Version: 0.1-2
Date: 2023-05-11
Title: Econometric Production Analysis with Ray-Based Distance Functions
Depends: R (≥ 4.2.0)
Imports: sfaR (≥ 0.1.1), stats (≥ 4.2.0)
Suggests: micEcon (≥ 0.6-18), quadprog (≥ 1.5-8)
Description: Econometric analysis of multiple-input-multiple-output production technologies with ray-based input distance functions as suggested by Price and Henningsen (2022): "A Ray-Based Input Distance Function to Model Zero-Valued Output Quantities: Derivation and an Empirical Application", https://ideas.repec.org/p/foi/wpaper/2022_03.html.
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Encoding: UTF-8
URL: https://github.com/micEcon/micEconDistRay
BugReports: https://github.com/micEcon/micEconDistRay/issues
NeedsCompilation: no
Packaged: 2023-05-11 09:34:26 UTC; gsl324
Author: Arne Henningsen [aut, cre], Juan José Price [aut]
Maintainer: Arne Henningsen <arne.henningsen@gmail.com>
Repository: CRAN
Date/Publication: 2023-05-12 08:40:02 UTC

Data on Museums in Denmark

Description

The MuseumsDk data set is a balanced panel data set of 93 state-recognized museums in Denmark over a six years (2012 and 2014-2018; 2013 is unavailable).

Usage

data( "MuseumsDk" )

Format

This data frame contains the following columns:

museum

Name of the museum.

type

Type of museum (Kulturhistorisk museum = cultural history museum; Kunstmuseer = arts museum; Naturhistorisk museum = natural history museum; Blandet museum = mixed museum).

munic

Municipality, in which the museum is located.

yr

Year of the observation.

units

Number of visit sites.

resp

Whether or not the museum has special responsibilities (0 = no special responsibilities; 1 = at least one special responsibility).

vis

Number of (physical) visitors.

aarc

Number of articles published (archeology).

ach

Number of articles published (cultural history).

aah

Number of articles published (art history).

anh

Number of articles published (natural history).

exh

Number of temporary exhibitions.

edu

Number of primary school classes on educational visits to the museum.

ev

Number of events other than exhibitions.

ftesc

Scientific labor (full-time equivalents).

ftensc

Non-scientific labor (full-time equivalents).

expProperty

Running and maintenance costs [1,000 DKK].

expCons

Conservation expenditure [1,000 DKK].

ipc

Consumer Price Index in Denmark (the value for year 2014 is set to 1).

Source

A subset of this data set is used for the empirical analysis in Price & Henningsen (forthcoming). It has been obtained from Statistics Denmark and the Danish Ministry of Culture.

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.

Calculate the Dependent Variable of a Ray-Based Input Distance Function

Description

Calculate the dependent variable (logarithmic distance) of a ray-based input distance function (Price & Henningsen, forthcoming).

Usage

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

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.

Value

A vector.

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

# Cobb-Douglas ray-based input distance function (with manually set parameters)
appleProdFr86$logDistCD <- distRayCalc( xNames = c( "qCap", "qLab", "qMat" ),
  yNames = c( "qApples", "qOtherOut" ), data = appleProdFr86,
  coef = c( "(Intercept)" = -11.116, alpha_1 = 0.082, alpha_2 = 0.615,
  beta_1 = -0.031, beta_2 = -0.388 ), form = "cd" )
summary( appleProdFr86$logDistCD )

# Translog ray-based input distance function (with estimated parameters)
estTL <- distRayEst( xNames = c( "qCap", "qLab", "qMat" ),
  yNames = c( "qApples", "qOtherOut" ),
  data = appleProdFr86 )
appleProdFr86$logDistTL <- distRayCalc( xNames = c( "qCap", "qLab", "qMat" ),
  yNames= c( "qApples", "qOtherOut" ), data = appleProdFr86,
  coef = coef( estTL ) )
summary( appleProdFr86$logDistTL )

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 )

Estimate a Ray-Based Input Distance Function

Description

Empirically analyse multiple-input-multiple-output production technologies by estimating a ray-based input distance function (Price & Henningsen, forthcoming).

Usage

distRayEst( xNames, yNames, zNames = NULL, sNames = NULL, 
  data, form = "tl", method = "sfa", fixThetas = FALSE, ... )

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.

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.

method

a character string that indicates the estimation method; currently, "lm" for the Ordinary Least-Squares method (using the lm() function of the stats package) and "sfa" for stochastic frontier estimation (using the sfacross() function of the sfaR package) are available.

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.

...

further arguments of distRayEst are passed to lm or sfacross.

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

# Cobb-Douglas ray-based input distance function
estCD <- distRayEst( xNames = c( "qCap", "qLab", "qMat" ),
  yNames = c( "qApples", "qOtherOut" ),
  data = appleProdFr86, form = "cd" )
summary( estCD )

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

Imposing Monotonicity on a Ray-Based Input Distance Function

Description

Create a matrix and vector for imposing monotonicity on a ray-based input distance function (Price & Henningsen, forthcoming).

Usage

distRayMonoRestr( xNames, yNames, zNames = NULL, sNames = NULL, 
  data, form = "tl", conDummy = NULL )

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.

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.

Value

A list that contains a matrix (RMat) and a vector (rVec).

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

# Cobb-Douglas ray-based input distance function (with manually set parameters)
estCD <- distRayEst( xNames = c( "qCap", "qLab", "qMat" ),
  yNames = c( "qApples", "qOtherOut" ),
  data = appleProdFr86, form = "cd" )
summary( estCD )

# the vector of unrestricted coefficients and their covariance matrix
nCoefCD <- length( coef( estCD ) ) - 2
uCoefCD <- coef( estCD )[ 1:nCoefCD ]
uCovInvCD <- solve( vcov( estCD )[ 1:nCoefCD, 1:nCoefCD ] )

# obtain the matrix and vector to impose monotonicity
restrCD <- distRayMonoRestr( xNames = c( "qCap", "qLab", "qMat" ),
  yNames = c( "qApples", "qOtherOut" ), data = appleProdFr86,
  form = "cd" )

# obtain the restricted coefficients
library( "quadprog" )
minDistCD <- solve.QP( Dmat = uCovInvCD, dvec = rep( 0, nCoefCD ),
  Amat = t( restrCD$RMat ), bvec = - restrCD$RMat %*% uCoefCD + restrCD$rVec )
rCoefCD <- minDistCD$solution + uCoefCD


# Translog ray-based input distance function (with estimated parameters)
estTL <- distRayEst( xNames = c( "qCap", "qLab", "qMat" ),
  yNames = c( "qApples", "qOtherOut" ),
  data = appleProdFr86 )
appleProdFr86$logDistTL <- distRayCalc( xNames = c( "qCap", "qLab", "qMat" ),
  yNames= c( "qApples", "qOtherOut" ), data = appleProdFr86,
  coef = coef( estTL ) )
summary( appleProdFr86$logDistTL )

# the vector of unrestricted coefficients and their covariance matrix
nCoefTL <- length( coef( estTL ) ) - 2
uCoefTL <- coef( estTL )[ 1:nCoefTL ]
uCovInvTL <- solve( vcov( estTL )[ 1:nCoefTL, 1:nCoefTL ] )

# obtain the matrix and vector to impose monotonicity
restrTL <- distRayMonoRestr( xNames = c( "qCap", "qLab", "qMat" ),
  yNames = c( "qApples", "qOtherOut" ), data = appleProdFr86 )

# obtain the restricted coefficientslibrary( "quadprog" )
minDistTL <- solve.QP( Dmat = uCovInvTL, dvec = rep( 0, nCoefTL ),
  Amat = t( restrTL$RMat ), bvec = - restrTL$RMat %*% uCoefTL + restrTL$rVec )
rCoefTL <- minDistTL$solution + uCoefTL