Package 'micEcon' reference manual

Title:	Microeconomic Analysis and Modelling
Description:	Various tools for microeconomic analysis and microeconomic modelling, e.g. estimating quadratic, Cobb-Douglas and Translog functions, calculating partial derivatives and elasticities of these functions, and calculating Hessian matrices, checking curvature and preparing restrictions for imposing monotonicity of Translog functions.
Authors:	Arne Henningsen
Maintainer:	Arne Henningsen <[email protected]>
License:	GPL (>= 2)
Version:	0.6-18
Built:	2024-11-19 06:32:56 UTC
Source:	CRAN

Data on French Apple Producers in 1986

Description

The appleProdFr86 data frame includes cross-sectional production data of 140 French apple producers from the year 1986. These data have been extracted from a panel data set that was used in Ivaldi et al. (1996).

Usage

data(appleProdFr86)data(appleProdFr86)

Format

This data frame contains the following columns:

vCap: costs of capital (including land).
vLab: costs of labour (including remuneration of unpaid family labour).
vMat: costs of intermediate materials (e.g. seedlings, fertilizer, pesticides, fuel).
qApples: quantity index of produced apples.
qOtherOut: quantity index of all other outputs.
qOut: quantity index of all outputs (not in the original data set, calculated as 580,000 $\cdot$ (qApples + qOtherOut)).
pCap: price index of capital goods
pLab: price index of labour.
pMat: price index of materials.
pOut: price index of the aggregate output (not in the original data set, artificially generated).
adv: dummy variable indicating the use of an advisory service (not in the original data set, artificially generated).

Source

This cross-sectional data set has been extracted from a panel data set that is available in the data archive of the Journal of Applied Econometrics: http://qed.econ.queensu.ca/jae/1996-v11.6/ivaldi-ladoux-ossard-simioni/.

References

Ivaldi, M., N. Ladoux, H. Ossard, and M. Simioni (1996) Comparing Fourier and Translog Specifications of Multiproduct Technology: Evidence from an Incomplete Panel of French Farmers. Journal of Applied Econometrics, 11(6), p. 649-667.

Artificial Prices and Quantities

Description

The Bleymueller251 data frame contains prices and quantities of 4 products for the years 1970, 1974 and 1978. This data are part of Exercise 25.1 of Bleymueller, Gehler und Guetlicher (1979).

Usage

data(Bleymueller79E25.1)data(Bleymueller79E25.1)

Format

This data frame contains the following columns:

p.A: Price of good A.
p.B: Price of good B.
p.C: Price of good C.
p.D: Price of good D.
q.A: Quantity of good A.
q.B: Quantity of good B.
q.C: Quantity of good C.
q.D: Quantity of good D.

Source

Bleymueller, J; G. Gehlert and H. Guelicher (1979) Statistik fuer Wirtschaftswissenschaftler. Verlag Vahlen, Muenchen.

Testing Theoretical Consistency

Description

Test theoretical consistency of microeconomic models.

Usage

checkConsist( object, ... )
checkConsist( object, ... )

Arguments

`object`	a microeconomic model
`...`	further arguments for methods

Details

This is a generic function.

Author(s)

Arne Henningsen

Calculate dependent variable of a Cobb-Douglas function

Description

Calculate the dependent variable of a Cobb-Douglas function.

Usage

cobbDouglasCalc( xNames, data, coef, coefCov = NULL, dataLogged = FALSE  )
cobbDouglasCalc( xNames, data, coef, coefCov = NULL, dataLogged = FALSE  )

Arguments

`xNames`	a vector of strings containing the names of the independent variables.
`data`	data frame containing the data.
`coef`	vector containing the coefficients: if the elements of the vector have no names, the first element is taken as intercept of the logged equation and the following elements are taken as coefficients of the independent variables defined in argument `xNames` (in the same order); if the elements of `coef` have names, the element named `a_0` is taken as intercept of the logged equation and the elements named `a_1`, ..., `a_n` are taken as coefficients of the independent variables defined in argument `xNames` (numbered in that order).
`coefCov`	optional covariance matrix of the coefficients (the order of the rows and columns must correspond to the order of the coefficients in argument `coef`).
`dataLogged`	logical. Are the values in `data` already logged?

Value

A vector containing the endogenous variable. If the inputs are provided as logarithmic values (argument dataLogged is TRUE), the endogenous variable is returned as logarithm; non-logarithmic values are returned otherwise.

If argument coefCov is specified, the returned vector has an attribute "variance" that is a vector containing the variances of the calculated (fitted) endogenous variable.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a Cobb-Douglas production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, linear = TRUE )

   # fitted values
   fitted <- cobbDouglasCalc( c( "qLabor", "land", "qVarInput", "time" ), germanFarms,
      coef( estResult )[ 1:5 ] )
   #equal to estResult$fitted

   # fitted values and their variances
   fitted2 <- cobbDouglasCalc( c( "qLabor", "land", "qVarInput", "time" ), germanFarms,
      coef( estResult )[ 1:5 ], coefCov = vcov( estResult )[ 1:5, 1:5 ] )
   # t-values
   c( fitted2 ) / attributes( fitted2 )$variance^0.5
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a Cobb-Douglas production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, linear = TRUE )

   # fitted values
   fitted <- cobbDouglasCalc( c( "qLabor", "land", "qVarInput", "time" ), germanFarms,
      coef( estResult )[ 1:5 ] )
   #equal to estResult$fitted

   # fitted values and their variances
   fitted2 <- cobbDouglasCalc( c( "qLabor", "land", "qVarInput", "time" ), germanFarms,
      coef( estResult )[ 1:5 ], coefCov = vcov( estResult )[ 1:5, 1:5 ] )
   # t-values
   c( fitted2 ) / attributes( fitted2 )$variance^0.5

Derivatives of a Cobb-Douglas function

Description

Calculate the derivatives of a Cobb-Douglas function.

Usage

cobbDouglasDeriv( xNames, data, coef, coefCov = NULL,
   yName = NULL, dataLogged = FALSE )
cobbDouglasDeriv( xNames, data, coef, coefCov = NULL,
   yName = NULL, dataLogged = FALSE )

Arguments

`xNames`	a vector of strings containing the names of the independent variables.
`data`	data frame containing the data.
`coef`	vector containing the coefficients: if the elements of the vector have no names, the first element is taken as intercept of the logged equation and the following elements are taken as coefficients of the independent variables defined in argument `xNames` (in the same order); if the elements of `coef` have names, the element named `a_0` is taken as intercept of the logged equation and the elements named `a_1`, ..., `a_n` are taken as coefficients of the independent variables defined in argument `xNames` (numbered in that order).
`coefCov`	optional covariance matrix of the coefficients (the order of the rows and columns must correspond to the order of the coefficients in argument `coef`).
`yName`	an optional string containing the name of the dependent variable. If it is `NULL`, the dependent variable is calculated from the independent variables and the coefficients.
`dataLogged`	logical. Are the values in `data` already logged?

Value

a list of class cobbDouglasDeriv containing following objects:

`deriv`	data frame containing the derivatives.
`variance`	data frame containing the variances of the derivatives (only if argument `coefCov` is provided). NOTE: if argument `yName` is specified, the variance of the endogenous variable is currently ignored.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a Cobb-Douglas production function
   estResult <- translogEst( "qOutput", c( "qLabor", "qVarInput", "land", "time" ),
      germanFarms, linear = TRUE )

   # compute the marginal products of the inputs (with "fitted" Output)
   margProducts <- cobbDouglasDeriv( c( "qLabor", "qVarInput", "land", "time" ),
      data = germanFarms, coef = coef( estResult )[1:5],
      coefCov = vcov( estResult )[1:5,1:5] )
   margProducts$deriv
   # t-values
   margProducts$deriv / margProducts$variance^0.5

   # compute the marginal products of the inputs (with observed Output)
   margProductsObs <- cobbDouglasDeriv( c( "qLabor", "qVarInput", "land", "time" ),
      data = germanFarms, coef = coef( estResult )[1:5], yName = "qOutput",
      coefCov = vcov( estResult )[1:5,1:5] )
   margProductsObs$deriv
   # t-values
   margProductsObs$deriv / margProductsObs$variance^0.5
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a Cobb-Douglas production function
   estResult <- translogEst( "qOutput", c( "qLabor", "qVarInput", "land", "time" ),
      germanFarms, linear = TRUE )

   # compute the marginal products of the inputs (with "fitted" Output)
   margProducts <- cobbDouglasDeriv( c( "qLabor", "qVarInput", "land", "time" ),
      data = germanFarms, coef = coef( estResult )[1:5],
      coefCov = vcov( estResult )[1:5,1:5] )
   margProducts$deriv
   # t-values
   margProducts$deriv / margProducts$variance^0.5

   # compute the marginal products of the inputs (with observed Output)
   margProductsObs <- cobbDouglasDeriv( c( "qLabor", "qVarInput", "land", "time" ),
      data = germanFarms, coef = coef( estResult )[1:5], yName = "qOutput",
      coefCov = vcov( estResult )[1:5,1:5] )
   margProductsObs$deriv
   # t-values
   margProductsObs$deriv / margProductsObs$variance^0.5

Optimal Values of Independent Variables of a Cobb-Douglas Function

Description

Calculate the optimal values of the variable independent variables of a Cobb-Douglas function.

Usage

cobbDouglasOpt( pyName, pxNames, data, coef,
   zNames = NULL, zCoef = NULL, xNames = NULL, dataLogged = FALSE  )
cobbDouglasOpt( pyName, pxNames, data, coef,
   zNames = NULL, zCoef = NULL, xNames = NULL, dataLogged = FALSE  )

Arguments

`pyName`	character string containing the name of the price of the dependent variable.
`pxNames`	a vector of strings containing the names of the prices of the variable independent variables.
`data`	data frame containing the data.
`coef`	vector containing the intercept and the coefficients of the variable independent variables: if the elements of the vector have no names, the first element is taken as intercept of the logged equation and the following elements are taken as coefficients of the variable independent variables with corresponding prices defined in argument `pxNames` (in the same order); if the elements of `coef` have names, the element named `a_0` is taken as intercept of the logged equation and the elements named `a_1`, ..., `a_n` are taken as coefficients of the variable independent variables with corresponding prices defined in argument `xNames` (numbered in that order).
`zNames`	optional vector of strings containing the names of the fixed independent variables.
`zCoef`	vector containing the coefficients of the fixed independent variables: if the elements of the vector have no names, they are taken as coefficients of the fixed independent variables defined in argument `zNames` (in the same order); if the elements of `coef` have names, the elements named `d_1`, ..., `d_m` are taken as coefficients of the fixed independent variables with corresponding prices defined in argument `zNames` (numbered in that order).
`xNames`	optional vector of strings containing the names that should be assigned to the returned variable independent variables.
`dataLogged`	logical. Are the prices and fixed independent variables in `data` with names defined in `pyName`, `pxNames`, and `zNames` already logged?

Value

A data frame containing the optimal values of the variable independent variables. If the prices and fixed independent variables are provided as logarithmic values (argument dataLogged is TRUE), the optimal values of the variable independent variables are returned as logarithms, too; non-logarithmic values are returned otherwise.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a Cobb-Douglas production function
   estResult <- translogEst( yName = "qOutput",
      xNames = c( "qLabor", "qVarInput", "land", "time" ),
      data = germanFarms, linear = TRUE )

   # calculate optimal quantities of variable inputs
   xCoef <- coef( estResult )[ 1:3 ]
   zCoef <- coef( estResult )[ 4:5 ]
   names( zCoef ) <- c( "d_1", "d_2" )
   optInput <- cobbDouglasOpt( pyName = "pOutput",
      pxNames = c( "pLabor", "pVarInput" ), coef = xCoef,
      data = germanFarms, xNames = c( "qLabor", "qVarInput" ),
      zNames = c( "land", "time" ), zCoef = zCoef )

   # compare observed with optimal input quantities
   plot( germanFarms$qLabor, optInput$qLabor )
   plot( germanFarms$qVarInput, optInput$qVarInput )
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a Cobb-Douglas production function
   estResult <- translogEst( yName = "qOutput",
      xNames = c( "qLabor", "qVarInput", "land", "time" ),
      data = germanFarms, linear = TRUE )

   # calculate optimal quantities of variable inputs
   xCoef <- coef( estResult )[ 1:3 ]
   zCoef <- coef( estResult )[ 4:5 ]
   names( zCoef ) <- c( "d_1", "d_2" )
   optInput <- cobbDouglasOpt( pyName = "pOutput",
      pxNames = c( "pLabor", "pVarInput" ), coef = xCoef,
      data = germanFarms, xNames = c( "qLabor", "qVarInput" ),
      zNames = c( "land", "time" ), zCoef = zCoef )

   # compare observed with optimal input quantities
   plot( germanFarms$qLabor, optInput$qLabor )
   plot( germanFarms$qVarInput, optInput$qVarInput )

Coefficients of a Quadratic Function

Description

These methods return the coefficients and their covariance matrix from an estimated quadratic function.

Usage

   ## S3 method for class 'quadFuncEst'
coef( object, ... )

   ## S3 method for class 'quadFuncEst'
vcov( object, ... )
## S3 method for class 'quadFuncEst'
coef( object, ... )

   ## S3 method for class 'quadFuncEst'
vcov( object, ... )

Arguments

`object`	an object of class `quadFuncEst`.
`...`	currently ignored.

Value

The coef method returns a vector containing all (linearly independent) coefficients of a quadratic function.

The vcov method returns the covariance matrix of all (linearly independent) coefficients of a quadratic function.

Author(s)

Arne Henningsen

Coefficients of a Translog Function

Description

These methods return the coefficients and their covariance matrix from an estimated translog function.

Usage

   ## S3 method for class 'translogEst'
coef( object, ... )

   ## S3 method for class 'translogEst'
vcov( object, ... )
## S3 method for class 'translogEst'
coef( object, ... )

   ## S3 method for class 'translogEst'
vcov( object, ... )

Arguments

`object`	an object of class `translogEst`.
`...`	currently ignored.

Value

The coef method returns a vector containing all (linearly independent) coefficients of a translog function.

The vcov method returns the covariance matrix of all (linearly independent) coefficients of a translog function.

Author(s)

Arne Henningsen

Calculating and returning elasticities

Description

These functions calculate and return elasticities of microeconomic models. elasticities is an alias for elas.

Usage

   elas( object, ... )
   elasticities( object, ... )
   ## Default S3 method:
elas( object, ... )
elas( object, ... )
   elasticities( object, ... )
   ## Default S3 method:
elas( object, ... )

Arguments

`object`	a microeconomic model
`...`	further arguments for methods

Details

This is a generic function. The default method just returns the element elas from object.

Author(s)

Arne Henningsen

Output and Inputs of Farms in West-Germany

Description

The germanFarms data frame contains annual data of an average full-time farm in West-Germany. Additionally, the price indices for agricultural output and agricultural variable input are included. 20 book-keeping years are included - starting in 1975/76 and ending in 1994/95.

Usage

data(germanFarms)data(germanFarms)

Format

This data frame contains the following columns:

year: the book-keeping year.
vCrop: the value of crop outputs (in current Deutschmark).
vAnimal: the value of animal outputs (in current Deutschmark).
vOutput: the value of outputs (in current Deutschmark).
pOutput: price index of agricultural outputs (1980/81 = 100).
vVarInput: the value of variable inputs (in current Deutschmark).
pVarInput: price index of variable agricultural inputs (1980/81 = 100).
qLabor: the number of full-time worker equivalents.
pLabor: costs of an agricultural worker (Deutschmarks per year).
land: land used for agricultural production (in ha).

Source

Bundesministerium für Ernährung, Landwirtschaft und Forsten (Federal Department for Food, Agriculture and Forests), Agrarbericht der Bundesregierung (Agricultural Report of the Federal Government), Jahrgänge 1977-1996 (years 1977-1996).

Creating a Data Set with the Logarithms of the Original Variables

Description

This function creates a data set with the logarithms of the original variables.

Usage

logDataSet( data, varNames, varNamesNum = NULL  )
logDataSet( data, varNames, varNamesNum = NULL  )

Arguments

`data`	a data frame containing the data (possibly a panel data frame created with `pdata.frame`).
`varNames`	vector of character strings that indicates names of variables in the data frame. The logarithm of these variables are included in the returned data frame.
`varNamesNum`	optional vector of character strings that indicates names of further variables in tha data frame. In case of numeric variables, the logarithms of these variabes are included in the returned data frame. In case of factor of logical variables, these variabes are included in the returned data frame without any transformation.

Author(s)

Arne Henningsen

Examples

   data( "germanFarms" )
   datLog <- logDataSet( germanFarms, c( "vAnimal", "vOutput", "vVarInput" ) )
   summary( datLog )
data( "germanFarms" )
   datLog <- logDataSet( germanFarms, c( "vAnimal", "vOutput", "vVarInput" ) )
   summary( datLog )

Meat Prices and Quantities in Germany

Description

The Missong03E7.7 data frame contains meat prices and demanded quantities of a representative (West-)German household for the years 1986 to 1989. This data are part of Exercise 7.7 of Missong (2003).

Usage

data(Missong03E7.7)data(Missong03E7.7)

Format

This data frame contains the following columns:

p.beef: Average price of beef (DM/kg).
q.beef: Demanded Quantity of beef (kg).
p.veal: Average price of veal (DM/kg).
q.veal: Demanded Quantity of veal (kg).
p.pork: Average price of pork (DM/kg).
q.pork: Demanded Quantity of pork (kg).

Source

Missong, M. (2003) Aufgabensammlung zur deskriptiven Statistik, Oldenbourg, Muenchen.

Statistisches Bundesamt (1989) Fachserie 15, Reihe 1, p. 76f.

Calculate dependent variable of a quadratic function

Description

Calculate the dependent variable of a quadratic function.

Usage

quadFuncCalc( xNames, data, coef, shifterNames = NULL, 
   homWeights = NULL )
quadFuncCalc( xNames, data, coef, shifterNames = NULL, 
   homWeights = NULL )

Arguments

`xNames`	a vector of strings containing the names of the independent variables.
`data`	dataframe or a vector with named elements containing the data.
`coef`	vector containing all coefficients: if there are `n` exogenous variables in `xNames` and `m` shifter variables in `shifterNames`, the `n+1` alpha coefficients must have names `a_0`, ..., `a_n`, the `n*(n+1)/2` beta coefficients must have names `b_1_1`, ..., `b_1_n`, ..., `b_n_n`, and the `m` delta coefficients must have names `d_1`, ..., `d_m` (only the elements of the upper right triangle of the beta matrix are directly obtained from `coef`; the elements of the lower left triangle are obtained by assuming symmetry of the beta matrix).
`shifterNames`	a vector of strings containing the names of the independent variables that should be included as shifters only (not in quadratic or interaction terms).
`homWeights`	numeric vector with named elements that are weighting factors for calculating an index that is used to normalize the variables for imposing homogeneity of degree zero in these variables (see documentation of `quadFuncEst`).

Value

a vector containing the endogenous variable.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- quadFuncEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   quadFuncCalc( c( "qLabor", "land", "qVarInput", "time" ), germanFarms,
      coef( estResult ) )
   #equal to estResult$fitted
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- quadFuncEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   quadFuncCalc( c( "qLabor", "land", "qVarInput", "time" ), germanFarms,
      coef( estResult ) )
   #equal to estResult$fitted

Derivatives of a quadratic function

Description

Calculate the derivatives of a quadratic function.

Usage

   quadFuncDeriv( xNames, data, coef, coefCov = NULL, 
      homWeights = NULL )
quadFuncDeriv( xNames, data, coef, coefCov = NULL, 
      homWeights = NULL )

Arguments

`xNames`	a vector of strings containing the names of the independent variables.
`data`	dataframe or a vector with named elements containing the data.
`coef`	vector containing all coefficients: if there are `n` exogenous variables in `xNames`, the `n+1` alpha coefficients must have names `a_0`, ..., `a_n` and the `n*(n+1)/2` beta coefficients must have names `b_1_1`, ..., `b_1_n`, ..., `b_n_n` (only the elements of the upper right triangle of the beta matrix are directly obtained from `coef`; the elements of the lower left triangle are obtained by assuming symmetry of the beta matrix).
`coefCov`	optional covariance matrix of the coefficients: the row names and column names must be the same as the names of `coef`.
`homWeights`	numeric vector with named elements that are weighting factors for calculating an index that is used to normalize the variables for imposing homogeneity of degree zero in these variables (see documentation of `quadFuncEst`).

Details

Shifter variables do not need to be specified, because they have no effect on the partial derivatives. Hence, you can use this function to calculate partial derivatives even for quadratic functions that have been estimated with shifter variables.

Value

A data frame containing the derivatives, where each column corresponds to one of the independent variables. If argument coefCov is provided, it has the attributes variance and stdDev, which are two data frames containing the variances and the standard deviations, respectively, of the derivatives.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- quadFuncEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # compute the marginal products of the inputs
   margProducts <- quadFuncDeriv( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), vcov( estResult ) )
   # all marginal products
   margProducts
   # their t-values
   margProducts / attributes( margProducts )$stdDev
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- quadFuncEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # compute the marginal products of the inputs
   margProducts <- quadFuncDeriv( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), vcov( estResult ) )
   # all marginal products
   margProducts
   # their t-values
   margProducts / attributes( margProducts )$stdDev

Elasticities of a Quadratic Function

Description

Calculate elasticities of a quadratic function.

Usage

quadFuncEla( xNames, data, coef, yName = NULL, 
   shifterNames = NULL, homWeights = NULL )

## S3 method for class 'quadFuncEst'
elas( object, data = NULL, yObs = FALSE, ... )
quadFuncEla( xNames, data, coef, yName = NULL, 
   shifterNames = NULL, homWeights = NULL )

## S3 method for class 'quadFuncEst'
elas( object, data = NULL, yObs = FALSE, ... )

Arguments

`xNames`	a vector of strings containing the names of the independent variables.
`data`	dataframe or a vector with named elements containing the data; if argument `data` of `elas.quadFuncEst` is not specified, the data frame that was used for the estimation is used for calculating elasticities.
`coef`	vector containing all coefficients.
`yName`	an optional string containing the name of the dependent variable. If it is `NULL`, the dependent variable is calculated from the independent variables and the coefficients.
`shifterNames`	an optional vector of strings containing the names of the independent variables that are included as shifters only (not in quadratic or interaction terms).
`homWeights`	numeric vector with named elements that are weighting factors for calculating an index that is used to normalize the variables for imposing homogeneity of degree zero in these variables (see documentation of `quadFuncEst`).
`object`	object of class `quadFuncEst` (returned by `quadFuncEst`).
`yObs`	logical. Use observed values of the endogenous variable. If `FALSE` (default) predicted values calculated by `quadFuncCalc` are used.
`...`	currently ignored.

Value

A data.frame of class quadFuncEla, where each column corresponds to one of the independent variables.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- quadFuncEst( yName = "qOutput", 
      xNames = c( "qLabor", "land", "qVarInput", "time" ),
      data = germanFarms )

   # compute the partial production elasticities with "fitted" output
   elaFit <- quadFuncEla( xNames = c( "qLabor", "land", "qVarInput", "time" ),
      data = germanFarms, coef = coef( estResult ) )
   elaFit
   # same as
   elaFit2 <- elas( estResult )
   all.equal( elaFit, elaFit2 )

   # compute the partial production elasticities with observed output
   elaObs <- quadFuncEla( xNames = c( "qLabor", "land", "qVarInput", "time" ),
      data = germanFarms, coef = coef( estResult ), yName = "qOutput" )
   elaObs
   # same as
   elaObs2 <- elas( estResult, yObs = TRUE )
   all.equal( elaObs, elaObs2 )
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- quadFuncEst( yName = "qOutput", 
      xNames = c( "qLabor", "land", "qVarInput", "time" ),
      data = germanFarms )

   # compute the partial production elasticities with "fitted" output
   elaFit <- quadFuncEla( xNames = c( "qLabor", "land", "qVarInput", "time" ),
      data = germanFarms, coef = coef( estResult ) )
   elaFit
   # same as
   elaFit2 <- elas( estResult )
   all.equal( elaFit, elaFit2 )

   # compute the partial production elasticities with observed output
   elaObs <- quadFuncEla( xNames = c( "qLabor", "land", "qVarInput", "time" ),
      data = germanFarms, coef = coef( estResult ), yName = "qOutput" )
   elaObs
   # same as
   elaObs2 <- elas( estResult, yObs = TRUE )
   all.equal( elaObs, elaObs2 )

Estimate a quadratic function

Description

Estimate a quadratic function.

Usage

quadFuncEst( yName, xNames, data, shifterNames = NULL,
   linear = FALSE, homWeights = NULL, 
   regScale = 1, ... )
quadFuncEst( yName, xNames, data, shifterNames = NULL,
   linear = FALSE, homWeights = NULL, 
   regScale = 1, ... )

Arguments

`yName`	a character string containing the name of the dependent variable.
`xNames`	a vector of strings containing the names of the independent variables.
`data`	data frame containing the data (possibly a panel data frame created with `pdata.frame`).
`shifterNames`	a vector of strings containing the names of the independent variables that should be included as shifters only (not in quadratic or interaction terms).
`linear`	logical. Restrict the coefficients of all quadratic and interaction terms to be zero so that the estimated function is linear in the exogenous variables?
`homWeights`	numeric vector with named elements that are weighting factors for calculating an index that is used to normalize the variables for imposing homogeneity of degree zero in these variables (see details).
`regScale`	a scalar or vector with length equal to `nrow( data )`. All regressors except for shifter variables that are logical or factors are divided by `regScale` (NOTE: quadratic and interaction terms are also divided by `regScale` and NOT divided by the square of `regScale`).
`...`	further arguments are passed to `lm` or `plm`.

Details

If argument homWeights is used to impose homogeneity of degree zero in some variables, the weighting factors in this vector must have names that are equal to the variable names in argument xNames. The order of the elements in homWeights is arbitrary and may or may not be equal to the order of the elements in xNames. Argument homWeights may contain less elements than xNames; in this case, homogeneity of degree zero is imposed only on variables with names in homWeights. Please note that the weighting factor of a variable ( $P_i$ ) in homWeights ( $w_i = \partial P / \partial P_i$ ) is not really its weight ( $( \partial P / \partial P_i ) ( P_i / P )$ ), in particular, if the numerical values of the variables ( $P_1, \ldots, P_n$ ) are rather different.

Value

a list of class quadFuncEst containing following objects:

`est`	the object returned by `lm` or `plm`.
`nExog`	length of argument `xNames`.
`nShifter`	length of argument `shifterNames`.
`residuals`	residuals.
`fitted`	fitted values.
`coef`	vector of all coefficients.
`coefCov`	covariance matrix of all coefficients.
`r2`	$R^2$ value.
`r2bar`	adjusted $R^2$ value.
`nObs`	number of observations.
`model.matrix`	the model matrix.
`call`	the matched call.
`yName`	argument `yName`.
`xNames`	argument `xNames`.
`shifterNames`	argument `shifterNames`.
`homWeights`	argument `homWeights`.
`regScale`	argument `regScale`.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- quadFuncEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   coef( estResult )
   estResult$r2
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- quadFuncEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   coef( estResult )
   estResult$r2

Residuals of a Translog function

Description

Extract the residuals from the estimation of a Translog function.

Usage

## S3 method for class 'translogEst'
residuals( object, ... )
## S3 method for class 'translogEst'
residuals( object, ... )

Arguments

`object`	an object of class `translogEst`.
`...`	currently not used.

Value

residuals.translogEst returns a vector containing the residuals of an estimated translog function.

Author(s)

Arne Henningsen

Summarizing the Estimation of a Translog Function

Description

summary.translogEst summarizes the estimation results of a Translog Function.

Usage

## S3 method for class 'translogEst'
summary( object, ... )

## S3 method for class 'summary.translogEst'
print( x, ... )
## S3 method for class 'translogEst'
summary( object, ... )

## S3 method for class 'summary.translogEst'
print( x, ... )

Arguments

`object`	an object of class `translogEst`.
`x`	an object of class `summary.translogEst`.
`...`	currently ignored.

Value

summary.translogEst returns a list of class summary.translogEst that is currently the provided object, but an element coefTable has been added and the class has been changed.

Author(s)

Arne Henningsen

Calculate dependent variable of a translog function

Description

Calculate the dependent variable of a translog function.

Usage

translogCalc( xNames, data, coef, shifterNames = NULL,
   dataLogged = FALSE  )
translogCalc( xNames, data, coef, shifterNames = NULL,
   dataLogged = FALSE  )

Arguments

`xNames`	a vector of strings containing the names of the independent variables.
`data`	dataframe containing the data.
`coef`	vector containing all coefficients: if there are `n` exogenous variables in `xNames` and `m` shifter variables in `shifterNames`, the `n+1` alpha coefficients must have names `a_0`, ..., `a_n`, the `n*(n+1)/2` beta coefficients must have names `b_1_1`, ..., `b_1_n`, ..., `b_n_n`, and the `m` delta coefficients must have names `d_1`, ..., `d_m` (only the elements of the upper right triangle of the beta matrix are directly obtained from `coef`; the elements of the lower left triangle are obtained by assuming symmetry of the beta matrix).
`shifterNames`	a vector of strings containing the names of the independent variables that should be included as shifters only (not in quadratic or interaction terms).
`dataLogged`	logical. Are the values in `data` already logged?

Value

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a Translog production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   translogCalc( c( "qLabor", "land", "qVarInput", "time" ), germanFarms,
      coef( estResult ) )
   #equal to estResult$fitted
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a Translog production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   translogCalc( c( "qLabor", "land", "qVarInput", "time" ), germanFarms,
      coef( estResult ) )
   #equal to estResult$fitted

Curvature of a Translog Function

Description

Check curvature of a translog function.

Usage

translogCheckCurvature( xNames, data, coef, convexity = TRUE,
   quasi = FALSE, dataLogged = FALSE, ... )

## S3 method for class 'translogCheckCurvature'
print( x, ... )
translogCheckCurvature( xNames, data, coef, convexity = TRUE,
   quasi = FALSE, dataLogged = FALSE, ... )

## S3 method for class 'translogCheckCurvature'
print( x, ... )

Arguments

`xNames`	a vector of strings containing the names of the independent variables.
`data`	dataframe containing the data.
`coef`	vector containing all coefficients.
`convexity`	logical. Check whether the function is (quasi)convex (default, `TRUE`) or (quasi)concave (`FALSE`).
`quasi`	logical. Check whether the function is quasiconvex/quasiconcave (`TRUE`) or convex/concave (default, `FALSE`).
`dataLogged`	logical. Are the values in `data` already logged?
`x`	an object returned by `translogCheckCurvature`.
`...`	arguments passed from `translogCheckCurvature` to `semidefiniteness` (if argument `quasi` is `FALSE`), `quasiconvexity` (if arguments `convexity` and `quasi` are both `TRUE`), or `quasiconcavity` (if argument `convexity` is `FALSE` and `quasi` is `TRUE`). Further arguments to `print.translogCheckCurvature` are currently ignored.

Value

translogCheckCurvature returns a list of class translogCheckCurvature containing following objects:

`obs`	a vector indicating whether the condition for the specified curvature is fulfilled at each observation.
`convexity`	argument `convexity`.
`quasi`	argument `quasi`.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a translog production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # check whether the production function is quasiconcave
   translogCheckCurvature( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), convexity = FALSE, quasi = TRUE )
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a translog production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # check whether the production function is quasiconcave
   translogCheckCurvature( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), convexity = FALSE, quasi = TRUE )

Monotonicity of a Translog Function

Description

Check monotonicity of a translog function.

Usage

translogCheckMono( xNames, data, coef, increasing = TRUE,
   strict = FALSE, dataLogged = FALSE,
   tol = 10 * .Machine$double.eps )

## S3 method for class 'translogCheckMono'
print( x, ... )

## S3 method for class 'translogCheckMono'
summary( object, ... )

## S3 method for class 'summary.translogCheckMono'
print( x, ... )
translogCheckMono( xNames, data, coef, increasing = TRUE,
   strict = FALSE, dataLogged = FALSE,
   tol = 10 * .Machine$double.eps )

## S3 method for class 'translogCheckMono'
print( x, ... )

## S3 method for class 'translogCheckMono'
summary( object, ... )

## S3 method for class 'summary.translogCheckMono'
print( x, ... )

Arguments

`xNames`	a vector of strings containing the names of the independent variables.
`data`	dataframe containing the data.
`coef`	vector containing all coefficients.
`increasing`	single logical value or vector of logical values of the same length as argument `xNames` indicating whether it should be checked if the translog function is monotonically increasing (default, TRUE) or decreasing (FALSE) in the explanatory variables.
`strict`	logical. Check for strict (TRUE) or non-strict (default, FALSE) monotonicity?
`dataLogged`	logical. Are the values in `data` already logged?
`tol`	tolerance level for checking non-strict monotonicity: values between `-tol` and `tol` are considered to be zero (ignored if argument `strict` is `TRUE`).
`x`	an object returned by `translogCheckMono` or by `summary.translogCheckMono`.
`object`	an object returned by `translogCheckMono`.
`...`	currently not used.

Details

Function translogCheckMono internally calls function translogDeriv and then checks if the derivatives have the sign specified in argument increasing.

Function translogCheckMono does not have an argument shifterNames, because shifter variables do not affect the monotonicity conditions of the eplanatory variables defined in Argument xNames. Therefore, translogCheckMono automatically removes all coefficients of the shifter variables before it calls translogDeriv.

Value

translogCheckMono returns a list of class translogCheckMono containing following objects:

`obs`	a vector indicating whether monotonicity is fulfilled at each observation.
`exog`	data frame indicating whether monotonicity is fulfilled for each exogenous variable at each observation.
`increasing`	argument `increasing`.
`strict`	argument `strict`.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a translog production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # check whether the production function is monotonically increasing
   # in all inputs
   test <- translogCheckMono( xNames = c( "qLabor", "land", "qVarInput", "time" ),
      data = germanFarms, coef = coef( estResult ) )
   test
   summary( test )

   # check whether the production function is monotonically decreasing
   # in time and monotonically increasing in all other inputs
   test <- translogCheckMono( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), increasing = c( TRUE, TRUE, TRUE, FALSE ) )
   test
   summary( test )
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a translog production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # check whether the production function is monotonically increasing
   # in all inputs
   test <- translogCheckMono( xNames = c( "qLabor", "land", "qVarInput", "time" ),
      data = germanFarms, coef = coef( estResult ) )
   test
   summary( test )

   # check whether the production function is monotonically decreasing
   # in time and monotonically increasing in all other inputs
   test <- translogCheckMono( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), increasing = c( TRUE, TRUE, TRUE, FALSE ) )
   test
   summary( test )

Estimate a translog Cost Function

Description

Estimate a translog cost function.

NOTE: this function is still under development and incomplete!

Usage

   translogCostEst( cName, yName, pNames, data, fNames = NULL, 
      shifterNames = NULL, dataLogged = FALSE, homPrice = TRUE, ... )
translogCostEst( cName, yName, pNames, data, fNames = NULL, 
      shifterNames = NULL, dataLogged = FALSE, homPrice = TRUE, ... )

Arguments

`cName`	a string containing the name of the variable for total cost.
`yName`	a string containing the name of the variable for the total output quantity.
`pNames`	a vector of strings containing the names of the input prices.
`data`	data frame containing the data (possibly a panel data frame created with `pdata.frame`).
`fNames`	a vector of strings containing the names of fixed inputs.
`shifterNames`	a vector of strings containing the names of the independent variables that should be included as shifters only (not in quadratic or interaction terms).
`dataLogged`	logical. Are the values in `data` already logged?
`homPrice`	logical. Should homogeneity of degree one in prices be imposed?
`...`	further arguments are passed to `lm` or `plm`.

Value

a list of class translogCostEst containing following objects:

`est`	the object returned by `lm` or `plm`.
`nExog`	length of argument `xNames`.
`nShifter`	length of argument `shifterNames`.
`residuals`	residuals.
`fitted`	fitted values.
`coef`	vector of all coefficients.
`coefCov`	covariance matrix of all coefficients.
`r2`	$R^2$ value.
`r2bar`	adjusted $R^2$ value.
`nObs`	number of observations.
`model.matrix`	the model matrix.
`call`	the matched call.
`cName`	argument `cName`.
`yName`	argument `yName`.
`pNames`	argument `pNames`.
`fNames`	argument `fNames`.
`shifterNames`	argument `shifterNames`.
`dataLogged`	argument `dataLogged`.
`homPrice`	argument `homPrice`.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # value of labor input
   germanFarms$vLabor <- germanFarms$pLabor + germanFarms$qLabor
   # total variable cost
   germanFarms$cost <- germanFarms$vLabor + germanFarms$vVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a translog cost function
   estResult <- translogCostEst( cName = "cost", yName = "qOutput", 
      pNames = c( "pLabor", "pVarInput" ), fNames = "land",
      shifterNames = "time", data = germanFarms, homPrice = FALSE )

   summary( estResult$est )
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # value of labor input
   germanFarms$vLabor <- germanFarms$pLabor + germanFarms$qLabor
   # total variable cost
   germanFarms$cost <- germanFarms$vLabor + germanFarms$vVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a translog cost function
   estResult <- translogCostEst( cName = "cost", yName = "qOutput", 
      pNames = c( "pLabor", "pVarInput" ), fNames = "land",
      shifterNames = "time", data = germanFarms, homPrice = FALSE )

   summary( estResult$est )

Derivatives of a translog function

Description

Calculate the derivatives of a translog function.

Usage

translogDeriv( xNames, data, coef, coefCov = NULL,
   yName = NULL, dataLogged = FALSE )
translogDeriv( xNames, data, coef, coefCov = NULL,
   yName = NULL, dataLogged = FALSE )

Arguments

`xNames`	a vector of strings containing the names of the independent variables.
`data`	dataframe containing the data.
`coef`	vector containing all coefficients.
`coefCov`	optional covariance matrix of the coefficients.
`yName`	an optional string containing the name of the dependent variable. If it is `NULL`, the dependent variable is calculated from the independent variables and the coefficients.
`dataLogged`	logical. Are the values in `data` already logged?

Value

a list of class translogDeriv containing following objects:

`deriv`	data frame containing the derivatives.
`variance`	data frame containing the variances of the derivatives (not implemented yet).
`stdDev`	data frame containing the standard deviations of the derivatives (not implemented yet).

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a translog production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # compute the marginal products of the inputs (with "fitted" Output)
   margProducts <- translogDeriv( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), vcov( estResult ) )
   margProducts$deriv

   # compute the marginal products of the inputs (with observed Output)
   margProductsObs <- translogDeriv( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), vcov( estResult ), "qOutput" )
   margProductsObs$deriv
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a translog production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # compute the marginal products of the inputs (with "fitted" Output)
   margProducts <- translogDeriv( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), vcov( estResult ) )
   margProducts$deriv

   # compute the marginal products of the inputs (with observed Output)
   margProductsObs <- translogDeriv( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), vcov( estResult ), "qOutput" )
   margProductsObs$deriv

Elasticities of a translog Function

Description

Calculate the elasticities of a translog function.

Usage

translogEla( xNames, data, coef, coefCov = NULL,
   dataLogged = FALSE  )

## S3 method for class 'translogEst'
elas( object, data = NULL, dataLogged = NULL,
   ... )
translogEla( xNames, data, coef, coefCov = NULL,
   dataLogged = FALSE  )

## S3 method for class 'translogEst'
elas( object, data = NULL, dataLogged = NULL,
   ... )

Arguments

`xNames`	a vector of strings containing the names of the independent variables.
`data`	dataframe containing the data; if argument `data` of `elas.translogEst` is not specified, the data frame that was used for the estimation is used for calculating elasticities.
`coef`	vector containing all coefficients: if there are `n` exogenous variables in `xNames`, the `n+1` alpha coefficients must have names `a_0`, ..., `a_n` and the `n*(n+1)/2` beta coefficients must have names `b_1_1`, ..., `b_1_n`, ..., `b_n_n` (only the elements of the upper right triangle of the beta matrix are directly obtained from `coef`; the elements of the lower left triangle are obtained by assuming symmetry of the beta matrix).
`coefCov`	optional covariance matrix of the coefficients: the row names and column names must be the same as the names of `coef`.
`dataLogged`	logical. Are the values in `data` already logged? If argument `dataLogged` of `elas.translogEst` is not specified, the same value as used in `translogEst` for creating `object` is used.
`object`	object of class `translogEst` (returned by `translogEst`).
`...`	currently ignored.

Details

Shifter variables do not need to be specified, because they have no effect on the elasticities. Hence, you can use this function to calculate elasticities even for translog functions that have been estimated with shifter variables.

Value

A data frame containing the elasticities, where each column corresponds to one of the independent variables. If argument coefCov is provided, it has the attributes variance and stdDev, which are two data frames containing the variances and the standard deviations, respectively, of the elasticities.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # calculate production elasticities of all inputs
   estEla <- translogEla( c( "qLabor", "land", "qVarInput", "time" ), 
      data = germanFarms, coef = coef( estResult ), 
      coefCov = vcov( estResult ) )
   # all elasticities
   estEla
   # t-values of all elasticities
   estEla / attributes( estEla )$stdDev
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # calculate production elasticities of all inputs
   estEla <- translogEla( c( "qLabor", "land", "qVarInput", "time" ), 
      data = germanFarms, coef = coef( estResult ), 
      coefCov = vcov( estResult ) )
   # all elasticities
   estEla
   # t-values of all elasticities
   estEla / attributes( estEla )$stdDev

Estimate a translog function

Description

Estimate a translog function.

Usage

   translogEst( yName, xNames, data, shifterNames = NULL,
      dataLogged = FALSE, ... )

   ## S3 method for class 'translogEst'
print( x, ... )
translogEst( yName, xNames, data, shifterNames = NULL,
      dataLogged = FALSE, ... )

   ## S3 method for class 'translogEst'
print( x, ... )

Arguments

`yName`	a string containing the name of the dependent variable.
`xNames`	a vector of strings containing the names of the independent variables.
`data`	data frame containing the data (possibly a panel data frame created with `pdata.frame`).
`shifterNames`	a vector of strings containing the names of the independent variables that should be included as shifters only (not in quadratic or interaction terms).
`dataLogged`	logical. Are the values in `data` already logged? If `FALSE`, the logarithms of all variables (`yName`, `xNames`, `shifterNames`) are used except for shifter variables that are factors or logical variables.
`x`	An object of class `translogEst`.
`...`	further arguments of `translogEst` are passed to `lm` or `plm`; further arguments of `print.translogEst` are currently ignored.

Value

a list of class translogEst containing following objects:

`est`	the object returned by `lm` or `plm`.
`nExog`	length of argument `xNames`.
`nShifter`	length of argument `shifterNames`.
`residuals`	residuals.
`fitted`	fitted values.
`coef`	vector of all coefficients.
`coefCov`	covariance matrix of all coefficients.
`r2`	$R^2$ value.
`r2bar`	adjusted $R^2$ value.
`nObs`	number of observations.
`model.matrix`	the model matrix.
`call`	the matched call.
`yName`	argument `yName`.
`xNames`	argument `xNames`.
`shifterNames`	argument `shifterNames`.
`dataLogged`	argument `dataLogged`.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   estResult
   summary( estResult )
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   estResult
   summary( estResult )

Hessian matrix of a translog function

Description

Calculate the Hessian matrices of a translog function.

Usage

   translogHessian( xNames, data, coef, yName = NULL,
   dataLogged = FALSE, bordered = FALSE )
translogHessian( xNames, data, coef, yName = NULL,
   dataLogged = FALSE, bordered = FALSE )

Arguments

`xNames`	a vector of strings containing the names of the independent variables.
`data`	dataframe containing the data.
`coef`	vector containing all coefficients.
`yName`	an optional string containing the name of the dependent variable. If it is `NULL`, the dependent variable is calculated from the independent variables and the coefficients.
`dataLogged`	logical. Are the values in `data` already logged?
`bordered`	logical. Should the bordered Hessians be returned?

Value

a list containing following the (bordered) Hessian matrices at each data point.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # compute the Hessian matrices (with "fitted" output)
   hessians <- translogHessian( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ) )
   hessians[[ 1 ]]

   # compute the Hessian matrices (with observed output)
   hessiansObs <- translogHessian( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), "qOutput" )
   hessiansObs[[ 1 ]]

   # compute the bordered Hessian matrices
   borderedHessians <- translogHessian( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), bordered = TRUE )
   borderedHessians[[ 1 ]]
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # estimate a quadratic production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # compute the Hessian matrices (with "fitted" output)
   hessians <- translogHessian( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ) )
   hessians[[ 1 ]]

   # compute the Hessian matrices (with observed output)
   hessiansObs <- translogHessian( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), "qOutput" )
   hessiansObs[[ 1 ]]

   # compute the bordered Hessian matrices
   borderedHessians <- translogHessian( c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms, coef( estResult ), bordered = TRUE )
   borderedHessians[[ 1 ]]

Monotonicity Restrictions of a Translog Function

Description

Create matrix to check or impose the monotonicity restrictions of a translog function.

Usage

translogMonoRestr( xNames, data,
   dataLogged = FALSE, box = FALSE )
translogMonoRestr( xNames, data,
   dataLogged = FALSE, box = FALSE )

Arguments

`xNames`	a vector of strings containing the names of the independent variables.
`data`	dataframe containing the data.
`dataLogged`	logical. Are the values in `data` already logged?
`box`	logical. Should monotonicity be imposed within an $n$ -dimensional box that includes all points in `data`? If `FALSE`, monotonicity is imposed (only) within an $n$ -dimensional polygon that includes all points in `data`. ( $n$ is the number of independent varables.)

Value

translogMonoRestr returns a matrix of dimension $( n \cdot N ) \times c$ , where $n$ is the number of independent varables, $N$ is the number of data points at which monotonicity should be imposed (if argument box is FALSE, $N$ is the number of rows in data; if argument box is TRUE, $N = 2^n$ ), and $c = 1 + n ( n + 3 ) / 2$ is the number of (linearly independent) coefficients. Multiplying a row of this matrix (e.g.\ the $k$ th row of $M$ ) by the vector of coefficients ( $\beta$ ) results in the derivative of the dependent variable ( $y$ ) with respect to one independent variable (e.g.\ $x_i$ ) at one data point (e.g.\ $j$ ):

$M[k,] \cdot \beta = \frac{ \partial \ln y }{ \partial \ln x_i}$

, evaluated at $x_{1j}$ , ..., $x_{nj}$ , where $k = ( i - 1 ) N + j$ . Hence, the observations run faster than the independent variables.

Author(s)

Arne Henningsen

Examples

   data( germanFarms )
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput

   # matrix to check or impose monotonicity at all observations
   monoRestrObs <- translogMonoRestr( c( "qLabor", "land", "qVarInput" ),
      germanFarms )

   # matrix to check or impose monotonicity within a box that includes all 
   # observations
   monoRestrBox <- translogMonoRestr( c( "qLabor", "land", "qVarInput" ),
      germanFarms, box = TRUE )
data( germanFarms )
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput

   # matrix to check or impose monotonicity at all observations
   monoRestrObs <- translogMonoRestr( c( "qLabor", "land", "qVarInput" ),
      germanFarms )

   # matrix to check or impose monotonicity within a box that includes all 
   # observations
   monoRestrBox <- translogMonoRestr( c( "qLabor", "land", "qVarInput" ),
      germanFarms, box = TRUE )

Marginal Costs of Translog Production Function

Description

Calculate the marginal costs of the output from a translog production function.

Usage

translogProdFuncMargCost( yName, xNames, wNames, data, coef,
   dataLogged = FALSE )
translogProdFuncMargCost( yName, xNames, wNames, data, coef,
   dataLogged = FALSE )

Arguments

`yName`	a single character string containing the name of the output quantity.
`xNames`	a vector of strings containing the names of the input quantities.
`wNames`	a vector of strings containing the names of the input prices.
`data`	dataframe containing the data.
`coef`	vector containing all coefficients: if there are `n` inputs in `xNames`, the `n+1` alpha coefficients must have names `a_0`, ..., `a_n` and the `n*(n+1)/2` beta coefficients must have names `b_1_1`, ..., `b_1_n`, ..., `b_n_n` (only the elements of the upper right triangle of the beta matrix are directly obtained from `coef`; the elements of the lower left triangle are obtained by assuming symmetry of the beta matrix).
`dataLogged`	logical. Are the values in `data` already logged?

Value

A vector containing the marginal costs of producing the output.

Author(s)

Arne Henningsen and Geraldine Henningsen

Examples

   data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # generate (artificial) prices
   germanFarms$pLand <- 200 + 15 * germanFarms$time
   germanFarms$pTime <- 1

   # estimate a single-output translog production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # compute the marginal costs of producing the output
   margCost <- translogProdFuncMargCost( yName = "qOutput",
      xNames = c( "qLabor", "land", "qVarInput", "time" ),
      wNames = c( "pLabor", "pLand", "pVarInput", "pTime" ),
      data = germanFarms, coef = coef( estResult ) )
data( germanFarms )
   # output quantity:
   germanFarms$qOutput <- germanFarms$vOutput / germanFarms$pOutput
   # quantity of variable inputs
   germanFarms$qVarInput <- germanFarms$vVarInput / germanFarms$pVarInput
   # a time trend to account for technical progress:
   germanFarms$time <- c(1:20)

   # generate (artificial) prices
   germanFarms$pLand <- 200 + 15 * germanFarms$time
   germanFarms$pTime <- 1

   # estimate a single-output translog production function
   estResult <- translogEst( "qOutput", c( "qLabor", "land", "qVarInput", "time" ),
      germanFarms )

   # compute the marginal costs of producing the output
   margCost <- translogProdFuncMargCost( yName = "qOutput",
      xNames = c( "qLabor", "land", "qVarInput", "time" ),
      wNames = c( "pLabor", "pLand", "pVarInput", "pTime" ),
      data = germanFarms, coef = coef( estResult ) )

Fossil Fuel Fired Steam Electric Power Plants

Description

The data frame utility is a panel data set of 72 investor-owned fossil fuel fired steam electric power plants in the United States over eleven years (1986-1996). This data set has 791 observations and, thus, is almost balanced (only one firm-year observation is missing). This data set is used as an example in Kumbhakar, Wang, and Horncastle (2015).

Usage

data(utility)data(utility)

Format

This data frame contains the following columns/variables:

firm: firm number (1-72).
year: last two digits of the year (86-96).
y: net steam electric power generation in MWh.
regu: a dummy variable indicating whether the firm is regulated.
k: capital input quantity (estimate of capital cost).
labor: quantity index of labor and maintenance input (costs of labor and maintenance divided by wl).
fuel: quantity index of fuel input. (costs of fuel divided by wf).
wl: cost-share weighted price of labor and maintenance.
wf: average price of fuel (coal, oil and gas) in USD per BTU.
wk: price of the capital input.

Details

This data set is a revised version of the data set that is used in Kumbhakar and Wang (2006). A detailed description of the data set and the variables can be found in Section 4 of Kumbhakar and Wang (2006).

Source

Companion website to Kumbhakar, Wang, and Horncastle (2015): https://sites.google.com/site/sfbook2014/.

References

Kumbhakar, Subal C. and Hung-Jen Wang (2006): Estimation of Technical and Allocative Inefficiency: A Primal System Approach, Journal of Econometrics 134(2), p. 419-440. (doi:10.1016/j.jeconom.2005.07.001)

Kumbhakar, Subal C., Hung-Jen Wang, and Alan P. Horncastle (2015): A Practitioner's Guide to Stochastic Frontier Analysis Using Stata. Cambridge University Press. (doi:10.1017/CBO9781139342070)

Package 'micEcon'

Help Index

Data on French Apple Producers in 1986

Description

Usage

Format

Source

References

Artificial Prices and Quantities

Description

Usage

Format

Source

Testing Theoretical Consistency

Description

Usage

Arguments

Details

Author(s)

See Also

Calculate dependent variable of a Cobb-Douglas function

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Derivatives of a Cobb-Douglas function

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Optimal Values of Independent Variables of a Cobb-Douglas Function

Description

Usage

Arguments

Value

Author(s)

See Also

Examples

Coefficients of a Quadratic Function

Description

Usage

Arguments

Value

Author(s)

See Also

Coefficients of a Translog Function

Description

Usage

Arguments

Value

Author(s)

See Also

Calculating and returning elasticities

Description

Usage

Arguments

Details

Author(s)

See Also

Output and Inputs of Farms in West-Germany

Description

Usage

Format

Source

Creating a Data Set with the Logarithms of the Original Variables

Description

Usage

Arguments

Author(s)

Examples

Meat Prices and Quantities in Germany

Description

Usage

Format