RCFRWorkingPaper#200801
ForeignReserveHoardingandRiskofGreaterForeignTradeDependence
JieLi[*] WukuangCun[†] RamkishenRajan[‡]
01/25/2008
Abstract: Therapidgrowthofforeignreservesinemergingmarkets,East-Asiacountries, inparticular,hasbeenassociatedwithgreaterforeigntradedependence,whichin turn,willpotentiallyexposethosecountrieswithmoreexternalrisks.This effect harmsthebenefits ofreservehoarding.Therefore,attheearlystage,reserveaccumulationmaybegoodforemergingmarketsintermsofcurrencycrisisprevention;however,withincreasedexternalrisksbroughtbygreaterforeigntradedependence,thecostsideofreserveaccumulationmaybedominating.Inthisregard,wecanderivetheoptimalreserveholdings.Basedonourestimate,themarginalcostforreserveaccumulationinChinaafterYear2012willbehigherthanthemarginalbenefits.Theoptimalreservesmayreach2.5trillionUSdollars.
KeyWord: ForeignReserves,ForeignTradeDependence,Risk
1Introduction
Therehave been large foreign reservehoardingamong emergingmarketsafterAsianFinancialCrises.Pre-cautionarydemandforforeignreserveshasbeenutilizedforexplainingsuchhoardingbehaviorinvarious articles.Reserveaccumulationisregardedasthewar chestagainstdifferentrisksarisingfromshort-term externaldebts,tradedeficits,large fiscaldebts, andsoon.
Thebenefitsideofreserveaccumulationhasbeen investigatedquitefully with much less serious research onthecostside. Frenkel and Jovanovic (1981) asserted that reserves serve as a buffer stock and the optimal stock of reserves depends positively on the extent of variability of international transactions and negatively on the market rate of interest. Aizenman and Marion (2004)considered reserve hoarding as a kind of precautionary demand of emerging markets to smooth consumption intertemporally. However, since reserves are only accumulated from sovereign borrowing and costly taxation in their model, the costs of reservesare merely taxation costs and the utility reductioncaused by less current consumption. This assumption can neither reflect the real process of reserve accumulation nor the increased risk brought by the larger foreign trade dependence. Olivier Jeanne and Romain Rancière (2006) regarded reserves as a buffer stock which allows the country to smooth domestic absorption in response to sudden stops, but yield a lower return than the interest rate on the country’s long-term debt. To sum up, therearefewliteratures to emphasizethecostofreservehoardingotherthanopportunitycost. Ourpaperwillfocusontherisksfromreservesaccumulationitself, the risk of greater foreign trade dependence in particular.
Reserveaccumulationisusuallyaccompaniedwithincreasedforeigntradedependence,whichinturn, exposestheeconomyunderhigherexternalrisks.It is a quite common practice among many emerging markets to pursue high growth in exporting sectors while depress domestic consumption. Since 1996, manyemerging markets have been through a decade-long processwith both current account surpluses and rising foreign trade dependences defined as Export / GDP.Figure 1 showslarge stockpiles of foreign reserves among some major emerging markets, such as China, Korea, Thailand and Russia, withhuge current accounts surpluses. Meanwhile, the foreign trade dependences of these countries are continuously risingfrom 21%, 32.4%,39%, and 40.5% to 37.5%, 42.5%,73.5% and 45.5%respectively during the period of 1996-2005. ThegrowthrateofreserveaccumulationisfargreaterthanGDPgrowth,which inevitablyincreasestheforeigntradedependence.
Increased foreigntradedependenceistheby-productofglobalizationwhichisbelievedtobegoodforglobalwelfare.However,italsomakestheemergingmarketsmorerelyonthoseexportdestinationcountries,usuallyUSandEU.ThedemandshocksfromUSorEUwouldbetransferredmoreeasilytotheemergingmarketsthrough increasedforeigntradedependence.Furthermore,these shocks may well be channeled toweakdomestic banking systems, which in turn, leadtomore serious bankingcrises.Inaddition,duringsurplusyears,it is very likely for the emerging markets togetaccusedforexchangeratemanipulationsaswellasothertradedisputes.
Therefore,reserveaccumulationwith greater foreigntradedependencemay expose emerging markets withhigherexternalrisks.Theneteffectofreservesaccumulationwillbe ambiguous.
Thispaperisstructuredasfollows.Wewilllayoutthetheoreticalmodelinnextsectionfollowedbyasimplercasestudyforthemodel in section 3 and its numerical solutions in section 4.ThenwewillfitthemodelintoChina’scase in section 5.In section 6, we will present a two-period model to show that it is not always optimal to accumulate reserves if foreign trade dependence is taken into account.The finalsectionconcludesourpaper.
2TheModel
2.1ObjectiveFunction
(1)
P:Probabilityforexternalshocks.
L:Totallosswithexternalshocks,currentaccountshocksinparticular[1].
R:Reserveholdings.
: Share of reserve holdings which a government is willing to use to defend.
NL:Netloss.
: Opportunity cost of reserves. It can be expressed as with the constant unit cost, c.
We should make it clear that NL is not the real loss of GDP, but a representative index which indicates expected external risk of an economy.
2.2 MoreaboutProbabilityFunctionP
Weassumethattheprobabilityfornegativeexternalshocksisassociatedwiththedegreeofforeigntradedependence:, whereisdefinedasExports/GDP.Thegreatertheforeigntradedependence,themorelikelyfortheeconomytobeaffectedbynegativeexternalshocks.With higher foreign trade dependence, domestic export industries are more likely to be subject to trade disputes, potentialtradebarricades, competition and retaliation from foreign counterpart industries, and troubles of such kind.Therefore,weassume.
2.3 MoreaboutLossFunctionL
L isthelossfunctionwhichdescribesthetotallossfromnegativeexternalshocks.WeassumethatLisafunctionof，.
2.4 Moreabout R and
Weassumethat.Thisassumptionisreasonablewhenthegrowthrateofreserveaccumulationismuchgreater than GDPgrowthwhilecapitalaccountsremain relativelystable.Thisassumption fits the situation in East Asian countriesaftertheCrises with huge current account surpluses.
2.5Modelsolution
The firstorderconditionof(1)determinestheoptimal R.
(2)
If, themarginalbenefitforaccumulatingonemoreunitofreservesisgreater than the risksitmaybring.If, themarginalcostofreserveaccumulationisdominating.
3ASimplerCase
Weassumethattheprobabilityfunctionfollowsthespecificform:
(3)
Theprobabilityfunctionisamonotonicallyincreasingconvexfunctionofforeigntradedependence.The greatertheforeigntradedependence,theeasierfortheeconomytogethitbynegativeexternalshocks.Wealsoassumethespecificfunctionalformforlossfunction L is:
(4)
where Y isdomesticGDP; = (Exports/GDP) GDP= Exports, representsexportsoftheemergingmarket,whichisalsotheforeigndemandfordomesticgoods. represents the share of demand loss when hit by external shocks. denotestheunitsofdomestic output losswhenforeigndemandreducesbyoneunit.is the Keynesian multiplier.
R isastockconcept,i.e.,theaccumulated flowsofannualreserveadditions.Thus,thereservelevelatyear t is:
(5)
whererepresentsreserveadditionatyear i.
Forsimplicity,weassumethat Y grows at aconstantrate n.
Define,
where. istakenasconstantacrosstime[2].InChina’scase,thevaluehasbeenquitestableat0.13afterthe AsianFinancialCrises (SeeFigure2).Then,(5)canberewrittenas
(6)
Whatisleftforustoestimateisthevalueof. Weclaimthatisalinearfunctionoftime.ThislinearrelationshipcanbedirectlyobservedfromChina’sdataaftertheCrises[3]. Theprecautionarydemandforreservesafter theCriseshasbeenpickedupquitesignificantly.InChina’scase,theslopeofthelinearelationshipisapproximately0.025.Theexport-orientedstrategiesaswellasaseriesofpolicieshavebeeninpracticetoboostforeigndemand.Thiscomeswiththeincreasedforeigntradedependence.ThegovernmentsarereluctanttochangethepoliciessincetheydonotwanttheslowerGDPgrowthduringtheirtenure.Therefore,wepredictthatthelinearrelationshipbetweenforeigntradedependenceandtimewillcontinueatleastintheshort and mediumrun.Itseemsplausibleforustoassumethefollowing:
(7)
whereandareconstants.
Foreasiercomputation,wecalculateundercontinuouscaseasfollows: (8)
Replace t with, andplugtheaboveinto(6),
(9)
Plugtheexpressionsof R, P,and L into(1),wehave
(10)
4 Numerical Solutions:
The optimization problem is:
(11)
While the analytical solution is difficult to obtain, we try the numerical methods. The initial parameter values are set as follows:
1 / 0.025 / 0.2 / 0.08 / 0 / 0.15 / 1.5 / 1 / 1[4]We set from 0 to 1 with a tick of 0.01, then we find the minimum NL and optimal and R accordingly.
As shown in Figure 2,NL reaches its minimum value (-1.308) at and the corresponding optimal reserve level is 4.75.
According to this result, the NL exhibits the typical U-shape when increases. When , reserve accumulation will reduce the NL value.But it will increase the NL value when . Therefore, a government should stop its mercantilism policy as well as the process of reserve accumulation before R andreach the critical values. However, the mercantilism policy is inelasticto some degree and hard to be abolished once put into practice. So even if the values of R andpass their critical levels, the government will feel it hard to reverse the reserve accumulation process.
Now, we vary the values of the parameters,,and, to find out the relationships between these parameters and critical levels of reserves and foreign trade dependence.
The policy intensity level
represents the intensity of the mercantilism policy. According to the expression , foreign trade dependence increases more quickly when gets larger.
As show in Figure 3, a largerwill decrease the critical levels of reserve and foreign trade dependence. It implies that anintensive mercantilismpolicy for reserve accumulation is more harmful than a moderate one. Even if accumulating reserve via current account surpluses is sensible for precautionary need, it should be accomplished in a longer term with a moderate trade policy.
The growth rate of economy n
As shown in Figure 4, when we change the valuesof, the critical values of foreign trade dependence moves in the same direction, leaving the direction of thecritical R uncertain.This result implies that it is not sensible for a government to adopt a mercantilism policy and accumulate reserves to satisfy its precautionary need when the economy grows rapidly. There may be not enough time for the economy to accumulate sufficient reserves when the risk/economy scale is too large.
The efficiency of reserve accumulation
According to the definition of, we interpret as the efficiency of reserve accumulation, that is, the quantity of reserve accumulated per unit of exports. Given other conditions unchanged, a largermeans more reserves be accumulated under the same risk or at the same level of foreign trade dependence.As shown in Figure 5, when we change the valuesof, the critical values of foreign trade dependence and reserve levels will change in the same direction.
In the economy like China or Thailand, where processing-trade accounts for a large proportion, it may not be sound to adopt mercantilism policy to boost its reserves. is very small in these economies. However, other economies like Korea withmost of export goods carrying their own brands (higher ) may be more “suitable” to accumulate reserves via current account surpluses.
It seems that not all economies can benefit from reserve accumulation. Only those with a relative low GDP growth rate orhigh accumulation efficiency can really get benefits. In addition, the mercantilism policy aimed to accumulate reserves should not be too intensive. In our view, Chinamay not be suited for such a policy while Korea may be a better place to adopt mercantilism policy.
5CalibrationsforChina
Figure7showsthattheestimatesforChina’s :after Asian Financial Crises.SeeFigure6fortheinthepasttenyears.Wetaketheaverageofthemabout0.13.
Thedataforforeigntradedependence,GDP,reserveholdingsfrom1998to2006is obtainedfromIFS.Weassumethegrowthrateofforeigntradedependencefrom2007onas0.025,GDPgrowrate10percent, 0.13.
Table1showstheestimatesofnetlossfrom1998to2022.Figure8showsthenetlosswhen=2, 1.75 and1.5.Thenetlossreacheslocalminimumatyear2012,2014and2017respectively.Thecorresponding reserve holdings are2.5,3.4and5.2trillionUSdollars.
6 Is it really sensible to hoard so much international reserve?
Large international reserve holdings in a number of Asian emerging markets areattributed to precautionary need. International reserves can be used to smooth consumption and distortions intertemporally in the face of volatility of macro economy (Aizenman et al. 2002). However, in most models developed from this idea, productivity shock is set to be exogenous, that is, irrelevant with the process of reserve accumulation. In this paper, we endogenize the productivity shock and relate it with foreign trade dependence.
Taking the basic setting in Aizenman et al. (2002), we study a two-period, two-states-of-nature model:
In time period t:
, whereis constant (12)
Foreign trade dependence of time t is: (13)
In time period t+1:
(14)
(15)
Whereis a stochastic term that represents productivity shock:
Whereis a function ofwhich can be expressed as.
According to the definition of, it is obviously that . Set and thenrepresents the natural variation of economy.
Objective function:
(16)
Input (12) & (13) & (14) into (16)
(17)
Where
(18)
Where
Comparisonbetween two cases when:
Case 1: when foreign trade dependence is included
The utility gain associated with acquiring the first unit of international reserves is:
(19)
The demand for international reserves is positive if obtaining a unit of reserves increases utility. The demand for international reserves is positive iff：
（20）
To simplify, suppose and (20) can be rewritten as:
(21)
Where
Since marginal utility decreases,
Ifis a linearfunction, for instance, inequation(21) cannot be held since. In this case, even the first unit of international reservewill bring a negative utility gain.
Only when, there may be positive demand for international reserves when agents have a proper.
Case 2: when foreign trade dependence is not included
If policy authority does not take “foreign trade dependence” into account when optimizing, then productivity shock has nothing to do with foreign trade dependence, that isand.Consequently,
(22)
Comparison:
Comparing (19) and (22), we can easily find that:
(23)
(19) and (22) can be regarded as the extent of inclination to hoard reserves. Conventionally, policy authority maximizing the expected total utility did not take “foreign trade dependence” and consequential risk increment into consideration, so they may find it optimal to hold sizeable international reserves. However, if risk increment caused by “foreign trade dependence” is included, they may find it not so optimal to hold so much international reserves.
7Conclusions
Though reserve can function as a war chest of the macro economy, the process of reserveaccumulationis always accompanied with greater foreign tradedependencewhich may expose emerging markets withhigherexternalrisks.Theneteffectofreservesaccumulationwillnotbethatbeneficial.
Even if the net effect of reserve accumulation is positive, not all economies can benefit from it. Only those with a relative low GDP growth rate and high accumulation efficiency can really get benefits. In addition, the mercantilism policy aimed to accumulate reserves should not be too intensive.
References:
[1]Joshua Aizenmanand Nancy Marion,2004, “International Reserve Holdings with Sovereign Risk and Costly Tax Collection”,The Economic Journal, 114(July),569-591.
[2]Joshua Aizenman and Nancy Marion, 2002, “The High Demand for International Reserves in the Far East: What’s going on?”, NBER working paper
[3]Jacob A. Frenkel and Boyan Jovanovic, Jun. 1981, “Optimal International Reserves: A Stochastic Framework”. The Economic Journal, Vol. 91, pp. 507-514
[4]JieLiandRamkishenRajan, CanHighReservesOffsetWeakFundamentals? ASimpleModelofPre-cautionaryDemandforReserves, EconomiaInternazionale,VolumeLIX,No.3,2006
[5]Olivier Jeanne and Romain Rancière, 2006, “The Optimal Level of International Reserves for Emerging Market Countries: Formulas and Applications”, IMF working paper.
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RCFRWorkingPaper#200801
Figure 1
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Figure 2
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Figure3
ALPHA/ R / NL /
0.81 / 11.33 / -3 / 0.02
0.75 / 4.75 / -1.308 / 0.025
0.7 / 2.55 / -0.695 / 0.03
0.65 / 1.52 / -0.412 / 0.035
0.6 / 0.961 / -0.261 / 0.04
0.56 / 0.66 / -0.173 / 0.045
0.53 / 0.49 / -0.118 / 0.05
Figure 4
GDP growth rate/ R / NL / n
0.86 / 4.84 / -1.376 / 0.05
0.82 / 4.86 / -1.351 / 0.06
0.78 / 4.75 / -1.33 / 0.07
0.75 / 4.75 / -1.308 / 0.08
0.73 / 4.92 / -1.289 / 0.09
0.7 / 4.73 / -1.271 / 0.1
Figure 5
SITA/ R / NL /
0.64 / 2.1 / -0.575 / 0.12
0.68 / 2.84 / -0.773 / 0.13
0.72 / 3.79 / -1.015 / 0.14
0.75 / 4.75 / -1.308 / 0.15
0.79 / 6.21 / -1.66 / 0.16
0.82 / 7.65 / -2.074 / 0.17
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Figure 6
Figure 7
Figure8
Table 1
YEAR /Exp/GDP / GDP
(USD Trillion) / Reserve
(USD Trillion) / Net loss
() / Net loss
() / Net loss
()
1998 / 0.197 / 1.096 / 0.145 / -0.132 / -0.130 / -0.128
1999 / 0.197 / 1.165 / 0.155 / -0.141 / -0.139 / -0.137
2000 / 0.225 / 1.289 / 0.166 / -0.143 / -0.140 / -0.136
2001 / 0.218 / 1.424 / 0.212 / -0.190 / -0.186 / -0.182
2002 / 0.243 / 1.563 / 0.286 / -0.253 / -0.247 / -0.242
2003 / 0.286 / 1.764 / 0.403 / -0.342 / -0.331 / -0.321
2004 / 0.328 / 2.076 / 0.610 / -0.500 / -0.482 / -0.463
2005 / 0.364 / 2.388 / 0.819 / -0.646 / -0.617 / -0.588
2006 / 0.403 / 2.739 / 1.066 / -0.798 / -0.753 / -0.708
2007 / 0.428 / 3.012 / 1.234 / -0.880 / -0.821 / -0.762
2008 / 0.453 / 3.314 / 1.429 / -0.968 / -0.891 / -0.814
2009 / 0.478 / 3.645 / 1.655 / -1.059 / -0.960 / -0.860
2010 / 0.503 / 4.010 / 1.917 / -1.153 / -1.026 / -0.898
2011 / 0.528 / 4.411 / 2.220 / -1.247 / -1.085 / -0.923
2012 / 0.553 / 4.852 / 2.569 / -1.339 / -1.135 / -0.930
2013 / 0.578 / 5.337 / 2.969 / -1.425 / -1.168 / -0.911
2014 / 0.603 / 5.870 / 3.430 / -1.501 / -1.180 / -0.858
2015 / 0.628 / 6.457 / 3.957 / -1.560 / -1.161 / -0.761
2016 / 0.653 / 7.103 / 4.559 / -1.596 / -1.102 / -0.608
2017 / 0.678 / 7.814 / 5.248 / -1.599 / -0.990 / -0.382
2018 / 0.703 / 8.595 / 6.033 / -1.558 / -0.812 / -0.066
2019 / 0.728 / 9.454 / 6.927 / -1.461 / -0.550 / 0.361
2020 / 0.753 / 10.400 / 7.945 / -1.291 / -0.182 / 0.928
2021 / 0.778 / 11.440 / 9.102 / -1.028 / 0.318 / 1.663
2022 / 0.803 / 12.584 / 10.415 / -0.650 / 0.978 / 2.605
*Net Loss values after 2006 are predicted values.
1
[*]TheCentralUniversityofFinanceandEconomics,Beijing,email:
[†]TheCentralUniversityofFinanceandEconomics,Beijing,email:
[‡]GeorgeMasonUniversity,email:
[1] Wedonotarguethattheshocksfromcapitalaccountsarenotimportantincrisis.Indeed,recentcrisesaremorelike capitalaccountcrises.However,whatweconcerninthispaperisforeigntradedependencewhichisapurecurrentaccountissue. Inaddition,aswementioned,themainsourcesofreserve accumulationforemergingmarketsarecurrentaccountsurplusinrecentyears.Therefore,weincludeonlycurrentaccountshocksintheassumptions.
[2] Inemergingmarkets,mostofinternationaltradesareprocessingtrades.Therawmaterialsarefrominternationalmarkets, so isthe destination of finalproducts.Emergingmarketsearnprocessingfeeonly.Therefore,theratioofexportsandimportstendstobestable acrosstime.
[3]SeeFigure 3.
[4]According to the definitions, andare determined by the specific characteristics of a country’s export industry and government, so we assumeto find a general solution. It should be noted that the values ofandcan only affect the optimal values of NL, R and, but not the relationships between them and the parameters.