Part I. Assemble your data.

1. The US Geological Survey maintains data on US mineral prices over time. Go to https://pubs.usgs.gov/sir/2012/5188/tables/ and locate the Excel workbook for your assigned mineral. It will list the (nominal) US price of the mineral by year. Download the workbook.

2. Examine the price data. Note the units of measurement of price. For example, the aluminum price is in dollars per pound. Note the earliest year in which a fairly continuous price series begins (i.e., the first year in which there is a long sequence of years with data on prices, even if there is a gap or two of 3-4 years with no price data). For example, for aluminum, a continuous price series begins in 1895. For some minerals, the price series begins in the 1950s or later. Note the last year with price data; this will usually be 2010 (or 2009). The number of years in the data does not affect the difficulty of the assignment. Finally note if there are any years in the middle of the data series with missing price observations – if that occurs, ask me how to handle it.

3. Insert a new worksheet into your workbook. Then transfer the data from the sheet you downloaded to this sheet, but starting with the first year in which a continuous price series begins (or with 1800, whichever is later). The first row in this sheet will be a header row with labels for the data appearing in the columns. For example, the entry in row 1, column A is “Year.” Fill in column A with the years for which you have a fairly continuous price series (aluminum entries in column A run from 1895 to 2010). In column B, under the heading “Nominal Price,” enter the price for each year from the data you downloaded.

4. In column C, under the heading CPI, enter the annual value of the CPI for each year in your data. You may use the data on the CPI from webcourses, which includes estimates of the CPI from 1800-1912, and the CPI from 1913-present. The base year is 1982-84. Information on the estimates of the CPI before 1913 can be found at the link below, if you are interested.

https://www.minneapolisfed.org/community/financial-and-economic-education/cpi-calculator information/consumer-price-index-1800

5. In column D, under the heading Inflator, compute the annual inflator to use to convert the nominal price data to the real price in $2010. As an economics major, you should know how to do this. If not, look it up.

6. In column E, under the heading Price_$2010, apply the inflator to compute the real price of the mineral in 2010 dollars. As an economics major, you should know how to do this. 7. In column F, under the heading Lag Price, compute the first lag of the real price of the mineral. In each year, this is the real price in the prior year. Thus the 1900 value of Lag Price is the real

price in 1899. Note this value cannot be computed for the first year in your data; leave the top cell (F2) blank.

8. In column G, under the heading FD Price, compute the first difference of the real price. In yeart the first difference of price equals Pt Pt ( ) ( 1), − − i.e., it is the price in one year minus the price in the previous year, or entries in column E minus entries in column F. Again, this cannot be computed in the first year of your data so leave cell G2 blank.

9. In column H, under the heading Proportionate Price Change, compute the annual rate of change of real price in each year. In yeart the proportionate rate of price change equals [Pt Pt Pt ( ) ( 1) ( 1). −− − ] For example, in 1980, the value is the real price difference between 1980 and 1979 divided by the real price in 1979, i.e., it is the entry in column G divided by the entry in column F. Again, this value cannot be computed in the first year of your data so leave cell H2 blank.

10. In column I, under the heading Log Price, compute the natural log of the real price of the mineral (the excel formula is LN). Make this computation for each year, including the first. 11. In column J, under the heading Time, enter a so-called trend variable which equals 1 in the first year of your data, 2 in the second, and so on until the last year in your data. 12. To illustrate, the spreadsheet containing the data for aluminum has the following entries for the first few and last few rows:

Year

Nominal

Price CPI Inflator Price_$2010

Lag Price

FD

Price

Proportionate Price Change

Log

Price Time

1895 0.587 8.3 26.213 15.387 2.73351 1 1896 0.507 8.3 26.213 13.290 15.387 -2.097 -0.1363 2.58699 2 1897 0.39 8.3 26.213 10.223 13.290 -3.067 -0.2308 2.32463 3 1898 0.306 8.3 26.213 8.021 10.223 -2.202 -0.2154 2.08207 4 1899 0.327 8.3 26.213 8.571 8.021 0.550 0.0686 2.14844 5 1900 0.327 8.3 26.213 8.571 8.571 0.000 0.0000 2.14844 6 1901 0.33 8.3 26.213 8.650 8.571 0.079 0.0092 2.15757 7 1902 0.33 8.7 25.204 8.317 8.650 -0.333 -0.0385 2.11835 8 1903 0.33 9.0 24.271 8.009 8.317 -0.308 -0.0370 2.08061 9 …

2008 1.205 215.3 1.013 1.221 1.286 -0.065 -0.0506 0.19940 114 2009 0.794 214.5 1.017 0.807 1.221 -0.413 -0.3386 -0.21403 115 2010 1.044 218.1 1.000 1.044 0.807 0.237 0.2932 0.04306 116

Part II. Analyze your data and construct your appendix.

1. Construct a clearly labeled time series graph (line chart) of the real price of the mineral over the time period in your data. Include a copy of the chart as Figure 1 in your appendix. See the end of this document for an example appendix for the data analysis of aluminum.

2. Construct a clearly labeled time series graph of the proportionate rate of real price change of the mineral (this series begins in the second year of your data), and include a copy as Figure 2 in your appendix.

3. Compute a log trend regression of the natural log of the real price of the mineral (dependent or Y-variable in the regression) on “Time,” the time-trend variable (independent or X-variable in

the regression). The population regression is Logprice Time u =+ + β β 0 1 , whereu is a random disturbance with E u Time ( | ) 0. = Under the standard assumptions of regression analysis, the slope coefficient β1 = d Logprice d Time dP P dt ( ) ( ) = ( / ) = the proportionate rate of price change. According to the Hotelling model, the slope should equal, approximately, (1+ r) , where r denotes the real rate of return to alternative investments. Also obtain a line fit plot of this regression.

4. Fully document the regression in your appendix (along with the line fit plot) as shown in the example appendix. Also report the fitted regression in summary terms in the text of your essay along the lines shown here for the aluminum regression:

*** *** 2 ˆ 2.041 0.0203 , 0.85, 116

Logprice Time R N

=− ==

( ) ( ) ( )

0.054 0.0008 1,114 655.284.

F

=

Part III. Use your data analysis to test the predictions of the Hotelling model for the mineral you examined.

Write a well-organized and succinct essay (2 pages double-spaced maximum, not including appendix, in 11- or 12-point font) that uses your data analysis for your mineral to assess how well the predictions of the Hotelling model match the data. Write in a professional style using the conventions of the English language.

You should turn in your essay and appendix as one document, and an electronic copy of your data and data analysis as a separate document, by Thursday, December 10 at 11:59 PM.

Do not write the essay as if answering a sequence of questions, but be sure to address the following points in any order that seems best to you.

1. What mineral are you examining? Very briefly, what is it used for?

2. Describe your data: its source, the years included, the units of measurement of the nominal price. Report the formula you used to compute the price inflator and to inflate nominal prices to 2010 dollars. Indicate how you measured the proportionate rate of price change.

3. Briefly explain what the basic Hotelling model of natural resource extraction predicts for the behavior of real mineral price over time.

4. Describe the actual behavior of the real price over time for your mineral, with reference to the time series graph you constructed for the real price, and discuss whether/to what extent the time-path of price seems to match, or not to match, the predictions of the Hotelling model.

5. Describe the behavior of the proportionate rate of real price change, with reference to the time series graph of this variable that you constructed, and again discuss whether/to what extent the time-path of the proportionate rate of price change seems to match the predictions of the Hotelling model.

6. Describe the log trend regression you computed in general terms. Then discuss whether the extent to which it supports/refutes the predictions of the Hotelling model. If there a hypothesis test you can conduct to test a Hotelling prediction, conduct the test and report results.

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Example Appendix

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Figure 1. Real price of aluminum ($2010 per pound), 1895-2010.

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Figure 2. Annual rate of real price change, aluminum, 1896-2010.

Trend Regression for Log Real Price of Aluminum

Regression Statistics

Multiple R 0.922935691

R Square 0.85181029

Adjusted R

Square 0.850510381

Standard Error 0.286607675

Observations 116

ANOVA

df SS MS F

Significance F

Regression 1 53.8276373 53.82764 655.2842 4.39889E-49 Residual 114 9.364411338 0.082144

Total 115 63.19204864

Coefficients

Standard

Error t Stat P-value

Intercept 2.041238595 0.053567683 38.10578 1.07E-66 Time -0.020343348 0.000794708 -25.5985 4.4E-49

Line Fit Plot for Log of Real Price

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Predicted Log Price

Figure 3. Line fit plot for log trend regression of real price of aluminum, 1895-2010.