We know that to measure real economic growth, we need to strip out the effects of inflation. The traditional way to do this was to pick a base year and value all future output using those prices. This works well for a few years, but over longer periods, it starts to create a distorted picture of the economy.

Imagine an economy in 1990 that produces two things: bread and personal computers. A loaf of bread cost $1 and a PC cost $2,000. Now fast-forward to today. Bread might cost $3, but a vastly more powerful PC costs $500. If we used 1990 prices to measure today's output, the massive increase in computer production would be valued at an outdated, sky-high price. This gives computers a much heavier weight in the GDP calculation than they actually have in the modern economy. It overstates real growth.

To solve this, economists use a more sophisticated method called chain weighting, which updates the price weights every year. This approach relies on two foundational quantity indexes.

To understand chain weighting, we first need to look at the two indexes that form its foundation: the Laspeyres Index and the Paasche Index. Both measure the change in output quantity between two periods, but they use different price weights.

The Laspeyres index asks: "How much would the value of production have changed if prices had remained the same as they were in the base year?" Because it uses old prices, it gives too much weight to goods whose prices have fallen (like technology) and doesn't account for consumers substituting away from goods that have become more expensive. This generally leads to an overstatement of growth.

The Paasche index asks a different question: "How much has the value of production changed, measured in today's prices?" This method can understate growth. It gives less weight to fast-growing sectors where prices have fallen, like electronics. It essentially assumes the substitution behavior of the current period existed in the base period.

So, we have one index that likely overstates growth (Laspeyres) and one that likely understates it (Paasche). The elegant solution is to combine them. The Fisher Ideal Index does this by taking the geometric average of the two.

This method provides a more accurate measure of the true change in quantity, neutralizing the biases inherent in each of the other indexes. Government agencies like the Bureau of Economic Analysis (BEA) use this approach to calculate the official GDP growth rate from one year to the next.

The final step is the "chaining." The BEA calculates the Fisher index growth rate for each year (e.g., 2021 to 2022, 2022 to 2023, etc.). They then pick a reference year and set its real GDP equal to its nominal GDP. To get the real GDP for any other year, they chain these annual growth rates together, either compounding forward or discounting backward to the desired year.

Using the data above, you can calculate the different growth rates:

• Laspeyres Index (using 2022 prices): ((110*$2) + (15*$1000)) / ((100*$2) + (10*$1000)) ≈ 1.49, or 49% growth.
• Paasche Index (using 2023 prices): ((110*$2.50) + (15*$800)) / ((100*$2.50) + (10*$800)) ≈ 1.48, or 48% growth.
• Fisher Index (geometric mean): sqrt(1.49 * 1.48) ≈ 1.485, or 48.5% growth.

In this simple case, the results are close. But over many years and with thousands of goods, the differences become significant.

Now let's check what you've learned about these measurement methods.