IDEAS home Printed from https://ideas.repec.org/p/ifs/cemmap/11-21.html
   My bibliography  Save this paper

Bias and consistency in three-way gravity models

Author

Listed:
  • Martin Weidner

    (Institute for Fiscal Studies and University College London)

  • Thomas Zylkin

    (Institute for Fiscal Studies)

Abstract

We study the incidental parameter problem for the “three-way” Poisson Pseudo-Maximum Likelihood (PPML) estimator recently recommended for identifying the effects of trade policies and in other panel data gravity settings. Despite the number and variety of fixed effects involved, we confirm PPML is consistent for fixed T and we show it is in fact the only estimator among a wide range of PML gravity estimators that is generally consistent in this context when T is fixed. At the same time, asymptotic confidence intervals in fixed-T panels are not correctly centered at the true point estimates, and cluster-robust variance estimates used to construct standard errors are generally biased as well. We characterize each of these biases analytically and show both numerically and empirically that they are salient even for real-data settings with a large number of countries. We also offer practical remedies that can be used to obtain more reliable inferences of the effects of trade policies and other time-varying gravity variables.

Suggested Citation

  • Martin Weidner & Thomas Zylkin, 2021. "Bias and consistency in three-way gravity models," CeMMAP working papers CWP11/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:11/21
    as

    Download full text from publisher

    File URL: https://www.cemmap.ac.uk/wp-content/uploads/2021/03/CWP1121-Bias-and-consistency-in-three-way-gravity-models.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Wooldridge, Jeffrey M., 1999. "Distribution-free estimation of some nonlinear panel data models," Journal of Econometrics, Elsevier, vol. 90(1), pages 77-97, May.
    2. Glick, Reuven & Rose, Andrew K., 2016. "Currency unions and trade: A post-EMU reassessment," European Economic Review, Elsevier, vol. 87(C), pages 78-91.
    3. Guido W. Imbens & Michal Kolesár, 2016. "Robust Standard Errors in Small Samples: Some Practical Advice," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 701-712, October.
    4. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
    5. Beverelli, Cosimo & Orefice, Gianluca, 2019. "Migration deflection: The role of Preferential Trade Agreements," Regional Science and Urban Economics, Elsevier, vol. 79(C).
    6. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," Review of Economic Studies, Oxford University Press, vol. 82(3), pages 991-1030.
    7. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    8. Head, Keith & Mayer, Thierry, 2014. "Gravity Equations: Workhorse,Toolkit, and Cookbook," Handbook of International Economics, in: Gopinath, G. & Helpman, . & Rogoff, K. (ed.), Handbook of International Economics, edition 1, volume 4, chapter 0, pages 131-195, Elsevier.
    9. James E. Anderson & Eric van Wincoop, 2003. "Gravity with Gravitas: A Solution to the Border Puzzle," American Economic Review, American Economic Association, vol. 93(1), pages 170-192, March.
    10. Koen Jochmans, 2017. "Two-Way Models for Gravity," The Review of Economics and Statistics, MIT Press, vol. 99(3), pages 478-485, July.
    11. Javier Alvarez & Manuel Arellano, 2003. "The Time Series and Cross-Section Asymptotics of Dynamic Panel Data Estimators," Econometrica, Econometric Society, vol. 71(4), pages 1121-1159, July.
    12. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2011. "Robust Inference With Multiway Clustering," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(2), pages 238-249, April.
    13. Fernández-Val, Iván & Vella, Francis, 2011. "Bias corrections for two-step fixed effects panel data estimators," Journal of Econometrics, Elsevier, vol. 163(2), pages 144-162, August.
    14. I-Hui Cheng & Howard J. Wall, 2005. "Controlling for heterogeneity in gravity models of trade and integration," Review, Federal Reserve Bank of St. Louis, vol. 87(Jan), pages 49-63.
    15. Moon, Hyungsik Roger & Weidner, Martin, 2017. "Dynamic Linear Panel Regression Models With Interactive Fixed Effects," Econometric Theory, Cambridge University Press, vol. 33(1), pages 158-195, February.
    16. Carro, Jesus M., 2007. "Estimating dynamic panel data discrete choice models with fixed effects," Journal of Econometrics, Elsevier, vol. 140(2), pages 503-528, October.
    17. Andrew K. Rose, 2019. "Soft power and exports," Review of International Economics, Wiley Blackwell, vol. 27(5), pages 1573-1590, November.
    18. repec:hal:spmain:info:hdl:2441/75dbbb2hc596np6q8flqf6i79k is not listed on IDEAS
    19. Chen, Mingli & Fernández-Val, Iván & Weidner, Martin, 2021. "Nonlinear factor models for network and panel data," Journal of Econometrics, Elsevier, vol. 220(2), pages 296-324.
    20. Baier, Scott L. & Bergstrand, Jeffrey H. & Feng, Michael, 2014. "Economic integration agreements and the margins of international trade," Journal of International Economics, Elsevier, vol. 93(2), pages 339-350.
    21. Koen Jochmans & Martin Weidner, 2019. "Fixed‐Effect Regressions on Network Data," Econometrica, Econometric Society, vol. 87(5), pages 1543-1560, September.
    22. Peter Egger & Mario Larch & Kevin E. Staub & Rainer Winkelmann, 2011. "The Trade Effects of Endogenous Preferential Trade Agreements," American Economic Journal: Economic Policy, American Economic Association, vol. 3(3), pages 113-143, August.
    23. Bergstrand, Jeffrey H. & Larch, Mario & Yotov, Yoto V., 2015. "Economic integration agreements, border effects, and distance elasticities in the gravity equation," European Economic Review, Elsevier, vol. 78(C), pages 307-327.
    24. William Greene, 2004. "Fixed Effects and Bias Due to the Incidental Parameters Problem in the Tobit Model," Econometric Reviews, Taylor & Francis Journals, vol. 23(2), pages 125-147.
    25. Kauermann G. & Carroll R.J., 2001. "A Note on the Efficiency of Sandwich Covariance Matrix Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1387-1396, December.
    26. Valentin Verdier, 2020. "Estimation and Inference for Linear Models with Two-Way Fixed Effects and Sparsely Matched Data," The Review of Economics and Statistics, MIT Press, vol. 102(1), pages 1-16, March.
    27. Costinot, Arnaud & Rodríguez-Clare, Andrés, 2014. "Trade Theory with Numbers: Quantifying the Consequences of Globalization," Handbook of International Economics, in: Gopinath, G. & Helpman, . & Rogoff, K. (ed.), Handbook of International Economics, edition 1, volume 4, chapter 0, pages 197-261, Elsevier.
    28. Hansen, Christian B., 2007. "Asymptotic properties of a robust variance matrix estimator for panel data when T is large," Journal of Econometrics, Elsevier, vol. 141(2), pages 597-620, December.
    29. Michael Pfaffermayr, 2019. "Gravity models, PPML estimation and the bias of the robust standard errors," Applied Economics Letters, Taylor & Francis Journals, vol. 26(18), pages 1467-1471, October.
    30. Mario Larch & Joschka Wanner & Yoto V. Yotov & Thomas Zylkin, 2019. "Currency Unions and Trade: A PPML Re‐assessment with High‐dimensional Fixed Effects," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(3), pages 487-510, June.
    31. Jinyong Hahn & Guido Kuersteiner, 2002. "Asymptotically Unbiased Inference for a Dynamic Panel Model with Fixed Effects when Both "n" and "T" Are Large," Econometrica, Econometric Society, vol. 70(4), pages 1639-1657, July.
    32. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09ij4j0h0h1 is not listed on IDEAS
    33. Manuel Arellano & Stéphane Bonhomme, 2009. "Robust Priors in Nonlinear Panel Data Models," Econometrica, Econometric Society, vol. 77(2), pages 489-536, March.
    34. Gaulier, Guillaume & Zignago, Soledad, 2004. "Notes on BACI (analytical database of international trade). 1989-2002 version," MPRA Paper 32401, University Library of Munich, Germany.
    35. Rose, Andrew, 2018. "Agent Orange: Trump, Soft Power, and Exports," CEPR Discussion Papers 13139, C.E.P.R. Discussion Papers.
    36. Iván Fernández-Val & Martin Weidner, 2018. "Fixed Effects Estimation of Large-TPanel Data Models," Annual Review of Economics, Annual Reviews, vol. 10(1), pages 109-138, August.
    37. J. M. C. Santos Silva & Silvana Tenreyro, 2006. "The Log of Gravity," The Review of Economics and Statistics, MIT Press, vol. 88(4), pages 641-658, November.
    38. Sergio Correia & Paulo Guimarães & Tom Zylkin, 2020. "Fast Poisson estimation with high-dimensional fixed effects," Stata Journal, StataCorp LP, vol. 20(1), pages 95-115, March.
    39. Hahn, Jinyong & Moon, Hyungsik Roger, 2006. "Reducing Bias Of Mle In A Dynamic Panel Model," Econometric Theory, Cambridge University Press, vol. 22(3), pages 499-512, June.
    40. Karyne B. Charbonneau, 2017. "Multiple fixed effects in binary response panel data models," Econometrics Journal, Royal Economic Society, vol. 20(3), pages 1-13, October.
    41. Jeffrey Brinkman & Jeffrey Lin, 2022. "Freeway Revolts! The Quality of Life Effects of Highways," Working Papers 22-24, Federal Reserve Bank of Philadelphia.
    42. Peter Egger & Kevin Staub, 2016. "GLM estimation of trade gravity models with fixed effects," Empirical Economics, Springer, vol. 50(1), pages 137-175, February.
    43. Baier, Scott L. & Yotov, Yoto V. & Zylkin, Thomas, 2019. "On the widely differing effects of free trade agreements: Lessons from twenty years of trade integration," Journal of International Economics, Elsevier, vol. 116(C), pages 206-226.
    44. Fally, Thibault, 2015. "Structural gravity and fixed effects," Journal of International Economics, Elsevier, vol. 97(1), pages 76-85.
    45. Tony Lancaster, 2002. "Orthogonal Parameters and Panel Data," Review of Economic Studies, Oxford University Press, vol. 69(3), pages 647-666.
    46. Hausman, Jerry & Hall, Bronwyn H & Griliches, Zvi, 1984. "Econometric Models for Count Data with an Application to the Patents-R&D Relationship," Econometrica, Econometric Society, vol. 52(4), pages 909-938, July.
    47. Elhanan Helpman & Marc Melitz & Yona Rubinstein, 2008. "Estimating Trade Flows: Trading Partners and Trading Volumes," The Quarterly Journal of Economics, Oxford University Press, vol. 123(2), pages 441-487.
    48. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    49. Kato, Kengo & F. Galvao, Antonio & Montes-Rojas, Gabriel V., 2012. "Asymptotics for panel quantile regression models with individual effects," Journal of Econometrics, Elsevier, vol. 170(1), pages 76-91.
    50. repec:hal:spmain:info:hdl:2441/2etjsneok98utpcm5s44jn4dlh is not listed on IDEAS
    51. Peter C. B. Phillips & Hyungsik R. Moon, 1999. "Linear Regression Limit Theory for Nonstationary Panel Data," Econometrica, Econometric Society, vol. 67(5), pages 1057-1112, September.
    52. Clément Bosquet & Hervé Boulhol, 2015. "What is really puzzling about the “distance puzzle”," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 151(1), pages 1-21, February.
    53. Andreas Dzemski, 2019. "An Empirical Model of Dyadic Link Formation in a Network with Unobserved Heterogeneity," The Review of Economics and Statistics, MIT Press, vol. 101(5), pages 763-776, December.
    54. Pfaffermayr, Michael, 2021. "Confidence intervals for the trade cost parameters of cross-section gravity models," Economics Letters, Elsevier, vol. 201(C).
    55. Jinyong Hahn & Whitney Newey, 2004. "Jackknife and Analytical Bias Reduction for Nonlinear Panel Models," Econometrica, Econometric Society, vol. 72(4), pages 1295-1319, July.
    56. Hinz, Julian & Stammann, Amrei & Wanner, Joschka, 2019. "Persistent zeros: The extensive margin of trade," Kiel Working Papers 2139, Kiel Institute for the World Economy (IfW Kiel).
    57. Baier, Scott L. & Bergstrand, Jeffrey H. & Clance, Matthew W., 2018. "Heterogeneous effects of economic integration agreements," Journal of Development Economics, Elsevier, vol. 135(C), pages 587-608.
    58. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-1426, November.
    59. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    60. Treb Allen & Cauê de Castro Dobbin & Melanie Morten, 2018. "Border Walls," NBER Working Papers 25267, National Bureau of Economic Research, Inc.
    61. Dzemski, Andreas, 2017. "An empirical model of dyadic link formation in a network with unobserved heterogeneity," Working Papers in Economics 698, University of Gothenburg, Department of Economics, revised Apr 2018.
    62. Bryan S. Graham, 2017. "An Econometric Model of Network Formation With Degree Heterogeneity," Econometrica, Econometric Society, vol. 85, pages 1033-1063, July.
    63. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    64. Baier, Scott L. & Bergstrand, Jeffrey H., 2007. "Do free trade agreements actually increase members' international trade?," Journal of International Economics, Elsevier, vol. 71(1), pages 72-95, March.
    65. Tiemen Woutersen, 2002. "Robustness against Incidental Parameters," University of Western Ontario, Departmental Research Report Series 20028, University of Western Ontario, Department of Economics.
    66. repec:hal:wpspec:info:hdl:2441/75dbbb2hc596np6q8flqf6i79k is not listed on IDEAS
    67. repec:hal:wpspec:info:hdl:2441/2etjsneok98utpcm5s44jn4dlh is not listed on IDEAS
    68. Jonathan Eaton & Samuel Kortum, 2002. "Technology, Geography, and Trade," Econometrica, Econometric Society, vol. 70(5), pages 1741-1779, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Chen, Mingli & Fernández-Val, Iván & Weidner, Martin, 2021. "Nonlinear factor models for network and panel data," Journal of Econometrics, Elsevier, vol. 220(2), pages 296-324.
    2. Fernández-Val, Iván & Weidner, Martin, 2016. "Individual and time effects in nonlinear panel models with large N, T," Journal of Econometrics, Elsevier, vol. 192(1), pages 291-312.
    3. Ivan Fernandez-Val & Martin Weidner, 2015. "Individual and time effects in nonlinear panel models with large N , T," CeMMAP working papers 17/15, Institute for Fiscal Studies.
    4. Koen Jochmans & Vincenzo Verardi, 2022. "Instrumental‐variable estimation of exponential‐regression models with two‐way fixed effects with an application to gravity equations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(6), pages 1121-1137, September.
    5. Ivan Fernandez-Val & Martin Weidner, 2013. "Individual and time effects in nonlinear panel models with large N, T," CeMMAP working papers 60/13, Institute for Fiscal Studies.
    6. Ivan Fernandez-Val & Martin Weidner, 2014. "Individual and time effects in nonlinear panel models with large N , T," CeMMAP working papers 32/14, Institute for Fiscal Studies.
    7. Adu, Raymond & Litsios, Ioannis & Baimbridge, Mark, 2022. "ECOWAS single currency: Prospective effects on trade," Journal of International Money and Finance, Elsevier, vol. 126(C).
    8. Baier, Scott L. & Yotov, Yoto V. & Zylkin, Thomas, 2019. "On the widely differing effects of free trade agreements: Lessons from twenty years of trade integration," Journal of International Economics, Elsevier, vol. 116(C), pages 206-226.
    9. Dutt, Pushan, 2020. "The WTO is not passé," European Economic Review, Elsevier, vol. 128(C).
    10. Pfaffermayr, Michael, 2020. "Constrained Poisson pseudo maximum likelihood estimation of structural gravity models," International Economics, Elsevier, vol. 161(C), pages 188-198.
    11. Geert Dhaene & Koen Jochmans, 2015. "Split-panel Jackknife Estimation of Fixed-effect Models," Review of Economic Studies, Oxford University Press, vol. 82(3), pages 991-1030.
    12. Benedikt Heid & Mario Larch & Yoto V. Yotov, 2021. "Estimating the effects of non‐discriminatory trade policies within structural gravity models," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 54(1), pages 376-409, February.
    13. repec:hal:spmain:info:hdl:2441/f6h8764enu2lskk9p2m9mgp8l is not listed on IDEAS
    14. Galvao, Antonio F. & Gu, Jiaying & Volgushev, Stanislav, 2020. "On the unbiased asymptotic normality of quantile regression with fixed effects," Journal of Econometrics, Elsevier, vol. 218(1), pages 178-215.
    15. repec:hal:spmain:info:hdl:2441/eu4vqp9ompqllr09ij4j0h0h1 is not listed on IDEAS
    16. repec:hal:wpspec:info:hdl:2441/f6h8764enu2lskk9p2m9mgp8l is not listed on IDEAS
    17. Anderson, James E. & Yotov, Yoto V., 2020. "Short run gravity," Journal of International Economics, Elsevier, vol. 126(C).
    18. Xuan Leng & Jiaming Mao & Yutao Sun, 2023. "Debiased inference for dynamic nonlinear models with two-way fixed effects," Papers 2305.03134, arXiv.org, revised Oct 2023.
    19. Bergstrand, Jeffrey H. & Larch, Mario & Yotov, Yoto V., 2015. "Economic integration agreements, border effects, and distance elasticities in the gravity equation," European Economic Review, Elsevier, vol. 78(C), pages 307-327.
    20. Scott L. Baier & Amanda Kerr & Yoto V. Yotov, 2018. "Gravity, distance, and international trade," Chapters, in: Bruce A. Blonigen & Wesley W. Wilson (ed.), Handbook of International Trade and Transportation, chapter 2, pages 15-78, Edward Elgar Publishing.
    21. Silviano Esteve-Pérez & Salvador Gil-Pareja & Rafael Llorca-Vivero & Jordi Paniagua, 2021. "Has the Euro paid off? A study of the trade-induced welfare effects of the EMU," Working Papers 2103, Department of Applied Economics II, Universidad de Valencia.
    22. Frensch, Richard & Fidrmuc, Jarko & Rindler, Michael, 2023. "Topography, borders, and trade across Europe," Journal of Comparative Economics, Elsevier, vol. 51(3), pages 816-832.
    23. Victor Chernozhukov & Ivan Fernandez-Val & Martin Weidner, 2018. "Network and panel quantile effects via distribution regression," CeMMAP working papers CWP70/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • F10 - International Economics - - Trade - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ifs:cemmap:11/21. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Emma Hyman (email available below). General contact details of provider: https://edirc.repec.org/data/cmifsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.