Tobit estimates gravity models in their additive form
by conducting a left-censored regression, which, after adding the
constant 1 to the dependent variable, utilizes log(1)=0
as the censoring value.
Tobit(y, dist, x, added_constant = 1, data, ...)name (type: character) of the dependent variable in the dataset
data, e.g. trade flows.
The number 1 is added and the transformed variable is logged and
taken as the dependent variable in the Tobit estimation with lower bound
equal to 0 as log(1)=0 represents the smallest flows
in the transformed variable.
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.
scalar (type: numeric); represents
the constant to be added to the dependent variable. The default value
is 1.
The minimum of log(y+added_constant) is taken as the
left boundary in the Tobit model.
In the often used case of added_constant=1, the
dependent variable is left-censored at value 0
as log(1)=0.
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 Tobit.
The function returns the summary of the estimated gravity model as a
censReg-object.
Tobit represents the left-censored Tobit (Tobin, 1958)
approach utilizing a known censoring threshold
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, in the execution of the function the number 1
is added to all flows and the log(flows+1) is
taken as the dependent variable.
The Tobit estimation is conducted using the censReg
function and setting the lower bound equal to 0 as
log(1)=0 represents the smallest flows in the transformed
variable.
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 more elaborate Tobit functions, see 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 or 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 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)
Tobit(y="flow", dist="distw", x=c("rta","lgdp_o","lgdp_d"),
added_constant = 1, data=Gravity_zeros)
# }
# NOT RUN {
# }
# NOT RUN {
# }
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