Matrices for repeat-sales price indexes

Calculate the matrices in Shiller (1991) that serve as the foundation for many repeat-sales price indexes.

Installation

Get the stable release from CRAN.

install.package("rsmatrix")

Install the development version from R-Universe

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

or directly from GitHub.

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.

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

##   id date price
## 1  1    1     1
## 2  1    2     3
## 3  1    3     2
## 4  2    1     1
## 5  2    3     1

In most cases data need to first be structured as sales pairs, which can be done with the rs_pairs() function.

# 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))

##   id date price date_prev price_prev
## 2  1    2     3         1          1
## 3  1    3     2         2          3
## 5  2    3     1         1          1

The rs_matrix() function can now be used to produce a function that constructs these matrices.

# 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

##    2 3
## 1  1 0
## 2 -1 1
## 3  0 1

matrices$X

##    2 3
## 1  3 0
## 2 -3 2
## 3  0 1

Standard repeat-sales indexes are just simple matrix operations using these matrices.

# Calculate the GRS index in Bailey, Muth, and Nourse (1963)
b <- with(matrices, solve(crossprod(Z), crossprod(Z, y))[, 1])
(grs <- exp(b) * 100)

##        2        3 
## 238.1102 125.9921

# Calculate the ARS index in Shiller (1991)
b <- with(matrices, solve(crossprod(Z, X), crossprod(Z, Y))[, 1])
(ars <- 100 / b)

##        2        3 
## 240.0000 133.3333

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.

Contributing

All contributions are welcome. Please start by opening an issue on GitHub to report any bugs or suggest improvements and new features. See the contribution guidelines for this project for more information.

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.