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Matrices forrepeat-sales price indexes

Calculate the matrices in Shiller (1991) that serve as the foundationfor 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 thematrices in Shiller (1991, sections I-II), e.g., S&P’s Case-Shillerindex, Teranet-National Bank’s HPI, and formerly Statistics Canada’sRPPI. Let’s consider the simplest non-trivial example to see how to makeand use these matrices.

library(rsmatrix)# Make some data for two products selling over three periodssales<-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, whichcan be done with thers_pairs() function.

# Turn into sales pairssales[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

Thers_matrix() function can now be used to produce afunction that constructs these matrices.

# Calculate matricesmatrix_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 usingthese 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

ThehpiR package has some functionality for makingrepeat-sales indexes, as does theMcSpatial package(formerly on CRAN). Although easier to use, these packages lack theflexibility to compute a number of indexes found literature (e.g., anyof the arithmetic repeat-sales indexes). The functions in this packagebuild off of those in thersi package in Kirby-McGregorand Martin (2019), which also gives a good background on the theory ofrepeat-sales indexes.

References

ILO, IMF, OECD, UN, World Bank, Eurostat. (2013).Handbook onResidential Property Prices Indices (RPPIs). Eurostat.

Kirby-McGregor, M., and Martin, S. (2019). An R package forcalculating repeat-sale price indices.Romanian StatisticalReview, 3:17-33.

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