Lecture34-2010

# Lecture34-2010 - Time Series Models Lecture XXXIV Charles B...

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Time Series Models: Lecture XXXIV Charles B. Moss December 2, 2010 I. Nonspherical Errors - Autocorrelation in Structural Models A. Time Series versus Structural Models 1. Theoretical models of supply and demand. a) Most students have been introduced to the utility model for the derivation of consumer demand. Taking for exam- ple the Cobb-Douglas utility function max x 1 ,x 2 x α 1 x β 2 s . t .p 1 x 1 + p 2 x 2 Y (1) yields two demand equations x 1 ( p 1 ,p 2 ,Y ) = Y p 1 ± α α + β ² x 2 ( p 1 ,p 2 ,Y ) = Y p 2 ± β α + β ² . (2) Taking the natural logarithms of the demand equations in Equation 2 yields structural models of demand ln ( x 1 ) = ln ± α α + β ² - ln ( p 1 ) + ln ( Y ) ln ( x 2 ) = ln ± β α + β ² - ln ( p 2 ) + ln ( Y ) ³ ln ( x 1 ) = α 01 + α 11 ln ( p 1 ) + α 21 ln ( p 2 ) + α 31 ln ( Y ) ln ( x 2 ) = α 02 + α 12 ln ( p 1 ) + α 22 ln ( p 2 ) + α 32 ln ( Y ) ´ (3) 1

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AEB 6571 Econometric Methods I Professor Charles B. Moss Lecture XXXIV Fall 2010 So the estimated model is directly linked to the theoretic model. b) The structural models can also be derived analytical ex- pansions of theoretic relationships. Speciﬁcally, in pro- duction economics we derive the existence of the cost function for a ﬁrm (and the expenditure function for the consumer) ± min x x 0 w s . t .f ( x,y ) = 0 ² C ( w,y ) (4) often this relationship is estimated a second order Taylor series expansion of an unknown function C ( w,y ) = α 0 + α 0 x + 1 2 x 0 Ax + β 0 y + 1 2 y 0 By + x 0 Γ y. (5) The cost function and input demand functions derived us- ing Shephard’s lemma are derived from economic theory. c) These models are typically referred to as structural models where economic theory can be used to directly justify the speciﬁcation. 2. Time series models model the current value of an economic
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Lecture34-2010 - Time Series Models Lecture XXXIV Charles B...

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