R/sfm.generate.R

In clemenshaerder/fepsfrontieR: Estimation of fixed-effect panel stochastic frontier models by MLE

#' @title Data Generation for Stochastic Frontier Models
#' @description Creates a fixed-effects panel stochastic frontier model.
#'     Data sets created by this function can be applied for sfmfep( ) of
#'     this package fepsfrontieR. The model specificiation are:
#'     alpha_i are fixed-effect parameters drawn from a uniform distribution in [0, 1].
#'     x_it is drawn from a normal distribution N(alpha_i, 1).
#'     z_it is drawn from a standard normal distribution.
#'     u_i (inefficency) is drawn from a truncated normal distribution with N(mu, sigma_u).
#' @param N is an integer and specifies the amount of panels
#' @param Time is an integer and specifies the amount of observations per panel
#' @param beta is a vector of k estimates.
#'     K explenatory varibles will be gerenated.
#' @param delta is a vector of r estimates.
#'     R inefficency determinats will be gerenated.
#' @param sigma_u is postivie numeric and is the variation
#'     of the stochastic inefficency
#' @param sigma_v is postivie numeric and is the variation
#'     of the zero-mean random error.
#' @param mu is numeric and is the mean of the truncated normal distribution
#'     of the stochastic inefficency.
#' @return A data.frame( ) including x, y, z & alpha variables
#' @examples
#' exampleSFM <- SFM.generate (N = 20, Time = 5, beta = c(0.5, 0.2, 9, 3),
#'         delta = c(0.5, 0.1, 2), sigma_u = 0.2, sigma_v = 0.1)
#'
#' exampleSFM
#' @importFrom truncnorm rtruncnorm
#' @importFrom dplyr as_tibble
#' @export

SFM.generate <- function(N, Time, beta, delta, sigma_u, sigma_v, mu = 0){

  if (!is.double (N) |
      !is.double (Time) |
      !is.vector (beta) |
      !is.vector (delta) |
      !is.numeric (sigma_u) |
      !is.numeric (sigma_v)  |
      !is.numeric (mu) |
      sigma_u <= 0 |
      sigma_v <= 0) {
    stop ("Invalid input format of parameters.")
  }

  K <- length (beta)
  R <- length (delta)

  # Generate inefficencys for each panel and repeat it
  # from truncated normal distribution (x>a)
  u_star <- rep (rtruncnorm (N, a = 0, mean = mu,
                             sd = sqrt (sigma_u)), each = Time)

  # Generate one alpha intercepts for each
  # panel and repeat it from a uniform distribution
  alpha  <- rep (runif (N, 0, 1), each = Time)


  # Generate data of the model ---------------------------
  v <- c(rnorm (Time*N, 0, sqrt (sigma_v)))
  # R inefficency determinants
  z <- matrix(rnorm (Time*N*R, 0, 1), nrow = Time*N, ncol = R)
  # K explenatory variables using alpha as mean
  x <- matrix(c(rnorm (Time * N * K, rep(alpha, each = K), 1)),
              nrow = Time * N, ncol = K)
  h <- exp (z %*% delta)
  u <- h * u_star
  epsilon <- v - u


  # Calculation of the response ---------------------------
  y <- alpha + x%*%beta + epsilon

  # nice output with dplyr -> need dplyr dependency anyhow for bootstrapping
  returnTibble <- as_tibble (data.frame (x = x, y = y, z = z, alpha = alpha))

  return (returnTibble)
}