Package {rsmatrix}

Title: Matrices for Repeat-Sales Price Indexes
Version: 0.2.11
Description: Calculate the matrices in Shiller (1991, <doi:10.1016/S1051-1377(05)80028-2>) that serve as the foundation for many repeat-sales price indexes.
Depends: R (≥ 4.0)
Imports: Matrix (≥ 1.5-0)
Suggests: litedown, piar, spelling, tinytest
License: MIT + file LICENSE
Encoding: UTF-8
URL: https://marberts.github.io/rsmatrix/, https://github.com/marberts/rsmatrix
BugReports: https://github.com/marberts/rsmatrix/issues
VignetteBuilder: litedown
Config/roxygen2/version: 8.0.0
Language: en-US
NeedsCompilation: no
Packaged: 2026-08-01 04:43:02 UTC; steve
Author: Steve Martin ORCID iD [aut, cre, cph]
Maintainer: Steve Martin <marberts@protonmail.com>
Repository: CRAN
Date/Publication: 2026-08-01 05:10:02 UTC

rsmatrix: Matrices for Repeat-Sales Price Indexes

Description

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Calculate the matrices in Shiller (1991, doi:10.1016/S1051-1377(05)80028-2) that serve as the foundation for many repeat-sales price indexes.

Author(s)

Maintainer: Steve Martin marberts@protonmail.com (ORCID) [copyright holder]

Authors:

See Also

Useful links:

Shiller's repeat-sales matrices

Description

Create a function to compute the Z, X, y, and Y matrices in Shiller (1991, sections I-II) from sales-pair data in order to calculate a repeat-sales price index.

Usage

rs_matrix(t2, t1, p2, p1, f = NULL, sparse = FALSE)

Arguments

t2, t1

⁠[Date | character]⁠ A pair of vectors giving the time period of the second and first sale, respectively. Usually a vector of dates, but other values are possible if they can be coerced to character vectors and sorted in chronological order (i.e., with order()).

p2, p1

⁠[numeric > 0]⁠ A pair of numeric vectors giving the price of the second and first sale, respectively.

f

⁠[factor]⁠ An optional factor the same length as t1 and t2, or a vector to be turned into a factor, that is used to group sales.

sparse

⁠[logical(1)]⁠ Should sparse matrices from the Matrix package be used (faster for large datasets), or regular dense matrices (the default)?

Details

The function returned by rs_matrix() computes a generalization of the matrices in Shiller (1991, sections I-II) that are applicable to grouped data. These are useful for calculating separate indexes for many, say, cities without needing an explicit loop.

The Z, X, and Y matrices are not well defined if either t1 or t2 have missing values, and an error is thrown in this case. Similarly, it should always be the case that t2 > t1, otherwise a warning is given.

Value

A function that takes a single argument naming the desired matrix. It returns one of two matrices (Z and X) or two vectors (y and Y), either regular matrices if sparse = FALSE, or sparse matrices of class dgCMatrix if sparse = TRUE.

References

Bailey, M. J., Muth, R. F., and Nourse, H. O. (1963). A regression method for real estate price index construction. Journal of the American Statistical Association, 53(304):933-942.

Shiller, R. J. (1991). Arithmetic repeat sales price estimators. Journal of Housing Economics, 1(1):110-126.

See Also

rs_pairs() for turning sales data into sales pairs.

Examples

# Make some data
x <- data.frame(
  date = c(3, 2, 3, 2, 3, 3),
  date_prev = c(1, 1, 2, 1, 2, 1),
  price = 6:1,
  price_prev = 1
)

# Calculate matrices
mat <- with(x, rs_matrix(date, date_prev, price, price_prev))
Z <- mat("Z") # Z matrix
X <- mat("X") # X matrix
y <- mat("y") # y vector
Y <- mat("Y") # Y vector

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

# Standard errors
vcov <- rs_var(y - Z %*% b, Z)
sqrt(diag(vcov)) * grs # delta method

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

# Standard errors
vcov <- rs_var(Y - X %*% b, Z, X)
sqrt(diag(vcov)) * ars^2 / 100 # delta method

# Works with grouped data
x <- data.frame(
  date = c(3, 2, 3, 2),
  date_prev = c(2, 1, 2, 1),
  price = 4:1,
  price_prev = 1,
  group = c("a", "a", "b", "b")
)

mat <- with(x, rs_matrix(date, date_prev, price, price_prev, group))
b <- solve(crossprod(mat("Z"), mat("X")), crossprod(mat("Z"), mat("Y")))[, 1]
100 / b

Sales pairs

Description

Turn repeat-sales data into sales pairs that are suitable for making repeat-sales matrices.

Usage

rs_pairs(period, product, match_first = TRUE)

Arguments

period

⁠[Date | factor]⁠ A vector that gives the time period for each sale. Usually a date vector, or a factor with the levels in chronological order, but other values are possible if they can be sorted in chronological order (i.e., with order()).

product

⁠[factor]⁠ A vector that gives the product identifier for each sale. Usually a factor or vector of integer codes for each product.

match_first

⁠[logical(1)]⁠ Should products in the first period match with themselves (the default)?

Value

A numeric vector of indices giving the position of the previous sale for each product, with the convention that the previous sale for the first sale is itself if match_first = TRUE, NA otherwise. Ties are resolved according to the order they appear in period.

Note

order() is the workhorse of rs_pairs(), so performance can be sensitive to the types of period and product, and can be slow for large character vectors.

See Also

rs_matrix() for using sales pairs to make a repeat-sales index.

rtCreateTrans() in the hpiR package for a feature-rich but slower and less flexible function to make sales pairs.

Examples

# Make sales pairs
x <- data.frame(
  id = c(1, 1, 1, 3, 2, 2, 3, 3),
  date = c(1, 2, 3, 2, 1, 3, 4, 1),
  price = c(1, 3, 2, 3, 1, 1, 1, 2)
)

pairs <- rs_pairs(x$date, x$id)

x[c("date_prev", "price_prev")] <- x[c("date", "price")][pairs, ]

x

Robust variance matrix for repeat-sales indexes

Description

Convenience function to compute a cluster-robust variance matrix for a linear regression, with or without instruments, where clustering occurs along one dimension. Useful for calculating a variance matrix when a regression is calculated manually.

Usage

rs_var(u, Z, X = Z, ids = seq_len(nrow(X)), df = NULL)

Arguments

u

⁠[numeric]⁠ An n \times 1 vector of residuals from a linear regression.

Z

⁠[matrix]⁠ An n \times k matrix of instruments.

X

⁠[matrix]⁠ An n \times k matrix of covariates.

ids

⁠[factor]⁠ A factor of length n, or something that can be coerced into one, that groups observations in u. By default each observation belongs to its own group.

df

⁠[numeric(1) > 0]⁠ An optional degrees of freedom correction. Default is Stata's small sample degrees of freedom correction.

Details

This function calculates the standard robust variance matrix for a linear regression, as in Manski (1988, section 8.1.2) or White (2001, Theorem 6.3); that is, (Z'X)^{-1} V (X'Z)^{-1}. It is useful when a regression is calculated by hand. This generalizes the variance matrix proposed by Shiller (1991, section II) when a property sells more than twice.

This function gives the same result as vcovHC(x, type = "sss", cluster = 'group') from the plm package.

Value

A k \times k covariance matrix.

References

Manski, C. (1988). Analog Estimation Methods in Econometrics. Chapman and Hall.

Shiller, R. J. (1991). Arithmetic repeat sales price estimators. Journal of Housing Economics, 1(1):110-126.

White, H. (2001). Asymptotic Theory for Econometricians (revised edition). Emerald Publishing.

Examples

# Makes some groups in mtcars
mtcars$clust <- letters[1:4]

# Matrices for regression
x <- model.matrix(~ cyl + disp, mtcars)
y <- matrix(mtcars$mpg)

# Regression coefficients
b <- solve(crossprod(x), crossprod(x, y))

# Residuals
r <- y - x %*% b

# Robust variance matrix
vcov <- rs_var(r, x, ids = mtcars$clust)

## Not run: 
# Same as plm
library(plm)
mdl <- plm(mpg ~ cyl + disp, mtcars, model = "pooling", index = "clust")
vcov2 <- vcovHC(mdl, type = "sss", cluster = "group")
vcov - vcov2

## End(Not run)