A DSGE model for a SOE with systematic interest and foreign exchange policy in which policymakers exploit the risk premium for stabilization purposes
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Escudé, Guillermo J. Working Paper A DSGE model for a SOE with systematic interest and foreign exchange policy in which policymakers exploit the risk premium for stabilization purposes Economics Discussion Papers, No. 2012-40 Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Escudé, Guillermo J. (2012) : A DSGE model for a SOE with systematic interest and foreign exchange policy in which policymakers exploit the risk premium for stabilization purposes, Economics Discussion Papers, No. 2012-40, Kiel Institute for the World Economy (IfW), Kiel This Version is available at: https://hdl.handle.net/10419/62000 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by-nc/2.0/de/deed.en
A DSGE Model for a SOE with Systematic Interest and Foreign Exchange Policy in Which Policymakers Exploit the Risk Premium for Stabilization Purposes Guillermo J. Escudé Central Bank of Argentina, Buenos Aires Abstract This paper builds a DSGE model for a small open economy (SOE) in which the central bank systematically intervenes both the domestic currency bond and the FX markets using two policy rules: a Taylor-type rule and a second rule in which the operational target is the rate of nominal currency depreciation. For this, the instruments used by the central bank (bonds and international reserves) must be included in the model, as well as the institutional arrangements that determine the total amount of resources the central bank can use. The ‘corner’ regimes in which only one of the policy rules is used are particular cases of the model. The model is calibrated and implemented in Dynare for 1) simple policy rules, 2) optimal simple policy rules, and 3) optimal policy under commitment. Numerical losses are obtained for ad-hoc loss functions for different sets of central bank preferences (styles). The results show that the losses are systematically lower when both policy rules are used simultaneously, and much lower for the usual preferences (in which only inflation and/or output stabilization matter). It is shown that this result is basically due to the central bank’s enhanced ability, when it uses the two policy rules, to influence capital flows through the effects of its actions on the endogenous risk premium in the (risk-adjusted) interest parity equation. JEL E58, F41, O24 Keywords DSGE models; small open economy; exchange rate policy; optimal policy Correspondence Guillermo J. Escudé, Banco Central de la República Argentina, Reconquista 266, Buenos Aires, Argentina; e-mail: gescud[email protected]v.ar The views expressed in this paper are the author’s and do not necessarily reflect those of the Central Bank of Argentina. A previous version was presented to the 7th Dynare Conference at the Federal Reserve Bank of Atlanta, September 9-10, 2011, under the title "Optimal (and simultaneous) Interest and Foreign Exchange feedback policies in a DSGE model for a small open economy”. Comments and suggestions by Horacio Aguirre to a previous version of this paper are gratefully acknowledged. © Author(s) 2012. Licensed under a Creative Commons License - Attribution-NonCommercial 2.0 Germany Discussion Paper No. 2012 -40 | August 21, 2012 | http://www.economics-ejournal.org/economics/discussionpapers/2012-40
2 1. Introduction According to John Williamson ‘the overwhelming conventional view in the profession is that it is a mistake to try to manage exchange rates’ (J. Williamson (2007)), although he does not subscribe this view. After having for a long time recommended a basket, band, and crawl (BBC) regime, Williamson lately confesses to have converted to the cause of in‡ation targeting, but with some signi…cant additional ingredients: ‘most of the time the only monetary policy objective that may merit consideration -other than in‡ation targetingis the maintenance of a su¢ - ciently competitive exchange rate to preserve the incentive to invest’... (in tradable sectors). He also argues that ‘the government can expect to reduce misalignments by a policy of intervention. The question is how those interventions should be structured: whether they should be ad-hoc or systematic and, if the latter, how the system should be designed.’ This paper attempts to deal with these issues in a novel way, integrating the usual ‘in‡ation targeting’(or Taylor rule) approach with a policy of systematic intervention in the foreign exchange market. In my view there is no justi…cation for having to choose between an in‡ation target anchor and an exchange rate target anchor. But it is by no means easy to escape this dichotomy in the absence of an accepted and adequate theoretical framework. My hunch is that this absence is due to the pervasive preference of modelers (theoreticians) to ‘sweep under the rug’some of the Central Bank ‘nuts and bolts’that are necessary to achieve a more general theory. Such ‘nuts and bolts’ as the Central Bank balance sheet (and the …nancial assets and liabilities within it), are detailed and analyzed in any IMF Article IV mission report pertaining to developing countries. However, when it comes to modeling the macroeconomy. such aspects are simply omitted in both academic and IMF models. What makes such an omission possible, of course, is that if we accept the dichotomy in question, an argument of system decomposability allows one to focus on the central block of equations. However, if we do not accept the dichotomy, the need to include such ‘nuts and bolts’arises merely to ensure a consistent policy model. This paper, and the model on which it is based, attempts to build such a consistent policy model. Using the model with various policy frameworks (simple policy rules, optimal simple policy rules, optimal policy under commitment) and implementing a …rst order approximation using Dynare, I …nd strong evidence that a proper systematic use by Central Banks (CBs) of small open economies (SOEs) of two policy rules, one for the nominal interest rate and another for the rate of nominal depreciation, outperforms the ‘corner’regimes of in‡ation targeting (‡oating exchange rate) and an exchange rate peg. The basic di¤erence between the model used here and the workhorse DSGE model of the profession is the inclusion of more detail in the modeling of the institutional structure that takes us closer to a formal representation of how most CBs (at least those in developing economies) implement their interest and foreign exchange policies. However, as far as I am aware no CB implements its FX policy the way that it is modeled in this paper. When FX policy is systematic, there tends to be an exchange rate-related target. And when there is an explicit in‡ation targeting framework, FX policy tends to be highly discretional. One of the conclusions of this paper is that it is perfectly possible to articulate a consistent model which conserves the systematic interest rate policy rule that prevails in the literature (Taylor rule models) yet incorporates
3 an additional policy rule to represent FX policy. Furthermore, the paper shows that when optimal simple rules or optimal policy under commitment are introduced through an ad-hoc CB loss function, signi…cant gains are obtained using two policy rules (or two control variables) for all the usual CB preferences (i.e. combinations of weights for in‡ation and output). The model used for this paper, ARGEMmin (a smaller version of two previous models: Escudé (2008) and Escudé (2009)), can represent the simultaneous (i.e. within the same quarterly period) intervention in the foreign exchange (FX) and the domestic currency bond markets. The simultaneous use of two policy rules is a generalization of standard models that are limited to having either a Taylor rule for the interest rate with a pure currency ‡oat or a pure pegged regime in which there is usually no feedback. The fact that most CBs of developing economies intervene regularly in both markets should make this generalization of practical interest.2And a model that only adds the essential features that are needed to include foreign exchange policy without excluding interest rate policy should help in obtaining intuition as to why the CB can better achieve its objectives, whatever they may be, by the use of two policy rules instead of one. It is shown that the gains the CB obtains using the two instruments are basically due its increased ability to exploit the foreign investors’risk premium function that constrains the domestic household’s optimal foreign debt decision. The household decision problem delivers the risk-adjusted uncovered interest parity (UIP) equation.3The use of an endogenous risk premium function that Rest of the World (RW) agents use to determine the interest rate at which they are willing to purchase the economy’s foreign currency bonds plays a fundamental role in the model’s dynamics of capital ‡ows. The use of a risk premium for foreign debt has a long history in open economy macroeconomics (see e.g. Bhandari, Ul Haque and Turnovsky (1990)). In the DSGE strand, Schmitt-Grohé and Uribe (2003) note that the simplest SOE models with incomplete asset markets use the assumption that the subjective discount rate equals the average real interest rate and, hence, present equilibrium dynamics that have a random walk component. They present …ve alternative modi…cations that have been used to eliminate this random walk component and show that they have quite similar dynamics. Among these modi…cations is the complete assets market model (i.e., doing away with the incomplete asset markets assumption altogether) and, more relevant for this paper, the use of a risk premium function by which the interest rate on foreign funds responds to the amount of debt outstanding. In the latter variant, combining the non-stochastic steady state (NSS) versions of the Euler and UIP equations gives 2IMF (2011), for example, notes that ‘on average about on-third of the countries in the region (Latin America) intervened in any given day’. Indeed, their Table 3.1 (Stylized facts of FX Purchases, 2004-10) shows that Colombia and Peru intervened in 32% and 39% of working days, respectively. This table also contains interesting information on other regions: in the same period, Australia and Turkey intervened in 62% and 66% of working days, respectively, while Israel intervened 24% of working days but with a cumulative intervention that represented 22.3% of GDP. 3This di¤ers from my two previous (and larger) models, where it was the decision of banks that delivered the model’s UIP equation. The simpli…cation in this paper seeks to obtain a model that is su¢ ciently close to the standard workhorse model that the speci…c di¤erence in modeling policy is highlighted.
4 an equation such as (1 + i)'D(d) = , where is the intertemporal discount factor, iis the RW’s NSS real interest rate, is the SOE’s in‡ation rate, dis the SOE’s foreign debt and 'D(:)is a risk premium function. This equation then determines das a function of model parameters (including those that de…ne the risk premium function 'D(:)and the policy target that de…nes ). Lubik (2007) adds that even if there is an exogenous risk premium function, to avoid the unit root problem it is necessary that it be fully internalized by the individual households, i.e., that each household take into account that other households’decisions are the same as its own and, hence, that the risk premium it faces is a function of the aggregate (and not its individual) foreign debt. The only signi…cant change that this paper presents with respect to such a risk premium is that 'D(:)is a function of the foreign debt to GDP ratio: ed=Y (where eis the SOE’s real exchange rate (RER) and Yis its GDP) and that there is an additional multiplicative shock (giving 'D(:)) that may represent either an exogenous component of the risk function or an international liquidity shock (or both).4 Simply for convenience, I call the policy framework where the CB uses two simultaneous policy rules a Managed Exchange Rate (MER) regime. I explicitly include the instruments that the CB uses for its intervention in the two markets as well as the CB balance sheet that binds them. Hence, the CB balance sheet is one of the model equations. It has cash mtand CB-issued domestic currency bonds bton the liabilities side, and foreign currency reserves rton the asset side. To make sure that there are no loose ends, I explicitly consider the CB’s ‡ow budget constraint and assume that the institutional framework is such that any ‘quasi-…scal’surplus (or de…cit) is handed over (…nanced) period by period to the Treasury, de…ning ‘quasi-…scal surplus’as …nancial ‡ows (speci…cally, those related to interest earned and capital gains on international reserves, and the interest paid on CB bonds) that could make the CB net worth di¤erent from zero. Hence, while there is overall …scal consistency (since the Treasury is assumed to be able to collect enough lump-sum taxes each period to …nance its expenditures in excess of the qusi-…scal surplus), the CB has a constraint each period on its two instruments (rtand bt): etrt=mt+bt, where etand mtare the real exchange rate (RER) and real cash held by households. This equation implicitly de…nes how much the CB ‘sterilizes’(through the issuance of domestic currency bonds) any unwanted monetary e¤ect of its simultaneous and systematic monetary and exchange policy. However, I avoid the expression ‘sterilized intervention’(in the foreign exchange market) because it implicitly gives the exchange rate policy a subordinate role (the undesired e¤ects of which must be ‘sterilized’to avoid disrupting the monetary equilibrium that is achieved through the use of conventional monetary policy). Generality is best preserved treating both interventions in a symmetrical way, neither of which ‘sterilizes’the e¤ects of the other. When the CB intervenes in both the money and foreign exchange market, it is subject to the set of constraints given by the equations of the model, among which is monetary equilibrium and the assumed institutional constraint 4In addition to , there are three more RW shocks that impinge on the SOE: the world nominal riskfree interest rate 1 + iand the rates of in‡ation of imported and exported goods. There are also two domestic shocks: a transitory productivity shock in the domestic output sector and a government expenditure ratio (to GDP) shock.
5 that the CB’s net worth is kept at zero.5Clearly, other similar constraints could be used for the same purpose of endogenizing the CB’s ‘sterilization’policy. The one I use has the virtue of simplicity. The important point is that the overall means that the CB has available be made explicit. To further ensure consistency, the model includes the balance of payments (where both household foreign debt and CB reserves play relevant roles) and the …scal equation. Since the 2008 …nancial meltdown and the consequent introduction of ‘unconventional’monetary policies it has become customary to stress the importance of central bank balance sheets in the sense that huge purchases of …nancial assets by central banks get re‡ected in their assets as well as their liabilities. Caruana (2012), e.g., stresses the need to start normalizing the situation before the risk of monetizing debts gets out of hand. In this paper the point is made that inclusion of the central bank balance sheet and its composition is important even in a more ‘normal’world with short term interest rates that are above zero and CB assets and liabilities that are closer to normal levels. In this paper, ‘normal’levels are given by the long run (i.e., the model’s nonstochastic steady state) CB foreign exchange reserves ratio to GDP, and actual CB reserves ‡uctuate around the corresponding long run level. Hence, a return to normal levels is automatically guaranteed whenever the model is dynamically stable. But the explicit consideration of the CB’s balance sheet opens the door for modeling the novel (‘unconventional’) types of CB monetary policies in which the CB, say, additionally intervenes in a market for long-period bonds in order to deepen its expansionary policy when the short run interest rate is at its zero lower bound. This, however, is for future research. The rest of the paper has the following structure. In section 2 I set up the model. In section 3 I study the functioning of the model under simple policy rules, optimal simple policy rules, and optimal policy under commitment and full information (as in Svensson and Woodford (2002)) and show that there are indeed gains from using these two simultaneous policy rules instead of only one of the ‘corner’ regimes. In section 4 I show that such gains are basically due to the central bank’s enhanced ability to in‡uence the risk premium in the UIP equation when it uses the two policy rules. Section 5 concludes. Appendix I shows how the model parameters and the NSS were jointly calibrated. Finally, Appendix 2 shows a selection of the impulse response functions for the optimal simple rules and the optimal policy under commitment. 2. The model 2.1. Households 2.1.1 The household optimization problem In…nitely lived identical households consume a CES bundle of domestic and imported goods and hold …nancial wealth in the form of domestic currency cash (Mt) and domestic currency denominated one period nominal bonds issued by the CB (Bt) that pay a nominal interest rate it. They also issue one period foreign currency bonds (Dt) in the international capital market that pay a nominal (foreign cur5Notice that the latter can be expressed as an institutional constraint of the CB preserving a ‘full backing’of its domestic currency liabilities with (the domestic currency value of) its foreign reserves.
6 rency) interest rate iD t. I assume that the CB fully and credibly insures investors in CB bonds, so the domestic currency nominal rate is considered riskfree. However, foreign investors are only willing to hold the SOE’s foreign currency bonds if they receive a risk premium over the international riskfree rate i t. Since I do not model the RW, the premium function is exogenously given. It has an exogenous stochastic and time-varying component t(that can represent general liquidity conditions in the international market) as well as an endogenous (more country risk-related) component D(:)that is an increasing convex function of the aggregate foreign debt to GDP ratio. Individual households are assumed to fully internalize the dependence of the interest rate they face on the aggregate (instead of individual) foreign debt based on to their knowledge that all households are (at least in this aspect) identical. The foreign currency gross interest rate households face is: 1 + iD t= (1 + i t) tDD t;(1) where D t=StDt PtYt =etdt Yt ; etStP t Pt ; dtDt P t :(2) D t,et, and dt, are the foreign debt to GDP ratio, the real exchange rate, and real foreign debt (in terms of foreign prices), respectively, Stis the nominal exchange rate, Ptis the domestic goods price index, P tis the price index of the goods the SOE imports, and Ytis GDP. I assume that the gross risk premium function DD tis increasing and convex (D1 + D>1,0 D>0and 00 D>0). The household holds cash Mtbecause doing so reduces its transaction costs. I assume that transaction frictions result in a loss of purchasing power (through the non-utility generating consumption of domestic goods) when households purchase consumption goods, and that this cost can be ameliorated using cash.6To purchase quantity Ctof the consumption bundle, households must spend MM tPC tCt, where PC tis the price index of the consumption bundle. All price indexes are in monetary units. The gross transactions cost function MM tis assumed to be a decreasing and convex function (M1 + M>1; 0 M<0; 00 M>0) of the cash/consumption ratio M t: M tMt PC tCt =mt pC tCt ;(3) where pC tPC t Pt ; mtMt Pt (4) are the relative price of consumption goods and real cash. The representative household maximizes an inter-temporal utility function which is additively separable in (constant relative risk aversion subutility functions of) goods Ctand labor Nt: Et 1 X j=0 j(C1C t+j 1CNNt+j1+N 1 + N);(5) 6The introduction of money is similar to the theoretical treatment in Montiel (1999), and also to the numerically implemented treatment in Schmitt-Grohé and Uribe (2004). It di¤ers from the latter in that instead of de…ning velocity I use its inverse (the cash/consumption ratio), and I use a di¤erent speci…cation of the transactions cost function.
7 where is the intertemporal discount factor, C, and Nare the constant relative risk aversion coe¢ cients for goods and labor, respectively, and Nis a parameter. The household receives income from pro…ts, wages, and interests, and spends on consumption, interests, and taxes. Its nominal budget constraint in period tis: MM tPC tCt+Mt+BtStDt=WtNt+ tTaxt(6) +Mt1+ (1 + it1)Bt1(1 + iD t1)StDt1 where itis the interest rate that CB bonds pay each quarter, Wtis the nominal wage rate, tis nominal pro…ts, and Taxtis lump sum taxes net of transfers. Introducing (1) in (6) and dividing by Pt, the real budget constraint is: MM tpC tCt+mt+btetdt=wtNt+t Pt taxt+mt1 t (7) + (1 + it1)bt1 t (1 + i t1) t1DD t1et dt1 t ; where btBt Pt ; wtWt Pt ; taxtTaxt Pt ; tPt Pt1 ; tP t P t1 are the real stock of domestic currency bonds, the real wage (in terms of domestic goods), real lump sum tax collection, and the gross rates of quarterly in‡ation for domestic goods and foreign goods, respectively. The household chooses the sequence fCt+j; mt+j; bt+j; dt+j; Nt+jgthat maximizes (5) subject to its sequence of budget constraints (7) (and initial values for the predetermined variables). The Lagrangian is hence: Et 1 X j=0 j(C1C t+j 1CNNt+j1+N 1 + N+t+jwt+jNt+j+t+j Pt+j +mt1+j t+j (8) + (1 + it1+j)bt1+j t+j (1 + i t1+j) t1+jDet1+jdt1+j Yt1+jet+j dt1+j t+j Mmt+j pC t+jCt+jpC t+jCt+jmt+jbt+j+et+jdt+jtaxt+j where jt+jare the Lagrange multipliers, and can be interpreted as the marginal utility of real income.7 The …rst order conditions for an optimum are the following: Ct:CC t=tpC t'Mmt=pC tCt(9) mt:t1 + 0 Mmt=pC tCt=Et(t+1=t+1)(10) bt:t=(1 + it)Et(t+1=t+1)(11) dt:tet=(1 + i t) t'D(etdt=Yt)Ett+1et+1= t+1(12) Nt:NNN t=twt(13) 7There is also a no-Ponzi game condition that I omit for simplicity and yields the transversality condition limt!1 tdt= 0 that prevents households from incurring in Ponzi games.
8 Notice that in (9) and (12) the auxiliary functions 'Mand 'Dhave been introduced merely to obtain a more compact notation: 'DDDD+D0 DD;(14) 'MMMMM0 MM: Combining (10) and (11) implicitly gives the demand for cash as a function of the nominal interest rate and consumption expenditure: 0 Mmt=pC tCt= 1 1 1 + it ;(15) Inverting 0 Mgives the explicit demand function for cash as a vehicle for transactions (or ‘liquidity preference’function): mt=L(1 + it)pC tCt;(16) where L(:)is de…ned as: L(1 + it)(0 M)111 1 + it;(17) and is strictly decreasing, since: L0(1 + it) = 00 M(L(1 + it)) (1 + it)21<0: Under the assumption that the Central Bank always satis…es cash demand, from now on I call (16) the money market clearing condition. Using (9) to eliminate tfrom (11) yields a version of the classical Euler equation that re‡ects the additional in‡uence of the use of money on transactions costs: CC t 'M(mt=pC tCt)=(1 + it)Et CC t+1 'Mmt+1=pC t+1Ct+11 C t+1 !;(18) where C tPC t=PC t1is the gross rate of in‡ation of the basket of consumption goods and I have used the identity: pC t pC t1 =C t t (19) (based on the de…nition of pC tin (4)) to eliminate the rate of in‡ation for domestic goods. The de…nition of the RER in (2) gives the following identity: et et1 =t t t ;(20) where tSt=St1is the rate of nominal depreciation of the domestic currency. Hence, (12) may be written as: 1 = (1 + i t) t'Detdt YtEtt+1 t t+1 t+1 :
15 Hence, if in the NSS there is price stability and hence no price dispersion, a loglinear approximation of the model will not give any dynamics for b tif initially there is no price dispersion (see Schmitt-Grohé and Uribe (2007)). Since in this paper I do not go beyond a log-linear approximation of the model and wish to see the dynamics of price dispersion in IRFs (that show the responses of the log-linear deviations of the variables from the NSS values to shocks when they are initially at the NSS), in Appendix I I calibrate a NSS with non-zero in‡ation. 2.3. Foreign trade, the public sector, and the balance of payments Firms in the export sector use domestic goods and ‘land’(representing natural resources) to produce an export commodity. Land is assumed to be …xed in quantity, hence generating diminishing returns. I assume that the export good is a single homogenous primary good (a commodity). Firms in this sector sell their output in the international market at the foreign currency price PX t. They are price takers in factor and product markets. The price of primary goods in terms of the domestic currency is merely the exogenous international price multiplied by the nominal exchange rate: StPX t: Let the production function employed by …rms in the export sector be the following: X t=QX tbAY1bA t;0< bA<1;(52) where QX tis the amount of domestic goods used as input in the export sector and Ytis real GDP. These …rms maximize pro…t StPX tX tPtQX tsubject to (52). In terms of domestic goods, they maximize: X t Pt =etp tQX tbAY1bA tQX t where I de…ned the SOE’s external terms of trade (XTT): p tPX t P t ; where P tis the price index of the foreign currency price of the SOE’s imports. Notice that the XTT is a ratio of two price indexes determined in the RW. Hence, the follow identity relates the rates of foreign in‡ation of exported and imported goods to the XTT (giving the dynamics of the XTT): p t p t1 =X t t ;where X tPX t PX t1 : The …rst order condition for pro…t maximization yields the export sector’s (factor) demand for domestic goods: QX t=bAetp t1 1bAYt:(53) Also, inserting the factor demand function in the production function shows that optimal exports vary directly with the product of the RER and the XTT and GDP: X t=bAetp tbA 1bAYt:(54)
16 The real value of exports in terms of domestic goods is: Xt=StPX tX t Pt =etp tX t=etp tbAetp tbA 1bAYt=X(etp t)bXYt(55) where for simplicity of notation I de…ne: bX1 1bA; XbAbA 1bA: Government expenditure is assumed to be a time-varying and stochastic fraction Gtof private consumption expenditure. De…ne the gross government expenditure fraction as: Gt1 + Gt. Hence, using (31) and (55), GDP in terms of domestic goods is: Yt=MM tGtpC tCt+Xt(1 aD)e1C tMM tGtpC tC Ct(56) =aDMM tGtpC tC Ct+Xt: In the domestic goods market, the output of domestic …rms Qtmust satisfy …nal demand from households (including the resources for transactions), the government, and the export sector:10 Qt=aDMM tGtpC tC Ct+QX t=Yt1bAXt:(57) The public sector includes the Government and the CB. The latter issues currency (Mt)and domestic currency bonds (Bt), and holds international reserves (Rt)in the form of foreign currency denominated riskfree bonds issued by the RW. I assume that the CB has no operational costs and that CB bonds are only held by domestic residents. The (‡ow) budget constraint of the CB is: Mt+BtStRt=Mt1+ (1 + it1)Bt1(1 + i t1)StRt1(58) = [Mt1+Bt1St1Rt1]QFt: where QFt=i t1StRt1+ (StSt1)Rt1it1Bt1 =i t1+ (1 1=t)StRt1it1Bt1 is the CB’s quasi-…scal surplus, which includes interest earned and capital gains on international reserves minus the interest paid on its bonds. I assume that the CB transfers its quasi-…scal surplus (or de…cit) to the Government every period. Hence, its net wealth is constant. Furthermore, assuming for convenience that the CB’s net worth is zero, the following holds for all t: Mt+BtStRt=Mt1+Bt1St1Rt1= 0:(59) 10Notice that intermediate output in the export sector (53) can be written as: QX t=bA1 1bA(etp t)bXYt=bAbAbA 1bA(etp t)bXYt=bAXt Hence, rearranging the second equality in (57) shows that GDP is the sum of the outputs of the domestic and export sectors, minus the intermediate use of domestic goods in the export sector Yt=Qt+XtbAXt.
17 The CB supplies whatever amount of cash is demanded by households, and can in‡uence these supplies by changing Rtor Bt, i.e. intervening in the foreign exchange market or in the domestic currency bond market. In terms of domestic goods, the CB balance, for all t, is: mt+bt=etrt:(60) This equation provides a constraint on the CB’s ability to simultaneously intervene in the foreign exchange market (through sales and purchases of foreign reserves rt) and in the domestic bonds market (through sales and purchases of domestic currency CB bonds bt).11 The Government spends on goods, receives the quasi-…scal surplus (or …nances the de…cit) of the CB, and collects taxes. I assume that …scal policy consists of an exogenous autoregressive path for real government expenditures as a (gross) fraction of private consumption (Gt) and collecting whatever lump-sum taxes are needed to balance the budget each period. The Public Sector ‡ow budget constraint is hence: Taxt=GtMM tPC tCtQFt:(61) So in real terms: taxt=GtMM tpC tCtqft;(62) qft=1 + i t11=tetrt1 t ((1 + it1)1) bt1 t : Inserting Yt=wtNt+t Pt ; in the household budget constraint (7) and consolidating the household, CB and government budget constraints yields the balance of payments equation: rtdt=CAt+rt1dt1; where the current account (in foreign currency) is: CAt=1 + i t1 t 1rt11 + i t1 t t1Det1dt1 Yt11dt1+TBt 11It is obviously unnecessary to restrict the CB net wealth to zero. Any …xed number would do. Moreover, there is clearly the possibility of adding a degree of freedom for a more general model in which the CB net wealth can vary (perhaps stochastically) or even be used as an additional control variable. The latter would require additional modeling, such as market perceptions of CB risk. For my purpose of modeling the simultaneous use of the interest rate and the rate of nominal depreciation as control variables, the simplest assumption of zero CB net wealth is su¢ cient.
18 and, using (32) and (56), the trade balance (in foreign currency) is: TBt=1 etXtetMM tGtCN t =1 ethXt(1 aD)e1C tpC tC MM tGtCti =1 etXt1aD aD e1C t(YtXt) =1 aDethpC t1C Xt(1 aD)e1C tYti: 2.4. Monetary and exchange rate policy In this paper the CB uses either policy rules or optimal policy under commitment (and full information) (OPC). The policy rules are simple (i.e., respond to a limited number of endogenous variables through constant coe¢ cients) and they may have either exogenous or endogenous and optimal coe¢ cients. Under simple rules with exogenous coe¢ cients, in the case of the rule for the nominal interest rate there is feedback (as in the typical Taylor-like rule) and the simple rule for nominal depreciation may or may not involve feedback. In the case of optimal simple rules, the CB is assumed to minimize a weighted average of the variances of some of the endogenous variables. In the case of OPC, the CB is assumed to minimize the expected discounted value of future losses for a suitably de…ned quadratic loss function of some of the endogenous variables. In any of these three cases, the CB can operate under one of three alternative monetary regimes. I use the expression ‘monetary regime’broadly. It expresses the combination of the CB’s operating procedures concerning the issuance of (base) money, and the intervention it may have in the bond and FX markets to in‡uence the nominal interest rate and the rate of nominal currency depreciation. As shown below, in this paper ‘monetary’policy (in the narrow sense) is passive, being money issuance whatever is needed to balance the money market once the other two policies are de…ned. For convenience, the three alternative monetary regimes are denominated: I) a Managed Exchange Rate (MER) regime, in which the CB uses both rules (or both instruments in the case of OPC), II) a Floating Exchange Rate (FER) regime, in which the CB only uses the Taylor-like rule (or only uses the interest rate as an instrument -in the case of OPC), and III) a Pegged Exchange Rate (PER) regime, in which the CB only uses the rule for the rate of nominal depreciation (or only uses the rate of nominal depreciation as an instrument, in the case of OPC). In the MER regime, through its regular and systematic interventions in the domestic currency bond (or ‘money’) market and in the foreign exchange market, the CB aims for the achievement of two operational targets: one for the interest rate it;and another for the rate of nominal depreciation t. When there are simple policy rules (whether they are optimal or not), the CB can respond to deviations of the consumption in‡ation rate (C t) from a target (T) which is the NSS value of this variable, to deviations of GDP from its NSS value, and to deviations of the RER from its NSS value. The rate of nominal depreciation can respond to the same variables and additionally to the deviations of the CB’s international reserves (IRs) ratio (to GDP ) from a long run target (R). There may be history
19 dependence (or inertia) in one or both of the two simple rules through the presence of the lagged operational target variable. The simple rules are the following: 1 + it 1 + i=1 + it1 1 + ih0C t T th1Yt Yh2et eh3(63) t =t1 k0C t T tk1Yt Yk2et ek3etrt=Yt Rk4 ;(64) where h16= 0 and k46= 0 and variables without time subscripts denote NSS values. The …rst of these is used in the MER and FER regimes, and the second is used in the MER and PER regimes. In a ‡oating exchange rate regime (FER), the CB abstains from intervening in the foreign exchange market. Hence, the international reserves that appear in its balance sheet remain constant. For simplicity, I assume that they remain constant at the NSS value rof the general model (with MER regime). In a pegged exchange rate regime (PER), the CB abstains from intervening in the domestic currency bond market. Hence, its stock of bonds remains constant, and I assume that they remain at the NSS value bof the MER regime. In both of the corner cases, one of the policy rules is dropped and one of the endogenous variables is turned into an exogenous parameter. But there is an alternative way of thinking about this issue which is more illuminating, particularly in an optimal control framework. The FER and PER regimes are extreme cases (‘corner regimes’) in which the CB chooses not to use one of its potential instruments. In the case of OPC this means that the optimal policy under any one of the ‘corner’ regimes cannot dominate the optimal policy under the MER regime. One can de…ne these regimes as cases in which the CB imposes an additional restriction on itself (‘ties its hands’) and relinquishes its use of one of its ‘control’variables. Hence that variable turns into a ‘non-control’variable.12 To obtain a generalization of the standard DSGE monetary policy model, I specify the instruments that the CB uses when it intervenes in each of the two markets and include them in the model. The CB purchases or sells domestic currency bonds, and thus changes its stock of bonds bt, to intervene with high frequency in this market in order to attain its operational target for the interest rate as determined by (63).13 And it purchases or sells foreign exchange to intervene in the foreign exchange market, thereby changing its stock of international reserves rt, in order to attain its operational target for the rate of nominal depreciation as determined by (64). While at high frequency (hours, days, weeks) the CB is active changing btand/or rt, at low frequency (quarters in this paper) these variables passively adapt to accommodate itand tas given by the feedback policy rules and the rest of the model equations. To represent the constraints that the CB faces it is necessary to broaden the usual policy model to include the CB balance sheet (60) and its arrangement with 12I hesitate to use the term ‘state variable’ because in this model both iand are nonpredetermined (or jump) variables and it is usual to call predetermined variables ‘state variables’. 13Notice that this high-frequency action may be modeled in di¤erent ways. But in the quarterly frequency of the model the instruments, operational target variables, and the rest of the model variables are related through the model equations that any higher frequency model must respect if it is designed to be consistent with the quarterly model.
20 the rest of the government (Treasury) as to the use of the …scal dimension of the CB’s ‡ow budget constraint (which I called CB quasi-…scal surplus qftabove). By assuming, as I do here, that the CB’s arrangement with the Treasury is that it hands over its quasi-…scal surplus (or receives automatic …nance for its quasi-…scal de…cit) period by period, the CB balance sheet equation is maintained period by period in the sense that the CB’s net worth is constant. This can be seen as a simple device for de…ning the CB’s ‘sterilization’policy, i.e. the value of bt, given the values of mt(‘determined’by money market balance), and the values of et and rt. But it is probably more adequate to think more symmetrically that (60) imposes a constraint on the simultaneous use of btand rt. From this vantage point, one should think of the ‘corner’regimes as the imposition of an additional constraint (instead of the dropping of an endogenous variable). In the case of the FER regime, the additional constraint is rt=r(an equation that replaces (64)). And in the case of the PER regime, the additional constraint is bt=b(an equation that replaces (63)). In terms of an optimal control framework (as is OPC), any one of the ‘corner’regimes imposes an additional constraint on the policymaker and, simultaneously, converts one of the ‘controls’(tin the case of the FER regime and itin the case of the PER regime) into a non-control variable. Hence, it quite evident that the MER regime cannot be inferior to any of the two ‘corner’regimes (in the sense of generating a larger loss). With the same loss function and the same (basic) model equations and endogenous variables, but with one additional constraint (equation) and one less ‘control’, the expected discounted loss cannot be lower. Indeed, I show below that it is very much higher in all of the usual CB preferences (represented through weights for in‡ation and output deviations). The policy framework in this paper is one in which monetary growth is passive.14 Indeed, de…ning the rate of money growth tMt=Mt1, (16) and (18) imply: t=C t L(1 + it) L(1 + it1)(1 + it)'M(L(1 + it)) 'M(1 + it1)1 C :(65) Hence, under the MER or FER regimes, achieving the operational target for the nominal interest rate bearing in mind the need to balance the money market implies that the growth in real money (t=C t) only depends on the current and lagged interest rate. However, (65) is equally valid under the PER regime, where there is no CB policy rule for the interest rate. 2.5. Functional forms for auxiliary functions For calibrations it is convenient to de…ne the net functions: DD t=DD t1; 'DD t='DD t1(66) MM t=MM t1; 'MM t='MM t1: 14See Olivera (1970).
21 I use the following functional forms:15 DD t1 12D t ; 1; 2>0;(67) MM t1 (1 + 2M t)3; 1; 2; 3>0(68) which, according to de…nitions (14), give: 'DD t=1 (1 2D t)2;(69) 'MM t=1 (1 + 2M t)31 + 3 2M t 1 + 2M t: The liquidity preference function (17) that results from (68) is: mt pC tCt M t=L(1 + it) = 1 22 4 123 11 1+it!1 3+1 13 5:(70) And to get a more compact notation in some of the equations the following auxiliary variables and equations are introduced: M;t = 1 + 1 (1 + 2M t)3 'M;t = 1 + (M;t 1) 1 + 3 2M t 1 + 2M t: 2.6. The nonlinear system of equations In this section I put together the model equations for simple feedback rules in a MER regime. Consumption Euler: CC t 'M;t =(1 + it)Et CC t+1 'M;t+1 1 C t+1 ! Risk-adjusted uncovered interest parity: 1 + it= (1 + i t) t"1 + 1 (1 + 2D t)2#Ett+1 (71) Phillips equations: t=Qt pC tCC t +Et1 t+1 t+1 t= 1 Qt pC tCC t mct+Et t+1t+1 t=11 t 11 1 t 15In calibrating the model parameters I found it important to include a third parameter in the the transactions cost function. Otherwise I could not obtain realistic money demand interest elasticities, and the variability of the instruments was systematically excessive.
22 Dynamics of price dispersion: t= tt1+ (1 )11 t 1 1 Exports: Xt=X(etp t)bXYt Trade Balance: TBt=1 aDethpC t1C Xt(1 aD)e1C tYti Current Account: CAt=1 + i t1 t 1rt11 + i t1 t t11 + 1 12D t11dt1+TBt: Balance of Payments: rtdt=CAt+rt1dt1 Real marginal cost: mct=wt t Labor market clearing: wt=NpC tCC t'M;tNN t Hours worked: Nt=Qt t t Domestic goods market clearing: Qt=Yt1bAXt GDP: Yt=aDM;tGtpC tC Ct+Xt Consumption relative price: pC t=aD+ (1 aD)e1C t1 1C Money market clearing: mt=1 22 4 123 11 1+it!1 3+1 13 5pC tCt; CB balance sheet: bt=etrtmt Consumption in‡ation: C t t =pC t pC t1
23 Real Exchange Rate: et et1 =t t t External terms of trade: p t p t1 =X t t (74) Tax collection: taxt=GtM;tpC tCtqft Quasi-…scal surplus: qft=1 + i t11=tetrt1 t ((1 + it1)1) bt1 t Great ratios: D t=etdt Yt ; M t=mt pC tCt ; Auxiliary functions: M;t = 1 + 1 (1 + 2M t)3; 'M;t = 1 + (M;t 1) 1 + 3 2M t 1 + 2M t: Interest rate feedback rule: 1 + it 1 + i=1 + it1 1 + ih0C t T th1Yt Yh2et eh3(75) Nominal depreciation feedback rule: t =t1 k0C t T tk1Yt Yk2et ek3etrt=Yt Rk4 (76) Notice that I am not constraining btnor rtto be non-negative, which may be quite unrealistic. Negative international reserves would mean borrowing from abroad and, in the context of this model, would require a risk premium as in the case of households. And many Central Banks are institutionally constrained in lending to the non-…nancial private sector, making btnon-negative. Here, I assume that the Central Bank’s target for reserves Ris su¢ ciently high and the household’s steady state demand for cash is su¢ ciently low to ensure that these non-negativity constraints hold for all tand all relevant stochastic shocks.16 In addition to these equations there are those that are subject to stochastic shocks, most of which are simple AR(1) processes. The external terms of trade (XTT) is a particularly important external e¤ect for most SOE’s. This justi…ed giving the calibration of its components a careful treatment. As a working hypothesis, I assumed that the in‡ation rates for imported and exported goods are interrelated in such a way that a shock to one of them a¤ects the other through 16In the parent model ARGEM, it is banks that invest in domestic currency bonds and usually Central Banks do have the institutional ability to assist banks, though usually with limitations.
24 the dynamics of the XTT (which is the ratio of the two corresponding foreign price levels). Hence, I assumed: X t=X t1XX1Xp t1Xexp X"X t;(77) t= t1 ()1p t1exp " t; p t=p t1 X t ( t): Notice that if the two price indexes are non-stationary, this implies that they are cointegrated. The XTT variable p tplays the role of a cointegration error term, X0; >0are the speeds of adjustment and (1;)plays the role of a cointegrating vector, with = 1 as in the identity (74). In Appendix I, I estimate these equations using data for Argentina and …nd evidence for the cointegration hypothesis with an additional in‡uence of X t1on t, as in the equation below. The equations subject to stochastic shocks are hence the following (where the NSS values ; ; Xare assumed equal to one): Productivity shock: t= (t1)exp (" t) Government expenditure shock: Gt= (Gt1)GG1Gexp G"G t Riskfree interest rate shock: 1 + i t=1 + i t1i (1 + i)1i exp i"i t Financing risk/liquidity shock: t= t1 ()1 exp " t Exports in‡ation shock: X t=X t1XX1Xp t1Xexp X" t Imported in‡ation shock: t= t1 ()1p t1X t1XN exp " t: 3. Numerical solution in Dynare A detailed calibration of the parameters and derivation of the NSS values of the endogenous variables can be found in Appendix 1. In this section I analyze the stabilizing role of the two policy rules under the di¤erent monetary and exchange rate regimes, mainly by studying the volatilities (standard deviations) of the main endogenous variables in the model. I also explore the policy parameter ranges that guarantee the Blanchard-Kahn (BK) stability conditions. Table 1 summarizes the calibrated values of the main model parameters that are used throughout, and also contains some comparisons with parameter values used in two other relevant SOE models.17 17‘E.S.’denotes ‘elasticity of substitution’, G_M stands for ‘Galí and Monacelli (2005)’, and De P for ‘De Paoli (2006)’.
31 The narrowing of the range of stability is more signi…cant in the case of the PER regime, especially in the cases of k2,k3, and k4. On the other hand, in the PER regime the stability range for k4includes 0, indicating that the need to respond to a target for international reserves is only valid in the more general MER regime. Because GDP is typically available with a signi…cant lag, it is of interest to see how these stability ranges are altered when the policy rules respond to output with a one quarter lag. Hence, the exercise was repeated by replacing Ytwith Yt1in both simple policy rules (including the IRs ratio to GDP). The resulting stability ranges are quite similar. For both the MER and FER regimes there is again no upper bound for h0and h1, and in this case there is no lower bound for h2, whereas the same upper bound subsists. There is no lower bound for h3in the case of the MER regime, and an increase in the upper bound to 5:99 in the FER regime. The stability ranges for the kiremain almost unaltered in the case of the MER regime. In the PER regime, however, k1is bounded above (by 0:67) whereas k2is not. Also, the stability range for k3is widened to [1:77;2:82] and the lower bound for k4becomes 2:45. Leaving behind the baseline calibration, it is interesting to verify that in the PER case there is stability when all the coe¢ cients are zero (kj= 0; j = 0;1;2;3;4). In this case the policy rule is to intervene in the FX market su¢ ciently to maintain the nominal exchange rate …xed at the existing level, letting the economy run its course, and not worrying about international reserves.19 7) The relatively narrow range of stability for the coe¢ cient on the interest rate response to GDP deviations (h2) in the MER case, along with the boundless range of stability for the corresponding coe¢ cient in the second policy rule (k2), naturally raises the question of the e¤ects of the latter coe¢ cient on the volatilities. Table 7 shows these e¤ects. Most the variables reach minimum volatilities for non-positive values of k2. And for a number of very signi…cant variables such as ,Y,C,N,m, and Utility, the minimum is reached for highly negative values of k2(-10 or -8). Indeed, the lowest volatility of Y,N, and Utility is lower than the lowest volatility they achieve, respectively, in any of the analogous tables above. Hence, reducing the rate of nominal depreciation (or perhaps even appreciating the currency) when GDP is above its NSS level has a very important stabilizing role for most of the variables of interest. Notice that this implies using both instruments with high volatility. 19However, one must bear in mind that here the nominal and real exchange rates are (in spirit) multilateral. If we modeled a multicountry RW, the nominal exchange rate would be the domestic currency price of a basket of the nominal exchange rates of the SOE’s trade partners, with weights equal to the shares in trade. Hence, our peg is completely di¤erent from pegging against the currency of a country with which only a small part of the SOE’s trade is done (as was the case of Argentina’s ill fated ‘Convertibility’).
32 Table 7: Means and standard deviations of main variables for di¤erent values of k2 h_0=0.4,h_1=0.8,k_4=-0.8 VARIABLE MEAN k_2=-10.0 k_2=-8.0 k_2=-4.0 k_2=-2.0 k_2=0.0 k_2=2.0 k_2=4.0 k_2=6.0 max/min piC 1.0150 0.0119 0.0117 0.0116 0.0117 0.0120 0.0128 0.0147 0.0183 1.58 DeltaP 1.0051 0.0013 0.0013 0.0013 0.0013 0.0013 0.0013 0.0014 0.0014 1.08 Y1.4430 0.0596 0.0610 0.0645 0.0669 0.0700 0.0741 0.0800 0.0886 1.49 C1.3108 0.0318 0.0318 0.0319 0.0320 0.0322 0.0325 0.0332 0.0346 1.09 N1.3220 0.0545 0.0554 0.0576 0.0590 0.0608 0.0631 0.0662 0.0706 1.30 real_ii 1.0101 0.0147 0.0146 0.0144 0.0145 0.0148 0.0158 0.0180 0.0226 1.57 mc 0.8302 0.0112 0.0111 0.0109 0.0109 0.0109 0.0110 0.0114 0.0122 1.12 e0.5951 0.0509 0.0503 0.0495 0.0494 0.0499 0.0511 0.0539 0.0592 1.20 TB 0.0082 0.0658 0.0637 0.0604 0.0600 0.0613 0.0655 0.0745 0.0907 1.51 d1.2125 0.1061 0.1059 0.1055 0.1051 0.1045 0.1037 0.1034 0.1057 1.03 m0.1154 0.0028 0.0028 0.0028 0.0029 0.0029 0.0029 0.0030 0.0031 1.11 Utility -2.2744 0.0486 0.0492 0.0509 0.0519 0.0532 0.0549 0.0572 0.0607 1.25 ii 1.0253 0.0114 0.0114 0.0113 0.0114 0.0116 0.0121 0.0130 0.0146 1.29 b0.0722 0.0908 0.0732 0.0369 0.0198 0.0167 0.0355 0.0616 0.0940 5.63 delta 1.0150 0.0669 0.0664 0.0659 0.0665 0.0687 0.0737 0.0843 0.1048 1.59 r0.3152 0.1622 0.1340 0.0778 0.0538 0.0448 0.0629 0.0988 0.1467 3.62 STANDARD DEVIATION 3.2. Optimal simple rules In view of these results, it is worthwhile to enquire what the optimal simple policy rules coe¢ cients are when using an objective function that represents the CB’s priorities with respect to to the volatilities it wants to minimize. In this subsection a (loss) function is de…ned that the CB wants to minimize and is de…ned using weights that re‡ect the CB’s priorities. It is an ad-hoc function, since it is not based directly on the maximization of household utility (or its second order approximation). 1) First I used Dynare’s ‘osr’(‘optimal simple rule’) command to obtain the policy coe¢ cients that minimized the variance of aggregate household Utility. In the case of the MER regime: arg min hi;ki f!UV ar (Utilityt)g = arg min hi;ki lim !1E0 1 X t=1 (1 )t!U(UtilitytUtility)2: A coe¢ cient !U=1000 was used in the loss function. The use of large coe¢ cients in the objective function is motivated by the need to have ‘osr’e¤ectively search the parameter space before settling on the optimal coe¢ cients. When I used low coe¢ cients (in the order of 1) the search was very short and I had to iterate the command (after putting the resulting coe¢ cients as the initial ones) many times before converging to the truly optimal ones. I obtained the following optimal coe¢ cients for the two simple policy rules (rounding o¤ to two digits): h0h1h2h3k0k1k2k3k4 0:97 1:53 2:59 0:06 2:41 0:04 0:80 3:60 0:44 Note that k4is negative, and the sum of h0and h1is above one.20 Also, the optimal value of k2is -0.8. These values are in accordance with what was 20Some of these values are outside the stability ranges shown in the table above. However,
33 obtained above. Under our simple rules, and assuming that the policymakers wish to reduce the variance of the utility of households, it is optimal to react strongly and positively to in‡ation and GDP in the interest rate rule and strongly and negatively to the RER in the nominal depreciation rule. A deviation of 1% in in‡ation above its target value here commands an increase of 1.5 p.p. in the interest rate (assuming it was at the NSS level the previous period) and a slight reduction of 0.04 p.p. in the rate of nominal depreciation (assuming it was at the NSS level the previous period). And a deviation of 1% in GDP above its NSS value commands an increase in the interest rate of 2.6 p.p. and a reduction of 0.8 p.p. in the rate of nominal depreciation. On the other hand, a deviation of 1% in the RER above its NSS value commands a tiny reduction in the interest rate (of 0.06 p.p.) and a signi…cant reduction in the rate of nominal depreciation of 3.6 p.p. The latter seems quite natural: if the currency is weak in real terms (e is high), it is optimal to depreciate less. Finally, it is optimal to make strong use of policy inertia in both rules (superinertial in the case of the second policy rule) even though no CB preference for such policies has been assumed. Table 8 shows the standard deviations of the main endogenous variables when using these optimal simple rules. Table 8: Means and standard deviations of main variables under optimal simple rules that minimize the variance of Utility VARIABLE MEAN Std.Dev. Std.Dev./Mean piC 1.015 0.065 0.06 DeltaP 1.005 0.044 0.04 Y1.443 0.052 0.04 C1.311 0.036 0.03 N1.322 0.033 0.02 real_ii 1.010 0.020 0.02 mc 0.830 0.037 0.04 e0.595 0.037 0.06 TB 0.008 0.058 7.11 d1.213 0.131 0.11 m0.115 0.005 0.05 Utility -2.274 0.032 -0.01 ii 1.025 0.053 0.05 b0.072 0.102 1.41 delta 1.015 0.079 0.08 r0.315 0.182 0.58 First, notice how small the standard deviation of Utility is. While the four tables above all had standard deviations above 0.0486, the ‘osr’routine reduced it to 0.032. Second, it is noteworthy that minimizing the volatility of Utility actually implies having substantial volatilities in many of the variables that ad-hoc CB loss functions usually try to minimize. While the highest s.d. of consumer in‡ation in the above four tables was 0.019, it is 0.065 when this optimal simple policy rule is that range was obtained keeping all the other coe¢ cients at their baseline levels, which is not done here. Dynare’s osr search changes direction whenever it goes into parameter values that do not comply with the Blanchard and Kahn conditions. In some cases, the search engine tended to obtain minor gains in loss with exceedingly high coe¢ cients (in absolute value, in the hundreds or thousands) when using some initializations. I always ignored such gains and kept to the more moderate coe¢ cient values.
34 used. The contrast with the price dispersion variable is even greater. The highest above was 0.008 and now it is 0.044. 2) Few CBs actually use models in which the explicit goal of the policymaker has to do with household utility. This is probably due to the fact that most models misrepresent reality in ways that CBs cannot take for granted: they assume homogenous households (except possibly for the heterogeneity derived from wage setting in a monopolistically competitive setting). The usual target variables of CB loss functions are in‡ation and GDP, and there is usually some explicit distaste for excessive movement in the operational target variable (the interest rate). This, of course, also brushes away, though in a di¤erent way, the incidence of CB actions on di¤erent sectors of the economy and di¤erent factor incomes. However, whereas aggregate household utility is an abstract concept because it is known that the model is misspeci…ed in the dimension of household heterogeneity, variables like in‡ation, GDP, or the RER, have clear empirical counterparts that are very present in the minds of policymakers when they make decisions. Hence, I now repeat the above exercise assuming that the CB minimizes a linear combination of the variances of its target variables: arg min hi;ki!V ar C t+!YV ar (Yt) + !eV ar (et) + !rV ar (rt) +!iV ar (it) + !V ar (t)g Aside from the usual terms (with weights !,!Y,!i), this loss function also allows for CB preferences with respect to the variances of the RER, of the CBs IRs, and of changes in the rate of nominal depreciation (with weights !e,!r,!). In Table 9 I de…ne six di¤erent CB styles (or preferences: A-F) according to the combinations of weights in each. In all of them I have given the same weight to the changes in each of the operational targets (50), and avoided zeros giving a weight of 1 to target variables with no importance. Hence, in style A only in‡ation matters and in style B only GDP matters, whereas both matter equally in style C. In style D (F) the real exchange rate (international reserves) matters as much as in‡ation and GDP. Finally, in style F in‡ation, GDP, the RER and the IRs all matter equally. Table 9: De…nition of CB styles Weights Styles A B C D E F !100 1 100 100 100 100 !Y1 100 100 100 100 100 !e1 1 1 100 1 100 !r1 1 1 1 100 100 !i50 50 50 50 50 50 !50 50 50 50 50 50 With Dynare’s ‘osr’command I obtained the optimal simple policy rules for each of the CB styles in each of the interest and exchange regimes. The coe¢ cients are shown in Table 10:
35 Table 10: Optimal simple policy rules for di¤erent CB styles and regimes MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER h_0 0.33 0.01 1.86 1.17 1.63 1.28 1.71 1.28 1.94 1.28 1.97 1.28 h_1 1.26 2.04 -1.01 -0.39 1.92 -0.20 -2.09 -0.22 0.56 -0.20 0.49 -0.22 h_2 0.02 -0.05 4.34 -3.72 1.43 -0.34 2.56 -0.34 -5.24 -0.34 -5.37 -0.34 h_3 0.12 0.04 -0.21 -0.40 0.82 -0.02 -0.05 -0.01 0.14 -0.02 0.14 -0.01 k_0 -0.03 -0.26 3.08 -0.47 0.44 -0.37 3.39 -0.43 0.26 -0.39 0.34 -0.41 k_1 -0.07 -2.08 -3.92 -2.13 -1.31 -2.82 -1.18 -3.70 1.28 -4.46 1.25 -3.71 k_2 -0.08 -2.36 -2.28 -4.66 -0.12 -3.85 -3.05 -3.92 -2.04 -5.09 -2.16 -4.32 k_3 -0.43 -1.09 1.18 0.46 -0.91 -0.10 1.40 0.08 0.16 0.11 -0.04 0.22 k_4 -0.08 -2.18 0.40 -0.87 -0.06 -2.57 0.13 -2.35 -0.74 -3.29 -0.84 -2.74 E F OPTIMAL SIMPLE POLICY RULES A B C D The inertial coe¢ cient for the interest rate (h0)is superinertial in all styles except A, in which only in‡ation matters. In the MER regime, the interest rate response to in‡ation deviations (h1)is greater than one in styles A and C, in both of which in‡ation matters. However, it is negative for styles B and D. Interestingly, with the latter styles the optimal nominal depreciation rule in the MER regime has k4>0. Furthermore, in both cases h0+h1is less than one and h1is negative, and yet there is Blanchard-Kahn stability since in both of these cases the interest rate response to GDP is su¢ ciently high (4.3 and 2.6, respectively). This is again in line with the Taylor Principle (see Woodford (2003), Proposition 4.4). Also, the depreciation rate response to to in‡ation and GDP are highly negative (-2.3 and -3.1, respectively). In the FER regime, central banks of style A practically respond only to in‡ation, with a coe¢ cient greater than two. However, in all the rest of the styles, h0is superinertial and h1is negative. The inequality h0+h1>1is valid in all CB styles except B where only GDP stabilization matters. Curiously, here it is a very negative interest rate reaction to GDP deviations maintains stability, quite the opposite from the MER regime case. And in the PER regime, all the coe¢ cients are negative except for k3, which is positive for styles B, D, E, and F. Hence, under the PER regime, high in‡ation and high GDP imply lowering the rate of nominal depreciation (or appreciating), and the previous’period rate of nominal depreciation a¤ects the present rate negatively. Finally, in the PER regime k4is negative for all the CB styles considered, and the highest coe¢ cient in absolute value is always k2. The latter means that responses to deviations of GDP tend to very …rm, regardless of the particular CB preferences. To see if the relatively high preference for inertia in the operational targets (!i=!= 50) in the de…nitions of the CB styles is the reason for the high superinertial coe¢ cients in Taylor rule under styles B-F, I made the same calculations using a much lower preference for inertia: !i=!= 10.21 Table 11 shows that the broad outline of the optimal policy rules remain very similar to the previous table. Paradoxically, h0actually increases in six of the twelve cases, and quite substantially for some, showing that it is de…nitely not the preference of avoiding changes in the operational targets that are behind the high inertial coe¢ cients in the Taylor rule. 21For notational simplicity I maintain the same names for the alternative CB preferences as in Table 9 although the last two rows of that table are modi…ed.
36 Table 11: Optimal simple policy rules for alternative CB styles with !i=!= 10 MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER h_0 0.79 0.29 1.13 1.38 1.14 1.28 5.33 1.27 4.11 1.28 3.59 1.27 h_1 1.53 3.01 -0.21 0.27 -0.66 -0.11 -2.54 -0.12 -0.15 -0.11 0.05 -0.12 h_2 -0.03 0.01 4.10 -4.66 1.58 -0.23 -4.80 -0.23 -2.25 -0.23 -2.94 -0.23 h_3 0.08 0.22 -0.19 0.32 0.02 -0.01 0.81 0.00 0.37 -0.01 0.52 0.00 k_0 -0.09 -0.38 2.88 -0.82 1.26 -1.11 -0.64 -0.91 0.09 -1.26 0.25 -1.16 k_1 -0.01 -10.58 -2.13 -1.64 1.72 -7.97 1.87 -5.43 -0.90 -8.80 -0.58 -8.08 k_2 -0.07 -3.66 -2.06 -4.93 -7.32 -7.57 -2.17 -5.38 -1.98 -9.49 -1.94 -7.76 k_3 -0.39 -1.52 1.00 0.28 -0.02 0.45 -1.97 0.53 0.71 0.75 -0.77 1.02 k_4 -0.15 -3.24 0.34 -1.52 0.02 -3.73 -0.18 -2.59 -3.53 -5.26 -4.65 -3.87 E F A B C D OPTIMAL SIMPLE POLICY RULES Table 12 shows the standard deviations of the main endogenous variables in each regime and CB style, as well as the total and relative losses. As expected, the loss is always lowest with the MER regime. For CB styles A and B the losses with the FER and PER regimes are between six and eleven times higher than with the MER regime. In style C, where both in‡ation and GDP matter, the losses in the FER and PER regimes are 3 and 2.4 times the loss with the MER regime. The di¤erences in the losses are lowest with CB styles E and F (where IRs matter). But the corner regimes still have losses that are between 30% and 70% greater than in the MER regime. It should be emphasized that the PER regime here is not the usual pegged exchange regime. The simple rule in the PER regime includes the typical peg, which has no feedback. But this section shows that it is in general optimal to operate the PER regime with feedback. And the feedback coe¢ cients are in general quite high (in absolute value). Hence, it is optimal to operate a very active peg for any of the CB styles. Table 12: Standard deviations of main variables and losses under optimal simple rules MEAN MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER piC 1.015 0.006 0.016 0.011 0.070 0.157 0.045 0.033 0.039 0.017 0.039 0.039 0.017 0.037 0.039 0.017 0.037 0.039 0.018 DeltaP 1.005 0.004 0.004 0.007 0.050 0.109 0.029 0.019 0.022 0.009 0.027 0.022 0.009 0.024 0.022 0.009 0.024 0.022 0.009 Y1.443 0.073 0.070 0.078 0.012 0.014 0.056 0.040 0.042 0.063 0.027 0.043 0.063 0.017 0.042 0.063 0.017 0.043 0.063 C1.312 0.037 0.039 0.074 0.086 0.089 0.053 0.078 0.072 0.048 0.077 0.072 0.049 0.082 0.072 0.044 0.082 0.072 0.045 N1.322 0.063 0.064 0.079 0.072 0.138 0.037 0.036 0.054 0.054 0.061 0.054 0.053 0.050 0.054 0.053 0.049 0.054 0.053 real_ii 1.010 0.011 0.035 0.052 0.017 0.035 0.035 0.028 0.022 0.035 0.023 0.021 0.036 0.032 0.022 0.032 0.031 0.021 0.032 mc 0.830 0.026 0.025 0.069 0.079 0.092 0.045 0.072 0.071 0.036 0.072 0.070 0.036 0.076 0.071 0.031 0.076 0.070 0.032 e0.594 0.038 0.052 0.048 0.037 0.052 0.048 0.044 0.055 0.048 0.034 0.055 0.048 0.050 0.055 0.049 0.049 0.055 0.048 TB 0.007 0.060 0.067 0.058 0.052 0.068 0.058 0.080 0.073 0.059 0.068 0.073 0.058 0.060 0.073 0.059 0.059 0.073 0.059 d1.214 0.135 0.081 0.099 0.123 0.072 0.094 0.144 0.087 0.094 0.126 0.086 0.094 0.094 0.087 0.094 0.095 0.086 0.093 m0.115 0.003 0.006 0.011 0.014 0.019 0.007 0.007 0.008 0.007 0.012 0.009 0.007 0.011 0.008 0.006 0.011 0.009 0.006 Utility -2.273 0.050 0.055 0.054 0.074 0.105 0.041 0.051 0.057 0.050 0.064 0.058 0.049 0.060 0.057 0.050 0.060 0.058 0.050 ii 1.025 0.011 0.036 0.048 0.076 0.136 0.049 0.026 0.033 0.036 0.055 0.034 0.038 0.042 0.033 0.034 0.042 0.034 0.035 b0.072 0.106 0.021 0.000 0.116 0.022 0.000 0.163 0.018 0.000 0.163 0.018 0.000 0.014 0.018 0.000 0.014 0.018 0.000 delta 1.015 0.029 0.081 0.058 0.066 0.166 0.078 0.044 0.093 0.066 0.036 0.092 0.066 0.073 0.093 0.068 0.072 0.092 0.067 r0.316 0.197 0.000 0.042 0.196 0.000 0.035 0.277 0.000 0.035 0.282 0.000 0.035 0.038 0.000 0.034 0.041 0.000 0.034 Loss 0.08 0.87 0.53 0.10 0.65 0.91 0.41 1.23 0.97 0.44 1.53 1.20 0.74 1.23 1.09 0.99 1.53 1.32 Relative Loss 10.9 6.6 6.5 9.1 3.0 2.4 3.5 2.7 1.7 1.5 1.5 1.3 OPTIMAL SIMPLE POLICY RULES STANDARD DEVIATION A B C D E F 3.3. Optimal policy under commitment In this section I use Dynare’s ‘ramsey’ command to obtain the optimal policy under commitment, i.e., the policy functions that yield the minimum expected value (conditional on the information at t=t0, including given initial conditions
37 for the predetermined variables) of the discounted ad-hoc loss function: Lt0=Et0 1 X t=t0 tt01 2Lt, (78) where the period loss function Ltis given by: Lt=!C tT2+!Y(YtY)2+!e(ete)2+!r(rtr)2+!i(it)2 (79) +!(t)2; subject to all the model equations (except, of course, the simple policy rules). I maintain the same de…nition of CB styles as in the previous section (with !i= != 50). Also, for simplicity I assume that the planner has the same intertemporal discount rate as households (= 0:99). In Table 13 I report the standard deviations of the main variables as well as the expected loss for the alternative CB styles (A-F) and the alternative policy regimes (MER, FER, PER). Table 13: Standard deviations of main variables and losses under optimal policy under commitment VARIABLE MEAN MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER piC 1.015 0.007 0.035 0.020 0.052 0.145 0.118 0.025 0.036 0.031 0.025 0.036 0.031 0.032 0.036 0.032 0.032 0.036 0.031 DeltaP 1.005 0.004 0.019 0.012 0.037 0.100 0.082 0.015 0.022 0.020 0.015 0.023 0.020 0.020 0.022 0.019 0.020 0.023 0.019 Y1.443 0.072 0.096 0.070 0.008 0.021 0.019 0.018 0.024 0.023 0.019 0.026 0.024 0.022 0.024 0.024 0.023 0.026 0.025 C1.312 0.043 0.058 0.060 0.080 0.090 0.089 0.073 0.078 0.077 0.068 0.077 0.077 0.075 0.078 0.072 0.074 0.077 0.073 N1.322 0.063 0.090 0.068 0.054 0.129 0.110 0.038 0.047 0.046 0.038 0.047 0.046 0.044 0.047 0.044 0.044 0.047 0.044 real_ii 1.010 0.012 0.036 0.047 0.017 0.050 0.043 0.023 0.044 0.037 0.020 0.045 0.038 0.033 0.044 0.035 0.033 0.045 0.035 mc 0.830 0.034 0.075 0.053 0.076 0.091 0.087 0.068 0.070 0.070 0.065 0.071 0.070 0.068 0.070 0.066 0.068 0.071 0.066 e0.594 0.039 0.049 0.048 0.037 0.051 0.050 0.038 0.052 0.049 0.028 0.051 0.049 0.049 0.052 0.049 0.048 0.051 0.049 TB 0.007 0.051 0.057 0.056 0.047 0.063 0.060 0.052 0.065 0.058 0.052 0.064 0.058 0.058 0.065 0.059 0.056 0.064 0.058 d1.214 0.135 0.071 0.091 0.121 0.066 0.082 0.129 0.073 0.089 0.112 0.071 0.087 0.091 0.073 0.088 0.090 0.071 0.087 m0.115 0.004 0.011 0.009 0.012 0.019 0.016 0.009 0.010 0.010 0.009 0.011 0.010 0.009 0.010 0.009 0.009 0.011 0.009 Utility -2.273 0.050 0.055 0.053 0.064 0.099 0.089 0.054 0.058 0.057 0.053 0.058 0.057 0.057 0.058 0.056 0.056 0.058 0.056 ii 1.025 0.010 0.057 0.044 0.058 0.125 0.103 0.032 0.046 0.040 0.031 0.048 0.042 0.037 0.046 0.038 0.038 0.048 0.039 b0.072 0.100 0.015 0.000 0.100 0.023 0.000 0.116 0.022 0.000 0.149 0.022 0.000 0.013 0.022 0.000 0.013 0.022 0.000 delta 1.015 0.027 0.076 0.059 0.051 0.150 0.123 0.036 0.080 0.068 0.034 0.080 0.067 0.067 0.080 0.069 0.066 0.080 0.068 r0.316 0.188 0.000 0.036 0.178 0.000 0.036 0.206 0.000 0.036 0.262 0.000 0.036 0.037 0.000 0.034 0.039 0.000 0.034 Loss 115.7 450.9 403.1 59.0 159.7 173.8 179.6 492.8 476.7 224.5 519.9 501.7 417.6 492.8 492.2 441.5 519.9 517.4 Relative Loss 3.90 3.48 2.71 2.95 2.74 2.65 2.32 2.24 1.18 1.18 1.18 1.17 OPTIMAL POLICY UNDER COMMITMENT STANDARD DEVIATION A B C D E F As expected, the MER regime always dominates the two ‘corner’regimes. Under CB styles A, B, and C, the losses under the FER and PER regimes are between 2.65 and 3.90 times the corresponding losses under the MER regime. Under CB styles E and F, where IRs matter for the CB, the losses under the FER and PER regimes are ‘only’ 17/18% higher than in the MER regime. In CB style B, in which only GDP matters, the FER regime achieves a signi…cantly lower cost than the PER regime. In CB styles A, C, and D, it is the PER regime that is second best. And in CB styles E and F, the two ‘corner’regimes obtain losses that are approximately the same. Tables 14 and 15 show the coe¢ cients of the policy functions in the reduced form (or ‘solution’of the DSGE model) corresponding to the instrument variables (in the sense of optimal control theory), i.e., the operational targets (in the economic sense), for the three alternative regimes. These variables22 are linear functions of 22Notice that we show the variables in the tables as they appear in the Dynare output. However, it is necessary to ‘read’the variables (contemporaneous or lagged) as their log-linear deviations with respect to their NSS values.
38 the 9 non-shock predetermined variables (i,,r,e,Y,d,,pC,p), the 6 shock variables23, and the Lagrange multipliers corresponding to the 5 equations with forward-looking terms (the UIP equation, the two dynamic Phillips equations, the consumption Euler equation, and the real interest rate equation). In all of the CB styles there is substantial inertia in the interest rate policy function (between 0.28 and 0.69) and in the nominal depreciation policy function (between 0.1 and 0.6). This is hardly surprising since all these CB styles have been de…ned to show a signi…cant preference for policy inertia. What is perhaps surprising is the dispersion in the inertial coe¢ cients, given that they all have the same weight for preference for inertia (50). The coe¢ cients on the Lagrange multipliers are relatively small, implying that the policy function coe¢ cients (for the rest of the variables) do not vary much from quarter to quarter when these e¤ects are cumulated (attributable to the commitment to never again re-optimize). The largest of these coe¢ cients correspond to the Lagrange multipliers for the Phillips equations under CB style B, where only GDP matters. Table 14: Reduced form policy functions under optimal policy under commitment and MER regime STYLES: ii delta ii delta ii delta ii delta ii delta ii delta Constant 1.025 1.015 1.025 1.015 1.025 1.015 1.025 1.015 1.025 1.015 1.025 1.015 ii(-1) 0.689 0.011 0.551 0.325 0.387 0.106 0.376 0.098 0.307 0.040 0.307 0.040 delta(-1) 0.011 0.358 0.325 0.604 0.106 0.302 0.098 0.240 0.040 0.131 0.040 0.130 r(-1) -0.021 -0.070 0.044 -0.044 0.022 -0.073 0.012 -0.054 -0.227 -0.353 -0.230 -0.344 e(-1) 0.029 -0.564 0.507 -0.484 0.372 -0.685 0.321 -0.883 -0.004 -1.314 -0.002 -1.322 Y(-1) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 d(-1) 0.021 0.070 -0.044 0.044 -0.022 0.073 -0.012 0.054 0.227 0.354 0.231 0.345 DeltaP(-1) 0.009 0.007 -0.019 0.016 -0.009 0.031 -0.006 0.042 0.014 0.069 0.014 0.069 pC(-1) -0.177 0.364 0.008 0.012 0.119 0.195 0.115 0.208 0.105 0.218 0.105 0.218 pStar(-1) -0.017 -0.182 0.194 -0.184 0.158 -0.235 0.148 -0.237 -0.141 -0.631 -0.145 -0.619 z_piStar(-1) -0.004 -0.106 0.073 -0.071 0.036 -0.123 0.024 -0.138 -0.058 -0.261 -0.059 -0.260 z_piStarX(-1) -0.021 -0.126 0.110 -0.106 0.069 -0.163 0.055 -0.136 -0.112 -0.412 -0.115 -0.405 z_G(-1) 0.012 -0.052 0.154 -0.124 0.115 -0.162 0.108 -0.216 -0.021 -0.404 -0.021 -0.402 z_epsilon(-1) -0.029 -0.031 0.066 -0.053 0.018 -0.114 0.008 -0.161 -0.069 -0.273 -0.069 -0.273 z_iStar(-1) 0.045 0.169 -0.117 0.117 -0.071 0.178 -0.044 0.136 0.390 0.725 0.397 0.708 z_phiStar(-1) 0.035 0.120 -0.075 0.075 -0.038 0.124 -0.022 0.093 0.360 0.583 0.365 0.567 mult_8(-1) 0.000 0.004 0.003 0.006 0.001 0.003 0.001 0.002 0.000 0.001 0.000 0.001 mult_15(-1) 0.005 0.026 0.123 0.165 0.016 0.021 0.016 0.023 0.019 0.027 0.019 0.027 mult_16(-1) -0.003 0.038 0.161 0.216 0.020 0.025 0.021 0.029 0.024 0.036 0.024 0.036 mult_22(-1) 0.007 -0.002 -0.002 -0.004 0.001 0.001 0.001 0.000 0.001 -0.001 0.001 -0.001 mult_30(-1) 0.001 -0.002 -0.004 -0.005 -0.001 -0.001 -0.001 -0.001 0.000 -0.001 0.000 -0.001 eps_epsilon -0.036 -0.039 0.083 -0.066 0.022 -0.143 0.011 -0.201 -0.087 -0.341 -0.087 -0.341 eps_G 0.014 -0.061 0.181 -0.145 0.135 -0.191 0.127 -0.254 -0.024 -0.476 -0.025 -0.473 eps_iStar 0.037 0.151 -0.111 0.111 -0.074 0.161 -0.048 0.125 0.266 0.582 0.271 0.570 eps_phiStar -0.033 -0.114 0.075 -0.075 0.041 -0.120 0.024 -0.089 -0.283 -0.513 -0.288 -0.500 eps_piStar 0.025 -0.255 0.121 -0.123 0.029 -0.257 0.001 -0.391 -0.045 -0.399 -0.041 -0.412 eps_piStarX -0.052 -0.306 0.269 -0.259 0.168 -0.398 0.135 -0.332 -0.273 -1.006 -0.281 -0.987 E OPTIMAL POLICY UNDER COMMITMENT MER A B C D F 23Notice that the shock variables appear here because Dynare automatically expresses the transition or policy functions of all variables (including those that are jump variables) in terms of lagged predetermined variables. If, as in Klein (2000) we were to express jump variables in terms of contemporaneous predetermined variables the shocks would not appear in the tables.
39 In order to study the sensitivity of the expected discounted loss under Ramsey to di¤erent parameter values, it is useful to know the structural parameter ranges under which (under a MER regime and Ramsey optimal policy rules) there is stability. A simple way to approach this is to start from the baseline set of parameters used above, and vary each parameter individually using a speci…c CB style until stability is impaired. I used CB style C. Table 16 shows that there are remarkably wide ranges within which the parameters can be moved individually while maintaining stability. Obviously, in some cases I did not bother to …nd the actual extremes. Table 15: Reduced form policy functions under optimal policy under commitment and FER and PER regimes Regimes: STYLES: A B C D E F A B C D E F ii ii ii ii ii ii delta delta delta delta delta delta Constant 1.025 1.025 1.025 1.025 1.025 1.025 1.015 1.015 1.015 1.015 1.015 1.015 ii(-1) 0.635 0.523 0.279 0.277 0.279 0.277 -0.139 0.351 0.002 0.003 0.002 0.003 delta(-1) -0.086 0.352 0.015 0.016 0.015 0.016 0.185 0.571 0.105 0.105 0.104 0.104 r(-1) -0.178 -0.014 -0.342 -0.354 -0.342 -0.354 -0.378 -0.056 -0.376 -0.375 -0.379 -0.379 e(-1) -0.322 0.514 -0.156 -0.153 -0.156 -0.153 -1.259 -0.593 -1.448 -1.450 -1.452 -1.453 Y(-1) 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 d(-1) 0.178 0.014 0.342 0.355 0.342 0.355 0.379 0.057 0.377 0.376 0.380 0.380 DeltaP(-1) 0.032 -0.019 0.022 0.023 0.022 0.023 0.043 0.020 0.074 0.074 0.074 0.074 pC(-1) -0.176 0.008 0.102 0.102 0.102 0.102 0.404 0.013 0.216 0.216 0.215 0.215 pStar(-1) -0.237 0.153 -0.273 -0.288 -0.273 -0.288 -0.599 -0.229 -0.676 -0.675 -0.681 -0.680 z_piStar(-1) -0.084 0.065 -0.098 -0.100 -0.098 -0.100 -0.249 -0.088 -0.272 -0.273 -0.272 -0.273 z_piStarX(-1) -0.167 0.091 -0.187 -0.197 -0.187 -0.197 -0.366 -0.134 -0.415 -0.416 -0.415 -0.416 z_G(-1) -0.104 0.149 -0.077 -0.081 -0.077 -0.081 -0.308 -0.155 -0.491 -0.490 -0.505 -0.505 z_epsilon(-1) -0.112 0.068 -0.101 -0.102 -0.101 -0.102 -0.165 -0.068 -0.290 -0.290 -0.292 -0.292 z_iStar(-1) 0.352 -0.023 0.600 0.622 0.600 0.622 0.737 0.151 0.745 0.745 0.745 0.746 z_phiStar(-1) 0.293 0.014 0.542 0.562 0.542 0.562 0.614 0.099 0.615 0.613 0.619 0.618 mult_9(-1) -0.001 0.004 0.000 0.000 0.000 0.000 0.002 0.006 0.001 0.001 0.001 0.001 mult_16(-1) 0.009 0.121 0.021 0.021 0.021 0.021 0.035 0.176 0.027 0.027 0.027 0.027 mult_17(-1) 0.003 0.158 0.026 0.026 0.026 0.026 0.052 0.232 0.036 0.036 0.036 0.036 mult_23(-1) 0.006 -0.002 0.001 0.001 0.001 0.001 -0.004 -0.005 -0.001 -0.001 -0.001 -0.001 mult_31(-1) 0.001 -0.004 0.000 0.000 0.000 0.000 -0.002 -0.006 -0.001 -0.001 -0.001 -0.001 eps_epsilon -0.140 0.085 -0.126 -0.128 -0.126 -0.128 -0.207 -0.085 -0.363 -0.363 -0.364 -0.365 eps_G -0.122 0.175 -0.090 -0.095 -0.090 -0.095 -0.362 -0.182 -0.578 -0.577 -0.594 -0.594 eps_iStar 0.275 -0.051 0.418 0.435 0.418 0.435 0.567 0.144 0.581 0.582 0.578 0.579 eps_phiStar -0.256 0.013 -0.426 -0.442 -0.426 -0.442 -0.515 -0.103 -0.526 -0.526 -0.528 -0.528 eps_piStar -0.053 0.127 -0.076 -0.066 -0.076 -0.066 -0.445 -0.145 -0.452 -0.453 -0.451 -0.451 eps_piStarX -0.406 0.222 -0.457 -0.480 -0.457 -0.480 -0.892 -0.328 -1.011 -1.014 -1.012 -1.016 FER PER OPTIMAL POLICY UNDER COMMITMENT The degree of price stickiness () in the New Keynesian Phillips equation is often considered an important factor in determining the desirability of alternative exchange regimes. Table 17 shows the losses under each CB style and exchange rate regime for six alternative degrees of price stickiness, which go from practically no price stickiness (=0.01) to very high price stickiness (=0.90). As expected, for each CB style and value of , the MER regime does better and in most cases much better. CB styles E and F are the ones for which the advantage of the MER regime is smallest, especially when there is little price stickiness: for =0.01, 0.10 and 0.30, the PER regime has a loss which is only 3-5% higher than in the MER regime. This is probably because the CB preference for stabilizing IRs makes it
40 behave similarly in MER and PER regimes. In the FER regime the excess loss is in the 7-10% range for CB styles E and F. However, for CB styles A, B, and C, the corner regimes have losses between 20% and 260% higher. The highest relative advantage for the MER regime is obtained for high degrees of price stickiness. In general, the PER regime is second best for low degrees of price stickiness (0.30). For =0.50, the FER regime is second best only for CB style B (where only GDP matters). And for higher values of , the FER regime is second best for CB styles A, B, E, and F. Another interesting feature is that the (absolute) losses are not always strictly increasing with . For example, under CB style B and regime MER, the loss reaches a peak for =0.30. For the same CB style but regimes FER and PER, the loss does increase monotonously with . But for CB style A, these regimes reach a peak at =0.70, while the MER regime has its loss increasing monotonously throughout. Table 16: Stability ranges for individual non-policy parameters with optimal policy under commitment, MER regime, and CB style C Parameter Baseline value Stability range TpiT 1.015 <0.8 - 1.07 betta 0.99 <0.8 - 0.999999 CsigmaC 1.5 0.01 - 50 NsigmaN 0.5 0.01 - 50 aDa_D 0.86 0.35 - 0.99 thetta 6 1.01 - 27 CthettaC 1.5 0.01 - 0.99 and 1.01 - 50 bAbA 0.5 0.01 - 0.99 alpha 0.66 0.01 - 0.91 "' Dvarepsvarphi_D 2 0.01 - 10000 "Lvarepsilon_L 1.02 0.3 - 100 DgammaD 0.5 0.01 - 50 Summing up, with or without price stickiness there is a gain from intervening in the FX market in the sense that the CB can better stabilize its target variables. The advantage is greater when the CB only cares about stabilization in‡ation and/or GDP (CB styles A, B, or C) and the degree of price stickiness is high (around 0.70 in CB style A, and around 0.90 in CB style B). Table 17: CB losses with optimal policy under commitment for di¤erent values of STYLE MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER A 78.2 144.1 131.3 78.7 149.5 134.9 82.9 182.0 157.2 93.8 295.1 234.1 125.8 432.6 437.5 168.1 230.9 249.3 B 50.0 74.7 64.7 52.8 75.4 65.6 74.3 97.7 89.0 73.3 139.6 141.8 57.4 163.5 179.8 60.6 193.5 218.4 C 148.4 211.3 194.8 154.9 218.9 201.9 186.8 279.5 256.6 211.3 432.9 399.1 172.2 490.3 480.1 183.1 520.9 520.4 D 162.1 242.8 221.8 169.0 250.0 228.6 202.9 309.7 282.4 238.9 462.7 425.0 219.4 516.6 504.6 235.9 545.7 543.6 E 198.2 211.3 204.0 205.4 218.9 211.7 256.3 279.5 268.4 373.3 432.9 412.9 416.3 490.3 496.2 447.6 520.9 536.6 F 225.2 242.8 231.1 232.4 250.0 238.5 282.8 309.7 294.3 398.7 462.7 439.0 439.9 516.6 520.9 470.7 545.7 559.8 A1.84 1.68 1.90 1.71 2.19 1.90 3.15 2.50 3.44 3.48 1.37 1.48 B1.49 1.29 1.43 1.24 1.31 1.20 1.90 1.93 2.85 3.13 3.19 3.60 C1.42 1.31 1.41 1.30 1.50 1.37 2.05 1.89 2.85 2.79 2.84 2.84 D1.50 1.37 1.48 1.35 1.53 1.39 1.94 1.78 2.35 2.30 2.31 2.30 E1.07 1.03 1.07 1.03 1.09 1.05 1.16 1.11 1.18 1.19 1.16 1.20 F1.08 1.03 1.08 1.03 1.10 1.04 1.16 1.10 1.17 1.18 1.16 1.19 RELATIVE LOSS SENSITIVITY TO PRICE STICKINESS UNDER OPTIMAL POLICY UNDER COMMITMENT LOSS alpha=0.01 alpha=0.10 alpha=0.30 alpha=0.50 alpha=0.70 alpha=0.90
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50 Appendix 1. Calibration of parameters and derivation of the corresponding non-stochastic steady state In this Appendix I obtain the calibrated values for the model’s parameters and the corresponding non-stochastic steady state (NSS) values of the model variables. There are always many ways of doing this. I calibrate some of the parameters, some ratios and some NSS values of endogenous variables, and obtain the rest sequentially from the static nonlinear equations so that a computer code can follow the same steps if one changes some of the calibrated values or estimates some of them from the data. A.1.1. Calibration of the components of the external terms of trade The terms of trade is a particularly important variable for any SOE. Hence, I made a preliminary investigation of the data pertaining to Argentina. To confront (77) with the data, notice that the …rst two of these equations can be written in terms of the (logs of) price indexes: log PX t=X log PX t1+1Xlog X+Xlog PX t1log PN t1 +X"X t; log PN t= log PN t1+ (1 ) log N+log PX t1log PN t1 +" t: A quick estimation for cointegration of Argentina’s trade price indexes during 1993Q3-2009Q2 gave the results in the table below (the notation should be obvious). Although empirically I was not able to impose a coe¢ cient of negative one for the second coe¢ cient in the cointegrating relation, I did impose it in the calibration to be consistent with the de…nition of the terms of trade. I also ignored the small deterministic trend in the cointegrating relation, the two time dummies (…rst and fourth quarters of 2008) that made the residuals normal, homoscedastic and devoid of serial correlation, as well as the non-signi…cant coe¢ cients. Hence, I use the following speci…cation in the model: log PX t= 0:41 log PX t1+ (1 0:41) log X0:25 log PX t1log PN t1 +0:0424" t; log PN t= 0:20 log PN t1+ (1 0:20) log N+ 0:18 log PX t1log PN t1 +0:18 log PX t1+ 0:0295" t; where, using the notation in (77), = 1, and XN = 0:18 is added for the e¤ect of log PX t1on log PN t(which did not appear in the original speci…cation). Hence, the …nal speci…cation of the XTT block (77) is: X t=X t10:41 X10:41 p t10:25 exp 0:0424" t; t= t10:20 ()10:20 p t10:18 X t0:18 exp 0:0295" t; p t=p t1 X t t :
51 Vector Error Correction Estimates Sample (adjusted): 1993Q3 2009Q2 Included observations: 64 after adjustments Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq: CointEq1 LPSTARXLEVEL(-1) 1.0000 LPSTARNLEVEL(-1) -1.4924 0.1263 [-11.8125] @TREND(93Q1) -0.0044 C2.3074 Error Correction: D(LPSTARXLEVEL) D(LPSTARNLEVEL) CointEq1 -0.25543 0.18115 0.09767 0.06597 [-2.61520] [ 2.74597] D(LPSTARXLEVEL(-1)) 0.40776 0.17699 0.13273 0.08965 [ 3.07203] [ 1.97414] D(LPSTARNLEVEL(-1)) 0.15719 0.20080 0.17834 0.12046 [ 0.88142] [ 1.66697] C-0.00273 -0.00498 0.00838 0.00566 [-0.32536] [-0.87938] @TREND(93Q1) 0.00021 0.00018 0.00023 0.00015 [ 0.95374] [ 1.17769] D081 0.08543 0.00287 0.03638 0.02457 [ 2.34827] [ 0.11686] D084 -0.15245 -0.12326 0.03296 0.02226 [-4.62518] [-5.53617] R-squared 0.48888 0.52026 Adj. R-squared 0.43508 0.46976 Sum sq. resids 0.05778 0.02636 S.E. equation 0.03184 0.02151 F-statistic 9.08656 10.30235 Log likelihood 133.50707 158.62000 Akaike AIC -3.95335 -4.73813 Schwarz SC -3.71722 -4.50200 Mean dependent 0.00581 0.00029 S.D. dependent 0.04236 0.02953 Determinant resid covariance (dof adj.) 0.00000045 Determinant resid covariance 0.00000035 Log likelihood 293.76131 Akaike information criterion -8.68004 Schwarz criterion -8.14032 A.1.2. The NSS relations between parameters and endogenous variables Eliminating time indexes from the model equations and simplifying gives a set of nonlinear equations that involve both the parameters and NSS values of the endogenous variables. I assume that in the NSS = 1. I also use the target value for the CB reserves ratio R=er=Y , the NSS household foreign debt ratio D=ed=Y and money ratio M=m= pCC:In some cases I divided the equation through by GDP. Consumption: 1 + i C=1 (84)
52 Risk-adjusted uncovered interest parity: 1 + i= (1 + i)'DD(85) Phillips in‡ation equations: = Q= pCCC 11(86) = 1mc Q= pCCC 1(87) =11 11 1 =ep()1(88) Dynamics of price dispersion: = 1 111 1 1 :(89) Exports: X=X(ep)bXY(90) Trade Balance: TB e Y=1 aDpC t1CX Y(1 aD)e1C(91) Current Account: CA e Y=1 + i 1R1 + i DD1D+TB e Y(92) Balance of Payments: CA = 0 (93) Real marginal cost: mc =w(94) Labor market clearing: w=NpCCC'MMNN(95) Hours worked: N=Q(96) Domestic goods market clearing: Q Y= 1 1bAX Y(97) GDP: 1 = aD MMG (pC)1C pCC Y+X Y(98)
53 Consumption relative price: pC=aD+ (1 aD)e1C1 1C(99) Money market balance: m=L(1 + i)pCC; (100) CB balance sheet: b Y=RMpCC Y(101) Consumption in‡ation: C=(102) Real Exchange Rate: =(103) External terms of trade: X=(104) Tax collection: tax =GpCCqf Quasi-…scal surplus: qf = (1 + i1=)er ((1 + i)1) b Interest rate feedback rule: 1 = C Th1 (105) Nominal depreciation feedback rule: 1 = C Tk1er=Y Rk4 (106) Exports in‡ation shock 1 = (p) (107) Imported in‡ation shock 1 = (p)XXN :(108) I now show one way in which the EENE values of the model’s variables and the calibrated values of parameters can be obtained sequentially. (105) implies C=T, since h16= 0 is assumed. Inserting this in (102) yields =T. Also, (107) implies that the XTT is p= 1, and hence (108) implies that X= 1, and (104) that = 1. Therefore, (103) implies =T. Summing up, we have: ==C=T;and =X=p= 1: Hence, (84) gives the nominal interest rate: 1+i=T= and (106) yields er=Y = R, since it is assumed that k46= 0, which implies that the CB’s target ratio of international reserves to GDP is attained in the NSS.
54 I assume = 0:99. For illustrative purposes I use as Argentina’s NSS GDP its 2010 level (at 2010 prices and in trillions of pesos): Y= 1:443. The gross exogenous risk/liquidity premium for households and the RW gross interest rate are assumed to be = 1:0050:25 and 1 + i= 1:030:25, respectively. Also, the household ratios are Ded=Y = 0:5,Mm=pCC= 0:095522, and Government to household consumption ratio is assumed to be G= 1:19. The home bias parameter (or share of domestic goods) in household consumption is calibrated to aD= 0:86. The constant relative risk aversion for labor (which is also the inverse of the elasticity of labor supply with respect to the real wage) and consumption are: N= 0:5and C= 1:5, respectively. Finally, I assume that the elasticity of substitution between varieties of domestic goods is = 6 and the elasticity of substitution between the bundles of domestic and imported goods is C= 1:5. Assuming that the exogenous parameter for exports demand is bA= 0:5, yields bX1bA1= 2 and XbAbAbX= 0:5. I now focus on the NSS values of the remaining endogenous variables and parameters. A.1.2.1 The endogenous risk premium Using (84), (102), and (103) in the UIP equation (85) gives the household foreign debt to GDP ratio as a function of parameters which I have already calibrated: Ded Y='1 D1= (1 + i)=='1 D1 (1 + i): However, calculating this requires the values of the exogenous parameters 1and 2which help de…ne the function 'D. I now seek to calibrate them in terms of the more intuitive elasticity of the risk premium function in the UIP (which plays a critical role in the present research). First, notice that the elasticity "Dof Dis "DD t2D t 12D t :(109) Dand 'Dare related to "Dby (see (67) and (69)): DD t=11 + "D(D t);(110) 'DD t=11 + "D(D t)2: Hence, if the NSS values of "Dand Dare calibrated, (109) gives the value of 2: 2=1 D1 "D+ 1:(111) Also, using (110), (66), and (84) in (85) yields: 'DD=1 + i (1 + i)1 = 1 (1 + i)1 = 1(1 + "D)2;(112)
55 which gives the value of 1: 1=1 (1 + "D)21 (1 + i)1=12D21 (1 + i)1;(113) where the second equality is derived from (111). However, because of the critical role of the derived function 'Din the UIP equation (71) it is perhaps more intuitive in calibrations to start with the value of the elasticity of 'D, which I denote as "' D, along with D, and derive the value of "D. It is straightforward to prove that "' Dand "Dare related by: "' D="D 2 D 'D 1 + 'D ="D 2 D[1 (1 + i)];(114) where the second equality uses (112). Hence, using (111), (113) and (109): 2=1 2 "' D[1 (1 + i)] + D 1=12D21 (1 + i)1: If, say, "' D= 2 then 2=1 (1 0:99 (1:030:25) 1:0050:25)+0:5= 1:994 4 1= (1 1:994 4 0:5)21 0:99 (1:030:25) 1:0050:25 1= 1:109 2 108 and hence: D=1:1092 108 11:9944 0:5= 3:9614 106 'D=1:1092 108 (1 1:994 4 0:5)2= 1:4148 103: A.1.2.2 The balance of payments Using the previous calibrations, (93) and (92) give the trade balance to GDP ratio necessary to sustain net interest payments abroad: TB e Y=1 + i D1D1 + i 1R 1:030:25 11:0050:25 (1:0000039368) 10:51:030:25 110:13 = 0:00337476
56 Then, using (91), (90), and (99), one can obtain the RER necessary to generate this trade surplus: X(ep)bXhaD+ (1 aD)e1Ci(1 aD)e1C=aDTB e Y 0:5e20:86 + (1 0:86) e11:5(1 0:86) e11:5= 0:86 (0:00337476) e= 0:595055 and hence the exports to GDP ratio and pC: X Y=X(ep)bX= 0:5 (0:595055)2= 0:177 045; pC=0:86 + (1 0:86) (0:595055)11:51 11:5= 0:921915 A.1.2.3 The transactions cost function and money demand The elasticity of L(1 + i)(see (70)) can be shown to satisfy the following relation: "LM=1 (3+ 1) i1 + 1 2M;(115) from which we obtain: 2=1 M 1 (3+ 1) "Li1: Also, reshuing (70) gives: 1=1 + 2M3+1 2311 1 + i: So using the last two expressions in (68) to eliminate 1and 2gives: MM=1 + 1 311 1 + ii"LMM:(116) Since transaction costs are dependent on the in‡ation rate (through the nominal interest rate) I cannot calibrate the three parameters 1; 2;and 3without …rst calibrating the in‡ation rate. I assume that the target in‡ation rate is T= 1:015. Hence, the nominal interest rate is given by (84): 1+i= 1:015=0:99 = 1:0253:Next, calibrate the value of the interest elasticity of money demand to, say, "L= 1:02. We also have M= 0:095522. Notice that to have 2positive, 3must be su¢ ciently high (and hence Msu¢ ciently low):26 26Although this level of transaction costs may seem unrealistically low, we really do not care much about transaction costs per se but only their e¤ect on money demand. To have more realistic levels of transaction costs we would need a di¤erent transaction costs function. As long as we are confortable with the resulting interest elasticity of money demand and the assumed stock of money, we can hold on to the present function.
63 Response to a positive shock to imports in‡ation: 510 15 20 -5 0 5x 10 -3 piC 510 15 20 -5 0 5x 10 -4 DeltaP 510 15 20 -0.01 0 0.01 Y 510 15 20 -0.01 0 0.01 C 510 15 20 -0.01 0 0.01 real_ii 510 15 20 -0.02 0 0.02 e 510 15 20 -0.01 0 0.01 TB 510 15 20 -0.01 0 0.01 X 510 15 20 -0.01 0 0.01 mc 510 15 20 -0.01 0 0.01 N 510 15 20 -0.01 0 0.01 ii 510 15 20 -0.02 0 0.02 delta 510 15 20 -0.01 0 0.01 b 510 15 20 -0.02 0 0.02 r 510 15 20 -0.02 0 0.02 d 510 15 20 -2 0 2x 10 -3 m 510 15 20 -5 0 5x 10 -3 Utility 510 15 20 -0.05 0 0.05 z_piStar
64 Response to a positive shock to exports in‡ation: X 510 15 20 -5 0 5x 10 -3 piC 510 15 20 -2 0 2x 10 -3 DeltaP 510 15 20 -0.05 0 0.05 Y 510 15 20 -0.02 0 0.02 C 510 15 20 -5 0 5x 10 -3 real_ii 510 15 20 -0.02 0 0.02 e 510 15 20 -0.05 0 0.05 TB 510 15 20 -0.02 0 0.02 X 510 15 20 -0.02 0 0.02 mc 510 15 20 -0.02 0 0.02 N 510 15 20 -5 0 5x 10 -3 ii 510 15 20 -0.02 0 0.02 delta 510 15 20 -0.1 0 0.1 b 510 15 20 -0.1 0 0.1 r 510 15 20 -0.1 0 0.1 d 510 15 20 -1 0 1x 10 -3 m 510 15 20 -0.01 0 0.01 Utility 510 15 20 -0.01 0 0.01 z_piStar
65 A.2.1.2 Central Bank style B != 1; !Y= 100; !e= 1; !r= 1; !i= 50; != 50 h0h1h2h3k0k1k2k3k4 1:86 1:01 4:34 0:21 3:08 3:92 2:28 1:18 0:40 Response to a positive shock to domestic sector productivity: 510 15 20 -5 0 5x 10 -3 piC 510 15 20 -5 0 5x 10 -3 DeltaP 510 15 20 0 0.5 1x 10 -3 Y 510 15 20 -1 0 1x 10 -3 C 510 15 20 -5 0 5x 10 -4 real_ii 510 15 20 -1 0 1x 10 -3 e 510 15 20 -2 0 2x 10 -3 TB 510 15 20 -1 0 1x 10 -3 X 510 15 20 -0.02 0 0.02 mc 510 15 20 -0.02 0 0.02 N 510 15 20 0 5x 10 -3 ii 510 15 20 0 5x 10 -3 delta 510 15 20 0 5x 10 -3 b 510 15 20 0 0.005 0.01 r 510 15 20 -2 0 2x 10 -3 d 510 15 20 -1 -0.5 0x 10 -3 m 510 15 20 -0.01 0 0.01 Utility 510 15 20 0 0.01 0.02 z_epsilon
66 Response to a positive shock to government expenditures: G 510 15 20 0 0.01 0.02 piC 510 15 20 0 0.01 0.02 DeltaP 510 15 20 -5 0 5x 10 -3 Y 510 15 20 -0.04 -0.02 0C 510 15 20 0 0.005 0.01 real_ii 510 15 20 -5 0 5x 10 -3 e 510 15 20 -5 0 5x 10 -3 TB 510 15 20 -2 0 2x 10 -3 X 510 15 20 -0.05 0 0.05 mc 510 15 20 0 0.01 0.02 N 510 15 20 0 0.01 0.02 ii 510 15 20 0 0.01 0.02 delta 510 15 20 0 0.01 0.02 b 510 15 20 0 0.02 0.04 r 510 15 20 0 2 4x 10 -3 d 510 15 20 -4 -2 0x 10 -3 m 510 15 20 -0.04 -0.02 0Utility 510 15 20 0 0.02 0.04 z_G
67 Response to a positive shock to the RW interest rate: i 510 15 20 -2 0 2x 10 -3 piC 510 15 20 -1 0 1x 10 -3 DeltaP 510 15 20 -1 0 1x 10 -3 Y 510 15 20 -2 0 2x 10 -3 C 510 15 20 -5 0 5x 10 -4 real_ii 510 15 20 -2 0 2x 10 -3 e 510 15 20 -5 0 5x 10 -3 TB 510 15 20 -2 0 2x 10 -3 X 510 15 20 -5 0 5x 10 -3 mc 510 15 20 -2 0 2x 10 -3 N 510 15 20 -1 0 1x 10 -3 ii 510 15 20 -1 0 1x 10 -3 delta 510 15 20 -5 0 5x 10 -3 b 510 15 20 -0.01 0 0.01 r 510 15 20 -0.01 -0.005 0d 510 15 20 -1 -0.5 0x 10 -4 m 510 15 20 -1 0 1x 10 -3 Utility 510 15 20 0 5x 10 -3 z_iStar
68 Response to a positive shock to the SOE’s exogenous risk/liquidity premium: 510 15 20 -0.02 -0.01 0piC 510 15 20 -0.01 -0.005 0DeltaP 510 15 20 -0.01 0 0.01 Y 510 15 20 -0.02 0 0.02 C 510 15 20 -5 0 5x 10 -3 real_ii 510 15 20 -0.02 0 0.02 e 510 15 20 -0.05 0 0.05 TB 510 15 20 -0.01 0 0.01 X 510 15 20 -0.02 -0.01 0mc 510 15 20 -0.02 -0.01 0N 510 15 20 -0.01 -0.005 0ii 510 15 20 -0.02 -0.01 0delta 510 15 20 -0.05 0 0.05 b 510 15 20 -0.1 0 0.1 r 510 15 20 -0.1 0 0.1 d 510 15 20 -5 0 5x 10 -4 m 510 15 20 -5 0 5x 10 -3 Utility 510 15 20 0 0.05 0.1 z_phiStar
69 Response to a positive shock to imports in‡ation: 510 15 20 0 0.005 0.01 piC 510 15 20 0 1 2x 10 -3 DeltaP 510 15 20 -5 0 5x 10 -3 Y 510 15 20 -5 0 5x 10 -3 C 510 15 20 -5 0 5x 10 -3 real_ii 510 15 20 -0.02 0 0.02 e 510 15 20 -0.01 0 0.01 TB 510 15 20 -5 0 5x 10 -3 X 510 15 20 0 0.005 0.01 mc 510 15 20 0 0.005 0.01 N 510 15 20 0 2 4x 10 -3 ii 510 15 20 -0.01 0 0.01 delta 510 15 20 -0.01 0 0.01 b 510 15 20 -0.02 0 0.02 r 510 15 20 -0.02 0 0.02 d 510 15 20 -1 0 1x 10 -3 m 510 15 20 -4 -2 0x 10 -3 Utility 510 15 20 -0.05 0 0.05 z_piStar
70 Response to a positive shock to exports in‡ation: X 510 15 20 0 0.01 0.02 piC 510 15 20 0 0.005 0.01 DeltaP 510 15 20 -0.01 0 0.01 Y 510 15 20 -0.01 0 0.01 C 510 15 20 -5 0 5x 10 -3 real_ii 510 15 20 -0.02 0 0.02 e 510 15 20 -0.02 0 0.02 TB 510 15 20 -0.02 0 0.02 X 510 15 20 -0.02 0 0.02 mc 510 15 20 0 0.01 0.02 N 510 15 20 0 0.01 0.02 ii 510 15 20 -0.02 0 0.02 delta 510 15 20 0 0.05 b 510 15 20 0 0.05 0.1 r 510 15 20 -0.05 0 0.05 d 510 15 20 -5 0 5x 10 -3 m 510 15 20 -5 0 5x 10 -3 Utility 510 15 20 -0.01 0 0.01 z_piStar
71 A.2.1.3 Central Bank style C != 100; !Y= 100; !e= 1; !r= 1; !i= 50; != 50 h0h1h2h3k0k1k2k3k4 1:63 1:92 1:43 0:82 0:44 1:31 0:12 0:91 0:06 Response to a positive shock to domestic sector productivity: 510 15 20 -5 0 5x 10 -3 piC 510 15 20 -2 -1 0x 10 -3 DeltaP 510 15 20 0 5x 10 -3 Y 510 15 20 -5 0 5x 10 -3 C 510 15 20 -2 0 2x 10 -3 real_ii 510 15 20 -5 0 5x 10 -3 e 510 15 20 -0.01 0 0.01 TB 510 15 20 -5 0 5x 10 -3 X 510 15 20 -0.02 0 0.02 mc 510 15 20 -0.02 -0.01 0N 510 15 20 -2 0 2x 10 -3 ii 510 15 20 -5 0 5x 10 -3 delta 510 15 20 0 0.01 0.02 b 510 15 20 0 0.01 0.02 r 510 15 20 -0.01 0 0.01 d 510 15 20 0 2 4x 10 -4 m 510 15 20 0 0.005 0.01 Utility 510 15 20 0 0.01 0.02 z_epsilon
72 Response to a positive shock to government expenditures: G 510 15 20 -0.02 -0.01 0piC 510 15 20 -0.01 -0.005 0DeltaP 510 15 20 0 0.01 0.02 Y 510 15 20 -0.04 -0.02 0C 510 15 20 -0.02 0 0.02 real_ii 510 15 20 -0.02 0 0.02 e 510 15 20 -0.05 0 0.05 TB 510 15 20 -0.02 0 0.02 X 510 15 20 -0.05 0 0.05 mc 510 15 20 0 5x 10 -3 N 510 15 20 -5 0 5x 10 -3 ii 510 15 20 -0.02 0 0.02 delta 510 15 20 0 0.05 0.1 b 510 15 20 0 0.05 0.1 r 510 15 20 0 0.02 0.04 d 510 15 20 -5 0 5x 10 -3 m 510 15 20 -0.04 -0.02 0Utility 510 15 20 0 0.02 0.04 z_G
79 Response to a positive shock to the RW interest rate: i 510 15 20 -5 0 5x 10 -4 piC 510 15 20 -2 0 2x 10 -4 DeltaP 510 15 20 -2 0 2x 10 -3 Y 510 15 20 -2 0 2x 10 -3 C 510 15 20 -5 0 5x 10 -4 real_ii 510 15 20 0 1 2x 10 -3 e 510 15 20 0 2 4x 10 -3 TB 510 15 20 0 1 2x 10 -3 X 510 15 20 -2 0 2x 10 -3 mc 510 15 20 -1 0 1x 10 -3 N 510 15 20 -5 0 5x 10 -4 ii 510 15 20 -1 0 1x 10 -3 delta 510 15 20 -5 0 5x 10 -3 b 510 15 20 -0.01 0 0.01 r 510 15 20 -0.01 -0.005 0d 510 15 20 -2 0 2x 10 -4 m 510 15 20 -1 -0.5 0x 10 -3 Utility 510 15 20 0 5x 10 -3 z_iStar
80 Response to a positive shock to the SOE’s exogenous risk/liquidity premium: 510 15 20 -2 0 2x 10 -3 piC 510 15 20 -1 0 1x 10 -3 DeltaP 510 15 20 -0.01 0 0.01 Y 510 15 20 -0.02 0 0.02 C 510 15 20 -5 0 5x 10 -3 real_ii 510 15 20 -0.01 0 0.01 e 510 15 20 -0.02 0 0.02 TB 510 15 20 -0.01 0 0.01 X 510 15 20 -0.02 0 0.02 mc 510 15 20 -0.01 0 0.01 N 510 15 20 -5 0 5x 10 -3 ii 510 15 20 -0.01 0 0.01 delta 510 15 20 -0.05 0 0.05 b 510 15 20 -0.1 0 0.1 r 510 15 20 -0.1 0 0.1 d 510 15 20 -2 0 2x 10 -3 m 510 15 20 -0.01 0 0.01 Utility 510 15 20 0 0.05 0.1 z_phiStar
81 Response to a positive shock to imports in‡ation: 510 15 20 -5 0 5x 10 -3 piC 510 15 20 0 5x 10 -4 DeltaP 510 15 20 -2 0 2x 10 -3 Y 510 15 20 -5 0 5x 10 -3 C 510 15 20 -5 0 5x 10 -3 real_ii 510 15 20 -0.02 0 0.02 e 510 15 20 -5 0 5x 10 -3 TB 510 15 20 -5 0 5x 10 -3 X 510 15 20 -2 0 2x 10 -3 mc 510 15 20 -5 0 5x 10 -3 N 510 15 20 -2 0 2x 10 -3 ii 510 15 20 -0.01 0 0.01 delta 510 15 20 -0.02 0 0.02 b 510 15 20 -0.02 0 0.02 r 510 15 20 -0.02 0 0.02 d 510 15 20 -2 0 2x 10 -4 m 510 15 20 -5 0 5x 10 -3 Utility 510 15 20 -0.05 0 0.05 z_piStar
82 Response to a positive shock to exports in‡ation: X 510 15 20 0 2 4x 10 -3 piC 510 15 20 -2 0 2x 10 -3 DeltaP 510 15 20 -0.05 0 0.05 Y 510 15 20 -0.02 0 0.02 C 510 15 20 -5 0 5x 10 -3 real_ii 510 15 20 -0.02 0 0.02 e 510 15 20 -0.02 0 0.02 TB 510 15 20 -0.02 0 0.02 X 510 15 20 -0.05 0 0.05 mc 510 15 20 -0.05 0 0.05 N 510 15 20 -5 0 5x 10 -3 ii 510 15 20 -0.02 0 0.02 delta 510 15 20 -0.05 0 0.05 b 510 15 20 -0.1 0 0.1 r 510 15 20 -0.1 0 0.1 d 510 15 20 -2 0 2x 10 -3 m 510 15 20 -0.01 0 0.01 Utility 510 15 20 -0.01 0 0.01 z_piStar
83 A.2.2.2 Central Bank style B != 1; !Y= 100; !e= 1; !r= 1; !i= 50; != 50: Response to a positive shock to domestic sector productivity: 510 15 20 -5 0 5x 10 -3 piC 510 15 20 -5 0 5x 10 -3 DeltaP 510 15 20 -5 0 5x 10 -4 Y 510 15 20 -1 0 1x 10 -3 C 510 15 20 -1 0 1x 10 -3 real_ii 510 15 20 -1 0 1x 10 -3 e 510 15 20 -2 0 2x 10 -3 TB 510 15 20 -1 0 1x 10 -3 X 510 15 20 -0.02 0 0.02 mc 510 15 20 -0.02 0 0.02 N 510 15 20 0 2 4x 10 -3 ii 510 15 20 -5 0 5x 10 -3 delta 510 15 20 -5 0 5x 10 -3 b 510 15 20 -5 0 5x 10 -3 r 510 15 20 -1 0 1x 10 -3 d 510 15 20 -4 -2 0x 10 -4 m 510 15 20 -0.01 0 0.01 Utility 510 15 20 0 0.01 0.02 z_epsilon
84 Response to a positive shock to government expenditures: G 510 15 20 -0.02 0 0.02 piC 510 15 20 -0.01 0 0.01 DeltaP 510 15 20 -2 0 2x 10 -3 Y 510 15 20 -0.04 -0.02 0C 510 15 20 0 0.005 0.01 real_ii 510 15 20 -2 0 2x 10 -3 e 510 15 20 -5 0 5x 10 -3 TB 510 15 20 -2 0 2x 10 -3 X 510 15 20 -0.05 0 0.05 mc 510 15 20 -0.02 0 0.02 N 510 15 20 0 0.01 0.02 ii 510 15 20 -0.02 0 0.02 delta 510 15 20 0 0.01 0.02 b 510 15 20 -0.02 0 0.02 r 510 15 20 0 0.005 0.01 d 510 15 20 -4 -2 0x 10 -3 m 510 15 20 -0.04 -0.02 0Utility 510 15 20 0 0.02 0.04 z_G
85 Response to a positive shock to the RW interest rate: i 510 15 20 -1 0 1x 10 -3 piC 510 15 20 -5 0 5x 10 -4 DeltaP 510 15 20 -5 0 5x 10 -4 Y 510 15 20 -2 -1 0x 10 -3 C 510 15 20 -5 0 5x 10 -4 real_ii 510 15 20 0 1 2x 10 -3 e 510 15 20 0 2 4x 10 -3 TB 510 15 20 0 1 2x 10 -3 X 510 15 20 -2 0 2x 10 -3 mc 510 15 20 -2 0 2x 10 -3 N 510 15 20 -1 0 1x 10 -3 ii 510 15 20 -1 0 1x 10 -3 delta 510 15 20 -5 0 5x 10 -3 b 510 15 20 -0.01 0 0.01 r 510 15 20 -0.01 -0.005 0d 510 15 20 -2 -1 0x 10 -4 m 510 15 20 -1 -0.5 0x 10 -3 Utility 510 15 20 0 5x 10 -3 z_iStar
86 Response to a positive shock to the SOE’s exogenous risk/liquidity premium: 510 15 20 -0.01 0 0.01 piC 510 15 20 -5 0 5x 10 -3 DeltaP 510 15 20 -5 0 5x 10 -3 Y 510 15 20 -0.02 0 0.02 C 510 15 20 -5 0 5x 10 -3 real_ii 510 15 20 -0.01 0 0.01 e 510 15 20 -0.02 0 0.02 TB 510 15 20 -0.01 0 0.01 X 510 15 20 -0.02 0 0.02 mc 510 15 20 -0.01 0 0.01 N 510 15 20 -5 0 5x 10 -3 ii 510 15 20 -0.01 0 0.01 delta 510 15 20 -0.05 0 0.05 b 510 15 20 -0.1 0 0.1 r 510 15 20 -0.1 0 0.1 d 510 15 20 -1 -0.5 0x 10 -3 m 510 15 20 -4 -2 0x 10 -3 Utility 510 15 20 0 0.05 0.1 z_phiStar
87 Response to a positive shock to imports in‡ation: 510 15 20 0 0.01 0.02 piC 510 15 20 0 2 4x 10 -3 DeltaP 510 15 20 -2 0 2x 10 -3 Y 510 15 20 -2 0 2x 10 -3 C 510 15 20 -2 0 2x 10 -3 real_ii 510 15 20 -0.02 0 0.02 e 510 15 20 -0.01 0 0.01 TB 510 15 20 -0.01 0 0.01 X 510 15 20 0 0.005 0.01 mc 510 15 20 0 0.005 0.01 N 510 15 20 0 5x 10 -3 ii 510 15 20 -5 0 5x 10 -3 delta 510 15 20 -0.01 0 0.01 b 510 15 20 -0.02 0 0.02 r 510 15 20 -0.02 0 0.02 d 510 15 20 -5 0 5x 10 -4 m 510 15 20 -4 -2 0x 10 -3 Utility 510 15 20 -0.05 0 0.05 z_piStar
88 Response to a positive shock to exports in‡ation: X 510 15 20 0 0.01 0.02 piC 510 15 20 0 0.005 0.01 DeltaP 510 15 20 -0.01 0 0.01 Y 510 15 20 -0.01 0 0.01 C 510 15 20 -5 0 5x 10 -3 real_ii 510 15 20 -0.02 0 0.02 e 510 15 20 -0.02 0 0.02 TB 510 15 20 -0.02 0 0.02 X 510 15 20 -0.01 0 0.01 mc 510 15 20 0 0.005 0.01 N 510 15 20 0 0.01 0.02 ii 510 15 20 -0.02 0 0.02 delta 510 15 20 -0.05 0 0.05 b 510 15 20 -0.1 0 0.1 r 510 15 20 -0.05 0 0.05 d 510 15 20 -5 0 5x 10 -3 m 510 15 20 -5 0 5x 10 -3 Utility 510 15 20 -0.01 0 0.01 z_piStar
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