OLS estimates gravity models in their traditional form
via Ordinary Least Squares (OLS). It does not consider Multilateral
Resistance terms.
OLS(y, dist, x, inc_d, inc_o, uie = FALSE, 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.
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.
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 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.
Interactions terms can be added.
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.
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.
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.
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. See the references for more information on panel data.
additional arguments to be passed to OLS.
The function returns the summary of the estimated gravity model as an
lm-object.
OLS estimates gravity models in their traditional, additive,
form via Ordinary Least Squares using the lm function.
MR 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. 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 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.
# NOT RUN {
data(Gravity)
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)
OLS(y="flow", dist="distw", x=c("rta", "comcur", "contig"), inc_o="gdp_o",
inc_d="gdp_d", uie=TRUE, vce_robust=FALSE, data=Gravity)
# }
# NOT RUN {
# }
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