Panel fixed effects model for competitiveness

Hi all,

I'm very new in econometrics and I'm having some problems in estimating my model and interpreting its coefficients.

What I'm trying to estimate is a panel fixed effects model in the following form:

ln(Qi,j,t/ 1-Qi,j,t) = -(φi + b1(time) + b2(ICOSi,t )), which is the log linear version of : Qi,j,t = 1/[1 + exp(φi + b1(time) + b2(ICOSi,t ) + ei,t )]


Qi,j,t : is the market share held by exporter i on market j at time t

Time: time trend variable;

ICOS i,t : relative labor cost index of exporter i at time t - calculated as (COS i, t /COS (competitors, t)) * 100

First question:
If I get a b2 coefficient equal to -0.5, do I interpret it in the reverse sign (+0.5) as I have the minus sign before brackets in my equation?
And concerning its interpretation, it means that an increase of one unit of ICOS will incrase my Y by 0.5?

Second question:
I'v tried to add to my panel gravitational variables with country pairs dummies in order take into account fixed effects. The problem is that I have to much parameters to estimate. For this reason I would like to first estimate the model in the original form (that I wrote above), get the fixed effects estimates and using them in a second equation of the following form:

log(Fe i,j) = b1*ln(dist) + b2* common_lang + b3* contig + b4* RTA + b5* colony + b6*ln(GDPi) + b7*ln(GDPj)

dist:is the geographic distance between countries;
common_lang: dummy which takes value 1 if importer and exporter share a language, otherwise 0
contig: dummy which takes value 1 if importer and exporter share a border
RTA: dummy for common free trade area which takes value 1 if both i and j belong to a RTA at time t and
colony: dummy which takes value 1 if country i and country j share a colonial relationship, otherwise 0

I would like to have an opinion about this.

Thanks a lot for your attention!