Money Demand & Interest Elasticity

The paper introduces a novel theory of money demand stemming from a general equilibrium, endogenous growth model. This model uniquely combines elements of a shopping time exchange economy and a cash-in-advance framework. A key departure from standard models is its prediction of a variable interest elasticity of money demand, unlike the constant elasticity typically found in shopping time specifications. The model posits that increases in both inflation and financial innovation (reducing credit costs) drive agents to substitute away from money towards exchange credit. This substitution effect is central to the model's mechanism. The interest elasticity of money demand, therefore, is not fixed; instead, it dynamically increases with higher inflation rates and more developed financial markets. This dynamic feature is a significant contribution, challenging the traditional assumption of a constant elasticity. The model anticipates that during periods of financial deregulation, as seen in the US and Australia from the late 1970s onwards, the interest elasticity should increase due to cheaper credit acting as a substitute for money. Conversely, decreases in nominal interest rates (resulting from falling inflation) would independently reduce the interest elasticity. The net effect of these opposing forces on money velocity is a significant area of investigation. The research employs a cash-in-advance constraint (Mt = at ct Pt) to capture the role of money in transactions, predicting a unitary consumption elasticity and a variable velocity of money (1/at). This provides a strong foundation for the subsequent empirical analysis and allows for a more nuanced understanding of money demand in a dynamic economic environment.

A crucial implication of the model is the impact of financial deregulation on money demand. The paper highlights that during periods of deregulation, such as those experienced by the US and Australia starting in the late 1970s and early 1980s, the interest elasticity of money demand would be expected to rise. This is attributed to the increased availability of less expensive credit, providing a more attractive alternative to holding money. The model incorporates financial sector productivity, arguing that productivity gains in this sector, exceeding overall productivity growth (as reflected in real wages), further increase the interest elasticity of money demand. This dynamic interplay between financial innovation, credit costs, and inflation creates a complex relationship influencing money demand. The paper acknowledges that deregulation unfolded in phases, with various banking laws contributing incremental productivity shocks. Consequently, the financial productivity variable used in the model captures these gradual changes over time rather than a single, immediate shock, ensuring that the time series analysis more accurately reflects the ongoing process of financial development and its influence on money demand. The model's internal consistency is enhanced by these considerations, avoiding potentially misleading results due to the simplification of a one-time shock.

The theoretical model's structure is only briefly outlined in the abstract. It is described as integrating a special case of the shopping-time exchange economy with the cash-in-advance framework. The model introduces equations to represent the consumer's choices between using money and exchange credit for consumption (Mt = at ct Pt), and a production function for credit services that is a constant returns to scale (CRS) function, using effective labor and deposited funds as inputs. The equilibrium conditions involve the firm's profit maximization, the money supply condition (with a constant rate of money growth), and the consumer's utility maximization subject to various constraints. These constraints include time allocation among goods production, leisure, credit services production, and human capital utilization. The model's mathematical representation is presented, demonstrating the integration of consumption, production, and monetary aspects within the general equilibrium framework. The complexity of the model highlights the integration of several economic concepts and the interdependency of various factors in influencing the demand for money. The introduction of a CRS production function for credit is a key distinguishing factor in the derivation of the model's implications, including the variable interest elasticity of money demand, which is a focal point of the research.

The empirical analysis utilizes quarterly data for the United States (1976:1 to 1998:2) and Australia (1975:1 to 1996:2). These periods are chosen because they encompass significant inflationary periods, financial deregulation, and the expansion of interest-bearing exchange credit. The data primarily originates from official government sources. However, some data series necessitated extrapolation or interpolation. The core data includes a measure of non-interest-bearing money (currency plus non-interest-bearing demand deposits), the nominal interest rate, and the real wage. A key variable is a measure of financial sector productivity; however, due to data limitations, the real wage in the finance and insurance sector is used as a proxy for Australian data. The authors acknowledge the limitations of this proxy for Australia, explaining the methodology used to derive this proxy due to the unavailability of a more direct productivity measure. The study uses Johansen and Juselius' (1990) and Johansen's (1995) cointegration techniques given the non-stationary nature of the time series data, focusing on long-run relationships among the variables. The non-stationary nature of the data necessitates using advanced econometric techniques, and the choice of Johansen and Juselius' (1990) and Johansen's (1995) cointegration method is justified given these characteristics of the data. This methodological detail is crucial for interpreting the results of the analysis.

Two models are estimated: a baseline model incorporating the nominal interest rate, the real wage, and financial sector productivity; and a conventional model omitting financial sector productivity. The study employs cointegration techniques to estimate long-run relationships. For both countries, unrestricted estimates show that money holdings are negatively associated with the nominal interest rate and financial sector productivity, and positively with the real wage—consistent with the model's predictions. However, large standard errors affect the precision of the unrestricted estimates. Restricted estimates, imposing a specific parameter restriction (based on theoretical considerations), are also presented and found to be significant in the case of Australia, providing stronger support for the model's predictions. The negative coefficients on the financial sector productivity measure consistently support the model's prediction that increased productivity in the credit sector leads to substitution away from cash. Comparing US and Australian results revealed differences in the magnitude of the estimated coefficients, indicating different sensitivities to financial developments across the two countries. Differences are discussed, highlighting that Australia provides more support for the model's specific parameterization than the US data.

The estimated model allows for a time-varying interest elasticity of money demand. The findings indicate that money demand becomes more elastic over time in both the US and Australia, a result consistent with the theoretical predictions of the model. This time-varying elasticity is a significant finding, challenging the typical assumption of constant interest elasticity. A direct comparison between the baseline model and a conventional money demand specification is undertaken. The baseline model, incorporating financial sector productivity, explains the long-run behavior of non-interest bearing money significantly better than the conventional model, which includes only income and the nominal interest rate. The conventional model produced either positive interest elasticities or a lack of cointegration between variables which highlights the importance of the contributions in the baseline model. The study finds strong support for the cointegration vector, especially for the Australian data. The robustness of the results is further analyzed by conducting tests using various sample sizes and lag lengths in the econometric models employed. Overall, these comparisons firmly support the superiority of the model that incorporates the impact of financial sector productivity on money demand.

Robustness checks are performed to assess the sensitivity of results to variations in sample size and lag length in the VAR model. The results indicate considerable robustness, particularly for the Australian data, providing greater confidence in the stability of the estimated relationships. Recursive estimation techniques, progressively expanding the estimation window, are employed to monitor the stability of the parameter estimates. These results demonstrate stability for Australia, while less stability is observed in the US data prior to 1995. Further analyses explore broader monetary aggregates (M1, M2, M3). Results using M1 and M2 show some support for the model's predictions, but results with M3 are less conclusive, likely due to M3 including interest-bearing instruments not directly addressed by the model's theoretical framework which focuses on non-interest bearing money. This suggests that the model's applicability is most strong for narrow definitions of the money supply, highlighting the limitations of applying the model to broader monetary aggregates, where the assumptions underpinning the model might not fully hold. The varying degrees of success across different monetary aggregates reinforce the importance of the theoretical focus on non-interest bearing money and the impact of financial innovation.

The robustness of the findings is assessed by examining their sensitivity to changes in sample size and the lag length of the Vector Autoregression (VAR) model used in the Johansen cointegration estimation. The results demonstrate substantial robustness across varying sample lengths, particularly for Australia where the point estimate of a key parameter varied only between 0.22 and 0.26. For Australia, recursive estimation, adding four quarters at a time, shows the model's stability. In contrast, the US data shows more variation until around 1995. Similarly, the impact of altering the lag length of the VAR model (tested with lags of 3, 4, and 5) is evaluated. The US results remain largely insensitive to lag length variations. For Australia, however, while the VAR(3) and VAR(5) specifications show weaker evidence of cointegration, the coefficient estimates remain qualitatively consistent with the banking time model's predictions and are comparable to the VAR(4) results. The consistency across different lag lengths demonstrates the robustness of the model and its ability to capture long-run relationships despite potential short-run variations. The analysis's rigorous approach, employing multiple robustness checks, enhances the credibility and generalizability of its findings.

To further examine the dynamics of the money demand relationship, dynamic models are estimated for both countries. These models incorporate lagged values of the dependent variable (m/y), lagged changes in the interest rate, and the lagged error correction term from the cointegration analysis. The dynamic model for Australia explains approximately 75% of the variation in m/y, with the error correction term being the most significant variable, reinforcing the long-run relationship established in the cointegration analysis. In contrast, for the United States, the dynamic model explains about half of the variation in m/y, and a lagged financial productivity variable is significant. This suggests that short-run dynamics differ slightly between countries, reflecting differing financial structures or market responsiveness. Diagnostic tests, including Lagrange multiplier tests for serial correlation and ARCH effects, revealed no significant evidence of misspecification up to five lags, confirming that the modeling assumptions are well-suited to the data. The use of White's (1980) heteroskedasticity-consistent covariance matrix estimator further ensures the robustness of the reported statistical significance. These comprehensive diagnostic checks provide further confidence in the validity and reliability of the findings.

As a final robustness check, the model is estimated using broader measures of the money supply (M1, M2, and M3) for both the US and Australia. Although detailed results are not presented, the main findings are summarised. While the model shows some degree of support, using broader monetary aggregates revealed varying degrees of success. All the aggregates provide some evidence of at least one cointegrating vector, though the overall fit and explanatory power may vary. Using M1 and M2 generally provides better results than M3, which is largely inconclusive. The diminished explanatory power when using M3, which incorporates interest-bearing components, highlights the model's focus on non-interest-bearing money. The success of the model varies depending on the specific monetary aggregate used. While the broader monetary aggregates provide some supporting evidence, they reveal that the theoretical model's explanatory power is strongest when focused on non-interest-bearing components of the money supply.

The study employs quarterly data for the United States, spanning from 1976:1 to 1998:2, and for Australia, covering the period from 1975:1 to 1996:2. These timeframes are specifically selected to encompass periods of high inflation, significant financial deregulation, and substantial growth in interest-bearing exchange credit. The data sources are primarily official government departments and statistical agencies. However, in certain instances, data interpolation or extrapolation was necessary to ensure data continuity. For the US, the money supply is measured as M1, excluding other checkable deposits, representing a measure of non-interest-bearing money. For Australia, the data on currency holdings is available from 1975:1. However, total current deposits are decomposed into interest-bearing and non-interest-bearing components only from 1984:3 to 1996:2. To address this data gap, an estimation method is applied, extrapolating interest-bearing deposits back to 1975:1 and then subtracting these from total current deposits. Other key variables include nominal interest rates and real wages (economy-wide and within the financial sector for Australia). For Australia, due to the absence of a suitable direct measure of labour productivity in the finance sector, the real wage in the finance and insurance sector is employed as a proxy. This proxy uses data from the Finance and Insurance (FI) sector, which is further processed to deal with incomplete data points (Interpolation of annual to quarterly, using broader sector data when sub-sector data is unavailable.) The specific details on data construction and limitations are crucial for evaluating the reliability and interpretation of the empirical results.

Given the non-stationary nature of the time series data, the study utilizes cointegration techniques developed by Johansen and Juselius (1990) and Johansen (1995) to estimate long-run relationships between money holdings and other macroeconomic variables. The application of cointegration methods is essential given the non-stationary characteristics of the data. The initial econometric models included several variables: money relative to income (m/y), the real wage, financial sector productivity, and a lagged error correction term. After testing for significance and parsimony, the models were refined and include variables that provided the best fit to the data. The authors explain the rationale behind using cointegration techniques: examining long-run equilibrium relationships. The choice of Johansen's method is clearly motivated by the presence of non-stationarity in the data series, ensuring appropriate handling of this statistical property to avoid spurious correlations in the analysis. The study uses the Johansen cointegration test, a sophisticated approach designed to test for the existence of a long-run relationship in the presence of non-stationary variables. This method allows for the simultaneous estimation of multiple cointegrating vectors, and the results are interpreted in terms of long-run equilibrium adjustments in money demand in response to changes in other economic factors. The inclusion of the error correction term suggests that deviations from the long-run equilibrium are adjusted in the short-term dynamics of money demand. Diagnostic testing, such as White's (1980) heteroskedasticity-consistent covariance matrix estimator, is performed to control for the presence of heteroskedasticity and potential serial correlation.