<p>Yes it does. According to the Verbeeks guide to modern econometrics (pp418) standard panel fixed effects binary model assumes that error has “a symmetric distribution with distribution function <span class="math-container">$F(.)$</span>, i.i.d. across individuals and time and independent of all <span class="math-container">$x_{is}$</span>” [with the model being  <span class="math-container">$y_{it}^*=x_{it}’ \beta+ \alpha_i+u_{it}$</span>].</p>

<p>Just a two pages later Verbeek also writes about Random effects probit model <span class="math-container">$y_{it}^*=x_{it}’ \beta +\epsilon_{it}$</span> that <span class="math-container">$\epsilon_{it}$</span> should also besides other things be independent of <span class="math-container">$x$</span>.</p>

<p>Now both of the above panel models are technically static since no lags are involved but I don’t see any reason why this assumption could be relaxed just by making model dynamic. In fact there is a such thing as panel IV logit/probit, probably people would not invest time into development of those if this assumption could be relaxed by just adding lags.</p>

CC BY-SA 4.0
2020-02-13T23:59:01.693Z
2020-02-13T23:59:01.693Z
1muflon1
<p>I am trying to understand how does the fact that a regressor is endogenous (as a result of reverse causality) in a dynamic probit model violate any assumptions that I may need to make for this model. E.g. for an OLS model, it is pretty straightforward - the orthogonality condition for the regressor being uncorrelated with the error term will not hold. Can similar logic be extended to probit models with panel data? I would appreciate simple explanations and/or references that explain this. </p>

<econometrics><paneldata>
Probit with panel data - assumptions violated with endogenous covariate?
Paul
# Probit with panel data - assumptions violated with endogenous covariate?

(Asked by: username_0 on 2020-02-13)

I am trying to understand how does the fact that a regressor is endogenous (as a result of reverse causality) in a dynamic probit model violate any assumptions that I may need to make for this model. E.g. for an OLS model, it is pretty straightforward - the orthogonality condition for the regressor being uncorrelated with the error term will not hold. Can similar logic be extended to probit models with panel data? I would appreciate simple explanations and/or references that explain this.

**Tags:** econometrics, paneldata

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## 1 answers

### Answer by username_1 on 2020-02-13. Score: 2 | Accepted answer

Yes it does. According to the Verbeeks guide to modern econometrics (pp418) standard panel fixed effects binary model assumes that error has “a symmetric distribution with distribution function $F(.)$, i.i.d. across individuals and time and independent of all $x\_{is}$” [with the model being $y\_{it}^\*=x\_{it}’ \beta+ \alpha\_i+u\_{it}$].

Just a two pages later Verbeek also writes about Random effects probit model $y\_{it}^\*=x\_{it}’ \beta +\epsilon\_{it}$ that $\epsilon\_{it}$ should also besides other things be independent of $x$.

Now both of the above panel models are technically static since no lags are involved but I don’t see any reason why this assumption could be relaxed just by making model dynamic. In fact there is a such thing as panel IV logit/probit, probably people would not invest time into development of those if this assumption could be relaxed by just adding lags.


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