Economics: Equilibrium Interest Rates

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Questions and Answers

What is the condition for equilibrium at the aggregate level?

Option A is less than option B

Option A is equal to option B (correct)

Option A is greater than option B

Option A is unrelated to option B

What is the relationship between the long rate and the short rate of interest in equilibrium?

The long rate is always less than the short rate

The long rate is always greater than the short rate

The long rate plus unity equals the geometric average of each year's expected short rate (correct)

The long rate is unrelated to the short rate

What happens to the yield curve if future short rates are expected to rise?

The yield curve will be flat

The yield curve will be horizontal

The yield curve will be downwards sloping

The yield curve will be upwards sloping (correct)

What is a limitation of the Expectations Hypothesis?

It assumes that all agents hold the same expectations with certainty Signup and view all the answers

What happens to the long-term rate if future short rates are expected to fall?

The long-term rate will be less than the current short rate Signup and view all the answers

What is the relationship between the slope of the yield curve and the expected change in the short rates?

The slope of the yield curve is directly related to the expected change in the short rates Signup and view all the answers

What is the empirical evidence for the liquidity premium hypothesis?

The upwards slope of the yield curve, especially for short maturities Signup and view all the answers

What is the main challenge in econometric testing of the hypotheses related to the yield curve?

Ex ante expectations need to be specified from ex post data Signup and view all the answers

What is the relationship between real and nominal interest rates according to Fisher?

(1 + 𝜌)(1 + 𝜋) = (1 + 𝑟) Signup and view all the answers

What does the Fisher relation suggest about the real interest rate if money is neutral?

It will be roughly constant Signup and view all the answers

According to Fama (1975), how can short-term interest rates be used to predict inflation expectations?

By using short-term interest rates as a proxy for inflation expectations Signup and view all the answers

What is the main assumption of the expectations hypothesis?

Expectations of future interest rates are reflected in current long-term rates Signup and view all the answers

What is a limitation of the traditional yield curve charts?

They only deal with differences in the maturity of the bonds Signup and view all the answers

What does the expected interest rate one year from now on a two-year bond refer to?

The rate we now expect to exist one year from now on a bond which, if bought at that time, has a term of two years from that date Signup and view all the answers

Which of the following theories of the term structure is considered the most general?

Expectations Hypothesis Signup and view all the answers

What is the primary assumption of the Expectations Hypothesis?

Market participants have different expectations about future interest rates Signup and view all the answers

What is the purpose of interpolation in the traditional yield curve charts?

To fill gaps in the maturity structure Signup and view all the answers

What is the notation for the expected interest rate one year from now on a bond that has a term of two years from that date?

r_t,t+1,1 Signup and view all the answers

Study Notes

The Expectations Hypothesis

The equilibrium is when option A = option B, where 𝑒 𝑒 𝑒 𝑃𝑏 (1 + 𝑅𝑡,𝑛 )𝑛 = 𝑃𝑏 (1 + 𝑅𝑡,1 )(1 + 𝑡𝑟𝑡+1,1 )(1 + 𝑡𝑟𝑡+2,1 ) ….(1 + 𝑡𝑟𝑡+𝑛−1,1 )𝑛
Cancelling Pb from both sides and rearranging gives: 𝑛 𝑒 𝑒 𝑒 𝑅𝑡,𝑛 = √(1 + 𝑅𝑡,1 )(1 + 𝑡𝑟𝑡+1,1 )(1 + 𝑡𝑟𝑡+2,1 ) ….(1 + 𝑡𝑟𝑡+𝑛−1,1 )𝑛 − 1

The Relationship Between Long and Short Rates

In equilibrium, there is a specific relationship between the long rate and the short rate of interest: the long rate plus unity equals the geometric average of each year's expected short rate over the period of the long bond.
If future short rates are expected to be the same in every year as the current long rate, then the yield curve will be horizontal.
If future short rates are expected to rise, the long-term rate will be greater than the current short rate and the yield curve will be upwards sloping.
If future short rates are expected to fall, the long-term rate will be less than the current short rate and the yield curve will be downwards sloping.

Limitations of the Expectations Hypothesis

The Expectations Hypothesis assumes that all agents hold the same expectations with certainty.
The hypothesis is limited in a practical sense, with two assumptions standing out as particularly impractical.

The Liquidity Premium Hypothesis

The frequently observed upwards slope of the yield curve, especially for short maturities, is the empirical evidence for the liquidity premium hypothesis.
Difficulties arise in econometric testing and specification of the various hypotheses.

The Fisher Relation

The Fisher relation is: 𝜌≅𝑟−𝜋
If money is neutral, then the real rate will be roughly constant and inflation expectations and nominal interest rates will move together.
Short-term interest rates may be used to predict inflation expectations.

Theories of the Term Structure

There are three theories of the term structure: the expectations, segmentation, and liquidity hypotheses.
The Expectations Hypothesis is the most general, with other models being discussed partly by way of a critique of this model.

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Test your understanding of the relationship between long and short interest rates in economics. Learn how to calculate the equilibrium interest rate and practice with our quiz.