snqProfitImposeConvexity: Imposing Convexity on a SNQ Profit function

Description

Imposing Convexity on a Symmetric Normalized Quadratic (SNQ) Profit function.

Usage

snqProfitImposeConvexity( estResult, rankReduction = 0,
   start = 10, ... )

Arguments

estResult

object returned by snqProfitEst.

rankReduction

an integer specifying the reduction of the rank of the $\beta$ matrix.

start

starting values of the triangular Cholesky matrix.

...

arguments passed to optim

Value

a list of class snqProfitImposeConvexity containing following objects:
mindistobject returned by . coef{a list containing the vectors/matrix of the estimated coefficients: * alpha = $\alpha_i$. * beta = $\beta_{ij}$. * delta = $\delta_{ij}$ (only if quasi-fix inputs are present). * gamma = $\gamma_{ij}$ (only if quasi-fix inputs are present). * allCoef = vector of all coefficients. } ela{matrix with the price elasticities at mean prices and mean quantities.} hessian{hessian matrix of the profit function with respect to prices evaluated at mean prices.} convexity{logical. Convexity of the profit function.} r2{$R^2$-values of all netput equations.} weights{the weights of prices used for normalization.} normPrice{vector used for normalization of prices.} estData{data frame used for estimation (contains the (scaled) netput prices, (scaled) netput quantities, (not scaled) fix inputs and the price index used for normalization.} fitted{data frame that contains the fitted netput quantities and the fitted profit.} residuals{data frame that contains the residuals of the netput quantities.} form{the functional form (see snqProfitEst).} pMeans{means of the (scaled) netput prices.} qMeans{means of the (scaled) netput quantities.} fMeans{means of the (quasi-)fix input quantities.}
Koebel, B., M. Falk and F. Laisney (2000), Imposing and Testing Curvature Conditions on a Box-Cox Cost Function. Discussion Paper No. 00-70, ZEW, Mannheim, ftp://ftp.zew.de/pub/zew-docs/dp/dp0070.pdf.
Koebel, B., M. Falk and F. Laisney (2003), Imposing and Testing Curvature Conditions on a Box-Cox Cost Function. Journal of Business and Economic Statistics, 21, p. 319-335.
snqProfitEst.
[object Object]
data( germanFarms ) germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput germanFarms$qVarInput <- -germanFarms$vVarInput / germanFarms$pVarInput germanFarms$qLabor <- -germanFarms$qLabor germanFarms$time <- c( 0:19 ) pNames <- c( "pOutput", "pVarInput", "pLabor" ) qNames <- c( "qOutput", "qVarInput", "qLabor" ) fNames <- c( "land", "time" ) estResult <- snqProfitEst( pNames, qNames, fNames, data = germanFarms ) estResult # Note: it is NOT convex in netput prices estResultConvex <- snqProfitImposeConvexity( estResult ) estResultConvex # now it is convex
models

Details

The procedure proposed by Koebel, Falk and Laisney (2000, 2003) is applied to impose convexity in prices on an estimated symmetric normalized quadratic (SNQ) profit function.