snqProfitEla {micEconSNQP}

Price Elasticities of SNQ Profit function

Description

Calculates the Price Elasticities of a Symmetric Normalized Quadratic (SNQ) profit function.

Usage

 snqProfitEla(  beta, prices, quant, weights,
   scalingFactors = rep( 1, length( weights ) ),
   coefVcov = NULL, df = NULL )

Arguments

beta

matrix of estimated \beta coefficients.

prices

vector of netput prices at which the elasticities should be calculated.

quant

vector of netput quantities at which the elasticities should be calculated.

weights

vector of weights of prices used for normalization.

scalingFactors

factors to scale prices (and quantities).

coefVcov

variance covariance matrix of the coefficients (optional).

df

degrees of freedom to calculate P-values of the elasticities (optional).

Value

a list of class snqProfitEla containing following elements:

ela

matrix of the price elasticities.

vcov

variance covariance matrix of the price elasticities.

stEr

standard errors of the price elasticities.

tval

t-values of the price elasticities.

pval

P-values of the price elasticities.

Note

A price elasticity is defined as

E_{ij} = \frac{ \displaystyle \frac{ \partial q_i }{ q_i } } { \displaystyle \frac{ \partial p_j }{ p_j } } = \frac{ \partial q_i }{ \partial p_j } \cdot \frac{ p_j }{ q_i }

Thus, e.g. E_{ij}=0.5 means that if the price of netput j (p_j) increases by 1%, the quantity of netput i (q_i) will increase by 0.5%.

Author(s)

Arne Henningsen

See Also

snqProfitEst.

Examples

# just a stupid simple example
snqProfitEla( matrix(101:109,3,3), c(1,1,1), 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$ela  # price elasticities at mean prices and mean quantities

   # price elasticities at the last observation (1994/95)
   snqProfitEla( estResult$coef$beta, estResult$data[ 20, priceNames ],
      estResult$data[ 20, quantNames ], estResult$weights,
      estResult$scalingFactors )
}