Abstract

The t-ratio has not one but two uses in econometrics, which should be carefully distinguished. It is used as a test and also as a diagnostic. I emphasize that the commonly-used estimators are in fact pretest estimators, and argue in favor of an improved (continuous) version of pretesting, called model averaging.

Highlights

  • The concept of ‘statistical significance’ appears in almost all scientific papers in order to form or strengthen conclusions, and the p-value or the t-ratio are commonly used to quantify this concept

  • There is a lot of confusion about statistical significance

  • Almost 25 years have passed since Hugo Keuzenkamp and I wrote on this issue (Keuzenkamp and Magnus 1995), but the confusion persists and does not seem to diminish over time

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Summary

Introduction

The concept of ‘statistical significance’ appears in almost all scientific papers in order to form or strengthen conclusions, and the p-value or the t-ratio are commonly used to quantify this concept. Despite many warnings in textbooks, there is confusion about the difference between significance and importance. This and other misuses of the p-value were recently well summarized by (Wasserstein and Lazar 2016). In this note, which draws heavily on my recent undergraduate textbook (Magnus 2017), I concentrate on another (mis)use of the t-ratio (or of the p-value)—one which is not mentioned in (Wasserstein and Lazar 2016), and needs attention and warning. This concerns the role of the t-ratio as a diagnostic. My aim is to explain that the t-ratio has not one but two uses in econometrics, which should be carefully distinguished; to emphasize (again) the difference between significance and importance; to show that the estimators that are used in practice are pretest (or post-selection) estimators (Leeb and Pötscher 2005); and to argue in favor of an improved (continuous) version of pretesting, called model averaging

Two Uses of the t-Ratio
Significance and Importance
Pretesting
Model Averaging
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