Investigating the effect the Cash Flow sensitivity and Market Value of family owned companies compared to widely held companies

Dear all,

I have a very specific problem for which I could not find a solution in the econometric books that I have and on the web, so I hope someone here could help me out.
I am currently writing my master thesis and I want to investigate whether family owned companies (EU companies in which the founding family or related family has more than 25% of the shares) i) in general invest more or less, ii) whether their investment behavior is more or less sensitive toward the internal cash flows of the company (CashFlow) and iii) whether the market valuates these companies more or less (as a measure of valuation I use the standard in the literature - Tobin's Q).

The final sample consists of 5181 companies for the time period between 2007 and 2016, for which we have 32091 observations. The key variables are KPIs like Sales, Total Assets, Long Term Debt, Short Term Debt, EBIT, EBITDA, Net Income, Dividends, Full Time Employees, Capital Expenditures, R&D etc.

FFF - bianary variable which takes the value of 1 if the company is qualifies as family owned, 0 otherwise
RoA - Return on Assets
year - control variables for the year from 2007 until 2016 (vector)
industry - industry variables for the different industries (vector)

My initial idea was to first regress Investment on FFF, , CashFlow, Sales, Total Debt, Dividends to see what is the effect of each independent variable on Investment.
Equation looks something like that:
Investment=Alpha+Beta1*FFF + Beta2*CashFlow+Beta3*Sales+Beta4*TotalDebt+Beta5*Dividends+Beta6*year+Beta7*industry

Then for the second hypothesis: ii) cash flow sensititvity, I wanted to include an interaction term between FFF and the CashFlow-variable to see how the investment behavior (in regard to Cash Flows) changes for family owned and widely held companies.
Equation looks something like that:
Inv.Sens.=Alpha+Beta1*FFF + (Beta2+Gamma*FFF)*CashFlow+Beta3*Sales+Beta4*TotalDebt+Beta5*Dividends+Beta6*year+Beta7*industry

So if FFF=0 (a widely held company) the effect of the cash flows on the investmet would be just Beta2. If FFF=1, then (Beta2+Gamma) would be the effect of CashFlow on Investment.

Then for the final hypothesis: iii) I initially wanted to regress Tobin's Q (The Tobin's Q ratio equals the market value of a company divided by its assets' replacement cost - used in the literature as an approximation of the market value of the company - market based view) on FFF, Sales, RoA, Investment.
Equation looks something like that:
Tobin's Q = Alpha + Beta1*FFF+Beta2*Sales+Beta3*RoA+Beta4*year+Beta5*industry

So my idea is to see whether Family owned companies (FFF) invest more or less compared to widely held firms, to investigate wheter they are more or less cash flow sensitive and then to see if there is an difference in the way the market valuates family owned and non-family companies. I expect that family companies invest less than non-family firms, but since they are more long-term oriented, their investments would be less sensitive toward changes in the cash flow, meaning that even in a bad economy those companies would not radically change their investment behavior. As a result they may be valued more or less by the market.

My problem:
I had a meeting with my tutor and he suggested the following methodology, which I am not familiar with:
First he suggested to regress Investment using the first equation i):
Investment=Alpha+Beta1*FFF + Beta2*CashFlow+Beta3*Sales+Beta4*TotalDebt+Beta5*Dividends+Beta6*year+Beta7*industry

Then to predict Beta2 and create a new variable in the data set let's say Beta2hat.

Then plug the Beta2hat in iii) . The idea is to see what is the effect CashFlow on Tobin's Q.
Equation should look like this:
Tobin's Q = Alpha + Beta1*Beta2hat + Beta2....

That is the part I do not really understand - why do we predict Beta2 in i), since Beta2 is only a number (the effect of CashFlow on Investment) and then plug it in iii)?

I would be very happy if someone could help me out or just give me direction what I could read to understand the theory behind it. Some terminology would be very helpful.

Kind regards
Mitio Chekanawa