Risky Mortgages in a DSGE Model Chiara Forlati 1 Luisa Lambertini 1 1 EPFL The Future of Monetary Policy, EIEF September 30, 2010 1 / 33
Motivation • The global financial crisis started with an increase in U.S. mortgage delinquencies Graph • Banks wrote down several hundred billion dollars in bad loans • Liquidity crisis brought several financial institutions into or on the brink of bankruptcy • Credit crunch and the Great Recession 2 / 33
Motivation • The global financial crisis started with an increase in U.S. mortgage delinquencies Graph • Banks wrote down several hundred billion dollars in bad loans • Liquidity crisis brought several financial institutions into or on the brink of bankruptcy • Credit crunch and the Great Recession 2 / 33
U.S. Seriously Delinquent Mortgages 10 8 6 4 2 0 1980 1985 1990 1995 2000 2005 2010 Percentage of total loans; Not seasonally adjusted Back Source: Mortgage Bankers Association, National Delinquency Survey 3 / 33
U.S. Seriously Delinquent Mortgages 10 8 6 4 2 0 1980 1985 1990 1995 2000 2005 2010 Percentage of total loans; Not seasonally adjusted Back Source: Mortgage Bankers Association, National Delinquency Survey 3 / 33
This Paper • Focuses on an increase in mortgage delinquencies and its transmission to the rest of the economy • Introduces endogenous default on mortgages in a DSGE model with housing • Analyzes an unanticipated increase in mortgage risk • Compares economies with different leverage ratios • Compares different degrees of interest rate inertia in monetary policy 4 / 33
Results 1. An increase in mortgage risk ◮ raises mortgage default and the mortgage premium ◮ produces a credit crunch that generates a recession 2. Economies with lower mortgage risk have higher leverage ratios 3. High leverage ratios amplify the effects of a mortgage risk shock 4. Inertial monetary policies amplify the effects of a mortgage risk shock (zero lower bound scenario) 5 / 33
Literature • Housing Sector : Iacoviello (2005), Iacoviello and Neri (2009), Calza, Monacelli and Stracca (2009), Aoki, Proudman and Vlieghe (2004) • Durable Consumption Goods : Barsky, House and Kimball (2007), Erceg and Levin (2006), Carlstrom and Fuerst (2006), Monacelli (2009) • Financial Accelerator : Bernanke and Gertler (1989), Carlstrom and Fuerst (1997), Bernanke, Gertler and Gilchrist (1999) • Risk, Default and Repayment Shocks : Christiano, Motto and Rostagno (2009), Cohen-Cole and Martinez-Garcia (2008), Iacoviello (2010), Dellas, Diba and Loisel (2010) 6 / 33
The Model Households Fraction ψ of impatient (Borrowers) and 1 − ψ of patient (Savers) households • Consume a non-durable good, C t • Consume services from and accumulate houses, H t + 1 • Supply two types of labor, N C , t and N H , t • Savers make loans to Borrowers, L t + 1 7 / 33
Borrowers ∞ � � � �� β t E 0 max U X t , N C , t , N H , t , 0 < β < 1 C t , H t + 1 , N C , t , N H , t , L t + 1 , ¯ ω t + 1 t = 0 where � � η η − 1 , η ≥ 0 , η − 1 η − 1 1 1 η C t η H t + 1 X t ≡ ( 1 − α ) + α η η subject to three constraints: Budget constraint (nominal terms) P C , t C t + P H , t H t + 1 + [ 1 − F (¯ ω t )]( 1 + R Z , t ) L t = L t + 1 + W C , t N C , t + W H , t N H , t + ( 1 − δ ) [ 1 − G (¯ ω t )] P H , t H t , Participation constraint Incentive-compatibility constraint 8 / 33
Mortgage Risk • Each household consists of many members • The household decides total housing investment H t + 1 • The i -th member receives H i t + 1 and finalizes the mortgage contract according to household instructions • Idiosyncratic shock ω i t + 1 (observable by the member only) such that the ex-post housing stock is ω i t + 1 H i t + 1 (or ex-post housing value is ω i t + 1 p H , t + 1 H i t + 1 ) • E t ( ω i t + 1 H i t + 1 ) = H t + 1 , i.e. there is no aggregate mortgage risk • For ω i t + 1 ∈ [ 0 , ¯ ω t + 1 ) loans are defaulted; for ω i t + 1 ∈ [¯ ω t + 1 , ∞ ] loans are repaid • Lenders pay the cost µ to monitor defaulting borrowers and seize the collateral • Perfect insurance among household members 9 / 33
The Mortgage Contract Participation constraint of lenders � ¯ ω t + 1 ( 1 + R L , t ) L t + 1 = ω t + 1 ( 1 − µ )( 1 − δ ) P H , t + 1 H t + 1 f ( ω ) d ω + 0 � ∞ ( 1 + R Z , t + 1 ) L t + 1 f ( ω ) d ω ω t + 1 ¯ Incentive-compatibility constraint ¯ ω t + 1 ( 1 − δ ) P H , t + 1 H t + 1 = ( 1 + R Z , t + 1 ) L t + 1 R L , t is the pre-determined and non-state-contingent rate of return on total loans R Z , t + 1 is the adjustable and state-contingent mortgage rate ω t + 1 is the threshold value of the idiosyncratic shock ¯ 10 / 33
Savers � � ∞ � γ t E 0 U ( � X t , � N C , t , � max N H , t ) , 0 < β < γ < 1 C t , � � H t + 1 , � N C , t , � N H , t � L t + 1 t = 0 subject to P C , t � C t + P H , t � H t + 1 + � L t + 1 = ( 1 + R L , t − 1 ) � L t + W C , t � N C , t + W H , t � N H , t ∆ t + ( 1 − δ ) P H , t � + � H t where � ∆ t are profits from firms 11 / 33
Intermediate Goods Producers • Each sector has monopolistically competitive intermediate goods producers • Continuum of differentiated goods i ∈ [ 0 , 1 ] • Firm i produces according to � � ς ς − 1 , 0 < ζ < 1 , ς > 0 1 ς − 1 1 ς − 1 ς � ς N j , t ( i ) Y j , t ( i ) = A j , t ζ + ( 1 − ζ ) N j , t ( i ) ς ς • Calvo price setting 12 / 33
Final Goods Producers • Each sector has perfectly competitive final goods producers • Flexible prices and CRS technology �� 1 � ε j ε j − 1 ε j − 1 ε j di Y j , t = Y j , t ( i ) , ε j > 1 , j = C , H 0 13 / 33
Monetary Policy Monetary policy rule: � 1 − φ r � 1 + R L , t − 1 � φ r � 1 + R L , t π φ π = A M , t φ π > 1 , φ r < 1 , C , t 1 + R L 1 + R L • Interest rate smoothing • Monetary policy targets inflation in the non-durable sector 14 / 33
Functional Forms Utility function: � � 1 + ϕ ν 1 + ξ , N 1 + ξ C , t + N 1 + ξ U ( X t , N C , t , N H , t ) ≡ ln X t − ϕ, ξ ≥ 0 H , t 1 + ϕ Leverage Ratio: l l + w C N c + w H N H Total output: Y t = Y C , t + p h , t Y H , t 15 / 33
Exogenous Shocks ln A C , t = ρ C ln A C , t − 1 + ǫ C , t ln A H , t = ρ H ln A H , t − 1 + ǫ H , t ln A M , t = ρ M ln A M , t − 1 + ǫ M , t Idiosyncratic risk in the housing sector: σ 2 ω, t 2 , σ 2 ln ω t ∼ N ( − ω, t ) Mortgage risk shock: ln σ ω, t = ρ σ ln σ ω, t − 1 + ǫ σ ω, t σ ω σ ω 16 / 33
Benchmark Calibration Parameter Value Description γ 0.99 Discount factor of Savers β 0.98 Discount factor of Borrowers ψ 0.5 Relative size of Borrower group δ 0.01 Rate of depreciation for housing ε C 7.5 Elasticity of substitution for C goods ε H 7.5 Elasticity of substitution for H goods 3 Elasticity of substitution across labor inputs ς ζ 0.5 Share of Borrower labor in the production function 0.871 Elasticity of substitution across labor types ξ α 0.16 Share of housing in consumption bundle 2.5 Disutility from work ν η 1 Elasticity of substitution between C and H goods ϕ 1 Inverse of elasticity of labor supply θ C 0.67 Calvo probability in C θ H 0 Calvo probability in H φ π 1.5 Taylor-rule coefficient on inflation φ r 0.9 Taylor-rule coefficient on past nominal interest rate ρ C 0.9 Serial correlation of productivity shocks in C ρ H 0.9 Serial correlation of productivity shocks in H ρ M 0 Serial correlation of monetary policy shocks σ ω 0.20 Standard deviation of idiosyncratic shocks 0.12 Monitoring cost µ 17 / 33
Low-Leverage Calibration: σ ω = 0 . 6 Steady State Values Variable Benchmark Low Leverage % Difference Output C 0.5407 0.5399 0.15 Output H 0.1465 0.1419 3.24 Consumption, Borrowers 0.4789 0.4887 -2.01 Consumption, Savers 0.6026 0.5912 1.93 Housing Demand, Borrowers 11.5421 10.5337 9.57 Housing Demand, Savers 17.7524 17.8431 -0.51 Hours Worked, Borrowers in C Sector 0.5879 0.5789 1.55 Hours Worked, Borrowers in H Sector 0.1617 0.1549 4.41 Hours Worked, Savers in C Sector 0.4948 0.5019 -1.41 Hours Worked, Savers in H Sector 0.1361 0.1343 1.37 Loans 2.1747 0.7980 172.54 Loan-to-Value Ratio * 59.17 24.37 142.80 Leverage Ratio * 80.12 60.01 33.51 Default Rate on Mortgages † 2.36 8.21 -71.22 External Finance Premium † 0.41 2.44 -83.20 Mortgage Interest Rate † 4.51 6.54 -31.04 * Percentage points. † Annual, percentage points. 18 / 33
Credit Crunch 2.5 σ ω =0.2 σ ω =0.28 2 Probability Distribution 1.5 1 0.5 0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 ω Mortgage Risk shock: increase in σ ω, t , the standard deviation of the distribution of idiosyncratic housing investment risk 19 / 33
Responses to a 40% Increase in σ ω, t : Benchmark Calibration Aggr Consumption Output Output H 0 0 -0.5 -0.2 -0.2 -1 -0.4 -0.4 -1.5 -0.6 -0.6 -2 -0.8 -2.5 -0.8 -1 -3 -1 -1.2 -3.5 5 10 15 5 10 15 5 10 15 Rel Price H Default Rate Loans 0.4 10 -10 0.3 9 8 0.2 -20 7 0.1 -30 6 0 5 -40 4 -0.1 -50 3 -0.2 2 5 10 15 5 10 15 5 10 15 Note: Default rate is annual and in percentage points. Loans are difference from steady state, multiplied by 100. All other variables are percentage point deviation from steady state 20 / 33
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