Money Demand: A Financial Approach

The core observation is that the distribution of money holdings across households mirrors the distribution of financial assets, exhibiting significantly higher inequality than the distribution of consumption levels. This is measured using the Gini coefficient. In the US during 2004, the Gini coefficient for consumption was approximately 0.3, income around 0.5, while both net wealth and money reached approximately 0.8. This pattern consistently held across various definitions of money, time periods, and after controlling for life-cycle effects. This stark contrast presents a challenge to prevailing macroeconomic theories directly linking money demand to consumption. These theories, which encompass various approaches like cash-in-advance constraints (CIA), money-in-the-utility function (MIUF) models, or shopping-time models, predict that money holdings and consumption should be similarly distributed, a prediction that the data clearly refutes. The empirical evidence reveals that the Gini coefficients for money and consumption should not be equal, highlighting a significant puzzle requiring further investigation.

The empirical analysis leverages data from both the US and Italy. For the US, the 2004 Survey of Consumer Finance is utilized, providing information on various aspects of household finances. In Italy, the 2004 Italian Survey of Households’ Income and Wealth serves as the corresponding data source. In both cases, the study focuses on households where the head is aged between 35 and 44, this age range being chosen to mitigate life-cycle effects on wealth accumulation and consumption patterns. The distribution of money is primarily characterized using the Gini coefficient, although the study notes that other inequality measures would yield consistent results. The analysis of the data reveals a strong positive correlation between money holdings, consumption, income, and wealth. However, importantly, the ratio of money to total financial assets shows a negative correlation with wealth. In other words, the wealthier the household, the smaller is the proportion of their portfolio held as money, which is inconsistent with simple models where money demand is directly proportional to consumption. The high level of inequality in money holdings in contrast to consumption levels, as evidenced by these high Gini coefficients, forms the basis of the research and the subsequent modelling approach.

Existing macroeconomic theories linking money demand directly to consumption, employing mechanisms such as CIA, MIUF, or shopping-time considerations, struggle to reconcile the observed disparities between the distribution of money and consumption. While some models suggest economies of scale in transaction technologies, with richer households needing proportionally less money to finance consumption due to credit use, these fail to fully explain the observed data. These theories often predict a homothetic relationship between money and consumption, leading to identical Gini coefficients for both, a stark departure from the empirical findings. The presence of unobserved heterogeneity in preferences or transaction technologies might seem like a possible explanation, but the amount of unobserved heterogeneity required to account for the observed differences is unreasonably large. Therefore, the paper's approach focuses on building a structural model to reproduce the observed joint distribution of money, financial wealth, and consumption, avoiding assumptions of extensive unobserved heterogeneity. This structural approach, using a heterogeneous agent model, aims to provide a more robust and comprehensive explanation for the puzzle.

The model successfully replicates the empirical distribution of money holdings, achieving a Gini coefficient of 0.80, which closely matches the observed value in the US data. This successful replication is particularly noteworthy given that the model's structure is relatively parsimonious, relying on only a few key parameters. The model's ability to reproduce this key characteristic of the data lends strong support to the model's underlying mechanisms and assumptions, particularly the inclusion of both transaction and financial frictions. The model also does a good job of replicating the money holdings of those at the lower end of the wealth distribution. The model's ability to capture this aspect suggests the financial motive for holding money is a critical component of understanding money distribution inequality. The generated Gini coefficient for consumption is slightly higher than that observed empirically, which could be a possible point for further refinement and model improvement. Further analysis shows that the model correctly simulates the fraction of wealth and money held by various wealth subpopulations, especially at the lower end of the wealth distribution, although some discrepancies remain for the wealthiest households.

To isolate the relative contributions of the two types of frictions (transaction and financial), the model is run under different scenarios. In one scenario, the financial market friction (portfolio adjustment cost) is removed, leaving only the transaction motive (cash-in-advance constraint). This produces a dramatically lower level of overall money holdings and a Gini coefficient for money significantly lower than the empirically observed value. Conversely, when the transaction friction is removed, leaving only the financial motive, a significant amount of money demand remains. This decomposition shows that financial motives account for the bulk (85-95%) of the total money stock, while the transaction motive explains only a small portion (15%). This result strongly indicates that the financial friction is the primary driver of the observed inequality in money holdings. The high inequality in observed money holdings can only be replicated if the financial motive is sufficiently large, showing the model's sensitivity to this parameter. The interaction of these two frictions is non-linear. The inclusion of both frictions produces a total money stock greater than the sum of money holdings that would be predicted under either friction alone. The combined effects of the two frictions are important for understanding the observed money distribution and dynamics.

The model generates insights into household-level saving behavior and portfolio choices. Low-income households tend to quickly deplete their financial assets and hold only minimal money balances due to the transaction cost. The combination of the financial motive and the cash-in-advance constraint result in agents holding both money and financial assets in equilibrium, even though money has a lower return than financial assets. High-income households exhibit different dynamics, accumulating financial assets and periodically participating in financial markets to adjust their portfolios, which contributes to the high inequality in money holdings. The simulation provides a visual illustration of this behavior by graphing the participation decisions of households with different income levels, where the size of the 'inaction region' - the amount of time the households do not participate in financial markets - varies depending on the amount of financial and money balances held. These findings highlight the critical role that infrequent participation in financial markets, due to the portfolio adjustment cost, plays in generating the observed high inequality in money holdings and in creating the empirical link between money holdings and financial assets.

The model's main contribution is demonstrating that incorporating both transaction and financial market frictions is crucial for generating a realistic distribution of money across households. The model accurately replicates the high level of inequality in money holdings observed in the data, a feature that existing macroeconomic models struggle to explain. A decomposition of money demand reveals a surprising finding: financial motives—stemming from the cost of adjusting financial portfolios—account for the overwhelming majority (85-95%) of total money demand. This contrasts sharply with standard models that emphasize transaction motives as the primary driver of money holdings. The model demonstrates that both transaction costs (via the cash-in-advance constraint) and financial market frictions are necessary to capture the full complexity of money demand. The transaction motive explains why many households hold only small amounts of money, while the financial motive explains the substantial inequality in money holdings by explaining why a few households hold disproportionately large amounts. The model's success in reproducing the empirical distribution of money provides strong support for the importance of considering these financial frictions within macroeconomic models.

The results challenge existing theories of money demand that predominantly focus on transaction motives. The study highlights the significant role of financial market imperfections in determining money holdings and their distribution. This has important implications for macroeconomic modeling and monetary policy analysis. Understanding the distribution of money is vital for assessing the real and welfare effects of inflation. The model's ability to replicate this distribution offers a more accurate framework for analyzing the impact of policy interventions. The findings imply that policies that affect financial market structure and transaction costs can have significant and potentially indirect impacts on money demand, effects which are often overlooked in simplified models. This research underlines the need for more sophisticated models incorporating household heterogeneity and financial frictions to better understand monetary phenomena and inform effective policy design.

The authors suggest several avenues for future research. One key area is the exploration of simpler methods for incorporating the model's key findings—the importance of both transaction and financial frictions in determining money distribution—into larger-scale macroeconomic models. This is important because the current model, while insightful, is relatively small-scale. This would make it easier to integrate these insights into broader macroeconomic analyses and simulations. Further research could also examine the welfare implications of the unequal distribution of money holdings revealed by the model. Investigating how this inequality affects aggregate economic outcomes and societal well-being would be beneficial. Additionally, exploring the interaction between the two frictions in more detail could offer further insights into the dynamics of money demand and its distribution. This might involve developing more nuanced representations of transaction technologies and financial market structures.