Specification (statistics)

In statistics and econometrics, the specification describes a process of model development in which an economically and statistically estimable model (estimation model) is established. The dependent variables and the explanatory variables, as well as their functional relationship, are determined by the specification. The specification is based on an economic model. From this economic model, an estimable econometric model is derived, the explanatory variables of which should be correctly specified. In time series analysis , the model specification is the determination of the order p, q of an ARMA process or p, d, q of an ARIMA process.

example

As an example, one could specify the functional relationship between household income and human capital as measured by the number of years of schooling and work experience : ${\ displaystyle y = f (s, x)}$ ${\ displaystyle y}$ ${\ displaystyle s}$ ${\ displaystyle x}$

{\ displaystyle \ ln y = \ ln y_ {0} + \ rho s + \ beta _ {1} x + \ beta _ {2} x ^ {2} + \ varepsilon}

.

Here denotes the unexplained error term that is assumed to be independent and identically distributed . If the model satisfies the Gauss-Markov assumptions , then the parameters and can be estimated accurately and efficiently using the least squares method . ${\ displaystyle \ varepsilon}$ ${\ displaystyle \ rho}$ ${\ displaystyle \ beta}$

Specification errors and distortions

A specification error occurs when the independent variable correlates with the error term . There are a variety of specification errors:

A wrong functional form could have been chosen
A variable that was not involved in the regression equation, could with the dependent variable and one or more explanatory variables correlate ( distortion by exuberant variables ( English omitted variable bias ))
An irrelevant variable was inserted into the regression model
Measurement errors could affect the dependent variable

Individual evidence

^ Rainer Schlittgen , Bernd Streitberg: Time series analysis. Oldenbourg Verlag, 2001., ISBN 978-3-486-71096-0 (accessed from De Gruyter Online). P. 253

[1] Rainer Schlittgen , Bernd Streitberg: Time series analysis. Oldenbourg Verlag, 2001., ISBN 978-3-486-71096-0 (accessed from De Gruyter Online). P. 253