 # Economics Laws and Curves

## Question

Phillips Curve
Phillips was A.W. Phillips, an economist from New Zealand who wrote an influential article about inflation in 1958. Let’s figure out a version of the Phillips Curve using a scatter diagram and a trendline. You can read about the Phillips Curve in MacroPolicy, pp. 245-48. Put the unemployment rate on the horizontal x-axis. Put the change in the core inflation rate on the vertical y-axis. To do that, first calculate the core inflation rate (you did that for Spreadsheet #4), then for each pair of years, subtract the earlier year’s inflation rate from the later year’s inflation rate. For example, the core inflation rate for 2010 is 1.0%, and for 2011 it’s 1.7%, so the change in the inflation rate for 2011 is +0.7%.

Calculate the correlation coefficient between the change in the core inflation rate, using only the unemployment rates and core inflation rate changes from 1987 through 2010.

Question 1. What is the correlation coefficient between the change in the core inflation rate and the unemployment rate 1987 to 2010? (The coefficient should be between -1.0 and +1.0; use 2 decimal places. Don’t type a “+” sign. Use a “-“ sign if the answer is negative.)

Now plot a scatter diagram with the unemployment rate for 1987 to 2010 on the horizontal axis, and the change in the core inflation rate on the vertical axis. Add a trendline through the scatter points, with the equation and R-squared. Scatter diagrams and trendlines are explained in the instructions to Spreadsheet #4.

Question 2. True/False. The correlation coefficient, the trendline slope and slope coefficient imply that higher unemployment rates correspond to decreases in the core inflation rate.

We can do something really cool with this trendline and its equation. All along we’ve been saying that the unemployment rate at potential output is about 5%. How do we know that? Where does that come from? Why not 4% like they thought at the beginning of the 1960s, or 6% like they thought at the beginning of the 1990s?

Well, according to our goods market model, if output is more than potential, input prices will rise and second shift #1 will decrease aggregate supply, causing an increase in the inflation rate. If output is less than potential, input prices will fall and second shift #1 will increase aggregate supply, causing a decrease in the inflation rate. So, if output equals potential, second shift #1 will have no effect, and the inflation rate will be stable.

The trendline shows the change in the inflation rate (y) as a function of the unemployment rate (x). If the inflation rate does not change, y=0 (that’s a zero change in the inflation rate from one year to the next). The unemployment rate that makes y=0, then, must be the unemployment rate at potential output!

So, do the calculation. Set y=0 and solve for x using the equation. Be sure to multiply by 100 (or click the “%” format button) to put your answer in percentage terms. Or, you can look at the unemployment rate where the trendline crosses the zero inflation change level on the graph.

Question 3. According to the Phillips Curve trendline or its equation, at what unemployment rate will the change in the inflation rate equal zero? This is an estimate of the unemployment rate at potential output. (Type your answer as a percent, that is, 6.5 not 0.065. Use 1 decimal place. Don't use a "%" or a “+” sign.)

Is your estimate of the unemployment rate at potential output about 5%, like we’ve been saying for months? Let’s give ourselves a margin of error, and say “true” if the estimate is between 4.5% and 5.5%--close enough to 5% for economics!

Question 4. True/False. According to the Phillips Curve trendline or its equation, the unemployment rate at potential output is close to 5% (within =/- 0.5 points).

We only used data through 2010. The trendline doesn’t take account of what happened from 2011 to 2017. Let’s check what the trendline or its equation says should have happened to the inflation rate in 2017.

Question 5. According to the Phillips Curve for 1987-2010, what should have happened to inflation in the year 2017?

a. the core inflation rate should have increased from 2016 to 2017.
b. the core inflation rate should have decreased from 2016 to 2017.

Now look to see what actually happened to the core inflation rate in 2017. How did the inflation rate actually change? Compare the actual change to the prediction from the trendline.

Question 6. True/False. The Phillips Curve for 1987-2010 correctly predicted the change in the core inflation rate from 2016 to 2017.

Question 7. What do the results from Questions 4, 5 and 6 imply for Federal Reserve Policy?

a. The core inflation rate is changing as expected. The Fed should increase the federal funds rate.
b. The core inflation rate is changing as expected. As a result, the Fed is uncertain about how to change the federal funds rate.
c. The core inflation rate is not changing as expected. The Fed should decrease the federal funds rate.
d. The core inflation rate is not changing as expected. As a result, the Fed is uncertain about how to change the federal funds rate.

Okun’s Law
Okun is Arthur Okun, an economist with the Council of Economic Advisors during the Kennedy and Johnson administrations. In the early 1960’s he was asked to figure out the relationship between the unemployment rate and real GDP growth. His fellow economists (as a joke) called his result “Okun’s Law,” and we still call it that. You can read about Okun’s Law in MacroPolicy, p. 238.

First, calculate a correlation coefficient between the change in the unemployment rate and the real GDP growth rate using the years 1987 to 2010.

Question 8. What is the correlation coefficient between the change in the unemployment rate and the real GDP growth rate 1987 to 2010? (The coefficient should be between -1.0 and +1.0; use 2 decimal places. Don’t type a “+” sign. Use a “-“ sign if the answer is negative.)

Now let’s figure out a version of Okun’s Law using a scatter diagram and a trendline. Put the change in the unemployment rate on the horizontal x-axis. To do that, calculate the unemployment rate, then for each pair of years, subtract the earlier year’s unemployment rate from the later year’s unemployment rate. For example, the unemployment rate for 2010 is 9.6%, and for 2011 it’s 8.9%, so the change in the unemployment rate for 2011 is -0.7%. Put the real GDP growth rate on the vertical y-axis. Use only the changes in the unemployment rates and the real GDP growth rates from 1987 through 2010 for your scatter diagram. Add a trendline through the scatter points, with the equation and R-squared.
Question 9. True/False. The correlation coefficient, the trendline slope and equation’s slope coefficient imply that higher real GDP growth rates correspond to decreases in the unemployment rate.

Let’s figure out how fast real GDP has to grow in order to hold the unemployment rate constant (to keep it from rising). A constant unemployment rate from one year to the next means the change in the unemployment rate is zero. The change in the unemployment rate is on the horizontal x-axis. Find zero on the x-axis and look at what the trendline says real GDP growth

must be. Or set x=0 in the trendline equation and solve for y. Remember to multiply by 100 or format as a percent to put the result in percentage form.

Question 10. (1 point) According to the Okun’s Law trendline or its equation, how fast must real GDP grow in order to hold the unemployment rate constant from one year to the next? (Type your answer as a percent, that is, 1.5 not 0.015. Use 1 decimal place. Don't use a "%" or a “+” sign. Don’t use a “-“ sign because your answer won’t be negative—that’s a hint!)
Again, we only used data through 2010. The trendline doesn’t take account of what happened from 2011 to 2017. Let’s check what the trendline or its equation says should have happened to the unemployment rate, with real GDP growth rates for 2011-2017. Then, look to see what actually happened to the unemployment rates in 2011-2017. How did the unemployment rates actually change? Compare the actual change to the prediction from the trendline.

Question 11. Which of the following is true?

a. The 1987-2010 Okun’s Law trendline says that the unemployment rate should have decreased in each year from 2011 to 2017, but in fact unemployment increased in each of those years.
b. The 1987-2010 Okun’s Law trendline says that the unemployment rate should have increased in each year from 2011 to 2017, and in fact unemployment did increase in each of those years.
c. The 1987-2010 Okun’s Law trendline says that the unemployment rate should have decreased in each year from 2011 to 2017, and in fact unemployment did decrease in each of those years.
d. The 1987-2010 Okun’s Law trendline says that the unemployment rate should have increased in each year from 2011 to 2017, but in fact unemployment decreased in each of those years.

Question 12. Which of the following might explain the result in Question 11?

a. When the unemployment rate falls, the labor force must be decreasing. But with fewer resources to employ, businesses produce less output. Real GDP grows more slowly.
b. When real GDP grows more slowly, fewer new jobs are created. But since the labor force is growing slowly, the unemployment rate can remain stable with slower real GDP growth.
c. When the unemployment rate rises, the labor force must be increasing. But with more resources to employ, businesses produce more output. Real GDP grows more rapidly.
d. When real GDP grows more rapidly, more new jobs are created. But since the labor force is growing slowly, the unemployment rate will fall with more rapid real GDP growth

## Solution Preview

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1. It was 1.00%
2. It’s 0.91. So, there is a strong positive relationship between the nominal federal fund rates and the core-inflation-less-unemployment-rate. It means that when the inflation goes up or the unemployement rate goes down, the Fed increases the federal fund rate, as Taylor rule predicts!
3. It’s 4.53% according to the Taylor Rule trend line....
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