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Monte Carlo methodology and the finite sample properties of statistics for testing nested and non-nested hypotheses

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Neil R. Ericsson

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Abstract

Using recently developed Monte Carlo methodology, this paper investigates the effect of dynamics and simultaneity on the finite sample properties of maximum likelihood and instrumental variables statistics for testing both nested and non-nested hypotheses. Numerical-analytical approximations (response surfaces) to the unknown finite sample size and power functions of those statistics are obtained for dynamic one-and two-equation models. The results illustrate the value of asymptotic theory in interpreting finite sample properties and certain limitations for doing so. Two practical finite sample results arise: the F form of the Wald statistic is strongly favored over its chi-squared form; and the effects of "large-sigma" and a small effective sample size are particularly pronounced for Sargan's (1958) instrumental variables statistic and Ericsson's (1983) Cox-type instrumental variables statistic. Re-examining Pesaran and Deaton's (1978) empirical example illustrates the additional information gained from the instrumental variables statistics.

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Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series International Finance Discussion Papers with number 317.

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Date of creation: 1987
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Keywords: Econometrics ; Statistics;

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  1. Sargan, J D, 1980. "A Model of Wage-Price Inflation," Review of Economic Studies, Blackwell Publishing, vol. 47(1), pages 97-112, January. [Downloadable!] (restricted)
  2. Hendry, David F. & Pagan, Adrian R. & Sargan, J.Denis, 1984. "Dynamic specification," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 18, pages 1023-1100 Elsevier. [Downloadable!] (restricted)
  3. Hendry, David F., 1982. "A reply to Professors Maasoumi and Phillips," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 203-213, August. [Downloadable!] (restricted)
  4. Hendry, David F & Srba, Frank, 1977. "The Properties of Autoregressive Instrumental Variables Estimators in Dynamic Systems," Econometrica, Econometric Society, vol. 45(4), pages 969-90, May. [Downloadable!] (restricted)
  5. Phillips, P C B, 1986. "The Exact Distribution of the Wald Statistic," Econometrica, Econometric Society, vol. 54(4), pages 881-95, July. [Downloadable!] (restricted)
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  6. Nicholls, D F & Pagan, A R, 1983. "Heteroscedasticity in Models with Lagged Dependent Variables," Econometrica, Econometric Society, vol. 51(4), pages 1233-42, July. [Downloadable!] (restricted)
  7. Hendry, David F., 1984. "Monte carlo experimentation in econometrics," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 16, pages 937-976 Elsevier. [Downloadable!] (restricted)
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  10. Hendry, David F & Mizon, Grayham E, 1978. "Serial Correlation as a Convenient Simplification, not a Nuisance: A Comment on a Study of the Demand for Money by the Bank of England," Economic Journal, Royal Economic Society, vol. 88(351), pages 549-63, September. [Downloadable!] (restricted)
  11. MacKinnon, James G. & White, Halbert & Davidson, Russell, 1983. "Tests for model specification in the presence of alternative hypotheses : Some further results," Journal of Econometrics, Elsevier, vol. 21(1), pages 53-70, January. [Downloadable!] (restricted)
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  12. Hendry, David F. & Richard, Jean-Francois, 1982. "On the formulation of empirical models in dynamic econometrics," Journal of Econometrics, Elsevier, vol. 20(1), pages 3-33, October. [Downloadable!] (restricted)
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  15. Kiviet, Jan F., 1985. "Model selection test procedures in a single linear equation of a dynamic simultaneous system and their defects in small samples," Journal of Econometrics, Elsevier, vol. 28(3), pages 327-362, June. [Downloadable!] (restricted)
  16. King, Maxwell L & McAleer, Michael, 1987. "Further Results on Testing AR (1) against MA (1) Disturbances in the Linear Regression Model," Review of Economic Studies, Blackwell Publishing, vol. 54(4), pages 649-63, October. [Downloadable!] (restricted)
  17. Godfrey, Leslie G, 1983. "Testing Non-Nested Models after Estimation by Instrumental Variables or Least Squares," Econometrica, Econometric Society, vol. 51(2), pages 355-65, March. [Downloadable!] (restricted)
  18. Ericsson, Neil R, 1983. "Asymptotic Properties of Instrumental Variables Statistics for Testing Non-Nested Hypotheses," Review of Economic Studies, Blackwell Publishing, vol. 50(2), pages 287-304, April. [Downloadable!] (restricted)
  19. Godfrey, L. G. & Pesaran, M. H., 1983. "Tests of non-nested regression models: Small sample adjustments and Monte Carlo evidence," Journal of Econometrics, Elsevier, vol. 21(1), pages 133-154, January. [Downloadable!] (restricted)
  20. Kiviet, Jan F, 1986. "On the Rigour of Some Misspecification Tests for Modelling Dynamic Relationships," Review of Economic Studies, Blackwell Publishing, vol. 53(2), pages 241-61, April. [Downloadable!] (restricted)
  21. Hausman, Jerry A, 1975. "An Instrumental Variable Approach to Full Information Estimators for Linear and Certain Nonlinear Econometric Models," Econometrica, Econometric Society, vol. 43(4), pages 727-38, July. [Downloadable!] (restricted)
  22. Maasoumi, Esfandiar & Phillips, Peter C. B., 1982. "On the behavior of inconsistent instrumental variable estimators," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 183-201, August. [Downloadable!] (restricted)
    Other versions:
  23. Davidson, James E. H. & Hendry, David F., 1981. "Interpreting econometric evidence : The behaviour of consumers' expenditure in the UK," European Economic Review, Elsevier, vol. 16(1), pages 177-192. [Downloadable!] (restricted)
  24. Hendry, D F, 1973. "On Asymptotic Theory and Finite Sample Experiments," Economica, London School of Economics and Political Science, vol. 40(158), pages 210-17, May. [Downloadable!] (restricted)
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  27. Neil R. Ericsson, 1986. "Post-simulation analysis of Monte Carlo experiments: interpreting Pesaran's (1974) study of non-nested hypothesis test statistics," International Finance Discussion Papers 276, Board of Governors of the Federal Reserve System (U.S.). [Downloadable!]
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  28. B. Pereira, 1978. "Empirical comparisons of some tests of separate families of hypotheses," Metrika, Springer, vol. 25(1), pages 219-234, December. [Downloadable!] (restricted)
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    Other versions:
  30. Sargan, J D & Mikhail, W M, 1971. "A General Approximation to the Distribution of Instrumental Variables Estimates," Econometrica, Econometric Society, vol. 39(1), pages 131-69, January.
  31. Granger, C. W. J. & Newbold, P., 1974. "Spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 2(2), pages 111-120, July. [Downloadable!] (restricted)
  32. Hendry, David F. & Harrison, Robin W., 1974. "Monte Carlo methodology and the small sample behaviour of ordinary and two-stage least squares," Journal of Econometrics, Elsevier, vol. 2(2), pages 151-174, July. [Downloadable!] (restricted)
  33. Sargan, J D, 1980. "Some Approximations to the Distribution of Econometric Criteria Which are Asymptotically Distributed as Chi-Squared," Econometrica, Econometric Society, vol. 48(5), pages 1107-38, July. [Downloadable!] (restricted)
  34. Anderson, T W, 1977. "Asymptotic Expansions of the Distributions of Estimates in Simultaneous Equations for Alternative Parameter Sequences," Econometrica, Econometric Society, vol. 45(2), pages 509-18, March. [Downloadable!] (restricted)
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