Risky Mortgages in a DSGE Model

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1 1 / 29 Risky Mortgages in a DSGE Model Chiara Forlati 1 Luisa Lambertini 1 1 École Polytechnique Fédérale de Lausanne CMSG November 6, 21

2 2 / 29 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

3 2 / 29 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

4 U.S. Seriously Delinquent Mortgages I Percentage of total loans; Not seasonally adjusted 198-I 1981-I 1982-I 1983-I 1984-I 1985-I 1986-I 1987-I 1988-I 1989-I 199-I 1991-I 1992-I 1993-I 1994-I 1995-I 1996-I 1997-I 1998-I Source: Mortgage Bankers Association, National Delinquency Survey Back 1999-I 2-I 21-I 22-I 23-I 24-I 25-I 26-I 27-I 28-I 29-I 3 / 29

5 U.S. Seriously Delinquent Mortgages I Percentage of total loans; Not seasonally adjusted 198-I 1981-I 1982-I 1983-I 1984-I 1985-I 1986-I 1987-I 1988-I 1989-I 199-I 1991-I 1992-I 1993-I 1994-I 1995-I 1996-I 1997-I 1998-I Source: Mortgage Bankers Association, National Delinquency Survey Back 1999-I 2-I 21-I 22-I 23-I 24-I 25-I 26-I 27-I 28-I 29-I 3 / 29

6 4 / 29 This Paper Introduces endogenous default on mortgages in a DSGE model with housing Analyzes an unanticipated increase in mortgage risk Focuses on an increase in mortgage delinquencies and its transmission to the rest of the economy Compares economies with different leverage ratios Compares different degrees of interest rate inertia in monetary policy

7 5 / 29 Results 1. An increase in mortgage risk raises mortgage default and the mortgage premium produces a credit crunch that generates a recession 2. In economies with lower mortgage risk: the leverage ratios are higher the effects of a mortgage risk shock are amplified 3. Inertial monetary policies amplify the effects of a mortgage risk shock (zero lower bound scenario)

8 6 / 29 Literature Durable Consumption Goods: Barsky, House and Kimball (27), Erceg and Levin (26), Carlstrom and Fuerst (26), Monacelli (29) Housing Sector: Iacoviello (25), Iacoviello and Neri (29), Calza, Monacelli and Stracca (29) Financial Accelerator: Bernanke and Gertler (1989), Carlstrom and Fuerst (1997), Bernanke, Gertler and Gilchrist (1999) Risk, Default and Repayment Shocks: Christiano, Motto and Rostagno (29), Iacoviello (21), Dellas, Diba and Loisel (21)

9 7 / 29 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

10 8 / 29 Borrowers max C t,h t+1,n C,t,N H,t,L t+1, ω t+1 t= where β t { ( )} E U Xt, N C,t, N H,t, < β < 1 X t [(1 α) 1 η C t η 1 η + α 1 η 1 ] η η 1 η H η t+1, η, subject to: 1. Budget constraint P C,t C t +P H,t H t+1 +[1 F t ( 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 t ( ω t )] P H,t H t, 2. Participation constraint 3. Incentive-compatibility constraint

11 9 / 29 Mortgage Risk Each household consists of many members The household decides total housing investment H t+1 and over total loan L t+1 The i-th member finalizes the mortgage contract (L i t+1 ) and buys Ht+1 i according to household instructions Idiosyncratic shock ωt+1 i (observable by the member only) such that the ex-post housing stock is ωt+1 i Hi t+1 E t (ω i t+1 Hi t+1 ) = H t+1, i.e. there is no aggregate mortgage risk For ω i t+1 [, 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

12 1 / 29 The Mortgage Contract Participation constraint of lenders (1+R L,t )L t+1 = ωt+1 ω t+1 (1 µ)(1 δ)p H,t+1 H t+1 f t+1 (ω t+1 )dω t+1 (1 + R Z,t+1 )L t+1 f (ω t+1 )dω t+1 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 : pre-determined rate of return on loans R Z,t+1 : state-contingent mortgage rate ω t+1 : threshold value of the idiosyncratic shock

13 11 / 29 Savers max ec t, H e t+1, N e C,t, N e H,t e Lt+1 t= subject to } γ t E {U( X t, ÑC,t, ÑH,t), < β < γ < 1 P C,t Ct + P H,t Ht+1 + L t+1 = (1 + R L,t 1 ) L t + W C,t Ñ C,t + W H,t Ñ H,t where t are profits from firms + t + (1 δ)p H,t Ht

14 12 / 29 Intermediate Goods Producers Each sector has monopolistically competitive intermediate goods producers Continuum of differentiated goods i [, 1] Firm i produces according to [ Y j,t (i) = A j,t ζ 1 ς Nj,t (i) ς 1 ς Calvo price setting ] + (1 ζ) 1 ς Ñj,t (i) ς 1 ς ς 1 ς, < ζ < 1, ς >

15 13 / 29 Final Goods Producers Each sector has perfectly competitive final goods producers Flexible prices and CRS technology Y j,t = ( 1 ) ε j ε j 1 ε j 1 ε Y j,t (i) j di, ε j > 1, j = C, H

16 14 / 29 Monetary Policy Monetary policy rule: 1 + R L,t 1 + R L = A M,t [ π φπ C,t ] [ ] 1 φr 1 + φr RL,t 1, φ π > 1, φ r < R L Interest rate smoothing Monetary policy targets inflation in the non-durable sector

17 15 / 29 Utility function Following Horvart(2) and Iacoviello e Neri (21) : U(X t, N C,t, N H,t ) ln X t ν [ ] N 1+ξ 1 + ϕ C,t + N 1+ξ 1+ϕ 1+ξ H,t, ϕ, ξ

18 16 / 29 Exogenous Shocks Monetary policy shock: ln A M,t = ρ M ln A M,t 1 + ɛ M,t Idiosyncratic risk in the housing sector: Mortgage risk shock: ln ω t N( σ2 ω,t 2, σ2 ω,t) ln σ ω,t σ ω = ρ σ ln σ ω,t 1 σ ω + ɛ σω,t

19 17 / 29 Credit Crunch 2.5 σ ω =.2 σ ω =.28 2 Probability Distribution Mortgage Risk shock: increase in σ ω,t, the standard deviation of the distribution of idiosyncratic housing investment risk ω

20 18 / 29 Benchmark Parametrization Parameter Value Description γ.99 Discount factor of Savers β.98 Discount factor of Borrowers ψ.5 Relative size of Borrower group δ.1 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 ς 3 Elasticity of substitution across labor inputs ζ.5 Share of Borrower labor in the production function ξ.871 Elasticity of substitution across labor types α.16 Share of housing in consumption bundle ν 2.5 Disutility from work η 1 Elasticity of substitution between C and H goods ϕ 1 Inverse of elasticity of labor supply θ C.67 Calvo probability in C θ H Calvo probability in H φ π 1.5 Taylor-rule coefficient on inflation φ r.9 Taylor-rule coefficient on past nominal interest rate ρ C.9 Serial correlation of productivity shocks in C ρ H.9 Serial correlation of productivity shocks in H ρ M Serial correlation of monetary policy shocks σ ω.2 Standard deviation of idiosyncratic shocks µ.12 Monitoring cost

21 Responses to a 4% Increase in σ ω,t : Benchmark Parametrization Cons B Cons S Aggr Consumption Hous Demand B Hous Demand S Rel Price H Infl C Wage B Wage S Wage S H Hours S H Output H Output C Output Default Rate Monit Cost Ext Fin Prem Loan-to-Value Loans Nom Int Rate / 29

22 2 / 29 Low-Leverage Parametrization: σ ω =.6 Steady State Values Variable Benchmark Low Leverage % Difference Output C Output H Consumption, Borrowers Consumption, Savers Housing Demand, Borrowers Housing Demand, Savers Hours Worked, Borrowers in C Sector Hours Worked, Borrowers in H Sector Hours Worked, Savers in C Sector Hours Worked, Savers in H Sector Loans Loan-to-Value Ratio* Leverage Ratio* Default Rate on Mortgages External Finance Premium Mortgage Interest Rate * Percentage points. Annual, percentage points.

23 Responses to a 4% Increase in σ ω,t : Low-Leverage Calibration Cons B Cons S Aggr Consumption Hous Demand B Hous Demand S Rel Price H Infl C Wage B Wage S Wage S H σ ω =.2 σ ω = Hours S H Output H Output C Output Default Rate Monit Cost Ext Fin Prem Loan-to-Value Loans Nom Int Rate / 29

24 Responses to a 4% Increase in σ ω,t with Non-inertial Rule Cons B Cons S Aggr Consumption Hous Demand B Hous Demand S φ r =.9 φ r = Rel Price H Hours S H -3 Infl C Output H -3 Wage B Output C Wage S Output Wage S H Default Rate Monit Cost Ext Fin Prem Loan-to-Value Loans Nom Int Rate / 29

25 Responses to a 25 basis points Monetary Shock Cons B Cons S Aggr Consumption Hous Demand B Hous Demand S Rel Price H Infl C Wage B Wage S Wage S H Wage B H Output H Output C Output Default Rate Monit Cost Ext Fin Prem Loan-to-Value Loans Nom Int Rate / 29

26 24 / 29 Monetary Policy Shock and Sectoral Co-movement Models with sticky non-durable and flexible durable prices display negative co-movement in response to monetary shocks (Barsky et al. (27)) Empirical evidence supports positive co-movement (Erceg and Levin (26)) There are models that display positive co-movement: Models with credit constraint (Monacelli (29)) Models with wage stickiness in the housing sector (Carlstrom and Fuerst (26)) Our model displays positive co-movement with sticky durable prices

27 25 / 29 Conclusions and Extensions A ricky shock to housing investment generates a recession. Our model under-predicts the fall in total output and real housing prices seen in the Great Recession Next steps: Reducing the perverse effects of monitoring costs Wage stickiness Financial intermediation to provide capital to firms Consider fixed-rate multi-year contracts

28 Responses to a 25 basis points Monetary Shock Cons B Cons S Aggr Consumption Hous Demand B Hous Demand S θ H = Rel Price H Infl C Wage B Wage S Wage S H θ H =.67 Wage B H Output H Output C Output Default Rate Monit Cost Ext Fin Prem Loan-to-Value Loans Nom Int Rate / 29

29 27 / 29 VAR Evidence: Innovation to Delinquencies.8 Response of DEL to DEL.1 Response of CC to DEL.12 Response of IH to DEL Response of INFLY to DEL.3 Response of QQ to DEL.2 Response of RRY to DEL

30 28 / 29 VAR Evidence: IR of Delinquencies to Innovation to All Variables.2 Response of DEL to RRY Response of CC to RRY Response of IH to RRY Response of INFLY to RRY Response of QQ to RRY Response of RRY to RRY

31 Responses to a 25 basis points Monetary Shock Cons B Cons S Aggr Consumption Hous Demand B Hous Demand S Rel Price H Infl C Wage B Wage S Wage S H.5 1 θ H = θ H = Hours S H Output H Output C Output Default Rate Monit Cost Ext Fin Prem Loan to Value Loans Nom Int Rate / 29

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