# Specification (regression)

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In regression analysis specification is the process of developing a regression model. This process consists of selecting an appropriate functional form for the model and choosing which variables to include. For instance, one may specify the functional relationship y = f ( s , x ) between personal income y and human capital in terms of schooling s and on-the-job experience x as:

## Contents

ln y = ln y 0 + ρ s + β 1 x + β 2 x 2 + ε

where ε is the unexplained error term that is supposed to be independent and identically distributed. If assumptions of the regression model are correct, the least squares estimates of the parameters ρ and β will be efficient and unbiased. Hence specification diagnostics usually involve testing the first to fourth moment of the residuals.

## 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:

• An incorrect functional form could be employed;
• 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);
• an irrelevant variable may be included in the model;
• the dependent variable may be part of a system of simultaneous equations (simultaneity bias);
• measurement errors may affect the independent variables.
• ## Detection

The Ramsey RESET test can help test for specification error.

## References

Specification (regression) Wikipedia

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