Kiel Institute for the World Economy Hindenburgufer 66 24105 Kiel Germany. Kiel Working Paper No 1881 November 2013,Monetary Union and Macroeconomic Stabilization. Dominik Groll, It is conventionally held that countries are worse off by forming a monetary union when it comes to. macroeconomic stabilization However this conventional view relies on assuming that monetary. policy is conducted optimally Relaxing the assumption of optimal monetary policy not only uncovers. that countries do benefit from forming a monetary union under fairly general conditions More. importantly it also reveals that a monetary union entails the inherent benefit of stabilizing private. sector expectations about future inflation As a result inflation rates are more stable in a monetary. Keywords Monetary union macroeconomic stabilization welfare analysis history dependence. inflation expectations,JEL classification F33 F41 E52. Dominik Groll,Kiel Institute for the World Economy. 24100 Kiel Germany,Telephone 49 431 8814 266,E mail dominik groll ifw kiel de. The responsibility for the contents of the working papers rests with the author not the Institute Since working papers are of. a preliminary nature it may be useful to contact the author of a particular working paper about results or caveats before. referring to or quoting a paper Any comments on working papers should be sent directly to the author. Coverphoto uni com on photocase com,M ONETARY U NION AND. M ACROECONOMIC S TABILIZATION,Dominik Groll, Kiel Institute for the World Economy Hindenburgufer 66 24105 Kiel Germany. This version February 14 2014, It is conventionally held that countries are worse off by forming a mon. etary union when it comes to macroeconomic stabilization However this. conventional view relies on assuming that monetary policy is conducted. optimally Relaxing the assumption of optimal monetary policy not only. uncovers that countries do benefit from forming a monetary union under. fairly general conditions More importantly it also reveals that a monetary. union entails the inherent benefit of stabilizing private sector expectations. about future inflation As a result inflation rates are more stable in a. monetary union, Keywords Monetary union macroeconomic stabilization welfare. analysis history dependence inflation expectations. JEL classification F33 F41 E52, E mail dominik groll ifw kiel de Phone 49 431 8814 266. 2 1 Introduction,1 Introduction, When do countries benefit from forming a monetary union This question is at least. as old as the Optimum Currency Area OCA literature initiated by Mundell 1961. One of the key insights of this literature is that for asymmetric countries to benefit. from forming a monetary union prices and wages have to be flexible and produc. tion factors have to be mobile More recently the New Keynesian literature by using. dynamic stochastic general equilibrium DSGE models has come to the consensus. that from the perspective of macroeconomic stabilization forming a monetary union. makes countries generally worse off in terms of welfare 1 This is because countries re. linquish one of their most important policy instruments for macroeconomic stabiliza. tion namely the short term nominal interest rate controlled by their national central. However this consensus is based on the assumption that the central bank conducts. monetary policy optimally While constituting a very useful theoretical benchmark. from a normative perspective the assumption of optimal monetary policy entails at. least two important disadvantages in the OCA context On the one hand it is widely. acknowledged that optimal monetary policy typically involves severe practical limita. tions in particular very demanding information requirements For example the cen. tral bank needs to be able to observe the households welfare function or the flexible. price equilibrium of the economy i e the equilibrium that would prevail under com. pletely flexible prices 2 On the other hand the assumption of optimal monetary policy. precludes the possibility to assess if and how the welfare performance of a monetary. union depends on the way monetary policy is conducted since deviations from opti. mality are ruled out by assumption Thus it seems at least debatable whether optimal. monetary policy is the best modeling choice when one wants to know the conditions. under which countries benefit from forming a monetary union 3. In light of these two disadvantages I take a different approach in this paper by. assuming that monetary policy follows Taylor type interest rate rules according to. which it responds only to observable variables such as inflation or output By being. able to vary the coefficients that determine the response of monetary policy to the. respective variables these interest rate rules are general enough to allow for a great. flexibility in specifying the behavior of monetary policy For example how aggressive. is monetary policy in its response to inflation Does it respond to output If so how. strongly Or does monetary policy smooth interest rates and to what extent In this. sense the way monetary policy is conducted can be viewed just as any other country. characteristic such as its size or the degree of price stickiness in its economy It is then. possible to assess if and how the welfare performance of a monetary union depends on. the behavior of monetary policy something that is not possible under the assump. tion of optimal monetary policy As it turns out the behavior of monetary policy is. absolutely critical for the welfare performance of a monetary union. Given this different approach the main finding of this paper is as follows In the. standard two country New Keynesian DSGE model in which monetary policy fol. 1 See surveys by Corsetti 2008 Dellas and Tavlas 2009 and Beetsma and Giuliodori 2010. 2 For more practical shortcomings of optimal monetary policy see Gali 2008 Ch 4 3 2. 3 In my view this doubt is supported by Adao Correia and Teles 2009 who conclude that every. currency area is an optimal currency area after having shown that the exchange rate regime is irrelevant. for stabilization policy if optimal monetary policy is complemented by optimal fiscal policy. 1 Introduction 3, lows interest rate rules countries may gain in welfare by forming a monetary union. The gain in welfare comes from a higher stability of inflation rates which outweighs. the costs of higher output gap and terms of trade gap instability Whether countries. gain in welfare depends strongly on the degree of price stickiness When prices are. relatively sticky countries are better off forming a monetary union when prices are. relatively flexible countries are better off maintaining a flexible exchange rate. Two effects are responsible for this higher stability of inflation rates First the benefit. of maintaining a flexible exchange rate diminishes as prices become stickier since the. nominal exchange rate inherits the stickiness of goods prices As a result an increas. ing degree of price stickiness reduces the effectiveness of the nominal exchange rate. as a stabilization mechanism Second forming a monetary union entails an inherent. benefit 4 Since the nominal exchange rate is fixed the terms of trade and therefore the. inflation rates display an inertial or history dependent behavior This history depen. dence has the advantage of affecting the inflation expectations of price setters in such a. way as to lower the responsiveness of inflation to changing economic conditions The. higher the degree of price stickiness is the stronger this effect is As a result inflation. rates are more stable in a monetary union, This second effect corresponds to an effect that is well known from the analysis of. optimal monetary policy in a closed economy There optimal monetary policy under. discretion is inferior to optimal monetary policy under commitment because the former. does not influence the inflation expectations of price setters in a favorable way It suf. fers from the so called stabilization bias In contrast optimal monetary policy under. commitment induces history dependence into the economy and therefore exploits. the fact that price setters are forward looking The intuition in this paper is completely. analogous Forming a monetary union may be superior to maintaining a flexible ex. change rate because fixing the exchange rate induces history dependence. This benefit which manifests itself in a higher stability of inflation rates and which. is related to the stabilization bias obtains in addition to the benefit of eliminating a. potential inflation bias which is stressed by Alesina and Barro 2002 and Cooley and. Quadrini 2003 5 Whereas the latter benefit has been acknowledged in the literature. e g Dellas and Tavlas 2009 Beetsma and Giuliodori 2010 the former still seems to. be unknown, It is important to realize that both effects described above are endogenous to the. model The first effect is due to the presence of the uncovered interest parity condition. on the one hand and monetary policy following Taylor type interest rate rules on the. other hand 6 The second effect is due to the fact that price setters are forward looking. in the presence of nominal price rigidities All these features belong to the core of new. open economy macroeconomics NOEM models and therefore are present also in. many medium to large scale models that are built around this core 7. Another important finding of this paper is that whether forming a monetary union. is beneficial or not depends heavily on the way monetary policy is conducted When. 4 Inherent refers to the fact that the benefit is not modeled explicitly like a reduction in transaction. costs but emerges from within the model, 5 Giavazzi and Pagano 1988 s advantage of tying one s hands follows the same logic although they. refer to the former European Monetary System 1979 1999. 6 Notably the uncovered interest parity condition need not hold exactly for this effect to exist It suffices. for the interest rates and the nominal exchange rate to be linked. 7 The introduction of nominal price rigidities in the spirit of Calvo 1983 into NOEM models goes back. to Kollmann 2001 Gali and Monacelli 2005 and Clarida Gali and Gertler 2002. 4 1 Introduction, monetary policy responds to inflation aggressively or when it implements a high de. gree of interest rate smoothing then maintaining a flexible exchange rate is superior. Thus it is the quality of monetary policy that is crucial for the welfare ranking between. the monetary union and the flexible exchange rate regime Since monetary policy is. more powerful under the flexible exchange rate regime it is also more harmful when. not conducted properly This is because the quality of monetary policy is reinforced. by the nominal exchange rate In this sense a monetary union provides a hedging. mechanism against monetary policy mistakes, Clearly the finding that countries benefit from forming a monetary union when. prices are relatively sticky but not when prices are relatively flexible stands in con. trast to the predictions of the traditional OCA theory Probably the most important. reason for this discrepancy is the fact that expectations are treated as endogenous in. New Keynesian models unlike in the theoretical framework of the traditional OCA. literature in which expectations are treated as exogenous Since the inherent benefit. of monetary unions works through expectations this channel is naturally missing in. models without such an expectational feedback mechanism 8. This paper is related along several dimensions to the New Keynesian literature. that analyzes the conditions under which countries benefit from forming a monetary. union In this literature only a few studies have considered an environment without. optimal monetary policy Devereux 2004 Dellas and Tavlas 2005 Dellas 2006 and. Ferreira Lopes 2010 The models used in these studies as well as their findings are. on the one hand quite diverse On the other hand none of these studies addresses the. inherent benefit of monetary unions the role of the degree of price stickiness nor the. closely related issue of the inherited stickiness of the exchange rate all of which are. crucial for the welfare ranking between the monetary union and the flexible exchange. rate regime, Several studies have introduced explicit benefits of monetary unions to create a. counterpart to the cost of giving up national monetary policy as a stabilization de. vice Such explicit benefits of monetary unions include the elimination of shocks to. the uncovered interest parity condition Kollmann 2004 the gain in potential output. Ca Zorzi De Santis and Zampolli 2005 the gain in central bank credibility Clerc. Dellas and Loisel 2011 and the possibility of higher consumption risk sharing across. countries Ching and Devereux 2003 In contrast no explicit benefits are introduced. into the model employed in this paper The benefit of stabilizing inflation expectations. is inherent to monetary unions as a result of a fixed nominal exchange rate. This paper is also related to Monacelli 2004 9 Among other things he finds that in. a small open economy a fixed exchange rate regime induces inertia into the economy. On the one hand I show that this benefit carries over to a two country environment. 8 See King 1993 for a critical assessment of the Old Keynesian IS LM models with respect to their treat. ment of expectations, 9 For a small open economy a fixed exchange rate regime may dominate a flexible exchange rate regime. with optimal monetary policy under discretion A flexible exchange rate regime with optimal monetary. policy under commitment however always dominates the other two regimes Comparing the same. three regimes Soffritti and Zanetti 2008 come to a different conclusion namely that a fixed exchange. rate regime fares worse than the two flexible exchange rate regimes One possible explanation for the. different finding could be the different weight attached to the output gap variance relative to the weight. attached to the inflation variance in the welfare loss function which is ad hoc in both studies Another. explanation could be the different assumption about whether the rest of the world is also subject to. shocks or not, and is inherent to monetary union regimes as well 10 On the other hand I show that. it does not hinge upon the stationarity of the price level as stressed by Monacelli. 2004 Stationarity of the price level is a special feature of the small open economy. environment and does not carry over to a two country setting employed here Also. Monacelli 2004 does not address the role of the degree of price stickiness the related. issue of the inherited stickiness of the exchange rate nor the role of monetary policy. The rest of this paper is organized as follows Section 2 outlines briefly the structure. of the model Section 3 provides important analytical results in the case of symmetric. countries and presents the welfare results graphically Section 4 presents the results in. the case of asymmetric countries Section 5 relates the results to the traditional OCA. theory Section 6 concludes, The model I use is a completely standard two country New Keynesian DSGE model. and thus I keep the description very brief It features two international monetary. 1 A monetary union MU regime Both countries share the same currency A com. mon monetary policy governs the common nominal interest. 2 A flexible exchange rate FX regime Each country maintains its national cur. rency and conducts its own independent monetary policy Nominal interest. rates are country specific The nominal exchange rate between the two curren. cies is flexible, The model is described in detail in Benigno 2004 and in Benigno and Benigno. 2008 and it includes a microfounded linear quadratic welfare measure Under both. regimes the model economy features two countries with trade in consumption goods. as opposed to trade in intermediate goods Consumption preferences are of the. Cobb Douglas type and are in addition identical across countries i e there is no. home bias in consumption These preferences imply that risk sharing is perfect in the. sense that consumption is equal across countries at all times Purchasing power parity. holds i e the real exchange rate is constant While these assumptions are clearly re. strictive they greatly simplify the analysis and relaxing them to allow for a home bias. in consumption i e no purchasing power parity and a variable real exchange rate. does not alter the findings significantly The only factor of production is labor which. is immobile between countries The only rigidity is the nominal price rigidity in the. spirit of Calvo 1983, Under the FX regime prices are set in the currency of the producer s country pro. ducer currency pricing i e the producer does not discriminate the price between. countries The nominal exchange rate converts the price into foreign currency i e the. law of one price holds and exchange rate pass through is complete Given the same. consumption preferences as under the MU regime purchasing power parity holds as. well The nominal exchange rate is determined by the uncovered interest parity. general fixed exchange rate regimes and monetary union regimes do not coincide This depends on. how the fixed exchange rate regime is implemented, In both regimes monetary policy is conducted via Taylor type interest rate rules. Importantly I assume that monetary policy is not able to observe the flexible price. equilibrium of the economy in particular the flexible price interest rate and flexible. price output Thus monetary policy reacts to inflation and to output deviation from. the steady state not to the output gap deviation from flexible price output The only. shocks considered are country specific productivity shocks However the findings are. robust with respect to other shocks such as government spending shocks or cost push. 2 1 Model equations, The equations of the complete log linearized model are displayed below for the full. derivation see Appendices B and C Deviations of the logarithm of a variable Xt from. its steady state are denoted by X t under flexible prices and by X t under sticky prices 12. Variables and parameters are defined in Table 1 and Table 2 respectively. Ct Consumption identical across countries,Yti Output of country i H F. YtW World output weighted average of country specific output. ti Producer price inflation in country i H F, tW World inflation weighted average of country specific inflation. tR Inflation differential between the two countries tF tH. Rit Nominal interest rate in country i H F,Rt Nominal interest rate in monetary union. Tt Terms of trade,St Nominal exchange rate,Yt Productivity shock in country i H F. ti White noise process in country i H F,Table 1 Variables. 11 In fact under cost push shocks the case for a monetary union becomes even stronger. 12 Notation is adopted from Benigno 2004,2 1 Model equations 7. Inverse of elasticity of intertemporal substitution in consumption. n Country size measured by population,Discount factor. Inverse of elasticity of producing the differentiated good. Elasticity of substitution between differentiated goods. i Probability of not being able to reset the price in country i H F. Inflation coefficient in interest rate rule,Y Output coefficient in interest rate rule. R Interest rate smoothing coefficient in interest rate rule. i Persistence of productivity shock in country i H F. kCi kCi i 1,kiT kiT i 1,Table 2 Parameters, 2 1 1 Flexible price equilibrium under both regimes. Under completely flexible prices the model equations are identical for both the FX. and MU regime and are given by,C t Yt 2 1,T t Yt 2 2. Y t Yt 2 3,Y t nY t 1 n Y t 2 4,Yt Yt Yt 2 5,Y t i Y t 1 ti 2 6. with i H F, 2 1 2 Sticky price equilibrium under the MU regime. Under sticky prices the model equations for the MU regime are given by. Et C t 1 C t R t Et tW,Y tH 1 n T t C t 2 8,Y tF n T t C t 2 9. tH 1 n k TH T t T t kCH C t C t Et tH 1 2 10,tF nk TF T t T t kCF C t C t Et tF 1 2 11. T t T t 1 tF tH 2 12,R t R R t 1 1 R tW Y Y tW 2 13. tW n tH 1 n tF 2 14, 2 1 3 Sticky price equilibrium under the FX regime. The model equations for the FX regime are given by. Et C t 1 C t n R tH Et tH 1 1 n R tF Et tF 1 2 15,Y tH 1 n T t C t 2 16. Y tF n T t C t 2 17,tH 1 n k TH T t T t kCH C t C t Et tH 1 2 18. tF nk TF T t T t kCF C t C t Et tF 1 2 19,T t T t 1 tF tH S t 2 20. Et S t 1 R tH R tF 2 21,R tH R R tH 1 1 R tH Y Y tH 2 22. R tF R R tF 1 1 R tF Y Y tF 2 23,2 2 Model description. Consumption is equal across countries at all times and is described by only one Eu. ler equation equation 2 7 under the MU regime and equation 2 15 under the FX. regime The only difference between the two Euler equations is that under the MU. regime the nominal interest rate is common to both countries The structure of aggre. gate demand is the same under both regimes and given by equations 2 8 2 9 2 16. and 2 17 Also the country specific New Keynesian Phillips curves are the same un. der both regimes and are given by 2 10 2 11 2 18 and 2 19 In contrast to a. closed economy framework not only the consumption gap but also the terms of trade. gap difference between sticky price and flexible price terms of trade matters for pro. ducer price inflation 13 The terms of trade identity is given by 2 12 under the MU. regime and by 2 20 under the FX regime the difference between the two being the. presence of the nominal exchange rate in the latter Equation 2 21 is the uncovered in. terest parity condition The expected change in the nominal exchange rate corresponds. to the interest rate differential across countries Finally monetary policy is conducted. via Taylor type interest rate rules given by equation 2 13 under the MU regime and. by equations 2 22 and 2 23 under the FX regime, Under flexible prices prices are set as a markup over marginal costs monetary pol. icy is neutral and consumption output and the terms of trade are driven by pro. ductivity shocks only given by equations 2 1 2 2 and 2 3 Since money is neutral. under flexible prices the international monetary regime does not affect real variables. which therefore behave identically under both monetary regimes. 2 3 Welfare loss function, The welfare analysis follows the logic of the familiar linear quadratic approach ac. cording to which the log linear model equations are used to evaluate a quadratic wel. fare loss measure Woodford 2003 The world welfare loss function is given by the. that the consumption gap is equal to the world output gap C t C t Y tW Y tW Accordingly the. New Keynesian Phillips curves can be expressed in terms of the world output gap as well. 2 4 Calibration 9, discounted value of a weighted average across countries of the average utility flow. of agents using a second order Taylor series expansion 14 Throughout the paper it is. assumed that the distortion induced by monopolistic competition is completely offset. by an appropriate subsidy see Appendix D for the full derivation Thus. Wt var C t C t 1 n 1 n var T t T t,1 1 n var t,t i p O k k3 2 24. As in the closed economy the welfare loss depends on the inflation rate and the. consumption gap 15 In the open economy the welfare loss depends additionally on. the terms of trade gap Intuitively when the terms of trade deviate from the terms of. trade that would prevail under flexible prices the resulting allocation of production. across countries is inefficient due to the presence of price stickiness. In the special case when prices are equally rigid in both countries H F. the welfare loss function simplifies to,Wt var C t C t 1 n 1 n var T t T t. 1 var t n 1 n var t,t i p O k k3 2 25,2 4 Calibration. The values for the baseline calibration are taken from Benigno 2004 except for the. interest rate rule coefficients Table 3 A value of 0 99 for the discount factor implies. a steady state real interest rate of around 4 1 percent annually A value of 7 66 for the. elasticity of substitution between differentiated goods implies a steady state markup. of prices over marginal costs of 15 percent A value of 0 75 for the probability of not. being able to reset the price i implies an average duration of price contracts of 4. quarters Following Rotemberg and Woodford 1998 and Benigno 2004 the inverse. of the elasticity of producing the differentiated good is calculated as. 14 Computing country specific welfare would complicate the calculations significantly because more ac. curate approximations of the non linear model equations would be necessary Benigno and Woodford. 2005 This is beyond the scope of this paper, 15 In the basic closed economy framework consumption usually equals output Note also that the welfare. loss function 2 24 can be expressed alternatively in terms of the world output gap or the country. specific output gaps see equation D 72 The specification in terms of the consumption gap was chosen. for analytical convenience,10 3 Results under symmetry. where wy denotes the elasticity of the average real wage with respect to production. and denotes the labor income share, 1 6 Inv of elasticity of intertemporal substitution in consumption. n 0 5 Country size measured by population,0 99 Discount factor. 0 67 Inv of elasticity of producing the differentiated good. wy 0 5 Production elasticity of average real wage,0 75 Labor income share. 7 66 Elasticity of substitution between differentiated goods. i 0 75 Probability of not being able to reset the price. 1 5 Inflation coefficient in interest rate rule,Y 0 Output coefficient in interest rate rule. R 0 Interest rate smoothing coefficient in interest rate rule. i 0 9 Persistence of productivity shock,var ti 1 Variance of white noise process. corr tH tF 0 Correlation between country specific white noise processes. Table 3 Baseline calibration, Under the baseline calibration monetary policy responds to inflation 1 5. but it does not react to output Y 0 and does not engage in interest rate smoothing. R 0 I assume throughout the paper that all interest rate rule coefficients are. identical across countries and regimes, I consider a broad range of values for the parameters of the model to check for the. validity of the results Table 4 In particular the interest rate rules will also feature a. reaction to output and interest rate smoothing, 0 1 1 1 Inv of elasticity of intertemporal substitution in consumption. n 0 05 0 95 Country size measured by population,0 9 1 0 Discount factor. 0 2 3 0 Inv of elasticity of producing the differentiated good. wy 0 2 1 2 Production elasticity of average real wage. 0 5 0 9 Labor income share, 5 25 Elasticity of substitution between differentiated goods. i 0 05 0 95 Probability of not being able to reset the price. 1 1 3 5 Inflation coefficient in interest rate rule. Y 0 3 Output coefficient in interest rate rule, R 0 0 95 Interest rate smoothing coefficient in interest rate rule. Table 4 Parameter range,3 Results under symmetry, First I conduct the analysis under the assumption that the two countries are sym. metric except for country size n In particular the degree of price stickiness is equal. 3 1 Analytical results 11, across countries The world welfare loss function under symmetry equation 2 25 is. repeated here for convenience,Wt var C t C t 1 n 1 n var T t T t. 1 var t n 1 n var t,t i p O k k3 3 1, It contains four components the variance of the consumption gap C t C t the. variance of the terms of trade gap T t T t the variance of the world inflation rate. tW and the variance of the inflation differential tR. 3 1 Analytical results, The analytical results in this subsection are crucial to understanding the main finding. of the paper I derive the recursive law of motion RLOM of the model equations for. each monetary regime using the method of undetermined coefficients to obtain the. analytical expressions for the variances contained in the welfare loss function The. derivations are based on the assumption that the degree of price stickiness and the. persistence of productivity shocks are identical across countries H F and H. F and that monetary policy does not engage in interest rate smoothing R 0. Fortunately it is not necessary to derive the RLOM for the variables consumption. and world inflation since they both behave identically across monetary regimes To. see this for the MU regime substitute out the nominal interest rate R t in the Euler. equation 2 7 by inserting the interest rate rule 2 13 and the equations for aggregate. demand 2 8 and 2 9,Et C t 1 Y C t tW Et tW, The same equation is obtained completely analogously for the FX regime. For world inflation inserting the New Keynesian Phillips curves which are identical. across regimes into the definition of world inflation tW n tH 1 n tF where. H F due to symmetry and therefore k TH k TF k T and kCH kCF kC yields. tW kC C t C t Et tW, The reason why world inflation is the same under both the MU and the FX regimes. is that the terms of trade vanish from the equation when the degree of price stickiness. is equal across countries The fact that both consumption and world inflation behave. identically across monetary regimes implies that the variance of consumption and the. variance of world inflation are identical as well As a result they do not produce dif. ferences in welfare across the two regimes,12 3 Results under symmetry. For the remaining two variables the terms of trade and the inflation differential the. reduced system of equations under the MU regime is given by. tR k T T t T t Et tR 1 3 4,T t T t 1 tR 3 5, The reduced system of equations under the FX regime is given by. tR k T T t T t Et tR 1 3 6,T t T t 1 tR S t 3 7,Et S t 1 tR Y T t 3 8. Equations 3 4 and 3 6 are obtained by subtracting the New Keynesian Phillips. curve of country H from that of country F Equations 3 5 and 3 7 are the terms. of trade identities Equation 3 8 is obtained by inserting the interest rate rules 2 22. and 2 23 and the equations for aggregate demand 2 16 and 2 17 into the uncovered. interest parity condition 2 21, The RLOM under the MU regime is then given by see Appendix A for the entire. derivation,T t b1 T t 1 c1 T t 3 9,tR b2 T t 1 c2 T t 3 10. with coefficients,1 kT 1 kT 2 4,1 k T 1 k T 2 4,1 k T 1 H b1. The RLOM under the FX regime is given by,T t b1 T t 1 c1 T t 3 11. tR b2 T t 1 c2 T t 3 12,S t b3 T t 1 c3 T t 3 13,3 1 Analytical results 13. with coefficients,H kT 1 H Y 1 H,H kT 1 H Y 1 H,H kT 1 H Y 1 H. Consequently the variances of the terms of trade gap and the variances of the infla. tion differential under each regime are given by,1 H b1 c2 2c. var MU T t T t 1 var T t 3 14,1 b21 1 H b1 1 H b1,var FX T t T t c1 1 2 var T t 3 15. var MU tR var T t 3 16,1 b1 1 H b1,var FX tR c22 var T t 3 17. var T t var t var t 2 cov t t 3 18, Two important differences exist between the MU and FX regime First in contrast to. the MU regime there is no persistence in the terms of trade nor in the inflation differ. ential under the FX regime b1 b2 0 Hence once the shock has vanished both. variables return immediately to their steady state This is due to the nominal exchange. rate Intuitively the coefficient b3 1 implies that if the terms of trade were for. example one percent below the steady state in the previous period the nominal ex. change rate would increase by one percent in the current period so that the terms of. trade are at steady state Naturally this mechanism is absent under the MU regime. since the nominal exchange rate is fixed Thus both the terms of trade and the infla. tion differential are inertial or history dependent in the sense that they depend on the. realization of the terms of trade in the previous period While the inertia of the terms. of trade in the context of a monetary union has been recognized before e g Benigno. 2004 Pappa 2004 it was regarded solely as an additional distortion in the economy. However as will be shown below the inertia of the terms of trade will also prove to. be beneficial namely from the perspective of stabilizing inflation expectations. Second in contrast to the MU regime monetary policy is able to influence the terms. of trade gap and the inflation differential under the FX regime i e monetary policy. is more powerful under the FX regime Technically the variance of the terms of trade. gap and of the inflation differential depend on the interest rate rule coefficients. and Y Moreover if monetary policy is extremely aggressive towards inflation under. the FX regime the variance of the terms of trade gap and of the inflation.

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