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In statistics, model specification is part of the process of building a statistical model: specification consists of selecting an appropriate functional form for the model and choosing which variables to include. For example, given personal income${\displaystyle y}$ together with years of schooling ${\displaystyle s}$ and on-the-job experience ${\displaystyle x}$, we might specify a functional relationship ${\displaystyle y=f(s,x)}$ as follows:^[1]

${\displaystyle \ln y=\ln y_0+\rho s+{\beta }_{1}x+{\beta }_2{x}^2+\epsilon }$

where ${\displaystyle \epsilon }$ is the unexplained error term that is supposed to comprise independent and identically distributedGaussian variables.

The statistician Sir David Cox has said, 'How [the] translation from subject-matter problem to statistical model is done is often the most critical part of an analysis'.^[2]

• 1Specification error and bias

Specification error and bias[edit]

Elements Of Econometrics Kmenta Pdf Creator Software

Specification error occurs when the functional form or the choice of independent variables poorly represent relevant aspects of the true. In the words of Burnham & Anderson, 'Modeling is an art as well as a science and is directed toward finding a good approximating model ... as the basis for statistical inference'.^[4]

Detection of misspecification[edit]

The Ramsey RESET test can help test for specification error in regression analysis.

Elements Of Econometrics Kmenta Pdf Creator Word

In the example given above relating personal income to schooling and job experience, if the assumptions of the model are correct, then the least squares estimates of the parameters ${\displaystyle \rho }$ and ${\displaystyle \beta }$ will be efficient and unbiased. Hence specification diagnostics usually involve testing the first to fourth moment of the residuals.^[5]

Model building[edit]

Building a model involves finding a set of relationships to represent the process that is generating the data. This requires avoiding all the sources of misspecification mentioned above.

One approach is to start with a model in general form that relies on a theoretical understanding of the.^[6]

Another approach to model building is to specify several different models as candidates, and then compare those candidate models to each other. The purpose of the comparison is to determine which candidate model is most appropriate for statistical inference. Common criteria for comparing models include the following: R², Bayes factor, and the likelihood-ratio test together with its generalization relative likelihood. For more on this topic, see statistical model selection.

See also[edit]

Notes[edit]

1. ^This particular example is known as Mincer earnings function.
2. ^Cox, D. R. (2006), Principles of Statistical Inference, Cambridge University Press, p. 197.
3. ^'Quantitative Methods II: Econometrics', College of William & Mary.
4. ^Burnham, K. P.; Anderson, D. R. (2002), Model Selection and Multimodel Inference: A practical information-theoretic approach (2nd ed.), Springer-Verlag, §1.1.
5. ^Long, J. Scott; Trivedi, Pravin K. (1993). 'Some specification tests for the linear regression model'. In Bollen, Kenneth A.; Long, J. Scott (eds.). Testing Structural Equation Models. SAGE Publishing. pp. 66–110.
6. ^Popper, Karl (1972), Objective Knowledge: An evolutionary approach, Oxford University Press.

Further reading[edit]

• Akaike, Hirotugu (1994), 'Implications of informational point of view on the development of statistical science', in Bozdogan, H. (ed.), Proceedings of the First US/JAPAN Conference on The Frontiers of Statistical Modeling: An Informational Approach—Volume 3, Kluwer Academic Publishers, pp. 27–38.
• Asteriou, Dimitrios; Hall, Stephen G. (2011). 'Misspecification: Wrong regressors, measurement errors and wrong functional forms'. Applied Econometrics (Second ed.). Palgrave Macmillan. pp. 172–197.
• Colegrave, N.; Ruxton, G. D. (2017). 'Statistical model specification and power: recommendations on the use of test-qualified pooling in analysis of experimental data'. Proceedings of the Royal Society B. 284 (1851): 20161850. doi:10.1098/rspb.2016.1850. PMC5378071. PMID28330912.
• Gujarati, Damodar N.; Porter, Dawn C. (2009). 'Econometric modeling: Model specification and diagnostic testing'. Basic Econometrics (Fifth ed.). McGraw-Hill/Irwin. pp. 467–522. ISBN978-0-07-337577-9.
• Harrell, Frank (2001), Regression Modeling Strategies, Springer.
• Kmenta, Jan (1986). Elements of Econometrics (Second ed.). New York: Macmillan Publishers. pp. 442–455. ISBN0-02-365070-2.
• Lehmann, E. L. (1990). 'Model specification: The views of Fisher and Neyman, and later developments'. Statistical Science. 5 (2): 160–168. doi:10.1214/ss/1177012164.
• MacKinnon, James G. (1992). 'Model specification tests and artificial regressions'. Journal of Economic Literature. 30 (1): 102–146. JSTOR2727880.
• Maddala, G. S.; Lahiri, Kajal (2009). 'Diagnostic checking, model selection, and specification testing'. Introduction to Econometrics (Fourth ed.). Wiley. pp. 401–449. ISBN978-0-470-01512-4.
• Sapra, Sunil (2005). 'A regression error specification test (RESET) for generalized linear models'(PDF). Economics Bulletin. 3 (1): 1–6.