Hi,

My research project is looking at the impact of financial development (bank development - proxied by private credit& stock market development proxied by stock market cap) on labour share(ls-pwt) using a panel dataset of 80 countries, period, 2000-2017. Here, some of my variables have unit root and as such I am using the first difference estimator as opposed to the fixed effects estimator. My main estimation model is as follows:
ΔLSit = β0 + β1Δprivatecreditit + β2ΔStockMcapit + ΔXit β + Өt + uit Equation 1
As part of one of the specifications, I am interested in ascertaining if the impact of financial development on labour share depends on the efficiency of that development process (2 diff efficiency variables are used) as follows:
ΔLSit = β0 + β1Δprivatecreditit*BankNIMargin + β2ΔStockMCapit*StockMTurnover + ΔXit β + Өt + uit

As such, I am interested in using an interaction term between the financial development variables and efficiency variables, both of which are continuous variables. From my readings, I gathered that it is advisable to center the relevant variables on meaningful values (mean) - which I have done as follows:
summarize pcredit, meanonly
gen pcredit_c=pcredit-r(mean)
by countryid: gen dpcredit_c=d.pcredit_c

summarize smcap, meanonly
gen smcap_c=smcap-r(mean)
by countryid: gen dsmcap_c=d.smcap_c

summarize bnimargin, meanonly
gen bnimargin_c=bnimargin-r(mean)
by countryid: gen dbnimargin_c=d.bnimargin_c

summarize smtratio, meanonly
gen smtratio_c=smtratio-r(mean)
by countryid: gen dsmtratio_c=d.smtratio_c


After this process I run the first difference estimator as follows:

regress dls_pwt c.dpcredit_c##c.dbnimargin_c c.dsmcap_c##c.dsmtratio_c $dcv4 i.year, robust cluster(countryid)


Basically, my query is whether, this centering process is the correct way to proceed in the context of using the first difference estimator. Here, I am centering the relevant variables on the mean of the variables across all countries (panels).