Welfare Cost of Inflation: A Microeconometric Analysis

The core of the research focuses on employing microeconomic data from Italian households to model the demand for currency. The researchers utilize a generalized Baumol-Tobin model, a framework well-suited for analyzing cash management behaviors. The dataset is rich, encompassing average currency holdings, deposits, interest-bearing assets, bank trip frequency, withdrawal sizes, and ATM card ownership and usage. Critically, the study incorporates the adoption of new transaction technologies, such as ATM cards, and the decision to hold interest-bearing assets as integral parts of the model. This approach acknowledges that the demand for currency is not static but evolves with technological advancements and financial choices. The resulting model offers a more nuanced understanding of the factors driving currency demand than traditional models. The paper's strength lies in its focus on individual-level data, which provides a more granular perspective compared to aggregate time-series data, overcoming issues of aggregation and allowing for detailed analysis of heterogenous cash management practices among households.

The empirical findings reveal interest rate and expenditure flow elasticities of the demand for currency that closely align with theoretical predictions derived from standard inventory models. However, a significant divergence emerges when comparing households with and without ATM cards. This highlights the substantial influence of financial innovation on the demand for money. The estimated parameters, which are robust across various econometric specifications, allow the researchers to construct a measure of the welfare cost of inflation, offering a more rigorous approach than traditional methods. The calculated welfare cost is comparatively low (approximately 0.1% of consumption or less) and varies significantly within the population. The analysis extends beyond the average currency stock, using data on bank trips and average withdrawals to corroborate the model's predictions. The consistency between these variables validates the model's efficacy and reinforces the study's findings.

The success of this study hinges on the unique characteristics of the data. The dataset provides exceptionally detailed information relevant for estimating inventory models of money demand, including average currency holdings, the number of trips to the bank, and withdrawal sizes. The Italian context proves beneficial because checking and saving accounts are predominantly interest-bearing assets, providing a clear and readily available measure of the opportunity cost of holding currency. The use of the nominal interest rate on deposits, as a proxy for the opportunity cost, strengthens the model's precision. The dataset's value is further enhanced by its tracking of ATM card ownership and usage, allowing the researchers to analyze the effect of technological progress on money demand. The Italian banking system, with its regional variation in nominal interest rates on deposits and the widespread adoption of ATM cards, offers valuable opportunities for identifying the parameters of the demand for currency. This combination of detailed data and a unique institutional context allows for a more rigorous and refined analysis of the demand for money.

The econometric specification tackles the inherent complexities of modeling household financial decisions. The decisions to hold interest-bearing assets and to adopt ATM cards are treated as discrete choices, acknowledging their endogenous nature and potential impact on the demand for currency. The model explicitly addresses selection bias, recognizing that only households holding interest-bearing deposits face a direct opportunity cost of holding currency. This is crucial because not all households in the sample utilize interest-bearing accounts, a factor that needs to be corrected for to obtain unbiased estimates. The model accounts for the potential endogeneity of ATM card adoption, thereby ensuring that the estimated parameters accurately reflect the true relationships. This sophisticated approach distinguishes this study from prior work, enhancing its accuracy and robustness.

The researchers adapt the McCallum-Goodfriend extension of the Baumol-Tobin model to incorporate the influence of technological innovations in the payments system and the heterogeneous behavior of consumers regarding interest-bearing assets. The model explicitly incorporates the choice to own both interest-bearing assets and ATM cards as choice variables, acknowledging that adoption decisions depend on a trade-off between benefits and costs. The consumer’s decision to open an account is contingent on whether the benefits (reduced transaction time and foregone interest) exceed adoption costs. The model allows for different demand parameters across households depending on their ATM ownership status. The use of ATM cards is modeled explicitly, recognizing that it affects the parameters of the demand for currency, although not its fundamental nature. This nuanced approach is crucial to understanding how technological advancements influence the demand for money.

Identification of the money demand equation requires variables that affect the adoption of banking services (accounts and ATM cards) but do not directly influence the average stock of currency. Fixed costs associated with these adoption decisions are ideal, but direct measurement is challenging. Instead, the number of ATM points in the area of residence is used as an instrumental variable (IV), leveraging potential network externalities. This IV is justified on the grounds that the cost of ATM card adoption is likely to be lower in regions with higher ATM availability, increasing adoption probability. However, the authors acknowledge potential endogeneity concerns (ATM installation may be demand-driven) and address them by employing alternative instruments reflecting the structure of the banking sector: the share of deposits held by the five largest banks and the share of deposits held by cooperative banks in the province. This robust methodology ensures that the estimated coefficients for the demand for currency are not spurious or influenced by omitted variables.

The empirical analysis yields precise estimates for key parameters of the demand for money. A crucial finding is the negative interest rate elasticity, ranging from -0.3 for households without ATM cards to -0.6 for those with ATM cards. This confirms the expected inverse relationship between the interest rate and currency holdings, with ATM users exhibiting a stronger response. Furthermore, the study reveals a consumption elasticity significantly below unity, indicating substantial economies of scale in cash management. This suggests that as consumption increases, the proportional increase in currency holdings is less than one-to-one. This finding is consistent with the theoretical predictions of inventory models, adding credence to the overall model's validity. The robustness of these elasticity estimates across several model specifications underscores their reliability. The precise nature of these estimates allows for a detailed investigation of how factors like access to ATM technology influence cash management practices.

The estimated parameters enable the calculation of the welfare cost of inflation, using a method analogous to Bailey's triangle but based on a rigorous microeconometric framework. This method delivers a more precise welfare cost estimate than traditional approaches. The results show that the welfare cost of inflation varies considerably across households, reflecting differences in behavior and access to financial technologies. Notably, however, this welfare cost is consistently low, never exceeding 0.1 percent of consumption. This contrasts sharply with estimates obtained by other researchers, suggesting that the presence of interest-bearing assets substantially reduces the welfare cost in economies where a large portion of the money stock pays interest. The low welfare cost estimation serves as a point of differentiation with previous research and highlights the significance of considering the complete financial landscape of households rather than only currency when modeling the implications of inflation.

The study conducts extensive robustness checks to ensure the reliability of its findings. The main results remain consistent across various changes in the econometric specification. For example, alternative definitions of consumption, exclusion of retired households, and the use of year dummies instead of a time trend did not materially alter the core findings of the model. The consistent finding of a higher interest rate elasticity among ATM cardholders across diverse model specifications adds weight to the conclusion that technological innovation dramatically affects cash management behavior and, thus, the demand for currency. The model's validation extends beyond the primary estimation of average currency holdings. The analysis of the number of bank trips and average withdrawals provides additional supportive evidence, strengthening the overall model's credibility and predictive power. The convergence of results across different aspects of the model offers significant validation for the chosen framework and its underlying assumptions.

The study's primary contribution lies in its rigorous quantification of the welfare cost of inflation, a cost stemming from the inefficiencies of transacting with non-interest-bearing currency. Unlike previous research relying on aggregate time-series data, this study uses a microeconometric framework, leveraging household-level data to estimate the welfare cost. This approach allows for a more precise calculation, accounting for the heterogeneity of household cash management practices and their access to financial technologies. The methodology mirrors Bailey's triangle but incorporates the nuanced estimations of interest and transaction sensitivities derived from the model. This refined method provides a more accurate and comprehensive understanding of the welfare cost of inflation. A key finding is that the welfare cost, though varying among households, remains notably low – at or below 0.1 percent of consumption – challenging previous higher estimations in the literature.

The study's findings on the welfare cost of inflation differ significantly from those of Lucas (2000) and Mulligan & Sala-i-Martin (2000). Lucas's estimation, based on aggregate US data, yielded a substantially higher welfare cost. This discrepancy is attributed to differences in the underlying data and the treatment of interest-bearing assets. The authors highlight that the aggregate interest rate elasticity, a crucial factor in calculating the welfare cost, is sensitive to the proportion of households holding such assets. Mulligan and Sala-i-Martin (2000) acknowledged this issue, noting that a considerable portion of US households held only currency and checking accounts, implying high transaction costs for investing in interest-bearing assets. Their approach focused on the extensive margin, evaluating the elasticity at low interest rates. In contrast, this research utilizes household-specific interest rate data and explicitly models both intensive and extensive margins, generating a more comprehensive and accurate assessment.

A central argument of the paper is that the significant difference in welfare cost estimations stems from the proportion of interest-bearing assets held by consumers. In economies where a substantial portion of the money stock is interest-bearing, the welfare cost of inflation is likely to be lower. This is because the opportunity cost of holding currency is significantly reduced when other interest-paying assets are readily available. The study meticulously analyzes the composition of monetary assets, emphasizing the importance of distinguishing between currency and interest-bearing deposits. Unlike previous studies that often treat a broader monetary aggregate (e.g., M1) as non-interest-bearing, this paper uses the nominal interest rate on deposits to provide a proper measure of the opportunity cost of holding currency, leading to different results. The choice of monetary aggregate is highlighted as a key source of the discrepancies with other studies such as that of Lucas (2000), who used a broader aggregate that does not account for interest-bearing characteristics of significant portion of the money stock.

The analysis extends beyond the average currency holdings to examine the determinants of withdrawal amounts. The study uses data on three types of withdrawals: those made at a bank counter by ATM cardholders, those at a bank counter by non-ATM cardholders, and ATM withdrawals. Across all three withdrawal types, the interest rate elasticity is consistently negative and statistically significant, indicating that larger withdrawals are associated with lower interest rates. The transaction variable (a proxy for the scale of transactions) shows a positive elasticity, suggesting that larger transactions lead to larger withdrawals. However, for ATM withdrawals, the elasticity of the transaction variable is significantly lower, highlighting the impact of technology in cash management. These results align closely with the model's predictions and demonstrate substantial economies of scale in cash management, particularly for ATM users. The consistency of these findings with the main estimates further strengthens the validity of the model.

The research further investigates the relationship between the number of trips to the bank (both for withdrawals and deposits) and the fraction of income received in cash. The analysis explores these variables to add more dimensions of cash management behavior under different interest rate scenarios. The number of trips is positively correlated with transaction volume, consistent with inventory models of money demand. The interest rate exhibits a positive elasticity in this context, suggesting that households adjust their bank visit frequency in response to interest rate changes. Separating ATM trips from total bank trips reveals a stronger interest rate responsiveness for ATM trips, reflecting the efficiency gains from this technology. Finally, examining the share of income received in cash indicates a negative association with the nominal interest rate. Households facing higher interest rates tend to reduce the proportion of their income received in cash, suggesting an active effort to minimize the time cash is held and reduce their exposure to inflation's effects. This behavior adds another layer of support for the core conclusions of the study.

The study acknowledges some limitations in the data. The variable ‘trips to the bank’ might not perfectly capture the theoretical concept due to ambiguities in its definition. This potentially impacts the precision of the estimations. Furthermore, the discrete nature of the ‘trips to the bank’ variable and the use of an ordered probit model for its estimation require considerations of potential selectivity biases, which the analysis does not fully address. Despite these limitations, the findings from the analysis of withdrawals and trips, while needing some cautious interpretation, consistently support the findings from the central analysis and further reinforce the model's overall validity. The findings related to the income received in cash, however, appear more robust and further support the model’s implications for household’s cash management strategies under different interest rates. This approach enhances the study's overall robustness and provides a more comprehensive perspective on the dynamics of cash management behavior.

The study's empirical analysis relies heavily on a unique dataset from the Italian Survey of Households Income and Wealth (SHIW). This dataset, covering the period from 1989 to 1995, offers unparalleled detail on household-level cash management practices. The data includes information on average currency holdings, deposits in interest-bearing accounts, the number of trips made to banks, the size of withdrawals, and ATM card ownership and usage. Furthermore, the data encompasses consumption and income flows, as well as demographic and occupational characteristics. The richness of this dataset allows researchers to address several challenges inherent in modeling money demand, particularly when considering the impact of new technologies on cash management. The availability of detailed information on a range of variables proves crucial for accurately estimating the parameters of a sophisticated version of the Baumol-Tobin model. The Italian context, where bank deposits are largely interest-bearing, simplifies the analysis by providing a readily available measure of the opportunity cost of holding currency, unlike in countries where some deposits might not offer interest.

All monetary variables in the SHIW dataset are carefully deflated using the Consumer Price Index (CPI) and converted into euros for consistency. This deflation is crucial for accurately analyzing the real demand for currency and avoiding spurious correlations caused by inflation. The dataset reveals high average currency holdings at home, exceeding 500 euros in 1989, indicating that Italy's demand for currency was exceptionally high by international standards during this period. However, the study observes a downward trend in the currency-consumption ratio, decreasing from 4% in 1989 to 2.8% in 1995. This decline is mainly attributed to the increased adoption of ATM cards, a key element of financial innovation during the period. The high proportion of households (approximately 85%) with interest-bearing accounts indicates a developed financial system. Furthermore, the data provides a crucial point for data validation: the total yearly cash expenditures, calculated independently through both average withdrawal and expenditure data, show a high degree of consistency. The study utilizes this feature to support the reliability of the data. The observed consistency serves as a critical check on the quality and integrity of the reported data.

The data exhibits substantial variation in nominal interest rates on deposits, offering both geographical and time-series variability. The researchers exploit this variation to precisely estimate the interest rate elasticity of the demand for currency. Importantly, this variation allows for a robust identification strategy, which is critical in econometric models to ensure unbiased and reliable estimates. The study specifically leverages data on the diffusion of ATM cards, whose ownership tripled during the sample period. The dataset tracks both ATM card ownership and usage, providing critical insights into the impact of technological innovation on money demand. The information on the number of ATM points in the province of residence complements the card ownership and usage data, strengthening the analysis of the impact of technological progress on cash management. This combination of interest rate data and information on ATM adoption provides a comprehensive and detailed picture of household behavior and allows the study to model the effects of technological progress on the demand for money and, ultimately, on the welfare cost of inflation.