Panel data basic question on right (best?) approach

Question

I have panel data that is structured like the example below only with more variables. I am using R and my goal is pretty straight forward - estimate the effect of the independent variables on my dependent variable.

        country   date        dependent     independent type1  independent type2
        Germany   01/01/2006  70            30                 0.754
        Germany   01/02/2006  72            36                 0.821
        ...  
        Germany   12/31/2016  70            16                 1.214
        Italy     01/01/2006  54            30                 0.213
        Italy     01/02/2006  59            36                 0.343
        ...

I assume that there are country specific effects that probably also vary across time in the long run which is why I wanted to include fixed effects and then split my panel into 4 time periods and run a regression that is simply like this:

time period 1 lm(dependent ~ independent1+independent2+independent3 ....+country)
time period 2 lm(dependent ~ independent1+independent2+independent3 ....+country)
...

However when skimming trough some books I became increasingly unsure (and confused) if this is an adequate approach. Thus my two questions would be:

1. Is what I intended to do the (or a) suitable approach to achieve my objective?

   2. Can you recommend some other ways to estimate this? I am also very interested in trying some "creative" things as long as they are not way over my head.

One more remark. I indicated type 1 and type 2 for the independent variables. While both vary across time the first one does not vary across countries. I am not sure if that is important on the other hand I feel like I am not sure about anything anymore after looking trough those statistics books.

Thank you.

EDIT:

What I mean with "fixed effects change over time" There are (for me) unobservable variables. The effect of these variables is of different magnitude for every country however it will also change to some extend over time. I thought that fixed effects might be able to improve my estimation in that they would capture something like "the average" effect of these variables for every country.

It might be difficult to explain without the economic context. I left it out before, because I thought it might be clearer when I express it in general terms but maybe this helps.

I look at the credit default swap (CDS) bond basis which is a spread so simply the difference between the two "yields". Now some of this spread I can explain with variables that I am able to proxy for like counter party risk that is involved in CDS etc. However some other parts like "embedded options in CDS contracts" I can not observe or proxy for. The impact of these variables will likely be large and also be different for every country. So for example the option value is connected to the default risk of the country thus it will vary over time (as the default probability will vary over time) but especially it will be different for say Greece and Germany.

Answer 1

What exactly do you mean by "fixed effects change over time"?

Usually, fixed effects in panel regression do not change over time.

You could try to test the hypothesis whether or not there is a level change in fixed country effects by setting country Germany to Germany2, say, after 1990. You could then test whether the coefficient of Germany is equal to the one of Germany2.

In your regression strategy, all coefficients are allowed to be different in time period 1 and 2, not only country fixed effects, as these are totally independent calculations.