DS280 - Intro to Statistics

Homework #5 - Using Index Numbers

The purpose of this homework exercise is to give you greater familiarity with the uses and applications of the Consumer Price Index. The assignment is due at the beginning of class on Friday, March 12. The assignment is worth 30 points toward your homework/quiz grade.

PROBLEM 1:
In this problem, you are asked to obtain data on the Consumer Price Index, project some future data for that series, and use the computer (Excel) to draw appropriate graphs of the data. While this looks complicated (or at least long), it’s actually a pretty straightforward process. It just takes a lot of words to describe it.

One good source for economic data is the website of the Bureau of Labor Statistics, a federal agency charged with (among other things) computing the Consumer Price Index. The address of their website is: http://www.bls.gov/ .

Step 1 - Find the data
To get CPI data: Access that site. On the right side of the homepage is a column headed "Latest Numbers." The Consumer Price Index is the first item on the list. Select the "Historical Data" link.

The resulting page will give you the data – rather, the most recent ten years of monthly percent change data (the default). To get the entire series, select "More Formatting Options." Request data from the beginning of the series (1947), and opt for "Original Data Value" rather than "One Month Change." Click "Retrieve Data" and you’ll have the entire data series.

The data can be cut-and-pasted directly into Microsoft Excel. (You may need to use the option to "Paste Special" and select "Unicode text.")

Step 2 - Graph the data
Your next task is to create two graphs of the data. One should show how the CPI has grown over time; the other should give the same information but on a logarithmic scale. Use just the end-of-year (rather than the monthly) CPI data.

Use the Excel graphing tools to create these graphs. (They are "X-Y (Scatter)" graphs in Excel terminology.) Make sure they are labeled appropriately. (The graph given on the BLS website does NOT logscale things – hence the need for Excel.)

You are to turn in (1) your two graphs, and (2) a brief commentary on what those two graphs tell you about the cost of living.

PROBLEM 2:
The last exercise focused on how prices have changed over time. This exercise then uses that information to investigate how the value of some other quantity has changed over time.

Pick some price-related measurement that has changed over time, and for which you can obtain a reasonably long series of data. (Ideally, your series should go back at least 20 years, and includes at least 15 data points.) Some examples might be: year-end value of the DowJones Industrial Average since its inception, or the cost of a postage stamp or a gallon of gas. You may find these data in the library or via the Web. (The Statistical Abstract of the United States is available online, by the way. Go to the Census Bureau website, www.census.gov, and under "Special Topics" select "Statistical Abstract." There numerous other online sources of data.) Your raw data should not already be adjusted for inflation. (After all, one purpose of the assignment is to have you make that adjustment!) You may need to consult older editions of the Statistical Abstract to extend a data series back far enough. (The library has old issues of the Statistical Abstract.)

Draw two graphs of the data, one showing how the actual dollar amounts have changed over time, the second showing the change in constant dollar terms (i.e., after adjusting for inflation, using the CPI). Turn in (1) the raw data (with source), (2) a written example, showing how you made the adjustment for inflation, (3) two graphs, and (4) a brief written commentary on what the graphs indicate.