# The U S Treasury Yield curve plots the interest rate of a security

```5-23-2002
Econ 240C
Takehome Project Two
Due: 6-12-2002
The U S Treasury Yield curve plots the interest rate of a security against its term or maturity. For
example, the current interest rate on a 3-month Treasury Bill is 1.69% and the current interest rate on a 30year Treasury Bond is 5.62%. So you receive a higher rate of interest for waiting. The question is how
much higher. In this exercise we examine the interest rate spread between the 5-year Treasury Bond and the
3-month Treasury Bill, and its dependence on the Federal Funds Rate.
The conventional wisdom is that the Federal Reserve influences short term interest rates much
more than it influences long term interest rates. The latter are more susceptible to market forces. Since the
Federal Funds Rate is the target rate of the Open Market Committee, when the Fed is trying to stimulate the
economy, it will purchase government securities in the secondary market, increasing excess reserves in the
private banking system. If, in turn, the private banks use these reserves to make more loans, the supply of
credit will increase, and short term interest rates should fall. The Open Market Committee will keep
purchasing treasuries until the Federal Funds Rate falls to the desired target rate. Thus an easy money
policy on the part of the Fed should increase the spread between the 5-year bond and the 3-month bill, if the
rate for the latter falls more than the rate for the former.
Conversely, if the Fed is concerned about inflation, or wishes to cool the economy, it will target a
high Federal Funds Rate and sell government securities in the secondary market, reducing excess reserves
in the private banking system and tightening credit. In this case the spread should fall.
1.
Estimate a distributed lag model between the first difference in the spread variable, dspread (t),
and the first difference in the Federal Funds Rate, dffr (t):
dspread(t) = h(z) dffr(t) + dresid(t) .
(1)
Consider only one-way causality, based on the argument that the Federal Funds Rate is a variable
determined by policy. Of course this policy might be influenced by the spread, a question this assumption
begs. Be sure to model the residual, dresid(t), in Equation (1).
2.
Use this model, i.e. Eq. (1), as a basis for estimating the distributed lag model in levels:
Spread(t) = c + h(z) ffr(t) + resid(t)
(2)
3.
How much of the variation in the interest rate spread is explained in model (2)?
4.
Show a plot of the actual and fitted Federal Funds Rate and the residual from model (2)
5.
Use model (2) to forecast the monthly spread for the rest of 2002, assuming no change in the
Federal Funds Rate for the rest of 2002 and plot your forecast of the spread along with 95%
confidence intervals with the spread dating from January 1995.
6.
Based on the Survey of Professional Forecasters, suppose the FFR is 1.8% in May, 1.9% in June
an increase by 0.1% per month for the rest of the year. Is your forecast much different than that
reported in 5 above?
7.
What would you recommend investing in now, the 5-year bond or the 3-month bill? Is there any
argument for investing in the 3-month bill now and waiting before investing in the 5-year bond?
The data is available at FRED and on the class page as an Excel file: Take2Data
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