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3

FE logit requires the idiosyncratic errors to be IID across $i$ and $t$, quite a strong assumption. Also the regressors should be strictly exogenous, but it's the same for linear FE models. In your application, the fact that FE logit wouldn't converge will make a good argument against FE logit, and will satisfy some referees but not all. An important ...

3

Having read up on your question it seems the fixed effect is fixed. If this is indeed the case it will have zero variance and hence zero covariance with any variable.

3

I asked exactly the same question on math.stackexchange: https://math.stackexchange.com/questions/1470490/fixed-effects-estimation In short, the answer is yes, it can be viewed as running separate OLS regressions- the weights, however, are not arbitrary. It is a weighted average of the separate OLS regressions.

2

The biggest difference between (1) and (3) is that (3) has incidental linear trends while (1) has common time effects. Differencing (1) gives (1a) $\Delta \log(uclms_{it}) = (\theta_t - \theta_{t-1}) + \beta_1 \Delta ez_{it} + \Delta \epsilon_{it}$. Comparing this to (3) you see that (3) has $\gamma_i$ in place of $\theta_t - \theta_{t-1}$ in (1a). So ...

2

The use of the natural $\log$ permits to obtain approximations of percentage changes instead of unit changes (assuming linear regression). For instance, the parameter associated with $\log$ of GDP per capita would give you the changes in education (in the unit you measured it, e.g., years) as a result of an increase of 1% in GDP per capita. Notice that if ...

2

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 ...

1

Assuming that you mean "fixed effects" of econometricians, not of statisticians, you can check it as follows. You have $v_{it} = u_i + e_{it}$ consistently estimated (as $\beta$ is consistently estimated), where $u_i$ are the fixed effects and $e_{it}$ are the idiosyncratic errors. Under the assumption that $x_{it}$ is strictly exogenous to $e_{it}$ (which ...

1

This is an interesting result, not a bad result. If there are no regressors other than time dummies, then I think OLS = RE = FE. (I've done a few experiments with reg y i.year, xtreg y i.year, fe, and xtreg y i.year, re, but I have not proved.) If $X_{it}$ have trends and are correlated with fixed effects, anything can happen. For example, run the following ...

1

Let $\hat\alpha^i = \left[\sum_t (x_{it}-\bar{x}_i)^2 \right]^{-1} \sum_t (x_{it}-\bar{x}_i) (y_{it}-\bar{y}_i)$, estimator from the individual OLS regression. Let $\hat\beta$ be the FE estimator using the panel data. Then, math gives the identity  \hat\beta = \sum_{i=1}^N w_i \hat\alpha^i,\quad w_i = \frac{\sum_t (x_{it}-\bar{x}_i)^2}{\sum_{j=1}^N \sum_t (...

1

I believe the second approach you suggest is equivalent to using an OLS on the whole sample and with dummy variables for each person, country or whatever. Therefore, the answer to your question should be yes.

1

This sounds like the standard "drop one dummy" requirement when binary characteristics are included in linear regression - because otherwise, we will get perfect mutlicollinearity and no-solution. Assume you have three subgroups, separated by age: Y(oung), A(dult), O(ld). You have reasons to believe that the effect of the treatment correlates with age-...

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