US Money Velocity: A Banking Explanation

The study's primary focus is on the long-term behavior of US M1 money velocity between 1919 and 2004. A key finding is the presence of long cycles in M1 income velocity, fluctuating around a consistent upward trend averaging 1.25% per year. This long-term upward trend in money velocity is a central observation of the research, setting the stage for further investigation into the underlying causes and mechanisms. The researchers aim to explain these cyclical patterns using a dynamic stochastic general equilibrium (DSGE) model and annual time series data. This time period encompasses significant economic events, providing a rich context for analyzing the relationship between money velocity and broader economic conditions. The selection of this particular period allows the researchers to study the behavior of M1 money velocity across diverse economic climates, including periods of relative stability and significant economic shocks. This detailed analysis establishes a baseline for understanding the long-term dynamics of M1 money velocity and serves as a foundation for the subsequent modeling and analysis within the paper.

To understand the observed long cycles, the researchers employ a DSGE model. The model incorporates three key shocks: shocks to credit productivity, money supply, and goods productivity. These shocks are introduced into the model and, together with observed data, are used to explain the movements in velocity. The model's design is crucial in capturing the intricacies of the relationship between the three shocks and money velocity, thus allowing for a detailed analysis of their individual and combined effects. The use of a DSGE model enables the researchers to analyze how these different economic forces interact and influence money velocity over time. The model's ability to capture the observed trends is then used to evaluate the success of the model and to make inferences about the underlying economic relationships. This methodological choice allows for a more nuanced understanding of the factors driving money velocity cycles compared to simpler approaches.

The paper examines velocity volatility across both business cycle and long-run frequencies. The analysis considers the volatility of M1 money velocity, investigating how this volatility is affected by the three shocks at both shorter and longer time horizons. A key aspect is the analysis of periods where filtered velocity turns negative. This occurred during the 1930s Great Depression, the 1987 stock market crash, and around 2003. The negative filtered velocity highlights potential economic instability that is associated with the behavior of money velocity. The research explores whether money and credit shocks are more influential during unstable economic periods, while goods productivity shocks may dominate during more stable times. The finding of a changing relative importance of these shocks across different economic periods adds to the paper's significance, demonstrating the model's applicability to distinct economic environments. The investigation into these contrasting economic phases allows for a comprehensive evaluation of the role of monetary phenomena in driving M1 money velocity.

The model's velocity is shown to be stable along a balanced growth path. This path is characterized by endogenous growth and decentralized banking. The decentralized banking system produces exchange credit, which is a unique element of the model. The existence of a stable balanced growth path demonstrates the model's internal consistency and helps to validate its theoretical underpinnings. This stable trajectory in the model provides a benchmark against which the observed cyclical fluctuations in M1 money velocity can be compared. The characteristics of the balanced growth path—endogenous growth and decentralized banking producing exchange credit—are important elements of the model's structure and contribute to its capacity to explain the observed long-term trends. The stability of the model's velocity is critical in providing a credible framework for analyzing the impact of shocks on money velocity. The ability to isolate the impact of the identified shocks against this stable background is a significant contribution of the study.

The core of the methodology is a DSGE model featuring endogenous growth and a decentralized banking sector. Unlike previous models that assume an ever-increasing money velocity, this model incorporates a banking sector that produces exchange credit using a constant-returns-to-scale technology (as in Clark, 1984). This approach is a significant departure from earlier work, offering a more realistic representation of how credit creation impacts money velocity. The model's inclusion of a realistic credit production mechanism leads to a stationary velocity along the balanced growth path, a key difference from other endogenous growth models. This approach also contrasts with models that postulate a general transaction cost form for credit. The model integrates endogenous growth with business cycles, allowing for the examination of the interaction of short-term and long-term factors. The resulting framework is designed to produce a stationary velocity along a well-defined balanced growth path, offering a new perspective on the determinants of money velocity.

The model incorporates three types of shocks: shocks to credit sector productivity, money supply, and goods sector productivity. These shocks serve as the driving forces behind the fluctuations in money velocity. The inclusion of a credit sector productivity shock is a novel aspect of the model and allows for analysis of how changes in the efficiency of credit production affect money velocity. This approach is different from earlier models that predominantly focused on money supply and goods productivity shocks. The methodology to construct these shocks draws on annual time series data and techniques from Ingram et al. (1994).The shocks' construction involves an iterative process, feeding estimated parameters back into the model until convergence is achieved. This process ensures consistency and reliability in the estimated parameters used to represent the shocks affecting the system, thus contributing to the model's accuracy and robustness.

The model is calibrated using average annual values from US time series data for the period 1919-2004. This calibration process ensures that the model's parameters reflect the actual macroeconomic conditions observed during that time frame, thereby increasing the model's relevance to the real-world economic context. The calibration targets specific macroeconomic variables and incorporates insights from other two-sector RBC models, aligning the model parameters with empirical evidence. Specific parameter values are derived from various studies, including Jones, Manuelli, and Siu (2005) for the capital share in the goods sector, and Benk et al. (2008) for the labor share in the banking sector. These specific parameter choices reflect the researchers’ attempt to match empirical data for a range of variables, enhancing the explanatory power and credibility of the model. The detailed approach taken in calibrating the model’s parameters illustrates a comprehensive engagement with empirical data in order to establish a robust analytical framework.

The model's equilibrium solution is obtained by normalizing variables and log-linearizing around the deterministic steady state. This method allows for the analysis of the model's dynamics under the influence of the three shocks. The process involves solving for each control variable as a function of the state variable and the three shocks, ultimately providing time series of crucial variables. These time series serve as the inputs for identifying and estimating each of the three shocks at every point in time. This innovative approach to identifying the shocks involves using more time series than are strictly needed for identification, resulting in an over-identified system. This over-identification allows for a more robust estimation process, reducing the impact of potential measurement errors and biases, improving the overall reliability of the analysis. The minimum distance approach employed enhances the reliability of the shock estimation and consequently enhances the accuracy of the model's empirical analysis.

The Christiano and Fitzgerald (2003) asymmetric frequency filter is applied to the data to achieve stationarity while preserving the business cycle and long-run components. This filtering technique is designed to isolate cyclical components from long-term trends in the data. The use of the Christiano-Fitzgerald filter is a key methodological choice because it allows the researchers to focus on the cyclical components of the data while minimizing distortions due to long-term trends. The application of this filter to both the target velocity series and the three shock series is critical for extracting the relevant frequency components, ensuring consistency across the various parts of the analysis. By using this filter, the researchers ensure that the analysis focuses on the relevant frequency bands for assessing the effects of the shocks. This methodologically sound step increases the accuracy and precision of the results.

Impulse response functions illustrate the effects of temporary one percent increases in each of the three shocks—credit, goods productivity, and money—on income velocity. All three shocks initially cause velocity to rise. However, the responses differ in their persistence. Credit and money shocks lead to an initial increase followed by a gradual return to equilibrium. The goods productivity shock shows an initial rise in velocity, followed by a decline before returning to the original level. The differing responses highlight the varied ways in which the shocks interact with the underlying model dynamics. The analysis of these impulse responses provides valuable insights into the short-term effects of each shock. For example, the goods productivity shock increases velocity primarily by temporarily increasing output, while the money shock increases inflation, reducing real money demand. The credit shock reduces the marginal cost of credit, which in turn reduces money demand, increasing velocity. The nuances revealed by these responses underscore the importance of a nuanced understanding of the interplay between the shocks and money velocity.

Variance decomposition analysis assesses the relative contribution of each shock to the overall volatility of M1 income velocity. This analysis is conducted across several sub-periods: 1919-1935, 1936-1954, 1955-1982, and 1983-2004, allowing for the examination of the changing importance of different shocks over time. The analysis considers both business cycle and long-run frequencies, offering a broader perspective on the sources of volatility. For the full 1919-2004 period and its sub-periods, the variance decomposition shows that money and credit shocks play substantial roles in explaining velocity fluctuations, particularly in the long-run spectrum. The results demonstrate that the relative importance of the three shocks is not constant over time but changes across these various sub-periods. Money and credit shocks contribute similarly to velocity volatility, although the relative dominance shifts between these two shocks across the sub-periods. The variance decomposition is performed separately for each sub-period using the estimated variance-covariance matrices from that sub-period, making the comparison more robust and meaningful.

The study compares the performance of the endogenous and exogenous growth model versions. The endogenous growth model proves more successful in explaining the actual filtered velocity levels, particularly in specific periods (1920s, 1939-1959, 1961-1970, and post-1990). This comparison highlights the importance of incorporating endogenous growth mechanisms into the model for accurately capturing the long-term trends and fluctuations in money velocity. This highlights the importance of endogenous growth in more accurately capturing the long-term trends and fluctuations in money velocity. Differences in the standard deviation and correlation of the shocks between the endogenous and exogenous growth versions of the model are also noted, although detailed results are not presented in the main text. The comparative analysis suggests that the endogenous growth model provides a significantly better fit to the observed data, particularly in explaining the level of filtered income velocity. This reinforces the importance of accounting for the endogenous nature of growth in the model.

The analysis extends to the UK, using data from 1978 to 2008. Unlike the US analysis which focused on M1, the UK analysis uses M0 as the money aggregate, due to differences in the composition of monetary aggregates between the two countries. The choice of M0 reflects the unique characteristics of the UK's monetary system and the need for consistency within the framework of the model. The UK's M1 aggregate, which includes overnight deposits, differs substantially from US or Euro area M1, making it less comparable for this analysis. The UK calibration uses an intermediate value of M/(Pc) = 0.33, which is close to the US value of 0.38, maintaining consistency while acknowledging the distinctions between the countries' financial structures. This calibration acknowledges the differences in the UK financial system, yet seeks to maintain comparability with the US analysis by using a similar model structure and calibration approach, which ensures consistency across different datasets and allows for direct comparison of the results.

The UK M0 income velocity exhibits an average annual increase of 2.1% during the study period, exceeding the US M1 velocity's growth rate of 1.25%. This faster growth rate in UK income velocity indicates potentially different dynamic characteristics of the UK economy when compared to the US. The model calibration remains similar to the US model, though parameters such as money supply growth rate, inflation rate, and the normalized money variable are adjusted to reflect UK-specific conditions. The shock processes in the UK data show higher autocorrelations and lower standard deviations compared to the US shocks. The longer-term trends observed in the UK M0 income velocity provide another perspective on the general relationships uncovered in the US data. These distinct shock processes and velocity trends highlight the importance of conducting country-specific analysis, to avoid generalization.

A direct comparison of the US (1983-2004) and UK (1978-2008) results is undertaken, focusing on the period with overlapping characteristics. The productivity shock emerges as the primary driver of velocity volatility in both countries during these more stable time periods, however the role of the credit shock is more significant in the US, highlighting possible structural differences in the financial sectors of these countries. Notably, both the goods and credit productivity shocks significantly affect the level of velocity in both countries, underscoring the importance of these factors in influencing long-term trends. The UK analysis extends beyond the US dataset's conclusion to encompass the recent financial crises. The findings suggest that during more stable periods, the goods productivity shock is the main driver of volatility. This pattern is consistent with both the US and UK data, indicating that even across different countries, stable periods show similar relationships between productivity and velocity volatility. The findings for similar time periods reinforce this, suggesting that the nature of credit shocks is different between the US and UK, even during comparable periods.

The paper successfully explains US money velocity cycles around a 1.25% upward trend using historically constructed shocks. These shocks encompass money, credit, and goods productivity. A substantial portion of the volatility in the 86-year band-pass filtered velocity is explained by these shocks, evident in both business cycle and long-run frequencies. The application of the model to UK data (1978-2008) supports the US findings, particularly for the 1983-2004 moderation period in the US. Stable economic periods correlate with velocity volatility primarily explained by goods productivity shocks. Conversely, during unstable monetary policy periods, money and credit shocks become dominant in explaining velocity variation. The research introduces a novel filtering methodology that incorporates both long-run and business cycle frequencies, providing a comprehensive analysis of velocity fluctuations.

The analysis reveals the varying importance of the three shocks across different economic periods. In stable periods, goods productivity shocks are the primary driver of velocity volatility. This suggests that stabilized monetary policy, such as inflation targeting, reduces the need for credit variations to offset inflation fluctuations. Only fluctuations in temporary income from productivity shocks then influence velocity volatility. However, during unstable monetary policy periods, money and credit shocks can overshadow the impact of goods productivity shocks, accounting for a larger portion of velocity variation. The high correlation amongst the identified shocks suggests a potential link where variable money and credit shocks may lead to increased volatility in goods productivity shocks, creating a feedback loop. This dynamic underscores the need for a multi-faceted approach to understanding the drivers of velocity and the role of policy interventions in mitigating or exacerbating velocity fluctuations.

The findings have significant implications for monetary policy. The paper suggests a state-dependent money supply rule that offsets velocity changes to maintain inflation targets. This contrasts with Taylor-type interest rate rules, which face constraints related to the zero nominal bound. The state-dependent rule, as envisioned by McCallum (1990) and Keynes (1923), would increase money supply growth during periods of falling filtered velocity (as seen during the Great Depression, the 1987 crash, the 1991 recession, and 2004 onward), thereby mitigating the impact of negative shocks. The sustained low nominal interest rates in the US from 2002-2004 and 2008 onwards are presented as examples potentially consistent with Friedman's (1968) observation that pegging low real interest rates can create new eras of unwanted volatility in government debt, money supply, and private credit. The study therefore proposes to use the band-pass filtered velocity to inform monetary policy decisions, advocating for a more dynamic and responsive approach than traditional rules.