Panel fixed effects model for competitiveness

#1
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 )]


where:

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)

where:
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!
viviana84