Specification Errors | Eonomics
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Specification errors in regression arise from mistakes in variables or model assumptions, and can occur due to the inclusion of irrelevant variables, omission of relevant ones, or incorrect functional form. While including irrelevant variables does not bias estimators, it makes them inefficient, whereas omitting relevant variables results in biased and inconsistent estimators that invalidate hypothesis tests. Various tests, such as the Ramsey RESET test, are recommended to detect these errors and ensure robust regression models.
Specification Errors | Eonomics
- 2. Definition and types of specification error • Specification errors in regression are the errors that occur because of a mistake in one of the variables or other assumptions of the model • A regression model will have a specification error when at least one of the following problems occur in that model: 1. Inclusion of irrelevant variable 2. Omission of relevant variable 3. Incorrect functional form
- 3. Inclusion of irrelevant variable • This is the least serious problem that leads to specification error • The hypothesis tests of a model which has included an irrelevant variable are still valid • The inclusion of irrelevant variable does not affect the relationship between other variables and the dependent variable because the estimator for such a variable turns out to be zero • The estimators of such a model are unbiased and consistent • However, the estimators are not efficient because the variances are larger than they would have been in the model excluding the irrelevant variable • The estimators violate the BLUE (Best Linear Unbiased Estimator) concept of regression because they are inefficient
- 4. Omission of relevant variable • Omission of a relevant variable has serious consequences for the regression analysis and almost everything goes wrong in this case • The estimators are biased and inconsistent • As a result the hypothesis tests do not hold • Even choosing a larger sample size does not make the estimators unbiased or consistent • The inconsistency of estimators is generated by a lower than normal variance in the regression analysis
- 5. Incorrect functional form and measurement errors • When you choose the wrong functional form for your regression model, the model will have a specification error • For example, if you choose a double log model for your analysis instead of the log-liner model (which describes the relation between the independent and dependent variables better) your model will suffer from a specification bias • Measurement errors are the errors that occur in measuring the magnitude of the variables and this too leads to larger variances for the model than there would have been if there were no measurement error
- 6. Tests for checking for the presence of specification errors • Given that specification errors lead to problems for the regression analysis, it is very important to check for these errors when we develop our model • F-test and t-test have been recommended by Gujrati but it is not advisable to use these tests for checking for the presence of specification errors • RESET is a test developed by J B Ramsey, a famous econometrician and has been gaining popularity • Other tests include Likelihood ratio test and Lagrange Multiplier test • One should run these tests on their models to ensure that there are no specification errors in the model so that they have a robust regression model
- 7. Helpful links • You can go through the steps for RESET test here: https://www.uvm.edu/~wgibson/Classes/200f09/Technical_n otes/Ramsey_RESET.pdf • These lecture notes will help in understanding the concept and consequences of specification errors in detail: http://ocw.uc3m.es/economia/econometrics/lecture-notes- 1/Topic5_logo.pdf/at_download/file
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