slides_Ch5_W[1] - Econometrics Textbook Reference Chapter 5...

Econometrics
Textbook Reference: Chapter 5, Wooldridge
Melissa Tartari
Yale
Melissa Tartari (Yale) Econometrics 1 / 27

Large Sample Theory: A Premise
In addition to °nite sample properties it is important to know the
asymptotic or large sample properties of estimators and test
statistics. These properties are not de°ned for a particular sample
size; rather, they are de°ned as the sample size grows without
bound .
Melissa Tartari (Yale) Econometrics 2 / 27

Large Sample Theory: A Premise
In addition to °nite sample properties it is important to know the
asymptotic or large sample properties of estimators and test
statistics. These properties are not de°ned for a particular sample
size; rather, they are de°ned as the sample size grows without
bound .
We will see that:
Melissa Tartari (Yale) Econometrics 2 / 27

Large Sample Theory: A Premise
In addition to °nite sample properties it is important to know the
asymptotic or large sample properties of estimators and test
statistics. These properties are not de°ned for a particular sample
size; rather, they are de°ned as the sample size grows without
bound .
We will see that:
The OLS estimator of β
j
has satisfactory large sample properties under
assumptions LR.1-LR.4.
Melissa Tartari (Yale) Econometrics 2 / 27

Large Sample Theory: A Premise
In addition to °nite sample properties it is important to know the
asymptotic or large sample properties of estimators and test
statistics. These properties are not de°ned for a particular sample
size; rather, they are de°ned as the sample size grows without
bound .
We will see that:
The OLS estimator of β
j
has satisfactory large sample properties under
assumptions LR.1-LR.4.
Even without normality (namely, LR.6), the t and F statistics have
approximately t and F distributions in large sample.
Melissa Tartari (Yale) Econometrics 2 / 27

A Review of Finite sample properties
Finite sample properties of estimators are properties that hold for a
sample of any size, no matter how large or small.
Melissa Tartari (Yale) Econometrics 3 / 27

A Review of Finite sample properties
Finite sample properties of estimators are properties that hold for a
sample of any size, no matter how large or small.
EXAMPLE: Unbiasedness
Melissa Tartari (Yale) Econometrics 3 / 27

A Review of Finite sample properties
Finite sample properties of estimators are properties that hold for a
sample of any size, no matter how large or small.
EXAMPLE: Unbiasedness
De°nition: An estimator W of θ is unbiased if, for all possible
values of θ ,
E [ W ] = θ
Melissa Tartari (Yale) Econometrics 3 / 27

A Review of Finite sample properties
Finite sample properties of estimators are properties that hold for a
sample of any size, no matter how large or small.
EXAMPLE: Unbiasedness
De°nition: An estimator W of θ is unbiased if, for all possible
values of θ ,
E [ W ] = θ
Meaning: if we could inde°nitely draw random (°nite) samples on Y
from the population, compute an estimate each time, and then
average them over all samples, we would obtain θ . Unbiasedness does