The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Model Selection

  • Jean-Marie Dufour
Reference work entry
DOI: https://doi.org/10.1057/978-1-349-95189-5_1964

Abstract

The problem of statistical model selection in econometrics and statistics is reviewed. Model selection is interpreted as a decision problem through which a statistical model is selected in order to perform statistical analysis, such as estimation, testing, confidence set construction, forecasting, simulation, policy analysis, and so on. Broad approaches to model selection are described: (1) hypothesis testing procedures, including specification and diagnostic tests; (2) penalized goodness-of-fit methods, such as information criteria; (3) Bayesian approaches; (4) forecast evaluation methods. The effect of model selection on subsequent statistical inference is also discussed.

Keywords

ARMA models Autocorrelation Bayesian statistics Deterministic models Econometrics Endogeneity Forecasting Forecast evaluation Heteroskedasticity Linear models Model selection Models Parsimony Probability models Serial correlation Specification problems in econometrics Statistical decision theory Statistical inference Stochastic models Structural change Testing Time series analysis 

JEL Classifications

C10 C50 D81 E52 O40 
This is a preview of subscription content, log in to check access

Bibliography

  1. Akaike, H. 1969. Fitting autoregressive models for prediction. Annals of the Institute of Statistical Mathematics 21: 243–247.CrossRefGoogle Scholar
  2. Akaike, H. 1970. Statistical predictor identification. Annals of the Institute of Statistical Mathematics 22: 203–217.CrossRefGoogle Scholar
  3. Akaike, H. 1973. Information theory and an extension of the maximum likelihood principle. In Second international symposium on information theory, ed. B.N. Petrov and F. Csaki. Budapest: Akademiai Kiado.Google Scholar
  4. Akaike, H. 1974. A new look at the statistical model identification. IEEE Transactions on Automatic Control AC-19: 716–723.CrossRefGoogle Scholar
  5. Allen, D.M. 1971. Mean square error prediction as a criterion for selecting variables. Technometrics 13: 469–475.CrossRefGoogle Scholar
  6. Amemiya, T. 1980. Selection of regressors. International Economic Review 21: 331–354.CrossRefGoogle Scholar
  7. Bhatti, M.I., H. Al-Shanfari, and M.Z. Hossain. 2006. Econometric analysis of model selection and model testing. Aldershot: Ashgate.Google Scholar
  8. Box, G.E.P., and G.M. Jenkins. 1976. Time series analysis: Forecasting and control. 2nd ed. San Francisco: Holden-Day.Google Scholar
  9. Box, G.E.P., and G.C. Tiao. 1976. Comparison of forecast and actuality. Applied Statistics 64: 195–200.CrossRefGoogle Scholar
  10. Burnham, K.P., and D.R. Anderson. 2002. Model selection and multi-model inference: A practical information theoretic approach. New York: Springer.Google Scholar
  11. Cartwright, N. 1983. How the laws of physics lie. Oxford: Oxford University Press.CrossRefGoogle Scholar
  12. Charemza, W.W., and D.F. Deadman. 1997. New directions in econometric practice: General to specific modelling, cointegration and vector autoregression. 2nd ed. Aldershot: Edward Elgar.Google Scholar
  13. Choi, B. 1992. ARMA model identification. New York: Springer.CrossRefGoogle Scholar
  14. Chow, G.C. 1960. Tests of equality between sets of coefficients in two linear regressions. Econometrica 28: 591–605.CrossRefGoogle Scholar
  15. Clements, M.P., and D.F. Hendry. 1998. Forecasting economic time series. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  16. Clements, M.P., and D.F. Hendry, ed. 2002. A companion to economic forecasting. Oxford: Blackwell.Google Scholar
  17. Danilov, D., and J.R. Magnus. 2004. On the harm that ignoring pretesting can cause. Journal of Econometrics 122: 27–46.CrossRefGoogle Scholar
  18. Davidson, J.E.H., D.F. Hendry, F. Srba, and S. Yeo. 1978. Econometric modelling of the aggregate time-series relationship between consumers’ expenditure and income in the United Kingdom. Economic Journal 88: 661–692.CrossRefGoogle Scholar
  19. Davidson, R., and J.G. MacKinnon. 1993. Estimation and inference in econometrics. New York: Oxford University Press.Google Scholar
  20. Diebold, F.X. 2004. Elements of forecasting. 3rd ed. Mason, OH: Thomson South-Western.Google Scholar
  21. Diebold, F.X., and R.S. Mariano. 1995. Comparing predictive accuracy. Journal of Business and Economic Statistics 13: 253–263.Google Scholar
  22. Draper, N.R., and H. Smith, ed. 1981. Applied regression analysis. rev ed. New York: Wiley.Google Scholar
  23. Dufour, J.-M. 1980. Dummy variables and predictive tests for structural change. Economics Letters 6: 241–247.CrossRefGoogle Scholar
  24. Dufour, J.-M. 1997. Some impossibility theorems in econometrics, with applications to structural and dynamic models. Econometrica 65: 1365–1389.CrossRefGoogle Scholar
  25. Dufour, J.-M. 2003. Identification, weak instruments and statistical inference in econometrics. Canadian Journal of Economics 36: 767–808.CrossRefGoogle Scholar
  26. Dufour, J.-M. and Ghysels, E. 1996. Recent developments in the econometrics of structural change. Journal of Econometrics 70(1).Google Scholar
  27. Dufour, J.-M., E. Ghysels, and A. Hall. 1994. Generalized predictive tests and structural change analysis in econometrics. International Economic Review 35: 199–229.CrossRefGoogle Scholar
  28. Gelman, A., J.B. Carlin, H.S. Stern, and D.B. Rubin. 2003. Bayesian data analysis. 2nd ed. London: Chapman and Hall/CRC.Google Scholar
  29. Godfrey, L.G. 1988. Misspecification tests in econometrics: The lagrange multiplier principle and other approaches. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  30. Gouriéroux, C., and A. Monfort. 1995. Statistics and econometric models. Vol. 1 and 2. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  31. Grasa, A.A. 1989. Econometric model selection: A new approach. Dordrecht: Kluwer.CrossRefGoogle Scholar
  32. Hannan, E.J., and B. Quinn. 1979. The determination of the order of an autoregression. Journal of the Royal Statistical Society B 41: 190–191.Google Scholar
  33. Harvey, D.I., S.J. Leybourne, and P. Newbold. 1997. Testing the equality of prediction mean squared errors. International Journal of Forecasting 13: 281–291.CrossRefGoogle Scholar
  34. Hocking, R.R. 1976. The analysis and selection of variables in linear regression. Biometrika 32: 1–49.CrossRefGoogle Scholar
  35. Hurvitch, C.M., and C.-L. Tsai. 1989. Regression and time series model selection in small samples. Biometrika 76: 297–307.CrossRefGoogle Scholar
  36. Judge, G.G., and M.E. Bock. 1978. The statistical implications of pre-test and stein-rule estimators in econometrics. Amsterdam: North-Holland.Google Scholar
  37. Judge, G.G., W.E. Griffiths, R. Carter Hill, H. Lütkepohl, and T.-C. Lee. 1985. The theory and practice of econometrics. 2nd ed. New York: Wiley.Google Scholar
  38. Keuzenkamp, H.A. 2000. Probability, econometrics and truth: The methodology of econometrics. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  39. Krishnaiah, P.R., and L.N. Kanal. 1982. Handbook of statistics 2: Classification, pattern recognition and reduction of dimensionality. Amsterdam: North-Holland.Google Scholar
  40. Lancaster, T. 2004. An introduction to modern Bayesian econometrics. Oxford: Blackwell.Google Scholar
  41. Le Cam, L. 1953. On some asymptotic properties of maximum likelihood estimates and related Bayes estimates. University of California Publications in Statistics 1: 277–330.Google Scholar
  42. Leamer, E. 1978. Specification searches: ad hoc inferences with nonexperimental data. New York: Wiley.Google Scholar
  43. Leamer, E.E. 1983. Model choice. In Handbook of econometrics, ed. Z. Griliches and M.D. Intriligator, Vol. 1. Amsterdam: North-Holland.Google Scholar
  44. Leeb, H., and B. Pötscher. 2005. Model selection and inference: Facts and fiction. Econometric Theory 21: 29–59.CrossRefGoogle Scholar
  45. Lehmann, E.L. 1986. Testing statistical hypotheses. 2nd ed. New York: Wiley.CrossRefGoogle Scholar
  46. MacKinnon, J.G. 1992. Model specification tests and artificial regressions. Journal of Economic Literature 30: 102–146.Google Scholar
  47. Mallows, C.L. 1973. Some comments on Cp. Technometrics 15: 661–675.Google Scholar
  48. Mariano, R.S. 2002. Testing forecast accuracy. In Clements and Hendry (2002).Google Scholar
  49. McCracken, M.W. and West, K.D. 2002. Inference about predictive ability. In Clements and Hendry (2002).Google Scholar
  50. McQuarrie, A.D.R., and C.-L. Tsai. 1998. Regression and time series model selection. Singapore: World Scientific.CrossRefGoogle Scholar
  51. Meese, R.A., and K. Rogoff. 1988. Was it real? The exchange rate-interest differential relation over the modern floating-rate period. Journal of Finance 43: 933–948.CrossRefGoogle Scholar
  52. Miller, A. 2002. Subset selection in regression. 2nd ed. Boca Raton, FL: Chapman & Hall/CRC.CrossRefGoogle Scholar
  53. Morgan, M.S., and M. Morrison. 1999. Models as Mediators: Perspectives on Natural and Social Science. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  54. Parzen, E. 1977. Multiple time series: Determining the order of approximating autoregressive schemes. In Multivariate analysis IV: Proceedings of the fourth international symposium on multivariate analysis, ed. P.R. Krishnaiah. Amsterdam: North-Holland/Elsevier.Google Scholar
  55. Pesaran, M.H., R.P. Smith, and J.S. Yeo. 1985. Testing for structural stability and predictive failure: a review. Manchester School 3: 280–295.CrossRefGoogle Scholar
  56. Poirier, D.J. 1994. The methodology of econometrics. Vol. 2. Aldershot: Edward Elgar.Google Scholar
  57. Popper, K. 1968. The logic of scientific discovery. rev ed. New York: Harper Torchbooks.Google Scholar
  58. Pötscher, B.M. 1983. Order estimation in ARMA-models by Lagrange multiplier tests. Annals of Statistics 11: 872–885.CrossRefGoogle Scholar
  59. Pötscher, B. 1991. Effects of model selection on inference. Econometric Theory 7: 163–185.CrossRefGoogle Scholar
  60. Pötscher, B. 2002. Lower risk bounds and properties of confidence sets for ill-posed estimation problems with applications to spectral density and persistence estimation, unit roots and estimation of long memory parameters. Econometrica 70: 1035–1065.CrossRefGoogle Scholar
  61. Sakamoto, Y., M. Ishiguro, and G. Kitagawa. 1985. Akaike information criterion statistics. Dordrecht: Reidel.Google Scholar
  62. Sawa, T. 1978. Information criteria for discriminating among alternative regression models. Econometrica 46: 1273–1291.CrossRefGoogle Scholar
  63. Schwarz, G. 1978. Estimating the dimension of a model. Annals of Statistics 6: 461–464.CrossRefGoogle Scholar
  64. Shibata, R. 1976. Selection of the order of an autoregressive model by Akaike’s information criterion. Biometrika 71: 117–126.CrossRefGoogle Scholar
  65. Shibata, R. 1980. Asymptotically efficient selection of the order of the model for estimating parameters of a linear process. Annals of Statistics 8: 147–164.CrossRefGoogle Scholar
  66. Theil, H. 1957. Specification errors and the estimation of economic relationships. Review of the International Statistical Institute 25: 41–51.CrossRefGoogle Scholar
  67. Theil, H. 1961. Economic forecasts and policy. 2nd ed. Amsterdam: North-Holland.Google Scholar
  68. West, K.D. 1996. Asymptotic inference about predictive ability. Econometrica 64: 1067–1084.CrossRefGoogle Scholar
  69. West, K.D., and M.D. McCracken. 1998. Regression-based tests of predictive ability. International Economic Review 39: 817–840.CrossRefGoogle Scholar
  70. White, H. 2000. A reality check for data snooping. Econometrica 68: 1097–1126.CrossRefGoogle Scholar
  71. Zellner, A. 1971. An introduction to Bayesian inference in econometrics. New York: Wiley.Google Scholar
  72. Zellner, A., H.A. Keuzenkamp, and M. McAleer. 2001. Simplicity, inference and modelling: Keeping it sophisticatedly simple. Cambridge: Cambridge University Press.Google Scholar

Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Jean-Marie Dufour
    • 1
  1. 1.