Generalized Price and Quantity Indexes.

Generalized Price and Quantity Indexes

Tools to build and work with bilateral generalized-mean price indexes (and by extension quantity indexes), and indexes composed of generalized-mean indexes (e.g., superlative quadratic-mean indexes, GEKS). Covers the core mathematical machinery for making bilateral price indexes, computing price relatives, detecting outliers, and decomposing indexes, with wrappers for all common (and many uncommon) index-number formulas. Implements and extends many of the methods in Balk (2008), von der Lippe (2007), and the CPI manual (2020).

Installation

Get the stable release from CRAN.

install.packages("gpindex")

The development version can be installed from R-Universe

install.packages("gpindex", repos = c("https://marberts.r-universe.dev", "https://cloud.r-project.org"))

or directly from GitHub.

pak::pak("marberts/gpindex")

Usage

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 percent-change 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)
lloyd_moulton <- 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
lloyd_moulton(p1, p0, q0)
#> [1] 1.592692
quadratic_mean(p1 / p0, s0)
#> [1] 1.592692

# Chained over time
lloyd_moulton(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 -0.02665039

Prior work

There are a number of R packages on the CRAN that implement the standard index-number formulas (e.g., IndexNumber, productivity, IndexNumR, micEconIndex, PriceIndices). While there is support for a large number of index-number formulas out-of-the box in this package, the focus is on the tools to easily make and work with any type of generalized-mean price index. Consequently, compared to existing packages, this package is suitable for building custom price/quantity indexes, calculating indexes with sample data, decomposing indexes, and learning about or researching different types of index-number formulas.

References

Balk, B. M. (2008). Price and Quantity Index Numbers. Cambridge University Press.

IMF, ILO, Eurostat, UNECE, OECD, and World Bank. (2020). Consumer Price Index Manual: Concepts and Methods. International Monetary Fund.

von der Lippe, P. (2007). Index Theory and Price Statistics. Peter Lang.