The Optimal Monetary and Fiscal Policy Mix in a Financially Heterogeneous Monetary Union

Transcription

1 The Optimal Monetary and Fisal Poliy Mix in a Finanially Heterogeneous Monetary Union Jakob Palek y February 4, 5 Abstrat Reent work on nanial fritions in New Keynesian models suggest that there is a sizable spread between the risk-less interest rate and the borrowing rate. We analyze the optimal poliy mix of monetary and sal authorities in a urreny union with a ountry-spei redit spread by introduing a ost hannel di erential. The ost hannel dereases the e ieny of monetary poliy and inreases the need for sal stabilization. We show that the importane of sal poliy in stabilizing shoks inreases, when there is a gap in the in ation di erential due to a relative shok, an idiosynrati shok or a redit spread di erential. The welfare losses will be inreasing (dereasing) in the size of the ost hannel, if the nominal interest rate is a demand- (supply-) side instrument. JEL-Classi ation: E 3, E 5, E 6, E 63. Keywords: ost hannel; nanial fritions; redit spreads; optimal monetary poliy; sal poliy; monetary union. Aknowledgements: I gratefully aknowledge helpful omments from Johen Mihaelis and Benjamin Shwanebek. y Department of Eonomis, University of Kassel, Nora-Platiel-Str. 4, D-347 Kassel, Germany; Tel.: + 49 () ; Fax: + 49 () ; palek@uni-kassel.de.

2 Introdution The onventional wisdom on the optimal poliy mix in a monetary union advoates monetary over sal poliy in stabilizing the union eonomy (see, for example, Beetsma and Jensen, 5, Gali and Monaelli, 8). Suh New Keynesian models typially assume that the riskless interest rate and the borrowing rate oinide. However, reent literature on the maroeonomi impliations of nanial fritions has shown that signifiant spreads do exist. This an be beause of information asymmetries between lenders and borrowers, ostly veri ation of nanial ontrats, bankrupties, ontagions et. (see, e.g., Carlstrom et al., ; Lombardo and MAdam, ; Brunnermeier et al., 3; Brzoza-Brzezina et al., 3). Espeially "tighter" nanial onditions inrease the size of these redit spreads whih have important impliations for the design and the e ieny of monetary poliy (see Cúrdia and Woodford,, and De Fiore and Tristani, 3). In this paper, we inorporate a ountry-spei spread between the riskless interest rate and the borrowing rate by introduing a ost hannel di erential. Using the ost hannel approah is isomorphi to a model where the redit spread ours due to a ollateral onstraint imposed on entrepreneurs (see Carlstrom et al., ). A ost hannel arises when rms marginal ost diretly depends on the nominal interest rate. This may be the ase as there are liquidity onstraints in the fator markets or ertain nanial fritions. If rms need to nane their operations by borrowing funds from nanial intermediaries, any hange in the borrowing rate will translate into hanges in the rms marginal ost and hene their optimal prie. This supply-side e et therefore lowers the e ieny of the monetary stabilization tool. Moreover, if the osts of nanial intermediation are not idential aross ountries, the redit spreads will be ountry-spei and so will the pass-through of union-wide (aggregate) shoks. This heterogeneity further ompliates the ondut of the interest rate poliy and lowers the pro ieny of the entral bank to at as a shok stabilizer even more. Given the fat that there is only one monetary poliy instrument in a urreny union, the deline in the e ieny of monetary poliy would indue large welfare losses, if the entral bank was the sole poliymaker responsible for stabilizing the eonomy. However, with national sal instruments available, we show that not only the derease in monetary e ieny an be (partially) ompensated, but also the ost hannel di erential an be treated appropriately by the use of the relative sal instrument. When the soure of the eonomi disturbane is a relative or an idiosynrati shok, the advantages of having national instruments inrease immediately as well. The ipside of the oin however, is that the use of government spending as a stabilization tool indues a welfare loss per se. A growing number of empirial studies estimate the extent of the interest rate e et

3 on marginal ost in the U.S. and the Euro area. Chowdhury et al. (6) nd the range of the ost hannel oe ient to lie approximately between. (Frane),.3 (the U.S.) and.5 (Italy). This is in aordane with estimates by Ravenna and Walsh (6) who nd a ost hannel of.76 for the U.S. Tillmann (8) and Henzel et al. (9) also provide supportive evidene for a signi ant ost hannel in the Euro area. Tillmann (9a) nds that the oe ient for the U.S. follows a U-shaped pattern. The ost hannel was most important in the pre-volker era and less important in the Volker-Greenspan period. De Fiore and Tristani (3) argue that the ost hannel gained quantitative importane during the reent nanial risis. From all these studies we onlude the ost hannel rst of all is quantitative important and seondly, that it varies aross ountries and over time. As there is a manageable amount of theoretial literature on the ost hannel, it is relatively straightforward to give a review in the following. Ravenna and Walsh (6) are the rst to implement the ost hannel in the New Keynesian framework of a losed eonomy. They show that under optimal monetary poliy, the output gap and in ation are allowed to utuate in response to both produtivity and demand shoks. Tillmann (9b) introdues unertainty about the true size of the ost hannel to the model of Ravenna and Walsh (6). With an unertain ost hannel, the monetary authority tends to overestimate the ost-push e et of an interest rate hike whih leads to a less aggressive interest rate response. Mihaelis and Palek (4) study the optimal monetary poliy in a urreny union with a ost hannel di erential and fous on demand shoks. The ost hannel makes monetary poliy less e etive in ombating in ation. On the one hand, the optimal response is a stronger use of the interest rate instrument. On the other hand, the larger the ost hannel di erential, the less aggressive will the optimal monetary poliy be. Lam (), Demirel (3) as well as Mihaelis and Palek (4) show that the value of a ommitment tehnology of monetary poliy is inreasing in the size of the ost hannel. Our model is losest to the framework of Mihaelis and Palek (4), but we di er by the expliit modelling of the publi setor and the fous on ost-push shoks. Sine the reation of the European Monetary Union (EMU), a large number of researhes investigated the role and interation of the entral bank and sal authorities within the urreny union. One part of the literature fouses on strategi interation between poliymakers: Dixit and Lambertini (, 3) study the poliy mix in a game theoretial framework, when the (adho) objetive funtion between the poliymakers di ers. Disagreement on a ommon objetive leads to an ine ient in ation/output outome. Agreement on an ideal level of output and in ation leads to ideal outomes, irrespetive of whih authority moves rst and despite any disagreement on the relative weights of the target variables. Andersen (5) studies the poliy-mix problem when the entral bank follows a strit in ation targeting poliy and sal poliymakers at 3

4 strategially. He nds that there are large oordination problems with respet to aggregate shoks whih inrease the need of poliy oordination. Badarau and Levieuge (3) analyze various poliy-mix senarios in a monetary union with nanial heterogeneity. In their setup, the entral bank ats as a leader while sal poliies follow in a oordinated or non-oordinated manner. A entralized monetary poliy should fous on stabilizing the union in ation rate rather than on the in ation di erential. Fisal oordination is ounterprodutive when monetary poliy is implemented regardless of the government s behavior. Sánhez (3) examines monetary stabilization in a urreny union in an open-eonomy framework where the entral bank interats with national sal poliies as well as wage-setting trade unions. In the event of an adverse union-wide supply shok, free-rider problems arise as eah government aims at mitigating the eonomi onsequenes on the domesti eonomy, leading to larger government de its. To remedy this problem, the entral bank is more aggressive in its interest rate response. Wage bargaining is found to dampen the resulting higher interest rate volatility by reduing the free rider problem. Note that all these studies lak a mirofounded welfare funtion in order to study the optimal poliy mix. Another strand of literature examines the joint optimization by monetary and sal authorities in the ontext of mirofounded models with derived loss funtions: Beetsma and Jensen (5) onsider the optimal poliy mix between sal and monetary poliy in a two-ountry version of a urreny union. The roles of the poliymakers are learut. Monetary poliy should stabilize the aggregate eonomy while sal poliy ought to be utilized for stabilizing the national eonomies. This result is on rmed by Gali and Monaelli (8) who study the poliy mix in a urreny union made up of a ontinuum of small open eonomies. Ferrero (9) goes one step further by introduing a government budget onstraint. He shows that a balaned budget rule generates welfare losses. Allowing for variations in government debt instead, is a superior poliy. Kirsanova et al. (7) also onsider a government budget onstraint but fous on simple sal poliy rules rather than optimal sal poliy. The use of sal poliy as a stabilization tool does not harm the longer term objetive of keeping publi debt under ontrol. Leith and Wren-Lewis () examine the interations between poliymakers in response to shoks in government debt. When the entral bank an ommit, the adjustment of reduing debt is undertaken largely by the sal authorities. When monetary poliy optimizes in a disretionary manner, reduing debts involves ostly interest rate adjustments. In this paper we show that the optimal poliy mix depends ritially on the size of the ost hannel (redit spread). The emergene of the ost hannel makes the entral bank generally less aggressive sine the sal authority supports the monetary poliymaker in stabilizing maroeonomi utuations. The larger the ost hannel, the smaller the interest rate response and the stronger the sal reation must be. Fisal poliy gains 4

5 even greater importane when an in ation di erential ours due to a relative shok, an idiosynrati shok or a ost hannel di erential. The welfare losses will be inreasing (dereasing) by the extent of the ost hannel s strength, if the nominal interest rate is a demand- (supply-) side instrument. The organization of the paper is as follows. In Setion we outline our model; the building bloks are the IS relation, the government budget onstraint and the Phillips urve. Setion 3 frames the joint poliy problem of the monetary and sal authority. In Setion 4, we present and disuss the in ation and output dynamis of various shoks. As our analysis will show, the nominal interest rate may turn into a supplyside instrument in the presene of a ost hannel. In Setion 5 we therefore disuss the determinants of this feature. Setion 6 ompares the in ation/output dynamis of shoks and the welfare onsequenes of optimal poliy under disretion with optimal poliy under ommitment. Setion 7 onludes. The Model Our model is a two-ountry version of a monetary union, extended to inlude a publi setor where government spending is naned either by lump-sum or distortionary taxes. Besides the union monetary poliy, the national sal poliies at as additional stabilization tools. Hene, sal authorities may vary government spending when faing shoks. Goods markets are haraterized by monopolisti ompetition and prie rigidity. All goods are traded and labor serves as the only prodution fator. Besides these New Keynesian features, we inorporate ountry-spei ost hannels as done by Mihaelis and Palek (4).. Optimal Consumption Choies There is a ontinuum of households in the union on the interval [; ]. The population of the segment [; n) belongs to (H)ome, while the population of [n; ] belongs to (F)oreign. The representative in nitely-lived household j will seek to maximize the following objetive funtion " X E t (C j t ) + (G t) t= # (L j t) + ; () + where [; ] is the disount fator, is the inverse of the intertemporal elastiity of substitution, and is the inverse Frish elastiity of labor supply. C j t, G t, L j t denote, respetively, private onsumption, publi onsumption and hours worked while the pa- 5

6 rameter [; ) measures the relative weight attahed to government spending. More preisely, the private omposite onsumption index is de ned as C j t " C j n H;t C j F;t n n ( n) n n # ; () where C j H;t and Cj F;t are the Home and Foreign private onsumption indies given by C j H;t " n " Z n # " " " Z # " C j t (h) " " dh ; C j F;t " " C j t (f) " " df ; (3) n n where " > is the elastiity of substitution between any two varieties. For publi onsumption, we assume that the national governments only purhase goods produed in their own ountry. The CES funtions for publi onsumption in ountries H and F are given by G H;t " Z # " " " n " Z # " G t (h) " " " " dh ; G F;t G t (f) " " df : (4) n n n There are no trade barriers and preferenes are assumed to be idential aross ountries. Therefore, absolute purhasing power parity holds and the onsumer prie indies are idential in H and F : P t = Pt H = Pt F : The onsumer prie index is given by P t = (P H;t ) n (P F;t ) n ; where P H;t = R n P n t(h) " dh h " R and P F;t = n P n t(f) " df are the produer pries in H and F, respetively: Let us de ne the terms of trade as the ratio of the Foreign produer prie index to the Home produer prie index: Q t = P F;t =P H;t : Furthermore, we assume perfet onsumption risk-sharing aross households, both within and aross ountries. The derivation of total demands for goods h and f onsists of ve steps: First, households divide their budget between savings and onsumption. The seond step implies solving the optimal alloation between Home and Foreign goods. Third, households deide on the optimal onsumption hoie between brands. This yields households demands for the individual goods, C j t (h) and C j t (f): Third, eah government hooses optimally the alloation of total publi onsumption expenditures among varieties produed in its own ountry, whih yields government s demands for the individual goods, G t (h) and G t (f). Finally, by aggregating onsumption over all households (C W t R Cj t dj) and ombining private and publi demands, the total demands for goods h and f are given by i " 6

7 " " Pt (h) Y t (h) = Q t n Ct W Pt (f) + G t (h); Y t (f) = Qt n Ct W + G t (f): (5) P H;t The demand for Home (Foreign) goods is inreasing (dereasing) in the terms of trade whih is the well-known open eonomy demand swithing e et. Though, there is no interation with publi spending sine governments onsume only domestially produed goods. Using the appropriate prodution indies, aggregate demands an be written as Yt H = Q t n Ct W + G H t ; Yt F P F;t = Q n t C W t + G F t: (6) In a ost hannel environment, there are liquidity onstraints for rms in the fator market. Firms have to pay for prodution fators before produt revenues are available. Thus, it is assumed that households engage in the asset market before the goods market opens. At the beginning of period t; the representative agent in ountry i has ash holdings Mt i, reeives wage inome Wt i L i t( i t) whih an be used as a mean of payment and is taxed with a tax rate i t (; ) if taxation is distortionary ( = ; see below). This ash payo is used for depositing funds Dt i at nanial intermediaries suh that the remaining ash balanes are equal to Mt i + Wt i L i t( i t) Dt i when leaving the asset market. Hene, the agent faes the following ash-in-advane onstraint in the goods market P t C W t M i t + W i t L i t( i t) D i t: (7) At the end of the period, agents reeive pro t from rms i t and get the deposits plus interest bak. Hene, the budget onstraint is given by P t Ct W + Dt i + Mt i R t Dt i + Mt i + Wt i L i t( i t) + i t P i;t Tt i i t (8) where R t is the gross nominal interest rate set by the entral bank, and T i t and i t are two types of lump-sum taxes. Let us shortly desribe our modelling approah of the way taxes are levied in general. We assume that there are two possible kinds of taxes households have to pay: If taxes are olleted in a lump-sum way, the dummy variable ( ) will be swithed on (o ). If taxation is distortionary, the dummy variable ( ) will be swithed o (on). The representative household in ountry i maximizes utility (), subjet to the ashin-advane onstraint (7) and the budget onstraint (8). By rearranging the resulting rst-order onditions, we get the Euler equation and labor supply deision respetively 7

8 = R t E t C W t C W t+ Pt P t+ L i t C W t = W t i ( i P t): (9) t Before we proeed, some simplifying notation is useful. Variables written in lower ase letters denote the log of the orresponding variable (i.e., x t ln X t ), while a "^" symbol (e.g. bx t ln(x t =X)) is used to denote the perentage deviation of X t from its steadystate value X. Moreover, an aggregate (union) variable x w t is de ned as the weighted average of the national variables, x W t nx H t + ( n)x F t, while the relative variable x R t is de ned as x R t x H t x F t. The log-linearized versions of (9) an be written as b W t = E t b W t+ brt E t W t+ () b i t + bw i t bp W;t = b l i t + b W t ; () where the aggregate produer prie equals the onsumer pries bp W;t nbp H;t + ( n)bp F;t = bp t ; and onsumer (and produer) prie in ation is de ned as i t bp i;t bp i;t : Furthermore, is de ned as follows:. Finally, let us log-linearize the aggregate demand funtions (6) and substitute aggregate onsumption by the Euler equation () in order to get the national IS-urves i by t H = h( n)q t + E t b W t+ brt E t W t+ + ( )bg t H + u H t () h i by t F = nq t + E t b W t+ brt E t W t+ + ( )bg t F + u F t ; (3) where C is the private onsumption share. Besides, we have added a ountryspei demand shok, whih is assumed to follow an AR() proess, u i t = u u i t + i u;t; Y where i u;t is a zero mean white noise proess, and u [; ].. The Government Budget Constraint The government budget onstraint in ountry i is given by P i;t G i t + i W i t L i t = i tw i t L i t + P i;t T i t + i t; (4) 8

9 where i is a steady-state employment subsidy. We follow Rotemberg and Woodford (997) and large parts of the literature by assuming that this steady-state subsidy is used to o set the distortions by monopolisti ompetition, distortionary taxation and the ost hannel. We assume that the steady-state subsidy is naned by the lump-sum tax i t, so that i Wt i L i t = i t. Given this assumption, the government budget onstraint an be written in real terms as W i t G i t = i t L i t + Tt i ; (5) P i;t and log-linearized as bg t i = b i t + bw t i bp i;t + b lt i + bt i t: (6) Substituting the labor supply deision () allows us to eliminate the nominal wage. Assuming that prodution is linear in labor (see (9) below), the national government budget onstraints an be written as.3 Firms bg H t = ( + )b H t + ( + )by H t + b w t + ( n)q t + bt H t (7) bg F t = ( + )b F t + ( + )by F t + b w t nq t + bt F t : (8) There is a ontinuum of rms of measure n in ountry H and of measure n in ountry F. Eah rm in ountry i produes a variety of the onsumption good i using a linear tehnology of the form by t i = b lt: i (9) The adjustment of pries follows the standard treatment of staggered pries based on Calvo (983). Only a fration i of rms an adjust pries eah period. Assuming that the steady state is haraterized by zero in ation in both ountries, the evolution of the produer in ation rate in region i is given by the marginal ost based (log-linearized) Phillips urve: i t = E t i t+ + i m i t + e i t; () where the omposite parameter i is given by i ( i )( i ) (see, e.g, Gali, 8). i Analogial to the assumption on the properties of the demand shok, the exogenous ost-push shok, e i t, is assumed to be an AR() proess, e i t = e e i t + i e;t, where i e;t is a zero mean white noise proess, and e [; ]. In a ost hannel environment, rms have to pay the wage bill before they enter 9

10 the goods market. Households deposit funds at the beginning of the period at nanial intermediaries who supply loans to rms at the nominal interest rate R l t: For simpliity we an approximate the lending rate R l t with the poliy-ontrolled risk-free interest rate R t. Any wedge between these two interest rates will be aptured by the parameter z i, whih measures the strength of the ountry-spei ost hannel. After goods have been produed and sold in the goods market, rms repay loans at the end of the period. Hene, the nominal interest rate enters the real marginal osts m i t = bw i t bp i;t + z i b Rt : () Real marginal osts are linear in the real wage and inreasing in the nominal interest rate. Note that it is not the real interest rate whih enters into the rms real marginal osts. The expeted in ation rate does not matter sine loans are assumed to be granted and repaid within a period. We proeed by eliminating the nominal wage with the help of equation (). Then, we insert the resulting equation into the original Phillips urve () and use the prodution funtion (9) to derive the following prie adjustment relations for Home and Foreign: H t = E t H t+ + H by H t + b W t + b H t + ( n)q t + z H b Rt + e H t () F t = E t F t+ + F by F t + b W t + b F t nq t + z F b Rt + e F t : (3) Finally, we substitue b i t by the government budget onstraints (7) and (8) in order to derive the national Phillips urves H t = E t H t+ + +e H t F t = E t F t+ + +e F t : H + ( )by H t + b W t + ( n)q t + bg H t F ( + )by t F + b W t nq t + bg t F + F z F Rt b + H z H b Rt Here, there are two additional arguments, b R t and, in the ase of distortionary taxation ( = ), bg i t, besides the standard features of a two-ountry Phillips urve. Positive government spending will have in ationary e ets via the supply side, sine an inrease in bg i t has to be naned by an appropriate inrease in labor inome tax revenues (see (5)). This inrease works analogially to a standard ost-push shok. The demand e et of an inrease in government spending - aggregate demand, prodution, employ- (4) (5)

11 ment, wages, real marginal ost and thus pries rise - works in the same diretion as long as the PC-urve is positively sloped ( > ), whih is the ase for all reasonable parameter onstellations. Hene, the total e et of an inrease in government spending on urrent in ation is de nitely positive. On the ontrary, if taxation is only lump-sum ( = ), there will be no supply-side e ets of a rise in government spending. Then, an inrease in bg t i only shifts the IS-urve and not the Phillips urve. Thus, we an summarize that the in ationary e ets of sal poliy are larger in the ase of distortionary taxation. An inrease in the entral bank interest rate above its steady-state value leads to a rise in real marginal osts und thus to a rise in the urrent in ation rate above its steady-state value. For H z H > F z F, the inrease in H t exeeds the inrease in F t : a positive in ation di erential R t H t F t > emerges. The demand e et of a higher interest rate - onsumption, prodution, employment, wages, real marginal osts and thus pries deline - works in the opposite diretion. Therefore, the overall e et of a higher interest rate on urrent in ation is a priori ambiguous. 3 Framing the Poliy Problem In this setion we desribe the nature of the optimal disretionary poliy and the optimal ommitment poliy by the monetary and sal authority. Following Gali and Monaelli (8) and Beetsma and Jensen (5), our analysis fouses on the ase of full optimization, i.e. the ommon sal-monetary regime hooses jointly the union-wide nominal interest rate R b t and the size of national government spending bg t i to maximize the utility of the representative household given by (). This ase of a entralized single poliymaker orresponds to that of full oordination of monetary and sal authorities. Sine we are interested in the output and in ation dynamis as well as the welfare losses arising from the ost hannel (di erential), we do not take into aount any strategi interation between both poliymakers (for an analysis of this topi, see Badarau and Levieuge, 3, or Sánhez, 3, among others). Instead, we are interested in the hange of the optimal poliy mix when monetary poliy beomes less e etive by the presene of a ost hannel (di erential).

12 3. Welfare Objetive We obtain the objetive funtion of the single poliymaker from a seond-order Taylor expansion of () around the deterministi steady state (see Appendix B for details): ( ) X E t t + t:i:p: + o k k 3 ; (6) t= where t:i:p: stands for terms independent of poliy and o (k k 3 ) represents terms of order three and higher. The per-period deadweight loss funtion t is given by t = b W h t + n by t H i + ( n) by F t + h n bg t H i + ( n) bg F t +n( n) (q t ) + n " H (H t ) + ( n) " F (F t ) ; (7) and ontains quadrati terms in b W t, by t H, by t F, bg t H, bg t F, q t, H t and F t. The weights of the respetive variables are all funtions of deep model parameters. Stabilizing onsumption and publi spending is desirable beause households are averse to private and publi onsumption risks. The national output gaps and the terms of trade are a part of the loss funtion beause individuals are averse to utuations of hours worked and shifts of these between Home and Foreign. In ation auses dispersion in pries and thus ine ient prodution of goods while di erenes at the national level ause undesirable relative prie dispersions. As rst pointed out by Benigno (4), the ountry with a higher degree of prie stikiness omes up with a higher degree of prie distortion, and thus it is optimal to put a higher weight to the ountry with stikier pries. This result is repliated in (7) where the weights of the national in ation rates are inreasing in the degree of prie stikiness (dereasing in i ). If the duration of prie ontrats was idential aross ountries, H = F =, the per-period loss funtion (7) ould be rewritten in area and relative terms as

13 t = b W t + (by W t ) + n( n) (by R t ) + (bg t W ) + n( n) (bg t R ) +n( n) (q t ) + Only then, monetary poliy should stabilize W t. 3. Calibration " ( W t ) + n( n) ( R t ) : (8) Let us outline the parametrization for the quantitative poliy analysis. The model is alibrated to a quarterly frequeny and the parameters are hosen in a manner that mathes the average features of ountries belonging to the EMU. The disount fator is set equal to.99, so that the steady-state real interest rate is 4% p.a. By alibrating the elastiity of substitution between goods " to a value of 7.66, we assume that the steadystate mark-up of pries over marginal osts is around 5% whih is a reasonable value for the European eonomies, aording to Benigno (4). The inverse of the intertemporal elastiity of substitution is set equal to, following the eonometri estimate of Leith and Malley (5). Following Gali and Monaelli (8), we assume the inverse of the Frish elastiity of labor supply to be 3 and the share of publi spending in GDP to be = :5; whih is roughly the average for the euro zone. Aording to the derived steady-state relationships in Appendix A, it follows that the relative weight of government onsumption in the utility funtion is = G=Y (+G=Y ) G=Y = 9. The steady-state tax rate is = = :. The prie rigidity is assumed to be equal in both ountries. We disregard di erenes in prie setting between ountries in order to highlight onsequenes from a ost hannel di erential. Therefore the Calvo parameter i is set equal to a standard value of.75 whih implies an average duration of prie ontrats of four quarters. We follow Benigno (4) and Beetsma and Jensen (5) and divide the monetary union into two equal-sized groups; thus, n = :5. For the benhmark alibration, we restrit our analysis to the ase of lump-sum taxation, i.e =, =. Moreover, we adopt a degree of persistene in the shoks of u = e = :5. 3

14 4 Dynamis The objetive of this setion is to analyze the dynami response of the relevant endogenous variables to di erent kind of supply and demand shoks. We distinguish between aggregate, asymmetri and idiosynrati shoks. In order to avoid (too) many ase di erentiations, the presentation fouses on the optimal disretionary poliy. Note that our analysis disregards all problems arising from the zero lower bound on nominal interest rates. For a disussion of this issue, see, e.g., Adam and Billi (7). Let us desribe our assumptions on the sequene of events before turning our fous on the in ation and output dynamis. First, the eonomy is in the deterministi steady state. Then, period t demand and/or ost-push shoks are revealed. Given the realizations of the shoks, the poliy authority deides on the optimal response of the nominal interest rate and (national) government spending. Next, wage setters deide on the wage, and rms deide on the produt prie and take up a loan to nane the wage bill. Employment is pinned down, and prodution takes plae. After selling the produts on the goods market rms repay the loan. 4. Cost-push Shoks 4.. Aggregate Cost-push Shoks Let us rst disuss the ase of idential ost hannels aross ountries, z H = z F : An aggregate ost-push shok (e H t = e F t = e W t > ) auses union in ation to go up, whereas on the union output gap remains initially unaltered. The ost-push shok drives a wedge between the output and the in ation target, even in the absene of a ost hannel. Figure displays the impulse responses to a positive one perent shok in aggregate supply e W t : Without a ost hannel and for symmetri eonomies, we on rm the result of Beetsma and Jensen (5), who nd that the roles of monetary and sal poliies are lear-ut: All deviations on the aggregate level will be met by the sole use of the monetary stabilization instrument, while sal poliy remains inative. On the ontrary, all deviations of relative target variables are within the responsibility of sal poliy, while monetary poliy does not respond. Thus, in the ase of the aggregate ost-push shok, the interest rate is raised by the entral bank in order to mitigate the in ationary e et of the ost-push. But there will be no full aommodation. Beause of a negative output gap the optimal monetary poliy will tolerate an in ation rate above the target rate. Fisal poliy would be able to repliate this result, but monetary and sal instruments are no perfet substitutes. Any deviation of government spending from its See setion 4.. for the disussion of a relative shok. 4

15 Union output gap Union inflation gap Consumption gap,5, ,3,, Nominal interest rate Union gov. spendings,5, Figure : Aggregate ost-push shok with idential ost hannels. z i = (blue line), z i = :5 (red line), z i = :5 (green line). steady-state value is, aording to our welfare funtion (7), ostly per se. Hene, the monetary instrument is superior and sal poliy remains inative. For z i >, the trade-o between in ation and output worsens. A given inrease in the interest rate and thus a given deline in output is now aompanied by a higher in ation rate. The ost hannel makes monetary poliy less e etive in ombating in ation, alling for ations in sal poliy. The optimal response to the deline in monetary e etiveness is a weaker use of that instrument and a (stronger) use of the sal instrument. This result is in ontrast to Mihaelis and Palek (4) who nd that the optimal interest hike is larger instead. However, in their analysis there are no substitutes to the nominal interest rate instrument, as it is the ase in our model. For a relatively small ost hannel, z i = :5, the interest hike is lower and government spending is dereased as ompared to the ase with no ost hannel. Similar to the demand-side interest rate e et, the redution in publi spending lowers union in ation and output. For a relatively large ost hannel, z i = :5, the interest rate turns into a supply-side instrument (see Setion 5). In order to redue in ation the entral bank now dereases the interest rate, as the ost hannel dominates the demand hannel. However, the interest rate redution stimulates the demand for goods, whih requires an even stronger reation of sal poliy. Regarding output and in ation dynamis, an 5

16 inreasing ost hannel lowers the union output gap and enlarges the union in ation gap. Proposition Suppose an aggregate ost-push shok and idential ost hannels aross ountries. a) For z i =, monetary poliy is superior to sal poliy and only an interest rate hike is used to respond to the shok. b) In the presene of a ost hannel, monetary poliy beomes less e etive and sal poliy steps in. Government spending is lowered to redue the in ation gap. The optimal poliy mix depends on the size of z W. The larger the ost hannel, ) the smaller the interest rate response and the stronger the sal reation must be; d) the smaller the union output gap and the larger the union in ation gap; e) the higher the probability of b R t turning into a supply-side instrument. Then it is optimal to redue the interest rate. For symmetri ountries, it is obvious that a hange in a union-wide instrument, like R b t and bg t W, is not able to in uene relative target variables. Only the relative sal instrument, bg t R, an take on this role. This is no longer true in the presene of a ost hannel di erential sine national variables matter for the ondut of monetary poliy as well. The monetary authority is now able to in uene both aggregate and relative variables. To illustrate the feedbak on the design of the optimal poliy mix we ompare the senario z F = z H = :5 with the senario z H = :5 and z F = (see Figure ). As the aggregate ost hannel is the same for both senarios, z W = :5, we are able to lter the omplete e et of introduing an asymmetry in the ost hannel. In the ase of full symmetry (blue line), all di erentials are zero; all losses arise from the variability of union wide variables. In the ase of a ost hannel di erential (red line), additional losses from deviations of relative target variables arise (see (8)). The entral bank takes into aount the e ets of union-wide instruments on the in ation di erential and the terms of trade, balaning the trade-o between a hange in aggregate and relative variables. As a result, heterogeneity leads to a less aggressive monetary poliy. The emergene of a ost hannel di erential lowers the optimal interest rate hike in response to the inrease in aggregate in ation. This reates a gap in the terms of trade. Sine z H > z F, so is q t p F;t p H;t < and thus, Home faes a deterioration of its terms of trade. Demand swithes from Home to Foreign and the relative output gap beomes negative. On the sal side, the union-wide instrument bg t W is used more aggressively due to the smaller interest rate response. The main sal tool however, is bg t R : The sal authority lowers relative government spending in order to redue relative in ation. This magni es the drop in the relative output and the terms of trade gap. The union output gap, the onsumption gap and the union in ation gap are only marginally di erent to the symmetry ase. The main results are summarized in the following. Proposition Suppose that there is a ost-push shok and a ost hannel di erential with z H > z F. The ost hannel di erential a) gives rise to a terms of trade gap, 6

17 .5 Union output gap.3.. Union inflation gap Consumption gap Relative output gap Nominal interest rate Relative inflation gap Union gov. spendings Terms of trade Relative gov. spendings Figure : Aggregate ost-push shok with di erent ost hannel values. z i = :5 (blue line); z H = :5, z F = (red line). 7

18 demand swithes from Home to Foreign; b) makes the optimal monetary poliy less aggressive and the optimal union-wide sal poliy more aggressive and ) lets relative sal poliy emerge. Fisal poliy reats stronger in that region, where the ost hannel is larger. So far we have disussed the benhmark senario of lump-sum taxes. Next, we want to analyze the impliations of distortionary taxes. When taxation is distortionary, the Phillips urve is atter ompared to the lump-sum ase, i.e. H =(+ )( ) < H, whih is true for <. A deline in the nominal interest rate, for example, inreases aggregate demand via the onventional demand hannel. In ontrast to lump-sum taxes, the inreased inome will initially lead to a rise in tax revenues, if taxation is distortionary. In order to maintain the government budget onstraint, the distortionary tax rate has to deline. Consequently, marginal osts deline and the Phillips urve beomes atter. What are the impliations of a atter PC-urve in the presene of a ost hannel? The slope of the Phillips urve determines the extent to whih an interest rate hange a ets in ation via the demand hannel. A unit deline in the nominal interest rate, for example, inreases output by (see (), (3)). For distortionary taxation, the demand-hannel e et on in ation is i =(+ )( ) whih is smaller than the demand-hannel e et for lump-sum taxes, i.e. i as shown above. In ontrast, the ost-hannel e et ( i z i ) is the same irrespetive of the type of taxation. Consequently, the ost hannel gains more weight - relative to the demand hannel - in the ase of distortionary taxation. Again, we onsider an aggregate ost-push shok whih initially pushes union in- ation up. In order to fous on the di erenes of the two tax systems for the optimal poliy mix, we display only the impulse response funtions of the nominal interest rate and government spending for di erent values of z i in Figure 3. As already disussed in Setion.3, a hange in government spending will hange in ation in the same diretion through the demand and supply side if taxation is distortionary. In other words, sal poliy beomes more e etive in losing the in ation gap. A hange of the nominal interest on the ontrary has opposing in ationary e ets via the demand and supply side. By looking at Figure 3, we see that Proposition a) (blue solid line) no longer holds true. Without a ost hannel, monetary poliy is no longer superior at all times. Furthermore, it an be observed that government spending is dereased (blue dashed line). Fisal poliy is more e etive than monetary poliy in losing the in ation gap. However a poliy mix is used beause sal poliy still inhabits welfare ost on its own. A seond result is a stronger use of the sal instrument and a smaller interest rate response (dashed lines always below sold lines). Monetary poliy is less aggressive as long as the nominal interest rate is a demand-side instrument, but more aggressive when it is a supply-side tool. Another feature of distortionary taxa- 8

19 Nominal interest rate Union government spendings 3,5,5, , Figure 3: Aggregate ost-push shok under di erent kinds of taxation and ost hannel values. Solid lines denote lump-sum taxation; dashed lines denote distortionary taxation. z i = (blue line), z i = :5 (red line), z i = :5 (green line). tion, whih has already been disussed above, is a atter Phillips urve and an inrease in the weight of the ost hannel relative to the weight of the demand hannel. This explains why the nominal interest rate rather turns into a supply-side instrument. For z i = :5 we see that the hange of the nominal interest rate is already negative in the ase of distortionary taxes (red dashed line), while it is still a demand-side instrument for lump-sum taxes (red solid line). Proposition 3 Suppose an aggregate ost-push shok. Distortionary taxes, relative to lump-sum taxes, are haraterized by a) a stronger use of the sal instrument; b) a smaller interest rate response and ) a higher probability of the nominal interest rate to turn into a supply-side instrument. 4.. Relative Cost-push Shoks We will fous on a perfet asymmetri (relative) ost-push shok, i.e. e H t = e F t (e R t > ), whereas e w t = (see Figure 4). The onsequene is initially an inrease in the in ation di erential, a negative terms of trade gap but a zero union in ation gap. The optimal poliy mix and the impat on union in ation and union output very muh depend on the sign of the ost hannel di erential. In the ase of no or idential ost hannels, z i = :5 (blue line), a perfet 9

20 Union output gap,4,,, Relative output gap,5, Nominal interest rate Union inflation gap,3,,, Relative inflation gap,5, Union gov. spendings,5, Consumption gap,3,,, Terms of trade, Relative gov. spendings Figure 4: Relative ost-push shok with di erent ost hannel values. z i = :5 (blue line), z H = :5, z F = (red line), z H =, z F = :5 (green line).

21 asymmetri shok does not a et aggregate variables, by t W = b W t = W t =. Sine the aggregates are not touhed and di erentials annot be in uened, the optimal monetary poliy is to do nothing, whih is in aordane to Lane (). Beause of the in ation di erential and the terms of trade gap, the poliy authority faes a loss, but due to the assumed symmetry in the transmission proess, the poliy authority annot a et ountry di erentials by the use of a union-wide instrument suh as R b t or bg t W : Instead, the poliy authority makes use of the relative instrument by lowering relative government spending, bg t R and thereby reduing the in ation di erential and terms of trade gap. The optimal poliy mix hanges in the ase of a ost hannel di erential. The "do nothing"- result of monetary poliy does not hold anymore as now the nominal interest rate a ets in ation di erentials and the terms of trade. From the disussion of the Home and Foreign Phillips urve (see (4) and (5)) we know that an inrease in the interest rate leads to an inrease (derease) in the in ation di erential for z R > (z R < ). Thus, for z R > the entral bank has to lower the interest rate (red line), and for z R < it has to raise the interest rate (green line). The deline in the in ation di erential omes at a ost. For z R > (z R < ) union output and union in ation inrease (derease). These deviations however are redued by the union sal poliy. For z R > (z R < ) union government spending is dereased (inreased). Proposition 4 Suppose a perfet asymmetri ost-push shok e H t = e F t (e R t > ). In all ases, it is optimal to redue relative government spending. The optimal poliy mix depends on the ost hannel di erential. a) For z H = z F, the optimal monetary poliy is to do nothing. Optimal sal poliy is restrained to the redution of relative government spending. b) For z R >, the entral bank redues the in ation di erential via a lower interest rate, aepting an inrease in aggregate output and aggregate in ation. This inrease is dampened by a redution of union government spending. ) For z R <, the poliy authority redues the in ation di erential via a higher interest rate aepting a deline in aggregate output and aggregate in ation. This derease is mitigated by an inrease of union government spending Idiosynrati Cost-push Shoks National (idiosynrati) shoks a et both aggregate and relative supply. Take, for instane, a Home ost-push shok: e H t > and e F t =. Suh a disturbane is an aggregate ost-push shok, e W t >, as well as relative ost-push shok, e R t >. A positive in ation di erential emerges, Home faes a deterioration of its terms of trade and the relative output gap beomes negative due to the deline in relative demand. Figure 5 displays the impulse responses of the endogenous variables for idential ost hannels. The results are similar to those of the aggregate ost-push shok. If there is no ost hannel, z i = (blue line), the roles of monetary and sal poliy are

22 Union output gap Relative output gap Nominal interest rate Union inflation gap Consumption gap Relative inflation gap Terms of trade Union gov. spendings Relative gov. spedings Figure 5: Home ost-push shok with idential ost hannels. z i = (blue line), z i = :5 (red line), z i = :5 (green line).

23 again lear-ut. Monetary poliy stabilizes the eonomy at the union level and sal poliy at the national (relative) level. Therefore, the optimal poliy mix onsists of an inrease in the interest rate, no hange in union government spending and a derease in relative government spending. The interest rate hike stabilizes aggregate in ation and output, whereas sal poliy redues deviations of the in ation di erential as well as the terms of trade from their steady-state values. In the presene of a ost hannel, the trade-o between output and in ation stabilization worsens. There is a drop in monetary e ieny and therefore room for sal stabilization at the union level. For a relatively small ost hannel, z W = :5 (red line), the optimal interest rate hike is smaller and union government spending is lowered ompared to the no ost hannel ase. For a relatively large ost hannel, z W = :5 (green line), the interest rate beomes a supply-side instrument and the optimal interest rate response is now negative. As the interest rate redution stimulates the demand for goods, union government spending is dereased to an even greater degree. Note that the size of the ost hannel does not alter the paths of all the relative variables. The relative instrument only stabilizes relative target variables and these are independent of z W : The results are summarized in the following. Proposition 5 Suppose a Home ost-push shok and idential ost hannels aross ountries. In all ases, only relative sal poliy redues the in ation di erential. a) Without ost hannels, solely monetary poliy stabilizes the eonomy at the union level. b) In presene of a ost hannel, monetary and sal poliy stabilize the eonomy at the aggregate level. The optimal poliy mix depends on the size of z W. The larger the ost hannel, ) the smaller the interest rate response and the stronger the (union) sal reation must be; d) the higher the probability of b R t turning into a supply-side instrument. Let us now shift our fous bak to the ost hannel di erential. Figure 6 also displays the impulse responses to a one perent Home ost-push shok. The optimal poliy strongly depends on the sign of the ost hannel di erential. Now the monetary authority an in uene the in ation di erential and the terms of trade. In all ases, a redution in relative government spending is still the main tool for lowering the in ation di erential. For z R = :5 (green line), any inrease in the interest rate redues the in ation di erential. The interest rate hike, whih is also optimal in the ase of idential ost hannels (blue line), has a positive side e et now; it helps to redue the in ation di erential. As a onsequene, it is optimal to magnify the interest rate hike and to redue the drop in relative government spending as ompared to the ase of symmetrial ost hannels. As the entral bank reats more aggressively, sal poliy will inrease union government spending in order to lower the negative e ets of the higher interest 3

24 ,5,5,5,5 3 Union output gap Relative output gap Nominal interest rate ,,5,,5,5,5,5,5,5,5 Union inflation gap Relative inflation gap Union gov. spendings ,5,5,5,5 3 5 Consumption gap Terms of trade Relative gov. spendings Figure 6: Home ost-push shok with di erent ost hannel values. z i = :5 (blue line), z H = :5, z F = (red line), z H =, z F = :5 (green line). 4

25 rate on the output gap. Relative to idential ost hannels, the deline in the union output gap turns out to be magni ed; the inline in the union in ation gap is smaller. For z R = :5 (red line), any inrease in the interest rate widens the in ation di erential. However, for this size of the ost hannel di erential the nominal interest rate turns into a supply-side instrument. Therefore, the entral bank lowers the nominal interest rate in order to redue union in ation. Furthermore, this poliy has the positive side e et of reduing the in ation di erential as well as boosting aggregate demand. Hene, the sal authority is less aggressive in reduing relative government spending and more aggressive in dereasing union publi spending ompared to the ase of having symmetry in the ost hannel. Following that, the deline in the union output gap turns out to be weaker; the inrease in the union in ation gap turns out to be stronger. Proposition 6 Suppose a Home ost-push shok in the ase of a ost hannel di erential. Relative government spending is the primary and monetary poliy is the seondary tool in reduing the in ation di erential. Comparing poliy responses to the ase of idential ost hannels: a) for z R <, monetary poliy is more aggressive, relative publi spending is less aggressive and union government spending swithes the sign (to positive); b) for z R >, the interest rate swithes the sign (to negative) as it is a supply-side instrument, relative government spending reats less aggressively and union publi spending delines stronger. 4. Demand Shoks In this subsetion we extend our analysis to the ase of aggregate and idiosynrati demand shoks for idential ost hannels. We will omit the straightforward extension of a relative demand shok or ost hannel di erentials, as these senarios are greatly similar to those already disussed in the setion of ost-push shoks. 4.. Aggregate Demand Shok Let us disuss the ase of idential ost hannels aross ountries, z H = z F : Figure 7 displays the impulse responses to a positive one perent shok in aggregate demand u W t : The demand shok reates initially in ation and a positive output gap. In absene of a ost hannel, z i =, our model repliates the "divine oinidene"-result of Blanhard and Gali (7): by w t = w t =. An aggregate demand shok will be o set perfetly by varying the interest rate. The interest rate neessary to bring in ation bak to the target value is idential to the interest rate neessary to lose the output gap. Similar to the ase of ost-push shoks (see Setion 4..), sal poliy would also be able to 5