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README.Rmd
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---
output: github_document
---
<!-- README.md is generated from README.Rmd. Please edit that file. -->
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
# Matrices for repeat-sales price indexes <a href="https://marberts.github.io/rsmatrix/"><img src="man/figures/logo.png" align="right" height="139" alt="rsmatrix website" /></a>
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[](https://cran.r-project.org/package=rsmatrix)
[](https://marberts.r-universe.dev)
[](https://github.com/marberts/rsmatrix/actions)
[](https://app.codecov.io/gh/marberts/rsmatrix)
[](https://zenodo.org/doi/10.5281/zenodo.10110159)
<!-- badges: start -->
Calculate the matrices in Shiller (1991) that serve as the foundation for many repeat-sales price indexes.
## Installation
Get the stable release from CRAN.
```{r, eval=FALSE}
install.package("rsmatrix")
```
Install the development version from R-Universe
```{r, eval=FALSE}
install.packages("rsmatrix", repos = c("https://marberts.r-universe.dev", "https://cloud.r-project.org"))
```
or directly from GitHub.
```{r, eval=FALSE}
pak::pak("marberts/rsmatrix")
```
## Usage
Most repeat-sales price indexes used in practice are based on the matrices in Shiller (1991, sections I-II), e.g., S&P's Case-Shiller index, Teranet-National Bank's HPI, and formerly Statistics Canada's RPPI. Let's consider the simplest non-trivial example to see how to make and use these matrices.
```{r}
library(rsmatrix)
# Make some data for two products selling over three periods
sales <- data.frame(
id = c(1, 1, 1, 2, 2),
date = c(1, 2, 3, 1, 3),
price = c(1, 3, 2, 1, 1)
)
sales
```
In most cases data need to first be structured as sales pairs, which can be done with the `rs_pairs()` function.
```{r}
# Turn into sales pairs
sales[c("date_prev", "price_prev")] <- sales[rs_pairs(sales$date, sales$id), c("date", "price")]
(sales <- subset(sales, date > date_prev))
```
The `rs_matrix()` function can now be used to produce a function that constructs these matrices.
```{r}
# Calculate matrices
matrix_constructor <- with(sales, rs_matrix(date, date_prev, price, price_prev))
matrices <- sapply(c("Z", "X", "y", "Y"), matrix_constructor)
matrices$Z
matrices$X
```
Standard repeat-sales indexes are just simple matrix operations using these matrices.
```{r}
# Calculate the GRS index in Bailey, Muth, and Nourse (1963)
b <- with(matrices, solve(crossprod(Z), crossprod(Z, y))[, 1])
(grs <- exp(b) * 100)
# Calculate the ARS index in Shiller (1991)
b <- with(matrices, solve(crossprod(Z, X), crossprod(Z, Y))[, 1])
(ars <- 100 / b)
```
## Prior work
The **hpiR** package has some functionality for making repeat-sales indexes, as does the **McSpatial** package (formerly on CRAN). Although easier to use, these packages lack the flexibility to compute a number of indexes found literature (e.g., any of the arithmetic repeat-sales indexes). The functions in this package build off of those in the **rsi** package in Kirby-McGregor and Martin (2019), which also gives a good background on the theory of repeat-sales indexes.
## References
ILO, IMF, OECD, UN, World Bank, Eurostat. (2013). *Handbook on Residential Property Prices Indices (RPPIs)*. Eurostat.
Kirby-McGregor, M., and Martin, S. (2019). An R package for calculating repeat-sale price indices. *Romanian Statistical Review*, 3:17-33.
Shiller, R. J. (1991). Arithmetic repeat sales price estimators. *Journal of Housing Economics*, 1(1):110-126.