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Unformatted text preview: The Constant Term Functional Forms One Tailed Tests for Unitary Elasticity Chapter 7 Specification: Choosing a Functional Form Lecture 1 Masao Ogaki Department of Economics, Ohio State University November 6, 2007 Masao Ogaki Department of Economics, Ohio State University Chapter 7 Specification: Choosing a Functional Form Lecture 1 The Constant Term Functional Forms One Tailed Tests for Unitary Elasticity The Use and Interpretation of Constant Term See Figure 7.1 to see the harmful effect of suppressing the constant term. Read Section 7.1 of Studenmund. Masao Ogaki Department of Economics, Ohio State University Chapter 7 Specification: Choosing a Functional Form Lecture 1 The Constant Term Functional Forms One Tailed Tests for Unitary Elasticity Alternative Functional Forms Linearity An equation is linear in the variables if plotting the function in terms of X and Y generates a straight line. For example, Y = + 1 X + (1) is linear in the variables, but Y = + 1 X 2 + (2) is not linear in the variables. We can apply OLS to Regression (2), using Z = X 2 as the explanatory variable. Masao Ogaki Department of Economics, Ohio State University Chapter 7 Specification: Choosing a Functional Form Lecture 1 The Constant Term Functional Forms One Tailed Tests for Unitary Elasticity An equation is linear in the coefficients if the coefficients appear in their simplest form. For example, Regression (1) is linear in the coefficients. Y = + 2 1 X + (3) is not linear in the coefficients. We cannot apply OLS to estimate 1 in Regression (3). Masao Ogaki Department of Economics, Ohio State University Chapter 7 Specification: Choosing a Functional Form Lecture 1 The Constant Term Functional Forms One Tailed Tests for Unitary Elasticity For a single explanatory variable (K=1), the equation is linear in the coefficients if f ( Y ) = + 1 g ( X ) + (4) for some functions f ( Y ) and g ( X ) . For example, f ( Y ) = log ( Y ) , and g ( X ) = X 2 . As long as these functions are known, we can apply the OLS to data on f ( Y ) and g ( X ) . Regression (4)is not linear in the variables, but OLS can be applied because it is linear in the coefficients. Masao Ogaki Department of Economics, Ohio State University Chapter 7 Specification: Choosing a Functional Form Lecture 1 The Constant Term Functional Forms One Tailed Tests for Unitary Elasticity In this course, we only use the natural logarithms (logarithms to the base e = 2 . 71828 . . . ), which we will denote either by ln( ) or log( ) . You only need to know the following four properties of the natural logarithms: 1. ln ( AB ) = ln ( A ) + ln ( B ) . This means that ln ( A n ) = n ln ( A ) 2. ln ( A / B ) = ln ( A ) ln ( B ) 3. ln ( e ) = 1, this is from the definition of the natural logarithm....
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 Fall '07
 OGAKI
 Economics, Econometrics

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