quadFuncDeriv: Derivatives of a quadratic function

Description

Calculate the derivatives of a quadratic function.

Usage

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

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

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

quadHalf

logical. Multiply the quadratic terms by one half?

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.

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.

Examples

Run this code

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