The Perils of Underestimation of Standard Errors in a Random-coefficients Model and the Bootstrap

  • Baldev Raj

Abstract

Simulation experiments provide an important extension to two standard components of econometrics, namely, mathematical statistics and data analysis. For over a decade Professor Henri Theil and his associates, among others, have made extensive use of simulation experiments to obtain considerable new insight into the problems of statistical inference in large systems of demand equations. These experiments can be particularly relevant in small sample situations where theoretical results generally correspond to larger sample approximations. The use and power of simulation experiments is clearly evidenced in Theil’s recent survey of simulation results of the econometrics of demand systems by his team of researchers (see Theil, 1987). Indeed, the use of simulation experiments in econometrics has a long and established tradition for statistical inference (for a comprehensive survey and related references, see Hendry, 1984).

Keywords

Covariance Anil Estima 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Efron, B. (1979) ‘Bootstrap Methods: Another Look at the Jackknife’, The Annals of Statistics, 7, 1–26.CrossRefGoogle Scholar
  2. Efron, B. (1982) The Jackknife, the Bootstrap, and Other Resampling Plans (Philadelphia: Society for Industrial and Applied Mathematics).CrossRefGoogle Scholar
  3. Efron, B. and Tibshirani, R. (1986) ‘Bootstrap Methods for Standard Errors, Confidence Intervals and Other Measures of Statistical Accuracy’, Statistical Science, 1, 54–77.CrossRefGoogle Scholar
  4. Fiebig, D.G. and Theil, H. (1983) ‘The Two Perils of Symmetry — Constrained Estimation of Demand Systems’, Economics Letters, 13, 105–11.CrossRefGoogle Scholar
  5. Freedman, D.A. and Peters, S.C. (1984) ‘Bootstrapping a Regression Equation: Some Empirical Results’, Journal of the American Statistical Association, 79, 97–106.CrossRefGoogle Scholar
  6. Geweke, J. (1986) ‘Exact Inference in the Inequality Constrained Normal Linear Regression Model’, Journal of Applied Econometrics, 1, 127–41.CrossRefGoogle Scholar
  7. Hall, P. (1983) ‘Inverting an Edgeworth Expansion’, The Annals of Statistics, 11, 569–76.CrossRefGoogle Scholar
  8. Hall, P. (1988) ‘Theoretical Comparison of Bootstrap Confidence Intervals (with discussion)’, The Annals of Statistics, 16, 927–84.CrossRefGoogle Scholar
  9. Hendry, D.F. (1984) ‘Monte Carlo Experimentation’, in Z. Griliches and M.D. Intriligator (eds), Handbook of Econometrics, vol. 2 (Amsterdam: North-Holland).Google Scholar
  10. Hildreth, C. and Houck, J.P. (1968) ‘Some Estimators for a Linear Model with Random Coefficients’, Journal of the American Statistical Association, 63, 584–95.Google Scholar
  11. Lee, L.F. and Griffiths, W.E. (1979) ‘The Prior Likelihood and Best Linear Unbiased Prediction in Stochastic Coefficient Linear Models’, Working Paper No. 1, Econometrics and Applied Statistics, University of New England, Armidale, NSW Australia.Google Scholar
  12. Manski, C.F. and Thomson, S. (1986) ‘Operational Characteristics of the Maximum Score Estimator’, Journal of Econometrics, 32, 85–108.CrossRefGoogle Scholar
  13. Parke, D.W. and Zagardo, J. (1985) ‘Stochastic Coefficient Regression Estimates of The Sources of Shifts into MMDA Deposits Using Cross-Section Data’, Journal of Econometrics, 29, 327–40.CrossRefGoogle Scholar
  14. Raj, B. (1975) ‘Linear Regression with Random Coefficients: the Finite Sample and Convergence Properties’, Journal of the American Statistical Society, 70, 127–37.CrossRefGoogle Scholar
  15. Raj, B., Srivastava, V.K. and Upadhaya, S. (1980) ‘The Efficiency of Estimating a Random Coefficient Model’, Journal of Econometrics, 12, 285–99.CrossRefGoogle Scholar
  16. Raj. B. and Ullah, A. (1981) Econometrics: A Varying Coefficient Approach (London: Croom Helm).Google Scholar
  17. Raj. B. and Taylor, T.G. (1989) ‘Do Bootstrap Tests Provide Significance Levels Equivalent to the Exact Tests? Empirical Evidence from Testing Linear Restrictions in Large Demand Systems’, Journal of Quantitative Economics, 5(1), 73–89.Google Scholar
  18. Srivastava, V.K. and Dwivedi, T.D. (1979) ‘Estimation of Seemingly Unrelated Regression Equations’, Journal of Econometrics, 10, 15–32.CrossRefGoogle Scholar
  19. Srivastava, V.K., Mishra, G.D. and Chaturvedi, A. (1981) ‘Estimation of Linear Regression Model with Random Coefficients Ensuring Almost Non-negativity of Variance Estimators’, Biometrical Journal, 23, 3–8.CrossRefGoogle Scholar
  20. Swamy, P.A.V.B. and Tinsley, P.A. (1980) ‘Linear Prediction and Estimation Methods for Regression Models with Stationary Stochastic Coefficients’, Journal of Econometrics, 12, 103–42.CrossRefGoogle Scholar
  21. Theil, H. (1987) ‘The Econometrics of Demand Systems’, Chapter 3 in H. Theil and K.W. Clements, Applied Demand Analysis: Results from System-Wide Approaches (Cambridge, Massachusetts: Ballinger).Google Scholar
  22. Theil, H., Rosalsky, M.C. and Finke, R. (1984) ‘A Comparison of Normal and Discrete Bootstraps for Standard Errors in Equation Systems’, Statistics and Probability Letters, 2, 175–80; erratum 2, 255.CrossRefGoogle Scholar
  23. Theil, H., Rosalsky, M.C., and McManus, W.S. (1985) ‘Lp-Norm, Estimation of Non-linear Systems’, Economics Letters, 17, 123–5.CrossRefGoogle Scholar
  24. Vinod, H.D. and Raj, B. (1988) ‘Economics Issues in Bell System Divestiture: A Bootstrap Application’, Applied Statistics, 37(2), 251–61.CrossRefGoogle Scholar

Copyright information

© Ronald Bewley and Tran Van Hoa 1992

Authors and Affiliations

  • Baldev Raj

There are no affiliations available

Personalised recommendations