Fed Model - Is The Fed Model Miss-specified?

Is The Fed Model Miss-specified?

The Fed model equilibrium remains an enigma. On one hand 30 years of data is available that shows how S&P earnings yield and 10-year government bond yield move in tandem. On the other hand there is no theoretical foundation to explain the relationship, and the best explanation academics came up with is that investors collectively suffer from 'money illusion'. A number of questions remain unanswered. Why was the relationship observed in the US and not in most other international markets? Do investors in the US (the world's largest equity market) suffer more from 'illusions' than investors in for example Austria and Finland? Why did the relationship not exist in the US before 1980 (or 1965) and why did the equilibrium break down during the 2008 crisis? And if government bonds and stocks are competing assets, what is the role of corporate bonds?

The recently proposed capital structure substitution theory argues that the Fed model indeed needs to be re-specified. It suggests that supply (company management), rather than demand (investors) drives the relationship between E/P and interest rates. Stock market earnings yield tends to equilibrium not with the government bond yield but with the average after-tax corporate bond yield as companies adjust capital structure (mix of equity and bonds) to maximize earnings per share. If managements consistently optimize capital structure by substituting stocks (repurchasing shares) for bonds or vice versa, equilibrium is reached when:

where E is the earnings-per-share of company x, P is the share price, R is the nominal interest rate on corporate bonds and T is the corporate tax rate. For a long time the after-tax interest rate on corporate bonds was roughly equal to the 10-year Treasury rate. But during the 2008 financial crisis this relationship broke down, as Baa rated corporate bonds peaked at over 9%, and 10-year treasuries bottomed under 2.5% (see figure 3). In the US, SEC Rule 10b-18 (explicitly allowing share repurchases) enabled fine adjustment toward equilibrium as of 1982, explaining why the equilibrium emerged around that time and not before. And in many other countries share repurchases were prohibited until 1998 or are still considered illegal, explaining why the Fed model equilibrium was observed in the US but not in many other international markets.

Re-specified Fed model comparing S&P 500 earnings yield with after-tax corporate bond yield (average rating=Baa). Before 1982 the equilibrium could not be reached due to legal limitations in repurchasing shares (SEC Rule 10b-18). Is the Fed model miss-specified? Thirty years of investor money illusion (left) or deliberate company policy (right)?