Compute period-over-period (chainable) or fixed-base (direct) elemental price indexes, with optional percent-change contributions for each product.
elemental_index(x, ...)# S3 method for default
elemental_index(x, ...)
# S3 method for numeric
elemental_index(
x,
...,
period = gl(1, length(x)),
ea = gl(1, length(x)),
weights = NULL,
product = NULL,
chainable = TRUE,
na.rm = FALSE,
contrib = FALSE,
r = 0
)
# S3 method for data.frame
elemental_index(x, formula, ..., weights = NULL, product = NULL)
elementary_index(x, ...)
A price index that inherits from piar_index. If
chainable = TRUE then this is a period-over-period index that also
inherits from chainable_piar_index; otherwise, it is a
fixed-based index that inherits from direct_piar_index.
Period-over-period or fixed-base price relatives. Currently there
are methods for numeric vectors (which can be made with
price_relative()) and data frames.
Further arguments passed to or used by methods.
A factor, or something that can be coerced into one, giving
the time period associated with each price relative in x. The
ordering of time periods follows of the levels of period, to agree
with cut(). The default makes an index for one time period.
A factor, or something that can be coerced into one, giving the
elemental aggregate associated with each price relative in x. The
default makes an index for one elemental aggregate.
A numeric vector of weights for the price relatives in x,
or something that can be coerced into one. The default is equal weights.
This is evaluated in x for the data frame method.
A character vector of product names, or something that can
be coerced into one, for each price relative in x when making
percent-change contributions. The default uses the names of x, if any;
otherwise, elements of x are given sequential names within each elemental
aggregate. This is evaluated in x for the data frame method.
Are the price relatives in x period-over-period
relatives that are suitable for a chained calculation (the default)? This
should be FALSE when x contains fixed-base relatives.
Should missing values be removed? By default, missing values
are not removed. Setting na.rm = TRUE is equivalent to overall mean
imputation.
Should percent-change contributions be calculated? The default does not calculate contributions.
Order of the generalized mean to aggregate price relatives. 0 for a
geometric index (the default for making elemental indexes), 1 for an
arithmetic index (the default for aggregating elemental indexes and
averaging indexes over subperiods), or -1 for a harmonic index (usually for
a Paasche index). Other values are possible; see
gpindex::generalized_mean() for details.
A two-sided formula with price relatives on the left-hand side, and time periods and elemental aggregates (in that order) on the right-hand side.
When supplied with a numeric vector, elemental_index() is a simple
wrapper that applies
gpindex::generalized_mean(r)() and
gpindex::contributions(r)() (if contrib = TRUE)
to x and weights grouped by ea and period. That
is, for every combination of elemental aggregate and time period,
elemental_index() calculates an index based on a generalized mean of
order r and, optionally, percent-change contributions. Product names should
be unique within each time period when making contributions, and, if not, are
passed to make.unique() with a warning. The default
(r = 0 and no weights) makes Jevons elemental indexes. See chapter 8
(pp. 175--190) of the CPI manual (2020) for more detail about making
elemental indexes, or chapter 9 of the PPI manual (2004), and chapter 5 of
Balk (2008).
The default method simply coerces x to a numeric vector prior to
calling the method above. The data frame method provides a formula interface
to specify columns of price relatives, time periods, and elemental
aggregates and call the method above.
The interpretation of the index depends on how the price relatives in
x are made. If these are period-over-period relatives, then the
result is a collection of period-over-period (chainable) elemental indexes;
if these are fixed-base relatives, then the result is a collection of
fixed-base (direct) elemental indexes. For the latter, chainable
should be set to FALSE so that no subsequent methods assume that a
chained calculation should be used.
By default, missing price relatives in x will propagate throughout
the index calculation. Ignoring missing values with na.rm = TRUE is
the same as overall mean (parental) imputation, and needs to be explicitly
set in the call to elemental_index(). Explicit imputation of missing
relatives, and especially imputation of missing prices, should be done prior
to calling elemental_index().
Indexes based on nested generalized means, like the Fisher index (and
superlative quadratic mean indexes more generally), can be calculated by
supplying the appropriate weights with gpindex::nested_transmute(); see the
example below. It is important to note that there are several ways to
make these weights, and this affects how percent-change contributions
are calculated.
elementary_index() is an alias for elemental_index() as this is more
common in the literature.
Balk, B. M. (2008). Price and Quantity Index Numbers. Cambridge University Press.
ILO, IMF, UNECE, OECD, and World Bank. (2004). Producer Price Index Manual: Theory and Practice. International Monetary Fund.
IMF, ILO, OECD, Eurostat, UNECE, 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.
price_relative() for making price relatives for the same products over
time, and carry_forward() and shadow_price() for
imputation of missing prices.
as_index() to turn pre-computed (elemental) index values into an
index object.
chain() for chaining period-over-period indexes, and
rebase() for rebasing an index.
aggregate() to aggregate elemental indexes
according to an aggregation structure.
as.matrix() and
as.data.frame() for coercing an index
into a tabular form.
library(gpindex)
prices <- data.frame(
rel = 1:8,
period = rep(1:2, each = 4),
ea = rep(letters[1:2], 4)
)
# Calculate Jevons elemental indexes
elemental_index(prices, rel ~ period + ea)
# Same as using lm() or tapply()
exp(coef(lm(log(rel) ~ ea:factor(period) - 1, prices)))
with(
prices,
t(tapply(rel, list(period, ea), geometric_mean, na.rm = TRUE))
)
# A general function to calculate weights to turn the geometric
# mean of the arithmetic and harmonic mean (i.e., Fisher mean)
# into an arithmetic mean
fw <- grouped(nested_transmute(0, c(1, -1), 1))
# Calculate a CSWD index (same as the Jevons in this example)
# as an arithmetic index by using the appropriate weights
elemental_index(
prices,
rel ~ period + ea,
weights = fw(rel, group = interaction(period, ea)),
r = 1
)
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