Aggregate Spending

Aggregate spending on the domestically produced good, ${\hat{y}}_t^d,$ is composed of domestic spending, ${\hat{c}}_t,$ plus exports, ${\hat{x}}_t^d:$

where:

$\overline{c}/{\overline{y}}^d\mathrm{a}\mathrm{n}\mathrm{d}\overline{x}/{\overline{y}}^d$ represent the respective shares of consumption and expoirts in domestic output in the steady state.

A fraction, λ of domestic spending is by optimizing (Ricardian) consumers, ${\hat{c}}_t^{\mathit{0}},$ and the rest is by “rule-of-thumb” (non-Ricardian) consumers, ${\hat{c}}_t^r:$

Spending by optimizing Ricardian consumers is derived from a standard separable utility function on consumption, C_t, and labor, N_t:

where:

σ is the coefficient of relative risk aversion

γ is the degree of habit formation in consumption.

This introduces an element of inertia into consumption, and is a fairly standard feature of New Keynesia models.

The first-order conditions of utility maximization provide the Euler equation that guides consumption:

where:

${\hat{i}}_t$ is the current nominal interest rate

${\hat{\mathrm{\pi }}}_{t+1}$ is the inflation rate expected in period t+1.

Rule-of-thumb or non-Ricardian consumers do not smooth consumption through borrowing and lending. The lack of consumption smoothing may reflect limited access of some households to financial markets.¹¹² As a consequence, for these consumers, spending is based on current income:

where:

ŵ_t is the nominal wage rate per unit of work a supplied

${\hat{P}}_t$ is the price level

${\hat{n}}_t$ is the number of units of work supplied.

In addition to domestic demand, there is also foreign demand for the domestically produced good, ${\hat{x}}_t^d\mathrm{.}$ Export demand depends on foreign real income and the real exchange rate:

where:

${\hat{y}}_t^{*}$is foreign real income

${\hat{q}}_t$ is the real exchange rate (the real cost of foreign currency)

ρ_x^d is the degree of persistence in domestically-produced exports

τ is the exchange rate elasticity of demand for domestically-produced exports.

Aggregate Production

Output in the economy consists of two types of goods. One is a composite good produced by monopolistically competitive firms using labor and imported goods as inputs. This good is both consumed domestically and exported. The second is a natural endowment commodity which is exported.

The composite good is produced using a CES production technology with inputs of labor and an imported input. This production function is particularly convenient because of its generality, given that it embeds a Cobb-Douglas or even a Leontief technology, depending on the size of the elasticity of input substitution chosen:

where:

σ_s is the elasticity of substitution in production

I_t is the imported intermediate input

N_t is the labor input

α is the share of the imported good in production—the openness of the economy

A_t is total factor productivity.

Production costs reflect the costs of the labor and the imported inputs, as well as labor. The real cost of imported inputs is determined by the real exchange rate, ${\hat{q}}_t,$ while the real wage, $({\hat{w}}_t-{\hat{p}}_t),$ is determined by the equilibration of producers’ demand for labor, ${\hat{n}}_t,$ with the supply of labor by households. The supply of labor is derived from maximization of utility in Equation (3)¹¹³ by both types of consumers. Aggregate supply depends positively on real wage and negatively on consumption. This is a typical result obtained from the first order condition with respect to labor of separable utility functions:

where:

v is the coefficient of disutility of labor.

With the production technology specified in Equation (7), the real marginal cost of production, $\hat{m}{c}_r^R$, is given by:

where:

ŵ_t is the nominal wage rate per unit of work supplied

${\hat{p}}_t$ is the price level ${\hat{q}}_t$ is the real exchange rate (the real cost of foreign currency)

${\hat{\alpha }}_t$ is the (log) deviation of At from its steady state value.

Equation (9) shows that the more open the economy, the larger the impact of exchange rate movements on production costs and inflation. The elasticity of substitution in production also plays an important role: the lower the possibility of substituting domestic labor for imported inputs, the larger the impact of an exchange rate movement on costs.

Production of the second endowment type good, ${\hat{x}}_t^{CM},$ is essentially exogenous and is completely exported. The amount produced of this commodity does not react to its price, and the requirement of local inputs to its production is negligible. Its value depends on the real exchange rate and its price, ${\overline{p}}_t^{CM},$ abroad, which is given by international markets. Consequently, the value of production is determined as:

Firms set the price of output for the domestic market in one of two ways. One group of firms, accounting for a fraction, μ of sales of the domestic good, follows a simple, backward-looking approach to adjusting their prices.¹¹⁴ In effect, this leads to an element of indexation of prices, generating persistence in inflation. Another group of price-setters takes a forward-looking optimization approach to price setting but only adjust their prices periodically, à la Calvo. In any given period, it is assumed that only a fraction, (1-8), of the optimizing firms adjust their prices. The backward-looking component of price setting can be motivated by uncertainty regarding the central bank’s inflation objective (Erceg, Henderson, and Levin, 2000) or limited credibility of the policy framework (Argov and others, 2007). In both cases, agents will tend to place a greater weight on recent inflation outcomes in forming inflation expectations than otherwise.

Taking these considerations into account, the aggregate inflation rate in the economy will be summarized by a New Keynesian Phillips curve of the form:

where:

β is the subjective rate of time preference

μ is the proportion of price adjustment based on a simple indexation formula, $\mathrm{\phi }=\frac{1-\mathrm{\theta }}{\mathrm{\theta }}(1-\mathrm{\beta }\mathrm{\theta }),$ where (1-θ) is the average frequency of price adjustment by optimizing firms

$\hat{m}{c}_r^R$ is the real marginal cost of production.

This Phillips curve has three elements. The first is an expected inflation component. This reflects the assumption that firms adjust their prices periodically rather than continuously, so that when prices are adjusted, firms take into account the expected evolution of inflation. The second term is a lagged inflation component reflecting the indexation applied to a fraction, μ of prices. The third term reflects the incorporation of marginal costs into optimizing firms’ prices. Exchange rate movements feed into inflation through their impact on marginal costs. The speed of pass-through into inflation depends both on the proportion of optimizing firms and on the average frequency of price adjustments.

Exchange Rate Determination

The real exchange rate is assumed to be determined by the real uncovered interest parity condition, together with a risk premium:

where:

${\hat{q}}_t={\hat{s}}_t+{\hat{p}}_t^{*}-{\hat{p}}_t$ is the real exchange rate (ŝ_t is the spot price of foreign exchange and ${\hat{p}}_t^{*}$ is the foreign price level)

${\hat{i}}_t^{*}$is the foreign nominal interest rate

${\hat{\mathrm{\pi }}}_{t+1}^{*}$ is the expected foreign inflation rate

${\hat{\mathrm{\phi }}}_t$ is the risk premium.

Following Céspedes, Chang, and Velasco (2004), the risk premium, ${\hat{\mathrm{\phi }}}_t\text{,}$ depends on debt, the exchange rate, and GDP:¹¹⁵

where:

• $({\hat{b}}_{t+1}^{*}-{\hat{y}}_t)$ is the projected external debt-to-GDP ratio.

• The risk premium consists of four elements:

• The first term in the equation, ${\mathrm{\phi }}_0({\hat{b}}_{t+1}^{*}-{\hat{y}}_t),$ says that the risk premium is an increasing function of the ratio of external debt to GDP. This friction in the international capital markets is required to ensure stationarity of the external debt-to-GDP ratio.¹¹⁶

• The second and third terms, ${\mathrm{\phi }}_1(\frac{{\overline{x}}^d}{{\overline{x}}^d+{\overline{x}}^{cm}}{\overline{x}}_t^d+(\frac{{\overline{x}}^{cm}}{{\overline{x}}^d+{\overline{x}}^{cm}}-1){\hat{q}}_t)+{\mathrm{\phi }}_1\left({\hat{I}}_t\right),$ relate the risk premium negatively to exports and positively to imports, so that a weakening of the current account raises the risk premium.

• The last term, ${\mathrm{\phi }}_3\left({\hat{q}}_t\right),$ captures the adverse impact of currency depreciation on the domestic currency value of external debt—the balance sheet effect. As the debt service burden on borrowers rises, the risk premium increases. For a financially vulnerable economy, the adverse impact of depreciation through the balance sheet effect must outweigh the beneficial effects of depreciation on the current account so that depreciation has a net harmful effect on activity. This imposes restrictions on the values of the parameters in the risk premium equation.¹¹⁷

Monetary Policy

Monetary policy is described by the alternative reaction functions presented in the main text.

Model Calibration

Differences in the calibration of the financially robust advanced and the financially vulnerable emerging economies are shown in Table A2.1 and reflect the following considerations:

• Domestic financial development. In the emerging economy, the share of “rule-of-thumb spending” based on current income is set at 30 percent, compared to 0 percent in the advanced economy, to reflect limited access of agents to borrowing opportunities and greater use of quantitative credit rationing rather than use of retail interest rates. Better access to borrowing and saving opportunities in advanced economies is also reflected in higher persistence in spending behavior, with the persistence coefficient set at 0.5 versus 0.3 in emerging economies.

• External financial constraints. More limited capital mobility and international asset substitutability in vulnerable emerging economies is reflected in: (1) a risk premium with a substantially higher coefficient related to the level of the external debt-to-GDP ratio (0.05 compared to 0.01 for the advanced economy (based on Schmidt-Grohé and Uribe, 2003)); and (2) a higher coefficient on the current account balance (0.3 compared to 0.2 for the advanced economy).¹¹⁸ In addition, the balance sheet vulnerability of the emerging economy is reflected in a much higher elasticity of the risk premium with respect to exchange rate movements than in the advanced economy (0.5 compared to 0.05).

Table A2.1.

Parameter Calibration of the Advanced and Emerging Economy Models

Table A2.1.

Parameter Calibration of the Advanced and Emerging Economy Models

	Advanced Economy	Emerging Economy
Utility function
Subjective Discount rate	β = 0.988	β = 0.988
Coefficient of relative risk aversion	σ= 1	σ= 2
Parameter of the labor supply (disutility)	ν = 2	ν = 2
Habit coefficient	γ= 0.5	γ= 0.3
Share of rule-of-thumb consumers	λ = o	λ = 0.3
Production function
Factor (input) elasticity of substitution in production function	σs=1	σs=1
Weight of imported factor (degree of openness)	α=0.25	α=0.3
Exports
Elasticity of home exports to exchange rate	τ= 5	τ= 5
Elasticity of commodity exports to exchange rate	0	0
Price-setting
Probability of not reoptimizing	θ = 0.75	θ = 0.75
Degree of indexation (for firms that are not reoptimizing)	μ = 0	μ = 0.8
Elasticity of demand	ε= 6	ε= 6
Mark-up	[ε/(ε-1)] = 1.2	[ε/(ε-1)] = 1.2
Wage-setting
Rigid wages (Dummy_WR)	D_WR = 0	D_WR =0
Parity condition and risk premium
Elasticity of country risk premium to foreign debt	0.01	0.05
Elasticity of country risk premium to exports	0.20	0.3
Elasticity of country risk premium to imports	0.20	0.3
Elasticity of risk premium to real exchange rate (balance sheet)	0.05	0.5
Exchange rate smoothing	0.6	0.6
Monetary Policy
Interest rate smoothing in Taylor rule	0.7	0.7
Parameter related to inflation gap	0.25 ≤ coeff. ≤ 3.11	0.26 ≤ coeff. ≤ 3.15
Parameter related to output gap	–0.28 ≤ coeff. ≤ 2.57	–0.28 ≤ coeff. ≤ 2.61
Parameter related to exchange rate	0.6	0.6
Aggressiveness	6.5	6.6
Shock Inertia
Shock persistence	Rho_R=0.8	Rho_R=0.8

View Table

Table A2.1.

Parameter Calibration of the Advanced and Emerging Economy Models

	Advanced Economy	Emerging Economy
Utility function
Subjective Discount rate	β = 0.988	β = 0.988
Coefficient of relative risk aversion	σ= 1	σ= 2
Parameter of the labor supply (disutility)	ν = 2	ν = 2
Habit coefficient	γ= 0.5	γ= 0.3
Share of rule-of-thumb consumers	λ = o	λ = 0.3
Production function
Factor (input) elasticity of substitution in production function	σs=1	σs=1
Weight of imported factor (degree of openness)	α=0.25	α=0.3
Exports
Elasticity of home exports to exchange rate	τ= 5	τ= 5
Elasticity of commodity exports to exchange rate	0	0
Price-setting
Probability of not reoptimizing	θ = 0.75	θ = 0.75
Degree of indexation (for firms that are not reoptimizing)	μ = 0	μ = 0.8
Elasticity of demand	ε= 6	ε= 6
Mark-up	[ε/(ε-1)] = 1.2	[ε/(ε-1)] = 1.2
Wage-setting
Rigid wages (Dummy_WR)	D_WR = 0	D_WR =0
Parity condition and risk premium
Elasticity of country risk premium to foreign debt	0.01	0.05
Elasticity of country risk premium to exports	0.20	0.3
Elasticity of country risk premium to imports	0.20	0.3
Elasticity of risk premium to real exchange rate (balance sheet)	0.05	0.5
Exchange rate smoothing	0.6	0.6
Monetary Policy
Interest rate smoothing in Taylor rule	0.7	0.7
Parameter related to inflation gap	0.25 ≤ coeff. ≤ 3.11	0.26 ≤ coeff. ≤ 3.15
Parameter related to output gap	–0.28 ≤ coeff. ≤ 2.57	–0.28 ≤ coeff. ≤ 2.61
Parameter related to exchange rate	0.6	0.6
Aggressiveness	6.5	6.6
Shock Inertia
Shock persistence	Rho_R=0.8	Rho_R=0.8

A crucial implication of these parameter configurations is that currency depreciation in the financially robust advanced economy will be expansionary as the stimulus to net exports will outweigh any adverse balance sheet effects. In contrast, currency depreciation has a net contractionary effect in the vulnerable emerging economy as the stimulus to net exports is more than offset by the adverse impact on balance sheets and, consequently, on consumption and investment.

• Openness. The share of imports in production rather than GDP (following McCallum, 2006) is set at 25 percent for the advanced economy and at 30 percent for the emerging economy, consistent with international evidence.

• Policy credibility. In the robust advanced economy, price formation is based on a purely forward-looking approach to formation inflation expectations (μ= 0). Implicitly, this assumes that agents know and believe the central bank’s policy rule. In the emerging economy, price formation is assumed to be much more backward looking (μ = 0.8), reflecting limited credibility of the central bank’s commitment to an inflation objective (following Rudebusch and Svensson, 1998; Erceg, Henderson, and Levin, 2000; and Argov and others, 2007).

Existing Studies of Hybrid Policy Rules

Taylor (2001) reviews the limited number of studies that had looked at the issue of whether it would be appropriate to take the exchange rate explicitly into account in monetary policy in an open economy.¹¹⁹ He concludes there was little evidence that including a systematic response to exchange rate movements would improve macroeconomic performance, even in an open economy. He attributes this to two principal factors: (1) even in the plain vanilla framework, monetary policy already responds to the indirect impact of exchange rate movements on output and inflation, and (2) the appropriate response to exchange rate movements should depend on the cause of the movement. He suggests that adding a mechanistic response to exchange rate movements in the policy reaction function could worsen performance, depending on the typical array of shocks affecting the economy. Both Taylor (2000) and Mishkin (2000), however, recognize that more research is needed in this area before any strong conclusions can be drawn.

More recent research has begun to examine whether differences in economic and financial structure between emerging and more advanced economies may explain the “fear of floating” evident in many emerging and developing economies and may justify including systematic dampening of exchange rate movements in the central bank policy reaction function.¹²⁰ Below is a brief summary of some of the main findings for each of the hybrid inflation-targeting exchange rate frameworks.

Open-Economy Inflation Targeting

Model-based analyses generally find little benefit from including the exchange rate in the monetary policy reaction function. Indeed, several studies argue that including the exchange rate worsens macroeconomic performance. However, in some other studies, including the exchange rate in the reaction function is found to be beneficial if the economy is financially fragile or if the central bank is very uncertain of how the exchange rate is determined:

• Céspedes, Chang, and Velasco (2004) consider the impact of exchange rate movements in economies with a high degree of dollarization and constrained access to international borrowing opportunities. In such circumstances, exchange rate movements can give rise to strong balance sheet effects opposite to the normal competitiveness effects of exchange rate movements. Which effect dominates depends on each country’s situation. However, the authors find that exchange rate flexibility outperforms a fixed exchange rate regime.

• Morón and Winkelried (2005) compare optimal hybrid reaction functions in financially vulnerable and financially robust economies. In general, the optimized rules for a vulnerable economy place much less weight on smoothing output and more weight on dampening exchange rates than in a robust economy. The analysis does not directly compare the performance of such hybrid rules against otherwise similar rules excluding exchange rate terms. Nonetheless, the finding that some exchange rate smoothing is involved in the optimal rules appears to imply that rules excluding exchange rate smoothing perform less well in minimizing inflation or output volatility or both. It is not clear, however, why some exchange rate smoothing appears optimal for both the vulnerable and robust economies.

• Cavoli and Rajan (2006) compare variations on plain vanilla and hybrid Taylor rules for a financially vulnerable economy (calibrated to the Thai economy). Key results of interest are that: (1) in optimally weighted, open-economy Taylor rules (including an exchange rate term), the optimal weight on the exchange rate is low; (2) open-economy Taylor rules may well lead to greater macroeconomic volatility than plain vanilla Taylor rules; and (3) the emphasis put on the level of the real exchange rate versus changes in the exchange rate has important consequences for macroeconomic outcomes. It is not clear, however, whether these results would carry over to a model with more forward-looking behavior, including more forward-looking policy formulation.

• Batini, Levine, and Pearlman (2007), using a calibrated model of the Peruvian economy with dollarization and financial “frictions,” compare fixed and flexible exchange rate regimes. They find that a fixed exchange rate delivers much poorer performance. They conclude that, because dollarization weakens the output gap channel of transmission relative to the exchange rate channel, nothing should be done to limit the flexibility of the exchange rate in order to achieve the inflation target.

• Ravenna and Natalucci (2008) use a model loosely calibrated to the transition economies of Eastern Europe to examine the implications of the Balassa-Samuelson effect. They find that when the economy is experiencing a prolonged period of more rapid productivity growth in the tradables than in the non-tradables sector, macroeconomic performance is much better with a flexible exchange rate than with a rule involving a high degree of exchange rate management.

• Leitemo and Söderstöm (2005) and Wollmershäuser (2006) both consider the performance of alternative policy rules when there is uncertainty surrounding the determination of the exchange rate. Although not specifically an emerging economy issue, uncertainty about the determination of the exchange rate may be even greater in such economies than in more advanced economies. The authors of both papers find a small gain from including the exchange rate in the reaction function when there is no uncertainty about exchange rate determination. However, when uncertainties are introduced, Leitemo and Söderstöm find that a Taylor rule is slightly more robust than an open-economy rule, while Wollmershäuser finds that open-economy rules are more robust to a wider range of exchange rate uncertainties.

Table A2.2.

Reaction Function Coefficients

Table A2.2.

Reaction Function Coefficients

	Inflation	Output
1	0.25	2.57
2	0.57	2.26
3	0.89	1.94
4	1.20	1.62
5	1.52	1.31
6	1.84	0.99
7	2.15	0.67
8	2.47	0.36
9	2.79	0.04
10	3.11	–0.28

View Table

Table A2.2.

Reaction Function Coefficients

	Inflation	Output
1	0.25	2.57
2	0.57	2.26
3	0.89	1.94
4	1.20	1.62
5	1.52	1.31
6	1.84	0.99
7	2.15	0.67
8	2.47	0.36
9	2.79	0.04
10	3.11	–0.28

Inflation Targeting with an Exchange Rate Band

It is unclear how well this type of framework compares with a more conventional inflation-targeting framework in terms of macroeconomic performance:

• Lahiri and Végh (2001) suggest that an exchange rate band may be appropriate if nominal exchange rate movements and higher interest rates have output costs and if intervention is costly. In such circumstances, a fairly free float within an exchange rate band may be optimal, at least in response to some kinds of shocks.

• Morón and Winkelried (2005) examine such a policy in their model of a financially vulnerable economy and find that it tends to outperform a policy involving a more linear response to exchange rate movements. The authors note, however, that the analysis fails to take into account the impact that limiting exchange rate movements will have on the behavior of economic agents. In particular, if the central bank limits the range of exchange rate movement, this could encourage agents to increase their foreign currency liabilities, accentuating the vulnerability of the economy. This would make the economy particularly vulnerable to real shocks shifting the equilibrium real exchange rate.

Exchange-Rate-Based Inflation Targeting

McCallum (2006) compares the performances of plain vanilla and exchange-rate-based approaches to inflation targeting in an economy with varying degrees of openness. The first key finding is that, as the degree of openness increases, an exchange-rate-based approach to inflation targeting does much better than the standard interest-rate-based approach in stabilizing output, with no adverse consequences for inflation variability. The second key finding is that, in the interest-rate-based approach, the variability of the interest rate is low while that of the exchange rate is high, whereas in the exchange rate-based approach, the opposite occurs. These results suggest, broadly, that in a very open economy, smoothing the exchange rate rather than interest rates may contribute to reducing output volatility.

Construction of Volatility Tradeoff Frontiers

The volatility trade-off frontiers shown in the main text are constructed as follows:

• For each of the two types of country models, 10 variants of each alternative policy reaction function were constructed, each with a slightly different weighting on the inflation and output objectives, as shown in Table A2.2. The sum of the coefficients on the two objectives was held constant, as were the coefficients on the exchange rate objective and the lagged instrument term.

• Each country model, with each variation of the parameterization of the alternative policy rules, is then simulated in response to each of three kinds of shocks: demand, cost-push, and risk premium shocks.

• Each simulation involves a 200-period run. In each period, the model is subjected to a shock drawn from a normal distribution.¹²¹ For each kind of shock, the 200-period simulation is replicated 50 times.¹²²

• These simulations provide 50 time series with 200 observations for each kind of shock, each policy rule variant, and each of the 29 endogenous variables. Of these, the variables of most interest are inflation, output, the interest rate, the exchange rate, and the current account balance. The standard deviation of the time series for each variable is then computed, between the 100th and 120th observation, and then averaged over each of the 50 replications to produce a representative standard deviation for each variable in response to each kind of shock and policy variant.¹²³