EK_Tobit estimates gravity models in their additive form
by conducting a censored regression.
It follows the Eaton and Kortum (2001) Tobit model where each country
is assigned specific ceonsoring bounds.
EK_Tobit(y, dist, x, vce_robust = TRUE, data, ...)name (type: character) of the dependent variable in the dataset
data, e.g. trade flows.
The variable is logged and then taken as the dependent variable in
the regression. 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.
name (type: character) of the distance variable in the dataset
data containing a measure of distance between all pairs of bilateral
partners. It is logged automatically when the function is executed.
vector of names (type: character) of those bilateral variables in
the dataset 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 variables such as country dummies or incomes can be added.
If unilateral metric variables such as GDPs should be used as independent
variables, those variables have to be logged first and the
logged variable can be used in x.
Interaction terms can be added.
robust (type: logic) determines whether a robust
variance-covariance matrix should be used. The default is set to TRUE.
If set TRUE the estimation results are consistent with the
Stata code provided at the website
Gravity Equations: Workhorse, Toolkit, and Cookbook
when choosing robust estimation.
name of the dataset to be used (type: character).
To estimate gravity equations, a square gravity dataset including bilateral
flows defined by the argument y, ISO-codes of type character
(called iso_o for the country of origin and iso_d for the
destination country), a distance measure defined by the argument dist
and other potential influences given as a vector in 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.
Zero trade flows are allowed.
additional arguments to be passed to EK_Tobit.
The function returns the summary of the estimated gravity model as a
survreg-object.
EK_Tobit represents the Eaton and Kortum (2001) Tobit model.
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.
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. Missing bilateral flows as well as incomplete rows should be excluded from the dataset. Zero trade flows are allowed.
EK_Tobit is designed to be consistent with the Stata code provided at
the website
Gravity Equations: Workhorse, Toolkit, and Cookbook
when choosing robust estimation.
Up to now, the function is designed for cross-sectional data,
but can be extended to panel data using the
survreg function.
For other Tobit functions, see Tobit
for a simple Tobit model where number 1 is added to all observations
and ET_Tobit for the Eaton and Tamura (1994)
threshold Tobit model where instead of simply adding number 1
to the data the threshold is estimated.
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>
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>
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.
Especially for Tobit models see
Tobin, J. (1958) <DOI:10.2307/1907382>
Eaton, J., & Tamura, A. (1994) <DOI:10.3386/w4758>
Eaton, J., & Kortum, S. (2001) <DOI:10.3386/w8070>.
See Carson, R. T., & Sun, Yixiao (2007) <DOI:10.1111/j.1368-423X.2007.00218.x> for the estimation of the threshold in a Tobit model.
See Gravity Equations: Workhorse, Toolkit, and Cookbook for gravity datasets and Stata code for estimating gravity models.
# NOT RUN {
# Example for data with zero trade flows
data(Gravity_zeros)
Gravity_zeros$lgdp_o <- log(Gravity_zeros$gdp_o)
Gravity_zeros$lgdp_d <- log(Gravity_zeros$gdp_d)
EK_Tobit(y="flow", dist="distw", x=c("rta","lgdp_o","lgdp_d"),
vce_robust=TRUE, data=Gravity_zeros)
EK_Tobit(y="flow", dist="distw", x=c("rta","iso_o","iso_d"),
vce_robust=TRUE, data=Gravity_zeros)
# }
# NOT RUN {
# }
# NOT RUN {
# }
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