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

Description Usage Arguments Details Value References See Also Examples

Tetrads estimates gravity models by taking the ratio of the ratio of flows.

1 2	Tetrads(y, dist, x, k = "USA", ell = "JPN", multiway_vcov = TRUE, data, ...)

`y`	name (type: character) of the dependent variable in the dataset `data`, e.g. trade flows. It is logged and taken 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 effects drop as the ratio of ratios is taken.
`k`	reference importing country, default is set to `"USA"`.
`ell`	reference exporting country, default is set to `"JPN"`.
`multiway_vcov`	(type: logic) optional; determines whether a function implementing Cameron, Gelbach, & Miller (2011) multi-way clustering of variance-covariance matrices in the package `multiway_vcov` is used for the estimation. In case `multiway_vcov=TRUE`, the `cluster.vcov` function is used. The default value is set to `TRUE`.
`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 functions used by `Tetrads`.

Tetrads is an estimation method for gravity models developed by Head et al. (2010) (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 Tetrads utilizes the multiplicative form of the gravity equation. After choosing a reference importer k and exporter ell one can eliminate importer and exporter fixed effects by taking the ratio of ratios. Only those exporters trading with the reference importer and importers trading with the reference exporter will remain for the estimation. Therefore, reference countries should preferably be countries which trade with every other country in the dataset. After restircting the data in this way, Tetrads estimates the gravity equation in its additive form by OLS. As, by taking the ratio of ratios, all monadic effects diminish, no unilateral variables such as GDP can be included as independent variables.

Tetrads estimation can be used for both, cross-sectional as well as panel data. Nonetheless, the function is designed to be consistent with the Stata code for cross-sectional data provided on the website Gravity Equations: Workhorse, Toolkit, and Cookbook when choosing robust estimation. The function Tetrads was therefore tested for cross-sectional data. If Tetrads is used for panel data, the user may has to drop distance as an independent variable as time-invariant effects drop. For applying Tetrads to panel data see Head, Mayer and Ries (2010).

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

For information on Tetrads see

Cameron, A. C., Gelbach, J. B., and Miller, D. L. (2011) <DOI:10.3386/t0327>

Head, K., Mayer, T., & Ries, J. (2010) <DOI:10.1016/j.jinteco.2010.01.002>

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. 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, cluster.vcov

## Not run: 
data(Gravity_no_zeros)

Tetrads(y="flow", dist="distw", x=c("rta"), k="USA", ell="JPN", 
multiway_vcov=TRUE, data=Gravity_no_zeros)

Tetrads(y="flow", dist="distw", x=c("rta", "comcur", "contig"), 
k="USA", ell="JPN", multiway_vcov=FALSE, data=Gravity_no_zeros)

## End(Not run)