Symbiosis and Coordination of Macroeconomic Policies in a Monetary Union

Transcription

1 Symbiosis and Coordination of Maroeonomi Poliies in a Monetary Union Georgios Chortareas Shool of Management & Business, King s College London, and Department of Eonomis, National & Kapodistrian University of Athens georgios.hortareas@kl.a.uk and Christos Mavrodimitrakis 1 Shool of Eonomis and Finane, Queen Mary University of London, and Department of Eonomis, National & Kapodistrian University of Athens xmaurod@eon.uoa.gr Abstrat This paper deals with strategi poliy interations in a monetary union. We use a stati two-ountry monetary-union model, whih inorporates the key features of the New-Keynesian framework. We investigate the poliy mix outome under non-onfliting but different objetives when the two poliy instruments an diretly affet inflation. Thus, we provide a reoniliation of the early literature, whih is mostly based on the supply-side of the eonomy with the most reent literature, whih mainly fouses on the demand side. We onsider the short-run maroeonomi stabilization and welfare impliations of the fisal-monetary poliy interations at both the union and national levels. We ompare and ontrast the alternative strategi regimes (simultaneous-move, fisal/monetary leadership) in the monetary union and we analyze both the horizontal (aross governments) and the vertial (between the monetary and the fisal authorities) oordination problems. We define the impat that the poliies diret effets on inflation has on (i) fisal authorities ooperation, (ii) poliies yliality, and (iii) the alternative strategi regimes (symbiosis). We draw important results on the preferable strategi and fisal regimes for the monetary authority. 1 (Corresponding Author) Queen Mary University of London, Shool of Eonomis & Finane, Graduate Centre, Banroft Road, London E1 4DQ, UK. .mavrodimitrakis@qmul.a.uk. Tel: +44 (0) ~ 1 ~

2 Keywords: Monetary union; Fisal/monetary poliies; Coordination; Symbiosis; Strategi regimes. JEL Classifiation: E52; E61; E62; E63; F Introdution There has been more than fifteen years sine the offiial launh of the Eonomi and Monetary Union (EMU) in Europe, the greatest monetary reform sine Bretton Woods (Buti, 2003, p. 24). However, the onsequenes of fisal and monetary poliy interations still remain an issue among both aademia and poliymakers. The reent travails of the Eurozone reveal that the institutional struture of poliymaking has been imperfet and motivate further researh on fisal-monetary poliy interations in monetary unions. Monetary poliy is onduted by an independent supranational authority, the European Central Bank (ECB), while fisal poliy remains deentralized at national level, respeting the debt sustainability onstraint imposed by the European Union (EU), meaning the Stability and Growth Pat (SGP), and more reent fisal developments desribed by the Fisal Compat 2 (FC). In this framework, fisal poliy remains the maroeonomi tool of national authorities to stabilize their eonomies under ountry-speifi shoks. However, non-oordinated fisal poliies in national level may reate externalities to other member-states, reating ineffiienies. This might indue the possibility of poliy oordination. Beetsma and Giuliodori (2010) provide an overview of the researh on the maroeonomi osts and benefits of the EMU. In Setions 6 and 7, the authors examine fisal poliy and onflits of interest in the monetary union, as well as fisal spillovers and oordination. Formal analysis of the poliy mix and fisal poliies oordination requires a framework to model strategi interations among fisal authorities and the ommon entral bank. 3 In partiular, assumptions regarding authorities objetives, their ability to ommit and the timing of their deisions are at the enter of the analysis. In a reent paper, Foresti (2017) analyzes the literature on strategi fisal/monetary poliy interations in a monetary union. The author presents a generi theoretial framework in order to highlight the main points of the literature, regarding unertainty issues, authorities preferenes, the role of ommitment to poliy rules, and oordination. All these issues have regained interest due to the Eurozone sovereign debt risis, being part of the appropriate institutional framework of poliymaking in the EMU. Following Plasmans et. al. (2006), the literature has been mainly foused on two poliy interations: (i) the links between defiits, debts, inflation and interest rates via the (dynami) government budget onstraints, and (ii) the links between fisal and monetary poliies in a maroeonomi stabilization 2 Its offiial name is The Treaty on Stability, Coordination and Governane (TSCG). 3 To quote Fragetta and Kirsanova (2010, p. 856), there is little doubt that authorities an at strategially. ~ 2 ~

3 perspetive. This paper follows the seond strand of the literature, abstrating from important long-run issues that are related to fisal poliy, suh as debt sustainability. 4 To quote Uhlig (2003, p. 43), we are dealing with the day-to-day poliy task of responding to business yle shoks. The literature so far has offered a plethora of different modeling assumptions that provided mixed results, while general onditions for ooperation and ommitment irrelevane provided by Kempf and von Thadden (2013) follow the lines of the traditional Barro-Gordon (1983) set-up, where the effets of monetary and fisal poliies are often set to work only on the supply side of the eonomy. Aording to Plasmans et. al. (2006), suh an approah seems rather narrow, onsidering also that the supply-side effets of monetary and fisal poliies may in pratie be of limited relevane, as they often take a very long time to materialize. On the ontrary, the most reent literature is based on the New-Keynesian framework, whih fouses on the demand side of the eonomy, where supply is often held fixed. This paper proposes a unified theoretial framework to analyze strategi poliy interations in a monetary union. We use a stati representation of the New-Keynesian model, following mainly Andersen (2005, 2008). We assume that the two (for simpliity) member-states in the monetary union are interonneted via a trade effet and a terms-of-trade effet, and that the poliy instruments, namely the ountry-speifi fisal stanes and the ommon nominal interest rate, an also diretly affet ountryspeifi inflation. Fisal poliy an have either positive or negative diret effets on inflation, as various fisal instruments an have (positive/negative) short-run effets on the supply-side of the eonomy (see, e.g., Andersen, 2005, 2008; Debrun, 2000), whereas monetary poliy an have a diret positive effet on inflation, following mainly the ost hannel (Ravenna and Walsh, 2006). Our motivation is to provide a reoniliation between the early literature that was mainly based on the supply-side of the eonomy with the most reent one that is mainly foused on the demand side. In the latter ase, the Phillips urve is only affeted by the output gap, whih means that the two poliy instruments are perfet substitutes in the stabilization proess. By omparing the two ases, we mainly fous on the ordering of moves and the resulting ylial behavior on the part of the authorities, for both ases of deentralized and entralized fisal poliies, where the latter ase defines fisal authorities ooperation. We thus investigate the poliy mix and the oordination problem in a monetary union under non-onfliting but different objetives, when both poliy instruments an diretly affet inflation. Beetsma and Debrun (2004) distinguish the oordination problem between a horizontal (aross governments) oordination problem and a vertial (between the monetary and the fisal authorities) one. By non-onfliting objetives we mean that all the authorities agree on the ideal targets of the onerned maroeonomi variables, being their long-run 4 For example, Aguiar et. al. (2015) study fisal and monetary poliies in a monetary union with the potential for rollover rises in sovereign debt markets. ~ 3 ~

4 equilibrium values (Uhlig, 2003). However, objetives may differ, as the national fisal authorities are about fisal stane stabilization and not about inflation. This reates the poliy onflit (Kempf and von Thadden, 2013). In a series of ritial papers, Dixit and Lambertini (2001, 2003a) studied strategi poliy interations (pure maroeonomi stabilization) in a monetary union in a Barro-Gordon (1983) framework where fisal poliy an also affet (ommon) inflation, together with monetary poliy, while the monetary authority is onerned with ountry-speifi data. The main results are: (i) under onfliting objetives, the simultaneous-move strategi regime is inferior to any leadership regime, while (ii) under non-onfliting objetives, there is symbiosis of monetary and fisal poliies, in that the atual targets an be obtained irrespetive of the ordering of moves, of fisal authorities ooperation or of idential preferene priorities. Under onfliting objetives, the Nash game produes a sub-optimal rae with fisal expansion aimed at raising output and monetary ontration aimed at offsetting the effet of fisal expansion on inflation, whih yields extreme outomes. The leadership regime, instead, produes improved outomes, as the leader moderates its poliy in antiipation of the follower s reation, who moderates its poliy, too. 5 Beetsma and Bovenberg (1998), following Alesina and Tabellini (1987), assume that the monetary authority diretly ontrols the ommon inflation rate, while they also inorporate a government budget onstraint. The authors find that fisal poliies oordination is welfare-reduing, as it makes the fisal authorities to set a high tax rate in order to indue a relax of their budget onstraints through an expansionary monetary poliy, hene strengthening their strategi position relative to the monetary authority. In this model, monetary unifiation is welfare-enhaning. Kempf and von Thadden (2013) provide the general onditions for the irrelevane of the ECB s ommitment apaity and the sequening of moves (symbiosis result), as well as for fisal poliies oordination irrelevane, in monetary unions under both private and fisal spillovers, ombining the work of Dixit and Lambertini (2001, 2003a) and Chari and Kehoe (2008) in a unified framework. The private spillovers refer to the (wage) deisions by (multiple) private agents (non-oordinated wage setters) within ountries (Chari and Kehoe, 2008). 6 The monetary authority is onerned with ountry-speifi data, there is a ommon inflation rate, and the omparison between the two fisal regimes is made on union-wide equilibrium solutions. The authors onsider alternative ommitment patterns (leadership regimes) in that eah player (the private setor; fisal authorities; the monetary authority) moves at a partiular stage of the game, where all private agents at at the same stage. The fisal authorities at at the same stage, too. The 5 In a losed-eonomy setting, the superiority of the fisal leadership regime is also stressed by Dixit and Lambertini (2003b) and Hughes Hallett and Weymark (2007), as it provides a regime of impliit oordination between the authorities. 6 In the Barro-Gordon (1983) framework, instead, there exists a representative private setor. ~ 4 ~

5 suffiient onditions are that the diret spill-over effets must have no strategi signifiane and that the number of instruments must math the number of squared gaps in all authorities payoff funtions. If further all the authorities agree on the objetives, then the bliss points an be also ahieved. In the absene of those onditions, both ooperation and ommitment (the sequene of moves) matter, while the differene between the non-ooperative and the ooperative outome depends on the number of ountries in the monetary union. The authors learly show that the monetary union benefits from fisal authorities ooperation under fisal leadership. The above disussion on the symbiosis result shows that it only holds under speifi assumptions of the model. In the opposite ase, both oordination and timing issues beome relevant, reating a poliy-mix bias (Foresti, 2017). Sine the offiial launh of the EMU, there are a lot of papers that deal with the maroeonomi poliy mix, fisal authorities ooperation, and the sequening of moves in monetary unions. Banerjee (2001) allows for fisal poliies to be subjet to potential time inonsistenies, while omparing different senarios of ommitment and disretion. The author finds that moving from the senario of full disretion to other senarios results in lower inflation and higher expenditure at the expense of lower output for the full ommitment and the fisal ommitment ones, whereas for the monetary ommitment we end up with lower publi spending. Godbillon and Sidiropoulos (2001) show that delegation of fisal poliy to a ounil of ountry representatives and monetary poliy to a ounil of governors is the appropriate institutional design to redue the inflation bias and better stabilize regional idiosynrati supply and demand shoks in a monetary union. Lambertini and Rovelli (2004) show that a vertial oordination problem arises even in an extremely simple setting of a simultaneous-move game in a stati two-ountry monetary-union model, where the two ountries are idential and there are no interonnetions between them. The authors further show that the ommon entral bank prefers national fisal authorities ooperation in minimizing a union-wide welfare funtion that also inludes prie stability. Cavallari and Di Gioahino (2005) show that fisal authorities ooperation leads to favorable outomes for output under demand/supply shoks and for inflation under demand shoks, while overall poliy oordination improves maroeonomi stabilization only under demand shoks. The authors further show that monetary-fisal symbiosis vanishes when there are other poliy goals than ylial stabilization, in partiular ostly poliy instruments, as there must also be agreement on preferenes weights. Della Posta and De Bonis (2009) rejet the symbiosis result in the presene of asymmetri shoks, showing that poliy oordination an be welfare improving even if the authorities have equal targets. Di Bartolomeo and Giuli (2011) also rejet the symbiosis result in a losed-eonomy setting, when there is unertainty about the effetiveness of the poliy instruments. ~ 5 ~

6 Oros and Zimmer (2015) onsider the impat of politial (entral bank) transpareny on the poliy mix in a monetary union under monetary poliy transmission heterogeneity. The authors onlude that when the monetary transmission mehanism is relatively weak, higher monetary unertainty may ontribute to redue inflation expetations, improving maroeonomi performane. Von Hagen and Mundshenk (2003) show that under strit inflation targeting the entral bank ontrols union-wide output gap, while the national fisal authorities determine the distribution of aggregate demand between them, engaging in a purely distributional game with ineffiient outomes unless poliies are oordinated. Uhlig (2003) shows that in the absene of fisal shoks and symmetrial ountries size-wise, all fisal authorities would be better off under a ooperative equilibrium haraterized by a ommon fisal poliy of zero defiits. Ferre (2005) finds that in expansive phases of the eonomy, fisal authorities ooperation leads to a higher defiit, while in Ferre (2008) the author shows that the non-ooperative ase leads to a more volatile unionwide fisal stane. Beetsma and Bovenberg (2005) onsider the impat of fisal authorities ooperation for the aumulation of debt, along with the interation with strutural distortions in labor markets. The authors find that ex-ante poliy oordination among all the authorities an be benefiial. Furthermore, Aoella et. al. (2007b) show that fisal authorities ooperation is benefiial when the labor market distortion is endogenously determined by trade union s strategy, while in Aoella et. al. (2007a) fisal leadership is desirable under a onservative entral banker, rendering fisal poliies oordination preferable. Andersen (2005, 2008) shows that in the fae of aggregate shoks, the fisal authorities underestimate the monetary reation, resulting in a more ounterylial fisal poliy, whereas in the ase of idiosynrati shoks, the monetary response is overestimated, and fisal poliy is insuffiiently ounterylial. Gatti and Wijnbergen (2002) show that, in the event of adverse symmetri output (demand) shoks, the ommon entral bank an impose fisal authorities ooperation under the form of fisal restraint by attahing a reward to the fisal authorities in the form of a disretional, nonstrategi level of the interest rate. There is also a parallel literature that uses miro-founded dynami stohasti general equilibrium (DSGE) models to examine optimal fisal/monetary poliies in a monetary union, where the fous is on transitional dynamis (see, e.g., Beetsma and Jensen, 2005; Gali and Monaelli, 2008; Ferrero, 2009). In a reent paper, Palek and Swanebek (2017) derive the welfare-maximizing (fisal-monetary) poliy response to demand and supply shoks in a two-ountry miro-founded DSGE monetary-union model with finanial fritions, where the ommon nominal interest rate an diretly affet inflation. The authors also allow for inflation to be diretly affeted by fisal poliy. Their analysis orresponds to that of full oordination of monetary and fisal poliies. Literally, the authors state: sine we are interested in the output and inflation dynamis as well as the welfare losses arising from the ost hannel, we do not take into aount any strategi interation between both poliymakers (Palek and Shwanebek, 2017, pp ~ 6 ~

7 6). On the ontrary, we expliitly onsider the strategi poliy interations in a monetary union when the two poliy instruments an diretly affet inflation. Their results are omparable to our regime of fisalmonetary (overall) poliy oordination. Naturally, we ompare our results with the standard ase in the literature that the two poliy instruments annot diretly affet inflation, whih makes them perfet substitutes in the stabilization proess. We an summarize our main results here: (i) the leader authority reats to the follower authority s reation parameter, hene to the follower s preferene parameter, depending on the sign of a speifi ombination of strutural parameters, (ii) the leader authority might hoose not to trade-off its objetives (i.e., ating pro-ylially), (iii) the symbiosis result ollapses at the union level, too, as both the strategi and the fisal regimes matter, (iv) the monetary authority hooses its preferable fisal regime under simultaneous move aording to the same before-mentioned ombination of strutural parameters, (v) the national fisal authorities prefer to oordinate their poliies under idiosynrati shoks for all strategi regimes, (v) fisal authorities ooperation an beome welfare-improving, (vi) the simultaneous-move strategi regime may even emerge as superior to the leadership ones, and (vii) fisal leadership with entralized fisal poliies an beome a superior institutional arrangement even to overall poliy oordination. The next setion presents the baseline model, while Setion 3 desribes the general solution at both the union and national levels for the alternative strategi regimes. In Setion 4, we analyze the poliy mix for all the alternative strategi and fisal regimes. Setion 5 proeeds to a welfare analysis for the two fisal regimes, while Setion 6 presents some results on the omparison among the alternative strategi regimes regarding union-wide pure ylial maroeonomi stabilization. Finally, Setion 7 onludes the paper. 2. The Model We onsider a monetary union onsisted of two idential ountries interonneted via traditional trade links and monetary poliy. We model the monetary union as a losed area, assuming that both ountries have no interonnetions with ountries outside the union. 7 The model is a stati representation of a redued-form New Keynesian model based on an Aggregate Demand (AD) and a Phillips Curve (PC) equation, whih onstitutes a first-order approximation to a DSGE model with monopolisti ompetition and nominal rigidities (see, e.g., Gali, 2008). In partiular, both equations an emerge from a miro-founded model that aptures monopolisti ompetition in produt and labor markets, along with stiky wages (see, 7 This assumption is ommon in this literature. Moreover, the model inludes various exogenous shoks that an be thought of as trade hannels with ountries outside the union. ~ 7 ~

8 e.g., Beetsma and Jensen, 2005; Gali and Monaelli, 2008). The stati representation provides analytial results, whih make the poliy transmission mehanisms tratable and the study of the orresponding interations manageable. This proves partiularly useful in poliy games, where a relatively simple analytial framework is required to allow omparisons of different solution onepts without resorting to numerial simulations. 8 The model is mainly based on Andersen (2005, 2008) extended to inlude a ost hannel of monetary poliy, while it follows the same notation, too. For eah ountry j, the non-poliy blok of equations is given by: y j = δ r (i π j e r j) δ τ (π j π k ) + δ y y k + δ g g j + u j (1) π j = ω y y j + ω g g j + ω i i ε j, (2) where the index k represents the other ountry. All variables represent log-deviations from long-run equilibrium values, apart from the deimal nominal interest rate, i. Thus, π represents inflation, y represents the output gap, while the variable g represents fisal poliy, aptured by the overall fisal stane. We assume that before the shoks both eonomies have balaned budgets. 9 The strutural parameter r j represents the long-run equilibrium real interest rate, whih for simpliity we set equal to zero for both ountries. The variables u j and ε j are independently and identially distributed (i.i.d.-random) demand and supply shoks, respetively, with zero means and onstant varianes. We assume that they both are pure and unorrelated. The inflation differential π j π k represents the real exhange rate and aptures intraunion ompetitiveness (the terms-of-trade effet); 10 in partiular, higher pries for domesti produts shift domesti demand to foreign. Finally, π j e denotes the private setor s (rational) expetation on ountry j s future inflation. Starting with the AD equation (1), all the parameters are positive. In partiular, the parameter δ r aptures the real interest rate elastiity of aggregate demand, while δ g aptures the effetiveness of fisal poliy. The parameters δ τ and δ y apture the interonnetions between the two ountries; in partiular, the effet of ompetitiveness on domesti output and the relative openness of the eonomy, respetively (Ferre, 2008). The former orresponds to a ost spill-over effet, sine higher domesti ativity leads to higher pries and thus makes it possible for foreign partners to inrease their market share, while the latter 8 As quoted in Hughes Hallett et. al. (2011), Blanhard (2009, p. 27) alls for the re-legalization of short-uts and of simple models, in order to improve intuition and ommuniation. 9 This is a trivial assumption, as our model departs from debt onsiderations and fouses on stabilization poliies. Thus, the model does not inlude an expliit government budget onstraint. For a model with suh a onstraint, see, e.g., Beetsma and Bovenberg (1998). 10 As the two ountries form a monetary union, the nominal exhange rate is fixed to unity, whih means that the real exhange rate is equal to their prie ratio. ~ 8 ~

9 orresponds to a demand spill-over effet, sine a domesti fisal expansion benefits trading partners by an inrease in demand for foreign produts. Both parameters are alled trade externalities and may lead to insuffiient stabilization (Andersen, 2005). The inflation differential works as a stabilization mehanism that ompensates for the lak of an independent monetary poliy. For example, if a ountry experienes a negative supply shok that inreases inflation, a real appreiation would derease exports to the other ountry (or to the rest of the union, in a mutli-ountry setting), reduing output demand. This means that the ountry loses in ompetitiveness vis-a-vis the other ountry. However, the resulting redution in demand eventually dereases inflation, thus ating as a stabilization mehanism (see, e.g., Landmann, 2012). Thus, the ompetitiveness hannel works as a fore of automati stabilizers. 11 The analysis does not hange allowing for different onsumption bundles aross member-states (see, e.g., Andersen, 2005). The existene of ountry-speifi Phillips urves means that the law of one prie does not hold (see, e.g., Bofinger and Mayer, 2007). The PC equation (2) represents the short-run Luass aggregate supply equation (see, e.g., Clarida et. al., 1999), whih links ountry-speifi inflation with the output gap. 12 The former an be also diretly affeted by the two poliy instruments, namely the domesti fisal stane and the ommon nominal interest rate. Starting with the output gap, the parameter ω y is assumed to be positive, apturing nominal (prie/wage) rigidities in the eonomy (see, e.g., Clarida et. al., 1999; Gali, 2008; Walsh, 2010). The existene of nominal rigidities provides a rationale for the monetary authority to influene output, as this passes through to inflation. The sign of the parameter for fisal poliy, namely ω g, an be either positive or negative, apturing the diret effet that the plethora of the available fisal instruments may have upon inflation (see, also, Chortareas and Mavrodimitrakis, 2016). Fisal poliy has a positive effet on output and through this a positive effet on inflation. However, following Andersen (2005, p. 5-6), it may also have (temporarily) separate effets on wage (prie) inflation depending on the partiular instrument used. For example, publi expansions finaned by value-added and exise taxes add (temporarily) to the inflationary pressure in the eonomy. However, it is also possible that tax inreases may lead to wage moderation; in partiular, high inome taxes may inrease labor supply ausing a downward pressure on the wage rate (see, e.g., Baxter and King, 1993). Aording to Dixit and Lambertini (2003a), it an also arise via publi investment or a prodution subsidy that raises private produtivity, inreasing the supply of goods. 13 In order to apture standard reasoning on fisal poliy, we follow Andersen (2005, 2008) by assuming that y j g j = δ g δ τ ω g > 0 and π j g j = ω g + ω y δ g > This proedure represents the adjustment of the real exhange rate through inflation differentials. 12 Following equation (2), ountry-speifi inflation does not depend on expeted inflation. We further examine this element on footnote Miro-foundations are provided by Gali and Monaelli (2008) for ω g < 0, and more reently by Palek and Swanebek (2017). ~ 9 ~

10 In our model, we also allow the ommon nominal interest rate to diretly affet inflation, following the ost hannel of monetary poliy effet of Ravenna and Walsh (2006), where ω i > 0 (see, also, Walsh, 2010). The ost hannel of monetary poliy reates a meaningful poliy trade-off for the entral bank without the need for an exogenous ost-push shok. 14 In partiular, the authors assume a finanial intermediary that monopolistially ompetitive firms must borrow from in order to pay for wages in advane. Thus, pries set by firms diretly depend on the ost of borrowing, i.e. the loan rate; e.g., under a high (low) loan rate, pries will be also high (low). Finanial intermediaries operate under perfet ompetition and the loan rate oinides with the basi interest rate set by the entral bank. 15 Moreover, as firms marginal ost is also a funtion of the loan rate, the PC equation depends also diretly on the basi interest rate set by the entral bank. This ost hannel generates a meaningful trade-off between the output gap and inflation, as they will both flutuate in response to supply and demand disturbanes under the optimal poliy. Thus, the authors provide theoretial justifiation for the fat that monetary poliy diretly affets the inflation adjustment equation if nominal interest rate movements diretly affet real marginal osts, whih has been empirially onfirmed (see, e.g., Chowdhury et. al., 2006; Henzel et. al., 2009). Similar to the assumption about fisal poliy, we assume that π j i = ω i δ r ω y < 0 δ r ω y ω i > 0 in order to guarantee that monetary poliy has the usual (expeted) overall effet upon inflation, maintaining the nominal interest rate as a demand-side poliy instrument. Alternative explanations for the (positive) diret effet of the nominal interest rate on inflation are provided by Ismihan and Ozkan (2012) and De Grauwe (2012). The former authors assume that the level of total bank redits affets output supply in a Barro-Gordon (1983) framework, where total bank redits are negatively affeted by the loan rate set by a monopolistially-ompetitive ommerial bank. Thus, the loan rate diretly affets inflation in a positive manner. De Grauwe (2012) let asset (stok) pries to affet both the aggregate demand and supply of a behavioral maroeonomi model. 16 Regarding aggregate supply, an inrease in stok pries makes external risk premia to derease, reduing firms redit osts. As the nominal interest rate affets negatively the stok pries, the former would diretly affet inflation in a positive manner For the importane of the exogenous ost-push shok in reating a meaningful poliy trade-off in the standard New Keynesian model, see Gali (2008, Chapter 5). 15 This means that there is omplete interest rate pass-through. Kobayashi (2008) examines the ase of inomplete interest rate pass-through resulting from real and nominal fritions in finanial markets. 16 De Grauwe (2012) proposes a behavioral maroeonomi model that modifies the standard New Keynesian model mainly in two aspets: (i) it enompasses inertia on the output gap and the inflation rate by inorporating bakward-looking elements, too, and (ii) it departs from rational expetations for forward-looking variables, introduing heuristis, instead. 17 Areosa and Areosa (2016) introdue an inequality hannel through whih the real interest rate an affet the PC equation in an otherwise standard New Keynesian DSGE model, by inorporating unskilled agents with no aess to finanial markets. The authors show that if there is an exess of unskilled agents, inequality rises with the interest rate and inreases inflation. This means that there is a diret positive link between the nominal interest rate and inflation through the inequality hannel. ~ 10 ~

11 In a reent paper, Palek and Shwanebek (2017) examine optimal fisal-monetary poliy in a monetary union under finanial fritions in a two-ountry DSGE model, assuming a ost hannel of monetary poliy, following Ravenna and Walsh (2006). The authors provide miro-foundations for the ountry-speifi Phillips urve (eq. 2), where both poliy instruments an diretly affet inflation. They are interested in the output and inflation dynamis, as well as in the welfare losses arising from the ost hannel of monetary poliy. However, the authors do not impose our assumption π j i < 0, allowing the ommon nominal interest rate to beome a supply-side poliy instrument. Moreover, they also onsider heterogeneous finanial fritions between the two member-states. In our model, this an be aptured by asymmetri supply shoks between the two member-states, as we only deal with disretionary poliies. We an find the desriptive non-poliy blok of equations at the union level by averaging the ountryspeifi equations (1)-(2). We get: y = 1 1 δ y ( δ r i + δ g g + u) (3) π = ω y y + ω g g + ω i i ε, (4) where for every variable x, it follows that x = 1 (x 2 j + x k ). The poliy instruments for the national fisal authorities and the monetary authority are g j, g k and i, respetively. Following Kydland and Presott (1977) and Barro and Gordon (1983), we assume that all the authorities have omplete ontrol over a poliy instrument and preferenes over some variables that an be approximated by a quadrati loss funtion. This methodology is standard in this literature and it is based on Theil s (1956) flexible target approah, where a poliymaker minimizes the inevitable deviations of some targets in the form of a quadrati objetive (loss) funtion under the eonomy s onstraints. The quadrati loss funtion illustrates that objetives are symmetri; i.e., the authorities weight the same either a positive or a negative deviation of a onerned variable from a target value. 18 The authorities loss funtions are given by: L M = 1 2 (π2 + a M y 2 ) (5) L Fj = 1 (g 2 j 2 + a F y 2 j ), (6) 18 Following Aoella et. al. (2013), quadrati funtions are used both beause they are mathematially tratable and beause they enompass useful eonomi properties. As deviations from the target are assoiated with inreasing osts, the marginal rate of substitution between any two target variables is never onstant, depending on the values of the two variables at the speifi point it is omputed. Moreover, quadrati forms an be obtained as seond-order approximations of more omplex funtions (see, e.g., Woodford, 2003). ~ 11 ~

12 where M stands for the Monetary authority and F for the national Fisal authorities. They all target long-run equilibrium values of onerned variables, assumed to equal zero; i.e., they all seek to minimize deviations of their onerned variables from long-run equilibrium. This means that they agree on the steady state of overall optimal poliy (Uhlig, 2003), hene they have non-onfliting objetives. In partiular, we assume that the national fisal authorities share idential preferenes and that they are onerned with the output gap and the deviation from the balaned budget, whereas the ommon entral bank is onerned with the average output gap and inflation in the union. The parameters a M and a F are both positive and represent the weights that the authorities plae on output-gap stabilization, meaning the monetary authority and the fisal authorities, respetively. These weights are relative to the preferene parameters for inflation and the fisal stane, respetively, whih for simpliity we have both set equal to unity. Regarding monetary authority, the larger a M, the more flexible is the inflation targeting approah that the ommon entral bank follows (Svensson, 1997). Naturally, a M < 1.0. The ase of a M = 0 orresponds to strit inflation targeting, where the ommon entral banker is only onerned with stabilizing union-wide inflation. The speifiation of the monetary and the fisal authorities loss funtions, namely equations (5) and (6), follows Uhlig (2003) and Andersen (2008). This set of loss funtions represents a realisti mapping of the atual poliy-making onerns in the EMU (see, also, Chortareas and Mavrodimitrakis, 2017). Following the most reent literature, we inlude eah ountry s fisal stane in the fisal authorities loss funtions, as ountries in the EMU are onstrained by both the SGP and the FC. Thus, the fisal stane is simultaneously a target and an instrument for the national fisal authorities. However, fisal poliymakers are not diretly onerned about inflation, sine the task of ontrolling inflation is delegated to the ommon entral bank. However, the inlusion of a terms-of-trade effet in the aggregate demand equation reates an impliit preferene for inflation stabilization for the national fisal authorities (see, e.g., Andersen, 2005, 2008). Andersen and Spange (2006) show that equation (6) an be derived from a representative household s utility funtion that depends positively on the private onsumption bundle and on the provision of publi goods and negatively on labor supply, where the private onsumption bundle is defined over the onsumption of the domesti and the foreign ommodity. The main objetive of this paper is to investigate the maroeonomi poliy mix in the monetary union we have just desribed that arises from the interation between the ommon entral bank and the two national fisal authorities when the two poliy instruments an also diretly affet the PC equation and when the authorities have non-onfliting but different objetives under alternative assumptions about the ordering of moves. The ordering of moves represents the institutional setting in the monetary union where poliies are being implemented. We analyze the standard one-shot poliy games of simultaneous move, ~ 12 ~

13 fisal and monetary leadership. 19 In all senarios, the time ontext begins with the private setor forming expetations about future inflation rationally and not strategially (Uhlig, 2003); then, demand and supply shoks are realized; finally, the authorities hoose their ontrol instrument in order to ahieve their goals aording to the partiular institutional setting (strategi regime), hene onsidering disretionary poliies. The strategi regime of simultaneous move demands all the authorities to at independently and simultaneously, where the equilibrium is desribed by a Cournot-Nash equilibrium. For the two leadership regimes we assume that the authority that has the lead makes its move before the follower authority, while it takes into aount the way the latter will reat to its hoie of the poliy instrument. These Stakelberg games are solved using bakward indution and the equilibrium rests on sub-game perfetion. The fisal leadership regime requires the two fisal authorities to lead the game with the ommon entral bank, while in the monetary leadership regime the monetary authority has the lead and the national fisal authorities follow. It follows that poliies are time-onsistent, hene π e j = π e = 0 (see, e.g., Uhlig, 2003; Andersen, 2008; among others). 20 In any ase, we assume that the national fisal authorities move simultaneously. 21 The model also assumes that there is no unertainty about strutural parameters between the two fisal authorities and between them and the monetary authority. 22 In every strategi regime we also onsider the ase of fisal authorities ooperation, where the national fisal authorities minimize a joint loss funtion aording to a straightforward utilitarian riterion that orresponds to simply averaging the two loss funtions given by equation (6). This is ommon in all papers in the literature that onsider an interonnetion between the ountries that form a monetary union (see, e.g., Debrun, 2000; Dixit and Lambertini, 2001, 2003a; Cavallari and Di Gioahino, 2005; Ferre, 2008, 2012; Andersen, 2005, 2008; among others). The joint loss funtion is given by: L F = 1 (L 2 F j + L Fk ) = 1 [g 4 j 2 + g 2 k + a F (y 2 j + y 2 k )] (7) We also investigate the ase of fisal-monetary (overall) poliy oordination, where the monetary authority and the two national fisal authorities hoose their poliy instruments so as to ahieve their joint objetives. In partiular, we reate a loss funtion that is the sum of eah authority s loss funtion, namely: 19 For a novel framework that generalizes the time struture through players rational inattention that reates rigidities in the timing of moves and makes the game more dynami and asynhronous, see Libih and Stehlik (2010). 20 We have already inorporated this result in equation (4). It needs rational expetations on the part of the private setor, the private setor to form its expetations prior to the shoks realization, and all the authorities to target long-run equilibrium values, in order for poliies to be time-onsistent. We follow Uhlig (2003) by using this result at the beginning, rather than deriving it as the last step of the alulation. 21 For models where the national fisal authorities in a monetary union do not move simultaneously but sequentially, see Chortareas and Mavrodimitrakis (2016, 2017). 22 We an think of this game as a regime that is in plae for long horizon; then, repeated play of this game would reveal the exat strutural parameters (Lane, 2003). ~ 13 ~

14 L OC = L M (L F j + L Fk ) = 1 2 [π (g j 2 + g k 2 ) + a M y a F(y j 2 + y k 2 )], (8) where OC stands for Overall Coordination. We follow Flotho (2012) by adding the mean of the fisal authorities loss funtions. Naturally, this joint loss funtion inludes both union-wide and ountry-speifi variables, while all spillover effets are fully internalized. We also define the soial planner s loss funtion by assuming that it enompasses the union-wide variables that the authorities are onerned with. For this speifiation, we follow Beetsma and Bovenberg (1998) and mainly Andersen (2008). We assume the following soial loss funtion 23 for the monetary union: L S = 1 2 (π2 + b S g 2 + a S y 2 ), (9) where S stands for Soiety (or the Soial planner ), and a S and b S are the weights that soiety plaes upon union-wide output gap and fisal stane, respetively, relative to inflation. Thus, the soial planner minimizes equation (9) subjet to the non-poliy blok of equations for the monetary union, namely equations (3) and (4). Andersen (2008) uses the above loss funtion in order to examine fisal-monetary (overall) poliy oordination in a monetary union, as the two ases deliver the same equilibrium solutions for the union-wide maroeonomi variables. Equation (9) an be also used as a welfare riterion for the omparison of the alternative strategi regimes. We onlude this setion by omputing the redued form ountry-speifi aggregate demand equations with respet to the poliy instruments and shoks. 24 We end up with: y j = Z i i + Z g g j + Z g g k + Z ε (ε j ε k ) + Z u u j + Z u u k, (10) where Z i = y j = δ r, Z i 1 δ g = y j y Z ε = y j ε = δ τ 1+δ y +2δ τ ω y, Z u = y j u j = = δ g δ τ ω g +δ τ (ω g δ y +ω y δ g ) g j (1 δ y )(1+δ y +2δ τ ω y ), Z g = y j 1+δ τ ω y (1 δ y )(1+δ y +2δ τ ω y ), Z u = y j u k = = δ τ(ω g +ω y δ g )+δ y (δ g δ τ ω g ) g k (1 δ y )(1+δ y +2δ τ ω y ) δ y +δ τ ω y. Equation (10) (1 δ y )(1+δ y +2δ τ ω y ) is a redued form equation that defines a target variable, namely ountry-speifi output demand, with respet to the poliy instruments and exogenous shoks. All the Z parameters are ountry-speifi output demand elastiities relative to the three poliy instruments (Z i, Z g, Z g ), to domesti and foreign demand shoks (Z u, Z u ) and to supply shoks asymmetries (Z ε ), where the latter is presented in absolute terms and, 23 Similar loss funtions an be also found in DSGE models that examine optimal fisal-monetary poliies in a monetary union, suh as Gali and Monaelli (2008), Ferrero (2009), and more reently Palek and Shwanebek (2017). In all models, soiety s loss funtion is derived from the representative household s utility funtion following the methodology of Woodford (2003). In the EMU ontext, we an think of the soial planner as the European Commission. 24 We solve together the two aggregate demand equations (eq. 1) for both ountries. We then subtrat the two PC equations (eq. 2) to reate π j π k, and we inorporate the latter to both the aggregate demand equations, whih we solve together. ~ 14 ~

15 defined as ε j ε k. It is straightforward that under 1 δ y > 0, all the Z parameters are positive. The orresponding ones that refer to the poliy instruments define poliy effetiveness, as long as they are different to zero. The importane of the interonnetions for those elastiities is profound. First, domesti output demand is diretly affeted by foreign demand shoks, by supply shoks asymmetries and by foreign fisal poliy only through the interonnetions; in the opposite ase of δ y = δ τ = 0, domesti aggregate demand is only affeted by domesti demand shoks, while supply shoks asymmetries are present only beause of the terms-of-trade effet. Seond, both domesti and foreign fisal poliy affet domesti aggregate demand. The former s diret effet is positive, while it affets it negatively through the terms-of-trade effet. The foreign fisal poliy affets positively domesti output through both the trade and the terms-of-trade effets. Third, all the above elastiities are independent of the ost hannel of monetary poliy, as it is assumed to be the same for the two ountries. This means that it does not affet the terms-of-trade effet and thus it annot affet aggregate demand The General Solution at the Union Level The monetary authority and the national fisal authorities have two targets but only one instrument: (i) the monetary authority ontrols the ommon nominal interest rate, i, to minimize its loss funtion (eq. 5), and (ii) eah national fisal authority ontrols its fisal stane, g j, in order to minimize its loss funtion (eq. 6). Both problems follow Theil s (1956) flexible target approah. Eah authority hooses its instrument of ontrol by equating the marginal rate of transformation with the marginal rate of substitution between the two target variables, where the latter is also based on the authorities preferene parameters, a M and a F. Eah authority s problem ends up with a orresponding poliy rule that ombines the onerned maroeonomi variables. The ountry-speifi fisal rule for the national fisal authorities under deentralization is given by: g j = φ gj y j, (11) where φ gj = a F dy j dg j is the ountry-speifi fisal reation parameter. The symmetry assumption for the two member-states ensures that dy j dg j = dy k dg k, whih leads to the two fisal rules being symmetri, too, meaning 25 Supply shoks asymmetries ould also represent a ost hannel heterogeneity between the two member-states, refleting possible differenes in the degree of ompetition in finanial markets. In this sense, the PC would depend on the loan rate, i l, as i lj = i + v j, where v j is an i.i.d. ost-push shok with zero mean and onstant variane. Then, it follows that ε j = ω i v j and ε j ε k = ω i (v j v k ). ~ 15 ~

16 φ gj = φ gk. For the entralized ase, where both fisal authorities minimize equation (7), the first order ondition beomes: g j + a F ( dy j dg j y j + dy k dg j y k ) = 0 (12) At the union level, the two rules an be found to be: MR: y = φ π π (13) FR: g = φ g y, (14) where MR stands for Monetary Rule and FR for Fisal Rule, and φ π = 1 a M dπ di dy di. The parameters φ π and φ g orrespond to the monetary and the (union-wide) fisal reation parameters, respetively. For the deentralized fisal regime, it is straightforward that φ gj = φ g, while for the entralized ase, we get φ g = a F ( dy j dg j + dy j dg k ). Both rules represent losed-form equilibrium solutions that show how both monetary and union-wide fisal poliy reat to a hange in the authorities onerned maroeonomi variables. Both reation parameters are funtions of the model s strutural (δ r, δ τ, δ y, δ g, ω y, ω i, ω g ) and preferene (a M, a F ) parameters, while they an be of either sign; in partiular, a possible positive sign defines a tradeoff between the authorities target variables. They depend upon the ordering of moves, namely the three strategi regimes of fisal/monetary leadership and simultaneous move, and also on whether fisal poliies are oordinated or not. At the union level, the two desriptive equations, namely the AD equation (3) and the PC equation (4), along with the monetary rule (eq. 13) and the fisal rule (eq. 14) reate a 4 4 system of (log)-linear equations, with unknowns the inflation rate, the output gap, the fisal stane and the ommon nominal interest rate. The two former variables represent the target variables, while the two latter the poliy instruments, although ountry-speifi fisal stanes are both targets and instruments, following the fisal authorities loss funtions (eq. 6). This assumption is responsible for the poliy onflit (see, e.g., Dixit and Lambertini, 2003a; Kempf and von Thadden, 2013). Solving all four equations simultaneously, we end up with the following equilibrium solutions: π = 1 Ω (ω iu δ r ε) (15) y = φ π Ω (ω iu δ r ε) (16) ~ 16 ~

17 where: g = φ gφ π Ω (ω iu δ r ε) (17) i = [1+(ω y ω g φ g )φ π ]u (1 δ y +δ g φ g )φ π ε, (18) Ω Ω = δ r [1 + (ω y ω g φ g )φ π ] (1 δ y + δ g φ g )ω i φ π = = δ r + [ω y δ r (1 δ y )ω i ]φ π (δ g ω i + δ r ω g )φ g φ π (19) We all Ω (eq. 19) the referene parameter, as it refers to a partiular institutional arrangement; thus, it aptures differenes on equilibrium solutions of the union-wide maroeonomi variables aross strategi and fisal regimes. Following the union-wide equilibrium solutions, namely equations (15)-(18), we an extrat some important remarks. Remark 1: The ost hannel of monetary poliy makes union-wide (pure) demand shoks not to be fully stabilized at the union level. The vast literature does not take into onsideration the ost hannel of monetary poliy. In this speial ase, union-wide pure demand shoks are fully stabilized at the union level. Countering pure demand shoks pushes both the output gap and inflation in the same diretion, as there is no trade-off between those two. Thus, the monetary authority sueeds in fully-stabilizing pure demand shoks (i = 1 u) and the unionwide fisal stane is passive. 26 This is the divine oinidene property of the standard losed-eonomy δ r New Keynesian model (Blanhard and Gali, 2007), whih illustrates the optimality of the strit inflation targeting monetary poliy framework (see, also, Clarida et. al, 1999). The irrelevane of demand shoks at the union level in a miro-founded monetary union model is also demonstrated by Beetsma and Jensen (2005). The existene of the ost hannel of monetary poliy, whih mainly intends to apture the existene of a finanial setor in the eonomy in the most simple way, makes demand shoks not to be fully stabilized at the union level by reating a trade-off between inflation and output gap, even in the absene of supply shoks, similar to Ravenna and Walsh (2006) (see, also, Palek and Shwanebek, 2017). In this ase, the 26 However, this does not mean that the ountry-speifi fisal poliies are passive. It only means that their reations either anel out at the union level or are ountered by the monetary authority. ~ 17 ~

18 union-wide fisal stane is not passive, whih means that the national fisal authorities supplement the monetary authority in the stabilization proess. Andersen (2008) onsiders shoks that are not pure, in the sense that they an simultaneously affet demand and supply in various ways. However, pure demand shoks emerge as a speial ase, where his result does not differ from the literature. Cavallari and Di Gioahino (2005), Lambertini and Rovelli (2004) and Oros and Zimmer (2015) ontrast from the literature in this aspet, as they all assume interest-rate smoothing on the part of the monetary authority, whih orresponds to the inlusion of the square of the ommon nominal interest rate in the monetary authority s loss funtion. 27 Beause of interest-rate smoothing, the monetary reation to shoks is milder, leaving demand shoks partially stabilized. Remark 2: At the union level, all maroeonomi variables are affeted by union-wide demand and supply shoks and not by shoks asymmetries. Thus, idiosynrati shoks are fully stabilized at the union level. Following equations (17) and (18), the two poliy instruments at the union level do not reat to shoks asymmetries. In spite of the ordering of moves, we will see that the two national fisal authorities respond to this shoks in exatly the opposite way, as the two ountries are idential; hene, their responses anel out at the union level. The ommon entral bank reats neither in the simultaneous move nor in the fisal leadership regime, as there is no average shok to the monetary union, whereas in the ase of monetary leadership it does not reat beause it antiipates that the reations of the fisal authorities will be offset. In a previous paper, we have shown that asymmetri demand shoks pass through to the union-wide maroeonomi variables when the two national fisal authorities follow a sequential game, hene they do not move simultaneously, and fisal poliy an diretly affet inflation (Chortareas and Mavrodimitrakis, 2016). Remark 3: If the two poliy instruments are not perfet substitutes in the stabilization proess, then the defiit bias result does not hold and fisal poliy beomes non-neutral at the union level. The standard ase in the vast literature that orresponds to a speial ase in our model is when the two poliy instruments do not diretly affet inflation, whih means that they are perfet substitutes in the 27 For an interest-rate smoothing entral bank in a losed-eonomy setting, see, e.g., Buti et. al. (2001). ~ 18 ~