quadFuncDeriv function

Derivatives of a quadratic function

Calculate the derivatives of a quadratic function.

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.

Returns

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.

See Also

quadFuncEst and quadFuncCalc

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