Question

Use 2 models to Predict how interest rate will behave when the Fed buys bond in the market. Draw relevant figures.

Answer 1

• The Taylor rule is a formula that can be used to predict or guide how central banks should alter interest rates due to changes in the economy.
• Taylor's rule recommends that the Federal Reserve should raise interest rates when inflation or GDP growth levels are higher than desired.
• Critics believe that the Taylor principle cannot account for sudden jolts in the economy.

Taylor's equation looks like:

r = p + 0.5y + 0.5(p – 2) + 2

Where:

• r = nominal fed funds rate
• p = the rate of inflation
• y = the percent deviation between current real GDP and the long-term linear trend in GDP

Or

Below is a simple formula used to calculate appropriate interest rates according to the Taylor rule:

Target Rate = Neutral rate + 0.5 (GDPe - GDPt) + 0.5 * (Ie - It).

Let's break down the formula and explore what each one of the terms means:

• Target rate: the interest rate that the central bank should target in the short term
• Neutral rate: the current short-term interest rate when the differences found among actual and expected inflation and GDP growth rates are equal to zero
• GDPe: expected GDP growth rate
• GDPt: long-term GDP growth rate
• Ie: expected inflation rate
• It: target inflation rate

IRVING FISHER

The irving fisher model is an economic theory created by economist Irving Fisher that describes the relationship between inflation and both real and nominal interest rates. The Fisher Effect states that the real interest rate equals the nominal interest rate minus the expected inflation rate. Therefore, real interest rates fall as inflation increases, unless nominal rates increase at the same rate as inflation

The economist Irving Fisher constructed a theory which is now referred to as the Fisher Effect, which depicts the relationship which is following between inflation and both the interest rates which are real and nominal interest rates. Here, the fisher states that the real rate of interest is equal to or derived as by subtracting the nominal interest rate with the expected inflation rate. Therefore, because of this relation, a change in the real rate of interest is due to the change in nominal rates.

So, we can say that the Fisher Effect is an economics theory dealing with the relationship between inflation and interest, where we are referring to

Fisher effect equation:

The fisher effect equation depicts or tells us the existing relationship of inflation and both the interest rates. Therefore, according to the Fisher relation equation, the nominal rate of interest is equivalent to the sum of the real rate of interest and the inflation, and this relationship can be depicted with the following equation:

i ≈ r + Pi

In the following fisher equation,

• i = the nominal rate of interest
• r = the real rate of interest, and the
• Pi = the inflation or the expected inflation rate

Or it can also be depicted by the following equation:

I = r + πe

Where,

• r refers to real interest rate,
• i refers to nominal interest rate, and
• πe refers to expected inflation

The fisher effect diagram shown above depicts the relation between the real rate of interest and inflation. As, I is the line of nominal interest rate, and π is the inflation that keeps on changing. So, the horizontal line shows us or represents the real rate of interest. And the point where the nominal rate of interest intersects the real rate of interest is the point where i=r or both the real and nominal rate of interest is equal.