A small package for calculating lots of different price indexes, and by extension quantity indexes. Provides tools to build and work with any type of bilateral generalized-mean index (of which most price indexes are), along with a few important indexes that don’t belong to the generalized-mean family (e.g., superlative quadratic-mean indexes, GEKS). Implements and extends many of the methods in Balk (2008), von der Lippe (2001), and the CPI manual (2020) for bilateral price indexes.
The development version can be installed from GitHub.
The examples here give a brief introduction to how to use the functionality in this package. The package-level help page (package?gpindex) gives much more detail.
library(gpindex)
# Start with some data on prices and quantities for 6 products
# over 5 periods
price6
#> t1 t2 t3 t4 t5
#> 1 1 1.2 1.0 0.8 1.0
#> 2 1 3.0 1.0 0.5 1.0
#> 3 1 1.3 1.5 1.6 1.6
#> 4 1 0.7 0.5 0.3 0.1
#> 5 1 1.4 1.7 1.9 2.0
#> 6 1 0.8 0.6 0.4 0.2
quantity6
#> t1 t2 t3 t4 t5
#> 1 1.0 0.8 1.0 1.2 0.9
#> 2 1.0 0.9 1.1 1.2 1.2
#> 3 2.0 1.9 1.8 1.9 2.0
#> 4 1.0 1.3 3.0 6.0 12.0
#> 5 4.5 4.7 5.0 5.6 6.5
#> 6 0.5 0.6 0.8 1.3 2.5
# We'll only need prices and quantities for a few periods
p0 <- price6[[1]]; p1 <- price6[[2]]; p2 <- price6[[3]]
q0 <- price6[[1]]; q1 <- price6[[2]]
# There are functions to calculate all common price indexes,
# like the Laspeyres and Paasche index
laspeyres_index(p1, p0, q0)
#> [1] 1.4
paasche_index(p1, p0, q1)
#> [1] 1.811905
# The underlying mean functions are also available, as usually
# only price relatives and weights are known
s0 <- p0 * q0; s1 <- p1 * q1
arithmetic_mean(p1 / p0, s0)
#> [1] 1.4
harmonic_mean(p1 / p0, s1)
#> [1] 1.811905
# The mean representation of a Laspeyres index makes it easy to
# chain by price-updating the weights
laspeyres_index(p2, p0, q0)
#> [1] 1.05
arithmetic_mean(p1 / p0, s0) *
arithmetic_mean(p2 / p1, update_weights(p1 / p0, s0))
#> [1] 1.05
# The mean representation of a Paasche index makes it easy to
# calculate quote contributions
harmonic_contributions(p1 / p0, s1)
#> [1] 0.02857143 0.71428571 0.04642857 -0.02500000 0.06666667 -0.01904762
# The ideas are the same for more exotic indexes,
# like the Lloyd-Moulton index
# Let's start by making some functions for the Lloyd-Moulton index
# when the elasticity of substitution is -1 (an output index)
lm <- lm_index(-1)
quadratic_mean <- generalized_mean(2)
quadratic_update <- factor_weights(2)
quadratic_contributions <- contributions(2)
# This index can be calculated as a mean of price relatives
lm(p1, p0, q0)
#> [1] 1.592692
quadratic_mean(p1 / p0, s0)
#> [1] 1.592692
# Chained over time
lm(p2, p0, q0)
#> [1] 1.136515
quadratic_mean(p1 / p0, s0) *
quadratic_mean(p2 / p1, quadratic_update(p1 / p0, s0))
#> [1] 1.136515
# And decomposed to get the contributions of each relative
quadratic_contributions(p1 / p0, s0)
#> [1] 0.03110568 0.51154526 0.04832926 -0.03830484 0.06666667 -0.02665039Balk, B. M. (2008). Price and Quantity Index Numbers. Cambridge University Press.
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.