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Laws and Limits of Econometrics

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  • Peter C. B. Phillips

    (Cowles Foundation for Research in Economics, Yale University)

Abstract

We discuss general weaknesses and limitations of the econometric approach. A template from sociology is used to formulate six laws that characterise mainstream activities of econometrics and their scientific limits. We discuss proximity theorems that quantify by explicit bounds how close we can get to the generating mechanism of the data and the optimal forecasts of next period observations using a finite number of observations. The magnitude of the bound depends on the characteristics of the model and trajectory of the data. We look at one possible future of econometrics using advanced econometric methods interactively with a web browser. Copyright Royal Economic Society 2003

Suggested Citation

  • Peter C. B. Phillips, 2003. "Laws and Limits of Econometrics," Economic Journal, Royal Economic Society, vol. 113(486), pages 26-52, March.
    • Handle: RePEc:ecj:econjl:v:113:y:2003:i:486:p:c26-c52
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    1. Dufour, J.M., 1995. "Some Impossibility Theorems in Econometrics with Applications to Instrumental Variables, Dynamic Models and Cointegration," Cahiers de recherche 9539, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    2. Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(5), pages 707-743, October.
    3. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    4. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    5. Dean Corbae & Sam Ouliaris & Peter C. B. Phillips, 2002. "Band Spectral Regression with Trending Data," Econometrica, Econometric Society, vol. 70(3), pages 1067-1109, May.
    6. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
    7. Phillips, P.C.B., 1989. "Partially Identified Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(2), pages 181-240, August.
    8. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    9. Park, Joon Y. & Phillips, Peter C.B., 1989. "Statistical Inference in Regressions with Integrated Processes: Part 2," Econometric Theory, Cambridge University Press, vol. 5(1), pages 95-131, April.
    10. Peter C.B. Phillips, 1992. "Bayes Methods for Trending Multiple Time Series with an Empirical Application to the US Economy," Cowles Foundation Discussion Papers 1025, Cowles Foundation for Research in Economics, Yale University.
    11. Stock, James H. & Watson, Mark W., 1999. "Forecasting inflation," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 293-335, October.
    12. Peter C. B. Phillips, 2005. "Econometric Analysis of Fisher's Equation," American Journal of Economics and Sociology, Wiley Blackwell, vol. 64(1), pages 125-168, January.
    13. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    14. Marcelo J. Moreira, 2003. "A Conditional Likelihood Ratio Test for Structural Models," Econometrica, Econometric Society, vol. 71(4), pages 1027-1048, July.
    15. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    16. Phillips, Peter C. B., 2002. "New unit root asymptotics in the presence of deterministic trends," Journal of Econometrics, Elsevier, vol. 111(2), pages 323-353, December.
    17. Michael P. Clements & David F.Hendry, 2001. "Forecasting with difference-stationary and trend-stationary models," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-19.
    18. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    19. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    20. Phillips, Peter C. B., 1995. "Bayesian model selection and prediction with empirical applications," Journal of Econometrics, Elsevier, vol. 69(1), pages 289-331, September.
    21. Hoover,Kevin D., 2001. "The Methodology of Empirical Macroeconomics," Cambridge Books, Cambridge University Press, number 9780521003216.
    22. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July.
    23. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    24. Sargan, J D, 1983. "Identification and Lack of Identification," Econometrica, Econometric Society, vol. 51(6), pages 1605-1633, November.
    25. Park, Joon Y. & Phillips, Peter C.B., 1988. "Statistical Inference in Regressions with Integrated Processes: Part 1," Econometric Theory, Cambridge University Press, vol. 4(3), pages 468-497, December.
    26. Forchini, Giovanni & Hillier, Grant, 2003. "Conditional Inference For Possibly Unidentified Structural Equations," Econometric Theory, Cambridge University Press, vol. 19(05), pages 707-743, October.
    27. Chao, John C. & Phillips, Peter C. B., 1999. "Model selection in partially nonstationary vector autoregressive processes with reduced rank structure," Journal of Econometrics, Elsevier, vol. 91(2), pages 227-271, August.
    28. Kim, Jae-Young, 1994. "Bayesian Asymptotic Theory in a Time Series Model with a Possible Nonstationary Process," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 764-773, August.
    29. Xiao, Zhijie & Phillips, Peter C. B., 2002. "Higher order approximations for Wald statistics in time series regressions with integrated processes," Journal of Econometrics, Elsevier, vol. 108(1), pages 157-198, May.
    30. Phillips, Peter C B & Ploberger, Werner, 1996. "An Asymptotic Theory of Bayesian Inference for Time Series," Econometrica, Econometric Society, vol. 64(2), pages 381-412, March.
    31. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
    32. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
    33. Peter C.B. Phillips, 1995. "Automated Forecasts of Asia-Pacific Economic Activity," Cowles Foundation Discussion Papers 1103, Cowles Foundation for Research in Economics, Yale University.
    34. David F. Hendry & Hans-Martin Krolzig, 1999. "Improving on 'Data mining reconsidered' by K.D. Hoover and S.J. Perez," Econometrics Journal, Royal Economic Society, vol. 2(2), pages 202-219.
    35. Cartwright,Nancy, 1999. "The Dappled World," Cambridge Books, Cambridge University Press, number 9780521643368.
    36. Phillips, Peter C.B. & Moon, Hyungsik Roger & Xiao, Zhijie, 2001. "How To Estimate Autoregressive Roots Near Unity," Econometric Theory, Cambridge University Press, vol. 17(1), pages 29-69, February.
    37. Cartwright,Nancy, 1999. "The Dappled World," Cambridge Books, Cambridge University Press, number 9780521644112.
    38. Jean-Marie Dufour, 1997. "Some Impossibility Theorems in Econometrics with Applications to Structural and Dynamic Models," Econometrica, Econometric Society, vol. 65(6), pages 1365-1388, November.
    39. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    40. Lahiri, Kajal, 1999. "Et Interview: Professor G.S. Maddala," Econometric Theory, Cambridge University Press, vol. 15(5), pages 753-776, October.
    41. Shimotsu, Katsumi & Phillips, Peter C B, 2002. "Exact Local Whittle Estimation of Fractional Integration," Economics Discussion Papers 8838, University of Essex, Department of Economics.
    42. Phillips, P C B, 1987. "Time Series Regression with a Unit Root," Econometrica, Econometric Society, vol. 55(2), pages 277-301, March.
    43. Nickell, Stephen J, 1981. "Biases in Dynamic Models with Fixed Effects," Econometrica, Econometric Society, vol. 49(6), pages 1417-1426, November.
    44. Joshua D. Angrist & Alan B. Keueger, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 106(4), pages 979-1014.
    45. Werner Ploberger & Peter C. B. Phillips, 2003. "Empirical Limits for Time Series Econometric Models," Econometrica, Econometric Society, vol. 71(2), pages 627-673, March.
    46. Phillips, Peter & Sul, Donggyu, 2002. "Dynamic Panel Estimation and Homogenity Testing Under Cross Section Dependence," Working Papers 194, Department of Economics, The University of Auckland.
    47. Peter C. B. Phillips, 1998. "New Tools for Understanding Spurious Regressions," Econometrica, Econometric Society, vol. 66(6), pages 1299-1326, November.
    48. Fisher, Irving, 1907. "The Rate of Interest," History of Economic Thought Books, McMaster University Archive for the History of Economic Thought, number fisher1907.
    49. repec:cup:etheor:v:10:y:1994:i:3-4:p:764-73 is not listed on IDEAS
    50. James H. Stock & Mark W. Watson, 1998. "Diffusion Indexes," NBER Working Papers 6702, National Bureau of Economic Research, Inc.
    51. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    52. Peter C. B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 12(5), pages 423-470, December.
    53. Durlauf, Steven N & Phillips, Peter C B, 1988. "Trends versus Random Walks in Time Series Analysis," Econometrica, Econometric Society, vol. 56(6), pages 1333-1354, November.
    54. P. Dorian Owen, 2003. "General‐to‐Specific Modelling Using PcGets," Journal of Economic Surveys, Wiley Blackwell, vol. 17(4), pages 609-628, September.
    55. Xiao, Zhijie & Phillips, Peter C. B., 1998. "Higher-order approximations for frequency domain time series regression," Journal of Econometrics, Elsevier, vol. 86(2), pages 297-336, June.
    56. Johansen, Soren, 1988. "Statistical analysis of cointegration vectors," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 231-254.
    57. Jeganathan, P., 1999. "On Asymptotic Inference In Cointegrated Time Series With Fractionally Integrated Errors," Econometric Theory, Cambridge University Press, vol. 15(4), pages 583-621, August.
    58. Michael P. Clements & David F. Hendry, 2001. "Forecasting Non-Stationary Economic Time Series," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262531895, December.
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    Cited by:

    1. Phillips, Peter C.B., 2005. "Challenges of trending time series econometrics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(5), pages 401-416.
    2. Allen, P. Geoffrey & Morzuch, Bernard J., 2006. "Twenty-five years of progress, problems, and conflicting evidence in econometric forecasting. What about the next 25 years?," International Journal of Forecasting, Elsevier, vol. 22(3), pages 475-492.
    3. Simón Sosvilla-Rivero & Javier Alonso Meseguer, 2005. "Estimación de una función de producción MRW para la economía española, 1910-1995," Investigaciones Economicas, Fundación SEPI, vol. 29(3), pages 609-624, September.
    4. Peter C. B. Phillips & Zhentao Shi, 2021. "Boosting: Why You Can Use The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 521-570, May.
    5. Phillips, Peter C.B., 2005. "Automated Discovery In Econometrics," Econometric Theory, Cambridge University Press, vol. 21(1), pages 3-20, February.
    6. John Rust, 2014. "The Limits of Inference with Theory: A Review of Wolpin (2013)," Journal of Economic Literature, American Economic Association, vol. 52(3), pages 820-850, September.
    7. Castle Jennifer L. & Doornik Jurgen A & Hendry David F., 2011. "Evaluating Automatic Model Selection," Journal of Time Series Econometrics, De Gruyter, vol. 3(1), pages 1-33, February.
    8. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2005. "Testing for Long Memory and Nonlinear Time Series: A Demand for Money Study," Trinity Economics Papers tep20021, Trinity College Dublin, Department of Economics.
    9. Razzak, Weshah, 2023. "Measuring the Deviations from Perfect Competition: International Evidence," MPRA Paper 119605, University Library of Munich, Germany.
    10. Bauer, Dietmar & Maynard, Alex, 2012. "Persistence-robust surplus-lag Granger causality testing," Journal of Econometrics, Elsevier, vol. 169(2), pages 293-300.
    11. Ernesto LEON CASTRO & Ezequiel AVILÉS OCHOA & Anna Maria GIL LAFUENTE, 2016. "Exchange Rate Usd/Mxn Forecast Through Econometric Models, Time Series And Howma Operators," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(4), pages 135-150.
    12. Peter C. B. Phillips & Sainan Jin, 2021. "Business Cycles, Trend Elimination, And The Hp Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 62(2), pages 469-520, May.
    13. Phillips, Peter C.B., 2003. "Vision And Influence In Econometrics: John Denis Sargan," Econometric Theory, Cambridge University Press, vol. 19(3), pages 495-511, June.
    14. W A Razzak, 2007. "A Perspective on Unit Root and Cointegration in Applied Macroeconomics," International Journal of Applied Econometrics and Quantitative Studies, Euro-American Association of Economic Development, vol. 4(1), pages 77-102.
    15. Pesaran, Hashem & Timmermann, Allan, 2005. "Real-Time Econometrics," Econometric Theory, Cambridge University Press, vol. 21(1), pages 212-231, February.
    16. David F. Hendry & Hans‐Martin Krolzig, 2004. "We Ran One Regression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(5), pages 799-810, December.
    17. Razzak, Weshah, 2024. "Measuring the Deviations from Perfect Competition: International Evidence (second version)," MPRA Paper 120200, University Library of Munich, Germany, revised 17 Feb 2024.
    18. Castle, Jennifer L. & Doornik, Jurgen A. & Hendry, David F., 2012. "Model selection when there are multiple breaks," Journal of Econometrics, Elsevier, vol. 169(2), pages 239-246.
    19. Dietmar Bauer & Alex Maynard, 2010. "Persistence-robust Granger causality testing," Working Papers 1011, University of Guelph, Department of Economics and Finance.
    20. Georgina Catacora-Vargas & Rosa Binimelis & Anne I. Myhr & Brian Wynne, 2018. "Socio-economic research on genetically modified crops: a study of the literature," Agriculture and Human Values, Springer;The Agriculture, Food, & Human Values Society (AFHVS), vol. 35(2), pages 489-513, June.
    21. Derek Bond & Michael J. Harrison & Edward J. O'Brien, 2007. "Demand for Money: A Study in Testing Time Series for Long Memory and Nonlinearity," The Economic and Social Review, Economic and Social Studies, vol. 38(1), pages 1-24.
    22. Victoria Zinde‐Walsh, 2011. "Presidential Address: Mathematics in economics and econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 44(4), pages 1052-1068, November.
    23. Shahidur Rahman, 2005. "An Alternative Estimation to Spurious Regression Model," Economic Growth Centre Working Paper Series 0507, Nanyang Technological University, School of Social Sciences, Economic Growth Centre.
    24. Simon Peters & Ken Clark & Pascal Ekin & Anja Le Blanc & Stephen Pickles, 2007. "Grid Enabling Empirical Economics: A Microdata Application," Computational Economics, Springer;Society for Computational Economics, vol. 30(4), pages 349-370, November.
    25. Duncan, Roberto & Toledo, Patricia, 2019. "Inequality in body mass indices across countries: Evidence from convergence tests," Economics & Human Biology, Elsevier, vol. 33(C), pages 40-57.

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    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C50 - Mathematical and Quantitative Methods - - Econometric Modeling - - - General
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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