aidsEst               package:micEcon               R Documentation

_E_s_t_i_m_a_t_i_o_n _o_f _t_h_e _A_l_m_o_s_t _I_d_e_a_l _D_e_m_a_n_d _S_y_s_t_e_m (_A_I_D_S)

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

     'aidsEst' does a full demand analysis with the Almost Ideal Demand
     System (AIDS): econometric estimation, calculation of
     elasticities, ...

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

      aidsEst( pNames, wNames, xtName, data = NULL,
           ivNames = NULL, qNames = wNames,
           method = "LA:L", hom = TRUE, sym = TRUE,
           elaFormula = "Ch", pxBase,
           estMethod = ifelse( is.null( ivNames ), "SUR", "3SLS" ),
           maxiterMk = 50, tolMk = 1e-5, alpha0 = 0, ... )

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

  pNames: a vector of strings containing the names of prices.

  wNames: a vector of strings containing the names of expenditure
          shares.

  xtName: a name of the total expenditure variable.

    data: a data frame containing the data.

 ivNames: a vector of strings containing the names of instrumental
          variables.

  qNames: an optional vector of strings containing the names of the
          quantities (just to label elasticities).

  method: the method to estimate the aids (see details).

     hom: should the homogeneity condition be imposed?

     sym: should the symmetry condition be imposed?

elaFormula: the elasticity formula (see 'aidsEla').

  pxBase: The base to calculate the LA-AIDS price indices (see
          'aidsPx').

estMethod: estimation method (e.g. "SUR", see 'systemfit').

maxiterMk: maximum number of iterations of the Michalek and Keyzer
          estimation.

   tolMk: tolerance level of the Michalek and Keyzer iteration.

  alpha0: the intercept of the translog price index (alpha_0).

     ...: arguments passed to 'systemfit'.

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

     At the moment two basic estimation methods are available: The
     'Linear Approximate AIDS' (LA) and the iterative estimation method
     of Michalek and Keyzer (MK).
      The LA-AIDS can be estimated with
      * Stone price index ('LA:S'),
      * Stone price index with lagged shares ('LA:SL'),
      * loglinear analogue to the Paasche price index ('LA:P'),
      * loglinear analogue of the Laspeyres price index ('LA:L'), and
      * Tornqvist price index ('LA:T').

     The iterative estimation method of Michalek and Keyzer needs
     starting values for the (translog) price index. Which price index
     is used to calculate the initial price index can be specified in
     the same way as for the LA-AIDS (e.g. 'MK:L')

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

     a list of class 'aidsEst' containing following objects: 

    coef: a list containing the vectors/matrix of the estimated
          coefficients (alpha = alpha_i, beta = beta_i, gamma =
          gamma_{ij}.

     ela: a list containing the elasticities (see 'aidsEla').

      r2: R^2-values of all budget share equations.

     r2q: R^2-values of the estimated quantities.

 wFitted: fitted budget shares.

  wResid: residuals of the budget shares.

    qObs: observed quantities / quantitiy indices.

 qFitted: fitted quantities / quantitiy indices.

  qResid: residuals of the estimated quantities.

    iter: iterations of SUR/3SLS estimation a vector containing the
          iterations of each iteration of the Michalek and Keyzer
          estimation.

  iterMk: iterations of the Michalek and Keyzer estimation.

  method: the method used to estimate the aids (see details).

     lnp: log of the price index used for estimation.

     hom: was the homogeneity condition imposed?

     sym: was the symmetry condition imposed?

estMethod: estimation method (see 'systemfit').

rcovformula: formula used to calculate the estimated residual
          covariance matrix (see 'systemfit').

_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:

     Deaton, A.S. and J. Muellbauer (1980) An Almost Ideal Demand
     System. _American Economic Review_, 70, p. 312-326.

     Michalek, J. and M. A. Keyzer (1992) Estimation of a two-stage
     LES-AIDS consumer demand system for eight EC countries. _European
     Review of Agricultural Economics_, 19 (2), p. 137-163.

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

     'aidsEla', 'aidsCalc'.

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

        ## Repeating the demand analysis of Blanciforti, Green & King (1986)
        data( Blanciforti86 )
        estResult <- aidsEst( c( "pFood1", "pFood2", "pFood3", "pFood4" ),
           c( "wFood1", "wFood2", "wFood3", "wFood4" ), "xFood",
           data = Blanciforti86, method = "LA:SL", elaFormula = "Ch",
           maxiter = 1, rcovformula = 1, tol = 1e-7 )
        print( estResult )

        ## Repeating the evaluation of different elasticity formulas of
        ## Green & Alston (1990)
        data( Blanciforti86 )
        pNames <- c( "pFood1", "pFood2", "pFood3", "pFood4" )
        wNames <- c( "wFood1", "wFood2", "wFood3", "wFood4" )

        # AIDS
        estResultA <- aidsEst( pNames, wNames, "xFood",
         data = Blanciforti86[ 2:nrow( Blanciforti86 ), ], maxiter = 1,
           elaFormula = "AIDS", rcovformula=1, tol=1e-7,
        method = "MK:L" )
        print( diag( estResultA$ela$marshall ) )

        # LA-AIDS + formula of AIDS
        estResultL1 <- aidsEst( pNames, wNames, "xFood",
           data = Blanciforti86, maxiter = 1, elaFormula = "AIDS",
           rcovformula=1, tol=1e-7, method = "LA:SL" )
        print( diag( estResultL1$ela$marshall ) )

        # LA-AIDS + formula of Eales + Unnevehr
        estResultL2 <- aidsEst( pNames, wNames, "xFood",
           data = Blanciforti86, maxiter = 1, elaFormula = "EU",
           rcovformula=1, tol=1e-7, method = "LA:SL" )
        print( diag( estResultL2$ela$marshall ) )

        # LA-AIDS + formula of Chalfant:
        estResultL3 <- aidsEst( pNames, wNames, "xFood",
           data = Blanciforti86, maxiter = 1, elaFormula = "Ch",
           rcovformula=1, tol=1e-7, method = "LA:SL" )
        print( diag( estResultL3$ela$marshall ) )

