Convention / standard methodology for calculating real prices?

Question

Is there an established professional standard used by economic / financial institutions for including or excluding i) the starting year/period, and ii) the end year/period when calculating real prices (i.e. when multiplying nominal values by a multiplier)?

Theoretically, there are four (mutually exclusive) possibilities

1. Include start period inflation, include end year inflation
2. Include start period inflation, exclude end year inflation
3. Exclude start period inflation, include end year inflation
4. Exclude start period inflation, exclude end year inflation

Example

Converting $100 from 2008 into 2010 dollars.

Suppose inflation was 2% in 2008, 3% in 2009, and 4% in 2010.

Applying the four methods gives four answers, like so

Method 1

Multiplying by the inflation in all of 2008, 2009, and 2010 (i.e. including start year and end year)

$100 * (1 + 0.02) * (1 + 0.03) * (1 + 0.04) = 109.26

Method 2

Multiplying by the inflation in all of 2008 and 2009 (not including end year)

$100 * (1 + 0.02) * (1 + 0.03) = 105.06

Method 3

Multiplying the 2008 price by the inflation in 2009 and 2010 (not including start year)

$100 * (1 + 0.03) * (1 + 0.04) = 107.12

Method 4

Multiplying by only the years in between (i.e. not including the start year nor end year) i.e.

$100 * (1 + 0.03) = 103

Would all professionals calculate the real value the same way and, if so, which way?

Answer 1

This is not an issue of "established practice", but of methodological and conceptual consistency.

In theoretical models, for "real" magnitudes we write, say $W_R = W_N/P$ where $P$ is the "price index" and we're done.

But in reality, in order to obtain an actual value for this price index (and hence also of inflation), we must specify a base period, against which we will evaluate the price index for the other periods (past and future). This in practice means that we set the value of the price index at the base period equal to $1$ (or $100$).

In the OP's example, the base period is 2010, since they want to express a 2008 amount in "2010 dollars". Let's see then:

The "start period inflation" is an indication of how much prices increased in 2008 compared to 2007. This cannot be relevant to the task at hand. We are examining the relation between 2008 and 2010, the year 2007 is out of the picture.

So conclusion 1: "Start period inflation" is NEVER included in the calculations.

This immediately eliminates the first two possibilities stated by the OP, as being wrong.

Then the issue is, do we include "end-period inflation"? In our example, end period inflation is how much prices increased in 2010 compared to 2009. This is certainly relevant to the task at hand, because we are examining the evolution from 2008 to 2010, and 2009 lies inside.

So conclusion 2: "end period inflation" is ALWAYS included in the calculations.

Combined the two conclusions, tell us that "possibility 3" is what should and is being used.

And it is also evidently logical, because, in order to have the same purchasing power in 2010 as in 2008, we want to cover for the prices increases that happened in 2009 compared to 2008, and the price increases that happened in 2010 compared to 2009.

Answer 2

You want to work with the price index. First, we can assume that the price index is 100 in 2008 (you would normally specify the month as well).

Your definition of “inflation” for a year is vague, but if the annual inflation is the change versus the previous year, your numbers imply that the index for 2009 is $103 = 100 \times 1.93.$

Then, the index for 2010 is $103 \times 1.04 = 107.12$.

To convert the value, use index values: (2010 value) = (2008 value)*(2010 index)/(2008 index), or \$107.12.

(This matches your method #3.)

The advantage of doing it this way is that you can align the index to any particular month of the year. Your description will be hard to adapt to partial years.

Answer 3

I also agree that method 3 is the best option. Just as the previous posted stated. You must chose the base year then use that value to adjust the time series, assuming this time series is annual. For 2008 the value would be 100 then 2009 would be 1.03 and 2010 would be 1.04.

$100 * (1.03) * (1.04) = 107.12