Assignment 1

INSTRUCTIONS: You should use a statistical software (e.g. Stata) for the relevant parts of the assignment, indicate the software you were using. The assignment must be edited with a text editor, which can include output (properly formatted) of the statistical software. Handwritten assignments will not be accepted.

You are allowed to work in groups. However, each student is required to submit his/her own personal copy of answers. Copies that qualify for improper collaboration (see course outline) will not be accepted. You need to hand in the assignment in paper form; e-mailed copies will not be accepted.

There are a total of 10 marks for this assignment. Money Demand

In the Keynesian theory of liquidity preference the transactions, precautionary and speculative motives for holding money lead to a function where the demand for money depends on income and the interest rate. Suppose that we can write the demand for money as the linear function:

where

\({{m}_{t}}\) represents money in the form currency and demand deposits (commonly
called M1),

\({{y}_{t}}\) is gross national product, and

\({{i}_{t}}\) is the interest rate on 6-month U.S. Treasury Bills.

Observations on these variables in the U.S. economy for the period 1960 to 1983 are given in the file money.dta. They are taken from the Economic Report of the President. Money m and gross national product y are in billions of dollars; the interest rate i is a percentage.

1. Using the datafile above, present a table with summary statistics (mean, standard deviation, maximum value, minimum value) of each of the variables. Comment briefly.
2. Present a graph where you plot the evolution of y over time and another graph where you plot m as a function of i.
3. What signs would you expect on \({{\beta }_{1}}\) and \({{\beta }_{2}}\) ? Why?

1. Find the least squares estimates of the coefficients \({{\beta }_{0}}\), \({{\beta }_{1}}\) and \({{\beta }_{2}}\) and the corresponding standard errors. Do the estimates have the expected signs? Give an interpretation to the estimates for \({{\beta }_{1}}\) and \({{\beta }_{2}}\).
2. Are the coefficients \({{\beta }_{1}}\) and \({{\beta }_{2}}\) statistically significant? What is the general goodness-of-fit of the model?
3. Predict money demanded for the next period (1984), assuming (i) a gross national product of 1000 billion dollars and an interest rate of 12%, (ii) a gross national product of 2000 billion dollars and an interest rate of 6%.

g) If the money demand equation is lagged by one period we get

Subtracting this equation from the original we get

where \(\Delta {{m}_{t}}={{m}_{t}}-{{m}_{t-1}}\), \(\Delta {{y}_{t}}={{y}_{t}}-{{y}_{t-1}}\), \(\Delta {{i}_{t}}={{i}_{t}}-{{i}_{t-1}}\) and \({{v}_{t}}={{u}_{t}}-{{u}_{t-1}}\) .

An assumption that we make when estimating the original equation is that the \({{u}_{t}}\) are independent random variables with mean zero and constant variance \({{\sigma }^{2}}\) Suppose that this assumption is not true, but, instead, the \({{v}_{t}}\) are independent random variables with mean zero and constant variance. Then, the equation in first differences \(\Delta {{m}_{t}}={{\beta }_{1}}\Delta {{y}_{t}}+{{\beta }_{2}}\Delta {{i}_{t}}+{{v}_{t}}\) is the correct one to estimate. Use it to find least squares estimates and standard errors for \({{\beta }_{1}}\) and \({{\beta }_{2}}\). Compare the results with those in part (b). What incorrect inferences might you make if you chose the original model when the first differenced model is the correct one?

h) Do the predictions obtained in part (c) change much if the estimated first-
differenced model is used for prediction?

Price: $13.54

Solution: The downloadable solution consists of 5 pages, 854 words and 6 charts.
Deliverable: Word Document