thesis_anthony locatelli

Predicting U.S. Recessions Using the Yield Curve

Anthony M Locatelli

Senior Research Project

Submitted in partial fulfillment of the graduation requirements

for the Economics major

School of Business and Economics

April 2014

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Abstract

The literature that focuses on the association between recessions and economic indicators

is constantly increasing in size and importance. In my research I examine a particular economic

indicator, the Treasury yield spread, and its correlation to recessions. Econometric models have

continually shown an exceptionally strong relationship between historical Treasury yield spread

and recessionary data. I use several Probit regression models with recession and yield spread

data spanning from the beginning of 1953 to end of 2013 to compare the robustness of the

correlation between these two variables over time. Even though the relationship shows constant

change over time, my research findings may initiate new government and public policies for the

future.

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I. Introduction

Predicting recessions and taking actions to resolve or diminish the impact of impending

recessions has been a major concern for policy makers for decades. Economists and policy

makers use economic indicators including the CLI (Composite Leading Indicators), Treasury

yield spread, growth rate of GDP, corporate bond yield spread, and Standard and Poor’s 500

stock returns to predict recessions. In this paper I focus on the relationship between the Treasury

yield spread and recessions because it has produced robust statistical results in the past, the

literature on the topic is seemingly endless, and I contribute to the already immense literature by

examining the results of numerous regressions of different time periods to determine the

historical robustness of the relationship between the Treasury yield spread and recessions.

The yield curve plots the yield of Treasury debt against their maturity date. Yield is

synonymous for interest rate and the Treasury securities are of equal credit quality. The curve is

depicted on an x,y-plane with maturity on the x-axis and yield on the y-axis. An example of

several yield curves are shown in Figure 1 in the Appendix.

For unknown reasons, the literature suggests that the reliability of the term spread in

predicting recessions has proven extremely lacking since roughly 1985. Some proposed theories

include thoughts that the Federal Reserve has incorporated more conservative and reliable

monetary policy techniques. Monetary authorities have proven to be much more responsive and

knowledgeable when responding to inflation and output. The best way to improve the reliability

of the yield curve Probit regression model is to continually monitor its performance in order to

determine when predictions are going to be true and when others are going to be false. This is

done through further testing. It is imperative to remember that this assessment is a statistical

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measure and that regardless of the accuracy of past signals this does not guarantee future results

that are as significant as past results.

In Section II, I discuss the previous literature dealing with the relationship between the

Treasury yield spread, specifically the difference between the 10-year and 3-month yields, and

imminent recessions. I also discuss other models that economists use and their findings. In

Section III, I explain the theory behind the relationship between the Treasury yield spread and

the economy, specifically recessions. I also describe the Probit model and the variables I use in

this particular model in Section III. I present the data and descriptive statistics for my variables

in section IV. In Section V, I present the results and analysis of the data pertaining to my

research. In Section VI, I discuss my conclusions and policy implications for future use of the

Probit model. The Appendix, Section VII, contains relevant tables and figures that I discuss

throughout this paper.

II. Literature Review

The importance of this topic cannot be overstated and consequently the literature dealing

with the yield curve as a recession predictor is unbounded. Assessing its accuracy is thus a

valuable endeavor for economists and practitioners. Economists and policy makers closely

examine and follow this economic indicator closely to determine its legitimacy as a recession

predictor. Table 7 contains information pertaining to past research and the findings of the

usefulness of the yield curve for predicting recessions.

Wheelock and Wohar (2009) stress that the future state of any country’s economic

activity is essential to “consumers, investors, and policy makers”. The vast majority of recession

forecasting studies estimate a Probit model to approximate the forthcoming economic conditions.

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Using Probit estimation, Estrella and Hardouvelis (1991) and Estrella and Mishkin (1996) find

that the yield curve substantially outperforms other macroeconomic variables in forecasting U.S.

recessions. Estrella and Mishkin (1996) compare interest rates, interest rate spreads, stock prices,

monetary aggregates, and the yield curve and find that the yield curve outperforms all other

variables beyond a one-quarter forecast horizon.

Dombrosky and Haubrich (1996) mention that individuals that closely follow market

activity choose to monitor the yield curve (which generally is upward sloping and slightly

convex). Dombrosky and Haubrich (1996), among other economists and consultants, notice that

in the past the yield curve has become flat and in extreme instances has inverted. In this instance

many researchers, analysts, economists, and other specialists see this trend as indication of an

impending recession. Clark (1996) proclaims the yield curve to be a virtually flawless economic

indicator used for economic predictions.

Estrella and Trubin (2006) classify recessions via the cyclical peaks and troughs

identified by the National Bureau of Economic Research (NBER). They use the NBER monthly

dates and convert them into a monthly recession indicator by classifying a “…recession as every

month between the peak and the subsequent trough, as well as the trough itself…” (Estrella and

Trubin, 2006). The peak is not considered because the economy had grown in the previous

month. Estrella and Trubin (2006) claim these conventions to be the most frequently used in

research on U.S. recessions, but not the only possible ones.

Filardo (1999) examines five popular recession prediction models, the “…simple rules of

thumb using the Conference Board’s composite index of leading indicators (CLI), Neftҫi’s

probability model of imminent recession using the CLI, a regression-based model of the

probability of a recession called a Probit model, a GDP forecasting model, and a recession

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prediction model recently proposed by Stock and Watson”, which I detail below. They also

assess the performance of each model by assessing the timeliness and accuracy. In regards to

timeliness, a long lead time is preferred over a short lead time because a longer lead time will

have a greater time span between which a signal occurs and when the recession originates

(Filardo, 1999). Accuracy pertains to the degree in which predictions and outcomes coincide

with each other (Filardo, 1999). These two measures are imperative to monetary policy decision

making (Filardo, 1999)

Filardo (1999) notes that the CLI is a composite of ten leading indicators that were

chosen specifically for recession prediction purposes. Specialists, including the NBER, study

past data trends to select variables that would best be suited as leading indicators (Filardo, 1999).

These characteristics include: “1) conformity to the general business cycle, 2) consistent timing

as a leading indicator, 3) economic significance based on accepted business cycle theories, 4)

statistical reliability of data collection, 5) smooth month-to-month changes, and 6) reasonably

prompt publication of the data” (Filardo, 1999, p. 37). The CLI rules of thumb are simplistic in

their use and understandability, but some rules present shortcomings in the form of false signals

due to consecutive, yet small, declines and less advance warning of imminent recessions

(Filardo, 1999). However, Philip Klein and Michael Niemira revise the CLI rules of thumb by

adding a threshold which requires “…two to three months of CLI declines of at least 1.3 percent”

to reduce the chance of false signals without compromising recession identification lead time

(Filardo, 1999, p. 37). Filardo (1999) states that the CLI rules of thumb would predict recessions

half a year prior to their occurrence. Lead times and the associated rules and recessions vary

substantially and this can complicate the rule’s use in policymaking.

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Neftҫi’s model offers theoretical advantages over the CLI rules of thumb (Filardo, 1999).

Filardo (1999) notes that the model is flexible to different ideas of how recessions begin. He

gives the example: “…if an analyst believes that expansions can die of old age, the analyst can

modify the Neftҫi model to reflect this belief” (p. 37-38). The CLI rules of thumb do not offer

such flexibility. Also, the Neftҫi model can evaluate other variables other than the CLI to predict

recessions (Filardo, 1999). However, it can only evaluate one variable at a time. Filardo (1999)

finds that the forecasting performance of the Neftҫi model is only marginally better than that of

the CLI rules of thumb.

The Probit model cannot be compared to the CLI rules of thumb and the Neftҫi model as

easily because it can predict recessions at any particular forecast horizon (Filardo, 1999).

However, Filardo (1999) notes that at short forecast horizons (one to three months) the model

provides advance warning of each recession except for the 1960-1961 recession. Unfortunately,

he also reports false signals in 1966, 1983, and 1988. At long horizons (ten to twelve months) he

finds results that were confirmed earlier by Estrella and Mishkin and Lamy. The false signals

were typically short-lived, weak, and associated with relatively weak periods of economic

activity (Filardo, 1999). It is reassuring that the probabilities of recession prior to actual

occurrences were long-lasting and strong.

Filardo (1999) claims that the GDP forecasting model is a regression based framework

but tries to predict recessions by forecasting consecutive declines in GDP. The GDP forecasting

model is specified as a multi-equation regression model. The growth rate of GDP depends on

past growth rates of GDP, past growth rates of the CLI, past changes in the interest rate spread

defined as the 10-year Treasury yield minus the 3-month Treasury yield, and past changes in the

3-month Treasury yield (Filardo, 1999). To spot future recessions, the model produces GDP

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forecasts. A forecast of two consecutive quarterly declines in GDP is taken as a recession

(Filardo, 1999).

As a regression-based framework, the GDP forecasting model has many of the

advantages of the Probit model. The GDP forecasting approach may also be attractive because

analysts can choose any model that produces forecasts of GDP (Filardo, 1999). The GDP

forecasting model is not without problems. Filardo (1999) note the shortcomings of the GDP

forecasting model: 1) it has some of the unstable lead time, 2) the GDP forecasting model

predicts recessions using a 2-quarter GDP decline, which is only an approximation of the

NBER’s definition of recession, and 3) the GDP forecasting equation is a small-scale version of

a large-scale forecasting model which makes it susceptible to inconsistent forecasting

performance around turning points in the business cycle.

The GDP forecasting model had roughly the same lead time and accuracy with real-time

data as with the recently published data. The model did send false signals of recession in the

early 1980s with real-time data. However, those signals were eliminated when the GDP and CLI

data was revised (Filardo, 1999). Filardo (1999) finds results did not necessarily contradict

earlier research that find important sensitivities of GDP forecasting to data revisions.

Dombrosky and Haubrich (1996) believe that due to interest rate data availability the

convenience and cost of analysis is appropriate, but the legitimacy of such analysis must be taken

into consideration. There are many stylish and complicated macroeconometric models being

utilized by the brightest professional forecasters and it seems that at first glance the use of such a

mundane indicator as the yield curve would be deemed irrelevant (Dombrosky and Haubrich,

1996). However, Dombrosky and Haubrich (1996) state that the simple yield curve model can be

used to reaffirm or disapprove the “assumptions or relationships” of the multifaceted

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macroeconometric models used by highly trained professionals. This comparison “increases

confidence in results” when data analysis produces similar results and “signals the need for a

second look” when the results are in disagreement (Dombrosky and Haubrich, 1996).

Chauvet and Potter (2001) claim that the predictive power of the yield curve is not stable

over time even though it has been a statistically significant predictor in the past. The majority of

models that incorporate the yield curve find difficulty in predicting the 1990 recession with the

exception of Laurent (1989), Harvey (1989), and Stock and Watson (1989) (Chauvet and Potter,

2001). The potential reasons for this instability can be contributed to: 1) whether the economy is

responding to real or monetary shocks, 2) the shifts in the market for U.S. Treasury debt, and 3)

increased volatility of the U.S. economy post 1984 (Chauvet and Potter, 2001).

Wheelock and Wohar (2009) find that the yield curve can forecast output growth and

forecast recessions. The yield curve is most useful for forecasting output growth at time horizons

of 6 to 12 months, even when other variables are added to the model (Wheelock and Wohar,

2009). Wheelock and Wohar (2009), among other researchers, notice that the spread has had

diminished predictability power since the mid-1980s.

Dueker (1997) and Estella and Mishkin (1995) use a recession dummy as the dependent

variable. As with other studies, Dueker (1997) proclaims the yield curve slope to be the best

recession predictor he examines and this reinforces the claim that the yield curve should

continuously be considered as a recession predictor. The two favorable characteristics of the

yield curve that contribute to its use as a recession indicator are: 1) “…it is readily observable at

high frequencies and gives a signal that is easy to interpret”, and 2) “the expectations theory for

the term structure of interest rates provides a theoretical foundation for the predictive power of

the yield curve” (Dueker, 1997, p. 49).

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Haubrich (2006) articulates that despite the evidence that links the yield curve and

economic growth, specialists in the field of economics suggest a decreased reliability in the yield

curve’s ability to predict recessions. Due to the constant dynamics and evolution of our

economy, past success stories of the yield curve are becoming less relevant, noting the

incidences in 1995 and 1998 when a flat curve did not signal low economic growth. Wright

(2006) notes that the slope of the yield curve has continuously been cited as a leading economic

indicator, with inversion of the curve being a hint at a forthcoming recession. He notes that

growth, recessions, and interest rates are all endogenous and that association between these

variables is a simple form of correlation. Wright (2006) suggests that the 3-month minus the 10-

year spread exhibits a negative statistical relationship with real GDP over subsequent quarters

and a positive relationship with the likelihood of a recession. The term spread may be useful

because it measures the difference between current short-term interest rates and the average of

expected future short-term interest rates over a time horizon. This brings into account monetary

policy and whether it is restrictive or not.

Wright (2006) uses four Probit regression models to forecast an NBER recession at some

point in the next h quarters. His first model, which he labels model A (equation 1), is:

𝑃(𝑁𝐵𝐸𝑅𝑡,𝑡+ℎ = 1) = 𝛷(ᾶ0 + ᾶ1𝑆𝑃𝑅𝐸𝐴𝐷𝑡3𝑀−10𝑌) (1)

where NBERt,t+h is the dummy variable that equals 1 if there is an NBER-defined recession at

some point during quarters t+1 through t+h, inclusive, 𝑆𝑃𝑅𝐸𝐴𝐷𝑡3𝑀−10𝑌 is the average 3-month

minus 10-year constant maturity Treasury term spread during quarter t and Φ(.) is the standard

normal cumulative distribution function. Wright’s second model, his model B (equation 2),

incorporates the nominal federal funds rate:

𝑃(𝑁𝐵𝐸𝑅𝑡,𝑡+ℎ = 1) = 𝛷(𝛽0 + 𝛽1𝑆𝑃𝑅𝐸𝐴𝐷𝑡3𝑀−10𝑌 + 𝛽2𝐹𝐹𝑡) (2)

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where FFt is the average effective federal funds rate during quarter t. Wright (2006) notes that, in

principle, the real federal funds rate should be a better measure of the expansion or contraction to

the economy due to the stance of monetary policy. Wright’s model C adds the real federal funds

rate to his model B to test which measure, the real or nominal federal funds rate, of the stance of

monetary policy has the best predictive power. Model C (equation 3) is shown below.

𝑃(𝑁𝐵𝐸𝑅𝑡,𝑡+ℎ = 1) = 𝛷(𝛿0 + 𝛿1𝑆𝑃𝑅𝐸𝐴𝐷𝑡3𝑀−10𝑌 + 𝛿2𝐹𝐹𝑡 + 𝛿2𝑅𝐹𝑡) (3)

RFt is the real federal funds rate during quarter t. Wright (2006) uses the “log difference in the

core Personal Consumption Expenditures (PCE) price index over the previous four quarters as a

proxy for expected inflation” (p. 4).

Wright (2006) argues that the expectations hypothesis and term premium components of

the slope of the yield curve have different associations for future growth. Controlling for the

level of the federal funds rate is, as Wright (2006) puts it, the “best indirect war of accounting for

this” (p. 4). Wright (2006) notes that Cochrane and Piazzesi (2005) build off the work of

Campbell and Shiller (1991) and Fama and Bliss (1987) and find that a single linear combination

of the term structure of forward rates has substantial predictive power for the excess returns from

holding a m-year bond for one year, over those from holding a one-year bond (for m from 2 to 5).

Wright calls the “return forecasting factor” a measure of the term premium on a longer-term

bond. Wright (2006) controls for the different implications of the expectations hypothesis and

term premium components of the yield by considering the term spread, the level of the funds

rate, and the “return forecasting factor” as predictors of an NBER recession. These are

incorporated into his model D (equation 4), which is:

𝑃(𝑁𝐵𝐸𝑅𝑡,𝑡+ℎ = 1) = 𝛷(𝛾0 + 𝛾1𝑆𝑃𝑅𝐸𝐴𝐷𝑡3𝑀−10𝑌 + 𝛾2𝐹𝐹𝑡 + 𝛾2𝑅𝐹𝐹𝑡) (4)

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where RFFt is the “return forecasting factor in quarter t estimates by a regression of the average

excess return from holding an m-year bond for one year, over those from holding a one-year

bond (averages over m from 2 to 5) on the term structure of a one-year forward rates at time t.

Wright (2006) notes that this equation introduces measurement errors because it is a “noisy

proxy for the term premium” (p. 5). These four models were tested using data from the first

quarter of 1964 to the fourth quarter of 2005 and tested at horizons of 2, 4, and 6 quarters.

In Model A the coefficient on the spread is statistically significant, thus reaffirming the

historical statistical association. Model B found the coefficients of the federal funds rate and the

term spread to be statistically significant. Model C preferred the nominal funds rate and found no

significance in the coefficient of the real funds rate as noted by Wright (2006). Model D found

the coefficient of the federal funds rate to be statistically positive while the coefficient of the

return forecasting factor was statistically negative at the six quarter horizon, but not at shorter

horizons. Model B, which used the term spread and the level of the funds rate along was the best

fitting model at all horizons out of the models studied.

Wright (2006) finds that more information is in the shape of the yield curve about the

likelihood of a recession than that provided by the term spread alone. The strongest predictability

captured within a yield curve occurred when the yield curve was inverted and the nominal funds

rate was high. The Probit model using term spread alone efficiently predicted recessions with

high certainty four quarters into the future while the other models did not. The funds rate being

statistically insignificant gives support to the idea that tight monetary policy does not necessarily

support the idea of a potential sharp slowdown in economic growth.

Movements in the spread between the discount equivalent yield of a 10-year U.S. and a

3-month Treasury bill precede changes in real GDP growth. These two variables are positively

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correlated with one another as past data has indicated. The term spread contains information

concerning economic variables because it is composed of a real term spread, the expected

difference in inflation, and a term premium (Dotsey, 1998). Dotsey (1998) attempts to

characterize the relationship between output growth and the spread and analyze the predictability

of the spread along different dimensions. The different dimensions include examinations of

nonlinearities in the relationship and whether monetary policy is closely related to the predictive

content of the spread. His findings indicate that when the yield curve inverts there is a high

probability (83 percent) of a forthcoming recession.

Dotsey (1998) analyzes the predictive content of the term spread cumulatively, up to two

years, and marginally using multiple regressions and specifications. The regressions for

cumulative growth are in the form

(400/k) ln(yt+k/yt) = α0 + α1st + et (5)

where y is quarterly real GDP and s is the spread. The values for k are 2, 4, 6, and 8. The

regressions for marginal predictability are of the form

(400/2) ln(yt+k/yt+k-2) = α0 + α1st + et (6)

and analyze whether the spread helps predict two-quarter output growth k periods in the future.

The regression used to evaluate the effects of a monetary tightening and spread is noted by

(400/k) ln(yt+k/yt) = α0 + α1dtst + α2st + et (7)

where dt is a dummy variable that takes on a value of 1 if the funds rate is raised by more than 50

basis points or more over the preceding two quarters. Nonlinearities are investigated by running

this regression:

(400/k) ln(yt+k/yt) = α0 + α1hst + α2mst + α3lst + et (8)

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where hst takes on the value of the spread when the spread exceeds the average by more than

0.425 standard deviations and is zero elsewhere. Also, lst equals the spread when the spread is

below its mean by more than 0.425 standard deviations and zero if it does not. The variable mst

equals the spread when each of the previous variables is zero and is zero elsewhere. Dotsey

(1998) uses 0.425 so that each variable equals the spread roughly one-third of the time. The sum

of the variables is the spread itself. By dividing the spread into these categories analysis can be

done to check if output growth is more response to extreme spread values.

Dotsey (1998) indicates that equation 5 is significant at the 5 percent level in predicting

cumulative output growth up to two years except during the 1985-1997 period and equation 6 is

helpful at predicting two-quarter growth rates two quarters and four quarters in the future, but

becomes less informative in the more distant future. Adding monetary tightening to the

regression equation does not help to forecast recessions and neither does adding a term for

nonlinearity within the spread. The term spread contains information that is absent from past

economic activity and monetary policy.

Estrella and Mishkin (1996) study the ability of financial variables to forecast recessions

and focus on out-of-sample performance rather than in-sample. They decide to do this instead

because earlier studies mostly focused on the ability of financial variables to produce

quantitative measures of economic activity and in-sample performance. Out-of-sample

performance provides a truer test of a variables forecasting ability.

Estrella and Mishkin (1996) use their model and results to compare their forecasting

performance to the NYSE price index, the Commerce Department’s index of leading economic

indicators, and the Stock-Watson index. The performance of the four variables as assessed by

Estrella and Mishkin (1996) suggest that 1) although all of the variables have some forecasting

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ability one quarter ahead the leading indicator indexes, particularly the Stock-Watson index,

produce the best forecast results over this horizon and 2) in predicting recessions two or more

quarters in the future the yield curve dominates the other variables, and this dominance increases

as the time horizon grows.

Results suggest that the yield curve spread can have useful macroeconomic prediction

capabilities and this is particularly true with long lead times. Long lead times are valued highly

by policymakers because policy actions involve substantial time lags. The yield curve can

supplement other econometric models for three key reasons. These reasons, as explained by

Estrella and Mishkin (1996), are 1) forecasting with the yield curve is quick and simple, 2) the

yield curve can be used to check econometric and judgmental predictions by identifying

problems that could have gone overlooked otherwise, and 3) the yield curve produces a

probability of recession that is of interest in its own right.

III. Theoretical Model

The intention of my research is to examine the yield spread and its correlation to

recessions prior to 2014. The Probit regression model used in my study is:

𝑅𝐸𝐶𝐸𝑆𝑆𝐼𝑂𝑁𝑡+4 = 𝛽0 + 𝛽1𝑆𝑃𝑅𝐸𝐴𝐷𝑡 + 휀𝑡 (9)

I examine the model nine times during different historical time periods. One regression is

a culmination of all recession and yield curve data from the second quarter of 1953 to the fourth

quarter of 2013. Two more regressions are used to predict recessions prior to the first quarter in

1986 and another beginning in the first quarter of 1986. I also run regressions to predict the

robustness over time by predicting recessions every ten years beginning in 1954 and ending in

the last quarter of 2013.

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In the Probit regression model I use in my study, SPREADt is the difference between the

10-year Treasury security and secondary market 3-month rate expressed on a bond-equivalent

basis in quarter t (lagged four quarters), β0 is a constant, t represents time (a quarter within a

particular year), β1 is my coefficient, εt is an error term, and RECESSIONt+4 is a dummy variable

that can take on two values: 0 if the observation is an expansion and 1 if it is a recession, in a

particular quarter. I obtain information for RECESSIONt-+4 via the NBER which dates the

official beginning and end of recessions. Table 1 gives a description of the variables and the

hypothesized sign of the variable’s effect.

Dombrosky and Haubrich (1996) and Wheelock and Wohar (2009) note that the

underlying economic theories concerning the predictive power of the yield curve are pertinent.

They note that under the expectations hypothesis theory, long-term interest rates are the average

of expected future short-term rates plus a term premium. The term premium is essentially the

extra interest received for holding a Treasury security with a longer maturity date. If today’s one-

year rate is 8 percent and next year’s one-year rate is expected to be 10 percent, the two-year rate

should be 9 percent ([8+10] / 2 = 8). Therefore if low interest rates are associated with

recessions, then an inverted term structure – which suggests that future rates will be lower –

should reasonably predict a recession. Wheelock and Wohar (2009) also note that the term

premium explains why the yield curve generally slopes upward (yields on long-term securities

exceed those on short-term securities).

The yield curve predicts future output because shifts in interest rates follow from the

same underlying cause: monetary policy. The yield curve reflects future output indirectly, by

predicting future interest rates or future monetary policy. It may also reflect future output

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directly, because the 10-year interest rate may depend on the market’s guess of output in 10

years. These explanations provide motivation for investigating yield curve predictions.

Estrella and Trubin (2006) note that current literature on the yield curve and recessions

has been largely empirical in nature and is generally concerned with the correlation between the

two instead of theorizing why this correlation exists. However, they recognize that there are

numerous explanations for such correlation and a large quantity of these explanations can be

found in the earliest literature dealing with this topic. They go on to explain why monetary

policy and investor expectations provide a robust explanation of why the relationship between

the yield curve and recessions exists.

Estrella and Trubin (2006) and Wheelock and Wohar (2009) illuminate the idea that a

tight monetary policy generally causes both short-term and long-term interest rates to rise which

causes the cost of borrowing to increase, thus lowering the amount of spending within an

economy. However, short-term rates are expected to rise more than long-term rates once

economic activity slows or inflation declines (Wheelock and Wohar, 2009). This process is

implemented during a booming economy when the Federal Reserve believes the economic

growth is occurring too quickly or when they foresee inflation rising beyond desirable levels.

Estrella and Trubin (2006) and Wheelock and Wohar (2009) find that this monetary tightening

slows down the economy and can flatten or invert the yield curve.

IV. Presentation of Data

Table 2 shows NBER dated recessions and the peak and trough year and accompanying

quarter for each economic contraction. The duration of each recession in Table 2 is in months.

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Table 3 provides descriptive statistics for my independent variable, the 10-year minus 3-month

spread, that I use in each of my nine regressions.

The 10-year constant maturity rate and the secondary market 3-month discount rate are

used for my spread. Estrella and Trubin (2006) suggest that maximum accuracy and predictive

power are achieved when the secondary market 3-month rate is expressed on a bond-equivalent

basis. Also, data on the three-month constant maturity rate is available only back to January 1982

which makes it an unfavorable choice for examining data prior to 1982. The secondary market 3-

month rate is expressed on a bond-equivalent basis. Estrella and Trubin (2006) make this

conversion possible via the following equation (“discount” is the yield expresses in percentage

points):

𝑏𝑜𝑛𝑑 − 𝑒𝑞𝑢𝑎𝑣𝑖𝑙𝑒𝑛𝑡 = 100 × (365 ×𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡

100)/(360 − 91 ×

𝑑𝑖𝑠𝑐𝑜𝑢𝑛𝑡

100) (10)

I also use this equation to convert my secondary market 3-month discount rate data to a bond-

equivalent. I use quarterly averages for my spread. I use term spread data from the second

quarter of 1953 through the fourth quarter of 2012 to analyze recessions that occurred from the

second quarter of 1954 through the fourth quarter of 2013. Wright (2006) notes that the data on

long-term yields before 1964 may be unreliable because at this time the vast majority of long

maturity bonds had distorted prices due to being callable or “flower bonds” (redeemable at par in

payment of estate taxes). The data for the Treasury yield curve spread (10-year constant maturity

rate and the secondary market 3-month discount rate) is obtained via the Board of Governors of

the Federal Reserve System’s H.15 Report.

I collect recession data from the National Bureau of Economic Research’s US Business

Cycle Expansions and Contractions. I use data lagged four quarters because Estrella and

Hardouvelis (1991), Estrella and Mishkin (1996), Deuker (1997), Chauvet and Potter (2005),

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Dotsey (1998), and Wright (2006) all find the spread useful for forecasting recessions 4-quarters

ahead. My research focuses more on the robustness of the correlation throughout history and

therefore using a 4-quarter lag was appropriate because prior research shows this particular lags

legitimacy. Figure 2 plots the spread I use in my regression analysis and the grey shaded areas

indicate recessions as designated by NBER.

The spread has been shown to predict recessions more effectively than output growth,

especially as the time horizon increases. It is vital to define recessions at the periods defined by

the NBER because they are most relevant and have also proven to produce very significant

results. Also, the treasury rates used for the model are best because they are very “naked” rates

meaning that they are not extremely complicated to interpret because their underlying “drivers”,

or “movers”, are generally basic in nature.

A. 1954 – 1963 Model

In this model, a recession ended in the second quarter of 1954 which is the start of the

data I used for recession dating. Another recession began in the third quarter of 1957 and ended

in the second quarter of 1958. A third recession began in the second quarter of 1960 and ended in

the first quarter of 1961. These were the three occurrences of recessions during this ten year

span. The mean 10-year less 3-month spread is 1.05%, the minimum spread is 0.24%, the

maximum spread was 1.95%, and the standard deviation is 0.46%.

19

B. 1964 – 1973 Model

In this model the first recession began in the fourth quarter of 1969 and ended in the last

quarter of 1970. The second recession began just years later in the fourth quarter of 1973, which

is the last observation for this particular model. The mean 10-year less 3-month spread is 0.66%,

the minimum spread is -0.39%, the maximum spread is 2.52%, and the standard deviation is

0.76%.

C. 1974 – 1983 Model

This model saw a recession occur from the first quarter of 1974 through to the first

quarter of 1975. Another recession begin in the first quarter of 1980 and ended shortly after in

the third quarter of 1980. A year later another recession began in the third quarter of 1981 and

ended in the fourth quarter of 1982. The mean 10-year less 3-month spread is 0.61%, the

minimum spread is -2.18%, the maximum spread is 3.44%, and the standard deviation is 1.63%.

D. 1984 – 1993 Model

In this model a recession began in the third quarter of 1990 and ended in the first quarter

of 1991. This was the only NBER dated recession in this ten year time span. The mean 10-year

less 3-month spread is 2.03%, the minimum spread is -0.01%, the maximum spread is 3.61%,

and the standard deviation is 1.02%.

20

E. 1994 – 2003 Model

The first recession that occurred in this model was in the first quarter of 2001 and the

recession ended in the fourth quarter of the same year. This was the only observed NBER

recession in this model. The mean 10-year less 3-month spread is 1.47%, the minimum spread is

-0.63%, the maximum spread is 3.35%, and the standard deviation is 1.09%.

F. 2004 – 2013 Model

The recession of 2007 began in the fourth quarter and lasted until the second quarter of

2009. As with the previous two models, only one recession was observed during this ten year

time span. The mean 10-year less 3-month spread is 1.99%, the minimum spread is -0.44%, the

maximum spread is 3.61%, and the standard deviation is 1.24%.

G. 1954 – 1985 Model

Seven recessions were observed prior to 1986. The average duration of these recessions

was eleven months. The mean 10-year less 3-month spread is 0.87%, the minimum spread is

-2.18%, the maximum spread is 3.44%, and the standard deviation is 1.12%.

H. 1986 – 2013 Model

Three recessions were observed post 1985. The average duration of these recessions was

eleven and one-third months. The mean 10-year less 3-month spread is 1.79%, the minimum

spread is -0.63%, the maximum spread is 3.61%, and the standard deviation is 1.17%.

21

I. 1954 – 2013 Model

Ten total recessions were observed for the data I used in my study and the average

recession duration was eleven and one-tenth months. The mean 10-year less 3-month spread is

1.30%, the minimum spread is -2.18%, the maximum spread is 3.61%, and the standard

deviation is 1.23%.

V. Results

Table 4 presents parameter estimates for my Probit regressions including coefficients,

constants, Wald test statistics, p-values, and McFadden pseudo R-squared statistics which are

detailed below in subsection A. Table 5 presents model fitting information which is discussed in

subsection B. Table 6 presents econometric results and probability of recessions occurring, based

on spread, which I discuss in subsection C. These tables are shown in the appendix. In my

analysis of results I use a significance level of 10%. Statistically significant coefficients are

bolded and italicized in Table 4 and Table 5.

A. Probit Parameter Estimates

In Table 4 I provide parameter estimates for β1 and β0 for each regression I run. The

Estimate column provides regression coefficients and the predicted probability of a recession can

be calculated using these coefficients. A negative β1 means that a decrease in SPREADt leads to

an increase in the predicted probability and vice versa. My regression outputs are designed to be

implemented in equation 11 below to assign an estimated probability of a recession four quarters

(t+4) into the future based on the yield spread at time at some point (t). For a particular spread,

β1, and β0, the predicted probability of a recession is

22

𝐹[𝛽0 + (𝑆𝑃𝑅𝐸𝐴𝐷𝑡 × 𝛽1)] (11)

where F is the standard normal cumulative distribution function (shown is equation 12).

𝐹(𝑧) = ∫ 1/√2𝜋 exp (−𝑥2

2) 𝑑𝑥

𝑧

−∞ (12)

I use Microsoft Excel and the standard normal cumulative distribution function to produce

results which I transpose onto Figure 3 in the Appendix. In Figure 3, P(10) represents the

predicted probability of a recession occurring based off of the outputs from the six regressions

that were broken into 10 year increments, P(54-85) represents the predicted probability of a

recession occurring based off of the outputs from the regression that uses data prior to 1986 and

after 1953, P(85-13) represents the predicted probability of a recession occurring based off of the

outputs from the regression that uses data after 1985 and prior to 2014, and P(comp) represents

the predicted probability of a recession occurring based off of the outputs from the regression

that includes all of the data that I utilize in my research. The grey shaded areas indicate periods

designated as national recessions by NBER.

The Wald statistic in Table 4 is the test statistic for the individual regression coefficients

and constants. The Wald test statistic is the squared ratio of the regression constant or

coefficient, β0 or β1 respectively, to the standard error of the respective constant or coefficient.

The test statistic follows a Chi-Square distribution which is used to test against a two-sided

alternative hypothesis that the Estimate is not equal to zero.

The Sig. column in Table 4 provides the p-value of the estimates, or probability that the

null hypothesis that a predictor’s regression coefficient is zero. The p-values are based on the

Wald test statistics of the predictor. The probability that a Wald test statistic is as extreme, or

more extreme, than what has been observed under the null hypothesis is defined by the p-values.

23

The McFadden column contains McFadden's pseudo R-squared which does its best to

mirror the R-squared obtained in OLS (ordinary least squares) regressions. The R-Squared in

OLS explains variability and improvement from a null model to a final (fitted) model. The

equation for McFadden's pseudo R-squared is shown below where MFull = model with predictors,

MIntercept = model without predictors, and Ḽ = estimated likelihood.

𝑅2 = 1 −𝑙𝑛 Ḽ(𝑀𝐹𝑢𝑙𝑙)

𝑙𝑛 Ḽ(𝑀𝐼𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡) (13)

The log likelihood of the intercept model mirrors a total sum of squares that goes into an OLS R-

squared calculation, and the log likelihood of the full model mirrors the sum of squared errors

that can be found in an OLS R-squared calculation as well. A likelihood falls between 0 and 1, so

the log of a likelihood is less than or equal to zero. If a model has a very low likelihood, then the

log of the likelihood will have a larger magnitude than the log of a more likely model. Therefore,

a small ratio of log likelihoods indicates that the full model is a far better fit than the intercept

model. If comparing two models, McFadden's would be higher for the model with the greater

likelihood.

B. Model Fitting Information

In Table 5, the -2 Log Likelihood columns show the product of -2 and the log likelihoods

of the null (β0) model and the final (β1) model. These measures are used to test whether or not the

coefficients of the predictors are zero. The Chi-Square column is the Likelihood Ratio Chi-

Square test that at least one of the predictors’ regression coefficient is not equal to zero in the

model (in my study there is only one predictor). The Likelihood Ratio Chi-Square statistic is

simply the difference between the null model and the final model which can be seen in Table 5.

The Sig. column is the probability of getting a Likelihood Ratio test statistic as extreme as, or

24

more so, than the observed under the null hypothesis. The null hypothesis is that all of the

regression coefficients in the model are equal to zero. Small p-values (less than 0.10) lead to

conclusions that the regression coefficient in the model is not equal to zero.

C. Probabilities based on spread.

Table 6 provides probability results for each of the nine regressions based on spread. For

each probability value, a specific spread is calculated. It is evident from this table that as the

difference in spread treads negatively, the probability of a recession increases. I use the inverse

of the standard normal cumulative distribution to obtain these results.

A. 1954 – 1963 Model

The 10-year less 3-month spread coefficient (β1) is -2.150. For a one unit increase in the

10-year less 3-month spread, the z-score decreases by 2.150. This means that an increase in the

spread decreases the predicted probability of a recession, and vice versa. The constant term

coefficient (β0) is -1.187 meaning that if the 10-year less 3-month spread is evaluated at zero the

predicted probability of a recession is F(-1.187) = 0.1176. So the predicted probability of a

recession occurring when the spread is 0 is 11.76%.

The Wald test statistic for RECESSIONt+4 is 3.823 and the p-value is 0.051 which means

that at my alpha level of 0.10 I reject the null hypothesis and conclude that the model intercept

(β0) has been found to be statistically different from zero given SPREADt is in the model. The

Wald test statistic for the predictor SPREADt is 10.184 and the p-value is 0.001 which means that

at my alpha level of 0.10 I reject the null hypothesis and conclude that the regression coefficient

(β1) has been found to be statistically different from zero in estimating SPREADt.

25

McFadden's pseudo R-squared for this model was 0.318. For the models that were split

into ten year increments this model had the third highest McFadden's pseudo R-squared and the

fourth highest out of the nine regressions.

The Chi-Square statistic for this model is 13.412 and the associated p-value is less than

0.000 which, at my alpha level of 0.10, leads to the conclusion that my regression coefficient in

this model is not equal to zero.

B. 1964 – 1973 Model




coefficient (β0) is 0.634 meaning that if the 10-year less 3-month spread is evaluated at zero the

predicted probability of a recession is F(0.634) = 0.7370. So the predicted probability of a





Wald test statistic for the predictor SPREADt is 3.045 and the p-value is 0.081 which means that

at my alpha level of 0.10 I reject the null hypothesis and conclude that the regression coefficient

(β1) has been found to be statistically different from zero in estimating SPREADt.


into ten year increments this model had the lowest McFadden's pseudo R-squared and the

absolute lowest out of the nine regressions.

26

The Chi-Square statistic for this model is 4.944 and the associated p-value is 0.026

which, at my alpha level of 0.10, leads to the conclusion that my regression coefficient in this

model is not equal to zero.

C. 1974 – 1983 Model








that at my alpha level of 0.10 I fail to reject the null hypothesis and conclude that the model

intercept (β0) has not been found to be statistically different from zero given SPREADt is in the

model. The Wald test statistic for the predictor SPREADt is 11.237 and the p-value is 0.001

which means that at my alpha level of 0.10 I reject the null hypothesis and conclude that the

regression coefficient (β1) has been found to be statistically different from zero in estimating

SPREADt.


into ten year increments this model had the second lowest McFadden's pseudo R-squared and the

third lowest out of the nine regressions.

27




D. 1984 – 1993 Model










model. The Wald test statistic for the predictor SPREADt is 2.569 and the p-value is 0.109 which

means that at my alpha level of 0.10 I fail to reject the null hypothesis and conclude that the

regression coefficient (β1) has not been found to be statistically different from zero in estimating

SPREADt.


into ten year increments this model had the highest McFadden's pseudo R-squared and also the

highest overall out of the nine regressions.

28




E. 1994 – 2003 Model











means that at my alpha level of 0.10 I reject the null hypothesis and conclude that the regression

coefficient (β1) has been found to be statistically different from zero in estimating SPREADt.


into ten year increments this model had the second highest McFadden's pseudo R-squared and

also the second highest overall out of the nine regressions.




29

F. 2004 – 2013 Model














into ten year increments this model had the third lowest McFadden's pseudo R-squared and

ranked fifth out of all nine regressions.




G. 1954 – 1985 Model



30








Wald test statistic for the predictor SPREADt is 22.955 and the p-value is less than 0.000 which



McFadden's pseudo R-squared for this model was 0.217. Out of the three models that

were not split into ten year increments this model had the lowest McFadden's pseudo R-squared

and the second lowest out of all nine regressions.




H. 1986 – 2013 Model





31






model. The Wald test statistic for the predictor SPREADt is 15.268 and the p-value is less than

0.000 which means that at my alpha level of 0.10 I reject the null hypothesis and conclude that

the regression coefficient (β1) has been found to be statistically different from zero in estimating

SPREADt.


were not split into ten year increments this model had the highest McFadden's pseudo R-squared

and the third highest out of all nine regressions.




I. 1954 – 2013 Model







32




Wald test statistic for the predictor SPREADt is 40.298 and the p-value is less than 0.000 which




were not split into ten year increments this model had the second highest McFadden's pseudo R-

squared and ranked sixth out of all nine regressions.




VI. Conclusions and Policy Implications

The research findings of this paper are quite encouraging. The results indicate that

models which use the yield curve spread may be useful in predicting recessions and thus may be

useful in policy making. The yield curve spread was significant at an alpha level of 0.10 in each

regression except the 1984-1993 model. I run regression models of yield curve data at a specific

time against recession data one year in the future. Due to my robust findings I am confident that

the yield curve can produce similar results in the future which can be used to predict imminent

recessions. It is important to lag the yield spread to predict future economic activity because the

action of policy makers generally has a lagged effect itself.

33

I find some similarities in using the yield curve that Estrella and Mishkin (1996) make

note of in their research. They note that the yield curve is quick and simple for forecasting, it can

be used to double-check econometric models and theoretical predictions, and it is useful in

predicting future recessions, which is of high interest to policy makers. An observer can simply

compare the 10-year and 3-month rates and instantly make assumptions about forthcoming

economic activity. One could take this a step further by running regressions and using the

outputs to assign a probability to a potential recession. These results can then be compared

against other econometric procedures used for predicting recessions.

The Probit model is certainly not perfect. Predictions are subject to error simply because

they are statistical estimates. However, the model I use in my research can be used in the future

by the Federal Reserve and government officials to test and reevaluate other models that are

currently used for predicting recessions. As always, caution must be taken in using this data

because future results may not be indicative of previous data. Also, the Federal Reserve is more

informed than ever before and controls rates to compensate economic swings. In the future I

would suggest economists who research recessions to test models with various other economic

indicators.

34

VII. Appendix

Table 1: Variables and Expected Coefficients

Variable Name Description Expected Coefficient Sign

RECESSIONt+4

A dummy variable for a recession

occurring in the quarter t + 4 from

the standpoint of the available

information in quarter t

Dependent Variable

SPREADt

The difference between the 10-year

Treasury security and 3-month

Treasury security interest rate in

quarter t

-

Table 2: Recessions According to NBER

Peak Trough Recession Duration

(Year & Quarter) (Year & Quarter) (In Months)

1953 Q2 1954 Q2 10

1957 Q3 1958 Q2 8

1960 Q2 1961 Q1 10

1969 Q4 1970 Q4 11

1973 Q4 1975 Q1 16

1980 Q1 1980 Q3 6

1981 Q3 1982 Q4 16

1990 Q3 1991 Q1 8

2001 Q1 2001 Q4 8

2007 Q4 2009 Q2 18

35

VII. Appendix (Continued)

Table 3: 10-Year Minus 3-Month Descriptive Statistics

Model Range Minimum Maximum Mean Standard

Deviation

1954-1963 1.71 0.24 1.95 1.05 0.46

1964-1973 2.91 -0.39 2.52 0.66 0.76

1974-1983 5.62 -2.18 3.44 0.61 1.63

1984-1993 3.62 -0.01 3.61 2.03 1.02

1994-2003 3.98 -0.63 3.35 1.47 1.09

2004-2013 4.05 -0.44 3.61 1.99 1.24

1954-1985 5.62 -2.18 3.44 0.87 1.12

1986-2013 4.24 -0.63 3.61 1.79 1.17

1954-2013 5.79 -2.18 3.61 1.30 1.23

36


Table 4: Probit Parameter Estimates

Model Estimate Wald Sig. McFadden

1954-1963 (β1) -2.150 10.184 0.001 0.318

1954-1963 (β0) -1.187 3.823 0.051

1964-1973 (β1) -0.931 3.045 0.081 0.146

1964-1973 (β0) 0.634 4.370 0.037

1974-1983 (β1) -0.535 11.237 0.001 0.266

1974-1983 (β0) 0.201 0.725 0.395

1984-1993 (β1) -3.084 2.569 0.109 0.674

1984-1993 (β0) -0.705 0.890 0.345

1994-2003 (β1) -1.959 5.053 0.025 0.463

1994-2003 (β0) -0.022 0.002 0.966

2004-2013 (β1) -0.750 8.911 0.003 0.317

2004-2013 (β0) -0.191 0.216 0.642

1954-1985 (β1) -0.679 22.955 0.000 0.217

1954-1985 (β0) 0.336 4.690 0.030

1986-2013 (β1) -0.962 15.268 0.000 0.344

1986-2013 (β0) 0.054 0.042 0.837

1954-2013 (β1) -0.753 40.298 0.000 0.275

1954-2013 (β0) 0.274 4.189 0.041

37


Table 5: Model Fitting Information

Model -2 Log Likelihood (β0) -2 Log Likelihood (β1) Chi-Square Sig.

1954-1963 42.136 28.724 13.412 .000

1964-1973 33.817 28.873 4.944 .026

1974-1983 51.796 38.043 13.752 .000

1984-1993 21.311 6.947 14.364 .000

1994-2003 26.007 13.959 12.048 .001

2004-2013 37.098 25.331 11.767 .001

1954-1985 136.467 106.810 29.657 .000

1986-2013 84.397 55.359 29.038 .000

1954-2013 225.265 163.399 61.867 .000

Table 6: Estimated Recession Probabilities from Nine Probit Regressions

Recession

Probability

Value of Spread (Percentage Points)

54-63 64-73 74-83 84-93 94-03 04-13 54-85 86-13 54-13

5% 0.213 2.448 3.450 0.305 0.828 1.938 2.919 1.766 2.548

10% 0.044 2.058 2.771 0.187 0.643 1.453 2.384 1.388 2.066

15% -0.070 1.794 2.312 0.108 0.518 1.127 2.022 1.133 1.740

20% -0.161 1.585 1.948 0.044 0.418 0.867 1.735 0.931 1.481

25% -0.239 1.406 1.636 -0.010 0.333 0.644 1.489 0.757 1.259

30% -0.308 1.244 1.355 -0.058 0.257 0.444 1.268 0.601 1.060

40% -0.434 0.953 0.848 -0.146 0.118 0.083 0.868 0.319 0.700

50% -0.552 0.681 0.375 -0.229 -0.011 -0.255 0.495 0.056 0.364

60% -0.670 0.409 -0.099 -0.311 -0.140 -0.593 0.121 -0.208 0.027

70% -0.796 0.118 -0.605 -0.399 -0.279 -0.954 -0.278 -0.490 -0.333

80% -0.944 -0.223 -1.198 -0.501 -0.441 -1.377 -0.746 -0.819 -0.754

90% -1.148 -0.696 -2.021 -0.644 -0.665 -1.963 -1.394 -1.277 -1.339

38


Table 7: Studies of the Usefulness of the Yield Curve for Predicting Recessions

Literature Methodology Data (years) Findings

Estrella and

Hardouvelis (1991) Probit model U.S. (1955-88)

Spread is useful for

forecasting recessions 4

quarters ahead.

Dotsey (1998) Probit model U.S. (1955-97) Spread is useful for

prediction.

Estrella and

Mishkin (1996) Probit model U.S. (1959-95)


prediction, especially at 2-

to 6-quarter horizons

Bernard and

Gerlach (1998) Probit model

8 industrialized

countries (1972-93)


prediction at 4- to 8-

quarter horizons

Estrella, Rodrigues,

and Schich (2003) Probit model

U.S. (1955-98) and

Germany (1967-98)


prediction at 12-month

horizons, less so at 24-

and 26-month horizons.

Chauvet and Potter

(2005)

Variants of Probit

model allowing for

multiple structural

breaks and

autoregression

U.S. (1954-2001)


prediction at 12-month

horizons.

Wright (2006) Probit model U.S. (1964-2005) Spread is useful for

predicting recessions.

Rosenberg and

Maurer (2008) Probit model U.S. (1961-2006)

The expectations

component of the spread

is more accurate than the

term premium component

at forecasting recessions.

SOURCE: Wheelock, David C. and Wohar, Mark E. 2009. “Can the Term Spread Predict

Output Growth and Recessions? A Survey of the Literature.” Federal Reserve Bank of St.

Louis, Review. Volume 91, Number.

39


0

2

4

6

8

10

12

14

16

18

3 -mo. 6-mo. 1-yr. 2-yr. 3-yr. 5-yr. 7-yr. 10-yr. 30-yr.

Per

cent

(Wee

kly

Aver

age)

Maturity

Yield Curves

2/18/1977

12/1/1978

3/28/1980

10/16/1987

2/15/2002

8/18/2006

Figure 1

-3.00

-2.00

-1.00

0.00

1.00

2.00

3.00

4.00

2 Q

1954

2 Q

1958

2 Q

1962

2 Q

1966

2 Q

1970

2 Q

1974

2 Q

1978

2 Q

1982

2 Q

1986

2 Q

1990

2 Q

1994

2 Q

1998

2 Q

2002

2 Q

2006

2 Q

2010

Per

cen

tage

Lagged Yield Spread & NBER Recessions

NBER Dated Recessions (Quarterly) 10-year, 3-month spread (Lagged 4 quarters)

Figure 2

40


0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

2 Q1954

2 Q1957

2 Q1960

2 Q1963

2 Q1966

2 Q1969

2 Q1972

2 Q1975

2 Q1978

2 Q1981

2 Q1984

2 Q1987

2 Q1990

2 Q1993

2 Q1996

2 Q1999

2 Q2002

2 Q2005

2 Q2008

2 Q2011

Predicted Probability of U.S. Recession Twelve Months Ahead

NBER Dated Recessions (Quarterly) P(10) P(54-85) P(85-13) P(Comp)

Figure 1

41

VIII. References

Board of Governors of the Federal Reserve System. Selected Interest Rates (Daily) - H.15.

from http://www.federalreserve.gov/releases/h15/data.htm (accessed November 2013 –

March 2014).

Campbell, John Y. and Shiller, Robert. 1991. “Yield Spreads and Interest Rate Movements: A

Bird’s Eye View.” Review of Economic Studies. Volume 58. Pp. 495-514.

Chauvet, Marcelle and Potter, Simon. 2005. “Forecasting Recessions Using the Yield Curve.”

John Wiley & Sons, Ltd., Journal of Forecasting. Volume 24, Number 2.

Cochrane, John and Piazzesi, Monika. 2005. “Bond Risk Premia.” American Economic Review.

Volume 95. Pp. 138-160.

Dombrosky, Ann M. and Haubrich, Joseph G. 1996. “Predicting Real Growth Using the Yield

Curve.” Federal Reserve Bank of Cleveland, Economic Review. Volume 32, Number 1.

Dotsey, Michael. 1998. “The Predictive Content of the Interest Rate Term Spread for Future

Economic Growth.” Federal Reserve Bank of Richmond, Economic Quarterly. Volume

84, Number 3.

Dueker, Michael J. 1997. “Strengthening the Case for the Yield Curve as a Predictor of U.S.

Recessions.” Federal Reserve Bank of St. Louis, Review. Volume 79, Number 2.

Estrella, Arturo and Hardouvelis, Gikas A. 1991. “The Term Structure as a Predictor of Real

Economic Activity.” The Journal of Finance. Volume, Number 2. Pp. 555-576.

Estrella, Arturo and Mishkin, Frederic S. 1996. “The Yield Curve as a Predictor of U.S.

Recessions.” Federal Reserve Bank of New York, Current Issues in Economics and

Finance. Volume 2, Number 7.

42

Estrella, Arturo and Trubin, Mary R. 2006. “The Yield Curve as a Leading Indicator: Some

Practical Issues.” Federal Reserve Bank of New York, Current Issues in Economics and

Finance. Volume 12, Number 5.

Fama, Eugene and Bliss, Robert. 1987. “The Information in Long-Maturity Forward Rates.”

American Economic Review. Volume 77. Pp. 680-692

Filardo, Andrew J. 1999. “How Reliable Are Recession Prediction Models?” Federal Reserve

Bank of Kansas City, Economic Review, Fourth Quarter.

Haubrich, Joseph G. 2006. “Does the Yield Curve Signal Recession?” Federal Reserve Bank of

Cleveland, Economic Quarterly. pp. 31-52.

The National Bureau of Economic Research. US Business Cycle Expansions and Contractions.

from http://www.nber.org/cycles.html (accessed November 2013 – March 2014).

UCLA: Idre Research Technology Group. Annotated SPSS Output.

from http://www.ats.ucla.edu/stat/spss/output/SPSS_probit.htm (accessed November

2013 – March 2014).

UCLA: Idre Research Technology Group. FAQ: What are pseudo R-squareds?

from http://www.ats.ucla.edu/stat/mult_pkg/faq/general/Psuedo_RSquareds.htm

(accessed November 2013 – March 2014).

UCLA: Idre Research Technology Group. SPSS Data Analysis Examples.

from http://www.ats.ucla.edu/stat/spss/dae/probit.htm (accessed November 2013 – March

2014).

Wheelock, David C. and Wohar, Mark E. 2009. “Can the Term Spread Predict Output Growth

and Recessions? A Survey of the Literature.” Federal Reserve Bank of St. Louis, Review.

Volume 91, Number.

43

Wright, Jonathan H. 2006. “The Yield Curve and Predicting Recessions.” Federal Reserve

Board of Washington D.C., Finance and Economics Discussion Series.

thesis_anthony locatelli

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