Matrices for repeat-sales price indexes (original) (raw)

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 the development version from R-Universe

or directly from GitHub.

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.

##   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.

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

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

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

##        2        3 
## 238.1102 125.9921

##        2        3 
## 240.0000 133.3333

Prior work

The McSpatial package (formerly on CRAN) has some functionality for making repeat-sales indices. 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.