8.1 Calculation of the lowest level index
An index calculated for an individual building material purchased by a construction organization represents the lowest level index. Graph #1 shows the structure of the construction section, where the price indices for materials A, B and C are the elementary (lowest level) indices. The lowest level index compared to the price reference period is obtained from the ratio of reporting period (t) and reference period prices.
Lowest level index
Iᵢt/0 = pᵢt / pᵢ0
where:
i — material purchased by the organization for which a comparable price is registered
Iᵢt/0 — lowest level index for material i in reporting period t, compared to the index reference period
pᵢt — price of material i in period t
pᵢ0 — price of material i in the price reference period
Graph #1. Structure of the price index for material inputs to construction industries
8.2 The index for separate groups and the whole section
The long-term index for the whole section compared to the price reference period is calculated using the following Laspeyres-type formula:
Laspeyres-type aggregate index
It/0 = Σni=1 Iᵢt/0 × sᵢb
where:
Iᵢt/0 — lowest level long-term index for material i compared to the price reference period
sᵢb = pᵢbqᵢb / Σpᵢbqᵢb — weight of material i in the weight reference period (share of material i in total material volume), Σsᵢb=1
pᵢb — price of material i purchased by the sampled organization in the weight reference period (b)
qᵢb — quantity of material i in the weight reference period (b)
The same formula is used for calculating all upper-level indices. For example, a sub-section index is obtained by weighting the long-term indices of materials within the sub-section, where the sum of those weights equals 1.
The short-term index compared to the previous month is obtained from the ratio of the long-term indices of the reporting and previous periods, each calculated relative to the price reference period.
8.3 Chain index
During the annual update of construction organizations and materials, prices are collected in December for materials in both the old and new samples. This enables chain-linking of indices calculated for two different samples. Chain-linking makes it possible to calculate an index with a long-term reference period regardless of changes in weights.
For example, before December 2016, the overall section index was calculated compared to December 2015 using wᵢ weights. From 2017 onwards, the index is calculated compared to December 2016 using kᵢ weights (see Table 5). X₁ is the chain index for January 2017 on a December 2015 base.
Table 5.
| 12.2015=100 | 12.2016=100 |
| 12.2016: I12.16/12.15 = ΣIᵢ12.16/12.15×wᵢ = 106 | 12.2016: I12.16/12.16 = ΣIᵢ12.16/12.16×kᵢ = 100 |
| X₁ | 01.2017: I01.17/12.16 = ΣIᵢ01.17/12.16×kᵢ = 102 |
Chain-linking formula
106 / X₁ = 100 / 102 ⇒ X₁ = 106 × 102 / 100 ≈ 108
I12.2016/12.2015 × I01.2017/12.2016 = 106 × 102/100 ≈ 108