# What is the most accurate way to calculate the difference in value of one dollar between two target years?

This question concerns only USD, and doesn't need to be more granular than a year-level.

I am trying to create a model that takes various features into account in explaining why a particular service cost more in 2018 than, say, 2016. A monetarily small but important feature in this model would be accounting for how much of the increase in price was due to inflation.

On the surface this sounded very straightforward, from a base year use inflation data to calculate the value of a dollar in two target years and apply the difference as a multiplier. As I've delved into how how inflation is calculated and how to compute the relative value of a dollar, this has become more opaque.

My question is this: what is the most accurate way to calculate the difference in value of one dollar between two target years?

• What data do you have to start with? Do you have inflation rates for each period or other relative data like CPI? Feb 11, 2019 at 19:57
• Define "accurate." If you mean "most widely accepted", then the standard way that everyone uses is to take the ratio of the CPI between the two times. Feb 11, 2019 at 19:58
• When you write "particular service", do you mean there's a specific service you have in mind, or it could be anything? For a specific service, there likely exists more appropriate inflation data than the general U.S. CPI, which covers a broader basket of goods/services. For instance, airline fares and communication service prices have gone down over the last few years, while car insurance and hospital services have gone up faster than average. See e.g. bls.gov/opub/ted/2019/consumer-price-index-2018-in-review.htm Feb 11, 2019 at 20:32
• @ChrisW.Rea I do have a particular service that I am evaluating, its unfortunately not tracked by name by the BLS in the way you describe but thats very useful info regardless Feb 11, 2019 at 20:51

Start with CPI data from BLS. You are looking at a specific service so it may be more accurate to use their industry-specific inflation rates rather than the general CPI inflation rate, which is an aggregate rate across all industries.

CPI data is updated monthly, so if you know the month you want to start with you can find both monthly and annual inflation rates on the BLS tables. If you only know the year (2016), best practice is to use the mid-point of the year, so you would look for the July 2016 - June 2017 inflation rate to calculate the value of a 2016 dollar in 2017.

One more point - remember that inflation rates are a measure of price change, not a cause of it, so make sure your model is not double-counting anything by incorporating an inflation factor. It's also important to remember that price is not the same as cost from the price-setter's perspective.

Inflation is a macro-economic phenomenon and can't directly be applied to individual prices.

That said, you would find the inflation rate for each period between your target dates, add 1 to each and multiply them together.

So if inflation for each quarter of 2106-2017 was (fictional numbers) 1%, 2%, -1%, 4%, 1.5%, 0%, 2%, 1.1%, your overall inflation factor would be:

1.01 * 1.02 * 0.99 * 1.04 * 1.015 * 1.0 * 1.02 * 1.011 = 1.011 = 11%

So 11% of the price increase could be attributed to inflation.