gravity (version 0.8.5)

nls: Non-linear Least Squares (NLS)

Description

nls estimates gravity models in their multiplicative form via Nonlinear Least Squares.

Usage

nls(dependent_variable, regressors, robust = TRUE, data, ...)

Arguments

dependent_variable

name (type: character) of the dependent variable in the dataset data (e.g. trade flows).

regressors

name (type: character) of the regressors to include in the model.

Include the distance variable in the dataset data containing a measure of distance between all pairs of bilateral partners and bilateral variables that should be taken as the independent variables in the estimation.

The distance is logged automatically when the function is executed.

Unilateral metric variables such as GDPs can be added but those variables have to be logged first.

Interaction terms can be added.

Write this argument as c(distance, contiguity, common curreny, ...).

robust

robust (type: logical) determines whether a robust variance-covariance matrix should be used. By default is set to TRUE.

data

name of the dataset to be used (type: character).

To estimate gravity equations you need a square dataset including bilateral flows defined by the argument dependent_variable, ISO codes or similar of type character (e.g. iso_o for the country of origin and iso_d for the destination country), a distance measure defined by the argument distance and other potential influences (e.g. contiguity and common currency) given as a vector in regressors are required.

All dummy variables should be of type numeric (0/1).

Make sure the ISO codes are of type "character".

If an independent variable is defined as a ratio, it should be logged.

The user should perform some data cleaning beforehand to remove observations that contain entries that can distort estimates.

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 function allows zero flows but will remove zero distances.

...

additional arguments to be passed to functions used by nls.

Value

The function returns the summary of the estimated gravity model similar to a glm-object.

Details

nls is an estimation method for gravity models belonging to generalized linear models.

It is estimated via glm using the gaussian distribution and a log-link.

As the method may not lead to convergence when poor starting values are used, the linear predictions, fitted values, and estimated coefficients resulting from a ppml estimation are used for the arguments etastart, mustart, and start.

For similar functions, utilizing the multiplicative form via the log-link, but different distributions, see ppml, gpml, and nbpml.

nls estimation can be used for both, cross-sectional as well as panel data.

It is up to the user to ensure that the functions can be applied to panel data.

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 a comprehensive overview of gravity models for panel data see Egger2003;textualgravity, Gomez-Herrera2013;textualgravity and Head2010;textualgravity as well as the references therein.

References

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

Anderson1979gravity

Anderson2001gravity

Anderson2010gravity

Baier2009gravity

Baier2010gravity

Head2010gravity

Head2014gravity

Santos2006gravity

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

Egger2003gravity

Gomez-Herrera2013gravity

and the references therein.

See Also

glm, coeftest, vcovHC

Examples

# NOT RUN {
# Example for data without zero trade flows
data(gravity_no_zeros)

gravity_no_zeros <- gravity_no_zeros %>%
   mutate(
     lgdp_o = log(gdp_o),
     lgdp_d = log(gdp_d)
   )

nls(dependent_variable = "flow", regressors = c("distw", "rta", "lgdp_o", "lgdp_d"),
robust = TRUE, data = gravity_no_zeros)
# }
# NOT RUN {
# }
# NOT RUN {
# }