2 Model specification

• Model specification refers to: (1) variables selection, (2) causality direction and (3) functional form selection

• Based on economic theory (specific subject of research) we should select appropriate variables, and assume causality directions between them in advance

TABLE 2.1: Examples of dependent and independent variables

$~~~~$Dependent	$~~~~~~~~~~~~~~~~~~~~$Independent(s)
$y=$ height	$x=$ age
$y=$ consumption	$x=$ income
$y=$ demand	$x=$ price
$y=$ production	$x_1=$ labour, $x_2=$ capital
$y=$ interest rate	$x_1=$ money supply, $x_2=$ inflation
$y=$ crop yield	$x_1=$ temperature, $x_2=$ rainfall, $x_3=$ number of sunshine days, …

• Variables in TABLE 2.1 are all numerical. However, standard econometric analysis requires continuous dependent variable, while independent variables are allowed to be qualitative (non-numerical) as well!

Qualitative variables can also be included in the equation on the right-hand side by using binary values of $0$ and $1$. These variables are known as dummy variables!

• In the most simple application a single dummy variable with two categories can be included, e.g. we could examine if there is a difference in average weight between males and females, i.e. if the weight (variable $y$) depends on the gender (variable $x$)?

$$\begin{equation}y_i=\beta_0+\beta_1x_i+u_i~~,~~~~~~y=weight~~,~~~x=\left\{\begin{array}{cl} 1& for~males,\\0& for~females\end{array}\right. \tag{2.1} \end{equation}$$