1 / 12

Econometrics

Econometrics. Chapter 7 Properties of OLS Estimators. Properties of Least Squares Estimators - Chapter 7. Unbiased Consistent Efficient Assumptions of the Classic Regression Model (Gauss-Markov) Homoskedasticity Serial Correlation Exogenous/Endogenous Linearity (Parameters/Variables).

nichole-osborn
Télécharger la présentation

Econometrics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Econometrics Chapter 7 Properties of OLS Estimators

  2. Properties of Least Squares Estimators - Chapter 7 • Unbiased • Consistent • Efficient • Assumptions of the Classic Regression Model (Gauss-Markov) • Homoskedasticity • Serial Correlation • Exogenous/Endogenous • Linearity (Parameters/Variables)

  3. Properties of OLS Estimators – continuedDefinitions/Desirable Characteristics of Estimators • Unbiased – An estimator’s expected value equals the true value of the parameter it estimates: • Consistent – As the data sample gets larger and larger, the difference between the Estimated Value and the True Value gets smaller and smaller • Efficient – There is no other unbiased estimator with a lower variance than

  4. Properties of OLS Estimators – continuedThe Classical Regression Model: Gauss-Markov Assumptions • A1:The true data generating process is seen by our model; • Yi = β0 + β1Xi + εi • A2:X does not take the same value for all observations • A3:Given the values for Xi, the variance of the error term is the same for each observation • A4:The error terms are Not correlated with each other • A5:The error terms are Not correlated with the value of X; the mean value of ε is 0 no matter what the value of X is

  5. Properties of OLS Estimators – continuedThe Classical Regression Model: Gauss-Markov Assumptions - Implications • A1:Model Matches Process (no way to confirm this – just build best model we can) • A2:Guarantees that Sum of Squared difference between observed and mean values of X is NOT equal to 0 • A3-A5:These are TESTABLE and can change the way we estimate the model if they are false

  6. Properties of OLS Estimators – continuedThe Classical Regression Model: Gauss-Markov Assumptions - Implications • A3:Error Terms have a common variance (Homoskedasticity not Heteroskedasticity) • A4:Error Terms are uncorrelated and do not influence each other (Error Terms are Not Serially Correlated) • A5:Knowing the value of X does not tell you anything about the value of ε (RHS Variables must not be Endogenous – must be Exogenous)

  7. Properties of OLS Estimators – continuedThe Classical Regression Model: Gauss-Markov Assumptions • Homoskedasticity: Each error term has the same variance → each data point is likely to lie just as far from the true model as any other • No Serial Correlation: Correlation of εi and εj equals 0 • Exogenous: Values determined outside the model (Independent) • Endogenous: Values determined within the model ( Y depends on X) • Linearity: WRT variables or Parameters or both

  8. Properties of OLS Estimators – continuedThe Classical Regression Model: Gauss-Markov Assumptions • Gauss-Markov Theorem: The estimators we get from OLS are efficient, that is; of all linear estimators, OLS provides ones with the lowest variance • A6: The Error Term is Normally Distributed; then OLS estimators have the Lowest Variance of other possible Unbiased Estimators • BLUE and BUE: A1-A5 → BLUE; add A6 and OLS estimators are BUE

  9. Properties of OLS Estimators – continuedSummary – Chapter 7 • An Estimator is Unbiased if its expected value is the True Value • An Estimator is Consistent if the chance of the Estimated Value being within any given distance of the True Value rises as the sample gets larger • An Estimator is Efficient within a class of unbiased estimators if it has a lower variance than other estimators in Its class

  10. Properties of OLS Estimators – continuedSummary – Chapter 7 • A1-A5 imply that Least Squares Estimators are Unbiased, Consistent, and More Efficient than any other Linear, Unbiased Estimator (BLUE) • A6 (Error Term is Normally Distributed) implies that OLS Estimator is BUE (linear or non-linear

  11. Properties of OLS Estimators – continuedSummary – Chapter 7 • The SER (Standard Error of the Regression) is an Unbiased and Consistent Estimator of the Variance of the Error Terms • The larger the SER, the larger the variances of the OLS parameters; but more observations imply smaller variances

  12. Properties of OLS Estimators – continuedSummary – Chapter 7 • The OLS Estimators are Normally Distributed if the Error Terms are Normally Distributed – They are approximately Normally Distributed, even if the Error Terms are not • We can use the OLS Estimates and their Standard Deviations to calculate Confidence Intervals for the True Values of β0 and β1 and to Test Hypothesis about those True Values

More Related