Surprise and Uncertainty Indexes: Real-Time Aggregation of Real-Activity Macro Surprises

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 1093r This Version: May 2016 Original Version: November 2013 Surprise and Uncertainty Indexes: Real-Time Aggregation of Real-Activity Macro Surprises Chiara Scotti NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from Social Science Research Network electronic library at http://www.ssrn.com/.

Surprise and Uncertainty Indexes: Real-time Aggregation of Real-Activity Macro Surprises Chiara Scotti Federal Reserve Board Abstract I construct two daily, real-time, real activity indexes for the United States, Euro area, the United Kingdom, Canada, and Japan: (i) a surprise index that summarizes recent economic data surprises and measures optimism/pessimism about the state of the economy, and (ii) an uncertainty index that measures uncertaintyrelatedtothestateoftheeconomy. Thesurpriseindexpreservesthe properties of the underlying series in affecting asset prices, with the advantage of being a parsimonious summary measure of real-activity surprises. For the United States, the real-activity uncertainty index is compared to other proxies commonlyusedtomeasureuncertaintytoshowthatwhenuncertaintyisstrictly related to real activity, it has a potentially milder impact on economic activity than when it also relates to the financial sector. Keywords: Business cycle, Dynamic factor model, State space model, Forecasting weights JEL: C38, E32 Email address: chiara.scotti@frb.gov I would like to thank for their useful comments Boragan Aruoba, David Bowman, Celso Brunetti, Domenico Giannone, Raffaella Giacomini, Rob Martin, Andrew Patton, Barbara Rossi, Jonathan Wright, Clara Vega as well as anonymous referees and various participants of conferences and seminars: 2012 Computing in Economics and Finance; 2012 European Meeting of the Econometric Society; 2012 Conference on Real-Time Data Analysis, Methods, and Applications at the Philadelphia Fed; 2012 NBER-NSF Time Series Conference; Third IFO conference on Macroeconomics and Survey Data; 2013 Econometric Society Australasian Meeting; Dallas Fed Conference on The Causes and Macroeconomic Consequences of Uncertainty; Boston College; and Board of Governors of the Federal Reserve System. For outstanding research assistance I thank Rebecca DeSimone, Eric English, Olivia Kim, and Margaret Yellen. The views expressed in this paper are solely the responsibility of the author and should not be interpreted as reflecting the view of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. (ChiaraScotti) Preprint submitted to IFDP May 16, 2016

1. Introduction This paper proposes a new methodology to construct two real-time, real activity indexes: (i) a surprise index that summarizes recent economic data surprises and measures deviation from consensus expectations and (ii) an uncertainty index that measures uncertainty related to the state of the economy. The indexes, on a given day, are weighted averages of the surprises or squared surprisesfromasetofreleases,wheretheweightsdependonthecontributionof the associated real activity indicator to a business condition index `a la Aruoba et al. (2009). The surprise index measures whether agents are ex-post more optimistic or pessimistic about the real economy than indicated by actual data releases.1 A positive (negative) reading of the surprise index suggests that economic releases have on balance been higher (lower) than consensus, meaning that agents were more pessimistic (optimistic) about the economy. The uncertainty index measures how uncertain agents are ex-post about current real activity conditions. A greater (smaller) reading of the uncertainty index suggests that agents have on balance been more (less) uncertain about the state of the economy. I apply this methodology to construct indexes for the United States, Euro Area, the United Kingdom, Canada, Japan, and an aggregate of the five countries over the 2003-2012 period. The Aruoba, Diebold, and Scotti (ADS) index maintained by the Federal Reserve Bank of Philadelphia has proven to be a successful economic indicator and as such it has been classified by the Wall Street Journal among the 50 economic indicators that really matter (Constable and Wright (2011)) and has beenaddedbyBloombergtothedatathatcanbefollowedinrealtimethrough itsplatform(ADSBCIIndex).2 TheADSindexmeasuresthestateoftheeconomy and serves as a summary statistic of the information market participants have received thus far about real activity. However, in efficient markets, asset prices react to new information. Thus it is important to measure the surprise 1 Ex-post optimism or pessimism differs from ex-ante optimism or pessimism. If we consider the weather, for example, the optimal, model-consistent forecast for the temperature tomorrowcouldbe15degreesFahrenheit. Icouldbeex-anteoptimisticandexpectittobe20 degrees Fahrenheit. If the forecast turns out to be wildly wrong, and the temperature turns up at a toasty 25 degrees, I was still ex-ante optimistic, even though, ex-post, my forecast looks pessimistic. Ex-post optimism or pessimism is neither necessary nor sufficient to say anythingaboutex-antebeliefs. AnotherdefinitionthatIthinkcaptureswellthesemeasures is realized optimismorpessimism. 2http://www.philadelphiafed.org/research-and-data/real-time-center/business-conditionsindex/ 2

component of the information that has just arrived and the uncertainty surrounding that information. To this end, the surprise index presented in this paperaggregatestheinformationcontainedinthesurprisestoconstructasummarymeasureofthedeviationoftherealeconomyfromconsensusexpectations, and the uncertainty index quantifies economic uncertainty, which is otherwise challenging to measure. The indexes are not competitors but complements to theexistingbusinessconditionindicatorssuchastheADSindexandtoexisting uncertainty indexes. This paper relates to several branches of the literature. First and foremost is the uncertainty literature, which has thrived in recent years. Because uncertaintyisnotobservable,anumberofproxieshavebeenusedtomeasureit,ranging from stock market realized and implied volatilities (Bloom (2009)), to the cross-sectional dispersion of survey-based forecasts (Bachmann et al. (2013)), the frequency of newspaper references to economic policy uncertainty (Baker et al. (2015)), or the common variability in the purely unforecastable component of the future value of a big number of variables (Jurado et al. (2015)). However, these measures tend to combine economic uncertainty with other notions. For example, stock return volatility combines information about stock market volatility with economic uncertainty, and forecast disagreement could measure divergence of opinions among forecasters rather than just the underlying uncertainty about the economy. My paper contributes to this literature by providingadaily macroeconomicinformationuncertaintymeasurewhichquantifies the part of uncertainty that specifically relates to the state of the real economy. It also contributes by helping to disentangle the impact of purely macro uncertainty from more general uncertainty. The index is daily in that it gets updated every time new information about the state of the economy gets released. Second, this paper relates to those papers that study the impact of news surprises on asset price such as Andersen et al. (2003), Andersen et al. (2007), and Gilbert et al. (2012), and contributes to this literature by providing a parsimonious summary measure of real-activity macroeconomic surprises. The paper also relates to papers that use similar factors models to extract a businessconditionindex(Aruobaetal.(2009),andBanburaetal.(2010)among others). It also employs the idea of forecasting weights developed in Koopman and Harvey (2003) and applied by Banbura and Runstler (2010) and Camacho and Perez-Quiroz (2009), among others, to study the impact of news releases on GDP forecast revisions. In order to construct the surprise and uncertainty indexes, I first employ a 3

dynamic factor model to estimate monthly business condition indexes for the aforementionedcountriesandcomputetheweightsrepresentingthecontribution of the economic indicators to these business condition indexes. I then use those weights to average the surprises or squared surprises in order to construct the surprise and the uncertainty indexes, respectively. The weights depend on (i) the time elapsed since the release of the associated information and (ii) the unbalancedness pattern of the underlying releases. The former is a time decay feature that reduces the contribution of each surprise over time. The latter is a missing data characteristic that sets to zero the contributions of an indicator in months in which no data is available. I find that surprise indexes tend to be negative during the recession associated with the 2008 financial crisis, the so-called Great Recession, suggesting that agents were more optimistic about the real economy than it warranted.3 There appear to be other episodes when the indexes are negative. Of note are severaldeclinesintheeuro-areasurpriseindexafter2011,thesharpdropinthe Japanese surprise index after the March 2011 earthquake, and the prolonged low levels of the U.K. index in 2010 and 2011. On the other hand, there are also several instances where the surprise indexes are positive, especially coming out of the recession in the United States, the United Kingdom and Canada. I show that the surprise index preserves the properties of the underlying series in affecting asset prices, with the advantage of being a parsimonious summary measure of real-activity surprises. In light of this, Demiralp et al. (2013) make useofitasacontrolvariablewheninvestigatingtheeffectsofpoliticalcommentaries on policy rate decisions and policy expectations in the United States and the Euro Area, and find it to be significant determinant of policy expectations. Similarly, Brunetti et al. (2013) employ it as a control variable in studying the impact of speculation activity in the crude oil market. The uncertainty indexes tend to be higher during recession periods. Interestingly, the euro-area uncertainty index reaches its highest values just before and after the 2008-2009 recession, suggesting that agents were more uncertain abouttheeconomyastheEuroAreawasenteringandexitingtherecession. The daily U.S. uncertainty index looks somewhat similar to the U.S. stock market implied volatility as measured by the VIX. Implied volatility, a forward-looking 3Unfortunately, we are not able to see whether this is a characteristic of all recessions because the surprise indexes only start in 2003 and hence only cover one recession episode. ExpectationdataareavailablefromBloombergforallcountriessince2003. 4

measure, is computed from option prices. The uncertainty index, a historical measure, is calculated from current and past macroeconomic news surprises. The former is a wider measure that combines information about risk aversion andfuturestockmarketvolatility/uncertainty,andtotheextentthatthesetwo movewithnewssurprises,theVIXalsocontainsinformationaboutcurrentand future economic uncertainty. Although understanding the exact linkages goes beyond the scope of this paper, I also decompose the VIX following Bakaert et al. (2013) into stock market uncertainty and variance risk premium, and observethattheVIXpatternsaremainlydrivenbytheBakaertetal.(2013)stock market uncertainty during the period analyzed.4 In a bivariate VAR exercise with employment and uncertainty proxies for the United States over the last decade, I find that, when uncertainty is strictly relatedtorealactivityasmeasuredbythereal-activityuncertaintyindex,ithas a potentially milder impact on economic activity. Just flipping the argument, whenuncertaintyismoregenerallyrelatedtoeconomicandfinancialconditions as measured by the VIX or Bakaert et al. (2013) stock market uncertainty proxy, its impact on real-activity variables seems to be stronger and faster. This finding supports recent work by Caldara et al. (2013) which finds that the financial channel is key in the transmission of uncertainty shocks. Of course, the different impact could also be more generally due to the fact that the VIX measures a more wide-ranging notion of uncertainty. Thesurpriseanduncertaintyindexestendtobenegativelycorrelated,meaning that bad news occurs together with increased volatility.5 This result is similartotheinverserelationshipbetweenfirstandsecondmomentsofassetreturns found in the financial literature, a phenomenon that Fostel and Geanakoplos (2012) provide a theoretical explanation for, together with explaining a decrease in leverage. The remainder of the paper is organized as follows: section 2 presents the data and the rationale behind using Bloomberg forecasts; section 3 presents the details of the model’s forecasting weights and the construction of the surprise and uncertainty indexes; section 4 covers the estimation details; section 5 presentstheresults;section6showssomeapplications;andsection7concludes. 4ThecorrelationbetweenthedailyU.S.uncertaintyindexandtheVIXis53percentover thesampleperiodanalyzed. 5Thecorrelationrangesbetween-0.26to-0.45fortheUnitedStates,EuroArea,theUnited KingdomandJapan,whereasitispositiveinCanadaoverthesampleperiodanalyzedinthe paper. 5

2. Data Before getting into the model, this section presents information about the data used to construct the surprise and uncertainty indexes. I use two different types of data: the actual first release of the macroeconomic variable, say gross domestic product (GDP) or nonfarm payroll, and its forecast as measured by theBloombergmedianexpectation. Ofnote, Bloombergexpectationsgenerally do not run the risk of being stale forecasts as they can be updated until one hour before the data release. The forecast that I use is the latest one recorded by Bloomberg.6 The actual releases of macroeconomic variables are used to estimate the underlying factor model from which I gather the weights. The difference between actual releases and Bloomberg expectations, also known as news surprise or forecast error, is then used together with the weights to construct the surprise and uncertainty indexes. In what follows, I describe the details of the data and study some of the properties of the news surprises. The analysis covers five countries: the United States, the Euro Area, the United Kingdom, Canada, and Japan. I use five indicators for each country, except the United States for which I use six. Several considerations guide the choice of variables. First, I want to use those variables that are regarded as the main real activity indicators and as such followed by the business community, governments, and central banks as indication of the state of the economy. Second, I choose indicators for which analysts form expectations that are publicly available (see Table B1 in the online Appendix).7 Theanalysisforthesurpriseanduncertaintyindexescoverstheperiodfrom May 15, 2003 through March 31, 2016. However, a longer dataset is used to estimate the underlying business condition indexes: January 1980 to March 31, 2016, except for the Euro area where the sample starts in January 1985. The first indicator is quarterly real GDP. For each country, the first GDP release for the corresponding quarter is used. The second indicator is industrial production(IP),whichisamonthlyindicator. Thethirdindicatorisemployees on nonagricultural payrolls, when available, or the unemployment rate.8 The 6The survey is done on a rolling basis and the Bloomberg news team run tables every weekday morning, as they get the forecasts. Economists can usually make changes up to an hourbeforereleasetime. 7The table lists the indicators, together with their frequency, publication lags and transformationsthatIusetoconstructtherealactivityfactor.Thetworightmostcolumnslistthe sourceofthedataseriesthatIusetoconstructthefactor,andthecorrespondingBloomberg dataseriesthatIusetoconstructthesurpriseanduncertaintyindexes. 8EmploymentdataandexpectationsareavailableonlyfortheUnitedStatesandCanada. 6

former tends to be more timely than the latter, but unfortunately it is not availableforallcountries.9 Thefourthindicatorisretailsales, whichisanother monthly variable. The fifth indicator is a survey measure of the manufacturing sector or the overall economy (composite) depending on the availability of the Bloomberg forecast. I use the ISM manufacturing index for the United States, the composite PMI for the Euro Area, the manufacturing PMI for the United Kingdom and Canada (Ivy survey), and the Tankan survey for Japan. The Tankansurveyisaquarterlyseries,whereastheothersurveysareallmonthly.10 Although monthly series are generally preferred when available, the Tankan survey has the advantage of being very timely, as it is released on average four daysbeforetheendofthequarteritrefersto.11 Theaveragepublicationlagfor the other series vary a lot as shown in table B1 in the online Appendix. Survey measures are the most timely of all: the euro-area Flash composite PMI is the first indicator to be released, followed by the Japanese Tankan survey, the U.S. ISM and the U.K. PMI. On the other hand, GDP and IP data tend to be the last information to be released. The additional indicator for the United States is the Bureau of Economic Analysis (BEA) personal income. Household income or personal income are generally available for the other countries but because their expectation is not, I drop them from the dataset. Asalreadymentioned,whiletheannouncementitselfisusedinconstructing the real activity factor, the news surprise, that is the difference between announcement realizations (yi) and their corresponding Bloomberg expectations t (E[yi|F ]), is used in constructing the surprise and uncertainty indexes. Bet t cause units of measurement vary across macroeconomic variables, I standardize the resulting surprises by dividing each of them by their sample standard deviation (σi). The standardized news surprise associated with the macroeconomic Fortheothercountriesweusetheunemploymentrate. 9Toavoidconfusion,becauseforalltheindicatorsahighernumbermeansthattheeconomy isdoingwell,Ifeedthenegativeoftheunemploymentrateintothemodel. 10ForCanada,Bloombergusedtoprovideexpectationsforthenon-seasonally-adjustedIVY index, but as of March 2011, it started to provide expectations for the seasonally adjusted series. Isplicethetwoseriestogetherbeingawareofthebreakpoint. 11The Tankan survey has an average publication lag of -4 days, but only Q4 numbers are released before the end of the quarter (around mid-December). Other releases occur at the beginningofthefollowingquarter. 7

indicator yi at time t is therefore computed as: yi−E[yi|F ] si = t t t . (1) t σi 2.1. News Surprises Marketparticipantswatch,andreactto,scheduledmacroeconomicannouncements because these announcements potentially contain new information that was not previously incorporated into market participants’ expectations about thestateoftheeconomy. Severalstudieshavelookedintotheforecastefficiency, or rationality, of market expectations. Under rationality, the surprise component, measured as difference between the actual release and its forecast, should truly represent “news,” meaning that market agents optimally use available information in forming their forecasts, and therefore the forecast error should be orthogonal to information available when the forecast is produced. This is equivalent to testing whether the error term εi is orthogonal to the forecast t yi,f =E[yi|F ] in the equation t t t yi,f =y +εi. (2) t t t Inparticular,testingforforecastefficiencyboilsdowntotestingthatαi =βi = 0 in the regression si =αi+βiyi,f +ui (3) t t t wheresi =yi−yi,f istheforecasterror, a.k.anewssurprise. Thisissometimes t t t known as the Mincer−Zarnowitz test (Mincer and Zarnowitz (1969)). Several earlier papers have applied these tests mainly using data revisions (among others, see Croushore and Stark (2001) and Faust et al. (2005)). Table 1 reports evidencefromthe baseline testsofforecastrationality − testsofthe hypothesis that αi =βi =0 in equation (3). As can be seen in the middle columns, αi and βi are very often significantly different from zero and the F test fails to reject the null hypothesis that αi =βi =0 only in 1/3 of the cases. ButgiventhatBloombergmedianforecastsarenotefficient,whyaretheyso important? WhydoIusethemratherthanusingefficientforecaststhatIcould construct within the factor model? The answer is simple: financial markets react neither to my own private forecast nor yours; financial markets react to Bloomberg forecasts, which are public and everyone can see. Awideliteraturehasdocumentedtheassetpriceresponsetomacroeconomic 8

news announcements. Andersen et al. (2007) and Gilbert et al. (2012) among others have looked into this question. Table 2 displays the results of univariate regressions of foreign exchange returns on the individual macro announcement surprises over the sample period 2003-2012. These results do not necessarily correspond to what reported in the existing literature because of the different samples used. However, they clearly state the point that Bloomberg forecasts (and surprises) are important because financial markets react to them. 3. The Model Iuseastandarddynamicfactormodelatamonthlyfrequencywhichexplicitly accounts for missing data and temporal aggregation (details can be found in the appendix). With it, each of the real-activity variables is used to extract information about the common (unobserved) factor. 3.1. Forecasting Weights The contribution of each real-activity variable to the determination of the factor represents the weight applied to construct the surprise index. As shown in Koopman and Harvey (2003), the weights w (α ) are used to calculate the j t|t estimatorofthestatevectorbasedoninformationavailableasoftimetandcan therefore be used to compute the contribution of variable yi in forecasting the j factor x at time t: t−1 (cid:88) x = w (α )y . (4) t|t j t|t j j=1 As in the previous section, y can contain vectors of monthly or quarterly series t (yM,yQ). Each series is indicated by yi. w is the vector of weights at time t t t j referring to the monthly and quarterly series. I consider the real-time release schedule of each real activity series yi. For example,ifIwanttocalculatethefactorforthemonthofMarch2012,informationaboutthatmonthwillbereleasedgradually. IntheUnitedStates,theISM indexwillbethefirstseriestobereleased, mostlikelyfollowedbyemployment, retail sales, industrial production, and personal income. The advance reading of GDP for the first quarter (i.e. the one which includes January) will be released with an average delay of 29 days from the end of the quarter. Based on this real-time schedule, I can recursively compute the underlying unobserved factor at time t based on the data availability until day t, that is x . Equation t|t (4) displays the factor at time t as a weighted average of the data y released 9

between day 1 and t. The weights implicitly display a time decay feature with more recent data exhibiting higher importance in determining the factor. Foreachdataseriesincludediny,sayyi,thereexistatimeseriesofweights wi, so that cumulative forecast weights can be computed as in Banbura and j Ru¨nstler (2010) t (cid:88) wi = wi. (5) cum j j=1 Forecast weights do not depend on time t, but depend on the forecast horizon and the real-time release pattern of the data. In this paper, I abstract from data revisions. An alternative to using the forecast weights as outlined above, would be to use the weights as described in Banbura and Modugno (2014). In this case, the weights would have a different interpretation, as they would represent the contribution of the news releases to the factor revision from period t to t+1. The Banbura and Modugno (2014) weights are represented by the b in: ν+1,j J (cid:88)ν+1 E[xi|Ω ]−E[xi|Ω ]= b (y −E[yi|Ω ]) (6) t ν+1 t ν ν+1,j t t ν j=1 where E[xi|Ω ]−E[xi|Ω ] represents the revision to the factor implied by t ν+1 t ν the new data release, (y −E[yi|Ω ]) is the news surprise, and Ω and Ω are t t ν ν ν+1 two consecutive data vintages with Ω ⊂ Ω . In the Banbura and Modugno ν ν+1 (2014) framework, E[yi|Ω ] is the model implied expectation of the variable y, t ν while in my framework E[yi|Ω ] would be the Bloomberg expectation for the t ν macro variable y. The advantage of their set-up is that the weights represents the impact of the news release of a variable y on the underlying factor forecast, ratherthantheimportanceoftheunderlyingseriesy indeterminingthefactor. The drawback, however, is that the weight b is practically the Kalman gain and as such, this set-up does not provide me with a time series of the weights similar to what I have in my framework. A way to overcome this issue could be toapplysomearbitrarytimedecayfeaturesimilartowhatappliedbyCitigroup toconstructtheso-called“CitigroupEconomicSurpriseIndexes.”Theseindexes are defined as weighted historical standard deviations of data surprises where theweightsofeconomicindicatorsarederivedfromtheannouncement’simpact thatthesedatasurpriseshaveonforeignexchangemarketstowhichasubjective decay function is applied. 10

3.2. The Surprise Index Iconstructthesurpriseindexstartingfromequation(4). Withtheideathat forecastweightsrepresenttheimportanceoftheseriesindeterminingtheunderlyingunobservablefactor,Iusethosesameweightstocombinethestandardized surprises so that the surprise index S at time t is: t (cid:88) S = w s (7) t j j j=1 where s =(sM,sQ)(cid:48) contains the vectors of the standardized surprise si correj t t spondingtoeachdataseriesyi.12 Intheapplication,Iconstructtheunderlying series that feed into the factor so that a higher (lower) number means that the economy is doing better (worse). Likewise, I construct each surprise such that a positive surprise means good (bad) news for the economy. This implies that the weights should be positive. The surprise indexes are daily: every time new information becomes available, i.e. newdataarereleased, thesurpriseindexgetsupdated. Ifthereareno new data, the index is equal by construction to its value on the previous day. Of course, more data releases imply that the surprise index gets updated more frequently. 3.3. The Uncertainty Index Theuncertaintyindexiscomputedstartingfromequation(4)andaveraging squared surprises (cid:118) (cid:117) t (cid:117)(cid:88) U t =(cid:116) w j s2 j . (8) j=1 Thelinkwithrealizedvolatilityisstraightforward. Justlikerealizedvolatility is computed as the square root of the average of squared returns, RV = n (cid:113) 1 (cid:80)n ret2, the uncertainty index is computed as the square root of the n t=1 t weighted average of the squared surprises.13 The weights are not simply 1/n 12Because s and w are vectors, I am practically aggregating over variables (through the productofsandw)andovertime(with(cid:80)t ). j=1 (cid:113) 13Realized volatility is more precisely defined as vol = n 1 (cid:80)ret2 i − (cid:0) n 1 (cid:80)reti (cid:1)2 but becausethesecondterm,theaveragereturn,tendstobezeroitisfrequentlydropped. Similarly, we abstract from using the second term, (cid:16)(cid:80)t j=1 wjsj (cid:17)2 in the definition of the uncertainty index. Inpractice,thistermisveryclosetozero. 11

but are time varying. Moreover, unlike the volatility which is computed on one instrument at a time using the history from t=1,...,n, the uncertainty index is computed across different instruments/surprises as well as across time. As mentioned in the introduction, these surprise and uncertainty indexes are ex-post, realized measures. Moreover, these indexes measure how optimistic / pessimistic or uncertain agents are about recent economic conditions. Bloombergforecastsareconstructedinsuchawaythatcontributorscansubmit and continuously revise their forecasts until one hour before the data release. The forecasts that I use are screen-shots of the latest submitted forecasts. For example, if we consider nonfarm payroll, a contributor can submit her forecast until7:30amETofthefirstFridayofthemonthforthereleaseofnonfarmpayrollreferringtothepreviousmonth. Inthissense,thesemeasuresarebackward lookingmeasuresastheyusetoday’sbestguess(forecast)aboutthestateofthe economyintherecentpast. BecausetheBloombergforecastsrefertothelatest macroeconomic statistics only, it is not possible to compute these measures for differenthorizons, sayt+1,t+2,...Infact, themacroeconomicannouncements analyzed in this paper are all released with a reporting lag, meaning that they are announced after the end of the period they refer to. Practically, this uncertainty measure can even be considered as a nowcasting/backcasting exercise in that it uses weighed forecast errors from the recent past. Similarly to the surprise indexes, the uncertainty indexes are also daily in that they get updated every time new information become available. 4. Estimation The construction of the indexes requires three steps: (i) estimation of the state space model, (ii) determination of the weights w as defined in equation (4) and j (iii) construction of the indexes as for equations (7) and (8). For step (i), the estimation of the model described in the online Appendix A and B requires estimation of the parameters θ = {µ,Z,T,Σ}. The missing data pattern complicates the estimation of the model. Missing data occur both becausethedataareatdifferentfrequenciesandbecauseindicatorsarereleased atdifferenttimesaftertheendofthereferenceperiod(raggededge). Anumber of papers have dealt with different frequencies and missing observations either 12

withinaKalmanfilterframework(seeamongothersAruobaetal.(2009),Giannone et al. (2008), and Banbura and Modugno (2014)) or within a mixed data sampling (MIDAS) regression framework (Andreou et al. (2011)). I estimate the parameters by maximum likelihood implemented by the Expectation Maximization (EM) algorithm as proposed by Doz et al. (2012) and extended by Banbura and Modugno (2014) to deal with missing observations and idiosyncraticdynamics.14 TheEMalgorithmiteratesovertwosteps: intheexpectation step,thelog-likelihoodconditionalonthedataiscalculatedusingtheestimated parameters from the previous iteration; in the maximization step, the parameters are re-estimated by maximizing the expected log-likelihood with respect to θ. Following Doz et al. (2011) and Doz et al. (2012), the initial parameters θ(0) are obtained through principal components and the iteration between the two steps is stopped when the increase in likelihood between two steps is small. In step (ii), once the parameters θ are estimated, the weights can be computed by running the algorithm defined in Koopman and Harvey (2003) to get the smoothed weights. The history of weights w (α ) for j = 1,...,t is comj t|t puted in real time for any t based on the information available up until that time. Finally,instep(iii),thesurpriseanduncertaintyindexesarecomputedbased on (7) and (8). Eachcountryisestimatedseparately. Theestimationoftheunderlyingbusiness condition index is based on the longest common sample across countries (1980-2012), except for the euro area for which not enough indicators are availablebefore1985. TheKalmanfilteristhenrunbasedontheestimatedparametersinarealtimeframework(i.e. basedondatathatarereleasedsequentially), and steps (ii) and (iii) are repeated to get the smoothed weight matrix and the real-time surprise and uncertainty indexes for each day from May 15, 2003 to September 30, 2012.15 Step (i) is run over the entire sample, unlike steps (ii) and (iii), because for countries in which data series become available later in the sample estimates are not accurate at first.16 For the United States, where therearenoissuesofdataavailability, therearenosignificantdifferencesinthe 14IthankBanbura,GiannoneandReichlinforsharingtheirEMcodes. 15The surprise index is computed on a shorter sample due to the limited availability of expectationdataforallthecountries. 16The underlying real activity factor is estimated on the full sample to avoid parameter instability problems due to the fact that, for some of the countries, some macroeconomic releasesbecomeavailablelaterinthesample(namelyretailsalesandPMIseries). 13

surprise indexes constructed according to the two methodologies.17 5. Results Here I discuss the results following the steps described in the estimation section. 5.1. Real Activity Indexes The real activity indexes that I estimate based on the indicators described above are displayed in figure 1. As mentioned, I use a longer history for the estimation of these factors in order to have more reliable estimates. The figure shows the latest factors, which include information as of March 31, 2016, for theUnitedStates,theEuroArea,theUnitedKingdom,Canada,Japan,andan aggregate of the five countries. The average value of each index is zero by construction. Therefore, a value of zero is interpreted as average economic activity for that country, whereas progressively bigger positive values indicate progressively better-than-average conditions and progressively more negative values indicate progressively worsethan-averageconditions. Importantly,averageconditionsdifferacrosscountries. For example, a value of zero for Japan corresponds to a number akin to 0.7 percent annual real GDP growth while a value of zero in the United States corresponds to around 2.5 percent annual real GDP growth. The shaded areas in the panels represent official recessions as defined by the NBER, CEPR, and ECRI. The indexes fall sharply during recessions and tend to reach relatively high values during good times, for example the late 1990s. As expected, the U.S.businessconditionindexisverysimilartotheADSindexmaintainedbythe Federal Reserve Bank of Philadelphia, with the difference that the ADS index isdailyandalsoincludesweeklydatasuchasinitialjoblessclaims.Becausethe other countries do not have relevant weekly data, I opted here for a monthly frequency. The last panel shows the aggregate business condition index, which is created by aggregating the other indexes weighing them by each country’s GDP. 17Thatmeans,running(i),(ii)and(iii)inrealtimeversusrunning(i)overtheentiresample, and(ii)and(iii)inrealtimedoesnotgivesignificantdifferencesfortheUnitedStates. 14

5.2. Weights Togaugetheimportanceofthevariousindicatorsinconstructingthesurprise and uncertainty indexes, I consider two different standpoints in analyzing the weights: (i) I construct the cumulative weights as in equation (5) and (ii) I analyze, at each time t, the vector of t×1 weights, wj, that are multiplied by t the announcements to get the time t surprise index based on equation (7). To be clear, for t=(cid:101)t, the variable w that represents the weights in equation (7)isamatrixofdimension(cid:101)t×MQwhichcontainsthoseweightsappliedtoall the announcements available up to time (cid:101)t that are used in the construction of theindex. Thesumoftheseweightsovertimerepresentsthecumulativeweight for indicator i at time (cid:101)t, that is w c i um = (cid:80)(cid:101)t j=1 w j i. Averagecumulativeweightscomputedoverthe2003-2016sampleshowthat employment (or unemployment) and industrial production have the highest value in the United States, the Euro Area, and in the United Kingdom. In Canada, most of the weight is concentrated on employment. In Japan, industrial production is the most important series followed by unemployment and retail sales.18 Cumulative weights, however, are not constant over time and therefore looking at their mean is not enough. They are affected by the pattern of missing observations due to the different release schedules of the underlying indicators(raggededge). Figure2showstheevolutionofthecumulativeforecast weightswi foreachindicatoroverthefirstquarterof2012. Eachpanelinthe cum figuredisplaystheweightsforaspecificcountry. Aclearpatternstandsout: as soonasnewinformationaboutanindicatorbecomesavailable,thecontribution of that particular indicator increases. So, for example, the weight of the U.S. nonfarm payroll series (NFP), represented by the green line in the top leftmost panel, increases on January 6, February 3, and March 9 (solid vertical lines) when the December, January and February figures are announced. Until the IP numbers are released (dotted vertical lines), nonfarm payroll has the biggest weight. With the release of the IP figures, the weight for IP (red line) increases and becomes the highest of all. However, as additional information about real activity in the United States is released, nonfarm payroll and IP weights start to decline gradually. A similar pattern can be observed in the other countries: as the more timely information becomes available, its weight jumps up and it 18DetailsoftheaveragecumulativeweightsarereportedintableB2intheonlineAppendix. For comparability across countries, the table shows standardized weights so that the sum of allweightsineachcountryisequalto1. 15

declinesasotherindicatorsaresubsequentlyreleased. Intheeuroarea(thetop rightmost panel), unemployment tends to have the highest weight overall, but when IP numbers are released, IP weights become slightly bigger than those of the unemployment data. In the United Kingdom, IP weights are always bigger thananyotherweight. InCanadaunemploymentisconsistentlyandbyfarthe highest weight. Finally, in Japan, the Tankan survey has the highest weight at the beginning of the quarter when it represents the only available information for that quarter, but its weight is immediately overtaken as other information become available and, in particular, as IP numbers are released. Turning to (ii), figure 3 shows the weights w when computed on March 31, 2012 for the six months prior to that day.19 The weights in all the countries display a time decay feature. For the United States, nonfarm payroll and IP (the green and red bars) have the highest weight for the month of February based on information as of March 31, 2012. Interestingly, IP weights are more persistent than the others, suggesting that past IP information continues to be importantwhereasthenonfarmpayrollinformationvalueislimitedtothelatest available month. Because no data about March are released as of March 31, all the weights are zero for the month of March. Weights are close to zero for all indicators after about six months. Of note, the time decay feature implies that an increase in the index might be due to a smaller weight given to an old negative surprise or to a new positive surprise. The Euro Area represents an interesting case because as of March 31, 2012, flash euro-area PMI numbers for February and March are available, whereas any other real activity information refers to January. While past PMI numbers haveaverysmallweight,theFebruaryandMarchPMIfigureshavearelatively high weight. Once more, the weights for IP are the slowest to decline, and the last available unemployment data displays the highest weight. The United Kingdom seems to have the slowest time decay in its weights comparedtotheothercountries. InCanada,theemploymentweightsdominate every other weight. Japan displays the quickest time decay with weights reaching practically zero already after only four months. Unlike the other countries, unemployment does not have the highest weight. These weights are computed based on the available information as of March 31, 2012. Of course, the pattern would be different if the weights were to be 19Theideaisthatwi representsthebarsinfigure3,whilewi representthelinesinfigure j cum 2. 16

computed on another day when different information was available. 5.3. Surprise Indexes The news surprise indexes for the United States, the Euro area, the United Kingdom, Canada, Japan, and the aggregate of the five countries are displayed in figure 4 (solid lines).20 A positive (negative) reading of the surprise index suggests that economic releases have on balance been higher (lower) than consensus, meaning that agents were ex-post more pessimistic (optimistic) about theeconomy. Apositivenumberdoesnotmeantheeconomyisdoingwellonany ordinary measure, but merely that economic forecasts were overly pessimistic. The surprise index reaches its lowest value during the global financial crisis of 2008-2009 in most countries. This suggests that, as the crisis was unfolding, agents were less pessimistic about its possible outcome and its impact on the real economy, while the actual data turned out to depict a grimmer picture of the stance of economic activity around the globe. The euro-area surprise index dropped sharply in March 2012. As agents became more optimistic on a resolution of the European debt crisis with the bond exchange taking place in Greece, real activity indicators for 2012 that were released in March were disappointing. The January unemployment rate, released on March 1, was 10.70 percent versus an expectation of 10.40 percent. The February and March euro-area PMIs released on February 22 and March 22 were 49.70 and 48.70 respectively, versus expected values of 50.50 and 49.60, respectively. Finally, based on data released on March 14, euro-area industrial production increased 0.2 percent from December 2011 to January 2012 versus an expectation of a 0.5 increase. Interestingly, the U.K. index dropped sharply on January 25, 2011 when a very disappointing Q4 GDP for 2010 was released (-0.5 percent versus an expectation of +0.5 percent). Although subsequent data helped the index to move higher, it continued to be depressed until the second half of 2011. Agents reportedlyattributedtheslowdowntoaseriesoftemporaryfactors(suchasbad weather, the Japanese earthquake, and the royal wedding) that were believed to be short-lived. The transitory nature of these events most probably made agents mark up their economic outlook, but, as a series of temporary factors occurred, these expectation were always disappointed. 20Theindexescontinuetobeupdateddailyandareavailablefromtheauthoruponrequest. 17

TheJapanesesurpriseindexdroppedsharplyonApril27,2011astheactual number for IP turned out to be a lot lower than expected following the March 2011 earthquake: IP decreased 15.30 percent between February and March versus the expectation of a 10.60 percent decrease. Ontheotherhand,therearealsoseveralinstanceswherethesurpriseindexes are positive, especially coming out of the recession in the United States, the United Kingdom, and Canada. More generally, the surprise indexes seem to be autocorrelated. Part of this feature comes from the fact that old surprises continue to receive a positive weight for some time after their release. Except for Canada, the surprise indexes are on average slightly negative, with a more negative value during recessionssuggestingthat,intheperiodconsidered,agentswereonaverageoverly optimistic about the state of the economy. Forcomparison,thedottedlinesinfigure4showtheCitiEconomicSurprise Indexes (CESI). Although CESIs also measure economic news, they are constructed based on a different methodology. CESIs are defined as weighted historical standard deviations of data surprises (actual releases versus Bloomberg median survey) and are calculated daily in a rolling three-month window. The weightsoftheeconomicindicatorsarederivedfromrelativehigh-frequencyspot foreign exchange impacts of 1 standard deviation data surprises adjusted to include a time decay feature so as to replicate the limited memory of markets. Because the index constructed in this paper does not rely on the impact that macroeconomic surprises have on asset prices, it represents a more objective measure of deviation from consensus expectations. Although the two indexes follow very similar patterns for all the countries, they also present some differences because both the set of indicators and the weights are different. For example, the euro-area surprise index tends to lag the CESI especially during the shaded area which represents the 2008-2009 recession. 5.4. Uncertainty Indexes The uncertainty indexes for the United States, the Euro area, the United Kingdom, Canada, Japan and the aggregate of the five countries are displayed in figure 5 (solid lines). These indexes measure how uncertain agents are about realized real activity conditions. A greater (smaller) reading of the uncertainty indexsuggeststhatagentshaveonbalancebeenmore(less)uncertainaboutthe stateofthecurrenteconomy. Theindexestendtobeelevatedduringrecessions, although there are other episodes when the indexes spike up. In the United 18

States,economicuncertaintywasalsorelativelyhighin2004andabigjumpwas observedattheendof2005andin2012. Theeuro-areauncertaintyindexreaches its highest values just before and after the 2008-2009 recession, suggesting that agents were more uncertain about the economy as the euro-zone was entering and exiting the recession. Increased macro uncertainty characterized also the beginningof2010,whentheGreece“problem”startedtoemerge,andtheperiod between the end of 2011 and the start of 2012. Uncertainty in the United Kingdom has been particularly elevated since early 2009, when compared to its value in the first part of the sample. Canada has experienced several episodes of elevated economic uncertainty, whereas in Japan, the period after the March 2011 earthquake was by far the one with the highest uncertainty regarding the state of the Japanese economy. Interestingly, higher volatility is associated with negative surprises. The correlation between the surprise index and the uncertainty index tends to be stronger when the surprise index is negative. The dotted lines in the panels show stock market implied volatilities in the United States, Euro Area, United Kingdom, Canada, and Japan as represented by the VIX, VSTOXX, VTFSE, VIXC and VXJ. The dashed lines display the stock market realized volatilities for the respective countries. Notably, especially in the latter part of the sample, the uncertainty index and the VIX look somewhat similar, whereas the uncertainty index of the euro area differs from the VSTOXX.21 The two measures (implied volatility and uncertainty index) are constructed in completely independent ways. Implied volatility, a forwardlooking measure, is computed from option prices. The uncertainty index, a historical measure, is calculated from current and past macroeconomic news surprises. The former is a wider measure that combines information about risk aversion and future stock market volatility, and to the extent that these two movewithnewssurprises,theVIXalsocontainsinformationaboutcurrentand future economic uncertainty. On the other hand, the uncertainty index presented here is a clean measure of agents’ uncertainty about the current state of the economy. In the analysis that follows, I will decompose the VIX into stock market uncertainty and variance risk premium, following Bakaert et al. (2013), to use the part of the VIX that is most comparable to uncertainty. 21TableB3intheonlineAppendixdisplaysthecorrelationbetweentheuncertaintymeasure andtheimpliedandrealizedvolatilitiesforeachcountry. 19

6. Applications In this section, I present a couple of applications for the surprise and uncertainty indexes. In the first application, the surprise index is shown to preserve thepropertiesoftheunderlyingmacroseriesinaffectingassetpricesinreplicating the regressions shown in table 2. Combining several macro series into one, the surprise index has the advantage of being potentially easier to use and very parsimonious. In light of this, Demiralp et al. (2013) make use of it as a control variable when investigating the effects of political commentaries on policy rate decisions and policy expectations in the United States and the Euro Area, and find it to be a significant determinant of policy expectations. Similarly, Brunetti et al. (2013) employ it as a control variable in studying the impact of speculation activity in the crude oil market. In the second application, the U.S. uncertainty index is compared to other uncertainty measures commonly used in the literature. The uncertainty index has a negative impact on real-activity series. Papers like Bloom (2009), Baker et al. (2015), and Bachmann et al. (2013) have documented a similar analysis withdifferentmeasuresofuncertainty. Ifindthat,intheUnitedStatesoverthe last decade, when uncertainty is strictly related to the state of the economy as measured by real activity, it has a potentially milder impact on macro activity thanwhentheuncertaintyisrelatedtoboththemacroandthefinancialsectors as measured by the VIX. 6.1. Surprise Indexes and News Impact on Foreign Exchanges As shown in section 2, macroeconomic news announcements affect asset prices. The surprise index presented in this paper represents a nice summary measure that can be used to parsimoniously control for news announcement surprises in more general models. Table3presentstheresultsofasetofregressionswheretheeuro/$,GBP/$, CAD/$, and JPY/$ exchange rate returns are regressed on the U.S. surprise indexandtherespectiveforeignsurpriseindex,i.e. theeuro/$returnisregressed on the U.S surprise index and the euro-area surprise index, the GBP/$ return is regressed on the U.S surprise index and the U.K. surprise index, etc. I cover approximately the sample period for which the surprise indexes are available (July 2003 to March 2016).22 As shown in the table, the surprise indexes tend 22For comparison with the exercise in table 2, I run the regression only on days in which 20

to have the right sign and be significant: a positive change in the U.S. surprise index (i.e. the U.S. economy doing better than expected) appreciates the U.S. dollar versus the foreign currency, whereas a positive change in the foreign surprise index depreciates the U.S. dollar. 6.2. Uncertainty Measures and the Business Cycle A “true” measure of economic uncertainty does not exist and stock market realized and implied volatilities have been commonly used as proxies for uncertainty. Bloom(2009), forexample,usestheChicagoBoardofOptionExchange VXO index as a proxy for uncertainty.23 More recently, a growing literature hasfocusedonfindingnewmeasuresofmacroeconomicuncertainty. Bachmann etal.(2013)usesurveyexpectationdatatoconstructtime-varyingbusiness-level uncertainty. For Germany and the United States, they construct a measure of uncertainty with forecast disagreement from the IFO Business Climate Survey and the Business Outlook Survey, respectively. Baker et al. (2015) create an economic policy uncertainty (EPU) measure based on the frequency of newspaperreferencestoeconomicpolicyuncertainty,thenumberandsizeofthefederal tax code provisions set to expire in future years, and the disagreement among economic forecasters about policy relevant variables. Leduc and Liu (2012) use ameasureofperceiveduncertaintyofconsumersandbusinessesfromtheThomson Reuters/University of Michigan Surveys of Consumers in the United States and the Confederation of British Industry (CBI) Industrial Trends Survey in the United Kingdom. Bakaert et al. (2013) decompose the VIX into variance riskpremium,ameasureofriskaversion,andstockmarketuncertainty. Jurado et al. (2015) define uncertainty as the variability in the purely unforecastable component of the future value of a variable and measure macro uncertainty as the uncertainty factors common to individual measures of uncertainty across a large number of series. Similarly to Jurado et al. (2015), my measure uses forecast errors, which, however, are not the objective and efficient forecast errors from a model. Instead they are market based forecast errors and as such myuncertaintyindexmeasurestheperceiveduncertaintyaboutthestateofthe therearenewsreleases. ThisimpliesthatIwillhave556,423,443,417,and298observations fortheU.S.,euro-area,U.K.,CanadianandJapanesenews,respectively. 23TheVXOisequivalenttotheVIX seriesthatIuse. TheVIXwaslaunched in1993. In 2003,itsformulawasmodifiedsubstantially. Datafromthenew2003VIXformula,alsoused to reconstruct historical data going back to 1990, is known as the VIX. The data associated with the original and revised VIX formulae is known as VXO. In my sub-sample VIX and VXOcoincide. 21

economy. Agents base decisions on their perceived uncertainty rather than an objective uncertainty that they do not observe. Figure6comparesthereal-activityuncertaintyindexdevelopedhereagainst some of the available other measures of uncertainty for the United States. All measures are de-meaned and standardized for comparison; they are all countercyclical, rising during economic downturns. The correlation of the uncertainty index ranges from about 20 percent between with the Baker, Bloom, and Davis EPU to over 60 percent with the VIX.24 The uncertainty index exceeds 1.65 standard deviations above its mean only few times but the peaks do not always correspond with the peaks of the other series suggesting that these uncertainty measures might indeed carry slightly different information. A growing literature has also focused on analyzing the relationship between real activity and uncertainty, and the latter has been generally found to have a significantroleinfirms’hiringdecisions(employment)andoutput. Toestimate such effects, I estimate a bivariate VAR with log employment and each one of the uncertainty proxies from figure 6, separately. Because of the short data set (monthly data from May 2003 to March 2016), the bivariate VAR represents a parsimonious way to model the joint dynamics between these variables. As shown in Bachmann et al. (2013), the results are robust to estimating a larger VARsimilartoBloom(2009).25 EachVARisestimatedselectingthelaglength based on the Schwarz Information Criterion; employment enters in log levels, while uncertainty measures in levels. Figure 7 shows the recursive impulse responses of employment to a onestandard-deviationuncertaintyshockasmeasuredbythedifferentproxies,where uncertainty is ordered first. The shaded region is the +/- one standard error confidence interval for the real-activity uncertainty shock. Employment decreases after an uncertainty shock, no matter which uncertainty proxy is used. However,howquicklyandhowdeeplyvariesacrossmeasures,withshockstothe VIXortheBakaertetal.(2013)stockmarketuncertaintybeingthemostquick to materialize and the ones with the deepest trough. Shocks to the macroeconomic uncertainty index, to the Baker et al. (2015) EPU measure and the 24ThesmallestcorrelationisbetweenBachmann,Elstner,andSimsandBaker,Bloom,and Davis measures (about 10 percent). The highest correlations are between the VIX and the Bakaertuncertainty/varianceriskpremiumdecompositionoftheVIX(about85-90percent), followedbythecorrelationbetweentheVIXbetweenBaker,Bloom,andDavisEPUmeasure (about70percent). 25Giventheshortdataset,IonlyestimatethebivariateVAR. 22

Bachmann et al. (2013) dispersion measure elicit a progressively lower impact on employment over this period. This result suggests that when uncertainty is strictly related to real activity, it has potentially milder impact on economic activity. Just flipping the argument, when uncertainty is more generally related to economic as well as financial conditions as measured by the VIX or the Bakaert et al. (2013) measure of stock market uncertainty, its impact on real-activity variables appears to be stronger.26 This finding supports recent work by Caldara et al. (2013) which finds that the financial channel is key in the transmission of uncertainty shocks. Although I do not explicitly introduce a financial channel, using the real-activity uncertainty index, the VIX and the Bakaert stock market uncertainty measure allows me to distinguish between purely macro versus the more general macro and financial uncertainty. Interestingly, the variance risk premium (not shown) does not seem to play a very importantrole.27 AnanalysisofthefractionoftheVARforecasterrorvariance of employment that is attributable to innovations in each of the uncertainty series over different forecast horizons confirms the results: the VIX and the Bakaert stock market uncertainty decomposition explain about 2-3 times the share of the forecast error of employment compared to the real-activity uncertainty index. For robustness, some alternative specifications are considered. The result justdescribedholdstruewithothermeasuresofrealactivity, suchasindustrial productionorunemploymentrate. Althoughasimilarcomparisonisnotshown for the other countries, the negative impact of an uncertainty shock on employment is generally significant across countries. As a robustness check, I estimate generalized impulse responses from Pesaran and Shin (1998) which do not depend on the ordering of the variables and the results remain quite consistent across uncertainty proxies and variables. 7. Summary and Concluding Remarks The goal of this paper is to construct measures of (i) real-time economic news and their deviation from consensus expectations and (ii) real-time uncertainty about the state of the economy. I view this paper as a “complement” 26Figure A1 shows the confidence intervals for the real-activity uncertainty index and the VIX. 27The variance risk premium, computed as in Bakaert et al. (2013), elicits an impulse responsetoemploymentsimilartothatofBakeretal.(2015)EPU. 23

to the Aruoba et al. (2009) business condition index updated on a daily basis by the Federal Reserve Bank of Philadelphia. While the ADS index is a real time measurement of the state of the economy, the surprise index presented in this paper measures agents’ optimism or pessimism about the economy by combining macroeconomic news surprises, and the uncertainty index measures agents’uncertaintyaboutthecurrentstateoftheeconomy. Thispaperisalsoa “complement”tootherpapersthatdevelopuncertaintymeasuresinthatitonly measures perceived uncertainty about the state of the economy and as such is mostly linked to Bachmann et al. (2013). I look forward to a variety of variations and extensions of this basic theme, including but not limited to: • constructing indexes for nominal variables to gauge optimism/pessimism about inflation stance • incorporating additional indicators and surprises for each country to construct a summary measure of real and nominal variables • extending the framework to include U.S. macro surprises into foreign economiesframeworkstoexploitthecorrelation/causationacrossbusiness cycles • including vintages of data so that the indexes change not only when new information is released but also when past information is revised • expanding the dataset to construct indexes with a longer history • analyzing in more depth the impact of different types of uncertainty. References Andersen, T. G., Bollerslev, T., Diebold, F. X., Vega, C., 2003. Micro effects of macro announcements: Real-time price discovery in foreign exchange. American Economic Review 93, 38–62. Andersen, T. G., Bollerslev, T., Diebold, F. X., Vega, C., 2007. Real-time price discovery in stock. Journal of International Economics 73, 251–27. Andreou, E., Kourtellos, A., Ghysels, E., 2011. Forecasting with mixedfrequency data. Oxford Handbook of Economic Forecasting, Chapter 8. 24

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Table1: Forecastefficiencyregressionresults(July2003-March2016) si =αi+βiyi,f +ui t t t Country Series Name α β F pvalue United States GDP -0.05 -0.02 0.65 0.53 IP -0.09∗∗∗ 0.27∗∗∗ 12.55 0.00 Employment -12.70∗∗ -0.01 2.87 0.06 RetailSales -0.05 0.18∗∗∗ 5.15 0.01 ISM 1.12 -0.02 0.67 0.51 PersonalIncome 0.04∗ -0.11∗∗∗ 4.17 0.02 Euro area GDP -0.02 0.11∗∗∗ 3.31 0.04 IP -0.08∗ -0.11∗∗ 3.81 0.02 Unemployment 0.10∗∗ -0.01∗∗ 3.13 0.05 RetailSales -0.07 -0.13∗ 1.93 0.15 PMI 1.03 -0.02 0.42 0.66 United Kingdom GDP -0.14 ∗∗∗ 0.26∗∗∗ 6.58 0.00 IP -0.21∗∗∗ -0.01∗∗∗ 9.22 0.00 Unemployment 0.05∗∗∗ -0.02∗∗∗ 7.73 0.00 RetailSales 0.20 ∗∗∗ 0.11∗∗∗ 5.88 0.00 PMI 3.28∗ -0.06∗∗ 1.93 0.15 Canada GDP 0.06 -0.01 0.23 0.80 IP -0.06∗∗∗ 0.06∗∗∗ 7.00 0.00 Employment 5.17 0.12∗∗∗ 2.98 0.05 RetailSales -0.07 0.35 ∗∗∗ 5.78 0.00 IveySurvey 19.95∗∗∗ -0.34∗∗∗ 7.23 0.00 Japan GDP 0.01 -0.05 0.25 0.78 IP -0.42∗∗∗ 0.04∗∗∗ 10.66 0.00 Unemployment 0.17∗ -0.05∗∗∗ 4.57 0.01 RetailSales 0.04 0.21 ∗∗∗ 6.02 0.00 Tankan 0.16 0.01 0.27 0.76 *10percentsignificance,**5percentsignificance,and***1percentsignificance. 27

Table2: Resultsofunivariateregressionsinwhichexchangeratereturnsareregressedoneach individualmacroeconomicnewsannouncementsurprise(July2003-March2016) dlog(FX )=α+β∗si+ε t t t Euro/$ GBP/$ CAD/$ JPY/$ Beta R2 Beta R2 Beta R2 Beta R2 US IP 0.029 0.003 0.021 0.001 0.043∗∗ 0.005 -0.034 0.003 Employment 0.271∗∗∗ 0.125 0.214∗∗∗ 0.130 0.002 0.000 0.342∗∗∗ 0.214 Retail sales 0.063 0.013 0.100∗∗∗ 0.030 -0.062 0.010 0.198∗∗∗ 0.099 Personal income 0.009 0.000 -0.040 0.004 0.020 0.001 -0.038 0.004 PMI 0.050 0.006 0.035 0.001 -0.013 0.000 0.169∗∗∗ 0.067 GDP 0.219∗∗∗ 0.097 0.017 0.000 0.084∗∗∗ 0.011 0.059 0.005 Foreign IP -0.066∗∗∗ 0.023 -0.147∗∗∗ 0.059 -0.028 0.005 0.077 0.023 Empl/unempl 0.064 0.066 -0.039 0.006 -0.252∗∗∗ -0.125 0.009 0.001 Retail sales -0.106 0.023 -0.148∗∗∗ 0.069 -0.013 0.071 -0.013 0.004 PMI/Ivey/Tankan 0.005 0.000 -0.238∗∗∗ 0.110 -0.064 0.006 0.020 0.001 GDP -0.113∗∗ 0.038 -0.371∗∗∗ 0.300 -0.090 0.025 -0.005 0.000 *10percent,**5percent,and***1percentsignificancewithNewey-Weststandarderrors. Table 3: Results of univariate regressions in which exchange rate returns are regressed on thechangeinthesurpriseindex(July2003-March2016) dlog(FX )=α+β∗d(S )+ε t t t Euro/$ GBP/$ CAD/$ JPY/$ β R2 β R2 β R2 β R2 US surprise index 0.418∗∗∗ 0.032 0.303∗∗∗ 0.019 -0.061 0.000 0.482∗∗∗ 0.037 Foreign surprise index -0.358∗∗∗ 0.016 -0.424 0.005 -0.830∗∗∗ 0.048 0.114 0.000 *10percent,**5percent,and***1percentsignificancewithNewey-Weststandarderrors. 28

Figure1: RealActivityIndexes(factors)fortheUnitedStates,EuroArea,UnitedKingdom, Canada, Japan, and aggregate of the five countries, as of March 31, 2016. The average valueofeachindexiszerobyconstruction. Avalueofzeroisinterpretedasaverageeconomic activityforthatcountry,whereasprogressivelybigger(morenegative)positivevaluesindicate progressivelybetter-than-average(worse-than-average)conditions. United States 0 = average economic activity 4 4 3 3 2 2 1 1 0 0 −1 −1 −2 −2 −3 −3 −4 −4 −5 −5 1980 1986 1992 1998 2004 2010 2016 Euro Area 0 = average economic activity 2 2 1 1 0 0 −1 −1 −2 −2 −3 −3 −4 −4 −5 −5 −6 −6 1985 1990 1995 2000 2005 2010 2015 United Kingdom 0 = average economic activity 2 2 1 1 0 0 −1 −1 −2 −2 −3 −3 −4 −4 1980 1986 1992 1998 2004 2010 2016 Canada 0 = average economic activity 2 2 1 1 0 0 −1 −1 −2 −2 −3 −3 1980 1986 1992 1998 2004 2010 2016 Japan 0 = average economic activity 3 3 2 2 1 1 0 0 −1 −1 −2 −2 −3 −3 −4 −4 −5 −5 1980 1986 1992 1998 2004 2010 2016 Aggregate 0 = average economic activity 3 3 2 2 1 1 0 0 −1 −1 −2 −2 −3 −3 −4 −4 −5 −5 1980 1986 1992 1998 2004 2010 2016 29

Figure 2: Average cumulative weights for the United States, Euro Area, United Kingdom, Canada,andJapanoverthefirstquarterof2012. United States 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Jan 01 Jan 18 Feb 05 Feb 23 Mar 12 Mar 30 Euro Area 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Jan 01 Jan 18 Feb 05 Feb 23 Mar 12 Mar 30 United Kingdom 0.5 0.4 0.3 0.2 0.1 0.0 Jan 01 Jan 18 Feb 05 Feb 23 Mar 12 Mar 30 Canada 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 Jan 01 Jan 18 Feb 05 Feb 23 Mar 12 Mar 30 Japan 0.40 0.35 IP, Monthly GDP 0.30 Employment, unemployment Surveys (ISM, PMI, IVEY, Tankan) 0.25 Retail Sales GDP 0.20 Personal Income 0.15 0.10 0.05 0.00 Jan 01 Jan 18 Feb 05 Feb 23 Mar 12 Mar 30 l 30

Figure 3: Time series of weights for each indicator over the 6-month period October 2011- March2012,basedontheinformationavailableasofMarch31,2012. United States Euro Area 0.35 0.35 0.30 0.30 0.25 0.25 0.20 0.20 0.15 0.15 0.10 0.10 0.05 0.05 0.00 0.00 Oct Nov Dec Jan Feb Mar Oct Nov Dec Jan Feb Mar 2011 2012 2011 2012 United Kingdom Canada 0.20 0.40 0.35 0.15 0.30 0.25 0.10 0.20 0.15 0.05 0.10 0.05 0.00 0.00 Oct Nov Dec Jan Feb Mar Oct Nov Dec Jan Feb Mar 2011 2012 2011 2012 Japan 0.25 0.20 IP, Monthly GDP Employment, unemployment 0.15 Surveys (ISM, PMI, IVEY, Tankan) Retail Sales GDP 0.10 Personal Income 0.05 0.00 Oct Nov Dec Jan Feb Mar 2011 2012 l 31

Figure4: ThesolidlinesshowthesurpriseindexesfortheUnitedStates,EuroArea,United Kingdom,Canada,Japan,andtheaggregateofthefivecountries,asofMarch31,2016. The dotted lines show the Citigroup Economic Surprise Indexes for the corresponding country (leftaxis). Apositive(negative)readingofthesurpriseindexsuggeststhateconomicreleases haveonbalancebeenhigher(lower)thanconsensus,meaningthatagentswere ex-post more pessimistic(optimistic)abouttheeconomy. United States 200 3 2 100 1 0 0 −1 −100 −2 −200 −3 2003 2005 2007 2009 2011 2013 2015 100 0 −100 −200 Euro Area 200 2 1 0 −1 −2 2003 2005 2007 2009 2011 2013 2015 United Kingdom 200 2 100 1 0 0 −100 −1 −200 −2 2003 2005 2007 2009 2011 2013 2015 100 0 −100 −200 −300 Canada 200 2 1 0 −1 −2 −3 2003 2005 2007 2009 2011 2013 2015 Japan 100 1 50 0.5 0 0.0 −50 −0.5 −100 −1.0 2003 2005 2007 2009 2011 2013 2015 80 60 40 20 0 −20 −40 −60 −80 −100 −120 Aggregate 100 0.4 0.2 0.0 −0.2 −0.4 −0.6 −0.8 −1.0 2003 2005 2007 2009 2011 2013 2015 32

Figure5: ThesolidlinesshowtheuncertaintyindexesfortheUnitedStates,EuroArea,United Kingdom,Canada,Japan,andtheaggregateofthefivecountries,asofMarch31,2016. The dottedanddashedlinesshowstockmarketimpliedandrealizedvolatilitiesrespectively(left axis). United States 100 4 90 3.5 80 3.0 70 60 2.5 50 2.0 40 1.5 30 1.0 20 10 0.5 0 0.0 2003 2005 2007 2009 2011 2013 2015 80 70 60 50 40 30 20 10 0 Euro Area 90 2.5 2.0 1.5 1.0 0.5 0.0 2003 2005 2007 2009 2011 2013 2015 United Kingdom 90 2.5 80 70 2.0 60 1.5 50 40 1.0 30 20 0.5 10 0 0.0 2003 2005 2007 2009 2011 2013 2015 60 50 40 30 20 10 0 Canada 70 2 1.5 1.0 0.5 0.0 2003 2005 2007 2009 2011 2013 2015 Japan 100 2.5 90 80 2.0 70 60 1.5 50 40 1.0 30 20 0.5 10 0 0.0 2003 2005 2007 2009 2011 2013 2015 70 60 50 40 30 20 10 0 Aggregate 80 1.8 1.6 1.4 1.2 1.0 0.8 0.6 2003 2005 2007 2009 2011 2013 2015 33

Figure 6: The solid line represents the uncertainty index which is compared against other commonproxiesforuncertainty,namelyBakaertetal.(2013)stockmarketuncertainty,Baker et al. (2015) economic policy uncertainty index, Bachmann et al. (2013) dispersion measure and the VIX. All series are demeaned and standardized. The horizontal line represents the 1.65standarddeviationlimit. 8 VIX Uncertainty Index 6 Bakaert et al Baker et al Bachmann et al 4 2 0 -2 -4 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 34

Figure 7: Employment response to a 1 standard deviation shock in the different uncertainty proxies, namely the uncertainty index, the Bakaert et al. (2013) stock market uncertainty, Baker et al. (2015) economic policy uncertainty index, Bachmann et al. (2013) dispersion measureandtheVIX. .4 VIX Baker et al EPU .2 Bachmann et al Bakaert et al Uncertainty Uncertainty Index .0 -.2 -.4 -.6 -.8 5 10 15 20 25 30 35 40 45 50 55 60 35

Online Material – Appendix A: The Dynamic Factor Model I model the unobserved factor as a VAR process of order p: x = Λx +η , (.1) t+1 t t η ∼ i.i.d.N(0,σ ). (.2) t η The model includes both monthly and quarterly variables. The monthly variables yM follow a single factor model representation of the type: t yM = µM +ZMx +εM (.3) t t t εM = αεM +eM (.4) t t−1 t where x represents the underlying real activity factor, ε is a vector of idt t iosyncratic components, and ZM represent the factor loadings for the monthly variables. ε follows an AR(1) process, as shown in equation (.4), and eM ∼ t t i.i.d.N(0,ΣM). e The quarterly variables yQ follow a similar factor model representation: t yQ = µQ+ZQx +εQ (.5) t t t εQ = ρεQ +eQ (.6) t t−1 t with eQ ∼ i.i.d.N(0,ΣQ). Quarterly variables in the model are GDPs for all t e countries and the Japanese Tankan survey. I follow Mariano and Murasawa (2003) in the way I incorporate quarterly GDP into the monthly factor model. I define YQ =100log(GDP), then t (cid:40) YQ−YQ if t=3,6,9,12 yQ = t t−3 (.7) t NA otherwise, and using the Mariano and Murasawa (2003) approximation I get that for t=3,6,9,12 YQ−YQ ≈(YM+YM +YM )−(YM +YM +YM )=y +2y +3y +2y +y . t t−3 t t−1 t−2 t−3 t−4 t−5 t t−1 t−2 t−3 t−4 (.8) 1

Based on this I can link the quarterly variables to the monthly factor as yQ = µQ+ZQx +2ZQx +3ZQx +2ZQx +ZQx (.9) t t t t t−1 t t−2 t t−3 t t−4 +εQ+2εQ +3εQ +2εQ +εQ t t−1 t−2 t−3 t−4 Asimilartreatmentcanbeappliedtoanyotherquarterlyseriesinthedataset.1 Stacking monthly and quarterly variables, this model can be easily cast in a state space representation:2 y = µ+Zα (.10) t t α = Tα +u , u ∼i.i.d.N(0,Σ) (.11) t t−1 t t where y = (yM,yQ)(cid:48), µ = (µM,µQ)(cid:48) and the state vector includes both the t t t common factor and the idiosyncratic components: (cid:16) (cid:17)(cid:48) α = x ,x ,x ,x ,x ,εM,εQ,εQ ,εQ ,εQ ,εQ (.12) t t t−1 t−2 t−3 t−4 t t t−1 t−2 t−3 t−4 We define the total number of indicators as nMQ. Of course, the model could be extended to a multiple factor model. Online Material – Appendix B: The State Space Representation We report below the details of the state space representation as specified by equations (.10) and (.11) when the only quarterly variable is GDP: 1The other quarterly series in the dataset is the Japanese Tankan survey. Because it is an index, I do not compute the log difference (growth rate) as for GDP. By defining YQ = t Tankanntandy t Q=Y t Q−Y t Q −3 =Tankannt−Tankannt−3,thesameargumentgoesthrough andequation(.8)holdsexactly. 2DetailsaboutthestatespacerepresentationcanbefoundinappendixB. 2

  x t  x   t−1     x t−2     x   t−3    (cid:34) yM (cid:35) (cid:34) µM (cid:35) (cid:34) ZM 0 0 0 0 I 0 0 0 0 0 (cid:35)  x t−4   t = + nM  εM  y t Q µQ ZQ 2ZQ 3ZQ 2ZQ ZQ 0 1 2 3 2 1    ε t Q    (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) t  yt Z  εQ   t−1    εQ    t−2   εQ   t−3  εQ t−4 (cid:124) (cid:123)(cid:122) (cid:125) αt        x Λ 0 0 0 0 0 0 0 0 0 0 x η t t−1 t  x   1 0 0 0 0 0 0 0 0 0 0  x   0   t−1    t−2            x t−2   0 1 0 0 0 0 0 0 0 0 0  x t−3   0          x   0 0 1 0 0 0 0 0 0 0 0  x   0   t−3    t−4            x t−4   0 0 0 1 0 0 0 0 0 0 0  x t−5   0          εM = 0 0 0 0 0 diag(α ,...,α ) 0 0 0 0 0  εM + eM   t   1 nM  t−1   t     εQ t       0 0 0 0 0 0 α Q 0 0 0 0       εQ t−1       eQ t     εQ   0 0 0 0 0 0 1 0 0 0 0  εQ   0   t−1    t−2      εQ     0 0 0 0 0 0 0 1 0 0 0     εQ     0    t−2    t−3     εQ   0 0 0 0 0 0 0 0 1 0 0  εQ   0   t−3    t−4    εQ 0 0 0 0 0 0 0 0 0 1 0 εQ 0 t−4 t−5 (cid:124) (cid:123)(cid:122) (cid:125) (cid:124) (cid:123)(cid:122) (cid:125) T ut with nMand nQ representing the number of monthly and quarterly variables, (cid:16) (cid:17)(cid:48) (cid:16) (cid:17)(cid:48) (cid:16) (cid:17)(cid:48) εM = ε1M,...,εnM , eM = e1M,...,enM , εQ = ε1Q,...,εnQ and eQ = t t t t t t t t t t (cid:16) (cid:17)(cid:48) e1Q,...,enQ . Because we are considering the case of only one quarterly varit t (cid:16) (cid:17) (cid:16) (cid:17) (cid:16) (cid:17) able, εQ = ε1Q and eQ = e1Q . Also ZM = Z1M,...,ZnM and t t t t 3

  σ ··· 0 η  0   σ 0 0    e1M Var(u t )=Σ=    . . . ΣM . . .    with Σ eM =   0 ... 0  .3  e     σQ  0 0 σ  e  enM 0 ··· 0 (cid:110) (cid:111) Theparameterstobeestimatedareθ = µM,µQ,ZM,ZQ,Λ,α ,...,α ,α ,σ ,σM,...,σM ,σQ . 1 nM Q η e1 enM e 3We use the notation Σ to indicate a variance-covariance matrix and σ to indicate its elements. 4

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TableB2: Averagecumulativeweightsforeachindicatorusedtoconstructthesurpriseindex. Forcomparabilityacrosscountries,weightsarestandardizedsothatthesumofallweightsin eachcountryisequalto1. Theaverageiscomputedovertheentiresample. United Euro United Canada Japan States area Kingdom GDP 0.03 0.07 0.11 0.00 0.01 IP 0.36 0.39 0.46 0.02 0.53 Employment/Unemployment 0.26 0.26 0.27 0.91 0.20 Retail Sales 0.18 0.18 0.11 0.01 0.14 PMI 0.06 0.10 0.05 0.04 0.12 Personal Income 0.10 TableB3: Correlationbetweentheuncertaintymeasureandtheimpliedandrealizedvolatilitiesforeachcountry. Correlation of Uncertainty vs: United Euro United Canada Japan States area Kingdom Implied Volatility 0.52 0.11 0.35 0.32 -0.01 Realized Volatility 0.53 0.11 0.31 0.33 0.06 CorrelationsareallsignificantexceptinthecaseofJapaneseuncertaintyvs. impliedvolatility. 6

FigureA1: +/-onestandarderrorconfidenceintervalforthereal-activityuncertaintyshock andtheVIX .02 .00 -.02 -.04 -.06 -.08 5 10 15 20 25 30 35 40 45 50 55 60 Uncertainty Index VIX 7