Using the yield curve to forecast economic growth

• DOI: http://doi.org/10.1002/for.2676
• Published date: 01 November 2020
• Author: Parley Ruogu Yang
• Date: 01 November 2020

Received: 6 August 2019 Accepted: 12 January 2020

DOI: 10.1002/for.2676

RESEARCH ARTICLE

Using the yield curve to forecast economic growth

Parley Ruogu Yang

Department of Statistics, University of

Oxford, Oxford, UK

Correspondence

Parley Ruogu Yang,Department of

Statistics, University of Oxford, Oxford

OX1 3LB, UK.

Email: ruogu.yang@st-annes.ox.ac.uk

Abstract

This paper finds the yield curve to have a well-performing ability to forecast

the real gross domestic product growth in the USA, compared to professional

forecasters and time series models. Past studies have different arguments con-

cerning growth lags, structural breaks, and ultimately the ability of the yield

curve to forecast economic growth. This paper finds such results to be dependent

on the estimation and forecasting techniques employed. By allowing various

interest rates to act as explanatory variables and various window sizes for the

out-of-sample forecasts, significant forecasts from many window sizes can be

found. These seemingly good forecasts may face issues, including persistent fore-

casting errors. However,by using statistical learning algorithms, such issues can

be cured to some extent. The overall result suggests, by scientifically deciding

the window sizes, interest rate data, and learning algorithms, many outperform-

ing forecasts can be produced for all lags from one quarter to 3 years, although

some may be worse than the others due to the irreducible noise of the data.

KEYWORDS

forecasting methods, interest rates, statistical learning

1INTRODUCTION AND

LITERATURE REVIEW

Time, by the well-known nature of it, is ordered and irre-

versible. As time cannot be traveled, any claim about the

future is probabilistic. Everyone wants to know what will

happen in the future. The future of economic growth is

a particular example: policymakers—for example, central

banks—could be more informed, and thus make moresuit-

able expansionary or contractionary policies at the right

time; investors could make better investment decisions

contingent on the future economic outlook.

The future is something that everyone wants to know

more about, yet no one can predict exactly due to the

nature of time. We try to make morereliable and convinc-

ing forecasts about tomorrow,based on the information we

have today.In the studies of forecasting economic growth,

one set of variables has been used and discussed—that is,

the yield curve data. The yield curve contains information

about short- and long-term interest rates that are priced

and used in the contemporaneous financial market. Such

information could be utilized to forecast the future state of

economic growth, and many empirical studies on differ-

ent countries have explored such a possibility, supported

by some theories developed alongside.

The empirical literature suggests different results when

using the yield curve to forecast different US economic

variables. To use yield curve data to forecast US economic

recessions, Rudebusch and Williams (2008) find the prob-

ability model using yield spread data to be “significantly

more accurate” than the benchmark forecast given by the

Survey of Professional Forecasters (SPF) for forecast hori-

zons of three and four quarters. However,when using yield

curve data to forecast US gross domestic product (GDP)

growth, Chinn and Kucko(2010) and De Pace (2013) argue

that the forecast results are not reliable and time varying.

On the theoretical side, Estrella (2005) links the spread

and economic activity in a small macroeconomic model,

Journal of Forecasting. 2020;39:1057–1080. wileyonlinelibrary.com/journal/for © 2020 John Wiley & Sons, Ltd. 1057

1058 YAN G

and such a relationship depends on the monetary policy

rule. Variousmodels given by Ljungqvist and Sargent, 2012

(2012, pp. 481–583) also provide such a link, depending on

the value of particular parameters.

To engage further with the empirical literature, the fol-

lowing part investigates three specific aspects. How long

do the spreads' predictive powers last? How is the spread

defined? How to model forecasts?

Let gt,t+kbe the real GDP growth from period tto period

t+k, where each point trepresents a quarter of a year; for

example, gt,t+1 means quarter-on-quarter growth.1Chinn

and Kucko (2010) investigate kup to 8, while Hvozden-

ska (2015) and De Pace (2013) focus on 6 and 4 respec-

tively. Indeed, a huge kmay not make sense—the point

of forecasting on this occasion is to predict the short-run

economic situation. All of them then assess and conclude

which of the lags are better forecasted or fitted. In Section

3, a similar method is utilized.

To the second question, denote Stto be the spread for

period t. While the more common definition to define2Stis

the yield spread between a 10-year Treasury note (T-note)

and a 3-month Treasurybill (T-bill), De Pace (2013) defines

Stas the spread between a 10-year T-note and 3-month

money market rates.3To gain a more hands-on under-

standing of the difference this implies, a replication is

made below, using the baseline fitting

gt,t+k=𝛼+𝛽St+𝜀t,

𝜀t∼i.i.d. N(0,𝜎

2),

t∈{1,…,T−k}.

(1)

Ordinary least squares (OLS) results are reported in

Table 1, where the data set starts from 1964:Q3 and ends

at 2019:Q1.4Indeed, at a small kthe models are dramati-

cally different in both the coefficient estimates and the R2,

while such difference decreases as kgets larger.

Such an observation motivates this paper to make a

different approach compared to the aforementioned liter-

ature, in terms of using which part of the yield curve to

define a spread. In Section 3, various maturities of the

T-note or T-bill, as well as interbank rates and the federal

funds rate, are used to provide representative information

from the yield spreads, and comparison is made across dif-

ferent combinations to see which pair does better at which

lags, and this may ultimately improve the fitting and fore-

casting performance. To this extent,the variables acquired

1All variables are defined properly in Section 2.

2Examples include Rudebusch and Williams (2008); Hvozdenska (2015).

3More precisely, the “3-Month or 90-day Rates and Yields: Interbank

Rates” from Federal Reserve Bank of St. Louis (2019).

4That is, 1964:Q3 corresponds to t=1and 2019:Q1 corresponds to t=T.

TABLE 1 Columns 2–4 are the OLS results obtained by using

3-month T-bill yield as part of the definition of the spread;

columns 5—8 are the results obtained by using 3-month money

market rate as part of the definition

3-month T-bill 3-month money market rate

k̂

𝛽sd(̂

𝛽)R2̂

𝛽sd(̂

𝛽)R2

1 0.571 0.143 0.069 0.627 0.109 0.134

20.594 0.128 0.092 0.597 0.097 0.149

3 0.611 0.117 0.114 0.568 0.090 0.159

40.611 0.109 0.129 0.539 0.084 0.163

5 0.589 0.102 0.137 0.496 0.079 0.158

60.564 0.095 0.143 0.456 0.074 0.152

7 0.521 0.090 0.138 0.411 0.071 0.139

80.470 0.085 0.127 0.365 0.067 0.124

9 0.417 0.082 0.111 0.314 0.065 0.102

10 0.365 0.079 0.093 0.266 0.063 0.080

11 0.319 0.077 0.077 0.226 0.061 0.062

12 0.277 0.075 0.063 0.192 0.059 0.049

are similar to Estrella and Mishkin (1998), Engstrom and

Sharpe (2018), and Bauer and Mertens (2018), where

various types of interest rates from the yield curve and

financial market are utilized, aiming to forecast economic

growth or recession.

To the last question, first the fitting-type models by

Hvozdenska (2015) and Engstrom and Sharpe (2018) are

reviewed. Although a straightforward fittingon past obser-

vations can be helpful, it does not support investigations

as to how good the out-of-sample forecast could be;5thus

out-of-sample forecasting is set as the focus throughout

this paper. There are two major ways to conduct the fore-

casting: recursive regressions and moving regressions (De

Pace, 2013).6The recursive one runs over the full samples

from the start to the time of the forecast, and thus the win-

dow size increases by a unit each step, whereas the moving

regressions run with fixed window size. In both Chinn and

Kucko (2010) and De Pace (2013), a window size of 40 is

chosen; however, no scientific results were generated to

support such a choice. Therefore, this paper takes a differ-

ent approach in this aspect. Rather than fixing a window

size, a variety of wide and narrow window sizes for fore-

casting are trialled, with the aim of improving forecasting

performance.

Motivated by the above reviews, this paper aims to

provide a further contribution to how good the forecast

could be, by considering scientific selections on the win-

5This could again be related to the concept of time—a fit overlooking the

entire period may be sensible in a data set that is not time related, but

a time series data set contains a fixed order over time, and forecasting

aims to make predictions out-of-sample rather than within the periods

observed (Harvey, 1989).

6Moving regressions are also called “rolling windows” in Chinn and

Kucko (2010).