Question

The Problems update with real-time data in MyLab Economics and are available for practice or instructor assignment. 1. On January 19, 2017, the Federal Reserve released its amended statement on longer-run goals and monetary policy strategy. It stated: “The Committee reaffirms its judgment that inflation at the rate of 2 percent, as measured by the annual change in the price index for personal consumption expenditures, is most consistent over the longer run with the Federal Reserve’s statutory mandate” and that “the median of FOMC participants’ estimates of the longer-run normal rate of unemployment was 4.8 percent.” Assume this statement implies that the natural rate of unemployment is believed to be 4.8%. Go to the St. Louis Federal Reserve FRED database, and find data on the personal consumption expenditure price index (PCECTPI), the unemployment rate (UNRATE), real GDP (GDPC1), and real potential gross domestic product (GDPPOT), an estimate of potential GDP. For the price index, adjust the units setting to “Percent Change From Year Ago.” Download the data into a spreadsheet.

1. For the most recent four quarters of data available, calculate the average inflation gap using the 2% target referenced by the Fed. Calculate this value as the average of the inflation gaps over the four quarters.
2. For the most recent four quarters of data available, calculate the average output gap using the GDP measure and the potential GDP estimate. Calculate the gap as the percentage deviation of output from the potential level of output. Calculate the average value over the most recent four quarters of data available.
3. For the most recent 12 months of data available, calculate the average unemployment gap, using 5.6% as the presumed natural rate of unemployment. Based on your answers to parts (a) through (c), does the divine coincidence apply to the current economic situation? Why or why not? What does your answer imply about the sources of shocks that have impacted the current economy? Briefly explain.

Short answer

1. The average of the inflation gaps over the four quarters is$-0.3$.
2. The average output gap is $3.654$.
3. The average unemployment gap will be $-1.25$.

Step-by-step solution

Part (a) Step 1: Concept Introduction

The inflation gap is the difference between the present rate of inflation and the inflation target. The following formula can be used to represent it:

Inflation Gap = Current inflation - Target inflation

Part (a) Step 2: Explanation

Given,

The inflation target is $2\%$.

The inflation gap is given as:

Inflation Gap = Current inflation - Target inflation

The index for calculation of current inflation is given by using the personal consumption expenditure price index and target inflation is 2%. Thus, the inflation gap for the recent four quarters is given in the table below:

Thus, the inflation gap of recent four quarters is $0,-0.4,-0.5,-0.3$respectively.

Formula to compute average inflation gap:

localid="1647923581008" $\mathrm{Average}\mathrm{inflation}\mathrm{gap}=\frac{\text{Sum of inflation of all periods}}{\text{Number of periods}}$

Substitute the value of total inflation from table 1 above:

localid="1647923588115" $$\begin{gathered} \mathrm{Average}\mathrm{inflation}\mathrm{gap}=\frac{-1.2}{4} \\ \mathrm{Average}\mathrm{inflation}\mathrm{gap}=-0.3 \end{gathered}$$

Therefore, the average inflation gap is $-0.3.$

Part (b) Step 1: Concept Introduction

The output gap is the total amount by which an economy's real output falls short of its potential level of output, or potential GDP. The following formula can be used to represent it:

Output Gap = Real GDP - Potential GDP

Part (b) Step 2: Explanation

Based on the statistics available from the Federal Reserve, the latest 4 quarters of real and potential GDP with the help of which the output gap can be calculated as given via the method above. Consequently, the output gap by the same is computed inside the table as shown:

From the table above the average output gap can be calculated with the formula given below:

$\mathrm{Average}\mathrm{output}\mathrm{gap}=\frac{\text{Sum of output of all periods}}{\text{Number of periods}}$

Substitute, the value of total output from the table above:

$$\begin{gathered} \mathrm{Average}\mathrm{output}\mathrm{gap}=\frac{14.616}{4} \\ \mathrm{Average}\mathrm{output}\mathrm{gap}=3.654 \end{gathered}$$

Part (c) Step 1: Concept Introduction

The difference between the unemployment rate and the natural rate of unemployment in a given economy is referred to as the unemployment gap. It can be calculated using the following formula:

Unemployment Gap = Unemployment Rate - Natural rate of Unemployment

Divine coincidence is a new Keynesian property that shows that the stability of inflation and the stabilization of output levels in an economy should not be mutually exclusive.

Part (c) Step 2: Explanation

As in line with the above system and the information from Federal Reserve, the unemployment gap is calculated and represented within the table under:

The average unemployment rate can be calculated as per the formula given below:

$\mathrm{Average}\mathrm{employment}\mathrm{gap}=\frac{\text{Sum of employment of all periods}}{\text{Number of periods}}$

Substitute the value of total unemployment gap from the table above,

$$\begin{gathered} \mathrm{Average}\mathrm{employment}\mathrm{gap}=\frac{-15}{12} \\ \mathrm{Average}\mathrm{employment}\mathrm{gap}=-1.25 \end{gathered}$$

Consequently, the common unemployment gap will be $-1.25$.

Both the unemployment rate and the inflation rate are negative, according to the answers in parts a. and c. above. The divine coincidence holds true in this instance.

Inflation rates are below the intended level, indicating that either individual has less money to demand or interest rates are not in line with the conditions for taking out a loan. Furthermore, because negative unemployment rates are a sign of improving labor growth, the output is altered in order to stabilize the economy, changing people's expectations for future inflation. Although labor conditions are improving, predicted inflation rates are not improving at the same pace.