Supplement 1:  Calculating the chain-weight GDP deflator
To address the problem associated with the substitution bias, a “chain weight” index may be used.  A chain weight index is essentially a geometric average of a Paasche and Laspeyres price index; the inflation rate for a year is calculated by averaging the inflation measures using the start of period basket and the end of period basket.  In fact, in the last few years, the official National Income and Product Accounts (NIPA) have used a chain weight index for real GDP and GDP deflator (now called a GDP chain weight price index) calculations.  Since the new NIPA measures calculate a real GDP index directly, and a price index indirectly (by dividing the nominal GDP figure by the chain weight real GDP figure), the equation that defines the GDP chain weight price index is difficult to teach to students.  This supplement will show how to set up a spreadsheet to calculate a chain weight real GDP figure, and the resulting GDP price index.  Overall, this example shows how spreadsheets can be used to limit the number of tedious calculations that a problem requires, allowing more interesting side topics to be explored.  In addition, the set-up of the sheet focuses attention on the process of creating the index.
The most straightforward way to calculate the chain-weight GDP price index is to first calculate the chain-weight growth rate of real GDP for each year.  To accomplish this, it is first necessary to find the annual growth rate of real output using the current year’s prices as weights and then find the annual growth rate of real output using the previous year’s prices as weights.  The chain-weight real growth rate is then computed as the geometric mean of these two real growth rates.  The next step is to choose a base year and calculate real GDP figures for each year by using the chain-weight real growth rates.  Finally, the chain-weight GDP deflator can be found by dividing the nominal GDP figure by the chain-weight real GDP figure.
While these steps may be easier for students to follow than the summation notation often used to describe the chain-weight price index, they do require tedious calculations.  A spreadsheet can help to keep the calculations organized, increase accuracy, and make the assignment less time consuming.  The three-step process described above is reflected in Figure S1.1.  Year 3 has been chosen as the base year for the real GDP and price index calculations.  Once the basic spreadsheet is set up, a wide variety of “what-if scenarios” can be explored.
Figure S1.1:  Chain-weight GDP deflator calculation
	An interesting follow-up to the calculations in rows 1 through 14 of Figure S1.1 would be to have students calculate real GDP, real GDP growth, and the GDP deflator using the prices in the base year as fixed weights, and then compare the results to the chain-weight results.  Because the chain-weight GDP deflator addresses the “substitution bias” issue detailed in section 3, traditional real GDP calculations using the prices in the base year as fixed weights tend to overstate real output growth after the base year and understate real output growth before the base year.  These errors tend to become worse farther from the base year.  This is exhibited in row 21 of Figure S1.1.  Similarly, the GDP deflator computed using the fixed-weight real GDP figures will tend to understate the rate of inflation implied by the chain-weight GDP deflator after the base year and overstate inflation before the base year.  This is exhibited in row 22.