FRED work:Real Interest Rates on One-month Treasury Bills

Use FRED database: https://fred.stlouisfed.org

You'll recall that we showed earlier in the term (and above!) that the real interest rate = nominal interest rate minus the inflation rate. Notationally, if i = nominal interest rate;, the rate of inflation; and r, the real interest rate; then r = i - .

An interesting exercise is to determine how the real interest rate on short-term (one-month) Treasury bills (T-bills) has fared over the past decade.This is trickier, however, than simply subtracting the inflation rate from the monthly T-bill rate.Why?Because the T-bill rate is "annualized."(We discussed what "annualized" means when we examined the quarterly rate of growth of GDP.)

To wit, consider the annualized rate of growth of a T-bill that pays0.5% for one month.If we invest $1 today that is compounded monthly, it will pay $1 (1 +. 005) at the end of the first month.And $1 (1+.005) * (1+.005) = $1 * (1+.005)²at the end of the second.And so on.So that at the end of 12 months, the $1 compounded 12 times = $1 * (1+.005)¹².So what is the compounded rate of return?As always, it is (new value - old value) / old value.

So:($1 * (1+.005)¹²- $1) / $1, which equals

$1(1+.005)¹²/ $1 - $1/$1 = (1+.005)¹²- 1

So a compounded 12-month rate of return of a one-month T-bill that pays0.5% per month =

(1+.005)¹²-1 = 0.0617 = 6.17%.

Call up the FRED one-month T-blll rate series by typing GS1M into the search.Remember, the series you just entered shows theannualizedmonthly T-bill rates as explained above.

So our next task is to add the CPI series "CPIAUCSL" and convert it to an annualized inflation rate.(You've already used, by the way, the CPIAUCSL series before.)

While in "Edit Line 1, "add the "CPIAUCSL" series, as before, remembering to click on the series and then to hit "add series."Change the "CPIAUCSL" series units to "compounded annual rate of change") to obtain the annualized percentage change in the inflation rate.This "CPIUCSL" series, of course, is series "b"; the one-month T-bill rate data, series "a."

Now, all you must do is enter the formula shown below to compute the real monthly T-bill rate, using series "a" and "b."

"a-b"

(a)Attach graph

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(b)So has the real (annualized) T-bill rate been for the most part positive or negative over the length of the series?What does this mean?

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(c)What happened to this real rate during the Great Recession of 2008-2009?

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(d)What's happened so far to the real rate during the Great Pandemic Recession?Predictions?

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(e)What is the March2021 value of the monthly (real) (annualized) T-bill rate, expressed as a percentage, rounded to 2 decimal places? Might this suggest a problem for the government going forward?Why or why not?

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