Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Econometric Methods

Ed. by Giacomini, Raffaella / Li, Tong

Mathematical Citation Quotient (MCQ) 2018: 0.06

See all formats and pricing
More options …

Testing Competing Models for Non-negative Data with Many Zeros

João M. C. Santos Silva / Silvana Tenreyro
  • London School of Economics and CfM, CREI, CEP, CEPR, Department of Economics, 32 Lincoln’s Inn Fields, 2.17, London WC2A 3PH, UK
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Frank Windmeijer
Published Online: 2014-03-29 | DOI: https://doi.org/10.1515/jem-2013-0005


In economic applications it is often the case that the variate of interest is non-negative and its distribution has a mass-point at zero. Many regression strategies have been proposed to deal with data of this type but, although there has been a long debate in the literature on the appropriateness of different models, formal statistical tests to choose between the competing specifications are not often used in practice. We use the non-nested hypothesis testing framework of Davidson and MacKinnon (Davidson and MacKinnon 1981. “Several Tests for Model Specification in the Presence of Alternative Hypotheses.” Econometrica 49: 781–793.) to develop a novel and simple regression-based specification test that can be used to discriminate between these models.

This article offers supplementary material which is provided at the end of the article.

Keywords: health economics; international trade; non-nested hypotheses; C test; P test

JEL Codes: C12; C52


  • Anderson, J., and Y. Yotov. 2010. “The Changing Incidence of Geography.” American Economic Review 100: 2157–2186.CrossrefGoogle Scholar

  • Anderson, J., and E. van Wincoop. 2003. “Gravity with Gravitas: a Solution to the Border Puzzle.” American Economic Review 93: 170–192.CrossrefGoogle Scholar

  • Arkolakis, C. 2008. “Market Penetration Costs and the New Consumers Margin in International Trade.” NBER Working Paper No. 14214.Google Scholar

  • Arkolakis, C., A. Costinot, and A. Rodríguez-Clare. 2009. “New Trade Models, Same Old Gains?” NBER Working Paper No. 15628.Google Scholar

  • Atkinson, A. C. 1970. “A Method for Discriminating Between Models.” Journal of the Royal Statistical Society, Series B 32: 323–353.Google Scholar

  • Bierens, H. J. 1982. “Consistent Model Specification Tests.” Journal of Econometrics 20: 105–134.CrossrefGoogle Scholar

  • Bierens, H. J. 1990. “A Consistent Conditional Moment Test of Functional Form.” Econometrica 58: 1443–1458.CrossrefGoogle Scholar

  • Chaney, T. 2008. “Distorted Gravity: The Intensive and Extensive Margins of International Trade.” American Economic Review 98: 1707–1721.CrossrefGoogle Scholar

  • Cox, D. R. 1961. “Tests of Separate Families of Hypotheses.” In Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Vol. I, 105–123. Berkeley: University of California Press.Google Scholar

  • Davidson, R., and J. G. MacKinnon. 1981. “Several Tests for Model Specification in the Presence of Alternative Hypotheses.” Econometrica 49: 781–793.CrossrefGoogle Scholar

  • Davidson, R., and J. G. MacKinnon. 2006. “Bootstrap Methods in Econometrics.” In Palgrave Handbook of Econometrics, edited by T. C. Mills and K. Patterson, Vol. 1, Ch. 23, 821–838. London: Palgrave Macmillan.Google Scholar

  • Deaton, A., and M. Irish. 1984. “Statistical Models for Zero Expenditures in Household Budgets.” Journal of Public Economics 23: 59–80.CrossrefGoogle Scholar

  • Dow, W. H., and E. C. Norton. 2003. “Choosing Between and Interpreting the Heckit and Two-Part Models for Corner Solutions.” Health Services & Outcomes Research Methodology 4: 5–18.Google Scholar

  • Duan, N. 1983. “Smearing Estimate: a Nonparametric Retransformation Method.” Journal of the American Statistical Association 78: 605–610.CrossrefGoogle Scholar

  • Duan, N., W. G. Manning, C. N. Morris, and J. P. Newhouse. 1983. “A Comparison of Alternative Models for the Demand for Medical Care.” Journal of Business and Economic Statistics 1: 115–126.Google Scholar

  • Duan, N., W. G. Manning, C. N. Morris, and J. P. Newhouse. 1984. “Choosing Between the Sample-Selection Model and the Multi-Part Model.” Journal of Business and Economic Statistics 2: 283–289.Google Scholar

  • Eaton, J., and A. Tamura. 1994. “Bilateralism and Regionalism in Japanese and US trade and Direct Foreign Investment Patterns.” Journal of the Japanese and International Economics 8: 478–510.Google Scholar

  • Feinstein, J. S. 1989. “The Safety Regulation of U.S. Nuclear Power Plants: Violations Inspections, and Abnormal Occurrences.” Journal of Political Economy 97: 115–154.CrossrefGoogle Scholar

  • Fisher, G., and M. McAleer. 1979. “On the Interpretation of the Cox Test in Econometrics.” Economics Letters 4: 145–150.CrossrefGoogle Scholar

  • Freedman, D. A. 1981. “Bootstrapping Regression Models.” Annals of Statistics 9: 1218–1228.CrossrefGoogle Scholar

  • Gaundry, M. J. I., and M. G. Dagenais. 1979. “The Dogit Model.” Transportation Research Part B: Methodological 13: 105–111.CrossrefGoogle Scholar

  • Gourieroux, C., A. Monfort, and A. Trognon. 1984. “Pseudo Maximum Likelihood Methods: Applications to Poisson Models.” Econometrica 52: 701–720.CrossrefGoogle Scholar

  • Gourieroux, C., and A. Monfort. 1994. “Testing Non-Nested Hypotheses.” In Handbook of Econometrics, edited by R. F. Engle and D. McFadden, Vol. IV, Ch. 44, 2583–2637. Amsterdam: Elsevier.Google Scholar

  • Hallak, J. C. 2006. “Product Quality and the Direction of Trade.” Journal of International Economics 68: 238–265.CrossrefGoogle Scholar

  • Heckman, J. J. 1979. “Sample Selection Bias as a Specification Error.” Econometrica 47: 153–161.CrossrefGoogle Scholar

  • Helpman, E., M. J. Melitz, and Y. Rubinstein. 2008. “Estimating Trade Flows: Trading Partners and Trading Volumes.” Quarterly Journal of Economics 123: 441–487.CrossrefGoogle Scholar

  • Helpman, E., M. J. Melitz, and S. R. Yeaple. 2004. “Export Versus FDI with Heterogeneous Firms.” American Economic Review 94: 300–316.CrossrefGoogle Scholar

  • Jones, A. M. 2000. “Health Econometrics.” In Handbook of Health Economics, edited by J. P. Newhouse and A. J. Culyer, Vol. 1A, Ch. 6, 265–344. Amsterdam: Elsevier.Google Scholar

  • La Porta, R., F. López-de-Silanes, and G. Zamarripa. 2003. “Related Lending.” The Quarterly Journal of Economics 118: 231–268.CrossrefGoogle Scholar

  • Lee, M.-J. 2010. Micro-Econometrics: Methods of Moments and Limited Dependent Variables. 2nd ed. New York, NY: Springer.Google Scholar

  • Leung, S. F., and S. Yu. 1996. “On the Choice Between Sample-Selection and Two-Part Models.” Journal of Econometrics 72: 197–229.CrossrefGoogle Scholar

  • Mukhopadhyay, K., and P. K. Trivedi. 1995. “Regression Models for Under-Recorded Count Data.” Paper presented at the Econometric Society 7th World Congress, Tokyo.Google Scholar

  • Melitz, M. J., 2003. “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity.” Econometrica 71: 1695–1725.CrossrefGoogle Scholar

  • Mullahy, J. 1986. “Specification and Testing in Some Modified Count Data Models.” Journal of Econometrics 33: 341–365.CrossrefGoogle Scholar

  • Mullahy, J. 1998. “Much ado About Two: Reconsidering Retransformation and the Two-Part Model in Health Econometrics.” Journal of Health Economics 17: 247–282.CrossrefPubMedGoogle Scholar

  • Newey, W. K. 1984. “A Method of Moments Interpretation of Sequential Estimators.” Economics Letters 14: 201–206.CrossrefGoogle Scholar

  • Newey, W. K. 1985. “Maximum Likelihood Specification Testing and Conditional Moment Tests.” Econometrica 53: 1047–1070.CrossrefGoogle Scholar

  • Newey, W. K., and D. McFadden. 1994. “Large Sample Estimation and Hypothesis Testing.” In Handbook of Econometrics, edited by R. F. Engle and D. McFadden, Vol. 4, Ch. 36, 2111–2245. Amsterdam: Elsevier.Google Scholar

  • Norton, E. C., W. H. Dow, and Y. K. Do. 2008. “Specification Tests for the Sample Selection and Two-part Models.” Health Services and Outcomes Research Methodology 8: 201–208.Google Scholar

  • Pierce, D. A. 1982. “The Asymptotic Effect of Substituting Estimators for Parameters in Certain Types of Statistics.” Annals of Statististics 10: 475–478.CrossrefGoogle Scholar

  • Pesaran, M. H., and A. S. Deaton. 1978. “Testing Non-Nested Nonlinear Regression Models.” Econometrica 46: 677–694.CrossrefGoogle Scholar

  • Quandt, R. E. 1974. “A Comparison of Methods for Testing Non-Nested Hypotheses.” Review of Economics and Statistics 56: 251–255.Google Scholar

  • Ramalho, E. A., J. J. S. Ramalho, and J. M. R. Murteira. 2011. “Alternative Estimating and Testing Empirical Strategies for Fractional Regression Models.” Journal of Economic Surveys 25: 19–68.CrossrefGoogle Scholar

  • Santos Silva, J. M. C. 2001. “A Score Test for Non-Nested Hypotheses with Applications to Discrete Data Models.” Journal of Applied Econometrics 16: 577–597.CrossrefGoogle Scholar

  • Santos Silva, J. M. C., and S. Tenreyro. 2006. “The Log of Gravity.” The Review of Economics and Statistics 88: 641–658.CrossrefGoogle Scholar

  • Santos Silva, J. M. C., and S. Tenreyro. 2011. “Further Simulation Evidence on the Performance of the Poisson Pseudo-Maximum Likelihood Estimator.” Economics Letters 112: 220–222.CrossrefGoogle Scholar

  • StataCorp. 2013. Stata Release 13. Statistical Software. College Station (TX): StataCorp LP.Google Scholar

  • Tauchen, G. 1985. “Diagnostic Testing and Evaluation of Maximum Likelihood Models.” Journal of Econometrics 30: 415–443.CrossrefGoogle Scholar

  • Tobin, J. 1958. “Estimation of Relationships for Limited Dependent Variables.” Econometrica 26: 24–36.CrossrefGoogle Scholar

  • van de Ven, W. P., and B. M. van Praag. 1981. “Risk Aversion of Deductibles in Private Health Insurance: Application of an Adjusted Tobit Model to Family Health Care Expenditures.” In Health, Economics and Health Economics, edited by J. van der Gaag and M. Perlman, 125–148. Amsterdam: North Holland.Google Scholar

  • Vuong, Q. H. 1989. “Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses.” Econometrica 57: 307–333.CrossrefGoogle Scholar

  • Winkelmann, R., and K. F. Zimmermann. 1993. “Poisson Logistic Regression.” Department of Economics, University of Munich, Working Paper No 93-18.Google Scholar

  • Wooldridge, J. M. 1992. “A Test for Functional Form Against Nonparametric Alternatives.” Econometric Theory 8: 452–475.CrossrefGoogle Scholar

  • Wooldridge, J. M. 2002. Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: MIT Press.Google Scholar

About the article

Corresponding author: João M. C. Santos Silva, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, UK and CEMAPRE, Rua do Quelhas 6, 1200-781 Lisboa, Portugal, E-mail:

Published Online: 2014-03-29

Published in Print: 2015-01-01

Citation Information: Journal of Econometric Methods, Volume 4, Issue 1, Pages 29–46, ISSN (Online) 2156-6674, ISSN (Print) 2194-6345, DOI: https://doi.org/10.1515/jem-2013-0005.

Export Citation

©2015 by De Gruyter.Get Permission

Supplementary Article Materials

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Peter H. Egger and Kevin E. Staub
Empirical Economics, 2016, Volume 50, Number 1, Page 137
Kenneth Gillingham and Tsvetan Tsvetanov
SSRN Electronic Journal , 2018
Rodolfo Metulini, Massimo Riccaboni, Paolo Sgrignoli, and Zhen Zhu
The World Economy, 2017

Comments (0)

Please log in or register to comment.
Log in