SILS: Structural Iterated Least Squares, SILS
In jpburgard/gravity: Estimation Methods for Gravity Models

Description Usage Arguments Details Value References See Also Examples

SILS estimates gravity models via Structural Iterated Least Squares and an explicit inclusion of the Multilateral Resistance terms.

1 2	SILS(y, dist, x, inc_o, inc_d, maxloop = 50, maxloop2 = 50, dec_places = 4, vce_robust = TRUE, verbose = FALSE, data, ...)

`y`	name (type: character) of the dependent variable in the dataset `data`, e.g. trade flows. This 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. The transformed variable is then used as the dependent variable 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.
`inc_o`	variable name (type: character) of the income of the country of origin in the dataset `data`. The dependent variable `y` is divided by the product of the incomes `inc_d` and `inc_o`.
`inc_d`	variable name (type: character) of the income of the country of destination in the dataset `data`. The dependent variable `y` is divided by the product of the incomes `inc_d` and `inc_o`.
`maxloop`	maximum number of outer loop iterations. The default is set to 50. There will be a warning if the iterations did not converge.
`maxloop2`	maximum number of inner loop iterations. The default is set to 50. There will be a warning if the iterations did not converge.
`dec_places`	number of decimal places that should not change after a new iteration for the estimation to stop. The default is set to 4.
`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.
`verbose`	(type: logic) determines whether the estimated coefficients of each iteration should be printed in the console. The default is set to `FALSE`.
`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. As, to our knowledge at the moment, there is no explicit literature covering the estimation of a gravity equation by `SILS` using panel data, cross-sectional data should be used.
`...`	additional arguments to be passed to functions used by `SILS`.

SILS is an estimation method for gravity models developed by Head and Mayer (2014) (see the references for more information). 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. The function SILS utilizes the relationship between the Multilateral Resistance terms and the transaction costs. The parameters are estimated by an iterative procedure. The function executes loops until the parameters stop changing significantly.

SILS is designed to be consistent with the Stata code provided at the website Gravity Equations: Workhorse, Toolkit, and Cookbook when choosing robust estimation. As, to our knowledge at the moment, there is no explicit literature covering the estimation of a gravity equation by SILS using panel data, we do not recommend to apply this method in this case.

The function returns the summary of the estimated gravity model as an lm-object. It furthermore returns the resulting coefficients for each iteration.

For information on SILS as well as more information on gravity models, theoretical foundations and suitable estimation methods in general see

Head, K. and Mayer, T. (2014) <DOI:10.1016/B978-0-444-54314-1.00003-3>

and

Anderson, J. E. and van Wincoop, E. (2003) <DOI:10.3386/w8079>

as well as

Anderson, J. E. (1979) <DOI:10.12691/wjssh-2-2-5>

Anderson, J. E. (2010) <DOI:10.3386/w16576>

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>

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.

lm, coeftest, vcovHC

## Not run:  
data(Gravity_no_zeros)

SILS(y="flow", dist="distw", x=c("rta"), inc_o="gdp_o", inc_d="gdp_d", 
maxloop=50, maxloop2=50, dec_places=4, vce_robust=TRUE, verbose=FALSE, 
data=Gravity_no_zeros)

SILS(y="flow", dist="distw", x=c("rta", "comcur", "contig"), 
inc_o="gdp_o", inc_d="gdp_d", maxloop=50, maxloop2=50, dec_places=4, 
vce_robust=TRUE, verbose=TRUE, data=Gravity_no_zeros)

## End(Not run)