Fixed Effects estimates gravity models via
OLS and fixed effects for the countries of origin and destination.
These effects catch country specific effects.
Fixed_Effects(y, dist, fe = c("iso_o", "iso_d"), x, vce_robust = TRUE, data,
...)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.
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.
vector of names (type: character) of fixed effects.
The default is set to the unilateral identifiers
"iso_o" and "iso_d" for cross-sectional data.
When using panel data, interaction terms of the iso-codes and time
may be added in either fe or 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.
The fixed effects catch all unilateral effects. Therefore,
no other unilateral variables such as GDP can be
included as independent variables in the estimation.
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 equal the Stata results for
robust estimation.
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.
The time variable can be used as a single dependent variable or interaction
term with other variables such as country identifiers by inserting it into
x or fe.
See the references for more information on panel data.
additional arguments to be passed to Fixed Effects.
The function returns the summary of the estimated gravity model as an
lm-object.
Fixed Effects
To account for MR terms, Feenstra (2002) and Feenstra (2004) 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 MR terms are not estimated
explicitly. Nevertheless, Head and Mayer (2014) highlight the importance of
the use of fixed effects.
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.
Country specific fixed effects are considered by incorporating
"iso_o" and "iso_d" in fe.
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
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. 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 (see also the references
included in the descriptions of the different functions). 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 more information on fixed effects as well as informaton on gravity models, theoretical foundations and suitable estimation methods in general see
Anderson, J. E. (2010) <DOI:10.3386/w16576>
Head, K. and Mayer, T. (2014) <DOI:10.1016/B978-0-444-54314-1.00003-3>
as well as
Anderson, J. E. (1979) <DOI:10.12691/wjssh-2-2-5>
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>
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.
# NOT RUN {
data(Gravity)
Fixed_Effects(y="flow", dist="distw", fe=c("iso_o", "iso_d"), x=c("rta"),
vce_robust=TRUE, data=Gravity)
Fixed_Effects(y="flow", dist="distw", fe=c("iso_o", "iso_d"),
x=c("rta", "comcur", "contig"), vce_robust=FALSE, data=Gravity)
# }
# NOT RUN {
# }
Run the code above in your browser using DataLab