Strengthening the Case for the Yield Curve As a Predictor of U.S. Recessions

M ARCH/APRIL 1997

Michael J. Dueker is a senior economist at the Federal Reserve Bank of St. Louis. Nick Meggos provided research assistance.

slope ought to contain information about Strengthening the future prospects of the economy. Estrella and Mishkin (1995) found the the Case for the yield curve slope to be a useful recession predictor; in this article, I examine results Yield Curve as from two econometric models that further test the predictive power of the yield-curve a Predictor of slope relative to other recession predictors such as stock prices and the Commerce U.S. Recessions Department’s index of leading indicators.

Michael J. Dueker WHY DOES THE YIELD CURVE TILT BEFORE RECESSIONS? hat is the message from stock and The yield curve shows prevailing bond markets about the likelihood market interest rates at various maturities. Wof a recession within the next The expectations hypothesis of the term year?” Monetary policymakers must structure of interest rates claims that, for examine such questions as part of a look- any choice of holding period, the expected at-everything approach to decision return is the same for any combination of making. Policymakers need quantitative bonds of different maturities one might analysis of the relevance of the answers, hold in that period. In other words, the because many touted indicators actually expectations hypothesis maintains that predict very little about the future course investors do not expect different returns of the economy. A quantitative appraisal from holding a 1-year note versus holding would establish whether a recession indi- two successive 6-month securities. For cator provides significant signals prior to the same 1-year holding period, they recessions and whether it gives false would also expect to realize identical signals outside of recessionary periods. returns from a 1-year note and from a Proponents of financial indicators of 30-year bond bought at the same time the economy maintain that financial mar- and sold at market price one year later. kets are good aggregators of information Obviously, if people had perfect foresight because of broad participation in the mar- about future short-term interest rates, kets. They suggest, further, that people holding-period returns would necessarily have strong incentives to price securities be equalized through arbitrage. However, as closely as possible to fundamental uncertainty regarding future short-term values. Recent research supports this interest rates causes the interest-rate term argument by showing that simple financial structure to deviate from the shape indicators, such as interest rates and stock implied by the risk-neutral expectations 1 Laurent (1989), Mishkin prices, often do better than composite hypothesis. In particular, the yield curve (1990), Estrella and indices of leading indicators in predicting normally is upward-sloping, even when Hardouvelis (1991), Hu economic recessions, especially at investors expect relatively constant short- (1993), Plosser and Rouwenhorst (1994), Estrella horizons beyond one quarter (Estrella and term rates, because holders of long-term and Mishkin (1995), Davis Mishkin, 1995). The predictive power of securities bear the risk that future interest and Fagan (1995) and the slope of the bond yield curve, in rates will be higher than expected, so they Haubrich and Dombrosky particular, has received notice in require a positive risk premium in long- (1996) all discuss the term numerous studies.1 This article begins term bond yields. Fluctuations in structure of interest rates as a with a discussion of why the yield curve interest-rate risk premiums are thought to forecasting variable.

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be relatively small, at least in the short short-term bonds throughout the period. run, so changes in market expectations of Therefore, we expect the yield curve to tilt future short-term rates are still considered down today if recession looms. the primary determinant of changes in the Historical experience shows that on slope of the yield curve. several occasions prior to recessions, If investors begin to suspect that a long-term interest rates dipped below pre- recession is near, the response of the yield vailing short-term rates, a phenomenon curve will depend on their assessment of known as an inverted yield curve. Figure 2 the magnitude and duration of the illustrates episodes when the gap between recession’s effect on short-term interest the 30-year bond rate and the 3-month rates. Rudebusch (1995) and Haubrich T-bill rate became negative—that is, the and Dombrosky (1996) observe that the yield curve became inverted.2 Since public anticipates that short-term interest 1960 the yield curve has become inverted rates will decline gradually in a recession prior to all five recessions. The extent to until the economy’s performance improves. which the yield curve is tilted away from These reductions in short-term interest its normal “slope” is identified by many rates may stem from countercyclical mone- researchers as a valuable indicator of tary policy designed to stimulate the recessions. Of course, the yield curve economy, or they may simply reflect low does not have to become inverted to real rates of return during the recession. signal that recession is imminent; it In either case, the anticipated severity and may simply flatten relative to normal. duration of the recession will strongly influence the expected path of short-term interest rates, which will show up in the QUANTIFYING THE YIELD shape of the yield curve. CURVE SLOPE AS A Figure 1 shows that a 2-year moving PREDICTOR OF RECESSIONS average of the change in the 3-month Estrella and Mishkin (1995) analyze Treasury bill rate generally conforms with candidate recession predictors and con- the notion that short-term rates fall in clude that the yield-curve slope is the recessions. According to the expectations single most powerful predictor of reces- hypothesis, when investors expect a recessions. They use a probit model to predict a sion, they believe that long-term interest recession dummy variable, Rt, where rates should fall immediately in order to equalize future expected holding-period Rt = 1 if the economy is in recession in returns. Current rates on securities with period t and different maturities will decline by different amounts, depending on how Rt = 0 otherwise. much of their repayment (in present value terms) will take place during the period of The decision to forecast a recession low short-term interest rates. Today’s 1- dummy, rather than output growth, has a year rate might not change at all if the purpose. A goodness-of-fit measure for a period of low short-term rates is not model of output growth would mix infor- expected to start for a year, whereas today’s mation on the predictability of the strengths 2 In this article, the slope of the 7-year rate might be the most affected if of recoveries and expansions with informa- yield curve is always taken over investors expect short-term rates to go tion on the timing of recessions. The the entire length, between down in a year and stay down for three recession dummy variable, in contrast, three months and the bench- mark 30-year rates. Some years. Under this theory, if long-term isolates the accuracy with which one can studies, especially those that rates, such as the 7-year rate, did not fall predict the date of the onset and the need internationally compara- today, then the expected holding-period expected length of recessions. With a ble data, take the slope return over the next four years would be recession dummy dependent variable, between three months and ten higher for those who held long-term bonds Estrella and Mishkin (1995) use the years. than for those who held a succession of probit, a standard econometric model in

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which the probability of recession at time Figure 1 t, with a forecast horizon of k periods, is described by the following equation: Changes in the 3-Month T-Bill: Two-year Moving Averages = =Φ() + Percent (1) Prob()Rt1 c 0 c1 Xt− k , 10 8 where Φ(.) is the cumulative standard 6 normal density function, and X is the set 4 of explanatory variables used to forecast 2 recessions. 0 The log-likelihood function for a -2 probit model, following from Equation 1, is -4 -6 = = -8 (2) LRRX∑ tlnProb () t 1 t− k 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 t + − = ()1RRXtlnProb() t 0 t− k .

Figure 2 As a measure of ﬁt for probit models, 2 Estrella (1995) proposed a pseudo-R in Yield-Curve Slope which the log-likelihood of a model, Lu, is compared with the log-likelihood of a Percent nested model, Lc, that by construction 4 must have a lower likelihood value: 3 2 −() 2 / n Lc  L  1 (3) pseudo−R2 =1 −  u  .   0 Lc -1 While many functions of the log- -2 likelihoods are monotonic between zero -3 and one, and could thus serve as meas- -4 ures of ﬁt, Estrella argues that Equation 3 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 corresponds well with the standard R2 function from linear regressions. Within this framework, Estrella and Poor’s 500 index of stock prices (stock); Mishkin (1995) obtain a quantitative and the percentage difference between 3 The explanatory variables stud- 2 measure of fit with the pseudo-R and the yields on 30-year Treasury bonds and ied by Estrella and Mishkin demonstrate that, among the variables 3-month T-bills (yield curve). Friedman (1995) are: the spread between they study, the yield-curve slope is the and Kuttner (1993) tout the quality the 10-year bond rate and the single-most powerful predictor, X, of spread between commercial paper and 3-month T-Bill rate (the slope of recessions for forecast horizons, k, the Treasury bill rates as a predictor the yield curve); the spread beyond one quarter.3 In this article, we of recessions. I use monthly data between the 6-month commer- examine probit results (Equation 1) for from January 1959 to May 1995 (437 cial paper rate and the corre- five explanatory variables: the change in observations). The recession binary sponding T-Bill rate; stock price indices; monetary aggregates; the Commerce Department’s index of variable follows from business-cycle indexes of leading indicators; leading indicators (lead); real M2 growth turning points determined by the and macroeconomic indicators, (money); the percentage spread between National Bureau of Economic Research such as the purchasing man- the 6-month commercial paper and 6- (NBER). The exact construction of agers' survey, housing starts month Treasury bill rates (spread); the the explanatory variables is given in and the trade-weighted percentage change in the Standard and the appendix. exchange rate.

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Table 1 from the model with the yield-curve slope and the constant-probability model that 2 Pseudo-R Measures of Fit for 2 has likelihood Lc = –197.2. The pseudo-R Recession Predictors is based on the difference in fit between these two models. The chart shows predic- Predictor Forecast Horizon tions of the recessionary state for that date, k=3 k=6 k=9 k=12 based on information that was available six months earlier. It is therefore interesting yield curve .153 .256 .305 .264 to see whether the model accurately (–164.3) (–142.7) (–133.0) (–141.8) predicted recessions six months ahead of lead .182 .122 .080 .032 time. Consistent with the conventional (–158.1) (–171.2) (–180.1) (–190.4) wisdom that most recessions arrive earlier money .098 .081 .090 .054 or later than the date predicted by most (–176.0) (–179.7) (–178.1) (–185.8) professional forecasters, Figure 3 shows stock .060 .061 .033 .017 that only in the 1980 and 1981 recessions (–184.2) (–184.0) (–190.1) (–193.6) was the forecast probability of recession clearly above 50 percent at the onset.4 spread .098 .052 .015 .013 Moreover, in the relatively severe 1974 (–176.1) (–186.1) (–194.0) (–194.5) recession, the six-month forecast probability Log-like. Lc (–197.2) (–197.2) (–197.2) (–197.2) of being in a recession never reached 75 percent, demonstrating that the recession Log-likelihood values are in parentheses. was always viewed as transitory, when actually it proved to be protracted. Similarly, Table 1 contains the pseudo-R2 for in the midst of the 1981 recession, the fore- these five variables at 3-month, 6-month, cast probability of recession fell below 9-month and 12-month forecasting horizons. 50 percent by 1982 and kept falling, The log-likelihood values are in parentheses. even as the recession continued through The baseline log-likelihood value, Lc, is November. Hence, although the yield from a model that contains only a constant, curve slope model surpasses all the others, which implies a constant probability of it still does not absolutely predict either recession each month. the onset or duration of recessions. The results of these simple probit models confirm the finding of Estrella and Mishkin (1995) that the slope of the yield THE PREDICTIVE POWER OF curve becomes the dominant predictor of A DYNAMIC MODEL recessions at horizons beyond three months. One drawback of the probit model of In fact, the log-likelihood improves for the Equation 1 that is typical of many limited- yield curve, unlike the other variables, up dependent-variable econometric models is to a nine-month horizon. The intuition the lack of a dynamic structure for applica- for this improvement is that, as the first tions to time series data such as the recession

section of this article explained, long-term variable, Rt. The recession predictor, Xt, is rates decline well before an anticipated a time series variable with its own autocor- recession in order to equalize holding- relation structure, but the model uses no period returns during the recession and information contained in the autocorrela- recovery. Thus the slope of the yield curve tion structure of the dependent variable to is likely to signal a recession well before form predictions. Univariate time-series the actual onset of a recession. Empirically, modeling of macroeconomic data has it appears that the yield curve slope, clearly demonstrated the relevance of a lagged nine months, is the best recession variable’s own history in generating predictor. forecasts. 4 I identify recessions by the year Figure 3 compares, at the six-month To demonstrate the statistical in which they began. forecast horizon, the recession probabilities importance of the dependent variable’s

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own autocorrelations, consider the assump- Figure 3 tions behind a probit model. Observable variables, X, and an unobserved, mean- Recession Probabilities from the Simple Probit Model: Six-Month Forecast Horizon zero random shock, u, determine the Percent value of the binary dependent variable 1.0 by way of an unobservable latent variable, 0.9 y*, that is assumed to be a linear function 0.8 of the explanatory variables and a mean- 0.7 zero, normally-distributed shock, u, 0.6 such that 0.5 0.4 * = − − + (4) yt c0 c 1 Xt− k ut . 0.3 0.2 By convention, the binary recession 0.1 0.0 variable is equal to 1 if y* Յ 0 and zero if 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 y* > 0, which implies that Φ( ) Φ( ) Prob (Rt=1) = c0+c1Yield Curvet-6 Prob (Rt=1) = c0

= ≤ + sion predictor. The unrestricted model (5) Rt1, if u t c0 c 1 Xt− k , and gives Lu. The restricted model, with c1 = 0, = > + Rt0, if u t c0 c 1 Xt− k . gives Lc. Note that in Equation 1 and in Estrella and Mishkin (1995), Lu comes In the probit model, the random shocks, u, from a model with c2 = 0, and Lc is from are assumed to be independent, identically the model with c1 = c2 = 0. Hence, distributed, normal random variables with Equation 6 imposes a higher standard at a mean of zero. For many time-series which a zero pseduo-R2 begins, because applications, however, it is implausible the recession predictor must now add to to assume that the conditional mean of the fit provided by the lagged dependent ut is zero if we condition only on Xt-k, variable. I repeat the exercise for different without reference to whether the economy forecasting horizons, k = 3, 6, 9, and 12 has actually been in recession in recent months. Three months is probably a min- periods. The obstacle to applying traditional imum recognition lag time for recessions. time-series techniques to address possible It would clearly not be reasonable to serial correlation in u is that y*, and there- include last month’s value of the recession fore u, are unobserved variables, so we binary variable as an explanatory variable, cannot apply an autoregressive moving- because it takes more time to recognize average (ARMA) filter, for example, to u. that the economy has entered a recession. The solution proposed here is to remove At three months, the NBER may not have serial correlation in u by conditioning officially designated and announced a explicitly on the recent history of R, as business cycle turning point, but people well as X. have acquired enough other information to Adding a lag of R to the specification infer with a reasonable degree of accuracy enhances the plausibility of the assump- whether the economy is in a recession or tion that ut has a mean of zero, conditional not. If three months seems less than the on information available through time minimum recognition lag time for t– k: recessions, then one can concentrate on the results for 6, 9, and 12 months. = =Φ + + (6) Prob()Rt 1 () c0 c 1 Xt− k c 2 R t − k . One difference between Table 1 and Table 2 is that Lc varies with the forecast The specification of Equation 6 is the horizon in Table 2. At the 3-month and probit analogue of adding a lagged depen- 6-month horizons, Lc is much higher than dent variable to a linear regression model. the –197.2 obtained in the constant-proba- I ran Equation 6 for each candidate reces- bility model in Table 1. The forecasting

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Figure 4 6, the slope of the yield curve dominates the other recession predictors at all Recession Probabilities from the Simple forecast horizons, not merely the longer Probit Model Using a Lagged Dependent ones. In particular, the index of leading Variable: Six-Month Forecast Horizon indicators does not have a high R2 at Percent short horizons in the presence of the 1.0 lagged dependent variable in Table 2, 0.9 whereas the R2 was high at short horizons 0.8 0.7 in Table 1. This difference suggests that 0.6 the explanatory power of the index of 0.5 leading indicators largely overlaps with 0.4 that of the lagged dependent variable. The 0.3 explanatory power of the slope of the yield 0.2 curve, in contrast, appears to complement 0.1 the lagged dependent variable. Thus, 0.0 rather than weakening the importance of 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 the yield-curve slope as a recession predictor, Prob (R =1) = Φ(c +c Yield Curve +c R ) Prob (R =1) = Φ(c +c R ) t 0 1 t-6 2 t-6 t 0 1 t-6 the addition of the lagged dependent variable has buttressed the dominance of the yield curve as a recession predictor. Table 2 Figure 4 contains two sets of recession Pseudo-R2 Measures of Fit for Recession probabilities—one from the baseline Predictors (with lagged dependent variable) model that uses the lagged dependent variable, and the other from the model that Predictor Forecast Horizon uses both the lagged dependent variable and the slope of the yield curve. Here the k=3 k=6 k=9 k=12 pseudo-R2 exceeds zero only to the extent Yield curve .163 .233 .284 .265 that a model’s explanatory variable adds to (–79.72) (–119.0) (–132.1) (–139.2) the fit provided by the lagged dependent Lead .069 .054 .055 .027 variable. In contrast to Figure 3, Figure 4 (–97.9) (–156.0) (–180.1) (–189.0) shows that the model predicts the severity and duration of the 1974 recession after Money .058 .048 .071 .047 (–100.0) (–157.1) (–176.7) (–184.9) lapsing briefly toward the beginning of the recession. The model with the lagged Stock .046 .039 .020 .002 dependent variable better captures the (–102.5) (–159.0) (–187.4) (–193.4) duration of recessions but still fails to Spread .020 .012 .002 .002 foresee, with six months’ notice and at (–108.0) (–164.8) (–191.3) (–194.4) least 50 percent probability, the onset of Log-like. L (–112.3) (–167.4) (–191.7) (–194.8) recessions in 1960, 1970, 1980 and 1990. c On the other hand, the lagged dependent Log-likelihood values are in parentheses. variable helps the model foresee the importance of the recessions in 1970 and 1990 better in Figure 4 than in Figure 3. power of the lagged dependent variable worsens at longer horizons, however, so the log-likelihood at which the recession A RICHER TIME-SERIES predictor begins to have a non-zero APPROACH pseudo-R2 decreases. For this reason, the The probit model with Markov pseudo-R2 of the slope of the yield curve switching further challenges the slope of actually increases up to the nine-month the yield curve to make a forecasting con- horizon, even though the log-likelihood tribution, because Lc is higher than in decreases. As the input, Xt-k, to Equation Table 2, making it more difficult to achieve

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COEFFICIENT VARIATION VIA MARKOV SWITCHING IN THE PROBIT MODEL With time-series data, one might also question the statistical assumption of independent, identically-distributed random shocks, in addition to the assumption of zero conditional means. One way to make the independence assumption more plausible is to allow for some time variation—that is, time-varying coefficients—in the structure of the model. For example, if the relationship between recessions and the slope of the yield curve were to undergo random fluctuations, these could cause a failure of the independence assumption, if left unmodeled. One simple yet tractable model allows the coefficients to change values according to an unobserved binary state variable, St, which follows a Markov process:

St ʦ {0,1}; cit = ci(St); Prob(St = 1 | St-1=1) = q; and Prob(St = 0 | St-1= 0) = p. In this way, the coefﬁcients take on either of two values, depending on the value of the state variable, changing the magnitude of the shock needed to induce a recession:

= ≤ + + (7) R t 1 , if u t c 0 () S t c 1 () S t Xt− k c 2 () St Rt − k , and = > + + Rt0,. if u t c0() S t c 1() S t Xt− k c 2 () St Rt − k

The transition probabilities, p and q, indicate the persistence of the states and determine the unconditional probability of the state St = 0 to be (1– q)/(2 – p – q). In the estimation, Bayes’ Rule is used to obtain ﬁltered probabilities of the states in order to integrate out the unobserved states and evaluate the likelihood function, as in Hamilton (1990): = = (8) Prob()SRt0 t 0

Prob()SXRRS= 0 Prob()= 0 = 0 = t t− k t − k t t 1 ; = − = = ∑ Prob()St s X t−1 , R t k Prob() R t0 S t s s=0 ′ ()Prob()SXRSXS= 0 Prob()= 1 (9) t t− k t − k t t − k t − k ′ =k = = GSXRSXR()Prob()tk−0 tktk − − , Pr ob() tk − 1 tktk − − , where G is the transition matrix of the Markov state variable. The function maximized is then

T  1  ()= ()= = (10) ∑Rt ln ∑ Prob St s Xt− k , R t − k Prob Rt1 S t s  t =1 s = 0   1  + − = = = ()1Rt ln∑ Prob() St s Xt− k , R t − k Prob() Rt 0 S t s  .  s=0 

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Table 3 a high pseudo-R2. Now the predictor vari- Pseudo-R2 Measures of Fit for Recession able has to show explanatory power above Predictors (with Markov switching) and beyond the predictions of not only the lagged dependent variable, but also the time-series Markov process governing the Predictor Forecast Horizon state variable. The Markov process helps

k=3 k=6 k=9 k=12 forecast, because a shifting c0(St), for Yield curve .159 .269 .294 .283 example, would help raise the likelihood (–79.70) (–111.6) (–128.4) (–123.6) value relative to a stationary c0. Results from estimating the Markov-switching Lead .086 .073 .095 .035 probit models in Table 3 show that the (–93.7) (–151.5) (–169.7) (–174.6) slope of the yield curve still dominates the Money .067 .054 .105 .052 other candidate predictor variables and (–97.6) (–155.4) (–167.6) (–171.0) attains significant pseudo-R2 values. Stock .043 .043 .034 0.0 The difference in log-likelihood values (–102.5) (–157.9) (–182.8) (–182.1) between entries in Table 3 and Table 2 Spread .063 .142 .049 .015 shows the gain from allowing Markov (–98.4) (–137.1) (–179.5) (–178.8) switching in the coefficients, at the cost of adding five parameters to the models. Log-like. L (–111.6) (–167.0) (–189.9) (–182.1) c Likelihood ratio statistics do not obey their Log-likelihood values are in parentheses. usual chi-square limiting distributions, however, because the transition probabilities are not identified under the null of no Markov switching. Therefore, we do not Table 4 present a formal test of the significance of Coefficient Estimates for the Markov switching, but it is reasonable to Markov-Switching Model of believe that large likelihood ratio test sta- the Yield-Curve Slope tistics, such as 31.2 for the yield curve at (six-month forecast horizon) the 12-month horizon, are significant. Generally, the Markov switching appears Parameter Estimate to be most relevant at longer horizons. At horizons less than one year, the c (S = 0) –1.18 0 t addition of Markov-switching coefficient Intercept (.275) variation is only of marginal benefit in

c0(St = 1) –.769 the log-likelihoods. One possible explana- Intercept (.125) tion—not easily proven—for less temporal stability in the coefﬁcients at a one-year c1(St = 0) –2.58 Yield curve (.549) horizon is that the degree of 12-month serial correlation in the business cycle

c1(St = 1) –.597 varies over time more than the degree of Yield curve (.086) 3-month serial correlation. Figure 5 plots the six-month-ahead c2(St = 0) 2.04 Lagged dep. (.577) recession probabilities for the models with Markov switching, both with and without c (S = 1) 1.30 2 t the slope of the yield curve. Relative to Lagged dep. (.241) Figures 3 and 4, the model with Markov switching does a better job at predicting p = Prob(St = 0 |St–1 = 0) .9898 (.0079) the length of recessions, once it recognizes .9997 that a recession is under way. As for q = Prob(S = 1 | S = 1) (.0037) forecasting the onset of recessions, the t t–1 model with Markov switching does reason- Standard errors are in parentheses. ably well for the “major” recessions: 1974,

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1980, and 1981, but it does not predict the Figure 5 onsets of the milder recessions in 1960, 1970, and 1990. The fit does not seem Recession Probabilities from the “worse” after 1985, as Haubrich and Probit Model Using a Lagged Dombrosky (1996) suggest; instead, the Dependent Variable and Markov- Markov-switching model suggests that Switching: Six-Month Forecast Horizon milder recessions, such as 1990, are less Percent accurately forecast throughout the 1.0 sample. 0.9 Table 4 contains the estimated coeffi- 0.8 cients and standard errors for the Markov 0.7 switching model when the slope of the 0.6 yield curve is the explanatory variable 0.5 and the forecast horizon is six months. 0.4 0.3 Equation 8 suggests that the coefficient 0.2 on the yield-curve slope, c1, should be 0.1 negative, because steep slopes ought to 0.0 indicate that recessions are less likely. 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 Φ( ) Φ( ) Similary, the expected sign for the coeffi- Prob (Rt=1) = c0+c1Yield Curvet-6+c2Rt-6 Prob (Rt=1) = c0+c1Rt-6 cient on the lagged dependent variable is positive, because a recent recession ought to make a subsequent recession more likely. The estimated coefficients in Table importance of allowing for dynamic serial 4 have the expected signs; they do not correlation in the model. They also suggest change signs across switches in the state that allowance for general coefficient varia- variable, only magnitudes. tion is not particularly significant at horizons less than one year. CONCLUSION As in Estrella and Mishkin (1995), I use REFERENCES a recession dummy as the dependent variable to focus on the timing of Davis, E. Phillip and S.G.B Henry. “The Use of Financial Spreads as recessions. The yield-curve slope remains Indicator Variables: Evidence from the United Kingdom and the single best recession predictor in the Germany,” IMF Staff Papers (September 1994), pp. 512-25. examined set of variables, even under two Engle, Robert F. “Autoregressive Conditional Heteroscedasticity with extensions of the basic time-series probit Estimates of the Variance of United Kingdom Inflation,” Econometrica, model. The robustness of this finding (July 1982), pp. 987-1007. strengthens the claim that the yield curve Estrella, Arturo, and Gikas Hardouvelis, “The Term Structure as a should be considered a useful recession pre- Predictor of Real Economic Activity,” Journal of Finance (June 1991), dictor. The yield curve has two factors in pp. 555-76. its favor as a recession indicator, other than ______and Frederic S. Mishkin, “Predicting U.S. Recessions: Financial the statistical backing outlined in this Variables as Leading Indicators,” NBER Working Paper 5379, 1995. article. First, it is readily observable at high frequencies and gives a signal that is easy to Friedman, Benjamin, and Kenneth Kuttner, “Why Does the Paper-Bill interpret. Second, the expectations theory Spread Predict Real Economic Activity?” Business Cycles, Indicators, for the term structure of interest rates pro- and Forecasting, James H. Stock and Mark W. Watson, eds., vides a theoretical foundation for the University of Chicago Press, 1993. predictive power of the yield curve. Hamilton, James D. “Analysis of Time Series Subject to Changes in This paper also attempts to address sta- Regime,” Journal of Econometrics (July-August 1990), pp. 39-70. tistical questions about the application of Haubrich, Joseph G., and Ann M. Dombrosky. “Predicting Real Growth probit models to time-series data. The Using the Yield Curve,” Economic Review, Federal Reserve Bank of results for recession dummies indicate the Cleveland (1996 Quarter 1), pp. 26-35.

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Hu, Zuliu, “The Yield Curve and Real Activity,” IMF Staff Papers (December 1993), pp. 622-37. Laurent, Robert. “Testing the Spread,” Economic Perspectives, Federal Reserve Bank of Chicago (July/August 1988), p. 13. Mishkin, Frederic S. “What Does the Term Structure Tell Us About Future Inﬂation?” Journal of Monetary Economics (January 1990), 77-95. Plosser, Charles I., and K. Geert Rouwenhorst. “International Term Structures and Real Economic Growth,” Journal of Monetary Economics, (February 1994), pp.135-55.

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Appendix Construction of the Explanatory Variables If we denote the constant-maturity, 30-year bond rate as TB30, the Commerce Depart- ment’s index of leading indicators as LI, the 6-month commercial paper rate as CP, and the 6-month Treasury bill rate as bill, then the explanatory variables found in the tables are as follows:

Yield curve ln((1 + TB30/100) / (1 + bill/100))

Lead LIt-LIt-1 Money ln(M1/P)t – ln (M1/P)t-1 Stock ln(S&P500t /S&P500t-1) Spread ln((1+ CP/100) / (1 + bill/100))

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