gpindex (version 0.6.3)

index_weights: Index weights

Description

Calculate weights for a variety of different price indexes.

Usage

index_weights(
  type = c("Carli", "Jevons", "Coggeshall", "Dutot", "Laspeyres", "HybridLaspeyres",
    "LloydMoulton", "Palgrave", "Paasche", "HybridPaasche", "Drobisch", "Unnamed",
    "Tornqvist", "Walsh1", "Walsh2", "MarshallEdgeworth", "GearyKhamis", "Vartia1",
    "MontgomeryVartia", "Vartia2", "SatoVartia", "Theil", "Rao", "Lowe", "Young",
    "HybridCSWD")
)

Value

A function of current and base period prices/quantities that calculates the relevant weights.

Arguments

type

The name of the index. See details for the possible types of indexes.

Details

The index_weights() function returns a function to calculate weights for a variety of price indexes. Weights for the following types of indexes can be calculated.

• Carli / Jevons / Coggeshall

• Dutot

• Laspeyres / Lloyd-Moulton

• Hybrid Laspeyres (for use in a harmonic mean)

• Paasche / Palgrave

• Hybrid Paasche (for use in an arithmetic mean)

• Törnqvist / Unnamed

• Drobisch

• Walsh-I (for an arithmetic Walsh index)

• Walsh-II (for a geometric Walsh index)

• Marshall-Edgeworth

• Geary-Khamis

• Montgomery-Vartia / Vartia-I

• Sato-Vartia / Vartia-II

• Theil

• Rao

• Lowe

• Young

• Hybrid-CSWD

The weights need not sum to 1, as this normalization isn't always appropriate (i.e., for the Vartia-I weights).

References

Balk, B. M. (2008). Price and Quantity Index Numbers. Cambridge University Press.

IMF, ILO, Eurostat, UNECE, OECD, and World Bank. (2020). Consumer Price Index Manual: Concepts and Methods. International Monetary Fund.

von der Lippe, P. (2007). Index Theory and Price Statistics. Peter Lang.

Selvanathan, E. A. and Rao, D. S. P. (1994). Index Numbers: A Stochastic Approach. MacMillan.

See Also

update_weights() for price-updating weights.

quantity_index() to remap the arguments in these functions for a quantity index.

Other price index functions: geks(), price_indexes, splice_index()

Examples

p1 <- price6[[2]]
p2 <- price6[[3]]
q1 <- quantity6[[2]]
q2 <- quantity6[[3]]
pb <- price6[[1]]
qb <- quantity6[[1]]

# Explicit calculation for each of the different weights
# Carli/Jevons/Coggeshall

all.equal(index_weights("Carli")(p2), rep(1, length(p1)))

# Dutot

all.equal(index_weights("Dutot")(p1), p1)

# Laspeyres / Lloyd-Moulton

all.equal(index_weights("Laspeyres")(p1, q1), p1 * q1)

# Hybrid Laspeyres

all.equal(index_weights("HybridLaspeyres")(p2, q1), p2 * q1)

# Paasche / Palgrave

all.equal(index_weights("Paasche")(p2, q2), p2 * q2)

# Hybrid Paasche

all.equal(index_weights("HybridPaasche")(p1, q2), p1 * q2)

# Tornqvist / Unnamed

all.equal(
  index_weights("Tornqvist")(p2, p1, q2, q1),
  0.5 * p1 * q1 / sum(p1 * q1) + 0.5 * p2 * q2 / sum(p2 * q2)
)

# Drobisch

all.equal(
  index_weights("Drobisch")(p2, p1, q2, q1),
  0.5 * p1 * q1 / sum(p1 * q1) + 0.5 * p1 * q2 / sum(p1 * q2)
)

# Walsh-I

all.equal(
  index_weights("Walsh1")(p1, q2, q1),
  p1 * sqrt(q1 * q2)
)

# Marshall-Edgeworth

all.equal(
  index_weights("MarshallEdgeworth")(p1, q2, q1),
  p1 * (q1 + q2)
)

# Geary-Khamis

all.equal(
  index_weights("GearyKhamis")(p1, q2, q1),
  p1 / (1 / q1 + 1 / q2)
)

# Montgomery-Vartia / Vartia-I

all.equal(
  index_weights("MontgomeryVartia")(p2, p1, q2, q1),
  logmean(p1 * q1, p2 * q2) / logmean(sum(p1 * q1), sum(p2 * q2))
)

# Sato-Vartia / Vartia-II

all.equal(
  index_weights("SatoVartia")(p2, p1, q2, q1),
  logmean(p1 * q1 / sum(p1 * q1), p2 * q2 / sum(p2 * q2))
)

# Walsh-II

all.equal(
  index_weights("Walsh2")(p2, p1, q2, q1),
  sqrt(p1 * q1 * p2 * q2)
)

# Theil

all.equal(index_weights("Theil")(p2, p1, q2, q1), {
  w0 <- scale_weights(p1 * q1)
  w1 <- scale_weights(p2 * q2)
  (w0 * w1 * (w0 + w1) / 2)^(1 / 3)
})

# Rao

all.equal(index_weights("Rao")(p2, p1, q2, q1), {
  w0 <- scale_weights(p1 * q1)
  w1 <- scale_weights(p2 * q2)
  w0 * w1 / (w0 + w1)
})

# Lowe

all.equal(index_weights("Lowe")(p1, qb), p1 * qb)

# Young

all.equal(index_weights("Young")(pb, qb), pb * qb)

# Hybrid CSWD (to approximate a CSWD index)

all.equal(index_weights("HybridCSWD")(p2, p1), sqrt(p1 / p2))