ˆ and ˆ 2 1 ˆ and 1 ˆ 3 ˆ var and ˆ var 4 1 ˆ

Info icon This preview shows pages 11–16. Sign up to view the full content.

View Full Document Right Arrow Icon
ˆ and * 0 ˆ 2. 1 ˆ and * 1 ˆ 3. 0 ˆ var( ) and * 0 ˆ var( ) 4. 1 ˆ var( ) and * 1 ˆ var( ) 5. 2 ˆ and * 2 ˆ 6. 2 XY R and * * 2 X Y R From least-squares theory, note and show the following results:
Image of page 11

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

View Full Document Right Arrow Icon
ECON 301 - Introduction to Econometrics I April, 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 12 1. * 0 1 0 ˆ ˆ w 2. * 1 1 1 2 ˆ ˆ w w   3. *2 2 2 1 ˆ ˆ w 4. * 2 0 1 0 ˆ ˆ var( ) var( ) w 5. 2 * 1 1 1 2 ˆ ˆ var( ) var( ) w w 6. * * 2 2 XY X Y R R One can draw some conclusions from the findings above. For example, if 1 w = 2 w , that is, the scaling factors are identical, the slope coefficient and its standard error remain unaffected in going from the ( t Y , t X ) to the ( * t Y , * t X ) scale, which should be intuitively clear. However, the intercept and its standard error are both multiplied by 1 w . 3. Functional Forms of Regression Models In particular, we discuss the following regression models: 1. The Double-log (loglinear) model 2. Semi-log models 3. Reciprocal models
Image of page 12
ECON 301 - Introduction to Econometrics I April, 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 13 A. The Double-log (Loglinear) Model (Constant Elasticity Model) Consider the following model, known as the exponential regression model: 1 0 t u t t Y X e which may also be expressed as follows: 0 1 ln ln ln t t t Y X u or more simply, * 0 1 t t t W Z u where * 0 0 ln , ln t t W Y and ln t t Z X . Note that this model is linear both in the parameters and variables, and hence can be estimated by OLS regression. Because of this linearity, such models are called log-log , double-log , or loglinear models 3 . 3 Do not confuse the expression of loglinear with log-lin . See: Erlat, H. (1997), Introduction to Econometrics , Chapter 2: The Simple Linear Regression Model, p.78. However, Ramanathan uses loglinear expression for log-lin models; this is not compatible what we use in this course. We follow the terminology of Erlat (1997, p.78) and Gujarati (2004, p.175) and hence use the term loglinear to denote double-log models.
Image of page 13

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

View Full Document Right Arrow Icon
ECON 301 - Introduction to Econometrics I April, 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 14 Here, note that 1 ln ln t t d Y d X . On the other hand, we can write that ln ln t t t t t XY t t t t t dY d Y Y dY X Y d X dX dX X . Hence, in this model the slope coefficient is elasticity (the X elasticity of Y, or elasticity of Y with respect to X). Examples: 1. Cobb Douglas Production Function ( 1 0 t u t t Q L e ) 2. Constant Elasticity Demand Function ( 1 0 t u t t Q P e ) Two special features of the log-linear model may be noted: 1. The model assumes that the elasticity coefficient between Y and X, 1 , remains constant throughout, hence the alternative name constant elasticity model .
Image of page 14
ECON 301 - Introduction to Econometrics I April, 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR
Image of page 15

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

View Full Document Right Arrow Icon
Image of page 16
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern