All Terrain Thinking

A Compendium of things I think are Important

Economics: It's not just whats' in your wallet

Answers for the Day
Data Analysis

1. Develop a 'story' to go with each of the following diagrams.

As with all stories, the richness of the story is dependent upon the depth of your background. For someone aware of the history of immigration into this country, the picture here looks very much different from what we saw in the late 19th and early 20th Centuries when immigration reached its peak. At that time immigrants came primarily from Europe and entered through New York City (Ellis Island should make it to your list of places to see). By 1991 Mexico accounted for more than 1 of every two immigrants into the US and approximately 7 of 10 moved from the the Americas and nearly 2 of 10 came from Asia. Europe which once accounted for most of US immigration, was the home to less than 1 of 10 immigrants.

The story here has two parts. The first has to do with the similarity in the two lines and the very real change in the trend. Although the growth was certainly not smooth, there was a definite upward trend in interest rates until the early 1980s at which time we saw rates begin to fall. To even the casual observer, the sharp turn around in the graph suggests something BIG happened here - and it did which will be the subject matter of a later section. There is also the relationship between the two lines. With only a few exceptions, the long term interest rate is above the short-term rate - another issue which we will look at during the semester. You should not be surprised that it will be the periods that the relationship switches that will be the focus of a good deal of attention - just as the turning point gets the attention.

What we have here is a scatter diagram - the most abused graph based on my experience with students in a quantitative analysis class. The graph contains a set of points where each point represents the combination of inflation and interest rates for one year. What you look for in a scatter diagram is a pattern to see if there is a relationship between the two variables. What you should do is attempt to draw a line through the points that captures the general pattern of the points. In this example it would be a line that slopes upward. The upward sloping line indicates a positive relationship between the two variables - when the inflation rate is higher we tend to see higher interest rates.

2 Develop a diagram to go with each of the following 'stories':

a. Percentage of the population supporting education rises to mid age and then begins to decline.

Here we have a graph with the percentage of the population in any age group supporting education measured on the vertical axis and age on the horizontal axis.  When the curve is positive sloped it shows us that as people get older they are more likely to support education.  This support is likely to continue until the age when their children are out of school.  As people get older, however, they are less likely to have school age children and thus they can be expected to be less supportive of education expenses.  We see this when the slope turns negative. 

b. One's grade on the exam tends to improve with hours studied, but the 'rate' of improvement tends to decline after 10 hours

c Max's Market sales for the next 12 months assuming that sales are currently $200,000 per month and will increase $2,000 per month for each of the next 12 months.

d Max's Market sales for the next 12 months assuming that sales are currently $200,000 per month and will increase 1 percent per month for each of the next 12 months.

These two sound very much the same, but as you will see they can produce very different results.  In the first part of the question we have a constant increase of $2,000 per month.  The increase will be $2,000 next month and it will be $2,000 in two years after sales have grown by $24,000.  In the second part we have a constant growth rate and here the rate will remain constant but the actual growth will increase.  In the first year sales will grow $2,000 ($200,000*.01) and after two years sales will have increased to approximately $250,000.  At this time a 1 percent increase will be approximately $2,500, a substantially bigger increase than the $2,000.   The lesson here is be very careful to distinguish growth from growth rate.

3. Election season is always a wonderful time to watch for outrageous claims and counterclaims. Tell me how you feel about the claim made by an incumbent that during her eight years in office the unemployment rate has fallen substantially. Are you ready to accept this as evidence that the economy has done well under the incumbent?

When dealing with this type of claim we begin by recognizing that most phenomena which we are interested in studying are truly multi-dimensional so there are a number of measures which we could use to describe performance. When we are talking about a firm we could use revenue, profit, market share, growth, debt, ... In your economics course you will learn about a number of measures of economic performance such as the unemployment rate, employment growth, inflation rate, and Gross Domestic Product (GDP) to describe . What you will note is that the messages that they are sending are not always consistent, that it is not uncommon for the economic news to be simultaneously good and bad. As you can see below, the economic expansion which produced lower unemployment rates during her tenure in office, came at a cost- higher inflation. If we evaluated her on inflation, we may find that we were unhappy with her and vote her out.

4. Recently a study was conducted to determine the extent to which the drug Ansylium could lower the level of chemical X in one's blood. The producer of Ansylium, in a recent advertisement, presented the graph below as evidence of the success of Ansylium as a treatment for high blood levels of chemical X. What do you believe? Is this conclusive evidence of Ansylium's success? Are you ready to buy into the claim?

Chemical X

There are two potential problems with the graphical proof.

a. There is no scale on the axes which means that you have no idea whether the decline represents a 'significant' decline. Consider the two graphs below-they are identical except for the vertical scale. Although both diagrams have identical shapes, in Diagram A there is a 50 percent decline in X between 1984 and 1990, while in Diagram B the decline is only 2 percent. So be careful when reading a graph. Be sure to read the labels and the units of measurement before you jump to any hasty interpretations.

b. The choice of the time period was such that it is impossible to see what was happening before the introduction of Ansylium. As you can see from the following two graphs, the introduction of the previous data changes substantially how you interpret the fall since the introduction of Ansylium. The graphs differ only in the length of the time series shown. In diagram A, we see only the time period since the introduction of Ansylium which certainly suggests that there has been a pronounced reduction in the blood level of Chemical X. This interpretation is not, however, supported by Diagram B where the time period in Diagram A appears as the shaded area. The recent decline in Chemical X appears to be more a continuation of a long term decline than a reaction to the introduction of Ansylium.

4. You have heard much about the plight of the American worker, how the average earnings for workers in this country are falling. But what is the story? Do you buy into the story after you see the graph below. It is pretty clear that average wages have been rising since the end of WWII.

So you are tired of the whining? Before you make a rash judgment, however, remember that prices have been rising during this period. The real question is, Have wages been growing more or less rapidly than inflation? If wages have been rising, but slower than inflation, then you would expect an inflation adjusted measure to account for that. If you follow the appropriate method of conversion, we get the following graph for real (inflation adjusted) wages. As you can see, which variable we use makes an enormous difference.

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