Modeling General-Equilibrium Macroeconomic Stress Scenarios in MATLAB

Jaromír BenešInternational Monetary Fund

MATLAB Computational Finance ConferenceMay 2015

Macroprudential Policy…Is What?

§ Narrow versus broader scope§ Broad policy objectives• Minimize incidence of balance sheet crises• Limit disruptions to key financial services

§ Key elements in macroprudential analysis• Tail-risk distress scenarios • Feedback between balance sheets and real economy• Possibility of severe nonlinearities

§ Models to support macroprudential policy

2

Plan of Presentation

3

Policymaking Perspective

Modeling Perspective

Programming Perspective

Simulation Experiment

POLICYMAKING PERSPECTIVE

4

Assess  risks

Macroprudential Policy Exercise

5

Design  macro(-­‐economic/-­‐financial)  stress  scenario(s)• Slow-­‐burn  (low-­‐frequency)   shocks  and  risks• Unlikely  yet  plausible   scenarios  with  large  impact

Evaluate  impact  of  scenario(s)• Resilience   of  sectoral balance  sheets• Feedback  between   financial  and  real  

sectorsCommunicate  with  policy  makers• Consider  possible  policy  responses

Communicate  to  public• Regular  Financial  Stability  Reports

6

3764 657 64724 87561

3638 1125 90354 4022

507 908 28384 78761

1209 8763 3321 20567

4545 284 374 3234

General  Equilibrium  Model  Framework

Structural  models

Sectoralanalysis

Time  series   analysis

CCA

Spreadsheet  scenarios

Empirical  estimates  (PD,  LGD,  EAD,  etc)

Financial  stability  analysis

Real  economy  and  monetary  policy  analysis

Role of General Equilibrium Models

§ Integrate all pieces of information§ Balance sheet consistency across sectors and time§ Facilitate internal communication

(explicit assumptions, most critical assumptions)§ Make process accountable§ Make external communication transparent, credible§ Model-based scenario analysis, not accurate

probabilistic predictions

7

Limitations…

§ Fundamental uncertainty§ Nonlinear feedback§ Corridor stability§ Estimation and backtesting difficult in crisis modeling• Distress episodes are few and far apart• Each has a different cause• Need to evaluate international evidence

è Common variety of macro models not well-suited

8

MODELING PERSPECTIVE

9

Macro Model with Credit Risk

Real economy§ Relatively standard

(DSGE) structure§ Monetary economy§ Optimizing agents with

finite (short) planning horizons

§ Mixed expectations

Financial sector§ Credit risk on loan

books§ Asymptotic single factor

risk model§ Advanced IRB to model

regulatory capital constraints

10

Rest  of  w

orldBank  

capital

Structure of Model

11

Loan  portfolio

Resident  deposits

Nonresiddeposits

Bank  capital

Other  assets

Banking  sector

Producers

Exporters

Households

Real  economy

Exports  and  imports

Bank  capital

12

Loan  portfolio

Resident  deposits

Nonresiddeposits

Bank  capital

Other  assets

Banking  sector

Producers

Exporters

Households

Real  economy

Exports  and  imports

Bank  capital

13

Loan  portfolio

Resident  deposits

Nonresiddeposits

Bank  capital

Other  assets

Banking  sector

Producers

Exporters

Households

Real  economy

Exports  and  imports

Demand for Deposits

Δt = Rt−1Dt−1− RL ,t−1Lt−1+NLt

Δt = φ PC ,tCt + PI ,tIt +κ PH ,tHt"#

$%

Bank  capital

14

Loan  portfolio

Resident  deposits

Nonresiddeposits

Bank  capital

Other  assets

Banking  sector

Producers

Exporters

Households

Real  economy

Exports  and  imports

Producers

Exporters

Households

Real  economy

Exports  and  imports

Individual Bank Loans

15

Bank  capital

15

Loan  portfolio

Resident  deposits

Nonresiddeposits

Bank  capital

Other  assets

Banking  sectorRL ,ti Lti > kexp ut+1

i( )PH ,t+1Hti ⇒ default

RL ,ti 1− λ Φ

logRL ,ti Lti

k PH ,tHti − E t log

PH ,t+1PH ,t

#$%

&'(

σ

)

*

+++

,

-

.

.

.

#

$

%%%

&

'

(((= Rt*

Bank  capital

16

Loan  portfolio

Resident  deposits

Nonresiddeposits

Bank  capital

Other  assets

Banking  sector

Producers

Exporters

Households

Real  economy

Exports  and  imports

Bank Capital Regulation

17

Bank  capital

17

Loan  portfolio

Resident  deposits

Nonresiddeposits

Other  assets

Banking  sector

Producers

Exporters

Households

Real  economy

Exports  and  imports

Bank  capital

Eti

Lti≥1−RL ,ti

Rt1− λht

i q( )#$

%&

hti q( ) =Φ

Φ−1 pdti( )−Φ−1 q( ) ρ

1− ρ

#

$

%%%

&

'

(((

PROGRAMMING PERSPECTIVE

18

IRIS Toolbox

19

60+  classes,  30+  packages,  2,300+  functionswww.iris-­‐toolbox.com

Structural  modeling  (DSGE)

MV  time  series  analysis

Time  series  and  database  

management

ReportingDocumentation

Model Related Classes and Packages

20

@economy

@agent @stock

@stocklike

@flow

@flowlike

@model

@userdataobj @getsetobj @fragileobj

@modelobj

@preparser @theparser

@estimateobj

+logdist @poster

@systempriors

+irisopt

@hlastsyst @hdataobj

@namedmat

Building Model Equations

§ Two types of equations• Behavioral rules• Stock-flow and other identities

§ Behavioral rules• Optimizing principles

• Rules of thumb• Empirical equations

§ Stock-flow identities• Logical structure of the model

21

Transactions Flow Matrix

22

Households Producers Exporters Banks Central Bank Rest of world Σ

Tra

nsac

tion

flow

s

Cur

rent

acc

oun

t

Consumption −PC×C PC×C 0

Wage bill W×N −W×NY −W×NX 0

Imports −PM×MY −PM×MX PM×M 0

Exports PX×X −PX×X 0

Distrib surplus producers Π −Π 0

Distrib surplus banks −Γ Γ 0

Distrib surplus CB Ω −Ω 0

Deposit interest RD(0)×D(0) −RD(0)×D(0) 0

Loan interest −RL(0)×L(0) RL(0)×L(0) 0

Loan loss L(0)[1+RL(0)]×UL −L(0)[1+RL(0)]×UL 0

CB liquidity surplus interest R(0)×B(0) −R(0)×B(0) 0

Net foreign liabs interest −RF(0)×F(0) RF(0)×F(0) 0

Cap

ital a

cco

unt Net acquisition of housing −PH×ΔH 0

Chng in deposits −ΔD ΔD 0

Chng in loans ΔL −ΔL 0

Chng in CB liquidity surplus −ΔB ΔB 0

Chng in foreign liabs ΔF −ΔF 0

Σ 0 0 0 0 0 0

Budget  constraints

Market  clearing

Net Worth Matrix

23

Households Producers Exporters Banks Central Bank Rest of world

Cha

nge

in n

et w

ort

h

Opening net worth VH0 0 0 VB(0) VC(0) VR(0)

Tra

nsac

tio

n ch

ng Net acquisition of housing PH×ΔHChng in deposits ΔD −ΔDChng in loans −ΔL ΔLChng in CB liquidity surplus ΔB −ΔBChng in foreign liabs −ΔF ΔF

Rev

al Revaluation of housing ΔPH×H(0)Revaluation of net foreign liabs

J×F(0)

Closing net worth VH 0 0 VB VC VR

Laws  of  motion  for  net  worth  (equity)

Delegated  agents

Stock-Flow Builder

24

Stock-Flow Builder

25

Stock-Flow Builder

26

Behavioral Equations (Regexp Parser)

27

SIMULATION EXPERIMENT

28

House Price Bubble and Burst

House  price  growth

Risk  perceptions  

down

Easier  cheaper  credit

Irrational  expectations

Consumption,  real  economy

House Price Bubble and Burst

§ Irrational expectations• Sequence of shocks

§ Burst of the bubble• Unexpected event• House prices go down to “fundamentals”

• Painful deleveraging in both real and financial sector

§ Re-simulate with loan-to-value caps• Inequality constraint in households decision• Complementary slackness translated into min(…)

30