ECON301_Handout_09_1213_02

However the intercept and its standard error are both

Info iconThis preview shows pages 12–16. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 12

Info iconThis 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 13 A. The Double-log (Loglinear) Model (Constant Elasticity Model) Consider the following model, known as the exponential regression model: 1 0 t u tt Y X e which may also be expressed as follows: 01 ln ln ln t t t Y X u  or more simply, * t t t W Z u where * 00 ln , WY and ZX . 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.
Background image of page 13
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 t t dY dX . On the other hand, we can write that t t t t t XY t ttt 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 tt Q L e ) 2. Constant Elasticity Demand Function ( 1 0 t u 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 .
Background image of page 14

Info iconThis 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 15 2. Another feature of the model is that although * 0 ˆ and 1 ˆ are unbiased estimates of * 0 and 1 , 0 (the parameter entering the original model) when estimated as * 0 ˆ 0 ˆ e is itself a biased estimator . 4 0 ˆ is not BLUE because, apart from unbiasedness, 0 ˆ is a non linear estimator. However, 0 ˆ will satisfy the large-sample properties and hence 0 ˆ is a consistent and asymptotically efficient estimator. B. The Semi-log Models: Log–Lin and Lin–Log Model These are called semilog models because only one variable (in this case the regressand) appears in the logarithmic form. For descriptive purposes a model in which the regressand (dependent variable) is logarithmic will be called a log-lin model . A model in which the regressand (dependent variable) is linear but the regressor(s) (independent variable) are logarithmic is called a lin-log model .
Background image of page 15
Image of page 16
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page12 / 23

However the intercept and its standard error are both...

This preview shows document pages 12 - 16. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online