## _wp10161 ## Source details **Canonical URL:** [_wp10161](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10161.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10161.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10161.pdf.json) --- ### Introduction: motivation, questions, and distinctive features of food - Motivation and empirical background - Dramatic swings in world commodity prices, especially food, renewed interest in how monetary policy in small open economies should react to imported price shocks. - Figure 1 correlation: relative food prices against the world price level since 1960; correlation coefficient is 0.54. - Empirical tests: - Over 1960-2008, Granger causality tests (Table 2) reject hypothesis that food prices do not Granger-cause global WPI (proxied by US WPI); the same hypothesis is not rejected for oil prices. - F-tests suggest food prices Granger-cause oil prices and not the other way around. - Recent episode (2006–mid-2008): global food-price hike occurred under inflation targeting regimes and led to breaches of central CPI targets; sharp decline since mid-2008 accompanied rapidly receding national inflation despite some large currency depreciations. - Country illustration (Chile): between 2007 and early 2008, 12-month CPI inflation rose to close to 10 percent while long-term inflation expectations hovered around 3 percent; after commodity price collapse, inflation receded to low single digit levels despite a depreciation of the peso relative to the US dollar. - Key questions - If world food price shocks are exogenous to a small open economy, should the monetary authority: - tolerate and accommodate a temporary but sizeable CPI fluctuation provided PPI remains within target (i.e., be lenient toward imported food-price driven CPI inflation)? or - react forcefully to CPI inflation, possibly requiring much lower inflation (or deflation) in non-commodity domestic sectors? - Which targeting rules deliver highest welfare: broad CPI targeting, domestic PPI targeting, or exchange rate targeting? - Distinctive features of food emphasized - 1. Large share in official CPI baskets, especially in lower income countries (Table 3). - 2. Low elasticities of substitution with other goods, particularly in poorer countries — combined with high spending share, implying non-trivial impact on marginal rates of substitution and labor supply. - 3. Food is highly competitive with fast pass-through from cost shocks to prices and high volatility. - 4. Many inflation-targeting countries are large net food importers or exporters, so swings in the relative world price of food can entail large terms of trade variations. ### Main high-level findings (summary) - Broad CPI targeting is often the welfare-dominant policy rule when the unconditional volatility of world commodity prices is sufficiently high. - Two key factors behind CPI-targeting superiority: - Large weight and peculiar nature of food in aggregate utility. - World relative food price shocks are sizeable relative to monetary and technology shocks used in prior studies. - Mechanism: food price shocks generate covariances between cost-push and demand shocks and induce real exchange rate volatility; targeting PPI or the exchange rate becomes suboptimal for sufficiently high risk aversion and high disutility of work. - Sensitivity and caveats: - If variance of external food price shocks is very low, strict PPI targeting or exchange pegging rules are typically superior. - Increasing the weight on the output gap in the monetary policy rule (responding to the correct natural output that incorporates world food-price fluctuations) can narrow the welfare gap between CPI and PPI targeting. - Policy implication: findings provide theoretical and empirical support for broad CPI targeting in many small open economies that face large imported food-price volatility. --- ### Model overview and setup - Environment and preferences - Representative-agent preferences: E sum_{τ=0}^∞ β^τ U_τ with 0<β<1, U_τ = C_τ^{1−σ}/(1−σ) − ∫_0^1 N_τ(φ)^{1+ϕ}/(1+ϕ) dφ. - Consumption aggregator: C_τ = [ (1−α)^{1/ξ} C_{hτ}^{(ξ−1)/ξ} + α^{1/ξ} C_{fτ}^{(ξ−1)/ξ} ]^{ξ/(ξ−1)}; ξ is elasticity of substitution; α measures openness. - CPI: Π_τ = [ (1−α) Π_{hτ}^{1−ξ} + α Π_{fτ}^{1−ξ} ]^{1/(1−ξ)}. - Full pass-through from world to domestic food prices: Π_{fτ} = S_τ Π^*_{fτ}; Π^*_{fτ} (world relative food price) taken exogenous. - Real exchange rate: X_τ = S_τ Π^*_{τ} / Π_τ; relation (6): 1 = (1−α) (Π_{hτ}/Π_τ)^{1−ξ} + α X_τ^{1−ξ} Z^*_{τ}^{1−ξ}, where Z^*_{τ} = Π^*_{fτ} / Π^*_{τ}. - Domestic production and pricing - Home final good assembled from intermediate varieties (CES with elasticity ε); intermediate firms face monopolistic competition and Calvo pricing with probability of price stickiness α̵. - Productivity shock A_τ common to all firms and a subsidy to employment at constant rate ϑ; nominal marginal cost Ψ_{φτ} = (1−ϑ) Ω_τ(φ) / A_τ. - Financial markets and international linkages - Complete financial markets and world consumption index enter via C_τ = κ C^*_τ X_τ^{−1/σ} (equation (4)) and the standard Euler equation for domestic safe interest rate (equation (5)). --- ### Equilibrium: recursive representation (section 2.4) - Market clearing and foreign demand - Yhτ = Chτ + ϖ [ (Phτ / Sτ / P∗τ) ]^(−θ) C∗τ (equation 12). - Combined form: Yhτ = (1−α) [ (Phτ / Pτ) ]^(−χ) + ϖ Xτ^(θ) [ (Phτ / Pτ) ]^(−θ) C∗τ (equation 13). - Pricing and recursive accounting variables - Intermediate pricing solution: 1 = (1−κ) [ (P̄τ / Phτ) ]^(1−ψ) + κ Πητ^(ψ−1) (equation 14). - Optimal pricing condition: P̄τ / Phτ Jτ = ψ / (ψ−1) Hτ (equation 15). - Recursive definitions: - Jτ = [ (P̄τ / Phτ) ]^(−ψ) Yhτ + κ Eτ M_{t+1} [ (P̄τ / Phτ) (P̄τ+1 / Ph,τ+1) ]^(−ψ) Πη,τ+1^(ψ) Jτ+1 (equation 16). - Hτ = Fτ [ (P̄τ / Phτ) ]^(−ψ(1+φ)) Yhτ^(1+φ) + κ Eτ M_{t+1} [ (P̄τ / Phτ) (P̄τ+1 / Ph,τ+1) ]^(−ψ(1+φ)) Πη,τ+1^(1+ψ(1+φ)) Hτ+1 (equation 17). - Supplementary relations - 1 / (1+it) = β [ (Cτ+1 / Cτ) ]^(−σ) (Pτ / Phτ) (Pτ+1 / Ph,τ+1) Πη,τ+1^(−1) (equation 18). - Fτ = (1−ω) ˙Cτ^(−σ) Aτ^(−(1+φ)) (Pτ / Phτ) (equation 19). - Closure - System comprised of equations 4, 6, 13, 14, 15, 16, 17, 18, 19 gives nine equations in ten variables (C, X, Ph/P, Yh, P̄/Ph, ...); specification of monetary policy (and Euler equation 5, if needed) closes the model. --- ### Marginal costs and the Phillips relation (sections 2.5–2.7) - First-order pricing approximations - P̄πτ − πh,τ−1 = (1−β α) Σ_{κ=0}^∞ (β α)^κ Eτ [ (mcτ+κ|τ − mc) + (πh,τ+κ − πh,τ−1) ] (equation 20). - πhτ = (1−α) P̄πτ + α πh,τ−1 (equation 21). - Real marginal cost decomposition - mcτ+κ|τ = −ω + wτ+κ|τ − ατ+κ − πh,τ+κ = −ω + [ log ˙ζ + σ cτ+κ|τ + φ nτ+κ|τ ] − ατ+κ + πτ+κ − πh,τ+κ. - Using production and pricing relations: mcτ+κ|τ = mcτ+κ + φ ψ(πh,τ+κ − P̄πτ) (equation 22). - Average marginal cost expression summarized in text; marginal costs depend on the term (ξτ + α θτ) — i.e., the real exchange rate and the terms of trade — in addition to domestic production yhτ and exogenous shocks (equation 23). - Relation between real exchange rate and terms of trade - ξτ = (1−α) θτ + (π∗τ − π∗fτ) = (1−α) θτ − ζ∗τ (equation 24), where ζ∗τ = π∗fτ − π∗τ is the shock to the world relative price of imports. - Producer-price Phillips relation - πhτ = β Eτ πh,τ+1 + λ (mcτ + ν) (equation 25), where λ = (1−β α)(1−α)/α × 1/(1+φ ψ). - New Keynesian Phillips Curve (in transformed variables) - πητ = β Eτ [πη,τ+1] + λ η (ψτ − ψνητ) + λ (θτ − θντ) (29). - In output-gap form: πητ = β Eτ [πη,τ+1] + R (ψτ − ψνητ), where R = λ{η + Θ} and Θ depends on structural parameters. - Natural rate of output - ψνητ given in closed form (32); natural output and natural terms of trade respond to ζ∗τ shocks and depend on (ξ − 1/σ), openness α, and home-good share φ. - Special parameterization: if ξ = τ = 1/σ then coefficients on foreign demand χ∗τ and world food prices ζ∗τ are zero and the model is isomorphic to a closed economy. --- ### Impulse responses to world food price shocks and policy-rule comparisons (section 2.7 and later) - Shock process for ζ∗τ: AR(1) ζ∗τ = ρζ ζ∗τ−1 + εζτ. - Representations under PPI and CPI Taylor rules - PPI rule (log-linearized): iτ = ϕψ ˜ψτ + ϕπ η πητ. - CPI rule (log-linearized): iτ = ϕψ ˜ψτ + ϕπ πτ. - Closed-form IRF coefficients (PPI case) - ˜ψτ = C PPI ψ ζ∗τ and πητ = C PPI π ζ∗τ with expressions (37)–(39); denominator ΩPPI defined in text. - Special case ξ = 1/σ - ˜θ = 1, Φ Θ = 1, and C PPI ψ = C PPI π = 0: neither the output gap nor PPI inflation respond to ζ∗ shocks under a PPI rule; terms of trade follow ζ∗τ path. On-impact effects include real exchange rate appreciation by  = 04 percent in a calibrated example and consumption falls by (1/σ). - General case ξ ≠ 1/σ - If ξ < 1/σ (limited substitutability) then ˜ψ < 0 and ˜θ < 1: natural output falls and natural terms-of-trade undershoot the shock; output gap and PPI inflation decline; nominal interest rate falls under PPI rule. - If ξ > 1/σ, positive world food-price shocks can be expansionary. - CPI vs PPI rule comparison: qualitative points - CPI targeting typically induces a stronger interest-rate response to ζ∗ shocks than PPI targeting, because CPI includes imported-food-price components. - Under CPI targeting, output and home inflation commonly move together and responses strengthen with larger ξ − 1/σ. - CPI targeting is typically less contractionary than PPI targeting in response to ζ∗ shocks; openness  amplifies CPI response relative to PPI. --- ### Welfare objective and numerical evaluation (section 2.7 and 5.2) - Second-order welfare approximation (following Gali 2008, Woodford 2003) - Representative-agent expected utility expanded to second order yields welfare-relevant variance terms including πητ^2 with coefficient Θ = 1/2 ϱ (1 + η ϱ) · α/(1 − α)(1 − β α). - Woodford mapping: E Σ βτ varφ(log πτ(φ)) = α/(1 − α)(1 − β α) E Σ βτ πητ^2. - Numerical solution method - Use second-order approximation methods (Schmitt-Grohé and Uribe (2004)) and conditional-starting-point approach (Schmitt-Grohé and Uribe (2007), Wang (2006)). - Welfare computed conditional on all state variables at non-stochastic steady state; control variable V_t added with recursive evolution V_t − β V_t = U(C_t, L_t). - Relative welfare loss τ (percentage of steady-state consumption): τ = 100 × (1 − ε^{(1−β)(V_1 − V_2)}). --- ### Calibration, baseline stochastic processes, and numerical experiment design (section 5.2 and related) - Key calibration and parameter ranges (selected) - Discount Factor  = 0.99. - Degree of Openness  = 0.4 (Table 4); baseline steady-state openness  = 0.75 (unless otherwise noted). - Coefficient of risk aversion  in ranges [0.5,4] and [1,4] in Table 4/5. - Average period between price adjustments  = 0.66. - Coefficient on domestic inflation in Taylor Rule   baseline 1.5; range [1.1,2]. - Coefficient on output gap in Taylor Rule   baseline 0 or 0.125 in robustness. - Persistence parameters:   = 0.85 (world relative food price),   in [0.6,0.8] (monetary shock). - Standard deviations: relative world price of food   = 0.05 (4.5% quarterly in text), productivity   = 0.012 (1.2% per quarter), world CPI VAR 1.3% quarterly for p* in one experiment. - Standar Deviation associated with monetary policy shock   in [0.0062,0.0167] (i.e., 0.62% baseline per quarter). - Index of foreign demand  ∗ = 0.27. - Baseline shock processes and values - World CPI AR(1): ρ = 0.99; quarterly standard deviation 1.3% (G-8 PPI 1990-2008). - Relative world price of food (z*): conditional (quarterly) standard deviation 4.5%; AR(1) coefficient 0.85. - Productivity (TFP) shocks (Chile-based): standard deviation 1.2% per quarter; AR(1) coefficient 0.7. - Baseline monetary policy shock v: standard deviation 0.62% per quarter; AR(1) coefficient 0.6. --- ### Main numerical welfare-ranking findings (section 5.2 and summary) - Baseline parametrization (strict inflation targeting: coefficient on output gap set to zero) - CPI ("rule 2") is the superior rule for the majority of − configurations, especially when  is low and  is high. - The classic closed-economy result of PPI dominance is overturned once realistic international relative price shocks (food price shocks) are allowed. - Low-variance z* (near zero) - Results revert to previous-author findings: either exchange rate peg or PPI targeting dominates. - For unit-elasticity case (===1) and negligible z* variance, trade is balanced at all times and the economy is isomorphic to the Gali-Monacelli benchmark where PPI is dominant. - Shock-type decomposition (Table 8) - If only food-price shocks are present, CPI targeting yields: - Lower RER volatility. - Lower consumption volatility. - Lower output (hence lower effort). - Higher consumption-to-output ratio (C/Y). - Average RER more appreciated by 0.32% above SS. - If only productivity or only monetary shocks are present, PPI targeting produces lowest consumption and RER volatility and (marginally) higher C/Y — PPI preferred when domestic productivity shocks dominate. - Effects of monetary shock variance and persistence - Doubling monetary shock standard deviation from 0.6% to 1.2% per quarter increases attractiveness of the peg. - Increasing persistence of v from 0.6 to 0.8 has a similar effect. - Larger monetary shocks can increase welfare differences; gaps may reach 0.6% of steady-state consumption in some cases. - TFP shock variance and persistence - Increasing volatility/persistence of domestic TFP shocks increases attractiveness of PPI; but with non-trivial z* variance (4.5% a quarter), PPI dominance is limited. - Policy-rule aggressiveness and output weighting - Raising inflation reaction parameter to  = 3.0 increases attractiveness of exchange rate pegs; a more hawkish stance increases PPI dominance over CPI though welfare gaps remain tiny for  above 1. - Introducing output-gap weighting (responding to the correct natural output that includes terms-of-trade fluctuations) reduces numerical gaps between rules; CPI vs PPI welfare differences shrink for higher . - Elasticities and openness experiments - Higher export price elasticity  (from 1 to 5) makes CPI even more attractive relative to PPI; CPI beats PEG more often. - Lower labor supply elasticity (raise  from 1 to 3, i.e., lower 1/) reduces attractiveness of the peg relative to both CPI and PPI. - Higher openness ( = 0.6) increases CPI rule dominance; for  above 0.5 CPI dominance becomes overwhelming. - Lower openness ( = 0.9) makes PPI more dominant, though welfare gains remain relatively tiny. - Magnitude of welfare differences - Under empirically realistic higher  and lower , welfare gains of CPI relative to PPI reported between 0.33 and 0.62 of steady-state consumption: - 0.33 ( = 2 and  = 025). - 0.62 ( = 2 and  = 075). - Numerical welfare differences are generally small but can be economically meaningful up to 0.6% of steady-state consumption. --- ### Mechanisms behind CPI dominance when food shocks matter - Food-in-utility channel - Large food weight and limited substitutability amplify welfare relevance of world food-price shocks. - Monetary-policy transmission and RER - CPI targeting induces more aggressive rate responses to world food-price shocks (tighten on price rises, loosen on falls) than PPI or peg. - Stronger CPI response yields greater real exchange rate (RER) stability and a more appreciated RER on average. - A more appreciated RER raises C/Y, allowing higher consumption for given output (exploits terms-of-trade externality). - Productivity-shock channel favoring PPI - Under Calvo pricing, covariance between income and marginal cost shocks is negative; PPI stabilizes Ph and reacts procyclically to productivity (α) shocks, limiting fall in marginal costs and producing higher C/Y under productivity-driven regimes. - Trade-offs - CPI’s benefits (lower consumption volatility, higher average C/Y) must offset PPI’s benefits (better offset of sticky-price distortions to raise output/employment); relative dominance depends on magnitudes and persistence of food shocks versus monetary and productivity shocks, preferences (risk aversion), and labor disutility. --- ### Sensitivity, robustness, and practical notes - Critical role of z* variance - Allowance for non-trivial z* variance (world food-price shocks) is crucial and can overturn closed-economy PPI dominance. - Sensitivity to: - Volatility and persistence of monetary shocks v. - Volatility and persistence of domestic TFP shocks a. - Degree of openness . - Elasticities: labor supply (1/) and export price (). - Policy instrument aggressiveness () and inclusion of the output gap in reaction function. - Practical measurement caveat - If the central bank can reliably measure the correct natural output (incorporating world relative food prices), responding to that output gap can approximate CPI targeting and narrow welfare gaps; measurement challenges limit practical implementation. --- ### Policy implications (concise) - Broad CPI targeting is theoretically and empirically supported for many small open economies with large food share in utility and large persistent world food-price shocks. - CPI targeting avoids ad hoc exclusions of food from the inflation index and mitigates regressive distributional effects (food is a larger share for poorer households). - Central banks should not be overly lenient toward imported food-price shocks; excessive accommodation (as in strict PPI or peg regimes) can be welfare-inferior for food-importing small open economies. - A more accurate natural-output measure that internalizes terms-of-trade fluctuations could reduce the need for headline CPI responses, but practical measurement limitations are substantial. *Source: _wp10161 (IMF Working Paper, sections 1, 2.4–2.7, 5.2, and related tables/figures as provided in the supplied content).* ### 1. Introduction ........................................................................................................ ### _wp10161 - 1. Introduction ### Motivation and empirical background - Dramatic swings in world commodity prices, and especially food prices, have renewed interest in how monetary policy in small open economies should react to imported price shocks. - Illustration: Figure 1 correlates relative food prices against the world price level since 1960; the correlation coefficient is 0.54. - Empirical tests reported: - Tables 1 and 2 present correlations and Granger causality tests. Over 1960-2008, Granger causality tests in Table 2 reject the hypothesis that food prices do not Granger-cause global WPI (proxied by US WPI); the same hypothesis is not rejected for oil prices. - F-tests suggest food prices Granger-cause oil prices and not the other way around. - Recent episode: the 2006–mid-2008 hike in global food prices occurred under inflation targeting regimes and led to breaches of central CPI targets; the subsequent sharp decline in US dollar food prices since mid-2008 accompanied rapidly receding national inflation rates despite some large currency depreciations. - Country illustration: Chile — between 2007 and early 2008, 12-month CPI inflation rose from low single digits to close to 10 percent while long-term inflation expectations hovered around 3 percent; after commodity price collapse, inflation receded to low single digit levels despite a depreciation of the peso relative to the US dollar. ### Key questions addressed - If world food price shocks are exogenous to a small open economy, should the monetary authority: - tolerate and accommodate a temporary but sizeable CPI fluctuation provided PPI remains within target (i.e., be lenient toward imported food-price driven CPI inflation)? or - react forcefully to CPI inflation, possibly requiring much lower inflation (or deflation) in non-commodity domestic sectors? - Which targeting rules deliver highest welfare: broad CPI targeting, domestic PPI targeting, or exchange rate targeting? ### Distinctive features of food emphasized - Four characteristics of food highlighted as crucial to the analysis: 1. Large share in official CPI baskets, especially in lower income countries (Table 3). 2. Low elasticities of substitution with other goods, particularly in poorer countries — combined with high spending share, implying non-trivial impact on marginal rates of substitution and labor supply. 3. Food is highly competitive with fast pass-through from cost shocks to prices and high volatility. 4. Many inflation-targeting countries are large net food importers or exporters, so swings in the relative world price of food can entail large terms of trade variations. ### Model setup (overview) - Setting: a small open economy that is a net food importer, where food accounts for a sizeable and relatively stable share of household spending. - Modeling framework: a stripped-down DSGE model akin to those in recent monetary policy literature (e.g., Woodford, 2003; Walsh, 2004; Gali, 2008). - Main modeling assumptions and elements (as presented): - Representative-agent preferences: E sum_{τ=0}^∞ β^τ U_τ with 0<β<1, and U_τ = C_τ^{1−σ}/(1−σ) − ∫_0^1 N_τ(φ)^{1+ϕ}/(1+ϕ) dφ. Parameters σ, ϕ, and ̇ are used as in source. - Consumption is a C.E.S. aggregate of home final good C_{hτ} and imported food C_{fτ}: C_τ = [ (1−α)^{1/ξ} C_{hτ}^{(ξ−1)/ξ} + α^{1/ξ} C_{fτ}^{(ξ−1)/ξ} ]^{ξ/(ξ−1)}, where ξ is the elasticity of substitution and α measures openness. - CPI (domestic currency) Π_τ = [ (1−α) Π_{hτ}^{1−ξ} + α Π_{fτ}^{1−ξ} ]^{1/(1−ξ)}. - Full pass-through from world to domestic food prices: Π_{fτ} = S_τ Π^*_{fτ}, where S_τ is the nominal exchange rate and Π^*_{fτ} the world currency price of food (taken exogenous). - Real exchange rate X_τ = S_τ Π^*_{τ} / Π_τ and relation (6): 1 = (1−α) (Π_{hτ}/Π_τ)^{1−ξ} + α X_τ^{1−ξ} Z^*_{τ}^{1−ξ}, where Z^*_{τ} = Π^*_{fτ} / Π^*_{τ} is the world relative price of food (exogenous). - Domestic production: home final good assembled from intermediate varieties (CES with elasticity ε), intermediate firms face monopolistic competition, Calvo pricing with probability of price stickiness α̵ (notation as in source), productivity shock A_τ common to all firms, and a subsidy to employment at constant rate ϑ, so nominal marginal cost Ψ_{φτ} = (1−ϑ) Ω_τ(φ) / A_τ. - Complete financial markets and world consumption index enter via C_τ = κ C^*_τ X_τ^{−1/σ} (equation (4) in source) and standard Euler equation for the domestic safe interest rate (equation (5) in source). ### Main findings and welfare results (summary) - Broad CPI targeting is often the welfare-dominant policy rule when the unconditional volatility of world commodity prices is sufficiently high, as it typically is in practice. This contrasts with previous studies that mostly found CPI targeting dominated by PPI targeting or an exchange rate peg. - Two key factors behind CPI-targeting superiority: - Large weight and peculiar nature of food in aggregate utility. - World relative food price shocks are sizeable relative to monetary and technology shocks considered in earlier studies. - Mechanism: Food price shocks generate a distinct pattern of covariances between cost-push and demand shocks and induce real exchange rate volatility such that targeting PPI or the exchange rate becomes suboptimal for sufficiently high risk aversion and high disutility of work. - Sensitivity: - Welfare dominance of CPI targeting is heavily dependent on the large variance of external food price shocks. When that variance is very low, strict PPI targeting or exchange pegging rules are typically superior (in line with previous studies). - Increasing the weight on the output gap in the monetary policy rule can narrow the welfare gap between CPI and PPI targeting, provided the output gap is properly measured. The correct natural output measure must incorporate fluctuations in the world relative price of food; a rule responding to the correct output gap effectively approximates CPI targeting. - Policy implication: Since many small open economy central banks practice broad CPI targeting, the findings provide theoretical and empirical support for that practice; CPI targeting is also more conducive to lower volatility in global inflation as it implies a less lenient attitude toward imported inflation. ### Structure of the paper (contents overview) - Section 2: lays out the model, recursive equilibrium representation, and Phillips curve relationships; shows how inflation and the appropriate output gap measure are affected by changes in world relative food prices. - Section 3: canonical representation of the linearized model and impulse responses to monetary policy shocks, world food price shocks, and technological shocks. - Section 4: second-order approximation to welfare, non-stochastic steady state, and welfare ranking of policy rules across a wide range of calibrated parameters. - Section 5: summary of results and policy discussion. - Appendices provide recursive representation, relationship between home pricing and covariance of income and price shocks, and references, tables, and figures. *Source: _wp10161 - 1. Introduction* ### 2.4 Equilibrium: Recursive Representation ### 2.4 Equilibrium: Recursive Representation ### Equilibrium conditions and foreign demand - Foreign demand for the domestic aggregate is a function of its price relative to Π∗τ and world consumption index C∗τ, leading to market clearing: - Yhτ = Chτ + ϖ [ (Phτ / Sτ / P∗τ) ]^(−θ) C∗τ (equation 12 as stated) - Combining with (2) and the real exchange rate definition yields: - Yhτ = (1−α) [ (Phτ / Pτ) ]^(−χ) + ϖ Xτ^(θ) [ (Phτ / Pτ) ]^(−θ) C∗τ (equation 13 as given) - Intermediate pricing solution (from (11)): - 1 = (1−κ) [ (P̄τ / Phτ) ]^(1−ψ) + κ Πητ^(ψ−1) (equation 14) - Optimal pricing condition can be written: - P̄τ / Phτ Jτ = ψ / (ψ−1) Hτ (equation 15) - Accounting variables Jτ and Hτ are recursive: - Jτ = [ (P̄τ / Phτ) ]^(−ψ) Yhτ + κ Eτ Mt+1 [ (P̄τ / Phτ) (P̄τ+1 / Ph,τ+1) ]^(−ψ) Πη,τ+1^(ψ) Jτ+1 (equation 16) - Hτ = Fτ [ (P̄τ / Phτ) ]^(−ψ(1+φ)) Yhτ^(1+φ) + κ Eτ Mt+1 [ (P̄τ / Phτ) (P̄τ+1 / Ph,τ+1) ]^(−ψ(1+φ)) Πη,τ+1^(1+ψ(1+φ)) Hτ+1 (equation 17) - With: - 1 / (1+it) = β [ (Cτ+1 / Cτ) ]^(−σ) (Pτ / Phτ) (Pτ+1 / Ph,τ+1) Πη,τ+1^(−1) (equation 18) - Fτ = (1−ω) ˙Cτ^(−σ) Aτ^(−(1+φ)) (Pτ / Phτ) (equation 19) - The system comprised of equations 4, 6, 13, 14, 15, 16, 17, 18, 19 gives nine equations in ten variables: C, X, (Ph/ P), Yh, (P̄/ Ph), ... and requires specification of monetary policy (and Euler equation 5, if needed) to close the model. *Source: _wp10161 - 2.4 Equilibrium: Recursive Representation* --- ### 2.5 Marginal Costs ### First-order log-linear approximation and pricing - Pricing equation (first-order) following Gali (2008, p.45): - Σ_{κ=0}^∞ α^κ Eτ [ Mτ,τ+κ Yτ+κ|τ (P̄τ / Ph,τ−1 − ψ/(ψ−1) MCτ+κ|τ Πη,τ−1,τ+κ ) ] = 0 - First-order approximation yields: - P̄πτ − πh,τ−1 = (1−β α) Σ_{κ=0}^∞ (β α)^κ Eτ [ (mcτ+κ|τ − mc) + (πh,τ+κ − πh,τ−1) ] (equation 20) - where mc = log(ψ−1)/ψ = −ν is steady-state marginal cost - Relation for wholesale/producer price: - πhτ = (1−α) P̄πτ + α πh,τ−1 (equation 21) ### Real marginal cost decomposition - Real marginal cost for firms that set prices in τ: - mcτ+κ|τ = −ω + wτ+κ|τ − ατ+κ − πh,τ+κ - = −ω + [ log ˙ζ + σ cτ+κ|τ + φ nτ+κ|τ ] − ατ+κ + πτ+κ − πh,τ+κ - From production function and (10): - nτ+κ|τ = yτ+κ|τ − ατ+κ = ψ(πh,τ+κ − P̄πτ) + yh,τ+κ − ατ+κ - Hence real marginal cost can be written: - mcτ+κ|τ = −ω + log ˙ζ + σ cτ+κ + φ ψ(πh,τ+κ − P̄πτ) + φ yh,τ+κ − (1+φ) ατ+κ + πτ+κ − πh,τ+κ ≡ mcτ+κ + φ ψ(πh,τ+κ − P̄πτ) (equation 22) - Average marginal cost: - mcτ = −ω + log ˙ζ + σ c∗τ + φ yh,τ − (1+φ) ατ + (ξτ + α θτ) − (1+φ) ατ (as derived below) ### Marginal costs and international variables - Define domestic price of food relative to home output (inverse of terms of trade): - Θτ = Pfτ / Phτ = Sτ P∗fτ / Phτ - Log-linear approximation of (1): - πτ − πhτ = α θτ - With complete markets, marginal utility relates to world consumption and real exchange rate (equation 4). Taking logs yields: - mcτ = −ω + log ˙ζ + σ log Λ + σ c∗τ + φ yh,τ + (ξτ + α θτ) − (1+φ) ατ (equation 23) - Summary statement: - Domestic marginal costs depend on the term (ξτ + α θτ) — i.e., the real exchange rate and the terms of trade — in addition to domestic production yhτ and exogenous shocks. - Relation between real exchange rate and terms of trade: - ξτ = (1−α) θτ + (π∗τ − π∗fτ) = (1−α) θτ − ζ∗τ (equation 24) - where ζ∗τ = π∗fτ − π∗τ is a shock to the world relative price of imports; if ζ∗τ = 0, ξτ is proportional to θτ. - Domestic (producer) inflation Phillips-type relation: - P̄πτ − πh,τ−1 = (1−β α) Σ_{κ=0}^∞ (β α)^κ Eτ [ 1 / (1+φ ψ) (mcτ+κ − mc) ] + Σ_{κ=0}^∞ (β α)^κ Eτ [ πh,τ+κ ] (rearranged) - Combining with (21): - πhτ = β Eτ πh,τ+1 + λ (mcτ + ν) (equation 25) - where λ = (1−β α)(1−α)/α × 1/(1+φ ψ) - Key point: - Marginal costs — and thus inflation via the Phillips relation — depend not only on domestic production but also on ξτ + α θτ = θτ − ζ∗τ (terms of trade and real exchange rate), so at least one of these must be treated as endogenous. *Source: _wp10161 - 2.4 Equilibrium: Recursive Representation* --- ### 2.6 Output and Relative Prices ### Market clearing and link between output and terms of trade - Market clearing (restate of 12 and manipulations): - Yhτ = Chτ + ϖ [ Phτ / Sτ / P∗τ ]^(−θ) C∗τ = (1−α) [ Phτ / Pτ ]^(−χ) + ϖ [ Phτ / Sτ / P∗τ ]^(−θ) C∗τ - = C∗τ { μ(1−α) [ Phτ / Pτ ]^(−χ) X^(1/σ)τ + ϖ [ Phτ / Sτ / P∗τ ]^(−θ) } (equation 26 as presented) - Log-linearization yields: - yhτ = c∗τ + { ι [ χ(πτ − πhτ) + (1/σ) ξτ ] + (1−ι) θ (σ τ − π∗τ − πhτ) } - Simplified and expressed in terms of θτ and ξτ: - yhτ = c∗τ + { ι [ χ α θτ + 1/σ ξτ ] + (1−ι) θ (ξτ + α θτ) } - Using ξτ = (1−α) θτ − ζ∗τ gives: - yhτ = c∗τ + θτ · { ι [ χ α + (1−α)/σ ] + (1−ι) θ } − ζ∗τ ( ι / σ + (1−ι) θ ) (equation 27) - where ι = Chh / Yh is the steady-state ratio of home consumption of home goods to domestic production. - Interpretation and implications: - Equation 27 establishes the equilibrium link between domestic production yhτ and terms of trade θτ. - Increases in domestic production must be associated with a deterioration in the terms of trade (an increase in θτ). - The magnitude of the terms of trade deterioration depends on elasticities and shares (χ, σ, θ, ι, α). - The equilibrium link is shifted by changes in world demand c∗ and by changes in the relative price of imports ζ∗τ. *Source: _wp10161 - 2.4 Equilibrium: Recursive Representation* ### 2.7 The Phillips Curve ### 2.7 The Phillips Curve ### Derivation and structure of the Phillips Curve - Starting point: deviations of marginal costs from their flexible-price (natural) value satisfy - μχτ + κ = η(ψτ − ψνητ) + (θτ − θντ) - Inserting the above into the price-setting relation (25) yields a New Keynesian Phillips Curve: - πητ = β Eτ [πη,τ+1] + λ η (ψτ − ψνητ) + λ (θτ − θντ) (29) - Using market-clearing under flexible prices and eliminating (θτ − θντ) gives the Phillips curve in conventional output-gap form: - πητ = β Eτ [πη,τ+1] + R (ψτ − ψνητ) - where R = λ{η + Θ} - Key analytical points: - The slope R depends on elasticities and structural parameters, including the degree of openness α (). - The Phillips curve incorporates both the conventional output-gap effect on marginal costs and the effects of the terms-of-trade gap. - The natural rate of output is endogenous and moves with shocks, including world relative price shocks ζ∗τ. ### Natural rate of output and terms-of-trade effects - Natural marginal-cost relation (flexible prices) (28): - −κ = −A + log ω̇ + σ log b + η ψντ + θντ + σ χ∗τ − ζ∗τ − (1 + η) ατ - Natural market-clearing condition (30): - ψνητ = χ∗τ + θντ · {φ [ξ α + (1 − α)/σ] + (1 − φ) τ} − ζ∗τ (φ/σ + (1 − φ) τ) - Relationship between deviations (31): - Θ(ψτ − ψνητ) = (θτ − θνητ) with 1/Θ = {φ [ξ α + (1 − α)/σ] + (1 − φ) τ} - Closed-form for the natural rate of output (32): - ψνητ = 1/(η + Θ) (−κ − (σ − Θ) χ∗τ + Θ[φ α (ξ − 1/σ)] ζ∗τ + A − log ω̇ − σ log b + (1 + η) ατ) - Special parameterization: - If ξ = τ = 1/σ then coefficients on foreign demand χ∗τ and world food prices ζ∗τ are zero and the model becomes isomorphic to a closed economy where natural output fluctuates only with productivity shocks. - Comparative-static intuition: - A unit shock to ζ∗τ shifts MM (marginal-cost relation) up by one unit; it shifts DD (market-clearing) up by Θ(φ/σ + (1 − φ) τ). - A positive ζ∗τ shock increases θνητ (deteriorates natural terms of trade). - The sign of the effect on ψνητ depends on whether Θ(φ/σ + (1 − φ) τ) < 1, which reduces to the sign of (ξ − 1/σ). - Demand adjustment to real exchange rate movements depends on ξ − 1/σ, openness α (), and home-good share φ (). ### Impulse responses to world food price shocks (ζ∗τ) - Natural levels solved (ignoring constants): - ψνητ = ˜ψ ζ∗τ - θνητ = ˜θ ζ∗τ - where ˜ψ = Θ[φ  (ξ − 1/σ)]/(η + Θ) and ˜θ = Θ[1 + η(φ/σ + (1 − φ) τ)]/(η + Θ) - Dynamic IS (in output-gap form) (33): - ˜ψτ = Eτ ˜ψτ+1 + 1/[Θ(1 − )] [iτ − Eτ πτ+1] + { [Θ φ  (ξ − 1/σ)/(η + Θ) + Φ − 1/(Θ(1 − ))] } Eτ Δζ∗τ+1 - where Φ = φ/σ + (1 − φ) τ - CPI vs PPI inflation relation: - πτ = πητ +  Δθτ (34) - Δθτ = Δθντ + Θ Δ˜ψτ = ˜θ Δζ∗τ + Θ Δ˜ψτ - Reduced-form IS in PPI terms (35): - ˜ψτ = Eτ ˜ψτ+1 + 1/Θ [iτ − Eτ πη,τ+1] + {[(1 − )(Φ + ˜ψ) − (1 − ) ˜θ]/Θ} Eτ Δζ∗τ+1 - NK Phillips curve (36): - πητ = β Eτ [πη,τ+1] + R ˜ψτ ### Responses under a PPI-based Taylor rule - PPI rule (log-linearized form used in section 3): - iτ = ϕψ ˜ψτ + ϕπ η πητ - Conjectured IRF form for ζ∗τ with AR(1): ζ∗τ = ρζ ζ∗τ−1 + εζτ and solutions: - ˜ψτ = C PPI ψ ζ∗τ - πητ = C PPI π ζ∗τ - Closed-form coefficients (37)–(39) and denominator ΩPPI: - C PPI ψ = 1/ΩPPI · [1 + Θ/η − (η + Θ)/η ˜θ − Θ ˜ψ] (37)/(38) - C PPI π = λ(η + ς)/(1 − β ρζ) C PPI ψ (39) - ΩPPI = [Θ − 1/(1 − ρζ) (ϕψ + (ϕπη − ρζ) λ(η + ς)/(1 − β ρζ))] - Calibrated example (as in the text): - food expenditure share set to 25% so that φ = 0.75 - elasticity parameter σ (risk version) set to 2 ( = 2) - baseline ρζ and other parameters from Table 4 (as in the source) - Special case ξ = 1/σ: - ˜θ = 1 and Φ Θ = 1 ⇒ C PPI ψ = C PPI π = 0: neither the output gap nor PPI inflation respond to ζ∗ shocks under a PPI rule. - Terms of trade follow ζ∗τ path; real exchange rate xτ = (1 − ) θτ − ζ∗τ = − θτ implies on-impact appreciation by  = 04 percent in the calibrated example. - Consumption falls by (1/σ) reflecting risk sharing; CPI inflation rises by  on impact, then falls by  Δθτ. - General case ξ ≠ 1/σ: - If ξ < 1/σ (limited substitutability), then ˜ψ < 0 and ˜θ < 1: natural output falls and natural terms-of-trade undershoot the shock. - Output gap and PPI inflation decline with a ζ∗τ shock; nominal interest rate falls under PPI rule. - If ξ > 1/σ, the opposite: positive world food-price shocks become expansionary. - The magnitude of effects depends on ξ − 1/σ, openness , and φ. ### Responses under a CPI-based Taylor rule - CPI rule used in section 3: - iτ = ϕψ ˜ψτ + ϕπ πτ - System to solve (CPI case) includes: - πητ = β Eτ [πη,τ+1] + R ˜ψτ - πτ = πητ + (˜θ Δζ∗τ + Θ Δ˜ψτ) - ϕψ ˜ψτ + ϕπ πτ = Eτ [(˜θ − 1) Δζ∗τ+1 + Θ Δ˜ψτ+1 + πη,τ+1] - Special case ξ = 1/σ (˜θ = 1): - Reduced equations (41) and the combined condition determine output-gap and PPI-inflation dynamics. - Even when ξ = 1/σ, CPI targeting implies Δζ∗τ appears in the equilibrium system; output gap and PPI inflation cannot both remain zero for a ζ∗τ shock. - Output-gap response under CPI targeting (42): - C CPI ψ = 1/Ω CPI · [ρζ (ρζ −  ϕπ) − Φ Θ − Θ^2 φ  (ξ − 1/σ)/(η + Θ)] - Comparison CPI vs PPI: - Output gap typically responds more strongly under CPI targeting when 0 <  ϕπ < 1 because ρζ(ρζ −  ϕπ) > 1. - Higher openness  amplifies the relative strength of the CPI response. - For sufficiently high ρζ and  ϕπ, the output gap may not contract even when ξ < 1/σ; PPI inflation then remains positive under CPI targeting. - Overall, CPI targeting is typically less contractionary than PPI targeting in response to ζ∗ shocks. - Transmission under CPI targeting: - CPI targeting makes the interest-rate respond to πητ and Δζ∗τ (through CPI), strengthening the interest-rate response to ζ∗ shocks relative to PPI rule. - Eτ πτ+1 = ρζ Cπ ζ ζ∗τ so Eτ πτ+1 rises by less than πτ ⇒ the real interest rate iτ − Eτ πτ+1 rises ⇒ by Euler, Eτ Δχτ+1 rises while current χτ falls ⇒ nominal exchange rate depreciation (Δsτ = −σ Δχτ + πτ). - Output and home inflation move together under CPI targeting (C PPI π = λ(η + ς)/(1 − β ρζ) C CPI ψ > 0), and responses strengthen with larger ξ − 1/σ. ### Welfare objective and evaluation - Second-order approximation of representative-agent expected utility (following Gali 2008, Woodford 2003) yields objective function components (consumption and labor) and terms in πητ variance: - Utility relevant terms (43): - Uτ = U + E Σ βτ { C̄1−σ/(1 − σ) (χτ + (1 − σ)/2 χτ^2) − N1+η [ψητ − ατ + (1 + η)/2 ψητ^2 − (1 + η) ατ ψητ + (1 + η)/2 ατ^2 + Θ πητ^2 ] } - Θ = 1/2 ϱ (1 + η ϱ) · α/(1 − α)(1 − β α) - Variance of idiosyncratic log prices maps to aggregate πητ^2 via Woodford result: - E Σ βτ varφ(log πτ(φ)) = α/(1 − α)(1 − β α) E Σ βτ πητ^2 - Numerical welfare evaluation: - Use second-order solution methods (Schmitt-Grohé and Uribe (2004) procedures) to compute welfare under alternative policy rules (PPI targeting, CPI targeting, nominal exchange-rate peg) given the full nonlinear equilibrium and stochastic processes for ζ∗τ and other shocks. ### Policy comparison setup (brief) - Policy rules considered: - PPI (producer-price) Taylor rule: log(1 + iτ) = (ρ + ϕπ (Πητ − 1) + ϕψ (ψητ − ψνητ) + vτ) - CPI Taylor rule: log(1 + iτ) = (ρ + ϕπ (Πτ − 1) + ϕψ (ψητ − ψνητ) + vτ) - Nominal exchange-rate peg: Sτ fixed at S, implying Xτ = S P∗τ / Pτ and additional equilibrium conditions - Model closure: - For peg, Euler equation is withdrawn from the monetary policy rule; system solved for eleven variables including domestic price level Pη. - World price process introduced: p∗τ = α + β p∗τ−1 + ετ *Source: IMF Working Paper section "2.7 The Phillips Curve" (from the supplied PDF content)._ ### 5.2 Policy Rankings ### 5.2 Policy Rankings ### Methodology and welfare metric - Welfare comparisons follow the numerical procedure and programs of Schmitt Grohe and Uribe (2004), and the conditional-starting-point approach of Schmitt-Grohe and Uribe (2007) and Wang (2006). - Welfare is computed conditional on all state variables being in their non-stochastic steady state. - The second-order approximation of the instantaneous discounted value of representative-agent welfare, conditional on the steady-state starting point, takes the form: - V_t = V + 1/2 γ''(−ξ,0) σ - where V is steady-state conditional utility, ξ is the vector of state variables evaluated at the model’s non-stochastic steady state, γ'' is the second derivative of γ with respect to the variance of the shocks (when control variables take the form ψ_t = γ(ξ_t, σ)), and σ is a scalar on the distribution of the shocks. - Computational implementation: add a control variable V_t to the S-U algorithm evolving according to V_t − β V_t = U(C_t, L_t). - Relative welfare loss of policy rule "1" relative to policy rule "2", expressed in percentage units of steady-state consumption, is: - τ = 100 × (1 − ε^{(1−β)(V_1 − V_2)}) ### Determinants of welfare rankings - Welfare-superiority of a policy rule depends on how it affects: - the volatility of consumption (negative effect) versus the level of consumption (positive effect); - variability in labor supply and the disutility of work (negative effects); - variability of home good inflation (negative effect). - The relative weights are given by intra- and inter-temporal elasticities, the weight of consumption in utility (φ), parameters pertaining to price stickiness, and food share in consumption. - With world consumption C* exogenously given, the risk sharing condition implies that both the level and volatility of domestic consumption depend on the volatility of the real exchange rate X_t. - X_t is directly affected by the world relative price of food and not necessarily one-to-one with the terms of trade. - Once departing from certainty-equivalence, volatility of relative prices can affect mean prices and quantities; variance of Z_t can affect level of X_t and hence consumption. - Under imperfect international competition, level and volatility of Z_t and X_t affect home output and thus level and volatility of work effort. - Domestic substitution between food and non-food home goods, together with price stickiness, makes volatility of Z_t affect home good prices. - Critical to welfare rankings is how each policy rule responds to volatility of world food prices. ### Calibration strategy and parameter ranges - Benchmarks: prototype emerging market (Chile) and other international data used to calibrate stochastic processes for: - relative world price of food; - TFP; - domestic and external interest rate shocks. - Taylor rule coefficients chosen close to those estimated for economies operating inflation-targeting regimes. - Robustness evaluated across: - standard deviation and persistence of shocks; - intra-temporal elasticity of consumption allowed to take values between 0.25 and 4; - coefficient of risk aversion (the inverse of the inter-temporal elasticity) allowed to take values between 0.5 and 4. - World income Y* and initial level of net foreign assets are fixed; φ is allowed to adjust to keep 1 − α fixed. - The ratio of home good consumption to income in steady state (α) is set to 0.75 and later varied in the range 0.6 to 0.9. ### Baseline shock processes and parameter values reported - World consumer price index initially fixed to unity, later allowed to evolve with: - AR(1) persistence ρ = 0.99; - quarterly standard deviation 1.3%; - obtained from a quarterly AR(1) regression of an unweighted average of advanced countries (G-8) PPIs during the 1990-2008 period. - Relative world price of food (z*) parameterized with: - conditional (quarterly) standard deviation 4.5%; - AR(1) coefficient 0.85; - consistent with regressions of the IFS-IMF index of food commodity prices relative to world (G-8) WPI between 1990 and 2008. - Productivity (TFP) shocks (based on Chilean estimates): - standard deviation 1.2% per quarter; - AR(1) coefficient 0.7; - note: Gali and Monacelli (2005) reported a Canadian TFP standard deviation of 0.7%, roughly half that for Chile. - Calibration of v_t: obtained by running a Taylor-rule type regression with Chilean data from 1991 to (text truncated in source). ### Numerical experiment focus - Numerical calibrations illustrate how different policy rules trade off consumption level versus volatility, labor variability, and home good inflation variability, especially in response to world food price volatility. - Robustness checks include varying TFP parameters and other shock characteristics. *Source: _wp10161 - 5.2 Policy Rankings* ### 2008. We obtain a standard deviation of ### _wp10161 - 2008. We obtain a standard deviation of ### Baseline parametrization and core numerical setup - Standard deviation of v (monetary policy shock) in baseline: 0.62% per quarter. - AR(1) coefficient for v: 0.6. - Labor supply elasticity (1/) calibration range: from 1 (benchmark) to 1/3. - Export price elasticity () calibration range: from 1 (benchmark) to 5. - Baseline steady-state openness: =0.75 (unless otherwise noted). - Secondary Monte Carlo: model solved to second order and simulated with 20,000 random draws of z*, a, and v shocks to compute moments. ### Main welfare-ranking findings - With baseline parametrization (Table 6: coefficient on the output gap set to zero — "strict" inflation targeting): - CPI ("rule 2") is the superior rule for the majority of − configurations, especially when  is low and  is high. - The classic closed-economy result of PPI dominance is overturned once realistic international relative price shocks (food price shocks) are allowed. - If variance of world food price shocks (z*) is set near zero (Table 7): - Results revert to previous-author findings: either exchange rate peg or PPI targeting dominates. - For unit elasticity case (===1) and with negligible z* variance, trade is balanced at all times and the economy is isomorphic to the Gali-Monacelli benchmark where PPI is dominant. - Table 8 (moments by shock-type): - If only food price shocks are present, CPI targeting yields: - Lower RER volatility. - Lower consumption volatility. - Lower output (hence lower effort). - Higher consumption-to-output ratio (C/Y). - Average RER more appreciated by 0.32% above SS (steady state). - If only productivity or only monetary shocks are present: - PPI targeting produces lowest consumption and RER volatility and (marginally) higher C/Y — hence PPI preferred when domestic productivity shocks dominate. - Monetary shock volatility and persistence (Tables 9 and 10): - Doubling monetary policy shock standard deviation from 0.6% per quarter to 1.2% per quarter increases attractiveness of the peg. - Increasing persistence of v from 0.6 to 0.8 has a similar effect. - Larger monetary shocks increase numerical magnitudes of welfare differences; in some cases welfare gaps reach 0.6% of steady state consumption. - Domestic TFP shock volatility (Tables 11 and 12): - Increasing volatility/persistence of domestic TFP shocks increases attractiveness of PPI relative to other rules. - Keeping z* standard deviation at non-trivial levels (4.5% a quarter) prevents far-reaching PPI dominance. - Stronger anti-inflation stance (Table 13): - Raising inflation reaction parameter to =3.0 increases attractiveness of exchange rate pegs. - For CPI vs PPI, a more hawkish stance increases PPI dominance over CPI, though welfare gaps remain tiny for  above 1. - More dovish monetary policy (Table 14): - Numerical welfare gaps between PPI and CPI rise, favoring CPI targeting. - Output-gap weighting in policy (Table 15): - Introducing output weighting (correct model measure of natural output) reduces numerical gaps between rules; CPI and PPI welfare differences shrink considerably for higher . - Higher export price elasticity (Table 16:  from 1 to 5): - Greater substitutability reduces scope to exploit terms-of-trade externality, but also implies greater RER volatility leads to greater domestic output and employment volatility. - Net effect: CPI becomes even more attractive than PPI; CPI beats PEG more often. - Lower labor supply elasticity (Table 17: raise  from 1 to 3, i.e. lower 1/): - Reduces attractiveness of the peg relative to both CPI and PPI. - World price p* stochasticity (Table 18): - Letting p* be very persistent with quarterly variance of 1.3% (close to data) increases dominance of CPI and PPI relative to peg; CPI still dominates for higher  and lower . - Openness experiments: - Higher openness (=0.6 in Table 19) increases CPI rule dominance; for  above 0.5 CPI dominance becomes overwhelming. - Under empirically realistic higher  and lower , welfare gains of CPI relative to PPI range between 0.33 and 0.62 of steady state consumption: - 0.33 (=2 and =025) - 0.62 (=2 and =075) - Lower openness (=0.9 in Table 20) makes PPI more dominant, though welfare gains remain relatively tiny. ### Mechanisms behind CPI dominance when food shocks matter - Food in utility: large weight and limited substitutability amplify the welfare relevance of world food price shocks. - CPI targeting implies more aggressive monetary policy response to world food price shocks (tighten on price rises, loosen on falls) than PPI or peg. - This yields greater real exchange rate (RER) stability and a more appreciated RER on average. - A more appreciated RER raises the consumption-to-output ratio (C/Y), allowing higher consumption for a given output and exploiting the terms-of-trade externality. - When only productivity shocks are present: - Under Calvo-pricing the covariance between income and marginal cost shocks is negative. - PPI aims to stabilize Ph and reacts more procyclically to productivity () shocks than CPI. - This limits the fall in marginal costs and makes the covariance less negative under PPI, raising the home price level and appreciating the RER under PPI. - Thus PPI produces higher C/Y under productivity shocks, explaining PPI preference in such environments. - Trade-offs: - CPI’s benefits (lower consumption volatility, higher average C/Y via appreciated RER) must offset PPI’s benefits (better offsetting of sticky-price distortions that raise output/employment). - Relative dominance depends on relative magnitudes and persistence of food shocks versus monetary and productivity shocks, plus preferences (risk aversion) and labor disutility. ### Sensitivity and robustness insights - Allowance for non-trivial z* variance (world food price shocks) is crucial: when sizable, it can overturn closed-economy PPI dominance. - Welfare rankings are sensitive to: - Volatility and persistence of monetary shocks (v). - Volatility and persistence of domestic TFP (z). - Degree of openness (). - Elasticities: labor supply (1/) and export price (). - Policy instrument aggressiveness () and inclusion of output gap in reaction function. - Numerical welfare differences are generally small in absolute terms but can reach economically meaningful magnitudes under some calibrations (up to 0.6% of steady state consumption; up to 0.62 of steady state consumption in high-openness CPI vs PPI cases reported). ### Policy implications - Rationale strengthened for broad CPI targeting when food plays a large role in utility and world food price shocks are large and persistent: - CPI targeting yields transparency and avoids ad hoc exclusions defining "core" inflation. - CPI targeting mitigates regressive distributional bias (food is a larger share of spending for poorer households who have limited smoothing capacity). - Central banks should not be overly lenient toward imported food price shocks; excessive accommodation that follows PPI or peg rules can be welfare-inferior for food-importing small open economies. - A correct output-gap measure that includes terms-of-trade fluctuations (relative world food prices) can narrow or overturn CPI superiority if the central bank reliably uses it; practical measurement challenges limit this route. - Less accommodative CPI-based policy by many central banks would reduce uncoordinated inward-oriented responses to world price shocks and help keep global inflationary pressures in check. ### Model and technical notes (appendices) - Model: small open economy with differentiated varieties, monopolistic competition with Calvo pricing, and complete asset markets. - Recursive representation and pricing relationships are derived in Appendix 1 and Appendix 2 (pricing function, recursive variables , , , , and equations relating home pricing to covariance of income and cost shocks). - Key symbolic relations preserved in the text include expressions for: - Pricing function summation over  expectations. - Definitions: +|, , , , and recursive formulas linking these variables. - Equation (44) representation linking aggregate sums of expectations and covariances relevant for home price level determination. *Italic: Source — content unit: _wp10161 - 2008. We obtain a standard deviation of* ### References ### References ### Bibliographic References - Aoki, K. (2001) "Optimal Monetary Policy Response to Relative Price Changes" Journal of Monetary Economics 48, pp55-80. - Benigno and Benigno, 2003, Price Stability in open economies, Review of Economic Studies 70, 743-764. - Bergin, P., Shin, H., Tchakarov, I., 2007. Does exchange rate variability matter for welfare? A quantitative investigation of stabilization policies. European Economic Review 51(4), 1041-1058. - Bodenstein, Martin, Christopher Erceg, and Luca Guerrieri, 2008, "Optimal Monetary Policy with Distinct Core and Headline Inflation Rates", Journal of Monetary Economics 55, pp.518-533. - Corsetti and Pesenti, 2001 Welfare and Macroeconomic Independence, Quarterly Journal of Economics, 116, 421-445. - Cova, P., Sondergaard, J., 2004. When should monetary policy target the exchange rate? Royal Economic Society Annual Conference, Paper Number 51. - Deaton, Angus., 1998. Getting Prices Right: What Should be done?. Journal of Economics Perspectives-Vol 12, Num 1. - Devereaux and Engle, 2003, Monetary Policy in the open economy revisited: price setting and exchange rate flexibility, Review of Economic Studies 70, pp. 765-783 - Deveraux, M., P. Lane and J. Xu, 2006, Exchange Rates and Monetary Policy in Emerging Market Economies, Economic Journal. - De Paoli, Bianca, 2009. Monetary policy and welfare in a small open economy. Journal of International Economics 77 (2009) 11—22. - Kiliam, Lutz, 2009, "Not All Price Shocks are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market," American Economic Review, 99(3), pp.1053-69. - Kollmann, R., (2002) "Monetary Policy Rules in the Open Economy: Exoects on Welfare and Business Cycles" CEPR Discussion Papers 3279, C.E.P.R. Discussion Papers. - Galí, Jordi. 2008. Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework - Galí, Jordi and Tommaso Monacelli, 2005. Monetary Policy and Exchange Rate Volatility in a Small Open Economy. Review of Economic Studies (2005) 72, 707-734. - Goodfriend, M. and R. King, 2001, The Case for Price Stability, NBER Working paper 8423. - Gouveia, Solange, 2007, Price Rigidity in Brazil: Evidence from CPI Micro Data, Working paper 143, Central Bank of Brazil. - Obstfeld and Rogoff, 2002, Global Implications of self-oriented national policy rules, Quarterly Journal of Economics, 117, pp. 503-535 - Rigobon, Robert, 2008. "“Distribution of Inflation Impact: The Recent Experience in Central America and Mexico” " - Rose, Andrew, 2007, "A Stable International System Emerges: Inflation Targeting is Bretton Woods Reversed", Journal of International Money and Finance 26, pp. 663-81 - Schmitt-Grohe, S. and M. Martin Uribe, 2004. Solving dynamic general equilibrium models using a second-order approximation to the policy function. Journal of Economic Dynamics & Control 28 (2004) 755 — 775 - Schmitt-Grohe, S. and M. Martin Uribe, 2007, "Optimal Simple and Implementable Monetary and Fiscal Rules", Journal of Monetary Economics, 54, 1702-1725. - Sutherland, A, 2005, Incomplete Pass-through and welfare effects of exchange rate variability, Journal of International Economics, 65, pp.375-399. - Woodford, Michael, Interest and Prices: Foundations of a Theory of Monetary Policy, Princeton University Press, 2003. ### Tables (titles and select exact statistics) - Table 1: Correlations between World Inflation Indicators and Food and Oil Prices, 1990-2008 (all series HP detrended) - Contemporary Correlations: USWPI 1 0.83689 0.74349 0.61911 0.7255 - Overall structure shows pairwise correlations among USWPI, World WPI, World CPI, Pfood, Poil. - Lagged Correlations: USWPI 1 0.83689 0.74349 0.44189 0.29036 - Table 2: Causality Tests (47 observations used for estimation from 1962 to 2008) - a) Food Prices -US WPI: Dependent variable is WPIGAP; Independent variables: ZGAP(-1) -ZGAP(-2). Lagrange Multiplier Statistic CHSQ(2)= 10.4873[.005]; Likelihood Ratio Statistic CHSQ( 2)= 11.8668[.003]; F Statistic F( 2, 42)= 6.0317[.005] - b) Oil Prices -US WPI: Lagrange Multiplier Statistic CHSQ( 2)= 1.4879[.475]; Likelihood Ratio Statistic CHSQ( 2)= 1.5119[.470]; F Statistic F( 2, 42)= .68653[.509] - c) Oil -Food: Lagrange Multiplier Statistic CHSQ( 2)= 1.1923[.551]; Likelihood Ratio Statistic CHSQ( 2)= 1.2077[.547]; F Statistic F( 2, 42)= .54659[.583] - d) Food -Oil: Lagrange Multiplier Statistic CHSQ( 2)= 14.1011[.001]; Likelihood Ratio Statistic CHSQ( 2)= 16.7653[.000]; F Statistic F( 2, 42)= 9.0010[.001] - Table 3: Food Expenditure Shares - Selected country values: Austria 15.50%; Belgium 16.10%; Bulgaria 43.36%; Costa Rica 13.11%; Romania 58.74%; United Kingdom 12.91% - Overall Median 23.55%; Overall Mean 25.26%; EM Median 32.69%; EM Mean 33.95%; Advanced Median 15.55%; Advanced Mean 16.81% - Table 4: Calibration of parameters - Discount Factor  0.99 - Coefficient of risk aversion  [1,4] - Degree of Openness  0.4 - Average period between price adjustments  0.66 - Coefficient on domestic inflation in Taylor Rule   1.5 - Coefficient on output gap in Taylor Rule   0.125 - Parameter of persistence associated with moderately persistent monetary policy shock   0.6 - Parameter of persistence associated with moderately persistent world relative food price shock   0.85 - Elasticity of substitution between varieties produced within country  6 - Ratio   /   in steady state  0.75 - Table 5: Calibration of parameters in Welfare Comparison of policy rules - Discount Factor  0.99 - Coefficient of risk aversion  [0.5,4] - Inverse of elasticity of labor supply  [0.5,1] - Coefficient on domestic inflation in Taylor Rule   [1.1,2] - Coefficient on output gap in Taylor Rule   0 - Parameter of persistence associated with persistent monetary policy shock   [0.6,0.8] - Parameter of persistence associated with persistent relative food’s price shock   [0.85,0.9] - Index of foreign demand  ∗ 0.27 - Standar Deviation associated with monetary policy shock   [0.0062,0.0167] - Standar Deviation associated with relative food’s price shock   0.05 - Standar Deviation associated with productivity shock   0.012 - Table 6 through Table 20: Welfare Comparisons and model sensitivity tables - Each table labeled with scenario (e.g., "Welfare Comparisons with Baseline Calibration", "Low Variance of Food Prices", "Higher Variance of Monetary Shocks", "Higher Persistence of Monetary Shocks", "Lower Variance of Productivity Shocks", "Higher Persistence of Productivity Shocks", "'Hawkish' Taylor Rule", "'Dovish' Taylor Rule", "Taylor Rule with Moderate Reaction to Output Gap", "High Export Price Elasticity", "Lower Elasticity of Labor Supply", "World Inflation Variability", "Higher Food Import Share", "Lower Food Import Share") - Tables present numeric welfare differences (e.g., Domestic Inflation-CPI Inflation, CPI Inflation - PEG, Domestic Inflation-PEG) across grids of \ = 0.25, 0.5, 0.75, 1, 2, 4 and report dominance relative to SS as digit matrices (examples: Dominance relative to SS entries such as rows "0.5 1 2 4" with strings like 0.513333, 0.7533232, 122212, etc.) - Exact numeric entries and scenario-specific parameter values are provided in each table (e.g., in Table 6 header:   =15   =06   =06%   =07   =12% =025; =1; =1;   =5% ; =075) - Table 8: Model statistics Under Simulated Random Shocks SS with Balance Trade and  = 075 - Standard deviations (in %), Means in % of SS deviation, and Consumption/Output ratio under various rules (PPI rule, CPI rule, PEG rule) and shock types; sample numeric entries include Domestic Output 0.367 1.137 0.863 0.000 0.936 0.945; Consumption 1.154 1.152 0.546 0.606 0.584 0.292; CPI-based Real Exchange rate 2.307 2.298 1.091 2.420 2.328 1.164 - Additional parameter blocks with =4; =025; =1 etc., and corresponding standard deviations such as Domestic Output 0.269 0.315 0.313 0.424 0.497 0.501 1.101 0.887 - Across Tables 6–20: numerous exact numeric welfare differences are tabulated under specified parameterizations (preserve numbers as shown in the source tables for scenario analysis and dominance metrics) ### Figures (titles and captions) - Figure 1: World WPI and World Relative Food Prices (in deviations from HP-trend) - Time series plotted from 1960 through 2008 with percent scale markers at -15% to 35%, labeled series "WPI" and "World Food/WPI". - Figure 2: Effects of Food Price Shocks on Natural Output and the Terms of Trade - Diagram with labels q n, y n, D D D’, M M M’, E E’ - Figures 3–6: Impulse Responses of one unit world food’s relative price shock with specified parameter sets - Figure 3: with  = 2 and  = [0.25, 0.5, 0.5, 2] and  = 1 with PPI rule - Figure 4: with  = 2 and  = [0.25, 0.5, 0.5, 2] and  = 5 with PPI rule - Figure 5: with  = 2 and  = [0.25, 0.5, 0.5, 2] and  = 1 with CPI rule - Figure 6: with  = 2 and  = [0.25, 0.5, 0.5, 2] and  = 5 with CPI rule *Source: _wp10161 - References (PDF)* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10161.pdf_