notes09 - Specification Errors and Specification Tests ECON...

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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
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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 0 + β 1 x i 1 β 2 x i 2 + u i (1) 2
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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 0 + 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. Ramsey’s RESET In Shazam, to perform Ramsey’s RESET on the model given in Equation (1) we would use OLS y x1 x2 DIAGNOS / RESET Shazam then computes the test using ˆ y raised to the powers 2, 3, and 4 Shazam reports an F -statistic as well as p - values for each power of ˆ y If any of the variants are significant ( p < 0 . 05) we conclude that we need
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