NBPML: Negative Binomial Pseudo Maximum Likelihood, NBPML
In jpburgard/gravity: Estimation Methods for Gravity Models

Description Usage Arguments Details Value References See Also Examples

NBPML estimates gravity models in their multiplicative form via Negative Binomial Pseudo Maximum Likelihood.

1	NBPML(y, dist, x, vce_robust = TRUE, data, ...)

`y`	name (type: character) of the dependent variable in the dataset `data`, e.g. trade flows.
`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 variables such as country dummies or incomes can be added. If unilateral metric variables such as GDPs should be used as independent variables, those variables have to be logged first and the logged variable can be used in `x`. Interaction terms can be added.
`vce_robust`	robust (type: logic) determines whether a robust variance-covariance matrix should be used. The default 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. Zero trade flows are allowed. 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 `NBPML`.

NBPML is an estimation method for gravity models belonging to generalized linear models. It is estimated via glm.nb using the negative binomial distribution and a log-link. 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. Zero trade flows are allowed. For similar functions, utilizing the multiplicative form via the log-link, but different distributions, see PPML, GPML, and NLS.

NBPML 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 Egger and Pfaffermayr (2003), Gomez-Herrera (2013) and Head, Mayer and Ries (2010) as well as the references therein.

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

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.

glm.nb, coeftest, vcovHC

## Not run: 
# Example for data with zero trade flows
data(Gravity_zeros)

NBPML(y="flow", dist="distw", x=c("rta","iso_o","iso_d"), 
vce_robust=TRUE, data=Gravity_zeros)

# Example for data without zero trade flows
data(Gravity_no_zeros)

Gravity_no_zeros$lgdp_o <- log(Gravity_no_zeros$gdp_o)
Gravity_no_zeros$lgdp_d <- log(Gravity_no_zeros$gdp_d)

NBPML(y="flow", dist="distw", x=c("rta","lgdp_o","lgdp_d"), 
vce_robust=TRUE, data=Gravity_no_zeros)

## End(Not run)