Dynamics of Money Market and Monetary Policy
Muhammad Ashfaq Ahmed1, Nasreen Nawaz1*
1Directorate General of Revenue Analysis, Federal Board of Revenue, Islamabad, Pakistan
*Correspondence to: Nasreen Nawaz, PhD, Chief Federal Board of Revenue, Directorate General of Revenue Analysis, Federal Board of Revenue, Constitution Avenue, Islamabad, Pakistan; Email: nawaznas@msu.edu
DOI: 10.53964/mem.2024014
Abstract
Objective: Contemporary research on monetary policy does not account for the loss/gain in efficiency during the adjustment of the market and the after-policy vis-a-vis pre-policy equilibrium in the money market. After a central bank exercises a monetary policy, the central bank’s cost as a supplier of money rises to pre-policy cost plus the per unit money cost incurred due to monetary policy, which affects money supply and pushes the money market out of equilibrium. Demand and supply of money along with the interest rate follow certain adjustment mechanism until the final equilibrium arrives. The basis of adjustment is lack of coordination regarding decisions of consumers and suppliers of money at the prevailing interest rate. For the design of an optimal monetary policy, efficiency considerations both during the adjustment of the market as well as in final equilibrium are important to be taken care of. This research designs a dynamic money market model and derives an optimal monetary policy.
Methods: A perfectly competitive money market with five agents has been modeled. The equations maximizing their objectives have been derived and solved simultaneously to solve the model. An optimal monetary policy has been derived by minimizing the objective function of efficiency loss, i.e., supply or consumption of money lost in post-policy equilibrium vis-a-vis the pre-policy one, and the loss during the time market is adjusting subject to central bank’s cost constraint.
Results: Derived mathematical expressions outline the optimal expansionary and contractionary monetary policies considering the adjustments in demand and supply over time.
Conclusion: The expressions are functions of demand, supply, and inventory curves’ slopes as well as initial pre-policy equilibrium quantity of funds.
Keywords: money market, monetary policy, dynamic efficiency, interest adjustment path
1 INTRODUCTION
A country’s central bank formulates and implements monetary policy for optimally controlling supply of money to achieve economic goals leading to a sustainable growth of economy. Money supply can either expand or contract as a result of implementation of monetary policy depending on whether the policy is expansionary or contractionary respectively. Monetary policy operates through following tools: open market operations, direct lending to banks, bank reserve requirements, unconventional emergency lending programs, and managing market expectations (depending upon the credibility of the central bank). Monetary policy is based on steps of designing, announcing, and implementing policy by central bank, currency board, or any other authority having a mandate of controlling money market in economy. It involves managing the interest rates and money supply through changing interest rates, regulations involving exchange rate, purchase/sale of government bonds, and decisions regarding reserve ratio, etc., in order to influence growth, inflation, production, consumption, and liquidity, etc. Monetary policy formulation depends on a variety of macroeconomic indicators, such as economic growth in terms of GDP and various sectors, inflation, oil markets, international market prices, etc., to achieve various objectives, e.g., reduce inflation, maintain a steady economic growth, address unemplyment, etc. Monetary policy along with other economic measures can achieve objectives which a fiscal policy can also achieve, e.g., a stable economic growth.
Generally a country’s central bank has the mandate to formulate and carry out the monetary policy with an objective of reducing inflation and unemployment, and allowing an inflation rate for a stable economic growth. The central bank is also responsible for managing interest rates for a long-term economic growth. It is responsible for regulating the financial sector and also liquidates commercial banks in crisis by acting as a lender of last resort.
An expansionary monetary policy is exercised if the aim is to increase the economic growth and expand the economic activity, in case the country faces a high unemployment rate during a crisis/recesssion or economic slowdown, etc. Lowering the interest rates through a variety of measures is also a part of an expansionary monetary policy, which promotes spending and discourages savings. This increases the money supply in the market, and may boosts spending on consumption as well as the investment goods. However, inflation can result from an expansionary monetary policy.
There are a number of monetary policy tools the central banks use. The open market selling and buying of short-term bonds, i.e., open market operations is one of those, which target the short-term interest rates, such as the federal funds rate. Through buying or selling assets, the central bank injects or removes money respectively into the banking system, and the banks either increase or decrease the interest rates, until the target set by central bank is achieved. Quantitative easing is also a process done through open market operations by the purchase of a specific quantity of assets to target specified increases in the money supply, so that the banks could provide loans more easily.
The central banks may also change the required collateral demanded by the central bank from the banks to fulfill its role as lender of last resort, i.e., the discount rate. The requirement of more collateral, and charging higher rates is a contractionary monetray policy and implies that the banks need to be careful of their lending with regard to risky loans. On the other hand, a lower requirement of collateral, and charging lower rates is an expansionary monetary policy and implies that the banks can make risky loans at lower rates, and can have lower reserves.
The central banks also have reserve requirements from the banks, i.e., an amount as a percentage of the deposits made by their customers, to be retained by them to make sure that their liabilities could be met. If the reserve requirement is low, the banks have more funds available to lend or purchase assets. If the requirement is high, it curtails the lending by banks leading to a lower money supply growth.
Besides standard monetary policies, unconventional monetary policies have also been popular in the central banks around the globe, i.e., USA, England, European Central Bank, and Japan, since the 2008 financial crisis, combining the quantitative easing, discount loans, and open market operations’ aspects.
The central banks can also influence the market expectations through their public announcements regarding their upcoming policies. The statements and policy announcements of the central banks move the markets by making the investors guess about the future course of action of the central banks. Some central banks deliberately choose to keep the monetray policy unpredictable, so that the expectations do not start showing up in the market prices in advance, while others choose to be more predictable and open to avoid the volatility in the market due to unexpected policies. However, the effectiveness of the policy announcements is contingent upon central bank’s credibility and other authorities which are responsible for designing the policy, making it public through announcement, and also implementing it.
Ideally speaking, the monetary institutions responsible for the monetary policy must be autonomous, to avoid any influence by the government, political elements, or any other institution. In practice, governments all over the world have varying degrees of interference in monetary institutions. The investors base their decisions on the announced monetary policy as well as the credibility of the monetary authority.
Monetarist theory came to the fore in the 1950s, drawing its cornerstone from the QTM and assuming that velocity in the quantity theory of money is generally stable, which implies that nominal income is largely a function of the money supply (Friedman[1]). Keynes rejected the quantity theory, both theoretically and as a tool of applied policy, in part arguing that velocity of money is unstable and not constant. QTM also assumed the absence of the trade-off between inflation and output (Keynes[2]). Keynesianism rationalized that prices are rigid and that the quantity of money adjusted rapidly. According to Hicks[3], the basic version of the IS_LM model assumes a fixed price level; and thus cannot be used to analyse inflation but output in the short run. Hicks IS/LM view of the Keynes’s general theory was, however, contested empirically (Leijonhufvud[4]). Brunner and Meltzer[5] develops an alternative to the standard IS-LM framework. There are two asset markets and three prices-the prices of real assets, financial assets, and output. Friedman[6] argues that there is least agreement about the role that various instruments of policy can and should play in achieving the several goals. Evans[7] finds that money is not neutral in the long run if it is not in the short run, in particular, if growth is endogenous. If growth is exogenous, long-run neutrality is found. Goodfriend and King[8] describes the key features of the New Neoclassical Synthesis and its implications for the role of monetary policy. Bullard[9] support the long term neutrality of money. Sims[10] reviews Monetary Policy Rules, edited by John Taylor. Insolvent firms must not be recapitalized with taxpayer funds. Mankiw[11] shows that only monetary policy (unexpected) surprises would have a temporary effect on real variables. Monetarist upheld the principle of trade-off between inflation and output but reformulated the Philips curve in terms of real wage and not nominal wages (Gottschalk[12]). Palley[13] contrasts the new classical, neo-Keynesian, and Post Keynesian frameworks, thereby surfacing the differences. Empirical evidence on the use of New Keynesian models remains slim, and that practicality of theory is contested in part on grounds of absence of the role of money (Arestis and Sawyer[14]). Nogueira et al.[15] using annual data for 14 emerging and developed countries offer overall support for the traditional economic theory that monetary policy is neutral over the long-run. Schwartz[16] concludes that a systematic procedure for examining portfolios of the financial institutions needs to be followed to identify which are insolvent. White et al.[17] challenged Monetarism on grounds of technological developments and the instability of the money demand function. Galí[18] provides a rigorous graduate-level introduction to the New Keynesian framework and its applications to monetary policy, according to which the New Keynesian framework is the workhorse for the analysis of monetary policy and its implications for inflation, economic fluctuations, and welfare. D’Amico and King[19] estimates how much of the impact from the Fed’s tightening cycle is to be felt in the U.S. economy in both absolute and relative terms. Storm[20] critically reviews the theoretical and empirical merits of three recent tweaks to the New Keynesian core: using the vacancy ratio as the appropriate measure of real economic activity; hammering on the considerable risk of an imminent wage-price spiral; and the resurrection of the non-linear Phillips curve. The paper concludes by drawing out sobering lessons concerning the art of paradigm maintenance as practiced by the “scientists of monetary policy”.
Contemporary research on monetary policy does not account for the loss/gain in efficiency during the adjustment of the market and the after-policy vis-a-vis pre-policy equilibrium in the money market. After a central bank exercises a monetary policy, the central bank’s cost as a supplier of money rises to pre-policy cost plus the per unit money cost incurred due to monetary policy, which affects money supply and pushes the money market out of equilibrium. Demand and supply of money along with the interest rate follow certain adjustment mechanism until the final equilibrium arrives. The basis of adjustment is lack of coordination regarding decisions of consumers and suppliers of money at the prevailing interest rate. For design of an optimal monetary policy, efficiency considerations both during the adjustment of the market as well as in final equilibrium are important to be taken care of. This research designs a dynamic money market model and derives an optimal monetary policy by minimizing the objective function of efficiency loss, i.e., supply or consumption of money lost in post-policy equilibrium vis-a-vis the pre-policy one, and also the loss during the time market is adjusting subject to central bank’s cost constraint.
The remainder consists of the following sections: Section 2 connects agents in the money market to construct a dynamic money market model. Section 3 solves the model with an expansionary monetary policy. Section 4 derives an optimal expansionary monetary policy. Section 5 solves the model with a contractionary monetary policy. Section 6 derives an optimal contractionary monetary policy. Section 7 presents the summary of findings and conclusion.
2 THE MODEL
There is a perfectly competitive money market in equilibrium, and have five agents, with two of them as suppliers of money, i.e., the household, and the central bank, consumer of money for investment, i.e., a producer or firm, a middleman, i.e., a financial intermediary/commercial bank, and central bank acting as the government for formulating and implementing monetary policy. Central bank influences the interest rate through exercising monetary policy, however, in the role of supplier of money, takes the interest rate as given. The interest rate is also given for the household. If the money supply changes due to an exogenous shock, e.g., the introduction of debit/credit cards for payment instead of cash in the shopping malls, restaurants, etc., the interest rate cannot jump on its own to bring money market in final equilibrium. The commercial bank in the role of middleman varies the interest rate in its own benefit due to which the interest rate follows an adjustment path before bringing the money market in equilibrium. After the market attains final equilibrium, the commercial bank finds it optimal not to change interest rate and stay put. Money is supplied to commercial bank by suppliers, who holds the stock of money to supply it further to consumer, i.e., producer/firm, which borrows from financial intermediary at market interest rate. Money suppliers maximize their benefit; financial intermediary maximizes profit, i.e., the amount of revenue generated through lending money to the consumer/borrower minus the cost of holding stock of money, subject to the constraints; and the consumer of money, i.e., the firm/producer maximizes profit.
The adjustment of interest rates hinges on the idea that when an external shock disrupts the money market’s equilibrium, sellers and buyers do not synchronize their decisions at the prevailing interest rate. To illustrate, let’s envision a scenario: Initially, the money market is balanced, and the commercial bank holds a stable quantity of money. However, if an unexpected increase in money supply occurs, exceeding consumer demand at the current interest rate, a surplus accumulates with the bank. In response, the bank lowers interest rates to incentivize lower quantity of money supply by suppliers. Ultimately, a new equilibrium is achieved, characterized by a higher money quantity and lower interest rates than the initial state. This equilibrium is defined as follows:
(i) Money suppliers aim to maximize their utility or benefit; consumers, producers, or firms strive to maximize profit; and commercial banks aim to maximize profit by balancing the revenue earned from lending money to borrowers or consumers against the cost of holding money, within certain constraints (refer to Section 2 for further details).
(ii) In equilibrium, the demand for money matches the supply, and the commercial bank’s money inventory remains unchanged.
In Section 3, the stability criterion of Routh–Hurwitz is discussed, which serves as the necessary and sufficient condition for equilibrium in a linear dynamical system. In a perfectly competitive money market, the financial intermediary or commercial bank operates as a price-taker, accepting the prevailing interest rate under market equilibrium. However, in times of market disequilibrium, the financial intermediary has an incentive to adjust interest rates until the money market reaches its final equilibrium, where it once again becomes a price-taker. When the central bank implements monetary policy, the market interest rate adjusts gradually rather than abruptly, facilitating the transition to a new equilibrium. This adjustment of interest rates is driven by endogenous decision-making processes involving households, the central bank, consumers of money, and financial intermediaries. During periods of steady-state equilibrium in the money market, both the financial intermediary and consumers borrow an amount of money equivalent to the supply provided by money suppliers in each time period. However, in the event of an expansionary monetary policy by the central bank—such as an increase in money supply—some portion of the supply may remain unutilized by consumers by the end of the policy period.
If money suppliers and the financial intermediary could instantly adjust money supply and market interest rates, and if the intermediary knew the new demand and supply patterns following the interest rate change, the commercial bank would set an optimal market interest rate to maximize profits and clear the money market. However, since this information is not available to the commercial bank or financial intermediary, they adjust interest rates based on their best estimate of the new market conditions, aiming to drive the market towards its final equilibrium. As the commercial bank reduces the interest rate, suppliers offer less money than before. The bank or intermediary continues lowering the interest rate until the market reaches its final equilibrium, which is gauged by the amount of unsold or unborrowed funds. Ultimately, the market settles into a new equilibrium, albeit with some efficiency losses during the adjustment period. These losses represent the unused funds during the money market adjustment due to monetary policy, and the total loss is the sum of the adjustment period loss plus or minus the loss or gain in the final equilibrium.
In mathematical terms, the first-order derivatives of the objective functions of all involved parties have been utilized to optimize their goals. These individual equations are then solved concurrently to derive a mathematical representation of their collective response. One simplifying assumption made is that the final equilibrium is not significantly distant from the pre-policy equilibrium. This implies that linearizing the demand and supply schedules is a reasonable approach. While Figure 1 illustrates that linearization is appropriate for the movement of equilibrium from point a to b, it’s not realistic to assume linearity of the supply curve when the equilibrium shifts from point a to c. In such cases, a non-linear dynamical system, which is beyond the scope of this paper, would need to be considered.
7 CONCLUSION
When a government exercises an expansionary/contractionary monetary policy, the central bank’s supply curve shifts downward/upward, which affects the money supply in the market and equilibrium no longer holds. Over time, the money supply and demand, along with the interest rate, dynamically adjust to guide the market towards its final equilibrium. Throughout this adjustment process and in the final equilibrium, there are efficiency gains or losses compared to the initial equilibrium in the money market. It’s crucial to consider these efficiency changes, including those during the adjustment period, when devising an optimal monetary policy. Equations and outline the optimal expansionary and contractionary monetary policies, respectively, taking into account the adjustments in demand and supply over time. The expressions are functions of demand, supply and inventory curves’ slopes as well as initial pre-policy equilibrium quantity of funds.
Acknowledgements
Not applicable.
Conflicts of Interest
The authors declared no conflict of interest.
Author Contribution
Ahmed MA conceived the main idea of the paper, planned on methodology, did literature review, and sketched outlines of the models. Nawaz N worked on details of the models and derived mathematical results. Both authors jointly prepared the working draft of the article, proofread, and agreed on the final draft for submission to the journal.
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