ECON301_Handout_03_1213_02

# Partial differentiation yields the following normal

This preview shows pages 3–7. Sign up to view the full content.

Partial differentiation yields the following “ normal equations :

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
ECON 301 (01) - Introduction to Econometrics I March, 2012 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: Lecture Notes 4 2 0 1 0 ˆ ( ) ˆ ˆ 2 ( ) 0 ˆ t t t u Y X   (1) 2 0 1 1 ˆ ( ) ˆ ˆ 2 ( ) 0 ˆ t t t t u Y X X   (2) From (1) 0 1 ˆ ˆ ( ) 0 t t Y X 0 1 1 1 ˆ ˆ . 0 T T t t t t Y T X 0 1 1 1 ˆ ˆ . T T t t t t T Y X 1 1 0 1 ˆ ˆ T T t t t t Y X T T 0 1 ˆ ˆ Y X From (2) 0 1 ˆ ˆ ( ) 0 t t t Y X X 2 0 1 1 1 1 ˆ ˆ 0 T T T t t t t t t t Y X X X 2 0 1 1 1 1 ˆ ˆ T T T t t t t t t t Y X X X 2 1 1 1 1 1 . ˆ ˆ T T T t t t t t t t T X Y X Y X X X 2 1 1 1 1 . ˆ ˆ . . . . T T t t t t t Y X T Y X T X X X 2 1 1 1 1 . ˆ ˆ . . . . T T t t t t t Y X T Y X X T X X
ECON 301 (01) - Introduction to Econometrics I March, 2012 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: Lecture Notes 5 2 2 1 1 1 ˆ . . . T T t t t t t Y X T Y X X T X 2 1 1 2 1 . . ˆ . T t t t T t t Y X T Y X X T X Note that 2 2 2 2 1 1 1 1 1 2 2 2 2 2 1 1 1 2 2 1 ( ) 2 2 . 2 . T T T T T t t t t t t t t t T T T t t t t t t T t t x X X X X X X X X X T X X TX T X X TX and 1 1 1 1 1 1 1 1 1 ( )( ) ( ) T T T t t t t t t t t t t t T T T T t t t t t t t t T T t t t t t t x y X X Y Y X Y X Y XY YX X Y X Y Y X YX X Y XTY YTX TYX X Y TXY Hence the OLS estimator can also be written as in mean-deviation form as follows: 1 1 2 1 ˆ T t t t T t t x y x

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
ECON 301 (01) - Introduction to Econometrics I March, 2012 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: Lecture Notes 6 A. Mean of 1 ˆ We assume that we draw repeated samples of size T from the population of Y and X , and for each sample we estimate the parameters 0 ˆ and 1 ˆ . This is known as hypothetical repeated sampling procedure. If all the possible samples are taken, then the mean value of 1 ˆ will be its expected value, (mean 1 ˆ )=E( 1 ˆ ) . To find the value of the mean in terms of the observations of our sample of Y and X we work as follows.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern