PRE-TEST ESTIMATION AND TESTING IN ECONOMETRICS: RECENT DEVELOPMENTS

This paper surveys a range of important developments in the area of preliminary-test inference in the context of econometric modeling. Both pre-test estimation and pre-test testing are discussed. Special attention is given to recent contributions and results. These include analyses of pre-test strategies under model misspecification and generalized regression errors; exact sampling distribution results; and pre-testing inequality constraints on the model's parameters. In many cases, practical advice is given to assist applied econometricians in appraising the relative merits of pre-testing. It is shown that there are situations where pre-testing can be advantageous in practice. Copyright 1993 by Blackwell Publishers Ltd

[1]  K. Ohtani Testing the disturbance variance after a pre-test for a linear hypothesis on coefficients in a linear regression , 1988 .

[2]  G. Judge,et al.  Pre-test estimation under squared error loss☆ , 1983 .

[3]  William E. Griffiths,et al.  The small-sample properties of some preliminary test estimators in a linear model with autocorrelated errors , 1984 .

[4]  Measuring the degree of severity of heteroskedasticity and the choice between the ols estimator and the 2sae , 1989 .

[5]  R. Muirhead Aspects of Multivariate Statistical Theory , 1982, Wiley Series in Probability and Statistics.

[6]  B. M. Bennett,et al.  On the use of preliminary tests in certain statistical procedures , 1956 .

[7]  C. Stein Inadmissibility of the usual estimator for the variance of a normal distribution with unknown mean , 1964 .

[8]  W. E. Taylor Small Sample Properties of a Class of Two Stage Aitken Estimators , 1977 .

[9]  Samaradasa Weerahandi,et al.  TESTING REGRESSION EQUALITY WITH UNEQUAL VARIANCES , 1987 .

[10]  Takeshi Hiromatsu,et al.  Minimax Regret Significance Points for a Preliminary Test in Regression Analysis , 1973 .

[11]  T. Wallace,et al.  Weaker Criteria and Tests for Linear Restrictions in Regression , 1972 .

[12]  The degree of severity of heteroskedasticity and the traditional goldfeld and quandt pretest estimator , 1990 .

[13]  J. S. Mehta,et al.  On Utilizing Information from a Second Sample in Estimating the Scale Parameter for a Family of Symmetric Distributions , 1972 .

[14]  Judith A. Giles Pre-testing for linear restrictions in a regression model with spherically symmetric disturbances☆ , 1991 .

[15]  J. Ghosh Statistics Independent of a Complete Sufficient Statistic , 1988 .

[16]  G. Judge,et al.  Some statistical implications of multivariate inequality constrained testing , 1990 .

[17]  B. M. Bennett,et al.  Estimation of means on the basis of preliminary tests of significance , 1952 .

[18]  M. King,et al.  Autocorrelation pre-testing in the linear model: Estimation, testing and prediction , 1984 .

[19]  G. Judge,et al.  Chapter 10 Biased estimation , 1983 .

[20]  T. A. Bancroft,et al.  On Biases in Estimation Due to the Use of Preliminary Tests of Significance , 1944 .

[21]  A NOTE ON THE LEVEL OF SIGNIFICANCE OF THE PRELIMINARY TEST IN POOLING VARIANCES , 1978 .

[22]  James Goodnight,et al.  OPERATIONAL TECHNIQUES AND TABLES FOR MAKING WEAK MSE TESTS FOR RESTRICTIONS IN REGRESSIONS , 1972 .

[23]  Thomas B. Fomby,et al.  On choosing the optimal level of significance for the Durbin-Watson test and the Bayesian alternative , 1978 .

[24]  Judith A. Giles Pre-testing in a mis-specified regression model , 1991 .

[25]  J. Ravichandran,et al.  Inference based on conditional speclfication , 1988 .

[26]  Peter E. Kennedy,et al.  Fighting the teflon factor: Comparing classical and Bayesian estimators for autocorrelated errors , 1991 .

[27]  Judith A. Giles Preliminary-test estimation of a mis-specified linear model with spherically symmetric disturbances , 1990 .

[28]  Toshihisa Toyoda,et al.  Estimation of regression coefficients after a preliminary test for homoscedasticity , 1980 .

[29]  Toshihisa Toyoda,et al.  Pre-testing on part of the data , 1979 .

[30]  G. Box MULTI-FACTOR DESIGNS OF FIRST ORDER , 1952 .

[31]  G. Seber Linear hypotheses and induced tests , 1964 .

[32]  K. Wallis Lagged dependent variables and serially correlated errors : a reappraisal of three-pass least squares , 1967 .

[33]  Carlos Enrique Toro-Vizcarrondo Multicollinearity and the mean square error criterion in multiple regression : a test and some sequential estimator comparisons , 1967 .

[34]  P. Sen,et al.  On shrinkage m-estimators of location parameters , 1985 .

[35]  Pranab Kumar Sen,et al.  On Some Shrinkage Estimators of Multivariate Location , 1985 .

[36]  Toshihisa Toyoda,et al.  Testing equality between sets of coefficients after a preliminary test for equality of disturbance variances in two linear regressions , 1986 .

[37]  G. Judge,et al.  Some risk results for a two-stage pre-test estimator in the case of possible heteroskedasticity , 1991 .

[38]  R. Mittelhammer Restricted least squares, pre-test, ols and stein rule estimators: Risk comparisons under model misspecification , 1984 .

[39]  Kōichi Inada ESTIMATION OF VARIANCE AFTER PRELIMINARY CONJECTURE , 1989 .

[40]  G. Mizon Inferential Procedures in Nonlinear Models: An Application in a UK Industrial Cross Section Study of Factor Substitution and Returns to Scale , 1977 .

[41]  T. A. Bancroft,et al.  A Note on Pooling Variances , 1983 .

[42]  E. Fama The Behavior of Stock-Market Prices , 1965 .

[43]  D. Giles,et al.  Preliminary-test estimation of the regression scale parameter when the loss function is asymmetric , 1993 .

[44]  A. Gelfand,et al.  Improved estimation of the disturbance variance in a linear regression model , 1988 .

[45]  K. Ohtani PRELIMINARY TEST PREDICTOR IN THE LINEAR REGRESSION MODEL INCLUDING A PROXY VARIABLE , 1983 .

[46]  Rand R. Wilcox,et al.  The statistical implications of pre-test and Stein-rule estimators in econometrics , 1978 .

[47]  W. Strawderman,et al.  Stein Estimation: The Spherical Symmetric Case , 1990 .

[48]  ötz Trenkler,et al.  Mean square error matrix comparisons of estimators in linear regression , 1985 .

[49]  D. Giles Preliminary-test estimation in mis-specified regressions , 1986 .

[50]  Arthur Cohen,et al.  Estimates of Linear Combinations of the Parameters in the Mean Vector of a Multivariate Distribution , 1965 .

[51]  R. Farebrother Minimax Regret Significance Points for a Preliminary Test in Regression Analysis: Comment , 1975 .

[52]  M. A. Chmielewski,et al.  Elliptically Symmetric Distributions: A Review and Bibliography , 1981 .

[53]  J. Gurland,et al.  TESTING EQUALITY OF MEANS AFTER A PRELIMINARY TEST OF EQUALITY OF VARIANCES , 1962 .

[54]  George G. Judge,et al.  Improved methods of inference in econometrics , 1986 .

[55]  Amy Hing-Ling Lau,et al.  The Distribution of Stock Returns: New Evidence against the Stable Model , 1990 .

[56]  Judith A. Clarke,et al.  Preliminary-test estimation of the scale parameter in a mis-specified regression model , 1989 .

[57]  William E. Taylor,et al.  The Heteroscedastic Linear Model: Exact Finite Sample Results , 1978 .

[58]  G. Judge,et al.  TESTINGAND ESTIMATING LOCATION VECTORS UNDER HETEROSKEDASTICITY , 1989 .

[59]  P. Schmidt,et al.  A Note on the Comparison of the Mean Square Error of Inequality Constrained Least Squares and Other Related Estimators , 1982 .

[60]  H. Folmer Autocorrelation Pre-Testing in Linear Models with AR(1) Errors , 1988 .

[61]  T. Wallace,et al.  Pretest Estimation in Regression: A Survey , 1977 .

[62]  Michael Thomson,et al.  Some results on the statistical properties of an inequality constrained least squares estimator in a linear model with two regressors , 1982 .

[63]  Offer Lieberman,et al.  The Optimal Size of a Preliminary Test of Linear Restrictions in a Misspecified Regression Model , 1992 .

[64]  Estimation of the variance in a normal population after the one-sided pre-test for the mean , 1991 .

[65]  Toshihisa Toyoda,et al.  Minimax Regret Critical Values for a Preliminary Test in Pooling Variances , 1978 .

[66]  Richard J. Brook,et al.  On the Use of a Regret Function to Set Significance Points in Prior Tests of Estimation , 1976 .

[67]  W. Jayatissa Tests of Equality between Sets of Coefficients in Two Linear Regressions when Disturbance Variances Are Unequal , 1977 .

[68]  N. D. Shukla Estimation of a regression coefficient after two preliminary tests of significance , 1979 .

[69]  Judith A. Giles Estimation of the scale parameter after a pre-test for homogeneity in a mis-specified regression model , 1993 .

[70]  C. K. Liew,et al.  Inequality Constrained Least-Squares Estimation , 1976 .

[71]  Judith A. Clarke,et al.  Estimating the error variance in regression after a preliminary test of restrictions on the coefficients , 1987 .

[72]  W. Krämer The Linear Regression Model Under Test , 1986 .

[73]  Judith A. Clarke,et al.  Preliminary-Test Estimation of the Error Variance in Linear Regression , 1987, Econometric Theory.

[74]  G. Judge,et al.  Inequality Restrictions in Regression Analysis , 1966 .

[75]  Luis A. Escobar,et al.  The bias of the least squares estimator over interval constraints , 1986 .

[76]  Hrishikesh D. Vinod,et al.  Recent Advances in Regression Methods. , 1983 .

[77]  Edward C. Prescott,et al.  Multiple Regression with Inequality Constraints: Pretesting Bias, Hypothesis Testing and Efficiency , 1970 .

[78]  James Durbin,et al.  Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables , 1970 .

[79]  D. Giles,et al.  Estimation of the Regression Scale After a Pre-Test for Homoscedasticity Under Linex Loss , 1992 .

[80]  D. Teichroew,et al.  The Mixture of Normal Distributions with Different Variances , 1957 .

[81]  Offer Lieberman,et al.  The optimal size of a preliminary test for linear restrictions when estimating the regression scale parameter , 1991 .

[82]  T. D. Wallace,et al.  A Test of the Mean Square Error Criterion for Restrictions in Linear Regression , 1968 .

[83]  Kazuhiro Ohtani,et al.  Optimal levels of significance of a pre-test in estimating the disturbance variance after the pre-test for a linear hypothesis on coefficients in a linear regression , 1988 .

[84]  M. L. King,et al.  Some aspects of statistical inference in the linear regression model , 1979 .

[85]  Masao Nakamura,et al.  On the Impact of the Tests for Serial Correlation Upon the Test of Significance for the Regression Coefficient , 1978 .

[86]  Kazuhiro Ohtani,et al.  SOME SMALL SAMPLE PROPERTIES OF A PRE-TEST ESTIMATOR OF THE DISTURBANCE VARIANCE IN A MISSPECIFIED LINEAR REGRESSION , 1987 .

[87]  K. Ohtani On pooling disturbance variances when the goal is testing restrictions on regression coefficients , 1987 .

[88]  R. Fletcher,et al.  Optimal significance levels of prior tests in the presence of multicollinearity , 1981 .

[89]  V. K. Srivastava,et al.  The exact distribution of a least squares regression coefficient estimator after a preliminary t-test , 1993 .

[90]  B. McCabe,et al.  The independence of tests for structural change in regression models , 1983 .

[91]  T. Wallace,et al.  Estimation of variance after a preliminary test of homogeneity and optimal levels of significance for the pre-test , 1975 .

[92]  D. Giles,et al.  Some properties of the Durbin-Watson test after a preliminary t-test , 1992 .

[93]  On Some Comparisons between Bayesian and Sampling Theoretic Estimators of a Normal Mean Subject to an Inequality Constraint , 1989 .

[94]  Toshihisa Toyoda,et al.  SMALL SAMPLE PROPERTIES OF THE TWO-STAGE TEST OF EQUALITY OF INDIVIDUAL COEFFICIENTS AFTER A PRE-TEST FOR HOMOSCEDASTICITY IN TWO LINEAR REGRESSIONS , 1988 .

[95]  Judith A. Giles Estimation of the error variance after a preliminary-test of homogeneity in a regression model with spherically symmetric disturbances , 1992 .

[96]  K. Ohtani The MSE of the least squares estimator over an interval constraint , 1987 .

[97]  K. V. Albertson,et al.  Pre-test estimation in a regression model with a mis-specified error covariance matrix , 1993 .

[98]  G. Judge,et al.  Sampling properties of an inequality restricted estimator , 1981 .

[99]  T. D. Wallace,et al.  Tables for the Mean Square Error Test for Exact Linear Restrictions in Regression , 1969 .

[100]  S. Adjibolosoo,et al.  A procedure foe improving upon the performance of the traditional heteroskedast1c1ty pretest estimator , 1990 .

[101]  Robert C. Blattberg,et al.  A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices: Reply , 1974 .

[102]  C. Morris,et al.  Non-Optimality of Preliminary-Test Estimators for the Mean of a Multivariate Normal Distribution , 1972 .

[103]  B. Mandelbrot The Variation of Certain Speculative Prices , 1963 .

[104]  George G. Judge,et al.  Wallace's weak mean square error criterion for testing linear restrictions in regression: a tighter bound / BEBR No. 88 , 1973 .

[105]  G. Judge,et al.  Some improved estimators in the case of possible heteroscedasticity , 1984 .

[106]  Peter Schmidt,et al.  The Theory and Practice of Econometrics , 1985 .

[107]  T. D. Wallace,et al.  Sequential Methods in Model Construction , 1972 .

[108]  B. V. Bahr,et al.  Inequalities for the $r$th Absolute Moment of a Sum of Random Variables, $1 \leqq r \leqq 2$ , 1965 .

[109]  G. Judge,et al.  Sampling Performance of Some Joint One-Sided Preliminary Test Estimators under Squared Error Loss , 1989 .

[110]  M. Morey The statistical implications of preliminary specification error testing , 1984 .

[111]  The Exact Distribution of a Simple Pre-Test Estimator , 1992 .

[112]  Edward Leamer 3 Things That Bother Me , 1988 .

[113]  Luis A. Escobar,et al.  Mean square error and efficiency of the least squares estimator over interval constraints , 1987 .

[114]  David F. Hendry,et al.  Small-Sample Properties of ARCH Estimators and Tests , 1985 .

[115]  A. Zellner Bayesian Estimation and Prediction Using Asymmetric Loss Functions , 1986 .

[116]  Invariant tests for the equality of k scale parameters under spherical symmetry , 1981 .

[117]  A. Gelfand,et al.  On the Estimation of a Variance Ratio. , 1988 .

[118]  T. Wallace,et al.  Optimal Critical Values for Pre-Testing in Regression , 1976 .

[119]  Some sampling properties of the two-stage test in a linear regression with a proxy variable , 1987 .

[120]  Robin C. Sickles,et al.  Some Further Evidence on the Use of the Chow Test under Heteroskedasticity , 1977 .

[121]  Judith A. Clarke,et al.  Preliminary-test estimation of the standard error of estimate in linear regression , 1990 .

[122]  George G. Judge,et al.  The Statistical Consequences of Preliminary Test Estimators in Regression , 1973 .

[123]  Brajendra C. Sutradhar,et al.  Estimation of the parameters of a regression model with a multivariate t error variable , 1986 .