8

When you control for not just year fixed effects but instead year-region or year-industry it adds flexibility. The year fixed effects controls in a flexible manner for the time-trend and is more flexible - less restrictive - than for example assuming that the time trend is for example linear $a \cdot t$, second order polynomial $at + bt^2$, exponential $exp(...


7

Consider the following regression specification where, $t$ is time, $c$ is the firm, $y$ is an outcome and $x$ is a variable of interest. $$ y_{c,t} = \alpha + \beta x_{c,t} + \varepsilon_{c,t} $$ There are three types of omitted variables: Variables that vary with time but are the same across firms. Examples might be weather conditions, inflation rate, ...


5

(1) whether we should not run the group and period fixed effect for simple DID because they will swallow the variables $P_t$ and $T_i$ as in the generalized case? In a simple 2 period 2 group regression, the $P_t$ and $T_i$ variables are capturing the time and group fixed effect. In fact, the regression with fixed effects is formally identical to the simple ...


5

What does industry * year fixed effect mean? $Industry \cdot year$ fixed effect is just an interaction term between industry and dummy year variables. For example, you can have dummy particular industry, let us say finance where $D=1$ if firm is a finance firm and $0$ otherwise, then you can have a year dummy which will be set to equal $1$ for particular ...


4

Think about a regression where you have two factors. Normally when you have a constant in the regression you would put one level of each factor to 0 as a reference level. Leaving out the constant you have two factors and put one reference level to 0 for one of these. The situation is similar here in the sense that you have firm and individual level fixed ...


4

I do not think the premise is correct. Following Brüderland and Volker in Best & Wolf The SAGE Handbook of Regression Analysis and Causal Inference [square brackets have my remarks]: Both estimators require strict exogeneity [Fixed Effects (FE) and First Differences (FD)]. However, while FE builds on the assumption of no serial correlation prior to ...


4

Let $i$ index firms and $t$ time. Consider the following type of regression: $$ y_{i,t} = \alpha + \beta_i + X_{i,t}\gamma + \varepsilon_{i,t} $$ where $\beta_i$ are the firm fixed effects and $X_{i,t}$ is a set of other covariates. If the number of time periods and firms goes to $\infty$ then both the estimates of $\beta_i$ and $\gamma$ will be consistent. ...


3

Consider the following specification: $$ Y_{i,g} = X_{i,g}\beta + u_{i,g} $$ Where the residuals have different mean across groups and have within group correlation: $$ \begin{align*} &\mathbb{E}(u_{i,g}) = \alpha_g,\\ &cov(u_{i,g} u_{j,g}) = \rho_{i,j},\\ &cov(u_{i,g}, u_{j,g'}) = 0 \text{ for } g \ne g' \end{align*} $$ Taking means gives: $$ \...


3

I guess this follows from the Frish-Waugh Lovell theorem. If you have $K$ dummies and say $n$ observations, so $F$ is $n \times K$, you need to regress every dummy in $F$ on all variables in $X$ separately ($K$ regressions). The residuals make up the matrix $\bar F$ which is again of dimension $n \times K$.


3

Here is an example where just from an economic perspective fixed effects are better than random effects. Suppose you have panel data and you want to regress earnings $y$ on some observable characteristics $X$ of an individual like education, tenure, experience, age, birthplace, etc. The regression you would estimate is $$y_{it} = \alpha + X'_{it} \beta + \...


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

You can't identify the effect of oil price when Year FE are applied, since the world oil price is perfectly correlated with year Fixed Effects. You can't identify the democracy indicator if you country does not change its value in your observed period. For the other variables, it should be possible to obtain estimates. You should apply a fairly large ...


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 ...


2

Note that you have an identification problem here because price is an endogenous variable. A way to deal with this problem would be to find an instrument (e.g. prices of the same good in other markets as in Hausman (1996)). Regarding your questions. Yes (although fixed effects are probably not the right wording here). Yes. If you want to capture a cross ...


2

You have the equation: $$ y_{it} = \delta y_{it-1} + x_{it}'\beta+ \alpha_i + v_{it}. $$ The left hand side runs from $t=2$ to $t = T$ as there is a $y_{it-1}$ on the right hand side. So taking the average over $t = 2$ to $t=T$ of this equation gives: $$ y_{it} - \bar y_{i[2,T]} = \delta y_{it-1} - \bar y_{i[1,T-1]} + x_{it}'\beta - \bar x_{i[2,T]} + v_{it} -...


2

Usually, the conditional mean and the conditional variance of a random variable are independent (of course there are exceptions). While the fixed effects introduce flexibility in the specification of the conditional mean, clustering introduce flexibility in the specification of the conditional variance.


1

Fixed effects model is estimated as: $$ y_{i t} − \bar{y_i} = ( X_{i t} − \bar{X_i} ) \beta + ( \alpha_i − \bar{\alpha_i} ) + ( u_{it} − \bar{u_i} )$$ So the country fixed effect is always relative to the average fixed effect. If a country has negative fixed effect that means it is less productive than average country in your sample. If you choose ...


1

You are correct in noting that, adding factor(FIPS) in side the regression formula should be equivalent to specifiying factor(FIPS) + YEARxQT in the felm() fixed effects block. I am less certain that your reg2 model that throws up the NA's is working correctly however, as that would typically throw up an error message before getting that result. Without ...


1

If I understand your question correctly, then in the current set up you describe, the answer is "maybe"--meaning, age might be effecting your estimate as an omitted variable, but you are currently not accounting for it if is doing so in anycase. To clarify, individual fixed effects are simply controlling for omitted variables that vary among ...


1

If you want to do unit-fixed effects (so eliminating any unobserved variable that varies cross-sectionally but remains the same over time), this should not be a problem, at least assuming that your explanatory variable varies over time (be it a dummy that is 1 in the year the policy was administered and 0 otherwise, or a continuous variable that changes over ...


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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