A DSGE model for a SOE with systematic interest and foreign exchange policies in which policymakers exploit the risk premium for stabilization purposes

Escudé, Guillermo J. Article A DSGE model for a SOE with systematic interest and foreign exchange policies in which policymakers exploit the risk premium for stabilization purposes Economics: The Open-Access, Open-Assessment E-Journal Provided in Cooperation with: Kiel Institute for the World Economy – Leibniz Center for Research on Global Economic Challenges Suggested Citation: Escudé, Guillermo J. (2013) : A DSGE model for a SOE with systematic interest and foreign exchange policies in which policymakers exploit the risk premium for stabilization purposes, Economics: The Open-Access, Open-Assessment E-Journal, ISSN 1864-6042, Kiel Institute for the World Economy (IfW), Kiel, Vol. 7, Iss. 2013-30, pp. 1-110, https://doi.org/10.5018/economics-ejournal.ja.2013-30 This Version is available at: https://hdl.handle.net/10419/78704 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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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/3.0/ Received July 5, 2012 Published as Economics Discussion Paper August 21, 2012 Revised July 5, 2013 Accepted July 11, 2013 Published July 18, 2013 © Author(s) 2013. Licensed under the Creative Commons License - Attribution 3.0 Vol. 7, 2013-30 | July 18, 2013 | http://dx.doi.org/10.5018/economics-ejournal.ja.2013-30 A DSGE Model for a SOE with Systematic Interest and Foreign Exchange Policies in Which Policymakers Exploit the Risk Premium for Stabilization Purposes Guillermo J. Escudé Abstract This paper builds a DSGE model for a small open economy (SOE) in which the central bank intervenes the domestic currency bond and FX markets using two policy rules: a Taylortype rule and a rule that determines the rate of nominal depreciation. The 2 'corner' regimes, in which only one policy rule is used, are particular cases. The model is calibrated and implemented in Dynare for simple and optimal simple policy rules, and optimal policy under commitment. Numerical losses are obtained for ad-hoc loss functions for different sets of central bank preferences. The results show that the losses are lower when both policy rules are used. This is due to the central bank's enhanced ability, when it uses the two policy rules, to influence private capital flows through the effects of its actions on the endogenous risk premium in the risk-adjusted uncovered interest parity equation. JEL E58 F41 O24 Keywords DSGE models; small open economy; exchange rate policy; optimal policy Authors Guillermo J. Escudé, Central Bank of Argentina, Ciudad Autónoma de Buenos Aires, Argentina, [email protected].ar Citation Guillermo J. Escudé (2013). A DSGE Model for a SOE with Systematic Interest and Foreign Exchange Policies in Which Policymakers Exploit the Risk Premium for Stabilization Purposes. Economics: The OpenAccess, Open-Assessment E-Journal, Vol. 7, 2013-30. http://dx.doi.org/10.5018/economics-ejournal.ja.2013-30 conomics: The Open-Access, Open-Assessment E-Journal 1 Introduction1 According to John Williamson `the overwhelming conventional view in the profession is that it is a mistake to try to manage exchange rates' (Williamson 2007), although he does not subscribe this view. He nds that `most of the time the only monetary policy objective that may merit consideration–other than ination targeting–is the maintenance of a sufciently competitive exchange rate to preserve the incentive to invest'. 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 Taylor rule approach with a policy of systematic intervention in the foreign exchange market. Although there doesn't seem to be any justication to having to choose between a policy that uses an operational target for the nominal interest rate (often with an ination target in mind) and a policy that uses foreign exchange (FX) market intervention to target the exchange rate, it is not easy to escape this dichotomy in the absence of an adequate and accepted theoretical framework (see, however, Wollmerhaüser 2003, Bonger and Wollmershaüser 2001, Kim 2003, Aguirre and Grosman 2010). This absence may be due to the pervasive preference of modelers (theoreticians) to `sweep under the rug' some of the Central Bank (CB) `nuts and bolts' that are necessary to achieve a more general theory. Such `nuts and bolts' as the CB and other nancial institutions' balance sheets (and the nancial assets and liabilities within them) 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, central bank, and IMF models. What makes such an omission possible, of course, is that if one accepts the dichotomy in question, an argument of system decomposability allows one to focus on the central block of equations. However, if one does not accept the dichotomy, the need to include such `nuts and bolts' arises merely to ensure a consistent policy model. 1A previous version of this paper 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". www.economics-ejournal.org 2 conomics: The Open-Access, Open-Assessment E-Journal This paper, and the model on which it is based, builds such a consistent policy model and uses it within various policy frameworks: simple policy rules, optimal simple policy rules, and optimal policy under commitment, implementing a rst order approximation to the model through Dynare. It nds strong evidence that a proper systematic use by CBs of small open economies (SOEs) of two operational targets, one for the nominal interest rate and another for the rate of nominal depreciation, outperforms the `corner' regimes which either control the nominal interest with a oating exchange rate or control the rate of nominal depreciation with a oating interest rate. The basic difference 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 comes closer to the way most CBs (at least those in developing economies) implement their interest and FX policies. However, as far as the author is aware no CB implements its FX policy using the type of model used in this paper. When FX policy is systematic, there tends to be an exchange rate level-related target that is discretionally moved around and this departs from the rule-based approach used here. And when there is an explicit framework of controlling the nominal interest rate (including `ination targeting'), FX policy tends to be even more discretional and opaque. 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 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 in the optimal control framework) for the usual CB preferences (i.e. combinations of weights for ination and output, and possibly the real exchange rate (RER). The model used for this paper (ARGEMmin) is a smaller version of the models described in two previous models: ARGEM in Escudé (2007) and ARGEMmy in Escudé (2009). They can all represent the simultaneous (i.e. within the same quarterly period) intervention in the 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 and the interest rate oats. The fact that most CBs of developing economies intervene www.economics-ejournal.org 3 conomics: The Open-Access, Open-Assessment E-Journal regularly in both markets should make this generalization of practical interest.2 And a model that only adds the essential features that are needed to include FX 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 decision problems of some sector of the economy. In this paper, it is the household decision problem that delivers the riskadjusted 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 basically due to its realism (see Bhandari et al. 1990 and the papers there cited, and Agenor 1997) since it has long been accepted as an empirical fact and measured econometrically, although various candidate variables can be statistically signicant in affecting the premium.4In the DSGE strand, SchmittGrohe and Uribe (2003) noted that the simplest SOE models with incomplete asset markets used the assumption that the subjective discount rate equals the average real interest rate and, hence, presented equilibrium dynamics with a random walk component. They considered several alternative modications that have been used 2IMF (2011), for example, notes that `on average about one-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 differs from the author's 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 sufciently close to the standard workhorse model so that the specic difference in modeling policy is highlighted. 4Outside of the open economy context, it goes back at least to Kalecki (1937), who says that `the entrepreneur who has invested in equipment his reserves (cash, deposits, securities) and taken "too much credit" is obliged to borrow at a rate of interest which is higher than the market one' and attributes this to `the danger of "illiquidity."' www.economics-ejournal.org 4 conomics: The Open-Access, Open-Assessment E-Journal to eliminate this random walk component and showed 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 foreign debt outstanding. In the present paper's framework, combining the non-stochastic steady state (NSS) versions of the Euler and UIP equations gives [(1+i)=π]ϕD(:) = 1=β, where βis the intertemporal discount factor, (1+i)=πis the RW's real interest rate, and ϕD(:)is an endogenous premium function that combines the exogenous risk premium function τD(:)that households face when getting funds abroad (d) and their rst order condition pertaining to d. Hence, it is a function of d(and possibly other endogenous variables). This equation determines the long run foreign debt level das a function of model parameters (including those that dene the risk premium function and possibly other endogenous variables). 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. In this paper the risk premium function τD(:)is assumed to be a function of the foreign debt to GDP ratio: ed=Y (where eis the SOE's RER and Yis its GDP). Furthermore, there is an additional multiplicative shock φthat may represent either an exogenous component of the risk function or an international liquidity shock (or both).5In an extension of the model, the risk premium function is made to also respond, but negatively, to the CB's international reserves to GDP ratio er=Y(see Fouejieu and Roger (2013) for econometric measurements). For convenience, the policy framework where the CB uses two simultaneous policy rules is called a Managed Exchange Rate (MER) regime. The instruments that the CB uses for its intervention in the two markets are explicitly included as model variables, and the CB balance sheet that binds them is a model equation. 5In addition to φ, there are three more RW shocks that impinge on the SOE: the world nominal riskfree interest rate 1+iand 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. www.economics-ejournal.org 5 conomics: The Open-Access, Open-Assessment E-Journal 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, the CB's ow budget constraint is explicitly considered and it is assumed that the institutional framework is such that any `quasi-scal' surplus (or decit) is handed over to (nanced by) 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 different 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) given by its balance sheet: etrt=mt+bt. This equation implicitly denes how much the CB `sterilizes' (through the issuance of domestic currency bonds) any unwanted monetary effect of its simultaneous and systematic monetary and exchange policy. The expression `sterilized intervention' (in the FX market) is avoided because it implicitly gives the exchange rate policy a subordinate role (the undesired effects 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 effects of the other. When the CB intervenes in both the `money' and FX markets, 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 that the CB's net worth is kept at zero. Clearly, other similar constraints could be used for the same purpose of endogenizing the CB's `sterilization' policy. The one used here 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. At the theoretical level, Curdia and Woodford (2010) study the CB balance sheet as an instrument of monetary policy in a very elaborate closed economy model in which www.economics-ejournal.org 6 conomics: The Open-Access, Open-Assessment E-Journal households are heterogenous in their spending opportunities. In a policy paper, Caruana (2011) 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 well above zero and CB assets and liabilities that are closer to normal levels. Here, `normal' levels are dened by the long run CB reserves/GDP ratio, 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 other policy combinations in open economies that may include, say, taxes on foreign debt to address a (possible) `trinity' of interest rate, FX, and capital control policies. This, however, is for future research. The rest of the paper has the following structure. In Section 2 the model is set up. Section 3 addresses the functioning of the model under simple policy rules, optimal simple policy rules, and optimal policy under commitment and full information and shows that there are indeed gains from using these two simultaneous policies instead of only one of the `corner' regimes. In Section 4 it is shown 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. This section also includes intuition (based on impulse response functions) on the expanded range of policy possibilities when the second simple policy rule is included, and extends the model to include CB reserves in the endogenous risk premium. Section 5 makes some additional robustness checks based on the sensitivity of CB losses to various parameter calibrations, and Section 6 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 in the context of optimal policy under commitment. www.economics-ejournal.org 7 conomics: The Open-Access, Open-Assessment E-Journal 2 The model 2.1 Households 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 currency) interest rate iD t. It is assumed 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 the RW is not modeled, the premium function is exogenously given. It has an exogenous stochastic and time-varying component φ t(that can represent general liquidity conditions in the international market) as well as an endogenous (more country risk-related) component τD(:)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 because they know that all households are (at least in this aspect) identical (Lubik 2007). The foreign currency gross interest rate households face is: 1+iD t= (1+i t)φ tτDγD t;(1) where γD t,et, and dt, are the foreign debt to GDP ratio, the RER, and real foreign debt (in terms of foreign prices), respectively: γD t=StDt P tYt =etdt Yt ;etStP t P t ;dtDt P t ;(2) Stis the nominal exchange rate, P tis the domestic goods price index, P tis the price index of the goods the SOE imports, and Ytis GDP. The gross risk premium function τDγD tis assumed to be increasing and convex (τD1+τD>1, τ0 D>0 and τ00 D>0). www.economics-ejournal.org 8 conomics: The Open-Access, Open-Assessment E-Journal Conditions (25), and (26) are necessary for the optimal allocation of household expenditures across domestic and imported bundles of goods. Similarly, for the optimal allocation across varieties of domestic goods within the rst of these classes, use of (33) yields the following necessary conditions: P t(i) = P tCD t(i) CD t1 θ : 2.2 Domestic goods rms The representative nal goods rm There is perfect competition in the production (or bundling) of nal domestic output Qt, with the output of intermediate rms as inputs. A representative nal domestic output rm uses the following CES technology: Qt=Z1 0 Qt(i)θ1 θdiθ θ1 ;θ>1 (34) where Qt(i)is the output of the intermediate domestic good i. The nal domestic output representative rm solves the following problem each period: max Qt(i)P tZ1 0 Qt(i)θ1 θdiθ θ1 Z1 0 P t(i)Qt(i)di;(35) the solution of which is the demand for each type of domestic good (as an input): Qt(i) = QtP t(i) P tθ :(36) Introducing (36) in (34) and simplifying, it is readily seen that the domestic goods price index is: P t=Z1 0 P t(i)1θdi1 1θ :(37) Also, introducing (36) into the cost part of (35) yields: Z1 0 P t(i)Qt(i)di =P tQt: www.economics-ejournal.org 15 conomics: The Open-Access, Open-Assessment E-Journal The monopolistically competitive rms A continuum of monopolistically competitive rms produce the intermediate domestic goods (that the nal goods producer bundles) using homogenous labor, with no entry or exit. The production function of each rm is: Qt(i) = εtNt(i)(38) where εtis an industry-wide transitory productivity shock. Since Nt(i)is rm i's labor demand, using (38) and (36) and integrating yields aggregate labor demand: ND t= 1 Z0 Nt(i)di = 1 Z0 Qt(i) εt di =1 εt 1 Z0 QtP t(i) P tθ di =Qt εt ∆t(39) where (as in Schmitt-Grohe and Uribe 2004 and 2005) a measure of price dispersion at period thas been dened : ∆t 1 Z0P t(i) P tθ di 1:(40) Notice that ∆t=1 when all prices are the same and ∆t>1 otherwise (SchmittGrohe and Uribe 2005). Equating labor supply (22) and demand (39) gives the labor market equilibrium real wage (in terms of domestic goods): wt=ξNQt εt ∆tσN pC tCσC tϕMmt=pC tCt(41) Each rm's cost is WtNt(i)=(Wt=εt)Qt(i). Hence, its marginal cost is Wt=εt and its real marginal cost (in terms of domestic goods) is: mct=wt εt :(42) www.economics-ejournal.org 16 conomics: The Open-Access, Open-Assessment E-Journal Notice that all rms face the same marginal cost. Also, (41) shows that increases in price dispersion raise the equilibrium real wage and hence the real marginal cost of rms. This is due to the positive effect of increased price dispersion on aggregate labor demand (see (39)) and, given the level of supply, on the equilibrium real wage. Furthermore, tighter monetary conditions increase marginal cost because an increase in itmakes households economize on cash (see (16)), lowering mt=pC tCt. Because ϕ0 M=γMτ00 M<0, this has a positive effect on ϕM, lowering labor supply (see (22)) and hence increasing the equilibrium real wage. The dynamics of ination and price dispersion Firms make pricing decisions taking the aggregate price and quantity indexes as parametric. Every period, each rm has a probability 1 αof being able to set the optimum price for its specic type of good (Calvo 1983). The rms that can't optimize must leave the same price they had last period. The pricing problem of rms that get to optimize is: max P t(i)Et ∞ ∑ j=0 αjΛt;t+jQt+j(i)P t(i) P t+j mct+j(43) subject to the demand they will face until they can again optimize: Qt+j(i) = Qt+jP t(i) P t+jθ :(44) Λt;t+jis the pricing kernel used by domestic rms for discounting, which, since rms are owned by households and respond to their preferences, is equal to households' intertemporal marginal rate of substitution in the consumption of domestic goods between periods t+jand t: Λt;t+jβjUCD;t+j UCD;t ; where U(Ct+j;Nt+j)is the function within brackets in (5). Notice that the marginal utility of consuming domestic goods can be obtained from the marginal utilwww.economics-ejournal.org 17 conomics: The Open-Access, Open-Assessment E-Journal ity of consuming the aggregate bundle of (domestic and imported) goods. Specically: UCD;t=UC;t dCt dCD t =UC;ta 1 θC DCD t Ct1 θC =CσC t P t PC t =1 pC tCσC t ; where the second equality is obtained by differentiating (23) with respect to CD t, and the third comes from using (25). Hence, the pricing kernel of domestic rms is: Λt;t+jβjpC tCσC t pC t+jCσC t+j :(45) Introducing (44) and (45) in (43) (and eliminating irrelevant multiplying terms that refer to time t) gives max P t(i)Et ∞ ∑ j=0 (βα)jQt+j pC t+jCσC t+j(P t(i) P t+j1θ mct+jP t(i) P t+jθ): Since by symmetry all optimizing rms make the same decision the optimum price can be denominated e P t(dropping the rm index). Hence, the rm's rst order condition is the following: 0=Et ∞ ∑ j=0 (βα)jQt+j pC t+jCσC t+jP t+j P tθe pt P t P t+j θ θ1mct+j(46) where e pte P t=P tis the relative price of rms that optimize and the general price level (which includes the prices of both optimizers and non-optimizers). In the Calvo setup, because optimizers (and hence non-optimizers) are randomly chosen from the population, the average price in t1 of non-optimizers (which must keep their price constant) is equal to the overall price index in t1 no matter when they optimized for the last time. Hence, (37) implies the following law of motion for the aggregate domestic goods price index: P1θ t=α(P t1)1θ+(1α)e P1θ t:(47) www.economics-ejournal.org 18 conomics: The Open-Access, Open-Assessment E-Journal Dividing through by P1θ tand rearranging yields the relative price of optimizers as an increasing function of the ination rate: e pt= 1απθ1 t 1α!1 θ1 e p(πt):(48) Hence, using this in (46) gives the (non-linear) Phillips equation that determines the dynamics of domestic ination: 0=Et ∞ ∑ j=0 (βα)jQt+j pC t+jCσC t+jP t+j P tθe p(πt)P t P t+j θ θ1mct+j:(49) In order to implement the Phillips equation in Dynare this equation is now expressed in a recursive (nonlinear) form. Dene: Γt=Et ∞ ∑ j=0 (βα)jQt+j pC t+jCσC t+jP t+j P tθ1 (50) Ψt=θ θ1Et ∞ ∑ j=0 (βα)jQt+j pC t+jCσC t+jP t+j P tθ mct+j and express (49) as: e p(πt)Γt=Ψt: Now write Γtand Ψtrecursively as follows: Γt=Qt=pC tCσC t+βαEtπθ1 t+1Γt+1 Ψt=θ θ1Qt=pC tCσC tmct+βαEtπθ t+1Ψt+1: Hence, the complicated Phillips equation (with innite summations) is transformed into these three simple nonlinear equations. Notice that collapsing the log-linear approximations of these equations yields the usual log-linearized Phillips equation: b πt=(1βα)(1α) αc mct+βEtb πt+1: www.economics-ejournal.org 19 conomics: The Open-Access, Open-Assessment E-Journal ∆tis an additional variable in the model, which hence needs an additional equation. A recursive equation for the dynamics of this variable is now derived in three steps. First, separate the set of non-optimizing rms Nfrom the set of optimizing rms Oand notice that in a given period the latter all set the same price e P tand have mass 1α: ∆tZ i2NP t(i) P tθ di +Z i2OP t(i) P tθ di =α∆N t+(1α)e pθ t(51) where an analogous measure of price dispersion for non-optimizers is used (see (40)): ∆N tZ i2N 1 αP t(i) P tθ di: Second, write ∆N trecursively using the fact that non-optimizers maintain in tthe same price as in t1: ∆N tZ i2N 1 αP t1(i) P t1 1 πtθ di =πθ tZ i2N 1 αP t1(i) P t1θ di =πθ t∆N t1 and use this and (48) in (51) to get: ∆t=απθ t∆N t1+(1α)e p(πt)θ: Third, since non-optimizers (as well as optimizers) are selected randomly from the set of all rms, the dispersion of non-optimizers in t1 is equal to the dispersion of the population: ∆N t1=∆t1. The new model equation is therefore: ∆t=απθ t∆t1+(1α)e p(πt)θ:(52) The log-linear approximation of this equation is: b ∆t=απθb ∆t1+θε e p(π1)b πt εe pαπθ1 1απθ1: www.economics-ejournal.org 20 conomics: The Open-Access, Open-Assessment E-Journal Hence, if in the NSS there is domestic price stability (π=1)and therefore no domestic price dispersion (∆=1), a linear approximation of the model will not give any dynamics for b ∆tif initially there is no price dispersion (Schmitt-Grohe and Uribe 2005). Since this paper does not go beyond a rst order approximation of the model, 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) it is necessary to assume that the target gross ination is different from one. And since it is also realistic to assume a positive target rate of ination, in the calibrations of Appendix I a target rate of 1.015 (1.5% quarterly ination, i.e., 6.1% annual ination), is assumed. 2.3 Foreign trade, the public sector, and the balance of payments Firms in the export sector use domestic goods and the composite of goods that denes GDP. It is assumed 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 PX 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: StPX t:Let the production function employed by rms in the export sector be the following: X t=QX tbA Y1bA t;0<bA<1;(53) where QX tis the amount of domestic goods used as input in the export sector. These rms maximize prot StPX tX tP tQX tsubject to (53). In terms of domestic goods, they maximize: ΠX t P t =etp tQX tbA Y1bA tQX t where the SOE's external terms of trade (XTT) is dened as: p tPX t P t ; www.economics-ejournal.org 21 conomics: The Open-Access, Open-Assessment E-Journal 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 t1 =πX t π t ;where πX tPX t PX t1 : The rst order condition for prot maximization yields the export sector's (factor) demand for domestic goods: QX t=bAetp t1 1bAYt:(54) Also, inserting this in (53) shows that optimal exports vary directly with the product of the RER and the XTT and with GDP: X t=bAetp tbA 1bAYt:(55) The real value of exports in terms of domestic goods is: Xt=StPX tX t P t =etp tX t=etp tbAetp tbA 1bAYt=κX(etp t)bXYt(56) where for simplicity of notation the following parameters are dened: bX1 1bA;κXbAbA 1bA: Government expenditure is assumed to be a time-varying and stochastic fraction Gtof private consumption expenditure. Dene the gross government expenditure fraction as: Gt1+Gt. Hence, using (31) and (32), GDP in terms of domestic goods is: Yt=GtτMγM tpC tCt+Xt(1aD)e1θC tGtτMγM tpC tθC Ct(57) =aDGtτMγM tpC tθC Ct+Xt: www.economics-ejournal.org 22 conomics: The Open-Access, Open-Assessment E-Journal 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:9 Qt=aDGtτMγM tpC tθC Ct+QX t=Yt1bAXt:(58) 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. It is assumed 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+BtStRt=Mt1+(1+it1)Bt1(1+i t1)StRt1(59) = [Mt1+Bt1St1Rt1]QFt: where QFt=i t1StRt1+(StSt1)Rt1it1Bt1 =i t1+(11=δt)StRt1it1Bt1 is the CB's quasi-scal surplus, which includes interest earned and capital gains on international reserves minus the interest paid on its bonds. It is assumed 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+BtStRt=Mt1+Bt1St1Rt1=0:(60) 9Notice that intermediate output in the export sector (54) can be written as: QX t=bA1 1bA(etp t)bXYt=bAbAbA 1bA(etp t)bXYt=bAXt Hence, rearranging the second equality in (58) 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+XtbAXt. www.economics-ejournal.org 23 conomics: The Open-Access, Open-Assessment E-Journal 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 FX market or in the domestic currency bond market. In terms of domestic goods, the CB balance, for all t, is: mt+bt=etrt:(61) This equation provides a constraint on the CB's ability to simultaneously intervene in the FX 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).10 The Government spends on goods, receives the quasi-scal surplus (or nances the decit) of the CB, and collects taxes. It is assumed 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=GtτMγM tPC tCtQFt:(62) So in real terms: taxt=GtτMγM tpC tCtq ft;(63) q ft=1+i t11=δtetrt1 π t ((1+it1)1)bt1 πt : Inserting Yt=wtNt+Πt P t ; 10In the present setup this equation can be interpreted as an institutional constraint that the CB must preserve a `full backing' of its domestic currency liabilities with (the domestic currency value of) its foreign reserves. But it is obviously unnecessary to restrict the CB net wealth to zero (or to full backing). Any constant amount 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 the 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 sufcient. www.economics-ejournal.org 24 conomics: The Open-Access, Open-Assessment E-Journal Price dispersion: ∆t=απθ t∆t1+(1α) 1απθ1 t 1α!θ θ1 Exports: Xt=κX(etp t)bXYt Trade Balance: TBt=1 aDetpC t1θC Xt(1aD)e1θC tYt Current Account: CAt=1+i t1 π t 1rt11+i t1 π t φ t1τD;t11dt1+TBt: Balance of Payments: rtdt=CAt+rt1dt1 Real marginal cost: mct=wt εt Labor market clearing: wt=ξNpC tCσC tϕM;tNσN t Hours worked: Nt=Qt εt ∆t Domestic goods market clearing: Qt=Yt1bAXt www.economics-ejournal.org 31 conomics: The Open-Access, Open-Assessment E-Journal GDP: Yt=aDτM;tGtpC tθC Ct+Xt Consumption relative price: pC t=aD+(1aD)e1θC t1 1θC Money market clearing: mt=1 β22 4 β1β2β3 11 1+it!1 β3+1 13 5pC tCt; CB balance sheet: bt=etrtmt Tax collection: taxt= (Gt1)τM;tpC tCtq ft Quasi-scal surplus: q ft=1+i t11=δtetrt1 π t ((1+it1)1)bt1 πt Identities: et et1 =δtπ t πt ;pC t pC t1 =πC t πt ;p t p t1 =πX t π t (76) Great ratios: γD t=etdt Yt ;γM t=mt pC tCt ;γR t=etrt Yt ; www.economics-ejournal.org 32 conomics: The Open-Access, Open-Assessment E-Journal Auxiliary functions: τD;t=1+α1 1α2γD t ;ϕD;t=1+(τD;t1)1+α2γD t 1α2γD t τM;t=1+β1 1+β2γM tβ3;ϕM;t=1+(τM;t1)1+β3 β2γM t 1+β2γM t: Notice that btnor rtare not constrained to 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 CBs are institutionally constrained in lending to the non-nancial private sector, making btnon-negative. Here, it is assumed that the CB's target for reserves γRis sufciently high and the household's steady state demand for cash is suf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 effect for most SOE's. This justied giving the calibration of its components a careful treatment. As a working hypothesis, it was assumed that the ination rates for imported and exported goods are interrelated in such a way that a shock to one of them affects the other through the dynamics of the XTT (which is the ratio of the two corresponding foreign price levels). Hence, the following equations are assumed: πX t=πX t1ρπXπX1ρπXp t1απXexpσπXεπX t;(77) π t=π t1ρπ (π)1ρπp t1απexpσπεπ t; p t=p t1 πX t (π t)βπ: 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, 16In the parent model ARGEM (Escudé 2007), 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. www.economics-ejournal.org 33 conomics: The Open-Access, Open-Assessment E-Journal απX0;απ>0 are the speeds of adjustment and (1;βπ)plays the role of a cointegrating vector, with βπ=1 as in the last identity in (76). In Appendix I, these equations are estimated using data for Argentina and evidence is found for the cointegration hypothesis with an additional inuence of πX t1on π t, as in the equation below. The equations subject to stochastic shocks are hence the following (where the NSS values ε;π;πXare assumed equal to one): Productivity shock: εt= (εt1)ρεexp(σεεε t) Government expenditure shock: Gt= (Gt1)ρGG1ρGexpσGεG t Riskfree interest rate shock: 1+i t=1+i t1ρi (1+i)1ρi expσiεi t Financing risk/liquidity shock: φ t=φ t1ρφ (φ)1ρφ expσφεφ t Exports ination shock: πX t=πX t1ρπXp t1απXexpσπXεπX t Imported ination shock: π t=π t1ρπp t1αππX t1ρπXN expσπεπ 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. This section studies the stabilizing role of the two policy rules under the different monetary and exchange www.economics-ejournal.org 34 conomics: The Open-Access, Open-Assessment E-Journal rate regimes, mainly by studying the volatilities (standard deviations) of the main endogenous variables in the model. The policy parameter ranges that guarantee the Blanchard-Kahn (BK) stability conditions are also explored. Table 1 summarizes the calibrated values of the main model parameters, and compares them with parameter values used in two other relevant SOE models. Table 1: Calibrated values of main model parameters Parameters Values G-M De P βIntertemporal discount factor 0.99 0.99 0.99 σCRelative risk aversion for goods 1.5 1 1 σNRelative risk aversion for labor 0.5 3 0.47 αProbability of not adjusting price 0.66 0.75 0.66 θE. of substitution between domestic goods 6 6 10 θCE. of substitution, domestic vs. imported goods 1.5 1 3 aDCoef. for share of domestic goods 0.86 0.6 0.6 bACoef. in production function for commodities 0.5 1 ετDE. of net risk function τD(ed=Y)10 εLE. of inverse cash velocity L(1+i)1.02 E.: Elasticity; G_M=`Gali and Monacelli (2002)'; De P=`De Paoli (2006)'. The standard errors and persistence parameters used for the six shock variables are given in Table 2. They were calibrated taking into account the available time series for Argentina and the RW during the period 1994.1–2009.2: public consumption to GDP σG;ρG, imported and exported goods ination as they conform Argentina's XTT σπ;σπX;ρπ;ρπX;ρπXN , Libor 3 months σi;ρi, and balance of payments information on private sector foreign debts and interest payments for the calculation of the spread over Libor 3 months σφ;ρφ. The standard deviations were not always taken exactly according to the data. Some were calibrated using both the data and the theoretical standard deviation and variance decomposition for GDP resulting from a baseline calibration of the two policy rules (h1=0:8, h2=0:8, k4=0:8, and the rest of the coefcients zero). This implied diminishing the observed standard deviation of G(from 0.054 in a simple AR(1) estimation, from which the persistence parameter ρGwas used), www.economics-ejournal.org 35 conomics: The Open-Access, Open-Assessment E-Journal which seemed to weigh too heavily in the volatility of Y, and increasing the standard deviation of φ(from 0.0034), which seemed not to weigh enough. The value of σεwas chosen so that the resulting theoretical standard deviation of Ywas similar to the data for detrended and s.a. GDP for Argentina leaving out the crisis years 2001/2002. Table 2: Calibration of shock variables Standard deviations σεσGσiσφσπσπX 0.01 0.03 0.0046 0.05 0.0295 0.0424 Persistence ρερGρiρφρπρπXρπXN 0.8 0.85 0.7 0.3 0.2 0.41 0.18 Speeds of adjustment απαπX 0.181 -0.255 3.1 Basic Blanchard-Kahn stability analysis First some of the general stability properties of the model are studied in relation to the parameters of the two simple policy rules in the MER regime. The coefcients on the policy rules not explicitly mentioned below are made equal to zero. When a particular conguration of parameters are said to give stability it means that all the requirements for determinacy and non-explosiveness are met, including the rank condition and absence of unit roots. Because the present model with 2 simple policy rules (or MER regime) is a generalization of the standard DSGE New Keynesian model, it is of some interest to explore how it stands in relation to the most characteristic stability requirement for the standard model: the Taylor Principle (in the generalization of Woodford 2003, Proposition 4.4), which states that Blanchard-Kahn (BK) stability requires that the sum of the inertial and ination coefcients in the interest rate feedback rule be grater than one (h0+h1>1). Obtaining necessary and sufcient conditions for BK stability is too complex, given the number of parameters and generalized www.economics-ejournal.org 36 conomics: The Open-Access, Open-Assessment E-Journal eigenvalues in the model. But the following observations concerning BK stability under the MER regime gives some idea of the richness of the model. 1) It is not necessary that any of the 4 kibe different from zero to have BK stability. Notice that when all 4 of the kiare zero, the second policy rule in log deviation form is b δt=0, which means that the operating target for the rate of nominal depreciation is its NSS value. In this case, two alternative sufcient (additional) conditions for BK stability are A) all hiexcept h3are zero and h3is positive (at any level), and B) all hiexcept h2are zero and h2is positive (at any level). Hence, two viable policy regimes are b δt=0 and either bit=h3b et(with h3>0), or bit=h3b Yt (with h2>0). In particular, this shows that the Taylor Principle is not necessary for BK stability. In the PER case (where the Taylor rule is substituted by bt=b)there is also BK stability when all the coefcients are zero (kj=0;j=0;1;2;3;4). In this case the policy rule implies intervening in the FX market sufciently to keep the nominal exchange crawling at the NSS rate δT, but otherwise letting the economy run its course, and not responding to international reserves (since they nevertheless return to their NSS ratio to GDP). More generally, in the PER regime BK stability is obtained if kj=0;j=0;1;2;3;and k42[1:6;1:6], which includes the previous case but also allows for explicitly responding to gaps in the CB reserves ratio. 2) Going back to the MER regime, it is not necessary that any of the 3 hibe different from zero to have BK stability. For sufciently small positive values of k4, a policy regime in which all the rest of the coefcients are zero is feasible. Hence, a policy regime where bit=0 and b δt=k4b et+brtb Ytwith k42[0:00001;0:0073] is viable. In such a regime, the operating target for the interest rate is its NSS value and the operational target for the rate of currency depreciation is a small fraction of the deviation of CB reserves ratio (relative to GDP) from the long run target. This again shows that the Taylor Principle is not necessary for BK stability. Perhaps even more surprising is that the Taylor Principle does not even hold in the FER regime. For example, (with rt=r) the two alternative policy rules dened by h3=h4=0, and either h0=2, h1=1 or h0=0:8, h1=10 are both feasible. If neither of h0and h1is negative, however, then their sum must be greater than one (Taylor Principle). But if it is not true that h3=h4=0, then even a rule where all the coefcients are negative may be feasible. For example, www.economics-ejournal.org 37 conomics: The Open-Access, Open-Assessment E-Journal the following policy rule satises the BK conditions in the FER regime: bit=0:5bit10:5b πC t0:5b Yt0:5b et: Before advancing any further, a few observations related to the previous points are worthwhile. First, if in the MER regime all 9 policy rule coefcients are zero the model generates a unit root and hence is not BK stable. Second, if (as in 1) above) all 4 of the kiare zero, there is a very active exchange rate policy: the CB is permanently intervening in the FX market to make the exchange rate crawl at the long run rate. In contrast, under the FER regime the CB lets the exchange rate oat, not intervening in the exchange market at all and hence keeping its international reserves constant. Third, if (as in 2) above) all 3 of the hiare zero, there is a very active interest rate policy: the CB is permanently intervening in the domestic currency bond market to keep the interest rate at the long run level. In contrast, under the PER (or FIR) regime the CB lets the interest rate oat, not intervening in the bond market at all and hence maintaining its stock of domestic currency bonds constant. Notice that in the standard New Keynesian model a FIR regime would never be feasible due to the validity of the Taylor Principle. 3) If in the MER regime all the kiexcept k4are zero and all the hiexcept h1 and h2are zero, then sufcient (additional) conditions for BK stability are that either a) k4<0 and h0+h1>1 or b) k4>0 and h0+h1<1. Notice that in the second case the Taylor Principle is turned on its head. For example, the following sets of policy rules are BK stable: bit=0:5bit1+0:51b πC tand b δt=0:001b et+brtb Yt bit=0:5bit1+0:49b πC tand b δt=0:001b et+brtb Yt but neither of the following are: bit=0:5bit1+0:51b πC tand b δt=0:001b et+brtb Yt bit=0:5bit1+0:49b πC tand b δt=0:001b et+brtb Yt: 4) The sign of k4plays a complex role in BK stability which is not always intuitive. If k0=k1=k2=k3=0 and k4<0, whenever there are insufcient www.economics-ejournal.org 38 conomics: The Open-Access, Open-Assessment E-Journal reserves (etrt=Yt<γRand hence) b et+brtb Yt<0, the CB depreciates the currency at a rate greater than in the NSS: b δt=logδt δ=k4b et+brtb Yt>0: Since a purchase of reserves (increase in rt) expands the money supply (ceteris paribus) one tends to associate it with a currency depreciation. But things are more complex here. First, it is the ratio between the real domestic value of reserves (etrt) and GDP that must increase if initially etrt=Yt<γR. Second, that increase must take place in the long run, so the direction of movement may be the opposite during a transition period. In fact, in Section 3.3 below (in the context of optimal simple rules) a positive k4is at times optimal. 5) To get a feeling for the range within each coefcient can vary without impairing BK stability, a baseline calibration for the coefcients in the two policy feedback rules is dened and the intervals within which each of the coefcients can be moved individually (leaving the rest at the baseline value) without impairing stability are found. The search is restricted to two decimal points accuracy and only checked for parameter values at most 10 in absolute value. The following is the baseline calibration for this exercise: Baseline calibration h0h1h2h3k0k1k2k3k4 0:8 0:8 0:0 0:0 0:0 0:0 0:0 0:00:8 The results for the three policy regimes are shown in the Table 3. Starting with the MER regime, both of the inertial coefcient intervals of stability are quite wide, both going into high superinertial levels (of 10). Because unity is included in the feasible intervals for h0and k0, one or both of the simple policy rules can be implemented as the feedback response of the rst difference (in the interest rate or the depreciation rate, respectively) to the various arguments on the r.h.s. In the case of the interest rate rule, there are no upper bounds for the reactions to ination or the RER, but, perhaps surprisingly, there is an upper bound of only 1.04 for the response to GDP. There is much more room for diminishing the interest rate (up to –3.03) when GDP is high. In the case of the nominal depreciation rule, there www.economics-ejournal.org 39 conomics: The Open-Access, Open-Assessment E-Journal are no upper or lower bounds for the reactions to ination, GDP, or the RER. In the case of k4, the only restriction is that it must be outside of a small interval around zero. The fact that there is a relatively low upper bound for the interest rate response to GDP while there is no bound for the nominal depreciation response to the same variable is interesting, since the stabilization of GDP is, of course, of primary interest in most CBs (along with the stabilization of ination). The wide negative intervals for h0and h1are also very interesting, since they invalidate the Taylor principle. For example a regime that combines either bit=5bit1+0:8b πC t or bit=0:8bit19b πC twith b δt=0:8b et+brtb Ytis BK stable. The FER regime shows stability ranges that are very similar to those of the rst policy rule of the MER regime. There is a narrowing of the negative range in the case of h3. But again those wide negative intervals for h0and h1that invalidate the Taylor Principle show up. The narrowing of the range of stability is more signicant in the case of the PER regime, especially in the cases of the positive and negative ranges for k0,k2and k4and the positive range for k3. On the other hand, in contrast to the MER regime, in the PER regime the stability range for k4 includes 0. Table 3: Stability ranges for individual coefcients of policy rules MER FER PER Interest rate rule h02[10;1:17][[0:21;10] [10;1:16][[0:21;10] h12[10;8:71][[0:21;10] [10;8:65][[0:21;10] h22[3:03;1:04] [3:02;1:03] h32[4:16;10] [1:97;10] Nominal depreciation rule k02[10;10] [1:18;0:67] k12[10;10] [10;10] k22[10;10] [1:16;1:80] k32[10;10] [10;2:47] k42[10;0:01][[0:01;10] [1:61;4:34] www.economics-ejournal.org 40 conomics: The Open-Access, Open-Assessment E-Journal (slightly) positive for style A. The interest rate response to the RER is negative for styles A and B, and positive for styles C and D. Finally, in the PER regime, k0,k1, and k2, are negative for all 4 styles, with the inertial coefcient k0between –0.6 and –0.8 and k1always greater than one in absolute value (and in the case of styles C and D, above 5). k3is negative for styles A and D. Finally, k4is positive for styles B, C, and D. Hence, under the PER regime, both high ination and high GDP demand lowering the rate of nominal depreciation, and the previous' period rate of nominal depreciation affects the present rate negatively. A caveat is that many of these observations on the sign and magnitude of the optimal simple rule coefcients are highly sensitive to parameter calibrations.19 Hence, there is no claim here of generality for the results obtained. The important point is that simple characteristics of the standard New Keynesian model to which we have been accustomed (such as the Taylor Rule) do not survive the type of model generalization introduced here, even in the case of the FER regime. 3.4 Optimal policy under commitment In this section Dynare's `ramsey' command is used 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 for the predetermined variables) of a discounted ad hoc loss function: Lt0=Et0 ∞ ∑ t=t0 βtt01 2Lt, (78) subject to all the non-policy model equations, where the period loss function Ltis given by20: Lt=ωππC tπT2+ωY(YtY)2+ωe(ete)2+ωr(rtr)2(79) +ω∆i(∆it)2+ω∆δ(∆δt)2; 19This is quite evident if one compares with the results of the `osr' exercise in the Discussion Paper, where the calibrations differ only in the NSS value of the elasticity of the foreign debt premium (which is here much lower). 20See Section 3.4 below for a discussion on the desideratum between using ad hoc versus utilitybased loss functions. www.economics-ejournal.org 47 conomics: The Open-Access, Open-Assessment E-Journal It is assumed that policymakers have the same intertemporal discount factor as households (β=0:99). The same denition of CB styles as in the previous section are maintained except that a small preference for rhas been introduced (with ωr= 1) in all the CB styles. Otherwise, to obtain BK stability it would be necessary to increase the policymaker discount factor (say to 0.999). Table 7 shows the losses and relative losses for the alternative CB styles (A-D) and policy regimes (MER, FER, PER). As expected, the MER regime always dominates the two `corner' regimes. The PER regime ranks above the FER regime when only ination matters (style A) but in the other 3 CB styles the FER regime has a lower relative loss than the PER regime. The `corner' regimes have losses between 0.8% and 4.7% higher than in the MER regime. For the baseline ετD=10 used, the increase in loss for forfeiting one of the policy rules does not appear to be very high. However, in Section 4 it is shown that for higher elasticities and for alternative calibrations of other parameters this increase in cost may be very substantial. Table 7: Losses under optimal policy under commitment STYLE MER FER PER MER FER PER A119.9 121.0 120.9 11.009 1.008 B112.0 114.5 117.3 11.023 1.047 C378.1 388.1 388.8 11.027 1.028 D394.5 405.2 405.7 11.027 1.028 LOSS RELATIVE LOSS www.economics-ejournal.org 48 conomics: The Open-Access, Open-Assessment E-Journal Table 8: Reduced form policy functions with optimal policy under commitment REGIMES: STYLES: A B C D A B C D ii delta ii delta ii delta ii delta ii ii ii ii delta delta delta delta ii(-1) 0.275 0.022 0.495 0.373 0.184 0.031 0.181 0.033 0.265 0.493 0.176 0.173 0.021 0.375 0.027 0.029 delta(-1) 0.022 0.377 0.373 0.562 0.031 0.179 0.033 0.174 0.022 0.375 0.027 0.029 0.375 0.559 0.172 0.168 r(-1) -0.031 -0.020 0.016 -0.017 -0.008 -0.042 -0.007 -0.038 -0.032 0.016 -0.009 -0.008 -0.020 -0.016 -0.042 -0.040 e(-1) -0.355 -0.484 0.452 -0.432 -0.175 -1.143 -0.164 -1.163 -0.366 0.454 -0.199 -0.187 -0.485 -0.442 -1.173 -1.188 d(-1) 0.031 0.020 -0.016 0.017 0.008 0.042 0.007 0.038 0.032 -0.016 0.009 0.008 0.020 0.016 0.042 0.040 Deltta(-1) -0.001 -0.008 -0.017 0.014 0.024 0.058 0.024 0.058 -0.001 -0.017 0.025 0.025 -0.009 0.014 0.059 0.059 tauD(-1) 0.038 0.024 -0.019 0.020 0.010 0.051 0.008 0.046 0.039 -0.019 0.011 0.009 0.024 0.020 0.051 0.048 pC(-1) 0.189 0.432 0.009 0.011 0.154 0.249 0.155 0.247 0.198 0.009 0.156 0.157 0.435 0.011 0.254 0.252 pStar(-1) -0.111 -0.121 0.161 -0.152 -0.022 -0.350 -0.027 -0.337 -0.114 0.162 -0.030 -0.035 -0.121 -0.155 -0.360 -0.348 z_piStar(-1) -0.068 -0.095 0.042 -0.043 -0.051 -0.151 -0.051 -0.164 -0.070 0.042 -0.054 -0.054 -0.095 -0.044 -0.155 -0.165 z_piStarX(-1) -0.075 -0.077 0.086 -0.083 -0.045 -0.225 -0.044 -0.206 -0.076 0.086 -0.050 -0.049 -0.076 -0.084 -0.229 -0.215 z_G(-1) -0.030 -0.039 0.182 -0.152 -0.093 -0.463 -0.091 -0.442 -0.031 0.182 -0.105 -0.103 -0.039 -0.158 -0.476 -0.460 z_epsilon(-1) 0.003 0.026 0.059 -0.047 -0.107 -0.233 -0.108 -0.234 0.004 0.059 -0.113 -0.114 0.026 -0.049 -0.236 -0.236 z_iStar(-1) 0.573 0.144 -0.042 0.051 0.398 0.534 0.396 0.475 0.587 -0.041 0.419 0.419 0.144 0.054 0.550 0.505 z_phiStar(-1) 0.231 0.028 0.013 -0.007 0.169 0.164 0.170 0.148 0.237 0.014 0.177 0.179 0.028 -0.006 0.169 0.157 mult_10(-1) 0.000 0.004 0.004 0.006 0.000 0.002 0.000 0.002 0.000 0.004 0.000 0.000 0.004 0.006 0.002 0.002 mult_17(-1) 0.026 0.027 0.137 0.152 0.024 0.027 0.024 0.027 0.027 0.137 0.024 0.024 0.028 0.152 0.027 0.027 mult_18(-1) 0.036 0.042 0.179 0.200 0.032 0.036 0.032 0.036 0.037 0.179 0.032 0.032 0.042 0.200 0.037 0.037 mult_24(-1) 0.000 -0.003 -0.003 -0.004 0.000 -0.001 0.000 -0.001 -0.001 -0.003 0.000 0.000 -0.003 -0.004 -0.001 -0.001 eps_epsilon 0.004 0.032 0.074 -0.059 -0.134 -0.291 -0.135 -0.292 0.005 0.074 -0.141 -0.142 0.033 -0.061 -0.295 -0.295 eps_G -0.035 -0.046 0.214 -0.179 -0.110 -0.544 -0.106 -0.520 -0.037 0.214 -0.123 -0.121 -0.046 -0.186 -0.560 -0.541 eps_iStar 0.779 0.180 -0.039 0.051 0.558 0.709 0.557 0.631 0.798 -0.038 0.586 0.588 0.180 0.057 0.732 0.671 eps_phiStar -0.643 -0.013 -0.107 0.089 -0.530 -0.376 -0.540 -0.341 -0.661 -0.110 -0.554 -0.566 -0.012 0.086 -0.393 -0.363 eps_piStar -0.179 -0.249 0.111 -0.114 -0.133 -0.397 -0.135 -0.432 -0.185 0.112 -0.141 -0.141 -0.250 -0.117 -0.408 -0.434 eps_piStarX -0.182 -0.187 0.209 -0.202 -0.111 -0.549 -0.108 -0.504 -0.187 0.210 -0.122 -0.120 -0.187 -0.206 -0.560 -0.524 FER MER B C D A PER Table 8 shows the coefcients of the policy functions in the reduced form (or `solution') that correspond to the instrument variables (in the sense of optimal control theory), i.e., the operational targets (in the economic sense) of the three alternative regimes. These variables21 are linear functions of the 9 non-shock predetermined variables (i,δ,r,e,d,∆,τD,pC,p), the 6 shock variables, and the Lagrange multipliers corresponding to the 4 equations with forward-looking terms (the UIP equation, the two dynamic Phillips equations, and the consumption Euler equation).22 In all of the CB styles there is substantial inertia in the interest rate policy function and in the nominal depreciation policy function. This is hardly 21Notice that the variables are shown 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. 22The real interest rate has been eliminated from the model for the construction of this table to avoid having an additional and unnecessary Lagrange multiplier variable. www.economics-ejournal.org 49 conomics: The Open-Access, Open-Assessment E-Journal surprising since all these CB styles have been dened to show a signicant preference for policy inertia. What is perhaps more surprising is the dispersion in the inertial coefcients, given that they all have the same weight for preference for inertia (ω∆i=ω∆δ=50). The coefcients on the Lagrange multipliers are relatively small, implying that the policy function coefcients (for the rest of the variables) do not vary much from quarter to quarter when these effects are cumulated (attributable to the commitment to never again re-optimize). Table 9 shows the variance decomposition for the 4 CB styles in the case of the MER regime. The corresponding variance decompositions for the FER and PER regimes are very similar and hence not shown. The table shows that the substantial shocks in explaining the variances of the target and operational target variables are G,φ,π, and πX. This is not surprising considering the assumed standard errors for the shocks (which are lowest for εand i). The shock to export price ination is explains around 50% of the variance of the RER for all CB styles. While 65% of the variance of ination is explained by the exogenous risk/liquidity shock φ when ination is the CB priority (style A), this drops to around 17% in styles C and D, where ination is equally important as GDP or both GDP and the RER. This shock also explains as much as 83% of the variance of the nominal interest rate under style A but only 29% under style B. Almost 60% of the variance of GDP is explained by this shock when the CB gives priority to stabilizing GDP, but only around 35% for the other CB styles. The shock to Ghas its highest relative effect on ination under styles C and D (around 65%) and also has high effect on GDP for styles A, C and D (around 40%). The shock to Ghardly explains any of the variance of ination under style A. Between 19% and 26% of the variance of GDP is explained by the shock to export price ination πXin all the CB styles. www.economics-ejournal.org 50 conomics: The Open-Access, Open-Assessment E-Journal Table 9: Variance decomposition (MER; `ramsey') eps_epsilon eps_G eps_iStar eps_phiStar eps_piStar eps_piStarX piC 0.26 0.27 1.36 64.87 19.42 13.82 Y2.36 35.29 0.63 33.49 1.85 26.38 e0.62 2.01 1.65 21.23 28.5 45.99 ii 0.09 0.38 1.66 82.77 3.86 11.25 delta 0.04 0.73 0.37 56.00 18.34 24.53 piC 1.57 29.51 0.75 44.04 5.53 18.61 Y0.07 9.9 1.33 57.97 4.4 26.33 e0.00 7.39 1.45 29.01 11.31 50.84 ii 2.07 48.16 0.32 29.14 3.21 17.11 delta 1.52 31.02 0.86 49.53 2.30 14.78 piC 4.76 63.67 0.39 17.13 5.06 8.99 Y2.01 42.3 0.75 34.17 2.15 18.62 e0.00 7.57 1.46 28.29 12.28 50.39 ii 1.84 44.39 0.62 47.63 1.66 3.85 delta 1.48 29.78 0.78 38.19 6.35 23.41 piC 4.88 65.43 0.40 16.86 4.91 7.54 Y1.66 36.44 0.81 36.20 1.41 23.47 e0.00 7.20 1.42 28.90 12.09 50.39 ii 1.82 43.95 0.67 49.43 1.37 2.77 delta 1.64 31.57 0.71 37.17 7.78 21.13 CB style C CB style D CB style A CB style B Table 10 explores to what extent the ranking of policy regimes depends on the shocks considered by eliminating 5 of the shocks and maintaining the same value for the standard error of the remaining shock. The table shows that the superiority of the MER regime is robust to any of the shocks taken separately. It also shows that with only one exception, the (ramsey-optimal) pure exchange rate oat is superior to the (ramsey-optimal) pure peg (or interest rate pure oat) for any of the individual shocks and CB preferences. The one exception is the case of the shock to the exogenous risk/liquidity premium φunder CB style A (in which only ination matters). It is to be noted that when all the 6 shocks are used (as in Table 7) the pattern of this one exception is repeated and the relative losses are www.economics-ejournal.org 51 conomics: The Open-Access, Open-Assessment E-Journal very similar to those of the central set of columns of Table 10. This points to the importance of the exogenous risk/liquidity shock in the overall model. Table 10: Losses for each individual shock STYLE MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER A103.4 104.0 104.1 103.7 104.3 104.5 116.5 117.5 117.5 104.6 105.2 105.3 104.9 105.5 105.6 B88.5 90.4 93.2 90.7 92.5 95.5 104.1 106.4 109.1 89.1 91.0 93.8 93.3 95.2 98.0 C333.7 342.0 343.2 344.5 353.0 354.3 355.8 365.3 366.1 334.8 343.2 344.4 341.0 349.6 350.7 D337.5 345.2 346.3 349.3 357.3 358.4 363.3 372.6 373.2 340.2 347.9 348.9 351.2 359.8 360.6 A1.006 1.007 1.006 1.007 1.009 1.008 1.006 1.007 1.006 1.007 B1.021 1.053 1.021 1.053 1.023 1.049 1.021 1.053 1.021 1.051 C1.025 1.029 1.025 1.028 1.027 1.029 1.025 1.029 1.025 1.028 D1.023 1.026 1.023 1.026 1.026 1.027 1.022 1.026 1.024 1.027 RELATIVE LOSS LOSS epsilon G phiStar piStar piStarX 3.5 Ad hoc vs. utility based loss functions In this paper policymakers are assumed to want to reduce the volatility of (a weighted average of) certain target variables that are deemed to be important for the success of their stabilizing efforts. These variables, ination, GDP, or the RER, are periodically measured by statistical agencies in most countries and their evolution is well publicized. Furthermore, most policymakers have an understanding of basic (more or less sophisticated) macroeconomic theory that links these variables in a unied framework. Any macroeconomic policy model will typically include the household decision problem in terms of a utility function that simply expresses in a mathematical way that people like to consume more and work less. Most macroeconomic policy models have tended to simplify reality in the dimension of household heterogeneity going to the extreme of postulating a `representative household' and thus completely overlooking aspects of the policy process, such as the consequences of policy decisions on sectorial income and risk distribution, that are in fact considered important by households and rms. An important strand of macro policy DSGE models, without going beyond the household homogeneity assumption, looks for the optimal policy that would deliver the highest expected household intertemporal utility. Without actually modeling policymakers as agents that have preferences and constraints, this research looks for the policy that would be followed if these policymakers were `benevolent' or `altruistic' in the sense that they unanimously decide to maximize the www.economics-ejournal.org 52 conomics: The Open-Access, Open-Assessment E-Journal utility of the representative household. A typical way of doing this is to obtain a second order approximation of the discounted intertemporal household utility, nd a way of doing away with the rst order terms to ensure that the resultant approximation adequately orders the losses obtained with different policy regimes, and use this, along with rst order approximations of the non-policy model equations to implement optimal policy under commitment in a linear-quadratic optimal control framework. Doing this is a very tedious process when one has a moderately complex model, but it does enrich the analysis in a sense. Not only does the optimum policy reect household utility maximization but also the loss function can be expressed in terms of welfare relevant gaps which depart from the simple gaps with respect to the NSS that are used in this paper. However, this enrichment is based on very strong assumptions that need not be universally accepted as true. First, the fact that the model used overlooks household heterogeneity is an important limitation. If instead of one class of households, the model had two classes that have sufciently different sources of income or risk, then the `benevolence' assumption loses meaning and some assumption has to be made as to what policymaker preferences are concerning the distributional consequences of their policy actions. Second, even if the household homogeneity assumption is maintained, it is at least controversial to assume that actual policymakers are not only homogeneous but also `benevolent'. Indeed, it is quite paradoxical that the combined assumptions that a) policytaking households care only for themselves and b) (non-modeled) policymakers care only for others, should exert such fascination. The ad hoc loss function approach can be considered more general since, if one has adequate target values in the loss function, the loss function that would be obtained from, say, a second order approximation to household utility is a particular case, i.e., gives specic (utility-related) values to the exogenous weights used in the ad hoc procedure. One can argue that if a sufciently varied set of exogenous weights were used, one of them would be close to the one that could be obtained through a second order approximation of utility. The ad hoc procedure is also more general in that it does not need to assume that policymakers are `benevolent'. Making monetary and exchange rate decisions is a complex process where many people intervene, with differing views with respect to the `correct' model and the `preferred' outcome of the policymaking. Usually, more than one www.economics-ejournal.org 53 conomics: The Open-Access, Open-Assessment E-Journal model is used in the process. One of the less defensible aspect of typical DSGE models is that they usually ignore distributive aspects by making households homogeneous or only heterogeneous in certain technical details. Distributive aspects are usually very important in policymaking, both in developed and less developed economies. The world economy has been recently hit by a crisis that many attribute to the lack of regulatory actions that could possibly have prevented the building up of bubbles in real estate sectors and nancial system vulnerability to the risks posed by insufciently understood derivatives. Monetary and exchange rate policy is an integral part of the political process in both developed and less developed economies. Unless a large amount of research effort is invested in trying to reect household heterogeneity, not much is actually gained by obtaining the policies that maximize the welfare of a ctitious `representative household' that is used in the model, presumably to avoid complexity. And if realistic household heterogeneity is actually reected in the model there remains the fact that there is also policymaker heterogeneity (say, between different members of the central bank board or between the central bank and the treasury). Different participants in the decision process may have different preferences with respect to the outcomes of the policy decisions. The principal objective of this paper is to show that using a relatively standard and simple SOE model in which there is an endogenous risk premium that affects the interest rate at which the private sector can borrow funds abroad there are signicant gains from simultaneously using interest and exchange rate policies (instead of only one of them) no matter what the specic policymaker preferences are. Although various caveats have been stated above with respect to using a utility based loss function, it is nevertheless a useful complement of the approach followed here since it can be used to make conditional statements such as, "if policymakers were homogeneous, had a high degree of condence in the appropriateness of the model used, and were only concerned with maximizing the welfare of the model's representative household, they would ..." However, such research clearly goes beyond the scope of the present paper. www.economics-ejournal.org 54 conomics: The Open-Access, Open-Assessment E-Journal 4 Monetary and exchange rate policy and capital ows in the SOE 4.1 The effectiveness of two simple policy rules in managing private capital ows for stabilization It has been shown that for a broad set of policy preferences the CB can better achieve its goals by simultaneously using interest and exchange rate policies. It remains to be seen what aspects of the model account for this. This subsection assumes the CB uses simple policy rules and starts by conjecturing that the gain in using two policy rules is related to the CB's ability to inuence, to a certain extent, households' foreign debt ratio. The latter determines the endogenous risk premium that foreign agents charge over the international interest rate and which, through the UIP equation, is a primary ingredient in determining the relation between the interest rate differential and the expected rate of nominal depreciation. The basic idea is that the corner regimes amount to forfeiting a part of the CB ability to affect this crucial relation. To substantiate this idea, consider the log-linear approximations of the UIP equation and the two simple policy rules equations under the MER regime: bit=Etb δt+1+bi t+b φ t+εϕDb dt+b etb Yt(80) bit=h0bit1+h1b πC t+h2b Yt+h3b et(81) b δt=k0b δt1+k1b πC t+k2b Yt+k3b et+k4brt+b etb Yt:(82) Leading the third equation, subtracting the resulting equation from the second, and using the rst, gives the following equation: bi t+b φ t+εϕDb dt+b etb Yt=h0bit1k0b δt+h1b πC tk1Etb πC t+1(83) +h2b Ytk2Etb Yt+1+(h3b etk3Etb et+1)k4Etbrt+1+Etb et+1Etb Yt+1: On the l.h.s. is the (log-linear deviation from the NSS of the) of the foreign currency riskless interest rate plus the risk premium in the UIP (with exogenous and endogenous components). On the r.h.s. is a complex term that exclusively depends on the log-linear deviations of the variables the CB uses for its simple policy rules www.economics-ejournal.org 55 conomics: The Open-Access, Open-Assessment E-Journal and the exogenous coefcients in the simple policy rules. Changes in the coef- cients on the CB policy rules can thus modify a crucial relation between the households' foreign debt ratio and a linear combination of lagged, current and expected endogenous variables to which the CB responds. The policy coefcients thus have an important role in determining what households' foreign debt is in each period, given the values of the international interest rate and risk/liquidity premium (bi t+b φ t), both exogenous. For example, when one of the latter is shocked, the policy coefcients help in determining the effects on the households' foreign debt and, hence, international capital ows. The constraints that the respective `corner' regimes impose (i.e., the constancy of one of the potential CB instruments: either bt=b;8t;or rt=r;8t, each replacing one of the simple policy rules), imply that the CB has less leeway in affecting international capital ows in the direction that helps it stabilize the economy according to its preferences (or style). Under the FER regime, in which (82) is replaced by brt=0, (83) is reduced to: bi t+b φ t+εϕDb dt+b etb Yt=h0bit1+h1b πC t+h2b Yt+h3b etEtb δt+1 and under the PER regime, in which (81) is replaced by bbt=0, it is reduced to:23 bi t+b φ t+εϕDb dt+b etb Yt=bitk0b δtEthk1b πC t+1+k2b Yt+1+k3b et+1 +k4brt+1+b et+1b Yt+1i: In both of the corner cases, the CB affects the foreign debt ratio through its interest rate or exchange rate policy, respectively. It therefore also affects the endogenous part of the risk/liquidity premium, and hence the (domestic) foreign currency interest rate that impinges on the economy. The exibility that the CB achieves by using two simultaneous policy rules generates gains that, at least for the most usual CB styles, can be signicant. Such gains have been measured above, in the context of this particular model and optimal simple rules, as the reductions in expected loss obtained from using the MER regime instead of any of the corner regimes. Although this argument is more clearly valid in the case of optimal simple 23Notice that in the particular PER regime in which there is no feedback, the r.h.s. of this equation is simply bitk0b δt, and in the xed exchange rate policy it reduces to bit. www.economics-ejournal.org 56 conomics: The Open-Access, Open-Assessment E-Journal Figure 2: Negative shock to φ FER 510 15 20 -0.02 0 0.02 piC 510 15 20 -0.05 0 0.05 Y 510 15 20 -0.02 0 0.02 real_ii 510 15 20 -0.05 0 0.05 e 510 15 20 -0.02 0 0.02 ii 510 15 20 -0.1 0 0.1 delta 510 15 20 -5 0 5x 10 -3 pii 510 15 20 -0.02 0 0.02 C 510 15 20 -0.05 0 0.05 X 510 15 20 0 0.05 0.1 d 510 15 20 0 0.01 0.02 gammaD 510 15 20 0 0.5 1x 10 -3 varphiD 510 15 20 -5 0 5x 10 -3 m 510 15 20 -2 0 2x 10 -3 gammaM 510 15 20 -0.02 0 0.02 CBbalsheet 510 15 20 -0.02 0 0.02 b 510 15 20 -5 0 5x 10 -3 gammaR www.economics-ejournal.org 63 conomics: The Open-Access, Open-Assessment E-Journal MER 510 15 20 -0.02 0 0.02 piC 510 15 20 -0.05 0 0.05 Y 510 15 20 -0.02 0 0.02 real_ii 510 15 20 -0.05 0 0.05 e 510 15 20 -0.02 0 0.02 ii 510 15 20 -0.1 0 0.1 delta 510 15 20 -5 0 5x 10 -3 pii 510 15 20 -0.02 0 0.02 C 510 15 20 -0.05 0 0.05 X 510 15 20 -2 0 2d 510 15 20 -0.5 0 0.5 gammaD 510 15 20 -0.05 0 0.05 varphiD 510 15 20 -2 0 2x 10 -3 m 510 15 20 -2 0 2x 10 -3 gammaM 510 15 20 -1 0 1CBbalsheet 510 15 20 -1 0 1b 510 15 20 -0.5 0 0.5 gammaR 510 15 20 -1 0 1r www.economics-ejournal.org 64 conomics: The Open-Access, Open-Assessment E-Journal Figure 3: Positive shock to π FER 510 15 20 -2 0 2x 10 -3 piC 510 15 20 -0.02 0 0.02 Y 510 15 20 -2 0 2x 10 -3 real_ii 510 15 20 -0.01 0 0.01 e 510 15 20 -2 0 2x 10 -3 ii 510 15 20 -0.05 0 0.05 delta 510 15 20 -1 0 1x 10 -3 pii 510 15 20 -5 0 5x 10 -3 C 510 15 20 -0.02 0 0.02 X 510 15 20 -0.02 0 0.02 d 510 15 20 0 0.01 0.02 gammaD 510 15 20 0 0.5 1x 10 -3 varphiD 510 15 20 -2 0 2x 10 -4 m 510 15 20 -2 0 2x 10 -4 gammaM 510 15 20 -2 0 2x 10 -3 CBbalsheet 510 15 20 -5 0 5x 10 -3 b 510 15 20 -5 0 5x 10 -3 gammaR www.economics-ejournal.org 65 conomics: The Open-Access, Open-Assessment E-Journal MER 510 15 20 -5 0 5x 10 -3 piC 510 15 20 -0.02 0 0.02 Y 510 15 20 -5 0 5x 10 -3 real_ii 510 15 20 -0.01 0 0.01 e 510 15 20 -5 0 5x 10 -3 ii 510 15 20 -0.02 0 0.02 delta 510 15 20 -1 0 1x 10 -3 pii 510 15 20 -5 0 5x 10 -3 C 510 15 20 -0.02 0 0.02 X 510 15 20 -2 0 2d 510 15 20 -0.5 0 0.5 gammaD 510 15 20 -0.05 0 0.05 varphiD 510 15 20 -2 0 2x 10 -3 m 510 15 20 -2 0 2x 10 -3 gammaM 510 15 20 -1 0 1CBbalsheet 510 15 20 -1 0 1b 510 15 20 -0.5 0 0.5 gammaR 510 15 20 -1 0 1r www.economics-ejournal.org 66 conomics: The Open-Access, Open-Assessment E-Journal Figure 4: Positive shock to πX FER 510 15 20 -0.01 0 0.01 piC 510 15 20 -0.01 0 0.01 Y 510 15 20 -0.01 0 0.01 real_ii 510 15 20 -0.02 -0.01 0e 510 15 20 -0.01 0 0.01 ii 510 15 20 -0.05 0 0.05 delta 510 15 20 -4 -2 0x 10 -3 pii 510 15 20 -0.02 0 0.02 C 510 15 20 -0.01 0 0.01 X 510 15 20 -0.04 -0.02 0d 510 15 20 -0.04 -0.02 0gammaD 510 15 20 -2 -1 0x 10 -3 varphiD 510 15 20 -2 0 2x 10 -3 m 510 15 20 -1 0 1x 10 -3 gammaM 510 15 20 -0.01 -0.005 0CBbalsheet 510 15 20 -0.01 -0.005 0b 510 15 20 -5 0 5x 10 -3 gammaR www.economics-ejournal.org 67 conomics: The Open-Access, Open-Assessment E-Journal MER 510 15 20 -5 0 5x 10 -3 piC 510 15 20 -0.02 0 0.02 Y 510 15 20 -5 0 5x 10 -3 real_ii 510 15 20 -0.02 -0.01 0e 510 15 20 -0.01 0 0.01 ii 510 15 20 -0.05 0 0.05 delta 510 15 20 -2 -1 0x 10 -3 pii 510 15 20 -0.01 0 0.01 C 510 15 20 -0.02 0 0.02 X 510 15 20 -0.5 0 0.5 d 510 15 20 -0.2 0 0.2 gammaD 510 15 20 -0.01 0 0.01 varphiD 510 15 20 -1 0 1x 10 -3 m 510 15 20 -1 0 1x 10 -3 gammaM 510 15 20 0 0.1 0.2 CBbalsheet 510 15 20 0 0.1 0.2 b 510 15 20 0 0.1 0.2 gammaR 510 15 20 0 0.2 0.4 r www.economics-ejournal.org 68 conomics: The Open-Access, Open-Assessment E-Journal In the case of shocks to Gor φ, the MER regime has been seen to be superior to the FER regime for any of the usual CB preferences. For the following two shocks, the effect of introducing the second policy rule will only be positive for some CB preferences but not all. The shock to imported goods ination π(Figure 3) under a FER regime generates nominal currency depreciation, increasing consumption ination on impact through its imported component. Hence, consumption falls, dragging GDP with it. This makes exports fall even though there is real depreciation. The CB, following its interest rate rule, increases the nominal interest rate. The fall in GDP makes the foreign debt ratio increase on impact (even though ddoes not change and the RER has increased) and hence the foreign currency interest rate households face when obtaining funds abroad also increases, which is consonant with the increased operational target for the domestic currency nominal interest rate. Households subsequently ameliorate their reduction in consumption by obtaining funds abroad. Under the MER regime, the second policy rule makes the CB purchase reserves on impact, generating a larger initial real depreciation. This makes exports and GDP fall less than in the FER regime and consumption fall more since there is greater ination (for both domestic and imported goods) and the expected real interest rate rises on impact. Households now increase their foreign debt on impact (as the CB is purchasing reserves) but thereafter reduce it along with the CB's rapid reversal of its purchases. Hence, the use of the second rule makes the shock less recessionary, but it also makes it more inationary and generate more real depreciation. Hence, in this case the MER regime should be favored over the FER regime whenever the CB cares more about stabilizing GDP than ination or the RER. Finally, a shock to exported goods ination πX(Figure 4) boosts exports and generates nominal and real appreciation. Ination falls on impact, boosting consumption and GDP, the increase in consumption being facilitated by the reduction in the target nominal interest rate (which makes the real interest rate fall). Under the MER regime, the action of the second policy rule makes the CB purchase reserves to obtain a lower reduction in the rate of nominal depreciation, which yields a lower real appreciation. Consequently, the shock is less deationary, more expansionary and generates less real appreciation. Hence the MER regimes should be favored over the FER regime for CB preferences that care more for stabilizing ination and the RER than stabilizing GDP. www.economics-ejournal.org 69 conomics: The Open-Access, Open-Assessment E-Journal 4.3 An extension: CB international reserves as an additional inuence on the risk premium The debt premium has so far been modeled as depending only on household foreign debt (as an endogenous variable). However, although a positive correlation between foreign debt and the risk premium is typically found in empirical research (Bellas et al. 2010, Di Cesare et al. 2012), a negative correlation between CB reserves and the risk premium is also measured.25 Fouejieu and Roger (2013), for example, place Gross external debt and Foreign exchange reserves (both as a ratio to GDP) at the top of their potential determinants of country risk and use system GMM estimation with annual data from 40 emerging and high income countries in the 1989 to 2010 period. In their Table 2, they report statistically signicant (at 1%) effects of both variables, and the positive inuence of foreign debt on country risk is around three times (the abolute value of) the negative inuence of CB international reserves. To address this additional inuence, the functional form of the endogenous risk premium τDis here extended to additionally include the negative inuence of CB international reserves (as a ratio of GDP). The new denition is hence: τDγD t;γR tα1 1α2γD t+α3γR t ;α1;α2;> 0;α30:(84) The sections above have centered in the special case α3=0. More generally, there are now two partial elasticities:26 ετD;1=α2γD 1α2γD+α3γR(85) ετD;2=α3γR 1α2γD t+α3γR t : The conditions under which α2and α3are equal may be deemed of special interest because in that case τD(:)is a function of net foreign liabilities (as a ratio 25I thank one of my anonymous referees for suggesting the expansion of the analysis in this direction. 26Notice that the Marshallian convention that makes the elasticies always positive is not used. www.economics-ejournal.org 70 conomics: The Open-Access, Open-Assessment E-Journal to GDP) γD tγR t. They are easily obtained: α2=α3<=>ετD;1 γD=ετD;2 γR<=>ετD;2=γR γDετD;1=0:13 0:5ετD;1=0:26ετD;1: Hence, if ετD;1=10 then ετD;2=2:6. However, notice that the risk function in the UIP equation continues to be a function of the two ratios individually, since the CB international reserves rtis not a household decision variable (whereas dtis). The following table assumes ετD;1=10 (as in the central set of columns of Table 11) and makes different assumptions with respect to ετD;2(including ετD;2=2:6).27 The second set of columns shows that ετD;2=2:6 gives the lowest relative advantage of the MER regime (at least among those shown), but it is still positive. Both lower and higher values of ετD;2give higher advantages for using the two policy rules. Also, according to the value of ετD;2either the FER or PER regime is second best. The important point is that the general argument is robust to the presence of the CB's international reserves in the risk premium. Table 12: Sensitivity of losses to alternative elasticities ετD;2under Ramsey (ετD;1=10) STYLE MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER A119.9 121.0 120.9 120.207 120.210 120.31 119.95 120.00 120.15 117.2 119.1 119.4 112.6 118.2 118.7 B112.0 114.5 117.3 114.3 114.3 115.2 114.1 114.3 114.6 109.2 114.0 112.0 99.6 113.7 109.4 C378.1 388.1 388.8 387.1 387.1 387.3 386.3 386.8 386.9 366.7 385.6 384.9 331.8 384.3 382.9 D394.5 405.2 405.7 404.0 404.1 404.2 403.2 403.7 403.8 382.4 402.3 402.0 348.5 400.8 400.1 A1.009 1.008 1.00002 1.0009 1.0004 1.0017 1.016 1.019 1.049 1.054 B1.023 1.047 1.0001 1.0079 1.00101 1.00437 1.044 1.026 1.141 1.099 C1.027 1.028 1.0001 1.0005 1.00128 1.00134 1.052 1.050 1.158 1.154 D1.027 1.028 1.0001 1.0005 1.00133 1.00153 1.052 1.051 1.150 1.148 ELASTtauBarD_2=-10; LOSS ELASTtauBarD_2=0; ELASTtauBarD_2=-2.6; ELASTtauBarD_2=-3.33; ELASTtauBarD_2=-6.66; RELATIVE LOSS 5 Some additional robustness checks In this section the optimal policy under commitment framework (`ramsey') is used to obtain the sensitivity of the losses and relative losses to several additional parameters. In all the tables below the elasticities used are ετD;1=10;ετD;2=0. 27In the Dynare code, ετD;iis ELASTtauBarD_i (i=1;2). www.economics-ejournal.org 71 conomics: The Open-Access, Open-Assessment E-Journal Taking into account the importance in the model of the shock to the exogenous risk/liquidity premium φ, the next exercise gauges how the losses and relative losses are affected by different levels of the standard deviation (or standard error) of the risk/liquidity shock (σφ). The results are shown in Table 13 for a range of values of σφthat go from 0.01 to 0.15. As expected, the losses are monotonically increasing in σφ. The relative losses of the FER regime for all CB styles and of the PER regime for styles A, C, and D are also increasing in σφ. The relative loss in the PER regime for style B (where only GDP matters), however, is decreasing with σφ. In this case, the FER regime is always second best. For the rest of the CB styles, low values of σφmake the FER regime second best and high values make the PER regime second best. Table 13: Losses for different values of σφ STYLE MER FER PER MER FER PER MER FER PER MER FER PER MER FER PER A106.7 107.4 107.5 107.2 107.9 108.0 119.9 121.0 120.9 159.6 161.8 161.1 225.6 229.9 228.1 B96.4 98.4 101.3 97.1 99.1 102.0 112.0 114.5 117.3 158.7 162.9 165.2 236.6 243.5 245.0 C355.3 364.2 365.3 356.2 365.1 366.2 378.1 388.1 388.8 446.4 459.9 459.4 560.4 579.5 577.1 D368.1 377.1 378.0 369.2 378.2 379.1 394.5 405.2 405.7 473.8 489.6 488.6 605.9 630.2 626.9 A1.0059 1.0071 1.0060 1.0071 1.009 1.008 1.014 1.010 1.019 1.011 B1.0206 1.0509 1.0207 1.0507 1.023 1.047 1.026 1.040 1.029 1.035 C1.0251 1.0282 1.0251 1.0282 1.027 1.028 1.030 1.029 1.034 1.030 D1.0245 1.0269 1.0246 1.0270 1.027 1.028 1.033 1.031 1.040 1.035 stderr(eps_phiStar)=0.15 LOSS RELATIVE LOSS stderr(eps_phiStar)=0.001 stderr(eps_phiStar)=0.01 stderr(eps_phiStar)=0.05 stderr(eps_phiStar)=0.1 The degree of price stickiness (α) in the New Keynesian Phillips equation is often considered an important factor in determining the desirability of alternative exchange regimes. Table 14 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 (α=0.01) to very high price stickiness (α=0.90). Starting with α=0.3, higher price stickiness generates higher losses for all regimes and styles. This is also true for lower values of αin the case of styles C and D. However, for (the extreme) styles A and B and very low values of price stickiness an increase in αgenerates a reduction in losses for the 3 regimes. As expected, for each CB style and value of α, the MER regime does signicantly better than the corner regimes. The smallest advantage for the MER regime appears in the intermediate range of price stickiness (including the baseline value). For all CB styles, the PER regime is second best for low degrees of price stickiness and the FER www.economics-ejournal.org 72 conomics: The Open-Access, Open-Assessment E-Journal Svensson, L. E.O, and M. Woodford (2003). Optimal Policy with Partial Information in a Forward-Looking Model: Certainty-Equivalence Redux. NBER Working Paper 9430. URL: http://www.nber.org/papers/w9430. Williamson, J. (2007). Do development considerations matter for exchange rate policy? In Current Account and External Financing, edited by K. Cowan, S. Edwards and R. O. Valdés, Central Bank of Chile. URL: http://www.bcentral.cl/ estudios/banca-central/pdf/v12/475-489.pdf Wollmerhaüser T. (2003). A Theory of Managed Floating. Inaugural-dissertation, Würzburg. URL: http://opusbibliothek.uniwuerzburg.de/volltexte/2004/867/pdf/ wollmershaeuser.pdf. Woodford, M. (2003). Interest and Prices. Foundations of a Theory of Monetary Policy. Princeton UP. www.economics-ejournal.org 79 conomics: The Open-Access, Open-Assessment E-Journal Appendix In this Appendix the calibrated values for the model's parameters are obtained as well as the corresponding NSS values of the model variables. There are always many ways of doing this. Some parameters, some ratios and some NSS values of endogenous variables are rst calibrated and the rest are obtained sequentially using the static nonlinear equations so that a computer code can follow the same steps if one changes some of the calibrated values. A.1 Calibration of parameters and derivation of the corresponding nonstochastic steady state Calibration of the components of the external terms of trade The terms of trade is a particularly important variable for any SOE. Hence, a preliminary investigation of the data pertaining to Argentina was made. 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: ∆logPX t=ρπX∆logPX t1+1ρπXlogπX+απXlogPX t1logPN t1 +σπXεπX t; ∆logPN t=ρπ∆logPN t1+(1ρπ)logπN+απlogPX t1logPN t1 +σπεπ 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 it was not possible to impose a coefcient of negative one for the second coefcient in the cointegrating relation, it was imposed in the calibration to be consistent with the denition of the terms of trade. The small deterministic trend in the cointegrating relation was also ignored, as well as the two time dummies (rst and fourth quarters of 2008) that made the residuals normal, homoscedastic and devoid of serial correlation and the non-signicant coefcients. Hence, the following specication was used in the model: www.economics-ejournal.org 80 conomics: The Open-Access, Open-Assessment E-Journal 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 www.economics-ejournal.org 81 conomics: The Open-Access, Open-Assessment E-Journal ∆logPX t=0:41∆logPX t1+(10:41)logπX0:25logPX t1logPN t1 +0:0424επ t; ∆logPN t=0:20∆logPN t1+(10:20)logπN+0:18logPX t1logPN t1 +0:18∆logPX t1+0:0295επ t; where, using the notation in (77), βπ=1, and ρπXN =0:18 is added for the effect of ∆logPX t1on ∆logPN t(which did not appear in the original specication). Hence, the nal specication of the XTT block (77) is: πX t=πX t10:41 πX10:41 p t10:25 exp0:0424επ t; π t=π t10:20 (π)10:20 p t10:18 πX t0:18 exp0:0295επ t; p t=p t1 πX t π t : 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. It is assumed that ε=1 and π=1. Several key ratios are used such as the target value for the CB reserves ratio γR=er=Y, the NSS household foreign debt ratio γD=ed=Yand money/consumption ratio γM=m=pCC:In some cases the equation is divided through by GDP. Interest rate feedback rule: 1=πC πTh1 (86) Nominal depreciation feedback rule: 1=πC πTk1er=Y γRk4 (87) www.economics-ejournal.org 82 conomics: The Open-Access, Open-Assessment E-Journal Consumption: 1+i πC=1 β(88) Risk-adjusted UIP: 1+i= (1+i)φϕDδ(89) Phillips equations: Γ= Q=pCCσC 1βαπθ1(90) Ψ=θ θ1mc Q=pCCσC 1βαπθ(91) Γ Ψ=1απθ1 1α1 θ1 (92) Price dispersion: ∆=1α 1απθ1απθ1 1αθ θ1 (93) Exports: X Y=κX(ep)bX(94) Trade Balance: TB e Y=1 aDpC1θCX Y(1aD)e1θC(95) Current Account: CA e Y=1+i π1γR1+i πφτD11γD+TB e Y(96) www.economics-ejournal.org 83 conomics: The Open-Access, Open-Assessment E-Journal Balance of Payments: CA =0 (97) Real marginal cost: mc =w(98) Labor market clearing: w=ξNpCCσCϕMNσN(99) Hours worked: N=Q∆(100) Domestic goods market clearing: Q Y=11bAX Y(101) GDP: 1=aD τMG (pC)1θC pCC Y+X Y(102) Consumption relative price: pC=aD+(1aD)e1θC1 1θC(103) Money market clearing: m Y=1 β22 4 β1β2β3 11 1+i!1 β3+1 13 5pCC Y;(104) CB balance sheet: b Y=γRγMpCC Y(105) www.economics-ejournal.org 84 conomics: The Open-Access, Open-Assessment E-Journal Tax collection: tax = (G1)pCCq f Quasi-scal surplus: q f = (1+i1=δ)er π((1+i)1)b π Identities: π=δ;π=πC;1=πX(106) Great ratios: γD=ed Y;γM=m pCC;γR=er Y; Auxiliary functions: τD=1+α1 1α2γD+α3γR;ϕD=1+(τD1)1+α2γD 1α2γD+α3γR τM=1+β1 (1+β2γM)β3;ϕM=1+(τM1)1+β3 β2γM 1+β2γM: Exports ination shock 1= (p)απX(107) Imported ination shock 1= (p)απXπXρπXN :(108) The NSS values of the model's variables and the calibrated values of parameters are obtained sequentially as follows. (86) implies πC=πT, since h16=0 is assumed. Inserting this in (106) yields π=δ=πT. Also, (107) implies that the XTT is p=1, and hence (108) implies that πX=1. Summing up, π=δ=πC=πT;and π=πX=p=1: www.economics-ejournal.org 85 conomics: The Open-Access, Open-Assessment E-Journal Hence, (88) gives the nominal interest rate: 1 +i=πT=β. It is assumed that β=0:99. For the NSS GDP, Argentina's 2010 level (at 2010 prices and in trillions of pesos) is used: Y=1:443. The gross exogenous risk/liquidity premium for households and the RW gross interest rate are assumed to be φ=1:0050:25 and 1+i=1:030:25, respectively. Also, the household ratios are calibrated to γDed=Y=0:5, γMm=pCC=0:095522, the CB international reserves/GDP ratio to γR=0:13, and the Government to household consumption ratio to 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 and consumption are: σN=0:5 and σC=1:5, respectively. Finally, it is assumed that the elasticity of substitution between varieties of domestic goods is θ=6 and the elasticity of substitution between the bundles of domestic and imported goods is θC=1:5. Assuming that the exogenous parameter in the export goods production function is bA=0:5, yields bX1bA1=2 and κXbAbAbX=0:5. The endogenous risk premium Using (88), (106) and (69) in the UIP equation (89) gives:28 α11+α3γR (1α2γD+α3γR)2=ϕDγD;γR=1 βφ(1+i)=π1:(109) The parameters on the r.h.s. have already been calibrated, as well as γDand γR. It is now necessary to calibrate the values of the exogenous parameters α1,α2 and α3. Assuming rst that α3=0, as in most of the paper, α1and α2can be expressed in terms of γDand ετD. First, notice that, according to (67), the elasticity of τDis ετDγD tα2γD t 1α2γD t :(110) 28Notice that the extension of the endogenous risk premium of Section 5 is used here. www.economics-ejournal.org 86 conomics: The Open-Access, Open-Assessment E-Journal Hence, if the NSS values of ετDand γDare calibrated (110) gives the value of α2: α2=1 γD ετD 1+ετD :(111) And (109) gives: α1=1α2γD21 βφ(1+i)=π1=1 βφ(1+i)=π1 (1+ετD)2:(112) More generally, when the endogenous risk premium also depends on the CB's international reserves, as in (84), there are two partial elasticities given by (85). In this case α1,α2and α3can be obtained by expressing them in terms of the 2 elasticities ετD;1,ετD;2, and the 2 great ratios γD,γR. First, notice that (85) implies: 1+ετD;1+ετD;2=1 1α2γD+α3γR:(113) Hence, (85) implies: 1+ετD;1=1+α3γR1+ετD;1+ετD;2(114) 1+ετD;2=1α2γD1+ετD;1+ετD;2:(115) Also, using (113) and (114) yields: ϕDγD;γR=α11+α3γR (1α2γD+α3γR)2=α11+ετD;11+ετD;1+ετD;2: Hence, using (109) gives: α11+ετD;11+ετD;1+ετD;2=1 βφ(1+i)=π1:(116) www.economics-ejournal.org 87 conomics: The Open-Access, Open-Assessment E-Journal Therefore, given the calibrated values of γD,γR,ετD;1and ετD;2(114), (115) and (116) yield the values of the three alphas: α1=1 βφ(1+i)=π1 1+ετD;1+ετD;21+ετD;1 α2=1 γD ετD;1 1+ετD;1+ετD;2 α3=1 γR ετD;2 1+ετD;1+ετD;2 : With ετD;2=0 (as in most of the paper) and assuming ετD;1=10: α1= 1 βφ(1+i)=π1 (1+)2= 1 0:99(1:030:25)1:0050:25 1 (1+10)2=1:1692 105 α2=1 γD ετD;1 1+ετD;1 =1 0:5 10 1+10 =1:8182 τD=1+α1 1α2γD+α3γR=1+α11+ετD;1+ετD;2 =1+1:1692 105(1+10) = 1:0001286 The elasticity that appears in the log-linearized UIP equation varies linearly with ετDas: εϕD=γD ϕD dϕD dγD=ϕD ϕDγD ϕD dϕD dγD= [1βφ(1+i)=π]εϕD = [1βφ(1+i)=π]2ετD=10:991:030:251:0050:252ετD =0:0028255ετD: www.economics-ejournal.org 88 conomics: The Open-Access, Open-Assessment E-Journal Response to a shock to the RW interest rate: i 510 15 20 -2 0 2x 10 -3 piC 510 15 20 -1 0 1x 10 -3 Deltta 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 -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 -0.02 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 -2 0 2x 10 -3 delta 510 15 20 -2 0 2x 10 -3 b 510 15 20 -0.01 -0.005 0r 510 15 20 -0.01 -0.005 0d 510 15 20 -2 0 2x 10 -3 m 510 15 20 -2 0 2x 10 -3 Utility 510 15 20 0 5x 10 -3 z_iStar www.economics-ejournal.org 95 conomics: The Open-Access, Open-Assessment E-Journal Response to a shock to the SOE's exogenous risk/liquidity premium: φ 510 15 20 -0.02 0 0.02 piC 510 15 20 -5 0 5x 10 -3 Deltta 510 15 20 -0.1 0 0.1 Y 510 15 20 -0.1 0 0.1 C 510 15 20 -0.05 0 0.05 real_ii 510 15 20 0 0.005 0.01 e 510 15 20 0 0.01 0.02 TB 510 15 20 -5 0 5x 10 -3 X 510 15 20 -0.1 0 0.1 mc 510 15 20 -0.1 0 0.1 N 510 15 20 -0.05 0 0.05 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 -0.01 0 0.01 m 510 15 20 -0.01 0 0.01 Utility 510 15 20 0 0.05 0.1 z_phiStar www.economics-ejournal.org 96 conomics: The Open-Access, Open-Assessment E-Journal Response to a shock to imports ination: π 510 15 20 -0.01 0 0.01 piC 510 15 20 -2 0 2x 10 -3 Deltta 510 15 20 -0.02 0 0.02 Y 510 15 20 -0.02 0 0.02 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 -5 0 5x 10 -3 X 510 15 20 -0.02 0 0.02 mc 510 15 20 -0.02 0 0.02 N 510 15 20 -0.01 0 0.01 ii 510 15 20 -0.01 0 0.01 delta 510 15 20 0 0.005 0.01 b 510 15 20 0 0.005 0.01 r 510 15 20 -0.02 0 0.02 d 510 15 20 -5 0 5x 10 -3 m 510 15 20 -2 0 2x 10 -3 Utility 510 15 20 -0.05 0 0.05 z_piStar www.economics-ejournal.org 97 conomics: The Open-Access, Open-Assessment E-Journal Response to a shock to exports ination: πX 510 15 20 -0.01 0 0.01 piC 510 15 20 -5 0 5x 10 -3 Deltta 510 15 20 -0.05 0 0.05 Y 510 15 20 -0.05 0 0.05 C 510 15 20 -0.02 0 0.02 real_ii 510 15 20 -0.02 -0.01 0e 510 15 20 -0.05 0 0.05 TB 510 15 20 -0.05 0 0.05 X 510 15 20 -0.05 0 0.05 mc 510 15 20 -0.05 0 0.05 N 510 15 20 -0.01 0 0.01 ii 510 15 20 -0.01 0 0.01 delta 510 15 20 -5 0 5x 10 -3 b 510 15 20 0 0.01 0.02 r 510 15 20 -0.1 -0.05 0d 510 15 20 -5 0 5x 10 -3 m 510 15 20 -5 0 5x 10 -3 Utility 510 15 20 -0.02 0 0.02 z_piStar www.economics-ejournal.org 98 conomics: The Open-Access, Open-Assessment E-Journal Central Bank style B ωπ=1;ωY=100;ωe=1;ωr=1;ω∆i=50;ω∆δ=50: Response to a shock to domestic sector productivity: ε 510 15 20 -5 0 5x 10 -3 piC 510 15 20 -5 0 5x 10 -3 Deltta 510 15 20 -1 0 1x 10 -3 Y 510 15 20 -5 0 5x 10 -4 C 510 15 20 -2 0 2x 10 -4 real_ii 510 15 20 -2 0 2x 10 -4 e 510 15 20 -5 0 5x 10 -4 TB 510 15 20 -2 0 2x 10 -4 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 0 0.5 1x 10 -3 b 510 15 20 0 1 2x 10 -3 r 510 15 20 -2 0 2x 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 www.economics-ejournal.org 99 conomics: The Open-Access, Open-Assessment E-Journal Response to a shock to government expenditures: G 510 15 20 0 0.01 0.02 piC 510 15 20 0 0.01 0.02 Deltta 510 15 20 -0.01 0 0.01 Y 510 15 20 -0.04 -0.02 0C 510 15 20 0 2 4x 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 -5 0 5x 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 -0.02 0 0.02 delta 510 15 20 0 0.005 0.01 b 510 15 20 0 0.01 0.02 r 510 15 20 0 0.05 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 www.economics-ejournal.org 100 conomics: The Open-Access, Open-Assessment E-Journal Response to a shock to the RW interest rate: i 510 15 20 -4 -2 0x 10 -3 piC 510 15 20 -2 -1 0x 10 -3 Deltta 510 15 20 -5 0 5x 10 -3 Y 510 15 20 -0.01 0 0.01 C 510 15 20 -5 0 5x 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 -0.01 -0.005 0mc 510 15 20 -0.01 -0.005 0N 510 15 20 -2 -1 0x 10 -3 ii 510 15 20 -5 0 5x 10 -3 delta 510 15 20 -4 -2 0x 10 -3 b 510 15 20 -0.01 -0.005 0r 510 15 20 -0.02 -0.01 0d 510 15 20 -5 0 5x 10 -4 m 510 15 20 -2 0 2x 10 -3 Utility 510 15 20 0 5x 10 -3 z_iStar www.economics-ejournal.org 101 conomics: The Open-Access, Open-Assessment E-Journal Response to a shock to the SOE's exogenous risk/liquidity premium: φ 510 15 20 -0.04 -0.02 0piC 510 15 20 -0.02 -0.01 0Deltta 510 15 20 -0.02 0 0.02 Y 510 15 20 -0.04 -0.02 0C 510 15 20 0 0.02 0.04 real_ii 510 15 20 0 0.01 0.02 e 510 15 20 0 0.02 0.04 TB 510 15 20 0 0.01 0.02 X 510 15 20 -0.04 -0.02 0mc 510 15 20 -0.04 -0.02 0N 510 15 20 -0.05 0 0.05 ii 510 15 20 -0.04 -0.02 0delta 510 15 20 -0.05 0 0.05 b 510 15 20 -0.1 -0.05 0r 510 15 20 -0.2 0 0.2 d 510 15 20 -5 0 5x 10 -3 m 510 15 20 -0.02 0 0.02 Utility 510 15 20 0 0.05 0.1 z_phiStar www.economics-ejournal.org 102 conomics: The Open-Access, Open-Assessment E-Journal Response to a shock to imports ination: π 510 15 20 0 0.01 0.02 piC 510 15 20 0 5x 10 -3 Deltta 510 15 20 -5 0 5x 10 -3 Y 510 15 20 -0.01 0 0.01 C 510 15 20 -0.01 0 0.01 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 0.01 0.02 mc 510 15 20 0 0.01 0.02 N 510 15 20 0 0.005 0.01 ii 510 15 20 -0.01 0 0.01 delta 510 15 20 0 0.005 0.01 b 510 15 20 0 0.005 0.01 r 510 15 20 -0.01 0 0.01 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 www.economics-ejournal.org 103 conomics: The Open-Access, Open-Assessment E-Journal Response to a shock to exports ination: πX 510 15 20 0 0.01 0.02 piC 510 15 20 0 0.005 0.01 Deltta 510 15 20 -0.02 0 0.02 Y 510 15 20 0 0.01 0.02 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 0.01 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 0.005 0.01 b 510 15 20 0 0.02 0.04 r 510 15 20 -0.05 0 0.05 d 510 15 20 -4 -2 0x 10 -3 m 510 15 20 -0.01 0 0.01 Utility 510 15 20 -0.02 0 0.02 z_piStar www.economics-ejournal.org 104 Please note: You are most sincerely encouraged to participate in the open assessment of this article. You can do so by either recommending the article or by posting your comments. Please go to: http://dx.doi.org/10.5018/economics-ejournal.ja.2013-30 The Editor © Author(s) 2013. Licensed under the Creative Commons License Attribution 3.0.