Specification (regression)

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:

$\ln y = \ln y_{0} + \rho s + \beta_1 x + \beta_2 x^2 + \epsilon$

where $\epsilon$ is the unexplained residual that is supposed to be independent and identically distributed. If assumptions of the regression model are correct, the least squares estimates of the parameters $\rho$ and $\beta$ will be efficient unbiased. Hence specification diagnostics usually involves 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:

• 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);
• 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.

See also

• Model risk
• Regression model validation