Specification (regression)

In regression analysis and related fields such as econometrics, specification is the process of converting a theory into a regression model. This process consists of selecting an appropriate functional form for the model and choosing which variables to include. Model specification is one of the first steps in regression analysis. If an estimated model is misspecified, it will be biased and inconsistent.^[1]

Specification error and bias

Specification error occurs when an independent variable is correlated with the error term. There are several different causes of specification error:

• incorrect functional form
• a variable omitted from the model may have a relationship with both the dependent variable and one or more of the independent variables (omitted-variable bias);^[2]
• an irrelevant variable may be included in the model
• the dependent variable may be part of a simultaneous equation (simultaneity bias)
• measurement errors may affect the independent variables.

Detection

The Ramsey RESET test can help test for specification error.

See also

• Model risk

References

1. ^ Lee, Cheng Few; Lee, John C.; Lee, Alice C.Statistics for Business and Financial Economics. World Scientific Publishing Company. 2nd edition. (December 1999). p 718.
2. ^ Untitled

• Thursby, Jerry G.; Schmidt, Peter (September 1977). "Some Properties of Tests for Specification Error in a Linear Regression Model". Journal of the American Statistical Association (Journal of the American Statistical Association, Vol. 72, No. 359) 72 (359): 635–641. doi:10.2307/2286231. JSTOR 2286231. 
• Sapra, Sunil (2005). "A regression error specification test (RESET) for generalized linear models" (PDF). Economics Bulletin 3 (1): 1–6. http://economicsbulletin.vanderbilt.edu/2005/volume3/EB-04C50033A.pdf.