price_indexes: Price indexes

Description

Calculate a variety of price indexes using information on prices and quantities at two points in time.

Usage

arithmetic_index(type)
geometric_index(type)
harmonic_index(type)
laspeyres_index(p1, p0, q0, na.rm = FALSE)
paasche_index(p1, p0, q1, na.rm = FALSE)
jevons_index(p1, p0, na.rm = FALSE)
lowe_index(p1, p0, qb, na.rm = FALSE)
young_index(p1, p0, pb, qb, na.rm = FALSE)
fisher_index(p1, p0, q1, q0, na.rm = FALSE)
hlp_index(p1, p0, q1, q0, na.rm = FALSE)
lm_index(elasticity)
cswd_index(p1, p0, na.rm = FALSE)
cswdb_index(p1, p0, q1, q0, na.rm = FALSE)
bw_index(p1, p0, na.rm = FALSE)
stuvel_index(a, b)
arithmetic_agmean_index(elasticity)
geometric_agmean_index(elasticity)
lehr_index(p1, p0, q1, q0, na.rm = FALSE)
martini_index(a)

Value

arithmetic_index(), geometric_index(), harmonic_index(), and stuvel_index() each return a function to compute the relevant price indexes; lm_index(), arithmetic_agmean_index(), and geometric_agmean_index() each return a function to calculate the relevant index for a given elasticity of substitution. The others return a numeric value giving the change in price between the base period and current period.

Arguments

type: The name of the index. See details for the possible types of indexes.
p1: Current-period prices.
p0: Base-period prices.
q0: Base-period quantities.
na.rm: Should missing values be removed? By default missing values for prices or quantities return a missing value.
q1: Current-period quantities.
qb: Period-b quantities for the Lowe/Young index.
pb: Period-b prices for the Lowe/Young index.
elasticity: The elasticity of substitution for the Lloyd-Moulton and AG mean indexes.
a, b: Parameters for the generalized Stuvel index or Martini index.

Details

The arithmetic_index(), geometric_index(), and harmonic_index() functions return a function to calculate a given type of arithmetic, geometric (logarithmic), and harmonic index. Together, these functions produce functions to calculate the following indexes.

Arithmetic indexes
Carli
Dutot
Laspeyres
Palgrave
Unnamed index (arithmetic mean of Laspeyres and Palgrave)
Drobisch (or Sidgwick, arithmetic mean of Laspeyres and Paasche)
Walsh-I (arithmetic Walsh)
Marshall-Edgeworth
Geary-Khamis
Lowe
Young
Hybrid-CSWD
Geometric indexes
Jevons
Geometric Laspeyres (or Jöhr)
Geometric Paasche
Geometric Young
Törnqvist (or Törnqvist-Theil)
Montgomery-Vartia / Vartia-I
Sato-Vartia / Vartia-II
Walsh-II (geometric Walsh)
Theil
Rao
Harmonic indexes
Coggeshall (equally weighted harmonic index)
Paasche
Harmonic Laspeyres
Harmonic Young

Along with the lm_index() function to calculate the Lloyd-Moulton index, these are just convenient wrappers for generalized_mean() and index_weights().

The Laspeyres, Paasche, Jevons, Lowe, and Young indexes are among the most common price indexes, and so they get their own functions. The laspeyres_index(), lowe_index(), and young_index() functions correspond to setting the appropriate type in arithmetic_index(); paasche_index() and jevons_index() instead come from the harmonic_index() and geometric_index() functions.

In addition to these indexes, there are also functions for calculating a variety of indexes based on nested generalized means. The Fisher index is the geometric mean of the arithmetic Laspeyres and Paasche indexes; the Harmonic Laspeyres Paasche (or Harmonic Paasche Laspeyres) index is the harmonic analog of the Fisher index (8054 on Fisher's list). The Carruthers-Sellwood-Ward-Dalen and Carruthers-Sellwood-Ward-Dalen-Balk indexes are sample analogs of the Fisher index; the Balk-Walsh index is the sample analog of the Walsh index. The AG mean index is the arithmetic or geometric mean of the geometric and arithmetic Laspeyres indexes, weighted by the elasticity of substitution. The stuvel_index() function returns a function to calculate a Stuvel index of the given parameters. The Lehr index is an alternative to the Geary-Khamis index, and is the implicit price index for Fisher's index 4153. The Martini index is a Lowe index where the quantities are the weighted geometric average of current and base period quantities.

References

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

Fisher, I. (1922). The Making of Index Numbers. Houghton Mifflin Company.

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.

Examples

Run this code

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

# Most indexes can be calculated by combining the appropriate weights
# with the correct type of mean.

laspeyres_index(p2, p1, q1)
arithmetic_mean(p2 / p1, index_weights("Laspeyres")(p1, q1))

geometric_index("Laspeyres")(p2, p1, q1)
geometric_mean(p2 / p1, index_weights("Laspeyres")(p1, q1))

# NAs get special treatment.

p_na <- replace(p1, 6, NA)

laspeyres_index(p2, p_na, q1, na.rm = TRUE) # drops the last price relative

sum(p2 * q1, na.rm = TRUE) /
  sum(p_na * q1, na.rm = TRUE) # drops the last period-0 price

# von Bortkiewicz decomposition

paasche_index(p2, p1, q2) / laspeyres_index(p2, p1, q1) - 1

wl <- scale_weights(index_weights("Laspeyres")(p1, q1))
pl <- laspeyres_index(p2, p1, q1)
ql <- quantity_index(laspeyres_index)(q2, q1, p1)

sum(wl * (p2 / p1 / pl - 1) * (q2 / q1 / ql - 1))

# Similar decomposition for geometric Laspeyres/Paasche.

wp <- scale_weights(index_weights("Paasche")(p2, q2))
gl <- geometric_index("Laspeyres")(p2, p1, q1)
gp <- geometric_index("Paasche")(p2, p1, q2)

log(gp / gl)

sum(scale_weights(wl) * (wp / wl - 1) * log(p2 / p1 / gl))

Run the code above in your browser using DataLab