Commodity Price Volatility with Endogenous Natural Resources

Transcription

1 Commodiy Prie Volailiy wih Endogenous Naural Resoures James Hansen a,, Isaa Gross b a Deparmen of Eonomis, Universiy of Melbourne b Keble College, Universiy of Oxford Absra Naural resoure reserves are exogenous in models of small ommodiy exporers. We onsider riher supply dynamis and model exploraion and depleion. These are imporan for apuring he effes of ommodiy prie shoks inluding a ommodiy urreny and rowding-ou of non-ommodiy aiviy. We also onsider how welfare and he ranking of opimal moneary and axaion poliies hange. Wihou exploraion or depleion, opimal moneary and axaion poliies an effiienly sabilise he eonomy in response o ommodiy prie shoks. However, when exploraion and depleion are aouned for, hanging ineres raes o offse prie shoks beomes ineffiien. Using axaion poliy, speifially an ad valorem royaly, remains effiien. Keywords: Commodiy urrenies, ommodiy pries, Duh Disease, non-renewable resoures, opimal poliy. JEL Codes: E63, F41, Q33, Q38 Corresponding auhor: James Hansen, 111 Barry Sree, Level 4 FBE Building, Universiy of Melbourne VIC 3010, Ausralia. Phone: , james.hansen@unimelb.edu.au. Isaa Gross: Keble College, Parks Road, Oxford, OX1 3PG, UK, isaa.gross@keble.ox.a.uk.... January 18, 2017

2 1. Inroduion Commodiy pries are volaile. In reen deades pries for non-renewable resoure ommodiies have more han doubled and hen halved. 1 Suh volailiy, alhough large, is no wihou preeden wih several large prie yles over he pas enury Figure 1; Jaks, 2013; Capuo and Chang, 2015). Over he pas wo deades, world ommodiy rade has inreased more han sevenfold and expor shares have been rising over ime. 2 The size of hese prie hanges ogeher wih he paern of inreasing expor onenraion, has renewed ineres in he quaniaive effes of ommodiy prie hanges. Two enral quesions are wheher prie volailiy is benefiial or osly, and how eonomi poliy should opimally respond. 3 Figure 1: Trends and Cyles in Real Commodiy Pries Sine 1900 Noes: Daa are from Jaks, D. 2013), From Boom o Bus: A Typology of Real Commodiy Pries in he Long Run, NBER Working Paper All indies have base period 1900=100 and are logged. A ommon assumpion when answering hese quesions is ha he sok of domesi resoure reserves deposis of minerals, oil or gas held in he ground is known, exogenous and non-exhausible. 4 There is no proess by whih firms an augmen ex- 1 Typial examples of hese ommodiies inlude oil, gas, iron-ore, oal and base meals suh as aluminium, opper, lead, nikel and zin. 2 Measured beween beween 1995 and 2011 UNCTADsa), as a share of oal merhandise rade i more han doubled from 10 o 22 per en. A he peak of he boom, ommodiy expor revenues made up 67 per en of oal merhandise expor revenue in Afria, 57 per en in Oeania, 24 per en in Ameria and 20 per en in Asia. 3 Defining a ommodiy exporer as exporing a leas 20 per en of is merhandise expors in he form of non-renewables, abou a fifh of he world s populaion resides in hese eonomies UNCTADsa, 1995 o 2014). 4 There is exensive lieraure on he effes of ommodiy prie shoks in small open eonomies. Reen examples inlude: Bjørnland and Thorsrud 2016), who fous on produiviy spillovers beween he resoure and non-resoure seors; Bodensein e al. 2011), on oil prie shoks and exernal adjusmen; Naal 2012) on opimal moneary poliy, and Jääskelä and Nimark 2011) who esimae a DSGE model for Ausralia. All of hese examples assume ha he supply of resoures is 2

3 ising reserves hrough exploraion. The depleion of exising reserves is also ignored. These wo hannels, emphasised in naural resoures lieraure, 5 are absraed from by assuming a Cobb-Douglas exraion ehnology where reserves play he role of exogenous ehnial hange. There is lile ha differeniaes naural resoures from oher seors of he eonomy. We onsider a riher model of supply by inegraing exploraion, depleion and reserve sariy ino an oherwise sandard small ommodiy exporing eonomy SCE). Unlike he reamen of reserves as fixed and invarian o ommodiy prie hanges exogenous), he supply of reserves is modelled as an endogenous sae variable. Firms an inves o find new reserves hrough exploraion. They also aoun for he fa ha exraing reserves resuls in heir depleion. We examine wheher hese addiional supply dynamis are imporan for modelling he ransmission of ommodiy prie shoks, he impliaions for domesi welfare and for opimal poliy rules. We fous on exploraion and depleion as hese are likely o be imporan for apuring he propagaion of ommodiy prie shoks. They have been emphasised in parial equilibrium models of naural resoures Devarajan and Fisher, 1982; Cairns, 1990; Halvorsen and Layon, 2015), where he opporuniy os of depleion he fa ha resoures exraed oday are no available for fuure exraion affes resoure firms opimal exraion deisions, while exploraion defines he feasible se from whih produion an our Pindyk, 1978; Lasserre, 1985; Livernois and Uhler, 1987). Boh are imporan for undersanding how resoure firms adjus o prie hanges. They may also be imporan from a maro perspeive. Wih limied propagaion of ommodiy prie shoks in he presene of exogenous reserves, sandard models have diffiuly in explaining orrelaion beween ommodiy prie and maro volailiy in SCEs Bidarkoa and Cruini, 2000; van der Ploeg, 2011; Berka, Cruini and exogenous, osless and inexhausible. Bems and de Carvalho Filho 2011) sudy preauionary saving and he urren aoun allowing for an exhausible supply whih is sill exogenous and osless o exra); Dib 2008) and Benkhodja 2014) allow for osly exraion, bu no exploraion or depleion; Wills 2013) and Arezki e al. 2015) sudy he effes of exogenous reserve disoveries when viewed as news abou fuure produion. None of hese sudies onsider reserves as an endogenous sae variable ha responds o prie signals. 5 See for example Hoelling 1931); Pindyk 1978); Heal 1993); Halvorsen and Layon 2015). 3

4 Wang, 2012). Given he magniude of adjusmen ha ours hrough produion quaniies when ommodiy pries hange, we invesigae wheher addiional wealh effes assoiaed wih he disovery of new reserves an help o reonile observaions abou ommodiy prie volailiy and maroeonomi performane. There are several dimensions in whih models wih exogenous reserves are a odds wih daa on how SCE s respond o ommodiy prie hanges. Perhaps mos noable, is he impliaion ha reserves growh is unorrelaed wih prie growh. Empirially, here is posiive omovemen in prie growh, exploraion aiviy and he subsequen disovery of new reserves. Firms have an inreased inenive o look for new reserves when pries are high, and alhough no all exploraion is suessful, on average hey find new deposis. Seond, sandard models imply signifian posiive omovemen beween prie growh and exraion growh onemporaneously. In he daa, he onemporaneous orrelaion is lose o zero and exraion inreases wih a lag. Exploraion o find new reserves and he addiional apial required o build new mines are imporan margins of adjusmen ha delay he exraion response. In erms of maro effes, models wih exogenous reserves do no generae a ommodiy urreny effe an appreiaion depreiaion) of he real exhange rae when ommodiy pries rise fall). Simple regression analysis suggess he orrelaion beween ommodiy pries and he real exhange rae is high a abou Chen and Rogoff, 2003; Cashin e al., 2004). Similar findings are observed in Sruural Veor Auoregressions VARs) and Dynami Faor Models. 6 Sandard models predi a muh lower orrelaion. 7 Lieraure on he effes of ommodiy prie volailiy has also emphasised a Duh Disease effe he rowding ou of aiviy in non-ommodiy seors in response o higher ommodiy pries, espeially in non-ommodiy expors. Evidene of i has been found in panel sudies see, for example, Sahs and Warner 2001), Sijns 2003) and van der Ploeg 2011), and in sruural ime series models Jääskelä 6 For SVAR evidene see Jääskelä and Smih 2013); for Dynami Faor Model evidene see Charnavoki and Dolado 2014) and Bjørnland and Thorsrud 2016). 7 For example, for Canada Dib, 2008), Chile Fornero e al., 2014), or in a sandard alibraed model Benkhodja, 2014), he peak response of he real exhange rae o a one peren posiive shok o ommodiy pries is an appreiaion of per en. 4

5 and Smih, 2013; Charnavoki and Dolado, 2014; Bjørnland and Thorsrud, 2016). 8 Nowihsanding, sandard models do no produe a large realloaion of goods or labour aross seors. 9 The maximal deline in non-ommodiy expors is abou a per en Dib, 2008; Benkhodja, 2014) and some models imply an absene of Duh Disease alogeher Fornero e al., 2014). Inorporaing exploraion and depleion beer apures he ransmission of ommodiy prie hanges. A model where reserves respond o hanges in prie an produe posiive omovemen in prie growh and exploraion growh, and in exploraion growh and reserves growh. I an also produe a weak or negaive orrelaion beween prie and exraion growh; a signifian appreiaion of he real exhange rae and large movemens of goods and labour aross seors. Exploraion, and he absene of depreiaion in reserves, are enral o hese resuls. Firms inrease exploraion when ommodiy pries rise and any new reserves found resul in a permanen inrease he feasible produion se ha is, new reserves found never depreiae. This generaes addiional omplemenariy in exraion, exploraion, invesmen and mining labour demand failiaing a greaer expansion of he resoure seor when ommodiies prie rise and a larger onraion when pries fall. 10 Assuming onsan reurns o sale in produion and an absene of priing power in world markes, reserves are an endogenous permanen rend ransiory hanges in prie an have permanen effes on he eonomy. Indeed, endogenous reserves magnifies he effes of ommodiy prie hanges on boh he resoure and non-resoure seors. The implied ommodiy urreny and seoral realloaion effes are similar o hose in he lassial heory of Duh-Disease in wo or hree-speed eonomies Corden and Neary, 1982; Corden, 2012). 8 Norway is an ineresing exepion. Bjørnland and Thorsrud 2016) find signifian produiviy spillovers offse he presene of Duh-Disease in Norway. 9 We are resriing aenion o dynami sohasi general equilibrium models. Models wihou expeaions or opimising behaviour have generaed signifian Duh Disease Corden and Neary, 1982; Corden, 2012). 10 A useful albei imperfe) analogy is o hink of a sandard firm wih Cobb-Douglas ehnology and aess o researh and developmen ha an permanenly inrease produiviy. Wih a higher prie for is produ, he firm an disover new ideas ha permanenly inrease oupu and produiviy, generaing larger effes on produion and faor usage when pries rise han in he ase in whih R&D anno be aessed. Exploraion works in muh he same way, hough he analogy is no perfe beause depleion will o some exen aenuae he mehanism. 5

6 In view of he differen prediions aross models, we ompare a sandard exogenous reserves model wih an endogenous ounerpar ha has exploraion and depleion. Parameerising he models o a prooypial SCE Ausralia), we firs sudy how ommodiy prie volailiy affes household welfare: is prie volailiy benefiial or is i osly? In he model wih exogenous reserves, welfare is no sensiive o prie volailiy. Households are willing o forgo only a small share of heir seady sae onsumpion, less han per en, o be insulaed from a small inrease in prie volailiy an inrease in he sandard deviaion of prie of 0.1 per en). 11 When reserves are endogenous he gloomy sory has more raion: households are signifianly more adverse o ommodiy prie volailiy and willing o forgo as muh as 0.13 per en of heir seady sae onsumpion o avoid he same inrease in prie volailiy. We nex onsider he ranking of opimal moneary and axaion poliy. 12 Wih exogenous reserves, opimal ineres rae and resoure axaion rules are lose subsiues and an eliminae he effes of ommodiy prie volailiy on welfare. In relaive erms, we find ha moneary poliy implemened hrough an opimised ineres rae rule is preferred o a ax on resoure seor profis, reserves or revenue. This suppors he emphasis on opimal moneary poliy in response o ommodiy prie shoks in previous lieraure Frankel, 2003; Cão and Chang, 2013; Hevia and Niolini, 2013; Berghol, 2014). When reserves are endogenous, however, he rankings hange. An opimal ineres rae rule an no longer eliminae he effes of prie volailiy on welfare and is an ineffiien ool for sabilising prie shoks. The reason is ha wih greaer spillover of ommodiy prie shoks ono he non-resoure seor, hanges in he ineres rae will only indue greaer volailiy in domesi non-mining produion hereafer domesi produion), non-resoure expors and onsumpion. In effe, a blun insrumen riique beomes imporan where i is no opimal o hange ineres raes o redue volailiy in he resoure seor as his will amplify volailiy in he res of he eonomy. 11 This is rue even in he presene of signifian asse marke friions ha preven households from insuring agains ommodiy prie shoks. 12 The opimaliy of alernaive axaion sruures has been invesigaed in parial equilibrium models in Gamponia and Mendelsohn 1985), Deaon 1993), Daniel e al. 2010) and Boadway and Keen 2015). 6

7 Opimal axaion rules, speifi o he resoure seor, remain effiien. For example, an opimally se revenue ax ad valorem royaly) miigaes hanges in resoure firm revenues. I reformulaes ommodiy prie shoks as lump-sum perurbaions o households budge onsrains. Wih lower onsumpion volailiy and less inerseoral flows of goods and labour, whih is osly in he presene of prie friions and onvex preferenes over labour supply, welfare is higher. Taxes on resoure rens or reserves an yield similar welfare gains, hough hese poliies are less effiien. The nex seion provides sylised observaions on reserves and ommodiy pries. Seion 3 disusses wo small open eonomies wih naural resoures, one wih exploraion and depleion and one where reserves are held fixed. Seion 4 presens our quaniaive resuls and sudies opimal poliy. The final seion onludes. 2. Sylised Observaions We begin wih summary evidene on he abiliy of he sandard and endogenous reserve models o explain simple empirial orrelaions ha are relevan o undersanding how SCEs respond o ommodiy prie hanges. 13 Table 1, olumns wo o four, provides summary orrelaions for hree prooypial SCE s Ausralia, Canada and Norway. I highlighs hree paerns: a) here is posiive omovemen beween ommodiy prie growh and exploraion growh, and subsequenly reserves growh; 14 b) exraion growh is onemporaneously unorrelaed wih prie growh and negaively orrelaed a lags; and ) invesmen and prie growh are posiively orrelaed boh onemporaneously and wih a lag. Similar paerns using miro daa for oil have been doumened by Anderson e al. 2014). The sandard model is only onsisen wih he hird fa Table 1, olumn five). Wih exogenous reserves here is no orrelaion beween prie and exploraion growh or exploraion and reserves growh. The sandard model also predis a srong posiive orrelaion beween exraion and prie growh, whereas he daa sugges lile onemporaneous orrelaion and negaive orrelaion a lags. The model wih endogenous reserves an produe posiive omovemen in prie, exploraion and reserves 13 These orrelaions are no model arges when we parameerise he models as disussed below). 14 The laer being onsisen wih a delay beween exploraion, disovery and hen lassifiaion of new reserves. 7

8 Table 1: Summary Correlaions τ Ausralia Canada Norway Exogenous Endogenous Exploraion Growh ) and Reserves Growh τ) Prie ) and Exploraion τ) N/A N/A N/A 0.13 Prie ) and Exraion τ) Prie ) and Invesmen τ) Noes: Correlaions are alulaed on annual growh raes; he periods overed are 1977 o 2011 Ausralia), 1976 o 2010 Canada), and 1981 o 2012 Norway), wih he exepion of Norwegian exploraion daa ha are only available from 2001; for a full desripion of he empirial daa, see Appendix A. Exogenous and Endogenous refer o orrelaions based on simulaed daa from he models disussed in Seion 3. growh, and lile or even negaive omovemen beween exraion growh and prie growh Table 1, olumn six). I also remains onsisen wih he hird sylised fa, produing a posiive orrelaion in invesmen and prie growh. Using he same daa for Ausralia and Canada, similar paerns an be observed in a panel-var in prie, exploraion and reserves. 15 Idenifying a prie shok by assuming ha ommodiy pries are onemporaneously unorrelaed wih shoks o exploraion and reserves, a one sandard deviaion inrease in prie leads o signifian inreases in exploraion expendiure and subsequenly reserves Figure 2). The persisene of he reserves response o a ransiory prie rise is a key feaure of he daa ha an endogenous reserves model an reprodue, while he exogenous model assumes he response is zero in all periods. The nex seion disusses he models for endogenous and exogenous reserves in deail and heir parameerisaion. 15 Norway ime series on exploraion are only available over a shor ime frame see Table 1 noes). 8

9 Figure 2: Comovemen in Prie, Exploraion and Reserves Noes: Based on a Panel-VAR ha uses annual daa on eonomially demonsrable reserves, ommodiy pries and exploraion from 1976 o 2010 for Ausralia and Canada. The shok is a one sandard deviaion inrease in ommodiy pries; 95 per en onfidene inervals are repored. 3. The Theoreial Models We assume ha here are four seors in he eonomy: resoures; non-radeables; impors; and non-resoure expors. Resoures are modelled as non-renewable and non-exhausible wih osly exraion. The seor is perfely ompeiive wih apial drawn from abroad and labour from he domesi eonomy, a paern ha is ommon in many SCEs. 16 When reserves are modelled as endogenous, firms have aess o a osly exploraion ehnology ha is a onvex funion of he level of exploraion underaken and he eonomy-wide aggregae) sok of naural resoure reserves. Firms also aoun for he fa ha exraion deplees he exising sok of reserves. When reserves are exogenous, here is neiher exploraion nor depleion and reserves are assumed onsan over ime. For he res of he eonomy, we onsider an environmen similar o ha in Adolfson e al. 2007), hough only he minimal se of friions hose required o mah he dynamis of a ommodiy prie shok are used. The hree remaining seors nonradeables, impors and expors are eah populaed by a oninuum of firms of uni 16 The assumpion of imporing mining speifi apial from abroad is onsisen wih he sylised fa ha a large fraion of he apial insalled in mining projes is impored. For example, reen large-sale floaing plaforms used o exra liquid naural gas in Ausralia have been enirely produed and assembled abroad. For broader evidene on he impored onen of apial, see Connolly and Orsmond 2011). 9

10 measure ha are monopolisially ompeiive and subje o seor-speifi Calvo priing rigidiies. Pries in all seors are se in loal urreny erms. Households make onsumpion and labour supply deisions opimally, hough finanial markes are inomplee wih an endogenous risk premium on foreign borrowing and parial domesi ownership of he resoure seor. The eonomy is losed hrough an opimal ineres rae rule. axaion rules The Resoure Seor In subsequen disussion, we will addiionally onsider opimal The resoure seor wih exploraion and depleion draws from previous work by Pindyk 1978), Heal 1993), Sweeney 1993), Bohn and Deaon 2000) and Halvorsen and Layon 2015). We assume many ompeiive resoure produers ha maximise profi aking ommodiy pries as given. They hoose exraion, X, invesmen in physial apial, I, labour, H r, expendiure on exploraion, D, and have value funion: V K, R ) = max {X,I,H r,d} S P r X W r H r S P I CD, R ) +βe M +1 V K +1, R +1 )) 1) wih onsrains: X = H r A r ) η K γ R 1 η γ 2) )) I K +1 = 1 δ) K + 1 Ξ I 3) I 1 R +1 = R + ω +1 D X 4) where K physial apial) and R firm-level reserves) are firm-speifi sae variables; and R aggregae reserves), W r wages), P r ommodiy pries), P he prie a whih apial goods are impored), and S he nominal exhange rae) are aggregae sae variables. 17 β is he rae of ime preferene and M +1 is is sohasi omponen refleing he ownership sruure of resoure firms. 17 Aserisks are used o denoe variables measured in foreign urreny erms. Aggregae reserves is he sum of reserves aross all domesi resoure firms in he eonomy, R = 1 0 R i)di. 10

11 Exploraion oss, CD, R ) : R 2+ R +, are an inreasing onvex funion of firm-level exploraion and he sok of aggregae reserves. The os funion is homogenous of degree one so ha he profi funion is homogenous of degree one, wih onsan reurns o sale in mining produion. Marginal oss ha are posiive and inreasing in he amoun of firm-level exploraion C D > 0, 2 C > 0) is a ommon D 2 assumpion in he naural resoures lieraure. I apures he idea ha larger deposis are ofen more osly o find and are affeed by rising oss of exploraory drilling as firms drill furher underground or in less aessible loaions. 18 Marginal oss ha are posiive and inreasing in he aggregae sok of reserves C R > 0, 2 C R 2 > 0) apures sariy when looking for new deposis. Alhough new reserves an be disovered in perpeuiy, i beomes inreasingly osly o find hem as he sok of exising reserves inreases. 19 Imporanly, we absra from a known finie bound on new reserves. This is useful beause he poliy funions ha solve he resoure firms program are ime invarian and an be inegraed wihin a broad lass of small open eonomy models. The heoreial raionale is ha, given a suffiienly high prie, firms will always have an inenive o look for new reserves and, a leas o some exen, will be able o find hem even if i beomes more osly o do so. Inreasingly sare, hough nonexhausible reserves, have been previously emphasised by Pindyk 1978), Devarajan and Fisher 1982), Lasserre 1985) and Livernois and Uhler 1987) amongs ohers. 20 Empirially, i has provided a reasonable approximaion as reserves have eiher grown or remained saionary over ime in many SCEs raher han being in rend deline Reen researh has foused on more granular produion sruures suh as soks of heerogenous qualiy and differen ypes of reserves, bu we absra from ha level of deail. 19 Our approah is moivaed by previous lieraure, whih assumes ha resoures are nonexhausible bu ha exploraion oss are inreasing in he umulaive sum of pas exploraion flows for example Lasserre 1985); Livernois and Uhler 1987)). We use he sok of reserves raher han he umulaive oal of pas exploraion as his allows for delineaion effes he fa ha drilling and exraing exising reserves redues he os of finding new linked deposis. 20 I is also ommon in naural resoures o allow for a non-exhausible baksop even if a given resoure may have finie supply van der Ploeg and Wihagen, 2012). 21 I is an alernaive approah o ha of a finie bound, where firms undersand wha reserves are available and simply exra hem a an opimal rae wihou he need for exploraion he sandard Hoelling model. For he sample over whih we esimae, he non-exhausible hough sare disoveries approah is a beer desripion of he daa produion and reserves have grown over ime insead of reserves exploraion) delining as predied by he ase of a finie bound wih a large small) iniial reserve sok Pindyk, 1978). 11

12 The exraion proess and he law of moion for apial, Equaions 2) and 3), are sandard. The former is Cobb-Douglas and allows for exogenous labour-augmening ehnial hange A r ). Invesmen adjusmen oss are inluded o apure he fa ha building new mines or expanding exising apial is osly and akes ime. Reserves are an endogenous sae variable ha an be inreased hrough exploraion and depleed via exraion, Equaion 4). Unerainy over exploraion is apured by he random variable ω +1, whih is assumed i.i.d. wih normalised mean E ω +1 ) = 1. The following neessary ondiions hold in equilibrium: S P r S P C D, R ) D where ϱ I I 1. = 1 + ζ) W r X ζ A r K µ R µ ζ + Q r 5) ) ) = Q k 1 Ξ ϱ ) Ξ ϱ ) ϱ + βe M+1 Q k +1Ξ ϱ +1 ) ϱ ) = Q r Equaion 5) equaes he marginal revenue of exraion wih he marginal os of exraion, where he laer inludes boh he os of exraion in period and he opporuniy os ha reserves exraed oday anno be exraed in he fuure. Equaion 6) equaes he marginal os of imporing apial o is marginal reurn, aouning for he presene of invesmen-adjusmen oss. Equaion 7) implies ha firms explore o he poin where he marginal os is equal o he expeed presen disouned value of an exra uni of reserves. The marginal values of reserves and apial are given by: 7) Q r = βe M +1 ζ µ) W r +1 Q k = βe M +1 µ W r A r A r +1 ) X 1+ζ +1 K+1R µ µ ζ M +1 Q r +1 ) X 1+ζ +1 K µ 1 +1 R µ ζ +1 + M +1 Q k +1 1 δ) 8) 9) Resoure firms are owned by domesi and foreign households, and use he real sohasi disoun faor: M +1 = ν Θ ) +1 P + 1 ν Θ P+1 where ν is a redued-form parameer apuring he domesi ownership share, Θ is he 12

13 marginal uiliy of domesi households in period and P he prie of onsumpion. If ν = 1, he model is onsisen wih domesi households having full ownership. In he ase ha ν = 0, resoure firms maximise heir real domesi urreny value, bu ake no aoun of domesi households preferenes a zero domesi ownership share). 22 To apure spillovers from resoure seor aiviy o domesi produion Rayner and Bishop, 2013; Berghol, 2014), we assume exploraion aiviy also requires nonraded goods as an inpu wih a fixed-proporions ehnology: Y r,n = D Q r φ m, where Q r is he seady sae shadow prie of one uni of reserves, φ m governs he sensiiviy of exploraion oss disussed in deail below) and Y r,n inpus. 23 is he demand for non-raded This assumpion will be imporan for obaining a hree-speed eonomy Corden, 2012), one where he resoures seor expands in response o posiive ommodiy prie shoks and here is rowding ou of non-resoure expor aiviy, bu he effes on non-raded produion an be posiive or negaive depending on he relaive size of spillovers aross seors Bjørnland and Thorsrud, 2016). In he eonomy where reserves are exogenous, Equaion 4), is replaed wih R = R and Equaion 7) is replaed wih D = 0. The wo eonomies are oherwise idenial. Domesi Households We assume a oninuum of idenial households of uni measure wih perfe onsumpion insurane wihin he period. Fousing on he represenaive household, preferenes are addiively separable wih onsan relaive risk aversion, an exernal habi over onsumpion and a onsan elasiiy of subsiuion beween he supply of resoure and non-resoure labour: U C, H n, H r ) = C V ) 1 ξ 1 ξ ς 1 1 Hn γ h H + Hr γ h n H r ξ h γ h 22 Similar assumpions are used in Favilukis e al. 2014) and Fornero e al. 2014). A heoreial moivaion for his approah an be found in Sanford J. Grossman 1979) and Careles-Poveda and Coen-Pirani 2010). 23 Noe ha for a given perenage hange in exploraion aiviy, he same hange will our in demand for non-raded inpus. Similar resuls are obained if we alernaively assume ha domesi labour is required o insall mining-speifi apial or exraion direly employs non-raded inpus. 13

14 C is an aggregae onsumpion bundle onaining non-raded and impored goods), V = 1 0 C 1 j) dj is he exernal habi, H n and H r are households supply of labour o he non-resoure and resoure seors respeively wih H n and H r heir orresponding seady sae values), ξ is he oeffiien of relaive risk aversion over onsumpion relaive o he habi, ξ h governs disuiliy over aggregae labour supply and γ h governs he elasiiy of subsiuion beween resoure and non-resoure labour. 24 Households an rade in wo risk-free bonds a domesi bond, B, and a foreign bond, B. To deouple he real exhange rae from he raio of foreign o domesi marginal uiliies of onsumpion and allow for inomplee sharing of ommodiy prie risk, we follow Benigno and Thoenissen 2008) and assume ha finanial markes are inomplee: when domesi residens issue laims in foreign urreny hey mus pay a premium on his borrowing, Φ. As we noe below, his premium will be imporan for generaing a ommodiy urreny when reserves are endogenous. The flow budge onsrain for households is: P C + B 1 + i ) + S B = W 1 + i n H n )Φ + W r H r + B 1 + S B 1 + νψ r + Ψ n + Ψ o + Ψ x T 10) where Ψ r, Ψ n, Ψ o, Ψ x are he aggregae profis dividends) paid o households from he resoure, non-raded, impor and non-resoure expor seors, T is a lump-sum ax or subsidy), 25 W n is he nominal wage paid for supplying non-resoure labour, and i and i are he domesi and foreign ineres raes. The Euler equaions are: Θ = βe 1 + i ) P ) Θ P+1 +1 ) Θ = βe 1 + i P S +1 ) Φ Θ P+1 +1 S 11) 12) where he marginal uiliy of onsumpion is Θ 1 C C V ) 1 ξ. 24 The exernal habi Abel, 1990) is useful as he level of onsumpion will be non-saionary in equilibrium. 25 In he subsequen disussion on opimal axaion rules, his will be he mehanism hrough whih axes are remied o households Seion 4.1). 14

15 Opimal labour supply in resoures is governed by: W r H r 1 γ 1 1 h Θ P = ςξ h Hn γ h H r H n 1 γ h + Hr H r ξ h γ h 1 13) and for non-resoures: W n P H n Θ = ςξ h 1 γ h 1 H n 1 γ h Hn H n 1 + Hr γ h H r ξ h γ h 1 14) We assume a onsan elasiiy of subsiuion beween non-raded and impored goods η ) and allow for home-bias in onsumpion α). 26 Domesi Non-mining Produion Y s,n i Eah non-raded produer, indexed by i, has aess o produion ehnology = An χ H n i where A n is a ommon ehnology shok, H n i is he quaniy of nonraded labour used by firm i, and χ is a ommon os-push shok. 27 Non-raded firms are monopolisially ompeiive and are subje o Calvo priing. For he fraion 1 φ n ) of firms able o se heir prie opimally, hey solve: where MC n χ is he marginal os of produion for a domesi non-raded produer and Y d,n max E P n 0 0 W n A n = 0 φ n β) 0 P 0 Θ n P P Θ 0 MC n 0 ) P n 0 P n ) θn Y d,n is a measure of aggregae non-raded demand. A reursive formulaion of he opimal prie P n ) is given by: P n = θn ) V n θ n 1 U n 15) where: V n = Y d,n Θ P n ) θn P W n ) χ A n + βφ n E V n +1 16) 26 See Equaions B.16) o B.18) in he Appendix. 27 This is a redued-form o aoun for he posiive orrelaion beween ommodiy pries and produion oss Sims, 1992; Roemberg and Woodford, 1996; Hamilon, 2003). We assume χ follows a similar auoregressive proess as ha modelled for ommodiy pries: ln χ = ρ r ln χ 1 + Υε r where Υ governs he elasiiy of marginal oss wih respe o ommodiy pries. 15

16 and U n = Y d,n Θ P n ) θn P + βφ n E U n +1 ) For he remaining fraion φ n ) of firms no able o hoose heir prie, hey simply reain heir prie from he previous period. The shadow prie of an exra uni of non-raded goods and non-raded profi are given by: Domesi Imporers 1 0 P n = 1 φ n ) P n ) 1 θn ) 1 + φn P 1 n1 θn 1 θn 17) 18) Ψ n idi = P n Y d,n 1 τ n ) W n H n 19) Imporing firms purhase final oupu from he foreign seor and use his o produe a differeniaed onsumpion impor. Real marginal oss, ommon o all imporers, are MC o = S P. Like non-radeable produers, imporers are also monopolisially ompeiive and fae a Calvo friion when reseing heir domesi urreny prie. 28 Non-Commodiy Exporers A non-ommodiy exporer, indexed by j, purhases a bundle of non-raded inpus from domesi produers and ransforms his ino a differeniaed expor good. The demand for inpus from non-raded produer i by exporer j is given by Y n,x i j) = ) P n θn i C x j), where C x j) is he demand for exporer j s oupu. The demand P n funion for expors of ype j is: C x j) = ) P x θx j C P x 20) where C = Y ) P x θ P Y is foreign oupu, P x j is a measure of ommon demand for non-resoure expors, is he prie of expor ype j in foreign urreny erms, P x an index of non-resoure expor pries in foreign urreny erms, and P is is he foreign prie index. As wih Adolfson e al. 2007), hese assumpions allow for ompeiion amongs firms wihin he exporing seor and wih he res of he world. Exporers 28 See Equaions B.24) o B.29) in he Appendix. 16

17 are monopolisially ompeiive, se heir pries in foreign urreny erms, and are also subje o Calvo priing. 29 Moneary Poliy Moneary poliy follows a Taylor rule and arges expeed inflaion wih gradual ineres rae adjusmen: ln 1 + i ) = 1 ρ i ) ln 1 + i ) + 1 ρ i )ρ π E ln P Marke Clearing and he Res of he World +1 P ) + ρ i ln 1 + i 1 ) 21) Supply equals demand for eah non-raded good i Y s,n i aross he oninuum of goods, i follows ha: = Y d,n i ). Aggregaing A n H n χ = P n P n ) θn Y d,n 22) Demand for non-raded goods arises from onsumpion, non-resoure expors and exploraion, Y d,n = 1 0 Cn + C x + Y r,n ) dj. The non-raded prie index is given by [ ] 1 P n 1 = P n 0 i θn θn di and markes for goods, labour, apial and bonds lear. 30 For he res of he world, we assume pries and quaniies saisfy he redued-form VAR: [ where y = Y i P P r y = p A j y j + ε 23) j=0 ] is a veor olleing all foreign pries and quaniies and ε is a 4 1 veor of redued-form shoks, inluding he primiive of ineres ommodiy prie shoks ε r ). A Saionary Represenaion Assuming onsan reurns o sale in he exraion ehnology, he soluion o he above sysem, and in pariular for reserves, is non-saionary. This arises from he assumpion ha reserves never depreiae, ha he resuling value funion of 29 See Equaions B.30) o B.35) in he Appendix. 30 Noe ha world demand for resoure and non-resoure expors are assumed perfely elasi given pries P r given P. and P x, while he supply of impored goods and apial are also perfely elasi 17

18 resoure produers is homogenous of degree one and ha domesi produion nonmining and mining) is assumed o be small in world markes. 31 In eonomi erms, i means ha ransiory shoks o ommodiy pries an propagae wih permanen effes ono he resoure seor and he res of he eonomy. 32 This resul has an esablished preeden in empirial work used o idenify he effes of ommodiy prie shoks Hamilon, 1983; Kilian, 2008; Jääskelä and Smih, 2013; Alquis and Coibion, 2014) and will be a key soure of amplifiaion in he model. To find a saionary represenaion of he eonomy, we require wo furher assumpions: i) ha ehnology in he non-raded and resoure seors share a ommon long-run rend wih reserves; and ii) ha world expor demand and reserves share he same rend. These assumpions ensure ha seor shares are saionary and ha he eonomy admis a balaned growh pah. The firs implies ha hanges in ommodiy pries do no aler he ehnial effiieny wih whih faor inpus are used in ommodiy produion in he long-run; he seond ha ommodiy and nonommodiy expors grow a he same long-run rae. The Appendix disusses hese assumpions in deail, inluding empirial suppor for hem Calibraion The models are alibraed o a prooypial SCE, Ausralia, a an annual frequeny. 33 Parameers speifi o he resoure seor are repored in he upper panel of Table 2. The disoun faor and depreiaion rae are hosen in aord wih exising lieraure. 34 The exponens on apial and labour in he exraion ehnology γ and η), are hosen o mah a seady sae rae of annual exraion of wo per en, and a wage bill relaive o oal revenue of 11 per en. 35 The seady sae value of exploraion oss Θ) is alibraed so ha firms earn zero profis on average. 31 For furher disussion on how general his propery is, see Hansen and Gross 2013). 32 Formally, ) even if he underlying ommodiy prie shok has a ransiory effe on prie P lim r +j = 0, i an sill have permanen effes on real variables for example, ɛ r ) ) R+j X+j lim 0 and lim 0. j E j E ɛ r j E ɛ r 33 This is he highes frequeny wih whih deailed reserves daa are available. Our resuls are robus o alernaively using Canadian or Norwegian daa Appendix C). 34 See for example Charnavoki 2010) and Garia and Gonzalez 2010). 35 The wo peren average annual exraion rae refles he average exraion rae in Ausralia s main resoure ommodiies Appendix A). The wage bill share is onsisen wih Topp e al. 2008). 18

19 Table 2: Calibraion Desripion Parameer Value Resoure Seor Disoun faor β 0.96 Labour faor exponen η 0.13 Capial faor exponen γ 0.49 Depreiaion rae δ 0.10 Seady sae exploraion oss Θ Res of he Domesi Eonomy Risk aversion ξ 1.01 Household disoun faor β 0.96 Labour onvexiy ξ h 4 Labour subsiuion γ h 0.5 Home-bias oeffiien 1 α 0.8 Subsiuion elasiiy onsumpion) η 1.01 Subsiuion elasiiy non-raded goods) θ n 7 Subsiuion elasiiy impors) θ o 7 Subsiuion elasiiy non-resoure expors) θ x 7 Subsiuion elasiiy res of he world) θ 1 Calvo parameer non-raded goods) φ n 0.2 Calvo parameer impors) φ o 0.2 Calvo parameer non-resoure expors) φ x 0.2 Domesi ownership share ν 0.35 Cos push parameer Υ 0.33 Coinegraion long-run adjusmen parameer ϑ 0.99 Coinegraion shor-run adjusmen parameer ϑ 1 For he res of he domesi eonomy, we use a alibraion in line wih Jääskelä and Nimark 2011), who esimae a medium-sale DSGE model for Ausralia ha is similar o he model in Adolfson e al. 2007). The domesi eonomy parameers are displayed in he lower panel of Table 2. We use idenial elasiiies of subsiuion wihin he non-raded goods, imporing and non-resoure expor seors, eah onsisen wih a mark-up of 17 per en, and idenial prie sikiness parameers o mah a 20 per en probabiliy ha a firm will no be able o re-opimise is prie wihin a year s ime. The degree of home bias in onsumpion mahes a 20 per en impor share in seady sae, and he elasiiy of subsiuion beween onsumpion of non-raded goods and impors is se o one. The elasiiy of subsiuion beween resoure and non-resoure labour supply is also one, and he overall disuiliy from working is se a four labour is relaively subsiuable aross seors bu households are averse o inreasing heir overall sup- 19

20 ply of labour. Togeher, hese assumpions imply Frish elasiiies of 0.35 in he non-raded seor and 0.88 in he resoure seor. Risk aversion is se a one onsumpion preferenes are logarihmi). For he domesi ownership share of resoure firms we se his a This is above he esimaes of one fifh in Connolly and Orsmond 2011) inferred from publily available daa. We use a higher share o aoun for he fa ha no all ross-firm holdings of resoure equiies are delared and ha nominee holding ompanies are used. 36 Viewed as an upper bound, using a share lower han 0.35 only srenghens our findings below. For he os-push effe of ommodiy prie shoks, we alibrae his elasiiy a 0.33, onsisen wih evidene from VARs wih ommodiy pries Esimaion For he exploraion os funion, we use: C D, R ) = P n Q r e φm φ m D R D R ) 1 Θ) ) R where R and D are he seady sae aggregae levels of reserves and exploraion and φ m governs he sensiiviy of oss o exploraion aiviy. This funion saisfies he resriions previously disussed being an inreasing onvex funion of exploraion aiviy and he aggregae sok of reserves. For invesmen adjusmen oss, a sandard quadrai funion is used wih Ξ 1) = 0, Ξ 1) = κ. The foreign deb risk-premium is a funion of he domesi eonomy s deb deflaed by is sok of reserves: S B ln Φ ϕ b S ) B P R P R implying ha inernaional lenders ake ino aoun boh he sok of deb held and he apaiy o repay i, as apured by he sok of domesi reserves, when hoosing o lend In Ausralia, domesi ross-firm holdings need need no be dislosed when hey are less han 5 per en of oal equiy Connolly and Orsmond, 2011). 37 The model-implied quarerly elasiiy of os-push inflaion o a ommodiy prie shok is This mahes esimaes of his elasiiy from a panel-var for G7 ounries Gerard, 2012) and from a New Keynesian Phillips urve for Ausralia as esimaed in he same paper). I is also in line wih esimaes in Hamilon 2003). 38 In effe, reserves are a pledgable asse when he domesi eonomy borrows. This is reasonable given he foreign speifiiy in apial required o build new mines and he high foreign ownership 20

21 Exploraion, invesmen adjusmen oss, he risk premium parameer, he persisene of ommodiy prie shoks, and he Taylor rule oeffiiens on inflaion and he lagged ineres rae are esimaed. Speifially, we use GMM o mah he modelheorei IRFs o he hose from an empirial VAR, weighing eah momen by he inverse of is sampling variane. The esimaes minimise: J = min g Model θ) ĝ V AR) W 1 g Model θ) ĝ V AR) θ where θ = {φ m, κ, φ b, A r, ρ π, ρ i } are he parameers o be esimaed, g are he impulse response funions eiher model-heorei or from he empirial VAR) and W is a diagonal weighing marix. 39 For he weighs, we use he sample varianes of eah IRF poin as esimaed using he empirial VAR. Using Ausralian daa, he empirial- VAR esimaed is: 40 A 0 z = Γz 1 + e where z is he veor of observables relaing o he IRFs being mahed ommodiy pries, he real exhange rae, he raio of domesi produion o reserves, he raio of mining invesmen o reserves and inflaion. The effes of a shok o ommodiy pries are idenified by assuming ha ommodiy pries are onemporaneously unorrelaed wih domesi variables and he real exhange rae. We separaely esimae he models wih endogenous and exogenous reserves, mahing he model-heorei IRFs o he empirial-var IRFs in eah ase. As noed by Ravenna 2007), wih unobserved sae variables he models admi a VARMA represenaion and i is no lear wheher model-irfs will be well approximaed by hose from a finie lag VAR. To verify he approximaion, we simulae daa from he endogenous and exogenous reserves models and hen esimae he equivalen empirial VAR on eah simulaed daa se. As shown in he Appendix Seion C), using reserves o deflae domesi produion and invesmen highlighs ha he empirial VAR an reover he rue model-heorei IRFs in eah ase. 41 share in resoures. 39 See for example Chrisiano e al. 2005). Ten equidisan momens are used for eah IRF mahed and over a 20-year response horizon. 40 We inlude a deerminisi ime rend and onsan. Similar esimaes are obained using a HP-filer or firs-differened daa. For a omplee desripion of he daa see he Appendix. 41 Alhough apial and he sok of deb are unobserved, he sok of reserves is he key sae 21

22 Table 3 repors he esimaed oeffiiens. The risk premium and invesmen adjusmen oss are similar aross models. However, he exogenous model requires greaer persisene in he proess for ommodiy pries, wih an AR1) oeffiien of 0.97 as ompared o I also requires a less aive ineres-rae rule wih a smoohing oeffiien lose o zero as ompared o 0.59) and a weigh on inflaion only slighly above ha required for he Taylor priniple o be saisfied, 1.18 as ompared o I is lear ha boh greaer shok persisene and less aive moneary poliy are required o mah he empirial effes of ommodiy pries shoks wih exogenous reserves. Table 3: GMM Esimaes Desripion Coeffiien Exogenous Model Endogenous Model Risk premium ϕ b ) 0.038) Exploraion oss parameer φ m ) Invesmen oss parameer κ ) 0.238) AR1) parameer ommodiy pries) A r ) 0.007) Ineres rae smoohing Taylor rule) ρ i ) 0.015) Weigh on inflaion Taylor rule) ρ π ) 0.036) Figure 3 highlighs he IRFs from he empirial VAR and from he models. Overall, boh models are able o mah he empirial responses hough a few exepions are noeworhy. 42 The exogenous reserves model is unable o generae a sizeable appreiaion in he real exhange rae ha is, here is no ommodiy urreny effe. I also implies a onraion in domesi produion relaive o reserves on impa ha lies ouside he 95 per en onfidene band. In onras, he endogenous reserves variable ha is observed. Deflaing real quaniies by his sok apures he underlying oinegraing relaionships implied by he endogenous model; in he exogenous model he sok of reserves is simply onsan. 42 Alhough i is emping o inerpre he model wih exogenous reserves as generaing a larger response in mining invesmen o a ommodiy prie shok, his aually refles he less aive ineres rae rule. As we show below, when boh models share he same rule, he endogenous reserves model generaes a muh larger effe of ommodiy prie hanges on invesmen. 22

23 Figure 3: Esimaed and Emprial IRFs Noes: Eah IRF is measured in erms of he perenage deviaion from is sample mean or perenage poin deviaion where appropriae); niney five peren onfidene inervals are repored for he empirial VAR. model an generae a signifian and persisen appreiaion of he real exhange rae, and almos preisely mahes he esimaed response of lile hange in he raio of domesi produion o reserves in he shor-run The Effes of Exploraion and Depleion We now ompare he differenes beween he wo models solely due o exploraion and depleion. We do so using he parameerisaion of he endogenous reserves model and hen urning off he exploraion and depleion hannels. 44 Figure 4 repors he resoure seor s response o a one sandard deviaion inrease in ommodiy pries an inrease of 12 per en) wih exploraion and depleion, and wihou hem. I highlighs a muh larger response when reserves are endogenous. The responses of mining invesmen and exraion are wo o hree imes as large, wih he maximal response of invesmen and exraion being an inrease of 17 9) per en and 10 3) per en for he endogenous exogenous) reserve eonomies. The responses of invesmen and exraion lag he inrease in prie and he effes on exploraion and reserves are highly persisen. Iniially, exploraion oss inrease as boh exploraion aiviy and he aggregae sok of reserves rise. However, sariy when exploring for new reserves beomes more imporan over ime wih he rising sok of aggregae reserves onibuing o he high os of exploraion in he longer erm. 43 A a longer horizon, he model wih endogenous reserves overesimaes he onraion in domesi produion o reserves, alhough he esimaes remain wihin he 95 per en onfidene band. Wih wider onfidene inervals a long horizons, hose momens are given less weigh in esimaion. 44 We ould alernaively fous on he parameerisaion of he exogenous model for he benhmark and urn on exploraion and depleion. The resuls are similar. 23

24 Figure 4: Resoure Seor Response o a Shok o Commodiy Pries Noes: Eah IRF is measured in erms of he perenage deviaion from is seady sae value. The shok is a one sandard deviaion inrease in ommodiy pries. The amplifiaion in he model arises from he fa ha exploraion resuls in a permanen inrease in fuure exraion possibiliies. Sine newly found reserves never depreiae and are omplemenary o labour and apial in produion, he marginal produiviy of he firm is raised in all periods, or unil he full amoun of any newly disovered reserves are exraed. Even small hanges in reserves an have long-erm effes on a resoure firms produiviy leading o larger and more persisen inreases in exraion, invesmen and labour demand. Figure 5 shows he responses for he res of he eonomy. The prie shok is ransmied o domesi aiviy wih larger delines in onsumpion and non-resoure expors, and a signifian appreiaion of he real exhange rae onsisen wih a rise in foreign deb and he risk premium. There is also an expansionary effe on domesi produion, and a sronger and more persisen response in inflaion and domesi ineres raes. There is signifian rowding ou of non-resoure expors refleing boh he appreiaion of he exhange rae and a higher os of domesi inpus. In shor, endogenous reserves have a posiive ne effe on overall demand, generae a ommodiy urreny and a realloaion of goods and labour aross seors Duh Disease). When reserves are exogenous he effe on domesi produion is onraionary, here is lile hange in he real exhange rae and less realloaion of goods and labour aross seors Welfare and Opimal Poliy Rules There are wo impliaions of endogenous reserves: on he one hand, hey inrease seoral realloaion he resoure movemen effe ); on he oher, hey imply higher 24

25 Figure 5: Domesi Eonomy Response o a Shok o Commodiy Pries Noes: Eah IRF is measured in erms of he perenage deviaion from is seady sae value. The shok is a one sandard deviaion inrease in ommodiy pries. wealh ied o he disovery of new reserves he spending effe ). In he presene of friions inluding seor-speifi prie rigidiies, a risk premium on foreign borrowing and an inabiliy o fully insure agains ommodiy prie shoks hrough asse markes, i is no lear a priori how ommodiy prie volailiy will affe welfare. We now explore his quesion and he impliaions for opimal poliy. Fousing on he unondiional mean of household uiliy household welfare), 45 we evaluae he perenage of seady sae onsumpion ha equalises mean household welfare in a sohasi eonomy ha has a small degree of prie volailiy a sandard deviaion in prie of 0.1 per en and in an eonomy wihou prie volailiy, he non-sohasi seady sae. 46 A he benhmark alibraion, households are willing o forgo 0.13 per en of seady sae onsumpion o avoid a 0.1 per en perurbaion 45 Tha is, W = E = 0 β 0 ) 1 ξ C V ς 1 ξ 1 γ h Hn H n 1 + Hr γ h H r ξ h γ h 46 Sine we use seond-order perurbaion mehods, we only evaluae he effes of a small hange in volailiy relaive o he non-sohasi seady sae. 25

26 o prie volailiy in he model wih exploraion and depleion, muh larger han he per en implied in he sandard model. Thus, endogenous reserves presen a muh gloomier view of ommodiy prie volailiy han in he sandard model. Given he magniude of he differene, an opimal poliy rules be used o miigae hese effes and is here any differene in opimal poliy wih endogenous and exogenous reserves? These are he quesions ha we now onsider Opimal Ineres-Rae Rules Our iniial fous is on opimal ineres rae rules where he nominal ineres rae is a funion of inflaion, he real exhange rae, ommodiy pries, he level of domesi produion deflaed by reserves) and he lagged ineres rae variables ha have also been emphasised in previous lieraure: 47 î = ρ i î ρ i ) ) ρ π π Y + ρ y R ) ) S r + ρ s + ρ P r P Has denoe log deviaions from seady sae and he weighs, {ρ i, ρ π, ρ y, ρ s, ρ r }, are hosen o maximise a seond-order approximaion of household welfare. Table 4 repors he opimised oeffiiens for he endogenous and exogenous reserves models. More aivis moneary poliy is opimal in response o ommodiy prie volailiy wih endogenous reserves, wih subsanially higher weighs on inflaion, 1.61 as ompared o 1.00, and he lagged ineres rae, 0.99 as ompared o For boh eonomies, here is lile emphasis on he raio of domesi produion o reserves, he real exhange rae or ommodiy pries. Thus, gains from non-onvenional poliies suh as a dire ineres rae response o ommodiy prie or exhange rae volailiy are small. In addiion, he welfare inreases in moving from he previous empirial ineres rae rules, o hose ha are opimised are also small: wih exogenous reserves here is a welfare gain of per en of onsumpion; when reserves are endogenous, he gain is 0.01 per en. 47 We use he raio of domesi produion o reserves as his is saionary while he level of domesi produion is no. Similar resuls are obained if an alernaive saionary ransformaion, suh as growh in domesi produion, is used. 26