Endogeneity versus unobserved heterogeneity What is the difference between endogeneity and unobserved heterogeneity? I know that endogeneity comes for example from omitted variables? But as far as I understand, unobserved heterogeneity causes the same problem. But where exactly lays the difference between these two notions?
 A: I understand heterogeneity to be any difference between individuals. Observed heterogeneity usually consists of the covariates and unobserved heterogeneity consists of any unobserved difference like ability or effort.
Endogeneity refers to the relationship between the observed and unobserved variables, namely that they are dependent on one another.
A: To wrap it up: 


*

*Unobserved heterogeneity is one possible cause of endogeneity.

*Endogeneity is therefore the broader term. 

*Unobserved heterogeneity implies endogeneity but not the other way around. 

A: the difference between the unobserved heterogeniety and endogeniety in the case of omitted variables lies in the orthogonality assumptions made. Whereas in the former, the assumption is that the unobserved omitted variable is independent of the observed (included) explanatory variable x,...in the latter this assumption is relaxed such that the unobserved (omitted) variable is correlated with some of the observed (included) explanatory variable.
A: I agree with @Michael's description of endogeneity---this is about a problem with the variables that you include and their relationship to the variables that you do not (i.e., the stuff in the error term). 
Unobserved heterogeneity is typically about unobservable componenents of the effects that you are estimating. Continuing with @Michael's education example, unobserved heterogeneity might be that some people have higher returns (e.g., increases in wages) from going to school than others. Let the returns for person $i$ be $\beta + b_i$ with $\mathbb{E}(b_i) = 0$. We have
$$\begin{equation*} y_i = x_i (\beta + b_i) + w^\prime_i \gamma + \epsilon_i, \end{equation*}$$
where $y_i$ is (typically, log) income, $x_i$ is years of education, and $w_i$ is a set of other controls. An example of endogeneity is when $x_i$ is correlated with $\epsilon_i$ (e.g., education is correlated with IQ, which is not among our other predictors).
If we estimate a single coefficient, we have
$$\begin{equation*} y_i = x_i \beta + w^\prime_i \gamma + (\epsilon_i + b x_i) = x_i \beta + w^\prime_i \gamma + \tilde{\epsilon}_i \end{equation*}$$
See that the included variable $x_i$ is correlated with the error term $\tilde{\epsilon}_i$, inducing the same problems as the case of endogeneity.
A: The terms endogeneity and unobserved heterogeneity often refer to the same thing but usage varies somewhat, even within economics, the discipline I most associate with the terms.  
In a regression equation, an explanatory variable is endogenous if it is correlated with the error term.
Endogeneity is often described as having three sources: omitted variables, measurement error, and simultaneity.  Though it is often helpful to mention these "sources" separately, confusion sometimes arises because they are not truly distinct.  Imagine a regression predicting the effect of education on wages.  Perhaps our measure of education is simply the number of years someone spent in formal education, regardless of the type of education.  If I have a clear idea of what type of education affects wages, I might describe this situation as measurement error in the education variable.  Alternatively, I could describe the situation as an omitted variables problem (the variables indicating type of education).
Perhaps wages also affect education decisions.  If wages and education are measured at the same time this is an example of simultaneity, but it too, might be reframed in terms of omitted variables.  
Unobserved heterogeneity is simply variation/differences among cases which are not measured.  If you understand endogeneity, I think you understand the implications of unobserved heterogeneity in a regression context.
A: Easy answer, without explanation because it is not wanted: if the omitted variables that cause endogeneity are not observable we call it unobserved heterogeneity. Easy :)
