Department of Economics, Macquarie University,North Ryde, NSW 2109,Australia

IdentifyingTermsofTradeShocksinaDevelopingCountryusingaSignRestrictionsApproach✩

Kagiso Mangadi1,, Jeffrey Sheen

Department of Economics, Macquarie University,North Ryde, NSW 2109,Australia

Abstract

UsingdataforBotswanafrom1960to2012,weexaminetheresponsesofmacroeconomicvariablestofourgeneralizedpositivetermsoftradeshocks—globaldemand,globalizing,sector-specific and global supply. A sign restricted structural vector autoregressionmodelwith a penalty function is estimated to identify the four shocks. While positiveglobaldemandandglobalizationshocksarebothexpansionary,theyhaveoppositeeffectsoninflation. A positive commodity market specific shock dampens real GDP growthandis inflationary, suggesting a possible Dutch disease response. A negative globalsupplyshocksuppressesbothoutputgrowthandinflation.Allbutthelastshockleadtoasignificant declining interest rate probably reflecting improved credit risk.Monetarypolicycontractionisrecommendedforthefirstshock,andexpansionfortheothers.

Keywords:TermsofTradeShocks,SVARmodels,SignRestrictions,MonetaryPolicyJEL Classification: C32, E52,F41

1.Introduction

The terms of trade play a prominent role in the macroeconomic performance ofmanyeconomies, and is one of the most important relative prices for small openeconomies(Cashinetal,2004),especiallydevelopingeconomies.Manyshockstothetermsoftradeoccur,buttheyarenotallthesamesincetheyariseinavarietyofglobalcontexts.Our contributions in this paper are to identify the impacts of these various shocksona developing country, using a sign restrictions approach on impulse responses, andtoconsider the appropriate policyresponses.

Terms of trade shocks tend to have persistent and volatile effects onmacroeconomicvariablessuchasoutputgrowth,exchangerates,inflation,realincomeandsavings,(see

Emailaddresses:(KagisoMangadi),

(JeffreySheen)

September 12,2016

Mendoza1995;KoseandRiezman2001;Broda,2004;Cashinetal,2004andAndrewsand Rees 2009). Such variability not only causes business cycle uncertainties, butcanalso have important implications for economic performance and growth (LoayzaandRaddatz, 2007). The identification of the context of these terms of trade shocksandhencetheireffectsonmacroeconomicvariabilityisnecessarytoinformtheappropriatepolicyresponse.Sincetheseshockscanhavedifferentmacroeconomicimplications,thenecessarypolicyresponsesarealsoboundtodiffer.

Theglobalcontextinwhichaninternationalrelativepriceshockoccursmustbedistin-guished. It has been argued in the literature that the response of macroeconomicvariablestoexternalshockswilllargelydependonthecharacteristicsoftheunderlyingshock. Forexample, Melolinna (2012), Peersman and Van Robays (2009) and Kilian (2009)showedthattheconsequencesofoilshocksontheUSandEuroeconomiesweredependentonthe features of the shocks. Kilian (2009) argued that there is a fundamental flaw inanapproach that analyzes the response of macroeconomic variables to variations in thepriceofoilalone,whileholdingallotherexternalvariablesconstant.Thesameargumentcanbe extended to the analysis of terms of trade shocks. It would be incorrect toanalyzetheconsequencesoftermsoftradeshocksonaneconomybyallowingonlythetermsoftrade to change while holding all other variables constant. This is because, thoughthetermsoftrademaybeexogenoustoasmalldomestic economy,itisendogenousintheworld economy. Failure to recognise this endogeneity between world variables andthe termsoftradecanleadtoconfusion,falseconclusionsandinappropriatepolicyresponses.Export and import prices are typically influenced by different external shocks, eachofwhichmayaffectthedomesticeconomydifferentlydependingonwhathappenstoworlddemand(KaragedikliandPrice,2012).Therefore,tobeabletounderstandtheeffectofterms of trade shocks on the domestic economy, it is crucial to determine theexternaldriversoftheactualexportandimportpriceshocks.

Theeffectsoftermsoftradeshockstendtobemorepronouncedindevelopingcountriesthaninthedevelopedworld.Thisisbecausemostdevelopingcountriesdependheavily on commodity exports. The structure of their economies is such that exports tendtobe concentrated in one or just a few primary commodities and account for asizeableproportionofGDPandgovernmentrevenues(KoseandRiezman,2001andHove,2015)whileimportstypicallycomprisemainlyintermediateinputs,fooditems,oilandmanu-factures. In addition, developing countries have little influence over the prices oftheirexports, which are also usually characterized by high volatility. In this way,developingcountries are highly vulnerable to terms of trade shocks. Because of thisvulnerability,theappropriatepolicyresponsewilllikelydependontheglobalcontextoftheidentifiedshock. While there is an extensive literature on the effects of terms of trade shockson

Africaneconomies(forexampleseeKoseandRiezman,2001,Cashinetal,2004,Hoveetal,2015andCashinandPattillo,2006),noneoftheliteratureondevelopingeconomies,toourknowledge,hasdisentangledtheglobalcontextoftermsoftradeshocks.Thusthispaperconsidersasignificantproblemfacedbymostdevelopingcountries,whichhasnotyet been properly addressed.

We estimate a sign restricted structural vector autoregression (SVAR) model withapenaltyfunctiontoidentifytheunderlyingdeterminantsofasetoflikelytermsoftradeshocksthathaveimpactedBotswanainthelastfiftyyears.Botswanaischosenbecauseitisaquintessentialsmallcommodity-dependentdevelopingcountrythathasahistoryofsoundmacroeconomicpoliciesandwell-managedresourcerevenueswhilebeingvulnerabletotermsoftradeshocks.Thismakesitagoodbenchmarkcaseformanyotherdevelopingcountriesinunderstandingtheimplicationsofexternalshocks,becausewecaninvestigate theeffectsofexternalshockswithoutbeingconcernedaboutthedistortionscreatedbythepitfallsassociatedwithalargenaturalresourceendowmentleadingtohugeinfusionsofforeignexchangeintothedomesticeconomy.Weuseannualdatafortheperiod1960to 2012, and investigate the effects of the likely set of external shocks on thecountry’skey macroeconomicvariables.

Fourgeneralizedexternalshocksareidentifiedfromthedatausingsignrestrictionsonimpulseresponses.Thefirstisapositiveglobaldemandshockthatisassumedtoraisebothexportandimportpricesaswellasglobaloutput.Thesecondisapositiveglobal-izing shock representing the experience of emerging economies into the globaleconomy—especiallyChina—thatisassumedtoraiseexportprices,reduceimportprices,andim-proveglobalGDP.Thethirdisapositivesector-specificshock,representingaboomingcommodity sector that could give rise to the ‘Dutch disease’. In this case, theexportpricealoneisassumedtosurge,andisnotassociatedwithaboomintheglobaleconomy.Finally,thefourthshockallowsforanegativeglobalsupplyshock,suchasinenergymarkets,whichisassumedtoreduceimportpricesandisaccompaniedbyadeclineinglobaloutput.

The first three shocks identified in this study are in line with the work of J¨a¨askel¨aandSmith(2013)andKaragedikliandPrice(2012),whoidentifiedsimilarshocksforAustraliaandNewZealandrespectively.Ourstudyintroducesafourthglobalsupply-sideshockto the model, which was not included in the aforementioned studies. This shocklikelyrepresents what essentially happened in the immediate aftermath of the financial crisisof2008.Inadditiontothis,ourworkfocusesonadevelopingeconomywithuniquefeaturessuchasBotswana,whiletheyfocusedondevelopedeconomies.SincethestructureoftheBotswanaeconomyissignificantlydifferentfromthatoftheAustralianandNewZealand

economies,theresultsoftheanalysisarebettersuitedforinformingappropriatepolicyin commodity exporting developing countries. Another point of difference is thatouranalysisisextendedtoincludeapenaltyfunctionintheidentificationprocess.Thisisavitaldifferencesinceithasbeenshownthatthealternativeuseofthemedianresponsefrommultiplemodelsislikelytobeflawed(forexample,seeUhlig(2005)).

Wefindthatourresultssupporttheargumentthatthedirectionandmagnitudeoftheresponseofmacroeconomicvariablestoexternalshockslargelydependonthecharac-teristicsoftheunderlyingshock.Theidentifiedworlddemandshockisfoundtobeexpansionaryandinflationary,whiletheglobalizationshockisexpansionarybutdrivesinflationdownasaresultoffallingimportprices.Apositivecommoditymarketspecificshockhasoppositeeffectstotheglobalizationshock.Unliketheglobalizationshock,thepositivespecificcommoditymarketshockmarginallydampensrealGDPgrowth,andisinsteadinflationaryduetorisingimportprices.Therealeffectiveexchangeratestrength-enstemporarily,causingothersectorstodeclineandcounteractingtheoutputeffectofthe booming sector. This is weakly consistent with a Dutch disease effect. Lastly,anidentifiednegativeglobalsupplyshockisfoundtosuppressbothoutputgrowthandin-flation.Allfourshocksareactually‘positive’termsoftradeshocksthatleadtoadeclineinthemarket(lending)interestrate,whichmaybeindicativeofadecliningcreditriskpremium. The appropriate monetary policy responses qualitatively differ for thefirstshock,andwillquantitativelydifferforallfourshocks.

Theremainderofthispaperisstructuredasfollows.Section2isareviewofboththe empirical and theoretical literature on the topic, with particular emphasisplacedon existing literature pertaining to Africa and the developing world, as well as ontheidentification of external shocks. Section 3 provides a discussion of themethodology,includinganoutlineoftheSVARmodelwithsignrestrictionsadoptedforthestudy,whilesections4and5discusstheresultsandprovideconcludingremarks.

2.Review of the Literature on Terms of TradeShocks

Shocks to the terms of trade and their effects on macroeconomic variables havebeenstudiedatlengthandusingdifferentmethodologies.Thissectiondiscussessomeoftheliteratureontermsoftradeshocks,aswellasonthedifferenttechniquesofdisentanglingtheseshocks,whichisacrucialpartofourstudy.

2.1.Identification ofShocks

Developingeconomies,arecharacterizedbyahighlevelofvolatilitythattendstonega-tivelyimpacteconomicperformanceandgrowth.Itisthereforeimportanttoinvestigatethe sources of this high volatility to ensure policies can be designed to maximisetheirgrowth performance. A large portion of variations in developing countrymacroeconomicfundamentalssuchasdomesticoutputandexchangeratesisattributedtotermsoftradefluctuations(seeBrodaandTille,2003;Kose,2002);KoseandRiezman,2001).Inad-ditiontothis,understandingthepatternsofpersistenceofexternalshocksiscrucialforformulating appropriate policyresponses1.

Past empirical work on the impact of various shocks to developed countries asserttheimportanceofunderstandingthesourcesoftheshocksinordertofullyascertaintheireffect on macroeconomic variables. The shocks are disentangled and identifiedusingdifferentidentificationschemes,eachwithitsownadvantagesanddisadvantages.Onepopular technique in this area is the SVAR method, which has been utilized widelyinthe literature to identify different types of shocks. Killian (2009) estimates anSVARmodeltodecomposeoilpriceshocksintoanaggregatedemandshock,aprecautionarydemand shock and an oil supply shock. Similarly, Peersman and Van Robays (2009)useasignrestrictionsapproachtoexaminethedifferenttypesofoilshocksaffectingtheeconomy of the Euro area, distinguishing between three types of oil shocks. Inrelatedwork,Melolinna(2012)usesapenaltyfunctionmethodtoidentifyoilshocksandothermacroeconomicshocksfortheUSeconomy.DungeyandFry(2009)proposeamethodfor decomposing shocks that involved combining three different identificationtechniques,namely, the traditional short run restrictions, the sign restrictions methodology andusingcointegratingrelationshipstoidentifymonetarypolicyshocks,fiscalpolicyshocksandother economicshocks.

Asmentionedabove,KaragedikliandPrice(2012)identifyhowthetermsoftradeprop-agatethroughtheNewZealandeconomyusingthesignrestrictionsmethodology.ThisstudycloselyfollowedsimilarworkbyJ¨aa¨skel¨aandSmith(2013)fortheAustralianecon-omy.ThesepapersappliedasimilarmethodologybyestimatingsignrestrictedVARswithcommonvariables,namelythegrowthofworldGDP,importpriceinflation,exportpriceinflation, the growth of domestic output, domestic CPI inflation, the interest rateandtheexchangerate.Thetwostudiesdifferedintheirmeasurementofvariablesandintheterms of trade shocks they sought to identify. Both studies identified a globaldemandshock. Karagedikli and Price (2012) also identified an import price shock, whichthey

1Interestingly, while clearly bothersome, terms of trade shocks tend to be relatively short-livedforsomedevelopingcountries(Cashinetal,2004),andlonger-livedforothers.

defined as a shock that leads to an increase in import prices and a decrease inworldoutput. They also identified an export price shock, which was restricted to have aneg-ative effect of world GDP and import prices. In addition to the global demandshock,J¨a¨askel¨a and Smith (2013) also identified a commodity market specific shock thatwasconstrainedto have apositiveeffectonexportprices,anegativeimpactonworldGDPand no effect on import prices. This study concluded that while a rising terms oftradetendstobeexpansionary,itisnotalwaysinflationarywiththeeffectlargelydependenton the nature of the shock as well as the response of policy. Even though thecurrentstudycloselyfollowsKaragedikliandPrice(2012)and J¨aa¨skel¨a andSmith(2013)insomeaspects,thesestudiesestimatedsign-restrictedSVARsfordevelopedeconomies,whosefeatures and structures are fundamentally different from developing countryeconomies.Byfocusingonabenchmarkdevelopingeconomy—Botswana,thisstudycontributestotheliteratureonunderstandingtheimpactofexternalshocksthatarerelevanttomostdeveloping economies.

2.2.Policy Options for Dealing with Terms of TradeShocks

Thereis much evidenceshowingthattheresponseofeconomiestomacroeconomicshocksis influenced by the policy framework in place (for example, see Aizenman andRiera-Crichton,2008,Aizenmanetal.,2012).TheFriedmanhypothesisrecommendsaflexibleexchange rate as a buffer against real shocks. The argument is that, in the presenceofprice stickiness, the speed at which relative prices adjust is mainly determined by theexchangerateregime.Aflexibleexchangerateisbettersinceitallowsforamorerapidadjustment of relative prices than a fixed exchange rate. The Friedman hypothesishassincebeenexaminedandsupported(seeBroda,2004;ChiaandAlba,2006;BrodaandTille,2003),leadingtotheconclusionthatflexibleexchangeratesarebettersuitedforinsulating the economy against terms of trade shocks. The strength of this supportislikelytodependontheprevalentsourcesofthetermsoftradeshocks.

The effectiveness of macroeconomic policies other than exchange rate policy hasalsobeenevaluated.Forinstance,AndrewsandRees(2009)foundthatalongwithaflexibleexchangerate,welldevelopedfinancialmarketsandamonetarypolicythatfocusesonlowinflationarealsoimportantforneutralizingthevolatileeffectsofthetermsoftradeon an economy. Hove et al (2015) assert that CPI inflation targeting, whencomparedwithnon-tradedinflationtargetingandexchangeratetargeting,isabetterpolicyoptionforeconomiesthataremorevulnerabletocommoditytermsoftradeshocks—thispolicyresponse can also reduce macroeconomic fluctuations and welfare losses. Onceagain,suchconclusionsshoulddependontheidentifiedsourceoftheexternalshocks,andwediscussbelowthepolicyimplicationsforeachoftheidentifiedtermsoftradeshocksto

Botswana.

Twomainconclusionsemergefromthisbriefliteraturereview.Thefirstisthatitiscrucialtoidentifywhichexternalshockstothetermsoftradematterfordevelopingeconomies,andtheappropriatepolicyresponsestoeach.TheotheristhattheSVARmethodologyisanimportanttoolfordisentanglingtheshocks.However,thestudiesdiscussedabovehavenotappliedthesignrestrictionsmethodologytounderstandingshockstothetermsoftradeinadevelopingcountrycontext.

3.Methodology

VAR models are often used for investigating interdependencies between variables. Insuchmodels,eachvariableisexpressedasafunctionofitsownlagsaswellasthelagsofothervariablesinthesystem.TheVARmodelyieldsimpulseresponsefunctions,varianceerrordecompositions and historical decompositions which contain important informationforinformingpolicy.However,inordertogivethesemeaningfuleconomicinterpretations,astructuralvectorautoregression(SVAR)modelhastobeestimated.Thestructuralerrortermsrepresentfundamentaleconomicshocks,anditisthroughthesethatmeaningfulmacroeconomic analysis can be carried out.

3.1.Identifying StructuralShocks

RecallthattheusefulnessofSVARmodelsmainlydependsontheidentificationofstruc-tural errors and that restrictions have to be imposed in order to identify theseshocks.Theserestrictionscaneitherbeparametricand/orsignrestrictions,withdifferentcon-clusionsdrawndependingonthetypeofrestrictionsimposed.

Parametricrestrictionsinvolveconstrainingtheparametersofthemodel.Thesesolvetheidentification problem “by reducing the number of parameters to be estimated sothat suitableinstrumentsaremadeavailableforestimation”(FryandPagan,2011).

There are different types of parametric restrictions. These include short run andlongrun restrictions. Short run restrictions are usually zero contemporaneousrestrictionsimposedontheshortrunparametersofthemodel.TheCholeskydecompositionisa popular example of such restrictions. This technique identifies structural shocksbyorderingthevariablesinthesystemsuchthatthemostexogenousvariableappearsfirst.They are short run restrictions because the response of variables is constrained inthe period immediately following theshock.

Longrunrestrictionsinvolveconstrainingtheimpulseresponsesinthelongruntohavevaluesthataremotivatedbyeconomictheory.Imposinglongrunrestrictionsrecognizesthatsomeshocksmayhaveapermanenteffectonthevariables.Here,“thecumulativeresponseofthevariableovertheentireperiodofanalysisiszero.”

The last class of parametric restrictions involve using a combination of short runandlong runrestrictions.

Theidentificationmethodsoutlinedabovehowever,arenotwithoutflaws.Zeroshortrunrestrictions have been criticized for being too stringent as well as for the fact thattheyaretypicallynotbasedoneconomictheory.Eventhoughlongrunrestrictionsaremoreconsistentwitheconomictheory,theyhavebeenfoundtohaveconsiderabledistortionsdue to small sample biases and measurement errors (Peersman,2005).

The sign restrictions methodology overcomes some of the shortfalls of conventionaliden-tificationtechniques.Thisprocedurerequiresnoparametricconstraintstobeplacedonthe short run or the long run effects of a shock. Furthermore, the sign conditionsareusuallytheoreticallyorientedinthattheyarebasedonmodels(suchasDSGE).Thesignrestrictions approach involves “placing restrictions on the direction that variableswillmoveoveragivenhorizon,inresponsetodifferenttypesofshocks”,(Ja¨a¨skel¨aandSmith,2013). This technique assumes that all shocks are uncorrelated. Here, restrictionsareplacedonthesignsoftheaccumulatedimpulseresponses.Thisidentificationprocedureis especially important in situations where variables are simultaneously determined,thusmaking it difficult to justify any parametric restrictions (Fry and Pagan, 2011). AbriefdiscussionoftheproceduretogeneratecandidateshockscanbefoundinAppendixAofthispaper.

3.2.ModelSpecification

A sign restricted VAR is estimated using data for the Botswana economy. Botswanaisa small open economy for which it is highly unlikely that domestic variables willhaveanimpactonforeignvariables. Therefore,ablockrecursivestructureisimposedonthemodel,i.e.themodelispartitionedintoadomesticblockofvariablesanda‘restoftheworld’orforeignblock.Thisallowsfornofeedbackfromvariablesinthedomesticblock to those in the world block. To achieve this, one has to ensure that there arenocontemporaneousorlaggeddomesticvariablesappearinginthesetofequationswhichdescribe the worldvariables.

Thefollowingmodelisestimated:

= αxt+

t−i+

(1)

dti=1

dt−iεt

wherewtanddtarevectorsofforeignanddomesticvariablesrespectively,xtisavectorofexogenousvariables,Bisthematrixofcontemporaneousimpactofthevectorsofmutually

uncorrelated foreign and domestic innovations (εw

and εd). The estimation precisionof

impulseresponsesisinfluencedbytheaccuracyofmodelparameterestimates,thereforeitiscrucialtoemployappropriateprocedurestodeterminetheoptimalVARorder.Wetherefore utilize the Akaike Information Criterion (AIC) to achieve this. This testhasbeenfoundtooutperformthemorepopularSchwarzInformationandFinalPredictionErrorcriteriainselectingtheoptimalorderforsmallsamples.TheAICselectedanoptimallaglengthof1,whichwasverifiedusingtheBayesianInformationCriterion(BIC).

Toimposethesmallopeneconomyassumption,theAimatrixisdefinedtobelowertriangular,ensuringthatlagsofthedomesticvariables have noinfluenceontheworldblock.

Thevariableswhichappearintheforeignblockarethegrowthofworldoutput(∆yw);

exportpriceinflation(πx)andimportpriceinflation(πm).

wt=(∆yw,πx,πm)!(2)

ttt

ThedomesticblockcontainskeyvariablesthatdescribeconditionsintheBotswana

economy—these are domestic output growth (∆yd), CPI inflation (πd), the shortterm

lendinginterestrate(id)andthechangeintherealeffectiveexchangerate(∆qt).

dt=(∆yd,πd,id,∆qt)!(3)

ttt

3.3.Identification

Thesignrestrictionsmethodologyisusedtoidentifytheshocksofinterest.Thisisinlinewithpaststudieswheresignrestrictionswereusedtoidentifymonetarypolicyshocks,fiscalpolicyshocks,technologyshocks,oilshocksandsoon(seeUhlig,2005;Peersmanand Van Robays, 2009; Liu, 2008; Dungey and Fry, 2009 and Karagedikli andPrice,2012).

Table1belowshowstherestrictionsimposedontheworldvariablesinordertoidentify theshocksofinterest.Apositivesign(+)meansthattheimpulseresponseofthevariable

isconstrainedtobepositive,whileanegativesign(-)impliesthattheimpulseresponseofthevariableisrestrictedtobenegative.A‘u’meansthatnorestrictionsareimposedonthevariableinquestion.

Table 1: VAR Sign Restrictions

ExportPrices / ImportPrices / WorldGDP / DomesticVariables
GlobalDemandShock / + / + / + / u
GlobalizationShock / + / - / + / u
CommodityMarketSpecificShock / + / u / - / u
GlobalSupplyShock / u / - / - / u

Four types of terms of trade shocks are identified by restricting the impulseresponsesof the variables in the foreign block. Since the interest is on the response ofdomesticvariables, these are left unrestricted.

Aglobaldemandshockisessentiallyashocktoincomes.Apositiveglobaldemandshockisonethatstimulatesoverallglobaleconomicactivityandincreasesthepricesofallproductsi.e.bothimportandexportproducts.Theglobaldemandshockisidentifiedbyrestrictingtheresponsesofworldoutput,exportpricesandimportpricestobepositive.ThisisbecauseaglobaleconomicboomisexpectedtoincreaseworldGDPaswellasthepricesofallproducts,whetherexportedorimported.

Recallthatapositiveglobalizationshockisonethatcapturestheincreasingparticipationand importance of emerging economies such as China and India in world markets.Itshould increase export prices due to the increase in global demand for rawmaterials,and at the same time import prices should fall as a result of the decline in the priceofmanufacturedgoodscomingoutoftheseemergingeconomies.Thisshockisthusonethat isrestrictedtoanincreaseinglobaleconomicactivityandexportprices,butareductioninimportprices.

LikeJ¨aa¨skel¨aandSmith(2013),wedefineapositivecommodity-marketspecificshockasashockthataccountsforincreasesinexportpricesnotcausedbyariseinglobaleconomic activity—to be sure, a fall is the restriction applied. This shock isthereforeidentified by restricting the responses of export prices and world output to bepositiveandnegativerespectively,whiletheresponseofimportpricesisleftunconstrained.Thisidentification allows for a test of the Dutch disease phenomenon, whereby aboomingexportsectorcrowdsoutothersectors.

Thefinalpositivetermsoftradeshockoccursthroughafallinimportpricesaccompaniedby a decline in global activity. This is essentially a global supply-side shock, whichcanbethoughtofasafallinpriceofenergypriceinputs.Thisisacontemporaryshockdriven by global excess supply for oil, which is influenced by the global businesscycle.Introducingthisshockisjustifiedinthatfallsinoilpricessincethefinancialcrisisof2008weredrivenbyglobalexcesssupplyinoilmarkets.ThistermsoftradeshockisidentifiedbyrestrictingtheresponsesofimportpricesandworldGDPtobothbenegative.

Based on table 1 above and the discussion in the preceding section, the followingsignrestricted model isestimated:

 πx

eπm

+++u000

+ −u−000

 εdemand

 εglobal 

t

 yw

 t 



++− −000



 comm.mkt



 yd



et

=uuuuu u u

×  εsupply

(4)





eπd

uuuuu u uεπ

 ∆q





et 

uuuuu u uε



uuuuu u uεi

A positive sign (+) means that the impulse response of the variable is constrainedtobe positive, a negative sign (-) is the reverse, while a ‘u’ means that no restrictionsareimposedonthevariableinquestion.

Equation 4 summarizes the sign restrictions discussed in the preceding section.Forinstance, the fourth column of the impact matrix in equation (4) above shows thattheglobalsupplyshockisidentifiedbyconstrainingtheresponsesofimportpricesandglobaloutput to be negative, while leaving export prices unrestricted. In the same way,theupperleftpositivesign(+)showsthatinordertoidentifyapositiveglobaldemand

shock,theresponseofexportpriceinflationisconstrainedtobepositive.The3×4upper

leftblockrepresentsthefourexternalshocksofinterest.Sincewearenotidentifyingany

domesticshocks,thelastthreecolumnsoftheimpactmatrixcontainaseriesofzerosand’u’s. The 3 × 3 upper right block illustrates the fact that shocks to domesticvariables

cannotinfluenceanyoftheworldvariables.

3.4.Sign Restrictions with a Penalty FunctionApproach

Oncetherestrictionshavebeenimposed,themodelisestimatedandsimulated.TherewillbemanyVARrepresentationswhichagreewiththepostulatedsigns—sowecanconsiderall the impulse response functions that are feasible and report the median responseateach horizon for each variable (Liu, 2008). The problem with this however is thatthe

orthogonality condition may be violated since the median response is calculatedwithimpulse responses from multiplemodels.

It is for this reason that sign restrictions have been criticized. They generateimpulseresponsesfrommultiplemodelsratherthanfromasinglemodel,whichmeansthattherecan be many impulses responses that are consistent with the sign constraints.Thisproblemisexacerbatedbythefactthatmanyoftheusesoftheinformation,suchasthe construction of variance decompositions, require that impulse responses beuncorrelated.The pure sign restrictions method thus fails to address the multiple modelsproblem,which can result in excess uncertainty about the model’s estimates andconsequentlymay lead to incorrect policy inference (Fry and Pagan, 2007 and Liu andTheodoridis,2012).

Onewayofdealingwiththeproblemdiscussedaboveistocomplementthesignrestric-tions method with the penalty function approach. This approach has been used intheliterature to find a unique solution from the set of impulse responses that producethecorrectsigns(seeUhlig,2005;MountfordandUhlig,2009andMelollina,2012).Thepenaltyfunctionmethodproducesauniquesetofstructuralinnovationsbyminimizingsomecriterionfunction.Theshocksofinterestareidentifiedbyfindingtheimpulsere-sponsewhichcomesascloseaspossibletosatisfyingthesignrestrictions.Thisisachievedbyminimizingapenaltyfortheimpulseresponsesthatviolatethesignrestrictions,andrewardingresponsesthatsatisfytheconstraints.Thishelpstoexactlyidentifythebestimpulseresponseoutofallthosethatsatisfythesignconditions,thusreducingtheun-certaintyoftheidentificationprocedure(LiuandTheodoridis,2012).Imposingapenaltyfunctionthushelpsustoexactlyidentifythebestimpulseresponseoutofallthosethatsatisfythesignconditions.

FromUhlig(2005),apenaltyfunctioncanbedefinedasfollows:

(wifw≤0

f(w)=

100∗wif w ≥0

wherewistheimpulseresponse.Thepenaltyfunctionaboveisasymmetricinthat whenimposingsignrestrictions,wrongresponsesarepenalizedmoretimesthancorrectresponses arerewarded.

Let rj,a(k) be the impulse response of variable j at horizon k to an impulse vector a, wherek=0,...,K. HereKisthelastperiodatwhichimpulseresponsesarerestricted. σj isthestandarddeviationofvariablej,suchthattheimpulseresponsesarere-scaled. Thismakesitpossibletocomparedeviationsacrossthevariousimpulseresponses. Let

ls+ be the set of variables for which the impulse response is constrained to bepositive,while ls− represents the set of variables for shock identification for which theimpulseresponses are restricted to be negative (Mountford and Uhlig, 2009; Uhlig, 2005).

Thecriterionfunctiontobeminimizedcanthusbegivenby:

Ψ(a)= f(−rj,a(k))+ f(rj,a(k))(5)

jEls+ k=0

σjσj

jEls k=0

−

In our case, a global demand shock impulse vector is one that minimizes thecriterionfunctionΨ(a),whichpenalizesnegativeimpulseresponsesofworldoutput,exportandimport prices. The globalization shock minimizes Ψ(a) which penalizes negativeimpulseresponses of world output and export prices, and positive responses of importprices.Thecommoditymarketspecificshockminimizesthecriterionfunctionwhichpenalizespositive responses of world GDP and negative responses of export prices. Finallythe globalsupply-sideshockimpulsevectorisonethatminimizesthecriterionfunctionwhichpenalizespositiveresponsesofimportpricesandworldoutput.

4.Data

Thedatasetforthisanalysiscomprises7keyvariablesrelevanttoBotswana—theseareexportpriceinflation,importpriceinflation,worldoutputgrowth,domesticoutputgrowth, domestic inflation, the real effective exchange rate and the domesticinterestrate.ThechoiceofvariablesisguidedbypastempiricalworkinthisareaaswellastheirrelevancetotheBotswanaeconomy.Weuseannualdatafortheperiod1960to2012,thefrequency is largely dictated by the availability ofdata.

ExportandimportpriceinflationarecalculatedusingexportandimportpriceindicesobtainedfromtheFederalReserveEconomicData(FRED),whileallotherdatawasobtainedfromtheWorldDevelopmentIndicatorsoftheWorldBank.Worldoutputgrowthiscalculatedasthetrade-weightedrealGDPofBotswana’smajortradingpartnercountries.2

DomesticoutputisBotswana’srealGDP.TheinflationrateistheheadlineinflationforBotswana,calculatedfromtheconsumerpriceindex,whiletheinterestrateusedhereistheprimelendingrate,whichisthelowestinterestrateatwhichfundscanbeloanedoutbycommercialbanks.Itisthusamarket-determinedrate,whichislargelyinfluencedbycreditriskpremiaaswellasmonetarypolicydecisions.

2Botswana’smajortradingpartnersincludeChina,theEuropeanUnion,Israel,Norway,SouthAfrica,the United Kingdom and the United States.

The real effective exchange rate (REER)3 is the trade weighted average of bilateralrealexchangeratesbetweenBotswanaanditsmajortradingpartners.

PreliminaryanalysisofthedataserieswascarriedoutandTableB.1inAppendixBshowsthedescriptivestatisticsofthedataseries.

5.Results

Thissectionreportstheresultoftheimpulseresponseanalysisundertakeninthestudy.Takingintoconsiderationtheshortcomingsofthesignrestrictionsmethodologyalreadydiscussedintheprecedingsection,wereporttheresultsofthesignrestrictionsapproachwithapenaltyfunction.Wethenexplainbrieflywhatwouldhappenwithoutthepenaltyfunction.

5.1.Impulse Response Analysis: Sign Restrictions with a PenaltyFunctionApproach

The sign restrictions with a penalty function methodology imposes morerestrictions,alongwiththesignconstraints,toresolvetheidentificationproblemthatarisesduetoweakinformation,andtonarrowdowntherangeofacceptableresponsesthatcarrythecorrectsign.4Inthisway,themultiplemodelsproblemisavoidedandauniquesolutionobtained.

Furthermore, since it has become common practice to impose contemporaneousrestric-tionsasopposedtoconstraininglongerlags,thesignrestrictionsareimposedforthefirstperiodonly.Theresultsoftheexperimentsarediscussedinthefollowingsubsection.

5.1.1.Responses to a Global DemandShock

Figure1belowshowstheresponsesofthevariablesofinterestfollowingapositiveglobaldemand shock. To reiterate, this type of shock is one that stimulates overallglobaleconomic activity and increases prices of all commodities. A positive globaldemandshockisthereforeidentifiedbyrestrictingtheimpulseresponsesofworldoutput,importpricesandexportpricestobepositive.

3REERt = NEERt × CPIt/CPI∗, where REERt is the real effective exchange rate in time t,

isthenominaleffectiveexchangerateintimet,calculatedastheweightedaverageofBotswana’s

NEERt

nominal bilateral exchange rates. CPIt and CPI∗

are domestic and foreign consumer price indices

respectively,whereCPI∗istheweightedaverageofconsumerpriceindexoftradingpartnercountries.

4Theanalysisisbasedon2000successfuldrawsfromtheposterioroftheVARandfromtheunitsphere. These are used to show the median target, 16th and 84th percentiles of the impulse responses.

0.09

0.08

0.07

0.06

0.05

0.04

0.03

0.02

0.01

0.00

ExportPriceInflation

012345

1.20

1.00

0.80

0.60

0.40

0.20

0.00

-0.20

-0.40

Inflation Rate

012345

0.06

0.05

0.04

0.03

0.02

0.01

0.00

ImportPriceInflation

012345

0.08

0.06

0.04

0.02

0.00

-0.02

-0.04

-0.06

Real Effective ExchangeRate

012345

1.20

1.00

0.80

0.60

0.40

0.20

0.00

-0.20

World GDPGrowth

012345

0.50

0.25

0.00

-0.25

-0.50

-0.75

InterestRate

012345

3.00

2.50

2.00

1.50

1.00

0.50

0.00

-0.50

Real GDPgrowth

012345

Figure1:Responsestoa Positive Global Demand ShockThe black line represents the median impulseresponsefunction of a positive one standard deviation shock,thebluelinesrepresentthe16thand84thpercentiles.

Asexpected,thepositiveshockleadstoapositivecontemporaneousresponseofworldoutputthatdeclinesovertimebutappearstoremainabovetrendgrowthforupto3periodsbeforenormalizing.Bothimportandexportpricesincreaseonimpact,butwiththeriseinexportpricesbeingslightlyhigherthanthatofimportprices,thussignifyinganimprovementinthetermsoftrade.

With the exception of the interest rate, the responses of the rest of the domesticvari-ablesareinsignificant,howevertheirmedianresponseswillstillbediscussed.Theglobaldemand shock results in a positive response of domestic output growth. Thepositiveeffectdeclinesovertimebutappearstobelong-lasting,whichmaybeattributedtothepositivegrowthofworldoutputandtheeventualrealdepreciationoftheexchangerate.Thecontemporaneousresponseoftheinflationratestrengthensovertimeandremainspositive,reinforcedbythehighpricesofimports.Interestingly,thenegativeeffectontheinterestratesuggeststhedeclineincreditriskpremiaintheboomingeconomyoutweighsanypossiblecountercyclicalresponsebythecentralbank.

In summary, a positive global demand shock leads to an improvement in the termsoftrade.Theshockalsostimulatesdomesticoutputandinducesupwardinflationarypres-suresontheeconomy.Withinterestrateslower,thecentralbankshouldbeinapositiontotightenmonetarypolicytomoderateinflation.

5.1.2.Responses to a GlobalizationShock

A globalization shock essentially captures the impact of the increasing dominanceofemergingeconomiessuchasChinaandIndiaintoworldproductmarkets.Thistypeofshockisexpectedtoincreaseexportpricesastheglobaldemandforrawmaterialsrises,atthesametimeimportpricesfallduetoinfluxofcheapmanufacturescomingoutoftheseeconomies.ApositiveglobalizationshockisthusidentifiedbyrestrictingtheresponsesofworldGDPandexportspricestobepositive,whiletheimportpricesareconstrainedto benegative.

Theresponsesofthevariablesinthemodeltoaglobalizationshockareshowninfigure2below.

ExportPriceInflation / InflationRate
1.00
0.04 / 0.50
0.03 / 0.00
0.01 / -0.50
0.01 / -1.00
-0.01 / -1.50
0 / 1 / 2 / 3 / 4 / 5 / 0 / 1 / 2 / 3 / 4 / 5
ImportPriceInflation / RealEffectiveExchange Rat / e
0.01 / 0.03
-0.00 / 0.01
-0.01 / -0.01
-0.03 / -0.03
-0.04 / -0.05
0 / 1 / 2 / 3 / 4 / 5 / 0 / 1 / 2 / 3 / 4 / 5
World GDPGrowth / InterestRate
1.75 / 0.60
1.50 / 0.40
1.25
1.00 / 0.20
0.75 / 0.00
0.50 / -0.20
0.25
0.00 / -0.40
-0.25 / -0.60
0 / 1 / 2 / 3 / 4 / 5 / 0 / 1 / 2 / 3 / 4 / 5
RealGDPgrowth
3.00
2.00
1.00
0.00
-1.00
-2.00
0 / 1 / 2 / 3 / 4 / 5

Figure2:Responsesto a Positive Globalization ShockThe black line represents the median impulseresponsefunction of a positive one standard deviation shock,thebluelinesrepresentthe16thand84thpercentiles.

Inkeepingwithaprioriexpectations,theshockcontemporaneouslyincreasesbothworldoutput and export prices, while decreasing import prices, once again signalling anim-provement in the terms of trade. The effect of the shock on export prices declinesovertimebutremainspositiveindefinitely.Theresponseofworldoutputgrowthalsodeclinesandnormalizesbytheendofthethirdyear.

EventhoughdomesticrealGDPisslightlynegativeonimpact,theimprovementinthetermsoftradeandtheincreaseinoutputoftradingpartnercountriesstimulateoutputgrowth,whichquicklybecomespositiveandremainsabovetrendgrowthfor5periods.

Thecontemporaneousresponseofinflationisnegativeduetofallingpricesofimports.Thepositiveshockalsoleadstoaslightdepreciationoftheexchangeratewhichlastsforlessthanhalfayear.Onceagain,thenegativeeffectontheinterestratesuggeststhatacreditriskpremiaeffectoutweighsanycountercyclicalmonetarypolicyresponsebythe centralbank.

Tosummarize,apositiveglobalizationshockisexpansionarybutnotinflationary,inthat not only does it stimulate the growth of domestic output over time, the fall inimportpricesexertsdownwardpressureontheinflationrate.Withinflationabatingmorethanthe nominal interest rate, the real rate of interest will be higher, and the centralbankmay choose to lower the interest rate further. However it should take into accountthebooming GDP, and be aware that this positive terms of trade shock will correctitselfovertime.

5.1.3.Responses to a Commodity Market SpecificShock

A positive commodity market specific shock relevant to Botswana is one thataccountsfor an increase in export prices not caused by a rise in global economic activity. Itisthereforeidentifiedbyrestrictingtheimpulseresponsesofworldoutputgrowthandexportpricestobenegativeandpositiverespectively.Figure3belowshowstheresponseofbothforeignanddomesticvariablestoapositivecommoditymarketspecificshock.

ExportPriceInflation / InflationRate
0.07 / 0.80
0.06 / 0.60
0.05
0.04 / 0.40
0.03 / 0.20
0.02 / 0.00
0.01
0.00 / -0.20
-0.01 / -0.40
0 / 1 / 2 / 3 / 4 / 5 / 0 / 1 / 23 / 4 / 5
ImportPriceInflation / RealEffectiveExchangeRate
0.07 / 0.06
0.06 / 0.04
0.05 / 0.02
0.04 / 0.00
0.03 / -0.02
0.02 / -0.04
0.01 / -0.06
0.00 / -0.08
0 / 1 / 2 / 3 / 4 / 5 / 0 / 1 / 23 / 4 / 5
WorldGDPGrowth / InterestRate
-0.00
-0.20 / -0.10
-0.40 / -0.30
-0.60
-0.80 / -0.50
-1.00 / -0.70
-1.20
-1.40 / -0.90
0 / 1 / 2 / 3 / 4 / 5 / 0 / 1 / 23 / 4 / 5
Real GDPgrowth
3.00
2.00
1.00
0.00
-1.00
-2.00
-3.00
0 / 1 / 2 / 3 / 4 / 5

Figure3:ResponsestoaPositiveCommodityMarketSpecificShock

The black line represents the median impulseresponsefunction of a positive one standard deviation shock,thebluelinesrepresentthe16thand84thpercentiles.

Thecontemporaneousresponsesofworldoutputandexportpricesareasexpected.In

identifyingthisshock,theresponseofimportpriceswasleftunrestricted,sotheresponsereported here is the unrestricted response. From figure 3, the positive shock leads toacontemporaneousincreaseinimportprices,thisisinlinewiththeresultJ¨a¨askel¨aandSmith(2013)obtainedforAustralia.Whilebothimportandexportpricesincrease,theincreaseinpricesofexportsisslightlyhigher,thereforethisparticularshockresultsinasmallimprovementofthetermsoftrade.

Theresponsesofthedomesticvariablesarerelativelyinsignificant,exceptfortheinterestrate,howevertheirmedianpatternswillstillbediscussed.

Thegrowthofdomesticoutputisnegativeonimpact.ThismaybelargelyexplainedbythenegativeresponseofworldGDPgrowthtotheshock.Theresponseofinflationisalittle sluggish on impact, but quickly becomes positive within a year where it staysforupto5periods.Thecentralbankrespondstofallingoutputlevelsbyadoptinganeasymonetary policy stance indefinitely. The exchange rate appreciates briefly onimpact,howeveracombinationofhighimportpricesandlowinterestratescontributetoarealdepreciationoftheexchangeratewithinafewmonthsoftheshock.Asexplainedearlier,thisresultmaybeinterpretedas(weak)evidenceofaDutchdiseaseeffect—aboomingsectorleadingtoatermsoftradeincreasestrengthenstherealexchangeratetemporarily,and compromises the competitiveness of other sectors. Overall GDP growth maythusdeclineintheshortterm.

Overall, the commodity market specific shock may dampen the growth of outputandinitially appreciate the real exchange rate. The central bank may respond byloweringthe interest rate further, which will moderate the real appreciation and ease theshortterm Dutchdisease.

5.1.4.Responses to a Global SupplyShock

Anegativeglobalsupplyshockisoneassociatedwithafallinimportpricesandaslowdownofglobaleconomicactivity.Thisshockisthereforeidentifiedbyrestrictingtheresponsesofimportpricesandworldoutputgrowthtobenegative.