*David F. Hendry*

- Published in print:
- 2014
- Published Online:
- January 2015
- ISBN:
- 9780262028356
- eISBN:
- 9780262324410
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262028356.003.0010
- Subject:
- Economics and Finance, Econometrics

We develop approximate bias corrections for the conditional distributions of the estimated parameters of retained variables after model selection, such that approximately unbiased estimates of their ...
More

We develop approximate bias corrections for the conditional distributions of the estimated parameters of retained variables after model selection, such that approximately unbiased estimates of their coefficients are delivered. Such corrections also drive estimated coefficients of irrelevant variables towards the origin, substantially reducing their mean squared errors (MSEs). We illustrate the theory by simulating selection from N = 1000 variables, to examine the impacts of our approach on estimated coefficient MSEs for both relevant and irrelevant variables in their conditional and unconditional distributions.Less

We develop approximate bias corrections for the conditional distributions of the estimated parameters of retained variables after model selection, such that approximately unbiased estimates of their coefficients are delivered. Such corrections also drive estimated coefficients of irrelevant variables towards the origin, substantially reducing their mean squared errors (MSEs). We illustrate the theory by simulating selection from N = 1000 variables, to examine the impacts of our approach on estimated coefficient MSEs for both relevant and irrelevant variables in their conditional and unconditional distributions.

*Robert J. Shiller*

- Published in print:
- 1998
- Published Online:
- November 2003
- ISBN:
- 9780198294184
- eISBN:
- 9780191596926
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/0198294182.003.0007
- Subject:
- Economics and Finance, Macro- and Monetary Economics, Financial Economics

This chapter addresses the fact that creating index numbers for settlement of contracts requires some judgement, and that no single method is likely to be applicable to all circumstances—there are ...
More

This chapter addresses the fact that creating index numbers for settlement of contracts requires some judgement, and that no single method is likely to be applicable to all circumstances—there are trade‐offs, and choices have to be made with limited information. Before applying a repeated‐measures method like the ones defined in the preceding chapter, a decision has to be made as to whether there are enough repeated measures to ensure that the standard errors are not going to be too high, and whether there is enough unmeasured quality variation across subjects to warrant the increase in error variances caused by the addition of many subject dummies. A choice has to be made as to which kinds of hedonic variables, if any, to include in the analysis, and not all quality measures are appropriate for index number construction, so a choice needs to be made as to whether these variables or the subject dummies are to be constrained in any of various ways. Prior information of an imprecise nature may be used to put probabilistic, rather than rigid, restrictions on the regression coefficients. There are also some fundamentally different variants of the hedonic repeated‐measures regression methods that could be considered, methods in which quality is inferred as an observed factor associated with each subject (factor analytic methods), and methods in which a separate selection equation is used to correct for possible selection bias in the mechanism by which it is determined which subjects are to be measured (selection bias correction methods).Less

This chapter addresses the fact that creating index numbers for settlement of contracts requires some judgement, and that no single method is likely to be applicable to all circumstances—there are trade‐offs, and choices have to be made with limited information. Before applying a repeated‐measures method like the ones defined in the preceding chapter, a decision has to be made as to whether there are enough repeated measures to ensure that the standard errors are not going to be too high, and whether there is enough unmeasured quality variation across subjects to warrant the increase in error variances caused by the addition of many subject dummies. A choice has to be made as to which kinds of hedonic variables, if any, to include in the analysis, and not all quality measures are appropriate for index number construction, so a choice needs to be made as to whether these variables or the subject dummies are to be constrained in any of various ways. Prior information of an imprecise nature may be used to put probabilistic, rather than rigid, restrictions on the regression coefficients. There are also some fundamentally different variants of the hedonic repeated‐measures regression methods that could be considered, methods in which quality is inferred as an observed factor associated with each subject (factor analytic methods), and methods in which a separate selection equation is used to correct for possible selection bias in the mechanism by which it is determined which subjects are to be measured (selection bias correction methods).

*David F. Hendry*

- Published in print:
- 2014
- Published Online:
- January 2015
- ISBN:
- 9780262028356
- eISBN:
- 9780262324410
- Item type:
- chapter

- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262028356.003.0008
- Subject:
- Economics and Finance, Econometrics

We now consider the special case in which a congruent, constant regression model in mutually orthogonal, valid conditioning variables can be successfully selected in one decision using the criteria ...
More

We now consider the special case in which a congruent, constant regression model in mutually orthogonal, valid conditioning variables can be successfully selected in one decision using the criteria discussed in chapter 5. This establishes a baseline, which demonstrates that the false null retention rate can be controlled, and that repeated testing is not an intrinsic aspect of model selection, even if there are 10300 possible models, as occurs here when N = 1000. Goodness-of-fit estimates, mean squared errors, and the consistency of the selection are all discussed. However, the estimates from the selected model do not have the same properties as if the DGP equation had been estimated directly, so chapter 10 develops bias corrections, after chapter 9 considers the 2-variable case in more detail.Less

We now consider the special case in which a congruent, constant regression model in mutually orthogonal, valid conditioning variables can be successfully selected in one decision using the criteria discussed in chapter 5. This establishes a baseline, which demonstrates that the false null retention rate can be controlled, and that repeated testing is not an intrinsic aspect of model selection, even if there are 10300 possible models, as occurs here when N = 1000. Goodness-of-fit estimates, mean squared errors, and the consistency of the selection are all discussed. However, the estimates from the selected model do not have the same properties as if the DGP equation had been estimated directly, so chapter 10 develops bias corrections, after chapter 9 considers the 2-variable case in more detail.