# Using the Federal Reserve's Implicit Price Deflator to Convert to 2020 Dollars

I have a list of government expenditures from 2011 to 2018 as shown below:

2011    2012    2013... 2018
$$30m$$35m    $$42m$$120m


How can I use the Federal Reserve's Implicit Price Deflator, to convert these figures into 2020 dollars? I'm not sure how to do this despite having read a lot online.

The index year for this table is 2012 equals 100 USD. I understand that this chart shows that 100 USD in 2012 is now worth approximately 112 USD, but I'm not sure how to use it if my index year changes etc.

The use case is I'm updating a report on short-run and long-run marginal costs associated with various activities and want to put them into 2020 dollars so that they are comparable.

If you want to change the base year of a deflator just divide all values by the value in base year and multiply by 100. For example, if you have deflator with base year 2012:

           2011  2012 2013 ... 2020
Def_2012:    87   100  101      112


Then deflator with base 2020 will be given as:

               2011             2012           2013     ...     2020
Def_2020:    87/112*100   100/112*100      101/112*100      112/112*100


This way you you rescale the implicit deflator to 2020. Afterwards you can just apply the deflator as you would normally do.

Edit:

In order to convert all values to 2020 you can use the following formula:

$$X_{2020} = \frac{X_{t}}{\frac{\text{deflator}_{2020}}{100}}$$

where $$X$$ is the nominal variable you want to adjust and subscripts indicate the years with $$t$$ being an arbitrary year.

• Thanks very much. Forgive my ignorance, but to apply the deflator do I take the base amount and multiply it by 1 + the deflator? In the example above, would I multiple the 2011 30m by 1 + (0.0078), which is the result of 87/(112*100), giving me 30m in 2011 dollars is now worth 30.2m in 2020 dollars?
– DJC
Commented Aug 13, 2020 at 16:03
• @DJC I eddited my answer
– 1muflon1
Commented Aug 13, 2020 at 16:10
• Got it. Thanks so much. Using that I'm getting 38.6m, which seems more reasonable.
– DJC
Commented Aug 13, 2020 at 16:13
• @DJC by the way also note you should be using 87/112*100 not 87/(112*100). Those are two very different things
– 1muflon1
Commented Aug 13, 2020 at 16:15
• Gotcha. Thanks for flagging me on that.
– DJC
Commented Aug 13, 2020 at 16:16