macroprudential regulation and macroeconomic activity · 2014-09-03 · tfp shock persistence ρ a...

Macroprudential Regulation andMacroeconomic Activity1

Sudipto Karmakar

Economic Research DepartmentBanco de Portugal

1Disclaimer: The views expressed are my own and do not necessarily reflect the views ofthe Bank of Portugal or the Eurosystem

1 / 30 Sudipto Karmakar (BDP) Macroprudential Regulation & Macro Activity

Questions

• Two important questions facing central bankers/bank regulatorsin the aftermath of the financial crisis:

• Given that we need to have stronger capital requirements, arethere any adverse welfare implications of such a policy?

• How can we solve the procyclicality problem caused by lowcapital requirements?


Literature

• Stricter Regulation• "Leverage Restrictions in a Business Cycle Model", Christiano and Ikeda,2012

• "Fallacies, Irrelevant Facts, and Myths in the Discussion of CapitalRegulation: Why Bank Equity is Not Expensive", Admati, De Marzo,Hellwig and Pfleiderer, 2010

• Giammarino et al. (1993), Diamond and Rajan (2000), Gorton andWinton (2000)

• Caution• "The Welfare Cost of Bank Capital Requirements", Van Den Heuvel, 2008• "The Bank Capital Channel of Monetary Policy", Van Den Heuvel, 2009


This Paper

• Incorporate costs and benefits of bank capital requirements in a DSGEframework

• Develop a counterfactual i.e. would we have been better of with highercapital requirements?

• How do countercyclical capital requirements solve the procyclicalityproblem and what are the implications for the real sector?

• Penalty function method to solve the model that is intuitive and makesthe model useful for policy analysis


Main Results

• Higher capital requirements and countercyclical requirements raisewelfare and reduce volatility

• For the first case, try κ = 8%, κ = 10%, κ = 14% and for the second casetry a mild and an aggressive countercyclical rule.

• By operating at 8% instead of 14%, the welfare loss (in terms ofconsumption) is 43bp

• By implementing countercyclical requirements as opposed to a flat rule,the welfare gain (in terms of consumption) is 111bp

• By implementing countercyclical requirements, the procyclicality problemis greatly reduced (business cycle statistics)


Overview

• Stylized Facts• The Model• Analytical Results• The Solution Method• Countercyclical Capital Requirements• Numerical Results• The Next Steps


Stylized Facts

−.0

1−

.005

0.0

05E

quity

Ass

et R

atio

1985q1 1990q1 1995q1 2000q1 2005q1 2010q1Date

Equity Asset Ratio NBER Recession

Figure 1


Stylized Facts (co-movement)

−.0

1−

.005

0.0

05E

quity

Ass

et R

atio

−.0

3−

.02

−.0

10

.01

.02

Rea

l GD

P

1985q1 1990q1 1995q1 2000q1 2005q1 2010q1Date

Real GDP Equity Asset Ratio

Real GDP and Equity−Asset Ratio

−.0

1−

.005

0.0

05E

quity

Ass

et R

atio

−.2

−.1

0.1

Inve

stm

ent

1985q1 1990q1 1995q1 2000q1 2005q1 2010q1Date

Investment Equity Asset Ratio

Investment and Equity−Asset Ratio

Figure 2


Flow Chart

Household

The Bank

Final Good

Producers

Capital

Good

Producers

Deposits (d) Dividend

(D)

Labor (l)

Capital goods (k)

Loans (s)

Wage

(w)

Return

on loans

Price (Q)


The Model (Physical Setup)

• In addition to a representative agent, there is a representative bank• There is also a non financial firms sector consisting of:

• capital goods producers who manufacture investment goods• final goods producers who use the technology, Yt = AtKα

t L1−αt

• Capital evolves according to:

Kt+1 = θt [It + (1 − δ)Kt ] (1)

• The household maximizes:

U (ct , dt , lt) =[ac1−b

t + (1 − a)d1−bt] 1−φ

1−b

1 − φ− χ

l1−ϕt1 − ϕ

(2)

ct + dt = Wt lt + Dt + Rtdt−1 (3)


The Model (The Bank)

• The bank maximizes the PDV of the dividends i.e

Vt = Et

∞∑i=0

Λt+iDt+i (4)

• Balance sheet:

(Qtst − dt) = [(Zt + (1 − δ)Qt)θtst−1 − Rtdt−1] − Dt (5)

• Capital requirement constraint:

(Zt + (1 − δ)Qt)θtst−1 − Rtdt−1 − Dt − κQtst > 0 (6)

• Further, we also require that:

Dt > 0 (7)

The bank can raise capital only through retained earnings.


The Model (Non Financial Firms)

• This sector is split into two parts• The capital goods producers manufacture the capital used in theproduction of the final good

• They solve:

maxEt

∞∑τ=0

Λt,τ [Qτ Iτ − c(Iτ/Kτ )Iτ ] (8)

and their FOC can be written as:

Qt = c′(It/Kt) (9)

• Final goods producers produce final output using labor and capital asinputs

• To buy the capital, they approach the bank for funds


The Model (Non Financial Firms)

• The first order conditions of these firms are:• Wage:

Wt = (1 − α)Yt

Lt(10)

• Gross profits per unit of capital:

Zt = Yt − WtLt

Kt= αAt(

Lt

Kt)1−α (11)

• Conditional on obtaining funds, these firms face no other financial frictionand can commit to pay all gross profits to the bank

• Alternative explanation..


The Model (Market Clearing)

• There are four markets in this model economy. The equilibriumconditions are as follows:

• Goods MarketYt = Ct + c(It/Kt) (12)

• Labor Marketu′(lt)u′(ct)

= (1 − α)Yt

Lt(13)

• Capital MarketSt = Kt+1 (14)

• Deposit market clears by Walras Law


Analytical Results

Solving the Bank’s problem we get:

Et [Λt,t+1(µt+1 + Ωt+1)Ret+1] + (1 − κ)µt = µt + Ωt (15)

Et [Λt,t+1(µt+1 + Ωt+1)Rt+1] = Ωt (16)

µt + Ωt = γt , γt > 1 and equal if Dt > 0

where, Ret+1 = Zt+1+(1−δ)Qt+1

Qt

And the excess returns are given by:

EtRet+1 − Rt+1 =

κµt − cov(Λt,t+1γt+1,Ret+1)

E(Λt,t+1γt+1) (17)


Analytical Results

• Remember,EtRe

t+1 − Rt+1 = κµt−cov(Λt,t+1γt+1,Ret+1)

E(Λt,t+1γt+1)

• Case 1 - (non binding today)µt = 0

• Case 2 - (binding today)µt > 0

• Case 3 - (non binding today but binds in the future)µt+1 > 0

Same as the last case because the covariance between γt+1 and Ret+1 is

negative.


Solution Technique: The Penalty FunctionMethod

• Standard perturbation methods cannot be applied to models withoccasionally binding constraints

• Use a smooth penalty model, with equality constraints only, that neststhe original model

• Modify the objective using a non linear asymmetric penalty function• Basic Idea: Allow anything to be feasible but alter the objective functionso that it has undesirable consequences if the constraint is violated

• Use a third order approximation solution to capture the asymmetry• Approach developed by Judd (1998) and used by Den Haan andOcaktan(2009), Kim, Kollman and Kim (2009), De Wind (2008) andPreston and Roca (2006)


The Modified Problem

• The Bank maximizes:

V Pt = Et

∞∑t=0

Λt [Dt − P(CB)] (18)

where,P(CB) = dt−1

ψ2 exp[− ψdt−1

((Zt + (1 − δ)Qt)θtst−1 − Rtdt−1 − Dt − κQtst)]

• The FOCs are same except that, µ is replaced by λ where,

λt = 1ψ

exp[− ψ

dt−1((Zt + (1 − δ)Qt)θtst−1 − Rtdt−1 − Dt − κQtst)] (19)

is the penalty term or the derivative of the penalty function with respectto the capital buffer


The Penalty Function

−0.05 −0.04 −0.03 −0.02 −0.01 0 0.01 0.020

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Capital Buffer (CB)

Pen

alty

(CB

)

psi=50psi=70psi=90psi=110psi=130

Figure 519 / 30 Sudipto Karmakar (BDP) Macroprudential Regulation & Macro Activity

Calibration

Shocks:lnAt = (1 − ρA)lnA + ρAlnAt−1 + ut (20)

lnθt = (1 − ρθ)lnθ + ρθlnθt−1 + vt (21)Table 1

Parameter Symbol ValueDiscount Rate β 0.99

Capital Requirement κ 0.08TFP shock persistence ρA 0.90

Std. Dev. of TFP shock σu 0.01Financial shock persistence ρθ 0.75

Std. Dev. of Financial shock σv 0.05Depreciation δ 0.025

Penalty parameter ψ 130Share of Capital α 0.33

Risk Aversion φ 1.5Disutility of labor χ 10.36

Inverse of Frisch Elasticity of labor supply ϕ 0.5Sub. between cons. & deposits 1/b 0.39

Share of cons. in utility a 0.95


Exploring the asymmetry

0 10 20 30 40−1

0

1

2

3

4

5x 10

−3

time

lam

bda

+ shock− shock+ shock reversed

0 10 20 30 40−12

−10

−8

−6

−4

−2

0

2x 10

−3

time

inve

stm

ent

0 10 20 30 40−12

−10

−8

−6

−4

−2

0

2x 10

−3

time

asse

t pric

e

0 10 20 30 40−12

−10

−8

−6

−4

−2

0

2

4x 10

−3

time

capi

tal

0 10 20 30 40−7

−6

−5

−4

−3

−2

−1

0

1x 10

−3

time

outp

ut

0 10 20 30 40−3

−2.5

−2

−1.5

−1

−0.5

0

0.5

1x 10

−3

time

cons

umpt

ion

SkewnessInvestment Output Cap. Buffer

Data -0.8462 -0.0054 -0.4782Model -0.7448 -0.0029 -0.5011


Business Cycle Statistics

Table 2

Output Consumption Cap-buffer InvestmentStandard Deviations

Data 0.0115 0.0056 0.0093 0.0419Model 0.0188 0.0058 0.0099 0.0320

First Order AutocorrelationsData 0.88 0.83 0.93 0.87Model 0.96 0.89 0.99 0.92

Correlations with OutputData 1.00 0.88 0.96 0.91Model 1.00 0.92 0.91 0.96


Altering the Capital Requirement

0 10 20 30 40−0.14

−0.12

−0.1

−0.08

−0.06

−0.04

−0.02

0

time

inve

stm

ent

kappa=8%kappa=10%kappa=14%

0 10 20 30 40−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

timeas

set p

rice

0 10 20 30 40−0.25

−0.2

−0.15

−0.1

−0.05

0

time

capi

tal

0 10 20 30 40−0.025

−0.02

−0.015

−0.01

−0.005

0

time

outp

ut

0 10 20 30 40−0.014

−0.012

−0.01

−0.008

−0.006

−0.004

−0.002

0

time

cons

umpt

ion

0 10 20 30 400

0.002

0.004

0.006

0.008

0.01

0.012

0.014

0.016

time

Exc

ess

Ret

urns


Countercyclical Capital Requirements

• Low capital requirements tend to generate procyclicality• Implement time varying requirements to mitigate business cyclefluctuations

• The capital requirement is written as:

κt = (1 − ρκ)κ+ (1 − ρκ)Λκ(logYt − logYt−1) + ρκκt−1 (22)

• Case 1: The capital requirement falls from 8% to 7.5% over six quarters• Case 2: The capital requirement falls from 8% to 6% over six quarters• Pick the parameters appropriately


Business Cycle Statistics

Table 3

Output Consumption Cap-buffer InvestmentStandard Deviations

Data 0.0115 0.0056 0.0093 0.0419Model 0.0188 0.0058 0.0099 0.0320

Model (cc κ) 0.01001 0.00529 0.00954 0.02801First Order Autocorrelations

Data 0.88 0.83 0.93 0.87Model 0.96 0.89 0.99 0.92

Correlations with OutputData 1.00 0.88 0.96 0.91Model 1.00 0.92 0.91 0.96

Model (cc κ) 1.00 0.79 0.64 0.94


Flat Vs Countercyclical Requirements

0 5 10 15 20−1

0

1

2

3

4

5x 10

−3

time

lam

bda

flat κcc κstrongly cc κ

0 5 10 15 20−0.012

−0.01

−0.008

−0.006

−0.004

−0.002

0

timein

vest

men

t

0 5 10 15 20−12

−10

−8

−6

−4

−2

0

2x 10

−3

time

asse

t pric

e

0 5 10 15 20−0.012

−0.01

−0.008

−0.006

−0.004

−0.002

0

time

capi

tal

0 5 10 15 20−7

−6

−5

−4

−3

−2

−1

0x 10

−3

time

outp

ut

0 5 10 15 20

−2.5

−2

−1.5

−1

−0.5

0x 10

−3

time

cons

umpt

ion


Welfare Implications

• Take the household’s utility as the objective• Following Faia & Monacelli and Gertler & Karadi, the households utilityin recursive form:

Wt = U (ct , dt , lt) + βEtWt+1 (23)

• Perform a third order approximation of the function, take policyparameters to be given


Welfare Implications (In consumption terms)

• Simulate the model for three different levels of capital requirement• Calculate the amount of compensation in consumption (∆C ) needed toget a steady state welfare as the benchmark

• Question: What is the loss in welfare by NOT operating atκ = 0.14?

Table 4

Variable κ = 0.14 κ = 0.10 κ = 0.08Consumption 0.4603 0.4600 0.4559

Welfare 20.29 19.98 19.32Welfare Decline (in cons. terms) – 0.35 % 0.43 %


Welfare Implications (Countercyclical κ)

• Solve the model for three different regimes:• Flat requirements, κ = 0.08• Mildly countercylcical κ• Strongly countercyclical κ

• Calculate the amount of compensation in consumption (∆C ) needed toget a steady state welfare as the benchmark

Table 5

Variable Flat κ Mildly cc κ Strongly cc κWelfare 19.32 20.07 21.78

Wel. Gain (in cons. terms) −− 0.76% 1.11%


Conclusion and future research

• Higher capital requirements reduce volatility and generate welfare gains• Countercyclical capital requirements mitigates the procyclicality problemand has positive welfare effects

• Asymmetric response to shocks capturing the idea that recessions aresharper than booms

• Optimal timeline for implementing macroprudential regulations and themagnitude of such policy changes

• Analyze the impact of macroprudential policies on key banking variablesand provide evidence from South East Asia


macroprudential regulation and macroeconomic activity · 2014-09-03 · tfp shock persistence ρ a...

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