Using econometric modelsto predict recessions

Mark W. Watson

1111 On April 25, 1991, the Busi-

ness Cycle Dating Committeeof the National Bureau ofEconomic Research (NBER)determined that the U.S.

econ¬omy had reached a businesscycle peak in July 1990 and had fallen into arecession. Could this recession have been pre-dicted by econometric models? In this article Idiscuss how econometric models can be used toforecast recessions and provide a partial answerto this question by documenting the forecastingperformance of one model, the NBER's Experi-mental Recession Index.

Econometric models describe statisticalrelationships between economic variables. Byextrapolating these relationships into the future,econometric models can be used for prediction.Carefully constructed econometric forecastscan predict recurring patterns in the economy,but even the best econometric model can notanticipate unique events that have not left astatistical footprint in past data.

Recognizing these strengths and weakness-es, most economists base their forecasts on acombination of econometric analysis and judg-ment (or economic instinct). The relativeweight given to judgment and econometricanalysis depends on how unique the forecastingperiod is expected to be. For example, econo-metric models can be expected to work well forpredicting the response of the economy to mon-etary expansions and contractions, since thestatistical record contains many similar epi-sodes. On the other hand, econometric modelsprobably will perform poorly for predicting

growth in economic activity in Eastern Europeover the next five years, since the statisticalrecord contains few transformations of com-mand to market economies.

Since the focus of this article is on how,and how well, econometric models forecastrecessions, I begin by defining a recession. Astatistical model requires a precise definition,and, as we will see, different definitions lead todifferent econometric approaches. After I de-scribe these econometric methods, I evaluatethe recent forecasting performance of oneeconometric method: the NBER's ExperimentalRecession Index, which I developed jointlywith James Stock of Harvard University. Itturns out that this index did not perform wellover the current recession. Unraveling thereasons for its poor performance says muchabout the causes of the current recession.

What is a recession?

Contrary to popular wisdom, the official(NBER) definition of a recession is not "two ormore quarters of consecutive decline in realGNP." The official definition is far less pre-cise. Indeed, it so imprecise that it is worthproviding in detail. Burns and Mitchell (1946)give the official definition of a recession as one

Mark W. Watson is senior consultant at theFederal Reserve Bank of Chicago, research associ-ate at the National Bureau of Economic Research,and professor of economics at NorthwesternUniversity. Much of the work discussed in thisarticle was carried out in collaboration with JamesH. Stock and was supported by grants from theNational Bureau of Economic Research and theNational Science Foundation. The author thanksSteven Strongin for comments on an earlier draft.

14 NLOWOVRL PN[\PNL]R`N\

phase of a business cycle. A business cycle isdefined as follows:

"Business cycles are a type of fluctuationfound in the aggregate economic activity ofnations that organize their work mainly in busi-ness enterprises: a cycle consists of expansionsoccurring at about the same time in many eco-nomic activities, followed by similarly generalrecessions, contractions, and revivals whichmerge into the expansion phase of the nextcycle; this sequence of changes is recurrent butnot periodic; in duration business cycles varyfrom more than one year to ten or twelve years;they are not divisible into shorter cycles ofsimilar character with amplitude approximatingtheir own."

Using this definition, the NBER BusinessCycle Dating Committee somehow determinedthat the U.S. economy reached a cyclical peakin July 1990. Actually, this is not as difficult asit appears. As lawmakers have claimed aboutobscenity, recessions may be difficult to define,but you know one when you see it.

Figure 1 presents an index of aggregateactivity constructed using four monthly coinci-dent indicators; the index of industrial produc-tion total nonagricultural ewzvyywex¬ manu-facturing and trade sales, and real personalincome. The precise details underlying the

construction of the index are given in the Ap-pendix. The shaded areas in the graph are thepostwar recessions, as determined by theNBER. As is evident from the graph, reces-sions are periods of sustained and significantdeclines in the index.

It is interesting to compare the NBERofficial peak and trough dates to those thatwould be determined using the rule of twoconsecutive quarters of declining GNP. I dothis in Table 1. The two sets of dates are moredifferent than one might imagine. Recessionsare often interrupted temporarily by one quarterof positive GNP growth; this causes the GNPrule to miss the peak or trough. This occurredduring the recessions of 1949, 1973-1975, and1981-1982. Moreover, two of the postwarrecessions determined by the NBER-1960-61and 1980—did not coincide with two quarterlydeclines in GNP. The NBER approach to dat-ing recessions yields more reasonable resultsthan the GNP method because it relies on alarge number of monthly indicators rather thana single quarterly indicator.

The NBER's experimental indicators

There are two distinct econometric meth-ods used for predicting recessions. The first isbased on traditional macroeconometric modelslike the Wharton, DRI, or Michigan models.

FIGURE 1

NBER Experimental Coincident Index

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TABLE 1

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NOTE: The GNP decline periods indicate periods during whichGNP was declining for two or more consecutive quarters.

The second is based on economic indicatorslike those originally developed by Burns andMitchell at the NBER in the 1930s, the Com-merce Department's Composite Index of Lead-ing Indicators, or the NBER experimental indi-cators that Stock and I developed. Traditionalmacroeconometric models were not developedto predict recessions, but they were developedto predict variables like real GNP. These mod-els can be used to construct approximate reces-sion predictions by using their forecasts tocalculate the likelihood of two consecutivedeclines in real GNP. In contrast, the indicators

approach, as implemented in mywork with Stock, predicts recessionsusing the official NBER definition.The remainder of this article willfocus on this approach. Readersinterested in a discussion of tradi-tional econometric models or amore technical description of theindicators approach should read thediscussion in the Box.

At the request of the Secretaryof the Treasury in 1937, a researchteam at the NBER led by Burns andMitchell identified a set of leading,coincident, and lagging indicatorsof economic activity for the U.S.economy. These indicators werechosen to ¬evv policymakers wherethe economy was going, where itwas, and where it had been. In theearly 1B=6}2 the WKN[ ceded re-

sponsibility for the system of economic indica-tors to the Commerce Department. Since then,the Department of Commerce has maintainedthe indicators, periodically updating the set ofvariables to reflect changes in the economy anddata availability. The Department of Com-merce publishes the indicators monthly, and thecomposite index of leading indicators is regu-larly reported in the financial and popular press.

In 1987, James Stock and I started anWKN[ sponsored project to rethink the systemof economic indicators.' We developed three

Nmyxywe¬|sm we¬ryn} py| z|ensm¬sxq |eme}}syx}Predicting recessions using traditionalmacroeconometric models

Traditional macroeconometric models describethe relationship between a set of "endogenous"variables, say Y,, "exogenous" variables, et3"anderrors, s¬ . The endogenous variables are the vari-ables that the model is attempting to explain; in atypical model they include real GNP, investment,the rate of inflation, interest rates, and other vari-ables. The exogenous variables are variables thatthe model takes as given and are important forexplaining changes in the endogenous variables; ina typical model they include government purchases,tax rates, and the monetary base. The error termscapture changes in the endogenous variables notexplained by the exogenous variables. They aremodeled as random.

Symbolically, the model is represented as

(1) Yt = Q/ft483 Yt-2 , Yt-p2 et0 +

which shows the relationship between the endoge-nous variables and their past values, the exogenousvariables, and the errors. Forecasts of the endoge-nous variables w"periods into the future constructedusing information through time t"are denoted asOf"that is, the conditional expectation of Yt+jgiven information available at time t5"This forecastis the best guess of the endogenous variables at timet2w"given information available to the forecaster attime t5"(The forecast is best in the sense that itminimizes the average squared forecast error.)

The forecast, Ot"ft2w"is just one summary of theinformation at time t"relevant for predicting the

16

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future. In principle, the macroeconometric modelcan be used to deduce the entire probability distri-bution of the future data conditional on informationavailable at date t, that is, Ft(Yt+1, Y t+2, Thepoint forecasts are the mean of this distribution, butone could also calculate, for example, the condition-al variance of Yr+j or the 95 percent conditionalconfidence interval for Indeed, given Ft( Y ¬1v,

, r,: ), one could calculate the probability ofany event characterized by future values of r. Inparticular, if a future recession is defined in termsof future rs, then the probability of a future reces-sion, conditional on information at date t, can bededuced. Fair (1991) uses this observation, togetherwith stochastic simulation techniques, to calculaterecession forecasts from his model. This procedureis simple, yet quite general.

Using stochastic simulation to predictrecessions in Fair's model

Fair's model contains 30 stochastic equationsand 98 identities for a total of 128 endogenousvariables; it also includes 82 exogenous variables.Given initial conditions, (r, r , r_ *,), futureexogenous variables, , X„ 2;, and futuredisturbances, (E,,, E , E„ 2), the model can bedynamically solved -forward to yield r *2 . Taking the

the only unvertainty about the

future involves the values of the exogenous vari-ables and the disturbances. Fair assumes that the asare independent and identically normally distributedand that exogenous variables follow simple autore-gressive models with normally distributed shocks.This makes it easy to simulate future values of theerrors and the exogenous variables by drawing froma random number generator. These simulated Xsand as are used to solve the model to yield r_„, r *„,Yr+h. This procedure is repeated many times and

a histogram of the realizations r*A) isan estimate of the conditional probability distribu-tion r„, ,

Fair uses this stochastic simulation method topredict recessions by defining a recession using the"two consecutive declines in real GNP" definition.That is, the economy is in a recession at time t+j, iftime t+j is in a sequence of two or more consecutivedeclines in real GNP. Since real GNP is an endoge-nous variable in Fair's model, this probability canbe calculated from FO7,,, , )7, ; /2 the distri-bution of future values of the endogenous variablesgiven information through time t. Using the simu-lated data, the probability of a recession at time t+jis approximated by the fraction of the simulationsthat were characterized by a recession at time t+j.

For example, to calculate the probability thatthe economy will be in recession in the first quarter

of 1992 using data through the first quarter of 1991,Fair proceeds as follows. First, he generates valuesfor the exogenous variables and disturbances in hismodel for 1990:2 through 1991:2. These values arechosen from a random number generator that mim-ics the variability in the future values of these vari-ables. Next, using these values, he solves for theendogenous variables over 1991:2-1992:2. Thisprocess is repeated many times, and the values ofthe endogenous variables are recorded after eachsimulation. The probability of a recession is calcu-lated as the fraction of the simulations in which thereal GNP growth in the first quarter of 1991 was ina sequence of two consecutive declines; that is, thefraction of simulations in which real GNP declinedin 1990:4 and 1991:1 or in 1991:1 and 1991:2.

The method can be generalized in many ways.First, the definition of the recession event can bechanged; the important thing is that it must be afunction of the future values of Y. Second, in mostcircumstances the parameters of the econometricmodel are not known and are estimated from pastdata. This introduces additional uncertainty into theforecasts, since the forecasts depend on the model'sparameters. This uncertainty can be incorporatedby drawing new model parameters from the appro-priate distribution for each simulation. As should

errors of the model are normally distributed, northat the exogenous variables follow simple autore-gressive processes. All that is required is that therealizations of the errors and the exogenous vari-ables can be simulated. More detailed discussioncan be found in Fair (1991).

The indicators approach to predictingrecessions

Stock and I developed an alternative approachto predicting recessions. Our approach uses theNBER's definition of a recession rather than thedeclining GNP definition and is in the tradition ofthe system of economic indicators developed byBums and Mitchell rather than large scale macro-econometric models. A description of our approachfollows.

Recessions are discrete events: we are either ina recession or we are not. Discrete events can bequantified using 0-1 "indicator" variables. Let R,denote a 0-1 indicator of a recession, so that R = 1if there is a recession at date t and R, = 0 otherwise.Let .7, denote a set of economic indicators that areuseful for predicting future economic activity. Thenthe probability forecast of a recession at date t+j,given information at date t, can be written as

(2) P(Rt+j= ' )

FEDERAL RESERVE BANK OF CHICAGO :D

P is the probability that the economy will bein a recession at date t+j, computed using informa-tion through time t. The statistical question is whatis the best way to parameterize this conditionalprobability, that is, what equation should be used toconvert the information in the indicators into arecession probability.

In research utilizing cross section data, this is awell studied problem. Applied researchers oftenestimate "probit" or "logit" models relating anindicator variable, such as "union membership" or"completed college," to a set of explanatory vari-ables.' While the prediction problem consideredhere is conceptually similar, it differs in two impor-tant ways. First, the data are temporally dependent,which suggests that some degree of temporalsmoothness should be incorporated in the functionalform. Second, since lagged values of the indicatorsmay be useful predictors, the number of explanatoryvariables is potentially very large.

The parameterization that Stock and I useborrows an important simplification from modelsdesigned to explain cross sectional data. Using thenotation above, and abstracting from lags, the crosssection model would parameterize the probability inEquation (2) as Pt+ j/t =p(z't B), where f(.) is a functionthat converts the "index" :13 into a probability, thatis, a number between 0 and 1. The single index, :13,summarizes all the relevant information in theexplanatory variables. Figure 1 suggests that theXCI might be a useful dynamic index, in the sensethat it adequately summarizes the relevant informa-tion in the explanatory variables for predictingrecessions. The problem is to convert this indexinto a recession forecast.

To see how this is accomplished, it is useful toproceed in three steps. In the first step, a probabili-ty model relating the XCI to observable variables isdeveloped. This serves to define the XCI. Next, aforecasting model for future values of the XCI isdeveloped. Finally, a model relating recessions tothe XCI is specified.

As mentioned above, the XCI is an index offour monthly indicators of aggregate activity: theindex of industrial production; aggregate employ-ment; personal income; and trade sales. Precisedefinitions are given in Table 2. The XCI is anindex of the common movement in these series. Itis calculated from a dynamic factor analysis modelusing statistical methods originally developed forsignal extraction. Thus, the XCI represents thecommon "business cycle signal" contained in thefour coincident indicators. The precise mathemati-

cal formulation of the XCI model is given in theAppendix, where the common business cycle signalis denoted by c 2 . The XCI, plotted in Figure 1, isnothing more than an optimal estimate of c 2 , con-structed from current and lagged values of thecoincident indicators. Thus, the first problemrelating the XCI to observed variables is solved.

To solve the next problem forecasting futurevalues of the XCI leading indicators are added tothe model. Prediction is carried out using a vectorautoregressive model or VAR, a common model formultivariate time series; the details are shown in theAppendix. The XLI is the "best guess" of growth inXCI over the next six months. Using the notationintroduced above, the XLI is Et (c t+6 -ct).

Recall that, using a standard macroeconometricmodel, we could go beyond "best guess" forecastsand obtain the entire probability distribution offuture values of the endogenous variables. Thesame is true here: the model can be used to deducethe entire distribution of past, current and futurevalues of c conditional on the observed indicators.For the purposes of predicting recessions this isimportant because the probability distribution offuture ct s summarizes all of the information in themodel about future recessions.

Our formulation allows us to break up theconstruction of P into two pieces. First, weconstruct the probability distribution of the cts giventhe observed leading and coincident indicators, asdescribed above. Next we relate the (ct s to the prob-ability of a recession. Figure 1 suggests that this iseasy to do; your eye can naturally pick out reces-sionary patterns from a graph of Recessions arethe periods of sustained and significant declines inthe index. The specification of the probability ofrecession given the ct s that Stock and R use capturesthis simple notion. Unfortunately, carefully speci-fying a pattern recognition algorithm that mimicswhat your eye does naturally requires the introduc-tion of much notation and many additional equa-tions. This will not be done here, but the interestedreader can see this detailed in Stock and Watson(1991b). It is sufficient to say that the specificationassigns a high probability of a recession to periodsof time in which c, undergoes a sustained sequenceof declines.

Oyy¬xy¬e'These models are discussed in any good econometricstextbook. A detailed discussion can be found in Maddala(1983).

:E UCO .FIRSPECT RW U\

indexes designed to track and forecast the mac-roeconomy. The first is the NBER Experimen-tal Coincident Index (the XCI). This is theseries plotted in Figure 1; we saw that expan-sions and contractions in the series coincidedwith NBER business cycle reference dates.The second index is the NBER ExperimentalLeading Index (the XLI), which forecasts thegrowth in the XCI over the next six months.The final index is the NBER ExperimentalRecession Index (the XRI), which shows theprobability that the economy will be in reces-sion six months hence. The framework used tocompute the XCI, XLI, and XRI is described inthe Box, and a more technical description isoffered in the Appendix.

The variables that are used to construct theXCI, XLI, and XRI are listed in Table 2. Thecoincident indicators are fairly standard; withone exception (total employee hours), they arethe same variables used in the Department ofCommerce's index of coincident indicators.Some of the leading indicators are standard(housing authorizations and manufacturers'unfilled orders); while others are not. For ex-

ample, we use two interest rate spreads (a yieldcurve spread and a commercial paper/Treasurybill spread). The set of leading indicators waschosen from a systematic investigation of over250 candidate series, which is documented inStock and Watson (1989).

The XRI focuses on six month ahead pre-diction, but the statistical framework allows usto calculate recession probabilities over anyhorizon. Figures 2-4 show the recession proba-bilities computed for three different forecastinghorizons from January 1962 through April 1991computed from the model. Figure 2 shows thecoincident recession indicator: the probabilitythat the economy is in recession at time t con-structed from data available at time t. Figure 3shows the three month ahead recession indica-tor: the probability that the economy will be ina recession at time t+3 given information avail-able at time t. Finally, Figure 4 shows the sixmonth ahead recession predictor; this predictoris the NBER's Experimental Recession Index(XRI). The series are plotted so that date tcorresponds to when the forecast was made.For example, the six month ahead predictor

TABLE 2Coincident and leading indicators

Coincident indicators

1. Industrial production.

2. Personal income, total, less transfer payments, 1982$.

3. Manufacturing and trade sales, total 1982$.

4. Total employee hours in nonagricultural establishments.

Leading indicators

1. Housing authorizations (building permits): new private housing.

2. Manufacturers' unfilled orders: durable goods industries, 1982$ (smoothed).

3. Trade-weighted index of nominal exchange rates between the U.S. and theU.K., West Germany, France, Italy, and Japan (smoothed).

4. Number of people working part-time in nonagricultural industries because ofslack work (smoothed).

5. The yield on a constant maturity portfolio of 10 year U.S. Treasury bonds(smoothed).

6. The spread (difference) between the interest rate on 6 month commercialpaper and the interest rate on 6 month U.S. Treasury bills.

7. The spread (difference) between the yield on a constant maturity portfolio of10 year U.S. Treasury bonds and the yield on 1 year U.S. Treasury bonds.

FEDERAL RESERVE RANK OF CHICAGO :F

FIGURE 2

Contemporaneous recession probability

probability1.0 —

0.8

0.6

0.4

0.2

0 .0 _ I I Ii it I LI 1 La 58 - 7. T

1962 '64 '66 '68 '70 '72 '74 76 '78 '80 82 '84 '86 '88 '90

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FIGURE 3

Three month ahead recession probabilityprobability1 .0 —

0.8

0.6

0.4

0.2

A. I 0.0 1962 '64 '66 '68 '70 '72 '74 '76 '78 '80 '82 '84 '86 '88 '90

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should tend to increase six months before theonset of each recession and decrease six monthsbefore the recession ends.

Looking first at Figure 2, the coincidentrecession indicator seems quite reliable. Themajor exceptions are the growth recession of1967 and the beginning of the current recession.Keep in mind that coincident "prediction" ismore difficult than it would appear; it was notuntil the end of April 1991 that the NBERdetermined that the economy hadpeaked in July 1990. Taken togeth-er, the Figures show that the abilityto forecast a recession declines asthe forecast horizon increases; thecoincident recession predictor ismore accurate than the three monthahead predictor, which in turn ismore accurate than the six monthahead predictor. But, at least forthe 1970, 1973-1975, 1980, and1981-1982 recessions, predictionsas far as six months ahead werereasonably accurate. The forecast-ing performance of the model forthe current recession, particularly atthe six month ahead horizon, wassignificantly worse than for theprevious recessions.

There are several possiblereasons for the failure of the model;

each is carefully analyzed in Stockand Watson (1991b). In the nextsection I will mention them all anddiscuss the most interesting in de-tail. First, here is some back-ground.

The NBER experimental lead-ing indicator model was constructedusing historical data from January1959 through September 1988. Allresults after September 1988 areout-of-sample. Figure 1 shows thatthe XCI continued to be an accuratecoincident indicator in the out-of-sample period: the XCI peaked inJuly 1990, precisely the peak cho-sen by the NBER's Business CycleDating Committee, and fell nearly 4percent from July 1990 throughApril 1991. Figures 5 and 6 showthe forecasting performance of theleading indicators over the out-of-

sample period. These Figures show how wellthe indicators predicted growth in the XCI threeand six months ahead. The forecasts trackedthe actual data reasonably well until the middleof 1990. The indicators correctly predicted theslowdown that occurred in 1989 and the subse-quent rebound in early 1990. But, as data fromthe fall of 1990 became available, it was clearthat the model was off track.

20 ECOYOYTT( T"TY"A5

FIGURE 4

Six month ahead recession probability

probability1.0 —

0.8

0.6

0.4

0.2

0.0

1962 '64 '66 '68 70 '72 '74 76 '78 '80 '82 '84 '86 '88 '90

NOTE: Shaded areas are recessions as determined by theNBER Business Cycle Dating Committee.

FIGURE 5

Three month predictions of XCIpercent (annual rate)

7

What went wrong?

Four possible reasons are analyzed in Stockand Watson (1991b). First, the statistical modelmay have been poorly determined, in the sensethat the parameters were poorly estimated andthe model "overfit." That is, the model mayhave been fit to match patterns in the historicaldata that did not persist into the future. Sec-ond, the model may have been correct, but thedata subject to large revisions. Third, the XCImay have become an unreliable coincidentindicator. Finally, the set of lead-ing indicators used in the modelmay have behaved differently thanin past recessions. In Stock andWatson (1991b), we present a vari-ety of evidence suggesting that thefirst three possible reasons were notimportant. However, the finalreason—the unusual behavior ofsome of the indicators, relative totheir behavior in past recessionswas important. Three of the sevenleading variables were primarilyresponsible for the index's opti-mism as the recession began: thespread between the yield on com-mercial paper and Treasury bills;the spread between the yield on 10year government bonds and 1 yeargovernment bonds; and the ex-change rate. The difference be-

tween the historical behavior ofthese variables and their behavior inthe current recession is the key tounderstanding why the index failedand why the current recession isunique in the postwar historicalrecord.

Table 3 documents the behav-ior of the interest rate spreads priorto the 1960 and subsequent reces-sions. During the 1959-1990 peri-od, the spread between commercialpaper and Treasury bills averaged57 basis points and increased sharp-ly prior to each of the 1960-1981cyclical peaks. In contrast, cominginto the current recession, thespread was essentially flat, averag-ing only 41 basis points during thefirst eight months of 1990.

The slope of the Treasury yieldcurve, measured as the yield spread

between 10 year and 1 year government bonds,also behaved differently than in past recessions.Over the 1959-1990 period, the yield curveusually sloped upwards; the average yield curvespread was 54 basis points. But, before eachrecession in the sample, the yield curve invert-ed and this spread became negative. FromJanuary 1990 to July 1990 the yield curvespread remains essentially constant, averaging+38 basis points. This was a slightly negativereading by this indicator, but nowhere near

FEDERAL RESERVE BANK OF CHICAGO

21

FIGURE 6

Six month predictions of XCI

Forecast

Actual

1 1 1 1 1 1 1 1 R 1

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significant enough to suggest a recession. Justas important, in August and September of 1990,the yield curve steepened significantly; thespread increased to 97 basis points in Augustand to 113 basis points in September. Typical-ly, such a steepening of the yield curve is asso-ciated with an increase in economic activity.

As the recession began, exchange rates alsoserved as a positive indicator. In general, as thedollar weakens, U.S. goods fall in price relativeto foreign goods, so that, controlling for theother indicators in the model, a depreciation inthe dollar is a positive indicator. While thevalue of the dollar was essentially flat duringthe first seven months of 1990, it fell by 11percent from July to November, suggesting anincrease in future demand for domesticallyproduced goods.

While the financial indicators behavedperversely during 1990, the real indicators usedin the model behaved qualitatively as they hadin earlier recessions. Building permits wereweak. The number of workers involuntarilymoving from full-time to part-time work in-creased. Manufacturers' unfilled ordersslowed. While these indicators provided nega-tive signals, these signals were not large enoughto forecast the recession.

Could the recession have beenpredicted?

The answer to this question is clearly yes:some analysts did accurately predict the reces-

sion. (An interesting question ishow many of these forecasters alsopredicted recessions in 1987 and1989.) Standard econometric mod-els and the consensus businessforecaster did not. For example, inMay 1990 only 19 percent of theforecasters surveyed by the BlueChip Economic Indicators expectedthe recession to begin in 1990. Inmid-1990 the consensus forecastcalled for 2.3 percent growth in realGNP over the 1990-1991 period.Variables that are typically used topredict economic activity did notpoint to a recession. This raises thequestion of what variables couldhave been used to help forecast thisrecession.

It is always easy in hindsight tofind a single variable that would

have predicted a specific event. To be usefulfor forecasting, a variable must not only havepredicted this recession, but also predict futurerecessions. Statistical procedures search forsuch variables by asking whether they haveconsistently predicted past recessions. In Stockand Watson (1991 b), a careful statistical searchfor such variables is documented. We foundthat the most important variables omitted fromour original model appear to be stock prices,help-wanted advertising, average weekly hoursin manufacturing employment, and consumersentiment. Interestingly, if the variables areadded to our original list of indicators and themodel is re-estimated, only marginal improve-ments are realized. The interest rate spreadspredict the previous recessions so well that theyget much of the weight in the statistical fit; thenew variables receive little weight. The newvariables lead to improved prediction only ifthe spreads are dropped from the model; in thiscase the new variables receive enough weightto be useful in the most recent recession. Whilethis modified model performs better during thecurrent recession, the original model performsbetter during previous recessions. The chal-lenge is to construct a new model, including theentire list of indicators, and perhaps more, thatwill perform well during the next recession.

22 1C1C11 f 111111. v-1.111.■■1.1D1C11■1D-2

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Behavior of interest rate spreads prior to recessions

A. Commercial paper—Treasury bill spread (basis points)

Lymvsmkv peak Months prior to cyclical peak

9 6 3 0

4/60 -7 3 88 10712/69 120 114 84 13311/73 62 106 160 1011/80 65 140 96 1477/81 185 78 113 1017/90 51 38 43 51

B. 10 year Treasury bond-1 year Treasury bond spread(basis points)

Cyclical peak Months prior to cyclical peak

9 6 3 0

4/60 -32 -45 23 7912/69 -10 -85 -75 -3511/73 -18 -126 -61 -431/80 -66 -151 -159 -3077/81 -204 -59 -139 -1207/90 12 24 38 113

What does this tell us aboutthe current recession?

These results suggest tentativeconclusions about the nature of thecurrent downturn. First and fore-most is that it differs from the re-cessions of the 1960s, 1970s, and1980s. This difference has beendocumented by other researchers,notably Strongin (1990) and Stron-gin and Eugeni (1991). In thepresent context, the most obvioussymptom of this difference is theunusual behavior of the interest ratespreads relative to their behavior inpast recessions. To understandwhat this difference suggests aboutthe nature of this recession, it isimportant to understand why theinterest rate spreads have tradition-ally been reliable indicators. Thisquestion has motivated much recentresearch [see Cook and Lawler(1983), Friedman and Kuttner(1990 and 1991b), Bernanke(1990), and Kashyap, Stein, and Wilcox(1991)1, and a variety of explanations havebeen offered. The most reasonable seems to goas follows.

It is widely (although not universally)accepted that a tightening of monetary policyleads, in the short run, to a slowdown in aggre-gate economic activity.' A tightening of mone-tary policy is accompanied by a rise in shortterm interest rates and a tightening in banklending. The increase in short term interestrates relative to long term rates leads to aninverted yield curve. The tightening in banklending leads some firms to raise capital byissuing new commercial paper. This increasesthe stock of commercial paper, which raises thecommercial paper rate relative to the rate onTreasury bills.

This explanation suggests that monetarypolicy, important for the recessions of the1960s, 1970s, and 1980s, was less importantduring the current recession.

An alternative explanation is that monetarypolicy played a major role in the current reces-sion but that structural changes in financialmarkets changed the relation between monetarypolicy and the interest rate spreads. This expla-nation is not convincing: the commercial paper/Treasury bill spread did widen significantly

before this recession, and the yield curve didinvert. But this occurred in early 1989 whenworries of inflation led the Fed to tightenpolicy. By the middle of 1990 the interest ratespreads had returned to normal levels, consis-tent with a more neutral monetary policy.

In the introduction, I noted that economet-ric methods are well suited for prediction overforecast periods with characteristics similar tothose found in the sample. Many characteris-tics of the current recession are unique; themost obvious is the sudden outbreak of hostili-ties in the Middle East and coincident increasein uncertainty and fall in consumer sentiment.These could not have been predicted by anyreasonable model. Thus, one can argue thatthis was a recession that should not have beenpredicted by an econometric model and thatXRI passed this specification test. While thereare elements of both truth and "cop out" here,I am not too concerned by the XRI's failure topredict the recession. What is of more con-cern is the XRI's failure to reflect the in-creased pessimism in the fall of 1990, bywhich time it was clear that the model was offtrack. Future research will focus on makingthe model more adaptive to changing circum-stances.

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JPPNWMRb

The probability model underlying the XCIis a dynamic factor model of the form:

(1) Ax, =13 + y(L)AcT +

(2)D(L)ut = s t,

(3) ep(L)Ac 8 +

where xt is a 4 x 1 vector of coincident indica-tors, c, is the scalar unobserved "state of thebusiness cycle," u, and e, are unobservedshocks, and y(L), D(L), and (1)(L) are polynomi-als in the lag operator L; so, for example,y(L)Act, represents a distributed lag of Act-i, with

weights y,. The coincident indicators in x, in-clude industrial production, real personal in-come, total employment (hours), and manufac-turing and trade sales. They are precisely de-fined in Table 2. It is assumed that the matrixpolynomial D(L) is diagonal, so that D(L) =diag[dii(L)], and and II, are mutually

uncorrelated Gaussian white noises. Theseassumptions imply that ct explains all of the co-movement between the indicators, but that eachindicator may move independently from theother because of innovations in its "uniqueness"ujt. Thus, ct is a natural index of co-movement

or covariation in the coincident variables andprovides an index of aggregate cyclical activity.For three of the variables, y(L) = y, and thisfixes the timing of c t : movements in c, are coin-cident with industrial production, personalincome, and manufacturing and trade sales.Since employment is slightly lagging, laggedvalues of ct enter its equation. The XCI, plottedin Figure I, is the minimum mean square errorestimate of ct, constructed from current andlagged values of xt.

Leading indicators are added to the modelto help predict future values of ct. The com-plete model, including leading indicators, is (1)and (2) together with the vector autoregression:

(4) Ac t = t + + (L)yt-1 + Vct

(5) Ay, ,= X,,,(L)Ac + (L)yt-1 +

where y, is a vector of leading indicators and1);=(1),, u',)' is NIID(0,k) and independent of

The definition of the leading indicators used inour analysis is given in Table 2; Stock andWatson (1989) provides a detailed discussion ofthe selection of variables, the estimated modeland diagnostic tests.

Equations (1)-(2) and (4)-(5) provide acomplete probability model for the index ct andits relation to the coincident and leading indica-tors. Forecasts of ct can be constructed in astraightforward way. The NBER's experimen-tal index of leading indicators (XLI) are theforecasts of ct over the next six months, that is,

The model can be used to construct theprobability distribution of past, current, andfuture values of the index, conditional on theobserved data, that is, F,(..., ct-1, 8, ).Given the assumptions made about the distur-bances in Equations (1)-(2) and (4)-(5), thisconditional distribution is multivariate normalwith a mean and covariance matrix that is easi-ly calculated using standard prediction formu-lae. The recession prediction problem is sim-plified by the following assumption whichcaptures the single index notion in this context:

(6)P[Rt2w = lI{c3 }:, z,, =P[Rt+j=1|{(c,}], for all t and j.

Thus, z, provides no information about a reces-sion at time t+j that is not included in {cd.Interpreting z, as the leading and coincidentindicators in the model implies:

(7) P(R,t = 11z,, z ii ,...) =J P[R = 11{cd:] dF

so that the probability of a recession at time t+j,given information through time t, can be calcu-lated in two steps. In the first step, the proba-bility of a recession at date t is calculated, giv-en the entire history of the index fct}, that is,P[R,+i = II{ c. r }:] is formed. In the next step,these probabilities are averaged using the prob-ability distribution of the index lc condi-tioned on the observed data, that is, the integra-tion is performed. This simplification is uti-lized to calculate P T+61„ which is the NBER'sExperimental Recession Index or XRI.

;A 11\ 411111 1.6:11:,P1,:1.1111r,

OOO]WO]N\

'This is an ongoing project, and our progress to date is 'The most thorough documentation of the relation between

summarized in three papers: Stock and Watson (1989), aggregate activity and the supply of money is Friedman and(1991a), and (1991M. Schwartz (1963).

[NON[NWLN\

Bernanke, Ben S., "On the predictive power ofinterest rates and interest rate spreads," NewEngland Economic Review, November/Decem-ber 1990, pp. 51-68.

Burns, Arthur, and Wesley C. Mitchell, Mea-suring Business Cycles, National Bureau ofEconomic Research, New York, 1946.

Cook, Timothy Q., and Thomas A. Lawler,"The behavior of the spread between Treasurybills and private money market rates since1978," Federal Reserve Bank of Richmond,Economic Review 69, November/December1983, pp. 3-15.

Fair, Ray, "Estimating event probabilities frommacroeconometric models using stochasticsimulation," Manuscript, Yale University,1991.

Friedman, Benjamin M., and Kenneth N.Kuttner, "Money, income, prices and interestrates after the 1980s," Federal Reserve Bank ofChicago Working Paper, No. 90-11, 1990.

, "Why is the paper-billspread such a good predictor of real economicactivity," Manuscript, Harvard University,1991 a.

, "Money, income,prices and interest rates," American EconomicReview, forthcoming, 1991b.

Friedman, Milton, and Anna J. Schwartz, AMonetary History of the United States, 1867-

1960, Princeton University Press, 1963.

Kashyap, Anil, Jermey C. Stein, and DavidWilcox, "Monetary policy and credit condi-tions: Evidence for the composition of externalfinance," Manuscript, Federal Reserve Board,1991.

Maddala, G.S., Limited-Dependent and Quali-tative Variables in Econometrics, CambridgeUniversity Press, Cambridge, UK, 1983.

Stock, James H., and Mark W. Watson,"New indexes of coincident and leading eco-nomic indictors," NBER Macroeconomics An-nual 1989, 1989, pp. 351-394.

, "A probability modelof the coincident indicators," in Leading Eco-nomic Indicators, edited by K. Lahiri and G.Moore, Cambridge University Press, Cam-bridge, UK, 1991a.

, "Predicting reces-sions," Manuscript, Northwestern University,1991 b.

Strongin, Steven, "Smoothing out the businesscycle," Chicago Fed Letter, March 1990.

Strongin, Steven, and Francesca Eugeni,"The cost of uncertainty," Chicago Fed Letter,March 1991.

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