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InvestmentEfficiencyandtheWelfareGainfrom InternationalFinancialIntegration* PhilipL.Brock UniversityofWashington September2016 Abstract I analyze international financial integration in a Ramsey growth model with capital adjustment costs that affect the efficiency of investment. The welfare gain relative to financial autarky is measuredbytheincreaseinthevalueofthecapitalstockatthetimeoffinancialintegration.My model offers an analytical structure that is consistent with four stylized facts of financial market liberalizationsinemergingmarketeconomies:thecostofcapitalfalls,stockmarketindexesrise, aggregate investment increases, and growth rates increase at rates that depend on country characteristics. The size of the welfare gain depends on structural parameters and is nonmonotonicinthedegreeofconvexityofthecapitaladjustmentcosts. JELClassificationNumbers:F43,F63,O16,O19 Keywords:CapitalAdjustmentCosts,InternationalFinancialIntegration,Tobin’sq ____________________________________________ *This is a substantially revised and expanded version of an earlier paper, circulated as “Growth RateAccelerationsandtheGainsfromInternationalFinancialIntegration”. The paper has improved as a result of comments at the 2016 Society for Nonlinear Dynamics and Econometrics Conference and the 2015 and 2016 Infiniti International Finance Conferences.IespeciallythankSebastianSosa, CharlesEngel,ManfredKremer,andJennyBerrillforextensivecommentsonearlierdrafts. Contactdetails:[email protected] 1Introduction Whatisthenatureofthewelfaregainsthatarecreatedbyfinancialintegrationofasmalleconomy with world capital markets? There are two important approaches to calculating the welfare gain frominternationalfinancialintegrationthatisassociatedwithcapitalaccumulation.Onestresses the gain due to the faster rate of capital accumulation induced by the lower world interest rate relativetotheautarkicinterestrate.Thesecondstressesthepotentialincreaseintherateofreturn tocapitalthatmaybeinducedbycontemporaneouschangesintotalfactorproductivity.Thispaper follows the first approach by extending the Ramsey growth model to include capital adjustment costsinfinancialautarkyaswellasininternationalfinancialintegration. In the theoretical literature, there appears to be little support for the proposition that one- sectoraggregategrowthmodelscangenerateasubstantialwelfaregainduetoareductionofthe interestratefromautarkictotheworldrateforasmalleconomy.GourinchasandJeanne(2006),in particular,showedthattheRamseygrowthmodelimpliesasmallwelfaregainfrominternational financial integration due to the fast rate of the economy’s convergence toward steady-state in financialautarky.1 In contrast to the welfare implications of the Ramsey model, a body of empirical evidence— originating in the work of Henry (2003, 2007) and Bekaert, Harvey, and Lundblat (2005)— demonstrates that there are empirically observed increases in the stock market value of firms as wellasgrowthrateaccelerationsthatfrequentlyaccompanymeasurestopromotetheinternational financialintegrationofaneconomy;thesesuggestawelfaregainarisingfromfinancialintegration.2 This paper revisits the theoretical hypothesis that a substantial part of the welfare gain from international financial integration may be attributable to the faster rate of capital accumulation. The analysis extends the Ramsey growth model by including capital adjustment costs; that is, it 1SeealsotherelatedpapersbyAoki,Benigno,andKiyotaki(2010);Mendoza,Quadrini,andRíos-Rull(2009); AngeletosandPanousi(2011);Corneli(2011);Hoxha,Kalemli-Ozcan,andVollrath(2013);AntunesandCavalcanti (2013);andCoeurdacier,Rey,andWinant(2013)forcontributionstothisliterature. 2SeealsoQuinnandToyoda(2008);anddeNicolòandJuvenal(2014). 2 generalizes the investment technology. With no adjustment costs, as in the Ramsey framework used by Gourinchas and Jeanne, the gains from integration are very small. Gains from financial integrationinthispaperaretiedtotheexistenceofcapitaladjustmentcosts—andthewelfaregain frominternationalfinancialintegrationisgreaterforeconomiesthathavelargercapitaladjustment costsandgreaterinitialcapitalscarcity(relativetothesteady-statecapitalstock). An important aspect of the analytical model is that adjustment of the capital stock in the financially integrated economy with non-zero adjustment costs is faster (but finite) than adjustmentinthefinanciallyautarkiceconomy.Thismeansthatthesizeofthewelfaregainfrom financialintegrationcanbeinferredfromthegrowthrateaccelerationthatfollowsintegration.In particular, given estimated parameter values of the initial relative capital scarcity, elasticity of intertemporal substitution, and convexity of capital adjustment costs (along with other standard parameters), the welfare gain can be estimated as a function of the observed growth rate acceleration. ThisfeatureofthemodelallowsittoaddressthefollowingconcernraisedbyGourinchasand Jeanne(2006): Henry(2003)andBekaert,HarveyandLundblad(2005)findthatopeningthestock markettoforeigninvestorsboostsgrowthby1-2%forfiveyearsinarow.Sucha result, however, is not obvious to translate in terms of domestic welfare. How persistent is the impact of capital account opening on growth? What share of the output increase is transferred to foreign investors? These questions are crucial in assessingthewelfareimpactofcapitalaccountopeningandcanbeaddressedonly bylookingatthedatathroughthelensesofamodel.[italicsadded] The lens of the model in this paper shows that the persistence of the impact of international financial integration depends on capital adjustment costs and other parameters that affect the speedofconvergence.Thewelfaregaincanbemeasuredbytheincreaseinthestockmarketvalue ofthecapitalstockorbythegrowthrateaccelerationatthetimeoffinancialintegration. Thepaper’splanisasfollows.Section2developsthemodelusedtoaddresstheissueofthe importance of capital accumulation for the welfare gain from international financial integration. Section3derivesthealgebraicexpressionforthewelfaregainfromfinancialintegration.Section4 3 calibrates the model and does a sensitivity analysis for Tobin’s q, growth rate acceleration, and welfaregaininrelationtothesizeoftheadjustmentcostparameter.Section5derivesamethodfor calculatingthewelfaregainfrominternationalfinancialintegrationbasedontheobservedgrowth rate acceleration. Section 6 extends the model to show that the proportional welfare gain from integrationisnon-monotonicwithrespecttoincreasingadjustmentcosts.Thesectionalsoderives thedynamicsassociatedwithanticipatedfinancialintegration.Section7concludes. 2TheModel ThissectionmodifiesthestandardRamseymodeltoincludecapitaladjustmentcosts.Thismodel was first developed by Abel and Blanchard (1983), and has subsequently been generalized by Rappaport(2006)fortheanalysisofbottleneckdevelopmentpaths. A representative infinitely-lived agent produces a single good with a linearly homogeneous production function Af (k) . A is the total factor productivity (TFP) of capital and labor inputs in theproductionfunction.FollowingUzawa(1969),LucasandPrescott(1971),andHayashi(1982), capital accumulation (dk dt) is subject to linearly homogeneous costs: γφ (i,k) . The parameter γ measurestheefficiencyoftransforminginvestmentintonewcapital;inthissenseitbearsaclose resemblancetoTFP.3Themaximizationproblemcanbeconsideredwitheitheraclosedoranopen capitalaccount.Theclosedcapitalaccountwillbereferredtoasfinancialautarky. 2.1 Financialautarky Therepresentativeagent’sutility-maximizationprobleminfinancialautarkyisthefollowing: ∞ V (k0 ,0,∞) = max ∫ u(ct )e− ρt dt subjectto i (2.1) 0 Af (kt ) = ct + it (2.2) 3Insection4,thespecificfunctionalformsfortheproductionfunctionandtheadjustmentcostfunctionwillbe adopted: Af (k) ≡ Ak α and γφ (i,k) ≡ (γ 2)(i k − δ )2 k . 4 dk = i − δ kt − γφ (it ,kt ) dt t k0 given (2.3) TheHamiltonianforthisproblemis: e ρt H (t) = u ⎡⎣ Af (kt ) − it ⎤⎦ + q!t ⎡⎣ it − δ kt − γφ (it ,kt ) ⎤⎦ (2.4) Theoptimalityconditionisgivenby(2.5): u ′(ct ) = q!t ⎡⎣1− γφi (it ,kt ) ⎤⎦ (2.5) where q! istheshadowpriceofcapitalmeasuredintermsofthemarginalutilityofconsumption. Theshadowpriceofcapitalevolvesovertimeaccordingtotheequationofmotiongivenby(2.6): dq! = − u ′(ct ) Af ′(kt ) + ⎡⎣ ρ + δ + γφk (it ,kt ) ⎤⎦ q!t dt (2.6) Thetransversalityconditionis lim q!t kt e− ρt = 0 (2.7) t→∞ The linearized dynamics of consumption and the capital stock around a steady state k and i are (seetheappendixforthederivation): ⎡ ⎡ di ⎤ ⎢0 ⎢ dt ⎥ ⎢ ⎢ ⎥ ⎢ ⎢ ⎥=⎢ ⎢ dk ⎥ ⎢ ⎢ ⎥ ⎢ ⎣ dt ⎦ ⎢ ⎣1 ⎤ ⎥ ⎡i − i ⎤ σ + γφii (i,k) ⎥ ⎢ ⎥ c ⎥⎢ ⎥ ⎥⎢ ⎥ ⎥⎢ ⎥ ⎥ ⎣k − k ⎦ ⎥⎦ ρ Af ′′(k) (2.8) where c = −cu ′′(c) u ′(c) is the inverse of the agent’s elasticity of intertemporal substitution in consumption(EIS). ThedynamicadjustmentissaddlepathstableandisillustratedinFigure1.Thehorizontalline at δ = i k corresponds to dk dt = 0 from equation (2.3), while the d(i k) dt = 0 locus is negativelysloped.TheinterpretationofFigure1isintuitivelyappealing:whentherelativepriceof capital is greater than one, the rate of investment is greater than the rate of depreciation, so the 5 capitalstockgrows.Onthesaddlepaththedeclineintherateofinvestmentleadstheeconomyto thestationarystate. Theconvergencespeedofthecapitalstockinfinancialautarkyis: 2 ⎛ ρ⎞ ρ Af ′′(k) µ= − ⎜ ⎟ − (2.9) σ 2 ⎝ 2⎠ + γφii (i,k) c Notethattheconvergencespeeddependsnegativelyontheconvexity( γφii )oftheadjustmentcost functionaswellasontheEIS. 2.2TheFinanciallyIntegratedEconomy The economy of 2.1 can be analyzed under the assumption of an open capital account, where borrowing and lending on international capital markets is permitted. The model extends the widely-employed representative agent small open economy model with adjustment costs for capital [e.g., Blanchard (1983), Cohen and Sachs (1986), Matsuyama (1987)] to include a limited commitmentconstraint.4 In the open economy capital accumulation takes place as in the autarkic economy. The resourceconstraintismodifiedtoallowforborrowing( d )oninternationalcapitalmarkets. The representative agent is able to pledge the incremental value of the capital stock, qt (kt − k0 ) , againstforeignborrowingwhere qt istherelativepriceoftheinvestmentgoodtotheconsumption good. Formally,theagentmaximizesutilityfromconsumptionsubjecttothedebtaccumulation constraint,thecapitalaccumulationconstraint,andthelimitedcommitmentconstraint: ∞ V ( k0 ,d0 ,0,∞ ) = max ∫ u(ct )e− ρt dt i 0 (2.10) 4SeealsoFrankelandRodriguez(1975)foranearlierversionofthisframework. 6 dd = ct + it + rdt − Af (kt ) dt dk = i − δ kt − γφ (it ,kt ) dt t dt ≤ qt (kt − k0 ) (2.11) k0 given (2.12) d0 = 0 (2.13) Inordertofocusonthewelfaregainfromfinancialintegrationarisingfromtransitionaldynamics,I assumethattheworldinterestraterisequaltorateoftimepreference( r = ρ ). TheHamiltonianforthisproblemis: e ρt H (t) = u(ct ) − λt ⎡⎣ ct + it + rdt − Af (kt ) ⎤⎦ + q!t ⎡⎣ it − δ kt − γφ (it ,kt ) ⎤⎦ + ω! t ⎡⎣ dt − qt (kt − k0 ) ⎤⎦ (2.14) where q! = λ q and ω! = λω are,respectively,theshadowvaluesofinstalledcapitalandthelimited commitmentconstraint.Necessaryandsufficientconditionsforanoptimumare: u ′(ct ) = λt (2.15) qt = 1 ⎡⎣1− γφi (it kt ) ⎤⎦ (2.16) dλ = λt ( ρ + ω t − r) dt (2.17) dq = − Af ′(kt ) + ⎡⎣ r + δ + γφk (it ,kt ) ⎤⎦ qt dt (2.18) Thetransversalityconditionsare: lim λt dt e− ρt = 0 (2.19) lim λt qt kt e− ρt = 0 (2.20) Linearizationof(2.18)and(2.12)aroundthesteadystategivesthelocaldynamicsoftheprice t→∞ t→∞ ofcapitalandthecapitalstock:5 5Thelinearizationisessentiallythesameasthatforsimilartextbookmodels,e.g.BlanchardandFischer(1989, Chapter2). 7 ⎡ di ⎤ ⎡ r ⎢ dt ⎥ ⎢ ⎢ ⎥ ⎢ ⎢ ⎥= ⎢ ⎢ dk ⎥ ⎢ ⎢ ⎥ ⎢ ⎣ dt ⎦ ⎢⎣1 Af ′′(k) ⎤ ⎡ i − i! ⎤ γφii (i,k) ⎥ ⎢ ⎥ ⎥ ⎢ ⎥ ⎥ ⎥ ⎥⎢ ⎥ ⎢ k − k! ⎥ ⎦ ⎥⎦ ⎣ 0 (2.21) Thedynamicadjustmentissaddlepathstable.Theconvergencespeed ( µ * ) inthefinanciallyopen economyis: 2 ⎛ r⎞ r Af ′′(k) µ = − ⎜ ⎟ − 2 ⎝ 2 ⎠ γφii (i,k) Acomparisonof(2.9)with(2.22)indicatesthattheconvergencespeedinthefinanciallyopen * (2.22) economy does not depend on the agent’s intertemporal elasticity of substitution because investmentexpenditurecanbefullyfinancedbyforeignborrowing,giventhelimitedcommitment constraint dt ≤ qt (kt − k0 ) .Asaresult,therateofinvestmentishigherintheopeneconomythanin the financially closed economy. Figure2 illustrates this difference between financial autarky and opennessbythedottedsaddlepaths,correspondingtofinancialautarky,andthesolidsaddlepaths, correspondingtofinancialintegration. In the financially autarkic economy consumption equals production minus investment: ct = Af (kt ) − it . Steady-state consumption in the autarkic economy is c = Af (k ) − δ k . Under limited commitment, the capital stock is financed by external borrowing. From (2.11) and a bindingconstraint(2.13),consumptioninthefinanciallyintegratedeconomycanbesolvedforas: ct = dd − i − rqt (kt − k0 ) + Af (kt ) dt t where dd dk dq = qt + (kt − k0 ) dt dt dt Using(2.12)and(2.18)for (2.23) dk dq ,andcollectingterms,consumptionintheopeneconomyis and dt dt 8 equaltotherealwage, w(kt ) = Af (kt ) − Af ′(kt )kt ,pluscapitalgainsincomefromtheinitialcapital stock: ⎛ 1 dq ⎞ ct = w(kt ) + qt k0 ⎜ r − qt dt ⎟⎠ ⎝ (2.31) Steady-state consumption (c * ) is equal to autarkic steady-state consumption minus interest paymentsonexternaldebt: c * = c − rd = c − r(k − k0 ) (2.32) Figure 3 compares the adjustment paths of consumption in financial autarky and financial openness. The limited commitment constraint allows the agent to smooth consumption by substitutingforeignfordomesticsavingtofinanceinvestmentinthecapitalstock.Thequasi-rents generated by the time-zero installed capital stock raise consumption above the wage and additionallyflattenthetimepathofconsumptioninthefinanciallyopeneconomy. 3TheWelfareGainfromFinancialIntegration The welfare gain from financial integration generally refers to the gain associated with moving from financial autarky to financial openness. Calculating this gain in this model involves making two assumptions. First, that the initial stock of debt at the time of integration is zero (d0 = 0) . Second,thatintegrationfollowsaone-offopeningofthecapitalaccount,referredtoas“aonce-andfor-all unanticipated regime change” by Mendoza, Quadrini, and Ríos-Rull (2009) and as an “unexpectedandirreversible”reformbyAngeletosandPanousi(2011).Thismeansthatfinancial integrationismodeledasaswitchattime0fromaperfectforesightpathunderfinancialautarkyto aperfectforesightpathwithanopencapitalaccount.6Thispapermakesanadditionalassumption 6AsHall(2011)hasnoted,“experiencehasshownthattheseperfectforesightpathsgivereasonablyaccurate measurementsoftheresponseofafullystochasticmodel,providedthattheinteractionswithuncertaintyarenot important.” 9 oflimitedcommitment, dt ≤ qt (kt − k0 ) .Thismeansthattheagentcancommitcurrentandfuture capitalincome,butnotwageincome. The welfare gain from capital account opening is the difference in the maximized present discountedvaluesofconsumptioninthefinanciallyintegratedandfinanciallyautarkiceconomies, as given by equations (2.10) and (2.1). In autarky, the economy’s resource constraint can be writtenas: ct = w(kt ) + Af ′(kt )kt − it (3.1) where is w(kt ) is the real wage. The value function (2.1) can then be linearized around a steadystateas: ∞ ∫ ∫ V (k) = u ⎡⎣ w(k ) ⎤⎦ e− ρt dt + u ′ ⎡⎣ w(k ) ⎤⎦ ⎡⎣ Af ′(kt )kt − it ⎤⎦ e− ρt dt 0 (3.2) ( ) From (2.3) and (2.6), the second term of (3.2) is equal to q!o k0 , where q! = u ′ ⎡⎣ w(k) ⎤⎦ 1− γφi (i,k) . Denoting q = q! u ′ ⎡⎣ w(k) ⎤⎦ , the value function (2.1), linearized around w(k ) , can be approximated by ∞ V (k) = ∫ u ⎡⎣ w(k ) ⎤⎦ e− ρt dt + u ′ ⎡⎣ w(k ) ⎤⎦ q0 k0 (3.3) 0 Followingfinancialintegration(i.e.,openingofthecapitalaccount),thevalueoftheinstalledcapital stock increases from q0 k0 to q0* k0 . The value function (2.10) can be linearized—using equations (2.11),(2.12),andabindingcommitmentconstraint(2.13)--as: ∞ ∫ V (k,d) = u ⎡⎣ w(k ) ⎤⎦ e− rt dt + u ′ ⎡⎣ w(k ) ⎤⎦ q0* k0 * (3.4) 0 Thewelfaregainfrominternationalfinancialintegration(assuming ρ = r )istherefore: ( ) ΔW! = V * (k,d) − V (k) = u ′ ⎡⎣ w(k ) ⎤⎦ q0* − q0 k0 Theappendixshowsthatthisgaincanalsobeapproximatedas: 10 (3.5) ( ΔW! ≈ u ′ ⎡⎣ w(k ) ⎤⎦ γ µ * − µ )( k − k ) ≥ 0 (3.9) 0 where µ and µ * are the convergence speeds of the capital stock in the autarkic and integrated economies.Expressedasafractionofthesteady-statecapitalstock,thewelfaregainis: ) ( ) ⎛ k − k0 ⎞ ΔW = q0* − q0 = γ µ * − µ ⎜ ≥0 k0 ⎝ k0 ⎟⎠ ( (3.10) where W = W! u ′ ⎡⎣ w(k ) ⎤⎦ . The size of the welfare increase is proportional to the adjustment cost parameter (γ ) , the relative adjustment speeds along the transition paths, and the relative capital scarcity (k0 k ) at the time of the capital account opening. It is worth noting that in the limiting caseofzeroadjustmentcosts (γ = 0) ,thereis(approximately)nowelfaregainfromcapitalaccount liberalization,aresultthatmirrorsthefindingofGourinchasandJeanne(2006). 4Calibration This section provides numerical estimates of the importance of capital adjustment costs to convergence speed, the price of capital (Tobin’s q), the rate of per capita income growth, the current account, and welfare. As derived in the appendix, the speed of convergence around a steady state in financial autarky can be expressed in terms of the model’s parameters as the following7: 2 ⎛ ρ⎞ ρ (1− α )(r + δ ) µ= − ⎜ ⎟ − ασ 2 ⎝ 2⎠ +γ ρ + (1− α )δ (4.1) In the financially open economy the adjustment speed does not depend on the elasticity of intertemporalsubstitution: 7In(4.1) ρ istherateoftimepreference, α istheshareofcapitalinproduction, δ istherateofdepreciation, σ is thecoefficientofrelativeriskaversion,and γ isthecapitaladjustmentconvexityparameter. 11 2 ⎛ r ⎞ (1− α )(r + δ ) r µ = − ⎜ ⎟ + 2 γ ⎝ 2⎠ * (4.2) Note that with r = ρ , the steady-state capital stock k is the same in a financially integrated economy as in autarky. This is because Af ′(k ) = ( ρ + δ ) in autarky and Af ′(k ) = (r + δ ) in a financiallyopeneconomy.With ρ = r ,thedifferencebetweenthetwoeconomiesisonlythespeed ofadjustmenttowardthesteady-statecapitalstock. TheresultsforTobin’sq,growthacceleration,debtaccumulation,andwelfaregaindependon the ratio of the capital stock to the steady-state capital stock at the time of the capital account liberalization. The results also depend importantly on the assumed value of the convexity parameter (γ ) for capital adjustment costs. Two studies using annual data estimate a capital installationcostfunctionwith γ = 2 : Hall(2002):approximately2fortheUnitedStatesusingannualdata(1958-1997) Garcia-Cicco,Pancrazi,andUribe(2010):2.3-3forArgentinausingannualdata (1900-2005) Onestudythatestimatesavalueof γ ≈ 0.5 (onanannualizedbasis)isMendoza(2010)forMexico usingquarterlydata(1993:1-2005:2). Figures 4, 5, and 6 plot Tobin’s q, the growth acceleration at the time of the capital account opening,andthewelfaregainfromcapitalaccountopeningfor γ = 0.5, 1, 2. Therearetwogeneral resultsthatthefiguresillustrate: 1)LargeradjustmentcostsareassociatedwithhighervaluesofTobin’s“q”andsmallergrowth accelerations, as shown in Figures 4 and 5. Although larger values of “q” are usually associated withfastergrowth,thepriceofcapitalisdeterminedbyboththepresentdiscountedvalueoffuture rentalsoncapitalandbyfuturemarginaladjustmentcosts.Anincreaseintotalfactorproductivity will raise the price of installed capital and increase the growth rate, while an increase in capital adjustmentcostswillraisethepriceofinstalledcapitalandlowerthegrowthrate. 12 2) The relative welfare gain from the opening of the capital account is greater for economies that have larger capital adjustment costs, as shown in Figure 6. This result does not imply that larger capital adjustment costs are better than small adjustment costs. It does mean that, in economies for which the marginal costs of adjusting the capital stock are high, capital account openingwillproduceasubstantialrevaluationoftheinitialcapitalstock. The welfare gain from capital account opening also depends on the agent’s elasticity of intertemporal substitution η = 1 σ . Most of the literature on the welfare gain from international financial integration makes the assumption that the EIS is one, following the specification of GourinchasandJeanne(2006).8AlargeliteraturesuggeststhattheEISmaybesubstantiallylower, with a recent meta-analysis by Havranke, Horvath, Irsova, and Rusnak (2013) of 169 studies covering104countriesfindingsubstantialheterogeneityinestimates,butwithameanestimateof 0.5. Table 1 shows the sensitivity of the welfare gain for combinations of three initial capital scarcity ratios, three adjustment cost parameters, and three intertemporal rates of substitution. Taking as a benchmark η = 1, k0 k = .83, and γ = 1 , the welfare gain from opening the capital accountwouldbeabout2.8percentofthevalueofthecapitalstockwitharangeof2.3–3.1percent for 0.5 ≤ γ ≤ 2 ; 2.2 – 3.3 percent for 2 ≥ η ≥ 0.5 ; and 1.4 – 4.2 percent for 0.91 ≥ k0 k ≥ 0.77 . Varying all three parameter values simultaneously generates a range of welfare gains from 1.0 percent of the initial capital stock (k0 k = 0.91, γ = 0.5, η = 2) to 5.9 percent of the value of the initialcapitalstock (k0 k = 0.77, γ = 2, η = 0.5) . 8SeeAntunesandCavalcanti(2013),Hoxha,Kalemli-Ozcan,andVollrath(2013),Corneli(2010),and AngeletosandPanousi(2011).Mendoza,Quadrini,andRíos-Rull(2009a,b)use η = 1 2 ,while Couerdacier,Rey,andWinant(2013)use η = 1 4 .ItshouldbenotedthatAPandCRWbothspecify Epstein-Zinpreferencestodistinguishriskaversionfromintertemporalsubstitution. 13 5GrowthRateAccelerations Aretherealternativewaystomeasurethewelfaregainfromfinancialintegration?Onewayisto try to estimate directly the magnitude of the increase in quasi-rents following a financial market liberalization. This literature, which was influenced by the work of Henry (2000), measures the gain from international financial market integration by calculating excess returns on capital associated with stock market liberalizations. Henry (2000) used a 12-country sample 9 of liberalizationstoconstructaneight-monthpanelwindowpriortotheofficialimplementationofa stockmarketliberalizations.10Hefoundacumulativerevaluationof38percent,withanestimated 26percentrevaluationafteradjustingfortheeffectsofforeignstockmarketfluctuationsandother concurrentdomesticeconomicliberalizationprograms. Kim and Singal (2000) used data on estimated stock market openings for 18 countries to comparethechangeinmeanstockmarketreturnsfortheone-yearperiodaftertheopeningwith two years prior to the opening.11 Using this window they estimated a cumulative increase of 12 percentacrossthe18countries. Bekaert and Harvey (2000) estimated duration windows of excess stock market returns for capital market liberalizations in 20 countries.12 For duration windows of twelve months (six months prior to a stock market liberalization and six months following), they found cumulative excessreturnsofabout15percent.13 Takenatfacevalue(andinthecontextofthispaper’smodel),thesefiguressuggestawelfare gain in the range of 10-20 percent of the value of the initial capital stock due to international financialmarketintegration.Butitisclearthatfirmslistedonthestockmarketsoftheliberalizing countriesinthesethreestudiesformarestrictedsampleofcompanies;inaddition,thestudiesdo 9Argentina,Brazil,Chile,Colombia,India,Korea,Malaysia,Mexico,thePhilippines,Taiwan,Thailand,andVenezuela. 10Stockmarketliberalizationsaredefinedasthemonththeliberalizationwasimplemented,basedoninformation takenfromseveralsourcesdocumentedbyHenry. 11ThecountriesareHenry’sminusMalaysiaplusGreece,Indonesia,Jordan,Pakistan,Portugal,Turkey,and Zimbabwe. 12ThecountriesareHenry’splusGreece,Indonesia,Jordan,Nigeria,Pakistan,Portugal,Turkey,andZimbabwe. 13Theseresultswereconsistentacrossstockmarketliberalizationsbasedeitheronofficialliberalizationdatesoron empirically-baseddatesfromstructuralbreaksinthedata. 14 notdifferentiatebetweencompaniesthathadincreasedaccesstointernationalcapitalmarketsand thosethatremainedshutoutfromexternalfinancing. Gozzi, Levine, and Schmukler (2008) directly compute a measure of (average) Tobin’s q for about9,000firmsin74countriesduring1989-2000.Inthismicroeconomicstudyoftheeffectof internationalizationonmarketcapitalization,theempiricalworkindicatesthat,forafirmthatgains access to international capital markets, “q” rises about twelve percent in the two-year period precedingtheinternationalization,andthenfallsbacktoitsinitiallevelduringthenextthreeyears. Theempiricalmeasureof“q”isthefollowingratio: q = ( market value of equity plus book value of debt ) ( book value of assets ) Abreakdownofthebehaviorofthenumeratoranddenominatorindicatesthattheincreasein“q” priortointernationalizationisdrivenbyprimarilybyanincreaseinthestockmarketvalueofthe firm, which remains high after the internationalization. The decline in “q” following the internationalization is primarily driven by the denominator, suggesting that firms expand rapidly bypurchasingothercompanies. In terms of this paper’s model, the increase in “q” is consistent with the revaluation of quasi- rentstoexistingcapitalatthetimeoffinancialintegration.Therapiddecreasein“q”forindividual firmssuggestsverysmallcapitaladjustmentcosts,whichwouldbethecaseatamicrolevelfora firm that can purchase capital assets from other domestic firms. However, the results do not addresstheimportanceofcapitaladjustmentcostsattheaggregate(economy-wide)level. A different approach is to look at growth accelerations that have followed financial market liberalizations.Henry(2003)findsthatcapitalaccountliberalizationsareassociatedwithgrowth rateaccelerationsofabouttwopercent(roughlystartingfromtwopercentperyearandthenrising to four percent per year). Bekaert, Harvey, and Lundblad (2005) find that equity market liberalizations lead to a growth acceleration for five years of about one percent, a finding that “is robust to alternative definitions of liberalization and does not reflect variation in the world businesscycle.” 15 Figure7takestheinformationfromTable1(plusotherinterpolatedpoints)andgraphsthem as iso-welfare curves. Each curve represents the different combinations of the adjustment cost technology (γ ) andinitialcapitalscarcity (k0 k ) thatgeneratetheequivalentrelativewelfaregain ( ) fromopeningthecapitalaccount,expressedasapercentoftheinitialcapitalstock ΔW k0 .For any given capital adjustment cost technology, the welfare gain from capital account liberalization increaseswithcapitalscarcity.Asadjustmentcostsbecomelinear,thewelfaregainassociatedwith capital account opening becomes smaller. There is no welfare gain from international financial integration when the economy is initially at its steady-state capital stock (the vertical axis, k0 k = 1 )orwhentherearenocapitaladjustmentcosts(thehorizontalaxis, γ = 0 ). Figure 7 also plots two growth rate acceleration curves. These curves comprise the sets of points k0 k and γ that generate an acceleration of the output growth rate by either one or two percentage points at the time of the capital account opening. The upward slopes of the curves reflectthe propertythat anincreaseinadjustmentcostslowerstheoutputacceleration,whilean increaseininitialcapitalscarcityraisestheoutputacceleration(thecurvesaredrawnforEIS=1). Thetwopercentcurveistotherightoftheonepercentcurvebecause,foranyinitiallevelofcapital scarcity,lessconvexadjustmentcostsraisethegrowthrate. Figure 7 shows that the welfare gain from capital account opening will depend on the initial levelofcapitalscarcityandtheconvexityofadjustmentcosts,givenotherparametersofthemodel. Gourinchas and Jeanne (2006) estimate that initial capital scarcity may be approximately 70 percentonaveragefornon-OECDcountries.Foracountrywithinitialcapitalscarcity k0 k = 0.71 , adjustment cost convexity parameter γ = 1.8 , and EIS=1, a one percent growth acceleration following a capital account liberalization would imply a welfare gain of about 6.0 percent of the value of the initial capital stock. An observed one-percent growth rate acceleration is also consistent with other parameter values. For example, k0 k = 0.8 and γ = 1 are consistent with a onepercentgrowthrateaccelerationandimplyawelfaregainofabout3.5percentofthevalueof 16 theinitialcapitalstock.Totheextentthatthesetwoparametervalues k0 k and γ areproblematic to estimate, the example given here illustrates the difficulty in attempting to make precise estimatesofthewelfaregainattributabletothegenerationofquasi-rentsontheinitialcapitalstock resultingfrominternationalfinancialintegration.14 6Extensions 6.1HigherValuesof γ Sections4and5haveworkedwithvaluesoftheefficiencyofinvestmentparameter γ between0.5 and 2.0, in line with several results reported for the U.S. and Argentina, using annual data over extended periods. However, other studies have estimated substantially higher values of γ . For example,CooperandHaltiwanger’s(2006)estimateforaggregateU.S.investment(usingquadratic adjustmentcosts)was γ = 5 for1972-1988.GilchristandHimmelberg(1995)estimated γ = 12 for theirfullsampleofU.S.firmsduring1979-1989.Hayashi(1982)estimated γ = 24 foraggregate U.S.investment1953-1976,whileSummersestimated γ = 8 forU.S.investmentbetween1932and 1978. In an open economy setting, Neumeyer and Perri (2005) simulated Argentinian business cyclesbetween1983and2001withthreealternative(annualized)valuesofthecapitaladjustment costparameter: γ = 2, 6, 10 . With regard to the substantial differences among estimated values of the capital adjustment parameter,KhanandThomas(2008)haveemphasizedthat: Throughoutthehistoryoftheiruse,theprimarypurposeofadjustmentcostshasbeentoreduce thedistancebetweenmodel-generatedandactualeconomictimeseries.Becausetheylargely representimplicitcostsofforgoneoutput,wehavelittleabilitytodirectlymeasureadjustment frictions.Thus,whenweadoptthemtoenhancetheempiricalperformanceofourmodels,the resultingimprovementsare,insomesense,ameasureofourignorance….Thisraisesanobvious, 14Itisevenpossiblethatanobservedtwo-percentagepointgrowthrateaccelerationrepresentsasmallerrelative welfaregainthanaone-percentagepointacceleration.Forexample,arelativecapitalscarcityofabout0.8combined withaconvexityparameterof0.5correspondstoawelfaregainofabout2percentofthevalueoftheinitialcapital stock,givenanobservedtwo-percentagepointgrowthrateacceleration.Arelativecapitalscarcityofabout0.7with aconvexityparameterof1.0correspondstoawelfaregainofabout3.5percentoftheinitialcapitalstock,givenan observedone-percentagepointgrowthrateacceleration. 17 butsometimesforgotten,point.Adjustmentcostsderivedwithinagivenclassofmodelmaybe quiteinappropriateinasecond,distinctclassofmodel. Inthispaper’smodel,asadjustmentcostsbecomemoreconvextherelativewelfaregainfrom internationalfinancialintegrationfirstrisesasafunctionof γ ,asemphasizedinsections4and5. Forsufficientlyhighvaluesof γ therelativewelfaregainisstillpositive,butdeclining.Figures8 and9illustratethisforaninitialcapitalscarcityof k0 k = 0.8 .Therelativewelfaregainfrom ! internationalfinancialintegrationrisesrapidlyfromzerowhen γ = 0 toabout3.5percentofthe valueofthecapitalstockwhen γ = 4 .Forhighervaluesof γ therelativewelfaregaindeclines, fallingtoalittlelessthan2.5percentofthevalueofthecapitalstockwhen γ = 64 . Thenon-monotonicityresultisduetothesupplyanddemandfactorsdeterminingthepriceof capital.Internationalfinancialintegrationlowersthecostofcapital,therebyraisinginvestment demandandthepriceofcapital,asshowninFigure8.Buttheefficiencyofinvestment—thatis, theconvexitycoefficient γ --alsoplaysaroleinthedeterminationofthepriceofcapital.When investmentisverycostly,thepriceofcapitalishighbeforefinancialintegration(asshownin Figure8),butthegainfromintegrationissmall,asshowninFigure9,sincethehigherinvestment demandonlyincreases q byasmallamount. 6.2AnticipatedInternationalFinancialIntegration Internationalfinancialintegrationisgenerallyagradualprocess,asemphasizedbyHenry (2000b),BekaertandHarvey(2000),Bekaert,Harvey,andLundblad(2001,2003,2005),Quinn andToyoda(2008),Gozzi,Levine,andSchmukler(2008),andBalakrishnan,Vashishtha,and Verrecchia(2014).Bekaert,Harvey,andLundblad(2003)tracethefinancialintegrationprocess ofBrazilandKoreaoveratwelveyearperiod(1989-2001)toshowthedifficultyofchoosinga singleimportantdateatwhichintegrationtookplace. 18 Inadditiontothegradualnessoftheprocessofintegration,importantequitymarket liberalizationdateswereoftenannouncedinadvance.BekaertandHarvey(2000),andBekaert, Harvey,andLundblad(2005)constructtimeseriesofliberalizationdatesfordevelopingcountry equitymarketsthatemployindicatorvariablesforthe“firstsigns”ofliberalizationaswellasan “official”liberalizationindicator.Thefirstsignsindicatoristhefirstofoneofthefollowingthree: “alaunchingofacountryfund,anAmericanDepositaryReceipt(ADR)announcement,andan OfficialLiberalization.”(BHL2005,p.12).Threeexamplesoftheestablishmentofcountryfunds precedingofficialliberalizationareChile(1989countryfund,1992officialliberalization),India (1986countryfund,1992officialliberalization),andKorea(1984countryfund,1992official liberalization).15BekaertandHarvey(2000)findsignificantexcessreturnsinequitymarkets followingfirstsigns,priortoofficialliberalizations.Henry(2000b)reportsexcessreturnof3.3 percentintheeightmonthspriortoaninitialstockmarketliberalizationforasampleof12 emergingmarketeconomies. Inrelatedresearch,Gozzi,Levine,andSchmukler(2008)examinethebehaviorofTobin’sqfor asampleof9,000firmsfrom74countriesduringthetimeperiod1989-2000.Usingasetof annualdummyvariables,theyfindthat“qstartstorisetwoyearsbeforefirminternationalization, whichisconsistentwiththemarketanticipatingthebeneficialeffectsofinternationalization.” Theynotethat“theevolutionofqhasadistincthump-shapedpattern….risingbefore internationalizationandevenfurtherduringtheyearofinternationalization,andthen relinquishingthesegainsafterinternationalization,”asshowninFigure10(takenfromtheir paper). Figure11graphsthepriceofcapitalbeforeinternationalfinancialintegrationalongthe saddlepathfrom (k0 ,q0 ) to (k ,1) .Iftheintegrationoffinancialmarketsisannouncedattime0, aheadoftheactualtimeofintegration,theanticipationofafuturedeclineinthecostofcapital 15Aclosed-endcountryfund“isaninvestmentcompanythatinvestsinaportfolioofassetsinaforeigncountrybut issuesafixednumberofsharesdomestically.(BHL2003). 19 leadstoanimmediateupwardjumpinthepriceofcapitalfrom q0 to q0* and,correspondingly,to anincreaseinwealthfrom q0 k0 to q0*k0 .Thepricecapitalcontinuestoriseastheintegrationdate (withitslowercostofcapital)approaches.Withinternationalfinancialintegrationtheeconomy convergestoitsnewsaddlepathtrajectoryat (k fi ,q fi ) ,leadingtothesteady-statecapitalstock k . Comparedtotheinitialsaddlepathtrajectory,thespeedofconvergenceishigherduetothelower costofcapital.16 Correspondingtothebehaviorofthepriceofcapital,thegrowthrateacceleratesuponthe announcementoftheplannedfinancialintegration.AsshownintheAppendix,thegrowthrateof thecapitalstockisthefollowingfunctionofthepriceofcapital: 1 dk 1 ⎛ q − 1⎞ = k dt γ ⎜⎝ q ⎟⎠ (6.1) ThusinFigure11theaccelerationofthegrowthratepeaksatthemomentofthefinancial integrationandthendeclinesmonotonicallyastheeconomygrowstowardthesteady-statecapital stock k . 7Conclusion ThispaperhasanalyzedthewelfaregainattributabletocapitalaccumulationinaRamseygrowth model that is augmented by the inclusion of capital adjustment costs. The paper provides an analytical framework that addresses the concern of Gourinchas and Jeanne (2006) regarding the measurement of the welfare gain from transitional dynamics following international financial integration. With no adjustment costs, as in the standard Ramsey model, the gains from 16ThisanalysisfollowsthatinAbel(1982)andBrock(1988).Moreformally,theannouncementofafuturedatefor financialintegrationdoesnotchangethesteady-statecapitalstockorpriceofcapital( q = 1 ).Duringtheperiod followingtheannouncementandpriortointegration,thedynamicsaredrivenbyboththenegativeeigenvalue µ in (2.9)aswellasthecorrespondingpositiveeigenvalue.Followingintegrationthedynamicsaredrivenbythe negativeeigenvalue µ * in(2.22).Ano-arbitrageconditiondeterminesthatthepriceofcapitalatthetimeof integration( q fi )cannotjump.Giventheseconstraints,thesizeofthejumpinthepriceofcapitalatthe announcementtimecanbeshowntobesmallerthefartherintothefutureistheactualliberalizationdate. 20 international financial integration are very small. Gains from financial integration are tied to the existenceofcapitaladjustmentcosts. Thepapershowsthatthesizeofthewelfaregainisrelatedtotheincreaseinthevalueofthe installed capital stock at the time of international financial integration. Even if this increase in value cannot be explicitly measured, the welfare gain from integration can be inferred from the growthrateaccelerationthatfollowsanopeningofthecapitalaccount. Inarelatedcontext,Bekaertet.al.(2005)conjecturethat“[T]hegrowtheffectshoulddepend on two factors: how much additional investment the reforms generate (e.g., because the cost of capital goes down) and the efficiency of new investments.” They add that “Countries with a relatively high physical and human capital stock, relatively efficient financial markets, good legal institutions,andsoon,mightseehighlyefficientinvestmentandalargegrowthresponse.” If one takes γ (the convexity of the adjustment cost function) as a reduced-form measure of investment-specific productivity, then more efficient investment (lower values of γ ) will, as suggested by Bekaert et. al. 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JournalofPoliticalEconomy77,628-52. 24 Table 1 Welfare Gain from International Financial Integration ⎛ k − k0 ⎞ ΔW = q0* − q0 = γ µ * − µ ⎜ k ⎝ k ⎟⎠ ( 0 k k0 k0 k η=2 γ = 0.5 η =1 η = .5 ) η=2 0 γ =1 η =1 η = .5 η=2 γ =2 η =1 η = .5 1.1 0.91 .010 .012 .013 .011 .014 .016 .011 .015 .020 1.2 0.83 .020 .023 .026 .022 .028 .033 .022 .031 .039 1.3 0.77 .029 .035 .039 .033 .042 .049 .033 .046 .059 2 ⎞ γ⎛i γ is the capital adjustment convexity parameter: γφ (i,k) = ⎜ − δ ⎟ k 2⎝k ⎠ η is the intertemporal elasticity of substitution: − u ′(c) cu ′′(c) Figure1 TransitionDynamicsinFinancialAutarky dk =0 dt 25 26 1.08 1.02 1.00 1.8 1.06 1.04 1.2 0.8 .80 0.4 0.0 .90 1.00 .80 .90 1.00 .08 .06 .04 .02 .00 .80 .90 1.00 Inallthreeofthefiguresthehorizontalaxisistheratiooftheinitialcapitalstocktothesteady-statestock. isameasureoftheefficiencyofinvestment—itparameterizestheconvexityofthecapitaladjustment costfunction. InFigure4“ ”isthepriceofinstalledcapitalafterfinancialintegration. InFigure5 isthepercentagepointincreaseinthegrowthratefollowingfinancialintegration. InFigure6thewelfaregainfrominternationalfinancialintegrationisexpressedasafractionoftheinitial capitalstockandtheefficiencyofinvestment. 27 Figure7 TheGainfromInternationalFinancialIntegration: WelfareandGrowthRateAccelerationCurves 28 Figure8 ThePriceofInstalledCapital 1.40 1.30 1.20 1.10 0.4 0.5 0.7 1 1.1 2 1.6 4 2.2 8 2.8 16 3.5 32 4.2 ln(1+γ) 64 γ Note:Thegraphshowstherelativepriceofinstalledcapitalattimezero,bothinfinancial autarky( )andwithinternationalfinancialintegration( )foraninitialrelativecapital scarcityof .Thevaluesof convexityparameter(rangingfrom areplottedagainstvaluesoftheadjustmentcost to 29 ). .04 Figure9 TheRelativeWelfareGainfromInternationalFinancialIntegration .03 .02 .01 0.4 0.5 0.7 1 1.1 2 1.6 4 2.2 8 2.8 16 3.5 32 4.2 ln(1+γ) 64 γ Note:Thegraphshowstherelativewelfaregainfrominternationalfinancialintegration foraninitialrelativecapitalscarcityof .Thewelfaregainisplotted againstvaluesoftheadjustmentcostconvexityparameter(rangingfrom 30 to ). Figure10 DynamicAdjustmentofTobin’sq for3,351FirmsthatInternationalizedBetween1989and2000 Source:Gozzi,Levine,andSchmukler(2008) 31 Figure11 AnticipatedInternationalFinancialIntegration andthePriceofCapital 32 Appendix:DerivationofEquations 1.DerivationofEquation(2.13) Fromequation(2.5)(withtimesubscriptssuppressed): u ′(c) = q! ⎡⎣1− γφi (i,k) ⎤⎦ weobtainthefollowing: u ′′(c) dc di di dq! = − q!φii + ⎡⎣1− φi ⎤⎦ di dt dt dt dq! q!φii − σ c di = dt 1− φi dt (a) Theco-stateequation(2.6)isthefollowing: dq! = − u ′(c) Af ′(k) + ⎡⎣ ρ + δ + γφk (i,k) ⎤⎦ q! dt (b) Substituteout dq! in(a)and(b)toget(c): dt (c) 2 ⎫ ⎧⎪ ⎡⎣ ρ + δ + γφk (i,k) ⎤⎦ ⎫⎪ ⎧⎪ ⎡⎣1− φi (i,k) ⎤⎦ di ⎪ = − ⎨ Af ′(k) − ⎬⎨ ⎬ dt 1− φi (i,k) ⎪⎩ ⎪⎭ ⎪⎩ ⎡⎣1+ φi (i,k) ⎤⎦σ c + φii (i,k) ⎪⎭ Linearizing(c)aroundasteadystategives: di Af ′′(k) = (k − k ) dt σ + φii (i,k) c Thisgivesthefirstlinearizationusedinequation(2.8). Thesecondlinearizationin(2.8)followsdirectlyfromthecapitalaccumulationconstraint(2.3)in conjunctionwiththeeconomy’sresourceconstraint(2.2). 2.Derivationoftheconsumptionequation(2.32): dd dk dq = qt + (kt − k0 ) (limited commitment constraint) dt dt dt 33 dd = ct + it + rdt − Af (kt ) dt (current account) { } qt ⎡⎣ it − δ kt − γφ (it ,kt ) ⎤⎦ + kt − Af ′(kt ) + ⎡⎣ r + δ + γφk (it ,kt ) ⎤⎦ qt − k0 dq dt = ct + it + rqt (kt − k0 ) − Af (kt ) * Cancellingoutcommontermsanddenotingopeneconomyconsumptionby ct leaves: ct* = Af (kt ) − Af ′(kt ) − k0 dq + rqt k0 dt ⎛ 1 dq ⎞ ct* = w(kt ) + qt k0 ⎜ r − qt dt ⎟⎠ ⎝ c * = w(k ) + rk0 3.Derivationoftherelativepriceofcapital(q): From(2.5)and(2.16): 1 dk qt − 1 = (*) kt dt γ qt Aroundasteady-stateequilibrium,thelinearizeddynamicsaregivenby: * kt = k + (k0 − k )e µ t dkt = µ * (k0 − k )e µt = µ * (kt − k ) dt ⎛k −k⎞ 1 dkt = µ* ⎜ t (**) kt dt ⎝ kt ⎟⎠ Substitutingoutthegrowthrateofcapitalaccumulationin(*)and(**)gives 1 qt = ⎛ kt − k ⎞ 1− γµ ⎜ ⎝ k ⎟⎠ t 34 ⎛k −k⎞ qt ≈ 1+ γµ ⎜ t ⎝ kt ⎟⎠ 4.Derivationofthenumericalexample: Let f (k) = Ak α , f ′(k) = α Ak α −1 = r + δ aroundasteadystate, f ′′(k) = α (α − 1) Ak α −2 .Then kf ′′(k) = α (α − 1) Ak α −2 = (α − 1)(r + δ ) . γ (i − δ k)2 2 k γ φi (i, k) = (i − δ k) k γ φii (i, k) = k Let φ (i, k) = Atasteadystateinaclosedeconomythefollowingholds: Then c f (k) = −δ k k α Ak α −1 = −δ α ρ +δ = −δ α ρ + (1− α )δ = α f ′′(k) kf ′′(k) (α −1)( ρ + δ ) = = σ σ ασ + φii k + kφii +γ c c ρ + (1 − α )δ Thetransitionspeedinfinancialautarkywiththesespecificfunctionalformsfortheutility, installation,andproductionfunctionsis: 2 ⎛ ρ⎞ ⎛ ρ⎞ (1− α )( ρ + δ ) µ=⎜ ⎟− ⎜ ⎟ + ασ ⎝ 2⎠ ⎝ 2⎠ +γ ρ + (1− α )δ Thecorrespondingconvergencespeedinafinanciallyopeneconomyis: 2 ⎛ r⎞ ⎛ r ⎞ (1− α )(r + δ ) µ =⎜ ⎟− ⎜ ⎟ + where r = ρ γ ⎝ 2⎠ ⎝ 2⎠ * 35