SNQ Profit function: Weights of prices for normalization
SNQ Profit function: Weights of prices for normalization
Returns a vector of weights to normalize prices on a Symmetric Normalized Quadratic (SNQ) Profit function.
snqProfitWeights( priceNames, quantNames, data, method ="DW92", base =1)
Arguments
priceNames: a vector of strings containing the names of netput prices.
quantNames: a vector of strings containing the names of netput quantities.
data: a data frame containing the data.
method: the method to determine the weights (see details).
base: the base period(s) for scaling prices (see details).
Details
If argument method is 'DW92' the method of Diewert and Wales (1992) is applied. They predetermine the weights by
θi=i=1∑n∣xi∣pi0∣xi∣pi0
Defining the scaled netput quantities as xit=xit⋅pi0
we get following formula:
θi=i=1∑nxixi
The prices are scaled that they are unity in the base period or - if there is more than one base period - that the means of the prices over the base periods are unity. The argument base can be either
(a) a single number: the row number of the base prices,
(b) a vector indicating several observations: The means of these observations are used as base prices,
(c) a logical vector with the same length as the data: The means of the observations indicated as 'TRUE' are used as base prices, or (d) NULL: prices are not scaled.