Precautionary Balances & Money Velocity

The study begins by highlighting the historically low velocity of money circulation in the United States from 1892 to 2004. Specifically, checkable deposits and currency in circulation (M1*) averaged three months' worth of GDP, even though households received income far more frequently. This implies significant unspent money. The recent decline to approximately one month's worth of GDP further emphasizes this anomaly. The authors posit that a precautionary motive for holding money, stemming from uncertain expenditure needs, explains this low velocity. This sets the stage for investigating the precautionary demand for money using a suitable theoretical model and empirical analysis of US data. The observed discrepancy between the frequency of income receipt and the relatively large amount of unspent money held by households directly motivates the need for a model of precautionary balances.

The authors position their work within the context of existing literature on precautionary demand for money, acknowledging both supporting and dissenting viewpoints. Svensson's (1985) work on precautionary demand in a representative agent model with cash-in-advance constraints is cited, highlighting the role of preference shocks. Conversely, the authors discuss Hodrick, Kocherlakota, and Lucas' (1991) influential critique which questioned the quantitative significance of precautionary demand in an aggregated model. Their study, however, aims to address these earlier criticisms by constructing a disaggregated search model. The chosen framework builds on the monetary search models of Kiyotaki and Wright (1989), Shi (1997), and Lagos and Wright (2005), incorporating features like divisible money and competitive search to provide a more realistic and tractable approach for understanding precautionary balances and their effects on the velocity of money.

This section delves into the details of the developed search model. The model explicitly incorporates preference shocks experienced by households, which are crucial for generating precautionary money holdings. The model structure involves a decentralized goods market where buyers and sellers interact bilaterally, with terms of trade determined through a competitive search process. The inclusion of a centralized credit market within each village allows for borrowing and lending but does not extend across villages to reflect limits in financial contract enforcement. The timing of preference shocks – occurring after credit markets close – is key to creating the precautionary demand. The buyer-seller decision and financial decisions are meticulously modeled, incorporating budget constraints and the need to hold sufficient money for contingent payments, which are directly related to precautionary balances and the need to handle unexpected expenditures.

The authors estimate their model using US data from 1892 to 2004, utilizing two measures of money supply: M1 and M1* (M1 excluding currency circulating abroad). M1* is chosen as the primary measure due to its greater relevance after 1964, when the importance of foreign currency became more substantial. The model successfully captures the positive correlation between velocity and interest rates, a key feature of the historical data. Critically, the empirical implementation demonstrates a significant decline in precautionary balances over the sample period, strongly influencing the elasticity of money demand and the welfare cost of inflation. This decline is closely related to interest rate changes and the overall velocity of money. The close fit between the model's predictions and the observed data validates the model's structure and its capacity to capture the essential dynamics of money demand and its impact on economic activity.

The study's key policy implication stems from the observed plummeting of precautionary balances in recent decades. This is attributed to advancements in information and communication technologies, allowing individuals to more easily manage unexpected expenditures without holding excessive precautionary balances. Consequently, the demand for money has decreased, and its elasticity has fallen. The model reveals that the seigniorage and the welfare cost of inflation are now significantly smaller than they were in earlier periods, leading to a call for reevaluating the established knowledge in monetary economics. The conclusions highlight the importance of understanding the impact of technological change on monetary policy and economic welfare, particularly how it affects precautionary savings and the overall velocity of money. The significant shift in monetary parameters underscores the need for adapting traditional frameworks to account for the effects of technological innovations.

The core of the paper's contribution lies in its development of a novel search model to explain precautionary money demand. Unlike previous aggregated models, this model is disaggregated, focusing on individual household behavior. A key feature is the introduction of idiosyncratic preference shocks, which directly affect households' willingness to purchase goods. These shocks, occurring after the decision to allocate money and bonds, are critical to modeling the precautionary demand for money. The model incorporates both decentralized and centralized markets: decentralized goods markets where buyers and sellers search for trading partners bilaterally, and a centralized credit market within each village that facilitates borrowing and lending. The assumption of competitive search, rather than Nash bargaining, determines the terms of trade endogenously, offering a more realistic representation of market dynamics. The strategic interaction between buyers and sellers in this competitive setting significantly impacts money demand and the resulting velocity of money.

The model utilizes competitive search as a mechanism to determine the terms of trade. This contrasts with the more common use of Nash bargaining in the literature. Competitive search determines the split of the trading surplus endogenously through competition among sellers, leading to efficient search decisions. The authors argue this is advantageous because it produces efficient search decisions, unlike Nash bargaining or Walrasian pricing which would be inefficient under the Friedman rule. This innovative approach avoids the need for exogenous bargaining weights, adding to the model's rigor. The model also introduces a simplifying assumption of efficient matching (the short side of the market is always served), abstracting from the uncertainty of meeting a trading partner. This simplification enables a more tractable analysis of the key mechanisms driving precautionary money demand and velocity, highlighting the impact of the preference shocks on household decisions.

A critical consequence of the model's structure is the emergence of precautionary balances and liquidity constraints. Because the preference shocks occur after credit markets close, individuals cannot readjust their money holdings after the shocks are revealed. This timing is essential for precautionary balances to persist. Some individuals might end up with unspent money, while others face binding cash constraints, leading to inefficiently low quantities of goods purchased. The model highlights the tradeoff between holding sufficient money to cover potential large preference shocks (thus decreasing velocity) and the opportunity cost of holding money. The authors contrast their model with the work of Berentsen, Camera, and Waller (2004), which introduces banks to eliminate precautionary balances. Their model focuses on the impact of unexpected expenditure needs and the role of money in a setting without continual rebalancing possibilities, directly influencing the velocity of money and the welfare implications of inflation.

To account for the observed upward trend in the velocity of money in the US, which the authors attribute to advancements in information technology, the model is extended. This extension introduces the possibility for a fraction of individuals to rebalance their portfolios after learning their preference shocks but before trading in the goods market. This reflects the improved ability to convert assets quickly and easily, reducing the need for large precautionary balances. The introduction of this parameter (θ, representing the fraction of individuals who can rebalance) adds a layer of realism and allows for a more nuanced investigation of the factors affecting precautionary balances and the resulting velocity of money. The model analyzes how this parameter impacts the interest elasticity of money demand and welfare consequences of inflation, emphasizing the role of technological change in altering the dynamics of money demand.

The empirical analysis uses US data from 1892 to 2004 on velocity of circulation and nominal interest rates. Two measures of money supply are considered: M1 (currency and checkable deposits) and M1* (M1 minus currency held abroad). The authors prioritize M1* for its greater accuracy after 1964, when data on foreign currency became available. The data sources include the US Bureau of the Census, the St. Louis Federal Reserve, and the DRI series. The choice of M1* is justified by its greater meaningfulness, but M1 is also included for comparison with prior studies. The analysis focuses on the velocity of M1* and its relationship to interest rates, attempting to validate the model's predictions against real-world data. Nonlinear least squares estimation is employed, treating velocity as the dependent variable and converting the annual data to bi-weekly frequency to align with the model's time period.

The model demonstrates a remarkably close fit to the historical data on velocity and interest rates. The authors visually represent this fit by plotting the actual and model-predicted annual velocities, demonstrating close alignment. To further examine the model's accuracy, they analyze the deviations of actual and predicted velocities from the trend velocity (calculated at the average interest rate of 4.53 percent). This detrending analysis reveals that the model accurately predicts deviations from the trend, even capturing significant fluctuations, such as those during the Great Depression and the period of high interest rates in the 1960s-1980s. The model's ability to accurately predict these fluctuations highlights its robustness and the validity of its underlying mechanisms in explaining the observed velocity of money.

The empirical results reveal a dramatic decline in precautionary balances over the latter part of the sample period. This has substantial implications for monetary policy. For example, the semi-elasticity of velocity (the responsiveness of velocity to interest rate changes) declined significantly over time. The government's ability to collect seigniorage at a given inflation rate also fell substantially. The welfare cost of inflation, previously estimated to be around 1 percent of consumption for a 10 percent increase in inflation above the Friedman rule, has also significantly reduced. This change is attributed to a shift from a high and elastic demand for money to a low and inelastic one. This dramatic reduction in the cost of inflation highlights a significant change in the monetary landscape and warrants a reassessment of conventional wisdom surrounding inflation and its impact on the economy, showing the direct consequence of the reduction in precautionary money holdings.

The dramatic reduction in precautionary balances has profoundly altered the welfare cost of inflation. Historically, a 10 percent increase in inflation from the Friedman rule resulted in approximately a 1 percent reduction in consumption—consistent with Lucas (2000) estimates. However, the model reveals that this cost has plummeted in recent decades due to the decline in precautionary balances. This reduction is directly linked to changes in the demand for money; the shift from a high and elastic demand to a low and inelastic one has compressed the area under the money demand curve, thus reducing the welfare cost. The decrease in precautionary balances has also impacted the relationship between inflation, GDP, and seigniorage, further emphasizing the need to reconsider the conventional wisdom surrounding inflation and its effects on the economy.

The decline in precautionary balances has significantly reduced the government's ability to collect seigniorage (revenue generated from printing money). The model shows that at a 4.53 percent nominal interest rate, seigniorage was considerably higher in earlier periods (0.4 percent of GDP from 1892-1948) compared to the later period (0.11 percent in 2004). The decreased reliance on precautionary balances has also reduced the elasticity of money demand. The semi-elasticity of velocity, which measures how velocity changes in response to changes in interest rates, also fell considerably. These findings suggest that traditional monetary policies may need to be recalibrated in light of these changes, necessitating a new understanding of how monetary policy instruments affect the economy when precautionary demand is significantly lower and less responsive to interest rate adjustments.

The authors attribute the observed decline in precautionary balances primarily to advancements in information and communication technologies. These advancements have enabled individuals, with the assistance of banks and other financial institutions, to more easily manage unexpected expenditure needs without the need for holding substantial precautionary cash balances. This has fundamentally altered numerous aspects of monetary economics, including the demand for money (both its level and elasticity) and the associated welfare costs of inflation. The authors explicitly state that the conventional wisdom surrounding many dimensions of monetary economics must be revisited to reflect the changed circumstances. This observation calls for a critical re-evaluation of established models and theories, emphasizing that technological progress has profoundly impacted how we view money demand and its implications for economic stability and policy making.

The conclusion reiterates the model's success in explaining the historically low velocity of money circulation and its correlation with interest rates. The rigorous microeconomic foundations of the model, incorporating precautionary balances, provide a robust explanation for these observed phenomena. The empirical analysis, based on US data from 1892 to 2004, strongly supports the model's predictions. The close fit between model predictions and actual velocity data, particularly when considering deviations from the trend, underscores the model's ability to capture the essential dynamics of money demand and velocity. The model's accuracy in forecasting velocity fluctuations across different economic periods, such as the Great Depression and the high-interest rate era of the 1960s-1980s, further strengthens its validity and relevance.

A central finding is the dramatic decline in precautionary balances over the past three decades. This observation is attributed to significant improvements in information and communication technologies. These advancements have facilitated easier and faster conversion of assets, enabling individuals to more effectively manage unexpected expenditure needs without excessive precautionary money holdings. This shift has fundamentally transformed various aspects of monetary economics, influencing not only the level of money demand but also its elasticity. The conclusion emphasizes the importance of recognizing these technological influences on monetary phenomena, highlighting how technological progress can alter the relationship between precautionary savings and the velocity of money.

The decreased reliance on precautionary balances has led to a lower demand for money and reduced elasticity. The implications are substantial for monetary policy, including reduced seigniorage and a significantly lower welfare cost of inflation compared to earlier periods. The authors strongly advocate for a reassessment of conventional wisdom in monetary economics, given the profound transformation brought about by technological advancements. Traditional policy frameworks need to be adjusted to account for the changed dynamics of money demand. This conclusion underscores the need for continued research and the development of new models that explicitly incorporate technological factors influencing the demand for money, its impact on velocity, and the broader implications for monetary policy and welfare.