ET_Tobit estimates gravity models in their additive form
by conducting a left-censored regression.
It follows the Eaton and Tamura (1994) Tobit model,
also called threshold Tobit model, where,
instead of adding number 1 to the dependent variable as done
in Tobit, the constant added to the
data is estimated and interpreted as a threshold.
For estimating this threshold, we follow Carson and Sun (2007).
ET_Tobit(y, dist, x, data, ...)name (type: character) of the dependent variable in the dataset
data, e.g. trade flows.
Following Carson and Sun (2007), the smallest positive flow value is
used as an estimate of the threshold.
It is added to y, the transformed variable is
logged and taken as the dependent variable in the Tobit estimation with
lower bound equal to the log of the smallest possible flow value.
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.
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 ET_Tobit.
The function returns the summary of the estimated gravity model as a
censReg-object.
ET_Tobit represents the Eaton and Tamura (1994) Tobit model
which is often used when several gravity models are compared.
When taking the log of the gravity equation flows equal to zero
constitute a problem as their log is not defined.
Therefore, a constant is added to the flows.
This constant, opposed to Tobit, is estimated.
Compared to the usual ET-Tobit approaches, in this package, the estimation
of the threshold is done before the other parameters are estimated.
We follow Carson and Sun (2007), who show that taking the minimum
positive flow value as an estimate of the threshold is super-consistent and that
using this threshold estimate ensures that the parameter MLE
are asymptotically normal with the asymptotic variance
identical to the variance achieved when the threshold is known.
Hence, first the threshold is estimated as the minimum positive flow.
This threshold is added to the flow variable. It is logged
afterwards and taken as the dependent variable.
The Tobit estimation is then conducted using the
censReg function and setting the lower bound
equal to the log of the minimum positive flow value which was added to all
observations.
A Tobit regression represents a combination of a binary and a
linear regression.
This procedure has to be taken into consideration when
interpreting the estimated coefficients.
The marginal effects of an explanatory variable on the expected value of
the dependent variable equals the product of both the probability of the
latent variable exceeding the threshold and the marginal effect of the
explanatory variable of the expected value of the latent variable.
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.
Up to now, the function is designed for cross-sectional data,
but can be easily extended to panel data using the
censReg function.
A robust estimations is not implemented to the present
as the censReg function is not
compatible with the vcovHC function.
For a more elaborate Tobit function, see EK_Tobit
for the
Eaton and Kortum (2001) Tobit model where each zero trade volume
is assigned a country specific interval with the upper
bound equal to the minimum positive trade level of the respective
importing country.
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)
ET_Tobit(y="flow", dist="distw", x=c("rta","lgdp_o","lgdp_d"),
data=Gravity_zeros)
# }
# NOT RUN {
# }
# NOT RUN {
# }
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