Inflation-Dynamics | Macro Paper Warehouse

A Theory of How Workers Keep up with Inflation

Mon, 01 Jan 0001 00:00:00 +0000

Beliefs About the Economy are Excessively Sensitive to Household-Level Shocks: Evidence from Linked Survey and Administrative Data

Mon, 01 Jan 0001 00:00:00 +0000

Complete Pass-Through in Levels

Mon, 01 Jan 0001 00:00:00 +0000

Mixing It Up: Inflation at Risk

Mon, 01 Jan 0001 00:00:00 +0000

This paper introduces a Bayesian Gaussian mixture density regression framework that estimates the complete forecast distribution of inflation — not just selected quantiles — and decomposes the entire risk outlook into contributions from individual economic predictors. The methodology accommodates multimodality, skewness, and fat tails without parametric restrictions, and allows construction of risk measures calibrated to the central bank’s own loss function rather than generic percentile-based measures. Applied to the recent U.S. inflation surge, the framework finds that post-pandemic inflation risk was primarily driven by the recovery of the U.S. business cycle and surging commodity prices, while adjustments in monetary policy contributed negatively — partially mitigating the increase in right-tail inflation risk — and credit spreads also offset some risk. The Gaussian mixture structure enables fast MCMC estimation and produces well-calibrated density forecasts across a range of macroeconomic variables.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the key methodological contribution relative to existing inflation-at-risk approaches?

Existing approaches to macroeconomic at-risk measures focus on specific quantiles of the forecast distribution — typically the 5th or 25th percentile — discarding information contained in the rest of the distribution; this paper redirects attention to the full forecast distribution while retaining the nonparametric flexibility of quantile regression. The Gaussian mixture density regression estimates a conditional distribution that is a weighted mixture of Gaussians, capturing multimodality, asymmetry, and fat tails simultaneously. The key innovation is decomposability: each predictor’s contribution to any region of the forecast distribution can be quantified, enabling a driver-level accounting of what generates tail risk in any given period.

Q2. What does the U.S. application reveal about the inflation surge?

The framework attributes the increase in right-tail U.S. inflation risk during 2021–2023 primarily to surging commodity prices and the recovery of the domestic business cycle, while monetary policy tightening contributed negatively — its effect partially offset the upward pressure from commodity and cycle drivers. Credit spreads also partially mitigated the risk. The decomposition implies that the dominant drivers of inflation risk were supply-side and aggregate-demand factors, and that monetary policy, when it tightened, reduced the right-tail risk as intended — providing quantitative support for the interpretation that policy was reactive but directionally correct.

Q3. How does the framework construct policy-relevant risk measures?

The framework allows weighting probability mass over the forecast distribution by any user-specified loss function, including asymmetric central bank preferences, yielding risk measures that integrate the full distributional information in proportion to the policymaker’s actual valuation of different inflation outcomes. A central bank that penalizes above-target inflation more heavily than below-target inflation (consistent with empirical evidence on CB loss functions) would weight the upper tail more, producing a risk statistic that is higher than a symmetric measure for the same distribution. This policy-preference-aligned risk measure could have provided a more accurate signal of the urgency of the 2021–2023 inflation risk than standard percentile measures.

Key concepts

inflation at risk : the quantile-based or distribution-based characterization of future inflation uncertainty; extended in this paper from a single quantile to the complete forecast distribution and its risk decomposition by driver.

density regression : a regression model in which the conditional distribution of the outcome — not just its mean or a specific quantile — is the object of estimation; the paper uses a Gaussian mixture density regression to capture non-standard distributional shapes.

risk decomposition : the attribution of shifts in the full forecast distribution to individual predictor variables; the paper’s key tool for identifying which economic factors drive right-tail inflation risk in any period.

CB-preference-aligned risk measure : a summary statistic constructed by weighting probability mass over the forecast distribution by the central bank’s loss function; captures asymmetric preferences and goes beyond standard percentile measures.

On measuring the welfare cost of inflation

Mon, 01 Jan 0001 00:00:00 +0000

Measuring the welfare cost of inflation requires specifying a money demand function, a definition of money, and an approach to consumer surplus; existing estimates vary widely because these choices are not standardized. This paper advances the literature by applying neoclassical monetary demand theory that integrates the demand for money with the demands for consumption and leisure, using the Normalized Quadratic (NQ) flexible functional form that avoids imposing specific elasticity assumptions. The main contribution is to extend the Serletis and Xu (2021, 2023) framework to derive Hicksian (compensating variation) money demand functions from the NQ model and compare welfare cost estimates based on these against estimates from the Marshallian (consumer surplus) approach—a comparison not previously made within this integrated demand-system framework. The paper uses U.S. CFS Divisia monetary aggregates across multiple levels of monetary aggregation and finds that the two approaches yield internally consistent but quantitatively different welfare cost estimates, with the Hicksian compensating variation approach providing theoretically preferred measures that are robust across specifications.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What is the neoclassical demand system approach and how does it differ from earlier methods?

The Serletis-Xu framework integrates the demand for money with the demands for consumption goods and leisure in a joint utility maximization problem, estimating a flexible NQ functional form in a systems context rather than fitting a single-equation money demand specification. Earlier approaches—such as the log-log specification (Lucas 2000) or semi-log specification (Ireland 2009)—estimate a single money demand equation under a maintained functional form assumption and a fixed interest elasticity (often −0.5 as in the Baumol-Tobin model). The NQ approach, derived from the dual demand system of Diewert (1974), makes no assumption about the functional form of money demand and allows demand interactions among consumption goods, leisure, and money (as recommended by Abbott and Ashenfelter 1976 and Barnett 1979), which is necessary for correct welfare measurement when money is consumed jointly with other goods.

Q2. What is the distinction between the Marshallian and Hicksian approaches to measuring welfare cost?

The Marshallian (Bailey 1956) approach measures the area under the inverse money demand curve between the zero-inflation and positive-inflation nominal interest rates, which corresponds to consumer surplus but does not hold utility constant. The Hicksian (compensating variation) approach measures the income that must be given to the consumer to restore the same utility after the inflation increase as before—holding utility constant rather than income. The Hicksian approach is theoretically preferred because it measures the true welfare loss from inflation under standard consumer theory; the Marshallian approach can under- or over-estimate the true cost depending on income effects. The paper’s main contribution is to derive the Hicksian demands from the NQ model and compute the compensating variation, previously not done within this flexible-functional-form demand system framework.

Q3. What role do Divisia monetary aggregates play?

The paper uses CFS (Center for Financial Stability) Divisia monetary aggregates—which aggregate monetary assets using economic quantity indices that weight components by their monetary service flows—rather than simple-sum aggregates such as M1 or M2. Simple-sum aggregates treat all monetary assets as perfect substitutes regardless of yield differentials, introducing a substitution bias that misrepresents the quantity of monetary services; Divisia aggregates are theoretically consistent with the neoclassical demand system approach used here. The paper reports welfare cost estimates across multiple levels of monetary aggregation to assess sensitivity to the definition of money.

Q4. How do the results compare with the prior literature?

The paper’s estimates, while internally consistent with the NQ flexible form and Divisia aggregates, are in the range of prior estimates in the literature; the Hicksian compensating variation estimates differ from Marshallian consumer surplus estimates in ways consistent with theory, providing a more theoretically grounded benchmark. The wide range of estimates in the existing literature (discussed in the paper’s Table 1)—from the Lucas (2000) log-log model to the Ireland (2009) semi-log model—reflects sensitivity to functional form, money definition, data frequency, and methodology; the paper’s NQ framework addresses functional-form sensitivity while comparing the two surplus measures.

Key concepts

compensating variation (Hicksian welfare cost of inflation) : the income required to restore a consumer’s utility to its pre-inflation level after an inflation increase, holding utility constant; the paper’s main new estimate, derived from Hicksian money demand functions.

Normalized Quadratic (NQ) flexible functional form : a globally flexible functional form (Diewert and Wales 1988) used to approximate the consumer’s cost function without imposing restrictions on substitution elasticities; allows derivation of both Marshallian and Hicksian demand functions.

Divisia monetary aggregates : theoretically consistent monetary aggregates that weight monetary assets by their monetary service flows (user costs) rather than summing them with equal weights; CFS Divisia aggregates are used here as the measure of money.

Quality Adjustment at Scale: Hedonic versus Exact Demand-Based Price Indices

Mon, 01 Jan 0001 00:00:00 +0000

Layer 1: Overview

This paper implements and evaluates methods for constructing quality-adjusted price indices from item-level retail scanner data at scale — across hundreds of product categories, heterogeneously encoded product attributes, and rapid product turnover. Using proprietary NPD Group data covering five general merchandise categories (2014–2018) and NielsenIQ scanner data covering 50+ food product groups (2006–2015), the paper compares hedonic superlative indices (using the Erickson-Pakes EP-TV methodology and a novel machine-learning extension) against exact demand-based indices (the Feenstra 1994 lambda-ratio adjustment and the Redding-Weinstein 2020 CES Unified Price Index, CUPI). The central finding is that quality adjustment is quantitatively large: the hedonic Tornqvist index shows roughly 2.5–2.9 percentage points per year faster price decline than the matched-model Tornqvist in high-tech categories (headphones, memory cards) and 4–5 percentage points of cumulative additional disinflation relative to matched-model indices for food. The Feenstra index agrees closely in magnitude with the hedonic approach, but the CUPI is highly sensitive to the choice of common-goods rule (CGR) and in some specifications shows 20–40 percentage points more cumulative disinflation than the Feenstra, a gap the paper attributes to the CUPI’s extreme sensitivity to low-share goods. The paper establishes that hedonic superlative price indices are feasible to implement at scale, including with machine learning on sparse text descriptions, and recommends them as the practical benchmark for re-engineering official price statistics.

Summary of a published paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. What problem in price index construction does the paper address?

The paper addresses the long-standing challenge of simultaneously accounting for consumer substitution and quality change due to product entry and exit in official price statistics, and shows these two corrections are now feasible to implement in real time from item-level retail transactions data. Standard official statistics (CPI, PCE) use an arithmetic Laspeyres index that holds spending weights fixed — the Boskin Commission documented this overstates the true cost of living due to substitution bias. Scanner data permit superlative indices (Tornqvist, Fisher) that correct for substitution at the item level, but further correcting for quality change requires dealing with the millions of products that enter and exit the market each quarter. The paper’s contribution is to show that both corrections can be combined at scale.

Q2. What data infrastructure does the paper use, and what does it reveal about product turnover?

The NPD Group data cover five product groups with quarterly turnover rates of 4.5–13.5 percent per quarter (both entry and exit), and exhibit a characteristic life-cycle pattern: prices peak at entry and decline steadily thereafter while market shares follow a hump shape — rising as products gain distribution and then declining as newer products displace them. Memory cards, for example, show approximately a 50 percent price decline over their life cycle and a 200 percent increase in market share in the first year after entry. These interrelated price-quantity dynamics mean that any matched-model index that ignores entering and exiting goods misses substantial quality improvement. The NielsenIQ data cover over 2.6 million UPCs across 40,000 stores, with nominal food sales closely tracking BEA PCE food expenditures, validating its representativeness.

Q3. What is the EP-TV hedonic method and why does the paper prefer it?

The Erickson-Pakes time-varying unobservables (EP-TV) method estimates hedonic price indices from item-level transactions data using a two-step procedure: first predict log price levels from observable characteristics to recover item-level residuals, then predict log price changes from characteristics plus the lagged residual, which allows the model to track changing valuations of unobservable attributes over time. This approach outperforms the simpler log-level hedonic and the EP-F (fixed unobservables) approach in model fit for price changes: EP-TV achieves R² of 0.13–0.50 versus 0.05–0.24 for log-level models across product groups. The paper extends EP-TV to the NielsenIQ data using deep neural networks to decode sparse abbreviated product descriptions (e.g., “ZR DT LN/LM CF NBP CT” for a diet soft drink), achieving out-of-sample R² of roughly 75% for price-level predictions and above 50% in-sample for price changes.

Q4. What are the main quantitative findings for the hedonic indices?

The EP-TV hedonic Tornqvist index indicates price declines approximately 2.9 percentage points per year faster than the matched-model Tornqvist for memory cards, 2.5 pp/year for headphones, 1.3 pp/year for boys’ jeans, 0.7 pp/year for coffee makers, and 0.4 pp/year for occupational footwear; for NielsenIQ food categories, the hedonic Tornqvist is approximately 4 percentage points lower cumulatively over 2006–2015 than the matched-model Tornqvist. These gaps represent the quality improvement embedded in product turnover — the fact that new memory cards at a given price embody more storage than their predecessors, new headphones better sound quality, etc. The paper also shows that the hedonic Laspeyres, which only adjusts for exiting goods (following the standard Pakes 2003 bounding result), is substantially lower than the matched-model Laspeyres, confirming that the selection bias from ignoring exiting goods in official statistics is quantitatively important.

Q5. How do the demand-based exact price indices compare with the hedonic approach?

The Feenstra (1994) lambda-ratio index, which adjusts the Sato-Vartia index for product entry and exit via the ratio of entering to exiting expenditure shares scaled by (1/(σ−1)), shows cumulative disinflation approximately 2 percentage points beyond the matched-model Sato-Vartia across all five NPD product groups and approximately 5 percentage points for NielsenIQ food, broadly comparable in magnitude to the hedonic adjustment. The estimated substitution elasticities (σ) range from about 5.2 to 7.8 across NPD product groups and have a median of about 6 across food product groups, consistent with the literature. The Feenstra-hedonic agreement is a reassuring finding: two methodologically distinct approaches based on different identifying assumptions yield similar magnitudes of quality correction.

Q6. What is the CUPI and why is it problematic?

The Redding-Weinstein (2020) CES Unified Price Index (CUPI) generalizes the Feenstra index by adding a taste-shock correction (S ratio) and a Jevons index (P ratio), both of which are unweighted geometric means across common goods — making the CUPI extremely sensitive to products with tiny expenditure shares, because any product with a low share is inferred to have low appeal, which the model translates into a large quality-adjustment downward.** Without a common-goods rule (CGR), the CUPI shows 30–40 percent per year price declines for high-tech goods and boys’ jeans, 10–30 percentage points below the Feenstra; with a 25th-percentile market-share CGR, the CUPI is still more than 40 percentage points below the Feenstra for food in 2015 on a cumulative basis. The key concern is that very low expenditure shares for entering or exiting products can reflect search frictions, limited distribution, or clearance-rack effects rather than genuinely low consumer appeal, so the CUPI’s unweighted components may conflate these factors with quality change. The paper concludes that more research on the appropriate CGR is needed before the CUPI can be recommended for official statistics.

Q7. Is the hedonic approach robust to missing or omitted product attributes?

Yes — omitting key observable characteristics (memory size for memory cards, major brand dummies for apparel and footwear) from the EP-TV estimation has only minimal effect on the resulting hedonic price index, in contrast to log-level hedonic models where such omissions produce much larger distortions. For memory cards, the baseline EP-TV Tornqvist index produces an average annual cumulative chained price change of −20.12%; excluding entering products whose size or speed is outside the range of continuing products changes this to −20.09%, even though roughly 50% of entering products (accounting for 25% of entering-product sales) are excluded. This robustness reflects the EP-TV design: the first-stage residual absorbs time-varying unobservable characteristics that would otherwise confound the hedonic mapping.

Q8. What are the implications for official statistics?

The paper argues that adopting hedonic superlative price indices from real-time scanner data would produce official CPI and PCE price measures that simultaneously correct for substitution bias and quality change, resulting in meaningfully lower measured inflation in categories with high product turnover — likely understating quality-adjusted price declines in current official statistics by several percentage points per year in high-tech consumer goods and by roughly half a percentage point per year in food. The practical case for adoption is that the EP-TV approach can be implemented across heterogeneously encoded data (both structured NPD attributes and unstructured NielsenIQ text), is feasible in real time with transaction data, is relatively insensitive to chain drift (full-imputation hedonic indices avoid the transitory price volatility that contaminates matched-model chained indices), and satisfies bounding properties under general conditions established by Pakes (2003). The paper thus operationalizes long-standing recommendations of the Boskin Commission (1998) that called for exactly these corrections.

Key Concepts

EP-TV hedonic index : the Erickson-Pakes time-varying unobservables hedonic price index, which imputes quality-adjusted price changes for entering and exiting products using a two-step regression that includes lagged residuals from a log-level hedonic to control for products whose unobservable attributes change their market valuations over time; the paper’s preferred hedonic approach.

Feenstra (1994) lambda-ratio adjustment : a correction to the Sato-Vartia CES price index that accounts for product entry and exit by multiplying by (λ_{t,t-1}/λ_{t-1,t})^{1/(σ-1)}, where the lambda terms are the expenditure shares of continuing goods relative to all goods in each period; larger entry shares relative to exit shares produce a downward adjustment reflecting quality improvement from new products.

CES Unified Price Index (CUPI) : the Redding-Weinstein (2020) extension of the Feenstra index that additionally incorporates time-varying product appeal shocks via an unweighted Jevons index (P* ratio) and an unweighted expenditure-share ratio (S* ratio); the paper finds this index is highly sensitive to the common-goods rule and may overstate quality adjustment in practice due to sensitivity to low-share goods.

common-goods rule (CGR) : a threshold rule that restricts the set of goods entering the CUPI’s unweighted components to those with sufficiently large or long-duration market shares, introduced by Redding and Weinstein (2020) to limit the influence of fringe products; the paper finds CUPI results are sensitive to the CGR specification in a way that varies across product groups.

full-imputation hedonic index : a hedonic price index that uses the hedonic mapping to impute price changes for all goods (including continuing goods), rather than only entering and exiting goods; reduces chain drift relative to partial-imputation approaches because imputed prices are less volatile than observed prices.

product turnover : the quarterly entry and exit of products from the market, ranging from 4.5% to 13.5% per quarter in NPD data; the primary mechanism through which quality change is embedded in item-level scanner data and the main source of mismeasurement in matched-model price indices.

Tell Me Something I Don't Already Know: Learning in Low- and High-Inflation Settings

Mon, 01 Jan 0001 00:00:00 +0000

This paper uses randomized control trials (RCTs) applied over time in multiple countries to study whether the economic environment — specifically the level of inflation — affects how agents learn from new information. The main finding is that as inflation rose in advanced economies, both households and firms became more attentive to and informed about publicly available news about inflation, causing them to respond less to exogenously provided information about inflation and monetary policy in the RCT treatments. When agents are already well-informed about the current inflation environment (because high inflation makes it salient), additional information provision moves their beliefs less — the marginal value of information is decreasing in prior attentiveness. Complementary evidence from Uruguay (persistently high inflation) and New Zealand (persistently low inflation) confirms the cross-sectional pattern: agents in high-inflation environments have stronger priors and respond less to information treatments. The results imply that central bank communication interventions are more effective during low-inflation periods when agents are less informed.

Summary of a forthcoming paper, AI-assisted and human-reviewed. See the linked original for the authoritative claims and full conditions.

In depth

Q1. How does the RCT design identify the effect of the inflation environment?

The paper exploits the within-country time variation in inflation — running comparable RCT information treatments before, during, and after the 2021-2023 surge in multiple countries — to identify whether the same information treatment has different effects depending on the prevailing inflation level. By holding the content of the information treatment constant and varying the macroeconomic environment, the paper isolates how environment-driven changes in agent attentiveness mediate the treatment effect.

Q2. Why do agents respond less to information when inflation is high?

When inflation is high and salient, agents actively monitor publicly available inflation news, reducing their prior uncertainty; the Bayesian posterior shift from a given information signal is smaller when the prior is more concentrated. This mechanism — decreasing marginal value of information with prior precision — means that information provision campaigns are subject to diminishing returns as the macroeconomic environment itself provides more signal.

Q3. What does this imply for central bank communication strategy?

Central bank forward guidance and information campaigns are most effective when agents have diffuse priors — i.e., during periods of low, stable inflation when inflation is not salient to households and firms. During high-inflation episodes, agents become more sophisticated but also more resistant to updating on any individual information signal, making communication a weaker tool precisely when the inflation challenge is most acute.

Key concepts

prior attentiveness : the degree to which agents actively monitor publicly available information about inflation; the paper shows this rises with inflation level, reducing the marginal value of additional information provided by RCT treatments.

decreasing marginal value of information : the property that additional information moves beliefs less when agents already have precise priors; the mechanism explaining why RCT treatment effects are smaller in high-inflation environments.