Price Index Aggregation.
Price Index Aggregation in R 
Most price indexes are made with a two-step procedure, where period-over-period elemental indexes are first calculated for a collection of elemental aggregates at each point in time, and then aggregated according to a price index aggregation structure. These indexes can then be chained together to form a time series that gives the evolution of prices with respect to a fixed base period. This package contains a collections of functions that revolve around this work flow, making it easy to build standard price indexes, and implement the methods described by Balk (2008), von der Lippe (2001), and the CPI manual (2020) for bilateral price indexes.
Installation
Get the stable version from CRAN.
install.packages("piar")
The development version can be installed from R-Universe
install.packages("piar", repos = c("https://marberts.r-universe.dev", "https://cloud.r-project.org"))
or directly from Github.
pak::pak("marberts/piar")
Usage
There is a detailed vignette showing how to use piar: browseVignettes("piar"). But the basic work flow is fairly simple.
The starting point is to make period-over-period elemental price indexes with the elemental_index() function.
library(piar)
# Make Jevons business-level elemental indexes
head(ms_prices)
#> period business product price
#> 1 202001 B1 1 1.14
#> 2 202001 B1 2 NA
#> 3 202001 B1 3 6.09
#> 4 202001 B2 4 6.23
#> 5 202001 B2 5 8.61
#> 6 202001 B2 6 6.40
elementals <- with(
ms_prices,
elemental_index(
price_relative(price, period, product),
period, business, na.rm = TRUE
)
)
elementals
#> Period-over-period price index for 4 levels over 4 time periods
#> 202001 202002 202003 202004
#> B1 1 0.8949097 0.3342939 NaN
#> B2 1 NaN NaN 2.770456
#> B3 1 2.0200036 1.6353355 0.537996
#> B4 NaN NaN NaN 4.576286
And an aggregation structure with the aggregation_structure() function.
# Make an aggregation structure from businesses to higher-level
# industrial classifications
head(ms_weights)
#> business classification weight
#> 1 B1 11 553
#> 2 B2 11 646
#> 3 B3 11 312
#> 4 B4 12 622
#> 5 B5 12 330
pias <- with(
ms_weights,
aggregation_structure(
c(expand_classification(classification), list(business)),
weight
)
)
pias
#> Aggregation structure for 5 elemental aggregates with 2 levels above the elemental aggregates
#> level1 level2 ea weight
#> 1 1 11 B1 553
#> 2 1 11 B2 646
#> 3 1 11 B3 312
#> 4 1 12 B4 622
#> 5 1 12 B5 330
The aggregate() method can then be used to aggregate the elemental indexes according to the aggregation structure. There are a variety of methods to work with these index objects, such as chaining them over time.
# Aggregate elemental indexes with an arithmetic index
index <- aggregate(elementals, pias, na.rm = TRUE)
# Chain them to get a time series
chain(index)
#> Aggregate fixed-base price index for 8 levels over 4 time periods
#> 202001 202002 202003 202004
#> 1 1 1.3007239 1.3827662 3.7815355
#> 11 1 1.3007239 1.3827662 2.1771866
#> 12 1 1.3007239 1.3827662 6.3279338
#> B1 1 0.8949097 0.2991629 0.4710366
#> B2 1 1.3007239 1.3827662 3.8308934
#> B3 1 2.0200036 3.3033836 1.7772072
#> B4 1 1.3007239 1.3827662 6.3279338
#> B5 1 1.3007239 1.3827662 6.3279338
References
Balk, B. M. (2008). Price and Quantity Index Numbers. Cambridge University Press.
Chiru, R., Huang, N., Lequain, M. Smith, P., and Wright, A. (2015). The Canadian Consumer Price Index Reference Paper, Statistics Canada catalogue 62-553-X. Statistics Canada.
ILO, IMF, OECD, Eurostat, UN, and World Bank. (2020). Consumer Price Index Manual: Theory and Practice. International Monetary Fund.
von der Lippe, P. (2001). Chain Indices: A Study in Price Index Theory, Spectrum of Federal Statistics vol. 16. Federal Statistical Office, Wiesbaden.