Financial Considerations in a Small Open Economy Model for ... · evidence in Mexico, CortØs...

Introduction The model Results Concluding Remarks ...

Financial considerations in a small open economymodel for Mexico

Francisco Adame Jessica Roldán-Peña Miguel Zerecero

Banco de México

BIS CCA Research Network on "Incorporating �nancial stability considerations into centralbank policy models", Mexico City.

October 2013


Two comments

This is work in progress.

The views expressed here are the author�s only and should not beinterpreted as re�ecting those of Banco de México.


Financial considerations in monetary policy

Quadrini (2011) FRB of Richmond Economic Quarterly

"There is a long and well-stablished tradition inmacroeconomics of adding �nancial market frictions in standardmacroeconomic models and showing the importance of the�nancial sector for business cycle �uctuations (...) Althoughthese studies had an impact in the academic �eld, formalmacroeconomic models used in policy circles have mostlydeveloped while ignoring this branch of economic research."

The �nancial crisis and its aftermath brought about new challengesfor the making of macroeconomic policy in general and of monetarypolicy in particular.


The Mexican case

Not much has been written in the context of DSGE models formonetary policy purposes that address these questions for theMexican case.

Some stylized facts to focus on:1 Credit �ows are procyclical and interest rate spreads arecountercyclical.

2 The baking sector works under monopolistic competition and interestrates are sticky (Negrin et al. (2012) and Mier-y-Terán (2013),respectively).

3 A great percentage of resources collected by �rms �nance workingcapital (Banxico (2013), Castellanos (2012), CNBV (2012)).


Credit �ows are procyclical

New loans vs output:

Firms Households

0.1

0

0.1

GD

P V

aria

tion

GDPCredit Flow

Q200 Q201 Q202 Q203 Q204 Q205 Q206 Q207 Q208 Q209 Q2100.02

0

0.02

Diff

eren

tial f

or F

irms

0.1

0

0.1

GD

P V

aria

tion

GDPCredit Flow

Q200 Q201 Q202 Q203 Q204 Q205 Q206 Q207 Q208 Q209 Q2100.02

0

0.02

Diff

eren

tial f

or H

ouse

hold

s

Correlations:ρ(new_loans_�rms, y) 0.58ρ(new_loans_HH, y) 0.56


Lending rate spreads are countercyclical

Di¤erence between lending rates and reference rate vs output:

Firms Households

0.1

0

0.1

GD

P V

aria

tion

GDPSpread

Q200 Q201 Q202 Q203 Q204 Q205 Q206 Q207 Q208 Q209 Q2101.02

1.04

1.06

Rat

io fo

r Int

eres

t Rat

es to

Firm

s

0.1

0

0.1

GD

P V

aria

tion

GDPSpread

Q200 Q201 Q202 Q203 Q204 Q205 Q206 Q207 Q208 Q209 Q2101.1

1.2

1.3

Rat

io fo

r Int

eres

t Rat

es to

Hou

seho

lds

Correlations:ρ(di¤_lendingrate_�rms, y) �0.57ρ(di¤_lendingrate_HH, y) �0.65


The Mexican case

Not much has been written in the context of DSGE models formonetary policy purposes that address these questions for theMexican case.

Some stylized facts to focus on:1 Credit �ows are procyclical and interest rate spreads arecountercyclical.

2 The baking sector works under monopolistic competition and interestrates are sticky (Negrin et al. (2012) and Mier-y-Terán (2013),respectively).

3 A great percentage of resources collected by �rms �nance workingcapital (Banxico (2013), Castellanos (2012), CNBV (2012)).


In this paper...

Main goals at this stage:

To develop an operational small open economy (SOE) model forthe Mexican economy that incorporates these features andsuccessfully accounts for the data.To use it to analyze the transmission mechanism of some shocksinto the economy.

Type of model:

Standard New-keynesian SOE model.Featuring linkages between real and �nancial sectors andimperfections in the intermediation of resources:

Credit demand frictions: collateral constraints with a working capitalchannel.Credit supply frictions: banking sector working under monopolisticcompetition and sticky interest rates.


So far...

Our contribution:

To estimate an operational DSGE model that considers both creditdemand and credit supply frictions for the Mexican economy.To analyze the role of a working capital channel embedded incollateral constraints in the transmission mechanism of bankingshocks into the economy.

Main results:

The model is able to reproduce some properties of business cycles.Preliminary estimation shows that the inclusion of working capital isrelevant. This ingredient has non-trivial e¤ects in the propagation ofdi¤erent shocks and the reproduction of the credit cycle.Sectorial banking shocks may have aggregate e¤ects in a contextwhere monetary policy reacts to o¤set them (is monetary policy tooblunt?).


Model�s main characteristics

New-keynesian SOE model (Adolfson (2007), successfully adaptedto other SOE countries):

Real rigidities: habit persistence, capital utilization, investmentadjustment costs.Nominal rigidities: price and wage stickiness.Incomplete exchange rate pass-through (according to empiricalevidence in Mexico, Cortés (2013)).

Financial frictions:

Limited enforceability of contracts give rise to collateral constraints(Iacovello (2005)).

Working capital channel associated to collateral constraints(as in Mendoza (2010) and Jermann and Quadrini (2011)).


Model�s main characteristics (contd.)

3 agents:

Patient households: consume, housing, di¤erentiated work, saveImpatient households: consume, housing, di¤erentiated work, borrowEntrepreneurs: consume, produce intermediate goods out of capitaland labor, borrow

2 assets:

housing goods (for households)capital good (for entrepreneurs)

Production side pretty standard of a SOE model


Real and �nancial linkages in the model


Real and �nancial linkages in the model (contd.)


Patient households

Patient household (i) chooses consumption, stock of housing andsavings to solve the following problem:

max E0 ∑ βtP

"εut(cPt (i )� hcPt�1(i ))1�σc

1� σc+ εxt

χPt (i )1�σχ

1� σχ� εnt

nPt (i )1+σn

1+ σn

#s.t.

PtcPt (i ) + Pχt

�χPt (i )� (1� δχ) χPt�1(i )

�+Dt (i ) �

�1�ΦP

�πPw ,t

��Ptw Pt (i )n

Pt (i )

+RHD ,t�1Dt�1(i )� Tt (i ) +ΠPt (i )

FOCs


Impatient Households

Impatient household (i) chooses consumption, stock of housing, andloans in order to solve the following problem:

max E0 ∑ βtI

"εut(c It (i )� hc It�1(i ))1�σc

1� σc+ εxt

χIt (i )1�σχ

1� σχ� εnt

nIt (i )1+σn

1+ σn

#s.t.

Ptc It (i ) + Pχt

�χIt (i )� (1� δχ)χ

It�1(i )

�+ RHL,t�1L

Ht�1(i ) �

�1�ΦI

�πIw ,t

��Ptw It (i )n

It (i )

+LHt (i )� T (i )

RHL,tLHt (i ) � mHt Et

hPχt+1(1� δχ)χ

It (i )

i

FOCs


Entrepreneurs

Representative entrepreneur chooses consumption, capital, capitalutilisation, labor and loans in order to solve the following problem:

max E0 ∑ βtE

"εut(cEt (i )� hcEt�1(i ))1�σc

1� σc

#s.t.

ywt (i ) = At [ut (i )kt�1(i )]α nt (i )1�α

RFL,tLFt (i ) + wtnt (i ) � mFt Et

hP kt+1(1� δk )kt (i )

i

Pt cEt (i ) + Ptwt nt (i ) + Pkt (kt (i )� (1� δk )kt�1 (i )) + Ptψ(ut (i ))kt�1 (i ) + R

FL,t�1L

Ft�1 (i ) � Pwt ywt (i ) + LFt (i )

FOCs


Working capital channel

The �rst order condition of labor for the entrepreneur is:

λEc ,t + µEt

λEc ,twt =

h(1� α)Pwt At (utkt�1)

α (nt )�αi

where λEc ,t and µEt are the Lagrangian multipliers of the budgetconstraint and the collateral constraint, respectively

If �nancial constraints are relaxed: µEt gets smaller ) lower laborcosts ) at the margin, higher demand for labor.

The opposite would happen if the �nancial constraints are tightened.


Banking sector

Follows Gerali et al. (2011):

Monopolistic competition: spreads between active and passive ratesand the reference rate.Sticky interest rates.Abstracts from bank�s �nancial soundness considerations.


Credit �ows


Credit �ows (contd.)

In order to illustrate the structure behind the banking system, wepresent the lending �ow of credit (the structure is similar forborrowing �ow).

Two types of �nancial intermediaries:1 Lending banks:

1 Operations: Obtain resources from the interbank market anduse them to make loans at di¤erentiated interest rates.

2 Features: Monopolistic competition and interest ratesstickiness.

2 Lending intermediaries:

1 Operations: They receive resources, package them and givesloans to households and �rms.

2 Features: perfect competition.



Credit �ow: from interbank market to real sector.



When carrying resources from the interbank market, the �ow of creditfaces an exogenous �nancial frictions:

Ljt (ijL) = z

jL,tL

jIB ,t (i

jL)

Every period each lending bank receives a signal about its ability to settheir price:

With probability θL it sets their interest rates to RjL,t�1.

With probability 1� θL they set its optimal interest rate, Rnewt (i jL) ,thus they must solve:

maxRj ,newL,t

Et∞

∑s=0

θsD βS+1I Λpt ,t+s+1hR j ,newL,t (i jL)L

jt+s (i

jL)� Rt+s L

jIB ,t+s (i

jL)i

Lending intermediaries solve:

maxLt (iL )

RjL,Ljt �

Z 10RjL,t (i

jL )Lt (iL )di

jL

s .t . Lt =

2664Z 10 Ljt (ijL )

11+µjL di jL

37751+µ

jL


The model vs the data

Unconditional MomentsData Model Data Model

σ (ey ) 2.81 2.73 ρ ((yH � � yF )/ey , ey ) �0.33 �0.23σ (c ) /σ (ey ) 1.52 1.59 ρ

�RD/R , ey � �0.23 �0.18

σ (ik + iχ) /σ (ey ) 3.28 4.01 ρ�RHL /R , ey � �0.69 0.002

σ (yH � ) /σ (ey ) 2.35 2.72 ρ�RFL /R , ey � �0.65 �0.02

σ (yF ) /σ (ey ) 2.70 2.64 ρ�∆LH , ey � 0.57 0.07

σ (RER ) /σ (ey ) 3.92 1.20 ρ�∆�LF + wn

�, ey � 0.62 0.13

σ�RD/R

�/σ (ey ) 0.18 0.20

σ�RHL /R

�/σ (ey ) 0.20 0.16

σ�RFL /R

�/σ (ey ) 0.04 0.08


IRF to a monetary policy shock

Working Capital


IRF to a banking shock in deposits

Working Capital


IRF to bank lending shock (households)

Working Capital


IRF to bank lending shock (�rms)

Working Capital


What have we learned so far?

Estimation: adding a working capital channel helps to match themodel to the data.

We have carefully inspected the implications of incorporating aworking capital channel in a model with collateral constraints. Theinteraction between both frictions could dampen the volatility ofvariables in reaction to some shocks.

The monetary policy rate could be a blunt instrument to address thee¤ects of sectorial banking shocks.


Next steps

To improve upon the estimation/calibration of the model.

To extend the modelling of the banking sector: to introduce capitalin bank�s balance sheets.

Allow for a better characterization of the shocks arising within thebanking sector.Allow for bank�s �nancial soundness considerations within our setup:macroprudential tool (capital adequacy ratio) would emerge thatallows to consider the coexistence of monetary and macroprudentialpolicies.


Consumption goods:

λPc ,t = εut(cPt � hcPt�1)�σc

Pt

Deposits:

λPc ,t = Et

(βPR

HD ,tλ

Pc ,t+1

πt+1

)

Housing goods:

ε{t (χPt )�σχ � λPc ,tP

χt + βPλPc ,t+1(1� δχ)P

χt+1 = 0

main


Consumption goods:

λIc ,t = εut(c It � hc It�1)�σc

Pt

Loans:Etn

λIc ,t+1

oλIc ,t

=1

βIRHL,t

"1� µHt

λIc ,tRHL,t

#

Housing goods:

ε{t (χIt )�σχ

Pχt

�λIc ,t +µHt mHt Et

�π

χt+1

(1� δχ)+ βIλIc ,t+1(1� δχ)π

χt+1 = 0

main


Comsumption goods

λEc ,t = εut(cEt � hcEt�1)�σc

Pt

Loans:Etn

λEc ,t+1

oλEc ,t

=1

βERFL,t

"1� µFt

λEc ,tRFL,t

#Labor demand:

wt�

λEc ,t + µFt

�= λEc ,t

�(1� α)Pwt At (utkt�1)

α (nt )�α�

Capital utilization:

PtΨ0(ut ) = αPwt At (ut (i )kt�1)α�1 (nt )

Capital demand:

λEc ,t �µFt mFt (1� δk )Et

nπkt+1

o= βE Et

8><>:λEc ,t+1

264 PWt+1Pkt+1

�α yw ,tkt

�+(1� δk )

Pkt+1Pkt

� Pt+1�

Ψ(ut )Pkt

�3759>=>;

main

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