Book contents
- Frontmatter
- Contents
- Preface
- User Guide
- 1 Introduction
- PART 1 DESCRIPTION
- PART 2 INFERENCE
- 9 Monte Carlo Simulation
- 10 Review of Statistical Inference
- 11 The Measurement Box Model
- 12 Comparing Two Populations
- 13 The Classical Econometric Model
- 14 The Gauss–Markov Theorem
- 15 Understanding the Standard Error
- 16 Confidence Intervals and Hypothesis Testing
- 17 Joint Hypothesis Testing
- 18 Omitted Variable Bias
- 19 Heteroskedasticity
- 20 Autocorrelation
- 21 Topics in Time Series
- 22 Dummy Dependent Variable Models
- 23 Bootstrap
- 24 Simultaneous Equations
- Glossary
- Index
14 - The Gauss–Markov Theorem
from PART 2 - INFERENCE
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- User Guide
- 1 Introduction
- PART 1 DESCRIPTION
- PART 2 INFERENCE
- 9 Monte Carlo Simulation
- 10 Review of Statistical Inference
- 11 The Measurement Box Model
- 12 Comparing Two Populations
- 13 The Classical Econometric Model
- 14 The Gauss–Markov Theorem
- 15 Understanding the Standard Error
- 16 Confidence Intervals and Hypothesis Testing
- 17 Joint Hypothesis Testing
- 18 Omitted Variable Bias
- 19 Heteroskedasticity
- 20 Autocorrelation
- 21 Topics in Time Series
- 22 Dummy Dependent Variable Models
- 23 Bootstrap
- 24 Simultaneous Equations
- Glossary
- Index
Summary
[J]ust a year after getting his degree, Mansfield Merriman, Ph.D. Yale 1876, wrote of Gauss's elegant demonstration of the “Gauss-Markov” theorem that “The proof is entirely untenable.” In charity to Merriman it might be added that no less a mathematician than Poincaré also misconstrued the nature of Gauss's result.
Stephen M. StiglerIntroduction
This chapter brings together all the key ideas in this book:
In order to do inference one must have a model of the data generating process.
There are many possible estimators of the population parameters.
Estimators can be classified according to whether they are unbiased – that is, on average correct.
Many, but by no means all, estimators are linear estimators.
One of the main criteria for comparing estimators is the variance of the estimator.
When the data are generated according to the classical econometric box model, ordinary least squares is the best estimator in the class of linear, unbiased estimators – best, that is, according to the criterion of finding the estimator with the minimum variance for a given sample size.
This last statement is often stated in shorthand as “OLS is BLUE” (best linear unbiased estimator) and is known as the Gauss–Markov theorem from which the title of this chapter is derived. This theorem explains the preeminence of the OLS estimator in econometrics.
The Gauss–Markov theorem also works in reverse: when the data generating process does not follow the classical econometric model, ordinary least squares is typically no longer the preferred estimator.
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- Chapter
- Information
- Introductory EconometricsUsing Monte Carlo Simulation with Microsoft Excel, pp. 335 - 377Publisher: Cambridge University PressPrint publication year: 2005