snqProfitImposeConvexity       package:micEcon       R Documentation

_I_m_p_o_s_i_n_g _C_o_n_v_e_x_i_t_y _o_n _a _S_N_Q _P_r_o_f_i_t _f_u_n_c_t_i_o_n

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

     Imposing Convexity on a Symmetric Normalized Quadratic (SNQ)
     Profit function.

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

     snqProfitImposeConvexity( estResult, rankReduction = 0,
        start = 10, ... )

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

estResult: object returned by 'snqProfitEst'.

rankReduction: an integer specifying the reduction of the rank of the
          beta matrix.

   start: starting values of the triangular Cholesky matrix.

     ...: arguments passed to 'optim'

_D_e_t_a_i_l_s:

     The procedure proposed by Koebel, Falk and Laisney (2000, 2003) is
     applied to impose convexity in prices on an estimated symmetric
     normalized quadratic (SNQ) profit function.

_V_a_l_u_e:

     a list of class 'snqProfitImposeConvexity' containing following
     objects: 

 mindist: object returned by '\optim'.

    coef: a list containing the vectors/matrix of the estimated
          coefficients:
           * alpha = alpha_i.
           * beta = beta_{ij}.
           * delta =  delta_{ij} (only if quasi-fix inputs are
          present).
           * gamma = gamma_{ij} (only if quasi-fix inputs are present).
           * allCoef = vector of all coefficients.


     ela: matrix with the price elasticities at mean prices and mean
          quantities.

 hessian: hessian matrix of the profit function with respect to prices
          evaluated at mean prices.

convexity: logical. Convexity of the profit function.

      r2: R^2-values of all netput equations.

 weights: the weights of prices used for normalization.

normPrice: vector used for normalization of prices.

 estData: data frame used for estimation (contains the (scaled) netput
          prices, (scaled) netput quantities, (not scaled) fix inputs
          and the price index used for normalization.

  fitted: data frame that contains the fitted netput quantities and the
          fitted profit.

residuals: data frame that contains the residuals of the netput
          quantities.

    form: the functional form (see 'snqProfitEst').

  pMeans: means of the (scaled) netput prices.

  qMeans: means of the (scaled) netput quantities.

  fMeans: means of the (quasi-)fix input quantities.

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

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

_R_e_f_e_r_e_n_c_e_s:

     Koebel, B., M. Falk and F. Laisney (2000), Imposing and Testing
     Curvature Conditions on a Box-Cox Cost Function. Discussion Paper
     No. 00-70, ZEW, Mannheim, <URL:
     ftp://ftp.zew.de/pub/zew-docs/dp/dp0070.pdf>.

     Koebel, B., M. Falk and F. Laisney (2003), Imposing and Testing
     Curvature Conditions on a Box-Cox Cost Function. _Journal of
     Business and Economic Statistics_, 21, p. 319-335.

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

     'snqProfitEst'.

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

        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" )
        fNames <- c( "land", "time" )
        estResult <- snqProfitEst( pNames, qNames, fNames, data = germanFarms )
        estResult  # Note: it is NOT convex in netput prices
        estResultConvex <- snqProfitImposeConvexity( estResult )
        estResultConvex  # now it is convex

