## _wp1670

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---

### Related Literature
- Major literatures connected to the paper:
  - New-Keynesian macroeconomics in closed and open economies (background literature for monetary policy design and inflation stabilization).
  - Structural transformation literature: Chenery and Syrquin (1975); Matsuyama (1992); Caselli and Coleman (2001); Kongsamut et al. (2001); Ngai and Pissarides (2007); Rogerson (2008).
  - Literature on inflation in emerging markets and LICs, with emphasis on the role of food: Walsh (2011); Adam et al. (2012); Anand and Prasad (2012); Anand et al. (2015); Andrle et al. (2013); Portillo and Zanna (2014); Catao and Chang (2013 and 2015).

- Positioning relative to existing work:
  - Follows structural-transformation literature by assuming a closed economy (Herrendorf et al. 2014).
  - Argues closed-economy assumption is less restrictive for many LICs due to limited integration of domestic grain markets with world markets (evidence: Gilbert (2011); FAO et al. (2011); Gollin and Rogerson (2010, 2014)).
  - Closest existing specifications: Anand and Prasad (2012) and Anand et al. (2015) (two-sector model with subsistence focus). Key contrasts:
    - Anand et al. assume some households excluded from financial markets and perfect labor segmentation; excluded households supply labor exclusively to food sector and included households to non-food sector.
    - Anand et al. include a traded good and shocks to non-food productivity and terms of trade.
    - Their numerical results show interest rate rules responding to headline inflation can be welfare-superior to rules responding to core inflation.
  - This paper extends the baseline model in Section 7 to include limited asset market participation and segmented labor markets to clarify differences with Anand et al.

- Empirical motivations (overview of stylized facts; data set period 1995-2011; country coverage: 28 OECD, 23 sub-Saharan African, 15 non-OECD (mostly emerging markets)):
  - Share of food in CPI falls as income rises; relationship appears convex when plotting food share against average income per capita in PPP dollars over 2001-2010 (US income per capita normalized to one).
  - Food prices are more flexible than non-food prices; unprocessed food prices change with markedly higher frequency than overall food prices; difference most pronounced in LICs.
  - Inflation volatility falls as income rises (business-cycle frequency focus using a band-pass filter that retains frequencies between 6 and 32 quarters).
  - Correlation between headline inflation and output increases with income per capita; many LICs display negative inflation/output correlations at business-cycle frequencies.

- Relevance of price-flexibility and subsistence assumptions:
  - Supported by micro-data studies (e.g., Bils and Klenow (2004) and subsequent CPI micro-data papers).
  - Higher frequency of price changes for (unprocessed) food and the larger share of unprocessed food in LICs justify modeling food as the flexible-price sector and non-food as the sticky-price sector.
  - Subsistence is central to generating endogenous structural transformation: low aggregate productivity implies higher resource allocation to food to satisfy subsistence needs, yielding a larger food share in the CPI; as productivity rises, the food share declines.

### The Consumer (Section 4.1)
- Setup and objective:
  - Representative consumer chooses consumption aggregate χ*_t, labor effort ν_t, and holdings of a nominal bond B_{t+1} to maximize lifetime utility:
    - E_0 Σ_{t=0}^∞ β^t [ Z ν(χ*_t) − (ν_t)^{1+ψ}/(1+ψ) ].
  - Budget constraint:
    - P_{F,t} c_{F,t} + P_{N,t} c_{N,t} + B_{t+1} = Ω_t ν_t + Π_{F,t} + Π_{N,t} + R_{t−1} B_t.
  - Consumption aggregate:
    - χ*_t = Z( c_{F,t} − c̄_F )^{α_F} c_{N,t}^{1−α_F}.
  - Definitions and primitives:
    - (c_{F,t}, c_{N,t}) consumption of food and non-food; prices P_{F,t}, P_{N,t}.
    - Ω_t nominal wage; Π_{F,t}, Π_{N,t} sector profits; R_{t−1} gross nominal interest rate.
    - c̄_F subsistence level of food consumption.
    - Z scaling parameter equal to (α_F)^{−α_F} (1−α_F)^{−(1−α_F)}.

- First-order conditions (exact notation preserved):
  - Intertemporal Euler equation:
    - (χ*_t)^{−1} = β E_t [ R_t / π^*_ {t+1} (χ*_{t+1})^{−1} ].  (Equation (2))
  - Labor FOC (Frisch condition):
    - (ν_t)^ψ = ω^*_t (χ*_t)^{−1}.  (Equation (3))
  - Intratemporal demand for food (notional):
    - c_{F,t} = c̄_F + α_F (P_{F,t} / P^*_t)^{−1} χ*_t = c̄_F + α_F π^{*−1}_{F,t} χ*_t.  (Equation (4))
  - Intratemporal demand for non-food (notional):
    - c_{N,t} = (1−α_F) (P_{N,t} / P^*_t)^{−1} χ*_t = (1−α_F) π^{*−1}_{N,t} χ*_t.  (Equation (5))
  - Notional price index:
    - P^*_t = P_{F,t}^{α_F} P_{N,t}^{1−α_F}.  (Equation (6))
  - Notional gross inflation and real wage relative to P^*_t:
    - π^*_t = P^*_t / P^*_{t−1};  ω^*_t = Ω_t / P^*_t.

- Measured vs notional (observed) variables:
  - Measured consumption:
    - c_t = p_F c_{F,t} + p_N c_{N,t}.  (Equation (7)), where p_F = P_F / P and p_N = P_N / P denote steady-state prices relative to measured price index.
  - Measured price index relationship:
    - P_t = [ ( p_{F,t} c_{F,t} / c_t ) P_{F,t} + ( p_{N,t} c_{N,t} / c_t ) P_{N,t} ].  (Equation (8))
  - Notation: starred variables (χ*_t, P^*_t, π^*_t, ω^*_t, π^*_{F,t}, π^*_{N,t}) are notional and used in consumer decisions; observed counterparts are (χ_t, P_t, π_t, ω_t, π_{F,t}, π_{N,t}) with π_t = P_t / P_{t−1} and ω_t = Ω_t / P_t.

### Optimal Monetary Policy under Subsistence (Section 6.1)
- Analytical result (core inflation stabilization suffices):
  - Despite food subsistence, optimal monetary policy requires complete stabilization of sticky-price non-food inflation.
  - Stabilizing sticky-price non-food inflation is sufficient to stabilize both aggregate output and the relative price of food around their efficient levels.
  - The "divine coincidence" of Blanchard and Galí (2007) holds in this model: stabilizing (core) inflation is equivalent to stabilizing the welfare-relevant output gap.

- Loss function and weighting (Proposition 1; equation numbering and structure preserved):
  - Assumption: labor share equals one (α = 1).
  - The average welfare loss per period is:
    - L = 1/2 · κ · [ (1−ω_F)·(ξ/μ)·var(ˆπ_{N,t}) + (ψ+κ)·var(˜y_t) + (α_F/(1−ω_F))·var(˜π_{F,t}) ]  (structure as in text, where κ = (1−α_F)/(1−ω_F) and μ = (1−θβ)(1−θ)/θ).
  - Interpretation and comparative statics:
    - Welfare loss is weighted sum of variances of sticky-price non-food inflation (ˆπ_{N,t}), aggregate output gap (˜y_t), and relative food price gap (˜π_{F,t}).
    - Weights depend on parameters α_F, ψ, ξ, β, θ, ω_F, and κ reflecting subsistence.
    - Subsistence parameters increase relative weights on output gap and relative food price gap versus sticky-price non-food inflation.
    - Numerical comparison (holding everything else constant):
      - Poor country (ω_F = 0.42) should assign almost twice the weight a rich country (ω_F = 0.08) should to stabilizing the output gap (Figure A.2 shows weight expressions are increasing in degree of subsistence).

- Corollary (strict targeting of sticky-price non-food inflation):
  - Welfare loss (33) can be rewritten to show optimal monetary policy corresponds to strict targeting of sticky-price non-food inflation, implemented by setting ˆπ_{N,t} = 0 for every t.
  - Targeting core inflation stabilizes aggregate output and relative food price around efficient levels.
  - Monetary authority should target core (sticky-price non-food) inflation ˆπ_{N,t} rather than headline inflation ˆπ_t = ω_F ˆπ_{F,t} + (1−ω_F) ˆπ_{N,t} to achieve the social optimum.

- Policy implications and costs of targeting headline inflation:
  - Food subsistence does not overturn strict targeting of core inflation as optimal, but raises the stakes for monetary stabilization.
  - Targeting headline inflation instead of core inflation is more costly for countries closer to subsistence.
  - Quantitative comparison (calibration; Table 4 referenced):
    - When both countries implement optimal core inflation targeting, standard deviations and welfare losses are zero.
    - Adopting headline inflation targeting increases volatility and reduces welfare; welfare loss for the poor country is much greater than for the rich country.
    - Mechanism after a negative food-sector productivity shock:
      - Shock raises relative price of food.
      - Keeping headline inflation stable requires large decreases in non-food inflation.
      - Decreases are bigger in poor countries because food has larger weight.
      - Sticky non-food prices imply these decreases are accompanied by larger contractions in non-food and overall output in poor countries.
      - Increase in output volatility receives larger weight in poor country (Figure A.2), inducing bigger welfare losses.
    - Similar policy ranking holds for Taylor rules responding to non-food inflation versus headline inflation.

### Subsistence is More Than a Higher Food Share (Section 6.2)
- Main argument:
  - Subsistence matters beyond a larger food share: a poor economy with subsistence (α_F = 0.0701, c̄_F = 0.0099, reported parametrizations in text with α_F = 0.07, ω_F = 0.42) behaves differently from same economy without subsistence (α_F = ω_F = 0.42).
  - For any positive weight on food inflation (ω > 0) both aggregate output volatility and welfare losses are larger with subsistence, and increase in that weight.

- Mechanisms raising volatility and welfare costs:
  - Reduced substitutability relative to food: subsistence limits reallocation away from agriculture after negative food-sector productivity shocks, amplifying aggregate effects of supply shocks.
  - Higher volatility of equilibrium relative food prices under subsistence increases cost of targeting the “wrong” price level because required real adjustment grows with relative food price volatility.
  - Economy with subsistence places larger weight on output volatility in the central bank’s loss function:
    - With subsistence the weight on output volatility corresponds to 1/2 · κ(ψ+κ) with κ ≥ 1.
    - Absent subsistence it reduces to 1/2 · (ψ+1).
  - Conclusion: subsistence raises the stakes for monetary policy at earlier development stages.

- Welfare loss and policy objective (baseline):
  - Welfare depends on stability of inflation in sticky-price sector (non-food/core inflation) rather than headline inflation; divine coincidence (stabilize inflation ⇒ stabilize output gap) not overturned.
  - Average welfare loss per period restated as:
    - L = 1/2 · κ · [ (1−ω_F)·(ξ/μ)·var(ˆπ_{N,t}) + (ψ+κ)·var(˜y_t) + (α_F/(1−ω_F))·var(˜π_{F,t}) ].
  - Perfect stabilization of sticky-price non-food inflation minimizes welfare loss (ˆπ_{N,t} = 0 ∀ t).

- Model extension: Limited Asset Market Participation (LAMP) and Segmented Labor Markets (SLM):
  - Two agent types introduced:
    - Urban agents (share λ* of total agents) supply labor exclusively to non-food sector and have access to financial assets.
    - Rural agents (share 1−λ*) supply labor exclusively to food sector and do not have access to financial assets.
  - For simplicity assume λ* = (1−ω_F) (urban share equals non-food sector share) and α = 1.
  - Key channels with subsistence + LAMP + SLM:
    - SLM prevent labor reallocation, amplifying sectoral shock effects and increasing relative food price responses.
    - LAMP implies rural agents’ consumption is insensitive to interest-rate movements; shocks cause large and opposing income effects across agent types.
    - Subsistence lowers food-sector price elasticity so a negative food productivity shock can raise real food income (relative price effect outweighs production fall), reducing rural labor supply and further contracting food output; urban agents’ real income falls and labor supply rises, expanding non-food production.
    - Depending on proximity to subsistence (food share), total output can even increase in response to a negative food supply shock (occurs when food share equals average in African countries).

- Welfare implications in extended model (Proposition 2; α = 1 and λ* = (1−ω_F)):
  - Average welfare loss per period, using weighted average of urban and rural utilities, is:
    - L = 1/2 · κ · [ (1−ω_F)·(ξ/μ)·var(ˆπ_{N,t}) + (ψ+κ)/(1−ω_F)·var(˜˜y_t) ]
    - where ˜˜y_t = ˆy_t − ˆy_alt_t and ˆy_alt_t ≠ ˆy_flex_t (an alternative output-gap measure appears because the economy’s response to food shocks is inefficiently low).
  - Implication: divine coincidence breaks down in principle — trade-off emerges between non-food inflation stabilization and output stabilization.
  - Policy consequence: optimal policy involves some tightening after negative food supply shocks to move economy toward a more efficient output (at cost of lower non-food inflation). Including food prices in the targeted inflation measure is an indirect way to achieve needed tightening.

- Quantitative evaluation and robustness (selected exact calibration values and quantitative findings):
  - Calibration selected parameters (Table 1 values as reported):
    - c̄_F = 0.0099
    - α_F = 0.0701
    - α (labor income share) = 0.7
    - β = 0.99
    - θ = 0.75
    - ς (response coefficient to non-food inflation in the rule) = 1.5
    - ψ (inverse Frisch elasticity) = 5
    - ε (elasticity of substitution between varieties) = 6
    - ρ_A (AR(2) food productivity process parameter) = 0.8
    - % (AR(2) parameter reported in text) = 0.01
    - σ_A_f (std. dev. of food productivity shocks) = 0.6
    - ρ_MP (persistence in AR(1) monetary policy shocks) = 0.8
    - σ_MP (std. dev. of monetary policy shocks) = 0.6
  - Quantitative findings:
    - Optimal weight on food inflation under targeting rules ≈ between zero and 2percent.
    - CPI food weight used in comparisons = 0.42.
    - Welfare losses and output-gap volatility are larger for the poor country with subsistence whenever any positive weight is placed on food inflation (ω > 0) — illustrated in Figure 4.
    - Under certain simple interest-rate instrument rules (Taylor-type), the optimal food weight can be 15percent (medium persistence) or 29percent (i.i.d. shocks), showing sensitivity to shock persistence.

- Policy takeaway and conclusions (chapter highlights):
  1. Incorporating food subsistence in a simple new-Keynesian two-sector model helps explain higher inflation volatility in poor countries and the negative inflation–output correlation in their business cycles.
  2. Subsistence does not overturn the result that monetary authorities should seek to stabilize core (non-food) inflation rather than headline inflation to maximize aggregate welfare.
  3. A subsistence threshold raises the stakes for monetary policy in poor countries: targeting the wrong inflation measure induces larger welfare losses the closer the economy is to subsistence.
  4. Adding LAMP and SLM creates the possibility of a trade-off between core inflation stability and a measure of output, but near-perfect core inflation stabilization remains near-optimal quantitatively.
  - Methodological conclusion: targeting rules aligned with the loss function are more robust to model structure than simple interest-rate instrument rules; instrument rules can give misleading prescriptions when structural features (subsistence, LAMP, SLM) interact with shock persistence.

*Source: _wp1670*

### 2.  Related Literature .................................................................................................

### 2.  Related Literature

### Major literatures connected to the paper
- New-Keynesian macroeconomics in closed and open economies (background literature for monetary policy design and inflation stabilization).
- Structural transformation literature:
  - Key references cited: Chenery and Syrquin (1975), Matsuyama (1992), Caselli and Coleman (2001), Kongsamut et al. (2001), Ngai and Pissarides (2007), Rogerson (2008).
- Literature on inflation in emerging markets and LICs, with emphasis on the role of food:
  - Key references cited: Walsh (2011), Adam et al. (2012), Anand and Prasad (2012), Anand et al. (2015), Andrle et al. (2013), Portillo and Zanna (2014), Catao and Chang (2013 and 2015).

### How this paper positions itself relative to existing work
- Follows the structural-transformation literature in assuming a closed economy (Herrendorf et al. 2014).
- Argues that for many LICs, limited integration of domestic grain markets with world markets makes the closed-economy assumption less restrictive:
  - Evidence cited: Gilbert (2011) on pass-through of international grain prices; FAO et al. (2011) on restrictive trade policies and high transport and transaction costs; Gollin and Rogerson (2010, 2014) on high overland trade costs in Africa.
- Notes that if food is nontraded, domestic supply and demand dominate determination of its relative price, independently of whether non-food is traded (non-food is nontraded in the model).

### Comparison with closely related models and papers
- Anand and Prasad (2012) and Anand et al. (2015) have the most similar specification (two-sector model with subsistence focused on appropriate inflation targets for LICs).
  - Contrasts in assumptions:
    - Anand et al. assume some households are excluded from financial markets and assume perfect labor segmentation (labor immobile across sectors).
    - In their setup, excluded households supply labor exclusively to the food sector and included households to the non-food sector.
    - Anand et al. also include a traded good and shocks to non-food productivity and terms of trade.
  - Their numerical results show interest rate rules responding to headline inflation can be welfare-superior to rules responding to core inflation.
  - This paper will extend its baseline model in Section 7 to include limited asset market participation and segmented labor markets to clarify and reconcile differences with Anand et al.

### Empirical data used to motivate model features (overview)
- Data set period: 1995-2011.
- Country coverage: 28 OECD countries, 23 sub-Saharan African countries, and 15 non-OECD countries (mostly emerging markets).
- Stylized facts motivating model design:
  - The share of food in the CPI falls as income rises (relationship appears convex when plotting food share against average income per capita in PPP dollars over 2001-2010; income per capita for the US normalized to one).
  - Food prices are more flexible than non-food prices; unprocessed food prices change with markedly higher frequency than overall food prices; this difference in price flexibility is most pronounced in LICs.
  - Inflation volatility falls as income rises (business-cycle frequency focus using a band-pass filter that retains frequencies between 6 and 32 quarters).
  - The correlation between headline inflation and output increases with income per capita; many LICs display negative inflation/output correlations at business-cycle frequencies.

### Relevance of price-flexibility and subsistence assumptions
- Price-flexibility assumptions are supported by micro-data studies (e.g., Bils and Klenow (2004) and subsequent papers examining CPI micro-data across countries).
- The paper emphasizes that the higher frequency of price changes for (unprocessed) food, and the larger share of unprocessed food in LICs, justify modeling food as the flexible-price sector and non-food as the sticky-price sector.
- The presence of subsistence in the model is central to generating endogenous structural transformation: low aggregate productivity implies higher resource allocation to food to satisfy subsistence needs, yielding a larger food share in the CPI; as productivity rises, the food share declines.

*Source: _wp1670 - 2.  Related Literature (IMF Working Paper content provided).*

### 4.1  The Consumer

### 4.1  The Consumer

### Setup and objective
- The representative consumer chooses a consumption aggregate ∗, labor effort , and holdings of a nominal bond B+1 to maximize lifetime utility:
  - E0 Σ=0 ∞  [ (∗) − ()1+/(1+) ].
- Budget constraint:
  - P F, c F, + P N, c N, + B+1 = Ω ν + Π F, + Π N, + R−1 B.
- Consumption aggregate composition:
  - ∗ = Z( c F, − ̄c F ) F c1− F N,.
- Definitions and primitives:
  - Pair (c F,, c N,) denotes consumption of food and non-food, priced at P F, and P N,.
  - Ω is the nominal wage; Π F, and Π N, are profits from food and non-food sectors.
  - R−1 is the gross nominal interest rate paid on bonds B.
  - ̄c F indicates the subsistence level of food consumption.
  - Z is a scaling parameter equal to ( F)− F (1− F)−(1− F) to simplify notation.

### First-order conditions (from utility maximization)
- Intertemporal Euler equation:
  - (∗)−1 =  E [ R/∗+1 (∗+1)−1 ].  (Equation (2))
- Labor FOC (Frisch condition):
  - () = ∗ (∗)−1.  (Equation (3))
- Intratemporal demand for food (notional):
  - c F, = ̄c F +  F ( P F, / P ∗ )−1 ∗ = ̄c F +  F ∗ F, −1 ∗.  (Equation (4))
- Intratemporal demand for non-food (notional):
  - c N, = (1− F) ( P N, / P ∗ )−1 ∗ = (1− F) ∗ N, −1 ∗.  (Equation (5))
- Notional price index arising from utility maximization:
  - P ∗ = P  F F, P 1− F N,.  (Equation (6))
- Notional gross inflation and real wage relative to P ∗:
  - ∗ = P ∗ / P ∗−1;  ∗ = Ω / P ∗.

### Measured vs notional (observed) variables
- Measured consumption definition:
  - c = p F c F, + p N c N,.  (Equation (7))
  - p F = P F / P and p N = P N / P denote steady-state prices of food and non-food relative to the measured price index.
- Relationship defining the measured price index P:
  - P = [ ( p F, c F, / c ) P F, + ( p N, c N, / c ) P N, ].  (Equation (8))
- Notational convention:
  - Variables with an asterisk (∗, P ∗, ∗, ∗, ∗ F,, ∗ N,) are relevant for consumer decisions but are not observed (notional).
  - Observed counterparts are (, P, , ,  F,,  N,) with  = P / P−1 and  = Ω / P.

*Source: _wp1670 - 4.1  The Consumer*

### 6.1  Optimal Monetary Policy under Subsistence

### 6.1  Optimal Monetary Policy under Subsistence

### Analytical result: core inflation stabilization suffices
- Despite food subsistence, optimal monetary policy requires complete stabilization of sticky-price non-food inflation.
- Stabilizing sticky-price non-food inflation is sufficient to stabilize both aggregate output and the relative price of food around their efficient levels.
- The "divine coincidence" of Blanchard and Galí (2007) holds in this model: stabilizing (core) inflation is equivalent to stabilizing the welfare-relevant output gap.

### Loss function and weighting (Proposition 1)
- Assumption: the labor share equals one–i.e., =1.
- The average welfare loss per period is given by the linear function:
  L=
  1
  2
  
  ∙
  (1−
  
  )
  
  
  (ˆ
  
  )+(+)( ̃
  
  )+
  
  
  1−
  
  ( ̃
  
  )
  ̧
  (33)
  where =
  1−
  
  1−
  
  and =
  (1−)(1−)
  
  .
- Interpretation:
  - Welfare loss is the weighted sum of variances of:
    - sticky-price non-food inflation (ˆ
      
      )
    - aggregate output gap ( ̃
      
      )
    - gap of the relative price of food ( ̃
      
      )
  - Weights depend on preference parameters (
    
    , , , ), degree of price stickiness (), share of expenditures on food (
    
    ), and parameter  reflecting subsistence.
  - Subsistence parameters increase the relative weights on output gap and relative food price gap versus sticky-price non-food inflation.
  - Figure A.2 (Appendix) shows both relative weights
    - (+)
      (1−
      
      )
    - 
      
      
      (1−
      
      )
      2
      
    are increasing in the degree of subsistence.
  - Numerical comparison (holding everything else constant):
    - Poor country (
      
      =042) should assign almost twice the weight a rich country (
      
      =008) should to stabilizing the output gap.

### Corollary: strict targeting of sticky-price non-food inflation (Corollary 1)
- The welfare loss (33) can be rewritten as:
  L=
  1
  2
  
  (
  (1−
  
  )
  
  
  (ˆ
  
  )+
  1
  
  
  "
  (+)+
  
  
  1−
  
  μ
  +
  
  ¶
  2
  #
  (ˆ
  
  −E
  
  ˆ
  +1
  )
  )
  (34)
- Therefore optimal monetary policy corresponds to strict targeting of sticky-price non-food inflation, implemented by setting ˆ
  
  =0 for every .
- Targeting core inflation completely stabilizes aggregate output and the relative price of food around their efficient levels.
- Monetary authority should target core (sticky-price non-food) inflation ˆ
  
  rather than headline inflation ˆ
  
  =
  
  ˆ
  
  +(1−
  
  )ˆ
  
  to achieve the social optimum.

### Policy implications and costs of targeting headline inflation
- Food subsistence does not overturn the result that strict targeting of core inflation is optimal, but it raises the stakes for monetary stabilization.
- Targeting headline inflation instead of core inflation is more costly (in welfare loss) for countries closer to the subsistence threshold.
- Quantitative comparison (calibration; Table 4 referenced):
  - When both countries implement optimal core inflation targeting, standard deviations and welfare losses are equal to zero.
  - Adopting headline inflation targeting increases volatility and reduces welfare; the welfare loss for the poor country is much greater than for the rich country.
  - Mechanism for larger welfare loss in poor countries facing a negative food-sector productivity shock:
    - Shock increases the relative price of food.
    - Keeping headline inflation stable requires large decreases in non-food inflation.
    - These decreases are bigger in poor countries because food has a larger weight.
    - Sticky prices in non-food sector imply these decreases are accompanied by larger contractions in non-food output and overall output in poor countries.
    - The resulting increase in output volatility receives a larger weight in the poor country (Figure A.2), inducing bigger welfare losses.
- Similar ranking of policies is found for Taylor rules that respond to non-food inflation versus Taylor rules that respond to headline inflation.

*Source: 6.1  Optimal Monetary Policy under Subsistence (excerpt).*

### 6.2  Subsistence is More Than a Higher Food Share

### _wp1670 - 6.2  Subsistence is More Than a Higher Food Share

### Main argument
- The importance of food subsistence is not reducible to a larger food share alone: a poor economy with subsistence (α_F = 0.0701, ᾱ_F = 0.0099, subsistence parameters discussed as _F = 007, _F = 042 in the text) behaves differently from the same economy without subsistence (_F = _F = 042).
- Comparing welfare costs of targeting various inflation measures (via equation (30)) shows that for any positive weight on food inflation (ω > 0) both the volatility of aggregate output and welfare losses are larger with subsistence and increase in that weight.

### Mechanisms driving higher volatility and welfare costs
- Reduced substitutability relative to food: subsistence limits relocation away from agriculture, especially after negative food-sector productivity shocks, constraining economy-wide factor reallocation and amplifying aggregate effects of supply-side shocks.
- Higher volatility of equilibrium relative food prices under subsistence increases the cost of targeting the “wrong” price level because the required real adjustment grows with relative food price volatility.
- The economy with subsistence also places a larger weight on output volatility in the central bank’s loss function:
  - With subsistence the weight on output volatility corresponds to 1/2 · (+) with  ≥ 1.
  - Absent subsistence it reduces to 1/2 · (+1).
- Conclusion: subsistence raises the stakes for monetary policy at earlier stages of development.

### Welfare loss and policy objective (baseline model)
- Welfare continues to depend on the stability of inflation in the sticky-price sector (non-food/core inflation) rather than headline inflation; the “divine coincidence” (stabilize inflation ⇒ stabilize output gap) is not overturned.
- The average welfare loss per period (equation (33), reproduced in the text and appendix) is:
  - L = 1/2 ·  · [ (1−_F)·(/)·var(ˆπ_N,t) + (+)·var(˜y_t) + (_F/(1−_F))·var(˜π_F,t) ] (structure preserved as in text).
- Perfect stabilization of sticky-price non-food inflation minimizes welfare loss (Corollary: ˆπ_N,t = 0 ∀ t is optimal in the baseline).

### Model extension: limited asset market participation (LAMP) and segmented labor markets (SLM)
- Extension introduces two agent types:
  - Urban agents (share * of total agents) supply labor exclusively to non-food sector and have access to financial assets.
  - Rural agents (share 1−*) supply labor exclusively to food sector and do not have access to financial assets.
- For simplicity the paper assumes * = (1−_F) (urban share equals non-food sector share) and  = 1 in this extension.
- Key channels with subsistence + LAMP + SLM:
  - Segmented labor markets (SLM) prevent labor reallocation, amplifying sectoral effects of shocks and increasing relative food price responses.
  - Limited asset market participation (LAMP) implies rural agents’ consumption is insensitive to interest-rate movements; shocks cause large and opposing income effects across agent types.
  - Subsistence lowers food-sector price elasticity so a negative food productivity shock can raise real food income (relative price effect outweighs production fall), reducing rural labor supply and further contracting food output; urban agents’ real income falls and their labor supply rises, expanding non-food production.
  - Depending on proximity to subsistence (food share), total output can even increase in response to a negative food supply shock (noted to occur when the food share equals the average in African countries).

### Welfare implications in the extended model
- Proposition 2 (extended model;  = 1 and * = (1−_F)):
  - The average welfare loss per period, using a weighted average of urban and rural utilities, is:
    - L = 1/2 ·  · [ (1−_F)·(/)·var(ˆπ_N,t) + (+)/(1−_F)·var(˜˜y_t) ]
    - where ˜˜y_t = ˆy_t − ˆy_alt_t and ˆy_alt_t ≠ ˆy_flex_t (an alternative measure of the output gap appears because the economy’s response to food shocks is inefficiently low).
- Implication: the divine coincidence breaks down in principle — there is a trade-off between non-food inflation stabilization and output stabilization; perfectly stabilizing non-food inflation is no longer theoretically optimal.
- Policy consequence: optimal policy involves some tightening after negative food supply shocks to move the economy toward a more efficient output (at the cost of lower non-food inflation). Including food prices in the targeted inflation measure is an indirect way to achieve the needed tightening.

### Quantitative evaluation and robustness
- Targeting rules evaluated (as in equation (30)) under the extended model show:
  - In all three persistence cases considered (AR(2), AR(1), i.i.d.), the optimal weight on food inflation (black vertical line in Figure 5) is minimal — between zero and 2percent.
  - This optimal weight is far lower than the CPI food weight at 042 (dashed grey line), implying near-perfect core inflation stabilization remains the main objective.
- Contrast with simple interest-rate (Taylor-type) instrument rules (as in Anand and Prasad / APZ):
  - Using an interest-rate rule ˆR_t = ρ_R ˆR_{t−1} + (1−ρ_R)[ φ_π ˆπ^ω_t + φ_y ˆy_t ] with parameters ρ_R = 067, φ_π = 15, φ_y = 05, the “optimal” weight on food inflation depends strongly on shock persistence:
    - Under the paper’s persistent AR(2) shocks, the optimal weight on food inflation is near zero.
    - As persistence decreases, the optimal weight increases: with APZ’s middle-panel persistence it jumps to 15percent; with i.i.d. shocks it increases to 29percent.
  - Explanation: instrument rules’ performance depends on their ability to replicate movements in the natural rate of interest; when subsistence + LAMP + SLM generate increases in equilibrium real rates after negative food shocks (size depending on shock persistence), assigning greater weight to food inflation can help produce desired real-rate increases — but this is not aligned with the central bank’s deeper objectives and is not robust.

### Stylized quantitative and calibration details (selected exact values from the chapter)
- Calibration (selected parameters as reported in Table 1):
  - ̄c_F Subsistence level of food consumption = 0.0099
  - α_F Non-subsistence food consumption share = 0.0701
  - α Labor income share = 0.7
  - β Discount factor = 0.99
  - θ Probability of not being able to reset price = 0.75
  - ς Response coefficient to non-food inflation in the rule = 1.5
  - ψ Inverse of Frisch elasticity of labor supply = 5
  -  Elasticity of substitution between different varieties = 6
  - ρ_A Parameter in the AR(2) process for food productivity shocks = 0.8
  - % Parameter in the AR(2) process for food productivity shocks = 0.01
  - σ_A_f Standard deviation of food productivity shocks = 0.6
  - ρ_MP Persistence in the AR(1) process for monetary policy shocks = 0.8
  - σ_MP Standard deviation of monetary policy shocks = 0.6
- Quantitative findings summarized:
  - Optimal weight on food inflation under targeting rules ≈ between zero and 2percent.
  - CPI food weight used in comparisons = 042.
  - Welfare losses and output-gap volatility are larger for the poor country with subsistence whenever any positive weight is placed on food inflation (ω > 0) — illustrated in Figure 4.
  - Under certain instrument-rule specifications the optimal food weight can be 15percent (medium persistence) or 29percent (i.i.d. shocks), illustrating sensitivity to shock persistence.

### Policy takeaway and conclusions
- Four key findings highlighted by the chapter:
  1. Incorporating food subsistence in a simple new-Keynesian two-sector model helps explain higher inflation volatility in poor countries and the negative inflation–output correlation in their business cycles.
  2. Subsistence does not overturn the result that monetary authorities should seek to stabilize core (non-food) inflation rather than headline inflation to maximize aggregate welfare.
  3. A subsistence threshold raises the stakes for monetary policy in poor countries: targeting the wrong inflation measure induces larger welfare losses the closer the economy is to subsistence.
  4. Adding LAMP and SLM creates the possibility of a trade-off between core inflation stability and a measure of output, but near-perfect core inflation stabilization remains near-optimal quantitatively.
- Methodological conclusion: targeting rules aligned with the loss function are more robust to model structure than simple interest-rate instrument rules; instrument rules can give misleading prescriptions when structural features (subsistence, LAMP, SLM) interact with shock persistence.

*Source: _wp1670 - 6.2  Subsistence is More Than a Higher Food Share (PDF chapter content).*

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*Source: _wp1670 - References*

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