## 6.  Comparing Impulse Responses

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---

### Major conclusion
- Central finding: tight management of the exchange rate through sterilized foreign exchange purchases/sales greatly enhances the viability of forward-looking IT.
- Exchange-rate-anchored IT delivers strongly positive, complementary results for:
  - targeting efficiency (actual inflation outcomes track targets better),
  - uniqueness of the equilibrium path (determinacy).
- Policy implication: successful IT in many LDCs requires two nominal anchors secured by two instruments (interest rate + sterilized FX interventions).

### Determinacy: managed vs. floating exchange rate regimes
- Criterion: monetary and exchange rate policies should guarantee determinacy – a unique equilibrium (Woodford, 2003).
- Flexible (pure) float:
  - IT incurs a high risk of indeterminacy; rules that target future inflation are subject to an upper bound on the Taylor coefficient.
  - The upper bound on the Taylor coefficient is much smaller than in the canonical closed-economy model.
  - The lower bound on the Taylor coefficient is often substantially above unity.
  - Result: the determinacy region is generally small and, in some important cases, non-existent.
- Mechanisms behind indeterminacy under floating rates:
  - Large flex-price tradables sector in small open LDCs reduces the upper bound on the Taylor coefficient.
  - Higher expected inflation spurs substitution away from domestic currency toward foreign currency; in a flexible exchange rate system, this causes spot depreciation and an upward jump in the real exchange rate, creating inflationary pressure in the sticky-price nontradables sector.
  - Easy substitution between domestic and foreign bonds alleviates pressure on the exchange rate but sharply reduces the upper bound on the Taylor coefficient. Sunspot equilibria can arise at ordinary Taylor coefficients (e.g., 1.5).
  - Finding the appropriate Taylor coefficient becomes akin to "guessing right" because policy makers do not know exact parameter values.
- Exchange-rate management (second instrument):
  - Pegging the real exchange rate via sterilized purchases/sales of foreign exchange restores the Taylor principle: active policy is necessary and sufficient for a unique equilibrium provided the coefficient on the inflation target does not exceed a large upper bound.
  - Pegging the rate of crawl of the currency at the target inflation rate and leaning against the wind in a managed float also produce well-behaved determinacy properties.
  - Targeting the real exchange rate directly in the interest-rate rule is not sufficient: sunspot equilibria remain a significant threat unless accompanied by FX intervention.

### Targeting efficiency and impulse responses
- Criterion: small inflation shocks should not escalate into much larger realized inflation increases.
- Under regimes that stabilize only the real exchange rate or that allow wide nominal exchange rate fluctuations (pure or lightly managed floats):
  - Impulse responses display large, erratic fluctuations in currency depreciation and frequent wide misses of the inflation target.
  - Example from simulations: quarterly rates of currency depreciation and inflation can jump from 1% to 4-6% following a shock that directly raises inflation by only a half percentage point.
- Under exchange-rate-anchored IT (peg the rate of currency depreciation or tightly managed float with strong leaning):
  - Active monetary policy suppresses inflationary shocks as expected; the problem of large erratic impulse responses disappears.
  - Conclusion reiterated: in LDCs, successful IT typically requires two nominal anchors and two instruments.

### Model structure and key features underlying results
- Framework: two-sector small open economy model with imperfect substitution between domestic and foreign financial assets; tradables (flex-price) and nontradables (Calvo sticky-price/New Keynesian).
- Private sector divides financial wealth among domestic bonds, domestic currency, foreign currency, and foreign bonds/loans.
  - Foreign currency provides liquidity services; purchases of foreign bonds/loans incur transaction costs (so uncovered interest parity does not bind).
- Central bank controls the path of the interest rate; sterilized FX interventions provide a second instrument.
- Liquidity services modeled as a CES aggregate of real holdings of domestic and foreign currency; elasticity of substitution between currencies denoted by parameter  (with  required for Edgeworth substitutability).
- Portfolio adjustment costs for foreign bond holdings captured by parameter Λ; small Λ implies elastic capital flows and domestic interest rates close to foreign rates, while large Λ (as in low-income countries) implies larger spreads and more variable domestic interest rates.
- Time is discrete; results also hold in continuous time.

### Representative equilibrium conditions (high-level)
- Consumption and Euler condition:
  - C^{-1/}_t =  R_t / _{t+1} C^{-1/}_{t+1}
- Sectoral marginal rate of substitution and real wage:
  - (η_i Λ_{s i,t}^{1/} C^{-1/}_t) = ω_{i,t}/P_t, for i = n, x.
- Currency and bond return relations (schematic):
  - Γ_F(...) =  C^{-1/}_{t+1} (P_t/P_{t+1})(R_t/^e_{t+1} − 1)
  - Γ_μ(...) =  C^{-1/}_{t+1} R_t^{-1} / _{t+1}
  - R_t = R^*_t ^e_{t+1} / (1 + Λ(β^*_t − β̄^*))

### Policy takeaways
- Relying solely on an interest-rate rule that lets the exchange rate float exposes LDCs practicing forward-looking IT to significant indeterminacy and large impulse-response volatility.
- Introducing a second instrument—sterilized foreign exchange purchases/sales—to manage the real or nominal path of the exchange rate substantially enlarges determinacy regions and improves targeting efficiency.
- Practical implication for policymakers in LDCs: pairing IT with active FX intervention (exchange-rate-anchored IT) can reconcile the needs of exchange rate management (export competitiveness, food-price stabilization, balance-sheet protection) with credible inflation targeting.

*Source: Excerpt from "6.  Comparing Impulse Responses" (content unit)._wp1655*

### 6.  Comparing Impulse Responses ........................................................................................

### 6.  Comparing Impulse Responses

### Major conclusion: exchange-rate-anchored IT strengthens forward-looking inflation targeting
- Central finding: tight management of the exchange rate through sterilized foreign exchange purchases/sales greatly enhances the viability of forward-looking IT.
- Exchange-rate-anchored IT delivers strongly positive, complementary results for:
  - targeting efficiency (actual inflation outcomes track targets better), and
  - uniqueness of the equilibrium path (determinacy).
- Policy implication: successful IT in many LDCs requires two nominal anchors secured by two instruments (interest rate + sterilized FX interventions).

### Determinacy: managed vs. floating exchange rate regimes
- Criterion: monetary and exchange rate policies should guarantee determinacy – a unique equilibrium (Woodford, 2003).
- With a flexible (pure) float:
  - IT incurs a high risk of indeterminacy; rules that target future inflation are subject to an upper bound on the Taylor coefficient.
  - The upper bound on the Taylor coefficient is much smaller than in the canonical closed-economy model.
  - The lower bound on the Taylor coefficient is often substantially above unity.
  - Result: the determinacy region is generally small and, in some important cases, non-existent.
- Mechanisms behind indeterminacy under floating rates:
  - Large flex-price tradables sector in small open LDCs reduces the upper bound on the Taylor coefficient.
  - Higher expected inflation spurs substitution away from domestic currency toward foreign currency; in a flexible exchange rate system, this causes spot depreciation and an upward jump in the real exchange rate, creating inflationary pressure in the sticky-price nontradables sector.
  - Easy substitution between domestic and foreign bonds alleviates pressure on the exchange rate but sharply reduces the upper bound on the Taylor coefficient. Sunspot equilibria can arise at ordinary Taylor coefficients (e.g., 1.5).
  - Finding the appropriate Taylor coefficient becomes akin to "guessing right" because policy makers do not know exact parameter values.
- With exchange-rate management (second instrument):
  - Pegging the real exchange rate via sterilized purchases/sales of foreign exchange restores the Taylor principle: active policy is necessary and sufficient for a unique equilibrium provided the coefficient on the inflation target does not exceed a large upper bound.
  - Pegging the rate of crawl of the currency at the target inflation rate and leaning against the wind in a managed float also produce well-behaved determinacy properties.
  - Targeting the real exchange rate directly in the interest-rate rule is not sufficient: sunspot equilibria remain a significant threat unless accompanied by FX intervention.

### Targeting efficiency and impulse responses
- Criterion: small inflation shocks should not escalate into much larger realized inflation increases.
- Under regimes that stabilize only the real exchange rate or that allow wide nominal exchange rate fluctuations (pure or lightly managed floats):
  - Impulse responses display large, erratic fluctuations in currency depreciation and frequent wide misses of the inflation target.
  - Example from simulations: quarterly rates of currency depreciation and inflation can jump from 1% to 4-6% following a shock that directly raises inflation by only a half percentage point.
- Under exchange-rate-anchored IT (peg the rate of currency depreciation or tightly managed float with strong leaning):
  - Active monetary policy suppresses inflationary shocks as expected; the problem of large erratic impulse responses disappears.
  - Conclusion reiterated: in LDCs, successful IT typically requires two nominal anchors and two instruments.

### Model structure and key features underlying results
- Framework: two-sector small open economy model with imperfect substitution between domestic and foreign financial assets; tradables (flex-price) and nontradables (Calvo sticky-price/New Keynesian).
- Private sector divides financial wealth among domestic bonds, domestic currency, foreign currency, and foreign bonds/loans.
  - Foreign currency provides liquidity services; purchases of foreign bonds/loans incur transaction costs (so uncovered interest parity does not bind).
- Central bank controls the path of the interest rate; sterilized FX interventions provide a second instrument.
- Liquidity services modeled as a CES aggregate of real holdings of domestic and foreign currency; elasticity of substitution between currencies denoted by parameter  (with  required for Edgeworth substitutability).
- Portfolio adjustment costs for foreign bond holdings captured by parameter Λ; small Λ implies elastic capital flows and domestic interest rates close to foreign rates, while large Λ (as in low-income countries) implies larger spreads and more variable domestic interest rates.
- Time is discrete; results also hold in continuous time.

### Households and key equilibrium conditions (model highlights)
- Consumption composite: traded consumption C_x and CES aggregate of nontraded varieties C_n.
- Euler equation linking consumption growth and real interest rate:
  - C^{-1/}_t =  R_t / _{t+1} C^{-1/}_{t+1}
- Marginal rate of substitution across labor and consumption equals real sectoral wage:
  - (η_i Λ_{s i,t}^{1/} C^{-1/}_t) = ω_{i,t}/P_t, for i = n, x.
- Marginal rate of substitution between consumption and currency holdings ties into returns on domestic bonds:
  - Γ_F(...) =  C^{-1/}_{t+1} (P_t/P_{t+1})(R_t/^e_{t+1} − 1)
  - Γ_μ(...) =  C^{-1/}_{t+1} R_t^{-1} / _{t+1}
- Domestic bond return relates to foreign return net of portfolio adjustment costs:
  - R_t = R^*_t ^e_{t+1} / (1 + Λ(β^*_t − β̄^*))

### Policy takeaways
- Relying solely on an interest-rate rule that lets the exchange rate float exposes LDCs practicing forward-looking IT to significant indeterminacy and large impulse-response volatility.
- Introducing a second instrument—sterilized foreign exchange purchases/sales—to manage the real or nominal path of the exchange rate substantially enlarges determinacy regions and improves targeting efficiency.
- Practical implication for policymakers in LDCs: pairing IT with active FX intervention (exchange-rate-anchored IT) can reconcile the needs of exchange rate management (export competitiveness, food-price stabilization, balance-sheet protection) with credible inflation targeting.

*Source: Excerpt from "6.  Comparing Impulse Responses" (content unit)._wp1655*

### 2.2  Firms

### 2.2  Firms

### Firms: production and labor demand
- Firms hire labor and fixed, sector-specific factors in competitive markets. Cobb-Douglas production functions:
  - Θ_{x,t} = α_x L_{x,t}^{θ_x} X_{x,t}, (14)
  - Θ_{n,t} = Z_1^0 q_φ dφ = α_n L_{n,t}^{θ_n} N_{n,t}, (15)
- Sectoral labor demands:
  - L_{x,t} = θ_x (w_{x,t})^{-1} Θ_{x,t}, (16)
  - L_{n,t} = (Θ_{n,t}/α_n)^{1/θ_n}. (17)
- Calvo pricing in nontradables sector: each period a fraction 1−ξ of firms receive the price-setting signal; the average price quote lasts (1−ξ)^{-1} periods and leads to the New Keynesian Phillips Curve.
- Define marginal cost:
  - H_t = w_{n,t}/θ_n (Θ_{n,t}/α_n)^{(1−θ_n)/θ_n}. (18)
- Resulting Phillips curve (percentage deviations indicated by circumflex):
  - ˆπ_{n,t} = β ˆπ_{n,t+1} + κ(ˆH_t − ˆP_{n,t}), (19)
  - where κ ≡ (1−β ξ)(1−ξ)/ξ.

### Monetary and fiscal policy (brief)
- Central bank rule (until Section 4): R_t = R^* (π_{t+1}/π^*)^α, (20)
  - π^* is target inflation, R^* = π^*/β is steady-state interest rate.
  - When α>1, monetary policy abides by the Taylor principle.
- Fiscal policy: lump-sum taxes adjust in the background to satisfy government budget constraint; transfers path does not affect equilibrium path.

### Market-clearing and accounting identities
- Labor market clearing: L_{i,t} = L^s_{i,t}. (21)
- Nontradables produced to demand:
  - Θ_{n,t} = ∫_0^1 c_φ dφ = [∫_0^1 (p_φ,t / P_{n,t})^{-ε} dφ] C_{n,t}. (22)
- Current account / net foreign assets identity:
  - X_t − X_{t−1} = (R^*_{t−1} − 1) β^*_{t−1} + Θ_{x,t} + P_{n,t} Θ_{n,t} − P_t C_t, (23)
  - X ≡ F + β^* + S (net foreign assets), S is stock of foreign exchange reserves.
- Law of motion for P_n:
  - P_{n,t} = P_{n,t−1} π_{n,t} / π^e_{t}. (24)

### Discussion: labor mobility and currency substitution
- Immobile vs. mobile labor:
  - Labor mobility matters: when central bank raises real interest rate, labor demand and wage usually fall more in sticky-price nontradables than tradables. If labor is intersectorally mobile, wage differentials disappear ex post, making monetary policy less effective the greater the labor mobility.
  - The authors analyzed a benchmark with full intersectoral labor mobility; many results similar, some differ significantly (results available upon request).
- Is currency substitution relevant in IT countries?
  - Yes. Dollarization ratios remain high in much of Latin America, Sub-Saharan Africa, East Asia (e.g., Cambodia, Vietnam, the Philippines), Eastern Europe, and former Soviet republics; majority of emerging market economies that practice IT are in high-dollarization group.
  - Empirical elasticity of currency substitution (σ) is very high. Estimates for Latin America (seventies and eighties) range from 1.5 to 7.
  - Average estimate of σ for the IT countries in Table 1 is 2.91.
  - Network externalities, global integration, electronic banking, and learning-by-experience plausibly sustain high dollarization even with low inflation.
  - Currency substitution may operate through cross-border deposits and near-monies; it affects domestic money demand and demand for foreign assets even where foreign currency is not used directly as medium of exchange.

### Key microfoundations linking money, currency substitution, and equilibrium
- Absent currency substitution, domestic money demand should not depend on rate of currency depreciation and demand for foreign currency should not depend on inflation rate (see first-order conditions in (11) and (12)).
- Model applies as long as substitution effects operate through some channel.

### Calibration: base case choices and interpretations
- Time period: one quarter; constants η_i chosen so ω_x = ω_n at steady state.
- Standard values for elasticity of labor supply and elasticity of substitution between differentiated varieties; other variables appropriate for a LDC.
- Parameters governing capital flows:
  - Base-case elasticity of currency substitution σ = 2 (conservative; biases results in favor of determinacy).
  - Median dollarization ratios in 2012: 30−35% in Latin America and Sub-Saharan Africa; 45% in Eastern Europe and Central Asian republics (Imam et al., 2014). Authors’ best-guess true dollarization ratio ≈ 50% (including cross-border deposits and holdings outside domestic banking system).
  - Parameter ϕ determines substitutability between domestic and foreign bonds. The value in base case, 1, implies a one percentage point increase in domestic interest rate induces capital inflows equal to one percent of annual GDP.
- Sticky-price quote length fixed at six months (ξ = 0.50) in base case; more common value is one year (ξ = 0.75). Evidence indicates ξ ≈ 0.5 or less in LDCs.
- Authors do not judge IT successful unless it performs well for ξ = 0.25−0.50 as well as ξ = 0.67−0.75.

### 3 Doing It By the Book: IT in a Pure Float — determinacy results (summary)
- The pure-float transition governed by six first-order difference equations in X, C, P_n, π_n, β^*, and π^e; three state variables (X, β^*, P_n) require three eigenvalues inside unit circle for saddle-point stability.
- Table 4 and Figures 1a–1h report lower and upper bounds on Taylor coefficient α across cases. Seven highlighted results:
  1. Weakly active monetary policy ensures determinacy when currency substitution does not operate:
     - Trade in bonds only (Figure 1a). Upper bound ranges from 1.34 to 1.97 depending on share of nontraded goods in aggregate consumption (ω) and elasticity of capital flows (ϕ); lower bound always equals unity.
     - Thus weakly active policy (α<1.20) guarantees determinacy in this special case.
  2. Lower bound increases strongly with elasticity of substitution between domestic and foreign currency (σ):
     - Effect especially damaging when average price quote is short-lived, consumption weight of tradables is large, and elasticity of labor supply is low.
  3. Determinacy region can be empty (entry "Null"): equilibrium indeterminate for passive and active policy alike.
     - Occurs frequently when ϖ<0.25, ξ = 0.25−0.33, and ω<0.40.
  4. Both lower and upper bounds on α sensitive to degree of demand-side openness (1−ω), degree of price stickiness (ξ), intertemporal elasticity of substitution (τ), and Frisch elasticity of labor supply (ψ):
     - Base case (ξ = 0.50, weight of traded goods in CPI = 60%): equilibrium unique for α = 1.84−2.07.
     - Determinacy region expands to 1.74−2.46 when ξ = 0.75.
     - Determinacy region is 1.53−2.40 when consumption weight of tradables decreases to 40% (ω = 0.60).
     - Determinacy region contracts sharply for τ = 0.50−0.80 and disappears when ψ < 0.22 or ξ < five months.
  5. Determinacy requires aggressive, highly active policy when currency substitution is moderately or highly elastic:
     - Taylor coefficient α = 1.5 delivers determinacy in 50% of runs for σ = 0.5−1.
     - Success rate plunges to 6.7% when σ = 1.5−3.
  6. Asset substitution (bond substitution) may expand or contract determinacy region depending on σ:
     - Easier substitution between domestic and foreign bonds decreases both upper and lower bounds on α. In Figure 1g, region size changes little as ϕ rises from 1 to 5.
     - When currency substitution is highly elastic (Figure 1h), upper bound decreases much faster than lower bound; gap contracts from 1.97−2.35 at ϕ = 0.50 to 1.94−2.13 at ϕ = 2 to a single point at ϕ = 3.05.
     - High capital mobility across currency and bonds may be incompatible with forward-looking IT in a flexible exchange rate system.
     - A second region of determinacy reappears near perfect capital mobility (e.g., around ϕ = 8 and higher), expanding slowly for very large ϕ.
  7. Upper and lower bounds are highly insensitive to degree of dollarization and net foreign debt:
     - Results for Φ = 0.16 and β^* = 1 virtually identical to base case (Φ = 0.32 and β^* = −1).
     - What matters are elasticities of currency and asset substitution, not dollarization level or net foreign debt size.

- Intuition and mechanisms:
  - Upper bound on α inversely related to overall degree of price stickiness and elasticity of aggregate demand w.r.t. interest rate: more price stickiness or larger tradables weight (1−ω) lowers upper bound.
  - Lower bound large when expectations of higher inflation can trigger capital outflows and depreciation even as central bank raises real interest rate. If σ > τ, domestic and foreign currency are Edgeworth substitutes: decreases in real money supply increase marginal utility of foreign currency, incentivizing capital flight.
  - Active policy must be strong enough that deflationary pull from lower aggregate demand outweighs inflationary pressure from real depreciation.
  - Asset substitution moderates or exacerbates these forces depending on whether bond flows offset or reinforce currency substitution flows; at high σ, bond and currency substitution can reinforce outflows, raising lower bound.

*Italic: Source: _wp1655 - 2.2  Firms*

### 3.1  Policy Issues

### 3.1  Policy Issues

### Challenges for IT in LDCs
- Locating the region of determinate equilibria is difficult because policy makers in LDCs operate with fuzzy, imprecise information about key parameters (, , , etc.).
- Parameter uncertainty examples (preserve original notation and precision):
  - The intertemporal elasticity of substitution probably lies between2 and75.
  - Estimates of  range from 1 to 6.
  - The “emerging stylized fact” that  ≤ 50 needs confirmation for additional countries.
- Practical consequence of uncertainty:
  - The central bank cannot be confident that its choice of  is compatible with determinacy.
  - Choosing  to exceed the largest lower bound is risky because the largest lower bound exceeds many upper bounds in the relevant parameter space. Example: setting  = 210 would be unfortunate when the country’s true coordinates are  = 50,  = 5, and  = 1 (where unique equilibria obtain only for  = 130−158).
- Amplification of policy errors:
  - Even if a Taylor coefficient of two ensures determinacy given parameter uncertainty, aggressive interest rate rules amplify policy errors; IT itself may become a source of macroeconomic instability (Orphanides, 2001; Benhabib and Eusepi, 2005).
- Socio-political constraints:
  - Internal and external shocks are larger and more frequent in LDCs. Highly activist policy may be infeasible.
  - A Taylor coefficient of 13 is probably acceptable when dealing with an 8−12 percentage point shock to annual inflation (e.g., the world food and oil price increases of 2007 - 2009).
  - If the coefficient must exceed two, IT is in trouble because policy makers cannot be expected to combat inflation shocks with brutal, intolerably large increases in the real interest rate (Fraga et al., 2003).
- Exchange rate neglect risk:
  - Benign neglect of the exchange rate can dampen inflationary shocks, but it can also allow an initial shock to escalate via depreciation of the real exchange rate into a much larger shock, causing wide misses of the inflation target (to be analyzed in Section 6).

### Coordinating Monetary and Exchange Rate Policy — key insight
- The key to reconciling active policy with determinacy is to limit nominal and/or real depreciation of the currency. The section investigates efficacy of alternative methods of targeting the exchange rate.

### Targeting the Exchange Rate the Wrong Way
- Wrong approach: encumber the Taylor rule with a target for the nominal () or real exchange rate (1

).
- Example rule:
  - ˆ
  
  
  = ˆ
  +1
  − 
  ˆ
  
    (equation (25))
- Effects of positive :
  - Raise the upper bound and reduce the lower bound for determinacy.
  - The increase in the size of the determinacy region is small even when  is large.
  - Indeterminacy remains virtually unavoidable when  and  are low.
- Conclusion: such rules undermine inflation-target credibility and are largely ineffective; a better approach exists.

### Targeting the Exchange Rate the Right Way — sterilized FX operations
- Right approach: sterilized sales/purchases of foreign exchange (two instruments for two targets). Two variants examined: pegging the real exchange rate and pegging the rate of crawl (

).

4.2.1 Pegging the Real Exchange Rate
- Problem in pure float: Taylor coefficient often must exceed a large lower bound for unique REE; when  is above unity but below that bound, increases in the real interest rate fail to prevent capital flight and real exchange rate depreciation, leading to self-validating inflation expectations and no macro anchor.
- Mechanism: using foreign exchange sales to peg the real exchange rate creates a firewall that insulates real marginal cost in the nontradables sector from capital flows and depreciation.
- Dynamics highlighted:
  - Since ˆ
    
    
     ˆ
    +1
    = ˆ
    +1
    = ˆ
    +1
    , the interest rate always increases more than the rate of currency depreciation.
  - Lower holdings of domestic currency can increase the non-pecuniary yield of foreign currency when the two currencies are Edgeworth substitutes (i.e.,   ). If the non-pecuniary yield rises more than 
    
     
    +1
    , demand for foreign currency increases and pressure on the exchange rate mounts; sterilized FX sales then buttress the real exchange rate and sever the link from depreciation to marginal costs and nontradables inflation.
- Result: the real exchange rate peg allows IT to function similarly to the closed economy; 
  
  and 
  
  drop out of the dynamic system and key equations decouple.
- Derived subsystem (equation (26)) and stability requirement:
  - ⎡ ⎣ ˆ
    
    +1
    ˆ
    +1
    ⎤ ⎦
    =
    ⎡ ⎣ 1−(−1)
    4
    (−1)
    −
    4
    1
    ⎤ ⎦
    ⎡ ⎣ ˆ
    
    
    ˆ
    
    ⎤ ⎦
    , where 
    4
    ≡  [1 + (1−
    
    )] + 
    
    
    
    
    
     0.
  - Stability of the full system requires that the subsystem in (26) possess two eigenvalues outside the unit circle.
- Proposition 1 (exact statement preserved):
  - Suppose the central bank pegs the real exchange rate. The necessary and sufficient condition for a unique equilibrium is then
    1    1 + 2(1 + )
    
    
    {[1 + (1−
    
    )] + 
    
    } .
- Remark 1 (preserved):
  - The upper bound is independent of the consumption share of traded goods (1−), the degree of dollarization (), the net foreign debt (
    ∗
    ), factor cost shares in tradables production (
    
    ), and the elasticities of currency substitution and bond substitution ( and ).
  - The upper bound in Proposition 1 equals the upper bound in the standard one-sector, sticky-price, closed-economy model; comparison with a closed-economy model that incorporates both sticky- and flex-price sectors is obtained by setting , 
    ∗
    , and  equal to zero.
  - IT works better in the open economy if the central bank pegs the real exchange rate (Table 5): the upper bound ranges from 122 to 220 in the closed economy, while in the open economy the upper bound is comfortably large except perhaps when prices adjust quickly in the nontradables sector ( = 25−33).
- Practical objection and reply:
  - Purist objection: mixing an instrument rule (interest rate) with a targeting rule (real exchange rate peg) is improper because it assumes FX sales/purchases adjust instantaneously.
  - Practical response: highly efficient targeting via an instrument rule can approximate the ideal target rule; however, concerns remain about how efficient the instrument rule must be to achieve the ideal.

4.2.2 Pegging the Rate of Crawl (

)
- Benign neglect allows depreciation, capital flight, real exchange rate increases, and nontradables inflation to form a self-validating loop.
- Pegging the real exchange rate or pegging the rate of crawl at the target inflation rate short-circuits that loop.
- With 
  
  constant, the real exchange rate always decreases (
  
  ↑) following a positive inflation shock. The exchange rate channel reinforces the interest rate channel; the equilibrium is saddle point stable under active policy, and passive policy can also work because appreciation of the real exchange rate neutralizes inflationary pressures and precludes sunspot equilibria.
- Proposition 2 (exact statement preserved):
  - When the central bank pegs the rate of crawl of the nominal exchange rate at the target inflation rate,
      1 + (1−)(1 + )
    {[1 + (1−
    
    )] + 
    
    }
    is necessary and sufficient for a unique equilibrium.
- Remark 2 (preserved):
  - The upper bound is independent of the degree of price stickiness (), the degree of dollarization (), the net foreign debt (
    ∗
    ), and the elasticities of currency substitution and bond substitution ( and ).
- Practical assessment:
  - Pegging the rate of crawl is competitive with pegging the real exchange rate only if the upper bound in Proposition 2 is sufficiently large. Outside a few runs where  = 7−8, the upper bounds in Table 6 are higher than any realistic value for  under aggressive, activist monetary policy.
  - Note: upper bounds are much larger when labor is intersectorally mobile (see online appendix).

4.2.3 Managed Floats
- Hard pegs (nominal or real) can be overkill: they always solve indeterminacy but may be inefficient because the upper bound can be much larger than necessary (example: hard nominal peg determinate as long as  < 43 in the base case).
- Intermediate regimes (managed floats) may offer better tradeoffs between exchange rate flexibility and determinacy region size, but their exact placement on the continuum is unclear.
- Managed-float rule (reserve sales that lean against the wind):
  - 
    
    − 
    −1
    
    −1
    = − (
    
    − 
    ∗
    ), with   0.  (equation (28))
- Interpretation of  into regime adjectives uses the ratio of reserve sales in the float to sales required for a hard peg. For shocks in Section 6, ratios for  = 25, 1, and 5 are 13−24, 37−54, and 70−84 respectively. Regime labels:
  - managedfloat lite when  ≤ 50,
  - medium when  = 1−150,
  - heavy when  ≥ 5.
- Empirical/analytical findings:
  - Small values of  (on the order of .25) reduce the lower bound to unity in every case covered by Table 4, so determinate equilibria exist for some  > 1.
  - The determinacy region is fairly large in many worst-case scenarios where pure float yields indeterminacy. Example: for  = 33, pure float loses determinacy when  exceeds 116; with a light managedfloat ( = 25), determinacy obtains for  = 192 even when  = 3.
  - The bad news: the upper bound is not very responsive to . For example, in one case the upper bound is only 131−138 for  = 5−10; another case yields 150−160. By contrast, hard nominal peg upper bounds are 29 and 47 (Table 6).
  - Conclusion: leaning against the wind always increases the determinacy region, but effectiveness varies across parameter space. A light lean is often highly effective; in some cases a heavily managedfloat is a poor substitute for a hard peg.

### Sensitivity Analysis — robustness and exceptions
- Overall robustness:
  - Results are robust to structural changes: limited asset market participation, inertial inflation, intersectorally mobile labor, imported intermediate inputs, alternative elasticities in preferences/technology (CES vs Cobb-Douglas), and combinations of structural changes. Alternative structural models typically show slightly higher upper and lower bounds than the benchmark.
- Important exception:
  - Equilibrium is always indeterminate when highly elastic currency substitution ( = 3) combines with easy substitution between domestic and foreign bonds —   305 in Figure 1h.
  - With intersectorally mobile labor, the threat intensifies: determinate equilibria disappear once  exceeds 157.

5.2 Targeting Core Inflation
- Switching the target from CPI to core inflation helps the indeterminacy problem provided the intertemporal elasticity of substitution is not too low.
- Key numeric findings:
  - The upper bound on the Taylor coefficient is no longer a worry in the base case or in runs where  and  exceed 5.
  - The lower bound drops to unity for  = 75−1 and the equilibrium is always unique when the average sticky-price quote lasts one year ( = 75).
  - Targeting core inflation solves indeterminacy for parameter values typical of developed countries ( = 50−1,  ≥ 67).
- Limitations and caveats:
  - Lower bounds still cluster between 15 and 28 when  ≤ 50 and  ≥ 1, so indeterminacy remains a threat in parts of the parameter space and the socio-political acceptability of highly active policy is still an issue.
  - Crucial caveat:  must not be too low. For  = 2 the lower bound soars from 165 at  = 50 to 4−71 at  = 1−15. The extreme sensitivity to  opens a large divide between developed and less developed countries: in LDCs (where  might be on the order of .2 - .3), targeting core inflation may help or may render the indeterminacy problem insoluble.

5.3 Flexible Inflation Targeting
- Flexible IT rule:
  - ˆ
    
    
    = ˆ
    +1
    + 
    ˆ
    
    
    , with   0 and 
    
    ≡ 
    
    + 
    
    
    
    . Empirical estimates place  between 1 and 5 in LDCs.
- Comparison with closed economy:
  - In the closed economy, flexible IT significantly improves prospects for determinacy (e.g., Galí et al., 2004; Huang and Meng, 2007).
  - In the open-economy model here, that result does not survive qualitatively. Sometimes the determinacy region expands slightly (lower bound decreases more than upper bound), but in other cases both bounds move toward each other and the determinacy region for flexible IT lies completely inside that for strict IT (example: Figure 4c).
  - Conclusion: flexible IT does not reliably improve determinacy in the open-economy setting examined.

*Source: _wp1655 - 3.1  Policy Issues*

### 5.4  Contemporaneous Inflation Targeting

### 5.4  Contemporaneous Inflation Targeting

### Contemporaneous IT: determinacy and realism
- Main theoretical result:
  - Contemporaneous IT guarantees determinacy in the closed economy and generalizes to the open economy: exchange rate policy and the choice of price index do not matter if the central bank targets current inflation. Even in a flexible exchange rate system, Core- and CPI-IT are compatible with a unique equilibrium under active policy (1).
- Practical caveats and literature:
  - Contemporaneous interest rate rules presume precise information on current inflation and other variables.
  - Bullard and Mitra (2002) and McCallum (1999) express concerns: information availability and operationality of contemporaneous rules.
  - Most central banks practice forward-looking IT; few, if any, target contemporaneous inflation.

### Determinacy vs. exchange rate management
- While contemporaneous IT guarantees determinacy under flexible exchange rates, this does not contradict the thesis that tight management of the exchange rate is essential for effective IT in LDCs.
- All flexible exchange rate regimes suffer from low targeting efficiency: without intervention to limit exchange rate volatility, aggressive interest-rate manipulation can fail to prevent small shocks from driving inflation far above target.

### Comparison framework for impulse responses
- Parameter subset for scenario analysis:
  - =75
  - =3
  - =15
  - =20
- Alternative benchmark run: perfect labor mobility (to test robustness across model specifications).
- Shock analyzed:
  - A 125% AR1 cost-push shock in the nontradables sector (equivalent to a5% inflation shock), with persistence parameter =90.
- Scenarios:
  - Scenario A: 
    
    =5.
  - Scenario B: 
    
    =01 and 
    
    =3 (limited wage flexibility in sticky-price nontradables and inelastic supply in a natural-resource-based export sector).
  - Scenario C: labor is intersectorally mobile and =20.
- Macro outcomes tracked: inflation, currency depreciation, sectoral output (
  
  , 
  
  ), the real exchange rate (=1
  
  ), and the real wage.
- For MF-IT, RERA-IT, NERA-IT: also report reserve sales/purchases as a percentage of initial annual GDP.

### Key findings from impulse responses
- Overall ranking:
  - NERA-IT is identified as the clear winner versus contemporaneous IT with a flexible exchange rate and versus other regimes considered.
- Summary of regime performance:
  - NERA-IT:
    - Dampens the inflation shock across all three scenarios.
    - Nontradables output and the real exchange rate fluctuate more than under flexible exchange rate regimes, but the real wage decreases much less.
    - Requires permanent reserve sales that are tolerable in Scenarios A and C and manageable, if large, in Scenario B.
  - Contemporaneous IT with flexible exchange rate:
    - Performs worse than NERA-IT; allows large inflation jumps.
    - Under contemporaneous IT, quarterly inflation increases 8−35percentage points despite exceptional downward flexibility of the real wage.
  - RERA-IT:
    - Accepts slightly higher inflation ( increases 12−4 points) and slightly larger real wage cuts as the price of stabilizing the real exchange rate.
  - Core IT and CPI IT under flexible rates:
    - Core and CPI inflation jump substantially following a large spot depreciation at =0:
      - Core inflation: from 1% to 28−55%
      - CPI inflation: from 1% to 32−64%
    - Core IT performs particularly poorly compared to contemporaneous IT and NERA-IT.
  - Irony: NERA-IT and contemporaneous CPI-IT target core inflation more effectively than core IT itself.
- Credibility concerns:
  - The model permits annual inflation to jump from 4% to 15−25% without losing IT credibility; in reality, such surges would likely destroy credibility, causing capital flight, faster depreciation, and escalating inflation.
  - Safeguard implication: stronger interest-rate responses to inflation are required in regimes that allow the exchange rate to float. True lower bounds on the Taylor coefficient are likely much larger than those suggested by earlier sections, and the number of indeterminate (Null) parameter combinations is probably greater.

### Reserve statistics and specific numeric outcomes
- Reserves:
  - Initial reserves: 16.7% of annual GDP (figure from Berganza and Broto’s (2012) sample).
  - Long-run decrease in reserves:
    - Scenarios A and C: 2.3-3% of GDP.
    - Scenario B: 5.2% of GDP.
  - Note: Some historical interventions required large reserve sales (e.g., 20% of the total stock in Brazil 2001).
- Contemporaneous IT inflation jumps and comparisons:
  - Contemporary IT quarterly inflation increases: 8−35percentage points (as reported).
  - Core and CPI inflation jumps (spot depreciation at =0):
    - Core: 1% → 28−55%
    - CPI: 1% → 32−64%

### NERA-IT vs. Managed Float (MFL / MFM)
- Determinacy regions:
  - The determinacy region for a lightly managed float is smaller than for NERA-IT but still large enough in most parameter space to accommodate highly active monetary policy.
  - If MFL matched NERA-IT in neutralizing shocks, more exchange rate flexibility would be preferable; however empirical runs show otherwise.
- Head-to-head reserve-sale comparisons ( denotes management intensity):
  - For =1 (first row):
    - Cumulative reserve sales amount to 37−54% of reserve sales under NERA-IT.
    - Quarterly inflation jumps from 1% to 33−39%.
    - The right label for =1 is MFM (Managed Float Medium), not MFL.
  - For =5 (second row):
    - Sales are 70−84% as large as under NERA-IT.
    - Results considerably better and perhaps acceptable, but =5 corresponds to a heavily managed float (on a line where zero = pure float and unity = fixed, =5 maps close to 75).
  - If  is dropped to 25 (MFL), inflation soars to 46−58%, undermining credibility and raising doubts about the existence of determinate, stable equilibria.
- Bottom line:
  - LDCs can tolerate some, but not much, exchange rate flexibility; effective IT requires tight management of the exchange rate, if not a hard peg.

### Fear of appreciation
- Flexible-rate regimes also frequently face unexpected large capital inflows and rapid appreciation.
- Under excessive nominal appreciation:
  - Floating-rate regimes experience large disruptive fluctuations in the real exchange rate and sectoral output.
  - NERA-IT eliminates much of the unwanted volatility:
    - Real exchange rate appreciates only 2% on impact.
    - Reductions in nontradables output and the real wage are small compared with floating-rate regimes.

### External shocks
- Oil price and world market interest rate shocks were examined (these hit the exchange rate directly).
- Comparison outcomes (interest rate shock example):
  - Under flexible exchange rate core IT:
    - A 50 basis point rise in the external borrowing rate increases inflation by 1−18 percentage points for =4−6 in Scenarios A-C.
  - Flexible exchange rate contemporaneous IT:
    - Allows inflation to jump 6−27 points.
  - NERA-IT:
    - The number is exactly zero (
      
      = 
      ∗
      , ∀). The interest rate shock affects output, the real exchange rate, and nontradables inflation only through its impact on the rate of depreciation; fixing the rate of depreciation at the target inflation rate neutralizes the shock.

*Source: _wp1655 - 5.4  Contemporaneous Inflation Targeting*

### 6.4  Reconciling Theory and Practice

### _wp1655 - 6.4  Reconciling Theory and Practice

### Targeting efficiency and empirical stylized facts
- Targeting efficiency explains why LDCs engaged in IT hold large stocks of foreign exchange reserves and intervene frequently in the foreign exchange market.
- Intervention is essential to counteract both domestic and external shocks and to prevent excessive depreciation in some cases and excessive appreciation in others.
- The dataset in Vavra (2014) classification and counts:
  - In 2006, all eight developed countries and eight of seventeen EMEs were classified as IT Pure.
  - At the end of 2013, six of eight developed countries were still classified as IT Pure, but twenty-four of twenty-five EMEs practiced IT with FXI.
- Reserves do not earn interest; in the model a shock financed by higher cost of debt service is financed entirely by a reduction in foreign exchange reserves (Reserves decrease permanently by 2.46% of annual GDP).

### Main analytical results: indeterminacy and instability under flexible exchange rates
- Conventional advice to let the exchange rate float is risky for LDCs:
  - In LDCs, foreign currency competes with domestic currency as a supplier of liquidity services; expectations of higher inflation can become self-fulfilling once capitalflight triggers rapid depreciation.
  - Sunspot equilibria proliferate in much of the potentially relevant parameter space.
  - The indeterminacy problem is especially acute in regimes that target future headline inflation (CPI-IT).
- Determinacy region properties for CPI-IT:
  - The set of Taylor coefficients compatible with a unique equilibrium is circumscribed by a lower bound substantially larger than unity and an upper bound much smaller than in the closed economy.
  - The gap separating the two bounds is small in many cases and nonexistent in some cases.
  - Location of upper and lower bounds is case sensitive; uncertainty about parameter values makes it easy for policy makers to choose a Taylor coefficient that falls outside the determinacy region.
- Under a flexible exchange rate system, CPI- and Core-IT fail the second robustness criterion (containment of inflationary shocks without excessive instability) badly:
  - Impulse responses indicate a small inflation shock may, via capitalflight and a precipitate spike in the exchange rate, be magnified into an increase in the inflation rate seven times larger.
  - In practice, such a surge in inflation is likely to destroy confidence in the central bank’s competence and/or commitment.

### Exchange-rate-anchored IT: relative performance of regimes
- Two ranking criteria used: (i) robust compatibility with the Taylor principle (determinacy), and (ii) containment of inflationary shocks without excessive instability.
- Pegging either the real exchange rate or the rate of nominal depreciation affords maximum flexibility:
  - The lower bound on the Taylor coefficient drops to unity.
  - The upper bound jumps to a level that is comfortably large in many parameterizations.
- Differences across regimes:
  - RERA-IT (peg the real exchange rate) still allows capitalflight and endogenous depreciation to strongly magnify inflation shocks.
  - Pegging the rate of crawl or leaning heavily against the wind in a managed float (MFH-IT) eliminates ripple effects and successfully contains inflation shocks.
  - NERA-IT always passes both determinacy and shock-containment tests.
  - MFH-IT also scores well and ranks slightly below NERA-IT because of marginal grades on determinacy.
- Summary conclusion: exchange-rate-anchored IT works both in practice and in theory; flexible exchange rate IT is problematic in theory and has performed poorly in practice.

### Policy trade-offs and practical costs
- Exchange-rate-anchored IT has shortcomings and well-known risks:
  - Difficulties in sustaining fixed exchange rate regimes in developing countries (risk of gradual reserve loss culminating in speculative attack).
  - Opportunity cost of amassing a large stockpile of reserves to support IT is not trivial.
- Practical lesson for LDC central banks: effective IT cannot be done on the cheap — “you get what you pay for.”

### Specific formal/analytical conditions (selected)
- For the real-exchange-rate peg (Appendix B, “Pegging the Real Exchange Rate”), the necessary and sufficient condition for a unique equilibrium in the reduced subsystem is
  11+2(1 +)
  
  
  {[1 +(1−
  
  )] +
  
  }
  (equation (B3) in the text).
- For the rate-of-crawl peg (Appendix B, “Pegging the Rate of Crawl”), the uniqueness condition stated in Proposition 2 is
  1−
  
  5
  
  4
  =
  1+
  (1−)(1 +)
  {[1 +(1−
  
  )] +
  
  }
  (equation (B8) in the text).
- Under a managed float that leans heavily against the wind (MFH-IT) or under NERA-IT, the determinacy region expands (lower bound at unity; upper bound large), and impulse-response amplification of inflation shocks is eliminated or greatly reduced.

### Recommendations and implications for policy makers in LDCs
- Reassess conventional advice to adopt a pure float under IT: in many LDC parameterizations, pure flexible exchange rate CPI-IT and Core-IT are prone to indeterminacy and extreme amplification of inflation shocks.
- Consider exchange-rate-anchored IT frameworks (NERA-IT, MFH-IT, or pegs of the real exchange rate or crawl rate) to improve both determinacy and shock containment.
- Recognize trade-offs: management of the exchange rate typically requires substantial reserve holdings and involves the standard risks of tightly managed exchange rate regimes.
- When implementing IT in LDCs, account explicitly for currency substitution (degree of dollarization) and liquidity-service competition between domestic and foreign currency; these features materially affect determinacy and policy performance.

### Extensions and future research
- Suggested extensions: include investment and rule-of-thumb consumers in the framework; these may influence determinacy analysis and could reinforce current results.
- Empirical work: estimate the model using LDC data and test for the presence of indeterminacy without restricting parameter space — a challenging task that warrants a stand-alone study. Recent empirical contributions (e.g., Farmer et al. (2015)) suggest these estimations may be feasible even in the presence of indeterminacy.

*Source: _wp1655 - 6.4  Reconciling Theory and Practice*

### References

### References

### Major themes covered by the referenced literature
- Monetary policy rules, inflation targeting, and policy design
  - Airaudo, M. and L.F. Zanna, 2012, “Equilibrium Determinacy and Inflation Measures for Interest Rate Rules rules.” Review of Economic Dynamics, 15, 573-592.
  - Batini, N., Levine, P. and J. Pearlman, 2007, “Monetary Rules in Emerging Economies with Financial Market Imperfections.” In, J. Galí and M. Gertler, eds., International Dimensions of Monetary Policy (Chicago, University of Chicago Press).
  - McCallum, B., 1999, “Issues in the Design of Monetary Policy Rules.” In Handbook of Macroeconomics, edited by J. Taylor and M. Woodford. Elsevier, 483—1530.
  - Orphanides, A., 2001, “Monetary Policy Rules Based on Real-Time Data.” American Economic Review, 91, 964-985.
  - Woodford, M., 2003, Interest and Prices: Foundations of a Theory of Monetary Policy, New Jersey: Princeton University Press.

- Inflation targeting in emerging and developing economies
  - Blejer, M. and A. Leone, 2000, “Introduction and Overview.” In, M. Blejer et al., eds., Inflation Targeting in Practice: Strategic and Operational Issues and Application to Emerging Market Economies (Washington, International Monetary Fund).
  - Fraga, A., Goldfajn, I. and A. Minella, 2003, “Inflation Targeting in Emerging Market Economies.” NBER Macroeconomics Annual 2003 (Cambridge, MA).
  - Mishkin, F., 2000a, “Inflation Targeting in Emerging-Market Economies.” American Economic Review, 90, 105-109.
  - Masson, P., Savastano, M. and S. Sharma, 1997, “The Scope for Inflation Targeting in Developing Countries.” IMF Working Paper No. 97/130.

- Currency substitution, dollarization, and seigniorage
  - Feige, E., 2002, “The Dynamics of Currency Substitution, Asset Substitution and De facto Dollarization Euroization in Transition Economies.” Paper presented at the conference Monetary Policy and Currency Substitution in the Emerging Markets.
  - Selcuk, F., 2003, “Currency Substitution: New Evidence from Emerging Economies.” Economics Letters, 78, 219-224.
  - Samreth, S., 2010, “Currency Substitution and Seigniorage-Maximizing Inflation: The Case of Cambodia.” Applied Economics 42, 1907-1916.
  - Imam, P., Corrales, J., Weber, S., and E. Yehoue, 2014, “Dollarization in Sub-Saharan Africa: Incipient Rise or Future Decline?” Mimeo.

- Exchange rate policy, interventions, and exchange rate management
  - Bank of International Settlements, 2005, “Foreign Exchange Market Interventions in Emerging Markets: Motives, Techniques and Implications.” BIS Papers No. 24 (Basel, Bank of International Settlements).
  - Berganza, J. and C. Broto, 2012, “Flexible Inflation Targets, Forex Interventions and Exchange Rate Volatility in Emerging Countries.” Journal of International Money and Finance, 31, 428-444.
  - Taylor, J., 2001, “The Role of the Exchange Rate in Monetary Policy Rules.” American Economic Review, 91, 263-267.
  - Ostry, J., Ghosh, A. and M. Chamon, 2012, “Two Targets, Two Instruments: Monetary and Exchange Rate Policy in Emerging Market Economies.” IMF Staff Discussion Note No. 12/01.

- Balance sheet effects, financial fragility, and crises
  - Cespedes, L., Chang, R. and A. Velasco, 2004, “Balance Sheet Effects and Exchange Rate Policy.” American Economic Review, 94, 1183-1193.
  - Burnside B., M. Eichenbaum, and S. Rebelo, 2001, “Prospective Deficits and the Asian Currency Crisis.” Journal of Political Economy, 109, 1155-1197.
  - Elekdag, E. and I. Tchakarov, 2004, “Balance Sheets, Exchange Rate Policy, and Welfare.” IMF Working Paper No. 04/63.
  - Kumhof, M., Li, S. and I. Yan, 2007, “Balance of Payments Crises Under Inflation Targeting.” Journal of International Economics, 72, 242-264.

- DSGE models, small open economy models, and model estimation
  - Alapanda, S., Kotze, K. and G. Woglom, 2010, “The Role of the Exchange Rate in a New Keynesian DSGE Model for the South African Economy.” South African Journal of Economics, 78, 170-191.
  - Benes, J., Berg, A., Portillo, R. and D.Vavra, 2013, “Modeling Sterilized Interventions and Balance Sheet Effects of Monetary Policy.” IMF Working Paper No. 13/11.
  - Del Negro, M., and F. Schorfheide, 2008, “Inflation Dynamics in a Small Open Economy Model Under Inflation Targeting: Some Evidence from Chile.” Staff Report 329 (Federal Reserve Bank of New York).
  - Ghironi, F. and A. Rebucci, 2002, “Monetary Policy Rules for Emerging Market Economies.” IMF Working Paper No. 02/34.
  - Farmer, R., V., Khramov, and G. Nicolò, 2015, “Solving and Estimating Indeterminate DSGE Models,” Journal of Economic Dynamics and Control, 54, 17-36.
  - Zheng, T. and H. Guo, 2013, “Estimating a Small Open Economy DSGE Model with Indeterminacy: Evidence from China.” Economic Modelling, 31, 642-652.

- Money demand, portfolio choices, and financial integration
  - Akhtaruzzaman, M., 2007, “Globalization, Financial Liberalization and the Behavior of the Long Run Money Demand in the Bangladesh Economy.” International Economic Journal, 21, 465-490.
  - Bjornland, H., 2005, “A Stable Demand for Money Despite Financial Crisis: The Case of Venezuela.” Applied Economics, 37, 375-385.
  - Rodriguez, M. and P. Turner, 2003, “Currency Substitution and the Demand for Money in Mexico.” Applied Economics Letters, 10, 59-62.
  - Lebre de Freitas, M. and F. Veiga, 2006, “Currency Substitution, Portfolio Diversification, and Money Demand.” Canadian Journal of Economics, 39, 719-743.

### Representative policy-relevant contributions and working papers
- IMF Working Papers and Staff Notes addressing policy tools and practical issues:
  - Benes, J., Berg, A., Portillo, R. and D.Vavra, 2013, “Modeling Sterilized Interventions and Balance Sheet Effects of Monetary Policy.” IMF Working Paper No. 13/11.
  - Elekdag, E. and I. Tchakarov, 2004, “Balance Sheets, Exchange Rate Policy, and Welfare.” IMF Working Paper No. 04/63.
  - Masson, P., Savastano, M. and S. Sharma, 1997, “The Scope for Inflation Targeting in Developing Countries.” IMF Working Paper No. 97/130.
  - International Monetary Fund, 2011, “Foreign Exchange Intervention: How Good a Defense Against Appreciation Winds?” Chapter 3 in Regional Economic Outlook, Western Hemisphere (Washington, International Monetary Fund).

_Italic: References (full list as provided in the source PDF)._

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2016/_wp1655.pdf_