Business Cycles, Optimal Interest Rate, and Recession Forecast From Yield Curve, Unemployment, GDP, and Payrolls

Abstract

We developed a factor regression model, nicknamed “GUPTY”, to study the business cycles, and their relation to the monetary policy. It covers several major macro-economic quantities, including unemployment rate, GDP, and weekly payrolls in the U.S. after WWII. The model postulates that these macro-economic quantities are predominantly a nonlinear function of the 10Y and 3M interest rates in the Treasury yield curve, and their regressions share similar model specification. The concept of the business cycle is injected into the model through the yield spread between 10Y and 3M rates. The notion of the natural rate of unemployment and GDP growth comes out of the model naturally. An optimization framework is proposed to determine the optimal short-term interest rate, which is a central concern for policymakers – Once the model parameters are obtained from regressions, the model is inverted to calculate the optimal 3M rate via optimization of the squared errors. Its first-order analytic solution is derived. We find that FED’s interest rate policy has leaned heavily on the unemployment data. We also observe that, on the optimality, the model GDP growth rate matches the realized data almost perfectly. We discuss some policy challenges, and attempt to provide an explanation for the plunge of GDP growth after 2009 due to super-low 10Y rate, in which the “2% GS10 floor hypothesis” is suggested. Unemployment’s 1Y momentum and its 6M acceleration are used to construct a Hidden Markov Model for real-time recession probability. Furthermore, a Random Forest model is developed to forecast recession up to 24 months ahead. And we show recession forecast is closely associated with yield spread inversion.