Monetary Policy & Price Dynamics: An Inventory-Theoretic Model

The paper presents a novel approach to understanding price dynamics, focusing on the heterogeneous responses of goods to monetary policy shocks. It introduces a multi-sector extension of the inventory-theoretic model of money demand, a segmented market model, to account for the diverse characteristics of goods. Key characteristics considered are durability, luxuriousness, and cash intensity (the proportion of a purchase paid in cash). The model suggests that the relative prices of durable, luxury, and less cash-intensive goods tend to fall during monetary contractions. This contrasts with existing research focusing primarily on aggregate price levels. The authors acknowledge and build upon previous work that's examined disaggregated price levels and noted heterogeneity in responses to monetary policy shocks, referencing studies by Bils et al. (2003), Erceg and Levin (2002), Barsky et al. (2007), and Boivin et al. (2007). The research aims to explore the reasons behind this heterogeneity using a combination of theoretical modeling and empirical analysis.

To investigate the heterogeneity in price responses, the study analyzes impulse response functions (IRFs) of prices for 189 Personal Consumption Expenditure (PCE) items following a contractionary monetary policy shock. The IRFs are calculated using the methodology of Romer and Romer (2004), normalizing price indices by an aggregate non-durables price index. The findings from this analysis reveal significant differences in how prices respond across goods. For instance, while some relative prices increase (15 items), a substantial number decline significantly (62 items), particularly amongst durable goods, which demonstrate relative price declines for over half of the observed items. The study further examines cumulative impulse responses (CIRs) using both Romer and Romer (2004) regressions and the Factor-Augmented VAR (FAVAR) model (Bernanke et al., 2005), applied to disaggregated price analysis as in Boivin et al. (2007). The analysis explores the relationship between CIRs and the frequencies of price adjustments reported in Nakamura and Steinsson (2007) and Bils and Klenow (2004). However, a clear link between CIRs and the frequency of price adjustment is not definitively established.

The paper then develops an inventory-theoretic model of money demand to provide a theoretical framework for understanding the observed price dynamics. The model expands upon the classic Baumol (1952) and Tobin (1956) models, incorporating subsequent advancements by Grossman and Weiss (1983) and Alvarez et al. (2003), allowing for analysis of the effects of monetary policy shocks on price responses of various goods. A key assumption is the presence of friction in accessing financial markets, where households withdraw money infrequently and spend it over multiple periods. This implies that changes in the aggregate money supply are not immediately reflected in price changes, leading to sluggish price adjustments in the wake of monetary policy shocks. The model integrates a multi-goods setup similar to Bils and Klenow (1998), focusing on the relationship between goods' characteristics (durability, luxuriousness, cash intensity) and price responses to monetary policy shocks. This builds on the existing literature which uses the ‘cash goods vs. credit goods’ distinction (Lucas and Stokey, 1987; Hodrick et al., 1991) by introducing cash intensity.

The model’s theoretical implications are then investigated using US data. The study estimates relative price responses to monetary policy shocks (using Romer and Romer (2004) and FAVAR) for PCE items, testing the relationships between these responses and depreciation rate, luxuriousness, and cash intensity. The findings reveal that depreciation rate and luxuriousness are significant determinants of price responses. The model suggests that price responses are linked to goods’ characteristics, assuming exogenous endowment and price determination based on household consumption decisions. The model considers household heterogeneity in access to financial markets, leading to varied impacts from monetary policy shocks. Simulations show that the relative prices of durable, luxury, and credit goods tend to fall (rise) after contractionary (expansionary) shocks. These findings hold even with changes in model parameters related to financial frictions or money supply shock dynamics.

The paper begins by highlighting the significant heterogeneity in price responses to monetary policy shocks observed across different goods. This heterogeneity contradicts simpler models that assume uniform price reactions. Recent macroeconomic research, including studies by Boivin et al. (2007), has shown a considerable cross-sectional dispersion in price responses at the item level, using data such as Personal Consumption Expenditure (PCE) and Producer Price Indices. These studies, while focusing on different levels of price aggregation, consistently find clear differences in the behavior of prices, especially when comparing durables versus non-durables. This inconsistency between theoretical predictions and empirical observations motivates the development of a more nuanced model.

To further analyze this heterogeneity, the researchers estimate impulse response functions (IRFs) for 189 PCE items following a contractionary monetary policy shock, employing the Romer and Romer (2004) approach. The findings from the IRFs show a considerable variation in how prices react; 15 items see a significant price increase relative to the aggregate non-durables price index, while 62 experience a significant decline. Durable goods show a particularly notable pattern, with over half experiencing price decreases. The study then shifts to analyzing cumulative impulse responses (CIRs) using two advanced econometric methods: Romer and Romer (2004) regressions and Factor-Augmented VAR (FAVAR) from Bernanke et al. (2005), as used in Boivin et al. (2007) The analysis investigates the link between these CIRs and the frequency of price adjustment reported in Nakamura and Steinsson (2007), but the results suggest that the frequency of price adjustment plays a limited role in explaining overall price dynamics after a monetary shock.

The core of the analysis focuses on how the inherent characteristics of goods influence their price responses to monetary policy shocks. The authors introduce a theoretical model incorporating three key characteristics: durability, luxuriousness, and cash intensity. Building upon the work of Bils and Klenow (1998), who demonstrate the impact of durability and luxuriousness on the cyclicality of consumption goods, the current study extends this to monetary policy responses. The inclusion of cash intensity, inspired by the 'cash goods vs. credit goods' distinction in monetary models such as Lucas and Stokey (1987) and Hodrick et al. (1991), adds another layer of complexity. The model suggests that the relative prices of durable, luxury, and less cash-intensive goods should decline following a monetary contraction. The study then tests the model's predictions using US data, evaluating the relationship between estimated price responses and goods’ characteristics such as depreciation rate, luxuriousness, and cash intensity.

The paper acknowledges that while some existing models, like that of Carvalho (2006), suggest a strong link between price adjustment frequency and relative price responses to monetary shocks, their empirical findings do not fully support this. The data, analyzed using both Romer and Romer (2004) and FAVAR methods, show an ambiguous relationship between price adjustment frequency and relative price changes following a contractionary shock. Some results align with the prediction of more negative relative price responses for more frequently adjusting prices, while others show an opposite relationship. This inconsistency raises questions about the role of price adjustment frequency and highlights the need to consider additional factors, such as goods’ characteristics, in explaining observed price dynamics. The study ultimately concludes that while price adjustment frequency might play a role, its impact is likely limited.

The empirical analysis uses US data, primarily focusing on Personal Consumption Expenditure (PCE) items. The study leverages goods-specific parameters from previous research, particularly Bils and Klenow (1998). Depreciation rates are calculated from reported 'expected life of service time' for 43 consumption goods, with an assumption of a unit depreciation rate for services lacking this data. Luxuriousness is assessed using goods-specific income elasticity from Bils and Klenow (1998)'s estimations of Engel curves using Bureau of Labor Statistics panel data. Cash intensity is determined using a dummy variable for food items, aligning with the premise in Kakkar and Ogaki (2002), where foods are considered cash goods. To test the model, impulse response functions (IRFs) are calculated for each PCE item using two econometric approaches: the Romer and Romer (2004) method and Factor-Augmented VAR (FAVAR), following methods employed by Davis and Haltiwanger (2001) and Boivin et al. (2007). The study then regresses the calculated cumulative impulse responses (CIRs) against the goods' characteristic parameters (depreciation rate, luxuriousness, and cash intensity) to examine their influence on price responses to monetary policy shocks. Data limitations, especially concerning the precise measurement of cash intensity, are noted.

The empirical findings largely support the model's predictions regarding the influence of goods' characteristics on price responses to monetary policy shocks. The analysis indicates a strong link between depreciation rate and luxuriousness, and price responses. More durable and more luxurious goods tend to exhibit larger price declines during a monetary contraction compared to the numeraire. The impact of cash intensity, however, is less clear. While the Romer and Romer measure shows a significant, correctly signed coefficient for food (as a cash good proxy), the FAVAR estimation results in an opposite sign, suggesting the role of cash intensity in shaping price responses to monetary shocks requires further investigation. The analysis highlights the limitations of the simplistic cash vs. credit goods categorization, suggesting that payment instruments might be more agent-specific than previously assumed. Data limitations regarding the precise measurement of cash intensity for various goods are also acknowledged.

The study conducts robustness checks by varying model parameters to assess the sensitivity of the findings. The results regarding the relationship between depreciation rates and price responses remain consistent across different parameterizations of money growth persistence (M) and household access frequency to brokerage accounts (N). A similar approach is taken regarding income elasticity (related to luxuriousness) showing a robust relationship between lower income elasticity (more luxurious goods) and greater price declines during contractionary shocks. These findings emphasize the robustness of the model's predictions concerning durability and luxuriousness, strengthening the overall validity of the model in explaining price dynamics following monetary policy shocks. The study emphasizes that the observed patterns are consistent across various time horizons (6-month, 12-month, and 24-month periods).

The model incorporates a key feature: segmented financial and goods markets. Access to the financial market incurs costs for households, resulting in infrequent withdrawals and spending of money over several periods. This creates a situation where only a fraction of the money supply is used for transactions in any given period. This mechanism is central to generating sluggish price adjustments to monetary policy shocks. The model assumes no price-setting friction; instead, the friction lies in accessing the financial market. Households act strategically, balancing the costs of accessing the financial market against the benefits of holding cash for transactions. This infrequent access means that changes in the aggregate money supply do not immediately and proportionally affect prices. The model's structure thus directly explains why prices adjust sluggishly following monetary policy interventions, particularly contractionary ones, a feature previously highlighted in Alvarez et al. (2003).

To analyze relative price movements, the model integrates a multiple-goods framework based on Bils and Klenow (1998), incorporating goods' characteristics such as durability, luxuriousness, and cash intensity. The model does not explicitly model production; therefore, price dynamics are determined solely by household consumption decisions. The model assumes goods are exogenously endowed. Given their differing income levels and access to financial markets, households make consumption decisions based on the characteristics of goods. The concept of a ‘numeraire’ good is used for comparative purposes. These consumption decisions then determine the aggregate demand for each good, ultimately shaping the equilibrium relative prices following a monetary policy shock. This highlights that consumption choices, influenced by goods' characteristics, are the primary driver of the observed dispersion in price responses.

The model incorporates household heterogeneity in their access to financial markets. Households are categorized by their type ('s'), representing the number of months until they can rebalance assets between their brokerage and bank accounts. This staggered access significantly influences how households respond to monetary shocks. Some households experience positive income shocks (becoming richer) and others negative ones (becoming poorer) following the shock. The model emphasizes that the impact of a policy intervention is not uniform, but rather differentially affects various groups of households depending on their type. This differential impact on households’ income, in turn, affects their consumption decisions, directly driving changes in the equilibrium relative prices. This staggered access mechanism is crucial to how monetary policy affects relative prices of goods with varying characteristics.

The study conducts simulation exercises to analyze the relationship between goods’ characteristics and relative price responses. The simulations demonstrate that the relative prices of durable, luxury, and credit goods tend to decline (increase) following a contractionary (expansionary) monetary policy shock. Importantly, these results are robust to various parameter specifications, such as the persistence of the money growth rate and the frequency of asset rebalancing. This robustness underscores the fundamental role of goods’ characteristics, as incorporated in the model, in driving price dynamics. The model demonstrates that the impact on relative prices is largely determined by the interaction between goods’ inherent characteristics and the heterogeneous responses of households to monetary policy shocks. The model's simplicity on the supply side, assuming equal endowments for all agents, focuses the attention on how consumer demand shaped by goods' traits and monetary shocks drives relative price adjustments.

The paper concludes by summarizing its key findings and their implications for understanding price dynamics and monetary policy transmission. The study provides a theoretical foundation for the heterogeneous price responses to monetary policy shocks, demonstrating that goods' characteristics are crucial determinants of price dynamics following such shocks. The inventory-theoretic model of money demand, incorporating goods' durability, luxuriousness, and cash intensity, successfully explains observed price patterns. The model predicts that more durable, luxurious, and less cash-intensive goods experience larger price declines during monetary contractions. This finding is consistent across different parameterizations of the model, emphasizing the robustness of the model's core predictions. The research highlights the limitations of simpler sticky-price models that fail to capture the nuances of price behavior across different goods, suggesting the importance of considering goods' heterogeneity for improved understanding of monetary policy effects.

The empirical analysis, using both Romer and Romer (2004) and FAVAR methodologies, largely confirms the model's predictions. The results show that durability and luxuriousness are significant determinants of price responses, aligning with the model's theoretical framework. However, the role of cash intensity remains ambiguous, with conflicting results depending on the econometric method used. This ambiguity is attributed to the limitations in data regarding the precise measurement of cash intensity for each good, and also to the limitations of the simplifying assumption of goods being purely cash or credit goods, ignoring the more agent-specific nature of payment instrument choice observed in studies such as Borzekowski et al. (2006) and Klee (2008). The paper further notes the ambiguous role of price adjustment frequency, with findings only partially supporting the theoretical predictions from models like Carvalho (2006).

The conclusion points towards areas for future research. The study calls for further investigation into the agent-specific nature of payment instruments rather than the goods-specific nature assumed in many models. The inconclusive results regarding the influence of cash intensity and price adjustment frequency suggest the need for more refined data and modeling techniques to fully capture the complexities of the monetary transmission mechanism. More research is needed to better quantify the role of cash intensity and price adjustment frequency in shaping relative price responses to monetary shocks. The model's success in highlighting the significant impact of goods' inherent characteristics indicates fruitful avenues for future research in incorporating even more fine-grained measures of goods' attributes or exploring alternative model specifications to improve our understanding of price dynamics in response to monetary policy changes.