“Monetary and Fiscal Rules in an Emerging Small Open Economy”

Contributor Notes

Author’s E-Mail Address: nbatini@imf.org

We develop a optimal rules-based interpretation of the 'three pillars macroeconomic policy framework': a combination of a freely floating exchange rate, an explicit target for inflation, and a mechanism than ensures a stable government debt-GDP ratio around a specified long run. We show how such monetary-fiscal rules need to be adjusted to accommodate specific features of emerging market economies. The model takes the form of two-blocs, a DSGE emerging small open economy interacting with the rest of the world and features, in particular, financial frictions It is calibrated using Chile and US data. Alongside the optimal Ramsey policy benchmark, we model the three pillars as simple monetary and fiscal rules including and both domestic and CPI inflation targeting interest rate rules alongside a 'Structural Surplus Fiscal Rule' as followed recently in Chile. A comparison with a fixed exchange rate regime is made. We find that domestic inflation targeting is superior to partially or implicitly (through a CPI inflation target) or fully attempting to stabilizing the exchange rate. Financial frictions require fiscal policy to play a bigger role and lead to an increase in the costs associated with simple rules as opposed to the fully optimal policy.


We develop a optimal rules-based interpretation of the 'three pillars macroeconomic policy framework': a combination of a freely floating exchange rate, an explicit target for inflation, and a mechanism than ensures a stable government debt-GDP ratio around a specified long run. We show how such monetary-fiscal rules need to be adjusted to accommodate specific features of emerging market economies. The model takes the form of two-blocs, a DSGE emerging small open economy interacting with the rest of the world and features, in particular, financial frictions It is calibrated using Chile and US data. Alongside the optimal Ramsey policy benchmark, we model the three pillars as simple monetary and fiscal rules including and both domestic and CPI inflation targeting interest rate rules alongside a 'Structural Surplus Fiscal Rule' as followed recently in Chile. A comparison with a fixed exchange rate regime is made. We find that domestic inflation targeting is superior to partially or implicitly (through a CPI inflation target) or fully attempting to stabilizing the exchange rate. Financial frictions require fiscal policy to play a bigger role and lead to an increase in the costs associated with simple rules as opposed to the fully optimal policy.

I. Introduction

Over the past decade, key emerging markets including Brazil, Chile, the Czech Republic, Mexico and South Africa, have adopted sound macroeconomic frameworks that have made them more resilient to domestic and external economic shocks. Many of these frameworks are characterized by the “three pillars macroeconomic policy framework”: a combination of a freely floating exchange rate, an explicit target for inflation over the medium run, and a mechanism that ensures a stable government debt-GDP ratio around a specified long run.

In this paper we develop a optimal rules-based interpretation of the “three pillars” and show how such monetary-fiscal rules need to be adjusted to accommodate specific features of emerging market small open economies (SOEs). Such emerging SOEs face substantially different policy issues from those of advanced, larger, more closed economies. The price of consumer goods depends on the exchange rate and exporting firms typically set their prices in foreign currency and bear the risk of currency fluctuations. They often borrow from international capital markets in foreign currency, so that debt repayment is similarly affected. Foreign shocks have significant effects on the domestic economy. Thus, we expect monetary and fiscal policy prescriptions in a emerging SOE to be fundamentally different from those in a advanced closed economy.

There is a large literature on optimal monetary and fiscal policy in response to exogenous shocks; Kirsonova et al. (2006); Schmitt-Grohe et al. (2007); Chadha et al. (2007); and Leith et al. (2007) are some recent examples for the closed economy; Wren-Lewis (2007) provides an insightful overview. We depart from these works in three principal ways. First, our focus is on a small open economy (SOE). Second, we want to consider an emerging economy where frictions and distortions are quantitatively important. To this end, we introduce financial frictions in the form of a “financial accelerator”. Finally we will impose a zero lower bound (ZLB) constraint on the nominal interest rate that limits its variability and increases the role for fiscal stabilization policy, a feature again absent in almost all the literature Schmitt-Grohe et al. (2007) is an exception).

We build a two-bloc DSGE emerging markets SOE - rest of the world model to examine the implications of financial frictions for the relative contributions of optimal Ramsey fiscal and monetary stabilization policy and the simple rules that will, as far as possible, mimic the Ramsey policy. Alongside standard features of SOE economies such as local currency pricing for exporters, a commodity sector, oil imports, our model incorporates liability dollarization,1 as well as financial frictions including a financial accelerator, where capital financing is partly or totally in foreign currency as in Gertler et al. (2003) and Gilchrist (2003). The model is calibrated to Chile and US data and uses estimates of shock processes taken from Medina et al. (2007b).

The rest of the paper is organized as follows. Section 2 presents the model. Sections 3 and 4 set out the form of monetary and fiscal rules under investigation. Section 5 addresses the requirement that monetary rules should be ‘operational’ in the sense that, in the face of shocks, the zero lower bound constraint on the nominal interest rate is very rarely hit. In Section 6 we examine the benchmark Ramsey policy as first the financial accelerator and then liability dollarization are introduced. In section 7 we derive and compare alternative simple monetary and fiscal policy rules including the ‘Structural Fiscal Stability Rule’ (SFSR) followed by Chile.2 Section 8 provides concluding remarks.

II. The Model

We start from a standard two-bloc microfounded model along the lines of Obstfeld and Rogoff (1995) to then incorporate many of the nominal and real frictions that have been shown to be empirically important in the study of closed economies (e.g. Smets and Wouters, 2003). The blocs are asymmetric and unequally-sized, each one with different household preferences and technologies. The single SOE then emerges as the limit when the relative size of the larger bloc tends to infinity. Households work, save and consume tradable goods produced both at home and abroad. At home there are three types of firms: wholesale, retail and capital producers. As in Gertler et al. (2003), wholesale firms borrow from households to buy capital used in production and capital producers build new capital in response to the demand of wholesalers. Wholesalers’ demand for capital in turn depends on their financial position which varies inversely with wholesalers’ net worth. Retailers engage in local currency pricing for exports, there is a commodity (that throughout we refer for simplicity as “copper”) sector and oil imports enter into consumption and production.

There are three departures from the standard open-economy model that lead to interesting results. First, money enters utility in a non-separable way and results in a direct impact of the interest rate on the supply side.3 Second, along the lines of Gilchrist (2003) (see also Cespedes et al (2004)), firms face an external finance premium that increases with leverage and part of the the debt of wholesale firms is financed in foreign currency (dollars), because it is impossible for firms to borrow 100 percent in domestic currency owing to “original sin” type constraints. Although not all emerging markets face this constraint, many have in the past and still do, for example Peru, where a great proportion of borrowing by firms continues to be in U.S. dollars–a phenomenon dubbed “liability dollarization”. Finally, there are frictions in the world financial markets facing households as in Benigno (2001). Departures two and three add an additional dimensions to openness.4 Details of the model are as follows.

A. Households

Normalizing the total population to be unity, there are v households in the “home”, emerging economy bloc and (1 − v) households in the “foreign” bloc. A representative household h in the home country maximizes


where Et is the expectations operator indicating expectations formed at time t, β is the household’s discount factor, Ct(h) is a Dixit-Stiglitz index of consumption defined below in (5), Mt(h) is the end-of-period holding of nominal domestic money balances, Pt is a Dixit-Stiglitz price index defined in (14) below, and Lt(h) are hours worked. An analogous symmetric intertemporal utility is defined for the ‘foreign’ representative household and the corresponding variables (such as consumption) are denoted by Ct*(h), etc.

We incorporate financial frictions facing households as in Benigno (2001). There are two risk-free one-period bonds denominated in the currencies of each bloc with payments in period t, BH,t and BF,t respectively in (per capita) aggregate. The prices of these bonds are given by


where ϕ(·) captures the cost in the form of a risk premium for home households to hold foreign bonds, Bt is the aggregate foreign asset position of the economy denominated in home currency and PH,tYt is nominal GDP. We assume ϕ(0) = 0 and ϕ′ < 0. Rn,t and Rn,t* denote the nominal interest rate over the interval [t, t + 1]. The representative household h must obey a budget constraint:


where Wt(h) is the wage rate, TFt are flat rate taxes net of transfers, τL,t and τГ,t are labor income and profits tax rates respectively and Гt(h), dividends from ownership of firms, PtC is the price of copper), (1χ)COP¯t(h) is an exogenous endowment of copper owned by household h, χ being the overall share of the government and τcop is the tax rate on copper income. In addition, if we assume that households’ labor supply is differentiated with elasticity of supply η, then (as we shall see below) the demand for each consumer’s labor supplied by v identical households is given by


where Wt=[1νr=1νWt(h)1η]11η and Lt=[(1ν)r=1νLt(h)η1η]ηη1 are the average wage index and average employment respectively.

Let the number of differentiated goods produced in the home and foreign blocs be n and (1 − n) respectively, again normalizing the total number of goods in the world at unity. We also assume that the the ratio of households to firms are the same in each bloc. It follows that n and (1 − n) (or v and (1 − v)) are measures of size. The per capita consumption index in the home country is given by


where µC is the elasticity of substitution between and composite of home and foreign final goods and oil imports,


where µZ is the elasticity of substitution between home and foreign goods,


where CH,t(f, h) and CF,t(f, h) denote the home consumption of household h of variety f produced in blocs H and F respectively and ζ > 1 is the elasticity of substitution between varieties in each bloc. Analogous expressions hold for the foreign bloc which indicated with a superscript “*” and we impose ζ = ζ* for reasons that become apparent in section Weights in the consumption baskets in the two blocs are defined by

wz=1(1n)(1ω);  wZ*=1n(1ω*)(7)

In (7), ω, ω*∊ [0, 1] are a parameters that captures the degree of “bias” in the two blocs. If ω = ω* = 1 we have autarky, while ω = ω* = 0 gives us the case of perfect integration. In the limit as the home country becomes small n → 0 and v → 0. Hence w → ω and w* 1. Thus the foreign bloc becomes closed, but as long as there is a degree of home bias and ω > 0, the home country continues to consume foreign-produced consumption goods.

Denote by PH,t(f), PF,t(f) the prices in domestic currency of the good produced by firm f in the relevant bloc. Then the optimal intra-temporal decisions are given by standard results:


where aggregate price indices for domestic and foreign consumption bundles are given by


and the domestic consumer price index Pt given by


with a similar definition for the foreign bloc.

Let St be the nominal exchange rate. If the law of one price applies to differentiated goods so that StPF,t*PF,t=StPH,t*PH,t=1. Then it follows that the real exchange rate RERt=StPt*Pt. However with local currency pricing the real exchange rate and the terms of trade, defined as the domestic currency relative price of imports to exports Tt=PF,tPH,t, are related by the relationships


Thus if μ = μ*, then RERt = 1 and the law of one price applies to the aggregate price indices iff w*= 1 w. The latter condition holds if there is no home bias. If there is home bias, the real exchange rate appreciates (RERt falls) as the terms of trade deteriorates.

We assume flexible wages. Then maximizing (1) subject to (3) and (4), treating habit as exogenous, and imposing symmetry on households (so that Ct(h) = Ct, etc) yields standard results:


where UC,t, UMH,t, UMF,t and −UL,t are the marginal utility of consumption, money holdings in the two currencies and the marginal disutility of work respectively. τC,t is a consumption tax rate. Taking expectations of (18), the familiar Keynes-Ramsey rule, and its foreign counterpart, we arrive at the modified UIP condition


In (19), the demand for money balances depends positively on the marginal utility of consumption and negatively on the nominal interest rate. If, as is common in the literature, one adopts a utility function that is separable in money holdings, then given the central bank’s setting of the latter and ignoring seignorage in the government budget constraint money demand is completely recursive to the rest of the system describing our macro-model. However separable utility functions are implausible (see Woodford 2003, chapter 3, section 3.4) and following Felices et al. (2006) we will not go down this route. Finally, in (21) the real disposable wage is proportional to the marginal rate of substitution between consumption and leisure, UL,tUC,t, and the constant of proportionality reflects the market power of households that arises from their monopolistic supply of a differentiated factor input with elasticity η.

1. Rule of Thumb (RT) Households

Suppose now there are two groups of household, a fixed proportion 1 λ¸ without credit constraints and the remaining proportion λ who consume out of post-tax income. Let C1,t(h), W1,t(h) and L1,t(h) be the per capita consumption, wage rate and labor supply respectively for this latter group. Then the optimizing households are denoted as before with Ct(h), Wt(h) and Lt(h) replaced with C2,t(h), W2,t(h) and L2,t(h). We then have the budget constraint of the RT consumers


where TF1,t is net flat-rate transfers received per credit-constrained household. Following Erceg et al. (2005) we further assume that RT households set their wage to be the average of the optimizing households. Then since RT households face the same demand schedule as the optimizing ones they also work the same number of hours. Hence in a symmetric equilibrium of identical households of each type, the wage rate is given by W1,t(r) = W1,t = W2,t(r) = W2,t = Wt and hours worked per household is L1,t(h) = L2,t(h) = Lt. The only difference between the income of the two groups of households is that optimizing households as owners receive the profits from the mark-up of domestic monopolistic firms.

As before, optimal intra-temporal decisions are given by


and average consumption per household over the two groups is given by


Aggregates C1H,t*, C1F,t*, Ct* etc are similarly defined.

B. Firms

There are three types of firms, wholesale, retail and capital producers. Wholesale firms are run by risk-neutral entrepreneurs who purchase capital and employ household labor to produce a wholesale goods that is sold to the retail sector. The wholesale sector is competitive, but the retail sector is monopolistically competitive. Retail firms differentiate wholesale good at no resource cost and sell the differentiated (re-packaged) goods to households. The capital goods sector is competitive and converts the final good into capital. The details are as follows.

1. Wholesale Firms

Wholesale goods are homogeneous and produced by entrepreneurs who combine differentiated labor, capital, oil and copper inputs with and a technology


where Kt is beginning-of-period t capital stock,


where we recall that Lt(h) is the labor input of type h, At is an exogenous shock capturing shifts to trend total factor productivity in this sector. The latter will provide the source of demand for copper shock that feeds into its world price.6 Minimizing wage costs h=1νWt(h)Lt(h) gives the demand for each household’s labor as


Wholesale goods sell at a price PH,tW in the home country. Equating the marginal product and cost of aggregate labor gives


Similarly letting PO,t and PC,t be the price of oil and copper respectively in home currency, we have


Let Qt be the real market price of capital in units of total household consumption. Then noting that profits per period are PH,tWYtWtLtPO,tOILtPC,tCOPt=α1PH,tWYt, using (29), the expected return on capital, acquired at the beginning of period t, net of depreciation, over the period is given by


where δ is the depreciation rate of capital. This expected return must be equated with the expected cost of funds over [t, t + 1], taking into account credit market frictions.7 Wholesale firms borrow in both home and foreign currency, with exogenously given proportion8 of the former given by ϕ ∊ [0, 1], so that this expected cost is


If φ = 1 or if UIP holds this becomes (1 + Θt)Et[1+Rt]. In (33), RERtPt*StPt is the real exchange rate, Rt1[(1+Rn,t1)Pt1Pt]1 is the ex post real interest rate over [t − 1, t] and Θt ≥ 0 is the external finance premium given by


where Bt = QtKt− Nt is bond-financed acquisition of capital in period t and Nt is the beginning-of-period t entrepreneurial net worth, the equity of the firm. Note that the ex post return at the beginning of period t, Rt1k, is given by


and this can deviate from the ex ante return on capital.

Assuming that entrepreneurs exit with a given probability 1 − ξe, net worth accumulates according to


where Vt the net value carried over from the previous period is given by


where τtk is the tax rate applied to capital returns. Note that in (37), (1+Rt1k) is the ex post pre-tax return on capital acquired at the beginning of period t − 1, (1 + Rt−1) is the ex post real cost of borrowing in home currency and (1+Rt1*)RERtRERt1 is the ex post real cost of borrowing in foreign currency. Also note that net worth Nt at the beginning of period t is a non-predetermined variable since the ex post return depends on the current market value Qt, itself a non-predetermined variable.

Exiting entrepreneurs consume Cte, the remaining resources, given by


of which consumption of the domestic and foreign goods, as in (9), are given

respectively by


2. Retail Firms

Retail firms are monopolistically competitive, buying wholesale goods and differentiating the product at a fixed resource cost F. In a free-entry equilibrium profits are driven to zero. Retail output for firm f is then Yt(f)=YtW(f)F where YtW is produced according to production technology (26). We provide a general set-up in which a fixed proportion 1 − θ of retailers set prices in the Home currency (producer currency pricers, PCP) and a proportion θ set prices in the dollars (local currency pricers, LCP).9 In the model used for the policy exercises we assume LCP only (θ = 1). Details are as follows:

3. PCP Exporters

Assume that there is a probability of 1 − ξH at each period that the price of each good f is set optimally to P^H,t(f). If the price is not re-optimized, then it is held constant.10 For each producer f the objective is at time t to choose P^H,t(f) to maximize discounted profits


where Dt,t+k is the discount factor over the interval [t, t + k], subject to a common11 downward sloping demand from domestic consumers and foreign importers of elasticity ζ as in (8) and MCt=PH,tWPH,t are marginal costs. The solution to this is

Etk=0ξHkDt,t+kYt+k(f) [P^Ht(f)ζ(ζ1)PH,t+kMCt+k]=0(41)

and by the law of large numbers the evolution of the price index is given by


For later use in the evaluation of tax receipts, we require monopolistic profits as a proportion of GDP. This is given by


For good f imported by the home country from PCP foreign firms the price PF,tp(f), set by retailers, is given by PF,tp(f)=StPF,t*(f). Similarly PH,t*p(f)=PH,t(f)St.

4. LCP Exporters

Price setting in export markets by domestic LCP exporters follows is a very similar fashion to domestic pricing. The optimal price in units of domestic currency is p^H,tSt,, costs are as for domestically marketed goods so (41) and (42) become


and by the law of large numbers the evolution of the price index is given by


Foreign exporters from the large ROW bloc are PCPers so we have


Table 1 summarizes the notation used.

Table 1.

Notation for Prices

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5. Capital Producers

As in Smets and Wouters (2003), we introduce a delayed response of investment observed in the data. Capital producers combine existing capital, Kt, leased from the entrepreneurs to transform an input It, gross investment, into new capital according to

Kt+1=(1δ)Kt+(1S(It/It1))It;  S,S0;  S(1)=S(1)=0(47)

This captures the ideas that adjustment costs are associated with changes rather than levels of investment.12 Gross investment consists of domestic and foreign final goods


where weights in investment are defined as in the consumption baskets, namely

WI=1(1n)(1ωI);  WI*=1n(1ωI*)(49)

with investment price given by


Capital producers choose the optimal combination of domestic and foreign inputs according to the same form of intra-temporal first-order conditions as for consumption:

IH,t=WI(PH,tPI,t)ρIIt;  IF,t=(1WI)(PF,tPI,t)ρIIt(51)

The capital producing firm at time 0 then maximizes expected discounted profits13


which results in the first-order condition


C. The Government Budget Constraint and Foreign Asset Accumulation

The government issues bonds denominated in home currency. The government budget identity is given by


Taxes are levied on labor income, monopolistic profits, consumption, capital returns and copper revenue at rates τL,t, τГ, τC,t, τK,t and τcop,t respectively. In the copper market, copper supply is an exogenous endowment given by COPt¯ and COP¯t* in the home and ROW blocs respectively. The government owns a share χ of the copper sector, but taxes this public firm at the same rate τcop,t. Then adding flat rate taxes14 levied on all consumers, TF2,t, and subtracting net flat rate transfers to the constrained consumers, TF1,t, per capita total taxation net of transfers is given

Tt=τL,tWtLt+τΓ,tΓt+τC,tPtCtλTF1,t+(1λ)TF2,t+τK,tRt1kPtQtKt +τcop,tPC,tCOPt¯(54)

In what follow we take flat rate taxes and transfers to be the dynamic fiscal instruments keeping tax rates constant at their steady-state values. For later use we then write Tt in (54) as a sum of the instrument TtI=λTF1,t+(1λ)TF2,t and remaining taxes which change endogenously, TtNI.

Turning to foreign asset accumulation, let h=1νBF,t(h)=νBF,t be the net holdings by the household sector of foreign bonds. A convenient assumption is to assume that home households hold no foreign bonds so that BF,t = 0, and the net asset position of the home economy Bt=BH,t*; i.e., minus the foreign holding of domestic government bonds.15 Summing over the household budget constraints (including entrepreneurs and capital producers), and subtracting (53), we arrive at the accumulation of net foreign assets:


where the trade balance, TBt, is given by the national accounting identity


Terms on the left-hand-side of (56) are oil revenues and the value of net output; on the right-hand-side are public and private consumption plus investment plus the trade surplus.

So far we have aggregated consumption across constrained and unconstrained consumers. To obtain separately per capita consumption within these groups, first consolidate the budget constraints (53) and (3), to give


Then using (23) and (55), we arrive at


In a balanced growth steady state with negative net foreign assets and government debt, the national and government budget constraints require a primary trade surplus (TB > 0) and a primary government surplus (T > PHG). Since private sector assets are exclusively owned by unconstrained consumers this may result in a higher consumption per head by that group. The same applies to profits from retail firms and income from copper firms since they are assumed to also be exclusively owned by unconstrained consumers. On the other hand flat rate transfers to constrained consumers plus flat rate taxes on unconstrained consumers, λTF1,t + (1 λ)TF2,t tend to lower the consumption gap.

D. The Equilibrium

In equilibrium, final goods markets, the copper market, money markets and the bond market all clear. Equating the supply and demand of the home consumer good and assuming that government expenditure, taken as exogenous, goes exclusively on home goods we obtain for the final goods market16


The law of one price applies in the copper market so we have


In this set-up, copper price shocks originate in shocks to copper supply. Other shocks are to technology in wholesale goods sectors, government spending in the two blocs, the interest rate rule in the foreign bloc and to the risk premia facing unconstrained households, in the modified UIP condition (22) and facing wholesale firms in their external finance premium given by (34). Following Medina et al. (2007b) we assume Chile is a small copper producer relative to world supply and therefore faces an exogenous copper price in dollars. The real price in dollars follows a process


The rationale for this modeling strategy is that whereas the rest of the world is reasonably captured by a US type economy for determining demand for non-copper exports, this is less plausible when it comes to copper exports where the two large emerging economies China and India are increasingly influential.

This completes the model. Given nominal interest rates Rn,t, Rn,t* the money supply is fixed by the central banks to accommodate money demand. By Walras’ Law we can dispense with the bond market equilibrium conditions. Then the equilibrium is defined at t = 0 as stochastic sequences C1,t, C2,t, Ct, Cte, CH,t, CF,t, PH,t, PF,t, Pt, PC,t, Mt, BH,t = BG,t, BF,t, Wt, Yt, Lt, PH,t0, PtI, Kt, It, Qt, Vt, foreign counterparts C1,t*, etc, RERt, and St, given the monetary instruments Rn,t, Rn,t*, the fiscal instruments and exogenous processes.

E. Specialization of The Household’s Utility Function

The choice of utility function must be chosen to be consistent with the balanced growth path (henceforth BGP) set out in previous sections. As pointed out in Barro et al. (2004), chapter 9, this requires a careful choice of the form of the utility as a function of consumption and labor effort. As in Gertler et al (2003), it is achieved by a utility function which is non-separable. A utility function of the form




and where labor supply, Lt(h), is measured as a proportion of a day, normalized at unity, satisfies this requirement.17 For this function, UΦL > 0 so that consumption and money holdings together, and leisure (equal to 1 − Lt(h)) are substitutes.

F. State Space Representation

We linearize around a deterministic zero inflation, zero net private sector debt, balanced growth steady state. We can write the two-bloc model in state space form as


where zt is a vector of predetermined exogenous variables, xt are non-predetermined variables, and ot is a vector of outputs.18 Matrices A, B, etc are functions of model parameters. Rational expectations are formed assuming an information set {z1,s, z2,s, xs}, st, the model and the monetary rule. Details of the linearization are provided in Appendix B.

G. The Small Open Economy

Following Felices et al. (2006), we can now model a SOE by letting its relative size in the world economy n → 0 whilst retaining its linkages with the rest of the world (ROW). In particular the demand for exports is modeled in a consistent way that retains its dependence on shocks to the home and ROW economies. We now need a fully articulated model of the ROW. From (7) we have that w → ω and w* 1 as n → 0. Similarly for investment we have wI →ωI and wI*1 as n → 0. It seems at first glance then that the ROW becomes closed and therefore exports from our SOE must be zero. However this is not the case. Consider the linearized form of the output demand equations in the two blocs:


where the elasticities and their limits as n → 0 are given by


Thus we see that from the viewpoint of the ROW our SOE becomes invisible, but not vice versa. Exports to and imports from the ROW are now modeled explicitly in a way that captures all the interactions between shocks in the ROW and the transmission to the SOE.

H. Calibration

1. Home Bias Parameters

The bias parameters we need to calibrate are: ω, ω*, ωI and ωI*. Let in the steady state Ce = seC be consumption by entrepreneurs, and cy=CY. Let csimports be the GDP share of imported consumption of the foreign (F) consumption good. Let csexports be the GDP share of exports of the home (H) consumption good. Then we have that


Similarly for investment define isimports to be the GDP share of imported investment of the F investment and isexports be the GDP share of exports of H investment good. Then with iy=IY, we have


in the steady state. We linearize around a zero trade balance TB = 0, so we require


in which case αC,H+αC,He+αC,H*+αI,H+αI,H*=cy+iy as required. Thus we can use trade data for consumption and investment goods, consumption shares and relative per capita GDP to calibrate the bias parameters ω, ω*, ωI and ωI*. We need the home country biases elsewhere in the model, but for the ROW we simply put ω*=ωI*=1 everywhere else, so these biases are not required as such.

2. Calibration of Household Preference Parameters

We now show how observed data on the household wage bill as a proportion of total consumption, real money balances as a proportion of consumption and estimates of the elasticity of the marginal utility of consumption with respect to total money balances can be used to calibrate the preference parameters ϱ, b and θ in (61).

Calibrating parameters to the BG steady state, we first note that from (21) we have


In (67), WLPC is the household wage bill as a proportion of total consumption, which is observable. From the definition of Φ in (62), we have that


where czC(1hC)Z is the “effective-consumption” –real money balance ratio (allowing for external habit). From (61), the elasticity the marginal utility of consumption with respect to total money balances, Ψ say is given by


From the first-order conditions in the steady state (A.30) and (??) with Rn=Rn*=R we have


Thus given σ, β, g, hC, W(1L)PC, cz and Ψ, equations (67)(70) can be solved for ϱ, b and θ. The calculations for these parameters for the calibrated values of σ, β, g, hC, W(1L)PC, and cz are out in Appendix C19 of Ψ ∊ [0, 0.01]. Since Ψ > 0 we impose on our calibration the property that money and consumption are complements.

3. Remaining Parameters

As far as possible parameters are chosen based on quarterly data for Chile. Elsewhere the parameters reflect broad characteristics of emerging economies. A variety of sources are used: for Chile we draw upon Kumhof et al. (2008) (KL) and Medina et al. (2007a), Medina et al. (2007b) (MS). For emerging economies more generally and for parameters related to the financial accelerator we use Gertler et al. (2003, “GGN”) and Bernanke et al. (1999, “BGG”). The rest of the world is represented by U.S. data. Here we draw upon Levin et al. (2006) (LOWW). In places we match Chilean with European estimates using Smets and Wouters (2003) (SW). Appendix C provides full details of the calibration.

III. Monetary Policy Interest Rate Rules

In line with the literature on open-economy interest rate rules (see, for example, Benigno et al. (2004), we assume that the central bank in the emerging market bloc has three options: (i) set the nominal interest to keep the exchange rate fixed (fixed exchange rates, “FIX”); (ii) set the interest rate to track deviations of domestic or CPI inflation from a predetermined target (inflation targeting under fully flexible exchange rates, “FLEX(D)” or “FLEX(C)”); or, finally (iii) follow a hybrid regime, in which the nominal interest rates responds to both inflation deviations from target and exchange rate deviations from a certain level (managed float, “HYB”). Many emerging market countries follow one or another of these options and most are likely to in the near future. Formally, the rules are:

Fixed Exchange Rate Regime, “FIX”. In a simplified model without an exchange rate premium analyzed in section 4 we show this is implemented by


where any θs 0 is sufficient to the regime. In our full model with an exchange rate premium, we implement “FIX” as a “HYB” regime below, with feedback coefficients chosen to minimize a loss function that includes a large penalty on exchange rate variability. (Note that values for the loss function reported below remove the latter contribution).

Inflation Targets under a Fully Flexible Exchange Rate, “FLEX(D)” or “FLEX(C)”. This takes the form of Taylor rule with domestic or CPI inflation and output targets:


where ρ ∊ [0, 1] is an interest rate smoothing parameter.

Managed Float, “HYB”. In this rule the exchange rate response is direct rather than indirect as in the CPI inflation rule, (73):20


In all cases we assume that the central bank and the fiscal authorities in the emerging market bloc enjoy full credibility. Although this assumption may have been considered heroic a few years ago, today there are several emerging market countries that have succeeded in stabilizing inflation at low levels and have won the trust of private agents, including economies with a history of high or hyper-inflation (e.g. Brazil, Israel, Peru and Mexico, among others. See IMF (2006). Accounting for imperfect credibility of the central bank remains nonetheless important for many other emerging market countries, and can lead to higher stabilization costs than under full credibility (under inflation targeting and floating exchange rate, see Aoki et al (2007) or even sudden stops and financial crises (under fixed exchange rates, see IMF (2005)).

IV. Fiscal Rules

First we rewrite the government budget identity (53) in terms of the market price of bonds B^G,t=PB,t*BG,t to give


where FSt is the fiscal surplus. In terms of GDP ratios this can be written as


defining a growth-adjusted real interest rate Rg,t−1 over the interval [t − 1,t] by


where πH,tPH,tPH,t1PH,t1 is the home price inflation rate and ΔytYtYt1Yt1 is output growth.

Given a target steady-state government debt-to-GDP ratio B^GPHY, the steady state primary (PS) and overall fiscal surpluses are given by


Thus if inflation and growth are zero the steady state fiscal surplus is zero, but if inflation and/or growth are positive, then a steady state fiscal deficit (but positive primary surplus) is sustainable.

In the exercises that follow fiscal policy is carried out in using a component of taxation as the instrument, keeping government spending exogenous. Then we can write total tax revenues as a sum of the chosen instrument TtI plus remaining non-copper taxes TtNI which change endogenously at fixed tax rates plus copper revenue TCOPt; i.e,.


where TCOPt=τcopPC,tCOPt¯. Since it is desirable to avoid frequent changes of distortionary taxes, our chosen tax instrument consists of flat-rate tax receipts paid by Ricardian households (1 λ)TF2,t minus flat-rate transfers to constrained households ¸ λTF1,t. Thus we have


All other tax rates are kept fixed at their steady-state values.21

We consider tax rules that acknowledge the following: while interest rates can be set very frequently, often monthly, fiscal policy is set less frequently and involves an implementation lag. We assume in fact that the fiscal authority set tax rates every two periods (quarters in our calibration) whereas the central bank changes the nominal interest rate every period. This means in quarter t, a state-contingent fiscal policy can only respond to outcomes in quarter t − 1 or earlier. It follows that the fiscal instrument Taylor-type (fixed feedback) commitment rule that is compatible with a two-period fiscal plan must take one of two forms


where Xt is a vector of macroeconomic variables that define the simple fiscal rule. We can express the rule in terms of adjustments to the two groups of households by writing (81) in linear-deviation form


where ttI=TtITITI, tf1,t = (TF1,tTF1)/TF1 etc are proportional changes in tax receipts relative to steady state values. We assume that


corresponding to forms (82) and (83) respectively. Thus fiscal expansion (contraction) involves reducing (increasing) real taxes for group 2 and increasing (reducing) real transfers to group 1. If k = 0 all the adjustment is borne by the unconstrained second group and if k = 1 by the constrained first group. In our results we put k = 0.5. It remains to specify the rule for tf2,t.

A. A Conventional Fiscal Rule

The form of our first fiscal rule is fairly standard: real tax receipts as a proportion of GDP feeds back on government debt as a proportion of GDP, B^G,tPH,tYt, and output, Yt. Denoting bG,t=B^G,tPH,tYtB^GPHY, the fiscal rule in linearized form corresponding to (82) and (83) is


B. The Structural Fiscal Surplus Rule

Chile is a strong commodity exporter, and its fiscal policy is designed to isolate fiscal spending from the large and unpredictable fluctuations in fiscal revenues that can ensue from swings in the price of its main exported commodity. Thus Chile’s fiscal rule, based on an explicit target for the structural surplus, is interesting for emerging markets that depend heavily on exports of commodities. In practice, Chile’s Structural Fiscal Surplus Rule (SFSR) is a targeting rule for the fiscal surplus of the form


where FS denotes the BGP steady state, αtax and αcop are constant feedback parameters set by the fiscal authority and T^tI, T^tNI and TCOP^t are revenues ‘at potential’; i.e., at current tax rates, but steady state levels of the economy.

Noting by definition that T^tNI=TNI(but T^tITI and TCOP^t=TCOP, we can now combine (76), (80) and (89) to obtain a fiscal instrument rule of the form


where ΔXtXtX denotes the deviation of the variable Xt about its BGP steady state. Notice if the instrument is either of the two lump sum taxes/subsidies TF1,t or TF2,t then T^tI=TtI and the rule becomes


Thus for αtax ∊ [0, 1) the rule adjusts the tax instrument in a negative direction in response to a rise in non-instrument tax and copper revenues, but positively to a rise in government spending and interest payments on accumulated debt. With an appropriate choice of αtax ∊ [0, 1), it is the latter feature that stabilizes the government debt-to-GDP ratio about a BGP steady state with FSt = FS.

In linear form the SFSR becomes


where trtI(TtIPH,tYtTIPHY) is the absolute deviation of flat-rate tax receipts as a proportion of GDP with trtI, tct, bG,t1 and grt similarly defined. However this form of the rule requires period-by-period state-contingent changes to the tax instrument. Substituting (84) and (85), the two forms of the rule that allow for a two-period fiscal planning horizon as in (82) and (83) are


V. Imposing the Nominal Interest Rate Zero Lower Bound

We now modify our interest-rate rules to approximately impose an interest rate ZLB so that this event hardly ever occurs. Although so far only a few emerging market countries have experienced deflationary episodes (Peru and Israel in 2007 are examples of this), most inflation-targeting emerging market countries have chosen low single digit inflation targets (see IMF, 2005), which makes the design of rules robust to ZLB problems germane. Our quadratic approximation to the single-period loss function can be written as Lt=ytQyt where yt=[zt,xt] and Q is a symmetric matrix. As in Woodford (2003), chapter 6, the ZLB constraint is implemented by modifying the single period welfare loss to Lt+wrrn,t2. Then following Levine et al. (2007), the policymaker’s optimization problem is to choose ωr and the unconditional distribution for rn,t (characterized by the steady state variance) shifted to the right about a new non-zero steady state inflation rate and a higher nominal interest rate, such that the probability, p, of the interest rate hitting the lower bound is very low. This is implemented by calibrating the weight ωr for each of our policy rules so that z0(p)σr < Rn where z0(p) is the critical value of a standard normally distributed variable Z such that prob (Zz0) = p, Rn=1β(1+guc)1+π* is the steady state nominal interest rate, σr2=var(rn) is the unconditional variance and π* is the new steady state inflation rate. Given σr the steady state positive inflation rate that will ensure rn,t ≥ 0 with probability 1 − p is given by22. Our approach to the ZLB constraint (following Woodford, 2003) in effect replaces it with a nominal interest rate variability constraint which ensures the ZLB is hardly ever hit. By contrast the work of a number of authors including Adam et al. (2007), Coenen et al. (2003), Eggertsson et al. (2003) and Eggertsson (2006 study optimal monetary policy with commitment in the face of a non-linear constraint it ≥ 0 which allows for frequent episodes of liquidity traps in the form of it = 0.


In our linear-quadratic framework we can write the intertemporal expected welfare loss at time t = 0 as the sum of stochastic and deterministic components, Ω0=Ω˜0+Ω¯0. Note that Ω¯0 incorporates in principle the new steady state values of all the variables; however the NK Phillips curve being almost vertical, the main extra term comes from the π2 term in (D.30). By increasing wr we can lower σr thereby decreasing π* and reducing the deterministic component, but at the expense of increasing the stochastic component of the welfare loss. By exploiting this trade-off, we then arrive at the optimal policy that, in the vicinity of the steady state, imposes the ZLB constraint, rt ≥ 0 with probability 1 − p.

VI. Optimal Monetary and Fiscal Policy with Financial Frictions

How do financial frictions in emerging market economies affect the transmission mechanism of monetary and fiscal policy and the subsequent contributions of each to stabilization in the face of shocks? To answer this question we parameterize three representations of the model with increasing frictions and solve them subject to the corresponding optimal monetary and fiscal policy rules based on maximizing the household’s utility. This then provides a benchmark against which to assess the welfare implications of the fixed-exchange rate regime and various Taylor-type flexible exchange rate rules alongside the fiscal policy.

We adopt a linear-quadratic framework for the optimization problem facing the monetary authority. This is particularly convenient as we can then summarize outcomes in terms of unconditional (asymptotic) variances of macroeconomic variables and the local stability and determinacy of particular rules. The framework also proves useful for addressing the issue of the zero lower bound on the nominal interest rate.

Following Woodford (2003), we adopt a “small distortions” quadratic approximation to the household’s single period utility which is accurate as long as the zero-inflation steady state is close to the social optimum. There are three distortions that result in the steady state output being below the social optimum: namely, output and labor market distortions from monopolistic competition and distortionary taxes required to pay for government-provided services. Given our calibration these features would make our distortions far from small. However there is a further distortion, external habit in consumption, that in itself raises the equilibrium steady state output above the social optimum. If the habit parameter hC is large enough the two sets of effects can cancel out and thus justify our small distortions approximation. In fact this is the case in our calibration.23

Results obtained below are for a single-period quadratic approximation Lt=ytQyt obtained numerically following the procedure set out in From Appendix D. Insight into the result can be gleaned from the special case where there are no oil inputs into production or consumption and copper is not a production input either. Then the quadratic approximation to the household’s intertemporal expected loss function is given by




and the weights ωc, ωτ, etc are defined in Appendix D. Thus from (97) welfare is reduced as a result of volatility in consumption adjusted to external habit, ct − hCct−1; the terms of trade, τt, labor supply lt, domestic inflation πH,t and foreign shocks. There are also some covariances that arise from the procedure for the quadratic approximation of the loss function. The policymaker’s problem at time t = 0 is then to minimize (96) subject to the model in linear state-space form given by (63), initial conditions on predetermined variables z0 and the Taylor rule followed by the ROW. Our focus is on stabilization policy in the face of stochastic shocks, so we set z0 = 0. The monetary instruments is the nominal interest rate and the fiscal instrument consists of flat-rate taxes net of transfers. By confining fiscal policy to flat-rate taxes on Ricardian households only we eliminate its stabilization contribution; this we refer to as “monetary policy alone”. Details of the optimization procedure are provided in Levine et al. (2007).

We parameterize the model according to three alternatives, ordered by increasing degrees of frictions:

  • Model I: no financial accelerator and no liability dollarization. (xθ=xθ*=0, Θ = Θ* = 0, ϵp=ϵp*=0, φ = 1). This is a fairly standard small open-economy model similar to many in the New Keynesian open-economy literature with the only non-standard features being a non-separable utility function in money balances, consumption, and leisure consistent with a balanced growth path and a fully articulated ROW bloc;

  • Model II: financial accelerator (FA) only; (χθ, χθ*<0, Θ, Θ* > 0, ϵp, ϵp*0, φ = 1).

  • Model III: financial accelerator (FA) and liability dollarization (LD), assuming that firms borrow a fraction of their financing requirements 1 − φ ∊ [0, 1] in dollars.(χθ, χθ*<0, Θ, Θ* > 0, ∊p, p*0, φ ∊ [0, 1)).

We subject all these variants of the model to nine exogenous and independent shocks: total factor productivity (at), government spending (gt) in both blocs; the external risk premium facing firms, P,t in the home country; a copper price shock; an oil shock; a risk premium shock to the modified UIP condition, UIP,t; and a shock to the foreign interest rate rule R,t*. The foreign bloc is fully articulated, so the effect of these shocks impacts on the domestic economy through changes in the demand for exports, though since the domestic economy is small, there is no corresponding effect of domestic shocks on the ROW.

The foreign bloc is closed from its own viewpoint so we can formulate its optimal policy without any strategic considerations. Since our focus is on the home country we choose a standard model without a FA in the foreign bloc and very simple monetary and fiscal rules of the form


Maximizing the quadratic discounted loss function in the four parameters ρ* ∊ [0, 1], θπ*[1,10],24 αy*, αbg*[0,] and imposing a ZLB constraint in a way described in detail below for the home country, we obtain for the calibration in that bloc: ρ* = 1, θπ*=10, θy*=0 and αbg*=0.87. The optimized monetary rule then is of a difference or “integral” form that aggressively responds to any deviation of inflation from its zero baseline but does not react to deviations of output.25

With the foreign bloc now completely specified we turn to policy in the home country. Table 2 sets out the essential features of the outcome under optimal monetary and fiscal policy and their relative contributions to stabilization. There are no ZLB considerations at this stage. We report the the conditional welfare loss from fluctuations in the vicinity of the steady state for optimal monetary and fiscal policy and for monetary policy alone as we progress from model I without a financial accelerator (FA) to model III with the FA alongside liability dollarization (LD). We also report the long-run variance of the interest rate.

Table 2.

Welfare Outcomes under Optimal Policy: No ZLB Constraint

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To assess the contribution of fiscal stabilization policy we calculate the welfare loss difference between monetary policy alone (Ω0M) and monetary and fiscal policy together (Ω0MF). From Appendix D in consumption equivalent terms this is given by


The results appear to indicate that the stabilization role of fiscal policy is rather small, but increases as financial frictions are introduced. At most in model III with both a FA and LD the consumption equivalent contribution of fiscal policy is at most around 0.1%. However this conclusion is misleading because we have ignored the ZLB constraint. The high variances reported in Table 1 indicate a very frequent violation of this constraint in the model economies under these optimal policies.

A. Imposing the ZLB

Table 3 imposes the ZLB constraint as described in the previous section. We first consider monetary policy alone. We choose p = 0.001. Given wr, denote the expected inter-temporal loss (stochastic plus deterministic components) at time t = 0 by Ω0(wr). This includes a term penalizing the variance of the interest rate which does not contribute to utility loss as such, but rather represents the interest rate lower bound constraint. Actual utility, found by subtracting the interest rate term, is given by Ω0(0). The steady-state inflation rate, π*, that will ensure the lower bound is reached only with probability p = 0.001 is computed using (95). Given π*, we can then evaluate the deterministic component of the welfare loss, Ω¯0. Since in the new steady state the real interest rate is unchanged, the steady state involving real variables are also unchanged, so from (97) we can write Ω¯0(0)=wππ*2.26

Table 3.

Optimal Policy with a ZLB Constraint: Monetary Policy Only for Model I

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The optimal policy under the constraint that the ZLB is violated with a probability p = 0.001 per period (in our quarterly model, once every 250 years) occurs when we put wr = 3.75 and the steady state quarterly inflation rises to π* = 0.29.

Notation: π*=max[z0(p)σr(1β(1+guc)1)×100,0]=max[3.00σr2.44,0] with p = 0.001 probability of hitting the ZLB and β= 0.99, guc = 0.014. Ω¯=12wππ*2=3.829π*2. Ω=Ω˜+Ω¯= = stochastic plus deterministic components of the welfare loss.

Table 4 repeats this exercise for monetary and fiscal policy together. With the benefit of fiscal stabilization policy the ZLB constraint is now more easily imposed at values wr = 0.5 and without any rise in the inflation rate from its zero baseline value. Figure 1 presents the same results in graphical form with Figure 2 providing analogous results for Model III.

Table 4.

Optimal Commitment with a ZLB Constraint. Monetary Plus Fiscal Policy for Model I

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Figure 1.
Figure 1.

Imposition of ZLB: Model I

Citation: IMF Working Papers 2009, 022; 10.5089/9781451871692.001.A001

Figure 2.
Figure 2.

Imposition of ZLB: Model III

Citation: IMF Working Papers 2009, 022; 10.5089/9781451871692.001.A001

Finally in this subsection we return to the question of how much stabilization role there is for fiscal policy, but now with the ZLB imposed. Table 5 recalculates the consumption equivalent contribution of fiscal stabilization with a ZLB. We now find this contribution to be significant, rising from ce = 0.10% to ce = 0.64% as we move from Model I to Model III.

Table 5.

Welfare Outcomes under Optimal Policy: ZLB Constraint

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B. Welfare Decomposition

Which shocks contribute the most to the welfare loss under optimal monetary and fiscal policy? We address this question in the three models by subjecting them to the nine shock processes one at a time. Table 6 shows the ‘welfare decomposition’ as % contributions to the whole welfare loss when all shocks are present.27 From the table we see that in Model I (no FA) the home productivity shock and the oil and copper price shocks contribute almost 96% of the loss from fluctuations. In model II with the FA this comes down by about 20%, the contribution from the volatility of the risk premium. Adding LD in model III (with 25% of firms’ finance requirements in dollars) has a dramatic effect on the decomposition. Ncontribution of foreign demandow the (gt*) and supply (at*) rise from 2.3% to almost 46%. These shocks impact on the FA through fluctuations in the real exchange rate and consequently net worth if there is LD.

Table 6.

Welfare Decomposition of Shocks(%)

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Crucial to the understanding of the effects of the FA and LD is the behavior of the net worth of the wholesale sector. In linearized form this is given by


where the ex ante cost of capital is given by rt1k. In (102) since leverage 1nk>1 we can see that net worth increases with the ex post return on capital at the beginning of period t, rt1k, and decreases with the risk premium θt−1 charged in period t − 1 and the the ex post cost of capital in home currency and dollars,φrt1+(1φ)(rt1*+(1+R)(rertrert1)), noting that (rert − rert−1) is the real depreciation of the home currency. Using


and starting at the steady state at t = 0, from (102) at t = 1 we then have


Thus net worth falls if Tobin’s Q falls and if some borrowing is in dollars (φ < 1), we see that a depreciation of the real exchange rate (rer1 > 0) brings about a further drop in net worth. However an appreciation of the real exchange rate (rer1 < 0) will offset the drop in net worth. Output falls through two channels: first, a drop in Tobin’s Q and a subsequent fall in investment demand and, second, through a reduction in consumption by entrepreneurs.

C. Impulse Responses

Insights into the working of optimal monetary and fiscal policy and of the transmission mechanism can be obtained deriving impulses responses of the model(s) following an unanticipated 1% negative productivity shock in Figure 3. Large welfare losses are associated with inflation so to prevent this happening both monetary and fiscal policy are tightened by raising the nominal interest rate (rn,t) and flat rate taxes as a proportion of GDP (ttI). As we introduce financial frictions and proceed from model I to model III, monetary policy becomes more constrained by the ZLB and fiscal policy plays a bigger role. Both the nominal and the expected interest rate falls with financial frictions and this offsets the downward effect on investment to some extent. Output falls as a direct result of the fall in productivity and indirectly owing to the fall in capital stock. This downward effect is offset by an increase in labor supply. In models I and II the real exchange rate appreciates, but in model III with LD a drawn out period lasting about 20 quarters sees the nominal interest rate drop below the baseline (rn,t becomes negative) causing both the nominal and real exchange rate to depreciate (rert becomes positive). This offsets the negative impact on investment of the FA plus the rise in foreign liabilities denominated in dollars.

Figure 3.
Figure 3.

Impulse Reponses to a -1% Technology Shock. Models I, II and III.

Citation: IMF Working Papers 2009, 022; 10.5089/9781451871692.001.A001

VII. The Performance of Optimized Simple Rules

The optimal monetary and fiscal policy with commitment considered up to now can be implemented as feedback rules but, as now acknowledged in the literature, the form these take is complex and would not be easy to monitor (see for example, Levine et al (1987a), Currie et al.(1993), Woodford (2003)). This point has added force when the need for a planning horizon of more than one period for fiscal policy is introduced into policy design. We therefore turn to simple rules and examine the ranking of various options and the extent to which they can match the fully optimal benchmark. For monetary policy we examine two of the options discussed in section 3: FLEX(D) where the nominal interest rate responds to current domestic inflation, πH,t and output, yt, as in (72); and the fixed exchange rate regime as in (71). In the first set of exercises the fiscal rule is the conventional type of the form (85) (with k = 0.5) and (87) which allow tax changes to be planned two periods ahead. We now maximize the quadratic discounted loss function in the five parameters ρ ∊ [0, 1], θ π ∊[1, 10], θy, αy, αbg ∊ [0, 5] and impose the ZLB constraint as before.

Table 7 summarizes the outcomes under this combination of rules. In addition to the the measure ceMF which as before quantifies the the contribution to welfare of fiscal stabilization in consumption equivalent terms, we provide a further measure of the costs of simplicity as opposed to implementing the fully optimal benchmark. Denoting the latter by OPT and any simple rule by SIM, this is given by

Table 7:

Welfare Outcomes under Optimized Simple Rules: FLEX(D) with a Conventional Fiscal Rule. Models I, II and III.

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Using this measure we see from Table 7 that the ability of the optimized simple rule to closely match the fully optimal benchmark deteriorates sharply as financial frictions are introduced rising from 0.12% in Model I to 0.66% and 2.07% in Models II and III respectively. The primary reason for this lies in the existence of a lower bound on σr2 as wr is increased. This is demonstrated in Figures 4 and 5.

Figure 4.
Figure 4.

Imposition of ZLB: Flex(D)+Conventional Fiscal Rule, Model I

Citation: IMF Working Papers 2009, 022; 10.5089/9781451871692.001.A001

Figure 5.
Figure 5.

Imposition of ZLB: Flex(D)+Conventional Fiscal Rule, Model III

Citation: IMF Working Papers 2009, 022; 10.5089/9781451871692.001.A001

What is the welfare cost of maintaining a fixed rate (FIX) and what are the implications of this regime for fiscal policy? We address these questions by introducing the interest rate rule (71) alongside the same simple fiscal rule as before. Table 8 sets out the outcome after imposing the ZLB.28. Under FIX there is no scope for trading off the variance of the nominal exchange rate with other macroeconomic variances that impact on welfare. Thus the only ways of reducing the probability of hitting the lower bound are to shift the stabilization burden onto fiscal policy or increase the steady state inflation rate. This imposes a very large welfare losses29 in all models which as before increase as financial frictions are introduced. This feature is reflected in the very large costs of simplicity ceMF which rise from almost 5% to over 11% as we progress from model I to III. The higher values for the measure of the role of fiscal policy, ceMF, indicate the shift to fiscal means of stabilization.

Table 8:

Welfare Outcomes under Optimized Simple Rules: FIX with a Conventional Fiscal Rule. Models I, II and III.

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Of course faced with these results there is an alternative of full dollarization, for example via a currency board, that would simply result in rn,t=rn,t* and the ZLB then ceases to be a concern for the domestic country. However this would still leave a significant welfare losses only slightly lower that those of the FIX regime. These can be calculated from the purely stochastic components of the welfare loss, Ω˜0 and the corresponding consumption equivalent measures c˜eMF and c˜eSIM.

We have now established that domestic inflation targeting, FLEX(D), alongside a counter-cyclical simple fiscal rule stabilizes the model economy far better than a fixed exchange rate regime. Two questions now remain: would a compromise ‘managed float’ of the type (74) improve upon FLEX(D)? How does CPI inflation targeting FLEX(C), the usual form of the target, compare with FLEX(D)?

Given the very poor performance of FIX one would not expect a hybrid regime to improve matters; nor do we expect a target that implicitly includes an element of an exchange rate target to outperform the domestic target. Indeed we find this to be the case. We find that the optimal feedback parameter in (74), θs with a ZLB imposed to be zero across all three models. Results for FLEX(C) are reported in Table 9. These confirm the FLEX(D) is vastly superior to FLEX(C); the costs of simplicity ceSIM now rise from 1.41% to 3.37% as we proceed from model I to model III compared with 0.12% to 2.07% for FLEX(D). CPI as opposed to domestic inflation targeting has a welfare cost of over a 1% permanent fall in consumption from the steady-state.

Table 9:

Welfare Outcomes under Optimized Simple Rules: FLEX(C) with a Conventional Fiscal Rule. Models I, II and III.

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Finally we consider the stabilization performance of the SFSR in the form (93) alongside a FLEX(D) monetary interest rate rule as in Table 7. It turns out that in this exact form its performance is very poor. Instead we consider a modified SFSR without any feedback on government spending shocks:


This form of the SFSR implies that the fiscal surplus defines in (89) must be defined with government spending assumed to be at its steady state. With this modification we see from Table 9 that the optimized SFSR has a very similar outcome to that of the conventional fiscal rule, but with the advantage that it can be formulated in terms of a state-contingent fiscal surplus rule as in (89) and so has added transparency. It involves a very active response to endogenous and copper taxes a with αtax above unity and αcop below, but close to unity for Model I. In Models II and III this procyclical responses of flat-rate taxes net of transfers is rather less and is switched to a monetary policy, especially in model III.

VIII. Conclusions

Our results provide broad support for the “three-pillars” macroeconomic framework such as that pursued by Chile in the form of an explicit inflation target, a floating exchange rate and a counter-cyclical fiscal rule either of a conventional type or the SFSR actually pursued in Chile. Domestic inflation targeting is superior to partially or fully attempting to stabilizing the exchange rate. Responding to the exchange rate explicitly or implicitly makes it more expensive in terms of output variability to stabilize inflation. A model corollary is that stabilizing domestic inflation (e.g., measured by changes in the producer price index) enhances welfare outcomes somewhat, since stabilizing changes in the consumer price index implies a partial response to the exchange rate via imported consumer goods.30

Financial frictions increase the costs of stabilizing the exchange rate, as shown in GGN and Batini et al. (2007), because the central bank cannot offset a drop in net worth by allowing the exchange rate to adjust. Emerging markets faced with financial frictions should thus “fear to fix” rather than “fear to float”.

Results for optimal monetary and fiscal policy compared with monetary stabilization alone indicate that potentially fiscal stabilization can have a significant role and more so if there are financial frictions. However the ability of best simple optimized counterpart to mimic the optimal policy deteriorates sharply as we first introduce the financial accelerator in model II and then liability dollarization in model III. This suggests that future research should explore alternative rules that respond to indicators of financial stress such as the risk premium facing firms in capital markets. Furthermore, given the sharp deterioration of the stabilization performance of both optimal policy and optimized rules as LD is introduced, future developments of the model could usefully attempt to endogenize the decision to borrow in different currencies.31 Finally, although we have drawn upon consistent Bayesian-ML estimates (BMLE) using Chilean data for the core model, and US data for the ROW, a BMLE of all three variants of the model, using data from a number of emerging SOEs, would both indicate the empirical importance of various financial frictions and enhance our assessment of the implications for policy.32

Table 10.

Welfare Outcomes under Optimized Simple Rules: FLEX(D) with a Modified SFSR. Models I, II and III.

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The zero-inflation, BGP steady state with consumption, wholesale output, the wage and capital stock are growing at a rate g per period, a balanced must satisfy


Since there are no investment adjustment costs at the steady state it follows that


It follows from (A.1) that


and hence the previous assumptions regarding S(·) become S(g + δ) = g + δ and S′ (g + δ) = 1.

In what follows we denote the (possibly trended) steady state of Xt by X. Then the rest of the steady state is given by


where gucis the growth rate of the marginal utility of consumption in the steady state,


plus the foreign counterparts.

The steady is completed with


Units of output are chosen so that PO = PC = PH = PF = 1. Hence T = P = PI = 1. Hence with our assumptions regarding S(·) we have that Q = 1. We also normalize S = 1 in the steady state so that PF*=PH*=P*=PI*=1 as well. Then the steady state of the risk-sharing condition (A.38) becomes C = kC* where k is a constant.


Appendix II. Linearization

Exogenous processes:

(Note grt = gtyt is estimated as a proportion of GDP.)

Predetermined variables

where rt−1 = rn,t−1 πt and rt1*=rn,t1*πt* are the ex post real interest rates.

Non-predetermined variables:
rn,t=exogenous instrument(B.34)
tf2,tpH,t=exogenous instrument(B.35)

(Note SOE results: w = ω, wI = ωI, w*=wI*=1)

pZ,tpH,t=(1wZ)τt(1ω)τt as n0(B.63)

(Note pZ,t*pF,t*=(1wZ*)τ*0)


(Note pI,t*pZ,t*=(1wI*)τt0)


(Note πZ,t*=πF,t*)


(Note qtk*=qt*)

check: ct=wCcZ,t+(1wC)cO,t(B.114)

The quadratic loss function for the home and ROW require the following:


tf2,t − pH,t, tf2,t*pF,t* the instruments.

Appendix III

Appendix III. Calibration and Estimation

We begin with estimates of the processes describing the exogenous shocks.

Shock parameters

We require the AR1 persistence parameters ρa, etc and the corresponding standard deviations of white noise processes, sda, etc.

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Table C1.

Parameterization of Shock Processes

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Note that officially CHILE has a zero Government-GDP target, but this is regarded as ignoring some government liabilities (see MS)