Fed Model Nuance

Is there a way to restore/enhance the relevance to investors of the Fed model, which is based on a putative investor-driven positive relationship between stock market earnings yield (equity earnings-to-price ratio) and U.S. Treasury bond (10-year) yield? In his February 2023 paper entitled "The Fed Model: Is it Still With Us?", David McMillan re-examines the predictive power of this relationship with the addition of regime shifts that may expose predictive power not persistent across the full sample. He considers three versions of the Fed model:

1. Fed1 - ratio of earnings yield to bond yield (yield ratio).
2. Fed2 - simple difference between earnings yield and bond yield (yield gap).
3. Fed3 - logarithmic version of Fed2 (log yield gap).

He tests the power of each model variation to predict stock market returns at horizons of 1, 3 and 12 months, either including or excluding earnings yield and the interest rate term structure (U.S. Treasury 10-year yield minus 3-month yield) as control variables. He considers two ways to detect regime shifts in each model variation: (1) regressing each series on a constant term and looking for a break in its value; and, (2) a Markov-switching approach. Using monthly S&P Composite index level and earnings, and 10-year and 3-month U.S. Treasury yields during January 1959 through December 2021, he finds that: