Magnitude X on the Richter Scale: Welfare Cost of Business Cycles in Developing Countries

Centre de recherchesur l’emploi et lesfluctuations economiques(CREFE)

Center for Research on EconomicFluctuations and Employment (CREFE)

Universite du Quebeca Montr eal

Cahier de recherche/Working Paper No. 124

Magnitude X on the Richter Scale:

WelfareCostof BusinessCyclesin DevelopingCountries�

StephanePallage

CREFE-UQAM

Michel A. Robe

AmericanUniversity

October2000

————————————————————–

Pallage: Departmentof Economics,University of Quebecat Montreal,CP 8888succ. Centre-Ville, Montreal,QC,

H3C 3P8,Canada.Tel: 514-987-3000(8370#).Fax: 514-987-8494.Email: [email protected].

Robe:KogodSchoolof Business,AmericanUniversity, 4400MassachussettsAvenueNW, Washington,DC 20015.

Tel: 202-885-1880.Email: [email protected].�We aregratefulto Kjetil Storesletten,Kevin Carey andRobertBuckley for usefuldiscussions.We alsothankGadi

Barlevy, EnriqueMendoza,David Reebandseminarparticipantsat the 2000Meetingof the Societyfor Economic

Dynamicsin CostaRicafor helpful suggestions.Xinxin Wangprovidedvaluableresearchassistance.

Abstract:

Economicfluctuationsaremuchstrongerin developingcountriesthanin theUnited States.Yet,

while a large literaturedebateswhatconstitutesa reasonableestimateof thewelfarecostof busi-

nesscyclesin theUS, it remainsanopenquestionhow large thatcostis in developingcountries.

Using several modeleconomies,we provide sucha measurefor a large numberof low–income

countries.Ourfirst mainresultis thatthewelfarecostof outputfluctuationsper se is far from triv-

ial in thosecountries,andtypically averages15to 30timesthecorrespondingestimatefor theUS.

Our secondmajor resultis that, in many poorcountries,thatcostmay in factexceedthewelfare

costof significantlylowergrowth.

Keywords:

Businesscycles,consumptionvolatility, welfarecost

JELclassification:E32,E60

1 Intr oduction

To theextentthatacountry’s residentsarerisk-averse,their inability to insureagainstfluctuations

in domesticaggregateconsumptionmustbringaboutwelfarelosses.Sincedevelopingnationsnot

only aresubjectto strongeconomicshocksbut alsofacedifficulties in sharingthat risk interna-

tionally, a naturalquestionis how mucheconomicfluctuationsaffect their welfare. Yet, muchas

policy adviceto thosecountriesconcentratesongrowth, researchonthecostsof economicvolatil-

ity in developing countriesfocuseson its deleteriouseffect on growth [e.g., Ramey & Ramey

(1995),Mendoza(1997)]. In fact,little is known aboutthewelfarecostof businesscyclesin those

countries,andhow it measuresup to thewelfarecostof significantlylowergrowth.

In the United States,numerousattemptshave beenmadeto computethat cost. Startingwith

Lucas(1987),estimatesrangefrom minor to substantial,dependingonthemodeleconomyusedin

thecomputations.A similardebate,aboutwhatconstitutesareasonablewayto measuretheactual

welfarecostof businesscycles,is likely to carryover to poorcountries.Consequently, we do not

endeavor to provideanabsolutecostestimatefor thelatter. Rather, thequestionsweanswerin this

paperarethefollowing: How large is thewelfarecostof businesscyclesin developingcountries,

relative to thatin theUS?Is thatcostevercomparableto thecostof significantlylowergrowth?

Usingseveralmodels,including theoriginal Lucas(1987)endowmenteconomy, we compute

thewelfarecostsof businesscyclesfor a largesampleof developingcountries.We thencontrast

thesecostswith estimatesobtainedfrom the samemodelsusingUS data. For eachcountry, we

calibratethemodelsusinglocal–currency figuresfrom theWorld Bankor extantstudies,andcarry

out robustnesschecks.

Acrossall modelspecifications,wefind thatthemediancostof businesscyclesin poorcountries

usuallyrangesbetween15 and30 timeswhat it is in the US. Even underthe mostconservative

assumptions,the deadweightloss is large – on average,removing businesscycles is equivalent

to increasingconsumptionby at least0.5% in perpetuity. In the ongoingdebateaboutwhether

economicfluctuationsper se have a significantimpacton welfare,our resultsthereforesuggest

that,at aminimum,oneshouldbeseveraltimesmorecarefulwhendealingwith poorcountries.

Indeed,despiteourabstractingaway from any negative impactof volatility ongrowth [Barlevy

(2000)],we show that thewelfarelossesbroughtaboutby businesscyclescouldwell bemassive

in developingcountries.In many of thosecountries,wefind thatevenmodestlyrisk–averseagents

mayin factstrictly preferseeingbusinesscycleseliminatedto receiving a permanentextra 1% of

1

yearlyconsumptiongrowth.

2 Modeling Considerations

In a path-breakingexercise,Lucas(1987) endeavored to measurethe welfare cost of business

cycles in the US. The idea was to obtainan upper-boundfor this cost, by simulatinga simple

economywhereconsumptionis generatedby a stochasticprocesswith i.i.d. shocksthatmatches

the varianceand meanof the observed consumptionseries. Agents in that economylack any

savings technology, andinvestmenthasno effect on the parametersof the stochasticprocessfor

consumption.

Surprisingly, the welfarecostof consumptionvolatility in suchan environmentis extremely

low. Shuttingoff all fluctuationsin USaggregateconsumptionamountsto giving therepresentative

agenta consumptionincrease,acrossall datesandstatesof theworld, of lessthan0.1%.By com-

parison,raisingthemeangrowth rateby 1%is equivalentto a17%across–the–boardconsumption

increase.Thatfindinghasledaseriesof authorsto consideralternativemodeleconomies.

A first considerationis market completeness.Unlike Lucas(1987), Imrohoroglu (1989) as-

sumesthat individuals are subjectto idiosyncraticemployment shocksand face liquidity con-

straints.Theresultingimperfectrisk–sharingamongagentsbringsabouta three–foldincreasein

thewelfarecostsof USbusinesscycles,relative to Lucas’estimate.Atkeson& Phelan(1994)and

Krusell& Smith(1999),however, find thatthewelfaregainfrom counter-cyclical policiesin such

anenvironmentis in factcloseto zero,oncetheadversewelfareeffectsof assetpricechangesare

takeninto account.Throughoutthis paper, we thereforeposit thatall idiosyncraticshockscanbe

perfectly insured. Consequently, sincemechanismsto shareidiosyncraticrisk arelikely far bet-

ter in theUS thanin low–incomeeconomies,our costestimatesfor developingnationsshouldbe

conservative– bothin absolutetermsandrelative to equivalentUSfigures.

A secondconsiderationis therepresentativeagent’spreferencesaswell asthestochasticprocess

governinghis consumption.Obstfeld(1994)andDolmas(1998)considernon–expected–utility

preferencesthatdecouplerisk aversionandintertemporalsubstitution.Whenconsumption–shock

persistenceis takeninto account,Obstfeld(1994)findsacostrangingfrom 0.1to 0.4%of expected

non–durableconsumptionin eachperiod,for reasonablevaluesof risk aversionandelasticityof

intertemporalsubstitution.Oncethegrowth rateof consumption[not just the level] is allowedto

fluctuate,Dolmas(1998)finds that thewelfarecostof businesscyclesis quitehigh: from 0.2 to

2

1%of permanentconsumption,for quarterlydataandsimilarvaluesof thepreferenceparameters.1

Overall, then,onecanreasonablyargueaboutthe“true” welfarecostof businesscyclesin the

UnitedStates.2 Whatis notdebatable,in contrast,is thatbusinesscyclesin developingeconomies

are of much higher magnitudethan any economicfluctuationexperiencedin industrializedna-

tions.3 A naturalquestionis how muchthoseeconomictremorsdecreasewelfarein developing

countries.In particular, is thewelfarecostof businesscyclesin thosecountriesa largemultipleof

thecostin theUS, regardlessof thechoiceof modeleconomy?Doesthatcostapproach,or even

exceed,thewelfarecostof significantlylower growth? We answerthesequestionsby computing

bothcostsunderthreespecifications,detailednext.

3 Thr eeModel Economies

We considerin turn threeeconomies,all populatedby a continuumof infinitely-lived, identical

individualsof mass1. In two of those,the representative consumerhasCRRA preferencesover

consumptionstreams���������

:� �� �������������� � �������� "!!� $# (1)

where�&%('*),+ !.- is thediscountfactorand#

is theconstantcoefficientof relative risk aversion.

In thelasteconomy, preferencesaredefinedby theEpstein& Zin (1989)–Weil (1990)recursion:� �� 0/�� ���21� 3 �54 ��� ' � �������6 � -879;:<9;:>=�? 99;:><(2)

where�1 is theelasticityof intertemporalsubstitution.Notethat(2) reducesto (1) when

�1 #.

Weconsiderthreelawsof motionfor consumption.In thefirst modeleconomy, thenaturallog-

arithmof realpercapitaconsumptionfluctuatesrandomlyandconsumptionshocksaretemporary:@BA �C�� �D 3FE �with

E ��G H '*)I+KJ�LM - (3)

1Theimportanceof shockpersistencealsoholdsunderfirst–orderrisk–aversepreferences:for moderateparameter

values,thecostcanreach2–5%with a stochasticgrowth rate[Dolmas(1998)]but is muchsmallerwith i.i.d. shocks

arounda deterministictrend[Pemberton(1996)].2In line with thatconclusion,therelatedliteratureon internationalrisk sharingshowsthatcomputationalestimates

of thewelfaregainsfrom betterinternationalinsurancedependheavily on theunderlyingmodeleconomy– seevan

Wincoop(1999)for a comprehensivereview of thatliterature.3Thevolatility of outputin developingcountries,for example,rangesfrom two to six timesthatin theUS[Mendoza

(1995);Carmichael,Samson,& Keita(1999);Agenor, McDermott,& Prasad(2000);Pallage& Robe(2000)].

3

We alsolook, for countriesin which it is a goodfit, at a consumptionprocessthathasa constant

time trendandin whichconsumptionshocksarepersistent:@BA �C�� @NA ��� �O� 3FP !Q J LR 3TS �with

S �,G H '*)I+KJ LR - (4)

While assuminga linear deterministictrend seemsappropriatein many cases,the long–term

growth rateof realpercapitaconsumptionis not constantin all African countries[e.g.,Pritchett

(2000)]. In onemodeleconomy, therefore,we follow Dolmas(1998)andconsideranautoregres-

siveprocessfor thegrowth rateof realpercapitaconsumption,U �V WYXW X :Z9 :U �V ' !� ([I- ' ! 3(\ - 3 [ U � �O� 3F] �with

] �IG H '*),+KJ^L_ - (5)

To summarize,weconsiderthreemodeleconomies.In thefirst, wepositCRRAutility (1) andlaw

of motion (3) for consumption.That economy, similar to Lucas(1987),providesthe traditional

benchmark.4 The secondspecificationcombinesCRRA utility (1) and stochasticconsumption

growth (5). Finally, thethird economy, proposedby Obstfeld(1994),allows shockpersistenceto

impactutilities by combiningEpstein& Zin–Weil preferences(2) andconsumptionprocess(4).

In eachmodeleconomy, wemeasurethecostof businesscyclesasthepercentageconsumption

increaseat all datesand in all states, , that would renderthe representative agentindifferent

betweena world of uncertainty[with consumptionfollowing (3), (4) or (5)] andoneof certainty

[i.e., with the samelaws of motion but J LM ) , J LR ) or J L_ ) , respectively]. AppendixA

summarizesthemethodsemployedto compute .

4 Calibration

In orderto quantify the costsof businesscycles in low–incomecountries,we mustparametrize

eachmodeleconomy, solve it numerically, andcarryout robustnesschecks.We focuson Africa,

for two reasons.First, in thelastthreedecades,African economieshaveexperiencedfewerforeign

exchangeandmonetarycrisesthantheirLatin Americanor Asiancounterparts.Second,andmost

importantly, African countriesareamongthepoorestin theworld: hence,concernsthatbusiness

cyclesmaybetruly onerousshouldbemostrelevantto thosenations.

4The stochasticprocesspositedin Lucas(1987)hasa linear time trend,which is appropriatefor the US but not

for many developingcountries.In our first economy, we wish to focussolelyon businesscycle fluctuations,defined

asthecyclical componentof Hodrick-Prescottfilteredseries.We seeka lower–boundestimateof thewelfarecostof

businesscycles.We will dealwith issuesrelatedto growth with theothertwo modeleconomies.

4

An African country is excludedfrom our sampleif it wasnot independentby 1975, if fewer

thantwenty-two consecutive yearsof dataareavailable for that country, or if it wasthe victim

of war [civil or otherwise]during the sampleperiod. Thosecriteria leave thirty–threecountries,

twenty–nineof which arefrom Sub–SaharanAfrica. AppendixB describesthesamplein detail.

To calibratethe preferenceparametersin (1) and(2), we rely on previous estimates.For de-

velopedaswell asdevelopingcountries,the discountfactor � typically is setbetween0.95and

0.97for yearlydata.We thereforechoose0.96asa basevaluefor our computations.5 Neitherthe

coefficientof relativerisk aversion#

nor theelasticityof intertemporalsubstitution�1 haveaccept-

edstandardvalues.We usethevalues# % � !badc + Q aec + c + ! ) � , which coversits recognizedrangeof

(0,10] [Mehra& Prescott(1985)]. In theexperimentsfor which�1 differs from

#, we take

�1 Qand

# % � !badc + Q adc + c � , which is in line with extantpapers[Obstfeld(1994),Dolmas(1998)]aswell

aswith estimatesof f in developingcountries[e.g.,Ostry& Reinhart(1992)].

We computeparameterestimates,for laws of motion of consumption(3)–(5),with datafrom

individual countriesover the 1968–1996period. We useannualdata,asquarterlyfigurestypi-

cally arenot available. For eachcountry, we calibratethe model to matchmomentsof the real

percapitatotal or privateconsumptionseries,6 in constantlocal currency prices,from theWorld

Bank’s World DevelopmentIndicatorsdatabase[WDI]. 7 For process(3), we parameterizeJ LM to

the varianceof the cyclical componentof Hodrick-Prescottfiltered logarithmsof real per capita

privateconsumption[with weight100,sincethedatais yearly]. By abstractingfrom any issuere-

latedto growth or from any impactthatvolatility in thenon-cyclical componentof theHP-filtered

seriescould have on the representative agent’s welfare,this parametrizationguaranteesthat cost

computationsin our first modeleconomyfocuspurelyon thewelfarecostof businesscycle fluc-

tuationsand,hence,yield conservative costestimates.8 For process(4), parametersareestimated

5Ostry& Reinhart(1992)documentthat therangemaybesomewhatbroaderin developingcountries,with a low

of 0.945in Africa. Usingthis alternativevalueleavesourmainresultsqualitatively unaffected.6We obtainqualitatively similar resultswith modeleconomiescalibratedto total, ratherthanprivate,consumption

in constantlocal–currency prices.Hence,theremainderof our discussionfocuseson privateconsumption.7For mostdevelopingcountries,comparable–USdollar figuresfrom the Summers& Heston(1991)PennWorld

Tables(1969-92)arebasedon few benchmarkpoints.Hence,our resultsshouldberobustto usingPWT figures[see

Pritchett(2000)for a similar point]. Indeed,consistentwith this premise,wefind qualitatively similar resultsin all of

theexperimentsrunwith bothPWT andWDI data.8Thisapproachpresentstheadditionaladvantageof allowing for directcomparisonof ourwelfarecostfigureswith

thoseof Lucas(1987),whousesasimilar calibrationprocedure,andof ourconsumptionvolatility figureswith output

5

by regressingconsumptionincreaseson a constant.For process(5), themeangrowth rate\, the

persistenceparameter[

andtheresidualvarianceJ L_ areobtainedfrom astandardgih ' !.- fit.

5 WelfareCostsof BusinessCycles

Table1 gives,for our sampleaswell asfor theUnitedStates,summarystatisticsof thevolatility

estimate,J LM , andof thewelfarecostsof businesscyclesfor differentvaluesof the representative

agent’s risk aversion,#. For eachcountry, thecostis computedundertheassumptionof a Lucas

(1987)treeeconomywith no growth, by comparing(i) an economyin which the representative

agenthasa constantstreamof real per capitaconsumption,correspondingto the meanof the

stochasticprocessand normalizedto unity, with (ii) an economyin which that streamhasthe

samemeanbut varianceJ LM . In the US we find, over the 1968-1996period, little consumption

volatility ( J M !baejZk�l) anda correspondinglyminusculewelfarecostof businesscycles,with `

rangingfrom 0.02%to 0.07%of permanentconsumption.African countrieshave muchstronger

andcostlierbusinesscycles: the median(average) volatility is 3.86%(4.18%), and the median

(average) welfarecostestimateis 15 (21) timestheUSfigure.9

By construction,Table1 explicitly abstractsfrom costsdueto economicfluctuationsthathave

beenHP-filteredout and,hence,from costsrelatedto possiblefluctuationsin thegrowth rateof

consumption.In contrast,PanelA of Table2 givessummarystatisticsfor the percentagecon-

sumptionincrease, , neededto makea representativeagentindifferentbetweena world in which

consumptiongrowth is stochasticandmovesaccordingto (5), anda world wheregrowth is deter-

ministic: m Xon 9m X ! 3(\qpsr.

Thewelfarecostof consumptionfluctuationsunderthissecondspecificationis muchlargerthan

underthepreviousone.10 Thecostapproaches3.4%of permanentconsumptionin theUS, while

volatility estimatesfrom otherpapersonbusinesscyclesin developingcountries.9It is well known that thequality of consumptiondatain low–incomecountriesoften leavesmuchto bedesired.

To ensurethat our resultsarenot data–specific,we ran the following experiment. In an economysimilar to Lucas

(1987),we gave the agentaccessto a risklessone–periodstoragetechnologyandcalibratedhis endowmentstream

to real local–currency GDP data[WDI]. The resultswerenot substantiallyaffected,in that the medianwelfarecost

of businesscycles in Africa remaineda non-trivial multiple of the cost in the United States. Similar resultswere

obtainedby calibratingthe outputprocessto comparable–USdollar datafrom the Summers& Heston(1991)Penn

World Tables(1969-92).Tablessummarizingthoseexperimentsareavailableuponrequest.10In orderto reducethelikelihoodthatwemightoverestimatevolatility – and,hence,costs– in Table2, weexclude

6

themediancostrangesfrom 8.3%to 22.5%in Africa dependingon therisk aversionparameter.11

Therelevantfindingin PanelA, though,is notmerelyhighercosts:thosecanbeanticipatedatleast

partly from extant resultsfor theUS [Dolmas(1998)]andtheobservation that,with a stochastic

growth rate,onemaymeasuremorethanthewelfarecostof consumptionvolatility per se. Rather,

whatis significantis that,despitevastlydifferentlawsof motionfor consumption,thewelfarecost

of businesscyclesin low–incomecountriesremainsa largemultipleof its UScounterpart.

The third modeleconomycombinesstochasticprocess(4), in which consumptionshocksare

persistent,andpreferences(2) thatmagnifytheimportanceof shockpersistence.PanelA of Table

3 showsthat,onceagain,all welfarecostestimatesaremuchhigherthantheircounterpartsin Table

1, whereasthemedianratio of US costto African costsremainsof thesamemagnitudeasbefore

[themedianratio rangesbetween18 and25,dependingon theparametrization].12

Overall, theseresultsdemonstratethat, even if businesscycles had no damagingimpact on

growth, their impact on developingcountries’welfare would neverthelessbe significant. First,

acrossall modelspecifications,thewelfarecostin thosecountriesis almostalwaysadouble–digit

multiple of thecostin theUS.Second,evenour lowestmeanwelfarecostestimate[with# !badc

anda lower–boundvolatility estimate]is nearly0.5%of permanentconsumption.To paraphrase

Lucas(1987)[p.29], “asdeadweightlossesgo, this is a largenumber.”

To furtherput our figuresin perspective,onecancomparethemto thewelfaregainthatwould

bebroughtabout,ceteris paribus, by a permanentadditional1% of growth peryear. Both for the

USandfor oursamplecountries,thatgaintypically rangesfrom 12.5%to 25%.Suchfiguresimply

that,in theUS,not evena highly risk–averserepresentative agent(# Q ) ) would preferreduced

uncertaintyto highergrowth [seealsoObstfeld(1994)andDolmas(1998)]. In strikingcontrast,in

many African countries,evena modestlyrisk–averserepresentativeagent(# Q aec

) might strictly

from thisexperimentall samplecountriesfor which (5) is not clearlyagoodfit. We alsoexcludecountrieswith mean

growth ratessonegativethattherepresentativeagent’sconsumptionwouldconvergeto negativelevelswithin 50years

– seeAppendixB.11Our costestimatefor the US [3.4%] is much larger thanthe onefound by Dolmas(1998)with quarterlydata

[0.5%]. In all likelihood,our largercostfigure is the resultof our highervolatility andshock–persistenceestimates

[whoseeffect is cumulative]. Thoselarger parameterestimatesmay be dueto the differencein estimationperiods.

They mayalsoreflectthefactthatthe tvuxwYy{z process(5) is not thebestof fit for annualUS consumptiondata.12In orderagainnot to biasvolatility andcostestimatesupwards,weeliminatefrom thesampleall countrieswhose

pathof log percapitaconsumptionis not clearly linear. Naturally, we alsoexcludeeconomiesthatshrankduringthe

sampleperiod,i.e.,countriesfor which |~}�� .7

preferseeingbusinesscycleseliminated[PanelA, Tables2 & 3] to beingaffordeda permanent

extra 1% of yearly consumptiongrowth [PanelB, Tables2 & 3]. This result is robust, in that it

holdsin bothspecificationsin whichweallow for shockpersistence.

6 Conclusion

In this paper, we computethewelfarecostof businesscyclesin a seriesof low–incomecountries,

usingvarioustechniquesthathave beenproposedin theliterature.Dependingon themodelused,

wefind thatthemedianwelfarecostof businesscyclesin thosecountriestypically rangesfrom 15

to 30 timesits estimatefor theUnitedStates.

Whetherthe true costof businesscyclesin poor countriesis massive or merely large, we do

not know. Dependingon themethodology, thereis significantvariancein thenumberswe report.

In fact, we do not think that any of our estimatesshouldbe taken asan absolutemeasureof the

welfarecostof economicfluctuationsin thosecountries.A constantof our analysis,however, is

that the costin poor countriesis never trivial, andalwaysa large multiple of that in theUS. For

many of thosecountries,furthermore,the welfaregain from eliminatingbusinesscyclesmay in

factbesolargeasto exceedthatof receiving anadditional1% of growth forever.

While policy adviceto developingcountrieshasfocusedheavily ongrowth, our resultssuggest

that policies (including financial reformsor institutional developments)meantsolely to reduce

outputvolatility maybring aboutsubstantiallyhigherwelfaregainsin thosecountriesthanin the

US.Stabilizationpolicies,at leastfor thosecountries,shouldnotbedismissedtoohastily.

8

Appendix

A WelfareCost Computation Methods

ThisAppendixsummarizeshow wecomputethewelfarecostof businesscycles, � . Closed–formsolutionsexist in the

first andthird modeleconomies[see,e.g.,Lucas(1987)andObstfeld(1994)]. For thesecondeconomy, we compute� by first simulating,for eachcountry, onethousand50–yearconsumptionpathsaccordingto (5), with the law of

motion’sparametersobtainedfrom ourcalibration[Section4]. We focuson50–yearsimulationrunssoasto simulate

African economieswith slightly negativemeangrowth rates.Wethenextractthepermanentconsumptionincreasethat

would equatethe representative agent’s lifetime expectedutility underthatprocessandhis lifetime utility underthe

constantgrowth consumptionpath.With thecalibrationusedby Dolmas(1998)[basedon quarterlyUS consumption

data],we find thatthis simplemethodyieldswelfarecostsestimatesextremelycloseto thosereportedby thatauthor.

B Countries and YearsCovered

This Appendix describesour African sample,as well as the sub-samplesfor eachmodel economy. Our sample

comprises33 countries:Algeria, Benin,BurkinaFaso,Burundi,Cameroon,CentralAfrican Republic,Congo,Cote

d’Ivoire, Egypt, Gabon,Gambia,Ghana,GuineaBissau,Kenya, Lesotho,Madagascar, Malawi, Mali, Mauritania,

Mauritius, Morocco, Niger, Nigeria, Rwanda,Senegal, Somalia,SouthAfrica, Sudan,Swaziland,Togo, Tunisia,

Zaıre [now theDemocraticRepublicof Congo]andZambia.

Percapitaconsumptionfigures,in constantlocal currency prices,areconstructedfrom the World Bank’s World

DevelopmentIndicators[CD-ROM, 2000]. Total consumptiondatais available for all 33 African countriesin the

sampleandfor theUSA,but thereis insufficientprivateconsumptiondatafor SwazilandandZaıre. Summarystatistics

for the first economyin Table1 arebasedon the remaining31 countries[robustnesscheckswith total consumption

arecarriedout for the full sample].Summarystatisticsfor the secondeconomyin Table2 arebasedon 8 countries

for which process(5) is a goodfit: Gabon,Gambia,Lesotho,Malawi, Morocco,Niger, SouthAfrica andTunisia.

Summarystatisticsfor the third economyin Table3 arebasedon 14 countriesfor which process(4) is a goodfit:

BurkinaFaso,Burundi,Congo,Egypt,Kenya, Mali, Mauritius,Morocco,Rwanda,SouthAfrica, Sudan,Swaziland,

Tunisia[robustnesschecksarealsocarriedout for an additional4 countriesfor which process(4) is a marginal fit:

Cameroon,Mauritania,SomaliaandTogo].

We useannualconsumptionfiguresfrom 1968to 1996for all countries,exceptfor: Burundi (1968-92),Guinea

Bissau(1975-96),Mauritania(private consumption:1968-90),Mauritius (1976-96),Somalia(1968-89),Rwanda

(1968-93),Sudan(1968-90)and Zaire (1968-91). When estimatingthe tvu�w�y{z process(5) for the secondmodel

economy, 28 data–yearsmight leave too few degreesof freedomto properlyascertainstatisticalsignificanceof the

regression.Reassuringly, we find thatusingannualfiguresfrom 1965to 1998insteadyieldsno relevantdifferencein

our parameterestimates[all countriesusedto constructTable2 have beenindependent,andat peace,sinceat least

1965].

9

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10

Table1: Welfarecostof businesscycles– Lucaseconomy

Private consumption Total consumption

costof businesscycles � (%) costof businesscycles � (%)��� (%) � � ��� � � � L � � � � � � � � � ��� (%) � � ��� � � � L � � � � � � � � �United States 1.73 0.02 0.04 0.07 0.15 1.50 0.02 0.03 0.06 0.11

Algeria 3.91 0.12 0.19 0.38 0.77 3.74 0.10 0.17 0.35 0.70Benin 4.16 0.13 0.22 0.43 0.85 3.78 0.11 0.18 0.36 0.71BurkinaFaso 4.80 0.17 0.29 0.58 1.15 4.36 0.14 0.24 0.48 0.95Burundi 5.19 0.20 0.34 0.67 1.35 5.33 0.21 0.36 0.71 1.42Cameroon 7.73 0.45 0.75 1.49 2.99 7.27 0.40 0.66 1.32 2.64CentralAfr. Rep. 5.32 0.21 0.35 0.71 1.42 4.48 0.15 0.25 0.50 1.00Congo 10.14 0.77 1.29 2.57 5.14 9.08 0.62 1.03 2.06 4.12Coted’Ivoire 6.66 0.33 0.56 1.11 2.22 6.81 0.35 0.58 1.16 2.32Egypt 3.46 0.09 0.15 0.30 0.60 2.53 0.05 0.08 0.16 0.32Gabon 9.30 0.65 1.08 2.16 4.32 7.03 0.37 0.62 1.24 2.47Gambia 11.14 0.93 1.55 3.10 6.20 9.83 0.72 1.21 2.41 4.83Ghana 6.13 0.28 0.47 0.94 1.88 5.41 0.22 0.37 0.73 1.46GuineaBissau 15.24 1.74 2.90 5.80 11.61 15.24 1.74 2.90 5.80 11.61Kenya 7.69 0.44 0.74 1.48 2.96 6.44 0.31 0.52 1.04 2.08Lesotho 6.60 0.33 0.54 1.09 2.18 5.52 0.23 0.38 0.76 1.52Madagascar 3.91 0.11 0.19 0.38 0.77 3.84 0.11 0.18 0.37 0.74Malawi 7.80 0.46 0.76 1.52 3.04 4.79 0.17 0.29 0.57 1.15Mali 4.78 0.17 0.28 0.57 1.14 4.60 0.16 0.26 0.53 1.06Mauritania 11.08 0.92 1.53 3.07 6.13 9.52 0.68 1.13 2.26 4.53Mauritius 4.99 0.19 0.31 0.62 1.25 5.80 0.25 0.42 0.84 1.69Morocco 3.85 0.11 0.18 0.37 0.74 4.66 0.16 0.27 0.54 1.09Niger 12.50 1.17 1.96 3.91 7.81 9.71 0.71 1.18 2.36 4.72Nigeria 9.22 0.64 1.06 2.13 4.25 9.10 0.62 1.03 2.07 4.14Rwanda 6.97 0.36 0.61 1.22 2.43 5.59 0.23 0.39 0.78 1.56Senegal 3.45 0.09 0.15 0.30 0.59 3.30 0.08 0.14 0.27 0.54Somalia 11.16 0.93 1.56 3.12 6.23 8.48 0.54 0.90 1.80 3.60SouthAfrica 2.82 0.06 0.10 0.20 0.40 2.22 0.04 0.06 0.12 0.25Sudan 9.11 0.62 1.04 2.07 4.15 7.70 0.44 0.74 1.48 2.97Swaziland - - - - - 10.93 0.90 1.49 2.99 5.97Togo 12.16 1.11 1.85 3.70 7.39 9.57 0.69 1.15 2.29 4.58Tunisia 2.88 0.06 0.10 0.21 0.42 2.60 0.05 0.08 0.17 0.34Zaıre - - - - - 7.73 0.45 0.75 1.49 2.99Zambia 9.65 0.70 1.16 2.33 4.65 7.54 0.43 0.71 1.42 2.84

Mean 7.22 0.47 0.78 1.57 3.13 6.50 0.38 0.63 1.26 2.51Median 6.66 0.33 0.56 1.11 2.22 5.81 0.25 0.42 0.84 1.69Std. deviation 3.29 0.41 0.68 1.36 2.72 2.87 0.34 0.57 1.13 2.27

LDC:US costratio

Mean 4.18 21 21 21 21 4.34 22.3 22.3 22.3 22.3Median 3.86 15 15 15 15 3.87 15 15 15 15Std. deviation 1.91 18.3 18.3 18.3 18.3 1.91 20 20 20 20

Notes: �Z� is the standarddeviation of the cyclical componentof the Hodrick-Prescottfiltered (weight=100)logarithmsof real percapitaprivateconsumptionin constantlocal currency prices[Source:World Bank (WDI2000)]. Annual figuresfrom 1968to 1996areused,exceptfor: Burundi (1968-92),GuineaBissau(1975-96),Mauritania(privateconsumption:1968-90),Mauritius(1976-96),Somalia(1968-89),Rwanda(1968-93),Sudan(1968-90)andZaire(1968-91).Thewelfarecostof businesscycles, � , is thepercentageconsumptionincreaseatall datesandin all statesneededto renderarepresentativeagent[with constantrelativerisk aversion� ] indifferentbetween(i) a constantstreamof realconsumptionequalto themeanof thestochasticprocessandnormalizedtounity, and(ii) a realconsumptionstreamwith thesamemeanbut variance���� .

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Table2: Welfarecosts:businesscyclesvs. lowergrowth – secondmodeleconomy

Panel A Panel B

costof businesscycles(%) costof lower growth (%)� (%) � ��� (%) � � ��� � � � L � � � � � � � ��� � � � L � � � � �United States 2.00 0.313 1.56 3.36 3.43 3.41 13.51 11.21 7.36

Gabon 1.44 -0.309 13.91 15.26 19.51 28.38 11.46 10.20 8.34Gambia -0.62 0.508 7.35 5.86 13.06 26.88 9.45 7.88 3.08Lesotho 1.06 0.425 7.37 8.22 14.06 25.55 11.35 9.87 7.33Malawi 1.29 -0.314 11.13 10.23 13.18 19.54 12.08 10.93 9.86Morocco 2.47 -0.572 4.71 3.98 4.01 3.85 13.83 11.10 6.89Niger -0.89 -0.402 13.87 11.81 16.34 26.14 9.28 8.70 5.89SouthAfrica 1.08 0.494 2.45 2.87 3.80 5.59 12.78 11.47 9.42Tunisia 3.63 0.291 4.55 8.32 8.84 8.61 13.91 10.20 5.96

Mean 1.18 0.015 8.17 8.32 11.60 18.07 11.77 10.04 7.10Median 1.18 -0.009 7.36 8.27 13.12 22.55 11.77 10.20 7.11Std. deviation 1.48 0.455 4.36 4.12 5.63 10.38 1.76 1.22 2.19

LDC:US costratio

Mean 0.6 0.0 5.2 2.5 3.4 5.3 0.9 0.9 1.0Median 0.6 0.0 4.7 2.5 3.8 6.6 0.9 0.9 1.0

Notes: ��� is the standarddeviation of the residualsfrom a standardfit of t�u�w�yKz process(5), with the growthrateof realpercapitaprivateconsumptionin constantlocal currency prices[Source:World Bank (WDI 2000)]asdependentvariable.Thesameregressionyields themeanconsumptiongrowth rate, � , andshockpersistencecoefficient, � . Annualfiguresfrom 1965to 1998areusedfor all countriesin theTable.Resultsarereportedonlywhenthe t�u�w�yKz fit is statisticallysignificantand the meanconsumptiongrowth rate, | , is not sonegative thatconsumptionwould convergeto negative levelswithin 50 years.Thecostof businesscycles, � , is thepercentageconsumptionincreaseat all datesandin all statesneededto rendera representative agent[with constantrelativerisk aversion � ] indifferent betweenbetweena world of uncertainty[with consumptionfollowing the t�u�w�yKzprocess(5)] andoneof certainty[i.e., with the samelaw of motion but ������ � ]. The costof lower growth ismeasuredastheacross–the–boardpercentageconsumptionincreasethatwould beneededfor thesameagenttogiveup a 1%increasein themeangrowth rate[i.e., ����yK� ] if volatility werekeptconstant.

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Table3: Welfarecosts:businesscyclesvs. lowergrowth – third modeleconomy

Panel A Panel B

costof businesscycles(%) costof lower growth (%)� (%) �K� (%) � � ��� � � � L � � � � � � � ��� � � � L � � � � �United States 1.96 1.61 0.31 0.52 1.05 16.03 16.07 16.16

BurkinaFaso 0.45 5.49 5.13 8.86 19.49 22.60 23.44 25.83Burundi 1.80 7.77 8.10 14.29 33.53 17.83 18.91 22.26Cameroon(*) 0.98 9.31 14.36 26.53 72.90 22.05 24.51 33.85Congo 2.23 12.02 20.09 38.86 129.79 18.54 21.59 36.38Egypt 2.87 3.83 1.55 2.62 5.38 14.04 14.20 14.61Kenya 1.48 9.59 13.80 25.40 68.75 19.95 22.09 30.07Mali 0.38 5.92 6.13 10.66 23.93 23.19 24.23 27.25Mauritania(*) 0.98 12.93 32.14 68.67 464.42 25.66 33.03 112.85Mauritius 3.35 4.75 2.24 3.79 7.90 13.20 13.42 13.99Morocco 2.35 5.40 3.40 5.81 12.36 15.51 15.90 16.94Rwanda 0.71 7.57 9.63 17.17 41.68 22.33 23.93 29.15Somalia(*) 0.49 16.14 72.95 242.00 - 37.50 75.13 -SouthAfrica 1.06 2.83 1.15 1.94 3.95 19.10 19.25 19.65Sudan 1.28 8.74 11.66 21.12 53.94 20.29 22.09 28.35Swaziland 2.31 12.72 22.69 44.81 166.83 18.72 22.27 41.88Togo(*) 2.84 16.76 42.24 99.39 - 20.17 28.68 -Tunisia 3.85 4.50 1.88 3.17 6.56 12.31 12.47 12.92

Mean 1.69 8.35 15.40 36.89 67.47 20.27 24.55 30.29Median 1.38 7.67 8.86 15.73 28.73 20.06 22.09 26.54Std.deviation 1.10 4.25 19.19 60.80 119.57 5.96 14.56 24.92

Mean (*) 1.82 6.54 7.06 12.81 33.94 18.24 19.29 23.12Median (*) 1.64 5.71 5.63 9.76 21.71 18.82 20.42 24.04Std. deviation (*) 1.13 2.66 5.86 11.25 36.65 3.74 4.29 7.52

LDC:US costratio

Mean 0.86 5.19 49.3 70.7 64.3 1.3 1.5 1.9Median 0.70 4.77 28.4 30.2 27.4 1.3 1.4 1.6Std.deviation 0.56 2.64 61.4 116.5 114.0 0.4 0.9 1.5

LDC:US costratio

Mean (*) 0.93 4.06 22.6 24.5 32.3 1.1 1.2 1.4Median (*) 0.84 3.55 18.0 18.7 20.7 1.2 1.3 1.5Std. deviation (*) 0.58 1.66 18.7 21.6 34.9 0.2 0.3 0.5

Notes: ��� is thestandarddeviationof theresidualsfrom regressingonaconstantfirst differencesof thelogarithmof real per capitaprivate consumptionin constantlocal currency prices[Source: World Bank (WDI 2000)].Resultsarereportedonly whensucha regressionis a goodfit to thedataand themeanconsumptiongrowth rate,| , is positive. Annualfiguresfrom 1968to 1996areused,exceptfor: Burundi(1968-92),Mauritania(1968-90),Mauritius(1976-96),Somalia(1968-89)andSudan(1968-90).Thecostof businesscycles, � , is thepercentageconsumptionincreaseat all datesand in all statesneededto rendera representative agent[with intertemporalelasticityof substitution �� �¡  andconstantrelative risk aversion � ] indifferentbetweenbetweena world ofuncertainty[with consumptionfollowing the martingale(4)] and one of certainty[i.e., with the samelaw ofmotion but ���� � � ]. The costof lower growth is measuredas the across–the–boardpercentageconsumptionincreasethatwouldbeneededfor thesameagentto giveup a 1%increasein themeangrowth rate[i.e., |¢�£y�� ]if volatility werekeptconstant.

(*) Datafrom a few countriesin this subsample,identifiedby a (*), area marginal fit to martingaleprocess(4).We computewelfarecostsfor thosecountriesto becomplete,but omit thoseestimateswhentabulatingsummarystatisticsin orderto not biasthelatterupwards.

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