R/BVU.R
In jpburgard/gravity: Estimation Methods for Gravity Models
Defines functions
BVU
Documented in
BVU
#' @title Bonus vetus OLS, BVU
#'
#' @description \code{BVU} estimates gravity models via Bonus
#' vetus OLS with simple averages.
#'
#' @details \code{Bonus vetus OLS} is an estimation method for gravity models
#' developed by Baier and Bergstrand (2009, 2010) using simple averages to center a
#' Taylor-series (see the references for more information).
#' 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.
#' The \code{BVU} function considers Multilateral Resistance terms and allows to
#' conduct comparative statics. Country specific effects are subdued due
#' to demeaning. Hence, unilateral variables apart from \code{inc_o}
#' and \code{inc_d} cannot be included in the estimation.
#' \code{BVU} is designed to be 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.
#' As, to our knowledge at the moment, there is no explicit literature covering
#' the estimation of a gravity equation by \code{BVU} using panel data,
#' we do not recommend to apply this method in this case.
#'
#' @param y name (type: character) of the dependent variable in the dataset
#' \code{data}, e.g. trade flows. This dependent variable is divided by the
#' product of unilateral incomes (named \code{inc_o} and \code{inc_d}, e.g.
#' GDPs or GNPs of the countries of interest) and logged afterwards.
#' The transformed variable is then used 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 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. Unilateral metric variables
#' such as GDPs should be inserted via the arguments \code{inc_o}
#' for the country of origin and \code{inc_d} for the country of destination.
#' As country specific effects are subdued due to demeaning, no further
#' unilateral variables apart from \code{inc_o} and \code{inc_d} can be
#' added.
#'
#' @param inc_o variable name (type: character) of the income of the country of
#' origin in the dataset \code{data}. The dependent variable \code{y} is
#' divided by the product of the incomes \code{inc_d} and \code{inc_o}.
#'
#' @param inc_d variable name (type: character) of the income of the country of
#' destination in the dataset \code{data}. The dependent variable \code{y} is
#' divided by the product of the incomes \code{inc_d} and \code{inc_o}.
#'
#' @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.
#' As, to our knowledge at the moment, there is no explicit literature covering
#' the estimation of a gravity equation by \code{BVU}
#' using panel data, cross-sectional data should be used.
#'
#' @param ... additional arguments to be passed to \code{BVU}.
#'
#' @references
#' For estimating gravity equations via Bonus Vetus OLS see
#'
#' 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>
#'
#' For more information on gravity models, theoretical foundations and
#' estimation methods in general see
#'
#' Anderson, J. E. (1979) <DOI:10.12691/wjssh-2-2-5>
#'
#' Anderson, J. E. (2010) <DOI:10.3386/w16576>
#'
#' Anderson, J. E. and van Wincoop, E. (2003) <DOI:10.3386/w8079>
#'
#' Head, K., Mayer, T., & Ries, J. (2010) <DOI:10.1016/j.jinteco.2010.01.002>
#'
#' Head, K. and Mayer, T. (2014) <DOI:10.1016/B978-0-444-54314-1.00003-3>
#'
#' 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.
#'
#' @examples
#' \dontrun{
#' data(Gravity_no_zeros)
#'
#' BVU(y="flow", dist="distw", x=c("rta"),
#' inc_o="gdp_o", inc_d="gdp_d", vce_robust=TRUE, data=Gravity_no_zeros)
#'
#' BVU(y="flow", dist="distw", x=c("rta", "contig", "comcur"),
#' inc_o="gdp_o", inc_d="gdp_d", 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,]
#' BVU(y="flow", dist="distw", x=c("rta"), inc_o="gdp_o", inc_d="gdp_d", 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
#'
BVU <- function(y, dist, x, inc_o, inc_d, 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(inc_d) | !inc_d%in%colnames(data) | length(inc_d)!=1) stop("'inc_d' must be a character of length 1 and a colname of 'data'")
if(!is.character(inc_o) | !inc_o%in%colnames(data) | length(inc_o)!=1) stop("'inc_o' must be a character of length 1 and a colname of 'data'")
# Transforming data, logging distances ---------------------------------------
d <- data
d$dist_log <- (log(d[dist][,1]))
d$count <- 1:length(d$iso_o)
# Transforming data, logging flows -------------------------------------------
d$y_inc <- d[y][,1] / (d[inc_o][,1] * d[inc_d][,1])
d$y_inc_log <- log(d$y_inc)
# Multilateral Resistance (MR) for distance ----------------------------------
mean.dist_log.1 <- vector(length=length(unique(d$iso_o)))
mean.dist_log.2 <- vector(length=length(unique(d$iso_o)))
for(i in unique(d$iso_o)){
mean.dist_log.1[i] <- mean(d$dist_log[d$iso_o == i])
}
for(i in unique(d$iso_o)){
mean.dist_log.2[i] <- mean(d$dist_log[d$iso_d == i])
}
mean.dist_log.3 <- mean(d$dist_log)
d$dist_log_mr <- d$dist_log - (mean.dist_log.1[d$iso_o] +
mean.dist_log.2[d$iso_d] -
mean.dist_log.3)
# Multilateral Resistance (MR) for the other independent variables -----------
num.ind.var <- length(x) #independent variables apart from distance
mean.ind.var.1 <- list(length=num.ind.var)
mean.ind.var.2 <- list(length=num.ind.var)
mean.ind.var.3 <- list(length=num.ind.var)
for(j in 1:num.ind.var){
mean.ind.var.1[[j]] <- rep(NA, times=length(unique(d$iso_o)))
mean.ind.var.2[[j]] <- rep(NA, times=length(unique(d$iso_o)))
names(mean.ind.var.1[[j]]) <- x[j]
names(mean.ind.var.2[[j]]) <- x[j]
}
ind.var <- list(length=num.ind.var)
for(j in 1:num.ind.var){
for(i in unique(d$iso_o)){
ind.var[[j]] <- ((d[d$iso_o == i,])[x[j]])[,1]
names(ind.var[[j]]) <- d$iso_d[d$iso_o == i]
mean.ind.var.1[[j]][i] <- mean(ind.var[[j]])
}
}
for(j in 1:num.ind.var){
for(i in unique(d$iso_o)){
ind.var[[j]] <- ((d[d$iso_d == i,])[x[j]])[,1]
names(ind.var[[j]]) <- d$iso_o[d$iso_d == i]
mean.ind.var.2[[j]][i] <- mean(ind.var[[j]])
}
}
for(j in 1:num.ind.var){
mean.ind.var.3[[j]] <- mean(d[x[[j]]][,1])
}
# MR
d_2 <- d
for(k in x){
l <- which(x == k)
d_2[k] <- d[k][,1] - (mean.ind.var.1[[l]][d$iso_o] +
mean.ind.var.2[[l]][d$iso_d] -
mean.ind.var.3[[l]])
}
# Model ----------------------------------------------------------------------
x_mr <- paste0(x,"_mr")
# new row in dataset for independent _mr variable
for(j in x){
l <- which(x == j)
mr <- x_mr[l]
d_2[mr] <- NA
d_2[mr] <- d_2[x[l]]
}
vars <- paste(c("dist_log_mr", x_mr), collapse=" + ")
form <- paste("y_inc_log","~",vars)
form2 <- stats::as.formula(form)
model.BVU <- stats::lm(form2, data = d_2)
# Return ---------------------------------------------------------------------
if(vce_robust == TRUE){
return.object.1 <- .robustsummary.lm(model.BVU, robust=TRUE)
return.object.1$call <- form2
return(return.object.1)}
if(vce_robust == FALSE){
return.object.1 <- .robustsummary.lm(model.BVU, robust=FALSE)
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 BVU
Documented in BVU
#' @title Bonus vetus OLS, BVU
#'
#' @description \code{BVU} estimates gravity models via Bonus
#' vetus OLS with simple averages.
#'
#' @details \code{Bonus vetus OLS} is an estimation method for gravity models
#' developed by Baier and Bergstrand (2009, 2010) using simple averages to center a
#' Taylor-series (see the references for more information).
#' 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.
#' The \code{BVU} function considers Multilateral Resistance terms and allows to
#' conduct comparative statics. Country specific effects are subdued due
#' to demeaning. Hence, unilateral variables apart from \code{inc_o}
#' and \code{inc_d} cannot be included in the estimation.
#' \code{BVU} is designed to be 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.
#' As, to our knowledge at the moment, there is no explicit literature covering
#' the estimation of a gravity equation by \code{BVU} using panel data,
#' we do not recommend to apply this method in this case.
#'
#' @param y name (type: character) of the dependent variable in the dataset
#' \code{data}, e.g. trade flows. This dependent variable is divided by the
#' product of unilateral incomes (named \code{inc_o} and \code{inc_d}, e.g.
#' GDPs or GNPs of the countries of interest) and logged afterwards.
#' The transformed variable is then used 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 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. Unilateral metric variables
#' such as GDPs should be inserted via the arguments \code{inc_o}
#' for the country of origin and \code{inc_d} for the country of destination.
#' As country specific effects are subdued due to demeaning, no further
#' unilateral variables apart from \code{inc_o} and \code{inc_d} can be
#' added.
#'
#' @param inc_o variable name (type: character) of the income of the country of
#' origin in the dataset \code{data}. The dependent variable \code{y} is
#' divided by the product of the incomes \code{inc_d} and \code{inc_o}.
#'
#' @param inc_d variable name (type: character) of the income of the country of
#' destination in the dataset \code{data}. The dependent variable \code{y} is
#' divided by the product of the incomes \code{inc_d} and \code{inc_o}.
#'
#' @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.
#' As, to our knowledge at the moment, there is no explicit literature covering
#' the estimation of a gravity equation by \code{BVU}
#' using panel data, cross-sectional data should be used.
#'
#' @param ... additional arguments to be passed to \code{BVU}.
#'
#' @references
#' For estimating gravity equations via Bonus Vetus OLS see
#'
#' 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>
#'
#' For more information on gravity models, theoretical foundations and
#' estimation methods in general see
#'
#' Anderson, J. E. (1979) <DOI:10.12691/wjssh-2-2-5>
#'
#' Anderson, J. E. (2010) <DOI:10.3386/w16576>
#'
#' Anderson, J. E. and van Wincoop, E. (2003) <DOI:10.3386/w8079>
#'
#' Head, K., Mayer, T., & Ries, J. (2010) <DOI:10.1016/j.jinteco.2010.01.002>
#'
#' Head, K. and Mayer, T. (2014) <DOI:10.1016/B978-0-444-54314-1.00003-3>
#'
#' 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.
#'
#' @examples
#' \dontrun{
#' data(Gravity_no_zeros)
#'
#' BVU(y="flow", dist="distw", x=c("rta"),
#' inc_o="gdp_o", inc_d="gdp_d", vce_robust=TRUE, data=Gravity_no_zeros)
#'
#' BVU(y="flow", dist="distw", x=c("rta", "contig", "comcur"),
#' inc_o="gdp_o", inc_d="gdp_d", 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$iso_o %in% countries_chosen,]
#' BVU(y="flow", dist="distw", x=c("rta"), inc_o="gdp_o", inc_d="gdp_d", vce_robust=TRUE, data=grav_small)
#' }
#'
#' @return
#' The function returns the summary of the estimated gravity model as an
#' \code{\link[stats]{lm}}-object.
#'
#' @seealso \code{\link[stats]{lm}}, \code{\link[lmtest]{coeftest}},
#' \code{\link[sandwich]{vcovHC}}
#'
#' @export
#'
BVU <- function(y, dist, x, inc_o, inc_d, vce_robust=TRUE, data, ...){
if(!is.data.frame(data)) stop("'data' must be a 'data.frame'")
if((vce_robust %in% c(TRUE, FALSE)) == FALSE) stop("'vce_robust' has to be either 'TRUE' or 'FALSE'")
if(!is.character(y) | !y%in%colnames(data) | length(y)!=1) stop("'y' must be a character of length 1 and a colname of 'data'")
if(!is.character(dist) | !dist%in%colnames(data) | length(dist)!=1) stop("'dist' must be a character of length 1 and a colname of 'data'")
if(!is.character(x) | !all(x%in%colnames(data))) stop("'x' must be a character vector and all x's have to be colnames of 'data'")
if(!is.character(inc_d) | !inc_d%in%colnames(data) | length(inc_d)!=1) stop("'inc_d' must be a character of length 1 and a colname of 'data'")
if(!is.character(inc_o) | !inc_o%in%colnames(data) | length(inc_o)!=1) stop("'inc_o' must be a character of length 1 and a colname of 'data'")
# Transforming data, logging distances ---------------------------------------
d <- data
d$dist_log <- (log(d[dist][,1]))
d$count <- 1:length(d$iso_o)
# Transforming data, logging flows -------------------------------------------
d$y_inc <- d[y][,1] / (d[inc_o][,1] * d[inc_d][,1])
d$y_inc_log <- log(d$y_inc)
# Multilateral Resistance (MR) for distance ----------------------------------
mean.dist_log.1 <- vector(length=length(unique(d$iso_o)))
mean.dist_log.2 <- vector(length=length(unique(d$iso_o)))
for(i in unique(d$iso_o)){
mean.dist_log.1[i] <- mean(d$dist_log[d$iso_o == i])
}
for(i in unique(d$iso_o)){
mean.dist_log.2[i] <- mean(d$dist_log[d$iso_d == i])
}
mean.dist_log.3 <- mean(d$dist_log)
d$dist_log_mr <- d$dist_log - (mean.dist_log.1[d$iso_o] +
mean.dist_log.2[d$iso_d] -
mean.dist_log.3)
# Multilateral Resistance (MR) for the other independent variables -----------
num.ind.var <- length(x) #independent variables apart from distance
mean.ind.var.1 <- list(length=num.ind.var)
mean.ind.var.2 <- list(length=num.ind.var)
mean.ind.var.3 <- list(length=num.ind.var)
for(j in 1:num.ind.var){
mean.ind.var.1[[j]] <- rep(NA, times=length(unique(d$iso_o)))
mean.ind.var.2[[j]] <- rep(NA, times=length(unique(d$iso_o)))
names(mean.ind.var.1[[j]]) <- x[j]
names(mean.ind.var.2[[j]]) <- x[j]
}
ind.var <- list(length=num.ind.var)
for(j in 1:num.ind.var){
for(i in unique(d$iso_o)){
ind.var[[j]] <- ((d[d$iso_o == i,])[x[j]])[,1]
names(ind.var[[j]]) <- d$iso_d[d$iso_o == i]
mean.ind.var.1[[j]][i] <- mean(ind.var[[j]])
}
}
for(j in 1:num.ind.var){
for(i in unique(d$iso_o)){
ind.var[[j]] <- ((d[d$iso_d == i,])[x[j]])[,1]
names(ind.var[[j]]) <- d$iso_o[d$iso_d == i]
mean.ind.var.2[[j]][i] <- mean(ind.var[[j]])
}
}
for(j in 1:num.ind.var){
mean.ind.var.3[[j]] <- mean(d[x[[j]]][,1])
}
# MR
d_2 <- d
for(k in x){
l <- which(x == k)
d_2[k] <- d[k][,1] - (mean.ind.var.1[[l]][d$iso_o] +
mean.ind.var.2[[l]][d$iso_d] -
mean.ind.var.3[[l]])
}
# Model ----------------------------------------------------------------------
x_mr <- paste0(x,"_mr")
# new row in dataset for independent _mr variable
for(j in x){
l <- which(x == j)
mr <- x_mr[l]
d_2[mr] <- NA
d_2[mr] <- d_2[x[l]]
}
vars <- paste(c("dist_log_mr", x_mr), collapse=" + ")
form <- paste("y_inc_log","~",vars)
form2 <- stats::as.formula(form)
model.BVU <- stats::lm(form2, data = d_2)
# Return ---------------------------------------------------------------------
if(vce_robust == TRUE){
return.object.1 <- .robustsummary.lm(model.BVU, robust=TRUE)
return.object.1$call <- form2
return(return.object.1)}
if(vce_robust == FALSE){
return.object.1 <- .robustsummary.lm(model.BVU, robust=FALSE)
return.object.1$call <- form2
return(return.object.1)}
}
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