R/gpml.R

In gravity: Estimation Methods for Gravity Models

#' @title Gamma Pseudo Maximum Likelihood (GPML)
#'
#' @description \code{gpml} estimates gravity models in their
#' multiplicative form via Gamma Pseudo Maximum Likelihood.
#'
#' @details \code{gpml} is an estimation method for gravity models
#' belonging to generalized linear models. It is described in \insertCite{Santos2006;textual}{gravity} and the model
#' is estimated via \code{\link[glm2]{glm2}} using the gamma distribution and a log-link.
#'
#' For similar functions, utilizing the multiplicative form via the log-link,
#' but different distributions, see \code{\link[gravity]{ppml}}, \code{\link[gravity]{nls}}, and \code{\link[gravity]{nbpml}}.
#'
#' \code{gpml} estimation can be used for both, cross-sectional as well as
#' panel data, but its up to the user to ensure that the functions can be applied
#' to panel data.
#'
#' Depending on the panel dataset and the variables -
#' specifically the type of fixed effects -
#' included in the model, it may easily occur that the model is not computable.
#'
#' Also, note that by including bilateral fixed effects such as country-pair
#' effects, the coefficients of time-invariant observables such as distance
#' can no longer be estimated.
#'
#' Depending on the specific model, the code of the
#' respective function might have to be changed in order to exclude the distance
#' variable from the estimation.
#'
#' At the very least, the user should take special
#' care with respect to the meaning of the estimated coefficients and variances
#' as well as the decision about which effects to include in the estimation.
#'
#' When using panel data, the parameter and variance estimation of the models
#' may have to be changed accordingly.
#'
#' For a comprehensive overview of gravity models for panel data
#' see \insertCite{Egger2003;textual}{gravity}, \insertCite{Gomez-Herrera2013;textual}{gravity} and
#' \insertCite{Head2010;textual}{gravity}.
#'
#' @param dependent_variable (Type: character) name of the dependent variable. This variable is logged and then used as
#' the dependent variable in the estimation.
#'
#' @param distance (Type: character) name of the distance variable that should be taken as the key independent variable
#' in the estimation. The distance is logged automatically when the function is executed.
#'
#' @param additional_regressors (Type: character) names of the additional regressors to include in the model (e.g. a dummy
#' variable to indicate contiguity). Unilateral metric variables such as GDPs can be added but those variables have to be
#' logged first. Interaction terms can be added.
#'
#' Write this argument as \code{c(contiguity, common currency, ...)}. By default this is set to \code{NULL}.
#'
#' @param robust (Type: logical) whether robust fitting should be used. By default this is set to \code{FALSE}.
#'
#' @param data (Type: data.frame) the dataset to be used.
#'
#' @param ... Additional arguments to be passed to the function.
#'
#' @references
#' For more information on gravity models, theoretical foundations and
#' estimation methods in general see
#'
#' \insertRef{Anderson1979}{gravity}
#'
#' \insertRef{Anderson2001}{gravity}
#'
#' \insertRef{Anderson2010}{gravity}
#'
#' \insertRef{Baier2009}{gravity}
#'
#' \insertRef{Baier2010}{gravity}
#'
#' \insertRef{Feenstra2002}{gravity}
#'
#' \insertRef{Head2010}{gravity}
#'
#' \insertRef{Head2014}{gravity}
#'
#' \insertRef{Santos2006}{gravity}
#'
#' and the citations therein.
#'
#' See \href{https://sites.google.com/site/hiegravity/}{Gravity Equations: Workhorse, Toolkit, and Cookbook} for gravity datasets and Stata code for estimating gravity models.
#'
#' For estimating gravity equations using panel data see
#'
#' \insertRef{Egger2003}{gravity}
#'
#' \insertRef{Gomez-Herrera2013}{gravity}
#'
#' and the references therein.
#'
#' @examples
#' # Example for CRAN checks:
#' # Executable in < 5 sec
#' library(dplyr)
#' data("gravity_no_zeros")
#'
#' # Choose 5 countries for testing
#' countries_chosen <- c("AUS", "CHN", "GBR", "BRA", "CAN")
#' grav_small <- filter(gravity_no_zeros, iso_o %in% countries_chosen)
#'
#' grav_small <- grav_small %>%
#'   mutate(
#'     lgdp_o = log(gdp_o),
#'     lgdp_d = log(gdp_d)
#'   )
#'
#' fit <- gpml(
#'   dependent_variable = "flow",
#'   distance = "distw",
#'   additional_regressors = c("rta", "iso_o", "iso_d"),
#'   data = grav_small
#' )
#' @return
#' The function returns the summary of the estimated gravity model similar to a
#' \code{\link[stats]{glm}}-object.
#'
#' @seealso \code{\link[glm2]{glm2}}, \code{\link[lmtest]{coeftest}},
#' \code{\link[sandwich]{vcovHC}}
#'
#' @export

gpml <- function(dependent_variable,
                 distance,
                 additional_regressors,
                 robust = FALSE,
                 data, ...) {
  # Checks ------------------------------------------------------------------
  stopifnot(is.data.frame(data))

  stopifnot(is.character(dependent_variable), dependent_variable %in% colnames(data), length(dependent_variable) == 1)

  stopifnot(is.character(distance), distance %in% colnames(data), length(distance) == 1)

  if (!is.null(additional_regressors)) {
    stopifnot(is.character(additional_regressors), all(additional_regressors %in% colnames(data)))
  }

  # Discarding unusable observations -------------------------------------------
  d <- discard_unusable(data, c(distance, dependent_variable))

  # Transforming data, logging distances ---------------------------------------
  d <- log_distance(d, distance)

  # Transforming data, renaming dependent variable -----------------------------
  d <- rename(d, y_gpml = !!sym(dependent_variable))

  # Model ----------------------------------------------------------------------
  if (!is.null(additional_regressors)) {
    vars <- paste(c("dist_log", additional_regressors), collapse = " + ")
  } else {
    vars <- "dist_log"
  }

  form <- stats::as.formula(paste("y_gpml", "~", vars))

  model_gpml <- glm2::glm2(form,
    data = d,
    family = stats::Gamma(link = "log"),
    control = list(maxit = 200, trace = FALSE)
  )

  if (robust == TRUE) {
    model_gpml_robust <- lmtest::coeftest(
      model_gpml,
      vcov = sandwich::vcovHC(model_gpml, type = "HC1", ...)
    )
  }

  if (robust == FALSE) {
    model_gpml$call <- form
    class(model_gpml) <- c(class(model_gpml), "gravity_gpml")
    return(model_gpml)
  } else {
    class(model_gpml_robust) <- c(class(model_gpml_robust), "gravity_gpml")
    return(model_gpml_robust)
  }
}