# In a two equation system, what is the meaning of the assumption "exogenous X is uncorrelated with ε1ε2"

Assume a triangular system such as

\begin{eqnarray*} Y = X'\beta_1 + D\gamma_1 + \varepsilon_1 \\ D = X'\beta_2 + \varepsilon_2 \end{eqnarray*}

with $Y$ and $D$ as observed endogenous variables, $X$ a vector of observed exogenous variables, and $\varepsilon_j$ as the unobserved error terms.

What is the meaning of this assumption $Cov(X, \varepsilon_1\varepsilon_2)=0$? When is it violated?

• What is the assumed relation between the two error terms? Dec 4, 2014 at 21:03
• ε1 and ε2 may be correlated and there is some heteroscedasticity in the form of $cov(X, e_2^2) != 0$ but I can't get my head around when the assumption is satisfied or violated.
– greg
Dec 4, 2014 at 22:21