Goal: This assignment introduces multiple regression by examining the problem of model specification known as near multicollinearity. Specifically, it introduces:

• Estimating the Demand for Money with Multiple Regression
• How Near Multicollinearity Effects the Quality of OLS regression
• How to change Model Specification to remove Near Multicollinearity.

The spreadsheet for this problem is CH5_Case1.xls. It contains the following data:

The series REALMONEY is the monthly demand for real money services. Monetary theory argues that people demand the real services (purchasing power) of money. Accordingly, our dependent variable must be expressed in real terms and transformed into logs to suppress any heteroscedasticity. Accordingly, we calculated monthly REALMONEY using a spreadsheet as the log of the ratio of the M1 money supply over the consumer price index (CPI):

The series INCOME is the log of seasonally adjusted Personal Income.

Note: The demand for money and income series are log transformations of the original data. This adjustment is made to suppress any heteroskedasticity in these series.

The series SHORTRATE is the Federal Funds interest rate, which is the rate banks charge on short-term reserves.

The series MEDRATE is Municipal Bond yield and represents the average rate of a portfolio of municipal notes.

The series LONGRATE is the Mortgage interest rate representing the average fixed mortgage interest rate.

Note: To help in the interpretation of our multiple regression results, we have named the interest rate variables according to their relative average maturity.

Explaining the Demand for Money

Milton Friedman is considered by many as the father of the "Monetarist" school of economic thought, which arose as a challenge to modern Keynesian macroeconomics in the late 1960s. Friedman argued that the supply of money effectively determined all nominal prices, and monetary policy was an effective tool of stabilization policy. Central to Friedman’s arguments was the assumption that the demand for money was stable, or at least, predictable. This led empirical researchers to develop forecasting models of the demand for money for purposes of macroeconomic forecasting.

The conventional theory of the demand for money concentrates on two motives for holding money:

1)People demand money to facilitate transactions, termed the Transactions Motive. Accordingly, the demand for money should have a positive correlation with Personal Income (a measure of aggregate economic activity).

2)Since money is an asset with special properties, the demand for money should be inversely related to the yields on substitute assets. This approach, termed the Portfolio Motive suggests that the demand for money is negatively related to interest rates and yields on substitute assets.

We can summarize these factors in a function, explaining behavior of the demand for money:

Real Demand for Money = f(Income, Shortrate, Medrate, Longrate),

Where we expect the slope coefficient on the income variable to be positive, whereas the slope coefficients on the interest rate variables should all be negative.

The demand for money can be estimated by applying Ordinary Least Squares to the following multiple regression model:

REALMONEY = a + b1INCOME + b2SHORTRATE + b3MEDRATE + b4LONGRATE + e

According to theory we expect b1> 0 and b2, b3, and b4 to be negative.

The fitted regression line is:

Details on coefficient estimates and their significance levels are reported in the table below.

Finally, some summary accuracy statistics are reported below.

Question #1: Do the coefficients on the interest rate variables have the correct signs? Can we reject the null that their respective slopes are zero using a two-tailed test with significance level of 5 percent?

ANSWER:

Past researchers have noted that any multiple regression estimated with three different interest rate variables as independent variables is likely to be plagued by Near Multicollinearity. Specifically, since interest rates tend to be highly correlated, OLS regression should produce large errors, i.e., unreliable results.

This is because OLS has trouble isolating the partial effects among independent variables because one or more are highly correlated, i.e., react to the same influence.

To examine for possible Near Multicollinearity we estimate the correlation matrix of the interest-rate variables summarized in the following table.

Question #2: Based upon the regression results above and the correlation matrix of interest rates, is near multicollinearity a problem in the former regression? Explain

ANSWER:

In addition, while the F-test for the complete model shows the presence of a significant relationship among the set of explanatory variables with the dependent variable, some of the individual parameter estimates are insignificant as shown by their t-ratios. This, once again, suggests that multicollinearity may be a problem.

A way to correct for multicollinearity is to change model specification. Specifically, since all three interest-rate variables measure the same effect (the cost of credit), we should try estimating the model with only one interest rate.

Using FORECASTX^TM we re-estimated the demand for money using only one interest rate variable, the short-term interest rate.

The fitted revised model is:

Coefficient estimates and standard errors of the revised model are reported below.

Finally, the following accuracy statistics were estimated for the revised model.

Question #3: Does the coefficient on the SHORTRATE variable now have the correct sign? Can we reject the null that this coefficient is zero at the 95 percent level of confidence?

ANSWER:

Question #4: Explain the differences between the first and second model specifications? Which model specification is superior?

ANSWER:

Question #1: Redo the assignment with the addition of an international variable to the list of explanatory variables used to predict the demand for money. Specifically, does the addition of the exchange rate or the trade balance increase our ability to forecast the demand for money? (Note: The fact that foreign interests influence the U.S. demand for money is a serious issue to monetary authorities).

Question #2: Select four macroeconomic variables at random and add to the explanatory variables used to predict the demand for money. Redo the regression with all the independent variables, including the four new ones. Contrast and compare the R² and AIC and SIC statistics between the two regressions. Comment.