## 3.1 The Cyclicality of Posted and Effective Prices

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### Measurement of posted and effective prices
- Effective price for good j in category c across stores in geographic area m is the quantity-weighted average price; monthly effective inflation is computed as log( P_eff_{j,c,m,t} / P_eff_{j,c,m,t-1} ).
- Category-level effective inflation rates are aggregated across goods j using UPC weights ω_{j,c,m} with three alternative weighting schemes: equal weights; city-specific expenditure shares; common cross-city expenditure shares. Weights are fixed within each calendar year (so the effective-price inflation measure does not include substitution across goods within the year).
- Monthly inflation rates are cumulated into the annual “across-store effective inflation rate” π_eff_{c,m}.
- Posted inflation measures π_post_{c,m} are constructed analogously using posted prices, with retailer weighting using fixed-expenditure weights updated at the annual frequency rather than time-varying expenditure weights.

### Baseline empirical specification and inference
- Baseline regression (specification (3.2)):
  - Y_{c,m,t} = β * u_{m,t} + γ_t + α_{c,m} + ε_{c,m,t},
    - m indexes markets, c indexes categories, t indexes month;
    - Y_{c,m,t} is the dependent variable (e.g., effective inflation);
    - u_{m,t} is the local seasonally-adjusted unemployment rate;
    - α_{c,m} are market-category fixed effects; γ_t are time fixed effects.
- Estimation is monthly. Standard errors constructed using Driscoll and Kraay (1998) to account for serial and cross-sectional correlation; these standard errors tend to be conservative. Time fixed effects control for aggregate shocks.

### Main empirical findings: posted versus effective prices
- Posted prices:
  - Little cyclical sensitivity in inflation of prices posted by retailers once city-category and time fixed effects are included; coefficients on unemployment are mostly negative but statistically indistinguishable from zero.
- Effective prices (prices actually paid by households):
  - Significantly pro-cyclical: inflation rate of prices paid by consumers falls when local economic conditions worsen.
  - Quantitative estimate: "a 2 percent point increase in the local unemployment rate lowers the effective price inflation rate by 0.5 percent at an annual rate below the inflation rate of posted prices."
  - Appendix Table 4: effect of unemployment on effective price inflation stronger than on posted price inflation for 25 out of 31 categories; for posted prices point estimates insignificantly different from zero for 19 out of 31 categories.

### The cyclicality of sales and regular price changes (summary)
- Sales (aggregate patterns):
  - Average size of sales: approximately 25 percent across all goods.
  - Less than 20 percent of goods are on sale in any given week.
  - More than 30 percent of all goods purchased are bought when goods are on sale.
  - Categories: frozen dinners and frozen pizzas are proportionally most bought on sale; cigarettes are least frequently bought on sale.
  - Empirical pattern: strong positive correlation between frequency and size of sales across categories; categories with higher sales frequency have larger fraction of goods bought on sale.
- Regular price changes:
  - Average size of price changes: 3.5 percent.
  - Average size of absolute price changes: 12 percent.
  - Average weekly frequency of regular price changes: 5 percent.
  - Average duration between regular price changes: approximately 5 months.
  - Observed asymmetry: increases in regular prices are more frequent than price decreases.
  - Categories with more frequent regular price changes tend to have smaller price changes.
- Cyclical behavior (preferred specification with city-category and time fixed effects):
  - Higher unemployment rates are associated with significantly less frequent sales and smaller sales (sales sizes measured as negative values, so a positive coefficient indicates smaller discounts).
  - Share of goods bought on sale declines as unemployment rises.
  - Regular price changes are close to acyclical:
    - Slightly reduced frequency of regular price changes observed in some specifications with marginal significance for price increases.
    - Using expenditure-weighted category averages, cyclical changes in frequency of regular price changes are no longer significantly different from zero.
    - Little evidence that the size of regular price changes varies with local economic conditions regardless of aggregation method.
- Robust result: frequency and average size of sales, and the share of goods bought on sale, are robustly lower when local unemployment rates are higher.
- Appendix Table 3 (alternative standard errors) and Table 2 report point estimates and significance for these moments; selected coefficients (equal-weights panel) include:
  - Sales — Frequency: -0.365*** (0.120)
  - Sales — Size: 0.256** (0.120)
  - Share of goods bought on sales: -0.461*** (0.133)
  - Changes of regular prices — Frequency (All): -0.100** (0.044)
  - Inflation of posted prices: 0.007 (0.034)
  - Inflation of effective prices: -0.206*** (0.045)

### Mechanism: store-switching and theoretical interpretation
- Puzzle: effective prices fall in downturns while posted regular prices are acyclical and sales become less frequent/smaller.
- Proposed mechanism:
  - Consumers reallocate expenditures toward low-price retailers when local conditions worsen (store-switching), lowering quantity-weighted effective prices even if posted prices do not decline and sales are less prevalent.
  - High-price (HiLo) stores face larger declines in the importance of sales and larger declines in revenue growth when unemployment rises; low-price (EDLP) stores may gain market share.
  - Reinforcing multiplier: as price-sensitive consumers shift to EDLP retailers, HiLo retailers reduce sales frequency/size, further encouraging switching.
- Simple two-retailer model (Lal and Rao (1997) framework in Appendix B):
  - EDLP (no sales) and HiLo (intermittent sales) with two consumer types: bargain hunters and loyal consumers.
  - An increase in the share of bargain hunters reduces HiLo’s incentive to offer large sales and increases EDLP share — consistent with observed pro-cyclicality of sales.

### Household-level evidence on store-switching
- Household panel (IRI Symphony) in Eau Claire, WI and Pittsfield, MA (2001–2007), 5,000–10,000 households tracked; about 2,000 continuously present.
- Household shopping-rank measure R̃_hmt = Σ_w_hsmt · R̃_smt (expenditure-share-weighted average store rank).
- Empirical findings:
  - Coefficient on unemployment is negative and significant across specifications.
  - Magnitude: a 1 percent point increase in the local unemployment rate is associated with a decrease in the average rank at which households shop between 0.05 and 0.13 depending on measures used.
  - Heterogeneity by income (income quintile ranges in IRI sample):
    - 1st quintile: $5000 to $22,500
    - 2nd quintile: $22,600 to $31,600
    - 3rd quintile: $31,700 to $50,000
    - 4th quintile: $50,100 to $70,000
    - 5th quintile: $70,100 to $120,000
  - Strongest store switching observed for households in the second and third income quintiles (annual income between $22,600 and $50,000); low-income households already shop at low-price stores; high-income households consistently shop at high-price stores.

### Cross-good substitution within categories
- Construction: within-category effective price at store s, market m: P̃_scm = Σ_j p_jsm · q̄_j / Σ_j q̄_j where q̄_j are quantity equivalents.
- Monthly inflation log(P̃_scm,t / P̃_scm,t−1); aggregated across stores using equal or expenditure weights; cumulated to annual Π̃_cm.
- Two substitution schemes: broad (all UPCs within category) and narrower (subcategories).
- Empirical results (Table 6):
  - Significant negative relationship between unemployment rates and within-category effective inflation rates.
  - Effect stronger when allowing larger set of goods within each category.
  - Quantitative magnitudes similar order as across-store substitution results.
  - Example estimates:
    - Substitution within broad categories (equal weights): -0.454* (0.251)
    - Substitution within broad categories (sales-share weights): -0.611** (0.265)
    - Substitution within narrower categories (equal weights): -0.377* (0.211)
    - Substitution within narrower categories (sales-share weights): -0.475* (0.250)

### New Keynesian model with expenditure reallocation across retailers (section 6.1) — overview and calibration
- Model features:
  - Households choose purchases across retailers; discount retailer purchases involve iceberg cost ߬ that can be reduced by shopping effort ܵ.
  - Time-intensive shopping effort trades off with leisure; diminishing returns to shopping effort imply countercyclicality of shopping intensity.
  - Intermediate goods under monopolistic competition with Calvo price stickiness; sales abstracted from in baseline model.
  - Shopping effort and iceberg-cost elasticity produce reallocation of expenditures and affect final consumption price dynamics.
- Key log-linearized conditions: consumption Euler, labor, shopping-effort first-order condition; marginal disutilities of labor and shopping equalized.
- Calibration (explicit parameter values):
  - Discount factor: ߚ = 0.99.
  - Calvo price-stickiness parameter: ߠ = 0.70 (firms update prices every 10 months on average).
  - Production and preference parameters:
    - ߙ = 0.66.
    - Elasticity across intermediate varieties: ߪ = 10.
  - Monetary policy coefficients (Coibion and Gorodnichenko (2011)):
    - Long-run response to inflation ߯గ = 1.5.
    - Long-run response to output growth ߯∆௬ = 0.5.
    - Long-run response to the output gap ߯௫ = 0.1.
    - Interest-smoothing ߩ௥ = 0.9.
  - Technology process:
    - Persistence ߩ௭ = 0.95.
    - Std. dev. of technology shocks = 0.0090.
    - Std. dev. of monetary policy shocks = 0.0024.
  - Store-switching and shopping-effort parameters:
    - Normalize steady-state iceberg cost so ߬ҧܵ(߬ҧ/ߤ) = 1 yielding equalized steady-state consumption shares across local and discount stores.
    - Relative posted price parameter ߤ = 1.5 (discount stores 33 percent cheaper on average).
    - Elasticity of substitution across stores: ߛ = 4.
    - Elasticity of iceberg costs w.r.t. shopping effort: ߶ = 0.3 (baseline).
  - Steady-state implied statistics:
    - Baseline implies steady-state labor-leisure ratio of 0.4.
    - American Time Use Survey averages: worked 3.7 hours/day, leisure 5.7 hours/day, sleep 8.6 hours/day — implying labor-leisure ratios of 0.65 (not counting sleep as leisure) or 0.26 (counting sleep as leisure).

### Empirical calibration check and model fit
- Empirical estimate (Table 4): a 1 percentage point increase in unemployment associated with decrease in average shopping rank ≈ 0.13 with standard error ≈ 0.04.
- Using Okun’s Law (1 percentage point increase in unemployment ≈ 2 percent decline in output gap) yields semi-elasticity of average shopping rank w.r.t. output gap ≈ 0.065 with 95 percent CI [0.028 0.102].
- Model implication with two retailers and baseline parameters (ߛ = 4, ߶ = 0.3, ߬ҧ/ߤ = 1): steady-state semi-elasticity ≈ 0.082 — close to empirical estimate and within the confidence interval.

### Model implications: transmission, Phillips curve, and quantitative effects
- Effective-price vs posted-price inflation:
  - Model’s observable effective-price index captures large fraction of final consumption price movements; given calibration (ఓిఓ)ߛ = 0.8, effective price measure captures 80 percent of movements in final consumption price index despite iceberg costs being unobservable.
- Quantitative example (2001–2003):
  - U.S. unemployment rose by approximately 2 percentage points → via Okun’s Law ≈ 4 percentage point decline in output gap.
  - Theory predicts a decline in the effective-posted price gap of 0.60 percentage points; empirical figure shows a decline very close to this value.
- Phillips curve and inflation measurement:
  - Shopping effort increases coefficient on contemporaneous output gap in NKPC expressed in consumption prices → steeper short-run Phillips curve between effective consumption price inflation and real activity than when using posted/input prices.
  - Simulations and micro-data:
    - Model simulation: unconditional relationship between CPI inflation and employment versus effective price inflation and employment shows steeper slope with effective prices (Panel A, Figure 3).
    - Aggregated monthly micro-data: both posted inflation and effective inflation decline with higher aggregate unemployment, but decline is larger for effective inflation; difference statistically significant at 1 percent level (Panel B, Figure 3).
- Monetary policy transmission:
  - In response to monetary policy shocks, nearly 50 percent of total adjustment in price of final consumption good paid by households occurs in the first quarter, while this ratio is less than 20 percent for underlying posted prices.
  - Consequence: contemporaneous effect of monetary policy shocks on output is smaller than implied by frequency of posted price changes alone, but persistence of output-gap response is not qualitatively affected.
  - Net result: dynamics dominated by underlying level of posted-price stickiness; response of output resembles New Keynesian model with high posted-price stickiness.

### Aggregate and welfare implications (section 6.3 and Appendix analysis)
- Business-cycle and labor-supply effects:
  - Shopping effort and store-switching alter effective Frisch labor supply elasticity and effective elasticity of output gap w.r.t. real interest rates when expressed in input-price terms.
  - Countercyclical shopping effort mitigates expected inflation declines via increased expected shopping effort when real rates rise, partially offsetting initial output declines.
- Welfare objective with endogenous shopping effort (second-order approximation, Appendix C and Figure 4 Panel C):
  - Welfare loss function coefficients on inflation volatility and output-gap volatility vary with elasticity of iceberg costs to shopping time ߶.
  - Higher ߶ systematically lowers coefficient on inflation volatility; net implication: welfare becomes relatively more sensitive to output-gap volatility relative to inflation volatility as steady-state shopping effort increases.
  - Policy implication: stabilizing output-gap volatility should play a more prominent role in policymakers' objective functions than in models omitting this channel.
- What price measure should policymakers target?
  - Under inflation-targeting: generally better to respond to posted price inflation than to effective price inflation for higher utility in most calibrated cases (Panel A, Figure 5).
  - Under price-level targeting (PLT): targeting effective or final consumption price levels yields significantly higher expected utility than targeting posted-price levels because effective prices respond more immediately to shocks and PLT forces corrective policy that stabilizes final consumption prices (Panel B, Figure 5).
  - Conclusion: optimal policy target depends on monetary regime; PLT favors targeting effective/final goods price levels while inflation-targeting may favor posted-price inflation.
- Measurement implications:
  - Store-substitution produces cyclical mismeasurement of cost-of-living by fixed-expenditure-weight price indexes (Boskin; Shapiro and Wilcox).
  - Effective price index using time-varying expenditure weights across retailers generally tracks final consumption price index despite not including household shopping-time costs.
  - Statistical agencies would be better served by tracking prices actually paid by consumers (effective prices) rather than prices charged by retail outlets to more precisely measure cost-of-living (Triplett (2003)).
  - Constructing time-varying expenditure weights in real time may be infeasible; scanner price data and household-level price-paid measures are promising approaches.

### Empirical robustness and auxiliary results
- Store-rank results (Table 3 and Appendix Tables 5–6):
  - Stores ranked by normalized price rank R̃_smt ∈ (0,1); rank persistence autocorrelation = 0.90 at annual frequency.
  - More expensive stores exhibit much larger declines in frequency of sales and share of goods bought on sale when unemployment rises; revenue growth declines more strongly in expensive stores when unemployment increases.
  - Appendix Table 6 store-level regressions (equal-weight rank construction) report strong negative UR×rank interactions, e.g. UR×rank on Sales Frequency: -8.285*** (0.785) in one specification.
- Robustness of standard errors:
  - Appendix Table 3 compares Driscoll-Kraay and clustered standard errors; main point estimates remain significant for key moments (sales frequency, share on sale, effective-price inflation).

### Concluding empirical and policy takeaways (summary)
- Empirical facts:
  - Sales are pro-cyclical: higher unemployment → declines in frequency and depth of sales and declines in share of goods bought on sale.
  - Posted regular prices exhibit little cyclical sensitivity; effective prices paid by households are substantially more flexible over the business cycle due primarily to store-switching and within-category substitution.
- Model interpretation and quantitative relevance:
  - Store-switching and time-varying shopping effort provide a mechanism for countercyclical effective prices and reallocation of expenditures toward low-price retailers in downturns.
  - Quantitatively, implications for monetary neutrality are present but relatively modest; dynamics remain influenced by posted-price stickiness.
- Policy and measurement:
  - Cyclical mismeasurement of household consumption prices occurs when fixed-expenditure weights ignore store-switching and shopping effort.
  - Under inflation-targeting, responding to posted-price inflation may be preferable; under price-level targeting, targeting effective/final consumption price levels can yield higher welfare.
  - Recommendation: statistical agencies should invest in measuring prices actually paid by households (effective prices) and reallocation across retailers to improve inflation measurement and policy design.
- Additional notes:
  - Rise of online retailing likely reduces shopping costs and increases the importance of the store-switching channel going forward.
  - Ignoring store-switching can bias structural interpretations of estimated relationships (e.g., intertemporal elasticity estimates).

*Source: _wp12207*

### 3.1 The Cyclicality of Posted and Effective Prices .......................................11

### 3.1 The Cyclicality of Posted and Effective Prices .......................................11

### Major sections covered
- 3.1 The Cyclicality of Posted and Effective Prices
- 3.2 The Cyclicality of Sales and Regular Price Changes
- 3.3 Implications of Sales and Effective Price Cyclicality
- IV. Household Store-Switching
  - 4.1 Cross-sectional variation in the sensitivity of pricing to business conditions
  - 4.2 Households’ choices of shopping outlets as a function of business conditions
- V. Cross-Good Substitution
- VI. Aggregate Implications of Store-Switching
  - 6.1 New Keynesian Model with Expenditure Reallocation across Retailers
  - 6.2 Testable Predictions of the New Keynesian Model with Store-Switching
  - 6.3 Business Cycle and Policy Implications of Store-Switching
- VII. Conclusion
- References

### Empirical and supplemental materials enumerated
- Tables:
  - 1. Descriptive statistics.
  - 2. Cyclical properties of selected moments of price changes.
  - 3. Cyclicality of pricing moments by store rank.
  - 4. Rank of the shore where households shop as a function of local unemployment rate.
  - 5. Rank of the shore where households shop as a function of local unemployment rate and household’s [text truncated in source].
  - 6. Within category substitution.
- Figures:
  - 1. Correlations between key moments
  - 2. Economic Conditions and the Reallocation of Consumption Expenditures Across Retailers.
  - 3. Correlation between unemployment rate and measures of inflation.
  - 4. Business Cycle and Policy Implications of Endogenous Shopping Effort and Store-Switching.
- Appendix content:
  - Appendix Figures: 1. Sensitivity of Output Gap Response to Contractionary Monetary Policy Shock
  - Appendix B: A Model of Store-Switching and Pro-Cyclical Sales
  - Shopping Effort and Store-Switching (appendix section)
  - Appendix D: Construction of Data Moments
  - Appendix Tables (numbered 1–6) with topics including Descriptive Statistics by Category; Moments for All (sales and regular) Price Changes; Alternative Standard Errors; Cyclical Behavior of Price Changes at the Category Level; Cyclicality of pricing moments by store rank, alternative aggregation across UPCs; Use Price Differentials to Construct Relative Price Ranks of Stores: Store-Level Results.

### Document pagination and organization notes
- Primary chapter/section numbering spans pages indicated by section headings (e.g., 3.1 on page 11).
- Appendix Figures and Appendix Tables are provided with explicit numbering (Appendix Figures start at 1; Appendix Tables 1–6).
- The document includes a set of Tables and Figures mapped to specific empirical and model components referenced in main sections IV–VI.

*Source: _wp12207 - 3.1 The Cyclicality of Posted and Effective Prices .......................................11*

### References

### _wp12207 - References

### I. Introduction — background and research question
- Research context: monetary non-neutrality commonly attributed to “sticky prices” (Woodford (2003)); alternative frictions include nominal and real wage rigidities and information rigidities.
- Motivation: firms change posted prices infrequently (example: Starbucks raised brewed coffee prices once per year since the 2007-2009 recession began), but “effective” prices actually paid by households may be more flexible due to consumer reallocation across goods, stores, or time.
- Key research question: How cyclical are posted prices versus effective prices paid by households, and what mechanisms (sales versus store-switching and shopping effort) account for any differences?

### II. Main empirical findings
- Cyclical sensitivity comparison:
  - Posted prices: little cyclical sensitivity in inflation of prices posted by retailers (consistent with Gali and Gertler (1999), Williams (2006), Roberts (2006)).
  - Effective prices: more cyclically sensitive than posted prices.
  - Quantitative estimate: a 2 percent point increase in the local unemployment rate lowers the local inflation rate in effective prices by 0.5 percent relative to the inflation rate in posted prices for a given UPC.
- Role of sales:
  - Regular price changes exhibit little cyclical sensitivity.
  - Frequency and size of sales, and the share of a given good bought on sale, decline when unemployment rates rise.
  - Conclusion: greater flexibility in effective prices does not stem from sales; sales behavior is the opposite of what would undo posted-price rigidities.
- Evidence for store-switching mechanism:
  - High-price stores experience larger declines in the importance of sales than low-price stores when local unemployment rates rise.
  - When unemployment increases, the growth rate of revenues in high-price stores declines more than in low-price stores, consistent with expenditure reallocation across retailers.
  - Household-level panel data: individual households reallocate expenditures toward low-price retailers when local economic conditions deteriorate; reallocation is most pronounced for households near the middle of the income distribution.

### III. Data description and measurement conventions
- Data source: panel dataset assembled by Symphony IRI (formerly Information Resources, Inc.), covering weekly scanner price and quantity data.
- Coverage:
  - Geographic: 50 U.S. metropolitan areas (MSA level with four broader areas and two smaller areas noted).
  - Time span: January 2001 to December 2007.
  - Products: 31 product categories, multiple chains per market, panel of stores (grocery and drug stores), and a household panel in two metropolitan areas.
- Retailer and product detail:
  - Weekly data at the UPC level, with brand information; private-label UPCs share same brand ID so retailer identity cannot be recovered from branding.
  - Retailers report total dollar value of weekly sales (TR) and total units sold (TQ); average retail price computed as TR/TQ (retail price includes retail features, displays and retailer coupons; manufacturer coupons excluded).
  - Retailers flag goods on sale; dataset provides average price and sales flag for each week-store-UPC observation.
- Sales and regular price definitions and filters:
  - Any change in prices between two periods when neither period has a sales flag is defined as a “regular” price change if the price difference exceeds 1 percent in value.
  - When a sales flag is listed and the price after the sale expires is the same as prior to the sale, assume no change in regular prices in intermittent periods.
  - Additional sales filter: consider a good on sale if a price reduction is followed by a price increase of the same magnitude within four weeks (Nakamura and Steinsson (2008)-style filter).
- Aggregation and weighting:
  - Frequencies of sales and regular price changes computed at UPC level in a given month, averaged across UPCs within a category in a city-month, then averaged across time and cities.
  - Weighting schemes used to aggregate across UPCs: i) equal weights; ii) expenditure shares for a given city and year (“city specific”); iii) cross-city expenditure shares for a given year (“common”).

### IV. Price-change statistics and patterns (exact figures)
- Sales:
  - Average size of sales: approximately 25 percent across all goods.
  - Less than 20 percent of goods are on sale in any given week.
  - More than 30 percent of all goods purchased are bought when goods are on sale.
  - Category examples: frozen dinners and frozen pizzas are proportionally most bought on sale; cigarettes are least frequently bought on sale.
  - Cigarettes and beer: sales, when they occur, tend to be smallest; frozen dinners and pizzas: sales are largest.
  - Empirical relationships documented: strong positive correlation between frequency and size of sales across categories; categories with higher sales frequency have larger fraction of goods bought on sale.
- Regular price changes:
  - Average size of price changes: 3.5 percent.
  - Average size of absolute price changes: 12 percent.
  - Average weekly frequency of regular price changes: 5 percent.
  - Average duration between regular price changes: approximately 5 months.
  - Observed asymmetry: increases in regular prices are more frequent than price decreases.
  - Category relationships: categories with more frequent regular price changes tend to have smaller price changes; little link between frequencies of sales and regular price changes across categories; positive relationship between average size of sales and average change in regular prices across categories; weak positive relationship between frequency of sales and average size of regular price changes across categories.
- Sampling frequency note:
  - Weekly sampling can yield higher estimated frequency of price changes than monthly sampling (Kehoe and Midrigan (2010)).

### V. Theoretical mechanism and model implications
- Mechanism summary:
  - Consumers switch across stores in response to economic conditions because of price dispersion across stores.
  - Shopping effort reduces iceberg costs of buying at discount retailers; when return to shopping effort is diminishing, shopping effort is countercyclical (higher when employment is low), lowering effective prices at discount retailers and inducing expenditure reallocation.
- Testable model predictions (three predictions):
  1. Effective prices are high relative to posted prices when the level of economic activity is high.
  2. High-price retailers of otherwise identical goods account for a larger share of total retail revenues when the level of economic activity is high.
  3. The unconditional Phillips curve relationship between inflation and economic activity is steeper when measured in terms of effective rather than posted prices.
- Monetary policy and dynamics:
  - In response to monetary policy shocks, nearly 50 percent of the total adjustment in the price of the final consumption good paid by households occurs in the first quarter, while only this ratio is less than 20 percent for underlying posted prices.
  - Consequence: contemporaneous effect of monetary policy shocks on output is smaller (less monetary non-neutrality) than one would expect from the frequency of posted price changes, but the impact effect is relatively small and persistence of output-gap response is not qualitatively affected.
  - Net result: dynamics of model responses remain dominated by underlying level of price-stickiness in posted prices; response of output to monetary policy shocks resembles that of a New Keynesian model with high price stickiness.

### VI. Business cycle, measurement, and policy implications
- Business cycle and labor supply:
  - Shopping effort and store-switching alter the effective Frisch labor supply elasticity and the effective elasticity of the output gap with respect to real interest rates when expressed in terms of input prices rather than final consumption good prices.
  - Interaction: when utility return to labor is high, return to shopping effort must be high (identical marginal disutilities), implying low shopping intensity under diminishing returns; lower shopping time reduces marginal disutility of labor so households supply more labor.
  - Countercyclical shopping effort mitigates expected inflation declines via increased expected shopping effort when real rates rise, thereby partially offsetting initial output declines.
- Inflation measurement and biases:
  - Store-substitution can bias measured inflation (Boskin Commission (1996); Shapiro and Wilcox (1996)).
  - Prior work focuses on entry of new low-price outlets and gradual inclusion in CPI; this paper emphasizes expenditure reallocation across retailers and time-varying shopping effort as additional sources of measurement differences.
  - Effective price index using time-varying expenditure weights across retailers generally tracks final consumption price index despite not directly including household costs from shopping effort.
  - Store-switching leads to cyclical mismeasurement of inflation in both data and model; substitution across similar goods within stores also varies with the business cycle, producing cyclical “substitution bias.”
  - Policy implication: statistical agencies would be better served by tracking actual prices paid by consumers (effective prices) rather than prices charged by retail outlets to more precisely measure cost-of-living (Triplett (2003)).
- Monetary policy targeting:
  - Welfare conclusions vary by regime:
    - Inflation-targeting central bank: generally better to respond to posted price inflation rather than measures of effective price inflation.
    - Price-level targeting regimes: significantly higher welfare can be obtained by targeting deviations of effective prices from a target level rather than traditional posted price gaps.
  - Suggestion: devoting more resources to constructing aggregate measures of effective prices paid by households could improve policy rules and economic stability/welfare.

*Source: _wp12207 - References (content unit provided).*

### 3.1 The Cyclicality of Posted and Effective Prices

### 3.1 The Cyclicality of Posted and Effective Prices

### Measurement of posted and effective prices
- Effective price for good j in category c across stores in geographic area m is the quantity-weighted average price (equation (3.1)), which can change because individual prices change or because consumers reallocate consumption across stores.
- Monthly effective inflation for each good j in category c and market m is computed as log( P_eff_{j,c,m,t} / P_eff_{j,c,m,t-1} ).
- Category-level effective inflation rates are aggregated across goods j using UPC weights ω_{j,c,m} with alternative weighting schemes: equal weights, city-specific weights, and common weights across UPCs within each product category. These weights are fixed within each calendar year, so the effective-price inflation measure does not include substitution across goods within the year.
- Monthly inflation rates are cumulated into the annual “across-store effective inflation rate” π_eff_{c,m}.
- Posted inflation measures π_post_{c,m} are constructed analogously using posted prices from (2.1), except retailer weighting uses fixed-expenditure weights updated at the annual frequency rather than time-varying expenditure weights.

### Baseline empirical specification and inference
- Baseline specification (3.2): Y_{c,m,t} = β * u_{m,t} + γ_t + α_{c,m} + ε_{c,m,t}, where:
  - m indexes markets, c indexes categories, t indexes calendar time (month);
  - Y_{c,m,t} is the variable of interest (e.g., effective inflation rate);
  - u_{m,t} is the local seasonally-adjusted unemployment rate;
  - α_{c,m} denotes market-category fixed effects;
  - γ_t denotes time fixed effects.
- Estimation is monthly because metropolitan unemployment is available monthly.
- Standard errors constructed using Driscoll and Kraay (1998) to account for serial and cross-sectional correlation; these standard errors tend to be conservative. Appendix Table 3 presents alternative standard-error estimates.
- Time fixed effects help control for aggregate shocks that could otherwise confound correlation between local unemployment and prices.

### Main empirical findings: posted versus effective prices
- Posted price inflation shows little cyclical sensitivity to local unemployment when including city-category and time fixed effects: coefficients on unemployment are mostly negative but statistically indistinguishable from zero.
- Effective prices (prices actually paid by households) show significant pro-cyclicality: the inflation rate of prices paid by consumers falls when local economic conditions worsen.
- Magnitude of the difference: "a 2 percent point increase in the local unemployment rate lowers the effective price inflation rate by 0.5 percent at an annual rate below the inflation rate of posted prices."
- Appendix Table 4 corroborates the main finding at the category level:
  - Point estimates of the effect of unemployment on effective price inflation are stronger than those on posted price inflation for 25 out of 31 categories.
  - For posted prices, point estimates of local unemployment on posted inflation rates are insignificantly different from zero for 19 out of 31 categories.

### The cyclicality of sales and regular price changes (summary of section 3.2)
- Specification (3.2) is re-estimated with dependent variables capturing:
  - frequency of sales,
  - size of sales,
  - share of monthly expenditures on sale,
  - frequency and size of regular (non-sale) price changes.
- Simple pooled estimates (no fixed effects) indicate higher local unemployment is associated with more frequent sales and larger share of goods on sale.
- Introducing geographic/category fixed effects removes much of the positive effect of unemployment on sales (addresses cross-sectional heterogeneity).
- Preferred specification includes city-category fixed effects and time fixed effects. In this specification:
  - Higher unemployment rates are associated with significantly less frequent sales and smaller sales (note: sales sizes are measured as negative values, so a positive coefficient indicates smaller discounts).
  - The share of goods bought on sale declines as unemployment rises.
  - Regular price changes are close to acyclical:
    - Slightly reduced frequency of regular price changes is observed in some specifications, with marginal significance for price increases.
    - When using expenditure-weighted category averages (city-specific or common weights), cyclical changes in the frequency of regular price changes are no longer significantly different from zero.
    - Little evidence that the size of regular price changes varies with local economic conditions regardless of aggregation method.
- Robust result: the frequency and average size of sales, and the share of goods bought on sale, are robustly lower when local unemployment rates are higher.
- Appendix Table 4 disaggregated results: for 22 out of 31 categories, higher unemployment is associated with less frequent sales; these effects are statistically significant for 15 categories. Only two categories (diapers and tooth-brushes) show reversed statistically significant effects.

### Mechanism: store-switching and theoretical interpretation
- Reconciliation of facts:
  - Effective prices fall when local conditions worsen while posted regular prices are acyclical and sales are less frequent/smaller.
  - Proposed mechanism: when local conditions worsen, price-sensitive consumers reallocate expenditures toward low-price retailers, lowering quantity-weighted effective prices even if posted prices do not decline and sales are less prevalent.
- Intuition and multiplier:
  - More price-sensitive consumers buying from low-price (EDLP) retailers reduces the incentive for high-price (HiLo) retailers to run sales, leading to fewer and smaller sales.
  - Reduced sales at HiLo stores further induces additional store-switching by price-sensitive consumers, creating a reinforcing multiplier between store-switching and sales reduction.
- Simple model (Appendix B, based on Lal and Rao (1997)):
  - Two retailers: EDLP (no sales) and HiLo (intermittent sales); unique Nash equilibrium yields market segmentation.
  - Two consumer types: "bargain hunters" (low transportation costs, observe all prices, buy from the lowest-cost retailer each period) and "loyal" consumers (higher transportation costs, do not observe current prices and purchase based on expected lowest net price).
  - An increase in the share of bargain hunters (interpreted as akin to increases in local unemployment) shifts more purchases to EDLP, reducing HiLo's incentive to offer large sales and increasing HiLo's relative price.
  - The model illustrates how variation in local economic conditions and household store-switching can generate the observed pro-cyclicality of sales.

### Policy and macroeconomic implications
- Effective price flexibility due to household reallocation across retailers is substantial relative to posted-price changes.
- This flexibility arises from store-switching rather than counter-cyclical sales, raising questions about implications for monetary non-neutrality:
  - Chevalier and Kashyap (2011) suggest effective price flexibility from sales could undo monetary non-neutralities associated with rigid posted prices.
  - The authors emphasize the need to quantify how much effective price flexibility from store-switching affects the degree of monetary non-neutrality and other business-cycle and policy implications.
- The paper builds a model (introduced in the next section) to quantify these effects and further assess implications for macroeconomic dynamics.

*Source: 3.1 The Cyclicality of Posted and Effective Prices (extracted content).*

### section 6 with shopping effort and store-switching on the part of households which allows us

### IV. HOUSEHOLD STORE-SWITCHING

### Cross-sectional variation in the sensitivity of pricing to business conditions
- Method to rank stores:
  - For each UPC-level good j in category c and market m, stores s in period t are ranked by price; rank R = 1 for lowest price, R = 2 for second lowest, etc.
  - Rank normalized by (number of stores selling the good + 1) so resulting rank R_sjm(t) ∈ (0,1).
  - Average rank for a store across UPC set Ω: R̄_smt, where Ω defined as:
    - Ω_all: UPCs sold in every store in a market (Ω_₪).
    - Ω_90: UPCs sold in 90 percent of stores (Ω_90).
    - Ω_75: UPCs sold in 75 percent of stores (Ω_75).
  - Store-level average rank normalized by city size to produce comparable store rank R̃_smt ∈ (0,1).
  - Store price ranking persistence: autocorrelation parameter = 0.90 at the annual frequency.
- Empirical specification (store-level) relates store price moments to unemployment and store rank (equation (4.1)).
- Main empirical findings:
  - More expensive stores (higher rank) exhibit much more pronounced declines in the frequency of sales when unemployment rises.
  - Share of goods bought on sale declines significantly in more expensive stores as unemployment increases.
  - The size of sales in expensive and cheap stores have similar reactions to unemployment.
  - Revenue growth declines more strongly in expensive stores when unemployment increases; the least expensive stores may experience an increase in revenue growth when unemployment increases.
  - Results are consistent across all definitions of Ω and alternative store ranking measures.

### Households’ choices of shopping outlets as a function of business conditions
- Data:
  - IRI Symphony household panel tracks between 5,000 and 10,000 households in Eau Claire, WI and Pittsfield, MA from 2001 to 2007.
  - About 2,000 households are continuously present between 2001 and 2007.
  - Expenditures on each UPC product and purchase location are tracked.
- Household-specific average shopping-rank measure:
  - R̃_hmt = Σ_w_hsmt · R̃_smt, where w_hsmt is household h’s expenditure share at store s in market m and month t (equation (4.2)).
  - Low (high) R̃_hmt means household shopped at low-price (high-price) stores in month t.
- Empirical specification across households (equation (4.3)) assesses response of R̃_hmt to local unemployment.
- Main empirical findings:
  - Coefficient on unemployment is negative and statistically significantly different from zero at standard levels across specifications and Ω choices.
  - Magnitude: a 1 percent point increase in the local unemployment rate is associated with a decrease in the average rank at which households shop of between 0.05 and 0.13 depending on measures used.
- Household heterogeneity by income:
  - Specification (4.4) interacts unemployment with income-quintile dummies to assess differential store-switching by income.
  - Income quintile ranges in the IRI sample:
    - 1st quintile ranges from $5000 to $22,500
    - 2nd quintile ranges from $22,600 to $31,600
    - 3rd quintile ranges from $31,700 to $50,000
    - 4th quintile ranges from $50,100 to $70,000
    - 5th quintile ranges from $70,100 to $120,000
  - Results (Table 5):
    - Strongest store switching observed for households in the second and third income quintiles (annual income between $22,600 and $50,000).
    - Interpretation: low-income households already shop in less expensive stores most of the time; high-income households consistently shop in most expensive stores; middle-income households (quintiles 2–3) drive most cyclical switching behavior.

### Cross-good substitution
- Construction of quantity-weighted “effective” price within category c, store s, market m:
  - P̃_scm = Σ_j p_jsm · q̄_j / Σ_j q̄_j (equation (5.1)), where q̄_j is the quantity equivalent of good j, making items comparable (e.g., 6-pack vs 12-pack).
  - Monthly inflation computed as log(P̃_scm,t / P̃_scm,t−1); aggregated across stores using equal or expenditure weights; cumulated to annual inflation Π̃_cm ("within-category effective inflation rate").
- Two classification schemes for substitution within categories:
  - Broad: all UPCs within a category.
  - Narrower: substitution allowed only within subcategories (adds a digit of disaggregation; e.g., whole milk vs 2 percent milk).
  - Subcategory inflation aggregated to category level using equal or expenditure weights.
- Empirical specification (5.2) regresses category-level within-category effective inflation rates on local unemployment.
- Main findings (Table 6):
  - Statistically significantly negative relationship between unemployment rates and cross-good inflation rates.
  - Effect stronger when allowing a larger set of goods within each category.
  - Quantitative magnitudes are of the same order as across-store substitution results.
- Note: categories excluded from this cross-good analysis because quantity equivalents unavailable or not comparable: deodorant; frozen dinner; photo; soup.

### Aggregate implications of store-switching
- Key message:
  - Significant flexibility in prices paid by households relative to retailers is driven primarily by store-switching by households rather than by retailer sales.
- Modeling approach:
  - A stylized New Keynesian model is presented in which households can reallocate expenditures across stores as economic conditions change.
  - The model delivers testable predictions that are confirmed in the data.
- Macro and policy implications discussed:
  - Store-switching is an important margin of adjustment over the business cycle and affects the cyclicality of retailer pricing decisions (especially for high-price stores).
  - Measured inflation dynamics and policy-relevant aggregates depend importantly on household reallocation across retailers and across goods.

*Source: _wp12207 - section 6 with shopping effort and store-switching on the part of households which allows us*

### 6.1 New Keynesian Model with Expenditure Reallocation across Retailers

### 6.1 New Keynesian Model with Expenditure Reallocation across Retailers

### Model overview and mechanism
- Incorporates a household decision over how much to purchase from different retailers into a standard New Keynesian framework (Clarida, Gali and Gertler (1999); Woodford (2003)).
- Retailers sell identical composite goods but at potentially different posted prices; the “local” retailer posts a higher price while purchases at the “discount” retailer come with an iceberg cost ߬௧ that can be reduced by household shopping effort ܵ௧.
- Households face a trade-off: reduce effective consumption prices by increasing time-intensive shopping effort ܵ௧ at the expense of leisure ܮ௧.
- Intermediate goods are produced under monopolistic competition with Calvo-style price stickiness; sales are abstracted from in the model (but noted would strengthen expenditure reallocation).
- Key theoretical implication: time-varying shopping effort and iceberg costs generate reallocation of expenditures across retailers and cause the “price of the final consumption good” to differ from standard price indexes because it includes shopping-time costs and expenditure-share reallocation (see equations (6.1)–(6.6)).

### Household problem and optimality conditions
- Lifetime utility maximization summarized by equation (6.1) with consumption bundle ܥ௧, labor supply ܮ௧, shopping effort ܵ௧, and discount factor ߚ.
- Consumption aggregator across retailers given by equation (6.2) where ߛ measures elasticity of substitution across stores.
- Budget constraint in retailer-specific form and in terms of the final consumption good (equations (6.3) and (6.6)).
- Iceberg cost ߬௧ is a function of shopping effort ܵ௧, normalized so that ߬(ܵ௧) has constant elasticity ߶: [ܵ௧/߬௧]ݍ = ߶ (text states a constant-elasticity assumption; see surrounding discussion).
- First-order conditions (log-linearized deviations denoted by “checks”):
  - Consumption Euler condition: equation (6.7).
  - Bonds condition: equation (6.8).
  - Labor optimality: equation (6.9) (labor condition includes shopping effort ܵ௧).
  - Shopping effort optimality: equation (6.10) — LHS is marginal disutility of shopping effort; RHS is marginal benefit via reduced expenditures at the discount retailer. Parameter ߱ௌ denotes steady-state elasticity of the utility flow with respect to shopping and requires ߱ௌ൏0 for an interior steady state.
- Equilibrium implications:
  - Marginal disutilities of labor and shopping are equalized (equation (6.11)), so hours spent shopping and hours worked are linked.
  - Relationship between labor and shopping time summarized in equation (6.12); diminishing marginal returns to shopping (߱ௌ൏0) produces countercyclicality of shopping intensity with respect to hours (ߝௌ൏0).
  - Shopping effort being countercyclical increases the effective Frisch labor supply elasticity (equation (6.13)).

### Firms and price-setting
- Retailer j assembles intermediate goods (continuum of varieties) into consumption goods using standard CES aggregators; elasticity across varieties is ߪ.
- Intermediate goods produced by monopolistic competitors with production function ݕ௧(݅) = ܼ௧ ܰ௧(݅)^{ߙ}, ߙ in (0,1).
- Technology follows a stationary AR(1) in logs with i.i.d. innovations ߳௧௭ and persistence ߩ௭.
- Calvo pricing: firms reset prices with probability (1-ߠ) each period; evolution of input-price aggregate leads to a New Keynesian Phillips Curve in input prices (equation (6.14)).

### Monetary policy rule
- Interest-rate rule after log-linearization: equation (6.15).
- Rule responds to inflation, output growth, and the output gap, with an i.i.d. monetary policy shock ߳௧௥.
- Long-run and smoothing parameters enter as ߯గ (inflation), ߯∆௬ (output growth), ߯௫ (output gap), and ߩ௥ (interest-smoothing).

### Parameterization and calibration (explicit values)
- Discount factor: ߚ ൌ 0.99.
- Calvo price-stickiness parameter: ߠ ൌ 0.70 (firms update prices every 10 months on average, consistent with Nakamura and Steinsson (2008)).
- Production and preference parameters:
  - ߙ ൌ 0.66.
  - Elasticity across intermediate varieties: ߪ ൌ 10.
- Monetary policy coefficients (following Coibion and Gorodnichenko (2011)):
  - Long-run response to inflation ߯గ ൌ 1.5.
  - Long-run response to output growth ߯∆௬ ൌ 0.5.
  - Long-run response to the output gap ߯௫ ൌ 0.1.
  - Interest-smoothing ߩ௥ ൌ 0.9.
- Technology process:
  - Persistence of technology shocks ߩ௭ ൌ 0.95.
  - Standard deviation of technology shocks ൌ 0.0090.
  - Standard deviation of monetary policy shocks ൌ 0.0024.
- Store-switching and shopping-effort parameters:
  - Normalize steady-state iceberg cost such that ߬ҧܵ(߬ҧ/ߤ) ൌ 1 so steady-state consumption shares across “local” and “discount” stores are equalized.
  - Relative posted price parameter ߤ ൌ 1.5 (implying “discount” stores in the model are 33 percent cheaper on average).
  - Elasticity of substitution across stores: ߛ ൌ 4 (noted as less than half the within-store elasticity ߪ).
  - Elasticity of iceberg costs with respect to shopping effort: ߶ ൌ 0.3 (baseline; discussed relative to empirical evidence).
- Steady-state implied statistics and time-use:
  - Baseline parameters imply a steady-state labor-leisure ratio of 0.4.
  - American Time Use Survey averages: worked 3.7 hours/day, leisure 5.7 hours/day, sleep 8.6 hours/day — implying labor-leisure ratios of 0.65 (not counting sleep as leisure) or 0.26 (counting sleep as leisure).

### Empirical calibration check for store-switching
- Empirical estimate from Table 4: a 1 percentage point increase in the unemployment rate is associated with a decrease in the average rank at which households shop of approximately 0.13 with a standard error of almost 0.04.
- Using Okun’s Law (1 percentage point increase in unemployment ≈ 2 percent decline in output gap) yields a semi-elasticity of the average shopping rank with respect to the output gap of approximately 0.065 with a 95 percent confidence interval of [0.028 0.102].
- Model implication: with two retailers and baseline parameters (ߛ ൌ 4, ߶ ൌ 0.3, ߬ҧ/ߤ ൌ 1), the steady-state semi-elasticity of the average price rank at which households shop with respect to the output gap is approximately 0.082 — close to the empirical estimate and within the confidence interval.
- Interpretation: baseline values for ߛ and ߶ produce expenditure reallocation rates across retailers consistent with observed household behavior.

### Simplified log-linearized representation and key implications
- Under the convenient normalization ߬ҧ/ߤ ൌ 1, the model reduces to the familiar three-equation New Keynesian system.
- Phillips Curve in terms of the output gap: equation (6.16).
- Euler equation for the output gap (log-linearized): equation (6.17), with parameter ߞ reflecting the effect of shopping effort on the intertemporal substitution channel; ൏0ߞ whenever shopping effort is countercyclical with respect to hours (ߝௌ൏0).
- Key mechanism in the Euler equation:
  - Larger elasticities of iceberg costs with respect to shopping effort (more negative ߶) decrease the contemporaneous sensitivity of the output gap to real interest rates (i.e., reduce ߞ), because anticipated changes in shopping intensity partially offset expected changes in consumption prices.
  - Shopping effort countercyclicality thus weakens the transmission of real interest-rate changes to contemporaneous output gaps.

*Source: _wp12207 - 6.1 New Keynesian Model with Expenditure Reallocation across Retailers*

### 6.2 Testable Predictions of the New Keynesian Model with Store-Switching

### 6.2 Testable Predictions of the New Keynesian Model with Store-Switching

### Store-switching mechanism and effective prices
- Low economic activity is associated with more shopping effort and therefore lower relative consumption prices, summarized by equation (6.18) in the source text.
- The model’s CPI-equivalent variable ܲρυ௧ corresponds, when log-linearized, to the CPI price index in the data; the model’s unobservable final consumption price ܲρυ௧஼ incorporates iceberg costs and reallocation across retailers.
- An alternative, observable effective price index ܲρυ௧ா that incorporates reallocation across stores is constructed and, after log-linearization, evolves according to equation (6.19).
- Given the model calibration, (ఓିଵ)(ఓାଵ)ߛ = 0.8, so ܲρυ௧ா captures 80 percent of the movements in the final consumption price index ܲρυ௧஼ despite iceberg costs being unobservable.
- Implication: the effective price measure ܲρυ௧ா (prices consumers actually pay) closely tracks the model’s final consumption price index ܲρυ௧஼ in the calibration.

### Empirical assessment: prices and mismeasurement
- Construction of empirical indices:
  - Average effective price level: average price paid by households for a given UPC in a metropolitan area, aggregated across UPCs and areas using constant expenditure weights (reflects price changes and consumer reallocation).
  - Posted price index: fixed expenditure-weights over individual UPC products and geographic areas.
- Empirical finding (Panel A, Figure 2): the difference between the average effective price index and the posted price index declines sharply relative to the posted-price index when the U.S. unemployment rate rises, and reverses when unemployment falls — consistent with the model’s prediction that consumer reallocation leads to non-trivial mis-measurement of household consumption prices by fixed-weight indexes.
- Quantitative magnitudes:
  - Model-implied elasticity of the difference (effective minus posted prices) ܲ(ρυ௧ா ܲρε௧) with respect to the output gap is approximately 0.15.
  - Between 2001 and 2003, the U.S. unemployment rate rose by approximately 2 percentage points, which via Okun’s Law translates to an approximate 4 percentage point decline in the output gap.
  - The theory predicts such a decline in the gap would be associated with a decline in the effective price index of 0.60 percentage points relative to the posted price index; the figure shows a decline very close to this value.
- Interpretation: both qualitative and quantitative implications of the store-switching channel align with the data.

### Empirical assessment: quantities and revenue shares
- Model prediction for relative quantities: relative quantities purchased at “local” versus “discount” retailers follow equation (6.20), implying households purchase relatively more goods from low-price stores when the output gap is low.
- Revenue-share prediction: defining the share of total revenues going to “local” retailers as specified, the cyclicality of the revenue share of high-price retailers is given by equation (6.21).
- Empirical finding (Panel B, Figure 2): the revenue share of “high-price” retailers (defined as rank above 0.5 per section 4.1) declined sharply during the 2001-2003 recession and then gradually recovered — consistent with model predictions of reallocation toward low-price outlets in downturns.
- Caveat: the revenue share of “high-price” retailers never fully recovers after 2001-2003, reflecting trend growth of discount retail stores in the U.S. over that period.

### Empirical assessment: Phillips curve slope and inflation measures
- Rewriting the NKPC in terms of consumption price inflation yields equation (6.22): consumption price inflation depends on expected next-quarter inflation, the current output gap, the previous period’s gap, and next-quarter expected gap.
- Shopping effort increases the coefficient on the contemporaneous output gap, implying a steeper short-run Phillips curve between effective consumption price inflation and real activity than when using input/CPI prices.
- Simulation and aggregation results:
  - Model simulation with time-varying shopping effort shows unconditional relationship between CPI inflation ߨ௧ and employment versus effective price inflation ߨ௧ா and employment (Panel A, Figure 3); slope is steeper with effective consumption prices.
  - Aggregated monthly micro-data (Panel B, Figure 3) plots posted price inflation ߨ௧posted and effective price inflation ߨ௧effective (weighted by expenditure shares across metropolitan areas and categories). Both inflation measures are lower at higher aggregate unemployment, but the decline is larger for effective price inflation; the difference between the two is statistically significant at the 1 percent level.
- Conclusion: store-switching and countercyclical shopping effort generate countercyclical effective prices, reallocation of expenditures toward low-price outlets during downturns, and steeper Phillips curves in terms of effective prices.

### Implications for measurement and policy
- Measurement implication: cyclical mismeasurement of the cost-of-living by fixed-expenditure-weight price indexes due to store-switching is relatively large; therefore, better measurement should focus on tracking prices paid by households rather than prices charged by specific retailers (as suggested in Triplett (2003)).
- Policy implication (previewed in 6.3): store-switching and shopping effort affect business-cycle dynamics and monetary policy effectiveness; these are examined in the subsequent section.

*Source: 6.2 Testable Predictions of the New Keynesian Model with Store-Switching, _wp12207*

### Appendix Figure 1 illustrates how the size of the contemporaneous response and the average response of the

### _wp12207 - Appendix Figure 1 illustrates how the size of the contemporaneous response and the average response of the

### Welfare objective function with endogenous shopping effort and store-switching
- Appendix Figure 1 shows that the size of the contemporaneous response and the average response of the output gap to monetary policy shocks increase in the elasticity of substitution across retailers and the elasticity of iceberg costs to shopping effort.
- Standard 2nd order approximations of utility (Woodford (2003)) deliver a loss function in terms of inflation and output gap volatility, but with shopping effort household welfare depends on effective prices rather than posted prices.
- The paper derives the 2nd order approximation to utility and expresses it in terms of posted inflation volatility and output gap volatility (Appendix C):  
  ܧ (ܷ௧) ൎെ ଵ ଶ ቀ ఙିଵ ఙఓ ܿቁ൛ గ ሺ ߶ ሻ ܧ ሺ ߨ ௧ ଶ ሻ ܿ൅ ௫ ሺ ߶ ሻ ܺ൫ܧ ั ௧ ଶ ൯ൟ, (6.23) ܿ గ ሺ ߶ ሻ ؠ ఙ Θ ఏ ሺ ଵିఏ ሻ మ ቀ ఠ ೄ ఌ ೄ ቁ, ܿ ௫ ሺ ߶ ሻ ؠ ଵ ఈ ൅ቀ ఙିଵ ఙఓ ቁ ് ర థ మ ି ഝ మ ାఠ ೄ మ ఌ ೄ మ .
- Panel C of Figure 4: coefficients on inflation and output gap volatility vary with the elasticity of costs to shopping time ߶.
  - Higher ߶ systematically lower the coefficient on inflation volatility, i.e., డ௖ ఏ డథ ൏0.
  - Interpretation: without shopping effort, high price dispersion requires high labor supply and less leisure, reducing welfare; with countercyclical shopping effort, higher labor supply associated with price dispersion is offset by fewer hours spent shopping, reducing sensitivity of leisure to inflation volatility.
  - The coefficient on output gap volatility reflects losses from volatility in leisure depending on variance in labor supply, shopping effort, covariance between the two, and changes in consumption dispersion across retailers.
  - Interaction of effects is nonlinear: low elasticities of shopping reduce cost of a given level of output gap volatility, but effect reverses at high elasticities.
  - Net implication: welfare becomes relatively more sensitive to output gap volatility relative to inflation volatility as steady-state shopping effort increases.
- Policy implication: presence of store-switching and shopping effort implies stabilizing output gap volatility should play a more prominent role in policymakers' objective functions than standard models omitting this channel suggest.
- Empirical caution: similarity of impulse responses does not justify ignoring endogenous variations in shopping effort; interpretation of estimated relationships in terms of structural parameters depends on whether consumers can re-allocate spending across stores. Ignoring store switching can lead to erroneous structural interpretations (e.g., reduced sensitivity of output gap to posted-price inflation misinterpreted as low inter-temporal elasticity of substitution).

### What price measure should policymakers target?
- Household welfare is associated with the price of the final consumption good ܲ௧஼, which are effectively more flexible than posted prices ܲ௧; this raises the question whether policymakers should respond to posted-price inflation ߨ௧, final good price inflation ߨ௧஼, or expenditure-weighted final goods inflation ߨ௧ா.
- The paper quantifies household welfare (6.23) when the central bank responds to:
  - posted price inflation ߨ௧ (baseline),
  - final good price inflation ߨ௧஼,
  - expenditure-weighted final goods inflation ߨ௧ா,
  holding other model parameters constant.
- Panel A of Figure 5 (inflation and output gap variances plotted for different long-run inflation response coefficients ߶ గ):
  - Responding to posted price inflation ߨ௧ leads to lower posted price inflation volatility but higher output gap volatility, particularly when the inflation response is high.
  - Because inflation volatility is more heavily weighted in the loss function, utility is higher in most cases when the central bank targets posted price inflation rather than final goods price inflation or expenditure-weighted inflation.
  - Result: even with store-switching and time-varying shopping effort, policymakers may be better served by responding to traditional measures of inflation than measures of effective price inflation under inflation-targeting regimes.
- Under price-level targeting (PLT) regimes:
  - Replace baseline interest rate rule with one that allows responses to deviations of price-levels from targets (equation (6.24)):  
    ݅௧ߩൌ௥݅௧ିଵ ൅ ሺߩ1െ௥ሻ߯ൣ௣ܲృ௧௠߯൅௫ܺృ௧߯൅∆௬ܻ∆ ŕ௧߳൧൅௧௥ (6.24)  
    where ܲృ௧௠ denotes deviation of posted prices ܲృ௧, final goods prices ܲృ௧஼, or expenditure-weighted prices ܲృ௧ா from a target path.
  - Panel B of Figure 5 plots implied inflation and output volatilities for different response coefficient ߯௣ to each price level, and expected utility losses for different ߯௣.
  - Under PLT, both inflation and output gap volatility are significantly reduced when the central bank targets the effective or final consumption price level rather than posted price levels.
    - Reason: effective prices (ܲృ௧஼ and ܲృ௧ா) respond much more immediately to shocks than posted prices ܲృ௧; targeting their levels forces policy to reverse immediate declines in effective prices after disinflationary shocks, requiring significant declines in nominal and real interest rates which raise contemporaneous output gaps via the dynamic IS curve and offset initial disinflation via the New Keynesian Phillips Curve.
  - Consequently, expected utility is strictly greater when the central bank targets deviations of effective final goods price levels rather than posted price levels under PLT.
- Conclusion on targeting:
  - Under inflation-targeting, targeting posted price inflation often yields higher utility.
  - Under price-level targeting, targeting effective/final goods price levels yields higher expected utility.

### Conclusion — empirical and policy takeaways
- Empirical findings:
  - Sales are pro-cyclical: higher unemployment leads to declines in frequency and absolute size of sales and declines in the share of goods bought on sale, implying sales differ fundamentally from regular price changes and are unlikely to undo high price-stickiness of regular price changes.
  - Actual prices paid by households are significantly more flexible than posted prices, reflecting store-switching.
- Model insights:
  - Consumer reallocation of expenditures across retailers charging different prices provides additional price flexibility, leading to smaller real effects of monetary policy shocks.
  - Store-switching rationalizes pro-cyclicality of sales: downturns increase incentives to search for bargains at low-price retailers, reducing incentives for high-price retailers to use sales.
  - Quantitatively, store-switching implications for monetary neutrality are relatively small, aligning with Eichenbaum et al. (2011), Kehoe and Midrigan (2010), Guimaraes and Sheedy (2011) though focusing on store-switching rather than sales for effective price flexibility.
- Welfare and policy implications:
  - Store-switching affects the relative importance of stabilizing output gap versus inflation variation in welfare calculations, the choice of price measures policymakers should target, and interpretation of estimated relationships in structural parameters.
  - There is cyclical mismeasurement of the price of households’ final consumption basket in standard aggregate inflation measures due to expenditure reallocation across retailers.
- Statistical and measurement implications:
  - Statistical agencies should devote more resources to measuring reallocation of household expenditures across retailers (not just across goods).
  - Constructing time-varying expenditure weights in real-time may be infeasible; tracking prices actually paid by households in real-time (e.g., via scanner price data) is a promising approach though challenges remain.
  - Ideal price index should measure both reallocation of expenditures across stores and shopping effort intensity, since shopping effort is a component of consumption cost; a measure incorporating expenditure reallocation across retailers will generally capture most missing cyclical variation in the final consumption price index.
- Additional considerations and extensions:
  - Rise of online retailing likely reduces shopping costs and facilitates expenditure reallocation across retailers, making this channel increasingly important.
  - Potential explanation for the missing disinflation in 2007-2009: nonlinear Phillips curve slope (flatter at low activity/inflation) could arise from downward wage rigidity or cyclical changes in price rigidities due to store-switching becoming more rigid in downturns, causing over-prediction of disinflation when using regular-time Phillips curve estimates.

*Source: _wp12207 - Appendix Figure 1 illustrates how the size of the contemporaneous response and the average response of the (PDF chapter/section).*

### REFERENCES

### _wp12207 - REFERENCES

### Key References
- Aguiar, Mark and Erik Hurst, 2005. “Consumption versus Expenditure,” Journal of Political Economy, 113(5), 919-948.
- Anderson, Eric, Emi Nakamura, Duncan Simester, and Jón Steinsson, 2012. “Decomposing Variation in Retail Prices,” manuscript.
- Aoki, Kosuke, 2001. “Optimal Monetary Policy Responses to Relative Price Changes,” Journal of Monetary Economics 48(1), 55-80.
- Ball, Lawrence and Sandeep Mazumder, 2011. “Inflation Dynamics and the Great Recession,” Brookings Papers on Economic Activity (Spring), 337-381.
- Bils, Mark, and Peter J. Klenow, 2004. “Some Evidence on the Importance of Sticky Prices,” Journal of Political Economy 112(5), 947-985.
- Boskin, Michael J., E. Dulberger, R. Gordon, Z. Griliches, and D. Jorgenson, 1996. “Toward a More Accurate Measure of the Cost of Living,” Final Report to the Senate Finance Committee, Dec. 4.
- Bronnenberg, Bart J., Michael W. Kruger, and Carl F. Mela, 2008. “Database Paper: The IRI Marketing Data Set,” Marketing Science 27(4), 745-748.
- Calvo, Guillermo, A. 1983. “Staggered Prices in a Utility-Maximizing Framework,” Journal of Monetary Economics 12(3), 383-398.
- Carlton, Dennis W., 1986. “The Rigidity of Prices,” American Economic Review 76(4), 637-658.
- Cecchetti, Stephen G., 1986. “The Frequency of Price Adjustment: A Study of the Newsstand Prices of Magazines,” Journal of Econometrics 31, 255–274.
- Chevalier, Judith A., and Anil K Kashyap, 2011. “Best Prices,” NBER Working Paper 16680.
- Christiano, Lawrence, Martin Eichenbaum, and Charles Evans, 1999. “Monetary Policy Shocks: What Have We Learned, and To What End,” in J. Taylor and M. Woodford, eds., Handbook of Monetary Economics.
- Clarida, Richard, Jordi Gali, and Mark Gertler, 1999. “The Science of Monetary Policy: A New Keynesian Perspective,” Journal of Economic Literature 37, 1661-1707.
- Cleeren, Kathleen, Frank Verboven, Marnik G. Dekimpe, and Katrijn Gielens, 2010. “Intra- and Intermarket Competition among Discounters and Supermarkets,” Marketing Science 29(3) 456-473.
- Coibion, Olivier and Yuriy Gorodnichenko, 2011. “Monetary Policy, Trend Inflation, and the Great Moderation: An Alternative Interpretation,” American Economic Review 101(1), 341-70.
- Coibion, Olivier, Yuriy Gorodnichenko, and Johannes Wieland, forthcoming. “The optimal inflation rate in New Keynesian models,” Review of Economic Studies.
- Diewart, Erwin, John Greenlees and Charles Hulten, 2009. Price Index Concepts and Measurement. The University of Chicago Press.
- Driscoll, John C., and Aart C. Kraay, 1998. “Consistent Covariance Matrix Estimation With Spatially Dependent Panel Data,” Review of Economics and Statistics 80(4), 549-560.
- Eichenbaum, Martin, Nir Jaimovich, and Sergio Rebelo, 2011. “Reference Prices and Nominal Rigidities,” American Economic Review 101(1), 234-262.
- Feenstra, Robert, and Matthew Shapiro, 2003. Scanner Data and Price Indexes. University of Chicago Press.
- Gali, Jordi, and Mark Gertler, 1999. “Inflation Dynamics: A Structural Econometric Analysis,” Journal of Monetary Economics 44, 195–222.
- Gali, Jordi, 2008. Monetary Policy, Inflation and the Business Cycle. Princeton University Press.
- Glandon, Philip J., 2011. “Sales and the (Mis)Measurement of Price Level Fluctuations,” Manuscript.
- Gorodnichenko, Yuriy, and Matthew D. Shapiro, 2007. “Monetary Policy When Potential Output Is Uncertain: Understanding the Growth Gamble of the 1990s,” Journal of Monetary Economics 54, 1132-1162.
- Guimaraes, Bernardo and Kevin Sheedy, 2011. “Sales and Monetary Policy,” American Economic Review 101, 844-874.
- Hausman, Jerry and Ephraim Leibtag, 2007. “Consumer Benefits from Increased Competition in Shopping Outlets: Measuring the Effect of Wal-Mart,” Journal of Applied Econometrics 22, 1157-77.
- Kashyap, Anil, 1995. “Sticky Prices: New Evidence from Retail Catalogs,” Quarterly Journal of Economics 110, 245-274.
- Kehoe, Patrick J. and Virgiliu Midrigan, 2010. “Price Are Sticky After All,” Federal Reserve Bank of Minneapolis Research Department Staff Paper 413.
- Knotek, Edward S. II, 2007. “How Useful Is Okun’s Law?” Federal Reserve Bank of Kansas City Economic Review, Fourth Quarter, 73-103.
- Kumar, V. and Robert P. Leone, 1988. “Measuring the Effect of Retail Store Promotions on Brand and Store Substitution,” Journal of Marketing Research 25(2) 178-185.
- Lal, Rajiv, and Ram Rao, 1997. “Supermarket Competition: The Case of Every Day Low Pricing,” Marketing Science 16, 60-80.
- Nakamura, Emi, and Jón Steinsson, 2008. “Five Facts About Prices: A Reevaluation of Menu Cost Models,” Quarterly Journal of Economics 123, 1415-1464.
- Reinsdorf, M. 1993. “The effect of outlet price differentials on the U.S. Consumer Price Index” in Price Measurements and Their Uses. M. Foss, M. Manser, and A. Young (eds.). NBER Studies in Income and Wealth, Vol. 57. Chicago: University of Chicago Press.
- Rhee, Hongjai, and David R. Bell, 2002. “The Inter-Store Mobility of Supermarket Shoppers,” Journal of Retailing 78, 225-237.
- Roberts, John M., 2006. “Monetary Policy and Inflation Dynamics,” International Journal of Central Banking 2, 193–230.
- Romer, Christina, and David H. Romer, 2004. “A New Measure of Monetary Shocks: Derivation and Implications,” American Economic Review 94, 1055-1084.
- Shapiro, Matthew D., and David W. Wilcox, 1996. “Mismeasurement in the Consumer Price Index: An Evaluation,” in NBER Macroeconomics Annual 1996, eds. Ben S. Bernanke and Julio J. Rotemberg, MIT Press, Cambridge, MA.
- Triplett, Jack E., 2003. “Using Scanner Data in Consumer Price Indexes: Some Neglected Conceptual Issues,” in Scanner Data and Price Indexes, eds. Robert C. Feenstra and Matthew D. Shapiro, University of Chicago Press.
- Walters, Rockney G., 1991. “Assessing the Impact of Retail Price Promotions on Product Substitution, Complementary Purchase, and Interstore Sales,” Journal of Marketing 55, 17-28.
- Warner, Elizabeth J., and Robert B. Barsky, 1995. “The Timing and Magnitude of Retail Store Markdowns: Evidence from Weekends and Holidays” Quarterly Journal of Economics 110(2), 321-352.
- Williams, John C., 2006, “The Phillips Curve in an Era of Well-Anchored Inflation Expectations,” Working Paper, Federal Reserve Bank of San Francisco.
- Woodford, Michael, 2003. Interest and Prices: Foundations of a Theory of Monetary Policy. Princeton University Press.

### Table 1 — Descriptive Statistics (weekly frequency, 2001 to 2007; city/category level)
- Dependent variable: Sales
  - Frequency (mean): 0.195 (equal weights to all UPCS), 0.237 (use expenditure shares as weights to aggregate UPCs, city specific), 0.237 (common)
  - Frequency (s.d.): (0.079), (0.108), (0.107)
  - Size (mean): -0.251 (equal weights), -0.249 (city specific), -0.252 (common)
  - Size (s.d.): (0.077), (0.088), (0.089)
  - Share of goods bought on sales (mean): 0.238 (equal weights), 0.319 (city specific), 0.317 (common)
  - Share of goods bought on sales (s.d.): (0.100), (0.146), (0.142)
- Dependent variable: Changes of regular prices — Frequency
  - All (mean): 0.048, 0.047, 0.048
  - All (s.d.): (0.031), (0.036), (0.038)
  - Positive (mean): 0.032, 0.031, 0.031
  - Positive (s.d.): (0.025), (0.028), (0.029)
  - Negative (mean): 0.016, 0.016, 0.017
  - Negative (s.d.): (0.012), (0.015), (0.015)
- Dependent variable: Changes of regular prices — Size
  - All (mean): 0.035, 0.034, 0.035
  - All (s.d.): (0.046), (0.043), (0.044)
  - Positive (mean): 0.120, 0.100, 0.102
  - Positive (s.d.): (0.053), (0.055), (0.057)
  - Negative (mean): -0.121, -0.089, -0.091
  - Negative (s.d.): (0.084), (0.069), (0.071)
- Notes: The table reports basic statistics about sales and regular price changes at the city/category level at the weekly frequency from 2001 to 2007.

### Table 2 — Cyclical properties of selected moments of price changes
- Estimation context:
  - Dependent variable panels: Equal weights to all UPCS; Use expenditure shares as weights to aggregate UPCs; City specific; Common
  - Estimated coefficients reported are on local seasonally-adjusted unemployment rate in specification (3.2).
  - Number of observation is 127,224.
  - Estimated specification is given by equation (1).
  - Driscoll and Kraay (1998) standard errors are in parentheses.
  - Significance notation: ***, **, * denote significance at 0.01, 0.05, and (text truncated in source).
- Selected coefficient estimates (columns labeled (1) to (5) and categories shown)
  - Sales — Frequency:
    - Column (1): 0.785*** (0.235)
    - Column (2): 0.327 (0.550)
    - Column (3): -0.365*** (0.120)
    - Column (4): -0.422*** (0.153)
    - Column (5): -0.475*** (0.141)
  - Sales — Size:
    - 0.245*** (0.086)
    - 0.321** (0.145)
    - 0.256** (0.120)
    - 0.183 (0.137)
    - 0.224* (0.128)
  - Share of goods bought on sales:
    - 1.126*** (0.237)
    - 0.512 (0.587)
    - -0.461*** (0.133)
    - -0.563*** (0.171)
    - -0.629*** (0.161)
  - Changes of regular prices — Frequency (All):
    - 0.083 (0.097)
    - -0.066 (0.222)
    - -0.100** (0.044)
    - -0.097 (0.065)
    - -0.070 (0.064)
  - Changes of regular prices — Frequency (Positive):
    - 0.015 (0.056)
    - -0.126 (0.128)
    - -0.053* (0.032)
    - -0.058 (0.040)
    - -0.050 (0.041)
  - Changes of regular prices — Frequency (Negative):
    - 0.067 (0.042)
    - 0.060 (0.097)
    - -0.047*** (0.019)
    - -0.040 (0.029)
    - -0.020 (0.028)
  - Changes of regular prices — Size (All):
    - -0.122 (0.098)
    - -0.292 (0.196)
    - -0.095 (0.062)
    - -0.008 (0.053)
    - -0.005 (0.052)
  - Changes of regular prices — Size (Positive):
    - 0.024 (0.046)
    - 0.142** (0.072)
    - -0.155* (0.092)
    - -0.020 (0.079)
    - -0.027 (0.080)
  - Changes of regular prices — Size (Negative):
    - 0.051 (0.092)
    - -0.014 (0.216)
    - -0.004 (0.129)
    - -0.026 (0.101)
    - -0.023 (0.101)
  - Inflation of posted prices:
    - -0.077*** (0.020)
    - -0.081 (0.054)
    - 0.007 (0.034)
    - -0.0273 (0.036)
    - -0.034 (0.039)
  - Inflation of effective prices:
    - -0.221*** (0.034)
    - -0.470*** (0.076)
    - -0.208*** (0.045)
    - -0.258*** (0.064)
    - -0.263*** (0.060)

*Italic: Source document _wp12207 - REFERENCES*

### 0.10 levels.

### _wp12207 - 0.10 levels.

### Cyclicality of pricing moments by store rank (Table 3)
- Specification: reports estimates of specification (4.1). Number of observation is 144,270. UR is the local seasonally-adjusted unemployment rate. Rank is the rank of the store in terms of level of prices. Expenditure shares are used to aggregate ranks across UPCs. Driscoll and Kraay (1998) standard errors in parentheses. ***, **, * denote significance at 0.01, 0.05, and 0.10 levels.
- Sales
  - Frequency: coefficients (for three UPC rank samples) reported as: -0.046; UR×rank: -1.398*** (0.177). Second sample: 0.052; UR×rank: -1.578*** (0.190). Third sample: 0.119; UR×rank: -1.709*** (0.193). Standard errors for main coefficients in parentheses: (0.155), (0.154), (0.156).
  - Size: 0.087; UR×rank: -0.181 (0.150). Second sample: 0.123; UR×rank: -0.251 (0.175). Third sample: 0.137; UR×rank: -0.277 (0.196). Std. errors for main coefficients: (0.102), (0.100), (0.099).
  - Share of goods bought on sales, ߱௠௖௧: 0.225; UR×rank: -1.677*** (0.210). Second sample: 0.332**; UR×rank: -1.874*** (0.227). Third sample: 0.412***; UR×rank: -2.030*** (0.235). Std. errors for main coefficients: (0.163), (0.168), (0.170).
  - Growth rate of revenue: 0.266; UR×rank: -0.620*** (0.089). Second sample: 0.432*; UR×rank: -0.919*** (0.086). Third sample: 0.605***; UR×rank: -1.251*** (0.111). Std. errors for main coefficients: (0.231), (0.225), (0.218).
- Changes of regular prices — Frequency (All / Positive / Negative)
  - All: 0.019; UR×rank: -0.157*** (0.052). Second sample: 0.026; UR×rank: -0.173*** (0.061). Third sample: 0.031; UR×rank: -0.183*** (0.066). Std. errors for main coefficients: (0.081), (0.084), (0.084).
  - Positive: main coefficients and interactions reported with significance: 0.010; UR×rank: -0.067** (0.035) [second column shows -0.081** and -0.087** across samples]. Std. errors for main coefficients: (0.050), (0.052), (0.052).
  - Negative: 0.009; UR×rank: -0.090*** (0.020). Second sample: 0.010; UR×rank: -0.093*** (0.023). Third sample: 0.012; UR×rank: -0.096*** (0.026). Std. errors for main coefficients: (0.037), (0.037), (0.037).
- Changes of regular prices — Size (All / Positive / Negative)
  - All: -0.121**; UR×rank: 0.034 (0.034). Second sample: -0.125**; UR×rank: 0.041 (0.036). Third sample: -0.123**; UR×rank: 0.037 (0.039). Std. errors for main coefficients: (0.055), (0.056), (0.057).
  - Positive: coefficients vary (examples shown include -0.140, -0.105***, -0.146, -0.094**, -0.139, -0.107**) with std. errors (0.091), (0.095), (0.097) for main coefficients and interaction std. errors (0.039), (0.046), (0.049).
  - Negative: 0.310***; UR×rank: -0.039 (0.056). Second sample: 0.320***; UR×rank: -0.058 (0.070). Third sample: 0.308***; UR×rank: -0.036 (0.082). Std. errors for main coefficients: (0.079), (0.084), (0.089).

### Store rank where households shop and local unemployment (Tables 4 and 5)
- Table 4 — specification (4.3). Dependent variable: average rank of stores where a household shops in a given month. Each regression has 471,615 observations. Driscoll and Kraay (1998) standard errors in parentheses. ***, **, * denote significance at 0.01, 0.05, and 0.10 levels.
  - Sample Ω௠௔௫ (Equal weights to all goods): coefficient on unemployment rate: -9.298*** (3.221).
  - Sample Ωଽ଴ (Equal weights): -9.210*** (3.006).
  - Sample Ω଻ହ: -10.585*** (3.238) when equal weights; other reported value: -4.908** (2.382) in the expenditure-weighted column.
  - Expenditure-weighted columns: Ω௠௔௫: -13.090*** (3.796); Ωଽ଴: -14.237*** (3.751); Ω଻ହ: -4.908** (2.382).
- Table 5 — specification (4.4). Dependent variable: average rank of stores where a household shops in a given month. D_g is dummy equal to one if household is in gth income quintile. Each regression has 471,615 observations. Driscoll and Kraay (1998) standard errors in parentheses.
  - For sample Ω௠௔௫:
    - Equal weights: constant: -8.961*** (3.149). Income quintile dummies: -0.671*** (0.174); -0.556** (0.240); additional coefficients reported: -0.631 (0.425); 0.025 (0.818).
    - Expenditure shares: constant: -12.735*** (3.820). Income quintile dummies: -0.744*** (0.238); -0.632** (0.314); additional coeffs: -0.516 (0.511); -0.007 (0.779).
  - For sample Ωଽ଴:
    - Equal weights: constant: -8.817*** (2.923). Income quintile dummies: -0.739*** (0.188); -0.604*** (0.250); additional coeffs: -0.688 (0.439); -0.117 (0.846).
    - Expenditure shares: constant: -13.830*** (3.725). Income quintile dummies: -0.704*** (0.218); -0.737*** (0.275); additional coeffs: -0.677 (0.437); -0.047 (0.785).
  - For sample Ω଻ହ:
    - Equal weights: constant: -10.160*** (3.160). Income quintile dummies: -0.828*** (0.194); -0.715*** (0.257); additional coeffs: -0.742* (0.392); -0.019 (0.822).
    - Expenditure shares: constant: -4.808** (2.321). Income quintile dummies: -0.430** (0.205); -0.312 (0.285); additional coeffs: -0.306 (0.343); 0.533 (0.689).

### Within-category substitution (Table 6)
- Specification: reports estimates of specification (5.2). Dependent variable: within-category effective inflation rate. Number of observations: 94,851. Driscoll and Kraay (1998) standard errors in parentheses. ***, **, * denote significance at 0.01, 0.05, and 0.10 levels.
- Results (two aggregation approaches)
  - Substitution within broad categories:
    - Equal weights for all stores: -0.454* (0.251).
    - Sales shares to aggregate stores: -0.611** (0.265).
  - Substitution within narrower categories:
    - Equal weights for all stores: -0.377* (0.211).
    - Sales shares to aggregate stores: -0.475* (0.250).

### Correlations between key moments (Figure 1)
- Figures report average (across time and goods) moments at the category level. Expenditure shares are used as weights to aggregate goods. Red line shows best fit linear projection.
- Panels illustrate relationships across product categories (list includes: beer, blades, carbbev, cigets, coffee, coldcer, deod, diapers, factiss, fzdinent, fzpizza, hhclean, hotdog, laundet, margbutr, mayo, milk, mustketc, paptowl, peanbutr, photorazors, saltsnck, shamp, soup, spagsauc, sugarsub, toitisu, toothbr, toothpa, yogurt) for:
  - Panel A: frequency of sales vs size of sales, log point.
  - Panel B: frequency of regular price changes vs absolute size of regular price changes, log points.
  - Panel C: share of goods sold on sale vs frequency of sales.
  - Panel D: frequency of sales vs frequency of regular price changes.
  - Panel E: frequency of sales vs absolute size of regular price changes, log points.
  - Panel F: (panel labels present; specific axes pairs reported above).

### Economic conditions and reallocation across retailers (Figure 2)
- Panel A: plots the difference between the “effective” price index and the “posted” price index (effective price - Average posted price) against Unemployment rate (right scale). Time series axis shows 2001–2008. Vertical scales include range .04 to .065 for price differential and unemployment rate plotted on right scale.
- Panel B: plots the share of total retailer revenues coming from high-price retailers (Share of high-price stores in total revenue) against Unemployment rate (right scale). Time series axis shows 2001–2008. Vertical scales include .4 to .55 for share; unemployment rate plotted on right scale.
- Notes: Posted price index is fixed-expenditure-weighted average of all UPC prices in each store and metropolitan area using average expenditure share weights. Effective price index is fixed-expenditure-weighted average of average price paid by households for each UPC across all retailers in a metropolitan area. “High-price” retailers defined as in text. Total share is a fixed expenditure-weighted average across metropolitan areas.

### Correlation between unemployment rate and measures of inflation (Figure 3)
- Panel A: Unconditional correlations in the model with endogenous shopping effort and store switching. Top figure plots relationship between negative employment gap and both posted (CPI) inflation and “effective” price inflation, annualized, from model simulation. Reported regression coefficients:
  - b1 = -1.56 (0.50)
  - b2 = -0.69 (0.38)
  - b1 - b2 = -0.86 (0.18)
- Panel B: Unconditional correlations in the data. Bottom figure presents relationships between the unemployment rate and the same two measures of inflation. Axes indicate inflation rate vs unemployment rate with example posted values: .045, .05, .055, .06, .065 for posted/ effective price.

### Business cycle and policy implications of endogenous shopping effort and store-switching (Figure 4)
- Panel A: Impulse responses to a contractionary monetary policy shock in model of section 6.1. Parameters: ߠ is degree of price stickiness and ߶ is elasticity of iceberg costs to shopping effort. Examples of parameter settings shown:
  - ߱ = 0.40, ϕ = 0.0
  - ߱ = 0.70, ϕ = 0.0
  - ߱ = 0.70, ϕ = -0.3
- Variables plotted include inflation, output gap, and shopping effort. Example axis ranges: inflation rate 5 10 15 20; output gap -6 to 0; shopping effort 0 to 5.
- Panel B: Substitution effects after monetary policy shock (ϕ = 0.3). Impulse responses include inflation rates for final consumption goods (ߨ஼), effective prices (ߨா), posted prices (ߨ); price levels P_C, P_E, P; and consumption measures C, C_A (consumption at high-price retailer), C_B (consumption at low-price retailer).
- Panel C: Welfare implications of endogenous shopping effort. Plots coefficients on inflation volatility (c_π) and output gap volatility (c_X) from second-order approximation to utility and ratio c_X / c_π. Axes examples include ranges 0 to 1600 for ϕ and small absolute values for coefficients.

### Which inflation measure should policymakers target? (Figure 5)
- Panel A: Inflation targeting. Top panel displays variance of inflation (left) and variance of output gap (middle) for different long-run responses to inflation by central bank when responding to posted price inflation (ߨ), effective price inflation (ߨா), or inflation of final goods prices (ߨ஼). Right panel shows expected utility loss in each case. Example axes show χ_π from 1 to 10 and Var(π) on order x 10^-6, Var(X) on order x 10^-4, Welfare Loss on order x 10^-3.
- Panel B: Price-level targeting. Bottom panel plots analogous figures when central bank responds to price levels: posted prices (P), effective prices (P_E), or final consumption goods prices (P_C). Axes examples: χ_p from 0 to 0.8; Var(π) and Var(X) scales and Welfare Loss on order x 10^-3.
- Notes: See section 6.3 for details on model setup and welfare calculations.

### Appendix material
- Appendix A: Additional tables and figures (label present: "APPENDIX A: ADDITIONAL TABLES AND FIGURES").

*Italic: Source — _wp12207 - 0.10 levels.*

### Appendix Table 1. Descriptive statistics by category.

### Appendix Table 1. Descriptive statistics by category.

### Sales share and changes of regular prices — key statistics by category
- Columns shown per category: Sales (Share of goods bought on sales, ߱௠௖௧), Changes of regular prices — Frequency (All; Positive; Negative), Changes of regular prices — Size (All; Positive; Negative).
- Note: UPCs have equal weights when aggregated to the category level.

- beer
  - Sales: 0.152; -0.122; 0.171
  - Frequency (All; Positive; Negative): 0.052; 0.034; 0.017
  - Size (All; Positive; Negative): 0.028; 0.077; -0.063
  - Standard errors (parentheses appear in source): (0.069) (0.035) (0.077) (0.032) (0.023) (0.012) (0.032) (0.030) (0.025)

- blades
  - Sales: 0.144; -0.267; 0.160
  - Frequency: 0.051; 0.036; 0.016
  - Size: 0.032; 0.119; -0.165
  - Standard errors: (0.038) (0.059) (0.042) (0.022) (0.017) (0.010) (0.044) (0.036) (0.087)

- carbonated beverages
  - Sales: 0.257; -0.239; 0.310
  - Frequency: 0.058; 0.036; 0.022
  - Size: 0.041; 0.132; -0.113
  - Standard errors: (0.055) (0.039) (0.063) (0.022) (0.015) (0.009) (0.024) (0.028) (0.030)

- cigarettes
  - Sales: 0.069; -0.122; 0.071
  - Frequency: 0.137; 0.102; 0.035
  - Size: 0.026; 0.079; -0.090
  - Standard errors: (0.046) (0.051) (0.047) (0.073) (0.069) (0.020) (0.035) (0.032) (0.039)

- coffee
  - Sales: 0.203; -0.237; 0.236
  - Frequency: 0.053; 0.035; 0.018
  - Size: 0.037; 0.126; -0.119
  - Standard errors: (0.069) (0.048) (0.076) (0.025) (0.020) (0.009) (0.037) (0.039) (0.050)

- cold cereals
  - Sales: 0.210; -0.314; 0.278
  - Frequency: 0.038; 0.027; 0.012
  - Size: 0.045; 0.112; -0.092
  - Standard errors: (0.066) (0.059) (0.081) (0.018) (0.013) (0.007) (0.029) (0.041) (0.047)

- deodorants
  - Sales: 0.198; -0.316; 0.226
  - Frequency: 0.043; 0.026; 0.016
  - Size: 0.030; 0.171; -0.219
  - Standard errors: (0.053) (0.055) (0.059) (0.019) (0.013) (0.010) (0.055) (0.048) (0.089)

- diapers
  - Sales: 0.242; -0.185; 0.269
  - Frequency: 0.058; 0.030; 0.027
  - Size: 0.008; 0.100; -0.107
  - Standard errors: (0.065) (0.039) (0.072) (0.028) (0.019) (0.016) (0.037) (0.033) (0.053)

- facial tissue
  - Sales: 0.219; -0.265; 0.279
  - Frequency: 0.043; 0.027; 0.016
  - Size: 0.040; 0.116; -0.093
  - Standard errors: (0.071) (0.058) (0.083) (0.024) (0.018) (0.010) (0.049) (0.053) (0.060)

- frozen dinner
  - Sales: 0.283; -0.308; 0.373
  - Frequency: 0.040; 0.027; 0.013
  - Size: 0.051; 0.138; -0.120
  - Standard errors: (0.081) (0.065) (0.098) (0.018) (0.012) (0.008) (0.036) (0.053) (0.060)

- frozen pizza
  - Sales: 0.306; -0.282; 0.395
  - Frequency: 0.044; 0.029; 0.015
  - Size: 0.052; 0.140; -0.119
  - Standard errors: (0.084) (0.050) (0.094) (0.021) (0.014) (0.009) (0.033) (0.047) (0.051)

- household cleaning
  - Sales: 0.173; -0.243; 0.198
  - Frequency: 0.035; 0.022; 0.012
  - Size: 0.035; 0.121; -0.129
  - Standard errors: (0.062) (0.054) (0.071) (0.017) (0.013) (0.009) (0.052) (0.050) (0.084)

- hot dog
  - Sales: 0.229; -0.336; 0.314
  - Frequency: 0.034; 0.025; 0.010
  - Size: 0.065; 0.134; -0.105
  - Standard errors: (0.074) (0.060) (0.090) (0.018) (0.014) (0.007) (0.045) (0.051) (0.063)

- laundry and detergents
  - Sales: 0.233; -0.272; 0.307
  - Frequency: 0.044; 0.028; 0.016
  - Size: 0.037; 0.118; -0.104
  - Standard errors: (0.063) (0.046) (0.076) (0.017) (0.012) (0.008) (0.031) (0.042) (0.048)

- margarine and butter
  - Sales: 0.177; -0.256; 0.229
  - Frequency: 0.041; 0.029; 0.012
  - Size: 0.042; 0.091; -0.064
  - Standard errors: (0.063) (0.068) (0.076) (0.023) (0.019) (0.007) (0.035) (0.039) (0.040)

- mayonnaise
  - Sales: 0.143; -0.246; 0.178
  - Frequency: 0.045; 0.032; 0.012
  - Size: 0.038; 0.093; -0.083
  - Standard errors: (0.055) (0.069) (0.064) (0.024) (0.020) (0.009) (0.035) (0.038) (0.051)

- milk
  - Sales: 0.133; -0.181; 0.156
  - Frequency: 0.055; 0.038; 0.017
  - Size: 0.029; 0.071; -0.055
  - Standard errors: (0.057) (0.043) (0.065) (0.032) (0.028) (0.011) (0.020) (0.024) (0.024)

- mustard and ketchup
  - Sales: 0.152; -0.212; 0.173
  - Frequency: 0.044; 0.031; 0.013
  - Size: 0.042; 0.114; -0.113
  - Standard errors: (0.061) (0.056) (0.067) (0.020) (0.016) (0.009) (0.046) (0.037) (0.066)

- paper towel
  - Sales: 0.204; -0.253; 0.273
  - Frequency: 0.043; 0.028; 0.015
  - Size: 0.039; 0.103; -0.082
  - Standard errors: (0.055) (0.050) (0.065) (0.022) (0.017) (0.009) (0.035) (0.040) (0.050)

- peanut butter
  - Sales: 0.156; -0.204; 0.200
  - Frequency: 0.046; 0.030; 0.016
  - Size: 0.026; 0.079; -0.065
  - Standard errors: (0.060) (0.065) (0.071) (0.024) (0.019) (0.011) (0.033) (0.034) (0.040)

- photo
  - Sales: 0.200; -0.285; 0.221
  - Frequency: 0.046; 0.025; 0.021
  - Size: 0.004; 0.171; -0.227
  - Standard errors: (0.055) (0.069) (0.059) (0.026) (0.017) (0.017) (0.095) (0.078) (0.131)

- razors
  - Sales: 0.226; -0.222; 0.238
  - Frequency: 0.061; 0.039; 0.023
  - Size: 0.010; 0.119; -0.186
  - Standard errors: (0.071) (0.069) (0.074) (0.034) (0.026) (0.020) (0.076) (0.059) (0.136)

- salt snacks
  - Sales: 0.210; -0.258; 0.251
  - Frequency: 0.031; 0.021; 0.010
  - Size: 0.055; 0.134; -0.110
  - Standard errors: (0.052) (0.037) (0.062) (0.013) (0.008) (0.005) (0.027) (0.033) (0.037)

- shampoo
  - Sales: 0.198; -0.283; 0.220
  - Frequency: 0.053; 0.032; 0.021
  - Size: 0.019; 0.161; -0.213
  - Standard errors: (0.044) (0.044) (0.047) (0.021) (0.013) (0.011) (0.047) (0.038) (0.075)

- soup
  - Sales: 0.173; -0.296; 0.225
  - Frequency: 0.044; 0.031; 0.012
  - Size: 0.047; 0.122; -0.117
  - Standard errors: (0.079) (0.074) (0.104) (0.019) (0.015) (0.007) (0.037) (0.040) (0.060)

- spaghetti sauce
  - Sales: 0.211; -0.262; 0.267
  - Frequency: 0.049; 0.033; 0.016
  - Size: 0.042; 0.119; -0.109
  - Standard errors: (0.072) (0.064) (0.085) (0.023) (0.016) (0.010) (0.039) (0.042) (0.058)

- sugar and substitutes
  - Sales: 0.100; -0.193; 0.114
  - Frequency: 0.035; 0.025; 0.010
  - Size: 0.032; 0.095; -0.099
  - Standard errors: (0.052) (0.076) (0.061) (0.022) (0.018) (0.010) (0.061) (0.055) (0.096)

- toilet tissue
  - Sales: 0.208; -0.255; 0.306
  - Frequency: 0.051; 0.032; 0.019
  - Size: 0.030; 0.096; -0.078
  - Standard errors: (0.060) (0.048) (0.074) (0.024) (0.019) (0.009) (0.029) (0.036) (0.035)

- tooth brush
  - Sales: 0.204; -0.337; 0.232
  - Frequency: 0.044; 0.025; 0.019
  - Size: 0.030; 0.206; -0.256
  - Standard errors: (0.058) (0.061) (0.067) (0.017) (0.012) (0.010) (0.064) (0.060) (0.089)

- tooth paste
  - Sales: 0.197; -0.287; 0.233
  - Frequency: 0.039; 0.024; 0.015
  - Size: 0.037; 0.153; -0.178
  - Standard errors: (0.052) (0.046) (0.062) (0.016) (0.011) (0.008) (0.041) (0.043) (0.073)

- yogurt
  - Sales: 0.224; -0.254; 0.291
  - Frequency: 0.036; 0.024; 0.012
  - Size: 0.037; 0.098; -0.075
  - Standard errors: (0.072) (0.063) (0.088) (0.020) (0.015) (0.008) (0.036) (0.041) (0.043)

*Notes: UPCs have equal weights when aggregated to the category level.*

*Appendix Table 2 that follows reports Moments for all (sales and regular) price changes (frequency and size) by category, including Total and per-category values.*

### Appendix Table 3. Alternative standard errors.

### _wp12207 - Appendix Table 3. Alternative standard errors.

### Appendix Table 3 — Baseline point estimates and alternative standard errors
- Dependent variable: Equal weights to all UPCs.
- Columns: (1) Point estimate; (2) Standard errors (Driscoll-Kraay); (3) Cluster by category/city (1550 clusters); (4) Cluster by month (84 clusters).

- Sales
  - Frequency: -0.365 (0.120)*** (0.085)*** (0.076)***
  - Size: 0.256 (0.120)** (0.084)*** (0.070)***

- Share of goods bought on sales
  - -0.461 (0.133)*** (0.098)*** (0.082)***

- Changes of regular prices — Frequency
  - All: -0.100 (0.044)** (0.027)*** (0.033)***
  - Positive: -0.053 (0.032)* (0.020)*** (0.026)**
  - Negative: -0.047 (0.019)*** (0.014)*** (0.013)***

- Changes of regular prices — Size
  - All: -0.095 (0.062) (0.042)** (0.053)*
  - Positive: -0.155 (0.092)* (0.064)*** (0.056)***
  - Negative: -0.004 (0.129) (0.093) (0.082)

- Inflation of posted prices
  - 0.007 (0.034) (0.024) (0.020)

- Inflation of effective prices
  - -0.206 (0.045)*** (0.045)*** (0.027)***

### Notes on Appendix Table 3
- The table shows the baseline point estimate (column 1) and standard error (column 2) which correspond to results presented in column 3 of Table 1.
- Columns 3 and 4 show alternative estimates of standard errors associated with column (1).
- Column (3) clusters standard errors by city and category (1550 clusters) which allows for arbitrary collation of errors across time.
- Column (4) clusters standard errors by month (84 clusters) which allow for arbitrary cross-sectional correlation.
- *,**,*** indicates statistical significance at 1, 5 and 10 percent.

### Appendix Table 4 — Cyclical Behavior of Price Changes at the Category Level (table header and notes)
- Title: Appendix Table 4. Cyclical Behavior of Price Changes at the Category Level.
- Aggregation: City-specific weights are used to aggregate across UPCs (corresponds to column 4 in Table 2).
- The table reports category-level coefficients for: Sales (Frequency, Size), Share of goods bought on sales, Changes of regular prices (Frequency, Size; All, Positive, Negative), Inflation of posted prices, Inflation of effective prices.
- Example category entries (coefficients and standard errors shown exactly as in the table):
  - beer: Sales Frequency -0.440*** (0.184); Sales Size -0.100 (0.159); Share of goods bought on sales -0.460*** (0.176); (additional entries and standard errors appear in the table)
  - coffee: Sales Frequency -1.262*** (0.397); Sales Size 0.080 (0.210); Share of goods bought on sales -1.466*** (0.403); (additional entries and standard errors appear in the table)
  - diapers: Sales Frequency 0.601** (0.267); Sales Size -0.550*** (0.212); Share of goods bought on sales 0.792*** (0.336); Changes of regular prices All -0.419*** (0.118); (additional entries and standard errors appear in the table)
  - yogurt: Sales Frequency -1.342*** (0.317); Sales Size -0.319 (0.271); Share of goods bought on sales -1.455*** (0.417); Changes of regular prices All -0.341*** (0.091); Changes of regular prices Positive -0.204*** (0.069); Changes of regular prices Negative -0.137*** (0.048)
- Notes: City-specific weights are used to aggregate across UPCs (corresponds to column 4 in Table 2).

### Appendix Table 5 — Cyclicality of pricing moments by store rank, alternative aggregation across UPCs (table header and notes)
- Title: Appendix Table 5. Cyclicality of pricing moments by store rank, alternative aggregation across UPCs.
- Dependent variable: UPC rank sample: Ω1  through Ω3 (three rank samples shown).
- Regressors include UR and UR×rank. The table corresponds to Table 3 in the text. The difference is that equal weights are used to aggregate ranks across UPCs.
- Selected reported coefficients (UR and UR×rank) with standard errors shown exactly:
  - Sales — Frequency (columns 1–3 sample): UR -0.069 (0.141); UR×rank -1.213*** (0.143)
  - Sales — Size (columns 1–3 sample): UR 0.175* (0.092); UR×rank -0.197 (0.141)
  - Share of goods bought on sales, ϑ̄: UR 0.225 (0.163); UR×rank -1.677*** (0.210)
  - Growth rate of revenue (month on month): UR 0.351 (0.226); UR×rank -0.779*** (0.088)
  - Changes of regular prices — Frequency All: UR -0.024 (0.072); UR×rank -0.129*** (0.043)
  - Changes of regular prices — Frequency Negative: UR -0.017 (0.029); UR×rank -0.093*** (0.016)
  - Changes of regular prices — Size All: UR -0.098* (0.055); UR×rank 0.043 (0.036)
  - Notes: See the note to Table 3. Equal weights are used to aggregate ranks across UPCs.

*Source: _wp12207 - Appendix Table 3. Alternative standard errors.*

### Appendix Table 6. Use Price Differentials to Construc

### _wp12207 - Appendix Table 6. Use Price Differentials to Construc

### Appendix Table 6 — Store-Level Regression Results (Price-Rank Construction)
- Dependent variable: UPC rank (store rank constructed from percent deviation of a given UPC’s price in a given store from the median price of the UPC in a given market and month); table corresponds to Table 3 in the paper; constructed using equal weights; Driscoll and Kraay (1998) standard errors in parentheses. ***, **, * denote significance at 0.01, 0.05, and 0.10 levels.
- Selected coefficient estimates and standard errors (preserve exactly as reported):
  - Sales Frequency:
    - Column (1): UR = -0.864*** (0.189); UR×rank = -8.285*** (0.785)
    - Column (2): UR = -0.811*** (0.202); UR×rank = -12.074*** (1.050)
    - Column (4): UR = -0.876*** (0.216); UR×rank = -15.767*** (1.068)
  - Size:
    - Column (1): UR = -0.014 (0.134); UR×rank = -0.533 (0.672)
    - Column (2): UR = -0.009 (0.133); UR×rank = -0.298 (0.972)
    - Column (4): UR = -0.012 (0.137); UR×rank = -0.554 (1.262)
  - Share of goods bought on sales, ߱௠௖௧:
    - Column (1): UR = -0.755*** (0.178); UR×rank = -9.907*** (1.021)
    - Column (2): UR = -0.693*** (0.193); UR×rank = -14.067*** (1.323)
    - Column (4): UR = -0.764*** (0.205); UR×rank = -17.678*** (1.396)
  - Growth rate of revenue:
    - Column (1): UR = 0.055 (0.233); UR×rank = -0.239*** (0.084)
    - Column (2): UR = 0.171 (0.228); UR×rank = -0.424*** (0.075)
    - Column (4): UR = 0.237 (0.218); UR×rank = -0.541*** (0.079)
- Changes of regular prices — Frequency (All / Positive / Negative) and Size (All / Positive / Negative):
  - Frequency — All:
    - UR: -0.072 (0.084); UR×rank: -0.898*** (0.223)
    - UR: -0.067 (0.084); UR×rank: -0.998*** (0.369)
    - UR: -0.073 (0.085); UR×rank: -1.310*** (0.514)
  - Frequency — Positive:
    - UR: -0.029 (0.049); UR×rank: -0.419*** (0.149)
    - UR: -0.027 (0.049); UR×rank: -0.394 (0.239)
    - UR: -0.030 (0.049); UR×rank: -0.638* (0.338)
  - Frequency — Negative:
    - UR: -0.043 (0.039); UR×rank: -0.479*** (0.091)
    - UR: -0.040 (0.039); UR×rank: -0.604*** (0.144)
    - UR: -0.043 (0.039); UR×rank: -0.672*** (0.194)
  - Size — All:
    - UR: -0.103** (0.050); UR×rank: -0.026 (0.206)
    - UR: -0.103** (0.050); UR×rank: 0.165 (0.262)
    - UR: -0.103** (0.050); UR×rank: -0.016 (0.297)
  - Size — Positive:
    - UR: -0.198*** (0.083); UR×rank: -0.253 (0.182)
    - UR: -0.196*** (0.084); UR×rank: -0.626*** (0.230)
    - UR: -0.200*** (0.084); UR×rank: -0.747*** (0.204)
  - Size — Negative:
    - UR: 0.286*** (0.069); UR×rank: -0.361 (0.245)
    - UR: 0.289*** (0.070); UR×rank: -0.334 (0.362)
    - UR: 0.286*** (0.070); UR×rank: -0.624 (0.421)
- Notes reiteration: rank constructed from percent deviations aggregated across UPCs using equal weights; see text and Table 3 note for further details.

### Appendix Table 7 — Household-Level Results (Price-Rank Construction)
- Table corresponds to Table 4 in the paper. Rank constructed as percent deviation of UPC price from market-month median; deviations aggregated across UPCs using equal weights (column 1) or expenditure shares (column 2); Driscoll and Kraay (1998) standard errors in parentheses; ***, **, * denote significance at 0.01, 0.05, 0.10.
- Reported estimates (columns labeled by sample of UPCs and weighting):
  - Sample Ω௠௔௫:
    - Equal weights (column 1): -0.994*** (0.354)
    - Expenditure shares (column 2): -0.611 (0.575)
  - Sample Ωଽ଴:
    - Equal weights (column 1): -0.790** (0.358)
    - Expenditure shares (column 2): -0.548 (0.588)
  - Sample Ω଻ହ:
    - Equal weights (column 1): -0.561** (0.292)
    - Expenditure shares (column 2): -0.567 (0.555)

### Appendix Figure 1 — Sensitivity of Output Gap Response to Contractionary Monetary Policy Shock
- Figure shows sensitivity of output gap response to a nominal shock as a function of two parameters: ߶ (elasticity of iceberg cost with respect to shopping effort) and ߛ (elasticity of substitution across stores).
- The mean response is the average response of output gap over 20 periods.
- Axes and tick marks preserved as presented: contemporaneous response and mean response over 5 years (right axis); parameter ranges indicated by ticks including -0.5, -0.4, -0.3, -0.2, -0.1 and 1.5, 2.5, 3.5, 4.5, 5.5, 6.5 in panels.

### Appendix B — Model of Store-Switching and Pro-Cyclical Sales (Lal and Rao (1997) framework)
- Objective: introduce a simple model of sales to explain pro-cyclicality of frequency and depth of sales and price-level differences across stores; builds on Lal and Rao (1997). Coexistence of EDLP and HiLo retailers is a unique Nash equilibrium in that framework.
- Retailer types:
  - EDLP (Every day low prices): sets constant lower regular price; denotes basket discount at EDLP store by ߜ.
  - HiLo: maintains a regular price and occasionally offers temporary sales with sales-depth D; assumed sales frequency = ½ (sales every other period). Footnote: model can extend to HiLo randomizing sales with frequency f.
- Price level R is fixed and taken as given; stores have zero marginal cost of obtaining goods from manufacturer.
- Location: stores on unit interval, EDLP at 0, HiLo at 1.
- Consumers:
  - Two types: bargain hunters (share ߣ) and loyal/time-constrained consumers (1-ߣ).
  - Bargain hunters: low transport cost, always observe prices, buy from lowest total cost store this period.
  - Loyal consumers: higher transport cost, do not observe current prices, buy from store with lowest expected price net of transport costs.
  - Travel cost for distance x is given by ݐ(2/x) for bargain hunters and ݐ(2/x) for loyal consumers with notation indicating different parameters (text denotes ݐሺ2/ݔ஻ுሻ and ݐሺ2/ݔ௅஼ሻ and assumes ݐ஻ுݐ௅஼).
- Demand and indifference conditions:
  - Loyal marginal buyer at location ݍ: equation equating total cost of EDLP and HiLo in expectation; resulting expression for ݍ: ݍ = 1/2 + (ݐ/2)(ߜ - ܴ)/(ݐߣ/஻ு + (ߣ1െ)ݐ௅஼) (symbols preserved as in source).
  - Bargain hunters: separate marginal locations depending on whether HiLo has a sale (ݏ) or not (݇); equations given with preserved forms including terms like 1/2 ݐ/஻ு (ܦ - ߜ) etc.
- Demand expressions:
  - Demand for HiLo with a sale: ܳௌߣ... (expression preserved in full form as in source).
  - Demand for HiLo without a sale: ܳேௌߣ... (expression preserved).
  - Expected demand for EDLP: ܳாൌ... (expression preserved).
- Profits:
  - Expected profit for HiLo: ߨு௜௅௢ = 1/2 ܳௌ (ܦെܴ) + 1/2 ܳேௌ ܴ = (full expression preserved exactly as in source).
  - Expected profit for EDLP: ߨா஽௅௉ = ܳൌ ܭ(ߜെܴ).
- First-order optimality conditions:
  - FOC w.r.t ߜ for EDLP and ܦ for HiLo given with exact expressions including fractions and summed terms.
- Closed-form solutions (as presented in source):
  - ܦכ = 3/ܴ2 (ݐߣ/஻ு + (ߣ1െ)ݐ௅஼) 1/(ݐߣ7/஻ு + 3(ߣ1െ)ݐ௅஼)
  - ߜכ = (long expression preserved verbatim) and identity ߜכ = 3(ߣ1െ)ݐ௅஼ݐߣ5 + ஻ு6… ܦכ ܦ൏כ (expressions preserved exactly as in source).
- Feasibility conditions to ensure 0 < ߜכ < ܦכ < ܴ: specified inequality conditions preserved exactly.
- Comparative statics — sensitivity to share of bargain hunters ߣ:
  - ܦ߲כ/ߣ߲ = -21ݐ஻ு (ݐܴ௅஼ - 1)ݐܴே3஻ுݐ௅஼ݐே9௅஼(ݐߣ7஻ு + 3(ߣ1െ)ݐ௅஼)ଶ (expression preserved verbatim).
  - If ݐ௅஼ = 1 (normalization), డ஽כ డఒ ≤ 0 meaning size of sales in HiLo decreases as there are more bargain hunters.
  - ߜ߲כ/ߣ߲ = ܦ߲כ/ߣ߲ ไฮ3(ߣ1െ)ݐ௅஼ݐߣ5 + ஻ு6… ܦכ and additional terms; interpretation: second term unambiguously positive and relative sizes determine sign; overall ߜ sensitivity less than ܦ sensitivity, interpreted as discount in EDLP less sensitive to business conditions.

### Appendix C — Second-Order Approximation to Utility with Endogenous Shopping Effort and Store-Switching
- Presents second-order approximation to utility and associated algebraic derivations following Woodford (2003) and references to Gali (2008). Main components preserved in symbolic form exactly as in source:
  - Second-order approximation: ܷ௧ = logܥ௧ + log(ܮ1െ௧ ܵെ௧) - series of higher-order terms (full expansion preserved in original notation).
  - Definitions and identities involving ߟ, ܺ, ܻ, ܰ, ܵ, ܮ and their steady-state and perturbation relationships preserved verbatim (including normalizations with ߬ҧߤ = and references to Woodford (2003) conditions).
  - Key steady-state and perturbation results preserved exactly:
    - Φഥ = 2 భ ంషభ, steady-state values for various variables, and expressions such as ܥ௧ܥെҧ = Φഥ (ܻ௧ ܻெത) ܻ + ... (full form preserved).
  - Linearization and variance relationships:
    - Δ௧ Δߠ = ௧ివ + ߠ/(ߠ1)െ ߨ௧ଶ ݐ݋݄… and subsequent variance scaling relations preserved as in source.
  - Final expected utility expression preserved as in source with symbolic rearrangements yielding expression referenced in the text.
- Notes: approximation and substitutions follow precisely the algebraic steps and notation in the appendix; steady-state simplifications and link between consumption and output preserved.

*Italic: Appendix tables, figures, and appendices summarized exactly as presented in the source content unit.*

### APPENDIX D: CONSTRUCTION OF DATA MOMENTS

### APPENDIX D: CONSTRUCTION OF DATA MOMENTS

### Frequency of sales
- Data source and flag:
  - The IRI data set provides a flag indicating whether a given good was on sale in a given store in a given week.
- Sale identification filters (following Nakamura and Steinsson (2008)):
  - Temporary reductions up to three weeks that return to the pre-cut level are identified as sales.
  - Two approaches to identify a price spell:
    - Approach “A”: missing values interrupt price spells. Example: price $4 for two weeks, missing one week, $4 for three weeks → two spells (durations two and three weeks).
    - Approach “B”: missing values do not interrupt price spells if price is the same before and after the missing period. Example above → one spell (duration five weeks).
  - Incidence of sales uses the union of: (i) the IRI sales flag, (ii) results from approach “A”, and (iii) results from approach “B”.
  - Using approaches “A” and “B” does not materially change the incidence of sales identified by the IRI sales flag alone.
- Aggregation/frequency metric:
  - The frequency of sales is computed at the weekly frequency as the fraction of weeks in a month when a good is identified by the sales flag as being on sale.

### Size of sales
- Measurement:
  - Size of a sale = (log) difference between the sales price (as identified by the sales flag) and the price preceding the sale.
- Monthly aggregation:
  - If more than one sale occurs in a month, take the average size of sales in that month.

### Share of goods sold on sale
- Calculation for a given good in a given city (or store) in a given month:
  - Numerator: number of units sold during episodes identified as sales by the sales flag.
  - Denominator: total number of sold units.
  - Share = numerator / denominator.

### Frequency of regular price changes
- Criteria for a week to be identified as a regular price change:
  - i) the sales flag does not identify this week as a period when a good is on sale;
  - ii) the sales flag does not identify the preceding week as a period when a good is on sale;
  - iii) the price change is larger than one cent or one percent in absolute value (or more than 0.5 percent for prices larger than $5).
    - The last criterion removes small price changes which could arise from rounding errors and the like.
- Use of approaches “A” and “B” to identify the price in the preceding period.
- Incidence of regular price changes is taken as the union of incidents identified by “A” and “B”.
- Aggregation/frequency metric:
  - The frequency of regular price changes is computed at the weekly frequency as the fraction of weeks in a month when a good is identified as having a regular price change.

### Size of regular price change
- Measurement:
  - Size = (log) difference between the price in the period identified as having a regular price change and the price in the preceding period (using approach “A” and “B” to identify the preceding period).
- Monthly aggregation:
  - If more than one regular price change occurs in a month, take the average size of regular price changes in that month.

### Weighting
- Aggregation across goods to the category level — three weighting schemes:
  - i) equal weights;
  - ii) expenditure shares for a given city and year (“city specific”);
  - iii) cross-city expenditure shares for a given year (“common”).
- City-specific expenditure share weights (as given in source):
  - ߱
    ௠௖௧௝
    ─
    ∑
    ܴܶ
    ௠௦௖௧௝௦
    ∑∑
    ܴܶ
    ௠௦௖௧௞௦௞
- Common expenditure share weights (as given in source):
  - ߱
    ௖௧௝
    ─
    ∑∑
    ܴܶ
    ௠௦௖௧௝௦௠
    ∑∑∑
    ܴܶ
    ௠௦௖௧௞௦௞௠
- Definitions:
  - m, s, c, t, and j index markets, stores, product categories, time, and UPC.
  - ܴܶ
    ௠௦௖௧௝
    is the revenue from selling good j in the year covering month t.
- Aggregation across goods and categories to the store level — two weighting schemes:
  - i) equal weights;
  - ii) expenditure shares for a given store, good and year.
- Store-level expenditure share weights (as given in source):
  - ߱
    ௠௦௖௧௝
    ─
    ܴܶ
    ௠௦௖௧௝
    ∑∑
    ܴܶ
    ௠௦௟௧௞௟௞
- Definition repeated for store-level formula:
  - ܴܶ
    ௠௦௖௧௝
    is the revenue from selling good j in the year covering month t.

*Source: APPENDIX D: CONSTRUCTION OF DATA MOMENTS (from the supplied IMF content unit)*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2012/_wp12207.pdf_