## _wp10200

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---

### Context and motivation
- Global financial crisis renewed debate on monetary policy objectives; consensus that low and stable inflation remains primary objective.
- Central operational issue: choice of price index for the inflation objective—determines level of inflation consistent with price stability and appropriate index to target.
- Literature guidance: core inflation (excluding food, energy, volatile components) often recommended because food and energy fluctuations are viewed as supply, non-monetary shocks (Wynne, 1999; Mishkin, 2007, 2008).
- Empirical facts motivating the analysis:
  - Share of food in total household expenditures much higher in emerging markets: nearly 40-50 percent versus 10-15 percent in advanced economies.
  - Average price elasticity of food in sample of 114 countries: -0.34.
  - Evidence on proportion of rule-of-thumb / credit-constrained consumers: Campbell and Mankiw estimate nearly 50 percent in the U.S.; Muscatelli, Tirelli and Trecroci (2004) estimate about 37 percent rule-of-thumb consumers accounting for 59 percent of total employment.
- Key conceptual point: under incomplete markets with credit-constrained consumers, stabilizing core inflation may not stabilize output; food-price (flexible-sector) fluctuations affect real wages and aggregate demand.

### Modeling approach and calibration
- Model structure:
  - Two sectors, two goods: flexible-price good = food (F_C), sticky-price sector = continuum of monopolistically produced non-food goods.
  - Heterogeneous households: fraction of consumers are credit-constrained (rule-of-thumb) who consume current labor income; others can buy one-period nominal bonds and smooth consumption.
  - Subsistence level of food consumption: minimum amount C* required for survival; all households assumed able to buy subsistence C*.
  - Price stickiness via Calvo mechanism with fraction α of firms unable to change prices each period.
- Key definitions and policy regimes:
  - Headline inflation Π_t ≡ P_t/P_{t-1}; sticky-sector (core) inflation Π_{s,t} ≡ P_{s,t}/P_{s,t-1}.
  - Monetary policy rule: log R_t = ρ_R log R_{t-1} + ρ_π log(Π_t/Π̄) + ρ_y log(Y_t/Ȳ) + ... (equation (34)).
  - Policy regimes evaluated:
    - Strict Core Inflation Targeting (stabilize Π_{s,t}) (eq. (35)).
    - Strict Headline Inflation Targeting (stabilize Π_t) (eq. (36)).
    - Flexible Core Inflation Targeting (stabilize Π_{s,t} and output gap) (eq. (37)).
    - Flexible Headline Inflation Targeting (stabilize Π_t and output gap) (eq. (38)).
- Baseline calibration (selected parameters):
  - Discount factor β = 0.9902.
  - Risk aversion σ = 2.
  - Elasticity of substitution between differentiated non-food goods θ = 10 (implies markup = 11 percent).
  - Price stickiness α = 0.66 (mean duration of fixed prices = 3 quarters).
  - Inverse Frisch elasticity ψ = 3 (Frisch elasticity = 0.33).
  - Elasticity between food and non-food η = 0.6.
  - Food weight γ = 0.3050.
  - Subsistence food parameter C* = 0.1013.
  - Calibration implies steady-state household expenditure on food = 42 percent (assumption: on average half of steady-state food consumption is subsistence).
  - Monetary policy parameters (Taylor rule baseline): i_ρ = 0.7, π_ρ = 2, Y_ρ = 0.5.
  - AR(1) persistence: food shock 0.25; non-food shock 0.95.
  - Shock volatilities: σ_af = 0.03; σ_as = 0.02.

### Baseline results and key quantitative findings
- Complete markets (representative-agent setting):
  - Strict core inflation targeting is welfare-maximizing.
  - Strict headline targeting: welfare loss relative to strict core (Table 6 shows Strict Headline Targeting: -0.07; Flexible Headline Targeting: -0.22; Flexible Core Targeting: -0.19 under Complete Markets).
  - Stabilizing inflation ≡ stabilizing output (Aoki, 2001); flexible targeting offers no additional welfare gains.
- Incomplete markets (credit-constrained consumers present):
  - Flexible headline inflation targeting is welfare-maximizing.
  - Table 6 (Incomplete Markets) — welfare gains (ω*100, percent increase in strict-core consumption needed to equate welfare; positive = alternative better than strict core):
    - Strict Headline Targeting: 3.21
    - Flexible Headline Targeting: 4.18
    - Flexible Core Targeting: 1.58
  - Mechanism: credit-constrained households consume current wage income; if core targeting ignores food-price inflation, food-sector wages rise more after a negative food productivity shock, boosting constrained-household consumption and potentially increasing aggregate demand despite monetary tightening. Targeting headline inflation damps relative-food-price and wage responses and makes monetary policy effective at stabilizing aggregate demand.
- Dynamics and persistence:
  - Empirical evidence: headline inflation more volatile than core inflation; volatility and persistence higher in emerging markets.
  - Representative episodes: Canada experienced headline inflation above core for 30 consecutive months (spring 1999–fall 2001); Thailand for more than 5 consecutive years after adopting IT.
- Impulse responses:
  - Impulse responses to a 1 percent negative food productivity shock: under incomplete markets, strict core targeting can raise aggregate demand while strict/flexible headline targeting can reduce aggregate demand appropriately.

### Sensitivity analysis and robustness (selected quantitative results)
- Robustness across parameter variations:
  - Elasticity η: flexible headline targeting dominates up to η = 0.8; for η ≥ 0.9 welfare gains shrink or become negative (Table 8).
    - Examples (Incomplete Markets, selected η values from Table 8):
      - η = 0.6 (baseline): Strict Headline 3.21; Flexible Headline 4.18; Flexible Core 2.10.
      - η = 0.7: Strict Headline 0.19; Flexible Headline 0.54; Flexible Core 0.23.
      - η = 0.8: Strict Headline -0.02; Flexible Headline 0.09; Flexible Core 0.02.
      - η = 0.9: Strict Headline -0.04; Flexible Headline -0.03; Flexible Core -0.05.
  - Subsistence consumption: main result does not depend on presence of subsistence C* (Table 7 shows similar patterns without subsistence).
  - Inverse Frisch elasticity ψ (Table 9): results robust; baseline ψ = 3 yields large gains (3.21; 4.18; 1.58).
  - Price rigidity α (Table 10): gains persist across α = 0.50, 0.66, 0.75; e.g., α = 0.75 gives Flexible Headline Targeting 5.24.
  - Share of credit-constrained consumers λ (Table 11): baseline λ = 1.00 yields large gains; with higher λ welfare gains decline but flexible headline often remains beneficial.
  - Taylor-rule parameters (Table 13): flexible headline targeting outperforms across wide ranges of π_ρ, Y_ρ, i_ρ; examples:
    - Varying π_ρ: baseline π_ρ = 2 gives Flexible Headline 4.18; π_ρ = 0.50 gives Flexible Headline 5.32.
    - Varying food-shock persistence and volatility (Table 14): welfare gains larger when shocks are less persistent and more volatile; selected entries for Flexible Headline Targeting:
      - Persistence 0.10 and volatility 0.03: 4.62
      - Persistence 0.25 and volatility 0.03: 4.18
      - Persistence 0.95 and volatility 0.03: 1.19
- Extensions:
  - Alternate complete-markets structures and generalized credit-constraint patterns preserve main qualitative result; Table 15 and Table 16 show flexible headline targeting often yields positive welfare gains under varied assumptions (e.g., Table 16 welfare gains range 0.21–0.38 for varied access combinations with overall 50 percent constrained).

### Policy implications
- Main policy recommendation: central banks operating under financial frictions (incomplete markets with significant credit constraints and high food expenditure shares) should consider targeting flexible headline inflation (headline inflation with some weight on output gap) rather than core inflation that excludes flexible-price (food) sector.
- Rationale:
  - Flexible-headline targeting damps relative-food-price and wage responses that otherwise boost constrained-household consumption and counteract monetary tightening under core targeting.
  - Flexible-headline targeting improves welfare for both credit-constrained and unconstrained households in the model (no distributional tradeoff found).
- Operational scope and caveats:
  - Model exhibits monetary super-neutrality and is analyzed around non-inflationary steady states; does not address optimal level of inflation or derive optimal policy rules.
  - Central banks should still use prudential and other tools to address asset-price bubbles while retaining IT-like frameworks focused on price stability.

### Appendix and equilibrium characterization (selected equations and definitions)
- Key equilibrium variables and definitions:
  - Relative price of food x_{f,t} = P_{f,t}/P_t; relative price of non-food x_{s,t} = P_{s,t}/P_t.
  - Gross headline inflation Π_t ≡ P_t/P_{t-1}; gross sticky-sector inflation Π_{s,t} ≡ P_{s,t}/P_{s,t-1}.
  - Competitive equilibrium defined by processes satisfying equilibrium conditions (equations (52)–(62) and main-text equations), bounded around deterministic steady state.
- Welfare measurement and solution method:
  - Lifetime utility V = sum_{t=0}^∞ β^t NCU(C_{i,j,t}, N_{i,j,t}) (equation (43)); totalV = λ V_f + (1-λ) V_s.
  - Welfare gains ω defined by equations (46)–(47); ω*100 = 1 represents one percentage point permanent consumption gain.
  - Solution method: second-order perturbation (Schmitt-Grohe and Uribe, 2004) required for accurate welfare comparisons.
- Representative equilibrium and market-clearing relations recorded in Appendix I (demand equations (52), (54); supply equations (53), (55); price indices (56); real marginal cost (57); market clearing and aggregation (58)–(62)).

*Source: _wp10200 - References (PDF content provided).*

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

### References

### Context and motivation
- Global financial crisis prompted debate over appropriate objectives for monetary policy; consensus that low and stable inflation remains a primary objective.
- Central operational issue: choice of price index for inflation objective—determining both the level of inflation consistent with price stability and the appropriate price index to target.
- Literature guidance: core inflation (excluding food, energy, volatile components) often recommended because food and energy fluctuations are viewed as supply, non-monetary shocks (Wynne, 1999; Mishkin, 2007, 2008).

### Modeling approach and contribution
- Objective: develop a model to study welfare implications of targeting different price indices in an incomplete markets setting and analytically determine the appropriate price index to target.
- Main modeling feature: heterogeneous agents with financial frictions—fraction of consumers are credit-constrained and simply consume current labor income.
- Financial frictions introduced similarly to Gali, Lopez-Salido and Valles (2004).
- Paper develops a two-sector, two-good model with heterogeneous agents to encapsulate empirical features relevant for emerging markets.

### Empirical facts motivating the analysis
- Share of food in total household expenditures is much higher in emerging markets: nearly 40-50 percent of household expenditures compared to 10-15 percent in advanced economies.
- Survey evidence: average price elasticity of food is -0.34 in a sample of 114 countries; this estimate is smaller in absolute terms than the elasticity normally used in other models (many assume unitary price elasticity).
- Literature estimates on proportion of rule-of-thumb / credit-constrained consumers:
  - Campbell and Mankiw estimate in the U.S. nearly 50 percent of income accrues to consumers who do not smooth their consumption.
  - Muscatelli, Tirelli and Trecroci (2004) find about 37 percent of consumers are rule-of-thumb consumers and they account for 59 percent of total employment.
  - Additional supporting studies: Jappelli (1990), Shea (1995), Parker (1999), Souleles (1999), Fuhrer (2000), Fuhrer and Rudebusch (2004).

### Key analytical insights and findings
- In complete markets models, core inflation targeting (sticky price sector) is welfare-optimal because price stickiness is the primary distortion; targeting sticky prices helps minimize mark-up fluctuations and relative price distortions (Aoki, 2001; Goodfriend and King, 1997, 2001).
- Under incomplete markets with credit-constrained consumers:
  - Welfare depends on the nature of idiosyncratic shocks; income distribution matters for consumption and welfare.
  - Low price elasticity of demand for food becomes important via its impact on household income and expenditure.
  - Relative price of goods produced in the flexible price sector affects not only aggregate supply but, through real wages, also aggregate demand—breaking the comovement of inflation and output seen under complete markets.
  - Stabilizing core inflation is no longer sufficient to stabilize output; targeting flexible headline inflation is a better policy choice in the presence of financial frictions.
- In emerging markets, high food expenditure shares, low price and income elasticities of food, and low income levels make welfare more sensitive to food price fluctuations; food price inflation can feed into inflation expectations via wage bargaining.

### Policy implications and scope limits
- Policy implication: central banks operating under financial frictions (incomplete markets) should consider targeting flexible headline inflation rather than core (sticky-sector) inflation.
- Central banks should continue to use prudential and other tools to counteract asset price bubbles while retaining IT-like frameworks focused on price stability.
- Model limitations:
  - Exhibits monetary super-neutrality; analysis limited to non-inflationary steady states (long-run price stability).
  - Does not address the optimal level of inflation or define optimal policy rules; focuses on evaluating welfare outcomes of alternative policy rules using different inflation measures.

*Italic: Source: _wp10200 - References*

### Section 6 concludes the paper.

### _wp10200 - Section 6 concludes the paper.

### II. BASIC STYLIZED FACTS
- Engel’s law: as average household income increases the average share of food expenditure in total household expenditure declines.
- Cross-country evidence (year 1996 used for illustration because data for a large number of countries were available for that year):
  - Expenditure on food (as a percentage of total expenditure) plotted against log real per capita income (Figure 1) shows countries with lower per capita income levels have a higher share of expenditure on food.
  - Table 1 (selected emerging and advanced economies) shows expenditure on food constitutes a much larger share of total household expenditure in emerging markets relative to advanced economies.
- Income elasticities of food:
  - Figure 2 plots income elasticity of food against real per capita GDP for 1996; income elasticity of food is low, suggesting food is a necessary good.
  - Table 2 (selected countries): the income elasticity of food in emerging markets is on average twice as large as that in advanced economies.
- Price elasticities of food:
  - Figure 3 (1996) plots Slutsky own price elasticity of food against log real per capita GDP. The price elasticity of food demand is nonlinear, decreasing at low income levels, then increasing, with a range from -0.4 to -0.1.
  - Table 2 reports Slutsky own-price elasticity values for selected countries; overall the price elasticity of food is very low (demand for food is inelastic).
  - Frisch elasticity values lie between Slutsky and Cournot values and can be considered as an average own price elasticity.
  - Implication: low price and income elasticities of food demand have considerable significance for the choice of price index.
- Credit constraints in emerging markets:
  - Table 3 presents percentage of adult population with access to formal finance (measured by share of population using financial services) in emerging markets.
  - On average, more than half of the population in emerging markets does not have access to the formal financial system.
- Characteristics of core and headline inflation (period March 1991–September 2009; Table 4; Figures 4–5):
  - Average inflation (both headline and core) has been higher in emerging market economies during the period reported.
  - Headline inflation is more volatile than core inflation in both advanced and emerging market economies.
  - The volatility of both inflation measures is much higher in emerging markets; core inflation has on average been more than twice as volatile in emerging market economies compared to advanced countries.
  - Both measures of inflation exhibit a high degree of persistence in both sets of economies.
  - Cross-country evidence (Walsh, 2010 cited in source): food price inflation is more persistent than non-food price inflation in both advanced and emerging market economies; food price inflation is more persistent in emerging markets.
- Dynamics of headline vs. core inflation (representative cases):
  - Expectation: headline inflation should revert to core inflation in a short period after transitory shocks to food and energy (Mishkin, 2007).
  - Canada (an advanced economy that adopted IT in 1991; targets core inflation excluding food, energy and indirect taxes): headline inflation remained above core inflation for 30 months in succession (spring 1999 to fall 2001) (Figure 4a).
  - Thailand (an emerging market that adopted IT in 2000; targets core inflation excluding food and energy): headline inflation remained above core inflation for more than 5 consecutive years (Figure 5a).
  - Policy implication: prolonged differences between headline and core inflation may have important welfare implications because the core measure excludes several expenditure items and is less representative of the cost of living.

### III. THE MODEL — structure and key features
- Model building blocks:
  - Dynamic sticky price model extended with two features relevant for emerging markets:
    - A fraction of consumers who are credit constrained.
    - A subsistence level of food consumption.
  - Two sectors and two goods:
    - Flexible price good: food (F_C), prices adjust instantaneously.
    - Continuum of monopolistically produced sticky price goods: non-food (indexed on z in (0,1)), prices adjust sluggishly.
  - Labor immobility across sectors assumed.
- Households:
  - Economy populated by a continuum of 1 + λ infinitely lived households, where 0 >? λ (source text uses 0; interpret as λ>0).
  - Representative consumer indexed by sector: f (flexible price sector) and s (sticky price sector).
  - Household maximization problem: maximize discounted lifetime utility sum_{t=0}^∞ β^t u_{i,t}(NC_{i,t}) with β in (0,1).
  - Utility functional form (generalized Klein-Rubin / Stone-Geary form):
    - u_{i,t}(NC_{i,t}) = [ψ + φ n_{i,t}]^(1-σ)/(1-σ) + ... (source retains exact notation in equations (1)–(4)).
    - Composite consumption index C_{i,t} defined by equations (3)–(4); elasticity of substitution between flexible and sticky goods is η ∈ [0,∞) and food weight γ ∈ [0,1].
    - Parameter θ > 1 is elasticity of substitution between differentiated goods; σ is risk aversion; ψ is inverse Frisch elasticity; n_φ is scaling factor.
  - Subsistence food consumption: minimum amount C* of food required for survival; all households always have enough income to buy subsistence C* (subsistence level alters elasticities and marginal utilities).
- Flexible price sector (food sector) — credit constrained consumers:
  - Households have no access to financial markets; they consume wage income each period (rule-of-thumb consumers).
  - Production: y_{f,t} = A_{f,t} N_{f,t} (equation (5)); A_{f,t} is sectoral productivity shock common to all food-sector households.
  - Budget constraint and demand relations:
    - Budget: P_{f,t} C_{f,t} + P_{s,t} C_{s,t} = W_{f,t} N_{f,t} (equation (7)); rearranged as in (9).
    - Composite price index P_t defined in (8).
    - Demand for flexible good: equation (10); demand for sticky good: equation (11); Dixit-Stiglitz price index for non-food given by (12) and demands by (13).
  - Labor supply first-order condition: equation (14).
- Sticky price sector (non-food) — unconstrained consumers:
  - Households can buy one-period nominal bonds and smooth consumption; identical budget constraints across households (Woodford (2003) setup).
  - Production for firm z: y_{s,t}(z) = A_{s,t} N_{s,t}(z) (equation (6)); A_{s,t} common shock.
  - Budget constraint: equation (15) with bonds B_t and gross nominal interest rate R_t.
  - Euler equation: equation (16). Labor supply to firm z: equation (17).
  - Demand for flexible and sticky goods: equations (18)–(20).
- Firms — flexible price sector:
  - Firms are price takers; set price so that P_{f,t} = A_{f,t} W_{f,t} (equation (21)).
  - Supply function: equation (22).
  - Market-clearing condition for food: equation (23) with aggregate definitions (24).
- Firms — sticky price sector:
  - Calvo (1983) price stickiness: fraction α ∈ (0,1) of firms cannot change price each period.
  - Firms that can change choose X_t to maximize objective in (25); future outputs when price set at t given by (26).
  - Market-clearing and demand relations for sticky sector: equations (27)–(29).
  - Sticky sector price index: equation (30).
  - First-order condition for price setting: equation (31) with marginal cost in (32); constant markup (1 - θ)/θ.
- System and equilibrium:
  - Key equilibrium equations: (8), (9), (16), (22), (23), (28), (30), (31), (32) plus a monetary policy rule determine equilibrium paths of consumption, output and price indices in both sectors.
  - Relative prices and inflation definitions:
    - Relative price of food x_{f,t} = P_{f,t}/P_t; relative price of non-food x_{s,t} = P_{s,t}/P_t; relative price firms set x_{t} = X_t/P_t.
    - Gross headline inflation Π_t ≡ P_t/P_{t-1}; gross sticky-sector inflation Π_{s,t} ≡ P_{s,t}/P_{s,t-1}.
    - Relationship between headline and core inflation: equation (33).
  - Stationary system given in Appendix I (source reference).
- Steady state:
  - Characterized by constant prices (zero inflation) and no price stickiness; Π_t = Π_{s,t} = 1 for all t.
  - Symmetric equilibrium: x_t = X_t = 1 and r MC_{s,t} = θ/(θ-1).
  - Productivity normalized to one.
  - Note: model exhibits monetary super-neutrality; steady state inflation level does not affect steady state real variables.
- Monetary policy rule:
  - Central bank sets short-term nominal interest rate R_t according to a log-linear Taylor-type rule (equation (34)):
    - log R_t = ρ_R log R_{t-1} + ρ_π log(Π_t/Π̄) + ρ_y log(Y_t/Ȳ) + ... with notation in source (exact functional form given in (34)).
    - R̄, Π̄, Ȳ denote steady state values; ρ_R is interest rate smoothing weight; ρ_π and ρ_y are weights on inflation and output gap respectively.
  - Core inflation defined as sticky-sector inflation Π_{s,t}; headline inflation defined as overall inflation Π_t.
  - Policy regimes evaluated:
    - Strict Core Inflation Targeting: central bank cares only about interest rate smoothing and stabilizing Π_{s,t} (equation (35)).
    - Strict Headline Inflation Targeting: central bank cares only about interest rate smoothing and stabilizing Π_t (equation (36)).
    - Flexible Core Inflation Targeting: central bank also stabilizes output gap in addition to Π_{s,t} (equation (37)).
    - Flexible Headline Inflation Targeting: central bank also stabilizes output gap in addition to Π_t (equation (38)).
- Exogenous shock processes:
  - Productivity shocks follow AR(1):
    - A_{f,t+1} = ρ_{af} A_{f,t} + ξ_t, with ξ_t ~ i.i.d. (0, σ_{af}) (equation (39)).
    - A_{s,t+1} = ρ_{as} A_{s,t} + υ_t, with υ_t ~ i.i.d. (0, σ_{as}) (equation (40)).
  - Focus on productivity shocks to compare with prior literature and to highlight role of adverse supply shocks on choice of price index.
- Competitive equilibrium:
  - Defined as a set of processes {y_t, x_{f,t}, x_{s,t}, C_{f,t}, C_{s,t}, mc_t, R_t, Π_t, Π_{s,t}, ...} that remain bounded around deterministic steady state and satisfy the equilibrium conditions (equations (52)–(62) referenced in source).

*Source: _wp10200 - Section 6 concludes the paper.*

### Appendix I, given the exogenous stochastic processes

### Appendix I, given the exogenous stochastic processes

### I. Complete markets specification
- Under complete markets (Aoki, 2001) all households fully insure idiosyncratic income risks and, given the same initial wealth, choose an identical consumption sequence.
- Aggregate demand and household consumption collapse to representative-consumer relations (see equations (41) and (42) in the source).
- The system of equilibrium equations under complete markets is defined by equations (53), (55)-(61) of Appendix I together with (41)-(42), the monetary policy rule (equation (34)), and the exogenous stochastic processes tfA and tsA.

### J. Welfare evaluations and measurement
- Lifetime utility for household type i in sector j is defined as V = sum_{t=0}^∞ β^t NCU(C_{i,j,t}, N_{i,j,t}) (see equation (43)); total welfare is totalV = λ V_f + (1-λ) V_s.
- Welfare comparisons condition on the economy starting at its non-stochastic steady state.
- Strict core inflation targeting allocation denoted r; alternative regime denoted a.
  - Conditional welfare under core allocation: sum_{t=0}^∞ β^t NCU(C^r_t, N^r_t) (equation (44)).
  - Conditional welfare under alternative regime a: sum_{t=0}^∞ β^t NCU(C^a_t, N^a_t) (equation (45)).
- Welfare gain ω defined as the fraction of the core-consumption process that must be added to regime a to make a household indifferent between a and core (equation (46)).
  - Rearranged expression for ω given in equation (47).
  - Interpretation: ω*100 = 1 represents a one percentage point of permanent consumption gain under the alternative policy regime.

### K. Solution method
- First-order approximations are inadequate for welfare comparisons; second-order approximations are required.
- The policy function is approximated using the perturbation method with a scale parameter for exogenous shock standard deviations and a second-order Taylor expansion (Schmitt-Grohe and Uribe, 2004, with modifications).
- The second-order accurate consumer welfare measure is computed following Schmitt-Grohe and Uribe (2004).

### L. Measuring welfare gains across policy regimes
- Benchmark: strict core inflation targeting.
- Alternative monetary policy regimes analyzed: strict headline inflation targeting, flexible headline inflation targeting, flexible core inflation targeting (defined by equations (35)–(38)).
- Welfare gains reported are conditional and expressed as additional lifetime consumption (fraction ω) that would equate welfare to the core allocation (positive ω implies welfare is higher under the alternative).

### M. Parameter selection (baseline calibration)
- Discount factor: β = 0.9902 (implies annual real interest rate of 4 percent).
- Representative consumers per sector: λ = 1.
- Risk aversion: σ = 2 (intertemporal elasticity of substitution = 0.5).
- Elasticity of substitution across differentiated goods: θ = 10 (implies markup = 11 percent).
- Price stickiness: α = 0.66 (implies mean duration of fixed prices = 3 quarters).
- Inverse Frisch elasticity baseline: ψ = 3 (Frisch elasticity = 0.33).
- Steady-state average hours worked target: 0.38 (n_φ chosen accordingly).
- Elasticity of substitution between food and non-food goods: η = 0.6 (baseline).
- Food subsistence and weight:
  - Subsistence level food consumption parameter: C* = 0.1013.
  - Weight on food in the consumption index: γ = 0.3050.
  - These choices imply steady-state household expenditure on food = 42 percent.
  - Assumption: on average half of households’ steady state food consumption is required for subsistence.
- Monetary policy parameters (Taylor rule baseline): i_ρ = 0.7, π_ρ = 2, Y_ρ = 0.5.
- AR(1) coefficients:
  - Food sector shock persistence = 0.25 (shock lasts four quarters).
  - Non-food sector shock persistence = 0.95.
- Shock volatilities:
  - Standard deviation of food productivity shock: σ_af = 0.03.
  - Standard deviation of non-food productivity shock: σ_as = 0.02.

### IV. Baseline results — main findings
- Under complete markets:
  - Strict core inflation targeting is the welfare-maximizing policy.
  - Strict headline inflation targeting yields higher volatility of consumption and output and a more aggressive policy response that leads to a further decline in output (impulse responses to a 1 percent negative food productivity shock).
  - Stabilizing inflation ≡ stabilizing output (Aoki, 2001); flexible inflation targeting offers no additional welfare gains.
- Under incomplete markets (presence of credit-constrained consumers):
  - Flexible headline inflation targeting becomes the welfare-maximizing policy.
  - Monetary tightening reduces aggregate demand only when the central bank targets headline inflation; under strict core targeting aggregate demand can instead rise following a negative food productivity shock.
  - Mechanism: unconstrained households’ consumption is interest-rate-responsive; credit-constrained households consume current wage income and are insensitive to interest-rate changes. If core targeting ignores food-price inflation, food-sector wages rise more, boosting constrained households’ consumption and potentially increasing aggregate demand despite tightening.
  - Aggregate demand link to relative food price formalized in log-linearized aggregate demand equation (49) and supporting expressions (50)-(51).
- Welfare distribution:
  - Flexible headline inflation targeting improves welfare for both credit-constrained and unconstrained households in the model (no tradeoff between groups).

### V. Sensitivity analysis (robustness)
- Main result (flexible headline inflation targeting optimal under incomplete markets) robust to variations in:
  - Elasticity of substitution between food and non-food goods (η): flexible headline targeting dominates up to η = 0.8; for higher η strict core targeting may do marginally better than strict headline targeting.
  - Presence/absence of subsistence food consumption: main result does not depend on subsistence.
  - Inverse Frisch elasticity (ψ), price stickiness (α), fraction of credit-constrained households (λ), mark-up in the sticky price sector (θ): results robust around baseline values (Tables 9–12).
  - Taylor rule coefficients: flexible headline targeting outperforms irrespective of Taylor coefficients; welfare gains remain positive even when comparing to optimal strict core rule parameters (search restricted to π_ρ in [0,3] and i_ρ in [0,1]; best strict-core rule found at π_ρ = 3 and i_ρ = 0.95 within search bounds).
  - Persistence and volatility of food shocks: results robust; welfare gains from flexible headline targeting are larger when shocks are less persistent and more volatile (Table 14). For advanced economies with much smaller shock volatility, potential gains are considerably smaller.

### A. Model extensions
- Alternative complete-markets characterization: allow insurance only after sector assignment (complete conditional on sector). For baseline calibration, flexible headline targeting still outperforms strict core targeting; for higher η welfare gains approach zero (Table 15).
- Generalized credit constraints: allow fractions λ1 and λ2 of households in flexible-price and sticky-price sectors, respectively, to be credit constrained, with combinations such that 50 percent of households are credit constrained. Flexible headline inflation targeting continues to outperform strict core targeting for considered combinations (Table 16).

### VI. Concluding remarks and policy implications
- Key model features relevant for emerging markets: incomplete markets with credit-constrained consumers; subsistence food consumption; low price elasticity of food demand; high share of food in total expenditures.
- Main policy implication: in the presence of financial frictions and significant food consumption exposure, targeting core inflation is not welfare maximizing. Flexible headline inflation targeting (targeting headline inflation while putting some weight on the output gap) is optimal.
- Rationale: credit-constrained households’ demand depends on real wages (linked to flexible-price sector prices); ignoring flexible-sector price fluctuations (core targeting) can produce counterproductive aggregate-demand responses. Targeting headline inflation damps the wage and consumption response of constrained households and makes monetary policy effective in managing aggregate demand.
- Relevance: results are particularly pertinent for emerging markets where food expenditure shares and credit constraints are large; traditional advice to focus on core CPI needs re-examination when financial frictions are important.

*Source: _wp10200 - Appendix I, given the exogenous stochastic processes*

### REFERENCES

### _wp10200 - REFERENCES

### References cited
- Extensive bibliography on monetary policy, consumption behavior, productivity, and food demand, including works by:
  - Amato, Jeffery D., and Thomas Laubach, 2003.
  - Aguiar, Mark, and Gita Gopinath, 2007.
  - Aoki, Kosuke, 2001.
  - Basu, Susanto, and collaborators (1994, 1995, 1996, 1997).
  - Bernanke, Ben S., Tomas Laubach, Frederic S. Mishkin, and Adam S. Posen, 1999.
  - Campbell, John Y., and N. Gregory Mankiw (1989, 1990, 1991).
  - Christiano, Lawrence, Martin Eichenbaum, and Charles Evans, 1996.
  - Clarida, Richard, Jordi Gali, and Mark Gertler (1998, 1999).
  - Devereux, Michael B., Philip R. Lane, and Juanyi Xu, 2004.
  - Ferrero, Andrea; Gertler, Mark; and Lars E.O. Svensson, 2008.
  - Fuhrer, Jeffrey C., and Glenn D. Rudebusch (2000, 2004).
  - Gali, Jordi, David J. Lopez-Salido, and Javier Valles, 2004.
  - Goodfriend, Marvin, and Robert King (1997, 2001).
  - Kydland, Finn E., and Edward C. Prescott, 1982.
  - Mishkin, Frederic S., and Klaus Schmidt-Hebbel, 2001; Mishkin, Frederic S., 2007, 2008.
  - Rotemberg, Julio J., and Michael Woodford (1997, 1999).
  - Schmitt-Grohe, Stephanie, and Martin Uribe (2004, 2007).
  - Woodford, Michael (1996, 2003).
- Additional citations cover microfinance, household surveys, commodity prices, inflation measurement, and solution methods for DSGE models.

### Figures (captions and notes)
- Figure 1. Share of Expenditure on Food, 1996
  - Source: WDI and International Food Consumption Patterns Dataset, Economic Research Service, USDA.
  - Note: Expenditure on food includes expenditure on food prepared at home and consumed plus beverages and tobacco.
- Figure 2. Income Elasticity of Demand for Food, 1996
  - Source: WDI and International Food Consumption Patterns Dataset, Economic Research Service, USDA.
  - Notes: Estimated percentage change in demand for food if total income increases by 1 percent. Food includes food prepared at home and consumed plus beverages and tobacco.
- Figure 3. Slutsky Own-Price Elasticity of Demand for Food, 1996
  - Source: WDI and International Food Consumption Patterns Dataset, Economic Research Service, USDA.
  - Notes: Percentage change in demand for food if food prices increase by 1 percent (keeping real income constant). Food includes food prepared at home and consumed plus beverages and tobacco.
- Figure 4. Levels and Volatility of Inflation
  - Source: CEIC and authors’ calculations.
  - Notes: Core index definitions for USA and Canada given; inflation is year-on-year using quarterly price index; volatility measured as standard deviation using rolling 20-quarter window; results similar with 8-year and 10-year windows.
- Figure 5. Levels and Volatility of Inflation (Korea and Thailand)
  - Source: CEIC and authors’ calculations.
  - Notes: Core index definitions for Korea and Thailand given; inflation and volatility measurement as in Figure 4.
- Figures 6–8. Impulse Responses to a 1% Negative Food Productivity Shock
  - Contexts: Complete markets with subsistence level food consumption; Incomplete markets with subsistence; Incomplete markets with different elasticity of substitution of food.
  - Notes: Responses expressed as percentage deviation from steady state. Definitions of strict core/headline and flexible headline inflation targeting refer to equations (35), (36), (38) in the main text.

### Tables — key values and statistics
- Table 1. Share of Food Expenditure in Total Household Expenditure
  - Emerging Markets (2005) examples:
    - Indonesia 53.0
    - Vietnam 49.8
    - India 48.8
    - China 36.7
    - Russia 33.2
    - Malaysia 28.0
    - Average 41.6
  - Advanced Economies (2006) examples:
    - Japan 14.7
    - Germany 11.5
    - Australia 10.8
    - Canada 9.3
    - United Kingdom 8.8
    - USA 5.7
    - Average 10.1
  - Note: Expenditure on food includes food consumed at home only and does not include beverages and tobacco.
- Table 2. Income (Expenditure) Elasticity and Slutsky Own-Price Elasticity of Food (1996)
  - Emerging Economies sample top entries:
    - Vietnam: Income Elasticity 0.73; Price Elasticity -0.37
    - Pakistan: 0.72; -0.38
    - Jordan: 0.70; -0.39
    - Indonesia: 0.69; -0.39
    - Average: Income Elasticity 0.63; Price Elasticity -0.38
  - Advanced Economies sample top entries:
    - New Zealand: Income Elasticity 0.39; Price Elasticity -0.29
    - Finland: 0.39; -0.29
    - Sweden: 0.36; -0.27
    - Netherlands: 0.36; -0.27
    - Average: Income Elasticity 0.30; Price Elasticity -0.22
  - Note: Elasticities represent percent changes in demand for a 1 percent change in income or price.
- Table 3. Composite Measure of Access to Financial Services in Emerging Markets (2008)
  - Country examples:
    - Argentina 28
    - Brazil 43
    - Chile 60
    - China 42
    - India 48
    - Korea 63
    - Mexico 25
    - Nigeria 15
    - Pakistan 12
    - Peru 26
    - Russia 69
    - Thailand 59
    - Turkey 49
  - Average 42
  - Note: Measures percent of adult population with access to an account with a financial intermediary.
- Table 4. Average Inflation, Volatility and Persistence of Inflation (March 1991–September 2009)
  - USA:
    - Average Headline Inflation 2.67
    - Average Core Inflation 2.58
    - Average Volatility Headline Inflation 0.80
    - Average Volatility Core Inflation 0.45
    - Persistence Headline Inflation 0.84*** (0.09)
    - Persistence Core Inflation 0.92*** (0.04)
  - Canada:
    - Average Headline Inflation 1.96
    - Average Core Inflation 1.78
    - Average Volatility Headline Inflation 0.80
    - Average Volatility Core Inflation 0.43
    - Persistence Headline Inflation 0.75*** (0.13)
    - Persistence Core Inflation 0.77*** (0.10)
    - Note: Data for Canada is for the period March 1996 – September 2009.
  - Korea:
    - Average Headline Inflation 4.23
    - Average Core Inflation 3.85
    - Average Volatility Headline Inflation 1.54
    - Average Volatility Core Inflation 1.32
    - Persistence Headline Inflation 0.85*** (0.05)
    - Persistence Core Inflation 0.88*** (0.03)
  - Thailand:
    - Average Headline Inflation 3.62
    - Average Core Inflation 2.87
    - Average Volatility Headline Inflation 1.78
    - Average Volatility Core Inflation 1.24
    - Persistence Headline Inflation 0.90*** (0.06)
    - Persistence Core Inflation 0.95*** (0.05)
  - Notes: Core definitions and measurement conventions specified in notes.
- Table 5. Parameter Calibration: Baseline Model (selected parameters and values)
  - Risk aversion σ = 2
  - Subjective discount factor β = 0.9902
  - Inverse of Frisch elasticity ψ = 3
  - Probability of firm not changing price α = 0.66
  - Elasticity of substitution between food and non-food η = 0.60
  - Weight on food in the price index γ = 0.3050
  - Households with credit constraints λ = 1
  - Elasticity of substitution between different non-food goods θ = 10
  - Weight on output gap in Taylor rule Yρ = 0.5
  - Weight on inflation gap in Taylor rule πρ = 2
  - Weight on interest rate smoothing in Taylor rule iρ = 0.70
  - Persistence of food productivity shock afρ = 0.25
  - Persistence of non-food productivity shock asρ = 0.95
  - Standard deviation of food productivity shock afσ = 0.03
  - Standard deviation of non-food productivity shock asσ = 0.02
- Table 6. Welfare Gains from Alternative Inflation Targeting Rules (baseline summary)
  - Complete Markets:
    - Strict Headline Targeting: -0.07
    - Flexible Headline Targeting: -0.22
    - Flexible Core Targeting: -0.19
  - Incomplete Markets:
    - Strict Headline Targeting: 3.21
    - Flexible Headline Targeting: 4.18
    - Flexible Core Targeting: 1.58
  - Note: Welfare gain (ω*100) defined as percent increase in strict core inflation targeting consumption needed to equate welfare; positive indicates higher welfare under alternative policy.
- Table 7. Welfare Gains Without Subsistence-Level Food (selected rows)
  - Elasticity of Substitution 0.4 (Incomplete Markets):
    - Strict Headline Targeting 1.15
    - Flexible Headline Targeting 1.42
    - Flexible Core Targeting 0.77
  - Elasticity 0.5 (Incomplete Markets):
    - Strict Headline Targeting 0.12
    - Flexible Headline Targeting 0.24
    - Flexible Core Targeting 0.16
  - Elasticity 0.6 (baseline a) (Incomplete Markets):
    - Strict Headline Targeting -0.03
    - Flexible Headline Targeting 0.02
    - Flexible Core Targeting 0.02
- Table 8. Welfare Gains for Different η (selected)
  - η = 0.6 (a): Complete Markets: Strict Headline Targeting -0.07; Flexible Headline Targeting -0.22; Flexible Core Targeting -0.19. Incomplete Markets: 3.21; 4.18; 2.10.
  - η = 0.7: Incomplete Markets: 0.19; 0.54; 0.23.
  - η = 0.8: Incomplete Markets: -0.02; 0.09; 0.02.
  - η = 0.9: Incomplete Markets: -0.04; -0.03; -0.05.
  - η = 1.5: Incomplete Markets: -0.01; -0.11; -0.11.
  - η = 2.0: Incomplete Markets: 0.00; -0.12; -0.12.
  - Note: a. Baseline value of this parameter.
- Table 9. Welfare Gains for Different Inverse of Frisch Elasticity ψ
  - ψ = 2: Strict Headline Targeting 0.00; Flexible Headline Targeting 0.38; Flexible Core Targeting 0.38
  - ψ = 3 (a): 3.21; 4.18; 1.58
  - ψ = 4: 1.32; 2.12; 1.01
  - Note: a. Baseline value of this parameter.
- Table 10. Welfare Gains for Different Price Rigidity α
  - α = 0.50: Strict Headline Targeting 2.30; Flexible Headline Targeting 2.90; Flexible Core Targeting 1.24
  - α = 0.66 (a): 3.21; 4.18; 1.58
  - α = 0.75: 3.64; 5.24; 2.89
  - Note: a. Baseline value of this parameter.
- Table 11. Welfare Gains for Different Shares of Credit-Constrained Consumers λ
  - λ = 1.00 (a): Strict Headline Targeting 3.21; Flexible Headline Targeting 4.18; Flexible Core Targeting 1.58
  - λ = 2.00: 0.05; 0.89; 0.73
  - λ = 3.00: -0.03; 0.75; 0.73
  - Note: a. Baseline value of this parameter.
- Table 12. Welfare Gains for Different θ (elasticity between non-food goods)
  - θ = 5: Strict Headline Targeting 2.65; Flexible Headline Targeting 3.27; Flexible Core Targeting 1.55
  - θ = 10 (a): 3.21; 4.18; 1.58
  - θ = 15: 3.36; 4.85; 2.54
  - Note: a. Baseline value of this parameter.
- Table 13. Welfare Gains for Different Taylor Rule Parameters
  - (a) Varying πρ (weight on inflation gap), baseline πρ = 2 (a):
    - For πρ = 0.50: Strict Headline Targeting -2.74; Flexible Headline Targeting 5.32; Flexible Core Targeting 3.76
    - πρ = 1.00: 2.40; 4.94; 2.95
    - πρ = 1.50: 3.12; 4.53; 2.45
    - πρ = 2.00 (a): 3.21; 4.18; 1.58
    - πρ = 2.50: 3.15; 3.87; 1.84
    - πρ = 3.00: 3.04; 3.62; 1.65
  - (b) Varying Yρ (weight on output gap), baseline Yρ = 0.5 (a):
    - Yρ = 0.00: Strict Headline Targeting 3.21
    - Yρ = 0.50 (a): Flexible Headline Targeting 4.18; Flexible Core Targeting 1.58
    - Yρ = 1.00: Flexible Headline Targeting 4.25; Flexible Core Targeting 2.72
    - Yρ = 1.50: Flexible Headline Targeting 2.26; Flexible Core Targeting 3.03
    - Yρ = 2.00: Flexible Headline Targeting 4.25; Flexible Core Targeting 3.23
    - Yρ = 2.50: Flexible Headline Targeting 4.25; Flexible Core Targeting 3.36
  - (c) Varying iρ (interest smoothing), baseline iρ = 0.70 (a):
    - iρ = 0.00: Strict Headline Targeting -5.58; Flexible Headline Targeting 3.79; Flexible Core Targeting 2.73
    - iρ = 0.10: -3.11; 4.01; 2.71
    - iρ = 0.20: -1.20; 4.16; 2.66
    - iρ = 0.30: 0.26; 4.25; 2.59
    - iρ = 0.40: 1.36; 4.28; 2.48
    - iρ = 0.50: 2.18; 4.27; 2.36
    - iρ = 0.60: 2.78; 4.23; 2.23
    - iρ = 0.70 (a): 3.21; 4.18; 2.10
    - iρ = 0.80: 3.52; 4.11; 1.97
    - iρ = 0.90: 3.73; 4.05; 1.86
  - Notes: Other Taylor rule parameters kept at baseline where stated.
- Table 14. Welfare Gains of Flexible Headline Inflation Targeting for Different Combinations of Persistence and Volatility of Food Productivity Shock
  - Volatility columns 0.02, 0.03, 0.04; Persistence rows 0.10, 0.25, 0.50, 0.95
  - Selected values:
    - Persistence 0.10: 2.27; 4.62; 7.99
    - Persistence 0.25: 2.08; 4.18; 7.18
    - Persistence 0.50: 1.81; 3.55; 6.04
    - Persistence 0.95: 0.77; 1.19; 1.75
  - Notes: Persistence is AR(1) coefficient in equation (39). Non-food shock persistence and volatility held at 0.95 and 0.02.
- Table 15. Welfare Gains from Flexible Headline Inflation Targeting under Alternate Complete Market Structures
  - η = 0.6 (a): 0.24
  - η = 0.7: 0.05
  - η = 0.8: -0.02
- Table 16. Welfare Gains from Flexible Headline Inflation Targeting under General Model
  - Fraction of households in sticky-price sector with access to formal finance / fraction in flexible-price sector with access / Welfare gains:
    - 0.10 / 0.90 / 0.38
    - 0.20 / 0.80 / 0.22
    - 0.30 / 0.70 / 0.21
    - 0.40 / 0.60 / 0.22
    - 0.50 / 0.50 / 0.24
    - 0.60 / 0.40 / 0.26
    - 0.70 / 0.30 / 0.28
    - 0.80 / 0.20 / 0.29
    - 0.90 / 0.10 / 0.30
  - Note: Combinations chosen so overall 50 percent of households are credit constrained.

*Italic: Source: _wp10200 - REFERENCES (PDF content provided).*

### Appendix I. Competitive Equilibrium with Incomplete Markets

### Appendix I. Competitive Equilibrium with Incomplete Markets

### Demand equations
- Demand equation for flexible price sector household:
  - C_t^f - x_t^f = C_{t}^{f} , (52)
- Demand equation for sticky price sector household:
  - { Π_t^{-1} [ β R_t (C_{t+1}^s)^{-σ} ] = (C_t^s)^{-σ} } , (54)

### Supply equations
- Supply equation of flexible price sector (food sector) firm:
  - A_{t}^f y_{t}^{f} = (1-ψ) (1-σ) / φ  )?  (53)
  - (As presented: ) )1( ,, , )()()( ψσψ φ +− = tf f ttfntf ACyx (53)
- Supply equation of sticky price sector (non-food sector) firm:
  - (55) (full expression as provided):
    - ...
    -  (long summation expression)
    - )()( )()(
    - 1
    - i
    - jts
    - jts
    - ts
    - jtt
    - j
    - t
    - j
    - r
    - jt
    - t
    - jt
    - jts
    - jts
    - ts
    - jtt
    - j
    - t
    - tst
    - Y
    - P
    - P
    - QE
    - zMC
    - P
    - P
    - Y
    - P
    - P
    - QE
    - xx
    - θ θ α β α β θ θ
    - = (55)

  (Equation (55) is reported in full in the source as a multi-line summation giving the sticky-sector supply condition in terms of price, quantity, marginal cost zMC, and parameters θ, α, β.)

### Price indices and real marginal cost
- Price index in sticky price good sector:
  - x_{t}^{s} = [ α^{α} (1-α)^{1-α} ]^{-(1/(1-α))} Π_{t}^{(1-α)/ (1-α)} ?  (56)
  - (As presented: [ ] θ θαα −−−− −+Π = 1 1 1)1( , )1()(1 tts x (56))
- Real marginal cost in the sticky price sector:
  - AC_{t} y_{t} - AC z y z MC = )1(,,)1(,,)()())(()()())(()( ψσψθψσψ φφ +−−+− = ts s ttstnts s ttsn r t ACYxACzyzMC (57)

### Market clearing conditions and aggregation
- Market clearing equation for flexible price good:
  - Y_{t}^{f} = C_{t}^{f} + (1-λ) (1-γ) C_{t}^{f,*}  (58)
  - (As presented: * ,,,, )1()(CCxCyY ttftftftf λγ η +++ = = = = −  ) (58)
- Market clearing condition for sticky price good:
  - Y_{t}^{s} = (1-η)^{-1} C_{t}^{s}  (59)
  - (As presented: ttststs CxCY η γ − − = = = ))(1( ,, , (59))
- Aggregate Price Index:
  - x_{t} = [ (1-γ)^{1-η} γ^{η} x_{t}^{f (1-η)} x_{t}^{s η} ]^{1/(1-η)}  (60)
  - (As presented: [ ] η ηη γ γ − − − − + = 1 1 1 , 1 , ))(1()(1 tstf xx (60))
- Relation between headline and sticky price index:
  - Π_{t}^{x_{t}^{s}} = Π_{t-1}^{,}  (61)
  - (As presented: t tsts ts x x Π Π = −1, , , (61))
- Aggregation equation:
  - Y_{t} = C_{t}^{s} + C_{t}^{f} = C_{t} + λ  (62)
  - (As presented: tt s t f t YCCC = = + λ (62))

### System characterization
- The appendix states: "This appendix gives the system of equations (in terms of stationary variables) characterizing the competitive equilibrium under the incomplete market settings."
- Equations listed here (including (52)–(62) and the detailed sticky-sector expression (55)) together characterize the competitive equilibrium with incomplete markets when written in stationary variables.

*Source: _wp10200 - Appendix I. Competitive Equilibrium with Incomplete Markets*

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