Substituting the Inflation Index?

Substituting the Inflation Index?

Gaargi Jamkar

B.Sc 2022 – 25

Inflation is like toothpaste. Once it’s out, you can hardly get it back in again…

Any layman knows the definition of inflation as a sustained increase in the general price level. This is a real-world phenomenon that affects every country and every individual’s purchasing power. Prices rise, and if the general income level doesn’t increase proportionately, there is a fall in the real income of all individuals. Nobody wants that.

Therefore, it is crucial for the central bank of any country to maintain a steady rate of inflation that does not hamper the spending power and growth of the economy. This can only be done if the central bank can accurately measure the economy’s inflation. You may think, “What’s the big deal in that?”. There exist measures like the Consumer Price Index (CPI) and the GDP deflator that have been constructed for the same reason. However, through this article, I aim to convince you that both measures have huge flaws, and it’s time that we develop a new measure for inflation. 

The Consumer Price Index (CPI) measures the affordability of a basket of goods and services with respect to a base year. It answers the question: how much do I have to pay in 2025 to buy a basket of goods and services compared to how much I had to pay for the same basket back in 2012? This index also assigns different weights to goods and services based on patterns of consumption and price volatility. It can be represented by the formula:

∑ [P₁Q₀ ፥ P₀Q₀] – Laspeyre’s Index

The GDP deflator measures the ratio between the nominal and real GDP of a year and can be denoted by the formula:

∑ (P₁Q₁ ፥ P₀Q₁) – Paasche’s Index

Effectively, the CPI controls for base quantities while the GDP deflator focuses on current ones. 

On the surface level there seems to be no problem with these two measures, but a simple example can expose a problematic flaw. 

Assume that there are only two goods to consume in the economy – red and green apples. 

	2012 (Base Year)		2025 (Current Year)
	P0	Q0	P1	Q1
Green Apples	1	10	2	0
Red Apples	2	0	1	10

Let us calculate the inflation measures

1) Consumer Price Index

CPI₂₀₁₂ = 10/10 = 1
CPI₂₀₂₅ = 20/10 = 2
Thus, inflation rate is (2-1)/1 = 1*100 = 100%

2) GDP Deflator
Deflator₂₀₂₅ = 10/20 = 0.5
Thus, inflation rate is (0.5-1)/1 = -0.5*100 = -50%

What should you believe? CPI tells you that prices in 2025 have gone up 100% compared to 2012 while the deflator tells you that the prices have in fact, fallen by 50%. This becomes even more confusing for the central bank that has to choose between an inflation controlling stance and a growth promoting stance.

The most interesting part of this example is the fact that the cost of living has not changed at all over the years. Technically, the inflation rate is 0%. The nominal GDP for both years was 10 and if we assume a constant income, there has in fact been no change in the purchasing power of the consumers. 

It becomes clear that the CPI overstates inflation due to the substitution effect (switching from type of apples depending on prices) and the deflator understates inflation due to the inclusion of base year prices. Given these flaws, don’t you think that these measures might get even noisier with an array of goods and services and a huge population?

The solution? 

A Substitution-Adjusted CPI can solve the overstating problem. This index is similar to the CPI but includes an ‘elasticity of substitution’ (σ) that adjusts with the type of product or service. A product with close substitutes like aerated beverages can have a higher σ, say 5, and products that show less degree substitutability can have lower σ (medicines). Thus, the formula would look like –

Source: Author’s calculations

Where,

W = weight of household expenditure on a product/service

σ = elasticity of substitution of a product. 

This formula is derived from the CES (constant elasticity of substitution) utility function because it’s the cleanest way to formally model how consumers substitute between goods when relative prices change. Now this formula controls for substitutability between products depending on prices and therefore can report a more accurate inflation rate. 

Now if we solve the same example with this formula (taking weights of each to be 0.5 and σ=1, the formula will decompose to:

√2^0.5 * 0.5^0.5 = 1

Therefore the inflation rate = 1-1/1= 0% 

But now you may question how to decide the elasticity of substitution for each product or service in the basket?

Use literature estimates: many papers already estimate σ for broad categories (food, housing, durables).

The RBI can use the following rule of thumb:

1. σ ≈ 0.3–0.6 for necessities (low substitutability, like housing).
2. σ ≈ 1 for balanced categories (like food staples).
3. σ ≥ 2 for luxuries / tech (high substitutability, like smartphones).

Thus inflation can now be calculated more precisely by making its calculation a bit more complex. 

All this index construction and research got me thinking that, maybe inflation is a societal construct and we’re just gullible enough to fall for it. 

But hey, that’s an article for another time…