gpindex

An R package for calculating generalized price and quantity indexes

https://github.com/marberts/gpindex

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An R package for calculating generalized price and quantity indexes

README.Rmd

---
output: github_document
---



```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  out.width = "100%"
)
```

# Generalized Price and Quantity Indexes 


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[![DOI](https://zenodo.org/badge/261861375.svg)](https://zenodo.org/doi/10.5281/zenodo.10097742)


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.

```{r, eval = FALSE}
install.packages("gpindex")
```

The development version can be installed from R-Universe

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

or directly from GitHub.

```{r, eval = FALSE}
pak::pak("marberts/gpindex")
```

## Usage

```{r}
library(gpindex)

# Start with some data on prices and quantities for 6 products
# over 5 periods.
price6
quantity6

# We'll only need prices and quantities for a few periods.
p1 <- price6[[1]]
p2 <- price6[[2]]
p3 <- price6[[3]]
q1 <- price6[[1]]
q2 <- price6[[2]]

# There are functions to calculate all common price indexes,
# like the Laspeyres and Paasche index.
laspeyres_index(p2, p1, q1)
paasche_index(p2, p1, q2)

# The underlying mean functions are also available, as usually
# only price relatives and weights are known.
s1 <- p1 * q1
s2 <- p2 * q2

arithmetic_mean(p2 / p1, s1)
harmonic_mean(p2 / p1, s2)

# The mean representation of a Laspeyres index makes it easy to
# chain by price-updating the weights.
laspeyres_index(p3, p1, q1)

arithmetic_mean(p2 / p1, s1) *
  arithmetic_mean(p3 / p2, update_weights(p2 / p1, s1))

# The mean representation of a Paasche index makes it easy to
# calculate percent-change contributions.
harmonic_contributions(p2 / p1, s2)

# 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(p2, p1, q1)
quadratic_mean(p2 / p1, s1)

# Chained over time
lloyd_moulton(p3, p1, q1)
quadratic_mean(p2 / p1, s1) *
  quadratic_mean(p3 / p2, quadratic_update(p2 / p1, s1))

# And decomposed to get the contributions of each relative.
quadratic_contributions(p2 / p1, s1)
```

## 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.

Owner

Citation (CITATION.cff)

# --------------------------------------------
# CITATION file created with {cffr} R package
# See also: https://docs.ropensci.org/cffr/
# --------------------------------------------
 
cff-version: 1.2.0
message: 'To cite package "gpindex" in publications use:'
type: software
license: MIT
title: 'gpindex: Generalized Price and Quantity Indexes'
version: 0.6.3
doi: 10.5281/zenodo.10097742
identifiers:
- type: doi
  value: 10.32614/CRAN.package.gpindex
abstract: 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, <https://doi.org/10.1017/CBO9780511720758>),
  von der Lippe (2007, <https://doi.org/10.3726/978-3-653-01120-3>), and the CPI manual
  (2020, <https://doi.org/10.5089/9781484354841.069>).
authors:
- family-names: Martin
  given-names: Steve
  email: marberts@protonmail.com
  orcid: https://orcid.org/0000-0003-2544-9480
preferred-citation:
  type: manual
  title: 'gpindex: Generalized Price and Quantity Indexes'
  authors:
  - family-names: Martin
    given-names: Steve
    orcid: https://orcid.org/0000-0003-2544-9480
    email: marberts@protonmail.com
  year: '2025'
  doi: 10.5281/zenodo.10097742
  url: https://cran.r-project.org/package=gpindex
  notes: R package version 0.6.3
repository: https://CRAN.R-project.org/package=gpindex
repository-code: https://github.com/marberts/gpindex
url: https://marberts.github.io/gpindex/
contact:
- family-names: Martin
  given-names: Steve
  email: marberts@protonmail.com
  orcid: https://orcid.org/0000-0003-2544-9480
keywords:
- cran
- economics
- inflation
- official-statistics
- r
- r-package
- rstats
- statistics
references:
- type: software
  title: 'R: A Language and Environment for Statistical Computing'
  notes: Depends
  url: https://www.R-project.org/
  authors:
  - name: R Core Team
  institution:
    name: R Foundation for Statistical Computing
    address: Vienna, Austria
  year: '2025'
  version: '>= 4.1'
- type: software
  title: stats
  abstract: 'R: A Language and Environment for Statistical Computing'
  notes: Imports
  authors:
  - name: R Core Team
  institution:
    name: R Foundation for Statistical Computing
    address: Vienna, Austria
  year: '2025'
- type: software
  title: knitr
  abstract: 'knitr: A General-Purpose Package for Dynamic Report Generation in R'
  notes: Suggests
  url: https://yihui.org/knitr/
  repository: https://CRAN.R-project.org/package=knitr
  authors:
  - family-names: Xie
    given-names: Yihui
    email: xie@yihui.name
    orcid: https://orcid.org/0000-0003-0645-5666
  year: '2025'
  doi: 10.32614/CRAN.package.knitr
- type: software
  title: quarto
  abstract: 'quarto: R Interface to ''Quarto'' Markdown Publishing System'
  notes: Suggests
  url: https://quarto-dev.github.io/quarto-r/
  repository: https://CRAN.R-project.org/package=quarto
  authors:
  - family-names: Allaire
    given-names: JJ
    email: jj@posit.co
    orcid: https://orcid.org/0000-0003-0174-9868
  - family-names: Dervieux
    given-names: Christophe
    email: cderv@posit.co
    orcid: https://orcid.org/0000-0003-4474-2498
  year: '2025'
  doi: 10.32614/CRAN.package.quarto
- type: software
  title: testthat
  abstract: 'testthat: Unit Testing for R'
  notes: Suggests
  url: https://testthat.r-lib.org
  repository: https://CRAN.R-project.org/package=testthat
  authors:
  - family-names: Wickham
    given-names: Hadley
    email: hadley@posit.co
  year: '2025'
  doi: 10.32614/CRAN.package.testthat
  version: '>= 3.0.0'

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