Modeling and Valuation of Energy Structures by Daniel Mahoney

Author:Daniel Mahoney
Language: eng
Format: epub
Publisher: Palgrave Macmillan

In the event that this picture is worth less than a thousand words, let us explain what we mean here. From an econometric model that expresses a relationship between structure and noise, we have an estimator mapping observables to estimates of underlying (structural) parameter values. The original model then allows us to derive residuals (i.e., estimates of the [unobservable] noise), as a function of the sample and estimated parameter values. In turn, these residuals can be used to construct synthetic samples from which reestimated parameter values can be obtained. Finally, the stability of the estimator and the robustness of the model, always in the context of a particular sample, can be assessed.

Note that this procedure can always be carried out, and it should be. The standard approach that views econometrics in terms of hypothesis testing of models and statistical significance of parameters is critically dependent on large samples and (largely) untestable assumptions about the underlying DGP.46 By contrast, viewing the problem as one of stability analysis is much broader in nature. For large enough samples and with sufficient knowledge of the DGP, stability analysis can of course be crafted as familiar testing of statistical significance. The reverse, however, is generally not true, and of course the usual situation is precisely one of small samples and insufficient information about the true DGP.

We are emphasizing two, although ultimately related, concepts in (6.134). First, we have the fact that all relevant information flows from the actual sample that we possess. (Obviously, if we have good prior reason to believe that this sample should be truncated or augmented, this should be done, but when the econometric analysis commences, we can only use that data for drawing conclusions.) Related to points we will raise when we discuss simulation in Chapter 7, imposing structure (through formal modeling) cannot create information not already present in the original sample. Furthermore, the residuals that arise from econometric analysis on this data are dependent on the model and associated estimator that are being employed. Second, as these residuals are resampled (in some model-dependent but otherwise still unspecified way) to produce synthetic samples, new estimates of the model parameter are produced. These new estimates can be used to assess, in light of the estimates derived from the original sample, the stability of the underlying estimator.

Thus, we have the following synergy:

• The sample as the central source of conditional information

• The residuals as dependent on sample, model, and estimator

• Resampled residuals as a means of assessing the robustness of the estimator given the model.

We can now turn attention to the operational question of how the generation of synthetic samples in (6.134) can be carried out, and shed more light on this synergy.

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