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r:;; Business t Review Federal Reserve Bank of Philadelphia May •June 1996 ISSN 0007-7011 Looking Ahead: Leading Indexes for Pennsylvania and New Jersey Theodore M . Crone & Kevin J. Bahyak Inflation Forecasts H ow Good Are They? Dean Cronshore Business Review The BUSINESS REVIEW is published by the Department of Research six times a year. It is edited by Sarah Burke. Artwork is designed and produced by Dianne Hallowell under the direction of Ronald B. Williams. The views expressed here are not necessarily those of this Reserve Bank or of the Federal Reserve System. SUBSCRIPTIONS. Single-copy subscriptions fo r individuals are available without charge. Insti tutional subscribers may order up to 5 copies. BACK ISSUES. Back issues are available free o f charge, but quantities are limited: educators may order up to 50 copies by submitting requests on institutional letterhead; other orders are limited to I copy per request. Microform copies are available fo r purchase from University Microfilms, 300 N. Zeeb Road, Ann Arbor, MI 48106. REPRODUCTION. Perm ission must be obtained to reprint portions o f articles or whole articles. Permission to photocopy is unrestricted. Please send subscription orders, back orders, changes o f address, and requests to reprint to Publications, Federal Reserve Bank o f Philadelphia, Department o f R esearch and Statistics, Ten Independence Mall, Philadelphia, PA 19106-1574, or telephone (215) 574-6428. Please direct editorial communications to the same address, or telephone (215) 574-3805. MAY/JUNE 1996 LOOKING AHEAD: LEADING INDEXES FOR PENNSYLVANIA AND NEW JERSEY Theodore M. Crone and Kevin Babyak Many policymakers and business persons are interested not only in the course of the national economy but also in the prospects for their region’s economy. Since 1994, the Philadelphia Fed has published monthly indexes of coincident indicators for the states in the Third Federal Reserve District. A natural complement would be a set of leading indexes. In this article, Ted Crone and Kevin Babyak introduce lead ing indexes for the two largest states in the District— Pennsylvania and New Jersey. INFLATION FORECASTS: HOW GOOD ARE THEY? Dean Croushore Forecasts of inflation affect decision-mak ing in many segments of the economy. But in the early 1980s, economists found that forecasts in surveys taken over the past 20 years systematically underpredicted infla tion. As a result, many economists stopped paying attention to forecasts. However, they may have abandoned them too quickly. In this article, Dean Croushore takes a closer look at survey forecasts and, after considering some relevant factors, concludes that inflation forecasts may not be as bad as you think. FEDERAL RESERVE BANK OF PHILADELPHIA Looking Ahead: Leading Indexes For Pennsylvania and New Jersey Theodore M . Crone* and Kevin J. Babyak* larly look for any sign of a change in the direc tion of the overall economy. Prudent budget directors will reduce their revenue projections when they see indications of a slowdown in the *Ted Crone is vice president in charge of the Regional Eco nomics section of the Philadelphia Fed's Research Depart ment. At the time this article was being prepared, Kevin Babyak was a research support analyst at the Federal Re serve Bank of Philadelphia. He is currently an assistant con troller for the City of Philadelphia. The authors thank Tom Stark for invaluable assistance in developing the models to estimate the leading indexes. economy. Likewise, prudent business manag ers will take steps to curtail their inventories. In these attempts to anticipate general business conditions, people look for signals about the economy. One signal of the future course of the na tional economy is the traditional composite in dex of leading indicators, now published by the Conference Board but maintained for many years by the U.S. Department of Commerce. Recently, the National Bureau of Economic Re search (NBER) began publishing an alternative leading index, developed as part of its project on cyclical indicators. Both these indexes are 3 BUSIN ESS REVIEW meant to foreshadow the direction of the na tional economy six to nine months ahead.1 Many policymakers and business persons, however, are interested not only in the course of the national economy but also in the course of their region's economy. Since 1994 the Fed eral Reserve Bank of Philadelphia has pub lished monthly indexes of coincident indicators for the three states in the Third Federal Reserve District (see the 1994 article by Crone). These indexes reveal that state recessions do not nec essarily coincide with national recessions. Therefore, a natural complement to the coinci dent indexes would be a set of leading indexes for the states. This article introduces leading indexes for the two largest states in the Dis trict—Pennsylvania and New Jersey—based on the methodology of the NBER's new alterna tive index for the nation. They are the first state indexes to be developed using this methodol ogy.1 2 LEADING INDEXES OF THE NATIONAL ECONOMY The origins of the current leading indexes for the nation go back to the late 1930s when Wesley Mitchell and Arthur Burns drew up a list of 71 statistical series that they considered to be reliable indicators of economic recover ies. The list was later extended to include lead ing indicators of recessions. Lists of coincident and lagging indicators were developed as well. These lists were periodically revised, and over time, the individual indicators were combined to construct composite indexes intended to 1The index of leading indicators formerly maintained by the Department of Commerce has been published by the Conference Board since late 1995. We will refer to it as the traditional leading index. 2In the late 1970s and early 1980s, the Federal Reserve Bank of Philadelphia published a leading index for the Philadelphia region using the Commerce Department's methodology (see Anthony Rufolo's article). 4 MAY/JUNE 1996 summarize the information in the individual indicators and give an overall assessment of the economy. Both the identification of individual indicators and the development of composite indexes have been part of a broader effort to explain business cycles, which Burns and Mitchell described as "a type of fluctuation found in the aggregate economic activity of nations that organize their work mainly in busi ness enterprises: a cycle consists of expansions occurring at about the same time in many eco nomic activities, followed by similarly general recessions, contractions, and revivals which merge into the expansion phase of the next cycle— ; in duration business cycles vary from more than one year to ten or twelve years; they are not divisible into shorter cycles . . . [that exhibit swings in economic activity of similar] amplitudes." From a List of Indicators to a Composite In dex. The early development of composite in dexes was based on the notion that there is a set of indicators that reflects the current state of the economy, a set that reflects the future state of the economy, and a set that reflects past eco nomic activity. Once researchers identified and categorized individual cyclical indicators as coincident, leading, or lagging, the next step was to combine at least some of those indica tors into single composite indexes. Since busi ness cycles are defined as broad-based contrac tions and expansions, combinations of indica tors or composite indexes are generally better at tracking the cycles than any single indicator (see the article by Geoffrey Moore). But which indicators should be included in each compos ite index? And should they all be given the same weight in forming the composite index?3 3To help answer these questions Geoffrey Moore and Julius Shiskin developed an explicit scoring system to gauge the value of the individual series as indicators of the busi ness cycle. They considered such factors as how large a portion of the economy is reflected in the series, how much FEDERAL RESERVE BANK OF PHILADELPHIA Looking Ahead: Leading Indexes for Pennsylvania and New Jersey The components of the traditional compos ite index of leading indicators and the weights assigned to them have changed over the years. Currently, the index is constructed from 11 com ponents (Table 1). As in the case of the coinci dent and lagging indexes, changes in the lead ing index are calculated as a weighted average of the monthly changes in each of the compo nents. The current weights for the monthly changes in the components of the index are pri marily designed to keep the more volatile se ries from dominating month-to-month move ments in the index.4 the series fluctuates with the cycle, how large and how fre quent revisions to the series are, and how promptly the data for the series are available. Moore and Shiskin used their scores not only to draw up short and long lists of indicators but also to weight the indicators in constructing composite indexes. Theodore M. Crone and Kevin J. Babyak How well does this leading index lead? A lead ing index can be evaluated either by how well it predicts turning points in the business cycle or by how well it predicts actual changes in some economic indicator at all points in the cycle (see Gary Gorton's article). The most fre quent use of the traditional leading index, how ever, has been to predict turning points in the business cycle, especially economic downturns or recessions. Several different rules of thumb have been applied to the leading index to determine whether it is signaling a recession. As Gorton points out, these rules of thumb are inherently arbitrary, but the most common rule is that three successive declines in the index forecast a re TABLE 1 Components of the Traditional Leading Index 4A standardized change is calculated for each component by dividing this month's change in the series by the average size of monthly changes over a his torical period. For example, be tween 1978 and 1989 the aver age absolute percentage change in hours worked by production workers in manufacturing was 0.42. If the actual change in the most recent month was only 0.21, or one-half the historical average, the stand ard ized change w ould be 0.5. The monthly change in the compos ite index is a weighted average of these "stan d ard ized changes" in the components. The weight is adjusted so that a 1 percent change (or one unit change) in each of the compo nents results in a 1 percent change in the composite index. The current formulas for calcu lating the index can be found in the article by George Green and Barry Beckman. • Average weekly hours of production workers in manufacturing • Average weekly initial claims for unemployment insurance • Manufacturers new orders in constant dollars for consumer goods and materials industries • Index of vendor performance • Contracts and orders for plant and equipment in constant dollars • Index of new private housing units authorized by local building permits • Manufacturers unfilled orders for durable goods in constant dol lars • Sensitive materials prices • Index of stock prices, S&P 500 common stocks • Money supply (M2) in constant dollars • Index of consumer expectations compiled by the University of Michi gan Research Center 5 BUSINESS REVIEW cession within the next nine months. By this rule the traditional index has successfully pre dicted eight of the nine U.S. recessions since 1948, with leads of two to eight months.5 But it has also given seven false signals. Once the economy is in a recession, the traditional lead ing index has generally been slow to signal a recovery using the popular three-month rule. Only three times in the last nine recessions has the index recorded three successive increases before the official beginning of the recovery.6 The record of the traditional leading index has not been perfect, but it has been helpful in predicting recessions. Questions are frequently raised, however, about how the index is con structed. A major issue is how the weights for the components are determined (see Vance M artin's article). While the current weights adjust for the volatility of the various compo nents, they do not reflect differences in how broadly the indicators represent the economy or of how consistent they have been in leading recessions or recoveries. Also, as their names suggest, the index of leading indicators ought to lead the index of coincident indicators. And although the same methodology is used to con struct the traditional coincident and leading indexes, no statistical technique is employed to ensure that the leading index actually "leads" the coincident index (see the article by Green and Beckman). A Forecasting Approach to a Leading In dex. In the late 1980s under the auspices of the NBER, James Stock and Mark Watson devel oped an alternative leading index that attempts to respond to some of the questions raised about 5The failure was for the 1990-91 recession. Three de clines in the leading index did occur between May and July 1989, one year before the onset of the 1990-91 recession. But we do not consider this to be a true recession signal, since the index later recorded three successive increases before the recession actually began. 6In four other cases the leading index registered its sec ond successive increase in the month the recession ended. MAY/JUNE 1996 the traditional index (see the 1994 article by Crone). In essence, their leading index is a sta tistical forecast of future economic conditions. The weights assigned to the various compo nents of the index are not set arbitrarily but are determined by how well each component helps predict future conditions. As a first step in their effort to develop alter native measures of the business cycle, Stock and Watson developed a new index o f coincident in dicators for the economy. With one slight modi fication this index includes the same series as the traditional one. The major difference be tween the two lies in the method by which they are constructed. Rather than use some average of the monthly changes in the individual coin cident indicators, Stock and Watson use a mod ern time-series technique known as dynamic factor analysis to estimate what they term the "unobserved state of the economy." This esti mated "state of the economy" is their alterna tive coincident index, and the implicit weights for the individual components are determined in the process of estimating their model. In prac tice, the historical pattern of Stock and Watson's new coincident index differs little from the pat tern of the traditional coincident index. Both tend to reach their peaks and troughs at or very near the NBER Dating Committee's official peaks and troughs of U.S. business cycles. But Stock and Watson's coincident index provides the basis for their leading index. Stock and Watson's new leading index differs from its traditional counterpart in more ways than their coincident index does. First, the list of individual indicators Stock and Watson use to construct their leading index varies substan tially from the traditional list (Table 2). Their leading index is constructed from their coinci dent index and seven other indicators, only two of which appear in the list of 11 leading indica tors used to construct the traditional index. More important than the differences in the lists of individual leading indicators is the dif ference in Stock and Watson's methodology. FEDERAL RESERVE BANK OF PHILADELPHIA Looking Ahead: Leading Indexes for Pennsylvania and New jersey Theodore M. Crone and Kevin /. Babyak effect of each indicator on the composite leading in Variables Used to Construct dex is statistically deter mined in the process of Stock and Watson's Leading Index estimating the forecast. How well does this new • Stock and Watson's Coincident Index index forecast recessions? Stock and Watson's lead • Index of new private housing units authorized by local building permits* ing index is available only from 1960. The U.S. • Manufacturers unfilled orders for durable goods in constant dol economy experienced a lars* recession that year and has suffered five others • Part-time work in nonagricultural industries because of lack of full since then. How well did time work this new index signal the • Trade weighted nominal exchange rate between the U.S. dollar and past five recessions? the currencies of the U.K., West Germany, France, Italy, and Japan Since Stock and Watson's leading index is a fore • Yield on 10-year Treasury bonds casted change in eco nomic activity, a negative • Spread between the yields on 10-year Treasury bonds and one-year value of their index is Treasury notes. analogous to a decline in • Spread between the interest rates on six-month commercial paper the traditional index. If and six-month Treasury bills we apply the rule of three consecutive negatives to Stock and Watson's lead *Also in the list of indicators for the traditional leading index. ing index, it forecasts four of the five U.S. reces Rather than constructing a leading index from sions since the end of 1960 with leads of two to some average change in the individual indica six months. Like the traditional index, Stock and tors, Stock and Watson tie their leading index Watson's would not have forecast the 1990-91 more closely to their coincident index. If the recession using the rule of three consecutive coincident index truly reflects the state of the negatives.7 But the Stock and Watson leading economy, a good forecast of the change in the index would have resulted in only one false coincident index should make a good leading recession signal since 1960 while the traditional index. Therefore, Stock and Watson use past changes in their coincident index as well as a 7Stock and Watson do not consider any absolute num number of other variables that have historically ber of negatives in their leading index as a recession signal. led the business cycle to forecast the change in Rather, they estimate a separate probability of being in re the coincident index over the next six months. cession in six months based on the components of their co This forecasted six-month change in the coin incident and leading indexes. But their recession probabil cident index becomes their leading index. To ity index also failed to forecast the 1990-91 recession. The estimated probability of recession did not exceed 10 per produce the forecast they use a common timecent in the nine months prior to that recession. In the nine series technique called vector autoregression, months prior to each of the four previous recessions, the or VAR (see The Basics o f VAR Forecasts). The estimated probability reached 77 percent or higher. TABLE 2 7 BUSIN ESS REVIEW MAY/JUNE 1996 The Basics of VAR Forecasts Vector autoregression (VAR) forecasts are based on the notion that in properly chosen sets (vec tors) of economic variables there are fundamental patterns among the variables (see the 1992 article by Crone). These fundamental patterns can sometimes be obscured by occasional deviations, and the purpose of the VAR system is to uncover the basic pattern by estimating a system of equations in which each variable is related to past values of itself and all the other variables in the system. In a simple two-variable model of housing starts and mortgage interest rates, for example, the two equa tions to be estimated would be Starts, = a0 + a, Starts, + a2 Starts, 2 . . . + b, Rates,, + b2 Rates, 2 . . . + es, Rates, = g0 + g, Rates, j + g2 Rates, 2 . . . + h, Starts,, + h2 Starts, 2 . . . + eR , Once the coefficients a, b, g, and h have been estimated from historical data, forecasts can be gener ated by successively calculating values for starts and rates one period ahead. Of course, the quality of the forecast will depend on choosing the proper variables for estimating a stable underlying pattern. One cannot, however, increase the number of variables or the number of lags on the variables arbitrarily in the hope of increasing the accuracy of the forecasts. Trying to estimate too many coefficients with a limited amount of historical data will cause the occasional past deviations from the fundamental pattern to be incorporated into the estimates of the coefficients. Forecasts from such an estimated model will reflect past one-time deviations as well as the true fun damental pattern. Most model builders overcome this difficulty by limiting the number of variables and lags included in the system based on their prior understanding of how certain variables affect others in the economy. For a more technical discussion of VAR models, see Thomas Sargent. index produced six false signals since then. Thus, over the period for which it is available, the Stock and Watson index foreshadows the same number of recessions as the traditional index but produces considerably fewer false signals (see Figures 1 and 2). Like the tradi tional index, Stock and Watson's leading index is less helpful in predicting recoveries than in predicting recessions. Using a rule of three consecutive increases, Stock and Watson's in dex would have predicted two of the last five national recoveries. LEADING INDEXES FOR THE STATES Since we have previously constructed coin cident or current economic activity indexes for Pennsylvania and New Jersey, we can use Stock and Watson's methodology to construct lead ing indexes for those two states.8Like Stock and Watson's national leading index, our state in dexes are forecasts of the change in the state's 8 current activity index. We chose a nine-month forecast to produce an index with a reasonable lead time.9 In other words, our leading index is 8We followed Stock and Watson's methodology in con structing the current economic activity indexes for the states. For a description of the methodology and a list of the vari ables used to construct the coincident indexes, see the 1994 article by Crone. We also constructed a coincident index for Delaware, but we were not successful in constructing a leading index for that state because we found no set of vari ables to adequately predict the state's coincident index. There is more month-to-month variability in Delaware's co incident index than in the indexes for Pennsylvania and New Jersey, so changes in Delaware's coincident index are more difficult to forecast. 9We also experimented with a six-month forecast, but the nine-month horizon produced a slightly better lead time for some recessions without introducing any more false sig nals. The longer the forecast horizon, the longer is the po tential lead time. The advantage of a longer lead time, how ever, must be weighed against the disadvantage of a less accurate forecast. FEDERAL RESERVE BANK OF PHILADELPHIA Theodore M. Crone and Kevin J. Babyak Looking Ahead: Leading Indexes fo r Pennsylvania and New Jersey FIGURE 1 Traditional Leading Index 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 90 92 94 96 FIGURE 2 Stock and Watson Leading Index 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 Note: Shaded areas represent national recessions. a forecast of the total change in the coincident index over the next nine months. Among the variables used in the traditional index or in Stock and Watson's index, only three are avail able at the state level— average hours worked in manufacturing, housing permits, and initial unemployment claims. Our basic model for the leading indexes includes past changes in hous ing permits and initial unemployment claims for the states plus past changes in the coinci 9 BUSINESS REVIEW MAY/JUNE1996 dent index.1 It does not include average hours 0 worked as a separate variable because this vari able is a component of the current activity in dexes for Pennsylvania and New Jersey and past changes in these indexes are already in cluded in the models for the leading indexes. We expanded these basic models by adding some interest-rate and regional variables that im proved the accu racy o f the forecasts w ith out diminishing their ability to signal recessions or without increasing the number of false sig nals. We found that adding the spread between the six-month commercial-paper rate and the six-month Treasury-bill rate improved our ba sic forecast model for New Jersey.1 For Penn 1 sylvania, the forecast was improved by adding the spread between the yield on 10-year Trea sury bonds and one-year Treasury notes. From the Philadelphia Fed's Business Out look Survey of manufacturers we also have some regional variables that correspond to com ponents of the national leading indexes, namely, new orders, unfilled orders, and delivery time (vendor performance).1 Neither the regional 2 variable for new orders nor the one for unfilled orders improved the performance of the lead ing indexes for the states. But the Pennsylva nia model was improved by adding the diffu sion index for delivery time from the Philadel phia Fed's survey. This diffusion index is the difference between the percentage of respon dents reporting an increase in delivery time and the percentage reporting a decrease. (For a com plete list of variables in the state models, see Table 3.) Figures 3 and 4 present the leading indexes for Pennsylvania and New Jersey from Janu ary 1973 to the present.1 Our leading indexes 3 10Because of the high month-to-month variability in the data on housing permits, we smoothed the data by taking a six-month moving average. 12The firms in this survey are located in eastern Penn sylvania, southern New Jersey, and Delaware. 11Improvement in the forecast was measured by the re duction in the average root mean squared error of the fore cast for the nine-month-ahead change in the state's eco nomic activity index. 13Because some of the data were not available prior to 1972 and our models used a number of lags in the data, we were not able to construct leading indexes for the states prior to 1973. TABLE 3 Variables Used to Construct Leading Indexes for the States Pennsylvania New Jersey The Philadelphia Fed's Economic Activity Index for Pennsylvania The Philadelphia Fed's Economic Activity Index for New Jersey Housing units authorized by local building permits Housing units authorized by local building permits State initial unemployment claims State initial unemployment claims Spread between the yields on 10-year Treasury bonds and one-year Treasury notes Spread between the rates on six-month commercial paper and six-month Treasury bills Diffusion index for vendor delivery time from the Philadelphia Fed's Business Outlook Survey 10 FEDERAL RESERVE BANK OF PHILADELPHIA Looking Ahead: Leading Indexes fo r Pennsylvania and New Jersey are the predicted nine-month growth rates for each state's current activity index based on these final models (see Appendix). Any posi- Theodore M. Crone and Kevin J. Babyak tive value of the state index is a prediction of a cumulative increase in activity over the next nine months; any negative value is a predic- FIGURE 3 Pennsylvania Leading Index Index FIGURE 4 New Jersey Leading Index Shaded areas represent state recessions. BUSINESS REVIEW tion of a cumulative decrease in activity. How Well Have These State Indexes Per formed? The rationale for developing leading indexes for the states is based on the notion that recessions in the states do not necessarily coin cide with national recessions. Using the cur rent economic activity index developed in 1994, we identified dates for four recessions in Penn MAY/JUNE1996 nal, and the New Jersey index two. The record of the state indexes is only slightly less accu rate than the record of the national Stock and Watson index, which would have given no false signals since 1973 but would have missed call ing the most recent recession. Like the national indexes, these state indexes are not as reliable in signaling the end of recessions. Using the sy lv an ia and N ew Je rse y b etw ee n 1973 and th ree-m onth rule P en n sy lv an ia's lead ing index 1994.1 How well would the leading indexes for 4 the two states have forecast those recessions? If we use the rule that three successive nega tive readings of the index signal a recession, Pennsylvania's leading index has predicted all four of the state recessions since 1973, with leads of 5 months or more. The index also gave a false signal last year when it was negative for seven consecutive months. Pennsylvania's economy was very weak in 1995, but it did not suffer a recession. New Jersey's leading index has also pre dicted all four of that state's recessions since 1973, with leads of one to seven months. New Jersey's index has given two false recession sig nals, one at the beginning of 1979 and one at the end of 1987. Both of these false signals oc curred a little more than a year before the onset of the next recession. Thus, in the last 23 years, the new leading indexes for the states would have predicted all four recessions in Pennsyl vania and New Jersey. In addition, the Penn sylvania index would have given one false sig would have predicted recovery from two of the state's four recessions since 1973; New Jersey's index would have predicted recovery from only one of four. At the end of 1995 the economies of both Pennsylvania and New Jersey were growing at a slower rate than the national average. A record-breaking snow storm in January 1996 reduced economic activity at the beginning of the year. New Jersey's leading index remained positive through the period, forecasting no re cession this year. Pennsylvania's index was negative in January 1996 but turned positive again in February; so it too is not signaling a recession this year. 14State recessions are dated from the peak to the trough of the state's current activity index in any business cycle. A decline in the index was recognized as a recession only if the cumulative decline was at least four times the average absolute monthly change in the index. Using these criteria, we marked with bars the state recessions in Figures 3 and 4. With two exceptions these recession dates are within three months of the cyclical peaks and troughs of employment in each of the two states. Digitized 1 2 FRASER for CONCLUSION Although they do not have a perfect record, leading indexes of the national economy have been helpful in foreshadowing turning points, especially economic downturns. The limited data available at the state and regional level and their greater volatility make it more difficult to construct leading indexes for the states. Despite these difficulties, we have been able to construct leading indexes for Pennsylvania and New Jer sey. These indexes have been rather successful in predicting downturns in the state economies over the past 23 years. Because there have been few business cycles over that time, however, a longer history will be necessary before we can make a full evaluation of these leading indexes for Pennsylvania and New Jersey. FEDERAL RESERVE BANK OF PHILADELPHIA Theodore M. Crone and Kevin ). Babyak Looking Ahead: Leading Indexes for Pennsylvania and New Jersey Appendix Model Specifications for the State Indexes Like Stock and Watson we used vector autoregression models to construct our leading indexes for the states. The Pennsylvania model contained five equations, and the New Jersey model, four. All the variables except the diffusion indexes and the interest rate spreads are expressed in log difference form, i.e., AlnX( = lnXt - lnXM. We applied some of the same restrictions that Stock and Watson used in their model. For example, the equation for each variable except the one for the changes in the state's economic activity index contained only one lag of itself and one lag of each of the other vari ables. Also, the equation for the change in the state's economic activity index contained four lags of the change in that index and a varying number of lags on the other variables. We used a commonly accepted statistical procedure to determine the number of lags for these other variables (see Akaike). We show the resulting equations forecasting the change in the economic activity index for Penn sylvania and New Jersey. Pennsylvania New Jersey 4 4 AlnPAI = a + X P;(A/nPAZ)t • AInNJl = a + £ (3 (A/nNJJ)t ■ 7=1 7=1 +ylAlnPermitst_1 3 +X 8k(AlnClaims)t_ k k=l +X +y]AlnPermitst_l 6 +X 5k(AlnClaims)t_ k k= 1 C (A elivery)^ m D m =1 + £$p(A Spread6)t_ p p=i + X 1 p(ASpreadlO)t_ 1 p p=i where: AlnPAI = log difference of the Pennsylvania current economic activity index, i.e., AlnPAIt = lnPAI( - lnPAIt ] = log difference of the New Jersey current economic activity index AlnNJI Alnpermits = log difference of the six-month moving average of state housing permits = log difference of state initial unemployment claims Alnclaims = change in the diffusion index for delivery time from the Federal Reserve Bank of Adelivery Philadelphia's Business Outlook Survey of manufacturers AspreadlO = change in the spread between the yields on 10-year Treasury bonds and oneyear Treasury bills = change in the spread between the interest rates on six-month commercial paper Aspread6 and six-month Treasury bills. Since our leading index is the forecasted nine-month change in each state's coincident index, we follow Stock and Watson in using the R2 between the forecasted nine-month change and the actual nine-month change as a measure of the "goodness of fit" for the model. For Pennsylvania this R2 is 0.48, and for New Jersey it is 0.42. 13 MAY/JUNE 1996 BUSINESS REVIEW REFERENCES Akaike, Hirotugu. "Likelihood of a Model and Information Criteria," Journal o f Econometrics, 16 (1981), pp. 3-14. Bums, Arthur F., and Wesley C. Mitchell. Measuring Business Cycles. New York: National Bureau of E conom ic R esearch, 1946. Crone, Theodore M. "A Slow Recovery in the Third District," Federal Reserve Bank of Philadelphia Business Review (July/August 1992). Crone, Theodore M. "New Indexes Track the State of the States," Federal Reserve Bank of Philadel phia Business Review (January/February 1994). Gorton, Gary. "Forecasting with the Index of Leading Indicators," Federal Reserve Bank of Philadel phia Business Review (November/December 1982). Green, George R., and Barry A. Beckman. "Business Cycle Indicators: Upcoming Revision of the Composite Indexes," Survey o f Current Business (October 1993). Martin, Vance L. "Derivation of a Leading Index for the United States Using Kalman Filters," Review o f Economics and Statistics, 72 (1990) pp. 657-63. Mitchell, Wesley C., and Arthur Burns. "Statistical Indicators of Cyclical Revivals," New York: NBER Bulletin No. 69,1938. Moore, Geoffrey H. Statistical Indicators o f Cyclical Revivals and Recessions. Occasional Paper 31. NY: National Bureau of Economic Research, 1950. Moore, Geoffrey H., and Julius Shiskin. Indicators o f Business Expansions and Contractions. NY: Na tional Bureau of Economic Research, 1967. Rufolo, Anthony M. "An Index of Leading Indicators for the Philadelphia Region," Federal Reserve Bank of Philadelphia Business Review (March/April 1979). Sargent, Thomas J. "Estimating Vector Autoregressions Using Methods Not Based on Explicit Eco nomic Theories," Federal Reserve Bank of Minneapolis Quarterly Review (Summer 1979). Stock, James H., and Mark W. Watson. "New Indexes of Coincident and Leading Economic Indica tors," NBER Macroeconomics Annual (1989), pp. 351-94. Stock, James H., and Mark W. Watson. "A Probability Model of the Coincident Economic Indicators," in Geoffrey Moore and K. Lahiri, eds., The Leading Economic Indicators: New Approaches and Forecasting Records. New York: Cambridge University Press, 1990. 14 FEDERAL RESERVE BANK OF PHILADELPHIA Inflation Forecasts: How Good Are They? F J L orecasts of inflation are important because they affect many economic decisions. Inves tors need good inflation forecasts, since the re turns to stocks and bonds depend on what hap pens to inflation. Businesses need inflation fore casts to price their goods and plan production. H om eow ners' decisions about refinancing mortgage loans also depend on what they think will happen to inflation. *Dean Croushore is an assistant vice president in charge of the Macroeconomics Section in the Philadelphia Fed's Research Department. Dean Croushore* In the early 1980s, economists tested the in flation forecasts in surveys taken over the pre vious 20 years and found that the forecasts sys tematically underpredicted inflation. But eco nomic theory suggests that this shouldn't hap pen. To some extent, forecasters' livelihoods depend on how well they forecast, so they have a strong incentive to avoid such systematic mistakes. Faced with evidence that forecasters make systematic errors, economists suggested that either those who surveyed the forecasters weren't collecting the proper data or forecast ers were irrational in their beliefs about infla 15 BUSIN ESS REVIEW tion. As a result, many economists stopped pay ing attention to the forecast surveys. If we look at the data on actual inflation and the forecasts of inflation, the problem with the forecasts is clear. In the mid-1970s, and again in the late 1970s, inflation increased dramati cally, rising to much higher levels than were forecast. But that doesn't mean that the fore casters w eren 't d oing the b est they could using the available information. Major increases in oil prices because of political events in the Middle East made the job of accurately fore casting inflation impossible. When oil prices rose, inflation rose sharply as well. Given that no one anticipated these huge increases in oil prices, it isn't surprising that the inflation fore casts underpredicted inflation. Another prob lem for forecasters was that, before 1973-74, they had never faced such a large increase in oil prices, so they didn't know how inflation would respond. So economists may have been too rash in abandoning the surveys of forecasters. The key question is this: does adding data from the 1980s and early 1990s suggest that the forecasts are better than when we just looked at data from the 1970s and before? The answer is yes: the forecasts are much better when you look at the entire period through 1994. One interpretation is simply that the sharp rise in oil prices caused a period of inflation underprediction; inflation forecasts are generally good otherwise. And it's understandable that forecasters facing such a huge economic shock w eren't sure what would happen. But the forecasts aren't perfect. Forecasters don't seem to account properly for changes in monetary policy. When inflation is increasing and the Federal Reserve raises short-term in terest rates, the forecasts suggest that inflation will stop rising much more quickly than it ac tually does. Systematic errors such as these sug gest that while inflation forecasts are correct on average, forecasters are inefficient in their use of information about monetary policy. These er 16 MAY/JUNE 1996 rors could arise because forecasters don't do their jobs well, because the economy is too com plicated and changes too frequently, because it takes tim e to learn about changes in the economy, or because monetary policy isn't fully credible. FORECASTS SHOULD BE UNBIASED The econom ic theory of rational expectations implies that forecasts for inflation should meet two criteria: (1) they must be unbiased, that is, forecast errors (actual inflation minus the fore cast) must average out to zero over time; and (2) they must be efficient, that is, forecasters must use all the relevant information at their disposal in forming forecasts. Forecasts are unbiased if, when you look at the data on inflation and on inflation forecasts over a long period, positive and negative er rors cancel each other out. But a look at actual inflation compared with expected inflation (as estimated from the Livingston Survey of econo mists from 1956 through 1979) shows a prob lem (Figure l) .1If the inflation forecasts are cor rect on average, they should be located sym metrically around the 45-degree line drawn in the figure. As you can see, the points tend to be above that line—actual inflation has usually been higher than expected inflation. These fore casts are biased because they show a system atic underprediction of inflation. Many formal statistical studies of the data available in the early 1980s also suggested that forecasts were biased.2This discovery, with sta tistical support behind it, persuaded economists 1The Livingston Survey, which collects economists' fore casts of inflation and other economic variables twice a year, has been in existence since 1946. For more information on the Livingston Survey, which is conducted by the Federal Reserve Bank of Philadelphia, see the article by Herb Tay lor. John Carlson discusses some statistical problems in using the survey. The figure shows the mean forecasts of CPI inflation over the 14 months following each survey, compared with actual inflation over those 14 months. FEDERAL RESERVE BANK OF PHILADELPHIA Inflation Forecasts: How Good Are They? Dean Croushore FIGURE 1 Actual and Expected Inflation Livingston Survey 1956H1 to 1979H2 A ctual Expected that there must be something wrong with sur veys of inflation expectations. Some economists believed that people didn't have a strong enough incentive to respond accurately to the surveys, because they weren't being paid to 2These studies include those by Stephen Figlewski and Paul Wachtel; Edward Gramlich; Eugene Fama and Michael Gibbons; and Michael Bryan and William Gavin. For a re view of the issues and the statistical results, see the article by G.S. Maddala. Technically, a biased forecast isn't neces sarily worse than an unbiased forecast, if the bias is small and if the biased forecast has smaller errors, on average. But the bias found in these studies was quite large. supply their fore casts, and they m ade their fore casts anonymously. An altern ativ e view was that the people being sur veyed weren't very good at forecasting in flation because they had no reason to be good at doing so; their livelihoods didn't depend on their inflation fore casts. As one par ticipant suggested, the ben efits of working on a joke for the speech he was about to give were greater than the benefits from a slight refinement in his inflation fore cast. INFLATION AND THE OIL SHOCK Economists had become interested in testing people's expecta tions about inflation at the worst possible time. In 1973 and 1974, the price of oil rose dramati cally on world markets in response to a sharp reduction in supply from the Arabian penin sula, catching everyone by surprise. As a result, inflation in the United States and many other countries rose sharply, and the forecasts of in flation looked very bad (Figure 2).2The oil-price 3 3A s before, the data in this figure are the mean responses from the Livingston Survey for the 14-month-ahead fore cast of CPI inflation. 17 BUSINESS REVIEW MAY/JUNE 1996 FIGURE 2 Actual and Expected Inflation Livingston Survey Percent Note: "Expected" is the inflation forecast for the year following the forecast date; "Actual" is the actual inflation rate over that period. shock of 1973-74 was followed by another one in 1978-79, which is also apparent in the figure. The two oil-price shocks were unexpected. But compounding the problem was the fact that people didn't know how the economy would respond. Would the oil price increases cause a recession in the United States? Would inflation rise permanently or temporarily and by how much? How would monetary policy respond? We know now that the sharp increases in oil prices led directly to a large increase in inflaDigitized for 18 FRASER tion, but at the time, no one knew what would hap pen.4 Since these were the first epi sodes of their kind in U.S. history, it isn't surprising that the fo recasters d id n 't do a very good job in forming inflation expecta tions. FORECASTS LOOK BETTER TODAY If we add the in flation data since 1980 to the chart, the forecasts look much better (Fig ure 3). There ap pears to have been some overpredic tion of inflation in the early 1980s and again in the early 1990s, but these er rors are m uch smaller than the er rors in the 1970s.5 Formal statisti cal tests on the 4CPI inflation rose from just over 3 percent in 1972 to almost 9 percent in 1973 and over 12 percent in 1974. In the second oil shock, inflation rose from just under 7 percent in 1977 to 9 percent in 1978, then to about 13 percent in 1979 and 1980. 5The error in a forecast is defined as the actual inflation rate over the period minus the forecast of the inflation rate over the period. If forecasts are good, forecast errors should be fairly small, and the plotted points should be close to the 45-degree line in the figure. FEDERAL RESERVE BANK OF PHILADELPHIA Inflation Forecasts: How Good Are They? d ata, w hich are id en tical to the ones econ om ists perform ed in the early 1980s, show m u c h -im p ro v e d performance.6 The forecasts no longer show any bias. In the figu re, the poin ts are fairly symmetric around the 45-degree line. W h at's m ore, this result holds up when we look at data from other surveys of forecasts or data other than the CPI in flation rate. W e've done the same statistical tests using the Sur vey of Professional Forecasters (Figure 4) and the Univer sity of M ichigan Survey of Consum ers (Figure 5).7 The expected inflation variable in the fig Dean Croushore FIGURE 3 Actual and Expected Inflation Livingston Survey 1956H1 to 1994H2 Actual 6In this analysis, we add data from the 1980s and 1990s to the original data from the 1950s through the 1970s. A similar figure for just the 1980s and 1990s shows a very impressive forecast pattern, with very small differences be tween actual and expected inflation. The formal results, which are based on regression analysis, are available from the author upon request. 7See my 1993 article for a detailed description of the Survey of Professional Forecasters, which began in 1968. See the article by Nicholas Noble and Windsor Fields for more details on the University of Michigan Survey of Con sumers, which, in 1969, began to collect inflation forecasts once a quarter. Expected ure for the Survey of Professional Forecasters is the mean of the survey participants' forecasts of the GNP implicit price deflator (GDP defla tor after 1991) over the next year, which is com pared to actual inflation over the next year; for the Michigan survey it is the mean of the sur vey participants' forecasts of the CPI inflation rate over the next year, which is compared to actual inflation over the next year. Though these surveys differ in the types of people respond ing to the survey and the type of inflation vari able being forecast, there is no apparent bias in the figures, a finding supported by formal sta tistical tests. 19 BUSINESS REVIEW MAY/JUNE 1996 biased , there is some evidence that they are inefficient. Actual and Expected Inflation The term inefficient Survey of Professional Forecasters 1968Q4 to 1994Q4 applies to forecasts that could be im Actual proved by using additional informa tion. That is, fore casters could have done a better job at forecasting if they had used all the data available to them in the right way. My research with Larry Ball of Johns H opkins U n iv ersity has found that forecast ers do not use infor mation about mon etary policy in the best way possible.8 Our research sug gests that when in flatio n is risin g, leading the Federal Reserve to tighten m onetary policy, Expected forecasters under estimate the degree to which inflation So it appears that the bias found in earlier continues to rise even after the Fed has taken studies of the surveys of inflation forecasts was action. Forecasters thus seem to assume that largely due to the oil-price shocks in the 1970s. tight monetary policy will have a more imme Those shocks made all forecasts of inflation look diate impact on inflation than is actually the bad. Still, these forecasts may have been the best case. In our research, we examine the correlation possible forecasts of inflation at the time; people should realize that unpredictable shocks some between the inflation forecast error (that is, the times occur. FIGURE 4 BUT FORECASTS MAY STILL BE INEFFICIENT Even though the forecasts appear to be un 20 8Detailed results can be found in our 1995 working pa per. Frederick Joutz, as well as John Schroeter and Scott Smith, also found that forecasters don't use information about monetary policy efficiently. FEDERAL RESERVE BANK OF PHILADELPHIA Dean Croushore Inflation Forecasts: Hoiv Good Are They? FIGURE 5 Actual and Expected Inflation Michigan Survey 1969Q1 to 1994Q4 A ctual tionship, which can be seen in a plot of the data (Figure 6). In this figure, we've shown the inflation forecast error from the Survey of Pro fessional Forecast ers plotted against the change in the federal funds rate. You can see that there is a positive relation sh ip b e tw een the tw o— w hen m onetary policy is tightening, actu al in flation tends to be higher than expected infla tion. And when m on etary policy is 0 2 4 6 Expected actual inflation rate over the next year minus the expected inflation rate) and the change in the federal funds rate (our measure of monetary policy) over the past year. If the forecasters are efficient in using information about monetary policy, there should be no relationship between the forecast error and the annual change in the federal funds rate; otherwise the forecasters should have used the relationship between the forecast error and the change in the federal funds rate to produce an improved forecast. But our formal statistical tests show a positive rela easing, actual infla tion tends to be less than expected infla tion. The solid line shown in the figure is the line through 8 10 12 the points of the figure that fits the data best. As shown by the line, an increase of one percentage point in the fed eral funds rate over the past year is associated with an increase in the forecast error of 0.32 percentage point, on average. Further investigation of this result shows that the forecasters' errors lie in the timing of the response of inflation to monetary policy, not in the magnitude. That is, the forecasters are right about the size of the effect that tighter monetary policy has in reducing inflation, but their forecasts suggest that inflation will re spond to monetary policy quickly. In fact, it 21 BUSINESS REVIEW MAY/JUNE 1996 ing this procedure over the last six years of the period Inflation Forecast Errors and we study w ould Monetary Policy have lowered fore Survey of Professional Forecasters 1968Q4 to 1994Q4 cast errors roughly 20 percent.9 For ex ample, after the fed eral funds rate de clined 2.4 percent age points in 1992, the forecasters pre dicted inflation in the GDP deflator of 2.87 percent, but a b etter forecast could have been made by predicting inflation of 2.87 (2.4 x .32), or 2.10 percent. Actual in flation for the GDP deflator turned out to be 2.13 percent, so the m odified fo recast would have been m uch better. This relationship -8 -6 -4 -2 0 2 4 6 8 betw een inflation forecast errors and Change in Federal Funds Rate past changes in M onetary Policy m onetary policy --------- Easing T ig h ten in g -------- ► also appears when we use the L iv ingston Survey or takes longer for monetary policy to work than the University of Michigan Survey of Consum the forecasters think. An improved inflation forecast can be de vised by using the information from Figure 6. 9Technically, the root mean squared forecast error is 17 To get a new inflation forecast, take the aver percent lower, while the mean absolute error is 24 percent age survey forecast for inflation (in the GDP lower. The root mean squared forecast error is found by taking the square of the forecast error at each date, calculat deflator) over the coming year and add to it an ing the average of these squared values, and taking the amount equal to 0.32 times the change in the square root. The mean absolute error is found by taking the federal funds rate over the past year. Follow average of the absolute values of the forecast errors. Digitized for 2 2 FRASER FIGURE 6 FEDERAL RESERVE BANK OF PHILADELPHIA Inflation Forecasts: How Good Are They? ers as the basis for expected inflation. This sug gests that forecasters could use information about monetary policy to make better forecasts. In particular, forecasters would need to make sure that their inflation forecasts reflected the proper timing of changes in inflation caused by recent movements in monetary policy. EXPLAINING FORECAST INEFFICIENCY Why do inflation forecasts suffer from inef ficiency? Don't forecasters have the incentive to provide optimal forecasts? If so, how can forecast errors be persistently related to mon etary policy measures? You might think that if forecasters continually made mistakes in their inflation forecasts, they would realize they were doing so and would correct those errors. So the real question is: why don't forecasters make adjustments so that they produce not only bet ter forecasts but also ones that are efficient with respect to monetary policy? There are a num ber of possible explanations for why forecast errors may persist, but no convincing explana tions for why the forecasts are inefficient in the first place. One possible explanation for the failure of forecasters to improve their forecasts is simply that forecasters don't do their jobs well. That is, they must not have enough incentive to form completely rational expectations of inflation, perhaps because their inflation forecasts aren't that important to them. It's possible that, ex cept for the few forecasters whose forecasts of inflation are used by traders to buy and sell bonds and thus have a lot of money riding on them, the forecasters in the survey may not care about inflation very much. If their forecasts are wrong, it doesn't hurt them. Another possible explanation for why fore cast errors may persist is that the m acro economy is very complicated, and no one has a complete understanding of how it works. The Phillips curve (which relates inflation to the unemployment rate) was thought to be a great model of inflation until the 1970s, when it failed Dean Croushore miserably. Nobody knew ahead of time that the oil-price shocks in the 1970s would raise infla tion so much. And the most popular theoreti cal models of the economy today seem far too abstract to use in forecasting. As a result, it isn't surprising that forecasting inflation is difficult. Related to our lack of understanding of ex actly how the economy works is the fact that it takes tim e for econom ists to learn about changes in the economy. They don't see trends emerging right away; it takes time for the data to come in and for economists to realize that the relationship between economic variables has changed. For example, in the late 1980s, the Federal Reserve developed a model of inflation called P* (pronounced P-star), which related the money supply (measured by M2) to the price level for the GNP deflator. But the changes in the demand for money that occurred in the early 1990s altered the relationship between M2 and inflation. As a result, the model no longer provided good forecasts. For example, it pre dicted a large reduction in inflation in the 199395 period, but inflation didn't decline nearly as much as predicted. Another possible explanation for the ineffi ciency of inflation forecasts concerns the cred ibility of monetary policy. In the early 1980s, people had doubts about how serious the Fed eral Reserve was about fighting inflation. They thought the Fed might allow inflation to drift upward, rather than keeping inflation at 4 per cent or less. That may be why forecasters per sistently overpredicted inflation in the mid1980s. So, clearly some degree of inefficiency in forecasting inflation may be due to uncer tainties about monetary policy. Credibility may also have played a role in the early 1990s. Again, forecasters kept predict ing a rise in CPI inflation from about 3 percent to about 3.5 percent. The overprediction was small, but it persisted for several years. This persistence may have resulted from a combi nation of doubts about the Fed's commitment to low inflation and the lack of a good macro 23 BUSINESS REVIEW economic model of inflation, since monetary aggregates (M l, M2, M3) seemed to have lost their predictive power. While these explanations may help us un derstand why forecasters have difficulty in fore casting inflation and perhaps also why they don't adjust their forecasts to better use the in formation about monetary policy, they don't tell us why the forecast errors are systematically related to monetary policy in the first place. Digitized for 4 2 FRASER MAY/JUNE 1996 CONCLUSION Surveys of inflation forecasts have had a bad reputation. Based on statistical tests in the early 1980s, economists had doubts about how ac curate the forecasts were. But that was largely the effect of the oil-price shocks in the 1970s. If we look at the data today, the forecasts look much better. Nonetheless, there appears to be some inefficiency in the forecasts with respect to their relationship to monetary policy. FEDERAL RESERVE BANK OF PHILADELPHIA Inflation Forecasts: Hoiv Good Are They? Dean Croushore REFERENCES Ball, Laurence, and Dean Croushore. "Expectations and the Effects of Monetary Policy," Federal Reserve Bank of Philadelphia Working Paper No. 95-22, October 1995. Bryan, Michael F., and William T. Gavin. "Models of Inflation Expectations Formation: A Comparison of Household and Economist Forecasts," Journal o f Money, Credit, and Banking 18 (November 1986), pp. 539-43. Carlson, John A. "A Study of Price Forecasts," Annals o f Economic and Social Measurement 6 (Winter 1977), pp. 27-56. Croushore, Dean. "Introducing: The Survey of Professional Forecasters," Federal Reserve Bank of Philadelphia Business Review (November/December 1993), pp. 3-15. Fama, Eugene F., and Michael R. Gibbons. "A Comparison of Inflation Forecasts," Journal o f Monetary Economics 13 (May 1984), pp. 327-48. Figlewski, Stephen, and Paul Wachtel. "The Formation of Inflationary Expectations," Re view o f Economics and Statistics 63 (February 1981), pp. 1-10. Gramlich, Edward M. "Models of Inflation Expectations Formation," Journal o f Money, Credit, and Banking 15 (May 1983), pp. 155-73. Joutz, Frederick L. "Informational Efficiency Tests of Quarterly Macroeconometric GNP Forecasts from 1976 to 1985," Managerial and Decision Economics 9 (1988), pp. 311-30. Maddala, G.S. "Survey Data on Expectations: What Have We Learnt?" in Marc Nerlove, ed., Issues in Contemporary Economics, vol. II. Aspects of Macroeconomics and Econo metrics. New York: New York University Press, 1991. Noble, Nicholas R., and T. Windsor Fields. "Testing the Rationality of Inflation Expecta tions Derived from Survey Data: A Structure-Based Approach," Southern Economic Journal 49 (October 1982), pp. 361-73. Schroeter, John R., and Scott L. Smith. "A Reexamination of the Rationality of the Livingston Price Expectations," Journal o f Money, Credit and Banking 18 (May 1986), pp. 239-46. Taylor, Herb. "The Livingston Surveys: A History of Hopes and Fears," Federal Reserve Bank of Philadelphia Business Review (January/February 1992), pp. 15-27. 25 Philadelphia/RESEARCH WORKING PAPERS The Philadelphia Fed's Research Department occasionally publishes working papers based on the current research of staff economists. These papers, dealing with virtually all areas within economics and finance, are intended for the professional researcher. The papers added to the Working Papers series thus far this year are listed below. To order copies, please send the number of the item desired, along with your address, to WORKING PAPERS, Department of Research, Federal Reserve Bank of Philadelphia, 10 Independence Mall, Philadelphia, PA 19106. For over seas airmail requests only, a $3.00 per copy prepayment is required; please make checks or money orders payable (in U.S. funds) to the Federal Reserve Bank of Philadelphia. A list of all available papers may be ordered from the same address. 96-1 Mitchell Berlin, Kose John, and Anthony Saunders, "Bank Equity Stakes in Borrowing Firms and Financial Distress" 96-2 Joseph P. Hughes and Loretta J. Mester, "Bank Capitalization and Cost: Evidence of Scale Economies in Risk Management and Signaling" 96-3 Tom Stark and Dean Croushore, "Evaluating McCallum's Rule When Monetary Policy Matters" 96-4 Sherrill Shaffer, "Capital Requirements and Rational Discount Window Borrowing" 96-5 Stephen Morris, "Speculative Investor Behavior and Learning" 96-6 Karen K. Lewis, "Consumption, Stock Returns, and the Gains from International RiskSharing" 96-7 Graciela L. Kaminsky and Karen K. Lewis, "Does Foreign Exchange Intervention Signal Future Monetary Policy?" 96-8 Satyajit Chatterjee and Dean Corbae, "Money and Finance with Costly Commitment" 96-9 Joseph P. Hughes, William Lang, Loretta J. Mester, and Choon-Geol Moon, "Efficient Banking Under Interstate Branching" 26 FEDERAL RESERVE BANK OF PHILADELPHIA FEDERAL RESERVE BANK OF PHILADELPHIA Business Review Ten Independence Mall, Philadelphia, PA 19106-1574
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