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Economics
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Community College / Lower Division, College / Upper Division
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Phillips Curve
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English
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Inflation/Unemployment Tradeoff and the Phillips Curve: Course Map & Recommended Resources

Overview

Presents a theoretical and statistical explanation of the negative relationship between inflation and unemployment known as the “Phillips Curve.”

Learning Objectives

  1. Demonstrate the short run tradeoff between inflation and unemployment through use of the short run Phillips curve
  2. Demonstrate the relationship between the short run and long run Phillips curves

  3. Discuss how expectations can impact the effectiveness of monetary policy

Learning Topics:

  1. Short run tradeoff between inflation and unemployment through use of the short run Phillips curve
  2. Relationship between the short run and long run Phillips curves
  3. How expectations can impact the effectiveness of monetary policy

Supplemental Content/Alternative Resources

Alternative Economics Sources (Grouped by Learning Topics)

Short run tradeoff between inflation and unemployment through use of the short run Phillips curve

 

Relationship between the short run and long run Phillips curves

  • Principles of Macroeconomics:  Chapter 16 – Inflation and Unemployment
    • Alternative open access text.
    • Authored by: Rittenberg & Tregarthen (2016). Retrieved on: October 26, 2018.
    • Note: There is a project in this chapter using data from the Bureau of Labor Statistics. While this is a good project, we present a similar project using data from FRED. In addition to creating a graph similar to the one proposed in this text, the FRED data allow the student to calculate correlation coefficients for different time periods, and thus quantitatively describe the relationship between inflation and unemployment at various times in the history of the United States. A summary of how to use FRED is included in the final portion of this module.
  • The Economy: Chapter 13.8
    • Important Notes for the instructor regarding this source:
    • Note: This resource, while very good, does not allow for “re-mixing” in a public way.

 

How expectations can impact the effectiveness of monetary policy

 

Non-open access texts:

  • Macroeconomics, Twelfth Edition

    • Authored by: Robert J. Gordon (2012). Provided by: Pearson Publishing.

  • Principles of Economics, Twelfth Edition

    • Authored by: Karl E. Case, Ray C. Fair and Sharon M. Oster (2017). Provided by: Pearson Publishing.

  • Economics, Fourth Edition

    • Authored by: Joseph E. Stiglitz (2007). Provided by: Pearson Publishing. 

Topic Exercise: Using Data to Explore the Phillips Curve

You and your classmates have been hired by the government to study the relationship between inflation and unemployment in the United States. To do this, you will use a data set compiled by the Federal Reserve Bank of St. Louis, known as “F.R.E.D.” (short for “Federal Reserve Economic Data.”) Instructions on how to use this resource are attached below.

  1. Find the relationship between inflation and unemployment between the years 1960 and 1969. To do this, use the variable “UNEMPLOY” (in thousands of persons) on the horizontal axis and the variable “CPIAUCSL” (“as percent change from a year ago”) on the vertical axis. At the same time, graph the unemployment rate on the horizontal axis.  Graph this as a “scatter plot”.

  2. Download the data from FRED into a CSV  file. (Once in this file, the data will look very similar to those found in Excel.) Print out the data set you have created, and then use these data to calculate a correlation coefficient between the two variables. (More details on how to calculate a correlation coefficient in this format are given later.) Briefly explain why this correlation coefficient might be expected, given the data you have been working with and the graph you produced.

  3. Use the same approach to find the relationship between inflation and unemployment in the years between 1970 and 1990. Once again, find and interpret the correlation coefficient for these variables in these new years.

  4. Write a short paper (2-3 pages, including theoretical graphs, as needed) to report to your superiors about what seems to be the relationship between inflation and unemployment when only the years between 1960 and 1969 are studied. Does this relationship seem to hold in the later years? What are some explanations given by economists for why this may be the case? What questions might you want to address in your future research? Why?

 

Thoughts for the Teacher

A possible rubric for this exercise:

A. 25 points for being able to graph these data in a way that illustrates this relationship. Of particular importance are: (5 points for each criteria.)

  • The variables used make sense and are in the correct units (percent or level)
  • The correct years were used to create the graph
  • The graph created is a scatter plot
  • A graph was created that generally shows a negative relationship between inflation and unemployment.
  • The graph is labeled correctly and a short explanation is given on the graph.

B. 25 points for being able to calculate the correlation coefficient for these two variables in this time frame. Of particular importance are: (5 points for each criteria.)

  • The data were downloaded correctly to a data set that is clearly labeled.
  • The data were used to calculate a correlation coefficient between the two variables.
  • The correlation coefficient is in the acceptable range (-1 <  r  <  1)
  • The student is able to correctly interpret the correlation coefficient.
  • The student is able to give insight as to why this correlation coefficient might hold.

C. 25 points for being able to repeat parts A and B for the later time period, which should illustrate that the previous relationship no longer holds. Of particular importance are:

  • A new graph is created correctly, showing the relationship in this new time period.
  • Data is correctly downloaded and presented clearly
  • The correlation coefficient for this time period is calculated correctly.
  • The new correlation coefficient is in the correct range and is interpreted correctly.
  • The student is able to give insight into why this correlation coefficient might differ from the one created earlier.    

D. 25 points for writing a report explaining what was found from the data and the statistics. Of particular importance are:

  • Grammatical structure is correct and the report begins with an opening paragraph and ends with a conclusion.
  • Statements are backed up by results from FRED
  • Graphs illustrating concepts are included to explain the results found
  • Historical events are used to explain why these results occur.
  • Student includes thoughts on direction for “future research.”


Answer Key

1960-1969:

1970-1990:

  • graph: https://fred.stlouisfed.org/graph/?g=lI21
  • Correlation coefficient: -0.00683 (very little relationship, showing a breakdown of the Phillips Curve)                                                                                 

Active Learning Exercise

Activity/Active Learning Exercise

To the students: You and your classmates have been hired to direct the Federal Reserve bank for the next four years (16 quarters).

Although your home office is in Washington, D.C, you report to work at the Federal Reserve Board of San Francisco.

Each quarter, in response to how the economy is doing (or to “exogenous” changes that are reported to you), you must decide what to do with the interest rate; keep it the same, or increase it or decrease it, and by how much. In response to your changes, the economy will react, with changes in unemployment, inflation and the GDP recorded on a graph.

  1. Each member of your group will take a turn setting interest rates. Even when you are not setting rates, be sure to pay attention to what happens in the economy in response to different changes made by your colleagues.

  2. After everyone has had a change to set rates, gather as a group and decide what changes seem to positively affect the economy, and the direction of changes necessary to bring about good outcomes.

  3. As a group, take one more turn setting rates, using what you learned from the previous trials as a guide.

  4. If your team is rehired, you may receive extra credit points on the next exam.


Thoughts for the Teacher

It is very difficult to be “rehired”, but it is possible, especially if one is thinking “outside the box.” If students are able to be successful, you may want to find out what they did, and to compare it to actual economic history (for example, lowering very high interest rates is one approach that seems to work, a situation that is comparable to some years of economic expansion in recent memory.)


A Possible Rubric for this exercise:

25 points for each part, A, B, C and D.

Of particular importance are :

  • Do students work together and watch what the other students are doing, taking their results into consideration when they have their own turn?

  • Does the group share their insights and build upon their colleagues thoughts?

  • Does the logic that the group uses to set rates make economic sense?

  • If the group is not re-hired, what do they suggest doing the next time, so as to improve their results? Can they relate this to any economic events from U.S. history?

Additional informaition on data exercise: FAQS about FRED

Some general links that will help with FRED:

1. What is FRED, and how do I get into it?

  • “FRED” stands for “Federal Reserve Economic Data” and is a collection of publicly available data maintained by the Federal Reserve Board of St. Louis.
  • FRED may be accessed at FRED. Upon entering the web site, either create a password (“register”) or use an already created password (“sign in”). The links to do this are found in the upper right-hand corner of the page.

2. How do I create a graph from a data set I am interested in using?

  • To find a data set, search using a keyword, and then select the appropriate data set from the list that appears. (Be sure to pay attention to which years are available for use. A companion collection of historical data is also available for earlier years.)
  • Upon selecting a data set, a graph of that data will appear on your screen.

3. How do I change the years covered by a graph?

  • Above your graph will be two spaces indicating the years that the graph is illustrating.
  • To change a year, click on the appropriate box and move the cursor through possible years until the correct one appears. Once in a year, select the appropriate month for that year.
  • Change the Time Range

4. How do I change the type of graph?

  • Go to “Format” and change the type of graph to the one desired. For example, you can create a scatter plot or a line graph using this dialogue box.

5. How do I create a two-dimensional graph?

  • Go to “edit graph” and you will be able to add a variable to your graph.
  • The first variable entered will become the variable on the vertical axis, while the second will be the variable on the horizontal axis. If you want to, you can in “Format” when editing the graph.
  • Customize Data, Add Series to Existing Line

6. How do I change a graph?

  • Once a graph is created, go to “edit graph” to make changes. In this dialogue box, you can make many changes. Some possible changes include adding more variables, changing which variable appears on the horizontal or vertical axis, changing the type of graph, and changing the dimensions of the graph.
  • Format the Graph and Line Settings

7. How do I save a graph?

  • In FRED, with your graph on the page, go to “Account tools” and click on “Save Graph”. This will bring up a dialogue box that will allow you to name your graph.
  • Save Your Graphs

8. How do I download data into a spreadsheet?

  • With the graph on the page, go to the “Download” button in the upper right hand corner of the page. Once there, select “CSV” from the options, and the data will soon appear in a spreadsheet.
  • Downloading Data from FRED

9. How do I do statistics with my data?

  • Use the statistical tools from CSV or Excel to do statistical analysis. You may need to upload a supplementary tool to allow you to do more advanced statistics, such as some types of regressions.

  10. How do I calculate a correlation coefficient in CSV?

  • To calculate a correlation coefficient in CSV, download your data and open as a spreadsheet. Once in the data, click on “Data”.
  • An option will appear on the upper right hand side that says “Data analysis”. Click on this, and a list of possible statistical options will appear. Click on “correlation”.
  • Once in “correlation”, highlight the part of your data set that you want to use to calculate a correlation coefficient (you may need to move columns around to be able to do this.) As you highlight the correct rows and columns (be sure you are calculating the coefficient for the correct parameter; either “rows” or “columns”), the labels for these spaces will appear in the dialogue box. Once they are correct, click on “ok”. A correlation coefficient will appear on the spreadsheet.
  • The  correlation coefficient, “r” is a numerical value that summarizes that relationship between two variables. Values close to 1 and negative 1 indicate a strong relationship, while values close to zero indicate very little relationship between two variables.
  • Calculating Correlation Coefficient R (Video)

11. How do I share graphs?

  • Go to “share links” and click on “paper short URL” to have the program create a shareable URL link for your graph.
  • Share my FRED Graph

12.  How do I re-access graphs I have created?

  • Go to “Account tools” and select “My Account” The graphs you have saved will appear, along with a notation as to when they were created.

 

Works cited in “FAQS about FRED”

Federal Reserve Board of St. Louis. “FRED: Economic Research” Retrieved on October 27, 2018 from https://fred.stlouisfed.org/.

Federal Reserve Board of St. Louis. “FRED: Master 10 tools in 10 minutes” Retrieved on October 27, 2018 from https://news.research.stlouisfed.org/2016/01/fred-master-10-tool-in-10-minutes/

Federal Reserve Board of St. Louis. “Frequently Asked Questions”  Retrieved on October 27, 2018 from https://fredhelp.stlouisfed.org/#fred-faq-frequently-asked-questions.

Federal Reserve Board of St. Louis. “Getting to Know FRED: Changing the Time Range” Retrieved on October 27, 2018 from https://fredhelp.stlouisfed.org/fred/graphs/customize-a-fred-graph/change-graph-time-range/

Federal Reserve Board of St. Louis. “Getting to Know FRED: Customize Data, Add Series to Existing Line.” Retrieved on October 27, 2018 from https://fredhelp.stlouisfed.org/fred/graphs/customize-a-fred-graph/data-transformation-add-series-to-existing-line/

Federal Reserve Board of St. Louis. “Getting to Know FRED: Downloading Data from FRED” Retrieved on October 27, 2018 from https://fredhelp.stlouisfed.org/fred/data/downloading/using-the-download-data-link/

Federal Reserve Board of St. Louis. “Getting to Know Fred: Save Your Graphs” Retrieved from https://fredhelp.stlouisfed.org/fred/account/fred-account-features/save/

Federal Reserve Board of St. Louis. “How can I find Data on FRED?” Retrieved on October 27, 2018 from https://fredhelp.stlouisfed.org/#fred-data-how-can-i-find-data-on-fred

Federal Reserve Board of St. Louis. “Getting to Know FRED: How Can I Share My FRED Graph?” Retrieved on  October 27, 2018 from https://fredhelp.stlouisfed.org/category/fred/graphs/share-my-fred-graph/

Kahn, Sal. “Calculating Correlation Coefficient r (video with text)” Retrieved on October 27, 2018 from https://www.khanacademy.org/math/ap-statistics/bivariate-data-ap/correlation-coefficient-r/v/cal

Deriving Phillips Curve from Macroeconomic Models

Deriving the Phillips Curve from Macroeconomic Models

In 1958, the British economist William Phillips discovered a negative statistical relationship between the inflation rate and the unemployment rate. This relationship became known as the “Phillips Curve.”

The statistical relationship, which holds for many countries at many times in history, but not under all conditions, can be derived from well-accepted macroeconomic theory and models. This section of this module seeks to derive the Phillips Curve using such models as a starting point. It is divided into five sections.

  1. The Keynesian model and the role of consumption and investment
  2. Monetary policy and the Keynesian model
  3. The Price Level and its effect on the Money Market
  4. The AD curve and its relationship to monetary policy and the price level, adding the AS curve to create the AS/Ad model
  5. The Phillips Curve in the short run and long run

We will discuss each step in the derivation of this curve using accepted economic models as starting points.

 

The Keynesian Model

In 1936, in part in response to the global wide Great Depression, John Maynard Keynes published his book, The General Theory of Employment, Interest and Money .

Central to this work is the idea that we did not have to wait for the economy to return to an equilibrium “in the long run” (as was commonly asserted by economists of the time), but could, instead, take action to move the economy towards a more desirable level of income. Of particular importance to Keynes were changes in “aggregate expenditure.” Such expenditure is often summarized by economists as a combination of consumption expenditures, investment expenditures and government spending, or, in equation form, “C + I + G”. Of course, there is the entire rest of the world to include, and it can be shown that including it under certain conditions will lead to results that augment the results found here.

Note that the “G” component of this sum is easily manipulated by the government, which can change aggregate expenditures easily by increasing expenditures, as when, for example, it decides to build a new bridge, or, as was done as part of the New Deal of the 1930s, the Hoover Dam.

However, aggregate expenditures can also be affected by changes in C and I. We will examine those cases more closely later.

 

Graphing the Keynesian Model

The Keynesian model can be drawn using a graph plotting aggregate expenditures (equal to, without an international sector, C +I+G) on the vertical axis, and income on the horizontal axis. With an upward sloping line beginning at some exogenous level of spending and sloping upwards with a slope equal to the marginal rate of consumption, we find the equilibrium income level at the point where aggregate expenditure line intersects the forty five degree line, indicating that the amount of people in the economy plan to spend is equal to the amount that is being produced. As, in equilibrium, all income must be spent by someone, the equilibrium level of income (where increasing or decreasing inventory investment does not induce firms to decrease or increase output, respectively) will be found where income, Y = C+I+G. A graph of this model is shown below.

 

                                   

           


A more detailed, interactive example of how this model works is found at: Wolfram Demonstrations Project which presents a graphic presentation of the Keynesian Cross diagram

Additional Resources

  • link to Keynesian Economics module

Study Question

For the following model:

  1. Find the equilibrium level of income:
    • C = 10 + 0.8Y

    • I = 20

    • G = 30

  2. What would happen to equilibrium income if G increased to 50? If it decreased to 20?
  3. How do these changes relate to the approach the U.S. used to get out of the Great Depression?

 

Monetary Policy and the Keynesian Model

The model presented above can be expanded to include a market for money.

“Money” can take on many different forms, from dollar bills to beads made of seashells to huge wheels on the island of Yap that don’t look anything like most think of as “money.” For this model, it is assumed that money is “fiat” money, that is, money that is declared to be money by fiat by the government. That means that the government determines the money supply, through mechanisms directed by the Federal Reserve system.

As the money market is just that, a market, it must operate using a price and according to the rules of supply and demand. As more money can be obtained when it is desired by borrowing at the going interest rate, “r” the price of money is seen as being the interest rate at which money can be borrowed. Further, it is clear that there is a downward sloping demand curve for money (MD). At high interest rates, less money will be demanded, while at lower interest rates, more money will be demanded. In the same market, the government creates a supply of money (MS), a supply that is not dependent on the interest rate but which can be seen as a vertical supply curve that is independent of the interest rate. Thus, the market for money may be drawn as shown below. Note that the intersection of money supply and money demand yield an equilibrium interest rate

 

Money Supply and Demand

It is through these changes in interest rate that changes in the money supply affect the level of total aggregate expenditure in an economy, which, in turn, affect the equilibrium level of output in that economy. This is done through the effect of interest rates on Consumption and Investment.

Consumption, often seen as consumer expenditure, depends on the interest rate. Lower interest rates induce consumers to purchase more goods, while higher interest rates cause them to refrain from purchasing goods. This applies even if a consumer pays cash for goods, as the opportunity cost of using cash to buy something is the interest that they could be earning if they would have left that money in the bank to earn interest on a savings account. Thus, when we focus on C, lower interest rates will shift the aggregate expenditures curve up, thus increasing equilibrium income.

A similar situation is found with investment, which is often seen from the point of view of a firm. Again, lower interest rates induce firms to invest more, while higher interest rates induce them to invest less. Again, the issue of whether they borrow to fund such investments or use cash is irrelevant, as the firm faces the question of whether to leave money to earn interest in the bank even if they can pay cash to purchase a machine or a building. Again, lower interests will shift the aggregate expenditures curve up, thus increasing equilibrium income.

An increase in aggregate expenditures from AE to AEˊ due to a decline in interest rates increases equilibrium income from Ye to Yeˊ.

Including the money market thus gives the government another tool to use to affect aggregate expenditures in the economy. It may now use either fiscal policy, through changes in G or T (or subsidies, which are negative taxes), or monetary policy, which manipulates the interest rate through changes in the money supply to bring about changes in aggregate expenditures, and therefore in equilibrium income.

Additional Resources

Study Question

Draw on the concept of “opportunity cost” to answer the following questions.

  1. What happens to the demand for bonds and stocks in the stock market when the equilibrium interest rate decreases? Why?

  2. What happens to the demand for bonds and stocks in the stock market when the equilibrium interest rate increases? Why?

 

The Price Level and its Effect on the Money Market

It is clear that the government can change the number of monetary units it produces, as it sees fit. The number of bills it prints or the number of stones it decides to call “money” is known as the “nominal money supply.”               

However, it may be that the purchasing power of that money supply will change with time, and so we are also concerned with “real” money supply, a value that takes into the effects of inflation and deflation. For example, a dollar bill today will buy less than a dollar bill bought in 1970, and even less than what the same dollar bought in 1950. Thus, regardless of the nominal money supply, the real money supply will change as a result of changes in the overall price level. As the real money supply is the nominal money supply divided by a measure of the price level, an increase in the price level will lead to a lower real money supply and therefore, as we saw when studying the money market, leading to higher interest rates. Meanwhile, lower price levels will lead to higher real money supply and therefore lower interest rates.

What does this mean for aggregate expenditure? Recall that aggregate expenditure can be seen as the sum of C+I+G. As price levels change and therefore affect the real money supply, changes in the interest rate will also occur, with results similar to those found for changes in the nominal money supply. Once we add an international sector, this Aggregate Expenditure can be expanded to C + I + G + (X - M), where X represents exports and M represents imports.

Consumption may be affected by changes in the price level when such changes influence the real money supply. An increase in the price level lowers the real money supply, thus causing the equilibrium level of interest to increase. As before, a higher interest rate leads to lower spending by consumers, while a lower interest rate (found when the price level decreases) leads to more consumer spending. Thus, from the point of view of C, a lower price level leads to lower interest rates will shift the aggregate expenditures curve up, thus increasing equilibrium income. As the price level decreases, equilibrium output increases, and vice versa.

A similar situation is found with investment, Again, a higher price level leads to a lower real money supply and therefore higher interest rates which induces firms to invest less, while a lower price level leads to a higher real money supply, and therefore lower interest rates which induce firms to invest more. As the price level increases, equilibrium output falls and vice versa.

Note that the result of changes in the price level is an inverse relationship between the price level and the equilibrium level of output derived from the Keynesian model.

Additional Resources

Study Question

  1. Graph the relationship between the price level in an economy and the level of equilibrium output in that economy, holding everything else constant. Graph the price level on the vertical axis and the equilibrium level of output on the horizontal axis.
  2. What is the economic term for “holding everything else constant”?

     

    The AD Curve and its Relationship to Monetary Policy and the Price Level

    This inverse relationship between the price level and the resulting equilibrium income level derived above is often depicted in the “Aggregate Demand curve” (AD). This curve maps levels of price with equilibrium levels of output, and illustrates a negative relationship, as illustrated in the discussion and study question above.

    To make use of this relationship, we will present another curve, mapped onto the same graph with price level as the vertical axis and equilibrium output as the horizontal axis. This new curve is a relationship that is dependent on the total resources that are available to an economy, and is called “Aggregate Supply curve (AS)”. While it, like the market supply curves learned earlier, is upward sloping, it is not merely a collection of supply curves. Note that the vertical price axis is not the price of a good but the price level of all goods in an economy, and the horizontal output axis is not the level of output produced by a firm but the total output in an economy, determined in part by the aggregate expenditures in that economy.

    The aggregate supply curve is a relationship between the price level and output that depends on the total resources available in an economy. It notes that there is some limit to the amount of resources available in an economy, and that to seek to produce more than can actually be produced will push wages and prices up, as firms bid for the limited number of workers or limited amount of other inputs. Alternatively, to produce less than can be produced in an economy will lead to no such pressure on wages and prices and will therefore allow for wages and prices to be at a lower level. The relationship between output and prices can therefore be graphed by combining several characteristics of several portions of this relationship. On the left side of the AS curve is a flat section at some low price level. There is also a section which is steep at some high level of income. These two sections can be connected with a section of the graph that is gently upwardly sloping, giving the entire Aggregate Supply Curve illustrating combinations of the price level and output that are possible with current resources and technology.

    Putting both the Aggregate Supply and Aggregate Demand curves on the same graph, gives the Aggregate Demand/Aggregate Supply (AD/AS) model. Recall, as mentioned earlier, that these curves (and the variables on the axes) have a very different meaning than do the simple supply and demand curves you learned earlier.    

    Note that an increase in government spending (G) or an increase in C or I due to expansionary monetary policy shifts the AD curve to the right to ADˊ for each price level, leading to a new, higher level of equilibrium output, Y. If the new AD curve intersects the AS curve on an upward sloping (but not vertical) portion of that curve, the price level will increase as output also increases.

    As outlined above, there are actually three regions of the AS curve. The first portion is on the left of the curve, where it becomes horizontal, indicating that equilibrium income can be increased without causing price levels to increase. This region is sometimes called the “Keynesian” region of the curve, and refers to the values of Y that are most associated with unemployment, as was the case when Keynes wrote, during the Great Depression.

    The second region occurs at high levels of equilibrium income, when the economy is facing the limits to its productive capacity. An effort to increase Y in this region will only lead to an increase in the price level, as wages and the price of inputs are bid up in an attempt to expand output. This is often called the “Classical” region, as classical economists believed that an increase in demand leads to an increase in prices.

    A third region is found between these two extremes, where the AS curve slopes up, leading to wages and prices being bid up as equilibrium output is successfully increased. It is in this region that the relationship known as the “Phillips Curve” is seen.

    Additional Resources

    Study Question

    1. What is the shift in the AD curve found when G is increased by an amount of 10 when the consumption function is C = 10 + 0.75Y?

    2. If G is increased by 10, what eventually happens to output inflation and unemployment in the Keynesian section of the AS curve? In the Classical section?


    The Phillips Curve (Short Run)

    What happens as AD shifts to the right along a stable AS curve? The result depends on which portion of the AS curve intersects with the AD curve. If the AD curve shifts to the right along the Keynesian section of the AS curve, prices are constant while output increases, as was the case as the U.S. recovered from the Great Depression (as well as other times of recession, as in 2008.) If the AD curve meets the AS curve on the vertical portion of the AS curve, such an effort to increase output only increases prices and not output.

    However, if the AD curve meets the AS curve on the upward sloping portion of the AS curve, an increase in output is accompanied by an increase in price level. One important aspect of this change in price is the percent change in price. It is possible to take the change in price and divide it by either the original price or an average of the original and final price, to find the percent change in price. The statistical relationship discovered by British economist William Phillips in the 1950s graphs the percent change in price level and the unemployment level.

    Recalling Calculus, the graph of the Phillips Curve may be seen as being a graph of the slope of (the derivative of) the Aggregate Supply curve on the upward sloping portion of the AS curve. Looking at it this way, the variable on the horizontal axis is the difference between full employment and the actual employment level.  As we move towards the flatter “Keynesian” region, where unemployment is high, the slope of the AS curve is small, leading to a low inflation.  As we move towards combinations where output is high, in the steeper “classical” region, unemployment is low but the slope of the AS curve is steep, implying high inflation.

    Alternatively, when the percent change in price is low, as is found on the flatter portion of the upward sloping part of the AS curve, unemployment is high.

    The percent change in price is actually the definition of the term “inflation”, or a general increase in the overall price level. As indicated above, when such a change is high, unemployment is low, while when such a change is low, unemployment is high. This inverse relationship between inflation and unemployment gives theoretical support to the short-run statistical relationship known as the short-run “Phillips Curve.”

     

    The Phillips Curve (The Breakdown)

    Why do we refer to this relationship as “short-run”? The answer to that can be found in the statistical data from the middle of the twentieth century. While the Phillips Curve relationship held for much of the early part of that century, it seemed to break down towards the end of that time period. Beginning in the 1970s, the clear trade-off between inflation and unemployment was no longer found, and economists were shocked to see a situation of both high inflation and high unemployment, a phenomenon they dubbed “stagflation.”  Clearly the neat menu illustrating combinations of inflation and unemployment that could be found in the economy at one time no longer held. A close study of what was happening in the economy at that time suggested some reasons for why this was happening.

    The 1970s saw the economy in the U.S., as well as in many countries throughout the world, being threatened by the decision of oil producing countries instituting an embargo on the sale of oil to countries severely dependent on such oil. This constraint in resources used for production might be seen as a shift in the AS curve to the left along a stable AD curve, leading to lower output at higher price levels. Indeed, while the values of unemployment and inflation seem to be inversely related during the early years of that century, such a relationship severely breaks down in the 1970s.

    It is proposed that, since the short run Phillips curve studied above can shift with changes in productive capacity in an economy, there is actually no long run trade-off between inflation and unemployment. Indeed, there may be only one long run level of output, at the “natural rate of unemployment”, this is that level of unemployment that consists of only frictional and structural unemployment. In the long run, the Phillips Curve is vertical and that natural rate of unemployment, a level that can be associated with any possible level of inflation, depending on the availability of labor and other resources.

    Additional Resources

    Study Question

    1. What historical economic events might have shifted the AS curve to the left?
    2. What historical economic events might have shifted the AS curve to the right?
    3. In each of the above cases, what would you expect to happen to the short run Phillips curve? Why do you say this? Be sure you can draw a graph backing up your thoughts
    4. In each case, what, if anything, would you expect to happen to the long fun Phillips curve? Why do you say this? Be sure you can draw a graph backing up your thoughts.

     

    The Phillips Curve (Long Run)

    For many years, economists thought that the inverse relationship between inflation and unemployment first found in Britain in the 1950s would always hold. There seemed to be a menu of combinations of inflation and unemployment from which policymakers could choose. However, after observing this hold relationship throughout the 1960s in the United States, something unexpected happened.

    Beginning in the 1970s in the United States, the negative relationship between these two variables seemed to break down, producing a pattern that was more “random” than expected. What should have been a smooth negatively sloped curve instead seemed to be combinations that did not follow any pattern at all. An explanation for this apparent challenge to the Phillips curve was proposed by economists Edmund Phelps and Milton Friedman, who proposed that there were short-run Phillips curves that shifted over time, responding to shifts in the Aggregate Supply curve from changes in resource availability (such as oil) and, in addition, to changing expectations in the anticipated level of inflation.

    Expectations of inflation influence the Phillips curve by shifting the underlying Aggregate Supply curve in response to wage contracts that are dependent on price expectations. Expectations of zero inflation lead to workers making wage contracts incorporating no inflation, while expectations of positive inflation led workers to sign contracts with higher wages to incorporate expected higher future prices. Contracts involving higher wages lead to an increase in costs for firms, therefore lowering the output attainable at any given price level. The change can be illustrated as a shift in the AS curve, leading to a shift in the short run Phillips Curve due to an increase in expected inflation, and this resulting inflation will no longer lead to the decline in unemployment seen as an effect of inflation when expectations for inflation are zero.

    In the long run, Friedman and Phelps proposed, there is only one level of output that is consistent with accurate expectations of inflation, a level of output in which any inflation is accurately predicted and incorporated into decisions about wage contracts. With the Aggregate Supply curve responding to changes in expectations about inflation through the mechanism of wage contracts dependent on such expectations, there is no longer a way to decrease either inflation or unemployment by trading off one for the other. This level of output is found at what they named the “long run Phillips Curve”

                   


    Work Cited in “Deriving the Phillips Curve From Macroeconomic Models”

    Goldstein, Jacob and David Kesterbaum. (December 10, 2010). “the Island of Stone Money”, Retrieved  from https://www.npr.org/sections/money/2011/02/15/131934618/the-island-of-stone-money. October 27, 2018.

    Keynes, John Maynard. (1936) The General Theory of Employment, Interest and Money. Retrieved from http://www.hetwebsite.net/het/texts/keynes/gt/gtcont.htm. October 27, 2018.

    Fiona Maclachlan (March 2011) “the Keynesian Cross Diagram” Wolfram Demonstrations Project. Retrieved from http://demonstrations.wolfram.com/KeynesianCrossDiagram/. October 27, 2018.