Earlier this year we discussed how the Volcker rule combined with Basel III is already reducing corporate bond liquidity by diminishing dealers' ability to make markets. It's just one of those "unintended consequences". Dealer inventories, which are essential for market making, have shrunk to the lowest level in 10 years. Some, including people at the Fed, have suggested that non-bank entities will step in to take the dealers' place as market makers. That is unlikely to happen in the near future.
One question that people are asking is why haven't we seen more lobbying from the corporate sector against the Volcker rule. There are multiple reasons for this, including corporations' unwillingness to put their reputation on the line by lobbying against this populist anti-bank regulation. But one of the key reasons is that the biggest impact will be on the medium to smaller US firms who simply don't have the resources to battle this legislation. With limited inventories the dealers increasingly make markets only in the largest bond issues, particularly those traded by the large corporate bond ETFs (LQD, HYG, etc.).
As liquidity in the smaller bond issues declines further, investors will demand a premium to hold them. Small to medium sized US firms will be disadvantaged relative to their large competitors due to higher cost of funds.