EK_Tobit: Eaton and Kortum (2001) Tobit model, EK_Tobit
In jpburgard/gravity: Estimation Methods for Gravity Models

Description Usage Arguments Details Value References See Also Examples

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.

1	EK_Tobit(y, dist, x, vce_robust = TRUE, data, ...)

`y`	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.
`dist`	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.
`x`	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.
`vce_robust`	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.
`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 `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`.

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.

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

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.

Surv, survreg

## 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)

## End(Not run)