fixed_effects estimates gravity models via OLS and fixed effects for the countries of origin and destination.

fixed_effects(dependent_variable, distance, additional_regressors = NULL,
  code_origin, code_destination, robust = FALSE, data, ...)



(Type: character) name of the dependent variable. This variable is logged and then used as the dependent variable in the estimation.


(Type: character) name of the distance variable that should be taken as the key independent variable in the estimation. The distance is logged automatically when the function is executed.


(Type: character) names of the additional regressors to include in the model (e.g. a dummy variable to indicate contiguity). Unilateral metric variables such as GDPs can be added but those variables have to be logged first.

Write this argument as c(contiguity, common currency, ...). By default this is set to NULL.


(Type: character) country of origin variable (e.g. ISO-3 country codes). The variables are grouped using this parameter.


(Type: character) country of destination variable (e.g. country ISO-3 codes). The variables are grouped using this parameter.


(Type: logical) whether robust fitting should be used. By default this is set to FALSE.


(Type: data.frame) the dataset to be used.


Additional arguments to be passed to the function.


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


To account for MR terms, Feenstra (2002) and Feenstra (2015) propose to use importer and exporter fixed effects. Due to the use of these effects, all unilateral influences such as GDPs can no longer be estimated.

A disadvantage of the use of fixed_effects is that, when applied to panel data, the number of country-year or country-pair fixed effects can be too high for estimation. In addition, no comparative statistics are possible with fixed_effects as the Multilateral Resistance terms are not estimated explicitly. Nevertheless, Head and Mayer (2014) highlight the importance of the use of fixed effects.

By including country specific fixed effects, all monadic effects are captured, including Multilateral Resistance terms. Therefore, no other unilateral variables such as GDP can be included as independent variables in the estimation.

fixed_effects 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 at the website Gravity Equations: Workhorse, Toolkit, and Cookbook when choosing robust estimation.

The function fixed_effects was therefore tested for cross-sectional data. Its up to the user to ensure that the functions can be applied to panel data.

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 might have 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) , Gómez-Herrera (2013) and Head et al. (2010) as well as the references therein.


For more information on gravity models, theoretical foundations and estimation methods in general see

Anderson JE (1979). “A Theoretical Foundation for the Gravity Equation.” The American Economic Review, 69(1), 106--116. ISSN 00028282.

Anderson JE, van Wincoop E (2001). “Gravity with Gravitas: A Solution to the Border Puzzle.” Technical Report 8079, National Bureau of Economic Research. doi: 10.3386/w8079 .

Anderson JE (2010). “The Gravity Model.” Technical Report 16576, National Bureau of Economic Research. doi: 10.3386/w16576 .

Baier SL, Bergstrand JH (2009). “Bonus vetus OLS: A simple method for approximating international trade-cost effects using the gravity equation.” Journal of International Economics, 77(1), 77 - 85. ISSN 0022-1996, doi: 10.1016/j.jinteco.2008.10.004 .

Baier SL, Bergstrand JH (2010). “The Gravity Model in International Trade: Advances and Applications.” In van Bergeijk PAG, Brakman S (eds.), chapter 4. Cambridge University Press. doi: 10.1017/CBO9780511762109 .

Feenstra RC (2002). “Border effects and the gravity equation: consistent methods for estimation.” Scottish Journal of Political Economy, 49(5), 491--506.

Head K, Mayer T, Ries J (2010). “The erosion of colonial trade linkages after independence.” Journal of International Economics, 81(1), 1 - 14. ISSN 0022-1996, doi: 10.1016/j.jinteco.2010.01.002 .

Head K, Mayer T (2014). “Chapter 3 - Gravity Equations: Workhorse,Toolkit, and Cookbook.” In Gopinath G, Helpman E, Rogoff K (eds.), Handbook of International Economics, volume 4 of Handbook of International Economics, 131 - 195. Elsevier. doi: 10.1016/B978-0-444-54314-1.00003-3 .

Silva JMCS, Tenreyro S (2006). “The Log of Gravity.” The Review of Economics and Statistics, 88(4), 641-658. 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). “The proper panel econometric specification of the gravity equation: A three-way model with bilateral interaction effects.” Empirical Economics, 28(3), 571--580. ISSN 1435-8921, doi: 10.1007/s001810200146 .

Gómez-Herrera E (2013). “Comparing alternative methods to estimate gravity models of bilateral trade.” Empirical Economics, 44(3), 1087--1111. ISSN 1435-8921, doi: 10.1007/s00181-012-0576-2 .

and the references therein.

See also


# Example for CRAN checks: # Executable in < 5 sec library(dplyr) data("gravity_no_zeros") # Choose 5 countries for testing countries_chosen <- c("AUS", "CHN", "GBR", "BRA", "CAN") grav_small <- filter(gravity_no_zeros, iso_o %in% countries_chosen) fit <- fixed_effects( dependent_variable = "flow", distance = "distw", additional_regressors = c("rta", "comcur", "contig"), code_origin = "iso_o", code_destination = "iso_d", robust = FALSE, data = grav_small )