SNQ Profit function: Hessian matrix
Returns the Hessian (substitution) matrix of a Symmetric Normalized Quadratic (SNQ) Profit Function.
snqProfitHessian( beta, prices, weights, scalingFactors = rep( 1, length( weights ) ) )
beta
: matrix of the coefficients.prices
: vector of netput prices at which the Hessian should be calculated.weights
: vector of weights of prices for normalization.scalingFactors
: factors to scale prices (and quantities).snqProfitEst
, snqProfitEla
and snqProfitHessianDeriv
.
Arne Henningsen
# just a stupid simple example snqProfitHessian( matrix(101:109,3,3), c(1,1,1), c(0.4,0.3,0.3) ) # now with real data if( requireNamespace( 'micEcon', quietly = TRUE ) ) { data( germanFarms, package = "micEcon" ) germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput germanFarms$qVarInput <- -germanFarms$vVarInput / germanFarms$pVarInput germanFarms$qLabor <- -germanFarms$qLabor germanFarms$time <- c( 0:19 ) priceNames <- c( "pOutput", "pVarInput", "pLabor" ) quantNames <- c( "qOutput", "qVarInput", "qLabor" ) estResult <- snqProfitEst( priceNames, quantNames, c("land","time"), data=germanFarms ) estResult$hessian # the Hessian at mean prices and mean quantities # Hessian at the last observation (1994/95) snqProfitHessian( estResult$coef$beta, estResult$data[ 20, priceNames ], estResult$weights, estResult$scalingFactors ) }