## _wp15205 ## Source details **Canonical URL:** [_wp15205](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15205.pdf) ## Other formats - [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15205.pdf.md) - [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15205.pdf.json) --- ### Role of price-index choice in monetary policy - Most central banks view low and stable inflation as a primary objective; core inflation excludes food, energy, and other volatile components. - Prior complete-markets literature shows targeting core inflation can maximize welfare by addressing distortions from infrequent price adjustments and fluctuating mark-ups (Goodfriend and King, 1997, 2001; Aoki, 2001; Benigno, 2004; Mankiw and Reis, 2003). ### Motivations and model overview for developing economies - Key departures from complete-markets assumptions: - A substantial fraction of agents cannot smooth consumption (hand-to-mouth). - Relatively high share of food in household consumption expenditures. - Three-sector model to capture developing-economy features: - Sector 1 (Food/informal): large, flexible prices, workers are hand-to-mouth. - Sector 2 (Sticky-price/formal): productivity and mark-up shocks, Calvo pricing, workers have access to credit markets. - Sector 3 (Open/commodity-exporting): flexible but highly volatile prices, faces large external shocks. - Financial frictions and heterogeneous agents emphasized; welfare depends on nature of idiosyncratic shocks and market incompleteness. ### Key empirical stylized facts (as used in calibration) - Expenditure on food: - Developing economies: 40-50 percent of household expenditures (Table 1 average 41.6). - Advanced economies: 10-15 percent (Table 1 average 10.1). - Income elasticity of food: average 0.63 in selected developing economies versus 0.30 in advanced economies. - Average price elasticity of food: about -0.38 in developing economies. - Access to formal finance: more than half the population in developing countries lacks access; median (29 Developing Economies) = 42; median (27 Advanced Economies) = 96 (Table 2). - Inflation characteristics: - Food and nonfood inflation higher on average in developing economies; food inflation more volatile and more persistent. ### Main theoretical result and mechanism - Main result: In the presence of financial frictions, targeting headline CPI inflation improves aggregate welfare relative to targeting core inflation (sticky-price sector inflation). - Mechanism: - Credit-constrained (hand-to-mouth) consumers have demand insensitive to interest rates; demand depends on real wages. - The relative price of the flexible-price good (food) affects real wages and therefore both aggregate supply and aggregate demand. - Under incomplete markets, stabilizing core inflation no longer stabilizes the output gap because financial frictions break the comovement of inflation and output. - Therefore, targeting a broader inflation measure (including food) improves welfare. - Computed optimal price index under baseline incomplete markets: - Includes a positive weight on food prices (Food Prices weight = 0.65). - Assigns zero weight to import prices (Import Prices = 0.00). ### Model structure and selected formal elements - Households: - Continuum of infinitely-lived households of two types: measure ߣ0 produce food (flexible-price) and are credit-constrained; measure ߣ1 produce sticky-price goods and can trade bonds. - Discount factor ߚ ∈ (0,1). - Utility: U(c) = c^{1-ߪ}/(1-ߪ); risk-aversion coefficient ߪ. - Composite consumption: weight ߛ ∈ (0,1) on food; elasticity between flexible and sticky goods ߟ ∈ (0,∞); differentiated goods elasticity ߠ > 1. - Subsistence consumption: food has minimum amount c*; assumed affordable by households. - Price and expenditure indices: - Expenditure price index P_t composed of P_{f,t} (food) and P_{n,t} (nonfood Dixit-Stiglitz index), with nonfood including imports share ζ ∈ (0,1) and elasticity ߦ. - Financial market segmentation: - Food households: no access to financial markets; consumption equals current labor income (equation (6)). - Nonfood households: can buy domestic and foreign one-period nominal bonds; budget constraint as in equation (10). ### Shocks, policy rule, and welfare evaluation - Exogenous shocks (innovations i.i.d. normal): - Food productivity shock: AR(1) with innovation ߝ ௧ ௙ ~ ܰ(0,ߪ ௔ ௙). - Sticky-price productivity shock: AR(1) with innovation ߝ ௧ ௦ ~ ܰ(0,ߪ ௔ ௦). - Sticky-price mark-up shock: AR(1) with innovation ߝ ௧ ఛ ~ ܰ(0,ߪ ఛ). - Terms of trade shock (exports): AR(1) with innovation ߝ ௧ ఙ ~ ܰ(0,ߪ ௦). - Monetary policy: Taylor-type rule (equation (12)) with interest rate smoothing ߩ and weights ߶ గ on inflation and ߶ ௬ on output gap; setting ߶ ௬ = 0 implies strict inflation targeting. - Welfare evaluation: - Compute second-order accurate consumer welfare measure (Schmitt-Grohe and Uribe approach). - Welfare gain ߱: fraction added to strict core inflation targeting consumption process to equate welfare under alternative regime a (equations (14) and (15)); ߱*100 = 1 means a 1 percentage point permanent consumption gain. ### Baseline calibration (selected parameters) - ߚ = 0.99. - Fraction credit-constrained households ߣ = 0.4 (40 percent). - Risk aversion ߪ = 2. - ߠ = 11 (markup 10 percent). - Calvo non-adjustment probability ߙ = 0.66 (mean duration 3 quarters). - Frisch elasticity benchmark: 0.33 (inverse ߰ = 3). - Monetary policy: ߩ = 0.7, ߶ గ = 2, ߶ ௬ = 0.5. - Food consumption: - Average expenditure on food ≈ 42 percent. - Subsistence ratio = 1/3 (one third of households' steady state food consumption subsistence); non-subsistence food consumption share 0.326. - Elasticity of substitution ߟ = 0.6 baseline → steady state price elasticity of demand for food ≈ -0.3. - Shock parameters: - Food AR(1) coefficient = 0.25; std. dev. ߪ ௔ ௙ = 0.03. - Nonfood AR(1) coefficient = 0.9; std. dev. ߪ ௔ ௦ = 0.02. - Terms of trade persistence ߩ ௦ = 0.77; std. dev. ߪ ௦ = 0.013. - Mark-up shock persistence ߩ ఛ = 0.9; std. dev. ߪ ఛ = 0.01. ### Baseline quantitative results and comparisons - Market completeness impact: - Incomplete markets: higher and more volatile inflation (food and nonfood) than complete markets. - Incomplete markets: consumption more volatile than output; opposite under complete markets. - Welfare comparisons (Table 4): - Complete Markets: - Financial Welfare Gain -0.09%; Headline 0.00%; Optimal 0.00. - Optimal price index weights: Food Prices 1.00; Sticky Prices 0.00; Import Prices 0.00. - Incomplete Markets: - Financial Welfare Gain 0.16%; Headline 0.20%; Optimal 0.35. - Optimal price index weights: Food Prices 0.65; Sticky Prices 0.00; Import Prices 0.00. - Interpretation: under incomplete markets, headline inflation targeting improves welfare relative to core targeting; the computed optimal index places two-thirds weight on sticky sector and one-third on food in the descriptive summary, but numerical table shows Food Prices 0.65 and Sticky Prices 0.00 for the incomplete-markets optimal index (optimal index composition in text: positive weight on food, generally zero weight on imports). - Impulse response to a 1 percent negative food productivity shock: - Complete markets: strict headline inflation targeting yields slightly higher volatility of consumption and output; policy response more aggressive under headline targeting causing further decline in output. - Incomplete markets: headline inflation targeting outperforms core targeting in stabilizing output because monetary policy is more effective at controlling aggregate demand when targeting headline inflation. ### Mechanics linking financial frictions and policy performance - Heterogeneous responses: - Unconstrained households: consumption responsive to interest rates. - Credit-constrained households: consumption independent of interest rates; depends on current wage income. - Policy transmission under a negative food productivity shock (incomplete markets): - Central bank raises interest rate → unconstrained households reduce demand. - Credit-constrained households' demand rises because higher relative food price raises food-sector wage income and they consume current income. - Under core-targeting: larger rise in food prices and wage income of food sector households → aggregate demand can increase. - Under headline-targeting: smaller food price increases → monetary tightening more effective in controlling aggregate demand. - Formalization: log-linearized aggregate demand (equation (16)) links demand to interest rate, inflation, lagged demand, and relative food price change Δ̂ ௙,௧; optimal food-sector labor supply (equation (17)) links food labor and relative price. ### Alternative policy rules and sensitivity (section 4.1) - Flexible versus strict targeting: - Baseline (strict, ߶ ௬ = 0): ordering of welfare gains — Optimal > Headline > Core; strict core is benchmark. - Flexible targeting (positive weight on output gap): ordering of rules preserved; weights in optimal price index essentially the same. - Adding output gap reduces welfare gains relative to strict targeting because output gap and sticky-sector inflation move together; including output gap weakens response to inflation deviations. - Search experiment yields optimal coefficient on output gap = 0. - Including real exchange rate or export price in optimal inflation target yields weight = 0. - Sensitivity tests (Table 6 highlights): - Share of rural (food) households (baseline 0.4): - At 0.3: Welfare Gain 0.36%; Headline 0.49%; Optimal 0.87; Food Prices 0.13. - At 0.4: Welfare Gain 0.16%; Headline 0.20%; Optimal 0.35; Food Prices 0.65. - At 0.5: Welfare Gain -0.02%; Headline 0.09%; Optimal 0.22; Food Prices 0.78. - At 0.6: Welfare Gain -0.15%; Headline 0.04%; Optimal 0.14; Food Prices 0.86. - Subsistence ratio (baseline 0.33): - 0.0: Welfare Gain -0.07%; Headline 0.00%; Optimal 0.08; Food Prices 0.92. - 0.1: Welfare Gain -0.06%; Headline 0.01%; Optimal 0.14; Food Prices 0.86. - 0.2: Welfare Gain -0.03%; Headline 0.03%; Optimal 0.21; Food Prices 0.79. - 0.3: Welfare Gain 0.08%; Headline 0.12%; Optimal 0.31; Food Prices 0.69. - 0.4: Welfare Gain 0.56%; Headline 0.63%; Optimal 0.48; Food Prices 0.52. - Price stickiness (baseline 0.66): - 0.5: Welfare Gain 0.13%; Headline 0.16%; Optimal 0.42; Food Prices 0.58. - 0.6: Welfare Gain 0.16%; Headline 0.19%; Optimal 0.39; Food Prices 0.61. - 0.7: Welfare Gain 0.14%; Headline 0.19%; Optimal 0.32; Food Prices 0.68. - 0.8: Welfare Gain 0.01%; Headline 0.11%; Optimal 0.20; Food Prices 0.80. - Financial frictions and portfolio access: - Introducing a portfolio holding cost to vary access: - Full access (portfolio cost = 0 but not full complete markets): food prices still enter with positive weight in optimal index but weight is substantially smaller than baseline. - Welfare gain from targeting optimal index small relative to core targeting when food-sector households can access bonds. - Common productivity shocks: - Replacing sector-specific shocks with a common productivity shock increases welfare gains from targeting headline CPI or optimal index; food prices retain significant weight in optimal target. ### Policy implications and concluding remarks - Introducing financial frictions overturns the classical complete-markets result that core inflation targeting is optimal: with credit-constrained consumers and other developing-economy features, core inflation targeting no longer maximizes welfare. - Stabilizing inflation alone is insufficient to stabilize output when markets are incomplete. - Headline inflation targeting improves welfare under baseline incomplete-markets calibration; the computed optimal index places positive weight on food prices and generally zero weight on import prices. - Practical extensions and dilemmas: - Including money explicitly could strengthen the case for headline inflation targeting by preserving value of monetary savings for hand-to-mouth consumers. - Including physical capital would reveal tradeoffs where raising policy rates to counter surging food inflation can hurt industrial activity; in incomplete markets raising rates after transitory negative agricultural shocks could be welfare improving when food accounts for a large consumption share. *Source: _wp15205 (sections 1, 3.3, 4.1, References as provided).* ### 1. INTRODUCTION ### _wp15205 - 1. INTRODUCTION ### Role of price-index choice in monetary policy - Most central banks view low and stable inflation as a primary, if not dominant, objective of monetary policy. - Core inflation (excluding food, energy, and other volatile components from headline CPI) is often targeted because fluctuations in food and energy prices are viewed as supply shocks and non-monetary (Wynne, 1999; Mishkin, 2007, 2008). - Prior literature (models with price and/or wage stickiness, complete markets) shows that targeting core inflation maximizes welfare by addressing distortions from infrequent price adjustments and fluctuating mark-ups (Goodfriend and King, 1997, 2001; Aoki, 2001; Benigno, 2004; Mankiw and Reis, 2003). ### Motivations for revisiting optimal price index in developing economies - Prior results rely on complete markets (full insurance against idiosyncratic risks). Developing economies differ: - A substantial fraction of agents cannot smooth consumption consistent with the permanent income hypothesis. - Relatively high share of food in household consumption expenditures. - Paper aims to provide an analytical framework for determining the optimal price index for developing-economy central banks, with three stated contributions: - Generalize Aoki (2001) and Benigno (2004) by developing a unifying model. - Show that incomplete financial markets and other characteristics of developing economies substantially alter key results. - Derive optimal price indexes and compare them with feasible rules (e.g., headline inflation targeting) that improve welfare relative to core inflation targeting while being easier to communicate and implement. ### Three-sector model structure (to represent developing economies) - Sector 1: Food (or informal) sector - Large fraction of the economy. - Prices are flexible. - Workers are hand-to-mouth (no access to credit markets); consume current labor income. - Sector 2: Sticky-price (formal) sector - Subject to productivity shocks and mark-up shocks. - Workers have access to credit markets. - Sector 3: Open to foreign trade (commodity-producing proxy) - Flexible but highly volatile prices. - Faces large external shocks. ### Financial frictions and heterogeneous agents - Financial frictions (credit constraints) are emphasized: agents differ in ability to smooth consumption; welfare depends on nature of idiosyncratic shocks. - Under incomplete markets: - Household income, influenced by shocks and price elasticities, affects consumption choices. - Example: a negative productivity shock to a good with low price elasticity of demand could increase income of net sellers and raise expenditure of net buyers. - Model allows analysis of welfare distribution under alternative inflation-targeting rules. ### Relevant features of developing economies (empirical stylized facts summarized) - Expenditure on food constitutes 40-50 percent of household expenditures in developing economies, compared to 10-15 percent in advanced economies. - Income elasticity of food: average of 0.63 in selected developing economies versus 0.30 in advanced economies. - Average price elasticity of food: about -0.38 in developing economies (much lower in absolute value than unitary elasticity). - Access to formal finance: data show on average more than half of the population in developing countries lacks access to formal financial services (World Bank, Demirguc-Kunt and Klapper, 2012); in advanced economies nearly all households have such access. - Inflation characteristics: - Both food and nonfood inflation are higher on average in developing economies than in advanced economies. - In developing economies, food inflation is more volatile than nonfood inflation; innovations to food price inflation are also more volatile. - Headline inflation is more volatile than core inflation in both groups. - Food price shocks tend to be quite persistent in developing economies. ### Key theoretical results and intuition - Main result: In the presence of financial frictions, targeting headline CPI inflation improves aggregate welfare relative to targeting core inflation (inflation in the sticky price sector). - Mechanism: - Credit-constrained (hand-to-mouth) consumers have demand insensitive to interest rates; demand depends only on real wages. - The relative price of the flexible-price good (food) affects real wages and therefore both aggregate supply and aggregate demand. - Under incomplete markets, financial frictions break the comovement of inflation and output; stabilizing core inflation no longer stabilizes the output gap. - Therefore, targeting a broader measure of inflation (including food) improves welfare. - Computed optimal price index: - Includes a positive weight on food prices. - Generally assigns zero weight to import prices (agents in the import sector have access to financial markets and the price elasticity of demand for goods produced in this sector is high). - Contrast with complete-markets literature: - In Aoki (2001) relative prices of the flexible-price sector appear only as a shift parameter of sticky-sector inflation; under incomplete markets, central bank must respond to flexible-price sector fluctuations to manage aggregate demand. - Results differ from Frankel (2008) and others who focus on commodity-exporting economies where targeting export price indices might be appropriate; ignoring sectors with nominal rigidities and targeting flexible-price sectors with small CPI weight would reduce welfare. ### Model outline and household specification (selected formal elements preserved) - Economy: continuum of infinitely-lived households of two types: - measure ߣ0 of households producing food (flexible price domestic good); - measure ߣ1 of households producing a continuum of monopolistically produced sticky-price goods (nonfood) for domestic consumption and a flexible-price good for export (nonfood exports). - Labor immobile across food and nonfood sectors (assumption noted; Gali et al. (2004) implication referenced). - Representative household indexed by i and sector f (food) or n (nonfood) maximizes discounted utility: - Discount factor ߚ ∈ (0,1). - Utility functional form: sum over t of ߚ^t U(c_{i,t}, n_{i,t}) (equation (1) and (2) in source). - Composite consumption index c_{i,t} aggregates food and nonfood with weight ߛ ∈ (0,1) on food (equation (3)). - Nonfood composite includes imported nonfood with share ζ ∈ (0,1) and elasticity ߦ ∈ (0,∞) between domestic and imported nonfood (equation (4)). - Elasticity of substitution between flexible-price and sticky-price goods: ߟ ∈ (0,∞); elasticity between differentiated goods: ߠ > 1. - Subsistence consumption: food has minimum amount c*; assumed households always afford c* (affects marginal utilities and elasticities). - Utility of consumption: U(c) = c^{1-ߪ}/(1-ߪ) where ߪ is risk aversion. - Disutility of labor in food sector: V_f(n_{i,f}) = χ_f n_{i,f}^{1+߰}/(1+߰) where ߰ is inverse Frisch elasticity and χ_f scaling factor. - Aggregate labor supply expression for nonfood households provided; s is share of nonfood households working in sticky-price sector. ### Financial market segmentation and budget constraints - Food-sector households: no access to financial markets; budget constraint implies consumption equals current labor income (rule-of-thumb consumers). Formal expression given in equation (6). - Expenditure price index P_t defined with P_{f,t} (food price) and nonfood price index P_{n,t} (equations (7), (8), (9) detailing Dixit-Stiglitz price index and nonfood composition). - Nonfood households: can buy one-period nominal domestic and foreign bonds to smooth consumption; budget constraint detailed in equation (10) with notation for nominal wages w_{x,t}, w_{n,t}, labor supplies, profits Π_t, and bond positions B_t and B_t^* with gross nominal interest rates R_t and R_t^*. ### Paper organization (as stated) - Section 2: empirical facts motivating model relevance. - Section 3: outline of model and contrast with prior literature. - Section 4: main results. - Section 5: sensitivity experiments and extensions. - Section 6: conclusion. *Source: _wp15205 - 1. INTRODUCTION (chapter/section content as provided).* ### 3.3 Production ### _wp15205 - 3.3 Production ### Production technologies and price setting - Food sector: - Each household owns one firm and produces food using a linear technology in labor ݕ ௙,௧: ݕ ௙.௧ ܣ ௙.௧ ܰ ௧ ௙, subject to a common productivity shock ܣ ௙,௧. - Firms are price takers; given market price ܲ ௙,௧ the zero profit condition determines labor demand. - Sticky price (nonfood) sector: - Firms use a linear technology in labor ݕ ௦,௧(ݖ) = ܣ ௦,௧ ܰ ௧ ௦(ݖ) and face a common productivity shock ܣ ௦,௧. - Calvo pricing with fraction ߙ ∈ (0,1) of firms unable to change price each period; firms free to change price choose ܺ ௧ by maximizing the discounted profit stream (equation (11)). - Marginal cost given by ܥܯ ௧ ௦ = (expression as in source). - Export sector: - Firms use linear technology ݕ ௫,௧ = ܣ ௫,௧ ܰ ௧ ௫ and face an exogenous price level every period. - Import prices follow the law of one price; export price ܲ ௫,௧ = ܵ ௧ ܲ ௠,௧, where ܵ ௧ is the terms of trade. - Firms are price takers; cost minimization determines wages and labor demand. ### Inflation definitions and monetary policy rule - Inflation measures (gross): - Headline inflation: ߨ ௧ = (݉ ೟ / ݉ ೟షభ) (expression as in source). - Sticky price sector inflation (core): ߨ ௦,௧ = (݉ ೞ.೟ / ݉ ೞ,೟షభ). - Imported goods inflation: ߨ ௠,௧ = (ݣ ೘,೟ / ݣ ೘,೟షభ). - Steady state: constant prices (zero inflation) and no price stickiness. - Taylor-type policy rule (equation (12)): - Central bank sets short-term nominal interest rate ܴ(௧) according to specified rule including interest rate smoothing parameter ߩ. - Parameters: ߶ గ and ߶ ௬ are weights on inflation and output gap; setting ߶ ௬ = 0 implies strict inflation targeting. - Definitions for policy experiments: - Core inflation = ߨ ௦,௧. - Headline inflation = ߨ ௧. - Inflation target used for optimal computation given by equation (13). ### Exogenous shock processes - Four shocks in the model, innovations drawn i.i.d. normal: - Productivity shock, food: - AR(1) process and innovation ߝ ௧ ௙ ~ ܰ(0,ߪ ௔ ௙). - Productivity shock, sticky price goods: - AR(1) process and innovation ߝ ௧ ௦ ~ ܰ(0,ߪ ௔ ௦). - Mark-up shock, sticky price goods: - AR(1) process and innovation ߝ ௧ ఛ ~ ܰ(0,ߪ ఛ). - Terms of trade shock, nonfood exports: - AR(1) process and innovation ߝ ௧ ఙ ~ ܰ(0,ߪ ௦). ### Welfare evaluation methodology - Objective: determine the policy rule that maximizes lifetime utility as a weighted sum of households' welfare, ܸ ௧௢௧௔௟ ܸߣ = ∑ (weights) ܸ ௧ ௡. - Compute second-order accurate consumer welfare measure under different monetary policy regimes (Schmitt-Grohe and Uribe approach). - Welfare gain ߱: - Defined as the fraction added to the strict core inflation targeting regime's consumption process to equate aggregate welfare to that under alternative regime a (equations (14) and (15)). - Interpretation: ߱*100 = 1 represents a gain of 1 percentage point of permanent consumption under the alternative policy regime. ### Parameter selection (baseline and calibration) - Discount factor: ߚ = 0.99 (annual real interest rate of 4 percent). - Fraction of credit-constrained households: ߣ = 0.4 (40 percent). - Risk aversion: ൌ2ߪ (baseline value). - Elasticity of substitution between differentiated goods: ߠ = 11 (implying a markup of 10 percent). - Calvo price non-adjustment probability: ߙ = 0.66 (mean duration of price fixation = 3 quarters). - Frisch elasticity (ݔ): benchmark assumption 0.33 (ൌ3߰). - Monetary policy parameters: ߩ = 0.7, ߶ గ = 2, ߶ ௬ = 0.5. - Food consumption calibration: - Average expenditure on food ≈ 42 percent. - One third of households' steady state food consumption assumed subsistence; demand inelasticity ߟ = 0.6 baseline. - Resulting steady state price elasticity of demand for food ≈ -0.3. - Shock persistence and volatility: - Food AR(1) coefficient = 0.25. - Nonfood AR(1) coefficient = 0.9. - Standard deviation of food productivity shock ߪ ௔ ௙ = 0.03. - Standard deviation of nonfood productivity shock ߪ ௔ ௦ = 0.02. - Terms of trade persistence ߩ ௦ = 0.77 and ߪ ௦ = 0.013. - Mark-up shock persistence ߩ ఛ = 0.9 and ߪ ఛ = 0.01. ### Baseline results and policy comparisons - Market completeness impact: - Incomplete markets model yields higher and more volatile inflation (food and nonfood) than complete markets. - Consumption more volatile than output in incomplete markets; reverse in complete markets. - Welfare comparisons (Table 4 summary from source): - Complete markets: optimal price index places entire weight on sticky price sector (identical to core inflation targeting); weight on food and traded goods = 0. Headline inflation targeting slightly reduces welfare. - Incomplete markets: headline inflation targeting improves welfare relative to core inflation targeting. - Optimal price index under incomplete markets assigns two-thirds weight to sticky price sector and one-third to food prices; traded goods weight = 0. - Targeting the optimal price index yields a slightly higher welfare gain than targeting headline inflation. - Impulse response to a 1 percent negative food productivity shock: - Complete markets: strict headline inflation targeting results in slightly higher volatility of consumption and output; policy response more aggressive under headline targeting, leading to further decline in output. - Incomplete markets: headline inflation targeting outperforms core targeting in stabilizing output because monetary policy is more effective at controlling aggregate demand when targeting headline inflation. ### Mechanics: financial frictions, heterogeneous households, and aggregate demand - Heterogeneity due to financial frictions: - Unconstrained households: consumption responsive to interest rates (optimize intertemporally). - Credit-constrained households: consumption independent of interest rates; depends only on current wage income. - Therefore, only a fraction of aggregate demand is interest-rate sensitive. - Response to negative food productivity shock under incomplete markets: - Central bank raises interest rate; unconstrained households reduce demand (postpone consumption). - Credit-constrained households' demand rises because relative food price increases raise wage income for food sector households, who consume current income. - Aggregate demand movement depends on which group's demand dominates. - Policy regime effect: - Under core inflation targeting: increase in food prices and wage income of food sector households is higher than under headline targeting → credit-constrained consumption rises enough to more than offset reduction by unconstrained households → aggregate demand increases. - Under headline inflation targeting: food price increases are lower → smaller rise in income and consumption of credit-constrained households → monetary tightening effectively controls aggregate demand. - Formalization: - Log-linearized aggregate demand equation (equation (16)) links aggregate demand to interest rate, inflation, lagged demand, and change in relative food price Δ̂ ௙,௧. - Optimal labor supply of food sector households (equation (17)) links food sector labor and relative price. - Conclusion: with financial frictions, relative prices affect aggregate demand in addition to aggregate supply; managing aggregate demand requires a policy regime that limits wage rises of credit-constrained consumers. *Source: _wp15205 - 3.3 Production* ### 4.1 Alternative Monetary Policy Rules ### 4.1 Alternative Monetary Policy Rules ### Flexible versus strict inflation targeting - Baseline comparison (first row of Table 5): all three inflation targets (optimal, headline and core) under strict inflation targeting (zero weight on the output gap). - Second row of Table 5: comparison of the three inflation targets under flexible inflation targeting (positive weight on the output gap) — ordering of rules in terms of welfare gains relative to core inflation targeting is preserved; weights on the different sectors in the optimal price index are essentially the same. - Third row of Table 5: flexible headline and flexible optimal inflation targeting compared against strict core inflation targeting — both flexible regimes still outperform strict core inflation targeting. - Adding the output gap into the monetary policy rule leads to lower welfare gains than strict targeting versions of those rules. Mechanism: - In the sticky price sector the output gap (level of output relative to trend) and inflation move in the same direction. - A negative productivity shock leads to a drop in output and an increase in inflation in this sector. - Including the output gap weakens the central bank's response to deviations of inflation from the target. - Experiment where the output gap coefficient was included in the search for the optimal rule: the optimal coefficient for the output gap is zero. - Related experiment findings: including the real exchange rate (current level, lagged level, changes) or the export price in the optimal inflation target yielded a coefficient/weight of zero. ### Sensitivity analysis — key parameter dimensions - General note: results held up quite well to changes in most parameters; comparisons are across regimes within a model (steady state values differ across models so cross-model comparison is not possible). - Share of households in the food sector (Panel A, Table 6): - As the share of households in the food sector rises, welfare gains from headline inflation or optimal inflation targeting decline relative to core inflation targeting. - Mechanism: larger rural household share ⇒ rural households poorer on average and nonfood households richer; for a given drop in agricultural output the relative price of food goes up by less when nonfood households' consumption of food (above subsistence) is larger. When rural share is small, relative price responds sharply to accommodate drop in food production. - Footnote: Reducing the share of food sector households even further leads to implausibly large welfare gains because the authors pinned down the average share of food expenditures in total household expenditures to be 0.42. - Subsistence level of food (Panel B, Table 6): - The subsistence constraint does not bind in equilibrium but reduces the elasticity of substitution between food and nonfood. - When there is no subsistence level of food consumption, the weight of food in the optimal inflation target is small and core inflation targeting delivers higher welfare than headline inflation. - As the subsistence level goes up, the weight of food in the optimal inflation index rises and core inflation targeting becomes inferior to headline inflation targeting. - Mechanism: a higher subsistence level implies lower nonsubsistence food consumption; for a given drop in food output, market clearing requires a larger increase in the relative price of food ⇒ more volatile impulse responses ⇒ larger welfare gain from headline inflation targeting. - Alternate approach: dropping subsistence assumption and lowering the elasticity of substitution to 0.38 yielded results similar to baseline; however the subsistence approach matches developing country data better because income elasticity of food consumption is smaller than one in developing economies. - Share of food in total household consumption: - When the food share is small, the optimal inflation target places most weight on the sticky price sector; core inflation targeting then delivers higher welfare than headline inflation targeting; gains from targeting the optimal index are modest. - As the food share rises, the optimal inflation index assigns increasing weight on food prices. - When food accounts for half of total consumption expenditures on average, gains from headline inflation targeting become large and the optimal inflation index puts nearly the entire weight on food prices. - Contrast with Mankiw and Reis (2003): their result that “the more important a price is in the consumer price index, the less weight that sector's price should receive in the stability price index” differs because the current model has incomplete markets and low elasticity of substitution between food and nonfood. Under complete markets the weight on food prices is zero irrespective of the food share. - Degree of price rigidity in the sticky price sector (Panel C, Table 6): - The weight of the sticky price sector in the optimal price index increases with the degree of price stickiness (consistent with Mankiw and Reis (2003) and Benigno (2004)). ### Financial frictions and portfolio access - Baseline assumption: food sector households face strong financial frictions and are hand-to-mouth consumers. - Relaxation: introduce a portfolio holding cost for these households to vary extent of common financial frictions. - When portfolio holding cost is zero, rural households have the same degree of access to the bond market as nonfood sector households (not equivalent to complete markets). - When portfolio holding cost is very high, rural households hold zero bonds and the economy converges to the baseline case. - Findings in the full access (but not complete markets) scenario: - Food prices enter with a positive weight in the optimal price index, but the weight is substantially smaller than in the baseline incomplete markets scenario. - Welfare gain from targeting the optimal price index is small relative to core inflation targeting because bond access allows food sector households to smooth consumption intertemporally though they cannot fully insure against sector-specific shocks. ### Common productivity shocks - Consideration: only aggregate rather than sector-specific productivity shocks. - Recomputed model with a productivity shock common to the food and the nonfood domestic goods sectors (and markup and terms of trade shocks as before). - Intuition and findings: - Common productivity shocks should increase welfare gain from targeting inflation in the headline CPI or the optimal price index because there are no shocks specific to the rigid price sector. - This is confirmed by the model: results hold whether the common productivity shock is transitory (food sector shock) or more persistent (sticky price sector shock). - Food prices consistently have a significant weight in the optimal inflation target under common shocks. ### Concluding remarks and policy implications - Context: prior research supporting core inflation targeting relied on complete markets and price stickiness as the only distortion. - The paper’s more realistic model for developing economies includes: - incomplete markets with credit-constrained consumers; - households requiring a minimum subsistence level of food; - low price elasticity of the demand for food; - a high share of expenditure on food in households' total consumption expenditure. - Main conclusions: - Introducing financial frictions overturns the classical result that core inflation targeting is optimal: in the presence of credit-constrained consumers, targeting core inflation no longer maximizes welfare. - Stabilizing inflation is not sufficient to stabilize output when markets are not complete. - Under these conditions, headline inflation targeting improves welfare. - The computed optimal price index includes a positive weight on food prices but generally assigns zero weight to import prices (agents in that sector have access to financial markets and high price elasticity of demand). - Possible extensions and practical dilemmas for developing-economy central banks: - Including money explicitly would provide a saving mechanism for hand-to-mouth consumers and could strengthen the case for headline inflation targeting to preserve the value of monetary savings. - Including physical capital would highlight tradeoffs: raising policy rates to counter surging food price inflation can hurt industrial activity. Raising interest rates in response to a transitory negative shock to agricultural productivity could be welfare improving in an incomplete markets setting where food consumption accounts for a large share of household consumption expenditures. *Source: 4.1 Alternative Monetary Policy Rules (extract).* ### References ### _wp15205 - References ### Major cited works - Aguiar, Mark, and Gita Gopinath, 2007, “Emerging Market Business Cycles: The Cycle Is the Trend,” Journal of Political Economy, Vol. 115, pp. 69-102. - Anand, Rahul, and Eswar Prasad, 2010, “Optimal Price Indices for Targeting Inflation Under Incomplete Markets,” NBER Working Paper No. 2010. - Aoki, Kosuke, 2001, “Optimal Monetary Policy Responses to Relative Price Changes,” Journal of Monetary Economics, Vol. 48, No. 1, pp. 55-80. - Ascari, Guido, 2004, “Staggered Prices and Trend Inflation: Some Nuisances,” Review of Economic Dynamics, Vol. 7, No. 3, pp. 642-667. - Basu, Priya, and Pradeep Srivastava, 2005, “Scaling-up Microfinance for India’s Rural Poor,” World Bank Policy Research Working Paper No. 3646. - Basu, Susanto, 1996, “Procyclical Productivity: Increasing Returns or Cyclical Utilization?” Quarterly Journal of Economics, Vol. 111, No. 3, pp. 719-751. - Basu, Susanto, and John G. 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Rolf Langhammer and Lucio Vinhas de Souza (Springer), pp. 205-245. - Oconnell, Steve, Rich Peck, Rafael Portillo, and Felipe Zanna, forthcoming, “Implications of Food Subsistence for Monetary Policy and Inflation,” IMF Working Paper. - Pallage, Stephane, and Michel A. Robe, 2003, “On the Welfare Cost of Economic Fluctuations in Developing Countries,” International Economic Review, Vol. 44, No. 2, pp. 677-698. - Pétursson, Thórarinn G., 2008, “How Hard Can it Be?: Inflation Control Around the World,” Central Bank of Iceland, Economics Department. - Rotemberg, Julio J., and Michael Woodford, 1997, “An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy,” in NBER Macroeconomics Annual, Vol. 12, eds. Ben S. Bernanke and Julio J. Rotemberg (Cambridge, MA: MIT Press), pp. 297-346. - Schmitt-Grohé, Stephanie, and Martın Uribe, 2003, “Closing small open economy models.” Journal of International Economics, Vol. 61, No. 1, pp. 163-185. - Schmitt-Grohé, Stephanie, and Martın Uribe, 2004, “Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function,” Journal of Economic Dynamics and Control, Vol. 28, pp. 755-775. - Schmitt-Grohé, Stephanie, and Martın Uribe, 2007, “Optimal Simple and Implementable Monetary and Fiscal Rules,” Journal of Monetary Economics, Vol. 54, No. 6, pp. 1702-1725. - Taylor, John B., 1993, “Discretion versus Policy Rules in Practice,” Carnegie-Rochester Conference Series on Public Policy, Vol. 39 (December), pp. 195-214. - Walsh, James, P., 2011, “Reconsidering the Role of Food Prices in Inflation,” IMF Working Paper No. 11/71. - Wynne, Mark A., 1999, “Core Inflation: A Review of Some Conceptual Issues,” Research Department Working Paper No. 9903, Federal Reserve Bank of Dallas. ### Key tables and exact figures Table 1: Share of Food Expenditure in Total Household Expenditure - Developing Economies: - Indonesia 53.0 - Vietnam 49.8 - India 48.8 - China 36.7 - Russia 33.2 - Malaysia 28.0 - Average 41.6 - Advanced Economies: - Japan 14.7 - Germany 11.5 - Australia 10.8 - Canada 9.3 - United Kingdom 8.8 - United States 5.7 - Average 10.1 - Notes: Data for developing economies are for 2005 while for advanced economies data are for 2006. Expenditure on food includes expenditure on food consumed at home only and does not include expenditure on beverages and tobacco. Table 2: Composite Measure of Access to Financial Services in Developing Countries - Selected Countries Percent with Access: - Argentina 33 - Brazil 56 - Chile 42 - China 64 - India 35 - Indonesia 20 - Kenya 42 - Malaysia 66 - Nigeria 30 - Philippines 27 - Poland 70 - Russia 48 - South Africa 54 - Thailand 73 - Turkey 58 - Median (29 Developing Economies): 42 - Median (27 Advanced Economies): 96 - Notes: Composite indicator measures percentage of adult population with access to an account with a financial intermediary. Table shows selected developing countries. Reported medians are based on a larger sample. Table 3: Parameter Values (selected) - Structural - ߣ Share of households in the food sector (who are credit-constrained) 0.4 - ߟ Elasticity of substitution between food and nonfood 0.6 - ܥ∗ Subsistence level of food consumption given subsistence ratio of 1/3 0.042 - ߛ Non-subsistence food consumption share 0.326 - General - ߚ Discount factor 0.99 - ߪ Risk-aversion coefficient 2 - ߠ Elasticity of substitution 11 - ߰ Inverse of Frisch elasticity of labor supply 3 - ߰௕ Interest rate elasticity of debt (for technical purpose only) 0.0007 - ߙ Probability not being able to reset price in each quarter 0.66 - ߦ Elasticity of substitution between domestic and foreign goods 0.7 - ߞ Share of imports in total nonfood consumption 0.3 - Policy - ߩ Degree of interest rate smoothing 0.7 - ߶గ Degree of response to inflation 2 - ߶௬ Degree of response to output gap 0.5 - Shock Parameters - ߩ௔௙ߪ,௔௙ Productivity shocks in the food sector: persistence, std. dev. 0.25, 0.030 - ߩ௔௦ߪ,௔௦ Productivity shocks in the sticky price sector: persistence, std. dev. 0.9, 0.020 - ߩ௦ߪ,௦ Terms of trade shocks in the export sector: persistence, std. dev. 0.77, 0.013 - ߩఛߪ,ఛ Markup shocks in the sticky price sector: persistence, std. dev. 0.9, 0.010 Table 4: Welfare Comparisons under Different Inflation Targets - Financial Welfare Gain and Weights in the Optimal Price Index - Complete Markets: Financial Welfare Gain -0.09%; Headline 0.00%; Optimal 0.00; Food Prices 1.00; Sticky Prices 0.00; Import Prices 0.00 - Incomplete Markets: Financial Welfare Gain 0.16%; Headline 0.20%; Optimal 0.35; Food Prices 0.65; Sticky Prices 0.00; Import Prices 0.00 - Notes: Optimal price index consists of food prices, sticky nonfood domestic goods prices, and import prices. Welfare gains are permanent consumption gains relative to strict core inflation targeting. Table 5: Welfare Comparisons between Strict and Flexible Inflation Targeting - Benchmark Target / Alternative Target / Welfare Gain / Weights in the Optimal Price Index - Strict / Core / Strict: Welfare Gain 0.16%; Headline 0.20%; Optimal 0.35; Food Prices 0.65; Sticky Prices 0.00; Import Prices 0.00 - Flexible / Core Flexible: Welfare Gain 0.12%; Headline 0.17%; Optimal 0.34; Food Prices 0.66; Sticky Prices 0.00; Import Prices 0.00 - Strict / Core Flexible: Welfare Gain 0.07%; Headline 0.11%; Optimal 0.34; Food Prices 0.66; Sticky Prices 0.00; Import Prices 0.00 - Notes: Optimal price index consists of food prices, sticky nonfood domestic goods prices, and import prices. Strict inflation targeting responds only to inflation; flexible targeting allows responses to output fluctuations. Welfare gains are permanent consumption gains relative to the respective benchmark. Table 6: Sensitivity Tests (selected entries) - Panel A. Share of Rural Households (baseline = 0.4) - 0.3: Welfare Gain 0.36%; Headline 0.49%; Optimal 0.87; Food Prices 0.13; Sticky Prices 0.00 - 0.4: Welfare Gain 0.16%; Headline 0.20%; Optimal 0.35; Food Prices 0.65; Sticky Prices 0.00 - 0.5: Welfare Gain -0.02%; Headline 0.09%; Optimal 0.22; Food Prices 0.78; Sticky Prices 0.00 - 0.6: Welfare Gain -0.15%; Headline 0.04%; Optimal 0.14; Food Prices 0.86; Sticky Prices 0.00 - Panel B. Subsistence Ratio of Food (baseline = 0.33) - 0.0: Welfare Gain -0.07%; Headline 0.00%; Optimal 0.08; Food Prices 0.92; Sticky Prices 0.00 - 0.1: Welfare Gain -0.06%; Headline 0.01%; Optimal 0.14; Food Prices 0.86; Sticky Prices 0.00 - 0.2: Welfare Gain -0.03%; Headline 0.03%; Optimal 0.21; Food Prices 0.79; Sticky Prices 0.00 - 0.3: Welfare Gain 0.08%; Headline 0.12%; Optimal 0.31; Food Prices 0.69; Sticky Prices 0.00 - 0.4: Welfare Gain 0.56%; Headline 0.63%; Optimal 0.48; Food Prices 0.52; Sticky Prices 0.00 - Panel C. Price Stickiness (baseline = 0.66) - 0.5: Welfare Gain 0.13%; Headline 0.16%; Optimal 0.42; Food Prices 0.58; Sticky Prices 0.00 - 0.6: Welfare Gain 0.16%; Headline 0.19%; Optimal 0.39; Food Prices 0.61; Sticky Prices 0.00 - 0.7: Welfare Gain 0.14%; Headline 0.19%; Optimal 0.32; Food Prices 0.68; Sticky Prices 0.00 - 0.8: Welfare Gain 0.01%; Headline 0.11%; Optimal 0.20; Food Prices 0.80; Sticky Prices 0.00 - Notes: Optimal price index consists of food price, sticky nonfood domestic goods price and import price. Welfare gains are permanent consumption gains relative to strict core inflation targeting. ### Figures and shock responses (notes) - Figure 1: Impulse Responses to a Negative Food Productivity Shock (Complete Markets) - Notes: Impulse responses are to a 1 percent negative shock to food productivity. Each variable's response is expressed as the percentage deviation from its steady state level. - Figure 2: Impulse Responses to a Negative Food Productivity Shock (Incomplete Markets) - Notes: Impulse responses are to a 1 percent negative shock to food productivity. Each variable's response is expressed as the percentage deviation from its steady state level. *Source: _wp15205 - References (PDF).* --- _Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2015/_wp15205.pdf_