Package 'rsmatrix'

Shiller's repeat-sales matrices

Description

Create a function to compute the $Z$, $X$, $y$, and $Y$ matrices in Shiller (1991, section 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 base::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, section 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 MJ, Muth RF, Nourse HO (1963). “A regression method for real estate price index construction.” Journal of the American Statistical Association, 53(304), 933-942.

Shiller RJ (1991). “Arithmetic repeat sales price estimators.” Journal of Housing Economics, 1(1), 110-126. doi:10.1016/S1051-1377(05)80028-2.

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 base::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

base::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); 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 RJ (1991). “Arithmetic repeat sales price estimators.” Journal of Housing Economics, 1(1), 110-126. doi:10.1016/S1051-1377(05)80028-2.

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)

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