distRayEla {micEconDistRay}

Elasticities and Derivatives of Ray-Based Input Distance Functions

Description

Calculate distance elasticities and derivatives based on ray-based input distance functions (Price & Henningsen, forthcoming).

Usage

distRayEla( xNames, yNames, zNames = NULL, sNames = NULL, 
  coef, data, form = "tl", conDummy = NULL, fixThetas = FALSE, ... )

distRayDeriv( xNames, yNames, zNames = NULL, sNames = NULL, 
  coef, data, form = "tl", conDummy = NULL, fixThetas = FALSE, 
  numDeriv = FALSE, eps = 1e-6 ) 

Arguments

xNames

a vector of character strings containing the names of the variables that indicate the input quantities.

yNames

a vector of two or more character strings containing the names of the variables that indicate the output quantities.

zNames

an optional vector of character strings containing the names of ‘environmental’ variables, i.e., variables that affect the production possibility set (i.e., the feasible combinations of input-output quantities) that—in the case of a Translog functional form—should be interacted with the input quantities and the angles of the output vector.

sNames

an optional vector of character strings containing the names of ‘environmental’ variables, i.e., variables that affect the production possibility set (i.e., the feasible combinations of input-output quantities) that—in the case of a Translog functional form—should not be interacted with the input quantities and the angles of the output vector.

coef

numeric vector containing the coefficients.

data

data frame containing the data.

form

a character string that indicates the functional form; currently, "cd" for the Cobb-Douglas functional form and "tl" for the Translog functional form are available.

conDummy

an optional numeric vector indicating the positions in argument zNames that are dummy variables so that quadratic terms of these variables are omitted.

fixThetas

logical value that indicates whether undefined angles of the output should be ‘fixed’ if the last two or more output quantities are zero for some of the observations.

numDeriv

logical value that indicates whether derivatives (and elasticities) should be calculated by numerical finite-difference differentiation.

eps

small positive value that is used as change in the variables when calculating derivatives (and elasticities) by numerical finite-difference differentiation.

...

further arguments of distRayEla are passed to distRayDeriv.

Value

A list that will be described here later.

Author(s)

Arne Henningsen and Juan José Price

References

Price, J.J. & Henningsen, A. (forthcoming): A Ray-Based Input Distance Function to Model Zero-Valued Output Quantities: Derivation and an Empirical Application. Journal of Productivity Analysis.

Examples

# load and prepare data set 
data( appleProdFr86, package = "micEcon" )
appleProdFr86$qCap <- appleProdFr86$vCap / appleProdFr86$pCap
appleProdFr86$qLab <- appleProdFr86$vLab / appleProdFr86$pLab
appleProdFr86$qMat <- appleProdFr86$vMat / appleProdFr86$pMat

# estimate Translog ray-based input distance function
estTL <- distRayEst( xNames = c( "qCap", "qLab", "qMat" ),
  yNames = c( "qApples", "qOtherOut" ),
  data = appleProdFr86 )
summary( estTL )

# calculate elasticities
ela <- distRayEla( xNames = c( "qCap", "qLab", "qMat" ),
  yNames = c( "qApples", "qOtherOut" ),
  coef = coef( estTL ), data = appleProdFr86 )
summary( ela )

# calculate derivatives
deriv <- distRayDeriv( xNames = c( "qCap", "qLab", "qMat" ),
  yNames = c( "qApples", "qOtherOut" ),
  coef = coef( estTL ), data = appleProdFr86 )
summary( deriv )