Estimating money demand using regression analysis and demand curves

Demand for Money

The international community is currently facing the most severe crisis since the Great Depression of 1929 -- 1933. It started within the American real estate sector and soon expanded to the rest of the sectors, as well as to the rest of the global economies.

The causes and impacts of the crisis have often been discussed in the media and within the specialized literature, and the discussion is far from over. Still, this approach to the crisis is more descriptive and reflective. At this stage nonetheless, it is necessary to implement a proactive approach through which to promote solutions to overcoming the crisis.

Governments across the globe have each developed and implemented their own solutions to the crisis, ranging primarily from injecting capitals in the troubled industry sectors and companies, to efforts aimed at reducing federal costs. In the completion of these efforts, a crucial role is played by money, especially by liquidity, which is becoming scarcer.

In this setting then, the current project strives to assess money as a source of overcoming the crisis. In order to attain this, emphasis is placed on estimating the demand curve for money, specifically the preference of people to hold their money rather than invest it in other assets that would generate higher returns than the cash or checking account.

The basis for the estimations would be represented by M1, or the money which does not generate any interest, as opposed to M2 or M3, which are broader categories of money. In order to assess the demand for money, a quantitative tool would be used in the form of the regression analysis. The advantage is that it uses facts and figures and retrieves reliable conclusions.

2. Literature review

The demand for money is often understood as the desire of individuals to possess financial resources. Still, it is necessary to make the distinction between this desire and the demand for money. Specifically, the demand for money refers to the decision of the individual / group / country and so on to hold part of their assets in the form of money, that is currency and bank accounts, without investing it in other assets.

In a traditional setting, money held do not generate any gains -- especially since the current project considers M1 (non-interest-bearing money), when money invested generate additional gains. In this context then, the opportunity cost to holding money is represented by the interest rate. Still, people often hold money and lose the interest rate. The economists found that there are three primary reasons as to why people hold their money. These refer to the following:

Since money is a medium of exchange, it is held to settle transactions

Money is held as liquidity to be used in the event of an unexpected situation arising, and last

Money is held to "reduce the riskiness of a portfolio of assets by including some money in the portfolio, since the value of money is very stable compared with that of stocks, bonds or real estate" (Nelson, 2011).

The demand for money is often volatile, and it can only be viewed as stable within restricted contexts, and in the background of strictly controlled economic variables. Within the modern day economies, which are dynamic and based on the principles of the free markets, the demand for money is unstable. Estimating it is necessary to ensuring that the policy makers develop and implement the adequate solutions to the identified problems.

Estimating the demand for money is often a challenging task and economists across the world have strived to devise various methods to approximating it. The classical economists for instance believe that the market is in equilibrium and that this is due to the price adjustments and flexibility. The market is in full employment -- with the exception of crisis situations. In such a setting, money only represents a means of exchanging goods; it is neutral and it does not impact interest rates, relative prices, the balance between commodities and the aggregate real income.

The quantity theory however, argued that money was more important and highlighted a direct link between money and interest rate. Furthermore, it argued that there existed a public demand for money and introduced the element of public and the larger economy into the demand for money.

Keynes built on this theory and concluded that people were driven by various motives to hold money and that the interest rate represented an additional explanatory variable to determine the demand for real balances. The post-Keynesian economists developed new means to assessing the demand for money. One model introduced the concept of cost as related to the demand for money and also linked it to uncertainty. Then, another model, the cash-advance model, perceived money again as a means f exchange, but approached it at the level of portfolio and risk management. The overlapping generations models disregarded the exchange function of money and only approached it through the lenses of its role as an asset. The consumer demand models recognized money as a common good ensuring transition within the markets. All in all, the approaches to money can as such be divided into three categories: money is used in transactions, money plays the role of asset, and last, money serves the customers.

"The interesting point is while all these models analyzed the demand for money in different angles, the resulting implications are almost the same. In all instances, the optimal stock of real money balances is inversely related to the rate of return on earning assets, that is the interest rate, and positively related to real income. The differences, of course, arise in terms of using the proper transaction (scale) variable and the opportunity cost of holding money" (Sriram, 1999).

From a quantitative standpoint, the efforts to estimating the demand for money are often completed with the aid of the regression analysis, focused on the interest rate, as either a logarithm of money demand on the interest rate, either the logarithm of money demand on the logarithm of the interest rate (Bae and De Jong, 2005).

The actual model used depends on the researcher, but the variables are often recurrent. In estimating the demand for money in Jamaica, Luciano Canova at the University of Sussex used a model based on three variables -- the log of real money balances, the log of real income at constant prices within the year of analysis (1995) and the government of Jamaica Bond Yield in percentage (Canova, 2006).

Richard Carl Barth, William Loehr Hemphill and Irina Aganina (2000) state that the demand for money can be estimated through the division of a specific equation, but also through the estimation of an equation. Both equations -- specific and estimated -- would be derived based on previous empirical studies. In both cases however, regression analyses would e used and these would trigger different conclusions, based on the aggregates used in the analysis (Barth, Hemphill and Aganina, 2000).

3. The model

The current project uses a quantitative model to estimating the demand for money. The usage of quantitative tools to assessing and discussing the demand for money is based on the belief that the topic is rather complex and it is best for it to be assessed in a numeric format in order to avoid subjectivism.

The quantitative model relies on factual and numerical data, which can be easily verified and attested. This usage of numbers and figures in based on the principles of direct research as it relies on primary sources of information to generate new findings. In other words, the demand for money has often been researched by the academic community and various findings have been generated, as it has been revealed throughout the previous section.

Still, the numerical figures which can be linked to the demand for money have yet to be exhausted and the application of this additional model creates new observations relevant to better understanding the phenomenon of the demand for money. Returning to the specifics of the quantitative model, it is advantageous as it is constructed on reliable information and it as such leads to relevant findings. Additionally, unlike research through qualitative methods, the quantitative model allows for the extrapolation of the results to explain the behavior of the overall community (Balnaves and Caputi, 2001).

The model to be used is that of a regression analysis applied to an estimated equation. The equation is as follows:

(1) M1 = a + b1 + b2, where

M1 represents the non-interest-bearing money a represents the intercept estimate b1 represents the coefficient estimate on an interest rate, with the mention that the interest rate is a proxy for the price of money and the interest rate is the opportunity cost for holding the money b2 represents the coefficient estimate on the variable time, with the mention that time is a proxy for all other things.

In the context of the research conducted, the proxy variable generically named time was replaced with the second variable of employment. In other words, it was sought to identify the relationship between employment and interest rate and to reveal if and how these impact the function of money supply.

To this end, data was collected from the FRED website, or the website of the Federal Reserve Economic Data. In both cases of the variables -- interest rate and employment -- data was collected for over half a decade. Specifically, the period assessed was that from 1948 through to 2000, with a monthly frequency of data collection.

The data for employment had been collected from the United States Department of Labor, the Bureau of Labor Statistics, and the information on the interest rate had been collected from the Board of Governors of the Federal Reserve System. Employment was expressed in real value and the interest rate was expressed in percentage. At this level, it should be noted that the interest rate taken into calculation was the interest rate established for long-term securities issued by the United States of America.

With these model specifics then, a regression was computed and it resulted in the following chart:

4. Results of the model

The regression analysis has revealed a rather intricate evolution of the interest rate and the employment of the American population. More particularly, throughout the assessed period -- 1948 through 2000 -- the employment levels of the population had followed a constant growth trend, meaning as such that the population was more and more likely to get better jobs, and even more so, better paid jobs.

The interest rate has however revealed a less constant evolution, showing both increases as well as decreases, observable in various time frames. For instance, as the population was reaching an employment level of over 100,000 thousand people with jobs, the interest rate was beginning to decrease and it has followed a decreasing trend ever since; within the same context nonetheless, the employment levels continued to steadily increase.

For a restricted period of time then, there seemed to exist a direct relationship between interest rate and employment in the meaning that the increase in employment would subsequently generate an increase in the interest rate. Gradually however, it was observed that a continued increase in the interest rate was not sustainable in the long run. Higher interest rates translated into costlier labor force, the need to constantly increase wages, as well as restricted access to funds, including loans. In such a setting then, the sustained increase in interest rates is not a means to support economic growth, but the excessive increase in the interest rate impedes economic development.

On the other hand, it is noted that an increase in the interest rate for long-term securities issued by the United States government would increase the gains registered by those investing in the respective securities. Nonetheless, these gains would only be collected in ten years time, for instance, or more, since they are long-term securities. But the employers and other economic agents needed the gains to be immediate so that they can be further used in investments. And furthermore, the gains were not expected to be increased as the policy of the government is that of offering low interest rates, due to the low levels of risk it assigns to its securities. And there was also the issue of inflation, which might exceed the gains registered on the long-term securities.

All in all then, the benefits associated with the increase in the interest rate were only sustainable within the short-term. Within the long-term, the scope was that of creating and using a stable interest rate, which would stimulate consumption and economic growth. Employment can as such be perceived as a variable of the economy, whereas the interest rate can be perceived as a variable of policy making.

Within the period assessed, the interest rate and the employment figures followed different trends, with an intercept at point Y. In other words, the linear function intersected the X axes at a point Y, which has been computed with the use of the following formula:

(2) Y = 8E -- 05x -- 0.7877

Based on the same series and computations, the correlation coefficient between the two variables -- employment and interest rate -- was set at 0.684631099. Subsequently, the slope for the demand of money curve was set at 5988.837.

Ultimately, these findings indicate that the demand for money is a function of both interest rate and employment, increasing when both variables increase. In other words, when the financial regulator implements higher interest rate, the population tends to hold on to the money, despite the higher opportunity cost. This feature could be explained by the fact that, when interest rates increase, the population expects an increase in the cost of living, and subsequently prefers to hold on to its money in liquidities.

In terms of employment, when more people become employed, they also tend to hold on to the money more. An explanation in this sense could be provided by the tendency towards consumption and the desire to use part of the new income for household purposes, rather than investments. All in all, the demand for money is a function of employment and interest rate in the United States, for the period assessed.