal distribution of the idiosyncratic shock → high number of defaulting entrepreneurs). Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator MP Shock 0 5 10 15 20 −0.2 −0.1 0 HDP 0 5 10 15 20 −0.2 −0.1 0 Investice 0 5 10 15 20 −0.2 0 0.2 Inflace QoQ p.a. 0 5 10 15 20 −0.2 0 0.2 Mzdová inflace QoQ p.a. 0 5 10 15 20 −1 0 1 Domácí úroková sazba 0 5 10 15 20 −0.2 0 0.2 Úvìry 0 5 10 15 20 −2 −1 0 Vlastní jmìní 0 5 10 15 20 0 0.1 0.2 Rozpìtí Rl/R SC SNC MP šok Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Sigma Shock (i) 0 0.5 1 1.5 2 2.5 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 sigma = 0.25 sigma = 0.5 Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Sigma Shock (ii) 0 5 10 15 20 −0.4 −0.2 0 Investice 0 5 10 15 20 −4 −2 0 x 10 −3 Inflace QoQ p.a. 0 5 10 15 20 −0.02 −0.01 0 Domácí úroková sazba 0 5 10 15 20 −1 −0.5 0 Úvìry 0 5 10 15 20 −5 0 5 Vlastní jmìní 0 5 10 15 20 −5 0 5 Rozpìtí (ex post) Rl/R 0 5 10 15 20 −5 0 5 Finanèní páka (úvìry / vlastní jmìní) 0 5 10 15 20 −5 0 5 Prahová hodnota idios. šoku SC SNC sigma shock Brno, Faculty of Science Financial Frictions in DSGE Models Brief Introduction to DSGE Models Monetary Transmission Channels Financial Frictions Modeling Financial Accelerator Thank you for your attention Jiri.Polansky@cnb.cz Brno, Faculty of Science Financial Frictions in DSGE Models