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Testing competing models for non-negative data with many zeros. (English) Zbl 1345.62185

Summary: 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 R. Davidson and J. G. MacKinnon [Econometrica 49, 781–793 (1981; Zbl 0472.62108)] to develop a novel and simple regression-based specification test that can be used to discriminate between these models.

MSC:

62P20 Applications of statistics to economics
62F03 Parametric hypothesis testing

Citations:

Zbl 0472.62108

Software:

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References:

[1] Anderson, J., and Y. Yotov. 2010. “The Changing Incidence of Geography.” American Economic Review 100: 2157-2186.;
[2] Anderson, J., and E. van Wincoop. 2003. “Gravity with Gravitas: a Solution to the Border Puzzle.” American Economic Review 93: 170-192.;
[3] Arkolakis, C. 2008. “Market Penetration Costs and the New Consumers Margin in International Trade.” NBER Working Paper No. 14214.;
[4] Arkolakis, C., A. Costinot, and A. Rodríguez-Clare. 2009. “New Trade Models, Same Old Gains?” NBER Working Paper No. 15628.;
[5] Atkinson, A. C. 1970. “A Method for Discriminating Between Models.” Journal of the Royal Statistical Society, Series B 32: 323-353.; · Zbl 0225.62020
[6] Bierens, H. J. 1982. “Consistent Model Specification Tests.” Journal of Econometrics 20: 105-134.; · Zbl 0549.62076
[7] Bierens, H. J. 1990. “A Consistent Conditional Moment Test of Functional Form.” Econometrica 58: 1443-1458.; · Zbl 0737.62058
[8] Chaney, T. 2008. “Distorted Gravity: The Intensive and Extensive Margins of International Trade.” American Economic Review 98: 1707-1721.;
[9] 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.; · Zbl 0201.52102
[10] Davidson, R., and J. G. MacKinnon. 1981. “Several Tests for Model Specification in the Presence of Alternative Hypotheses.” Econometrica 49: 781-793.; · Zbl 0472.62108
[11] 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.;
[12] Deaton, A., and M. Irish. 1984. “Statistical Models for Zero Expenditures in Household Budgets.” Journal of Public Economics 23: 59-80.;
[13] 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.;
[14] Duan, N. 1983. “Smearing Estimate: a Nonparametric Retransformation Method.” Journal of the American Statistical Association 78: 605-610.; · Zbl 0534.62021
[15] 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.;
[16] 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.;
[17] 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.;
[18] 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.;
[19] Fisher, G., and M. McAleer. 1979. “On the Interpretation of the Cox Test in Econometrics.” Economics Letters 4: 145-150.;
[20] Freedman, D. A. 1981. “Bootstrapping Regression Models.” Annals of Statistics 9: 1218-1228.; · Zbl 0449.62046
[21] Gaundry, M. J. I., and M. G. Dagenais. 1979. “The Dogit Model.” Transportation Research Part B: Methodological 13: 105-111.;
[22] Gourieroux, C., A. Monfort, and A. Trognon. 1984. “Pseudo Maximum Likelihood Methods: Applications to Poisson Models.” Econometrica 52: 701-720.; · Zbl 0575.62032
[23] 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.;
[24] Hallak, J. C. 2006. “Product Quality and the Direction of Trade.” Journal of International Economics 68: 238-265.;
[25] Heckman, J. J. 1979. “Sample Selection Bias as a Specification Error.” Econometrica 47: 153-161.; · Zbl 0392.62093
[26] Helpman, E., M. J. Melitz, and Y. Rubinstein. 2008. “Estimating Trade Flows: Trading Partners and Trading Volumes.” Quarterly Journal of Economics 123: 441-487.; · Zbl 1179.91174
[27] Helpman, E., M. J. Melitz, and S. R. Yeaple. 2004. “Export Versus FDI with Heterogeneous Firms.” American Economic Review 94: 300-316.;
[28] 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.;
[29] La Porta, R., F. López-de-Silanes, and G. Zamarripa. 2003. “Related Lending.” The Quarterly Journal of Economics 118: 231-268.; · Zbl 1074.91532
[30] Lee, M.-J. 2010. Micro-Econometrics: Methods of Moments and Limited Dependent Variables. 2nd ed. New York, NY: Springer.; · Zbl 1177.91003
[31] Leung, S. F., and S. Yu. 1996. “On the Choice Between Sample-Selection and Two-Part Models.” Journal of Econometrics 72: 197-229.; · Zbl 0881.62132
[32] Mukhopadhyay, K., and P. K. Trivedi. 1995. “Regression Models for Under-Recorded Count Data.” Paper presented at the Econometric Society 7th World Congress, Tokyo.;
[33] Melitz, M. J., 2003. “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productivity.” Econometrica 71: 1695-1725.; · Zbl 1154.91551
[34] Mullahy, J. 1986. “Specification and Testing in Some Modified Count Data Models.” Journal of Econometrics 33: 341-365.;
[35] Mullahy, J. 1998. “Much ado About Two: Reconsidering Retransformation and the Two-Part Model in Health Econometrics.” Journal of Health Economics 17: 247-282.;
[36] Newey, W. K. 1984. “A Method of Moments Interpretation of Sequential Estimators.” Economics Letters 14: 201-206.; · Zbl 1273.62278
[37] Newey, W. K. 1985. “Maximum Likelihood Specification Testing and Conditional Moment Tests.” Econometrica 53: 1047-1070.; · Zbl 0629.62107
[38] 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.;
[39] 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.;
[40] Pierce, D. A. 1982. “The Asymptotic Effect of Substituting Estimators for Parameters in Certain Types of Statistics.” Annals of Statististics 10: 475-478.; · Zbl 0488.62012
[41] Pesaran, M. H., and A. S. Deaton. 1978. “Testing Non-Nested Nonlinear Regression Models.” Econometrica 46: 677-694.; · Zbl 0379.62089
[42] Quandt, R. E. 1974. “A Comparison of Methods for Testing Non-Nested Hypotheses.” Review of Economics and Statistics 56: 251-255.;
[43] 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.;
[44] 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.;
[45] Santos Silva, J. M. C., and S. Tenreyro. 2006. “The Log of Gravity.” The Review of Economics and Statistics 88: 641-658.;
[46] 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.;
[47] StataCorp. 2013. Stata Release 13. Statistical Software. College Station (TX): StataCorp LP.;
[48] Tauchen, G. 1985. “Diagnostic Testing and Evaluation of Maximum Likelihood Models.” Journal of Econometrics 30: 415-443.; · Zbl 0591.62094
[49] Tobin, J. 1958. “Estimation of Relationships for Limited Dependent Variables.” Econometrica 26: 24-36.; · Zbl 0088.36607
[50] 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.;
[51] Vuong, Q. H. 1989. “Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses.” Econometrica 57: 307-333.; · Zbl 0701.62106
[52] Winkelmann, R., and K. F. Zimmermann. 1993. “Poisson Logistic Regression.” Department of Economics, University of Munich, Working Paper No 93-18.;
[53] Wooldridge, J. M. 1992. “A Test for Functional Form Against Nonparametric Alternatives.” Econometric Theory 8: 452-475.;
[54] Wooldridge, J. M. 2002. Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: MIT Press.; · Zbl 1441.62010
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