Credit frictions and co-movement of durable and non-durable goods in a small open economy

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1 Credi fricions and co-movemen of durable and non-durable goods in a small open economy Hilary Paroba ERSA working paper 73 February 28 Economic Research Souhern Africa ERSA is a research programme funded by he Naional Treasury of Souh Africa. The views expressed are hose of he auhors and do no necessarily represen hose of he funder, ERSA or he auhor s affiliaed insiuions. ERSA shall no be liable o any person for inaccurae informaion or opinions conained herein.

2 Credi fricions and co-movemen of durable and non-durable goods in a small open economy July 25, 26 Absrac In his paper I invesigae, numerically, he co-movemen puzzle by esing he abiliy of borrowing and lending consrains o couner he opposie movemen of durable and non-durable goods in response o foreign moneary policy and inernaional bond shocks. I do his by simulaing a small open economy sicky price model calibraed o he Souh African economy over he period 99Q24Q4. I show ha inroducing borrowing and lending consrains ino a small open economy sicky price model, in he face of foreign moneary policy ighening and an inernaional bond shock, parially solves he co-movemen puzzle. This is because he shadow value of durable goods reduces he incenive o accumulae durables for collaeral because foreign lenders are less efficien han domesic lenders a recovering loans. In he case of sicky durables and sicky non-durables, he sicky price model mimics a fall in he relaive price of durable goods observed in he daa. Thus, financial fricions such as borrowing and lending consrains make i possible o reconcile he sicky price model wih he daa. JEL codes: E44, E52, F4, F42 Keywords: Credi fricions, borrowing consrain, lending consrain, durable goods, nondurable goods, sicky prices, co-movemen puzzle, small open economy Inroducion Muli-secor sicky price models produce unusual oucomes when he prices of durable goods are flexible. This is because, on he one hand, as empirical evidence suggess, a moneary policy shock resuls in he posiive movemen of aggregae consumpion in boh durable and non-durable goods secors. On he oher, i is because he movemen of durable goods is greaer han ha of nondurable goods, as suggesed by Erceg and Levin 22, 26. On he oher hand, Barsky e al. 23 show ha in a wo-secor economy wih flexibly priced durable goods and sicky priced

3 non-durable goods, he flexibiliy of prices of durable goods governs he response of aggregae consumpion o a moneary policy ighening. This is because he shadow value of durable goods is approximaely consan owing o he ypically high sock-o-flow raio of durable goods. Thus, he responsiveness of he user cos of durable goods does no resul in an improvemen in oal uiliy for he households. The phenomenon in which he consumpion of durable goods and he consumpion of nondurable goods co-move in he same direcion in he daa bu in he opposie direcion in sicky price models is known as he co-movemen puzzle Barsky e al., 23; Monacelli, 29. puzzle is due o he negaive correlaion beween he user cos and he relaive price of durable goods durables. This is because consumpion of non-durable goods non-durables is condiional on consumpion smoohing, as prediced by he permanen income hypohesis Barsky e al., 23. In he face of a moneary policy shock, households can subsiue ineremporally in reacion o changes in he relaive price of non-durables, bu he shadow value of durables is nearly consan, allowing lile ineremporal elasiciy of subsiuion for durables. Thus, a small, ineremporal increase in he relaive price of durables resuls in a large shif of consumpion away from he durables secor. To solve he co-movemen puzzle, Barsky e al. 23 propose he inroducion of fricions in he form of credi consrains, sicky wages and sicky inpus ino sicky price models. Incorporaing a binding borrowing consrain ino a sicky price model generaes a disconnec beween he marginal uiliy of exra durable purchases and he relaive price of durables. This is because, assuming ha incomes rise in he wake of a moneary policy shock, consrained borrowers may spend heir exra income purchasing durables alhough non-durables have become relaively cheaper. The The exra income also relaxes he borrowing consrain, hus making he demand for durables dependen on income GDP raher han on he aggregae sock of durables. Monacelli 29 formalizes his idea in a wo-secor sicky price model in which borrowing households face a borrowing consrain. He shows ha whenever prices of durable goods are flexible and prices of non-durable goods are sicky, a moneary policy ighening resuls in a decrease in he relaive price of durables. The user cos of consumpion rises in he durable goods and falls in he non-durables secor. The comovemen puzzle is hus solved by connecing he shadow value of durables o he shadow value of borrowing. Serk 2 and Chen and Liao 24 revisi he Monacelli 29 framework and show ha flexible durable prices are required o solve he co-movemen puzzle. This paper invesigaes, numerically, he co-movemen puzzle by examining he abiliy of bor- In he lieraure, he erms sock, purchases and consumpion are also used o refer o goods durable and non-durable. For clariy, in his paper I have used goods hroughou. 2

4 rowing and lending consrains o explain he opposie movemen of durable and non-durable goods in response o a foreign moneary policy shock and an inernaional bond shock. The aim is o discover wheher a small open economy sicky price SOE-SP model ha is augmened wih credi fricions can solve he co-movemen puzzle. I augmen he SOE-SP model wih a borrowing consrain, following Iacoviello and Manei 26 and lending consrain, following Manei and Peng 23. Similar models ha use credi fricions o explain he co-movemen puzzle have been esed in recen milesone papers by Monacelli 29, Serk 2 and Chen and Liao 24. The conribuion of he paper is ha i invesigaes he co-movemen puzzle for small open economies, hus expanding he new-keynesian DSGE lieraure on credi fricions and he fundamenal characerisics of durable goods and non-durable goods. Mehodologically, he paper enhances Monacelli 29 and Serk 2 by inroducing he dynamics of small open economies. To he bes of my knowledge, his is he firs paper o ackle he co-movemen puzzle for small open economies. The resuls show ha in response o foreign moneary policy ighening and an inernaional bond shock, he inroducion of credi fricions ino a SOE-SP model parially solves he comovemen puzzle. In he case of sicky durables and sicky non-durables, he SOE-SP model mimics a fall in he relaive price of durable goods observed in he daa. Thus, credi fricions such as borrowing and lending consrains make i possible o reconcile he SOE-SP model wih he daa. The res of paper is organized as follows. The nex secion presens he SOE-SP model, Secion 3 repors he numerical resuls, and Secion 4 concludes. 2 A SOE-SP model wih credi fricions The main framework of his paper is a wo-secor SOE-SP model. In each secor, here are households consising of savers and borrowers, perfecly compeiive final goods producers and monopolisically compeiive inermediae goods producers. Households supply labor hours of work o producers from which hey earn wage paymen. The model incorporaes credi fricions in he form of a lending consrain, and domesic and foreign borrowing consrains subjec o an exogenous inernaional bond shock. Durables are used as collaeral agains borrowing. Moneary policy is implemened using a foreign nominal ineres rae via he counry specific risk premium. 2. Borrowers Represenaive borrowers of measure ς maximize he expeced lifeime uiliy funcion: 3

5 E o β log X = ] +ϕ νn, + ϕ where β is he borrowers discoun facor, N is he labor hours, ν is he preference parameer for hours worked, ϕ is he inverse elasiciy of labor supply and X is he oal aggregae consumpion specified as: X = ω κ κ C κ ] κ κ + ω κ κ D κ, 2 where ω is he share of durable goods, κ is he elasiciy of subsiuion beween durables and non-durables irrespecive of counry of producion, C is consumpion of non-durable goods and D is he sock of durable goods. Consumpion of non-durable goods is specified by a Dixi-Sigliz aggregaor: C α η C η η h, + α η C η η f, ] η η, 3 where αɛ, ] is inversely conneced o he degree of home bias. Tha is, he porion of domesic non-durable goods assigned o impored goods is aken as an index of openness, following Gali and Monacelli 25. η > is a measure of subsiuabiliy beween domesic and foreign goods. C h, and C f, are respecively given by he consan elasiciy of subsiuion CES funcions: C h, = C J ε J ε J dj ε J ε J and C f, = C f, J γ γ dj where Jɛ, ] denoes a coninuum of differeniaed final non-durables produced by each counry, ε J > is he elasiciy of subsiuion beween varieies of goods produced in any given counry and γ is he subsiuabiliy of goods produced in differen foreign counries. The opimal allocaions of expendiure beween domesic and impored non-durables afer derivaion of heir respecive demand funcions, as in Gali and Monacelli 25, are: γ γ, where P P h η C h, = α P h η C and C f, = α C, P P α P η h, ] + αp η η f, is he consumer price index CPI. Borrowers maximize Eq. subjec o a budge consrain specified as: 4

6 P c, C +P d, D δd +R h B h +Ξ F A e R f Bf = Bh +e B f +W N +T. 4 where B is end-of-period nominal deb, R is he nominal lending rae on loan conracs required a ime, e is he real exchange rae, W is he nominal wage, N is he oal labor supply and T is governmen ransfers. The upper and lower case leers denoe nominal and real variables respecively. Labor is assumed o be perfecly mobile across secors, implying ha he nominal wage rae is common across secors Monacelli, 29. B f is an exogenous inernaional bond and follows an AR process, B f = ρ B B f ɛ B f wih ɛ B f i.i.d., σ 2 B. Ξ F f A is he counry-specific risk premium funcion, following Gelain and Kulikov 29 and Schmi-Grohe and Uribe 23, specified as: where F A ebf P h parameer. Ξ F A φ fa F A. is he ne foreign asse posiion and φ fa is he counry-specific risk premium In real erms, budge consrain Eq. 4 is expressed as: C + q D δd + R B h h + Ξ F A R f B f e = Bh + B f + w N + τ. 5 e where he relaive price of durables is q P d, P c,, and gross inflaion is in unis of non-durable goods π c, Pc, P c,. In addiion o he period budge consrain Eq. 4, borrowers face an endogenous domesic consrain and foreign borrowing consrains, following Iacoviello and Minei 26 and Minei and Peng 23, specified in real erms as: R h B h E σχ h q + D, 6 R f Bf E σ χ f q + D, 7 where σ is he share of durable goods D used by borrowers as collaeral and χ is he loano-value raio. Borrowers would prefer o exhaus heir credi in he domesic marke. However, 5

7 because savers face a lending consrain, ha is χ h > χ f, full domesic borrowing is no achievable. Borrowers herefore supplemen domesic borrowing wih foreign borrowing. Leing he shadow value of domesic borrowing consrains be λ h and he shadow value of foreign borrowing consrains be λ f, borrowers firs-order condiions in unis of non-durables are: w = ν α η + α η ] ω κ ] N ϕ C, 8 = β E C C + R h π c,+ = β E Ξ F A e + C C + e + λ h R h, 9 R f π c,+ + λ f Rf, q = β ] E + q + + E λ h σχ h q + + λ f C C + D σ χ f q +. Eq. 8 is he real wage equaion. Eq. 9 is he Euler equaion for holding domesic bonds. Eq. is he Euler equaion for holding foreign bonds. Eq. is he borrowers demand for durable goods where λ h σχ h q + + λ f σ χ f q + is he shadow value of durables. The shadow value of durables implies ha he opimal selecion of he share of durables σ equaes o he marginal benefi of domesic and foreign collaeral as λ h χ h = λ f χ f. Therefore, by purchasing more durables, borrowers shif consumpion from non-durables. This in urn increases heir curren credi limi and fuure consumpion of non-durables. Eq. can be expressed in erms of he user cos of durables Z = D C 2.2 Savers as: Z q { β E D q + + D E C + λ h σχ h q + + λ f σ χ f q + ] }. 2 Savers of measure ς inves in domesic governmen bonds earning a gross nominal ineres rae in period and own monopolisic producers in each secor. They maximize he uiliy funcion: E o ζ log X = ] +ϕ νñ, 3 + ϕ wih ζ β implying ha savers are more paien han borrowers and herefore discoun he fuure less heavily. Subjec o he budge consrain: 6

8 P c, C + P d, D δ D + B h = R h B h + W Ñ + T, 4 where C, D, B, Ñ, and T are respecively savers consumpion of non-durables, savers consumpion of durables, end-of-period nominal deb, labor supply and governmen ransfers. I is assumed ha here are no aggregae nominal profis from he holdings of monopolisic compeiive producers in secor j. In real erms, he budge consrain Eq. 4 is expressed as: C + q D δ D + B h = R h B h + w Ñ + τ, 5 Savers also face a lending consrain, following Minei and Peng 23, specified as: B h σ R h B h + q D, 6 where σ is a consan used as savers proxy for capial-adequacy raio. Leing λ be he shadow value of he savers lending consrain, savers firs-order condiions in unis of non-durables are: w = ν α η + α η + λ = ζ E C C + π c,+ ] ω κ R h Ñ ϕ C, 7 + λ + σr h, 8 q = j D + ζ E q + + λ + σq +. 9 C C + Eq. 7 is savers real wage equaion. Eq. 8 is savers Euler equaion for holding domesic bonds. Eq. 9 is savers ineremporal consumpion of non-durables. 2.3 Final goods producers Perfecly compeiive final goods producers purchase unis of inermediae good i and operae he producion funcion: Y j, = ε j ε j ε j ε Y j, j j dj, where j = c, d and ε j is he elasiciy of subsiuion beween differen varieies in secor j. The final goods producers maximize profis. The demand funcions for he ypical inermediae 7

9 good i in secor j, expressed as: Y j, i = P h εj j, i Y j,. P h j, ] for all i. Therefore, Pj, h Pj, h i ε j ε di j goods producer in secor j earning zero profis. is he price index consisen wih he final 2.4 Inermediae goods producers Monopolisic compeiive inermediae goods producer i in secor j hires labor supplied by borrowers and faces a linear producion echnology funcion given by: Y j, i = N j, i. 2 where N j, i is oal demand for labor by producer i in secor j. Labor produciviy is assumed o be consan and normalized o in boh secors. Each producer i has monopolisic power o se is prices and face a Roemberg 982 ype quadraic price adjusmen cos proporional o 2 υ oupu: j Pj, h i 2 Pj, h i Y j,. Where υ j is he degree of secoral nominal price rigidiy and deermines he size of he price adjusmen cos. Prices are flexible in he case υ j =. The inermediae goods producer i maximizes he expeced discouned nominal profi: E = Λ j, P h j, i Y j, i w N j, i υ j 2 P h 2 j, i Pj, h i P h j,y j,. 2 subjec o Eq. 2. In Eq. 2, Λ j, ζe λ+ λ is savers sochasic discoun facor in which λ is savers marginal uiliy of nominal income. Leing P j, h i be he relaive price of variey i in Pj, h secor j, in a symmeric equilibrium in which P j, h i = for all i and j, and all producers employ Pj, h he same amoun of labor in each secor, he firs order condiion for inermediae goods producer i s maximizaion problem is: { } ε j + ε j mc j, = υ j π j, h πj, h Λ j,+ Pj,+ h Y j,+ υ j E Λ j, Pj, h πj,+ h πj,+ h. 22 Y j, where π h j, is mc j, = W. Pj, h P h j, P h j, is he gross inflaion rae in secor j, and he real marginal cos in secor j 8

10 Log-linearizing around a secoral zero-inflaion seady sae, Eq. 22 akes he form of a forwardlooking new-keynesian Phillips curve: π h j, = ζ E π h j,+ + ε j υ j mc j,. 23 where a ha denoes he percenage deviaion from he respecive seady sae value. 2.5 Small open economy dynamics In he SOE-SP model, bilaeral erms of rade beween he domesic and he foreign counry are defined by leing erms of rade S i, = P f. This is he price of non-durables produced in foreign P h counry i in erms of he domesic counry. Therefore, he effecive erms of rade are given by: S P f, = P h, S γ γ i, di. 24 Dividing hrough households demand funcions yields he relaion, C f, C h, = α α Sη. Gross inflaion in unis of non-durables π c, is linked o he CPI inflaion hrough he CPI index Gali and Monacelli, 25. Thus, in seady sae, he CPI index saisfies a purchasing power pariy condiion given by: π = π h α + α S η α + α S η η. 25 η In addiion, exchange rae dynamics are derived from Eq. 24 as follows. The index of openness and he erms of rade are he gap beween he wo measures of change in price as a fracion of percenage change in erms of rade. Assuming ha he law of one price applies for households non-durables and defining P i, j = g i, P i i, j for all counries, where g i, is he bilaeral nominal exchange rae and Pi, i j is he price of differeniaed goods in counry i expressed in he producer s currency, subsiuing for P i, j and log linearizing around a seady sae yields: p f, = i, + p i i, di = + p f, 26 where i, di is he log nominal effecive exchange rae and Pi, i Pi, i j dj represens he log domesic price index for counry i. Defining he bilaeral real exchange wih counry i o be e i, g i, P i P, and leing e e i, di be he log effecive real exchange rae, where e i, loge i,, he real exchange rae is given by Gali and Monacelli, 25; Faia and Iliopulos, 2: 9

11 ] e = α S η η + α = e S, 27 Durable goods are assumed o be non-radable, herefore he real exchange rae e does no cause changes in he relaive price of durable goods. Following Gelain and Kulikov 29, Eqs. 9 and resul in a modified uncovered ineres rae pariy UIP ha akes ino accoun a counry specific risk specified as: R h = Ξ F A R f Foreign moneary policy and marke clearing condiions The UIP condiion in Eq. 28 implies ha he domesic nominal ineres rae is conneced o he foreign nominal ineres rae hrough he counry specific risk premium funcion. Therefore, he moneary policy is conduced by means of an AR process foreign ineres rae rule: R f = ρ RR f + ɛ R f. 29 where ɛ R f i.i.d., σr 2. The necessary marke clearing condiions are as follows. For markes o clear in he domesic economy, domesic households expendiure on durables mus equal aggregaed domesic producion and coss associaed wih prevailing resources originaing from price adjusmens. The aggregae consumpion of he durables secor and he non-durables secor is he same in domesic and foreign economies. Therefore: Y c, = ςc + ς C + υ c 2 π c, 2 Y c,, 3 Y d, = ς D δ D + ς D δ D ] + υ d 2 π d, 2 Y d,. 3 The deb marke clears as follows: ςb h + ς B h = and B f =. 32 The labor marke clears as follows: Y = ςn + ς Ñ. 33

12 Finally, he fiscal auhoriy does no issue ransfers o miigae economic flucuaions. Hence: τ = Deerminisic seady sae condiions The deerminisic seady sae condiions are as follows. Inflaion is zero in boh he durable and non-durable goods secors. The shadow value of deb is always posiive. This implies ha households prefer o hold posiive amouns of credi. Evaluaing Eq. 9 using he sandard seady sae Lucas asse price equaion R = β yields: λ = ζ β. 35 Furher, evaluaing Eq. in seady sae combined wih Eq. 35, domesic borrowers consumpion of durables is presened as: D C = α α q { δ β + χ β ζ]} η. 36 whereas δ non-durabiliy of goods coupled by β = ζ, non-binding collaeral consrains, λ =, implies ha q is he only deerminan of he margin on consumpion of durable or nondurable goods. Noice ha collaeral as a requiremen for borrowing is isomorphic o he deb elasic ineres rae. Tha is, an increase in he credi limi resuls in a decrease in demand for durable goods as collaeral. Inuiively, as i becomes more difficul for domesic borrowers o conver collaeral ino new foreign deb, he araciveness of durable goods as collaeral diminishes. 3 Numerical analysis The model is solved using simulaion echniques calibraed o he Souh African economy by compuing he averages of quarerly ime series daa for he period 99Q-24Q4. 2 Parameers are also se following he lieraure. 3. Calibraed parameers Table presens he calibraed parameer coefficiens. The durables depreciaion rae δ, is obained from quarerly values of D Y, Following Paroba and Rapusoane 26. This resuls in an annual 2 The daa are also obained from he Souh African Reserve Bank s Quarerly Bullein.

13 depreciaion rae of.9. The share of durables ω =.8 is calculaed from quarerly values of D C+D. The value is consisen wih Hoosain 22, who obained a raio of.2 for Souh Africa. In seady sae, he gross real ineres rae equals he inverse of he subjecive discoun facor + R = β. The average annual deposi rae, proxied by he discoun rae on 9-day reasury bills, is calculaed o be percen and he average annual lending rae, proxied by he prime overdraf rae, is calculaed o be 5 percen. This implies ha he discoun facor for savers ζ =.9 and he discoun facor for borrowers β =.87. The degree of openness is obained from he sum of expors and impors as a share of GDP per capia resuling in α =.54, compared o.48 esimaed by du Plessis e al. 24. The value is.3 in he empirical lieraure for developed counries. The degree of nominal rigidiy in he non-durables secor υ c is se o creae a frequency of four quarers on price adjusmen. Tha is, following he sandard Calvo-Yun model by leing θ be he probabiliy of no re-seing prices, θ = 4. This implies ha θ =.75 and an average frequency of price adjusmen of one year. In each secor, herefore, he sickiness parameer saisfies υ j = θ ε j / θ ζθ. The simulaion ess alernaive degrees of price sickiness wih full flexibiliy achieved by seing υ j =. The elasiciy of labor supply ϕ =. The elasiciy of subsiuion beween domesic and foreign goods η =.59 as in Seinbach e al. 29. The elasiciy of subsiuion beween varieies of goods ε = 6 as in Alpanda e al. 2, implying a seady sae mark-up µ =.2. The elasiciy of subsiuion beween durables and non-durables κ =.2. The preference parameer ν =.3, implying ha, on average, Souh African households prefer o work a hird of heir ime endowmen. The share of durable goods used as domesic collaeral σ =.5. The domesic loan-o-value raio χ h =.8 and he foreign loan-o-value raio χ f =.4 following Minei and Peng 23. Finally, he persisence of he foreign moneary policy shock ρ R,f =.9 wih a sandard deviaion of.. Table : Calibraed parameers Parameer δ ω ζ β α θ φ η ɛ χ ν σ χ h χ f Value The effecs of a foreign moneary policy ighening Figure plos he impulse response funcions IRFs of non-durables, durables, relaive price of durables, user cos of durables and domesic deb in response o a foreign moneary policy shock. The IRFs predic a varied resricion of price sickiness, namely sicky non-durables and flexible durables prices, sicky durables and flexible non-durables prices and equally sicky durables and non-durables prices. In he IRFs, he unbroken green line shows he reacion of he SOE-SP 2

14 model when non-durables have sicky prices and durables have flexible prices. The figure shows ha he co-movemen problem occurs up o he hird period, hrough which he relaive price of durables is consan. Afer he hird period, he relaive price of durables now falls and is accompanied by a rise in consumpion of boh non-durables and durables. The relaive price of durables falls afer he hird period because he prices in he non-durables secor rise more han hose in he durables secor. The broken blue line shows he reacion of he SOE-SP model when durables have sicky prices and non-durables have flexible prices. The figure shows ha he co-movemen problem occurs again up o he fifh period, during which he relaive price of durables falls. This is because here is a disconnec beween he relaive price and user cos of durables in response o he moneary policy shock Monacelli, 29. Tha is, he drop in he relaive price of durables causes a ighening of borrowing requiremens, resuling in a decrease in he demand for durables. This is paricularly eviden in Figure in he iniial increase in he demand for durables followed by a seep decline in demand up o he hird period and an equally seep decline in domesic deb up o he fourh period. The marginal increase in he user cos of durables causes a subsiuion effec from durables o non-durables up o he fourh period, followed by larger increases in he durables secor han in he non-durables secor. From he fifh period, he relaive price of durables is consan and is accompanied by consan movemen of consumpion of non-durables and a marginal rise in consumpion of durables. The spiky red line shows he reacion of equally sicky non-durables and durables o foreign moneary policy ighening. The figure shows ha he co-movemen problem occurs up o he fifh period, during which he relaive price of durables falls. Subsequenly, he relaive price of durables becomes consan and is accompanied by a marginal decline in consumpion of non-durables and near consancy in consumpion of durables. I can herefore be concluded from Figure ha he co-movemen problem occurs up o he hird period, afer which he problem is resolved in he face of a moneary policy ighening. According o Barsky e al. 27, Monacelli 29, Serk 2 and Chen and Liao 24, solving he co-movemen puzzle requires ha a model predics a decrease in boh non-durables and durables. This is because of a ypically high sock-o-flow raio of durables ha is due o he marginal benefi of durables being dependen on he sock of durables and he almos infinie elasiciy of subsiuion beween durables and non-durables. This implies ha addiional purchase of durables by households, due o he responsiveness o he durables own user cos, does no improve he households oal uiliy. The drop in he relaive price of durables, in he case of sicky durables, is as a resul of he 3

15 2 x 3 Non durables.5 Durables Relaive price of durables x 65 User cos of durables.2 Domesic deb 2 x 3 Foreign deb Shadow value of domesic borrowing 5 x Shadow value of foreign borrowing 5 x Sicky non durables Sicky durables Equally sicky Figure : Impulse responses o a foreign moneary policy ighening: effec of varying he degree of sickiness ineracion beween he borrowing consrain and he lending consrain, as shown by Minei and Peng 23. On he one hand, he decrease in he relaive price of durables caused by he foreign moneary policy ighening resuls in a reducion in he ne worh of he domesic lenders, hereby ighening he borrowing consrain. This in urn compels domesic borrowers o borrow from foreign lenders o mee heir loan demand. On he oher hand, given ha borrowers have borrowed parly from he domesic marke, heir borrowing from he foreign marke, up o heir deb limi, is dependen on he value of durables no commied for domesic borrowing. This implies ha he amoun of credi borrowed from he domesic marke is greaer han ha borrowed from he foreign marke. Therefore, he drop in he relaive price of durables causes ighening of he lending consrain and helps o achieve equilibrium in he durables marke. In Figure 2, I es he effecs of he shadow value of durables o consumpion of durables and consumpion of non-durables for boh savers and borrowers. To do his, I esablish he impac of he shadow value of durables given is imporan characerisics in deermining he direcion of movemen beween durables and non-durables. The figure shows a negaive co-movemen of consumpion of durables and consumpion of non-durables in response o a foreign moneary policy shock, and a posiive co-movemen beween he wo variables in response o an inernaional bond 4

16 shock. 2 x 3 Non durables Panel : Foreign monaary policy shock x 3 Non durables Panel 2: Inernaional bond shock Durables Durables x 3 Shadow value of durables x 29 Shadow value of durables Borrowers Savers Figure 2: Impulse responses o a foreign moneary policy ighening and an inernaional bond shock: effecs of shadow value of durable goods I can be concluded from Figures and 2 ha, in response o a foreign moneary policy ighening, he inroducion of credi fricions ino a SOE-SPM parially solves he co-movemen puzzle. ] This can be aribued o he shadow value of durables λ h σχ h q + + λ f σ χ f q + in Eq.. Tha is, χ h > χ f and implies ha here is a reduced incenive o accumulae durables for collaeral because foreign lenders are less efficien han domesic lenders a recovering loans. I is also eviden ha he marginal benefi of durables purchased by borrowers depends on he proporion of he domesic loan-o-value raio χ h =.8 o he foreign loan-o-value raio χ f =.4 and wheher he borrowing consrains are binding or no. As borrowers reallocae he purchase of durables from he domesic o he foreign marke and vice versa, he collaeral consrain is relaxed. 3.3 The effecs of an inernaional bond shock Figure 3 shows he impulse response funcions IRFs of non-durables, durables, he relaive price of durables, he user cos of durables, and domesic deb in he face of an inernaional bond shock. The resricions are he same as hose in Figure. In he IRFs, he unbroken green line shows he reacion of he SOE-SP model when non-durables have sicky prices and durables have 5

17 flexible prices. The figure shows a decrease in boh consumpion of non-durables and consumpion of durables. Decreases in consumpion of durables are seeper han hose of consumpion of nondurables. Whereas he relaive price of durables increases a an almos uniary rae, he user cos of durables increases up o lag six before converging o zero. Domesic deb, on he oher hand, decreases monoonically wih decreases in consumpion of durables. The broken blue line shows he reacion of he SOE-SP model when durables have sicky prices and non-durables have flexible prices. I reveals an increase in he consumpion of boh non-durables and durables. Furher, he increase in he consumpion of durables is larger han he increase in he consumpion of non-durables. The relaive price of durables decreases while he user cos of durables increases. Domesic deb, on he oher hand, increases sharply before declining o zero in he ninh period. The spiky red line shows he reacion o equally sicky consumpion of non-durables and durables. Non durables x 3 Durables x 3 5 Relaive price of durables 5 x x 64 User cos of durables 5 x 3 Domesic deb Foreign deb Shadow value of domesic borrowing x Shadow value of foreign borrowing 5 x Sicky non durables Sicky durables Equally sicky Figure 3: Impulse responses o an inernaional bond shock: effec of varying he degree of sickiness I is eviden from he figure ha here is a decrease in he consumpion of boh non-durables and durables, wih he decline in he former being seeper han in he laer. Whereas he relaive price of durables and he domesic deb level decrease in he face of an inernaional bond shock, he user cos of durables increases a an almos uniary rae. 6

18 4 Conclusion This paper has simulaed an small open economy sicky price SOE-SP model calibraed o he Souh African economy. I shows ha inroducing borrowing and lending consrains ino a SOE- SP model, in he face of a foreign moneary policy ighening and an inernaional bond shock, parially solves he co-movemen puzzle. In paricular, sicky durables and sicky non-durables help he SOE-SP model o mimic a decline in he relaive price of durable goods observed in he daa. Tha is, inroducing credi fricions such as borrowing and lending consrains makes i possible o reconcile he sicky price model wih he daa. References Alpanda, S., Koze, K., Woglom, G., 2. The role of he exchange rae in a new Keynesian DSGE model for he Souh African economy. Souh African Journal of Economics 78 2, 7-9. Barsky, R., House, C., Kimball, M., 23. Do flexible durable goods prices undermine sicky price model? Naional Bureau of Economic Research Working Paper, No Barsky, R., House, C., Kimball, M., 27. Sicky-price models and durable goods. American Economic Review 97 3, Chen, B., Liao, S., 24. Capial, credi consrains and he co-movemen beween consumer durables and non-durables. Journal of Economic Dynamics and Conrol 39, du Plessis, S., Smi, B., Seinbach, R., 24. A medium sized open economy DSGE model of SA. Souh African Reserve Bank Working Paper, No. 4. Erceg, C.J., Levin, A., 22. Opimal moneary policy wih durable consumpion goods. Board of Governors of he Federal Reserve Sysem, Inernaional Finance Discussion Paper No Erceg, C.J., Levin, A., 26. Opimal moneary policy wih durable consumpion goods. Journal of Moneary Economics 53, Faia, E., Iliopulos, E., 29. Financial openness, financial fricions and opimal moneary policy. Journal of Economic Dynamics and Conrol 35, Gali, J., Monacelli, T., 25. Moneary policy and exchange rae volailiy in a small open economy. Review of Economic Sudies 72, Gelain, P., Kulikov, D., 29. An esimaed dynamic sochasic general equilibrium model for Esonia. Eesi Pank Working Paper, No. 59. Hoosain, A., 22. Relaionship beween consumer credi and consumpion spending in Souh Africa. Gordon Insiue of Business Science, Universiy of Preoria. Mimeo. 7

19 Iacoviello, M., Minei, R., 26. Inernaional business cycles wih domesic and foreign lenders. Journal of Moneary Economics 53 8, Minei, R., Peng, T., 23. Lending consrains, real esae prices and business cycles in emerging economies. Journal of Economic Dynamics and Conrol 37, Monacelli, T., 29. New Keynesian models, durable goods, and collaeral consrains. Journal of Moneary Economics 56, Paroba, H., Rapusoane, L., 26. Souh Africa s real business cycles: The cycle is he rend. Economic Research Souhern Africa Working paper No. 69. Roemberg, J., 987. Sicky prices in he Unied Saes. The Journal of Poliical Economy 9 6, Schmi-Grohe, S., Uribe, M., 23. Closing Small Open Economy Models. Journal of Inernaional Economics 6, Seinbach R., Mahuloe, P., Smi, B., 29. An open economy new Keynesian DSGE model of he Souh African economy. Souh African Journal of Economics 77 2, Serk, V., 2. Credi fricions and he co-movemen beween durable and non-durable consumpion. Journal of Moneary Economics 57 2, Appendix This appendix recaps he full non-linear model. Borrowers: C + q D δd + R h B h π c, e + Ξ F A R f B f e π c, = B h + B f + w N + τ, B. R h B h E σχ h q + D, B.2 R f Bf E σ χ f q + D, B.3 w = ν α η + α η ] ω κ ] N ϕ C, B.4 = β E C C + 8 R h π c,+ + λ h R h, B.5

20 = β E Ξ F A e + C C + e R f π c,+ + λ f Rf, B.6 Z q { β E D q + + D E C + λ h σχ h q + + λ f σ χ f q + ] }. B.7 Savers: C + q D δ D + B B h = R h h + w Ñ + τ, B.8 π c, B h σ R h B h + q D, B.9 w = ν α η + α η + λ = ζ E C Firms: Inermediae goods producers C + π c,+ ] ω κ R h Ñ ϕ C, B. + λ + σr h, B. q = j D + ζ E q + + λ + σq +. B.2 C C + π h c, = ζ E π h c,+ + ε c υ c mc c,, B.3 Marke clearing condiions: π h d, = ζ E π h d,+ + ε d υ d mc d,. B4. Y c, = ςc + ς C + υ c 2 π c, 2 Y c,, B.5 Y d, = ς D δ D + ς D δ D ] + υ d 2 π d, 2 Y d,. B.6 B h = B h, B.7 9

21 B f =, B.8 τ =. B.9 Definiions: X = ω κ κ C κ ] κ κ + ω κ κ D κ, B.2 C α η C η η h, + α η C η η f, ] η η, B.2 P α P η h, ] + αp η η f,, B.22 Ξ F A φ fa F A, B.23 F A e B f P h, B.24 q P d, P c,, B.25 Y j, i = N j, i, B.26 λ+ Λ j, ζe, B.27 λ D Share = ω C, B.28 D Shadow = α q C, B.29 Y = Y c, + Y d,. B.3 2

22 Small open economy dynamics: π = π h e = α + α S η α + α S η η, B.3 η ] α S η η + α, B.32 R h = Ξ F A R f. B.33 Exogenous AR shock process: B f = ρ BB f ɛ B f, B.34 R f = ρ RR f + ɛ R f. B.35 2