# The Theory Behind Yield Curve Prediction

## CommentarySince the U.S. yield curve inverted, predicting recession ahead, there have been voices again arguing “this time is different.” Like previous recessions, contrarians challenged the lack of theoretical basis behind it, others accused the yield curve slope as mainly governed by Fed policy which should be the true cause of boom-bust. In terms of reasoning, this time is no different. Having said that, they all got wrong practically even though their “theories” might be correct. Since data began, the curve predicted nine recessions, with only one turning out not happening. Although it is widely regarded that the seminal work by Arturo Estrella and Gikas A. Hardouvelis (working paper in 1989, published in 1991) was the first demonstration of a yield curve predicting a recession, Campbell R. Harvey was asserting the curve as a predictor to consumption earlier (his Ph.D. thesis in 1986, published in 1988). Despite the consumption bust not being equivalent to the recession, the concepts behind it are highly similar; most recessions were indeed consumption driven. Estrella and Hardouvelis were smart in pushing this one step further. The idea probably originated from one of Harvey’s Ph.D. supervisors, Eugene Fama, who published a series of journal articles on term structure (and term premium) around 1984. Term structure is nothing but a fancy (academic) name for a yield curve, and term premium refers to the long-short yield gap. While Fama specialized in predicting future spot rates forward, Harvey linked the term structure to consumption. Such an idea naturally arises from the popularity of models with dynamic optimization of lifetime consumption in the 1970–80s. In Harvey’s simple setup, everyone is maximizing one’s lifetime utility function, which is the sum of many future periods’ utility, each being a function of consumption at that period. Basically, everyone is deciding how much to spend in one’s future life. As the decision is intertemporal (across time), it is not hard to imagine the solution to this problem should involve price across time, which is the interest rate. Then the change in consumption over time is naturally related to the change of interest rate over time, which is conceptually linked to term premium. Given the derivation starts from economic optimization—a typical economic behavior, one cannot say the yield curve predicting consumption change (growth) lacks a theoretical basis. However, such a prediction is not generally true across the whole term structure. It has been documented in the literature that the yield curve can only be a successful predictor when there is a sign change, i.e., positively sloped versus inverted yield curve. Else it is not a powerful predictor. Illustration of Long-short Yield Gap on Lagged GDP Growth, 1962–2022 by Law Ka-chung. (Courtesy of Law Ka-chung) The accompanying chart above links up the 10-year-3-month yield gap and real GDP year-over-year growth with five quarters lag. The proportional relationship applies only when the yield gap goes between –1.5 percent and +1.5 percent; the relationship breaks down when above this range. The true reason is not well known, but one possibility is Taylor approximation has been used in the result derivation, which holds only for small changes (of yield). Thus, the theory fails to apply when the yield gap is wide. Views expressed in this article are the opinions of the author and do not necessarily reflect the views of The Epoch Times. Law Ka-chung is a commentator on global macroeconomics and markets. He has been writing numerous newspaper and magazine columns and talking about markets on various TV, radio, and online channels in Hong Kong since 2005. He covers all types of economics and finance topics in the United States, Europe, and Asia, ranging from macroeconomic theories to market outlook for equities, currencies, rates, yields, and commodities. He has been the chief economist and strategist at a Hong Kong branch of the fifth-largest Chinese bank for more than 12 years. He has a Ph.D. in Economics, MSc in Mathematics, and MSc in Astrophysics. Email: [email protected]

*Commentary*

Since the U.S. yield curve inverted, predicting recession ahead, there have been voices again arguing “this time is different.” Like previous recessions, contrarians challenged the lack of theoretical basis behind it, others accused the yield curve slope as mainly governed by Fed policy which should be the true cause of boom-bust. In terms of reasoning, this time is no different. Having said that, they all got wrong practically even though their “theories” might be correct. Since data began, the curve predicted nine recessions, with only one turning out not happening.

Although it is widely regarded that the seminal work by Arturo Estrella and Gikas A. Hardouvelis (working paper in 1989, published in 1991) was the first demonstration of a yield curve predicting a recession, Campbell R. Harvey was asserting the curve as a predictor to consumption earlier (his Ph.D. thesis in 1986, published in 1988). Despite the consumption bust not being equivalent to the recession, the concepts behind it are highly similar; most recessions were indeed consumption driven. Estrella and Hardouvelis were smart in pushing this one step further.

The idea probably originated from one of Harvey’s Ph.D. supervisors, Eugene Fama, who published a series of journal articles on term structure (and term premium) around 1984. Term structure is nothing but a fancy (academic) name for a yield curve, and term premium refers to the long-short yield gap. While Fama specialized in predicting future spot rates forward, Harvey linked the term structure to consumption. Such an idea naturally arises from the popularity of models with dynamic optimization of lifetime consumption in the 1970–80s.

In Harvey’s simple setup, everyone is maximizing one’s lifetime utility function, which is the sum of many future periods’ utility, each being a function of consumption at that period. Basically, everyone is deciding how much to spend in one’s future life. As the decision is intertemporal (across time), it is not hard to imagine the solution to this problem should involve price across time, which is the interest rate. Then the change in consumption over time is naturally related to the change of interest rate over time, which is conceptually linked to term premium.

Given the derivation starts from economic optimization—a typical economic behavior, one cannot say the yield curve predicting consumption change (growth) lacks a theoretical basis. However, such a prediction is not generally true across the whole term structure. It has been documented in the literature that the yield curve can only be a successful predictor when there is a sign change, i.e., positively sloped versus inverted yield curve. Else it is not a powerful predictor.

The accompanying chart above links up the 10-year-3-month yield gap and real GDP year-over-year growth with five quarters lag. The proportional relationship applies only when the yield gap goes between –1.5 percent and +1.5 percent; the relationship breaks down when above this range.

The true reason is not well known, but one possibility is Taylor approximation has been used in the result derivation, which holds only for small changes (of yield). Thus, the theory fails to apply when the yield gap is wide.

*Views expressed in this article are the opinions of the author and do not necessarily reflect the views of The Epoch Times.*