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```
# IndexNumR: a package for index number computation
# Copyright (C) 2018 Graham J. White (g.white@unswalumni.com)
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU General Public License
# as published by the Free Software Foundation; either version 2
# of the License, or (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, see <http://www.gnu.org/licenses/>.
#' Evaluate product overlap between periods
#'
#' Evaluate the counts and expenditure for each period with and without
#' matching items across periods.
#'
#' @param x A dataframe containing price, quantity, a time period identifier
#' and a product identifier. It must have column names.
#' @param pvar A character string for the name of the price variable
#' @param qvar A character string for the name of the quantity variable
#' @param prodID A character string for the name of the product identifier
#' @param pervar A character string for the name of the time variable. This variable
#' must contain integers starting at period 1 and increasing in increments of 1 period.
#' There may be observations on multiple products for each time period.
#' @param output A character string specifying whether the matching should be
#' done assuming a chained index or a fixed base index. No index is actually computed,
#' but the matching needs to know which periods are being compared. Default is chained.
#' @return A list of two matrices, one for expenditures and one for counts.
#' The first four columns present the base period information
#' base_index (the base time period), base (base period expenditure or count),
#' base_matched (the expenditure or count of the base period after matching),
#' base_share (share of total expenditure in the base period that remains after
#' matching). Columns 5-8 are defined analogously for the current period. The matched
#' numbers for the base period should be interpreted as the count or expenditure
#' that remains after removal of products that exist in the base period, but not
#' in the current period. That is, products that existed in the base period but no
#' longer exist in the current period are removed by the matching. If new products
#' exist in the current period that were not available in the base period, this
#' does not affect the matched base period expenditure or count. The appearance
#' of new products is captured in the current period matched expenditure and counts.
#' Therefore, a base period share that is less than 1 indicates that products have
#' disappeared, while a current period share less than 1 indicates that new products
#' have appeared.
#'
#' The count matrix has two additional columns, "new" and "leaving". The new column
#' gives the number of products that exist in the current period but not the base period.
#' The leaving column gives the count of products that exist in the base period
#' but not the current period. Matching removes both of these types of products.
#' @examples
#' # create CES_sigma_2 dataset removing the observation in time period 4
#' # on product 1
#' df <- CES_sigma_2[!(CES_sigma_2$time==4 & CES_sigma_2$prodID==1),]
#' # evaluate the overlap between periods for this dataset assuming
#' # a chained index
#' evaluateMatched(df, pvar="prices", qvar="quantities", pervar="time",
#' prodID = "prodID", output="chained")
#' @export
evaluateMatched <- function(x,pvar,qvar,pervar,prodID,output="chained"){
# check that a valid output type is chosen
validOutput <- c("chained","fixedbase")
if(!(tolower(output) %in% validOutput)){
stop("Not a valid output type. Please choose from chained or fixedbase.")
}
# initialise some things
n <- max(x[[pervar]], na.rm=TRUE)
colheadsExp <- c("base_index","base","base_matched","base_share",
"current_index","current","current_matched","current_share")
colheadsCount <- c(colheadsExp, "new", "leaving")
expenditure <- matrix(NA,n-1,8)
colnames(expenditure) <- colheadsExp
counts <- matrix(NA,n-1,10)
colnames(counts) <- colheadsCount
# if fixed base requested, set xt0 to the first period data
if(tolower(output)=="fixedbase"){
xt0 <- x[x[[pervar]]==1,]
expenditure[,"base_index"] <- 1
expenditure[,"base"] <- sum(xt0[[pvar]]*xt0[[qvar]])
counts[,"base_index"] <- 1
counts[,"base"] <- length(unique(xt0[[prodID]]))
}
for(i in 2:n){
# calculate expenditure and counts prior to matching
if(!(tolower(output)=="fixedbase")){
xt0 <- x[x[[pervar]]==i-1,]
expenditure[i-1,"base_index"] <- i-1
expenditure[i-1,"base"] <- sum(xt0[[pvar]]*xt0[[qvar]])
counts[i-1,"base_index"] <- i-1
counts[i-1,"base"] <- length(unique(xt0[[prodID]]))
}
else {
xt0 <- x[x[[pervar]]==1,]
}
xt1 <- x[x[[pervar]]==i,]
expenditure[i-1,"current_index"] <- i
expenditure[i-1,"current"] <- sum(xt1[[pvar]]*xt1[[qvar]])
counts[i-1,"current_index"] <- i
counts[i-1,"current"] <- length(unique(xt1[[prodID]]))
counts[i-1,9] <- length(xt1[[prodID]][!(xt1[[prodID]] %in% xt0[[prodID]])])
counts[i-1,10] <- length(xt0[[prodID]][!(xt0[[prodID]] %in% xt1[[prodID]])])
# remove the unmatched items
xt1 <- xt1[xt1[[prodID]] %in% unique(xt0[[prodID]]),]
xt0 <- xt0[xt0[[prodID]] %in% unique(xt1[[prodID]]),]
# calculate the matched expenditures and counts
expenditure[i-1,3] <- sum(xt0[[pvar]]*xt0[[qvar]])
counts[i-1,3] <- length(unique(xt0[[prodID]]))
expenditure[i-1,7] <- sum(xt1[[pvar]]*xt1[[qvar]])
counts[i-1,7] <- length(unique(xt1[[prodID]]))
}
# compute the shares
expenditure[,4] <- expenditure[,3]/expenditure[,2]
expenditure[,8] <- expenditure[,7]/expenditure[,6]
counts[,4] <- counts[,3]/counts[,2]
counts[,8] <- counts[,7]/counts[,6]
return(list(expenditure = expenditure, counts = counts))
}
#' Product ID's for appearing/disappearing products
#'
#' This function will give the product ID's of products that appear
#' or disappear in each period.
#'
#' @inheritParams priceIndex
#' @return a list containing one element for each time period, each element of
#' which contains two vectors (one for appearing products, and one for disappearing products)
#' @export
#' @examples
#' # create a dataset with some missing products
#' df <- CES_sigma_2[-c(3,4,15),]
#'
#' # show the products that changed
#' productChanges(df, "time", "prodID")
#'
productChanges <- function(x, pervar, prodID){
# initialise some things
n <- max(x[[pervar]], na.rm=TRUE)
result <- list()
# sort the dataset by time period and product ID
x <- x[order(x[[pervar]], x[[prodID]]),]
# for each period
for(i in 1:n){
if(i != 1){
xt <- x[x[[pervar]] == i,]
xtminus1 <- x[x[[pervar]] == i-1,]
appearing <- unique(xt[[prodID]][!(xt[[prodID]] %in% xtminus1[[prodID]])])
disappearing <- unique(xtminus1[[prodID]][!(xtminus1[[prodID]] %in% xt[[prodID]])])
if(length(appearing) > 0 & length(disappearing) == 0){
result[[as.character(i)]] <- list(appearing = appearing)
} else if(length(appearing) == 0 & length(disappearing) > 0){
result[[as.character(i)]] <- list(disappearing = disappearing)
} else if(length(appearing) > 0 & length(disappearing) > 0){
result[[as.character(i)]] <- list(appearing = appearing,
disappearing = disappearing)
}
}
}
return(result)
}
```

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