Terms of Trade Shocks and Heterogeneous International Portfolio Positions

Transcription

1 Terms of Trade Shocks and Heerogeneous Inernaional Porfolio Posiions Jonahan J Adams and Philip Barre PRELIMINARY DRAFT!!! This version: February 15, 2018 Link o Mos Curren Version Absrac How do erms of rade shocks affec open economies? We use a panel of exogenous erms of rade shocks for 93 counries o esimae he dynamic effecs on macroeconomic variables. We find ha erms of rade shocks resemble wealh shocks: a erms of rade improvemen increases consumpion and invesmen by more han oupu and decreases ne expors, conrary o prior evidence and sandard heory. To explain his oucome, we also show ha erms of rade improvemens increase counries ne foreign asse posiion, due o valuaion effecs of nominal ne asses. To make sense of hese resuls, we augmen a sandard business cycle model wih realisic inernaional porfolio choice. We esimae he model for a large sample of counries, and show ha i can replicae our empirical findings: erms of rade improvemens look like wealh shocks, and heir imporance for business cycles is heerogeneous, depending on he counry s inernaional porfolio posiion. JEL-Codes: F30, F41 Keywords: Terms of rade, counry porfolios, inernaional business cycles, small open economies, home bias, gross asse posiions, exchange raes We are graeful for helpful commens from our colleagues. The views expressed in his paper are hose of he auhor(s) and do no necessarily represen he views of he IMF, is Execuive Board, or IMF managemen. Universiy of Florida. Websie: adamsjonahan@ufl.edu Inernaional Moneary Fund. Websie: pbarre@imf.org 1

2 1 Inroducion How do erms of rade shocks affec macroeconomies? In radiional business cycle models (e.g. Mendoza 1995) erms of rade improvemens ac like produciviy improvemens, where income effecs lead households o consume and inves more, bu wih subsiuion effecs such ha households work more and oupu increases by more han consumpion. We challenge his convenional wisdom. Insead, we argue ha erms of rade shocks resemble wealh shocks more han produciviy shocks, and demonsrae a channel hrough which his occurs: nominal exchange rae exposure in counries inernaional asse posiions. Firs, we examine he effecs of counry-specific erms of rade shocks on a variey of macroeconomic aggregaes, and find resuls ha resemble wealh effecs. The shocks we consider are unexpeced changes o a panel of counry-specific commodiy erms of rade indices consruced by Be and Peluffo (2017). The radiional empirical mehodology is o consider shocks o he measured erms of rade, bu his may include may include endogenous facors on boh he impor and expor side. Insead, world commodiy prices are mosly homogenous and more likely o be exogenous o counries wih small marke shares, as argued by Chen and Rogoff (2003). We run a series of dynamic panel regressions and find ha erms of rade shocks look like a wealh shock, increasing consumpion, invesmen, and impors by more han oupu 1. This sraegy is relaed o he approaches of Fernandez, Gonzalez, and Rodriguez (2018) and Shousha (2015), who consruc counry-specific indices of commodiy expor prices and analyze heir effecs on business cycles. The Be-Peluffo indices improve upon hese approaches in hree ways: he Be-Peluffo panel is longer, sreching from 1970 o 2004; he panel is wider, covering 96 counries; and he index capures he enire erms of rade, insead of only expor prices. Second, we documen a source for large wealh effecs from erms of rade shocks: nominal exchange rae exposure in counries inernaional asse posiion. Mos counries choose porfolios of nominal asses and liabiliies ha are long in heir domesic currency and shor in foreign currency. In he Benerix, Lane, and Shambaugh (2015) panel of inernaional asse posiions, 1 Oher papers have also discovered his volaile consumpion response, including Drechsel and Tenreyro (2017) in Argeninian daa, and Fernandez, Gonzalez, and Rodriguez (2018) in an esimaed small open economy model, 2

3 107 of 116 counries have his ype of porfolio posiion, such ha heir ne asse posiions gains value when heir exchange rae appreciaes 2. When we examine he effecs of erms of rade shocks on inernaional porfolio posiions, we find ha a erms of rade improvemen increases a counry s ne asse posiion, and his is driven almos enirely by appreciaion of he counry s ne foreign posiion in nominal, raher han real, asses and liabiliies. Third, we consider a small open economy model wih many poenial sources of aggregae flucuaions. We augmen his sandard model wih a meaningful porfolio decision and show ha counries wih larger exchange rae exposure in heir inernaional porfolio will exhibi higher business cycle volailiy. In paricular, we allow for rend shocks o produciviy as in Aguiar and Gopinah (2007), who argue ha hese shocks are imporan source of variaion for developing counries. This is an imporan inclusion because we demonsrae ha erms of rade shocks can cause consumpion o be more volaile han oupu, which could also be explained by rend shocks. We esimae he model for many small open economies, and show ha in counries where porfolios are more exposed o exchange raes, consumpion is more sensiive o erms of rade shocks. Given he variey of exchange rae exposures observed in inernaional porfolio posiions, our findings sugges ha we should consider he imporance of erms of rade shocks for business cycles o be heerogeneous across counries. This paper joins a large lieraure assessing he imporance of erms of rade shocks for macroeconomic flucuaions. There is no general consensus. Tradiional business cycle models such as Mendoza (1995) and Kose (2002) find ha erms of rade shocks represen a large source of flucuaions. Bu less srucural analysis, ofen using SVARs as in Broda (2004) and Schmi- Grohe and Uribe (2017), esimae he conribuion of erms of rade shocks is small 3. Our model esimaion uses Bayesian mehods like he SVAR lieraure, we find ha he conribuion of erms of rade shocks o macroeocnomic volailiy is small. However, our analysis differs in ha 2 This panel covers , and Adams and Barre (2017) repor ha he average exchange rae exposure is 40% of GDP, such ha a 1% appreciaion in a counry s nominal exchange rae would increase is ne asse posiion by 0.4%, ceeris paribus. 3 Alhough his generalizaion is no perfec: Fernandez, Schmi-Groh, and Uribe (2017) show ha a SVAR wih disaggregaed world prices will assign more imporance o erms of rade shocks, while Zeev, Pappa, and Vicondoa (2017) argue ha accouning for news shocks o erms of rade increases heir esimaed effec. 3

4 we esimae he model separaely for many counries, and find ha he imporance of erms of rade shocks is heerogeneous and depends on he counry s inernaional porfolio posiion. The remainder of he paper is organized as follows. Secion 2 esimaes macroeconomic responses o he commodiy erms of rade shocks. Secion 3 presens he small open economy model wih gross asse posiions. Secion 4 presens he model resuls and esimaes for many counries. Secion 5 characerizes he counries porfolio selecion problem and compares he soluion o he daa. Secion 6 concludes. 2 Empirical Analysis How do erms of rade shocks affec economies? In his secion, we address his quesion by esimaing he dynamic effecs of plausibly exogenous erms of rade shocks on various macroeconomic variables. The source of our plausibly exogenous erms of rade shocks is he daase compiled by Be and Peluffo (2017). The inpus o his index are he prices, relaive o manufacuring uni values, of six major commodiy groups (food, fuels, raw maerials, meals, gold, and beverages). The erms of rade index is hen he raio of he expor- o impor-share weighed geomeric averages of hese prices: T OT i = c (P c/muv i ) Xc i c (P c/muv i ) M c i where P c is he world price of commodiy c a ime, MUV i he manufacuring uni value index in counry i a ime, and X c i and M c i are he average expor and impor shares of commodiy c in counry i. The goods covered by his index are imporan, making up some XX% of global rade in commodiies. And producion of he underlying commodiies is widely dispersed; no counry is responsible for more han YY% of any one of he six caegories. So from he perspecive of any individual counry, his index will capure variaion in he erms of rade which is economically imporan, and exogenous o domesic condiions. To isolae he shocks o his index, we esimae auoregressive processes for T OT i for each i, wih lag lengh deermined by he Akiake Informaion Crierion. The esimaed residuals are 4

5 hen our erms-of-rade shock series, Z i. Furher deails of he shock esimaion can be found in Appendix A. Ten real macroeconomic variables are considered: oupu, consumpion, hours, invesmen, governmen spending, expors, impors, real exchange rae, ne foreign asse posiion, and he measured erms of rade. In mos cases, he daa are from naional accouns, as colleced and sandardized by Feensra, Inklaar, and Timmer (2015). The real exchange rae is calculaed relaive o he Unied Saes, and he raio of consumpion prices is used o normalize he nominal exchange rae. The ne foreign asse posiion is relaive o GDP, as calculaed by Benerix, Lane, and Shambaugh (2015). All daa are annual. To be included in he panel, counries mus have consecuive observaions for all of hese variables, concurren o he erms of rade shocks; 93 counries are included 4. To evaluae he dynamic effecs of a erms of rade shock on a macroeconomic quaniy X, we regress he log difference of X on lags of iself, as well as several lags of he log difference of shock. We deviae from he ypical approach of esimaing a panel VAR for wo reasons. Firs, wih a plausibly exogenous shock, we can consisenly esimae he impulse response funcion wihou needing o make idenifying assumpions abou he srucure of he marices in a VAR. Secondly, our esimaion is more parsimonious han a VAR, which esimaes many cross-erms in he coefficien marices, allowing spurious esimaes o affec calculaed dynamic effecs. Neverheless, we esimae a panel VAR in Appendix B and find similar resuls. For a macroeconomic quaniy X,i in counry i, we run a regression of he following form: N M X,i = α + β j X j,i + γ j Z,i + δc i + ε,i (1) j=1 j=0 where represens aking he year-over-year difference, Z i, is he erms of rade shock, ε is an error erm, C i is a vecor of counry-specific conrols, and α is he consan. For N 1 and M 1, X is specified as an ARMA(N, M) in he erms of rade shock. Firs differences are used o remove he linear rend componen, which is capured by α (he common componen) and δc i (poenial counry-specific componens). We avoid more sophisicaed derending or filering 4 LIST THEM IN AN APPENDIX 5

6 for wo reasons: linear derending is simple, eliminaing any poenial for a researcher o selec a paricular filer o achieve desired resuls; and he linearly derended variables map direcly ino he model in Secion 3. The esimae of ineres is he Toal Dynamic Effec (TDE). The TDE of he erms of rade shock on he quaniy X is given by T DE X = M j=0 γ j 1 N j=1 β j (2) In cos passhrough sudies, his saisic is he oal passhrough of a cos shock. In his macroeconomic conex, he saisic is he oal permanen effec of a erms of rade shock. Table 2 repors TDEs for several macroeconomic quaniies, and regression specificaions. The firs line repors he baseline esimaes, wih N = 3 and M = 3 and no counry conrols. The full regression resuls for his specificaion are repored in Table 1, while full resuls for oher specificaions are repored in Appendix D. Table 2 also repors esimaes when counry conrols are included, ime conrols o accoun for global macroeconomic changes, and a specificaion wih N = 0 which is used elsewhere in he lieraure. To calculae he sandard errors, we boosrap by randomly sampling counries wih replacemen 100 imes. The impulse response of a quaniy X o a shock Z is calculaed by equaion 3. The prediced response in period + k is given by ˆX +k = α + γ k Z + min(n,k) j=1 β j ˆX +k j (3) The esimaed impulse response funcions are repored in Figure 1. The 95% confidence inervals are calculaed by boosrapping he esimaes ˆX +k for each k 0, again by sampling counries wih replacemen 100 imes. Terms of rade shocks resemble wealh shocks. For all specificaions, a erms of rade improvemen increases consumpion and invesmen. Consumpion increases by more han oupu, which is inconsisen wih radiional models of erms of rade shocks wihou gross asse posiions. In a sandard small open economy RBC model erms of rade improvemens ac like produciviy improvemens, increasing hours and oupu by more han consumpion, as he subsiuion effec 6

7 from higher real wages ouweighs he income effec. Oupu and hours are esimaed o increase as well, bu heir TDEs are no saisically significan. To achieve higher consumpion and invesmen wihou more oupu, counries impor more and expor less in response o he erms of rade improvemen. If consumers do no produce or expor more afer a erms of rade improvemen, how do hey afford heir increased consumpion and invesmen? Their nominal and real exchange raes boh fall (i.e. heir currency and consumpion bundles appreciae), which appreciaes he counry s ne foreign asse posiion. To documen his channel, we run regression (1) for hree addiional quaniies: he ne foreign asse posiion (NFA); he ne foreign deb asse posiion, which is foreign deb asses less deb liabiliies (NFDA); and he ne foreign equiy asse posiion, which is foreign non-deb asses less non-deb liabiliies (NFEA). These series are calculaed by Benerix, Lane, and Shambaugh (2015) and are scaled relaive o GDP. Table 3 repors heir oal dynamic effecs. Afer a erms of rade improvemen, he ne foreign asse posiion appreciaes. This appreciaion allows counries o consume and inves more despie small changes o producion and expors. In paricular i is ne foreign deb asses ha drive he appreciaion, versus non-deb asses which have lile response. Deb asses are unique because hey are nominal conracs which are exposed o exchange rae risk. Mos counries NFDA posiions are biased owards he domesic currency so ha hey increase afer an exchange rae appreciaion (Adams and Barre, 2017). Therefore, when a erms of rade improvemen causes he domesic currency o appreciae, he inernaional porfolio posiion does he same, increasing he counry s wealh. These resuls sand in conras o much of he lieraure, which ypically find ha oupu rises and consumpion falls in response o a erms of rade improvemen (Schmi-Grohe and Uribe, 2017). We also find evidence conrary o he sandard Harberger-Laursen-Mezler effec, in which erms of rade improvemens increase ne expors. Counries do no appear o use heir inernaional porfolio exposure o nominal exchange raes o hedge agains erms of rade shocks. Given ha erms of rades improvemens cause 7

8 Oupu Consumpion Hours Invesmen Gov. Spending Expors Impors Real Ex. Rae Nom. Ex. Rae Terms of Trade L. X (14.50) (4.02) (5.22) (-3.46) (2.60) (1.57) (5.49) (5.80) (40.75) (-3.88) L2. X (-0.11) (1.33) (6.76) (-3.72) (2.32) (1.26) (-2.04) (-1.71) (-1.99) (-7.86) L3. X (5.93) (2.71) (-0.50) (0.57) (1.22) (2.68) (1.62) (-0.91) (2.62) (0.40) ToT Shock (3.25) (0.96) (-0.32) (0.50) (0.94) (3.37) (2.12) (-0.85) (0.60) (21.38) L.ToT Shock (1.59) (3.62) (1.29) (4.62) (3.71) (-0.13) (7.81) (-3.16) (-1.11) (12.01) L2.ToT Shock (2.87) (4.07) (1.06) (4.87) (3.65) (-0.87) (6.71) (-1.03) (1.12) (9.08) L3.ToT Shock (2.17) (2.09) (-0.11) (3.93) (1.09) (0.17) (3.42) (-3.07) (-0.72) (4.03) Consan (9.67) (10.10) (2.72) (4.60) (7.91) (11.47) (9.93) (0.57) (5.81) (-1.25) Observaions saisics in parenheses p <.1, p <.05, p <.01 Table 1: Effecs of Terms of Trade Shocks losses o porfolios wih NFDA biased owards he domesic currency, we expec ha counries which are more exposed o erms of rade shocks would choose deb porfolios wih less home bias. On he conrary, he relaionship beween home bias and erms of rade exposure is weak or even posiively correlaed. Figure 2 plos his correlaion for several quaniies, agains he counry s median NFDA home bias. Firs, median counry openness impors plus expors relaive o GDP has nearly zero correlaion wih home bias, bu higher rade dependence increases an economy s exposure o erms of rade shocks ceeris paribus. Nex, counries wih a higher sandard deviaion of nominal exchange rae growh end o have more home bias, despie he associaed increase in porfolio exchange rae risk. Finally, counries wih greaer home bias also have higher erms of rade volailiy, which is ploed for boh he measured erms of rade as well as he consruced commodiy erms of rade. These correlaions are uncondiional, omiing oher variables ha mus be accouned for wih a model, so in Secion 5 we calculae he opimal deb porfolios implied by our model, and find furher evidence supporing his puzzle. 8

9 Figure 1: Esimaed Impulse Responses o a Terms of Trade Shock 3 A Small Open Economy Model wih Gross Asse Posiions 3.1 Households The represenaive household in he small open economy maximizes E 0 =0 β U(C, L ) (4) where C is domesic consumpion in period, and L is labor hours in period. The uiliy funcion is King and Rebelo (1999) s Consan Frisch uiliy funcion, U(C, L ) = 1 ( ( C 1 γ 1 (1 γ)χ ɛ ) 1 γ 1 + ɛ L ɛ+1 γ ) ɛ 1 (5) 9

10 Oupu Consumpion Hours Invesmen Gov. Spending Expors Impors Real Ex. Rae Nom. Ex. Rae Terms of Trade No Conrols (0.74) (2.41) (1.03) (3.59) (2.02) (-0.20) (6.02) (-2.04) (-0.27) (5.94) Counry Conrols (0.94) (2.55) (0.70) (3.55) (2.07) (0.14) (6.14) (-2.11) (-0.39) (5.98) Year Conrols (0.74) (2.41) (1.01) (3.54) (2.00) (-0.20) (5.96) (-1.99) (-0.27) (5.86) MA only (1.06) (2.58) (0.65) (3.86) (2.18) (-0.02) (6.79) (-2.00) (-2.23) (5.29) Observaions Table 2: Toal Dynamic Effecs of Terms of Trade Shocks NFA NFDA NFEA Toal Dynamic Effec (2.41) (2.52) (0.29) Observaions saisics in parenheses p <.1, p <.05, p <.01 Table 3: Toal Dynamic Effecs: Financial Exposure where ɛ is he Frisch labor supply elasiciy and 1 γ is he ineremporal elasiciy of subsiuion along he balanced growh pah. 5 The household earns wage income W i, per hour of labor, denominaed in domesic currency 6. The price level is P C,. The household has access o hree asse markes. I can hold nonconingen domesic bonds B +1 a price 1 R +1, which pays one uni of domesic currency in period + 1, and i can hold non-coningen foreign bonds B+1 F a price 1, which pays one R+1 F uni of a global foreign currency. Boh of hese bonds are in zero ne supply. The household can also hold domesic capial K. Capial is governed by he law of moion K +1 = I (1 ϕ 2 ( I I 1 1) 2 )τ I, δk (6) where he ϕ 2 ( I I 1 1) 2 is an invesmen adjusmen cos, following he Chrisiano, Eichenbaum, and Evans (2005) formulaion, and τ I, is a sochasic invesmen produciviy shock. Households choose a uilizaion rae U for heir capial, a cos κu ω in unis of he generic oupu good. Capial services U K reurn he renal rae R K. 5 Traband and Uhlig (2011) prove ha his is he unique uiliy funcion which feaures a consan Frisch elasiciy, consan ineremporal elasiciy of subsiuion. 6 Currency here serves he role only of a uni of accoun, no a means of exchange nor a sore of value. Given ha we are mos ineresed in wealh effecs induced by relaive flucuaions in compeing unis of accoun, his is an appropriae simplificaion for our purposes. 10

11 Figure 2: Counries Domesic Currency Home Bias and Relaed Risks The household can spend is income on consumpion C, invesmen in capial I, and financial asses for he nex period. Therefore he household s period budge consrain (denominaed in domesic currency) is W + R K U K + B + E B F = P C + P I + P κu ω + B +1 R +1 + E B F +1 R F +1 (7) where E is he nominal exchange rae beween he domesic and global foreign currencies, and P is he price level for boh consumpion and invesmen. Households choose consumpion, invesmen, labor, uilizaion, and asses o maximize heir uiliy (4) subjec o consrains (6) and (7). Opimaliy implies ha heir labor supply is deermined by seing he real wage equal o he marginal rae of subsiuion beween consumpion and labor: 1 ɛ W γχc L = τ L, P 1 (1 γ)χ ɛ 11 1+ɛ L ɛ+1 ɛ (8)

12 where τ L, is a sochasic labor wedge, which represens fricions in he labor marke. The choice of capial uilizaion requires ha he marginal real renal income be equal o he marginal cos: R K, P = κωu ω 1 (9) Households have hree asses, which hey price wih hree Euler equaions. The Euler equaion for domesic nominal bonds is 1 = R +1 E [ P Λ +1 P +1 ] (10) where Λ +1 is he household s sochasic discoun facor in period + 1. The Euler equaion for foreign nominal bonds is [ ] 1 = R+1E F E +1 P Λ +1 E P +1 (11) and he Euler equaion for capial is [ ( )] RK,+1 Q = E Λ +1 + Q +1 (1 δ) P +1 (12) where Q is Tobin s Q, he cos of a marginal uni of capial in erms of oupu. Q is deermined by he firs order condiion for invesmen, which is a dynamic equaion: ( 1 = Q τ I, 1 ϕ 2 ( I 1) 2 ϕ( I ) [ ) 2 + E Λ +1 Q +1 τ I,+1 ϕ( I ] +1 ) 3 I 1 I 1 I (13) Finally, he uiliy funcion implies ha he sochasic discoun facor is given by ( ) Λ +1 = β C γ 1 (1 γ)χ 1+ɛ ɛ L ɛ+1 γ ɛ +1 C γ ( ) γ τ EE, (14) +1 1 (1 γ)χ ɛ ɛ 1+ɛ L ɛ+1 We assume global demand for asses is characerized by wo equaions. The ineres rae on inernaional bonds is fixed a R F = β 1, and uncovered ineres rae pariy holds: R F E [ E +1 E ] = R (15) 3.2 Firms There are four ypes of firms in each counry: inermediae goods producers, inermediae assemblers, imporers and final reailers. 12

13 The inermediae goods producers produce a variey of inpus, indexed by i I. These producers are monopolisic compeiors, and use a Cobb-Douglas producion funcion o combine labor L i, and capial services K i, ino oupu Y i, by Y i, = A Kα i, L 1 α i, (16) where A is he sochasic oal facor produciviy which is shared by all primary producers. Primary producers hire labor a wage rae W and hire capial services a renal rae R K. Primary producers are monopolisic, so hey choose heir oupu price P i,. However, hey face Calvo-syle price sickiness, and can only updae heir price wih probabiliy λ. The inermediae assemblers aggregae inpus ino a homogeneous domesic oupu good Y D which will be used for consumpion and invesmen, by a CES producion funcion: ( Y D = i I Y η 1 η i, ) η η 1 (17) where η is he elasiciy of subsiuion. These firms are perfecly compeiive, purchasing variey i a price P i, and selling oupu a price P D. Imporers aggregae homogeneous oupu goods X j, from oher counries, which are indexed by j J. Imporing firms produce a homogeneous impored oupu good Y M by a CES producion funcion: ( Y M = j J µ j, X ζ 1 ζ j, ) ζ ζ 1 where ζ is he elasiciy of subsiuion, and µ j, is a sochasic demand shifer ha saisfies j J µ j, = 1. Imporers are perfecly compeiive, purchasing inpu j a price Pj, M and selling oupu a price P M. (18) Lasly, final reailers combine assembled domesic goods Y D and aggregaed impored goods Y M ino he final oupu good Y by a CES producion funcion: ( Y = θ 1 ξ (Y D ) ξ 1 ξ + (1 θ) 1 ξ (Y M ) ) ξ 1 ξ ξ 1 ξ (19) where ξ is he elasiciy of subsiuion and he share parameer θ capures he degree of home bias. Final reailers are perfecly compeiive, and sell oupu a he aggregae price level P. 13

14 Oupu goods are used for consumpion C, invesmen I, governmen spending G, and expors X, implying he marke clearing condiion 3.3 Prices Y = C + I + G + X (20) Profi maximizaion in he reail secor implies ha demand for he domesic aggregae Y D impored aggregae Y M are given by and (θ Y Y D ) 1 ξ = P D P ((1 θ) Y Y M ) 1 P M ξ = (21) P Profi maximizaion in he impor secor implies ha demand for he impored bundle from counry j is given by The impored good Y M Y M (µ j, ) 1 ζ X j, = P j, P M is he same across counries so he law of one price holds: (22) P M = E P M W, (23) where P M W, is he world price of he impored good, expressed in he global currency. X is P M j, The expor demand funcion holds in all counries as well, so he aggregae demand for expors X = µ j J Y M j, ( E P M j, E j, P ) ζ is he price of impors in counry j s currency. E is he domesic counry s exchange rae wih he global currency, so E /E j, is he exchange rae wih counry j. The law of one price (23) implies ha his expor demand equaion can be wrien as X = µ ( E PW, M ) ζ Yj, M P j J Then, by defining world rade as YW, M j J Y j, M and he erms of rade as S P E P, he W, M demand for expors is given by µ Y M W, X = S ζ (24) 14

15 Profi maximizaion in he inermediae assembly secor implies ha demand for he inermediae good of ype i is given by ( Y D ) 1 η Y i, = P D P i, (25) Inermediae goods firms face a dynamic problem, because hey can only updae heir prices sochasically. Appendix C characerizes his problem and shows ha i leads o a sandard linearized New Keynesian Philips Curve: where Π D P D P D 1 log(π D ) = β log(π D +1) Θ log( η(1 α)p DY D ) (26) (η + 1)W L is inflaion of he domesic aggregae and Θ > 0. This equaion operaes as he labor demand equaion. The capial services demand can eiher be described by a similar dynamic equaion, or equivalenly by seing he marginal rae of ransformaion o he relaive inpu price: The aggregae price level P is deermined by a cash consrain: αl (1 α) K = RK W (27) P Y = νm (28) where M is he exogenous sochasic money supply, and ν is he money velociy. 3.4 Exogenous Shocks There are four exogenous shocks which we assume follow a saionary AR(1) process in logs. Money: log M +1 = ρ M log M + ε M,+1 (29) expor demand: log µ +1 = ρ µ log µ + ε µ,+1 (30) he labor wedge: log τ L,+1 = ρ L log τ L, + ε L,+1 (31) 15

16 and invesmen produciviy: log τ I,+1 = ρ I log τ I, + ε I,+1 (32) We also assume ha log produciviy log A follows an AR(1) process wih drif, as in Aguiar and Gopinah (2007): log A +1 = ρ A log A + (1 α) log Γ +1 + ε A,+1 (33) where Γ +1 is he rend componen. The inclusion of labor share 1 α as a coefficien on he rend implies ha variables wih a balanced growh rae can be saionarized by dividing by Γ. This rend is iself sochasic, following he process Γ +1 = e z+1 Γ where z is he average growh rae. 3.5 Equilibrium Definiion z +1 = ρ z z + (1 ρ z ) z + ε z,+1 (34) A compeiive equilibrium in his economy consiss of sequences of 28 quaniies: asses K, B, B F ; prices, W, R K,, R, P, P D, P M, E ; allocaions, Y, Y D, Y M, C, I, U, L, X ; and oher quaniies, Q, Λ, S, Π D ; and realizaions of he exogenous sochasic saes A, z, M, µ, τ L,, τ I,, such ha: 1. Households maximize heir ineremporal uiliy subjec o consrains, which implies ha 10 equaions mus be saisfied: he capial law of moion (6); he budge consrain (7); 3 Euler equaions: (10), (11), and (12); foreign demand for domesic asses (uncovered ineres rae pariy) (15); he cash consrain (28); and 3 firs order condiions for labor (8), uilizaion (9), and invesmen (13). 2. Firms maximize profis, saisfying 9 equaions: inpu demand by he inermediae producers (26) and (27); domesic and foreign inpu aggregaion (19) and wo demand funcions in 16

17 (21); global expor demand (24); he law of one price (23); he resource consrain (20), and o a firs order approximaion oupu aggregaes by Y D A (U K ) α L 1 α (35) 3. Three variable definiions mus be saisfied: he definiions of he erms of rade, domesic producer inflaion, and sochasic discoun facor (14). 4. The exogenous sochasic saes mus saisfy he laws of moion (29)-(34). 4 Model Esimaion and Resuls 4.1 Soluions Mehods and Equilibrium Selecion To solve he model, we linearize around a deerminisic seady sae, and calculae equilibrium using Dynare (Adjemian, Basani, Juillard, Mihoubi, Perendia, Rao, and Villemo, 2011). Linearized small open economy models are no generally sable (Schmi-Grohe and Uribe, 2003), so we sabilize he model by adding an ad hoc Endogenous Discoun Facor (EDF). Specifically, we assume ha insead of β, he household s discoun facor is βe ϑ( C C ), where C is seady sae consumpion and ϑ > 0. Moreover, we assume ha households do no inernalize he effec of C on he EDF, or equivalenly ha aggregae consumpion eners he EDF insead of household consumpion. Finally, we mus selec he seady sae asse posiion, and we choose zero NFA. Linear models wih porfolio problems also suffer from mulipliciy. In he linear approximaion, households are risk neural, and herefore indifferen beween all poenial asse allocaions for a given level of wealh. To resolve his indeerminacy, we assume ha counries choose an allocaion of bonds ha maches heir empirical home bias (Figure 2). In Secion 5 we compare his equilibrium wih empirical porfolios o equilibrium where households choose he model s opimal porfolio, using a higher order soluion mehod. 4.2 Calibraion and Esimaion TO BE COMPLETED Here deail he calibraion arges/choices, and Bayesian priors for esimaed parameers. 17

18 4.3 Response o a Terms of Trade Shock Figure 3 plos he model response o a posiive ε µ, shock, which increases foreign demand for domesic goods µ and improves he erms of rade. The impulse responses are ploed for wo differen calibraions. In he firs calibraion, he counry has no home bias in bonds. In he second calibraion, he counry has home bias worh 100% of GDP, (i.e. a 1% domesic currency appreciaion would appreciae he counry s porfolio by 1% of GDP). All oher parameers are se o he esimaes for Mexico. The ploed values are log deviaions (excep for NFA) so he impulse responses can be inerpreed as elasiciies. Figure 3: Equilibrium Impulse Responses o a Terms of Trade Shock Oupu rises afer a erms of rade improvemen. Labor and capial uilizaion boh fall, so his increase is final oupu is driven by increasing impors o use in producion. The counry akes advanage of is improved erms of rade by exporing more goods, even reducing invesmen 18

19 Percen of Variance Absolue Variance Mean 3.46% Median 2.83% Minimum 0.02% Maximum % Sandard Deviaion 2.69% Observaions Table 4: Conribuion of Terms of Trade Shocks o Log Consumpion Variance and consumpion emporarily o do so. The resuling rade surplus leads o an accumulaion of ne foreign asses. The erms of rade slowly rever o he seady sae, households begin o enjoy heir increased wealh, increasing consumpion, invesmen, and leisure. If a counry has a home-biased bond porfolio, i undergoes a more exreme response o he shock. The erms of rade improvemen reduces he real exchange rae, because he domesic consumpion bundle becomes more expensive relaive o he foreign consumpion bundle. The price level moves bu no by enough o offse he real exchange rae, so he nominal exchange rae decreases (i.e. he currency appreciaes) as well. If he counry has home-biased porfolio bond porfolio, he exchange rae movemen appreciaes he counry s ne foreign asse posiion. This is increases household wealh, so hey choose more consumpion. Moreover, his consumpion increase is long-lasing, and would be permanen if no for he endogenous discoun facor. Households also choose o work less, which slighly decreases he oupu response. 4.4 Imporance of Terms of Trade Shocks Afer esimaing he model for each counry, we decompose he variance of consumpion ino he conribuion from each fundamenal shock. The firs column of Table 4 repors summary saisics for he percen of consumpion variance ha is driven by erms of rade shocks across counries. The second column repors summary saisics for he oal consumpion variance ha is driven by erms of rade shocks. We can esimae he model for 70 counries, which is less han he 93 counries sudied in Secion 2. For mos counries, erms of rade shocks are a small componen of consumpion variance. Much more imporan are labor demand shocks and rend produciviy shocks. Bu here is con- 19

20 siderable heerogeneiy across counries. While he average counry sees erms of rade deermine only 2-3% of heir consumpion variance, ohers are much larger, such as Zimbabwe (8.9%), Nepal (11.1%), and Nigeria (12.5%). Wha deermines his heerogeneiy? Counries for whom erms of rade shocks are more imporan o he business cycle end o have porfolios ha are more home biased in heir currency exposure. Figure 3 illuminaes he channel: when counries receive erms of rade improvemens, heir consumpion rises by more when hey are more home biased. Figure 4 plos his correlaion. Among counries wih low home bias, he correlaion is weak. Bu nearly all counries wih a home bias above 75% of GDP feaure a relaively large percenage of heir consumpion variance ha is driven by erms of rade shocks. Figure 4: Porfolio Home Bias and Percen of Variance due o ToT Shocks I could be ha counries who are oherwise more exposed o erms of rade shocks choose a more home biased porfolio. So we conrol for he oher counry-specific parameers and sill find ha counries ha are more home biased have greaer conribuions of erms of rade shocks o heir consumpion variance. Figure 5 shows his relaionship, ploing he condiional correlaion 20

21 beween porfolio home bias and he absolue log consumpion variance ha is due o erms of rade shocks. Why are counries wih a greaer consumpion exposure o erms of rade shocks choosing financial porfolios ha reinforce his exposure? We explore his quesion in he nex secion. Figure 5: Porfolio Home Bias and Absolue Variance due o ToT Shocks (Condiional) 5 Opimal Porfolios IN PROGRESS Here we use global mehods from Adams and Barre (2017) o calculae opimal counry porfolios and compare versus observed porfolios. 6 Conclusion TBD 21

22 References Adams, J., and P. Barre (2017): Why are Counries Asse Porfolios Exposed o Nominal Exchange Raes?, IMF Working Paper. Adjemian, S., H. Basani, M. Juillard, F. Mihoubi, G. Perendia, M. Rao, and S. Villemo (2011): Dynare Reference Manual, version 4,. Aguiar, M., and G. Gopinah (2007): Emerging Marke Business Cycles: The Cycle Is he Trend, Journal of Poliical Economy, 115(1), Benerix, A. S., P. R. Lane, and J. C. Shambaugh (2015): Inernaional currency exposures, valuaion effecs and he global financial crisis, Journal of Inernaional Economics, 96(Supplemen 1), S98 S109. Be, G., and C. Peluffo (2017): Weak Insiuions as a Barrier o Economic Growh, Working Paper. Broda, C. (2004): Terms of rade and exchange rae regimes in developing counries, Journal of Inernaional Economics, 63(1), Chen, Y.-c., and K. Rogoff (2003): Commodiy currencies, Journal of Inernaional Economics, 60(1), Chrisiano, L., M. Eichenbaum, and C. Evans (2005): Nominal Rigidiies and he Dynamic Effecs of a Shock o Moneary Policy, Journal of Poliical Economy, 113(1), Drechsel, T., and S. Tenreyro (2017): Commodiy booms and buss in emerging economies, Journal of Inernaional Economics. Feensra, R. C., R. Inklaar, and M. P. Timmer (2015): The nex generaion of he Penn World Table, The American Economic Review, 105(10), Fernandez, A., A. Gonzalez, and D. Rodriguez (2018): Sharing a ride on he commodiies roller coaser: Common facors in business cycles of emerging economies, Journal of Inernaional Economics, 111, Fernandez, A., S. Schmi-Groh, and M. Uribe (2017): World shocks, world prices, and business cycles: An empirical invesigaion, Journal of Inernaional Economics, 108, S2 S14. King, R. G., and S. T. Rebelo (1999): Chaper 14 Resusciaing real business cycles, Handbook of Macroeconomics, 1,

23 Kose, M. A. (2002): Explaining business cycles in small open economies: How much do world prices maer?, Journal of Inernaional Economics, 56(2), Mendoza, E. G. (1995): The Terms of Trade, he Real Exchange Rae, and Economic Flucuaions, Inernaional Economic Review, 36(1), Schmi-Grohe, S., and M. Uribe (2003): Closing small open economy models, Journal of Inernaional Economics, 61(1), Schmi-Grohe, S., and M. Uribe (2017): How imporan are erms of rade shocks?, Inernaional Economic Review. Shousha, S. (2015): Macroeconomic Effecs of Commodiy Booms and Buss, manuscrip, Columbia Universiy. Traband, M., and H. Uhlig (2011): The Laffer curve revisied, Journal of Moneary Economics, 58(4), Zeev, N. B., E. Pappa, and A. Vicondoa (2017): Emerging economies business cycles: The role of commodiy erms of rade news, Journal of Inernaional Economics, 108,

24 A Shock Esimaion Here we show our shock esimaion procedure in deail. B Panel Vecor Auoregression Here show he VAR resuls (I have already calculaed hese) C New Keynesian Phillips Curve Derive New Keynesian equaions here. D TDE Regression Resuls Pu full regression ables from TDE calculaion here. 24