snqProfitHessian           package:micEcon           R Documentation

_S_N_Q _P_r_o_f_i_t _f_u_n_c_t_i_o_n: _H_e_s_s_i_a_n _m_a_t_r_i_x

_D_e_s_c_r_i_p_t_i_o_n:

     Returns the Hessian (substitution) matrix of a Symmetric
     Normalized Quadratic (SNQ) Profit Function.

_U_s_a_g_e:

     snqProfitHessian( beta, prices, weights )

_A_r_g_u_m_e_n_t_s:

    beta: matrix of the beta coefficients.

  prices: vector of netput prices at which the Hessian should be
          calculated.

 weights: vector of weights of prices for normalization.

_A_u_t_h_o_r(_s):

     Arne Henningsen ahenningsen@agric-econ.uni-kiel.de

_S_e_e _A_l_s_o:

     'snqProfitEst', 'snqProfitEla' and 'snqProfitHessianDeriv'.

_E_x_a_m_p_l_e_s:

        # just a stupid simple example
        snqProfitHessian( matrix(101:109,3,3), c(1,1,1), c(0.4,0.3,0.3) )

        # now with real data
        data( germanFarms )
        germanFarms$qOutput   <- germanFarms$vOutput   / germanFarms$pOutput
        germanFarms$qVarInput <- -germanFarms$vVarInput / germanFarms$pVarInput
        germanFarms$qLabor    <- -germanFarms$qLabor
        germanFarms$time <- c( 0:19 )
        pNames <- c( "pOutput", "pVarInput", "pLabor" )
        qNames <- c( "qOutput", "qVarInput", "qLabor" )

        estResult <- snqProfitEst( pNames, qNames, c("land","time"), data=germanFarms )

        estResult$hessian  # the Hessian at mean prices and mean quantities

        # Hessian at the last observation (1994/95)
        snqProfitHessian( estResult$coef$beta, estResult$estData[ 20, pNames ],
           estResult$weights )

