# 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 (2001), 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)

# This index can be calculated as a mean of price relatives
lloyd_moulton(p1, p0, q0)
#> [1] 1.592692
#> [1] 1.592692

# Chained over time
lloyd_moulton(p2, p0, q0)
#> [1] 1.136515
#> [1] 1.136515

# And decomposed to get the contributions of each relative