# The What and Why of Inflation Adjustment

Here it is again:We can express Equation (IV) in terms of (I) by expressing the denominator of Equation (IV) as follows:Now referring back to Equation I, CPI for 2020 is the index value and CPI for 2018 is always 100 since its the base year.

Therefore,Which is the same as what we got before using a different but equivalent formula.

Either way, we now have the cost of soup for both 2019 and 2020 adjusted to the same base i.

e.

2018 dollars.

Therefore like we did before, let’s compare the real percentage change in the price of soup from 2019 to 2020 after discounting the effect of overall price inflation.

This ‘core’ change in price is:We can now state the general formula for calculating the real (intrinsic) change in the price of an item with respect to a CPI of interest:Formula for intrinsic inflation in an itemThe following table shows the inflation in soup price in Gotham in the years 2019 through 2023 before and after adjusting for overall inflation.

That was a healthy dose of math.

Let’s take a break and enjoy some soup before ploughing ahead.

Image credit: GeoTrinity CC BY-SA 3.

0Our fictitious CPI example has served us well.

So far it showed us how to calculate the index, how to calculate inflation in the index, how to interpret inflation adjusted values and how to calculate the intrinsic growth of an item w.

r.

t.

an appropriate index.

But now, at the risk of deflating the interest (and egos) of all us Batman fans, we must return to reality.

A quick dose of realityEach year the BLS in the US, (or the corresponding government agency in other countries) interviews thousands of households across different financial strata (low, middle, high income), and different professions in order to gather data about their spending habits.

The result of this exercise is the calculation of dozens of smaller, more focused indexes.

These indexes are then aggregated to form the several top-level CPIs using a system of weights.

The exact calculations can get complicated, but the concept is simple.

You want to find out how much money the ‘average’ household spends on goods and services and then index that amount to some arbitrary base year.

Then repeat this calculation each month, quarter and year to get a sense for how much more expensive (or cheap) the cost of living has become as compared to the previous time period.

If you are training a model on currency denominated data…If you are training a model, your training will not fail if you do not deflate your currency denominated data.

At the same time, you should consider deflating it because doing so will remove the portion of the ‘signal’ from your data that is due to general inflationary pressure.

Along with deflation, you should also consider one or more of other transformations such as the log transformation (which makes the trend linear), seasonal adjustment, and differencing.

All these operations will remove the corresponding portions of the signal from your data.

What will remain is the residual trend that your training algorithm can now focus on.

Plus of course there will be the noise — this, your algorithm will have to learn to ignore!Happy deflating!.