bargaining_tariff {trade}

Tariff Simulation With A Nash Bargaining Game

Description

Simulate the effect of tariffs when firms play a Nash Bargaining game and consumer demand is Logit.

Usage

bargaining_tariff(
  demand = c("logit"),
  prices,
  shares,
  margins,
  owner = NULL,
  mktElast = NA_real_,
  insideSize = NA_real_,
  diversions,
  tariffPre = rep(0, length(shares)),
  tariffPost = rep(0, length(shares)),
  bargpowerPre = rep(0.5, length(prices)),
  bargpowerPost = bargpowerPre,
  normIndex = ifelse(isTRUE(all.equal(sum(shares), 1, check.names = FALSE)), 1, NA),
  priceOutside = ifelse(demand == "logit", 0, 1),
  priceStart,
  control.slopes,
  control.equ,
  labels = paste("Prod", 1:length(shares), sep = ""),
  ...
)

Arguments

demand

A character vector indicating which demand system to use. Currently allows logit (default).

prices

A length k vector product prices.

shares

A length k vector of product shares. Values must be between 0 and 1.

margins

A length k vector of product margins. All margins must be in levels (not w.r.t to price), or NA.

owner

EITHER a vector of length k whose values indicate which firm produced a product before the tariff OR a k x k matrix of pre-merger ownership shares.

mktElast

A negative number equal to the industry pre-merger price elasticity. Default is NA .

insideSize

An integer equal to total pre-merger units sold. If shares sum to one, this also equals the size of the market.

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.

tariffPre

A vector of length k where each element equals the current ad valorem tariff (expressed as a proportion of the consumer price) imposed on each product. Default is 0, which assumes no tariff.

tariffPost

A vector of length k where each element equals the new ad valorem tariff (expressed as a proportion of the consumer price) imposed on each product. Default is 0, which assumes no tariff.

bargpowerPre

A length k vector of pre-tariff bargaining power parameters. Values must be between 0 (sellers have the power) and 1 (buyers the power). NA values are allowed, though must be calibrated from additional margin and share data. Default is 0.5.

bargpowerPost

A length k vector of post-tariff bargaining power parameters. Values must be between 0 (sellers have the power) and 1 (buyers the power). NA values are allowed, though must be calibrated from additional margin and share data. Default is ‘bargpowerPre’.

normIndex

An integer equalling the index (position) of the inside product whose mean valuation will be normalized to 1. Default is 1, unless ‘shares’ sum to less than 1, in which case the default is NA and an outside good is assumed to exist.

priceOutside

price of the outside good. Equals 0 for logit and 1 for ces. Not used for aids.

priceStart

For aids, 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. For ces and logit, the default is prices.

control.slopes

A list of optim control parameters passed to the calibration routine optimizer (typically the calcSlopes method).

control.equ

A list of BBsolve control parameters passed to the non-linear equation solver (typically the calcPrices method).

labels

A k-length vector of labels.

...

Additional options to feed to the BBsolve optimizer used to solve for equilibrium prices.

Details

Let k denote the number of products produced by all firms. Using price, and quantity, information for all products in each market, as well as margin information for at least one products in each market, bargaining_tariff is able to recover the slopes and intercepts of a Logit demand system. These parameters are then used to simulate the price effects of an ad valorem tariff under the assumption that the firms are playing a Nash Bargaining game.

Value

bargaining_tariff returns an instance of class TariffBargainingLogit

References

Simon P. Anderson, Andre de Palma, Brent Kreider, Tax incidence in differentiated product oligopoly, Journal of Public Economics, Volume 81, Issue 2, 2001, Pages 173-192.

See Also

bertrand_tariff to simulate the effects of a tariff under a Bertrand pricing game and monopolistic_competition_tariff to simulate the effects of a tariff under monopolistic competition.

Examples

## Calibration and simulation results from a 10% tariff on non-US beers "OTHER-LITE"
## and "OTHER-REG"
## Source: Epstein/Rubenfeld 2004, pg 80

prodNames <- c("BUD","OLD STYLE","MILLER","MILLER-LITE","OTHER-LITE","OTHER-REG")
owner <-c("BUD","OLD STYLE","MILLER","MILLER","OTHER-LITE","OTHER-REG")
price    <- c(.0441,.0328,.0409,.0396,.0387,.0497)
shares   <- c(.066,.172,.253,.187,.099,.223)
margins <- c(.3830,.5515,.5421,.5557,.4453,.3769) # margins in terms of price
tariff <- c(0,0,0,0,.1,.1)

names(price) <-
 names(shares) <-
 names(margins) <-
 prodNames


result.barg <- bargaining_tariff(demand = "logit",prices=price,shares=shares,
                                margins = margins,owner=owner,
                                 tariffPost = tariff, labels=prodNames)

print(result.barg)           # return predicted price change
summary(result.barg)         # summarize merger simulation