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Assume the simplest linear regression model $$y = bx + u$$ The OLS etimator for $b$ is $$\hat b_{OLS} = \frac {\sum x_iy_i}{\sum x_i^2} = b + \frac {\sum x_ie_i}{\sum x_i^2}$$ Whatever the true $b$ is (it is zero in your case, as another answer pointed out) , the fact is that $$\text{plim} \frac {n^{-1}\sum x_ie_i}{n^{-1}\sum x_i^2} \neq 0$$ and so ...

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What you are referring to is two-stage least squares. This is an instrumental variable commonly applied to correct for endogeniety and selection bias. It is a pretty hot topic in economics at the moment and, when applied correctly, can be very useful and will remove the selection bias. There are a few conditions and assumptions - Suppose you want to ...

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Windmeijer (2000, Economics Letters) presents a treatment of the estimation of count-data models with fixed effects and endogeneity. http://www.sciencedirect.com/science/article/pii/S0165176500002287 See this slideshow by Wooldridge for a pedagogic and progressive presentation of panel data models with endogeneity. Count-data models are introduced slide ...

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Your first point is valid for not using fixed effects as you are interested in the entire border not just these 16 roads. Random effects can be advantageous when you have such a small sample compared to the population for your treatment group. Also note, if the unobserved effect has a large variance or T is very large then RE will be close to FE anyway. ...

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The question is not totally clear, but I will attempt to give you some guidance. To answer your first questions, confounding variables are not a type of endogenous variable. We do not observe nor are we interested in the confounding variables, which means they are not endogenous variables in our model. You later give the correct definition of an ...

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You are completely correct that mathematically endogeneity is defined $\text{cov(X,e)}\neq0$, which is true not only when it’s correlated with omitted variable but also with measurement error or reverse causation/simultaneity. However, every single variable in economics can be subject to correlation with omitted variables or measurement error, so if you ...

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No, I don't see how the dummy variable you are proposing would give you the same (or even similar) analysis as in the original model. I would recommend dealing with the endogeneity in another way. IV estimation, or one of the more recent methods, difference-in-difference, matching etc. One of the will be suitable.

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In principle, there is nothing to exclude the case where all regressors are endogenous. My issue is that the Hurlin-Dumitrescu test has to do with Granger-causality, and Granger-causality examines the relation between the regressors and the dependent variable, not the relation between the regressors and the error term. On the other hand, endogeneity refers ...

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In a typical OLS model, $Y=\alpha+\beta X+\epsilon$, endogeneity exists when $E[\epsilon\,|\,X]\ne 0$, which results from $X$ and $\epsilon$ being correlated with one another. In your case, $Y$ uncorrelated with $\epsilon$ implies only that $E[\epsilon]=0$, which is not the same as the exogeneity condition $E[\epsilon\,|\,X]= 0$. Moreover, $Y$ ...

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I looked a bit more into this and I think I found the confirmation of my suspicion into this article, which describes the command ivreg2 in STATA. I am not a super-techy econometrician but from my understanding it can apparently be done using the orthog() option, and under certain conditions it is equivalent to a Hausman test. http://www.stata-journal.com/...

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(i) I think your idea makes sense. Under the null, $[X,Z]$ is orthogonal to $\varepsilon$. Under the alternative, $X$ is correlated with $\varepsilon$. (ii) Your statement that it's "basically a test of whether the OLS residual are orthogonal to $Z$" is exactly what I think. (iii) Your thought about the power depending on the relevance of $Z$ also makes ...

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