Similarly consider the following model 1 1 t t t t t

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Similarly, consider the following model: 1 1 0 0 ( ) ( ) t t t t t t t q q x g p g u (4)12.35
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 9 Notice that, Model (4) can be obtained from Model (3) by imposing single restriction that 0 0 0 0 or 0 0 0   , since: 1 1 0 0 0 t t t t t t q q x p g u (3)12.34 1 1 0 0 0 0 ( ) t t t t t t q q x p g u   1 1 0 0 0 0 t t t t t t t q q x p g g u 1 1 0 0 ( ) ( ) t t t t t t t q q x g p g u Model (4) is therefore nested within Model (3) 5 . The relationship between the above models is illustrated in Figure 1 below. It is important to realize that different models or equations are not necessarily nested within each other. For example, Model (3) and Model (4) are non-nested models because neither can be obtained from the other by the imposition of a restriction. This is reflected by the fact that they appear in different “branches” of the structure in Figure 1. Both models are, however, nested within the general model (GUM), of course. 5 If variables are defined in logarithmic terms, so that 0 , 0 and 0 are elasticities then Model (4) implies that demand for food is homogenous of degree zero, as predicted by microeconomic theory: if all prices and income doubles at the same time, the optimum consumption choice of consumer will not change.
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 10 Figure 1 Nested Models In practice, a general-to-specific investigation of the demand for food would commence with an initial equation such as (GUM). In general, it is important that the initial model (GUM) should: (a) have nested within it all competing hypothesis or theories concerning the phenomenon under investigation; (b) Be able to explain existing data and be able to satisfy various tests for misspecification. If an important theory has been overlooked, and consequently a relevant variable has been omitted from the initial general equation (GUM), then that equation is likely to fail many tests of
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ECON 301 - Introduction to Econometrics I May 2013 METU - Department of Economics Instructor: Dr. Ozan ERUYGUR e-mail: [email protected] Lecture Notes 11 misspecification that we have described before. Therefore, the initial equation is generally exposed to a bunch of such diagnostic tests to ensure, for example, that functional form has not been mis-specified, that variables have not been omitted (RESET test can be used), or that lag lengths are not too short (Durbin Watson, DW, autocorrelation test can be used).
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