What is the behavior of a "high-hedging needs" firm at refinancing points? What about its profitability impact on the financial package it will choose/ accept from the bank or the market? Do you know papers on that subject?
But I can add that firms have apparent future refinancing needs, have higher risk cost than firms with a "hedged" approach to investment, and firms where the sources of future financing are known and negotiated in advance for the entire duration of the long term investments.
The extremes has been investigated in the field of distress cost, where you can find some resources easily. By extremes I mean that in distress dost it is bankruptcy cost that is investigated.
It is more tricky with risk cost that does not lead to bankruptcy. However, in such cases we have experimentally been able to show that risk cost is also higher in high risk companies, than in hedged or de-risked companies.
You may want to take a look at Bowmans Paradoks for documentation that high risk can lead to impaired financial performance by firms.
Yes I think that "High hedging needs" firms are riskier than "Low-refinancing needs" companies. Thus I may imagine that profitability of these "High hedging needs" firms should be an important criteria to get loans at the precise refinancing times. A high profitability may open a lot of possibilities, a lower one will perhaps constrain the firm to some of them?
Financially constrained firms are expected to exhibit higher investment or growth sensitivity to cash-flow than non-constrained firms. This is the standard approach at least, and there is a lively debate still ongoing to a large extent. You can find an overview with some important references here in one of my papers... but there are of course many others you can look at.
Your paper is interesting and relevant. It is quite different from the Hadlock and Pierce approach (2010) RFS vol 23, N°5,p 1909 -1940 that tested the Kaplan and Zingales index (1997) or the Whited and Wu index (2006). Moreover as you said firm size and age are relevant for predicting financial constrants.