Excessive zeros, fixed effect & time effect

[Mohamad Saoud]

Hello everyone, this is my first post here, I hope to make a clear post.
My research is about the effect of the refugee crisis in Germany in 2015 on crimes against foreigners.
I have yearly data for 2014 and 2015, my data is in county level (402 observations for each year). My dependent variable is the incidents or crimes that happened against refugees, it is excessive zeros variable, 276 out of 402 in 2014 is zeros, and 107 in 2015. my main explanatory variable is the number of refugees.
Since I have this zero issue I should use count models Negative Binomial or Poisson, or I could standardize the number according to population then using Tobit model with censored from below (zero).
I cannot use first difference because I will have some observations with negative values where I cannot use any of the aforesaid models. Hence, I must use panel data technique.
Now my questions:
First: when I add the fixed effect about 30% of the observations dropped automatically because there is no variation between groups. Do you think that doesn't ruin the result ? or I should not control for fixed effect? Please let me know about any good book highlights such issue.
Second: when I control for the time fixed effect “i.year” most of the variables change their signs and go insignificant including my main variable, however, the year variable is only one with highly significant. It looks that the time absorbed the shock of the refugees' crisis. so shall I drop the time dummy or that will be wrong? I really do not know, wherever I read I find that I should add the time dummy but in my case, I think it is legitimized not to add it. Please let me know what do you think or if you know any reference might help. Thank in advance, I appreciate every single support.

[Phil Bromiley]

You didn't get a quick answer. You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex.

If including year in the rhs eliminates the effect of number of refugees, then that is a result. Depending on signs, it probably means that antagonism towards refugees increased over time and it appears that local number of refugees didn't matter. That makes sense to me. If someone wants to attack a refugee, that person will probably find one assuming there are some around. I would check that you don't have any counties with zero reported refugees and non-zero incidents...

There is a pile of different ways to do this. You could imagine the data set as each refugee in each year as an observation and estimate the probability of an incident. This could be done with a logit with an expanded data set or a gee/glm model where number of refugees appears as exposure. You could use panel regression with random effects, You could use a hybrid model (search Stata Journal for recent articles on hybrid models). You could use a count model like poisson.

I think you need year as a control. Beyond that, I can't give you a quick answer.