Nothing
R/AIDSFunctions.R
In antitrust: Tools for Antitrust Practitioners
Defines functions
pcaids.nests
pcaids
aids
Documented in
aids
pcaids
pcaids.nests
#' @title (Nested) AIDS Calibration and Merger Simulation
#' @name AIDS-Functions
#' @aliases aids
#' pcaids
#' pcaids.nests
#' @description Calibrates consumer demand using (nested) AIDS and then
#' simulates the price effect of a merger between two firms
#' under the assumption that all firms in the market are playing
#' a differentiated products Bertrand game.
#' @description Below let k denote the number of products produced by all firms.
#'
#' @param shares A length k vector of product revenue shares. All shares must
#' be between 0 and 1.
#' @param margins A length k vector of product margins. All margins must
#' be either be between 0 and 1, or NA.
#' @param prices A length k vector product prices. Default is missing, in
#' which case demand intercepts are not calibrated.
#' @param knownElast A negative number equal to the pre-merger own-price
#' elasticity for any of the k products.
#' @param mktElast A negative number equal to the industry pre-merger
#' price elasticity. Default is NA for \code{aids} and -1 for \code{pcaids}.
#' @param diversions A k x k matrix of diversion ratios with diagonal
#' elements equal to -1. Default is missing, in which case diversion
#' according to revenue share is assumed.
#' @param ownerPre EITHER a vector of length k whose values
#' indicate which firm produced a product before the merger OR a
#' k x k matrix of pre-merger ownership shares.
#' @param ownerPost EITHER a vector of length k whose values
#' indicate which firm produced a product after the merger OR
#' a k x k matrix of post-merger ownership shares.
#' @param knownElastIndex An integer equal to the position of the
#' \sQuote{knownElast} product in the \sQuote{shares} vector. Default is 1, which
#' assumes that the own-price elasticity of the first product is
#' known.
#' @param insideSize Total expenditure (revenues) on products included in the simulation.
#' @param nests A length k vector identifying which nest a product
#' belongs to. Default is that all products belong to a single nest.
#' @param mcDelta A vector of length k where each element equals the
#' proportional change in a product's marginal costs due to
#' the merger. Default is 0, which assumes that the merger does not
#' affect any products' marginal cost.
#' @param subset A vector of length k where each element equals TRUE if
#' the product indexed by that element should be included in the
#' post-merger simulation and FALSE if it should be excluded.Default is a
#' length k vector of TRUE.
#' @param parmStart \code{aids} only. A vector of length 2 who elements equal to an
#' initial guess for "known" element of the diagonal of the demand matrix
#' and the market elasticity.
#' @param priceStart A vector of length k who elements equal to an
#' initial guess of the proportional change in price caused by the
#' merger. The default is to draw k random elements from a [0,1] uniform
#' distribution.
#' @param isMax If TRUE, checks to see whether computed price equilibrium
#' locally maximizes firm profits and returns a warning if not. Default is FALSE.
#' @param nestsParmStart A vector of starting values used to solve for
#' price coefficient and nest parameters. If missing then the random
#' draws with the appropriate restrictions are employed.
#' @param control.slopes A list of \code{\link{optim}} control parameters passed to
#' the calibration routine optimizer (typically the \code{calcSlopes} method).
#' @param control.equ A list of \code{\link[BB]{BBsolve}} control parameters passed to
#' the non-linear equation solver (typically the \code{calcPrices} method).
#' @param labels A k-length vector of labels.
#' @param ... Additional options to feed to the \code{\link[BB]{BBsolve}}
#' optimizer used to solve for equilibrium prices.
#'
#' @details Using product market revenue shares and all of the
#' product product margins from at least two firms, \code{aids} is able to
#' recover the slopes in a proportionally calibrated Almost Ideal Demand System (AIDS)
#' without income effects. \code{aids} then uses these slopes to simulate the
#' price effects of a merger between
#' two firms under the assumption that all firms in the market are
#' playing a differentiated Bertrand pricing game.
#'
#' If prices are also supplied, \code{aids} is able to recover the
#' intercepts from the AIDS demand system. Intercepts are helpful because
#' they can be used to simulate pre- and post-merger price \emph{levels} as well as price
#' \emph{changes}. Whatsmore, the intercepts are necessary in order to
#' calculate compensating variation.
#'
#' \code{aids} assumes that diversion between the products
#' in the market occurs according to revenue share. This assumption may be relaxed
#' by setting \sQuote{diversions} equal to a k x k matrix of diversion
#' ratios. The diagonal of this matrix must equal -1, the off-diagonal
#' elements must be between 0 and 1, and the rows must sum to 1.
#'
#' \code{pcaids} is almost identical to \code{aids}, but instead of
#' assuming that at least two margins are known, \code{pcaids} assumes
#' that the own-price elasticity of any single
#' product, and the industry-wide own-price elasticity, are
#' known. Demand intercepts cannot be recovered using \code{pcaids}.
#'
#' \code{pcaids.nests} extends \code{pcaids} by allowing products
#' to be grouped into nests. Although products within the same nest still
#' have the independence of irrelevant alternatives (IIA) property,
#' products in different nests do not. Note that the \sQuote{diversions}
#' argument is absent from \code{pcaids.nests}.
#'
#' \code{pcaids.nests} assumes that the share diversion between nests is symmetric
#' (i.e for 2 nests A and B, the diversion from A to B is the same as B to
#' A). Therefore, if there are \eqn{w} nests, \eqn{2\le w \le k}{2 <= w <=k}, then the model
#' must estimate \eqn{w(w-1)/2} distinct nesting parameters. To accomplish
#' this, \code{pcaids.nests} uses margin information to produce estimates of
#' the nesting parameters. It is important to note that the number of
#' supplied margins must be at least as great as the number of nesting
#' parameters in order for PCAIDS to work.
#'
#' The nesting parameters are constrained to be between 0 and
#' 1. Therefore, one way to test the validity of the nesting structure is
#' to check whether the nesting parameters are between 0 and 1. The value
#' of the nesting parameters may be obtained from calling either the \sQuote{summary} or
#' \sQuote{getNestsParms} functions.
#'
#' @return \code{aids} returns an instance of class
#' \code{\linkS4class{AIDS}}, a child class of \code{\linkS4class{Linear}}.
#' \code{pcaids} returns an instance of class
#' \code{\linkS4class{PCAIDS}}, while \code{pcaids.nests} returns an
#' instance of \code{\linkS4class{PCAIDSNests}}. Both are
#' children of the \code{\linkS4class{AIDS}} class.
#'
#' @seealso \code{\link{linear}} for a demand system based on quantities
#' rather than revenue shares.
#' @author Charles Taragin \email{ctaragin+antitrustr@gmail.com}
#' @references Epstein, Roy and Rubinfeld, Daniel (2004).
#' \dQuote{Merger Simulation with Brand-Level Margin Data: Extending PCAIDS
#' with Nests.}
#' \emph{The B.E. Journal of Economic Analysis and Policy}, \bold{advances.4}(1), pp. 2.
#'
#' Epstein, Roy and Rubinfeld, Daniel (2004).
#' \dQuote{Effects of Mergers Involving Differentiated Products.}
#'
#' @examples
#' ## Simulate a merger between two single-product firms A and B in a
#' ## three-firm market (A, B, C). This example assumes that the merger is between
#' ## the firms A and B and that A's own-price elasticity is
#' ## known.
#' ## Source: Epstein and Rubinfeld (2004), pg 9, Table 2.
#'
#'
#' prices <- c(2.9,3.4,2.2) ## optional for aids, unnecessary for pcaids
#' shares <- c(.2,.3,.5)
#'
#'
#' ## The following are used by aids but not pcaids
#' ## only two of the margins are required to calibrate the demand parameters
#' margins <- c(0.33, 0.36, 0.44)
#'
#' ## The following are used by pcaids, but not aids
#' knownElast<- -3
#' mktElast <- -1
#'
#'
#' ## Define ownership using a vector of firm identities
#' ownerPre <- c("A","B","C")
#' ownerPost <- c("A","A","C")
#'
#' ## Alternatively, ownership could be defined using matrices
#' #ownerPre=diag(1,length(shares))
#' #ownerPost=ownerPre
#' #ownerPost[1,2] <- ownerPost[2,1] <- 1
#'
#'
#' ## AIDS: the following assumes both prices and margins are known.
#' ## Prices are not needed to estimate price changes
#'
#'
#'
#' result.aids <- aids(shares,margins,prices,ownerPre=ownerPre,ownerPost=ownerPost,labels=ownerPre)
#'
#'
#'
#' print(result.aids) # return predicted price change
#' summary(result.aids) # summarize merger simulation
#'
#' elast(result.aids,TRUE) # returns premerger elasticities
#' elast(result.aids,FALSE) # returns postmerger elasticities
#'
#' diversion(result.aids,TRUE) # return premerger diversion ratios
#' diversion(result.aids,FALSE) # return postmerger diversion ratios
#'
#'
#' cmcr(result.aids) #calculate compensating marginal cost reduction
#' upp(result.aids) #calculate Upwards Pricing Pressure Index
#'
#'
#' ## Implement the Hypothetical Monopolist Test
#' ## for products A and B using a 5\% SSNIP
#'
#' HypoMonTest(result.aids,prodIndex=1:2)
#'
#'
#' CV(result.aids) #calculate compensating variation as a percent of
#' #total expenditure
#' #CV can only be calculated if prices are supplied
#'
#'
#' ## Get a detailed description of the 'AIDS' class slots
#' showClass("AIDS")
#'
#' ## Show all methods attached to the 'AIDS' Class
#' showMethods(classes="AIDS")
#'
#' ## Show which class have their own 'elast' method
#' showMethods("elast")
#'
#' ## Show the method definition for 'elast' and Class 'AIDS'
#' getMethod("elast","AIDS")
#'
#'
#'
#' ## PCAIDS: the following assumes that only one product's elasticity is
#' ## known as well as the market elasticity.
#'
#'
#'
#' result.pcaids <- pcaids(shares,knownElast,mktElast,
#' ownerPre=ownerPre,ownerPost=ownerPost,
#' labels=ownerPre)
#'
#' print(result.pcaids) # return predicted price change
#' summary(result.pcaids) # summarize merger simulation
#'
#' elast(result.pcaids,TRUE) # returns premerger elasticities
#' elast(result.pcaids,FALSE) # returns postmerger elasticities
#'
#' diversion(result.pcaids,TRUE) # return premerger diversion ratios
#' diversion(result.pcaids,FALSE) # return postmerger diversion ratios
#'
#'
#' cmcr(result.pcaids) #calculate compensating marginal cost reduction
#'
#'
#' ## Implement the Hypothetical Monopolist Test
#' ## for products A and B using a 5\% SSNIP
#'
#' HypoMonTest(result.pcaids,prodIndex=1:2)
#'
#'
#'
#' ## Nested PCAIDS: in addition to the PCAIDS information requirements,
#' ## users must supply the nesting structure as well as margin infromation.
#'
#' nests <- c('H','L','L') # product A assigned to nest H, products B and C assigned to nest L
#'
#'
#' result.pcaids.nests <- pcaids.nests(shares,knownElast,mktElast,margins=margins,
#' nests=nests,ownerPre=ownerPre,
#' ownerPost=ownerPost,labels=ownerPre)
#'
#' @include DiagnosticsMethods.R
NULL
#'@rdname AIDS-Functions
#'@export
aids <- function(shares,margins,prices,diversions,
ownerPre,ownerPost,
mktElast = NA_real_,
insideSize = NA_real_,
mcDelta=rep(0, length(shares)),
subset=rep(TRUE, length(shares)),
parmStart= rep(NA_real_,2),
priceStart=runif(length(shares)),
isMax=FALSE,
control.slopes,
control.equ,
labels=paste("Prod",1:length(shares),sep=""),
...){
if(missing(prices)){ prices <- rep(NA_real_,length(shares))}
if(missing(diversions)){
diversions <- tcrossprod(1/(1-shares),shares)
diag(diversions) <- -1
}
## Create AIDS container to store relevant data
result <- new("AIDS",shares=shares,mcDelta=mcDelta,subset=subset,
margins=margins, prices=prices, quantities=shares, mktElast = mktElast,
ownerPre=ownerPre,ownerPost=ownerPost, parmStart=parmStart, insideSize = insideSize,
diversion=diversions,
priceStart=priceStart,labels=labels)
if(!missing(control.slopes)){
result@control.slopes <- control.slopes
}
if(!missing(control.equ)){
result@control.equ <- control.equ
}
## Convert ownership vectors to ownership matrices
result@ownerPre <- ownerToMatrix(result,TRUE)
result@ownerPost <- ownerToMatrix(result,FALSE)
## Calculate Demand Slope Coefficients
result <- calcSlopes(result)
## Solve Non-Linear System for Price Changes
result@priceDelta <- calcPriceDelta(result,isMax=isMax,subset=subset,...)
## Calculate marginal cost
result@mcPre <- calcMC(result,TRUE)
result@mcPost <- calcMC(result,FALSE)
## Calculate Pre and Post merger equilibrium prices
result@pricePre <- calcPrices(result,TRUE)
result@pricePost <- calcPrices(result,FALSE)
return(result)
}
#'@rdname AIDS-Functions
#'@export
pcaids <- function(shares,knownElast,mktElast=-1,
prices,diversions,
ownerPre,ownerPost,
knownElastIndex=1,
insideSize = NA_real_,
mcDelta=rep(0, length(shares)),
subset=rep(TRUE, length(shares)),
priceStart=runif(length(shares)),
isMax=FALSE,
control.slopes,
control.equ,
labels=paste("Prod",1:length(shares),sep=""),
...){
if(missing(prices)){ prices <- rep(NA_real_,length(shares))}
if(missing(diversions)){
diversions <- tcrossprod(1/(1-shares),shares)
diag(diversions) <- -1
}
## Create PCAIDS container to store relevant data
result <- new("PCAIDS",shares=shares,prices=prices,
quantities=shares, margins=shares,mcDelta=mcDelta,
subset=subset, insideSize = insideSize,
knownElast=knownElast,mktElast=mktElast,
ownerPre=ownerPre,ownerPost=ownerPost,
knownElastIndex=knownElastIndex,
diversion=diversions,
priceStart=priceStart,labels=labels)
if(!missing(control.slopes)){
result@control.slopes <- control.slopes
}
if(!missing(control.equ)){
result@control.equ <- control.equ
}
## Convert ownership vectors to ownership matrices
result@ownerPre <- ownerToMatrix(result,TRUE)
result@ownerPost <- ownerToMatrix(result,FALSE)
## Calculate Demand Slope Coefficients
result <- calcSlopes(result)
## Solve Non-Linear System for Price Changes
result@priceDelta <- calcPriceDelta(result,isMax=isMax,subset=subset,...)
## Calculate marginal cost
result@mcPre <- calcMC(result,TRUE)
result@mcPost <- calcMC(result,FALSE)
## Calculate Pre and Post merger equilibrium prices
## These are equal to NA in pcaids
result@pricePre <- calcPrices(result,TRUE)
result@pricePost <- calcPrices(result,FALSE)
return(result)
}
#'@rdname AIDS-Functions
#'@export
pcaids.nests <- function(shares,margins,knownElast,mktElast=-1,
prices,ownerPre,ownerPost,
nests=rep(1,length(shares)),
knownElastIndex=1,
insideSize = NA_real_,
mcDelta=rep(0, length(shares)),
subset=rep(TRUE, length(shares)),
priceStart=runif(length(shares)),
isMax=FALSE,
nestsParmStart,
control.slopes,
control.equ,
labels=paste("Prod",1:length(shares),sep=""),
...){
if(is.factor(nests)){nests <- nests[,drop=TRUE] }
else{nests <- factor(nests)}
if(missing(nestsParmStart)){
nNests <- nlevels(nests)
nestsParmStart <- runif(nNests*(nNests -1)/2)
}
if(missing(prices)){ prices <- rep(NA_real_,length(shares))}
diversions <- tcrossprod(1/(1-shares),shares);diag(diversions) <- -1.000000001 #'diversions' slot not used by pcaids.nests
## Create PCAIDS Nests container to store relevant data
result <- new("PCAIDSNests",shares=shares,
prices=prices,
quantities=shares,
margins=margins,mcDelta=mcDelta,subset=subset,insideSize = insideSize,
knownElast=knownElast,mktElast=mktElast,nests=nests,
nestsParms=nestsParmStart, diversion=diversions,
ownerPre=ownerPre,ownerPost=ownerPost,knownElastIndex=knownElastIndex,
priceStart=priceStart,labels=labels)
if(!missing(control.slopes)){
result@control.slopes <- control.slopes
}
if(!missing(control.equ)){
result@control.equ <- control.equ
}
## Convert ownership vectors to ownership matrices
result@ownerPre <- ownerToMatrix(result,TRUE)
result@ownerPost <- ownerToMatrix(result,FALSE)
## Calculate Demand Slope Coefficients
result <- calcSlopes(result)
## Solve Non-Linear System for Price Changes
result@priceDelta <- calcPriceDelta(result,isMax=isMax,subset=subset,...)
## Calculate marginal cost
result@mcPre <- calcMC(result,TRUE)
result@mcPost <- calcMC(result,FALSE)
## Calculate Pre and Post merger equilibrium prices
result@pricePre <- calcPrices(result,TRUE)
result@pricePost <- calcPrices(result,FALSE)
return(result)
}
Try the antitrust package in your browser
Any scripts or data that you put into this service are public.
antitrust documentation built on Aug. 24, 2022, 9:05 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Defines functions pcaids.nests pcaids aids
Documented in aids pcaids pcaids.nests
#' @title (Nested) AIDS Calibration and Merger Simulation
#' @name AIDS-Functions
#' @aliases aids
#' pcaids
#' pcaids.nests
#' @description Calibrates consumer demand using (nested) AIDS and then
#' simulates the price effect of a merger between two firms
#' under the assumption that all firms in the market are playing
#' a differentiated products Bertrand game.
#' @description Below let k denote the number of products produced by all firms.
#'
#' @param shares A length k vector of product revenue shares. All shares must
#' be between 0 and 1.
#' @param margins A length k vector of product margins. All margins must
#' be either be between 0 and 1, or NA.
#' @param prices A length k vector product prices. Default is missing, in
#' which case demand intercepts are not calibrated.
#' @param knownElast A negative number equal to the pre-merger own-price
#' elasticity for any of the k products.
#' @param mktElast A negative number equal to the industry pre-merger
#' price elasticity. Default is NA for \code{aids} and -1 for \code{pcaids}.
#' @param diversions A k x k matrix of diversion ratios with diagonal
#' elements equal to -1. Default is missing, in which case diversion
#' according to revenue share is assumed.
#' @param ownerPre EITHER a vector of length k whose values
#' indicate which firm produced a product before the merger OR a
#' k x k matrix of pre-merger ownership shares.
#' @param ownerPost EITHER a vector of length k whose values
#' indicate which firm produced a product after the merger OR
#' a k x k matrix of post-merger ownership shares.
#' @param knownElastIndex An integer equal to the position of the
#' \sQuote{knownElast} product in the \sQuote{shares} vector. Default is 1, which
#' assumes that the own-price elasticity of the first product is
#' known.
#' @param insideSize Total expenditure (revenues) on products included in the simulation.
#' @param nests A length k vector identifying which nest a product
#' belongs to. Default is that all products belong to a single nest.
#' @param mcDelta A vector of length k where each element equals the
#' proportional change in a product's marginal costs due to
#' the merger. Default is 0, which assumes that the merger does not
#' affect any products' marginal cost.
#' @param subset A vector of length k where each element equals TRUE if
#' the product indexed by that element should be included in the
#' post-merger simulation and FALSE if it should be excluded.Default is a
#' length k vector of TRUE.
#' @param parmStart \code{aids} only. A vector of length 2 who elements equal to an
#' initial guess for "known" element of the diagonal of the demand matrix
#' and the market elasticity.
#' @param priceStart A vector of length k who elements equal to an
#' initial guess of the proportional change in price caused by the
#' merger. The default is to draw k random elements from a [0,1] uniform
#' distribution.
#' @param isMax If TRUE, checks to see whether computed price equilibrium
#' locally maximizes firm profits and returns a warning if not. Default is FALSE.
#' @param nestsParmStart A vector of starting values used to solve for
#' price coefficient and nest parameters. If missing then the random
#' draws with the appropriate restrictions are employed.
#' @param control.slopes A list of \code{\link{optim}} control parameters passed to
#' the calibration routine optimizer (typically the \code{calcSlopes} method).
#' @param control.equ A list of \code{\link[BB]{BBsolve}} control parameters passed to
#' the non-linear equation solver (typically the \code{calcPrices} method).
#' @param labels A k-length vector of labels.
#' @param ... Additional options to feed to the \code{\link[BB]{BBsolve}}
#' optimizer used to solve for equilibrium prices.
#'
#' @details Using product market revenue shares and all of the
#' product product margins from at least two firms, \code{aids} is able to
#' recover the slopes in a proportionally calibrated Almost Ideal Demand System (AIDS)
#' without income effects. \code{aids} then uses these slopes to simulate the
#' price effects of a merger between
#' two firms under the assumption that all firms in the market are
#' playing a differentiated Bertrand pricing game.
#'
#' If prices are also supplied, \code{aids} is able to recover the
#' intercepts from the AIDS demand system. Intercepts are helpful because
#' they can be used to simulate pre- and post-merger price \emph{levels} as well as price
#' \emph{changes}. Whatsmore, the intercepts are necessary in order to
#' calculate compensating variation.
#'
#' \code{aids} assumes that diversion between the products
#' in the market occurs according to revenue share. This assumption may be relaxed
#' by setting \sQuote{diversions} equal to a k x k matrix of diversion
#' ratios. The diagonal of this matrix must equal -1, the off-diagonal
#' elements must be between 0 and 1, and the rows must sum to 1.
#'
#' \code{pcaids} is almost identical to \code{aids}, but instead of
#' assuming that at least two margins are known, \code{pcaids} assumes
#' that the own-price elasticity of any single
#' product, and the industry-wide own-price elasticity, are
#' known. Demand intercepts cannot be recovered using \code{pcaids}.
#'
#' \code{pcaids.nests} extends \code{pcaids} by allowing products
#' to be grouped into nests. Although products within the same nest still
#' have the independence of irrelevant alternatives (IIA) property,
#' products in different nests do not. Note that the \sQuote{diversions}
#' argument is absent from \code{pcaids.nests}.
#'
#' \code{pcaids.nests} assumes that the share diversion between nests is symmetric
#' (i.e for 2 nests A and B, the diversion from A to B is the same as B to
#' A). Therefore, if there are \eqn{w} nests, \eqn{2\le w \le k}{2 <= w <=k}, then the model
#' must estimate \eqn{w(w-1)/2} distinct nesting parameters. To accomplish
#' this, \code{pcaids.nests} uses margin information to produce estimates of
#' the nesting parameters. It is important to note that the number of
#' supplied margins must be at least as great as the number of nesting
#' parameters in order for PCAIDS to work.
#'
#' The nesting parameters are constrained to be between 0 and
#' 1. Therefore, one way to test the validity of the nesting structure is
#' to check whether the nesting parameters are between 0 and 1. The value
#' of the nesting parameters may be obtained from calling either the \sQuote{summary} or
#' \sQuote{getNestsParms} functions.
#'
#' @return \code{aids} returns an instance of class
#' \code{\linkS4class{AIDS}}, a child class of \code{\linkS4class{Linear}}.
#' \code{pcaids} returns an instance of class
#' \code{\linkS4class{PCAIDS}}, while \code{pcaids.nests} returns an
#' instance of \code{\linkS4class{PCAIDSNests}}. Both are
#' children of the \code{\linkS4class{AIDS}} class.
#'
#' @seealso \code{\link{linear}} for a demand system based on quantities
#' rather than revenue shares.
#' @author Charles Taragin \email{ctaragin+antitrustr@gmail.com}
#' @references Epstein, Roy and Rubinfeld, Daniel (2004).
#' \dQuote{Merger Simulation with Brand-Level Margin Data: Extending PCAIDS
#' with Nests.}
#' \emph{The B.E. Journal of Economic Analysis and Policy}, \bold{advances.4}(1), pp. 2.
#'
#' Epstein, Roy and Rubinfeld, Daniel (2004).
#' \dQuote{Effects of Mergers Involving Differentiated Products.}
#'
#' @examples
#' ## Simulate a merger between two single-product firms A and B in a
#' ## three-firm market (A, B, C). This example assumes that the merger is between
#' ## the firms A and B and that A's own-price elasticity is
#' ## known.
#' ## Source: Epstein and Rubinfeld (2004), pg 9, Table 2.
#'
#'
#' prices <- c(2.9,3.4,2.2) ## optional for aids, unnecessary for pcaids
#' shares <- c(.2,.3,.5)
#'
#'
#' ## The following are used by aids but not pcaids
#' ## only two of the margins are required to calibrate the demand parameters
#' margins <- c(0.33, 0.36, 0.44)
#'
#' ## The following are used by pcaids, but not aids
#' knownElast<- -3
#' mktElast <- -1
#'
#'
#' ## Define ownership using a vector of firm identities
#' ownerPre <- c("A","B","C")
#' ownerPost <- c("A","A","C")
#'
#' ## Alternatively, ownership could be defined using matrices
#' #ownerPre=diag(1,length(shares))
#' #ownerPost=ownerPre
#' #ownerPost[1,2] <- ownerPost[2,1] <- 1
#'
#'
#' ## AIDS: the following assumes both prices and margins are known.
#' ## Prices are not needed to estimate price changes
#'
#'
#'
#' result.aids <- aids(shares,margins,prices,ownerPre=ownerPre,ownerPost=ownerPost,labels=ownerPre)
#'
#'
#'
#' print(result.aids) # return predicted price change
#' summary(result.aids) # summarize merger simulation
#'
#' elast(result.aids,TRUE) # returns premerger elasticities
#' elast(result.aids,FALSE) # returns postmerger elasticities
#'
#' diversion(result.aids,TRUE) # return premerger diversion ratios
#' diversion(result.aids,FALSE) # return postmerger diversion ratios
#'
#'
#' cmcr(result.aids) #calculate compensating marginal cost reduction
#' upp(result.aids) #calculate Upwards Pricing Pressure Index
#'
#'
#' ## Implement the Hypothetical Monopolist Test
#' ## for products A and B using a 5\% SSNIP
#'
#' HypoMonTest(result.aids,prodIndex=1:2)
#'
#'
#' CV(result.aids) #calculate compensating variation as a percent of
#' #total expenditure
#' #CV can only be calculated if prices are supplied
#'
#'
#' ## Get a detailed description of the 'AIDS' class slots
#' showClass("AIDS")
#'
#' ## Show all methods attached to the 'AIDS' Class
#' showMethods(classes="AIDS")
#'
#' ## Show which class have their own 'elast' method
#' showMethods("elast")
#'
#' ## Show the method definition for 'elast' and Class 'AIDS'
#' getMethod("elast","AIDS")
#'
#'
#'
#' ## PCAIDS: the following assumes that only one product's elasticity is
#' ## known as well as the market elasticity.
#'
#'
#'
#' result.pcaids <- pcaids(shares,knownElast,mktElast,
#' ownerPre=ownerPre,ownerPost=ownerPost,
#' labels=ownerPre)
#'
#' print(result.pcaids) # return predicted price change
#' summary(result.pcaids) # summarize merger simulation
#'
#' elast(result.pcaids,TRUE) # returns premerger elasticities
#' elast(result.pcaids,FALSE) # returns postmerger elasticities
#'
#' diversion(result.pcaids,TRUE) # return premerger diversion ratios
#' diversion(result.pcaids,FALSE) # return postmerger diversion ratios
#'
#'
#' cmcr(result.pcaids) #calculate compensating marginal cost reduction
#'
#'
#' ## Implement the Hypothetical Monopolist Test
#' ## for products A and B using a 5\% SSNIP
#'
#' HypoMonTest(result.pcaids,prodIndex=1:2)
#'
#'
#'
#' ## Nested PCAIDS: in addition to the PCAIDS information requirements,
#' ## users must supply the nesting structure as well as margin infromation.
#'
#' nests <- c('H','L','L') # product A assigned to nest H, products B and C assigned to nest L
#'
#'
#' result.pcaids.nests <- pcaids.nests(shares,knownElast,mktElast,margins=margins,
#' nests=nests,ownerPre=ownerPre,
#' ownerPost=ownerPost,labels=ownerPre)
#'
#' @include DiagnosticsMethods.R
NULL
#'@rdname AIDS-Functions
#'@export
aids <- function(shares,margins,prices,diversions,
ownerPre,ownerPost,
mktElast = NA_real_,
insideSize = NA_real_,
mcDelta=rep(0, length(shares)),
subset=rep(TRUE, length(shares)),
parmStart= rep(NA_real_,2),
priceStart=runif(length(shares)),
isMax=FALSE,
control.slopes,
control.equ,
labels=paste("Prod",1:length(shares),sep=""),
...){
if(missing(prices)){ prices <- rep(NA_real_,length(shares))}
if(missing(diversions)){
diversions <- tcrossprod(1/(1-shares),shares)
diag(diversions) <- -1
}
## Create AIDS container to store relevant data
result <- new("AIDS",shares=shares,mcDelta=mcDelta,subset=subset,
margins=margins, prices=prices, quantities=shares, mktElast = mktElast,
ownerPre=ownerPre,ownerPost=ownerPost, parmStart=parmStart, insideSize = insideSize,
diversion=diversions,
priceStart=priceStart,labels=labels)
if(!missing(control.slopes)){
result@control.slopes <- control.slopes
}
if(!missing(control.equ)){
result@control.equ <- control.equ
}
## Convert ownership vectors to ownership matrices
result@ownerPre <- ownerToMatrix(result,TRUE)
result@ownerPost <- ownerToMatrix(result,FALSE)
## Calculate Demand Slope Coefficients
result <- calcSlopes(result)
## Solve Non-Linear System for Price Changes
result@priceDelta <- calcPriceDelta(result,isMax=isMax,subset=subset,...)
## Calculate marginal cost
result@mcPre <- calcMC(result,TRUE)
result@mcPost <- calcMC(result,FALSE)
## Calculate Pre and Post merger equilibrium prices
result@pricePre <- calcPrices(result,TRUE)
result@pricePost <- calcPrices(result,FALSE)
return(result)
}
#'@rdname AIDS-Functions
#'@export
pcaids <- function(shares,knownElast,mktElast=-1,
prices,diversions,
ownerPre,ownerPost,
knownElastIndex=1,
insideSize = NA_real_,
mcDelta=rep(0, length(shares)),
subset=rep(TRUE, length(shares)),
priceStart=runif(length(shares)),
isMax=FALSE,
control.slopes,
control.equ,
labels=paste("Prod",1:length(shares),sep=""),
...){
if(missing(prices)){ prices <- rep(NA_real_,length(shares))}
if(missing(diversions)){
diversions <- tcrossprod(1/(1-shares),shares)
diag(diversions) <- -1
}
## Create PCAIDS container to store relevant data
result <- new("PCAIDS",shares=shares,prices=prices,
quantities=shares, margins=shares,mcDelta=mcDelta,
subset=subset, insideSize = insideSize,
knownElast=knownElast,mktElast=mktElast,
ownerPre=ownerPre,ownerPost=ownerPost,
knownElastIndex=knownElastIndex,
diversion=diversions,
priceStart=priceStart,labels=labels)
if(!missing(control.slopes)){
result@control.slopes <- control.slopes
}
if(!missing(control.equ)){
result@control.equ <- control.equ
}
## Convert ownership vectors to ownership matrices
result@ownerPre <- ownerToMatrix(result,TRUE)
result@ownerPost <- ownerToMatrix(result,FALSE)
## Calculate Demand Slope Coefficients
result <- calcSlopes(result)
## Solve Non-Linear System for Price Changes
result@priceDelta <- calcPriceDelta(result,isMax=isMax,subset=subset,...)
## Calculate marginal cost
result@mcPre <- calcMC(result,TRUE)
result@mcPost <- calcMC(result,FALSE)
## Calculate Pre and Post merger equilibrium prices
## These are equal to NA in pcaids
result@pricePre <- calcPrices(result,TRUE)
result@pricePost <- calcPrices(result,FALSE)
return(result)
}
#'@rdname AIDS-Functions
#'@export
pcaids.nests <- function(shares,margins,knownElast,mktElast=-1,
prices,ownerPre,ownerPost,
nests=rep(1,length(shares)),
knownElastIndex=1,
insideSize = NA_real_,
mcDelta=rep(0, length(shares)),
subset=rep(TRUE, length(shares)),
priceStart=runif(length(shares)),
isMax=FALSE,
nestsParmStart,
control.slopes,
control.equ,
labels=paste("Prod",1:length(shares),sep=""),
...){
if(is.factor(nests)){nests <- nests[,drop=TRUE] }
else{nests <- factor(nests)}
if(missing(nestsParmStart)){
nNests <- nlevels(nests)
nestsParmStart <- runif(nNests*(nNests -1)/2)
}
if(missing(prices)){ prices <- rep(NA_real_,length(shares))}
diversions <- tcrossprod(1/(1-shares),shares);diag(diversions) <- -1.000000001 #'diversions' slot not used by pcaids.nests
## Create PCAIDS Nests container to store relevant data
result <- new("PCAIDSNests",shares=shares,
prices=prices,
quantities=shares,
margins=margins,mcDelta=mcDelta,subset=subset,insideSize = insideSize,
knownElast=knownElast,mktElast=mktElast,nests=nests,
nestsParms=nestsParmStart, diversion=diversions,
ownerPre=ownerPre,ownerPost=ownerPost,knownElastIndex=knownElastIndex,
priceStart=priceStart,labels=labels)
if(!missing(control.slopes)){
result@control.slopes <- control.slopes
}
if(!missing(control.equ)){
result@control.equ <- control.equ
}
## Convert ownership vectors to ownership matrices
result@ownerPre <- ownerToMatrix(result,TRUE)
result@ownerPost <- ownerToMatrix(result,FALSE)
## Calculate Demand Slope Coefficients
result <- calcSlopes(result)
## Solve Non-Linear System for Price Changes
result@priceDelta <- calcPriceDelta(result,isMax=isMax,subset=subset,...)
## Calculate marginal cost
result@mcPre <- calcMC(result,TRUE)
result@mcPost <- calcMC(result,FALSE)
## Calculate Pre and Post merger equilibrium prices
result@pricePre <- calcPrices(result,TRUE)
result@pricePost <- calcPrices(result,FALSE)
return(result)
}
Try the antitrust package in your browser
Any scripts or data that you put into this service are public.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.