EME Business Cycles: Evidence and Theory - IJuly 2015 (Indian Statistical Institute - Delhi Center) EME Business Cycles July 2015 1 / 53. ... Indian business cycle in the pre and post

EME Business Cycles: Evidence and Theory - I

Chetan Ghate

Indian Statistical Institute - Delhi Center

July 2015

(Indian Statistical Institute - Delhi Center) EME Business Cycles July 2015 1 / 53

EME Business Cycles

A substantial literature exists on business 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 the empirical regularitiesof EMDE business cycles (Agenor et al., 2000; Rand and Tarp, 2002;Aguiar and Gopinath, 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 IndiaResearch agenda on building, calibrating, and estimating DSGE modelsfor EMEs


Overview

Preliminaries

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

Stylized Facts for EME Business Cycles

India business cycle evidence (Ghate, Pandey, and Patnaik (2013))Rand and Tarp (2002), Agenor et al. (2000), Male (2010), Chang andFernandez (2013)

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

Trend productivity shocks vs. interest rate shocksRole of frictionsCriticisms

Solving the model/calibration/estimation

Conclude


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 byde�ned ?

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 de�nition 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 de�nitions

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


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 de�ning 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

"N

∑t=1(yt � xt )2 + λ

N�1∑t=2

((xt+1 � xt )� (xt � xt�1))2#, λ > 0

(1)

First term is the penalty on the distance between the trend and theoriginal series. Second term is the penalty on changes in growth rates.

The second term, (xt+1 � xt � (xt � xt�1) = 42xt , is anapproximation to the 2nd derivative of x at t.

λ is the smoothing parameter (penalty parameter). As λ gets largerthe HP estimated trend gets smaller (smoother the growthcomponent)

As λ �! ∞ growth component becomes a linear trend



λ = 1600 generates a cyclical residual that accords with expectationsof what is generally believed to be a business cycle (for quarterly data)

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 trend is identi�ed by

x = (λF+ I)�1y

andc = y� x

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=1ct = 0


Criticisms of 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) versus 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 (exacerbate 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 spuriouslygenerating business cycles where there is no cycle present in theoriginal data.


The Baxter King Filter

The BK �lter belongs to the category of band-pass �lters that extractdata corresponding to chosen 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 quarters 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 in�niteorder 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

NI = ∆L� ∆A


Transition away from Autarky - 2

Two questions

relevance of the SOE assumption

appropriateness of the business cycle approach in studying�uctuations in EMEs


Growth Cycle Approach

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

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

We use the HP Filter to extract 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 fallenOutput volatility �2.13 vs 1.78 (consistent with other other Asianeconomies)

Increases consumption volatility0.85 vs 1.05 ( σc

σydriven largely by decreases in σy )

Increased pro-cyclicality of investment0.22 vs 0.77

Increased pro-cyclicality of imports�0.19 vs 0.70 (imports �uctuating more with BC activity which is apro-cyclical feature of AEs)

Counter-cyclical net exports0.24 vs �0.69 (X not pro-cyclical, M signi�cantly pro-cyclical)

Counter-cyclical nominal exchange rate0.10 vs �0.48 (" in bad times, # in good times)


Takeaways









Takeaways









Takeaways









Takeaways









Takeaways









Statistical signi�cance of di¤erence in correlation

Procedure : see footnote 28�29 (Ghate et al. (2013))


Lower volatility not driven by good luck but better policies

Good Luck Hypothesis: Variance of exogenous shocks is smaller (s.d.for TFP " from 0.21 to 0.27; s.d. for crude " from 2.29 to 4.83)


India�s Transition


Sensitivity tests: Quarterly data


Detrended path of key variables with GDP: quarterly data


Detrended path of key variables with GDP: quarterly data


Sensitivity tests: choice of detrending procedure


Sensitivity tests: rede�ning the sample period


Other EME Experience

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

Use a sample of 15 developing countries (Table 2)

Average length of the business cycle for developing countries is onlybetween 7 and 18 quarters (� 4.5 years)

Fewer comovements in terms of common peaks and troughsDeveloping countries typically move relatively quickly from peak totough and vice-versa



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

Use a sample of 15 developing countries (Table 2)

Average length of the business cycle for developing countries is onlybetween 7 and 18 quarters (� 4.5 years)

Fewer comovements in terms of common peaks and troughsDeveloping countries typically move relatively quickly from peak totough and vice-versa



See Rand and Tarp (2002). Truncation lag parameter of k = 20


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 signi�cant volatility between DEs and EMDEs in imports, exports,terms of trade, and the REER

Cross Correlations

Foreign trade (in general) counter-cyclicalConsumption and investment strongly pro-cyclicalIn�ation negatively correlated with output (supply side models forEMDEs appropriate)



Volatility


Cross Correlations




Volatility


Cross Correlations




Volatility


Cross Correlations




Volatility


Cross Correlations




Volatility


Cross Correlations




See Rand and Tarp (2002)


Developed versus EMEs : How are they Di¤erent?


AG 2007

Mendoza (1991) + Trend productivity shocks

See also Garcia-Cicco et al. (2010), Correia et al. (1995), Kydlandand Zargaza (2002), Chang and Fernandez (2013)

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 productivity to account foremerging versus developed economy experiences.

In their view,EMEs are characterized by frequent changes in economicpolicy, hence shocks to trend growth are the primary source of�uctuations 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.

Frictions? Financial and labor market (see Altug and Kabaca (2015))


Intuition of AG 2007

After εgt " productivity " permanently" in permanent income ) consumption can " more than currentincome ) σc

σy> 1

The representative agent may want to issue debt in the world marketto �nance consumption in excess of current income

This leads to a counter-cyclical current account


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 (ε

zt ) = 0, Var(ε

zt ) = σ2z .

In the standard model εzt is the only source of uncertainty



The permanent shock to productivity evolves according to

Γt = gtΓt�1 =t

∏s=0

gs

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

here fεgt g∞t=0 is distributed i .i .d with E (ε

gt ) = 0, Var(ε

gt ) = σ2g .

Γt allows for labor augmenting tech. progress. In a standard model Γtassumes a deterministic path

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



See Jaimovich and Rebelo (2009) who embed CD and GHHpreferences as special casesCobb Douglas preferences

ut =

�Cγt (1� Lt )1�γ

�1�σ

1� σ0 < γ < 1, σ � 0

Reduces the extent to which BCs can be driven by interest rate shocksRobustness check done with Grossman, Hercowitz, and Hu¤man(GHH) preferences

ut =(Ct � τΓt�1Lυ

t )1�σ

1� σ, υ > 1, τ > 0

Allows labor supply to be independent of consumption levels.Technically if u (c , l) = v (c � h (1� l))) MRScl = 1

h0(1�l) )MRS only depends on the real wage, not consumption



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 inindebtednessInterest on borrowing by the residents of the country is inverse of qt



Need a well de�ned steady state (see Schmidt-Grohe and Uribe(2003)). Therefore assume

rt = r � + p�edt� , where p0 (.) > 0

In the steady state,

1 = βh1+ r + ψ

nexp

�d � ed�� 1oi

=) interest rate premium is nil


AG 2007 - Solving the model

Model expressed in "hatted" variables can be solved by standardrecursive methods

De�ne bxt = xtΓt�1

Value function de�ned in the terms of the transformed variables isgiven by

V (Kt , Bt , zt , gt ) = maxCt ,Lt ,Kt+1,Bt+1

�u(Ct , Lt )+

ftEtV (Kt+1, Bt+1, zt+1, gt+1)

�where ft = f (β, gt )

subject to

Ct + gt Kt+1 = Yt +(1� δ)Kt +φ

2(gtKt+1Kt

�µg )2Kt � Bt +qtgt Bt+1



Substituting for Ct using the resource constraint, the �rst orderconditions with respect to Kt+1, Bt+1, and Lt are

uc (Ct , Lt )�gt + φ

�gtKt+1Kt

� µg

�gt

�= f (β, gt )Et

�∂V

∂Kt+1

�uc (Ct , Lt )gtqt + f (β, gt )Et

�∂V

∂Bt+1

�= 0

uL(Ct , Lt ) + uc (Ct , Lt )∂Yt∂Lt

= 0



The envelope conditions are given by

∂V (Kt , Bt , zt , gt )∂Kt

= uc (Ct , Lt )

8>><>>:∂Yt∂Kt+ (1� δ)+

φ�gtKt+1Kt� µg

�gtKt+1Kt

� φ2 (gt

Kt+1Kt� µg )

2

9>>=>>;∂V (Kt , Bt , zt , gt )

∂Bt= �uc (Ct , Lt )


AG 2007 - Solving the model with GHH Preferences

The stationary competitive equilibrium satis�es the followingequations�Ct � τLυ

t

��σ�1+ φ(gt

Kt+1Kt� µg )

�=

βg σtEt

8>>><>>>:�Ct+1 � τLυ

t+1

��σ

266641� δ+ expzt+1(1� α)g α

t+1

�Lt+1Kt+1

�α

+φ�gt+1

Kt+2Kt+1

� µg

�gt+1

Kt+2Kt+1

� φ2 (gt+1

Kt+2Kt+1

� µg )2

377759>>>=>>>;�

Ct � τLυt

��σ= β(1+r )

g σtEtn�Ct+1 � τLυ

t+1

��σo

τυLν�1t = expzt αg α

t

�KtLt

�1�α

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




t

��σ�1+ φ(gt

Kt+1Kt� µg )

�=

βg σtEt

8>>><>>>:�Ct+1 � τLυ

t+1

��σ

266641� δ+ expzt+1(1� α)g α

t+1

�Lt+1Kt+1

�α

+φ�gt+1

Kt+2Kt+1

� µg

�gt+1

Kt+2Kt+1

� φ2 (gt+1

Kt+2Kt+1

� µg )2

377759>>>=>>>;�

Ct � τLυt

��σ= β(1+r )


t+1

��σo


t

�KtLt

�1�α





t

��σ�1+ φ(gt

Kt+1Kt� µg )

�=

βg σtEt

8>>><>>>:�Ct+1 � τLυ

t+1

��σ

266641� δ+ expzt+1(1� α)g α

t+1

�Lt+1Kt+1

�α

+φ�gt+1

Kt+2Kt+1

� µg

�gt+1

Kt+2Kt+1

� φ2 (gt+1

Kt+2Kt+1

� µg )2

377759>>>=>>>;�

Ct � τLυt

��σ= β(1+r )


t+1

��σo


t

�KtLt

�1�α



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

See Chang and Fernandez (IER, 2013); goodness of �t can be doneby matching moments and likelihood based measures (BayesianEstimation � see Lubik and Schorfheide (2005))

Also need IRFs and variance decomposition exercise


AG 2007 - Calibration results

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

Important �ndings:

The relative importance of trend productivity shocks over transitoryshocks for Canada and Mexico depend on the speci�cation forpreferencesFor Canada: σg

σz= f0.25 or 0.41g ; for Mexico: σg

σz= f2.5 or 5.4g

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

Main �nding: volatility of innovations much stronger in thepermanent technology process than in the transient one. Major roleof trend shock

presence of more persistent trade de�cits in EMEs than in SOEs.σcσy> 1 for EMEs unlike in SOEs







σz= f2.5 or 5.4g










σz= f2.5 or 5.4g










σz= f2.5 or 5.4g










σz= f2.5 or 5.4g





Garcia-Cicco et al. 2010 and Chang and Fernandez (2013)

Garcia-Cicco et al. (2010) challenge AG�s results

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

The show that output �uctuations in post WWII are as large as the preWWII 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

Chang and Fernandez (2013) say that trend shocks play a small rolein explaining the variance in output



























They also show that

Investments are insu¢ ciently volatileAutocorrelations of output growth and NX

Y do not match the data. Infact NXY actually tends to follow a random-walk

Therefore Garcia-Cicco et al. (2010) argue that EME-RBC models arenot purely driven by the in�uence of permanent/transitory shocks,other sources of shocks matter.

In Chang and Fernandez (2013), relative importance of trend shocksincreases when they shut o¤ interest rate shocks and �nancial frictions



They also show that

Investments are insu¢ ciently volatileAutocorrelations of output growth and NX

Y do not match the data. Infact NXY actually tends to follow a random-walk

Therefore Garcia-Cicco et al. (2010) argue that EME-RBC models arenot purely driven by the in�uence of permanent/transitory shocks,other sources of shocks matter.

In Chang and Fernandez (2013), relative importance of trend shocksincreases when they shut o¤ interest rate shocks and �nancial frictions


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


Documents

EME Business Cycles: Evidence and Theory - IJuly 2015 (Indian Statistical Institute - Delhi Center) EME Business Cycles July 2015 1 / 53. ... Indian business cycle in the pre and post