Matrices for repeat-sales price indexes

A small package for calculating the matrices in Shiller (1991) that serve as the foundation for many repeat-sales price indexes. Builds on the ‘rsi’ package by Kirby-McGregor and Martin (2019).

Installation

install.package("rsmatrix")

Get the development version from GitHub.

devtools::install_github("marberts/rsmatrix")

Usage

library(rsmatrix)

# Make some data
sales <- data.frame(id =    c(1, 1, 1, 2, 2), 
                    date =  c(1, 2, 3, 1, 3), 
                    price = c(1, 3, 2, 1, 1))

# 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

# 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

# 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

References

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.