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Cited by 6,408Global trade and economicsAdvanced Statistical Methods and ModelsSpatial and Panel Data Analysis

The Log of Gravity

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Silva, J. M. C. Santos, Tenreyro, Silvana·2006·The Review of Economics and Statistics
DOI 10.1162/rest.88.4.641
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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.

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  • PPML is recommended for estimating the log-linearized model.

    “They recommended using PPML for estimating the log-linearized model.”

    From Do Japan’s Free Trade Agreements Increase Its International Trade? (2022) · cites this paper as Santos Silva and Tenreyro (2006)

    In the estimation discussion, the paper specifies that PPML uses exports measured in levels, not a log-transformed dependent variable. Its comparison of estimators distinguishes PPML for the multiplicative model from estimators of the log-linearized model. The authors recommend PPML as an alternative to estimating the log-linearized model, not as a way to estimate it. (LLM, conf=0.90)

    Checked by a reasoning model — may be wrong.

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  • The Poisson regression is less sensitive to bias in the presence of heteroscedasticity than OLS.

    “Firstly, it is less sensitive to bias in the presence of heteroscedasticity (Silva and Tenreyro, 2006).”

    From The joint impact of the European Union emissions trading system on carbon emissions and economic performance (2023) · cites this paper as Silva and Tenreyro, 2006

  • PPML can estimate gravity in multiplicative form, which does not lead to dropping zero trade flows from gravity estimations.

    “Due to its ability to handle heteroskedasticity in the trade data, which renders OLS estimates inconsistent, and to estimate gravity in multiplicative form, which does not lead to dropping the zero trade flows from gravity estimations, PPML established itself as the leading gravity estimator (Santos Silva & Tenreyro, 2022).”

    From Estimating the effects of trade agreements: Lessons from 60 years of methods and data (2024) · cites this paper as Santos Silva and Tenreyro (2006)

  • PPML can handle heteroskedasticity in trade data, which renders OLS estimates inconsistent.

    “Due to its ability to handle heteroskedasticity in the trade data, which renders OLS estimates inconsistent, and to estimate gravity in multiplicative form, which does not lead to dropping the zero trade flows from gravity estimations, PPML established itself as the leading gravity estimator (Santos Silva & Tenreyro, 2022).”

    From Estimating the effects of trade agreements: Lessons from 60 years of methods and data (2024) · cites this paper as Santos Silva and Tenreyro (2006)

  • The OLS estimates may indeed be biased.

    “Consistent with the main argument from Santos Silva and Tenreyro (2006), this suggests the OLS estimates may indeed be biased.”

    From Estimating the effects of trade agreements: Lessons from 60 years of methods and data (2024) · cites this paper as Santos Silva and Tenreyro (2006)

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Cites

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Research works printed but not linked: 34

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Authors
Silva, J. M. C. S., & Tenreyro, S.
Affiliations
  • ISEG/Universidade Técnica de Lisboa and CEMAPRE
  • Centre for Economic Policy Research (GB)
ORCID
Tenreyro, Silvana
Venue
The Review of Economics and Statistics
Publisher
MIT Press
Published
2006-11-01
Volume
88
Issue
4
Pages
641-658
ISSN
  • 0034-6535 (ISSN-L)
  • 1530-9142
DOI
10.1162/rest.88.4.641
OpenAlex
W2100130392
Cited by
6,408
References
0
Citations by year
2026: 673 · 2025: 555 · 2024: 497 · 2023: 428 · 2022: 433 · 2021: 510 · 2020: 381 · 2019: 294 · 2018: 323 · 2017: 271 · 2016: 311 · 2015: 328 · 2014: 342 · 2013: 249 · 2012: 209
FWCI
175.61
Type
journal article
Language
en
Open access
Licence
Locations
  • The Review of Economics and Statistics (publishedVersion, cc-by)
  • London School of Economics and Political Science Theses Online (London School of Economics and Political Science) (acceptedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • Open Research (University of Surrey) (submittedVersion)
  • Surrey Research Insight Open Access (The University of Surrey) (submittedVersion)
Topics
  • Social Sciences › Economics, Econometrics and Finance › General Economics, Econometrics and Finance › Global trade and economics
  • Physical Sciences › Mathematics › Statistics and Probability › Advanced Statistical Methods and Models
  • Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
Keywords
Jensen's inequality, heteroscedasticity, log-linearization, elasticity estimation, OLS bias, gravity model, trade flows, estimator bias correction

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