snqProfitImposeConvexity {micEcon}R Documentation

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 β matrix.
start starting values of the triangular Cholesky matrix.
... arguments passed to optim

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.

Value

a list of class snqProfitImposeConvexity containing following objects:

mindist object returned by \optim.
coef a list containing the vectors/matrix of the estimated coefficients:
* alpha = α_i.
* beta = β_{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.

Author(s)

Arne Henningsen ahenningsen@agric-econ.uni-kiel.de

References

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.

See Also

snqProfitEst.

Examples

   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

[Package micEcon version 0.1-6 Index]