Question

1. One of the concerns the Federal Reserve has had is the expansionary fiscal policy in light of Covid-19. Included in this policy is the budget deficits. This may lead to inflation. In the context of the material we have reviewed, please answer each question in regards to the idea of inflation and Economic Growth.
   1. Given the Fisher Equation, what is the impact of a zero nominal interest rates (we have approached very low rates recently—although not zero, it has been close) and deflation on the real interest rate. You need to write down the Fisher Equation along with this answer. (6 Points)
   2. If the Federal Reserve’s actions result in extremely low Nominal Rates, how would this impact the Demand for Bonds? What would this response do to the Price of Bonds and Interest Rates? If the Government is running a budget deficit, how does this impact the Supply of Bonds? Note—this creates a dilemma in regards to the ultimate goal of low Nominal Rates—explain this dilemma. (6 Points)
   3. If short term interest rates are lowered to approximate zero percent, how does this impact the Bond Yield Curve (is it normal or inverted—there is an answer that involves one of these issues only). Please draw the curve with the axes labeled properly. In many cases, students draw the figures and graphs on a sheet of paper and scan it—they submit it to the canvas site as a separate attachment. Other students use programs, like excel and Microsoft paint, and put it directly in their exam. Either approach is acceptable. However, if requested, the figures and graphs are required. (4 Points)

Answer 1

Fisher Equation

The Fisher Equation is a mathematical formula that describes the theoretical relationship between the interest rates we observe and the expected rate of inflation.

The formula for the Fisher effect is usually expressed as a mathematical equation:

i_rf = (1 + i_r)(1 + π) – 1,

where i_rf = the nominal risk-free rate, i_r = the real interest rate, and π = expected inflation. In this equation the real interest rate and the inflation rate are compounded, following the mathematical logic. However, not much accuracy is lost by omitting the cross term in the multiplication since it is usually a small number. Doing so, we arrive at a simplified version of the Fisher equation:

i_rf ≈ i_r + π

Economists generally consider deflation to be very negative for an economy and its citizens. Declining prices can lead buyers to sit on their hands, waiting for a better price. This can seriously cramp economic activity, leading to lower demand, lower profits, and higher unemployment.

But let’s take a look at how deflation affects real rates. The following scenario again assumes a nominal rate of return of 1.5%, but this time the inflation rate is -0.5%. (Note that the inflation rate is negative in a deflationary environment.) Here’s how the real rate would look:

Real Rate = 1.5% – (-0.5%) = 2.0%

Impact on bonds

Imagine a pension fund is holding a deposit with a commercial bank. If the interest rate drops, the fund might seek to buy financial assets with a higher return, such as bonds (which are like long-term loans). This increases demand for, and therefore the price of, these assets, which is how the rate cut is transmitted to the broader financial market.

The national debt may seem as far removed from your investments as your parents' debt is from your bank account. But, like your parents' debt, if the federal government's budget deficit grows too large, it will impact your daily life and investments in a painful way.

As the U.S. government issues more Treasury securities to cover its budget deficit, the market supply of bonds increases. For bondholders this is both a boon and a burden: New bonds will provide higher yields but the prices on old bonds will fall. For stock investors, higher rates are only a burden.

Yield Curve

In many of the world’s advanced economies, central banks have set policy rates close to or below zero. Indeed, negative rates have been relatively common for an extended time in many countries.

The yield curve refers to the relationship between short-term interest rates, intermediate interest rates, and long-term interest rates. Under normal economic and market conditions, short-term interest rates are the lowest because there is less embedded inflation risk, while long-term interest rates are the highest.

The most important concern when it comes to negative interest rates is that we do not know at which point people, corporations or financial institutions will want to sell all their bonds and bank deposits and demand cash instead. We don’t know where the lower bound is, and inadvertently reaching this point could be bad for the trust and smooth functioning of the financial system.