@incollection{Head2014,
 title = "Chapter 3 - Gravity Equations: Workhorse,Toolkit, and Cookbook",
 editor = "Gita Gopinath and Elhanan Helpman and Kenneth Rogoff",
 series = "Handbook of International Economics",
 publisher = "Elsevier",
 volume = "4",
 pages = "131 - 195",
 year = "2014",
 booktitle = "Handbook of International Economics",
 issn = "1573-4404",
 doi = "10.1016/B978-0-444-54314-1.00003-3",
 author = "Keith Head and Thierry Mayer",
 keywords = "Bilateral trade, Heterogeneous firms, Distance, Borders, Trade cost elasticity, Poisson"
}

@Article{Egger2003,
 author = "Egger, Peter and Pfaffermayr, Michael",
 title = "The proper panel econometric specification of the gravity equation: A three-way model with bilateral interaction effects",
 journal = "Empirical Economics",
 year = "2003",
 month = "Jul",
 day = "01",
 volume = "28",
 number = "3",
 pages = "571--580",
 abstract = "We argue that the proper specification of a panel gravity model should include main (exporter, importer, and time) as well as time invariant exporter-by-importer (bilateral) interaction effects. In a panel of 11 APEC countries, the latter are highly significant and account for the largest part of variation.",
 issn = "1435-8921",
 doi = "10.1007/s001810200146"
}

@Article{Gomez-Herrera2013,
 author = "Gómez-Herrera, Estrella",
 title = "Comparing alternative methods to estimate gravity models of bilateral trade",
 journal = "Empirical Economics",
 year = "2013",
 month = "Jun",
 day = "01",
 volume = "44",
 number = "3",
 pages = "1087--1111",
 abstract = "The gravity equation has been traditionally used to predict trade flows across countries. However, several problems related with its empirical application still remain unsolved. The unobserved heterogeneity, the presence of heteroskedasticity in trade data or the existence of zero flows, which make the estimation of the logarithm unfeasible, are some of them. This paper provides a survey of the most recent literature concerning the specification and estimation methods of this equation. For a dataset covering 80{\%} of world trade, the most widely extended estimators are compared, showing that the Heckman sample selection model performs better overall for the specification of gravity equation selected.",
 issn="1435-8921",
 doi="10.1007/s00181-012-0576-2"
}

@article{Head2010,
 title = "The erosion of colonial trade linkages after independence",
 journal = "Journal of International Economics",
 volume = "81",
 number = "1",
 pages = "1 - 14",
 year = "2010",
 issn = "0022-1996",
 doi = "10.1016/j.jinteco.2010.01.002",
 author = "Keith Head and Thierry Mayer and John Ries",
 keywords = "Trade, Gravity, Colonies"
}

@article{Santos2006,
 author = "J. M. C. Santos Silva and Silvana Tenreyro",
 title = "The Log of Gravity",
 journal = "The Review of Economics and Statistics",
 volume = "88",
 number = "4",
 pages = "641-658",
 year = "2006",
 doi = "10.1162/rest.88.4.641",
 abstract = "Abstract Although economists have long been aware of Jensen's inequality, many econometric applications have neglected an important implication of it: under heteroskedasticity, the parameters of log-linearized models estimated by OLS lead to biased estimates of the true elasticities. We explain why this problem arises and propose an appropriate estimator. Our criticism of conventional practices and the proposed solution extend to a broad range of applications where log-linearized equations are estimated. We develop the argument using one particular illustration, the gravity equation for trade. We find significant differences between estimates obtained with the proposed estimator and those obtained with the traditional method."
}

@techreport{Anderson2001,
 title = "Gravity with Gravitas: A Solution to the Border Puzzle",
 author = "James E. Anderson and Eric van Wincoop",
 institution = "National Bureau of Economic Research",
 type = "Working Paper",
 series = "Working Paper Series",
 number = "8079",
 year = "2001",
 month = "January",
 doi = "10.3386/w8079",
 abstract = "The gravity model has been widely used to infer substantial trade flow effects of institutions such as customs unions and exchange rate mechanisms. McCallum [1995] found that the US-Canada border led to trade between provinces that is a factor 22 (2,200{\%}) times trade between states and provinces, a spectacular puzzle in light of the low formal barriers on this border. We show that the gravity model usually estimated does not correspond to the theory behind it. We solve the 'border puzzle' by applying the theory seriously. We find that national borders reduce trade between the US and Canada by about 44{\%}, while reducing trade among other industrialized countries by about 30{\%}. McCallum's spectacular headline number is the result of a combination of omitted variables bias and the small size of the Canadian economy. Within-Canada trade rises by a factor 6 due to the border. In contrast, within-US trade rises 25{\%}.",
}

@techreport{Anderson2010,
 title = "The Gravity Model",
 author = "James E. Anderson",
 institution = "National Bureau of Economic Research",
 type = "Working Paper",
 series = "Working Paper Series",
 number = "16576",
 year = "2010",
 month = "December",
 doi = "10.3386/w16576",
 abstract = "The gravity model in economics was until relatively recently an intellectual orphan, unconnected to the rich family of economic theory. This review is a tale of the orphan's reunion with its heritage and the benefits that have flowed from it. Gravity has long been one of the most successful empirical models in economics. Incorporating the theoretical foundations of gravity into recent practice has led to a richer and more accurate estimation and interpretation of the spatial relations described by gravity. Recent developments are reviewed here and suggestions are made for promising future research."
}

@article{Anderson1979,
 ISSN = "00028282",
 author = "James E. Anderson",
 journal = "The American Economic Review",
 number = "1",
 pages = "106--116",
 publisher = "American Economic Association",
 title = "A Theoretical Foundation for the Gravity Equation",
 volume = "69",
 year = "1979"
}

@article{Baier2009,
 title = "Bonus vetus OLS: A simple method for approximating international trade-cost effects using the gravity equation",
 journal = "Journal of International Economics",
 volume = "77",
 number = "1",
 pages = "77 - 85",
 year = "2009",
 issn = "0022-1996",
 doi = "10.1016/j.jinteco.2008.10.004",
 author = "Scott L. Baier and Jeffrey H. Bergstrand",
 keywords = "International trade, Gravity equation, Multilateral resistance terms, Border barriers"
}

@inbook{Baier2010, 
 place = "Cambridge",
 title = "The Gravity Model in International Trade: Advances and Applications",
 author = "Baier, S. L. and Bergstrand, J. H.",
 editor= "van Bergeijk, Peter A. G. and Brakman, StevenEditors",
 chapter = "4",
 DOI = "10.1017/CBO9780511762109",
 publisher = "Cambridge University Press",
 year = "2010"
}

@article{Tobin1958,
 ISSN = "14680262",
 author = "James Tobin",
 journal = "Econometrica",
 number = "1",
 pages = "24--36",
 publisher = "Econometric Society",
 title = "Estimation of Relationships for Limited Dependent Variables",
 volume = "26",
 year = "1958"
}

@techreport{Eaton1995,
 title = "Bilateralism and Regionalism in Japanese and U.S. Trade and Direct Foreign Investment Patterns",
 author = "Jonathan Eaton and Akiko Tamura",
 institution = "National Bureau of Economic Research",
 type = "Working Paper",
 series = "Working Paper Series",
 Number = "4758",
 year = "1995",
 month = "March",
 doi = "10.3386/w4758",
 abstract = "We apply a modified 'gravity model' incorporating measures of factor endowments to analyze Japanese and U.S. bilateral trade flows and direct foreign investment positions with a sample of around 100 countries for the period 1985-1990. Country features that our analysis takes into account are population, income, the land-labor ratio, the average level of education, and region. We find that features of a country associated with more trade with either Japan or the United States also tend to be associated with more DFI from Japan or the United States. U.S. economic relations with Japan and Western Europe provide an important exception. Despite U.S. concern about its trade deficit with Japan, we find Japan to be much more open to the United States, not only as a source of imports, but also as a destination for U.S. exports than most countries in Western Europe. Taking other factors into account, however, Western Europe is more open to U.S. direct foreign investment. We also find that a country's level of education tends to increase significantly U.S. interaction of all types with that country, even after correcting for per capita income. Education does not play a significant role in Japanese trade patterns. As factor endowments theory would predict, the United States tends to trade more with densely-populated countries, while Japan tends to import more from sparsely-populated countries. There is a substantial degree of 'bilateralism' in Japanese and U.S. economic relationships in that the residual correlation among exports, imports, and outward direct foreign investment is much larger than would be the case if these magnitudes were independent across countries."
}

@techreport{Eaton2001,
 title = "Trade in Capital Goods",
 author = "Jonathan Eaton and Samuel Kortum",
 institution = "National Bureau of Economic Research",
 type = "Working Paper",
 series = "Working Paper Series",
 number = "8070",
 year = "2001",
 month = "January",
 doi = "10.3386/w8070",
 URL = "http://www.nber.org/papers/w8070",
 abstract = "Innovative activity is highly concentrated in a handful of advanced countries. These same countries are also the major exporters of capital goods to the rest of the world. We develop a model of trade in capital goods to assess its role spreading the benefits of technological advances. Applying the model to data on production and bilateral trade in capital equipment, we estimate the barriers to trade in equipment. These estimates imply substantial differences in equipment prices across countries. We attribute about 25 percent of cross-country productivity differences to variation in the relative price of equipment, about half of which we ascribe to barriers to trade in equipment.",
}

@article{Carson2007,
 author = "Carson, Richard T. and Yixiao Sun",
 title = "The Tobit model with a non-zero threshold",
 journal = "The Econometrics Journal",
 year = "2007",
 volume = "10",
 number = "3",
 pages = "488-502",
 keywords = "Exponential distribution, Maximum likelihood, Order statistic, Threshold determination",
 doi = "10.1111/j.1368-423X.2007.00218.x",
 abstract = "Summary The standard Tobit maximum likelihood estimator under zero censoring threshold produces inconsistent parameter estimates, when the constant censoring threshold γ is non‐zero and unknown. Unfortunately, the recording of a zero rather than the actual censoring threshold value is typical of economic data. Non‐trivial minimum purchase prices for most goods, fixed cost for doing business or trading, social customs such as those involving charitable donations, and informal administrative recording practices represent common examples of non‐zero constant censoring threshold where the constant threshold is not readily available to the econometrician. Monte Carlo results show that this bias can be extremely large in practice. A new estimator is proposed to estimate the unknown censoring threshold. It is shown that the estimator is superconsistent and follows an exponential distribution in large samples. Due to the superconsistency, the asymptotic distribution of the maximum likelihood estimator of other parameters is not affected by the estimation uncertainty of the censoring threshold."
}

@article{Cameron2011,
 ISSN = "07350015",
 author = "A. Colin Cameron and Jonah B. Gelbach and Douglas L. Miller",
 journal = "Journal of Business & Economic Statistics",
 number = "2",
 pages = "238--249",
 publisher = "American Statistical Association",
 title = "Robust Inference With Multiway Clustering",
 volume = "29",
 year = "2011",
 abstract = "In this article we propose a variance estimator for the OLS estimator as well as for nonlinear estimators such as logit, probit, and GMM. This variance estimator enables cluster-robust inference when there is two-way or multiway clustering that is nonnested. The variance estimator extends the standard cluster-robust variance estimator or sandwich estimator for one-way clustering (e.g., Liang and Zeger 1986; Arellano 1987) and relies on similar relatively weak distributional assumptions. Our method is easily implemented in statistical packages, such as Stata and SAS, that already offer cluster-robust standard errors when there is one-way clustering. The method is demonstrated by a Monte Carlo analysis for a two-way random effects model; a Monte Carlo analysis of a placebo law that extends the state-year effects example of Bertrand, Duflo, and Mullainathan (2004) to two dimensions; and by application to studies in the empirical literature where two-way clustering is present."
}

@Manual{rlang,
  title = {rlang: Functions for Base Types and Core R and 'Tidyverse' Features},
  author = {Lionel Henry and Hadley Wickham},
  year = {2018},
  note = {R package version 0.2.2},
  url = {https://CRAN.R-project.org/package=rlang}
}
    
@Manual{tidyverse,
  title = {tidyverse: Easily Install and Load the `Tidyverse'},
  author = {Hadley Wickham},
  year = {2017},
  note = {R package version 1.2.1},
  url = {https://CRAN.R-project.org/package=tidyverse}
}
    
@Manual{baser,
  title = {R: A Language and Environment for Statistical Computing},
  author = {{R Core Team}},
  organization = {R Foundation for Statistical Computing},
  address = {Vienna, Austria},
  year = {2018},
  url = {https://www.R-project.org/}
}

@article{WoelwerBressleinBurgard2018, 
  title = {Gravity Models in R},
  volume = {47},
  url = {https://ajs.or.at/index.php/ajs/article/view/688},
  DOI = {10.17713/ajs.v47i4.688}, 
  number = {4},
  journal = {Austrian Journal of Statistics},
  author = {Wölwer, Anna-Lena and Breßlein, Martin and Burgard, Jan Pablo},
  year = {2018},
  month = {Jun.},
  pages = {16-35}
}

@article{Feenstra2002,
  title={Border effects and the gravity equation: consistent methods for estimation},
  author={Feenstra, Robert C},
  journal={Scottish Journal of Political Economy},
  volume={49},
  number={5},
  pages={491--506},
  year={2002},
  publisher={Wiley Online Library}
}

@book{Feenstra2004,
  title={Advanced International Trade: Theory and Evidence},
  author={Feenstra, Robert C},
  year={2015},
  publisher={Princeton University Press}
}
