ek_tobit: Eaton2001;textualgravity Tobit model (EK Tobit)

Description

ek_tobit estimates gravity models in their additive form by conducting a censored regression.

Usage

ek_tobit(dependent_variable, distance, additional_regressors = NULL,
  code_destination, robust = FALSE, data, ...)

Arguments

dependent_variable

(Type: character) name of the dependent variable. This variable is logged and then used as the dependent variable in the estimation. As the log of zero is not defined, all flows equal to zero are replaced by a left open interval with the logged minimum trade flow of the respective importing country as right border.

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.

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 GDP should be inserted via the arguments income_origin and income_destination.

Write this argument as c(contiguity, common currency, ...). By default this is set to NULL.

code_destination

(Type: character) country of destination variable (e.g. country ISO-3 codes). The variables are grouped using this parameter.

robust

(Type: logical) whether robust fitting should be used. By default this is set to FALSE.

data

(Type: data.frame) the dataset to be used.

...

Additional arguments to be passed to the function.

Value

The function returns the summary of the estimated gravity model as a survreg-object.

Details

ek_tobit represents the Eaton2001;textualgravity Tobit model where each country is assigned specific censoring bounds.

When taking the log of the gravity equation flows equal to zero constitute a problem as their log is not defined. Therefore, in ek_tobit all values of the dependent variable are redefined as intervals.

The positive observations have both interval bounds equal to their original value.

For zero flows the interval is left open. The right border of the interval is set to the log of the minimum positive trade flow of the respective importing country.

The defined data object of class Surv is then inserted in survreg for the parameter estimation.

ek_tobit is designed to be consistent with the Stata code provided at Gravity Equations: Workhorse, Toolkit, and Cookbook when choosing robust estimation.

For other Tobit functions, see tobit for a simple Tobit model where number 1 is added to all observations and et_tobit for the Eaton1995;textualgravity threshold Tobit model where instead of simply adding number 1 to the data the threshold is estimated.

The function is designed for cross-sectional data, but can be extended to panel data using the survreg function.

References

For more information on gravity models, theoretical foundations and estimation methods in general see

Anderson1979gravity

Anderson2001gravity

Anderson2010gravity

Baier2009gravity

Baier2010gravity

Feenstra2002gravity

Head2010gravity

Head2014gravity

Santos2006gravity

and the citations therein.

See Gravity Equations: Workhorse, Toolkit, and Cookbook for gravity datasets and Stata code for estimating gravity models.

For estimating gravity equations using panel data see

Egger2003gravity

Gomez-Herrera2013gravity

and the references therein.

Examples

Run this code

# NOT RUN {
# 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(
    flow = ifelse(flow < 5, 0, flow), # cutoff for testing purposes
    lgdp_o = log(gdp_o),
    lgdp_d = log(gdp_d)
  )

fit <- ek_tobit(
  dependent_variable = "flow",
  distance = "distw",
  additional_regressors = c("distw", "rta", "lgdp_o", "lgdp_d"),
  code_destination = "iso_d",
  robust = FALSE,
  data = grav_small
)
# }

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