notes09 - Specification Errors and Specification Tests ECON...

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Unformatted text preview: Specification Errors and Specification Tests ECON 399 Neil Hepburn Contents 1 Introduction 1 2 The Nature of Specification Errors 1 3 Consequences of Misspecification 2 4 Detecting Misspecification 2 4.1 Ramsey’s Regression Error Specification Test (RESET) . . . . . 2 4.2 Non-Nested Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 4.3 Information Criteria . . . . . . . . . . . . . . . . . . . . . . . . . 5 4.4 Choosing Between Log and Linear Specifications . . . . . . . . . 6 5 Unobservable Regressors 7 6 Measurement Error 8 1 Introduction Introduction • Early in the course we looked at the issue of omitted variable bias - this is an example of a misspecified model • There are many ways in which a model can be misspecified • We now turn to the issue of detecting specification errors in our regression models. 2 The Nature of Specification Errors The Nature of Specification Errors • Specification errors can result from the wrong functional form (log vs linear) 1 • Missing interaction terms • Missing variables 3 Consequences of Misspecification Consequences of Misspecification • Misspecification can have quite serious consequences for us • Our OLS estimators will generally be biased and not consistent • This means that any results that we get from a model are junk • Specification problems cannot be ignored. 4 Detecting Misspecification Detecting Misspecification • There are some tests that we can make use of to detect specification errors and choose between competing specifications • We also need to rely on judgement and a sound understanding of economic theory 4.1 Ramsey’s Regression Error Specification Test (RE- SET) Ramsey’s RESET • Ramsey’s RE gression S pecification E rror T est can assist us in deciding whether or not higher powers of our regressors or interaction terms are needed • The idea with Ramsey’s RESET is that we begin by assuming that the model is correctly specified against an alternative that higher powers and cross products should be included • To illustrate this, we will look at the following simple model: y i = β + β 1 x i 1 β 2 x i 2 + u i (1) 2 Ramsey’ RESET • If add higher powers of x i 1 and x i 2 as well as their cross products, we get the following y i = β + β 1 x i 1 β 2 x i 2 + β 3 x 2 i 1 + β 4 x 2 i 2 + β 5 x i 1 x i 2 + u i (2) • Under the null hypothesis, the coefficients β 3 , β 4 , and β 5 should all be zero • Thus, Ramsey’s RESET is actually quite straight forward. Ramsey’s RESET • Often we want to go beyond simple squares and cross products and include cubic terms • This can make the auxiliary regression model rather unwieldy • To solve this problem, we can use squares and cubes of ˆ y i • Most regression packages can do this test for us....
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This note was uploaded on 10/04/2011 for the course ECONOMICS 399 taught by Professor Neil.h during the Spring '11 term at University of Alberta.

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notes09 - Specification Errors and Specification Tests ECON...

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