ECON301_Handout_09_1213_02

# However the intercept and its standard error are both

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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

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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.
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 .

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

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