# Do Not Add Chain Weighted Quantities, Illustrated

I’ve discussed in an earlier post the fact that the sum of chain weighted quantities does not usually sum to the corresponding total chain weighted quantity. Here is a more recent example, that demonstrates the dramatic shifts in relative prices of consumption types.

Figure 1: Total consumption in bn. Ch.2012\$ (brown), and sum of durables, nondurables and services consumption, each measured in bn.Ch.2012\$ (blue), all SAAR (on log scale). Source: BEA 2020Q4 advance release, and author’s calculations.

The gap in the two series is 1.3% in 2020Q4 (log terms).

This outcome is most pronounced when relative prices shift dramatically.

Figure 2: Price of durables (blue), nondurables  (red) and services consumption (green), each in logs, 2019Q4=0. Source: BEA 2020Q4 advance release, and author’s calculations.

## 1 thought on “Do Not Add Chain Weighted Quantities, Illustrated”

1. Moses Herzog

Isn’t this kind of like saying you can’t add up jumping heights from a marked measurement on a wall, if the ground the jumpers are jumping from is on an incline?? I was trying to think of a way people can think of this in their heads, that simplifies the concept. I mean if they are all going from the same height/distance mark written on a wall, as measured from the lowest part of the incline, the jumper jumping from the higher part of the ground incline is going to get a higher reading, and therefor adding them up gives a false number??