**Introduction:**

Money plays a crucial role in the economy. The key reason for holding money is to facilitate economic transaction. A stable long run money demand function is vital in selecting appropriate monetary policy actions. The stability of money demand function is an important pre-requisite for effective money targeting because it helps to predict the future money supply growth.

Demand for money is the amount that the people of a particular economy holds. Holding money is associated with an opportunity cost – that is interest rate. If people hold money then he has to forego the interest rate that can be earned in other form of assets. Demand for money is associated with transaction, precautionary and speculative motives. While precautionary and transaction motive shows a positive relation between the income and the money demand the speculative motive shows an inverse relation between the money demand and the interest rate.

Our study examines the causality between real money demand, real GDP and interest rate and price level.

**Key objective of the study:**

The key objective of this research paper is to estimate the money demand function for United States for the period of 1970-2017. Macroeconomic study suggest money demand function depends on several variables that includes interest rate, real GDP, price level and transaction cost. The current study only considers two variables namely real GDP , interest rate and the price level that affects the money demand function. The current study uses the multiple linear regression tool to estimate the money demand function. With the help of linear regression technique, this study puts an attempt to formulate the money demand function. The primary aim of this paper is to figure out how the money demand responds when the income level and interest rate changes.

**Literature Review:**

Several studies have estimated the money demand function on a country by country basis. There are few groups of studies that have used panel cointegration testing procedure. Mark and Sul( 2003) have estimated the money demand function for 19 OECD countries using Pedroni’s panel cointegration procedure. Harb (2004) also used the same procedure to figure out the money demand function for six middle east countries. Harb has found strong evidence that M1 is cointegrated with its key determinants. Paresh Kumar Narayan · Seema Narayan ·Vinod Mishra ( 2008) has estimated the money demand function for South Asian countries. They found that money demand and its determinants that includes real income, real exchange rate, both domestic and foreign interest rate are well cointegrated for all individual south Asian countries as well as for the panel. The research study provides a strong evidence of statistically significant relationship between money demand and its determinants. They further conducted the test for Granger causation and found strong money demand function for all countries except Nepal. The findings of their study suggest that all countries except Nepal can consider the money targeting as the viable option to conduct monetary policy. The study failed to find a stable money demand function for Nepal thereby sceptical about the money targeting option for Nepal. (Mishra, June 2009)

Sober Mall ( 2013), in his research study attempts to estimate the real money demand function for Pakistan. They have collected time series data for the period of 1973-2010 and used bounds test based cointegration technique to estimate the money demand function. The study has considered three key variables: real income, foreign exchange rate and the call money rate. They figured out the elasticities for real income, exchange rate and the call money rate both for the short run and long run. The model strongly recommends M2 as an important monetary aggregate for Pakistan in terms of policy implications. (Mall, October 2013)

Casey b mulligan & Xavier sala-i- martin (1992) has estimated the demand for money for US for the time period of 1929- 1990 by using the cross-section analysis. This cross-section analysis helps to avoid the difficulties that occurs in the time series analysis. The study has interesting findings: the cross-sectional elasticities are observed to be greater than 1 for a longer period of time. It ranges between 1.3 to 1.5. The study further observes that the demand for money in agricultural regions has come out to be more that predicted. (SALA-I-MARTIN, 1992)

Mariana KAZNOVSKY( 2008), in his paper estimates the money demand function for Romanian economy with the help of two econometric models. The first model comprised with the multiple regression between money demand and inflation rate, industrial production and foreign exchange rate. The second model was unrestricted Vector Auroregressive model ( VAR) that was used for the for the same variables to estimate the demand for money function. The later one is found to be strong model that provides stable estimates of money demand function for Romanian economy. (KAZNOVSKY, 2008)

Similar work has been conducted by Luciano Canova( 2007) to estimate the demand for money for the small open economy of Jamaica. Demand for money estimation is important for the developing country like Jamaica because it would provide an instrument to the government to guarantee a stable growth policy in the long run. The dataset comprised of real money balance ( M) , real income (Y) and the bond yield parentage in Jamaica covering the time period of 1962-1997. This research study also considers the log linear model to estimate the demand function which is very similar to our current study. (Canova, January 2006)

**Research Objective:**

The key objective of the research is to estimate the demand for money function. The primary purpose is to gain a deep insight on how the money demand depends on other macroeconomic variables like the interest rate, real GDP and the price level. The research is conducted with the help of multiple regression technique. It helps to formulate the money demand equation and figure out the individual effect of each explanatory variables. The coefficient of each explanatory variable shows how the money demand changes if there is a change in any particular explanatory variable keeping the other variables as constant. The purpose of the analysis is to find out if there is any evidence of a stable relation between demand for money and other three variables and their relative contributions as a single variable.

**Data set:**

The data set for this research study is composed by annual data for United States covering the period of 1960-2016. In order to estimate the money demand function, we have considered total four set of variables:

- Real money balance (M1)
- Real GDP (at current US$)
- Interest rate
- Inflation rate, GDP deflator.

The data set is collected from Federal Reserve Economic Data and the World Bank website. The data is collected and shown in the attached excel.

**Methodology to be used:**

Several methods are used to estimate the money demand function in various research study. In the current study, we have used the linear multiple linear regression model to predict the money demand function. Log linear model is used to predict the money demand equation. The data that have collected from Fred and World bank are transformed to log form before conducting the regression analysis. Based on the summary output, the study has estimated the money demand function.

**Selection of variables: one dependent and two independent variables**

There are one dependent variable and three independent variables in the current research study.

**Money
demand M1: Dependent variable**

Macroeconomic theory suggests four major components of money : M0 ( Monetary base) M1, M2 and M3. The study has used M1 has the dependent variable that consists currency outside the U.S treasury, Travelers check, demand deposits and many other checkable deposits.

**Interest
rate: Independent variable**

It is the opportunity cost of holding money. Instead of holding money rather than an interest-bearing asset, the individual has to forego the interest rate. Hence a rise in interest rate will decrease the demand for money because the opportunity cost becomes too high.

While considering the money demand curve, macroeconomic theory suggests a downward sloping money demand curve showing an inverse relation between real money demanded M/P and the interest rate . holding all other variables that influence the money demand held constant. (Ghosh, 2005)

**Real
GDP: Independent variable**

Higher real GDP implies the expansion of volume of expenditure in the economy. When the GDP is substantially high, people are likely to increase their consumption expenditure. It would increase the demand for real money that people plan to hold.

**Price
level: Independent variable **

A rise in the price level leads to increase the nominal quantity of money but it does not change the real variable of money that people plan to hold.

**The Model:**

The econometric model for multiple regression can be represented as

M1t= α0+α1It+α2Yt+α3Pt

Where M1 is the dependent variable, demand for money

i is the independent variable, interest rate

Y is the independent variable, real GDP

P is the independent variable, price level

α0 is the intercept of the trend line

Since we are using the log – linear form of regression model, the equation takes the form of

Ln(M) = α0+α1ln( I)+ α2ln( Y) + α3ln( P)

In case of log linear model, the coefficient itself represents the elasticity for that particular variable. For example, the value and magnitude of α1 is the interest elasticity that shows how much the money demand changes if there is 1% change in interest rate. Similarly, the value of the coefficient α2 shows how the money demand responds when the real GDP changes by 1%.

**Demand for Money equation: theoretical prediction**

The real volume of economic activity is one of the key determinants of demand for money. We can expect a positive relation between the demand for money and real GDP. Higher the economic output, greater will be the demand for money. Money is primarily valued for its purchasing power which is measured by the price level. People will demand more money when the price level is increased showing a positive relation between the price level and the demand for money. Interest rate is one of the key determinants for the demand for money. It is the opportunity cost that the firms and the household face while holding wealth in the form of money. People are discouraged in holding the wealth in terms of money when the interest rate is too high. Therefore, the money demand shares a negative relation with interest rate. Transaction cost is another major determinant. People usually want to hold more money when the transaction cost is so high. There is a positive relationship between the money demand and transaction cost. (Demand for Money)

This theoretical prediction is investigated with a qualitative analysis through an appropriate econometric method.

Money demand function can take the form of

M=f( Y,P,I,C)

In this research study we have considered only three independent variables that include real GDP interest rate and inflation rate Thus the money demand function takes the form ( after taking logarithms)

Log Mt= lnα0 + α1ln Yt + α2It+ α3Pt

**Testing the hypothesis:**

The major goal of statistical testing is to observe whether there is sufficient evidence to reject the null hypothesis and accept the alternative hypothesis.

We need to transform the research question into null hypothesis H0 and the alternative hypothesis H1.

The Null hypothesis is,

H0: α0= α1 = α2=α3=0

The alternative hypothesis,

H1: α1≠0, α2≠0 and α3≠0

The null hypothesis implies that there is no relation between the dependent variable (money demand) and explanatory variables (interest rate real income and the price level)

Alternative hypothesis implies that there exists a significant relation between the dependent variable and independent variable.

t statistics is used to confirm the hypothesis testing.

We can only reject the null hypothesis if our sample t value is more than the critical t value

Alternatively we fail to reject the null hypothesis if the sample t value is less than the critical value.

**Regression Results:**

SUMMARY OUTPUT | ||||||||

Regression Statistics | ||||||||

Multiple R | 0.992593 | |||||||

R Square | 0.985241 | |||||||

Adjusted R Square | 0.98439 | |||||||

Standard Error | 0.112883 | |||||||

Observations | 56 | |||||||

ANOVA | ||||||||

| df | SS | MS | F | Significance F | |||

Regression | 3 | 44.23397 | 14.74466 | 1157.122 | 1.44E-47 | |||

Residual | 52 | 0.662611 | 0.012743 | |||||

Total | 55 | 44.89658 | ||||||

| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% |

Intercept | -15.9265 | 0.475698 | -33.4803 | 7.35E-37 | -16.8811 | -14.972 | -16.8811 | -14.972 |

X Variable 1 | -0.07796 | 0.028327 | -2.7521 | 0.008133 | -0.1348 | -0.02112 | -0.1348 | -0.02112 |

X Variable 2 | 0.773376 | 0.015831 | 48.85063 | 3.96E-45 | 0.741608 | 0.805145 | 0.741608 | 0.805145 |

X Variable 3 | -0.06393 | 0.034382 | -1.85947 | 0.068622 | -0.13292 | 0.00506 | -0.13292 | 0.00506 |

The estimated demand for money equation can be written as

**L****N( M)= -15.9265 – (0.07796) ln ( I) + ( 0.773376) ln (Y ) –
(0.06393)ln (P)**

The coefficients of each explanatory variables shows how the money demand changes when each of the variable changes, keeping others remaining same.

**Specifications of the model**:

Number of observations (n) in the model: 56

Number of variables: total 4 Variables that includes one dependent variable and three independent variables

Degrees of freedom df= (n-k-1) = 56- 4-1 = 56-5=51

**C. Interpretation of the model: **

1. The intercept for estimated equation is . This implies the trend line has a negative intercept. Actually, the intercept value does not have any meaningful interpretation as long as the coefficients of all explanatory variables are equal to zero.

2. The value of α2 coefficient is . This shows the negative relation between the money demand and the interest rate. The negative value of the coefficient supports the theoretical prediction of money demand model. The elasticity value implies that 1% increase in interest rate will lead to reduce the demand for money by 0.07%.

3. The value for α3
coefficient is **+ 0.773376**. This
shows the positive relation between the money demand and the real output. The
positive value of the coefficient supports the theoretical prediction of money
demand model. The elasticity value implies that 1% increase in real GDP will
lead to increase the demand for money by 0.773%.

4. The value of α3
coefficient is **-0.06393** . This shows the negative relation between the
money demand and the inflation rate. The negative value of the coefficient
contradicts the theoretical prediction of money demand model. This is an
interesting observation. The elasticity
value implies that 1% increase in inflation rate will lead to reduce the demand
for money by 0.063%.

**XI.
Statistical significance of the model:**

1. **R^2 value:**

R^2 value shows how much percentage of variation been explained by estimated equation.

The formula for coefficient of determination = Regression SS/ Total SS

The value of R square is 0.985241 that implies 98.52 % of the total variation is explained by the regression model. In other words, 1.4759 % of total variation remains unexplained in the model. An R2 near 1.0 indicates that the regression line fits the data well.

**2.
t statistics**

The critical value of the t statistics with 51 degrees of freedom at 5% level of significance is 2.069 (from the t distribution table).

The estimated t value for the intercept is -33.4803 – since the computed t value is greater than the critical value, it is statistically significant.

The estimated t value in the model for the dependent variable interest rate is –2.7521

Since the absolute value of estimated t stat is greater than the critical value it is statistically significant.

The estimated t value for the dependent variable income is 48.85063. Since the estimated value is greater than the critical value, it is said to be statistically significant at 5% level of significance

The estimated t value in the model for the dependent variable inflation rate is -1.85947

Since the absolute value of estimated t stat is less than the critical value it is not statistically significant at 5% level of significance

Though the interest rate and income are found to be statistically significant, t stat confirms that the rice level is not statistically significant at the 5 % level of significance.

**3.
P value**

Since the P value is less than 0.05, so we can reject the null hypothesis in favour of the alternative hypothesis. F statistic can also be used to determine the statistical significance in deciding to support or rejects the null hypothesis. If the estimated F value is greater than the table F value, there is sufficient evidence to reject the null hypothesis and accept the alternative hypothesis.

**Key findings of the model:**

With the help of multiple regression tool, this study has estimated the money demand function for US. The study has found that income is positively and statistically significantly related with the money demand whereas the interest rate is negatively and statistically significantly related with the demand for money. Both the findings are very much consistent with the theoretical predictions. The model has figured out an important observation. Though there is strong evidence that the income and the interest are statistically significant and consistent with theoretical prediction, the model observes third variable (price level) is not consistent with the theoretical prediction. The value of the coefficient of the variable as well as t stat fails to find out a strong statistically significant relation.

**Conclusion:**

The current study has estimated the money demand function for US economy using the data for the years 1960-2016. The results confirm the theoretical prediction of an inverse relation between the money demand and the interest rate and the positive relation between money demand and real output. The results fails to establish a positive relation between the price level and the money demand. Estimating of a statistically strong model for money demand is the pre-requisite to the application for an effective monetary policy. Definitely there is scope for improvement. We can include financial innovation as another independent variable for the future research study. Financial innovation also influence the money demand function as it lowers the cost of switching between the money and other interest bearing assets thereby decrease the demand for money people plan to hold.

**References**

Canova, L. (January 2006). Estimating
demand for money in Jamaica. *Research Gate *.

*Demand for Money.* (n.d.). Retrieved from
http://www3.econ.muni.cz/~hlousek/teaching/money_demand.pdf

Ghosh, D. S. (2005). *Money, Interest
Rate, Price Level and Real GDP.* Retrieved from
http://www3.uakron.edu/econ/ghosh/201-004/chapter_11_for_web.pdf

KAZNOVSKY, M. (2008). MONEY DEMAND IN
ROMANIAN ECONOMY, USING MULTIPLE REGRESSION METHOD AND UNRESTRICTED VAR MODEL. *Journal
of Applied Quantitative Methods*.

Mall, S. (October 2013). Estimating a
Function of Real Demand for Money in Pakistan: An Application of Bounds Testing
Approach to Pakistan. *International Journal of Computer Applications*.

Mishra, P. K. (June 2009). Estimating money
demand functions for South Asian countries. *Research Gate*, 685-696.

SALA-I-MARTIN, C. B. (1992). U.S. Money
Demand: Surprising Cross sectional Estimates . *Brookings Paper on Economic
Activity *.

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