OLS: OLS
In jpburgard/gravity: Estimation Methods for Gravity Models

Description Usage Arguments Details Value References See Also Examples

OLS estimates gravity models in their traditional form via Ordinary Least Squares (OLS). It does not consider Multilateral Resistance terms.

1	OLS(y, dist, x, inc_d, inc_o, uie = FALSE, vce_robust = TRUE, data, ...)

`y`	name (type: character) of the dependent variable in the dataset `data`, e.g. trade flows. This variable is logged and taken as the dependent variable in the estimation. If `uie=TRUE` the dependent variable is divided by the product of unilateral incomes `inc_o` and `inc_d`, e.g. GDPs or GNPs of the countries of interest and logged afterwards. If `uie=FALSE` the dependent variable is logged directly. The transformed variable is then used as the dependent variable and the logged income variables are used as independent variables in the estimation.
`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 metric variables such as GDPs should be inserted via the arguments `inc_o` for the country of origin and `inc_d` for the country of destination. Interaction terms can be added.
`inc_d`	variable name (type: character) of the income of the country of destination in the dataset `data`. If `uie=TRUE`, the dependent variable `y` is divided by the product of the incomes `inc_d` and `inc_o`. If `uie=FALSE`, the incomes are logged and taken as independent variables in the estimation. If one wants to use more than one unilateral variable, e.g. GDP and population, those variables have to be merged into one variable, e.g. GDP per capita, which can be inserted into `inc_d`.
`inc_o`	variable name (type: character) of the income of the country of origin in the dataset `data`. If `uie=TRUE`, the dependent variable `y` is divided by the product of the incomes `inc_d` and `inc_o`. If `uie=FALSE`, the incomes are logged and taken as independent variables in the estimation. If one wants to use more than one unilateral variable, e.g. GDP and population, those variables have to be merged into one variable, e.g. GDP per capita, which can be inserted into `inc_o`.
`uie`	Unitary Income Elasticities (type: logic) determines whether the parameters are to be estimated assuming unitary income elasticities. The default value is set to `FALSE`. If `uie` is set `TRUE`, the flows in the dependent variable `y` are divided by the product of the country pairs' incomes before the estimation. If `uie` is set to `FALSE`, the income variables are logged and taken as independent variables in the estimation. The variable names for the incomes should be inserted into `inc_o` for the country of origin and into `inc_d` for destination country.
`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. Furthermore, flows equal to zero should be excluded as the gravity equation is estimated in its additive form. When using panel data, a variable for the time may be included in the dataset. Note that the variable for the time dimension should be of type: factor. See the references for more information on panel data.
`...`	additional arguments to be passed to `OLS`.

OLS estimates gravity models in their traditional, additive, form via Ordinary Least Squares using the lm function. Multilateral Resistance terms are not considered by this function. 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. Make sure the ISO-codes are of type "character". Missing bilateral flows as well as incomplete rows should be excluded from the dataset. Furthermore, flows equal to zero should be excluded as the gravity equation is estimated in its additive form. As the coefficients for the country's incomes were often found to be close to unitary and unitary income elasticities are in line with some theoretical foundations on international trade, it is sometimes assumed that the income elasticities are equal to unity. In order to allow for the estimation with and without the assumption of unitary income elasticities, the option uie is built into OLS with the default set to FALSE.

OLS estimation can be used for both, cross-sectional and panel data. Nonetheless, the function is designed to be consistent with the Stata code for cross-sectional data provided at the website Gravity Equations: Workhorse, Toolkit, and Cookbook when choosing robust estimation. The function OLS was therefore tested for cross-sectional data. For the use with panel data no tests were performed. Therefore, it is up to the user to ensure that the functions can be applied to panel data. Depending on the panel dataset and the variables - specifically the type of fixed effects - included in the model, it may easily occur that the model is not computable. Also, note that by including bilateral fixed effects such as country-pair effects, the coefficients of time-invariant observables such as distance can no longer be estimated. Depending on the specific model, the code of the respective function may has to be changed in order to exclude the distance variable from the estimation. At the very least, the user should take special care with respect to the meaning of the estimated coefficients and variances as well as the decision about which effects to include in the estimation. When using panel data, the parameter and variance estimation of the models may have to be changed accordingly. For a comprehensive overview of gravity models for panel data see Egger and Pfaffermayr (2003), Gomez-Herrera (2013) and Head, Mayer and Ries (2010) as well as the references therein.

The function returns the summary of the estimated gravity model as an lm-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.

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

Egger, P., & Pfaffermayr, M. (2003) <DOI:10.1007/s001810200146>

Gomez-Herrera, E. (2013) <DOI:10.1007/s00181-012-0576-2>

and the references therein.

lm, coeftest, vcovHC

## Not run: 
data(Gravity_no_zeros)

OLS(y="flow", dist="distw", x=c("rta", "contig", "comcur"), 
inc_o="gdp_o", inc_d="gdp_d", uie=FALSE, 
vce_robust=TRUE, data=Gravity_no_zeros)

OLS(y="flow", dist="distw", x=c("rta", "comcur", "contig"), 
inc_o="gdp_o", inc_d="gdp_d", uie=TRUE, 
vce_robust=TRUE, data=Gravity_no_zeros)

## End(Not run)