EME Business Cycles: Evidence and Theory · business cycles where there is no cycle present in the...

EME Business Cycles: Evidence and Theory

Chetan Ghate1

IGC-ISI Summer School 2014

June 2014

1Indian Statistical Institute Delhi Center(IGC-ISI Summer School 2014) EME Business Cycles June 2014 1 / 122

EME Business Cycles

A substantial literature exists on busniess cycle stylized facts fordeveloped economies (Kydland and Prescott, 1990; Stock andWatson, 1999; King and Rebelo, 1999; Rebelo, 2005).

A number of papers have recently focused on stylized facts forEMDEs (Agenor et al., 2000; Rand and Tarp, 2002; Aguiar andGopinath, 2007; Male, 2010; Ghate et al. 2013)

Ghate et al. (2013) compare the changes of the properties of theIndian business cycle in the pre and post reform period, taking datafrom 1950-2010.

Research agenda on general equilibrium models with policy relevantimplications for IndiaGhate (2012), Ghate and Wright (2012, 2013), Ghate, Glomm and Liu(2012), Das, Ghate, and Robertson (2013), Ghate, Glomm and Stone(2014), Callaghan, Ghate, Pickford, and Rathinam (2014), Ghate,Gopalakrishnan, Tarafdar (2014).

(IGC-ISI Summer School 2014) EME Business Cycles June 2014 2 / 122

Overview

PreliminariesWhat is a growth cycle?The HP Filter / Baxter King Filter

India business cycle evidence (Ghate, Pandey, and Patnaik (2013))Stylized Facts for EME Business Cycles

Rand and Tarp (2002), Agenor et al. (2000), Male (2010)

Can a SOE RBC model account for both developed and emergingmarket business cycles?

Aguiar and Gopinath (2007)Criticism: Garcia-Cicco et al. (2010)Also see Mendoza (1991), Correia et al. (1995), Kydland and Zargaza(2002).

Neumeyer and Perri (2005)Solving linear rational expectation models, Uhligs general approachIndia: Ghate, Gopalakrishnan, and Tarafdar (2014)

Conclude(IGC-ISI Summer School 2014) EME Business Cycles June 2014 3 / 122

Preliminaries

Burns and Mitchell (1946)

Business cycles are a type of uctuation found in aggregateeconomic activity of nations that organize their work mainly inbusiness enterprises; a cycle consists of expansions occurring atabout the same time in many economic activities, followed bysimilar general recessions, contractions, and revivals which mergeinto the expansion phase of the next cycle; this sequence ofchanges is recurrent but not periodic; in duration business cyclesvary from one year to ten or twelve years; they are not divisibleinto shorter cycles of similar cycles with amplitudesapproximating their own.


Preliminaries

"Fluctuations in the aggregate economic activity of nations...

Should one worry about di¤erences in business cycle activity of nations?

"Expansions occurring in many economic activities..."

How broadly should the aggregates that are being considered bydened ?

The notion that changes in economic activity occur "at about thesame time.."

Admits the possibility of economic variables that lead or lag the cycle

In seeking to identify "recurring changes.."

How should we deal with seasonal changes, random uctuations,secular trends?

Bottom Line:

This denition has formed the basis of modern thinking about businesscycles (measurement, theory).


Preliminaries - Classical business cycles versus growthcycles

Growth cycles: measured by a deviation from its long run trendClassical cycles: based on the absolute downturn of the level of output


Preliminaries - Some denitions

Expansion

movement from trough to peak

Recession

movement from peak to trough

Duration

length of time the economy spends between two troughs or peaks

Amplitude

deviation from trend


Preliminaries - The HP Filter

If we choose to use growth cycles

how do we identify the cyclical component of a given series?

Linear trend (de-trend) vesus stochastic trend (modeled as a unitroot, rst di¤erence)

Properties of the HP Filter have been studied by many authors

King and Rebelo (1993)Cogley and Nason (1995)Stock and Watson (1999) - neither linear trends (generate spuriouscycles in de-trended series) or rst di¤erences (exacebate the role ofshort term noise) eliminate unit roots, and therefore not a satisfactoryapproach identifying the cyclical component of a series!

Cogley and Nason (1995) criticize the HP lter for spuriously geratingbusiness cycles where there is no cycle present in the original data.


The HP Filter

Hodrick and Prescott (1980) proposed the HP lter to decompose amacroeconomic time series into a non-starionary trend componentand a stationary cyclical residual component

in practice, rst seasonally adjust the data

As a general principle all macroeconomic series can be decomposedinto

seasonal variations, a business cycle component , irregular short termmovements, long term trend component

The HP method involves dening cyclical output, ct , as currentoutput, yt less a measure of trend output, xt , with trend output beinga weighted average of past current, and future observations.Given anobserved time series, yt , let

yt = xt + ct

with yT = (y1,y2....yN ), xT = (x1,x2,..xN ) and cT = (c1,c2, .., cN ),where xT denotes the unobserved trend component at time t and ctthe unobserved cyclical residual at time t.


The HP Filter - Continued

The HP trend bxt can be obtained as the solution to the followingconvex minimization problem

minfxtgNt=1

"(yt � xt )2 + λ

N�1∑t=2

((xt+1 � xt )� (xt � xt�1))2#, λ > 0

(1)λ is the smoothing parameter (penalty parameter). As λ gets largerthe HP estimated trend gets smaller.The term, (xt+1 � xt � (xt � xt�1) = 42xt , is an approximation tothe 2nd derivative of x at t.λ = 1600 generates a cyclical residual that accords with expectationsof what is generally believed to be a business cycle.Two opposing forces: one force minimizes the sum of squared cyclicalresiduals; the other force is attempting to minimize the sum ofsquared ∆2xt . The smoothing parameter gives relative weight thesetwo opposing forces.


The HP Filter- Continued

The HP rst order conditions are derived by setting the gradientvector of the above equation

c1 = λ(x1 � 2x2 + x3)c2 = λ(�2x1 + 5x2 � 4x3 + x4)ct = λ(xt�2 � 4xt�1 + 6xt � 4xt+1 + xt+2), ..t = 3, 4, 5...N � 2

cN�1 = λ(xN�3 � 4xN�2 + 5xN�1 � 2xN )cN = λ(xN�2 � 2xN�1 + xN )

or,c = λFx

which implies thaty = (λF+ I)x


The HP Filter - Continued

The HP trend is identied by

x̂ = (λF+ I)�1y

andĉ = y� x̂

Except for the four endpoints, the rst order conditions state that

ct = λ∆4xt , .......for t = 3, 4, 5, ....N � 2.

HP procedure renders stationary time series di¤erence stationary andintegrate of a higher order (King and Rebelo, 1993)

no apparent economic reason why the cyclical residual should beproportional to the fourth di¤erence of the trend.

Another property (directly derived from the FOCs)

N∑t=1ĉt = 0


The Baxter King Filter

The BK lter belongs to the category of band-pass lters that extractdata corresponding to choosen frequency components."Band pass lters" lter out both the long run trend and thehigh-frequency movements in a given time series while retainingperiodicities of typical business cycle durations (typically, periodicitesbetween six quaters and eight years)

this approach is based on a spectral analysis of economic time series

In the time domain, the BK bandpass lter is obtained by applying aK-th order moving average to a given time series

y �t =K∑k=1

akyt�k

where the moving average coe¢ cients are chosen to be symmetric,ak = a�k , for all k = 1, .....K .

i.e., the time domain representation of the band pass lter is an inniteorder moving average.


The Baxter King Filter - Continued

BK show that if the sum of the moving average coe¢ cients is zero,i.e.,

K∑k=1

ak = 0

then it has trend elimination properties.

In particular, Baxter-King show that the lag polynomial describing theKth order moving average can be written as

a(L) = (1� L)(1� L)�1Ψ(L)

where Ψ(L) is an order symmetric moving average polynomial.The Baxter King lter will eliminate deterministic quadratic trends orrender stationary series that are integrated up to order two, i.e., I (2)or less


Developed versus EME/LDCs: Broad Features


The Indian Business Cycle - Evidence

India provides an interesting example to the study the changingnature of stylized facts

The Indian policy environment changed after the liberalizationreforms of 1991

The economy changed from a largely planned, closed, and agriculturaldependent economy to a market determined, industrial, andincreasingly globalized economy

Three transitions: away from socialism, away from autarky, and awayfrom agriculture.

How did this change the properties of the Indian business cycle.


Transition away from Agriculture


Transition away from Autarky -1


Transition away from Autarky - 2

Two questions

relevance of the SOE assumption

appropriateness of the business cycle approach in studyinguctuations in EMEs


Growth Cycle Approach

The log transformed series is ltered to extract the cyclical(stationary) and trend (non-stationary) component

The cylical component of the series is used to derive the businesscycle chatacteristics of volatility, persistence, and cross-correlations

We use the HP Filter to extact the cyclical component of the series

Robustness check done with respect to the BK Filter

approach followed by other papers (see Rand and Tarp, 2002).

The next set of slides follow Ghate et al. (2013)


Annual data analysis


Takeaways

Volatility of key macro variables have fallen

Output volatility 2.13 vs 1.78

Increases consumption volatility

0.85 vs 1.05

Increased pro-cyclicality of investment

0.22 vs 0.77

Increased pro-cyclicality of imports

�0.19 vs 0.70

Counter-cyclical net exports

0.24 vs �0.69

Counter-cyclical nominal exchange rate

0.10 vs �0.48


Statistical signicance of di¤erence in correlation

Procedure : see footnote 2829 (Ghate et al. (2013))


Decline in volatility not driven by Good Luck

But better policies


Indias Transition


Sensitivity tests: Quarterly data


Detrended path of key variables with GDP: quarterly data


Sensitivity tests: choice of detrending procedure


Sensitivity tests: redening the sample period


Other EME Experience

Rand and Tarp (2002) question whether length of business cycles inEMDEs is comprable to the duration in industrialized countries.

Use a sample of 15 developing countries

Average length of the business cycle for developing countries is onlybetween 7 and 18 quarters

Fewer comovements in terms of common peaks and troughsDeveloping countries gypically move relatively quickly from peak totrough and vice versa


Other EME Experience

See Rand and Tarp (2002)


Rand and Tarp - other results

Volatility

Output in their sample is a little more volatile than in the OECD region(but by no more than 15-20%)Consumption is generally more volatile than outputNo signicant volatility between DE and EMDEs in imports, exports,terms of trade, and the REER

Cross Correlations

Foreign trade (in general) counter-cylicalConsumption and investment strongly pro-cyclicalInation negatively correlated with output (supply side models forEMDEs appropriate)


Rand and Tarp - other results

See Rand and Tarp (2002)


Developed versus EMEs: How are they Di¤erent?


AG 2007

Can a SOE RBC model account for both developed and emergingmarket business cycles?

AG examine a version of a small open economy RBC model withpermanent and transitory shocks to productivty to account foremeging versus developed economy experiences.

In their veiw,EMEs are characterized by frequent changes in economicpolicy, hence shocks to trend growth are the primary source ofuctuations as opposed to transitory uctuations around the trend

In contrast, developed economies typically face stable political andeconomic policy regimes so that change to productivity are transitory.


AG 2007 - Description of the Model

Production function

Yt = expzt K 1�αt (ΓtLt )α, 0 < α < 1

where fztg and fΓtg represent two alternative productivity processesThe shock, zt , represents the transitory component of productivity,and evolves as a stationary AR(1) processεzt

zt = ρzzt�1 + εzt , jρz j < 1

where fεzt g∞t=0 is distributed i .i .d with E (εzt ) = 0, Var(εzt ) = σ2z .The permanent shock to productivity evoves according to

Γt = gtΓt�1 =t

∏s=0

gs

ln(gt ) = (1� ρg ) ln(µg ) + ρg ln(gt�1) + εgt ,

��ρg �� < 1here fεgt g

∞t=0 is distributed i .i .d with E (ε

gt ) = 0, Var(ε

gt ) = σ

2g .



Thus, gt , denotes shocks to the growth rate of productivity and µgdenotes average long run productivity growth.

Cobb Douglas preferences

ut =

�Cγt (1� Lt )1�γ

�1�σ1� σ 0 < γ < 1, σ � 0

Robustness check done with Grossman, Hercowitz, and Hu¤man(GHH) preferences

ut =(Ct � τΓt�1Lυt )

1�σ

1� σ , υ > 1, τ > 0



Economy wide resource constraint given by:

Ct +Kt+1 = Yt + (1� δ)Kt +φ

2Kt

�Kt+1Kt

� µg�2

| {z }Adjustment cost of capital

� Bt + qtBt+1

Price of debt for the country depends on the quantity of debtoutstanding:

1qt= 1+ rt = 1+ r � + ψ

�exp

�Bt+1

Γt� b�� 1�

| {z }Country spread risk due to indebtedness

where r � is the world interest rate, b is the steady state normalizeddebt, and ψ > 0 governs the elasticity of interest rate to changes inindebtednessModel expressed in "hatted" variables can be solved by standardrecursive methods


AG 2007 - Solving the model

Dene, bxt = xtΓt�1Value function dened in the terms of the transformed variables isgiven by

V (K̂t , B̂t , zt , gt ) = maxĈt ,Lt ,K̂t+1,B̂t+1

�u(Ĉt , Lt )+

ftEtV (K̂t+1, B̂t+1, zt+1, gt+1)

�where ft = f (β, gt )

subject to

Ĉt + gt K̂t+1 = Ŷt +(1� δ)K̂t +φ

2(gtK̂t+1K̂t

�µg )2K̂t � B̂t +qtgt B̂t+1



Substituting for Ĉt using the resource constraint, the rst orderconditions with respect to K̂t+1, B̂t+1, and Lt are

uc (Ĉt , Lt )�gt + φ

�gtK̂t+1K̂t

� µg�gt

�= f (β, gt )Et

�∂V

∂K̂t+1

�uc (Ĉt , Lt )gtqt + f (β, gt )Et

�∂V

∂B̂t+1

�= 0

uL(Ĉt , Lt ) + uc (Ĉt , Lt )∂Ŷt∂Lt

= 0



The envelope conditions are given by

∂V (K̂t , B̂t , zt , gt )∂Kt

= uc (Ĉt , Lt )

8>>>:∂Ŷt∂Kt+ (1� δ)+

φ�gtK̂t+1K̂t� µg

�gtK̂t+1K̂t

� φ2 (gtK̂t+1K̂t� µg )2

9>>=>>;∂V (K̂t , B̂t , zt , gt )

∂B̂t= �uc (Ĉt , Lt )


AG 2007 - Solving the model with GHH Preferences

The stationary competitive equilibrium satises the followingequations�Ĉt � τLυt

��σ �1+ φ(gt

K̂t+1K̂t� µg )

�=

βg σtEt

8>>>>>:�Ĉt+1 � τLυt+1

��σ266641� δ+ expzt+1(1� α)g αt+1

�Lt+1K̂t+1

�α+φ

�gt+1

K̂t+2K̂t+1

� µg�gt+1

K̂t+2K̂t+1

� φ2 (gt+1K̂t+2K̂t+1

� µg )2

377759>>>=>>>;�

Ĉt � τLυt��σ

= β(1+r )g σtEtn�Ĉt+1 � τLυt+1

��σoτυLν�1t = exp

zt αg αt�K̂tLt

�1�αsubject to the production function, the laws of motion for the shocks, theresource constraint, and the equation describing the real interest rate.


AG 2007 - solving the model

Solution of the model obtained by implementing a log-linearapproximation of the equilibrium conditions above

Subset of parameters is set at values determined a priori

The remainder of the parameters are estimated using GMM


AG 2007 - Calibration results

AG (2007) calibrate their model to match Mexico (EME) and Canada(SOE) data for the period 1980-2003

Important ndings:

The relative importance of trend productivity shocks over transitoryshocks for Canada and Mexico depend on the specication forpreferences

For Canada: σgσz = f0.25 or 0.41g ;for Mexico:σgσz= f2.5 or 5.4g

The autocorrelations of transitory shocks and φ are roughly similar forboth countries

Because shocks to productivity growth are more important thantransitory shocks

presence of more persistent trade decits in EMEs than in SOEs.σcσy> 1 for EMEs unlike in SOEs


Garcia-Cicco et al. 2006

Garcia-Cicco et al. (2006) challenge AGs results (the 2004 NBERversion of the AG 2007 paper).

Results in AG are driven due to the choice of a short sample toestimate low-frequency movements in productivity.

They show that output uctuations in post WWII are as large as thepre WWII periodSimilar results were not obtained when Garcia-Cicco et al. worked withlong-run Argentine data (1913-2005).They estimate that consumption smoothing in response to transitoryshocks are more important than in response to permanent shocks.In their estimated model,σ (consumption growth) < σ (output growth) .σ( NXY )σ(Y ) > 4


Garcia-Cicco et al. 2006

They also show that

Investments are insu¢ ciently volatileAutocorrelations of output growth and NXY do not match the data. Infact NXY actually tends to follow a random-walk

Therefore Garcia-Cicco et al. (2006) argue that EME-RBC models arenot purely driven by the inuence of permanent/transitory shocks,other sources of shocks matter.


Argentina (1900-2005): Model versus Data

The Predicted Autocorrelation Function of the Trade Balance-to-OutputRatio


Mexico (1900-2005): Model versus Data

The Predicted Autocorrelation Function of the Trade Balance-to-OutputRatio


Interest Rate Shock Models: NP 2005

Neumeyer and Perri (2005) build a SOE-RBC model where interestrate shocks play a crucial role

Compared to Advanced Economies (AEs), in Emerging MarketEconomies (EMEs)

output (Y ) is more volatileconsumption (C ) is pro-cyclical and more volatilenet exports (NX ) are more volatile than output and are morecounter-cyclical than in AEs

In addition

Interest rates (R) are also counter-cyclical


Brief digression - solving linear rational expectation models

Follows Uhlig (1999)

Uhlig shows how to nd the conditions for solving the log-linearizedversion of the model once it has been divided into a set of equtionswithout expectations and a set of equations in expectations (also see,McCandless, Chapter 6, 2008).

The model is divided into a set of matrix equations

0 = Axt + Bxt�1 + Cyt +Dzt0 = Et [Fxt+1 + Gxt +Hxt�1 + Jyt+1 +Kyt + Lzt+1 +Mzt ]

and a stochastic prcocess

zt+1 = Pxt�1 +Qztyt = Rxt�1 + Szt

Problem is to nd the values for the matrices P,Q,R,S


NP 2005 - A snapshot

Firms face a working capital constraint + preferences are GHH.

R " ) LD #Agents face GHH preferences ) LS remain unchanged ) equilibriumlabor falls, Y falls ) ρ (R,Y )EME < 0Intertemporal substitution e¤ect ) C # instantaneously, S "R " ) X #(S � X ) " ) ρ (NX ,Y ) < 0


NP 2005 - A snapshot

In their model, real interest rates are decomposed into twocomponents

Rt = R�t Dt

where R is the domestic real interest rate, R� is the world realinterest rate (US real interest rates), and D is the country spread riskcomponent

They model D in two ways the exogenous case, and the inducedcase (more on this later).

They calibrate their model to match the Argentine data and theyshow that lowering the country spread risk shocks can lower outputvolatility by around 27%.


NP 2005 - Solution Procedure

Setup of the model

FOCs

Steady state

Log-linearization

Impulse responses


NP 2005 - Timeline


Firms

The rm maximizes

πt = Atkαt�1�(1+ γ)t lt

�1�α � wt lt � rtkt�1 � (Rt�1 � 1) θwt lt .(2)

wt and rt are obtained


Firms

We transform all variables to their stationary values. For any variablext , we dene its stationary transformation as ext such that,

ext = xt(1+ γ)t

.

All variables in our model grow at the same exogenous rate (1+ γ) .All variables are therefore transformed to their correspondingstationary values except lt , which is assumed to be at the stationary.

Further, as in Uhlig (1997), any stationary variable ext can belog-linearized as

ext = xebxt' x(1+ bxt ).


Firms

Therefore

eyt = yt(1+ γ)t

=Atkαt�1l

1�αt (1+ γ)

t(1�α)

(1+ γ)t(3)

=At

(1+ γ)αekαt�1l1�αt .

Hence prots can be re-written as

eπt = eyt � rtekt�1(1+ γ)

� (1� θ) ewt lt � ewt ltRt�1θ.The rms prot maximization yields the following rst orderconditions for labor, lt , and capital, ekt�1, respectively.

fltg :(1� α)eyt

lt= ewt [(1� θ) + θRt�1] (4)nekt�1o : αeytekt�1 = rt(1+ γ) .


Firms steady state

In steady state,

(1� α)yl

= w�(1� θ) + θR

�αy

k=

r(1+ γ)

.


Firms Log-linear expressions

Log-linearizing the output yields

byt = bAt + αbkt�1 + (1� α)blt (5)Log-linearizing fkt�1g yields

byt = brt + bkt�1. (6)Log-linearizing fltg yields

byt = (bwt +blt ) + θR�(1� θ) + θR

� bRt�1. (7)


Households

Households supply labor and rent out capital in the competitive laborand capital markets respectivelyA stand-in representative agent maximizes

E0∞

∑t=0

βt�ct � ψ (1+ γ)t lvt

�(1�σ)(1� σ) , (8)

wherev > 1, and ψ > 0

subject to

ct + xt + bt + κ(bt ) � wt lt + rtkt�1 + Rt�1bt�1. (9)

Note that

wt lt + rtkt�1 � ct � xt = yt � ct � xt = st � xt= bt + κ(bt )� Rt�1bt�1 = nxt .


Households

κ(bt ) is the bond holding cost such that

κ(bt ) =κ

2yt

��btyt

��by

��2(10)

which is required for ensuring stationarity

xt is private investment such that;

xt = kt � (1� δ)kt�1 +Φ(kt , kt�1), (11)

where Φ(kt , kt�1) is the investment adjustment cost.

Φ(kt , kt�1) =φ

2kt�1

��ktkt�1

�� (1+ γ)

�2. (12)

which is required for keeping the relative volatility of xt under check.


Households

The agent therefore maximizes the following utility function

E0∞

∑t=0

eβt [ect � ψlvt ](1�σ)(1� σ) ,

where eβ = β (1+ γ)(1�σ) ,subject to (3), (9), (10), (11) and (12).


Households Lagrangian

Therefore the Lagrangian is given by

E0∞

∑t=0

eβt [ect � ψlvt ](1�σ)(1� σ) + λt fCONSTRAINTg


Households Lagrangian

Where the constaint is given by

0 �

8>>>>>>>>>>>:

ewt lt + rtekt�1(1+γ) + Rt�1ebt�1(1+γ) � ect � ekt � ebt+(1� δ) ekt�1

(1+γ)

� φ2ekt�1(1+γ)

h�(1+γ)ektekt�1

�� (1+ γ)

i2� κ2eyt h� ebteyt �� by �i2

9>>>>>>=>>>>>>;


Households - First Order Conditions

The rst order condition with respect to consumption is given by

fectg : λt = [ect � ψlvt ]�σ (13)The rst order condition with respect to labor supply is given by

fltg : λt ewt = [ect � ψlvt ]�σ ψvlv�1t (14)This implies ewt = ψvlv�1t .


Households - First Order Conditions

Other FOCs are as followsnebto : 1+ κ "ebteyt � by#=

eβ(1+ γ)

Et

�λt+1λt

Rt

�(15)

nekto : 1+ φ (1+ γ) " ektekt�1!� 1#= eβEt �λt+1

λtz�. (16)

where,

z = (1� δ) + rt+1(1+ γ)

+φ

2(1+ γ)

8

Households steady state

Fromnebto : eβR

(1+ γ)= 1

We get the following "No-Arbitrage" combiningnebto and nekto :

r = RP � (1� δ)

We get the following labor supply equation combining fectg and nelto :w = ψv l

v�1


Households steady state

Other steady state equations

x =γ+ δ

1+ γk

Φ(k, k) = 0κ(b) = 0

c +γ+ δ

1+ γk + b = wl +

rk(1+ γ)

+Rb

(1+ γ)


Households Log-linear expressions

From (13) and (14), labor supply is given by

lt = (ψv)11�v (ewt ) 1v�1 (17)

Log-linearizing (17) gives us

blt = bwtv � 1 . (18)Therefore equilibrium labor supply in log-linear terms is obtained bycombining (5), (7), and (18) to yield

blt = 1(α+ v � 1)

(bAt + αbkt�1 � θR�(1� θ) + θR

� bRt�1) (19)



On log-linearizingnebto we get

1� κby+

κby

�1+ bbt � byt� = eβ

(1+ γ)RPEth1+ bλt+1 � bλt + bRti

This implies

1+κby

�bbt � byt� = Et h1+ bλt+1 � bλt + bRti (20)) κb

y

�bbt � byt� = Et hbλt+1 � bλt + bRti



On log-linearizingnekto we get

φ (1+ γ)�bkt � bkt�1� (21)

= Etnbλt+1 � bλto+ eβr

(1+ γ)Etbrt+1 + eβφ (1+ γ)Et nbkt+1 � bkto .

where

Etnbλt+1 � bλto = � cσ

c � ψlv

!Et fbct+1 � bctg (22)

+

ψvσl

v

c � ψlv

!Etnblt+1 �blto



Note that log-linear approximations of κ(bt ) and Φ(kt , kt�1) areequal to zero!

Therefore the law of motion of capital can be log-linearized as

bxt = 1+ γγ+ δ

bkt � (1� δ)(1+ γ)

kxbkt�1 (23)

and nally the CBC is log-linearized as

wly

�bwt +blt�+ r ky�brt + bkt�1�(1+ γ)

+

Rby

�bRt + bbt�1�(1+ γ)

(24)

=cybct + kbkt � (1� δ) ky bkt�1

(1+ γ)+bybbt


Shocks

TFP bAt = ρAbAt�1 + εAt . (25)For interest rates,

Rt = R�t Dt . (26)

R�t is the US real interest rate. Therefore,bRt = bR�t + bDt . (27)


Interest rates and country spreads

bR�t is estimated as bR�t = ρR bR�t�1 + εRt . (28)There are two di¤erent models for country spreads

The Exogenous Case

bDt = ρD bDt�1 + εDt . (29)The Induced Case bDt = �ηEt bAt+1 + ut . (30)


Calibration of Parameters

For persistence of TFP, NP assume bAt to follow the same persistenceas in the US. Hence ρA = 0.95 and σ (εAt ) is set so as to match themoments of the Argentine data.bRt is obtained from the 3-month real yield on Argentine dollardenominated sovereign bonds, bR�t is obtained from 90 day-UStreasury bill rates.

The values of η and σ (εut ) are again chosen so as to match themoments of the Argentine data.



The value of the parameters v and σ of the GHH utility function havebeen chosen from the literature.

The value of θ is set to be equal to 1

The cost parameters κ and φ are set to match the moments of theArgentine data



Other parameters such as γ, α, β, δ, µ, and ψ are set so that thebalanced growth paths in the model are consistent with the long runArgentine data.

γ = 0.025 to match the average long-run Argentine growth rate of realoutputFrom (15) in steady state, eβ = R1+γ . Therefore β is chosen to matchthe average real interest rate of R = 14.8% during the sample of theirstudyThe parameter values of µ and ψ are so as to match l = 0.2.The parameter α is chosen such that from (4) in steady state,

(1�α)[(1�θ)+θR ]lt

= w ly = 0.6

δ is obtained by matching the the average investment/output ratio of0.21 during the period of 1983-2001Finally by is obtained from

NFA = θwly� by= �0.42


Summarizing the equations

Equations (31) to (38) below (obtained from (5), (6), (19), (20),(21), (22), (23), (24), (25), (27), (28)) and (29), or (30) representour system of equations.

0 = �byt + bAt + αbkt�1 + (1� α)blt (31)0 = �byt +brt + bkt�1 (32)

0 = �blt + 1(α+ v � 1)

(bAt + αbkt�1 � θR�(1� θ) + θR

� bRt�1) (33)

0 = �wlvblt � rk�brt + bkt�1�(1+ γ)

�Rb�bRt + bbt�1�(1+ γ)

(34)

+cbct + kbkt � (1� δ)kbkt�1(1+ γ)

+ bbbt(IGC-ISI Summer School 2014) EME Business Cycles June 2014 79 / 122

Summarizing the equations (contd)

0 = �κby

�bbt � byt�� cσc � ψlv

!Et fbct+1 � bctg (35)

+

ψvσl

v

c � ψlv

!Etnblt+1 �blto+ bRt

0 = �

cσ

c � ψlv

!Et fbct+1 � bctg+ ψvσlv

c � ψlv

!Etnblt+1 �blto(36)

+eβr

(1+ γ)Etbrt+1 + eβφ (1+ γ)Et nbkt+1 � bkto

�φ (1+ γ)�bkt � bkt�1�


Summarizing the equations (contd)

And nally the shocks

0 = �bAt + ρAbAt�1 + εAt (37)0 = �bR�t + ρR bR�t�1 + εRt . (38)

with either exogenous shocks to bDt or induced shocks to bDt as given inequations (29) and (30) respectively.


Uhligs Method applied

Following Uhlig, the above equations (31) to (38) along with (29) or(30) can be written in the following form

0 = Axt + Bxt�1 + Cyt +Dzt0 = Et fFxt+1 + Gxt +Hxt�1 + Jyt+1 +Kyt + Lzt+1 +Mztg

where

xt =� bkt bbt �0

yt =� byt bct blt brt �0

zt =� bAt bR�t�1 bDt�1 �0 .

The structural model is then obtained using Uhligs approach suchthat each yt variable is a linear policy function of xt�1 and zt .

We then use Uhligs toolkit to generate the impulse responsefunctions and the second order moments.


A Single Period interest rate shock

Note from equations (7) and (18), labor supply does not change due to aninterest rate shock since it is independent of consumption and labordemand at t depends on the interest rates of t � 1.


Impulse responses


Transmission of the interest rate shock

R " =) C # instantaneously, S " due to the intertemporalsubstitution e¤ect

R " =) LD # after one time period; LS remain unchanged due toGHH preferences =) equilibrium labor falls, Y falls after one timeperiod (k is brought forward from t � 1) =) ρ (R,Y ) < 0R " =) X # =) (S � X ) " =) NX " =) ρ (NX ,Y ) < 0


Calibration results


An Extension of NP (2005)

Usually, ρ (R,Y )AE > 0In EMEs, R is more volatile than output, but there is mixed evidenceon ρ (R,Y )EMEρ (R,Y ) < 0 in Latin American economies, but ρ (R,Y ) > 0 inEastern Europe, Africa and Asia (Male (2010)).

For India see Ghate et al. (2013).


Government expenditures - EMEs

In EMEs government expenditures are more volatile (Male (2010))and scal policy is less stabilizing and less counter-cyclical (Talvi andVegh (2005)) although there is no clear consensus.

Political pressures/temptations during boom-time governments cantlower expenditures or raise taxes.Pressure to reduce spendings during recessions lack of access tocredit.

Several EMEs in the last decade have "graduated" from pro-cyclicalto counter-cyclical scal policy improvements in institutional quality(Frankel et. al (2013)).

Government expenditure has been counter-cyclical in India post reforms(Ghate et al. (2013)).


Mixed experience

Male (2010)


The Indian business cycle

Ghate et al. (2013)


Is there a unied BC model for EMEs?

In Ghate, Gopalakrishnan, and Tarafdar (2014), we extend Neumeyerand Perri (2005) to capture this disparity. To do this

we add scal policy.we make preferences Cobb-Douglas - enables ρ (R,Y ) 7 0.

We then calibrate the model to qualitatively match Indian businesscycles using

TFP shocksinterest rate and country spread shocks.


Main result of the paper

By adding scal policy, we are able to explain the disparity inρ (R,Y )EME and in ρ (G ,Y )EMEKey Feature : Fiscal policy also acts as a stabilizer in ourframework, which makes real interest rates a-cyclical/pro-cyclical inour framework. This is because

a time varying tax wedge a¤ects the labor supply and,a subsidy on the interest rate on a portion of the rms totalborrowings a¤ects the labor demand.

Causal Mechanism: Interest rate shocks ! stabilizing scalpolicy ! the labor market


The Model: Firms


The Model: Firms

The rm maximizes

πt = Atkαt�1�(1+ γ)t lt

�1�α � wt lt � rtkt�1 (39)��RGt�1 � 1

�θGwt lt �

�RPt�1 � 1

�(θ � θG )wt lt .

The government lends θG < θ portion of the working capital at

RGt�1 = RPt�1(1� s) > 1, 0 < s < 1. (40)

We obtain wt and rt .


The Model: Households

A stand-in representative agent maximizes

E0∞

∑t=0

βt

h(c�t )

µ(1� lt )(1�µ)i(1�σ)

(1� σ) , (41)

where 8t c�t = ct +ΘGt , such that Θ > 1

subject to

(1+ τc )ct + xt + bt + κ(bt ) � (1� τw )wt lt (42)+(1� τk )rtkt�1 + RPt�1bt�1.

κ(bt ) is the bond holding cost, xt is private investment such that;

xt = kt � (1� δ)kt�1 +Φ(kt , kt�1). (43)

Φ(kt , kt�1) is the investment adjustment cost.


The Model: Government

The government balances its budget 8t

TRt|{z}After Prod.

+ RGt�1θGwt lt| {z }After Prod

= Gt|{z}After Prod.

+ St|{z}Before Prod.

where TRt isTRt = τcct + τwwt lt + τk rtkt�1. (44)

St is the loan extended to rms

St = θGwt lt .

Therefore

Gt = τcct +nhRPt�1(1� s)� 1

iθG + τw

owt lt + τk rtkt�1. (45)


Firsr Order Conditions

fectg : λt (1+ τc ) = h(ec�t )µ(1� lt )(1�µ)i�σ µ(ec�t )µ�1(1� lt )(1�µ)where λt is the Lagrangian multiplier

fltg : λt (1� τw )ewt = h(ec�t )µ(1� lt )(1�µ)i�σ (1� µ)(ec�t )µ(1� lt )�µ


Firsr Order Conditions

nebto : 1+ κ "ebteyt � by#= Et

" eβ(1+ γ)

λt+1λt

RPt

#nekto : 1+ φ (1+ γ) " ektekt�1

!� 1#= Et

�eβ λt+1λt

z�.

where,

z = (1� δ) + (1� τk )rt+1(1+ γ)

+φ

2(1+ γ)

8

The Labor Market Supply side

Proposition

Labor supply, lSt ,is given by:

lSt = 1�ectewt�1� µ

µ

�Γt (46)

where

Γt =�1+ τc1� τw

�ΨtDt�1

(47)

And τc > τw , τc >�RPt�1(1� s)� 1

�θG , and µ > 0.5 =) Γt > 1.



Γt is the "scal policy wedge" where

Γt =�1+ τc1� τw

�ΨtDt�1

such that

Dt�1 = 1+Θ�1�µ

µ

� �1+τc1�τw

� ��RPt�1(1� s)� 1

�θG + τw

and

Ψt =�1+Θτc +

Θτk rtekt�1(1+γ)ect + Θf[R

Pt�1(1�s)�1]θG+τwgewtect

�Clearly, when Θ = 0,

Γt = Γ =�1+ τc1� τw

�.



Note that

Dt�1 = D

+

RPt�1; parameters

!

Ψt = Ψ

+rt ,

�ect , +ekt�1, +RPt�1, +ewt ; parameters!.



Dt�1, does not change on impact. Ψt " in time period t because ect #and rt " (no-arbitrage condition).Therefore Γt " on impact due to a positive interest rate shock.Hence the outward shift of lSt due to a positive interest rate shock isdampened by an increase in Γt .



Proposition

For a positive shock to RPt

∂ect∂RPt

< 0 =) ∂lSt

∂RPt> 0

Further, a positive interest rate shock always increases the scal policywedge,i.e., ∂Γt

∂RPt> 0 An increase in Γt therefore dampens the outward

shift of the labor supply:�� ∂lSt∂RPt��Γt=0

>

�� ∂lSt∂RPt��Γt 6=0

> 0.


Labor supply interest rate shocks

From a one period shock in R at time period t

Lst " to Ls0t because ect instantaneously falls due to the intertemporal

substitution e¤ect. However, Lst shifts to Ls 00t with Γt " .


The Labor Market Equilibrium Demand side

We get ldt from the rms FOC

lDt =

"(1� α)Atewt �(1� θ) + RPt�1 (θ � sθG )�

# 1α ekt�1(1+ γ)

.

Proposition

A positive shock to interest rate RPt lowers labor demand only in timeperiod t + 1. However, the presence of θG and s, dampens the reductionin lDt+1. That is ��∂lDt+1∂RPt

��s 6=0,θG 6=0

<

��∂lDt+1∂RPt��s=0,θG=0

.


Labor Demand interest rate shocks

At time period t + 1

ldt+1 # because it depends on RPt(IGC-ISI Summer School 2014) EME Business Cycles June 2014 106 / 122

Labor Demand interest rate shocks

At time period t + 1 - with a working capital loan subsidy


Nota Bene: GHH preferences

Under GHH preferences,

E0∞

∑t=0

βt[ec�t � ψlvt ](1�σ)

(1� σ) ,

focs from fectg and fltg will give us l st from�1� τw1+ τc

�| {z }tax wedge

ewt = ψv (l st )v�1 .l st is not a¤ected by private or public consumption, although the tax

wedge�1�τw1+τc

�a¤ects the slope of the labor supply.



Without working capital loan subsidy



With working capital loan subsidy


Calibration

We estimate the DGP for India assuming annual HP-lteredde-trended series from 1980 - 2008. All shocks are for the momentassumed to be uncorrelated.

TFP (Penn World Tables Version 8.0 (2014))

bAt = ρAbAt�1 + εAt .ρA = 0.42 (0.012)

We use annual World Bank data on real lending rates, i.e.,

RPt = R�t Dt . (48)

R�t is the US real interest rate. Therefore,bRPt = bR�t + bDt .(IGC-ISI Summer School 2014) EME Business Cycles June 2014 111 / 122

Interest rates and country spreads

bR�t is estimated as bR�t = ρR bR�t�1 + εRt .ρR = 0.462 (0.004)

Country spreads are modelled as

bDt = �ηEt bAt+1 + ut .η = 0.4425 (0.006)

ut is a random shock

This is the "Induced Case" as in Neumeyer and Perri (2005), which isthe relevant case for India.


Parameters


Fiscal policy parameters

We assume:

θ = θG = 1τc = 0.12τk = τw = 0.01s = 0.11,Θ = 75


Experiment 1: Single period TFP shock

Figure: Single period TFP (bA) shock(IGC-ISI Summer School 2014) EME Business Cycles June 2014 115 / 122

Experiment 2: Single period interest rate shock

5 10 15 20 25 30 35 40-10

-5

0

5x 10

- 3 l y

5 10 15 20 25 30 35 40-0.03

-0.02

-0.01

0lc

5 10 15 20 25 30 35 40-0.01

-0.005

0

0 .005

0 .01l l

5 10 15 20 25 30 35 40-4

-2

0

2x 10- 3 l g

5 10 15 20 25 30 35 40-6

-4

-2

0

2lnx

5 10 15 20 25 30 35 400

2

4

6x 10- 3 R

5 10 15 20 25 30 35 40-0.2

-0.15

-0.1

-0.05

0lx

5 10 15 20 25 30 35 40-0.03

-0.02

-0.01

0

0 .01tr_gp

5 10 15 20 25 30 35 40-0.05

0

0 .05

0 .1

0 .15s i_gp

Figure: Single period world interest rate (bR�) shock(IGC-ISI Summer School 2014) EME Business Cycles June 2014 116 / 122

Experiment 3: Single period u-shock

5 10 15 20 25 30 35 40-15

-10

-5

0

5x 10- 3 ly

5 10 15 20 25 30 35 40-0.04

-0.03

-0.02

-0.01

0lc

5 10 15 20 25 30 35 40-0.02

-0.01

0

0.01l l

5 10 15 20 25 30 35 40-4

-2

0

2

4x 10- 3 lg

5 10 15 20 25 30 35 40-10

-5

0

5lnx

5 10 15 20 25 30 35 400

2

4

6

8x 10- 3 R

5 10 15 20 25 30 35 40-0.2

-0.1

0

0.1

0.2lx

5 10 15 20 25 30 35 40-0.06

-0.04

-0.02

0

0.02tr_gp

5 10 15 20 25 30 35 40-0.1

0

0.1

0.2

0.3s i_gp

Figure: Single period country spread (bD) shock(IGC-ISI Summer School 2014) EME Business Cycles June 2014 117 / 122

Calibration Results


Takeaway

Counter-cyclical government expenditures act as stabilizers

Interest rate shocks have implications for labor market dynamics andtherefore in EME business cycles

However, scal policy dampens the transmission of interest rate shocksto labor market dynamicsGoodness of t improves for the Indian business cycles when we addgovernment expenditures and subsidies.Government expenditure is counter-cyclical for high subsidies and lowtax rates

But,

Our t needs to improve knife-edge!Welfare?Government debt; e¤ect on spreads?


Thank you!


IGC Summer School 2014.

EME Business Cycles: Evidence and Theory · business cycles where there is no cycle present in the...

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