## 1. Gains from Cooperation in the Basic Case for Different Values of mu

## Source details

**Canonical URL:** [1. Gains from Cooperation in the Basic Case for Different Values of mu](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp0401.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp0401.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp0401.pdf.json)

---

### Introduction and objective
- Focus: quantifying gains from international monetary coordination in a dynamic New Open Economy Macroeconomics (NOEM) framework.
- Two policy scenarios evaluated:
  - Decentralized (Nash): each country maximizes its own agents’ welfare taking the other country as given.
  - Coordinated (Cooperative): a centralized policymaker maximizes welfare of both countries together.
- Motivation: reassess Obstfeld and Rogoff (2002) claim that coordination yields trivial gains by building a richer microfounded NOEM model and using a full second-order solution.

### Model structure and key features
- World: two countries, "Home" and "Foreign", with complete asset markets (except insofar as incomplete markets are considered later).
- Goods and sectors:
  - Traded and nontraded differentiated goods produced on unit intervals l∈[0,1] and lN∈[0,1].
  - Homogeneous imported good indexed by lI∈[0,1].
  - Reprocessed imported goods used in domestic production and consumption.
- Consumption and pricing:
  - C_t = C_{T,t}^ξ C_{N,t}^{1−ξ} with (1−ξ) the weight of nontraded goods.
  - Traded goods CES index with elasticity μ>1 between home and foreign goods.
  - Monopolistic competition with Calvo-style staggered price setting: mass (1−κ_H) can reoptimize, κ_H cannot.
  - Fraction s of firms exhibit local currency pricing (LCP); fraction (1−s) exhibit producer currency pricing (PCP).
  - Firms producing nontraded goods: flexible prices.
  - Imported goods marginal cost MC_{F,t} = (1−s)e_t P^*_{F,t} + s P_{F,t}.
- Labor and wages:
  - Households supply differentiated labor; CES labor aggregators with elasticity λ>1.
  - Sticky wages in traded sector with renegotiation probability (1−χ_H); nontraded sector wages flexible.
- Production technologies:
  - Traded good: Y_t(l) = A_{H,t} IM_{F,t}(l)^α L_{H,t}(l)^{1−α}.
  - Nontraded good: Y_{N,t}(lN) = A_{N,t} L_{N,t}(lN).
- Preferences and money:
  - Representative household utility: E_t Σ_{k=0}^∞ β^k [ C(h)_{t+k}^{1−ρ}/(1−ρ) + 1/(1−ε) (μ M_{t+k}(h)/P_{t+k})^{1−ε} − L_{H,t+k}(h)^{1+ψ_H}/(1+ψ_H) − L_{N,t+k}(h)^{1+ψ_N}/(1+ψ_N) ].
  - Inter-temporal discount factor β satisfying 0<β<1.

### Solution method and welfare evaluation
- Uses Sims (2003) second-order accurate solution method; system expanded to second order around steady state Ψ(η, η, 0).
- Solution representation includes second-order terms and quadratic tensors; unconditional moments computed using second-order expansion.
- Loss function derived by second-order Taylor approximation to utility (Woodford (2001) techniques); unconditional expected welfare rearranged as equation (14) with explicit dependence on first and second moments.
- Key conceptual point: first moments of equilibrium variables depend on second moments of shocks; second-order solution required for correct welfare rankings.

### Monetary policy rules (model closure)
- Home money supply rule:
  - M_t = M_A A_{H,t}^{θ1} A_{N,t}^{θ2} A^*_{F,t}^{θ3} A^*_{N,t}^{θ4}.
- Foreign money supply rule:
  - M^*_t = M^*_A A^*_{H,t}^{θ^*_1} A^*_{N,t}^{θ^*_2} A_{F,t}^{θ^*_3} A_{N,t}^{θ^*_4}.
- Authorities respond actively to productivity disturbances in traded and nontraded goods production home and abroad; commitment to these rules assumed.

### Calibration (reasonable calibration)
- ξ = 0.5.
- λ = φ = 7.66.
- ψ = 1.
- β = 0.99.
- Interest-elasticity-of-money-demand inverse (ι) = 4 (i.e., 1/ι = 0.25).
- ρ = ε = 4.
- μ experimented between 1 and 10; sensible assumption μ = 6 in many exercises.
- χH = κH = 0.75 (prices sticky for four periods).
- Steady-state value of imported goods in traded goods consumption index: 0.5.
- Technology shocks: standard deviation = 0.01, persistence = 0.95.

### Experiments and frictions considered
- Baseline: imperfect competition + sticky prices (Obstfeld and Rogoff (2002)–type setup).
- Additional frictions (separately and jointly):
  - Sticky nominal wages.
  - Differential productivity disturbances across traded vs nontraded sectors.
  - Imports used as inputs to domestic production (α denotes share).
  - Combination of producer and local currency pricing; varying s.
  - Non-unitary elasticity of substitution between home and foreign goods (μ≠1).
  - Nonlogarithmic real money balances in utility.
- Shocks: country-specific and global shocks; robustness checks and incomplete asset market variants.

### Main quantitative findings (preserved as stated)
- Non-unitary intratemporal elasticity of substitution (μ>1) gives rise to gains from coordination.
- With local currency pricing and wage rigidities the gains from coordination are nontrivial even with a unitary elasticity μ=1.
- Differential productivity shocks across sectors, nonlogarithmic real money balances, and imports used in production do not lead to cooperation gains with a Cobb-Douglas consumption index.
- When those three factors are combined with a CES consumption index, gains increase relative to the Cobb-Douglas case.
- For a reasonable calibration of parameters, the biggest gains realized are found to be around two percent of steady state consumption.
- Global shocks do not imply coordination failure once multiple inefficiencies are present; gains can arise under predominantly global shocks.
- Incomplete asset markets increase gains from cooperation compared with complete asset markets, though not dramatically.

### Selected numerical results and illustrative statistics
- Basic case (imperfect competition + sticky prices):
  - μ = 1: no gains from coordination.
  - μ = 6: gains can be as high as 0.26 percent of steady state consumption; this gain represents about 15.5 percent of the overall gain from active monetary policy; R = 0.18 (comparable to largest value reported by Obstfeld and Rogoff (2002) for ρ = 8).
  - For higher μ the Nash solution can be welfare-inferior to inactive policy.
- Robustness (μ = 6, ρ = 4): gains ≈ 0.46 percent of steady state consumption and account for about 92 percent of possible gain from active monetary policy in one reported calibration.
- Wage case (sticky wages + sticky prices):
  - With wages and prices sticky for four periods (μ = 1): benefits = 0.35 percent of steady state consumption, about half of overall gain from active stabilization.
  - With μ = 6 and wages/prices sticky four periods: gains ≈ 1.23 percent of steady state consumption and represent 235 percent of the overall gain from active monetary policy.
- Nontraded goods case:
  - Calibrated analog of Canzoneri et al. scenario: traded shock sd = 0.01, nontraded = 0 → gains ≈ 0.02 percent of steady state consumption; R = 0.0586.
  - For ρ = ε = 4, μ = 6 and nontraded shocks more important: gains up to 1.11 percent of steady state consumption and represent 206 percent of overall welfare gain.
- Import case (productive imported inputs; example α = 0.2, γ = 0.5, μ = 6):
  - Welfare gains reach 2.41 percent of steady state consumption and constitute about 81 percent of overall gain from active monetary policy.
  - Sensitivity: gains decrease with lower γ (for fixed α) or lower α (for fixed γ). Importance of α > γ for generating gains.
  - Empirical example γ = 0.2, α = 0.3 → gains ≈ 2.18 percent of steady state consumption and represent close to half of overall welfare benefits.
- Local Currency Pricing (LCP):
  - μ = 1: no gains from cooperation.
  - Increasing s (exchange rate pass-through) generates welfare benefits up to an intermediate s; example s = 0.4 → gains 0.11 percent of steady state consumption and 16.7 percent of overall gain.
  - With full LCP gains equal those with PCP.
  - Selected entries from reported table (unit risk aversion and ι=4, unitary μ unless noted):
    - s: 0 0.2 0.4 0.6 0.8 1.0 0.4(µ=6)
    - W_N − W_I: 0.7817 0.6716 0.5810 0.7274 0.7664 0.8490 0.8988
    - W_C − W_I: 0.7880 0.7366 0.6981 0.7589 0.7780 0.8517 1.1800
    - W_C − W_N: 0.0063 0.0650 0.1171 0.0315 0.0118 0.0027 0.2812
    - R = (W_C − W_N)/(W_N − W_I): 0.0081 0.0968 0.2015 0.0433 0.0154 0.0032 0.3129
    - V = (W_C − W_N)/(W_C − W_I): 0.0080 0.0882 0.1677 0.0415 0.0152 0.0032 0.2383
- Global shocks (perfectly correlated productivity disturbances across countries):
  - Basic price rigidity case: no gains.
  - Wage case: small gains ≈ 0.04 percent of steady state consumption; R and V can be significant.
  - LCP (s=0.4): gains = 0.10 percent of steady state consumption and close to 10 percent of overall welfare gain.
  - Import case: gains present but vanish if μ=1.
  - Nontraded goods case (shocks correlated across countries but not across sectors): gains can reach almost 0.55 percent of steady state consumption and 587 percent of overall gain; if shocks also perfectly correlated across sectors, no gains.
  - Selected Table 8 excerpts (ρ,ε = 4 4 4 4 4; μ = 6 6 6 6 6):
    - Cases: Price, Wage, Trade, Import, LCP
    - W_N − W_I: 0.1285 0.0674 −0.4584 1.1294 0.9878
    - W_C − W_I: 0.1285 0.1088 0.0941 1.2932 1.0898
    - W_C − W_N: 0.0000 0.0414 0.5525 0.1638 0.1020
    - R = (W_C − W_N)/(W_N − W_I): 0.0000 0.6142 −1.2063 0.1450 0.1032
    - V = (W_C − W_N)/(W_C − W_I): 0.0000 0.3855 5.8714 0.1267 0.0935
- Incomplete asset markets:
  - Stationarity achieved by introducing adjustment costs for foreign bond positions: AC_H,t = 1/2 ψ_f ((B_F,t + B_F)/e_t)^2 P*_F,t Y*_t.
  - Gains from coordination are higher with incomplete asset markets but not dramatically so; example basic case gains now account for almost all gains from active monetary policy, namely 98%.
  - Selected Table 9 excerpts (ρ,ε = 4 4 4 4 4; μ = 6 6 6 6 6):
    - Cases: Price, Wage, Trade, Import, LCP
    - W_N − W_I: 0.0145 −0.1134 −0.9866 0.5294 0.9124
    - W_C − W_I: 1.2283 0.5961 0.1161 3.1932 1.4258
    - W_C − W_N: 1.2138 1.7095 1.1027 2.6638 0.5134
    - R = (W_C − W_N)/(W_N − W_I): 83.7101 −15.0749 −1.1176 5.0317 0.5626
    - V = (W_C − W_N)/(W_C − W_I): 0.9881 2.8678 9.4978 0.8324 0.3600

### Mechanisms generating coordination gains
- Non-unitary elasticity μ>1 introduces cross-border substitution effects that make foreign stabilization relevant.
- Wage rigidity and local currency pricing (LCP) create additional nominal frictions that raise the value of coordinated responses.
- Imported inputs in production (α>0) interact with μ>1 to amplify coordination gains; interaction matters more than the presence of imported inputs alone.
- Differential sectoral productivity shocks alter relative supplies and prices, producing gains when combined with CES consumption aggregator.
- Global shocks do not mechanically eliminate gains; model augmentations can sustain nontrivial coordination benefits.

### Policy implications and recommendations
- Individual countries should account for foreign stabilization problems when formulating domestic monetary policies; ignoring foreign stabilization can imply significant welfare losses.
- International monetary policy cooperation can be welfare-improving under realistic model augmentations (wage rigidity, LCP, nontraded sectors, imported productive inputs) and parameter calibrations.
- Incomplete asset markets tend to increase gains from coordination, reinforcing the case for cooperation when international financial frictions exist.
- Second-order solution and welfare evaluation methods are essential for reliable policy ranking; linearization may mis-rank regimes unless restrictive assumptions hold.

### Technical and methodological contributions
- First study to quantify gains from cooperation in a dynamic NOEM model with a complex structure using second-order solution methods.
- Demonstrates constructing a NOEM model where international coordination matters significantly is possible, challenging prior claims of negligible gains.
- Extends Woodford methodology to an open-economy setting using Sims (2003) quadratic-quadratic solution method; shows need for second-order approximations to evaluate country-specific welfare correctly.

*Source: _wp0401 - 1. Gains from Cooperation in the Basic Case for Different Values of mu (PDF chapter/section).*

### 1. Gains from Cooperation in the Basic Case for Different Values of mu...................26

### 1. Gains from Cooperation in the Basic Case for Different Values of mu...................26

### Major themes and sections
- 1. Gains from Cooperation in the Basic Case for Different Values of mu...................26
- 2. Gains from Cooperation in the Basic Case for Different Values of rho and the  
  Inverse of the Interest Elasticity of Real Money Balances (with mu equal to one)..27
- 3. Gains from Cooperation in the Basic Case for Different Values of rho and the  
  Inverse of the Interest Elasticity of Real Money Balances (with mu equal to six)... 28
- 4. Gains from Cooperation in the Wage Case...............................................................29
- 5. Gains from Cooperation in the Nontraded Goods Case............................................30
- 6. Gains from Cooperation in the Import Case..... ........................................................31
- 7. Gains from Cooperation in the Local Currency Pricing Case..... .............................32
- 8. Gains from Cooperation with Global Shocks ...........................................................33
- 9. Gains from Cooperation with Incomplete Asset Markets.........................................34

### Appendices
- Appendix I .........................................................................................................................35
- Appendix II ........................................................................................................................37
- Appendix III...............................................................................................................................38
- Appendix IV........................................................................................................................40

*Source: _wp0401 - 1. Gains from Cooperation in the Basic Case for Different Values of mu...................26 (PDF chapter/section).*

### References..............................................................................................................

### _wp0401 - References..............................................................................................................

### Introduction and objective
- Focus: quantifying gains from international monetary coordination in a dynamic New Open Economy Macroeconomics (NOEM) framework.
- Two policy scenarios evaluated:
  - Decentralized (each country maximizes its own agents’ welfare taking the other country as given).
  - Coordinated (a centralized policymaker maximizes welfare of both countries together).
- Motivation: reassess Obstfeld and Rogoff (2002) claim that coordination yields trivial gains by building a richer microfounded NOEM model and using a full second-order solution.

### Model structure and key features
- World: two countries, "Home" and "Foreign", with complete asset markets.
- Goods and sectors:
  - Traded and nontraded differentiated goods produced on unit intervals l∈[0,1] and lN∈[0,1].
  - Homogeneous imported good indexed by lI∈[0,1].
  - Reprocessed imported goods used in domestic production and consumption.
- Consumption aggregator:
  - C_t = C_{T,t}^ξ C_{N,t}^{1−ξ} with (1−ξ) the weight of nontraded goods.
  - Traded goods CES index with elasticity μ>1 between home and foreign goods.
- Pricing and market structure:
  - Monopolistic competition; Calvo-style staggered price setting with mass (1−κ_H) allowed to reoptimize and κ_H that do not.
  - Fraction s of firms exhibit local currency pricing (LCP); fraction (1−s) exhibit producer currency pricing (PCP).
  - Firms producing nontraded goods: flexible prices.
  - Imported goods marginal cost MC_{F,t} = (1−s)e_t P^*_{F,t} + s P_{F,t}.
- Labor and wages:
  - Households supply differentiated labor; CES labor aggregators with elasticity λ>1.
  - Sticky wages in traded sector with renegotiation probability (1−χ_H); nontraded sector wages assumed flexible.
- Production technologies:
  - Traded good production: Y_t(l) = A_{H,t} IM_{F,t}(l)^α L_{H,t}(l)^{1−α}.
  - Nontraded good production: Y_{N,t}(lN) = A_{N,t} L_{N,t}(lN).
- Preferences and money:
  - Representative household utility: E_t Σ_{k=0}^∞ β^k [ C(h)_{t+k}^{1−ρ}/(1−ρ) + 1/(1−ε) (μ M_{t+k}(h)/P_{t+k})^{1−ε} − L_{H,t+k}(h)^{1+ψ_H}/(1+ψ_H) − L_{N,t+k}(h)^{1+ψ_N}/(1+ψ_N) ].
  - Inter-temporal discount factor β satisfying 0<β<1.
- Market clearing conditions (home and foreign):
  - Y_t = Y_{H,t} + Y^*_{H,t} = C_{H,t} + C^*_{H,t} + IM^*_t.
  - Y^*_t = Y_{F,t} + Y^*_{F,t} = C_{F,t} + C^*_{F,t} + IM_t.
  - Y_{N,t} = C_{N,t}; Y^*_{N,t} = C^*_{N,t}.

### Solution method
- Uses Sims (2003) second-order accurate solution method for dynamic stochastic systems.
- System cast as Ψ(η_t, η_{t−1}, ε_t) + Π(t−1,t) = 0 and expanded to second order around steady state Ψ(η, η, 0).
- Solution representations:
  - y_t = F(y_{t−1}, ε_t), x_t = M(y_t) with second-order expansions including terms F_{1ij}, F_{2ij}, F_{3i}σ^2 and quadratic tensors.
- Unconditional moments computed using second-order expansion; higher-order terms disregarded.

### Monetary policy rules (model closure)
- Home money supply rule:
  - M_t = M_A A_{H,t}^{θ1} A_{N,t}^{θ2} A^*_{F,t}^{θ3} A^*_{N,t}^{θ4}.
- Foreign money supply rule:
  - M^*_t = M^*_A A^*_{H,t}^{θ^*_1} A^*_{N,t}^{θ^*_2} A_{F,t}^{θ^*_3} A_{N,t}^{θ^*_4}.
- Authorities respond actively to productivity disturbances in traded and nontraded goods production home and abroad.
- Assumption: monetary authorities can commit to these rules.

### Scenarios and experiments
- Baseline: model close to Obstfeld and Rogoff (2002) with sticky prices and monopolistic competition in production sector only.
- Additional frictions introduced (separately and jointly) to generate potential coordination gains:
  - Staggered nominal wage contracts by monopolistically competitive households (Erceg, Henderson, Levin (2000) style).
  - Differential productivity disturbances in traded vs nontraded sectors (Canzoneri, Cumby, Diba (2002) suggestion).
  - Imports used as inputs to domestic production rather than directly in consumption (McCallum and Nelson (2001); Clarida, Gali, Gertler (2002) conjecture).
  - Combination of producer and local currency pricing, including intermediate degrees of local currency pricing (Corsetti and Pesenti (2001) qualitative results).
  - Non-unitary elasticity of substitution between home and foreign goods (Benigno (2002) specification).
  - Nonlogarithmic real money balances in utility.
- Experiments conducted for global and country-specific shocks.
- Robustness checks: sensitivity to calibrated parameter values, e.g., case with unit intertemporal elasticity of substitution.

### Main quantitative findings (preserved as stated)
- A non-unitary intratemporal elasticity of substitution gives rise to gains from coordination.
- With local currency pricing and wage rigidities the gains from coordination are nontrivial even with a unitary elasticity of substitution between home and foreign goods.
- Differential productivity shocks across sectors, nonlogarithmic real money balances, and imports used in production do not lead to cooperation gains with a Cobb-Douglas consumption index.
- When the latter three factors are combined with a constant elasticity of substitution consumption index, gains are increased relative to the Cobb-Douglas case.
- For a reasonable calibration of parameters, the biggest gains realized are found to be around two percent of steady state consumption.
- Global shocks do not imply coordination failure once multiple inefficiencies are present; gains from cooperation can arise under predominantly global shocks.
- Incomplete asset market structures increase gains from cooperation compared with complete asset markets, although not dramatically.

### Analytical and methodological contributions
- First study to quantify gains from cooperation in a dynamic NOEM model with a complex structure using second-order solution methods.
- Demonstrates that constructing a NOEM model where international coordination matters significantly is possible, challenging Obstfeld and Rogoff (2002).
- Argues that a quadratic-quadratic approach (quadratic approximation of the utility evaluated by a quadratic approximation of equilibrium conditions) is needed for strategic open-economy policy analysis; linearization alone may mis-rank policy regimes unless restrictive assumptions (per Woodford (2001)) hold.
- Emphasizes that second-order solution techniques (Sims (2003); Schmitt-Grohe and Uribe (2001); Sutherland (2002a)) enable correct construction and evaluation of country-specific welfare functions.

### Policy implications and interpretation
- Welfare losses from purely self-oriented monetary rules might be substantial enough to warrant considering cooperation.
- The presence of multiple inefficiencies implies that optimal domestic monetary policy may involve some price stickiness; centralized and decentralized solutions can diverge, creating scope for beneficial coordination.
- Although some previous theoretical results suggest negligible gains from coordination, richer NOEM specifications and second-order welfare evaluation can uncover economically meaningful gains.
- The paper does not undertake design of individual objective functions that implement cooperative equilibria in Nash solutions, noting such implementations are restrictive and may not coincide with actual country welfare in richer frameworks.

### Paper organization (as stated)
- Section breakdown:
  - I. INTRODUCTION
  - II. A GENERAL TWO-COUNTRY MODEL
  - Section 3: derives the welfare loss functions.
  - Section 4: describes the game.
  - Section 5: discusses the results.
  - Section 6: concludes.

*Source: _wp0401 - References..............................................................................................................*

### Appendix IV shows how this can be done.

### _wp0401 - Appendix IV shows how this can be done.

### III. LOSS FUNCTION
- The loss function is derived using a second-order Taylor approximation to the utility function of the representative consumer and techniques described by Woodford (2001).
- Representative-agent per-period utility (equation (12)):
  - Wt = μ C1−ρt/(1−ρ) − ∫0 1 LH,t(h)1+ψH/(1+ψH) dh − ∫0 1 LN,t(h)1+ψN/(1+ψN) dh
- Appendix I yields the second-order approximation (equation (13)) containing:
  - Terms in bCt, bLH,t, bLN,t and their second moments.
  - Cross-sectional dispersions varh[bLH,t(h)] and varh[bLN,t(h)].
  - An O(||ξ||3) remainder.
- Key conceptual points:
  - Calculating expected first moments of bCt, bLH,t, bLN,t is problematic because equilibrium depends on variances of productivity shocks; thus first moments depend on second moments (following Obstfeld and Rogoff (1998)).
  - Woodford (2001) eliminates first-order terms by introducing a subsidy that removes monopolistic distortions, enabling a linear-quadratic framework; but in open economies achieving a first-best steady state is more challenging.
  - Benigno and Benigno (2003a) show monopolistic distortions may need a positive setting in open economies due to coexisting deflationary and inflationary biases.
  - A second-order approximation of equilibrium conditions (Sims (2003) sense) allows expansion around a steady state not necessarily close to the first-best and retains the role of monopolistic competition linked to sticky prices.
- Rearranged unconditional expectation of welfare (equation (14)):
  - E(Wt − W) / C1−ρ = E bCt − φ1N E(bYN,t − bAN,t) − φ1H E(bYt − bAH,t − α[IMt) + 1/2 (1−ρ) E bC2t − φ2N E(bYN,t − bAN,t)2 − φ2H E(bYt − bAH,t − αdIMt)2 − φ3H E(π2H) − φ4H E[ω2H] + O(||ξ||3)
- Interpretation (equation (15)):
  - Loss increases with variances of price and wage inflation, variances of technology shocks, and variance of consumption (provided ρ>1).
  - Loss depends on first moments of consumption and technology shocks; first-row terms are usually eliminated by a production subsidy.

### IV. OPTIMAL COOPERATIVE AND NASH MONETARY POLICY
- Policy definitions:
  - Cooperative: monetary authorities choose θ1−θ4 and θ*1−θ*4 in money supply rules (11) and (12) to maximize joint welfare E(Vt) = 1/2 E(Wt − W) + 1/2 E(W*t − W*).
  - Nash: each policymaker chooses its money rule parameters to maximize its own loss taking the other's policy as given.
- Numerical solution algorithm:
  - Cooperative: start with initial θ parameters, solve model, compute first and second unconditional moments of vector ηt via (9) and (10), evaluate joint welfare, then numerically search for parameters that maximize joint welfare.
  - Nash: iterate optimization—home chooses θ1−θ4 given foreign θ*1−θ*4 to maximize E(Wt − W); foreign then chooses θ* given home; iterate until convergence.

### V. RESULTS — Overview and Reporting Conventions
- Table row meanings (first three rows reported in all tables):
  - Row 1: gains from pursuing active Nash monetary policy relative to inactive (constant money supply; response coefficients set to zero).
  - Row 2: welfare benefits from active coordinated policy relative to inactive monetary policy.
  - Row 3: difference between coordinated and Nash optimal policies.
  - Row 4: ratio of row 3 to row 1 (importance of coordination relative to stabilization gains; analogous to Obstfeld and Rogoff (2002)).
  - Row 5: gains from coordination relative to overall gains from active monetary policy (comparable to Sutherland (2002b)).
- Note: E(π2H) is retained (usually written as var(π2H) since E(πH) is second-order).

### A. Calibration
- Parameter choices labeled "reasonable calibration":
  - ξ = 0.5 (relative weight of traded goods).
  - Degree of monopolistic competition in goods and wage sectors: λ = φ = 7.66.
  - Inverse of elasticity of labor supply: ψ = 1.
  - Discount factor: β = 0.99.
  - Interest-elasticity-of-money-demand inverse (ι): reasonable calibration ι = 4 (i.e., 1/ι = 0.25).
  - Set ρ = ε = 4 (empirical studies estimate income elasticity of real money demand ρ/ι ≈ 1).
  - Elasticity of substitution between home and foreign goods μ: experiments between 1 and 10; sensible assumption μ = 6 in many exercises.
  - Price stickiness parameters: χH = κH = 0.75 (prices sticky for four periods).
  - Steady-state value of imported goods in traded goods consumption index: 0.5 (sensitivity analysis performed).
  - Technology shocks: standard deviation = 0.01, persistence = 0.95.

### B. Basic Case (imperfect competition + sticky prices)
- Setup: two inefficiencies only—imperfect competition and sticky prices; similar to Obstfeld and Rogoff (2002) but without traded goods.
- Main findings:
  - When μ = 1 there are no gains from coordination (domestic Nash policy can achieve objectives without foreign help).
  - Increasing μ generates gains from coordination (consistent with Benigno (2002) and Sutherland (2002b)).
  - For μ = 6 (reasonable calibration), gains can be as high as 0.26 percent of steady state consumption.
    - This gain represents about 15.5 percent of the overall gain from active monetary policy.
    - R = 0.18 (comparable to largest value reported by Obstfeld and Rogoff (2002) for ρ = 8).
  - For higher values of μ the Nash solution can be welfare-inferior to inactive monetary policy.
- Robustness (Table 2):
  - Varying ρ and ε with μ = 1 shows negligible gains from coordination for higher ρ and ε.
  - Confirms basic results are robust to non-log real balances in utility.
- Further parameter combinations (Table 3):
  - For μ = 6 and ρ = 4 gains ≈ 0.46 percent of steady state consumption and account for about 92 percent of possible gain from active monetary policy.

### C. Wage Case (sticky wages + sticky prices)
- Setup: introduce sticky wages in addition to sticky prices.
- Main findings:
  - Even with μ = 1, introducing sticky wages creates additional friction and yields non-trivial gains from coordination.
  - Example: wages rigid for four periods and prices sticky for four periods → benefits = 0.35 percent of steady state consumption, about half of overall gain from active stabilization.
  - As wage stickiness increases, welfare gains increase.
  - In some parameterizations inactive monetary policy may deliver higher welfare than Nash policy (Nash frictions severe enough that non-response is preferable).
  - With CES consumption index μ = 6 and prices and wages inflexible for four periods, gains rise to about 1.23 percent of steady state consumption and represent 235 percent of the overall gain from active monetary policy.
- Conceptual note:
  - Monetary authorities must trade off price and wage stickiness jointly to minimize welfare loss.
  - The wage case shows Cobb-Douglas consumption index need not preclude sizable gains from cooperation.

### D. Nontraded Goods Case
- Context: relates to the "Workhorse model" and Canzoneri and others (2002) conjectures.
- Scenarios considered (per Canzoneri et al.):
  - Scenario 1: shocks to traded goods sectors more important than nontraded → reported R = 1/15 in their analysis.
  - Scenario 2: shocks to nontraded goods more important → reported R = 1/3 in their analysis.
  - Scenario 3 (not considered here): shocks to export sector dominant → R = ∞ in their analysis.
- Results (Table 5):
  - Calibrated scenario: standard deviations of traded shock = 0.01, nontraded = 0 (scenario 1 analog) → small welfare gains ≈ 0.02 percent of steady state consumption; R = 0.0586 (3.5 times smaller than Canzoneri et al. (2002) reported).
  - Scenario 2 analog (nontraded shocks std = 0.01, traded = 0) → no gains from coordination.
  - Conclusion: presence of nontraded shocks alone does not necessarily add frictions for the "Workhorse" calibration; contrasts with Canzoneri et al. (2002) and suggests static models may miss dynamic features.
  - For reasonable calibration ρ = ε = 4 and μ = 6, if nontraded shocks are more important, gains from cooperation can be as high as 1.11 percent of steady state consumption and represent 206 percent of overall welfare gain.
- Empirical note:
  - Canzoneri, Cumby, and Diba (1999) find evidence that stochastic properties of shocks to traded and nontraded sectors differ.

### E. Import Case (imported inputs in production)
- Motivation: Clarida et al. (2002) and McCallum and Nelson (2001) considerations; α denotes steady-state share of imported goods in production; γ denotes steady-state value of imported goods in consumption.
- Findings (Table 6):
  - With μ = 1 there are no gains from coordination (column 1).
  - Example calibration: μ = 6, α = 0.2, γ = 0.5 → welfare gains reach 2.41 percent of steady state consumption and constitute about 81% of overall gain from active monetary policy.
  - Sensitivity:
    - For given α (or γ), gains decrease with decrease of γ (or α).
    - Importance of imported goods in production (α) appears larger than imported goods in consumption (γ) for generating gains.
  - Empirically relevant example: γ = 0.2 and α = 0.3 → gains ≈ 2.18 percent of steady state consumption and represent close to half of overall welfare benefits.
- Conceptual implication:
  - Mere presence of imported inputs is not sufficient; interaction with intratemporal elasticity μ > 1 is critical for large coordination gains.

*Source: _wp0401 - Appendix IV shows how this can be done.*

### introduction of productive imported inputs in production is not an independent source of gains

### introduction of productive imported inputs in production is not an independent source of gains

### Local Currency Pricing Case (LCP)
- Framework and parameterization:
  - s denotes the fraction of firms that set their prices in the currency of the foreign consumer.
  - μ denotes the elasticity parameter; results shown for μ=1 and μ=6 in Table 7.
- Main findings:
  - When μ=1, there are no gains from cooperation (replicating the PCP familiar result).
  - Increasing the degree of exchange rate pass-through (s) leads to welfare benefits.
  - Example: when s=0.4 the gains are 0.11 % of steady state consumption and also 16.7 % of the overall gain.
  - Raising s further reduces the gains and with full LCP the gains are identical to those with PCP.
  - Table 7 reports gains for a CES consumption index with μ=6.
- Quantitative table excerpts (from Table 7, with coefficient of risk aversion and inverse of the interest elasticity of real money balances equal to 4, and unitary elasticity between home and foreign goods):
  - s: 0 0.2 0.4 0.6 0.8 1.0 0.4 (last is µ=6 case column label)
  - W_N - W_I: 0.7817 0.6716 0.5810 0.7274 0.7664 0.8490 0.8988
  - W_C - W_I: 0.7880 0.7366 0.6981 0.7589 0.7780 0.8517 1.1800
  - W_C - W_N: 0.0063 0.0650 0.1171 0.0315 0.0118 0.0027 0.2812
  - Ratios:
    - R = (W_C − W_N) / (W_N − W_I): 0.0081 0.0968 0.2015 0.0433 0.0154 0.0032 0.3129
    - V = (W_C − W_N) / (W_C − W_I): 0.0080 0.0882 0.1677 0.0415 0.0152 0.0032 0.2383

### Gains from Coordination with Global Shocks
- Setup:
  - Global productivity shocks introduced by assuming home and foreign productivity disturbances are perfectly correlated.
  - Cases considered: Price rigidities, Wage rigidities, Trade (nontraded), Import, LCP (s=0.4 in reported LCP case).
- Main findings:
  - In the basic case with only prices rigid there are no gains (consistent with Obstfeld and Rogoff (2002)).
  - Wage case: small gains from coordination ~0.04 % of steady state consumption, but relative magnitudes (R and V) can be significant.
  - LCP case (s=0.4): gains reach 0.10 % of steady state consumption and are close to 10 % of the overall welfare gain.
  - Import case: gains present but vanish if μ=1.
  - Nontraded goods case: largest gains; assuming shocks to traded and nontraded sectors are perfectly correlated across countries but not across sectors, gains can reach almost 0.55 % of steady state consumption and 587 % of the overall gain. If shocks were perfectly correlated across sectors as well, there would be no gains from coordination.
- Quantitative table excerpts (Table 8, ρ,ε = 4 4 4 4 4; μ = 6 6 6 6 6):
  - Cases: Price, Wage, Trade, Import, LCP
  - W_N - W_I: 0.1285 0.0674 −0.4584 1.1294 0.9878
  - W_C - W_I: 0.1285 0.1088 0.0941 1.2932 1.0898
  - W_C - W_N: 0.0000 0.0414 0.5525 0.1638 0.1020
  - R = (W_C − W_N)/(W_N − W_I): 0.0000 0.6142 −1.2063 0.1450 0.1032
  - V = (W_C − W_N)/(W_C − W_I): 0.0000 0.3855 5.8714 0.1267 0.0935

### Gains from Coordination with Incomplete Asset Markets
- Modeling adjustments:
  - Equation (2) rewritten to include home and foreign bond positions and an adjustment cost for buying foreign bonds: AC_H,t = 1/2 ψ_f ((B_F,t + B_F)/e_t)^2 P*_F,t Y*_t to induce stationarity and eliminate the unit root in the first-order solution.
  - Home and foreign bonds are one-period risk-free securities paying gross nominal rates of (1 + i_{t-1}) and (1 + i^*_{t-1}).
  - Second-order solution not obtainable without stationarity-inducing adjustment costs.
- Main findings:
  - Gains from coordination are higher with incomplete asset markets but not dramatically so.
  - Example: in the basic case gains from cooperation now account for almost all gains from pursuing active monetary policy, namely 98%.
- Quantitative table excerpts (Table 9, ρ,ε = 4 4 4 4 4; μ = 6 6 6 6 6):
  - Cases: Price, Wage, Trade, Import, LCP
  - W_N - W_I: 0.0145 −0.1134 −0.9866 0.5294 0.9124
  - W_C - W_I: 1.2283 0.5961 0.1161 3.1932 1.4258
  - W_C - W_N: 1.2138 1.7095 1.1027 2.6638 0.5134
  - R = (W_C − W_N)/(W_N − W_I): 83.7101 −15.0749 −1.1176 5.0317 0.5626
  - V = (W_C − W_N)/(W_C − W_I): 0.9881 2.8678 9.4978 0.8324 0.3600

### Broader Quantitative Results Across Model Variants (selected table highlights)
- Basic case (Table 1): gains from Nash active versus inactive and coordinated versus inactive shown for different μ (1,2,4,6,8,10) with logarithmic consumption and real money balances. Example figures:
  - For μ=1: W_N - W_I = 0.8112; W_C - W_I = 0.8112; W_C - W_N = 0.0000; R = 0; V = 0.
  - For μ=6: W_N - W_I = 0.1190; W_C - W_I = 0.6208; W_C - W_N = 0.5018; R = 4.2168; V = 0.8083.
- Sensitivity to preference and money demand parameters (Tables 2 and 3): variations in the coefficient of risk aversion and inverse interest elasticity of real money balances affect absolute gains and ratios R and V; negative and positive gains appear depending on parameter combination.
- Wage stickiness (Table 4): gains vary substantially with the number of periods wages are sticky (0,4,6,8,10,104) for μ = 1 and μ = 6; W_C - W_N can exceed 1.0 for some calibrations.
- Nontraded goods case (Table 5): gains depend on sd(traded goods shock) and sd(nontraded goods shock) combinations and can be large or undefined (n.a.) for certain parameterizations.
- Import case (Table 6): with μ=6 and various steady-state shares of processed goods (γ) and output process share (α), W_N - W_I, W_C - W_I, and W_C - W_N can be sizable; example first column (γ=0.5, α=0.2): W_N - W_I = 2.6523; W_C - W_I = 2.6635; W_C - W_N = 0.0112; R = 0.0042; V = 0.0042.

### Mechanisms and Model Contributions
- Key mechanisms generating coordination gains:
  - More empirically relevant calibration of the intratemporal elasticity of substitution between home and foreign goods (μ) can generate welfare benefits.
  - Rigidity in real wages or local currency pricing can give rise to gains even with a Cobb-Douglas consumption index.
  - Trade-offs in the Phillips curves, differential productivity shocks across sectors, and imported goods as productive inputs can magnify gains.
  - Presence of global shocks is not in itself sufficient to eliminate coordination gains; under realistic augmentations gains can emerge even for global shocks.
- Methodological contribution:
  - Extension of the Woodford methodology to an open-economy setting using the Sims (2003) quadratic-quadratic solution method, allowing richer environments and strategic analysis of optimal monetary policy.

### Policy implications and recommendations
- Individual countries should account for foreign stabilization problems when formulating domestic monetary policies; ignoring foreign stabilization can imply significant welfare losses.
- International monetary policy cooperation can be welfare-improving under realistic model augmentations (wage rigidity, LCP, nontraded sectors, imported productive inputs) and parameter calibrations.
- Incomplete asset markets tend to increase the gains from coordination (though not always dramatically), reinforcing the case for cooperation in environments where international financial frictions exist.

### Technical notes from appendices (method and solution details)
- Stationarity with incomplete asset markets is achieved by introducing adjustment costs for foreign bond positions to eliminate unit roots and allow second-order approximations.
- Variance expressions and second-order approximations are derived for labor aggregators, wage dispersion, and price-setting under Calvo pricing; representative expressions include:
  - var_h(logL_H,t(h)) = λ^2 var_h(logW_H,t(h)). (B.1)
  - Recursive definitions for price-setting state variables F_t and G_t and the timing (t−1,t) cast of Calvo optimal price equations: P_new_H,t = φ/(φ−1) F_t / G_t. (D.6)
- Second-order expansions link aggregate labor and production variables with cross-sectional variances (see Appendices I–III for full derivations and the exact functional forms).

*Italic: Source: _wp0401 - introduction of productive imported inputs in production is not an independent source of gains (IMF working paper PDF content provided).*

### References

### _wp0401 - References

### Monetary policy, exchange rates, and open-economy frameworks
- Benigno, Gianluca, and Pierpaolo Benigno, 2000, “Monetary Policy Rules and the Exchange Rate,” (unpublished; Berkeley: UC Berkeley; New Jersey: Princeton University).
- ———, 2003a, “Price Stability in Open Economies,” Review of Economic Studies, Vol. 70(4) No. 245, pp. 743–764.
- ———, 2003b, “Designing Targeting Rules for International Monetary Cooperation,” (unpublished; London: Bank of England; New York: New York University).
- Benigno, Pierpaolo, 2001, “Price Stability with Imperfect Financial Integration,” (unpublished; New York, New York: New York University).
- Benigno, Pierpaolo, 2002, “A Simple Approach to International Monetary Policy Coordination,” Journal of International Economics, Vol. 57, No. 1, pp. 177–96.
- Clarida, Richard, Jordi Gali, and Mark Gertler, 2002, “A Simple Framework for International Monetary Policy Analysis, Journal of Monetary Economics, Vol. 49, pp.879–904.
- Devereux, M., and Charles Engel, 2000, “Monetary Policy in Open Economy Revisited: Price Setting  and Exchange Rate Flexibility,” NBER Working Paper No. 7655 (Cambridge, Massachusetts: National Bureau of Economic Research).
- McCallum, B., and E. Nelson, 2001, “Monetary Policy for an Open Economy: an Alternative Framework with Optimizing Agents and Sticky Prices,” NBER Working Paper No. 8175 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Kollmann, Robert, 2002, “Monetary Policy in the Open Economy: Effects on Welfare and Business Cycles,” Journal of Monetary Economics, Vol.49, pp. 989–1015.
- Smets, Frank, and Raf Wouters, 2002, “Openness, Imperfect Exchange Rate Pass-through and Monetary Policy,” ECB Working Paper No. 128 (Frankfurt, Germany: European Central Bank).
- Pappa, Evi, 2002, “Should the ECB and the FED Cooperate? Optimal Monetary Policy in a Two-Country World,” (unpublished; London: London School of Economics and Political Science).
- Obstfeld, M., and K. Rogoff, 1995, “Exchange Rate Dynamics Redux,” Journal of Political Economy, Vol. 103, pp. 624–60.
- Obstfeld, M., and K. Rogoff, 1998, “Risk and the Exchange Rate,” NBER Working Paper No. 6694 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Obstfeld, M., and K. Rogoff, 2002, “Global Implications of Self-oriented National Rules,” Quarterly Journal of Economics, Vol. 117, pp. 503–35.
- Goodfriend, M., and Robert King, 2000, “The Case for Price Stability,” (unpublished; Virginia: FRB of Richmond; Massachusetts: Boston University).
- Woodford, Michael, 1996, “Control of the Public Debt: a Requirement for Price Stability,” NBER Working Paper No. 5684 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Woodford, Michael, 2001, “Inflation Stabilization and Welfare,” NBER Working Paper No. 8071 (Cambridge, Massachusetts: National Bureau of Economic Research).

### International policy coordination, game-theoretic approaches, and model uncertainty
- Canzoneri, Matthew, and JoAnna Gray, 1985, “Monetary Policy Games and the Consequences of Noncooperative Behavior,” International Economic Review, Vol. 26, No. 3, pp. 547–64.
- Canzoneri, Matthew, and Dale Henderson, 1991, "Noncooperative Monetary Policies in Interdependent Economies" (Cambridge: MIT Press).
- Canzoneri, Matthew, Robert Cumby, and Behzad Diba, 1999, “Relative Labor Productivity and the Real Exchange Rate in the Long Run: Evidence for a Panel of OECD Countries,” Journal of International Economics, Vol. 47, pp. 246–65.
- Canzoneri, 2002, “The Need for International Policy Coordination: What's Old, What's New, What's Yet to Come?” (unpublished; Washington, DC: Georgetown University).
- Ghosh, J., and P. Masson, 1988, “International Policy Coordination in a World with Model Uncertainty,” IMF Staff Papers, Vol. 35 (Washington, DC: International Monetary Fund).
- ———, 1991, “Model Uncertainty, Learning and the Gains from Coordination,” American Economic Review, Vol. 81.
- ———, 1994, “Economic Cooperation in an Uncertain World,” (Cambridge, Massachusetts: Blackwell).
- Hamada, Koichi, 1974, “Alternative Exchange Rate Systems and the Interdependence of Monetary Policies,” in National Monetary Policies and the International Financial System, ed. by Robert Aliber (Chicago: University of Chicago Press).
- Hamada, Koichi, 1976, “A Strategic Analysis of Monetary Interdependence,” Journal of Political Economy, Vol. 84, No. 4, pp. 677–700.
- Hamada, Koichi, 1979, “Macroeconomic Strategy and Coordination under Alternative Exchange Rates,” in International Economic Policy: Theory and Evidence, ed. by R. Dornbusch and J. Frenkel  (Baltimore: John Hopkins University Press).
- Oudiz, Gilles, and J. Sachs, 1984, “Macroeconomic Policy Coordination Among the Industrial Economies,” Brookings Papers on Economic Activity, Vol. 1 (Washington, DC: The Brookings Institution Press).
- Oudiz, Gilles, and J. Sachs, 1985, "International Policy Coordination in Dynamic Macroeconomic Games," ed. by M. Buiter and R. Marston.
- Rogoff, Kenneth, 1985, “Can International Monetary Cooperation be Counterproductive?” Journal of International Economics, Vol. 18, pp. 199–217.
- Buiter, M., and Richard Marston, 1985, ed., "International Economic Policy Coordination" (Cambridge: Cambridge University Press).
- McKibbin, W., 1997, “Empirical Evidence on International Economic Policy Coordination,” in Handbook of Comparative Economic Policies, Vol.5, ed. by M. Fratianni, D. Salvatore, and J. Von Hagen (Westport: Greenwood Press).
- Cooper, Richard, 1968, The Economics of Interdependence (New York: McGraw-Hill), pp. 157–58.
- Ghosh and Masson works listed above on model uncertainty and gains from coordination.

### Price setting, sticky prices, nominal rigidities, and microfoundations
- Calvo, G., 1983, “Staggered Price Setting in a Utility-maximising Framework,” Journal of Monetary Economics, Vol. 12, pp. 983–98.
- Christiano, Lawrence J., M. Eichenbaum, and C. Evans, 1997, “Sticky Price and Limited Participation Models of Money: A Comparison,” European Economic Review, Vol. 41, pp. 1201–249.
- Christiano, Lawrence J., M. Eichenbaum, and C. Evans, 2001, “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy,” NBER Working Paper No. 8403 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Erceg, C., Dale Henderson, and Andrew Levin, 2000, “Optimal Monetary Policy with Staggered Wage and Price Contracts,” Journal of Monetary Economics, Vol. 46, pp. 281–313.
- Fuhrer, J., 1997, “A Comment on Optimization Based Econometric Framework for the Evaluation of Monetary Policy,” NBER Macroeconomics Annual 1997 (Cambridge, Massachusetts: MIT Press).
- Fuhrer, J., 2000, “Habit Formation in Consumption and its Implications for Monetary Policy Models,” American Economic Review, Vol. 90, pp. 367–90.
- Rotemberg, J., and M. Woodford, 1998, “An Optimization-based Econometric Framework for the Evaluation of Monetary Policy,” in NBER Macroeconomic Annual, ed. by B. Bernanke and J. Rotemberg (Cambridge: MIT Press).
- Yun, Tack, 1996, “Nominal Price Rigidity, Money Supply Endogeneity and Business Cycles,” Journal of Monetary Economics, Vol. 37, pp. 345–70.
- Chari, V.V., Patrick Kehoe, and Ellen McGrattan, 1998, “Can Sticky Price Models Generate Volatile and Persistent Real Exchange Rates?” Staff Report No. 223, (December) (Minneapolis: Federal Reserve Bank of Minneapolis).
- Dotsey, M., Robert King, and A. Wolman, 1999, “State Dependent Pricing and the Dynamics of Business Cycles,” Quarterly Journal of Economics, Vol. 114, pp. 655–90.
- Gali, Jordi, Mark Gertler, and J. David Lopez-Salido, 2002 “Markups, Gaps, and the Welfare Costs of Business Fluctuations,” NBER Working Paper No. 8850 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Devereux and Engel work listed above on price setting and exchange rate flexibility.

### Welfare, gains from trade, risk-sharing, and real exchange rates
- Bergin, Paul, and Ivan Tchakarov, 2003, “Does Exchange Rate Risk Matter for Welfare? A Guantitative Investigation,” NBER Working Paper No. 9900 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Canzoneri, Cumby, and Diba, 1999, “Relative Labor Productivity and the Real Exchange Rate in the Long Run: Evidence for a Panel of OECD Countries,” Journal of International Economics, Vol. 47, pp. 246–65.
- Cole, H., and M. Obstfeld, 1991, “Commodity Trade and International Risk Sharing: How Much do Financial Markets Matter?” Journal of Monetary Economics, Vol. 28.
- Trefler, D., and H. Lai, 1999, “The Gains from Trade: Standard Errors with the CES Monopolistic Competition Model,” (unpublished; Toronto, Canada: University of Toronto).
- Rogoff, Kenneth, 1985, “Can International Monetary Cooperation be Counterproductive?” Journal of International Economics, Vol. 18, pp. 199–217.
- Sutherland, Alan, 2002b, “International Monetary Policy Coordination and Financial Market Integration,” (unpublished; Fife, Scotland: University of St. Andrews).

### Model solution methods, numerical techniques, and second-order approximations
- Scmitt-Grohe, S., and Martin Uribe, 2001, “Solving Dynamic General Equilibrium Models Using a Second-order Approximation to the Policy Function,” CEPR Discussion Paper No. 2963 (London: Centre for Economic Policy Research).
- ———, 2002, “Closing Small Open Economy Models,” NBER Working Paper 9270 (Cambridge, Massachusetts: National Bureau of Economic Research).
- Sims, C., 2003, “Second-order Accurate Solution of Discrete Time Dynamic Equilibrium Models,” (unpublished; Princeton, New Jersey: Princeton University).
- Sutherland, Alan, 2002a, “A Simple Second-order Solution Method for Dynamic General Equilibrium Models,” (unpublished; Fife, Scotland: University of St. Andrews).
- Smets and Wouters, 2002, “Openness, Imperfect Exchange Rate Pass-through and Monetary Policy,” ECB Working Paper No. 128 (Frankfurt, Germany: European Central Bank).
- Christiano, Eichenbaum, and Evans works listed above on dynamic effects and nominal rigidities.

### Other theoretical and empirical contributions cited
- Bryant, Ralph, 1993, Evaluating Policy Regimes: New Research in Empirical Macroeconomics (Washington, DC: The Brookings Institution Press).
- Dixit, A., and J. Stiglitz, 1977, “Monopolistic Competition and Optimum Product Diversity,” American Economic Review, Vol. 67, pp. 297–308.
- Hall, Robert, 1988, “Intertemporal Substitution in Consumption,” Journal of Political Economy, Vol. 96, No. 2, pp. 339–57.
- Hansen, G., 1985, “Indivisible Labor and the Business Cycle,” Journal of Monetary Economics, Vol. 16, pp. 309–27.
- Harrigan, J., 1976, “OECD Imports and Trade Barriers in 1983,” Journal of International Economics, Vol. 35, pp. 91–112.
- Kim, Jinill, and Sunghyun Kim, 1999, “Spurious Welfare Reversals in International Business Cycles Models,” forthcoming, Journal of International Economics.
- Mankiw, N. Gregory, and Lawrence H. Summers, 1986, “Money Demand and the Effects of Fiscal Policies,” Journal of Money, Credit and Banking, Vol. 18, pp. 415–29.
- McCallum and Nelson, 2001, works listed above on open-economy monetary policy.
- Weerapana, Akila, 2000, “The Performance of Monetary Policy Rules in a Backward Looking Model of the U.S. and the EMU,” (unpublished; Wellesley, Massachusetts: Wellesley College).
- Rotemberg and Woodford, 1998, work listed above on optimization-based econometric frameworks.
- Chari, Kehoe, and McGrattan, 1998, Staff Report No. 223 (Minneapolis: Federal Reserve Bank of Minneapolis).

*References list from _wp0401 - References*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp0401.pdf_