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

44 Pages Posted: 18 Jul 2019

See all articles by Stephen H.T. Lihn

Stephen H.T. Lihn

Novus Partners, Inc.; Atom Investors LP

Date Written: July 18, 2019


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.

Keywords: business cycle, GDP growth, interest rate policy, Treasury yield spread inversion, unemployment, weekly payrolls, UNRATE momentum, recession probability, recession forecast, GS10 floor hypothesis

JEL Classification: C38, C53, E32, E43, J64

Suggested Citation

Lihn, Stephen H.T. and Lihn, Stephen H.T., Business Cycles, Optimal Interest Rate, and Recession Forecast From Yield Curve, Unemployment, GDP, and Payrolls (July 18, 2019). Available at SSRN: or

Stephen H.T. Lihn (Contact Author)

Atom Investors LP ( email )

3711 S Mopac Expressway
Austin, TX 78746
United States
917-603-4133 (Phone)

Novus Partners, Inc. ( email )

521 5th Ave
29th Floor
New York, NY 10175
United States
917-603-4133 (Phone)

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