R/Fixed_effects.R
In jpburgard/gravity: Estimation Methods for Gravity Models
Defines functions
Fixed_Effects
Documented in
Fixed_Effects
#' @title Fixed_Effects
#'
#' @description \code{Fixed_Effects} estimates gravity models via
#' OLS and fixed effects for the countries of origin and destination.
#' These effects catch country specific effects.
#'
#' @details To account for MR terms, Feenstra (2002) and Feenstra (2004) propose to use
#' importer and exporter fixed effects. Due to the use of these effects, all
#' unilateral influences such as GDPs can no longer be estimated.
#' A disadvantage of the use of \code{Fixed_Effects} is that, when applied to
#' panel data, the number of country-year or country-pair fixed effects can be
#' too high for estimation. In addition, no comparative statistics are
#' possible with \code{Fixed_Effects} as the MR terms are not estimated
#' explicitly. Nevertheless, Head and Mayer (2014) highlight the importance of
#' the use of fixed effects.
#' To execute the function a square gravity dataset with all pairs of
#' countries, ISO-codes for the country of origin and destination, a measure of
#' distance between the bilateral partners as well as all
#' information that should be considered as dependent an independent
#' variables is needed.
#' Make sure the ISO-codes are of type "character".
#' Missing bilateral flows as well as incomplete rows should be
#' excluded from the dataset.
#' Furthermore, flows equal to zero should be excluded as the gravity equation
#' is estimated in its additive form.
#' Country specific fixed effects are considered by incorporating
#' \code{"iso_o"} and \code{"iso_d"} in \code{fe}.
#' By including country specific fixed effects, all monadic effects
#' are captured, including Multilateral Resistance terms.
#' Therefore, no other unilateral variables such as GDP can be
#' included as independent variables in the estimation.
#'
#' \code{Fixed_Effects} estimation can be used for both, cross-sectional as well as
#' panel data.
#' Nonetheless, the function is designed to be consistent with the
#' Stata code for cross-sectional data provided at the website
#' \href{https://sites.google.com/site/hiegravity/}{Gravity Equations: Workhorse, Toolkit, and Cookbook}
#' when choosing robust estimation.
#' The function \code{Fixed_Effects} was therefore tested for
#' For the use with panel data no tests were performed.
#' Therefore, it is 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 may has 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 Egger and Pfaffermayr (2003), Gomez-Herrera (2013) and Head, Mayer and
#' Ries (2010) as well as the references therein.
#'
#' @param y name (type: character) of the dependent variable in the dataset
#' \code{data}, e.g. trade flows. This variable is logged and taken as the
#' dependent variable in the estimation.
#'
#' @param dist name (type: character) of the distance variable in the dataset
#' \code{data} containing a measure of distance between all pairs of bilateral
#' partners. It is logged automatically when the function is executed.
#'
#' @param fe vector of names (type: character) of fixed effects.
#' The default is set to the unilateral identifiers
#' \code{"iso_o"} and \code{"iso_d"} for cross-sectional data.
#' When using panel data, interaction terms of the iso-codes and time
#' may be added in either \code{fe} or \code{x}.
#'
#' @param x vector of names (type: character) of those bilateral variables in
#' the dataset \code{data} that should be taken as the independent variables
#' in the estimation. If an independent variable is a dummy variable
#' it should be of type numeric (0/1) in the dataset. If an independent variable is
#' defined as a ratio, it should be logged.
#' The fixed effects catch all unilateral effects. Therefore,
#' no other unilateral variables such as GDP can be
#' included as independent variables in the estimation.
#'
#' @param vce_robust robust (type: logic) determines whether a robust
#' variance-covariance matrix should be used. The default is set to \code{TRUE}.
#' If set \code{TRUE} the estimation results are consistent with the
#' Stata code provided at the website
#' \href{https://sites.google.com/site/hiegravity/}{Gravity Equations: Workhorse, Toolkit, and Cookbook}
#' when choosing robust estimation.
#'
#' @param data name of the dataset to be used (type: character).
#' To estimate gravity equations, a square gravity dataset including bilateral
#' flows defined by the argument \code{y}, ISO-codes of type character
#' (called \code{iso_o} for the country of origin and \code{iso_d} for the
#' destination country), a distance measure defined by the argument \code{dist}
#' and other potential influences given as a vector in \code{x} are required.
#' All dummy variables should be of type numeric (0/1). Missing trade flows as
#' well as incomplete rows should be excluded from the dataset.
#' Furthermore, flows equal to zero should be excluded as the gravity equation
#' is estimated in its additive form.
#' When using panel data, a variable for the time may be included in the
#' dataset. Note that the variable for the time dimension should be of
#' type: factor.
#' The time variable can be used as a single dependent variable or interaction
#' term with other variables such as country identifiers by inserting it into
#' \code{x} or \code{fe}.
#' See the references for more information on panel data.
#'
#' @param ... additional arguments to be passed to \code{Fixed_Effects}.
#'
#' @references
#' For more information on fixed effects as well as informaton on gravity models,
#' theoretical foundations and suitable estimation methods in general see
#'
#' Anderson, J. E. (2010) <DOI:10.3386/w16576>
#'
#' Head, K. and Mayer, T. (2014) <DOI:10.1016/B978-0-444-54314-1.00003-3>
#'
#' as well as
#'
#' Anderson, J. E. (1979) <DOI:10.12691/wjssh-2-2-5>
#'
#' Anderson, J. E. and van Wincoop, E. (2003) <DOI:10.3386/w8079>
#'
#' Baier, S. L. and Bergstrand, J. H. (2009) <DOI:10.1016/j.jinteco.2008.10.004>
#'
#' Baier, S. L. and Bergstrand, J. H. (2010) in Van Bergeijk, P. A., & Brakman, S. (Eds.) (2010) chapter 4 <DOI:10.1111/j.1467-9396.2011.01000.x>
#'
#' Head, K., Mayer, T., & Ries, J. (2010) <DOI:10.1016/j.jinteco.2010.01.002>
#'
#' Santos-Silva, J. M. C. and Tenreyro, S. (2006) <DOI:10.1162/rest.88.4.641>
#'
#' 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
#'
#' Egger, P., & Pfaffermayr, M. (2003) <DOI:10.1007/s001810200146>
#'
#' Gomez-Herrera, E. (2013) <DOI:10.1007/s00181-012-0576-2>
#'
#' and the references therein.
#'
#' @examples
#' \dontrun{
#' data(Gravity_no_zeros)
#'
#' Fixed_Effects(y="flow", dist="distw", fe=c("iso_o", "iso_d"),
#' x=c("rta"), vce_robust=TRUE, data=Gravity_no_zeros)
#'
#' Fixed_Effects(y="flow", dist="distw", fe=c("iso_o", "iso_d"),
#' x=c("rta", "comcur", "contig"), vce_robust=TRUE, data=Gravity_no_zeros)
#' }
#'
#' \dontshow{
#' # examples for CRAN checks:
#' # executable in < 5 sec together with the examples above
#' # not shown to users
#'
#' data(Gravity_no_zeros)
#' # choose exemplarily 10 biggest countries for check data
#' countries_chosen <- names(sort(table(Gravity_no_zeros$iso_o), decreasing = TRUE)[1:10])
#' grav_small <- Gravity_no_zeros[Gravity_no_zeros$iso_o %in% countries_chosen,]
#' Fixed_Effects(y="flow", dist="distw", fe=c("iso_o", "iso_d"), x=c("rta"), vce_robust=TRUE, data=grav_small)
#' }
#'
#' @return
#' The function returns the summary of the estimated gravity model as an
#' \code{\link[stats]{lm}}-object.
#'
#' @seealso \code{\link[stats]{lm}}, \code{\link[lmtest]{coeftest}},
#' \code{\link[sandwich]{vcovHC}}
#'
#' @export
Fixed_Effects <- function(y, dist, fe=c("iso_o", "iso_d"), x, vce_robust=TRUE, data, ...){
if(!is.data.frame(data)) stop("'data' must be a 'data.frame'")
if((vce_robust %in% c(TRUE, FALSE)) == FALSE) stop("'vce_robust' has to be either 'TRUE' or 'FALSE'")
if(!is.character(y) | !y%in%colnames(data) | length(y)!=1) stop("'y' must be a character of length 1 and a colname of 'data'")
if(!is.character(dist) | !dist%in%colnames(data) | length(dist)!=1) stop("'dist' must be a character of length 1 and a colname of 'data'")
if(!is.character(x) | !all(x%in%colnames(data))) stop("'x' must be a character vector and all x's have to be colnames of 'data'")
if(!is.character(fe) | !all(unique(unlist(strsplit(fe,c("[:]|[*]"))))%in%colnames(data)) | length(fe)<2) stop("'fe' must be a character vector of length >=2 and all main variables of the fe's have to be colnames of 'data'")
# Transforming data, logging flows and distances -----------------------------
d <- data
d$dist_log <- (log(d[dist][,1]))
d$y_log <- log(d[y][,1])
# Model ----------------------------------------------------------------------
vars <- paste(c("dist_log", x, fe), collapse = " + ")
vars2 <- paste(vars)
form <- paste("y_log", "~", vars2)
form2 <- stats::as.formula(form)
model.fe <- stats::lm(form2, data = d)
# Return ---------------------------------------------------------------------
return.object.1 <- .robustsummary.lm(model.fe, robust=vce_robust)
return.object.1$call <- form2
return(return.object.1)
}
jpburgard/gravity documentation built on Sept. 16, 2019, 12:38 p.m.
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Defines functions Fixed_Effects
Documented in Fixed_Effects
#' @title Fixed_Effects
#'
#' @description \code{Fixed_Effects} estimates gravity models via
#' OLS and fixed effects for the countries of origin and destination.
#' These effects catch country specific effects.
#'
#' @details To account for MR terms, Feenstra (2002) and Feenstra (2004) propose to use
#' importer and exporter fixed effects. Due to the use of these effects, all
#' unilateral influences such as GDPs can no longer be estimated.
#' A disadvantage of the use of \code{Fixed_Effects} is that, when applied to
#' panel data, the number of country-year or country-pair fixed effects can be
#' too high for estimation. In addition, no comparative statistics are
#' possible with \code{Fixed_Effects} as the MR terms are not estimated
#' explicitly. Nevertheless, Head and Mayer (2014) highlight the importance of
#' the use of fixed effects.
#' To execute the function a square gravity dataset with all pairs of
#' countries, ISO-codes for the country of origin and destination, a measure of
#' distance between the bilateral partners as well as all
#' information that should be considered as dependent an independent
#' variables is needed.
#' Make sure the ISO-codes are of type "character".
#' Missing bilateral flows as well as incomplete rows should be
#' excluded from the dataset.
#' Furthermore, flows equal to zero should be excluded as the gravity equation
#' is estimated in its additive form.
#' Country specific fixed effects are considered by incorporating
#' \code{"iso_o"} and \code{"iso_d"} in \code{fe}.
#' By including country specific fixed effects, all monadic effects
#' are captured, including Multilateral Resistance terms.
#' Therefore, no other unilateral variables such as GDP can be
#' included as independent variables in the estimation.
#'
#' \code{Fixed_Effects} estimation can be used for both, cross-sectional as well as
#' panel data.
#' Nonetheless, the function is designed to be consistent with the
#' Stata code for cross-sectional data provided at the website
#' \href{https://sites.google.com/site/hiegravity/}{Gravity Equations: Workhorse, Toolkit, and Cookbook}
#' when choosing robust estimation.
#' The function \code{Fixed_Effects} was therefore tested for
#' For the use with panel data no tests were performed.
#' Therefore, it is 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 may has 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 Egger and Pfaffermayr (2003), Gomez-Herrera (2013) and Head, Mayer and
#' Ries (2010) as well as the references therein.
#'
#' @param y name (type: character) of the dependent variable in the dataset
#' \code{data}, e.g. trade flows. This variable is logged and taken as the
#' dependent variable in the estimation.
#'
#' @param dist name (type: character) of the distance variable in the dataset
#' \code{data} containing a measure of distance between all pairs of bilateral
#' partners. It is logged automatically when the function is executed.
#'
#' @param fe vector of names (type: character) of fixed effects.
#' The default is set to the unilateral identifiers
#' \code{"iso_o"} and \code{"iso_d"} for cross-sectional data.
#' When using panel data, interaction terms of the iso-codes and time
#' may be added in either \code{fe} or \code{x}.
#'
#' @param x vector of names (type: character) of those bilateral variables in
#' the dataset \code{data} that should be taken as the independent variables
#' in the estimation. If an independent variable is a dummy variable
#' it should be of type numeric (0/1) in the dataset. If an independent variable is
#' defined as a ratio, it should be logged.
#' The fixed effects catch all unilateral effects. Therefore,
#' no other unilateral variables such as GDP can be
#' included as independent variables in the estimation.
#'
#' @param vce_robust robust (type: logic) determines whether a robust
#' variance-covariance matrix should be used. The default is set to \code{TRUE}.
#' If set \code{TRUE} the estimation results are consistent with the
#' Stata code provided at the website
#' \href{https://sites.google.com/site/hiegravity/}{Gravity Equations: Workhorse, Toolkit, and Cookbook}
#' when choosing robust estimation.
#'
#' @param data name of the dataset to be used (type: character).
#' To estimate gravity equations, a square gravity dataset including bilateral
#' flows defined by the argument \code{y}, ISO-codes of type character
#' (called \code{iso_o} for the country of origin and \code{iso_d} for the
#' destination country), a distance measure defined by the argument \code{dist}
#' and other potential influences given as a vector in \code{x} are required.
#' All dummy variables should be of type numeric (0/1). Missing trade flows as
#' well as incomplete rows should be excluded from the dataset.
#' Furthermore, flows equal to zero should be excluded as the gravity equation
#' is estimated in its additive form.
#' When using panel data, a variable for the time may be included in the
#' dataset. Note that the variable for the time dimension should be of
#' type: factor.
#' The time variable can be used as a single dependent variable or interaction
#' term with other variables such as country identifiers by inserting it into
#' \code{x} or \code{fe}.
#' See the references for more information on panel data.
#'
#' @param ... additional arguments to be passed to \code{Fixed_Effects}.
#'
#' @references
#' For more information on fixed effects as well as informaton on gravity models,
#' theoretical foundations and suitable estimation methods in general see
#'
#' Anderson, J. E. (2010) <DOI:10.3386/w16576>
#'
#' Head, K. and Mayer, T. (2014) <DOI:10.1016/B978-0-444-54314-1.00003-3>
#'
#' as well as
#'
#' Anderson, J. E. (1979) <DOI:10.12691/wjssh-2-2-5>
#'
#' Anderson, J. E. and van Wincoop, E. (2003) <DOI:10.3386/w8079>
#'
#' Baier, S. L. and Bergstrand, J. H. (2009) <DOI:10.1016/j.jinteco.2008.10.004>
#'
#' Baier, S. L. and Bergstrand, J. H. (2010) in Van Bergeijk, P. A., & Brakman, S. (Eds.) (2010) chapter 4 <DOI:10.1111/j.1467-9396.2011.01000.x>
#'
#' Head, K., Mayer, T., & Ries, J. (2010) <DOI:10.1016/j.jinteco.2010.01.002>
#'
#' Santos-Silva, J. M. C. and Tenreyro, S. (2006) <DOI:10.1162/rest.88.4.641>
#'
#' 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
#'
#' Egger, P., & Pfaffermayr, M. (2003) <DOI:10.1007/s001810200146>
#'
#' Gomez-Herrera, E. (2013) <DOI:10.1007/s00181-012-0576-2>
#'
#' and the references therein.
#'
#' @examples
#' \dontrun{
#' data(Gravity_no_zeros)
#'
#' Fixed_Effects(y="flow", dist="distw", fe=c("iso_o", "iso_d"),
#' x=c("rta"), vce_robust=TRUE, data=Gravity_no_zeros)
#'
#' Fixed_Effects(y="flow", dist="distw", fe=c("iso_o", "iso_d"),
#' x=c("rta", "comcur", "contig"), vce_robust=TRUE, data=Gravity_no_zeros)
#' }
#'
#' \dontshow{
#' # examples for CRAN checks:
#' # executable in < 5 sec together with the examples above
#' # not shown to users
#'
#' data(Gravity_no_zeros)
#' # choose exemplarily 10 biggest countries for check data
#' countries_chosen <- names(sort(table(Gravity_no_zeros$iso_o), decreasing = TRUE)[1:10])
#' grav_small <- Gravity_no_zeros[Gravity_no_zeros$iso_o %in% countries_chosen,]
#' Fixed_Effects(y="flow", dist="distw", fe=c("iso_o", "iso_d"), x=c("rta"), vce_robust=TRUE, data=grav_small)
#' }
#'
#' @return
#' The function returns the summary of the estimated gravity model as an
#' \code{\link[stats]{lm}}-object.
#'
#' @seealso \code{\link[stats]{lm}}, \code{\link[lmtest]{coeftest}},
#' \code{\link[sandwich]{vcovHC}}
#'
#' @export
Fixed_Effects <- function(y, dist, fe=c("iso_o", "iso_d"), x, vce_robust=TRUE, data, ...){
if(!is.data.frame(data)) stop("'data' must be a 'data.frame'")
if((vce_robust %in% c(TRUE, FALSE)) == FALSE) stop("'vce_robust' has to be either 'TRUE' or 'FALSE'")
if(!is.character(y) | !y%in%colnames(data) | length(y)!=1) stop("'y' must be a character of length 1 and a colname of 'data'")
if(!is.character(dist) | !dist%in%colnames(data) | length(dist)!=1) stop("'dist' must be a character of length 1 and a colname of 'data'")
if(!is.character(x) | !all(x%in%colnames(data))) stop("'x' must be a character vector and all x's have to be colnames of 'data'")
if(!is.character(fe) | !all(unique(unlist(strsplit(fe,c("[:]|[*]"))))%in%colnames(data)) | length(fe)<2) stop("'fe' must be a character vector of length >=2 and all main variables of the fe's have to be colnames of 'data'")
# Transforming data, logging flows and distances -----------------------------
d <- data
d$dist_log <- (log(d[dist][,1]))
d$y_log <- log(d[y][,1])
# Model ----------------------------------------------------------------------
vars <- paste(c("dist_log", x, fe), collapse = " + ")
vars2 <- paste(vars)
form <- paste("y_log", "~", vars2)
form2 <- stats::as.formula(form)
model.fe <- stats::lm(form2, data = d)
# Return ---------------------------------------------------------------------
return.object.1 <- .robustsummary.lm(model.fe, robust=vce_robust)
return.object.1$call <- form2
return(return.object.1)
}
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