S-values: Conventional context-minimal measures of the sturdiness of regression coefficients

This paper proposes a context-minimal range of alternative regression models that is used to generate a range of alternative estimates. A prior distribution is assumed with a zero mean but an ambiguous covariance matrix. The choice of the prior covariance matrix is facilitated by transformation to standardized variables which makes the prior expected R2 equal to the sum of the prior variances. Three different ranges of the prior expected R2 are used to define three different intervals of prior covariance matrices which are used to produce three different sets of s-values.

[1]  D. Rodrik.  Why We Learn Nothing from Regressing Economic Growth on Policies , 2012 .

[2]  S. Geisser.  BAYESIAN ESTIMATION IN MULTIVARIATE ANALYSIS , 1965 .

[3]  X. Sala-i-Martin,et al.  I Just Ran Two Million Regressions , 1997 .

[4]  Edward E. Leamer,et al.  Matrix Weighted Averages and Posterior Bounds , 1976 .

[5]  Edward Leamer.  A result on the sign of restricted least-squares estimates , 1975 .

[6]  William A Brock,et al.  Policy Evaluation in Uncertain Economic Environments , 2003 .

[7]  M. Steel,et al.  Model uncertainty in cross-country growth regressions , 2001 .

[8]  D. Mccloskey,et al.  The Cult of Statistical Significance: How the Standard Error Costs Us Jobs, Justice, and Lives , 2008 .

[9]  Ramon E. Henkel.  Tests of Significance , 1976 .

[10]  W. Brock,et al.  Growth empirics and reality , 2001 .

[11]  P. Aghion,et al.  Growth, Inequality, and Globalization: Theory, History, and Policy , 1999 .

[12]  R. Levine,et al.  A Sensitivity Analysis of Cross-Country Growth Regressions , 1991 .

[13]  Charles A. Ingene,et al.  Specification Searches: Ad Hoc Inference with Nonexperimental Data , 1980 .

[14]  S. Jaggi.  TESTS OF SIGNIFICANCE , 2003 .

[15]  Edward E. Leamer,et al.  Sets of Posterior Means with Bounded Variance Priors , 1982 .

[16]  S. J. Press,et al.  Posterior distribution for the multiple correlation coefficient with fixed regressors , 1978 .

[17]  X. Sala-i-Martin,et al.  Determinants of Long-Term Growth: A Bayesian Averaging of Classical Estimates (Bace) Approach , 2000 .

[18]  Edward E. Leamer,et al.  A Bayesian Interpretation of Pretesting , 1976 .

[19]  S‐values and All Subsets Regressions , 2014 .

[20]  A. E. Hoerl,et al.  Ridge regression: biased estimation for nonorthogonal problems , 2000 .

[21]  Mark F. J. Steel,et al.  On the effect of prior assumptions in Bayesian model averaging with applications to growth regression , 2009 .

[22]  A. Raftery.  Bayesian Model Selection in Social Research , 1995 .