gerardi {pricelevels}

Gerardi index

Description

Calculation of regional price levels using the multilateral Gerardi index (Eurostat, 1978).

Usage

gerardi(p, r, n, q, w=NULL, base=NULL, simplify=TRUE, settings=list())

Arguments

p

A numeric vector of prices.

r, n

A character vector or factor of regional entities r and products n, respectively.

q, w

A numeric vector of non-negative quantities q or expenditure share weights w (see details). If both q and w are provided, q will be used.

base

A character specifying the base region to which all price levels are expressed. When NULL, they refer to the (unweighted) regional average.

simplify

A logical indicating whether a named vector of estimated regional price levels (TRUE) should be returned, or also the average product prices.

settings

A list of control settings to be used. The following settings are supported:

• chatty : A logical specifying if warnings and info messages should be printed or not. The default is getOption("pricelevels.chatty").

• connect : A logical specifying if the data should be checked for connectedness or not. The default is getOption("pricelevels.connect"). If the data are not connected, price levels are computed within the biggest block of connected regions or the block of regions to which the base region belongs. See also connect().

• plot : A logical specifying if the calculated price levels should be plotted or not. If TRUE, the price ratios of each region are displayed as boxplots and the price levels are added as colored points. The default is getOption("pricelevels.plot").

• variant : for original, the international prices are calculated as unweighted geometric means. This is the original approach. With adjusted, the international prices are calculated as weighted geometric means.

Details

Before calculations start, missing values are excluded and duplicated observations for r and n are aggregated, that is, duplicated prices p and weights w are averaged and duplicated quantities q added up.

The weights w must represent expenditure shares defined as w_i^r = p_i^r q_i^r / \sum_{j=1}^{N} p_j^r q_j^r. They are internally (re-)normalized such that they add up to 1 for each region r.

Value

For simplify=TRUE, a named vector of regional price levels. Otherwise, for simplify=FALSE, a list containing the named vector of international product prices and regional price levels.

Author(s)

Sebastian Weinand

References

Balk, B. M. (1996). A comparison of ten methods for multilateral international price and volume comparisons. Journal of Official Statistics, 12 (1), 199-222.

Eurostat (1978), Comparison in real values of the aggregates of ESA 1975, Publications Office, Luxembourg.

Examples

require(data.table)

# example data:
set.seed(123)
dt1 <- rdata(R=3, B=1, N=5)

# Gerardi price index:
dt1[, gerardi(p=price, q=quantity, r=region, n=product)]

# add price data:
dt2 <- rdata(R=4, B=1, N=4)
dt2[, "region":=factor(region, labels=4:7)]
dt2[, "product":=factor(product, labels=6:9)]
dt <- rbind(dt1, dt2)
dt[, is.connected(r=region, n=product)] # non-connected now

# compute expenditure share weights:
dt[, "share" := price*quantity/sum(price*quantity), by="region"]

# Gerardi index with quantites or expenditure share weights:
dt[, gerardi(p=price, q=quantity, r=region, n=product)]
dt[, gerardi(p=price, w=share, r=region, n=product)]