The Importance of Updating: Evidence from a Brazilian Nowcasting Model

Finance and Economics Discussion Series Divisions of Research & Statistics and Monetary Affairs Federal Reserve Board, Washington, D.C. The Importance of Updating: Evidence from a Brazilian Nowcasting Model Daniela Bragoli, Luca Metelli, and Michele Modugno 2014-94 NOTE: Staff working papers in the Finance and Economics Discussion Series (FEDS) are preliminary materials circulated to stimulate discussion and critical comment. The analysis and conclusions set forth are those of the authors and do not indicate concurrence by other members of the research staff or the Board of Governors. References in publications to the Finance and Economics Discussion Series (other than acknowledgement) should be cleared with the author(s) to protect the tentative character of these papers.

The Importance of Updating: Evidence from a Brazilian Nowcasting Model Daniela Bragoli1 Luca Metelli2 Michele Modugno3 Abstract: How often should we update predictions for economic activity? Gross domestic product is a quarterly variable disseminated usually a couple of months after the end of the quarter, but many other macroeconomic indicators are released with a higher frequency, and financial markets react very strongly to them. However, most of the professional forecasters, including the IMF, the OECD, and most central banks, tend to update their forecasts of economic activity only two to four times a year. The main exception is the Central Bank of Brazil which is responsible for collecting and publishing a daily survey on GDP and other variables. The aim of this article is to evaluate the forecasting performance of the Central Bank of Brazil Survey and to compare it with the mechanical forecasts based on state-of-the-art nowcasting techniques. Results indicate that institutional forecasts perform as well as model-based forecasts. The latter finding suggests that, on the one hand, judgmental forecasters do not have computational limitations and are able to incorporate very quickly new information in a way that is as efficient as a machine. On the other hand, it confirms what has been found in other studies, namely that a linear time invariant model does a good job and hence that eventual nonlinearities, time variations and soft information (such as weather conditions or government decisions)thatcouldbeincorporatedbyjudgment,donotprovidenewimportantinformation. JELClassification: C33,C53,E37. Keywords: Nowcasting,Updating,DynamicFactorModel. 1Universita` Cattolica,viaNecchi9,29100Milano(Italy),e-mail:daniela.bragoli@unicatt.it 2LondonSchoolofEconomics,LondonWC2A2AE(UK),e-mail:L.Metelli@lse.ac.uk 3FederalReserveBoard,WashingtonD.C.20551(US),e-mail:Michele.Modugno@frb.gov Acknowledgements:WeareindebtedtoDomenicoGiannoneandJonathanWrightfortheirusefulcommentsand twoanonymousreviewersfortheirconstructivesuggestions.WealsowouldliketothankNow-CastingEconomics foradvice,feedback,andaccesstodata.

1 Introduction Monitoring short-term economic developments, in particular real GDP growth, is the instrument through which market participants and policy institutions all over the world make their decisions on how to invest or on how to conduct monetary and fiscal policy. Real GDP growth in many countries, including Brazil, is a quarterly variable that is released by the national statistical office with a delay that could be, at times, significant. In the case of Brazil the delay is two months. In other words, real GDP growth related to the first quarter (January to March)isdisclosedonlyinMay. Given this limitation it is nevertheless reasonable to think that it is possible to learn the current economic condition by monitoring other indicators that are linked to GDP growth and thatarereleasedatahigherfrequency. Newspapers,statisticaloffices,andcentralbankwebsites release daily data (for instance releases on industrial production, on the number of vehicles sold, on the confidence of consumers, etc.) that can be used to produce early estimates of GDP growth. Market participants monitor these data too. Global information services, such as Bloomberg and Forex Factory, report a calendar of data releases that is highly regarded by the markets. Bloomberg and Forex Factory also assign a measure of importance to each release, which reflects the usage by markets. Bloomberg, in addition, conducts a survey and collects forecasts from analysts and economists on each release they report and publishes it the day beforethereleaseisdisseminated. Academia has also moved toward incorporating this more timely information into formal econometric forecasting models. Two seminal papers (Evans, 2005, and Giannone et al., 2006) have modeled, within the same statistical framework, the joint dynamics of GDP and the monthly indicators. According to this literature, it is worth while to update economic predictions often, as the incorporation of the continuous data flow makes the forecasts more and moreaccurate. Professionalforecasters,however,donotpublishshort-termeconomicforecastsfrequently. The Organisation for Economic Co-operation and Development (OECD) and the International Monetary Found (IMF) report their forecast twice a year, many central banks (e.g. Bank of 2

England, Bank of Canada, and the Federal Reserve Open Market Committee) four times a year and, only a few institutions update their forecasts monthly (e.g. Banque de France, Bank of Japan, Bundesbank, the Conference Board). The process through which they revise their forecastsisnotclear. The Central Bank of Brazil (BCB), though, is an exception to this framework. It is, in fact, responsible for the set up of an interesting Market Expectation System, a web interface where financial institutions, consulting firms, and universities report their expectations for various macroeconomicvariablesincludingGDP. Theaimofthispaperistounderstandhowsensibleitisforaninstitution,suchastheBCB, to produce such regular predictions of GDP growth. The aim is to evaluate the forecasting performance of the BCB Survey and to compare it with the mechanical forecasts based on state-of-the-artnowcastingtechniques. Results indicate that market participants’ predictions are well behaved, i.e. as more informationbecomesavailabletheiraccuracyandcorrelationwiththeout-turnincreases. Inaddition,itturnsoutthatinstitutionalforecastsperformaswellasmodel-basedforecasts. The latter result suggests that, on the one hand, judgmental forecasters do not have computationallimitationsandtheyareabletoincorporateveryquicklynewinformationinawaythatis as efficient as a machine. On the other hand, it confirms what has been found in other studies, namely that a linear time invariant model does a good job and hence that eventual non linearities,timevariations,andsoftinformation(suchasweatherconditionsorgovernmentdecisions) that could be incorporated by judgment, do not provide new important information. According to this last result, the often-cited superiority of professional forecasts (see Ang et al., 2007, Clements, 2010, Jansen et al., 2012) turns out to be weak in our sample confirming findings in Giannoneetal. (2006)andLiebermann(2011). Recently, there has been a lot of interest in applying this statistical environment to various economies, including the United States (Lahiri and Monokroussos, 2013), the Euro Area (Angelini et al., 2010; Angelini et al., 2011; Camacho and Perez-Quiros, 2010), France (Barhoumi et al., 2010), Germany (Marcellino and Schumacher, 2010), Ireland (D’Agostino et al., 2008; 3

Liebermann, 2012), the Netherlands (de Winter, 2011), the Czech Republic (Arnostova et al., 2011; Rusna´k, 2013), New Zealand (Matheson, 2010), Norway (Aastveit and Trovik, 2012), Switzerland(Siliverstovs,2012)andforChina(YiuandChow,2010). Forasurvey,seeBan´bura etal. (2012)andBan´buraetal. (2013). In the case of Brazil, Issler and Notini (2013) propose an interpolation method based on state-space models to estimate monthly Brazilian GDP, through the use of coincident indicators. Thismethodologyispartoftotheliteratureoncoincidentindicatorsofeconomicactivity, where an unobserved state of the economy is estimated from a multivariate model. Chauvet (2001) constructs an indicator of Brazilian monthly GDP through the use of a Markov switchingdynamicfactormodel. Inthisarticle,instead,weaimatpurenowcasting,definedastimely estimationofGDP. The rest of the paper is structured as follows. Section 2 describes the structure of the data releasesinBrazil. Section3introducesthemodelandestimationtechnique. Section4describes the BCB survey and the other benchmarks. Section 5 introduces the empirical analysis and commentsontheresults. Section6concludes. 4

2 The Data Set The Brazilian statistical office publishes real GDP growth two months after the end of the quarter. The aim of the statistical model we propose in this paper is to predict GDP before the official figures are published by taking advantage of the information in the flow of economic datareleasesthatprecedethemandupdatingourpredictionwitheachsuccessivedatarelease. We include in our model those variables whose headline number is reported by the main statistical sources and central banks; in addition we consider those indicators monitored by financial markets and by the press. We choose the transformations that guarantee stationarity of the variables (see Table 1), which are the same as the ones reported by the media and Bloomberg, making the comparison easier.4 We consider only real data and surveys. We disregard prices and financial variables, nominal variables, and sector-specific series. This choice reflects the results of previous research, in which the inclusion of these variables does not improve the model’s forecasting performance (see Ban´bura and Modugno, 2010, and Ban´bura et al.,2012).5 Table1reportssomedetailsontheselectedseries,inparticularthetimingofthereleaseand theimportancethatthefinancialmarketsattachtotheseries,accordingtotheBloombergindex. ThepeculiarityoftheBraziliandatasetisthefactthatitincludestwoindicatorsthatarestrictly related to the target variable (quarterly GDP). The first is the monthly nominal GDP, published by the BCB, based on monthly indicators for economic activity and prices. The second is the economic activity index (EAI), also published by the BCB. The EAI is a monthly coincident indicator based on the same methodology used to measure the Brazilian quarterly GDP, which 4Mostofthevariablesareinmonth-on-month(MoM)changeinordertoguaranteestationarity,withtheexceptionofRegisteredJobsCreatedwhichisayearlychangetoaccountforseasonalityissuesgiventhatthevariableis notseasonallyadjusted,PMIManufacturingisinlevelsbutbehaveslikeaMoMchangeforhowitisconstructed andRealGDPisthetargetvariableanditisquarter-on-quarter(QoQ). 5Itis true thatfinancialvariables, which are availableatvery high frequencymight, inprinciple, carry informationonexpectationsoffutureeconomicdevelopments(Andreouetal.,2008),howeverweonlyconsidermacro indicatorsandsurveysgiventhatotherstudiesonthistopic-seeBan´buraetal. (2013),StockandWatson(2005) andFornietal. (2003)-indicatethat“financialvariablesdonothelpimprovingtheprecisionofGDPnow-cast”, becausethenewsfromfinancialvariablesishighlyvolatileandleadstorevisionsindifferentdirections.Moreover, Ban´bura et al. (2013) show that there is correlation between some financial variables and GDP, but only at low frequency: thisindicatesthatwhilefinancialvariablesarenotimportantforshorttermforecasttheycouldinstead beimportantforlongtermforecast. Thisisalsoconfirmedbythefactthatmarketparticipantsmostlymonitorreal variables. 5

Table1: Seriesusedinthemodel Name Timing Publishinglag Frequency Source Starting Transf. Relevance Date Bloomberg Registeredjobscreated 20thmonth 20days M MTE May-99 Yearlychange - Formalemployment 20thmonth 20days M IBGE Jan-85 Monthlychange 63.5 Merchandiseexports firstdays 2days M MDIC Jan-54 MoM 40.4 Merchandiseimports firstdays 2days M MDIC Jan-59 MoM 36.5 Capacityutilization firstweek onemonth M CNI Dec-91 Monthlychange 32.7 Industrialproduction firstdays onemonth M IBGE Jan-91 MoM 90.4 Consumerconfidenceindex lastweek currentmonth M FGV Sep-05 Monthlychange 17.3 Economicactivityindex middle 1-2months M BCB Jan-03 MoM 23.2 MonthlyGDP end onemonth M BCB Mar-90 MoM - Manufacturingsales firstdays onemonth M CNI Dec-91 MoM - PMImanufacturing firstdays 2days M BancoRl Feb-06 Levels 75.0 Extendedretailtrade middle 1-2months M IBGE Jan-03 MoM - Retailtrade:volume middle 1-2months M IBGE Jan-03 MoM 71.1 RealGDP firstdays 2months Q IBGE Q1-90 QoQ 80.1 Notes. Timing: isapproximatelythenumberofdaysfromtheendofthereferenceperiod;Frequency: indicateswhethertheseriesis monthly(M)orquarterly(Q);Sources: MTE(Ministe´riodoTrabalhoeEmprego),IBGE(Fundac¸aˆoInstitutoBrasileirodeGeografia eEstat´ıstica),MDIC(Ministe´riodoDesenvolvimento,Indu´striaeCome´rcioExterior),CNI(Confederac¸aˆoNacionaldaIndu´stria),FGV (Fundac¸aˆoGetu´lioVargas),BCB(BancoCentraldoBrasil),BancoRL(BancoReal);Bloomberg: reportsthemarketrelevanceofeach variableaccordingtoBloomberg’srelevanceindex,thatrangesfrom0to100. consists of a set of proxies of economic behavior in the different economic sectors (agriculture, industry, distributive trade, transportation, services). As the EAI is a recent indicator, it still does not relate directly to the monthly nominal GDP, whose calculations follow an older methodology. Therestofthevariablescanbedividedintofourcategories: surveys,labor,production/demand, and trade indicators. Among surveys, we consider the consumer confidence index and the purchasing manager index (PMI). The consumer confidence index is very timely and it is the only piece of information in Brazil published within the reference period, though Bloomberg does not rank it as important (17.3%). The PMI is released at the beginning of the following month andisarelevantseriesaccordingtothemarkets(75.0%). Forlabour,weincluderegisteredjobscreated(RJC)andformalemployment(FE).Thelatter is rated fairly important by Bloomberg (63.5%). Both variables are timely. For production, we track industrial production (IP), which is rated highly for importance by Bloomberg (90.4%). For domestic demand, we track capacity utilization (CU), real manufacturing turnover (RMT), extended retail trade (ERT) and retail trade (RT). ERT, differently from RT, reports the volume of sales of formally established companies with 20 or more employed persons and whose main activity is retail trade which includes “Vehicles, motorcycles, parts and accessories” and 6

“Construction material”. Bloomberg comments RT and rates it fairly high in terms of importance (71.1%). The trade category is particularly important for the Brazilian economy given its timeliness. ExportsandImportshavethesamepublicationlagasthePMI. Most of the hard data series (employment, retail sales and industrial production) are published with a three to six weeks lag after the end of the reference month. Trade variables (exports and imports) are published at the beginning of the following month. Differently from othercountriesthestatisticaloffice,theBrazilianInstituteofGeographyandStatistics(IBGE), disseminatesamonthlyGDPindicator,whichispublishedfourweeksafterthereferenceperiod. 3 The Nowcasting Problem and the Econometric Framework The problem of nowcasting lies in estimating GDP in the interval of time between the beginningofthereferencequarteranditsofficialrelease,exploitingtheinformationcomingfrom otherhigherfrequencyvariables6. More formally, the nowcast of GDP (yQ) can be defined as the orthogonal projection of t yQ on the available information set Ω , which contains mixed-frequency variables (x ) and is t v j characterized by a “ragged edge” structure given that the time of the last available information variesfromseriestoseries. Each time new information arrives, a new nowcast is produced. This nowcast can be decomposedasfollows: E[yQ|Ω ] = E[yQ|Ω ]+E[yQ|I ]. (1) t v+1 t v t v+1 The new forecast E[yQ|Ω ] is just the sum of the old forecast E[yQ|Ω ] and the revision t v+1 t v E[yQ|I ],where t v+1 I = x −E[x |Ω ]. (2) v+1 j j v 6InthissectionwecloselyfollowGiannoneetal., 2006; Ban´buraModugno, 2010; Ban´buraetal., 2012; and Ban´buraetal.,2013. 7

Thisrevision(I )istheexpectedvalueofourtargetvariableconditionaltothedifferencebev+1 tweentheactualreleaseofanyvariable(x ∈ Ω )andwhatourmodelwaspredictingforthat j v+1 release (E[x |Ω ]). The only element that leads to a change in the nowcast is the “unexpected” j v (withrespecttothemodel)partofthedatarelease,I ,whichwecallthe“news”. v+1 AsshownbyBa´nburaandModugno(2010),themagnitudeoftheforecastrevisiondepends bothonthesizeofthenewsandonitsrelevanceforthetargetvariable. Throughthisinteresting mechanism, it is possible to trace the contribution of each series to the revision of the nowcast, in particular putting in relation the revision of the target with the unexpected developments of theinputs. Themodel weuse inorder tocomputethe nowcastand thenews isadynamic factormodel (DFM).Thismodelproducesagoodrepresentationofthedataandguarantees,atthesametime, parsimony. It exploits the fact that there is a large amount of co-movement among macroeconomic data series, and hence that relatively few factors can explain the dynamics of many variables (see Sargent and Sims, 1977; Giannone et al., 2005; Watson, 2004; and Stock and Watson,2011). Themodelcanbewrittenasasystemwithtwotypesofequations: ameasurementequation (Equation 3) linking the observed series (i.e GDP and all the indicators listed in Table 1) to a latent state process, and the transition equation (Equation 4), which describes the state process dynamics. Equations 3 and 4, written in a state space form, allow the use of the Kalman filter to obtain an optimal projection for both the observed and the state variables. The Kalman filter generates projections for all of the variables in the model (GDP but also all the other data releases). TheDFMmodelisdescribedbythefollowingequations: y = Λf +e , (3) t t t f = A f +A f +...+A f +u u ∼ i.i.d.N(0,Q), (4) t 1 t−1 2 t−2 p t−p t t 8

e = ρ e +v v ∼ i.i.d.N(0,σ2), (5) i,t i i,t−1 i,t i,t i where y = [y ;y ;...;y ](cid:48) denotes a set of standardized stationary monthly variables, f t 1,t 2,t n,t t is a vector of r unobserved common factors with zero mean and unit variance, Λ is a matrix of coefficients collecting the factor loadings for the monthly variables, ande = [e ;e ;...;e ](cid:48) t 1,t 2,t n,t isan-dimensionalvectorofidiosyncraticcomponentsuncorrelatedwithf atallleadsandlags. t Thislastassumption,whichmeansthatallofthejointcorrelationbetweenobservablesisexplainedbythecommonfactors,isstrongandunrealistic,howeverDozetal. (2006)haveshown thattheeffectsofthismispecificationontheestimationofthecommonfactorsisnegligiblefor largesamplesize(T)andthecross-sectionaldimension(n). We consider only one factor and two lags in Equation 4 and an AR(1) process for the idiosyncraticcomponentsdescribedinEquation5.7 In order to incorporate quarterly variables into the model, we construct for each of them a partially observed monthly counterpart in which the value of the quarterly variable is assigned to the third month of the respective quarter. We assume that the “unobserved monthly” growth rateofGDP(yUM)admitsthesamefactormodelrepresentationasthemonthlyrealvariables: t yUM = Λ f +eQ, (6) t Q t t eQ = ρ eQ +vQ vQ ∼ i.i.d.N(0,σ2). (7) t Q t−1 t t Q To link yUM with the observed GDP data, we construct a partially observed monthly series t andweusetheapproximationofMarianoandMurasawa(2003): yQ = yUM +2yUM +3yUM +2yUM +yUM . (8) i,t i,t i,t−1 i,t−2 i,t−3 i,t−4 The estimation procedure is quasi maximum likelihood. As shown in Doz et al. (2006), the 7WeuseBaiNg(2002)InformationCriteriatoselectthenumberoffactorsinEquation3andAkaikeInformationCriteriatoselectthelagorderofEquation4. Seetheappendixfordetails. 9

estimator, apart from being robust to model mispecification, is feasible when n is large (as in thecaseofBrazil)andeasilyimplementableusingtheKalmansmootherandtheEMalgorithm, initializedusingprincipalcomponents,asintraditionalfactoranalysis. Given that most of the indicators we include in our model are characterized by missing data at the beginning of the sample (as it is in the case of the consumer confidence index, which starts in September 2005, or the PMI, which starts in February 2006) and by a “ragged edge” structure,duetounsynchronizeddatareleasesattheendofthesample,weadapttheestimation proceduretothepresenceofarbitrarypatternsofmissingdatafollowingBan´buraandModugno (2014). 4 The BCB Survey and Other Benchmarks The BCB has set up a Market Expectation System, a web interface where financial institutions, consulting firms, and universities, which are required to have a specialized team on macroeconomic projections, report their expectations for various macroeconomic variables including GDP growth. The process through which these institutions revise their forecasts is not clear, nevertheless it is reasonable to think that these predictions are not entirely model based, but that a certain amount of judgment is also used.8 Every business day at 5:00 pm (GMT-2) the information is consolidated and several statistics are generated: averages, medians, standarddeviations,coefficientsofvariation,andminimumandmaximumvaluesoftheprojections recorded by the participants. Of the universe of qualified institutions, most of them alter their expectationsweekly. Forthepurposesofourexercise,weconsiderthemedianprojection. The other important benchmark we consider is Bloomberg, which conducts a survey and collects forecasts from analysts and economists in order to produce predictions for GDP and other market-relevant variables before their release dates. Bloomberg publishes predictions as soon as they have at least three respondents to their questionnaire, which is generally around twoweeksbeforethereleaseoftherelevantdataseries. Thereafterthepredictioniscontinually 8ThisstatementwasconfirmedbyaBCBforecastingexpert. 10

reviseduntil24hoursbeforetherelease. Thefinalnumberisusuallyclosetotheactualrelease value. Surveys of professional forecasters are averages and according to the literature on forecast combination should have the advantage of performing better than single forecasts (see Bates and Granger, 1969; Diebold and Lopez, 1996; Newbold and Harvey, 2002; and Clements and Hendry, 2004). In addition, short term forecasts, produced by the surveys, are based on realtimeinformation. We also consider as benchmarks the OECD, IMF (released twice a year), and the BCB quarterlyforecaststocomparethemodelresultsoncalendaryearforecasts. 5 Model Evaluation In order to evaluate the performance of the model we report a “pseudo real time” historical reconstruction from 2007:Q1 to 2013:Q1. We estimate the model recursively and we take account of information from each new data release (real-time), but we do not consider revisions (pseudo).9 This last point can in principle distort the results in favour of the model, given that the BCB short term forecasts and the Bloomberg survey rely on real time information. However,giventherobustnessoffactormodelstodatarevisionerrors(seeGiannoneetal.,2006and Ban´buraetal.,2013),weexpectthisnottobethecase. The results of the historical evaluation are reported in the figures below. Figure 1 comparesboththeyear-on-yearGDPnowcastwiththeBCBSurvey(panela)andthecalendaryear nowcastwiththeIMFandOECDforecasts(panelb). Figure 2 compares the root-mean-squared forecast error (RMSFE) of the model - on average for all of the calendar quarters in the historic reconstruction period - with the short-term forecast of BCB, the Bloomberg’s survey of independent forecasters (published the day before the preliminary GDP release) and an auto-regressive forecast, which changes only when GDP 9We cannot conduct a real time analysis given that we do not have real time information for all the data series included in the model. To our knowledge only the OECD reports real time information on Brazil, but only on a small number of series, namely GDP, industrial production, retail trade, export and import. See http://stats.oecd.org/mei/default.asp?rev=1. 11

Figure1: GDPnowcast 10 8 6 4 2 0 -2 -4 -6 a) YoY Nowcast b) Calendar Year Nowcast 70-neg-20 70-rpa-20 70-gul-20 70-tto-20 80-neg-20 80-rpa-20 80-gul-20 80-tto-20 90-neg-20 90-rpa-20 90-gul-20 90-tto-20 01-neg-20 01-rpa-20 01-gul-20 01-tto-20 11-neg-20 11-rpa-20 11-gul-20 11-tto-20 21-neg-20 21-rpa-20 21-gul-20 21-tto-20 31-neg-20 31-rpa-20 10 8 6 4 2 0 -2 -4 out turn YoY nowcast Banco do Brazil Survey (median) 70-neg-2 70-rpa-2 70-gul-2 70-tto-2 80-neg-2 80-rpa-2 80-gul-2 80-tto-2 90-neg-2 90-rpa-2 90-gul-2 90-tto-2 01-neg-2 01-rpa-2 01-gul-2 01-tto-2 11-neg-2 11-rpa-2 11-gul-2 11-tto-2 21-neg-2 21-rpa-2 21-gul-2 21-tto-2 31-neg-2 31-rpa-2 Out Turn Calendar Year Nowcast IMF OECD Banco do Brasil Notes. Comparison between GDP nowcast, GDP actual value, and the BCB survey. PanelareportstheYoYgrowthrate,panelbthecalendaryear. is released. Given that the BCB GDP Survey reports YoY figures, we evaluate the model on a YoYbasis. ResultsdonotdiffersignificantlyifweconsiderQoQfigures. Themodel’squarterlyGDPgrowthpredictionisfirstmade90daysbeforethestartofagiven quarter. ItisthenupdatedwitheachsuccessivedatareleaseuntilthereleaseofpreliminaryGDP, which takes place 145 days after the start of the calendar quarter. Thereby for each calendar quarter there is a period of 235 days (the “prediction period”) over which the prediction is continuously updated. This period is measured by the X-axis. The Y-axis measures the rootmean-squaredforecasterror(RMSFE)foreachdifferentseriesofpredictions. In Table 2, we report the RMSFE reduction by release, in each of the three months of the reference quarter. Specifically, real GDP, Exports, industrial production, PMI and formal employment are the data releases that have the most impact in improving the accuracy of the 12

Figure2: RMSFE 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 98- 38- 67- 56- 26- 65- 94- 83- 53- 92- 32- 81- 9- 3 31 81 72 03 04 54 45 75 36 86 97 19 79 401 511 811 421 131 241 541 151 model AR BCB Bloomberg Notes. The Y-axis reports the root-mean-squared forecast error (RMSFE) over theperiod2007:Q1to2013:Q1. Theforecastaccuracyisevaluatedfromthefirst month of the previous quarter to the time when GDP is released. The X-axis reportsthedistanceintermsofdaysfromthebeginningofthecurrentquarter. 13

Table2: AverageMSFEReductionbyVariable m1 m2 m3 Merchandiseexports -0.5 -21.8 4.9 Merchandiseimports 0.0 -1.1 -0.9 PMImanufacturing 7.4 -23.5 -10.9 Industrialproduction -34.1 -14.9 -3.9 Manufacturingsales -4.8 -1.9 4.8 Capacityutilization -5.3 1.9 0.9 Economicactivityindicator -7.0 -6.4 -0.9 Extendedretailtrade -7.1 -4.3 -5.6 Retailtrade: volumeofsales -1.6 -0.5 -0.7 Registeredjobscreated -6.1 -11.7 -2.5 Formalemployment -17.7 -11.5 -0.5 Consumerconfidenceindex -1.0 -0.5 0.0 MonthlyGDP -2.0 10.3 -0.5 RealGDP -42.5 Notes. These results are referred as the first (m1), second (m2),andthird(m3)monthsofthenowcastperiod. model’sprediction. 14

5.1 Tests The BCB professional forecasts seem to be highly collinear with the nowcasts and equally accurate. In Table 3, we report the Diebold-Mariano (2002) test of equal predictive accuracy to check whether the difference in forecasting performance between models is significant. For each month, we report the sample average of the difference between the squared errors of the ARandtheBCBprofessionalforecastsbothwithrespecttothenowcastingmodel(benchmark), in coincidence with the first Brazilian release (exports). We report the value of the DM test and its standard deviation estimated using heteroskedasticity and autocorrelation robust (HAC) standard errors (see appendix A.2 for details). The test confirms better performance in terms of accuracy of the nowcasting model in comparison with the AR (in the forecast, nowcast and backcast) and a slightly better performance in comparison with the BCB forecasts (only in the secondandthirdmonthofthenowcastandinthebackcast). FromFigure2wecanseethatthemodel’sRMSFEdeclinesmoreorlesscontinuouslyover the prediction period, which means that new information has a monotonic and negative effect onuncertainty. Inordertoformallytestthedeclineinuncertainty,asmoredataarriveweapply the test for forecast rationality proposed by Patton and Timmerman (2012). Table 4 reports the p-values of three monotonicity tests for, respectively, the forecast errors, the mean-squared forecast, and covariance between the forecast and the target variable (see the appendix for a description of the test). Monotonicity cannot be rejected by any of the three tests confirming the evidence of Figure 2 and proving the importance of incorporating new information as it arrivesintheforecastupdate. 15

Table3: Diebold-Marianotestofequalforecastingaccuracy Forecast Nowcast Backcast AR BCB AR BCB AR BCB 1m 6.09 0.26 6.61 0.85 3.76 0.96 (3.00) (1.18) (3.03) (0.78) (1.46) (0.35) 2m 7.80 1.27 8.01 1.49 3.93 0.55 (3.21) (1.14) (3.24) (0.74) (1.50) (0.22) 3m 9.17 1.71 8.50 1.31 (3.34) (1.17) (3.31) (0.52) Notes. ThetablereportstheestimatedconstantandtheHACestimatorofitsstandarderrorinthefirst,second,andthirdmonth of the forecast, nowcast, and backcast, respectively. The AR and BCB professional forecasts are compared against the nowcastmodel. Table4: MonotonicityTests ∆e ≥ 0 ∆f ≥ 0 ∆c ≥ 0 nowcastmodel 0.4963 0.4977 0.5024 Notes. The table reports the p-values of three monotonicity test for, respectively, the forecast errors, the mean-squared forecast, and covariance between the forecastandthetargetvariable. 16

5.2 The News The importance of calculating the news is twofold: first, given that the news is defined as the difference between the actual value of the data release and the value predicted by the model, it is possible to check whether the model is well specified in all of its dimensions. The average ofthenewsforeachreleaseshouldbeclosetozero,andthestandarddeviationshouldbesmall (|mean| < 2 standard deviation). Table 5 confirms the previous statement. In addition, the table also compares the model’s performance in predicting each of the series with that of the Bloombergsurvey. Weshowthat,formostseries,themodel’spredictionsarecomparabletothe Bloomberg survey predictions. Finally, we include in Table 5 the mean and standard deviation of the revisions for each of the series in the data set. As the means of the revisions are close to zero and the standard deviations are small, this suggests that the model’s relative performance wouldhavebeensimilarinrealtime.10 Table5: Averagenewsandstandarddeviation Model Bloomberg Revisions Units/ Mean StD Mean StD Mean StD Transformation Merchandiseexports US$/MoM -0.25 7.04 0.74 11.68 0.85 8.95 Merchandiseimports US$/MoM 0.89 6.27 0.39 10.31 0.43 8.53 PMIManufacturing D.I./Levels -0.16 1.77 -0.07 0.22 0.01 0.13 Industrialproduction Index/MoM -0.10 1.92 0.38 1.09 -0.05 0.54 Manufacturingsales Index/MoM -0.15 2.39 Capacityutilization Percentage/Diff. -0.01 0.37 -0.81 0.68 -0.80 0.46 Economicactivityindex Index/MoM -0.07 0.78 Extendedretailtrade Index/MoM 0.08 2.63 -0.10 2.00 -0.08 2.67 Retailtrade:volume Index/MoM 0.30 0.85 -0.05 0.85 -0.01 0.60 Registeredjobscreated Thous.Units/YoY -4,369.9 72,134.4 1,069 46,725 - - Formalemployment Index/Diff. 0.03 0.17 Consumerconfidenceindex Index/Diff. -0.24 3.34 -0.48 6.06 0.22 4.41 Monthlygrossdomesticproduct Mil.Reais/MoM -0.23 2.31 Realgrossdomesticproduct Index/MoM 0.14 0.59 0.04 0.45 -0.07 0.56 Notes. D.I.=diffusionindex; Diff.=differences; Thous. Units=ThousandUnits; Manuf. =Manufacturing; Mil. Reais=MillionReais. The second important feature of the news within a nowcasting framework is that it allows interpretation of all the data releases in terms of the signals they give about current economic conditions (Ban´bura and Modugno, 2010). The impact that a given release has on the GDP 10NotethattheBloombergsurveyisconductedinrealtime,andtherespondentswhoseforecastsitreflectsare attemptingtopredictthefirstreleaseofeachseries,whereasthereconstructionofthemodel’spredictionsisbased onthelastavailablevintageofdata,ignoringrevisions. 17

nowcast is the product of two variables: the news (or the unexpected component of the release value), and the relevance of the series in relation to GDP, which is expressed as its weight (i.e., impact=newsxweight). Figure3showstheaverageimpactofeachvariableinthefirst,second, andthirdmonthofthequarter. SeeappendixA.4forthedecompositionoftheaverageimpact. Figure3: Variables’relevance Real GDP Monthly GDP Consumer Confidence Index Formal Employment Registered Jobs Created Retail Trade: Volume of Sales m3 Extended Retail Trade m2 Economic Activity Indicator m1 Capacity Utilization Manufacturing Sales Industrial Production PMI Manuf. Imports Exports 0 5 10 15 20 25 30 35 impact Notes. Variables’averageimpactinthefirst(m1),second(m2),andthird(m3) monthofthenowcast. 18

6 Conclusions ThenowcastingmodelforBrazil,presentedinthisarticle,provestherelevanceofupdating GDPforecaststotakeadvantageoftheflowofdatareleases. Institutional forecasts, which in Brazil are revised as often as once a week, perform as well asmodel-basedforecasts. Thisresultisinterestingbecauseitsuggeststhatjudgmentalforecasts areabletoincorporatetheinformationasefficientlyasalineartimeinvariantmodel. Thisfinding proves, on the one hand, that professional forecasters consider appropriate information to formtheirpredictions. Ontheotherhand,itprovesthatpurejudgment(whichcanbetranslated in nonlinearities, time variations, and soft information) turns out to be no more accurate to the scopeofforecasting. Thenowcastingmodelisalsoausefulinstrumenttostressthesinglevariable’srelevanceto the updating process. In Brazil, trade variables (in particular exports), given their timeliness, turn out to have a huge impact on the forecasting revisions. Industrial production, manufacturingPMIandemploymentvariablesarealsorelevant. 19

Appendix A1. Selecting the Number of Factors and Lags We select the optimal number of factors using an information criteria approach. The idea is to choose the number of factors that maximizes the general fit of the model using a penalty function to account for the loss in parsimony. Bai and Ng (2002) derive information criteria to determine the number of factors in approximate factor models when the factors are estimated by principal components. They also show that their information criterion (IC) can be applied to any consistent estimator of the factors provided that the penalty function is derived from the correctconvergencerate. Table A.1 reports the information criterion and the sum of the variance of the idiosyncratic componentsforthedifferentspecifications,whichallowforadifferentnumberoffactors. The TableA1: Modelselection(numberoffactors) Sample1 Sample2 Sample3 IC V IC V IC V 1 -0.03 0.67 -0.01 0.71 -0.04 0.69 2 -0.02 0.47 0.07 0.55 0.08 0.56 3 0.32 0.46 0.26 0.48 0.18 0.44 4 0.23 0.30 0.41 0.40 0.17 0.31 T 11 47 128 N 14 12 14 Notes. IC stands for Information Criteria, V is the sumofthevarianceoftheidiosyncraticcomponent. IC selects the model with one factor. Given that our data set is strongly unbalanced at the top, and some series are more recent than others, we report the test on three different samples. The first (sample 1) considers a balanced panel in the estimation period 1995:Q1 to 2006:Q4 (14 seriesand11observations),thesecond(sample2)arestrictedbalancedpanelwhereweexclude twoofthemostrecentseries(12series47observations),thethird(sample3)isabalancedpanel thatincorporatesthewholesample(estimationandforecastingperiod). Thechoiceofonefactor isconfirmedacrossthedifferentsamples. 20

In order to select the number of lags in Equation 4 of the model, we report in Table A.2 the resultsontheAkaikeinformationcriterion,whichselectstwolags. TableA2: Modelselection(numberoflags) Numberoflags Akaikeinformationcriteria 1 0.96 2 0.74 3 0.79 4 0.79 Notes. The lag is chosen in correspondence with the minimumAICvalue. A2. Diebold-Mariano Test Denotethelossassociatedwithforecasterrore byL(e )andthetime-tlossdifferentialbetween t t forecasts 1 and 2 as d = L(e )−L(e ). The Diebold-Mariano (DM) requires only that the 12t 1t 2t lossdifferentialiscovariancestationary: E(d ) = µ,∀t 12t cov(d ,d ) = γ(τ),∀t 12t 12t−τ 0 < var(d ) = σ < ∞ 12t 2 The key hypothesis of equal predictive accuracy (i.e., equal expected loss) corresponds to E(d ) = 0,inwhichcase,underthemaintainedassumptionDM: 12t ¯ d 12 d DM = → N(0,1), 12 σˆ d¯ 12 where d ¯ = 1 (cid:80)T d is the sample mean loss differential and σ is a consistent estimator 12 T t=1 12t d¯ 12 ¯ ofthestandarddeviationofd . 12 DM is thus an asymptotic z −test of the hypothesis that the mean of a constructed but observed series (the loss differential) is zero. Forecast errors, and hence loss differential, though, 21

may be serially correlated for various reasons. In this paper, we calculate the DM statistics by regression of the loss differential on an intercept, using heteroskedasticity and autocorrelation robust (HAC) standard errors. In a fully articulated econometric model in which we have pseudo out-of-sample forecasts, following West (1996), we define the test on the sample mean quadraticlossasfollows: (cid:80)T (e2 −e2 ) ¯ t=t∗+1 1,t|t−1 2,t|t−1 d = , 12 T −t∗ where e is a time-t pseudo out-of-sample one-step ahead forecast error. We do not cont|t−1 sider a rolling scheme, so results should be taken with caution, as the test ignores estimation uncertainty. A3. Monotonicity Test We rely on the first three tests of Patton and Timmermann (2012), and we report the p-values forthenowcastmodel. Test1: Monotonicityoftheforecasterrors Let us define y˜ = yk and e = y˜ −E[y˜|Ω ] as the forecast error obtained on the basis t t,1 t|Ωv t t v of the information set corresponding to the data vintage Ω and by e that obtained on the v t|Ωv+1 basisofalargermorerecentvintagev +1andv = 1,...,V. ThemeansquaredError(MSE)differentialis∆e = E[e2 ]−E[e2 ]. v t|Ωv t|Ωv+1 Thetestis: H0: ∆e ≥ 0vsH1:∆e (cid:11) 0,wherethe(V −1)×1vectorofMSE-differentials isgivenby∆e ≡ (∆e,...,∆e )(cid:48). 1 V−1 Test2: Monotonicityofthemeansquaredforecast Definethemeansquaredforecast(MSF)foragivenvintageasE[y˜2 ] = E[E[y˜2|Ω ]]and t|Ωv t v considerthedifference∆f = E[y˜2 ]−E[y˜2 ]anditsassociatedvector∆f. v t|Ωv t|Ωv+1 22

ThetestisH0: ∆f ≤ 0vsH1: ∆f (cid:10) 0. Test3: Monotonicityofcovariancebetweentheforecastandthetargetvariable Here we consider the covariance between the forecast and the target variable for different vintages v and the difference ∆c = E[y˜ y˜]−E[y˜ y˜]. The associated vector is defined v t|Ωv t t|Ωv+1 t as∆c andthetestisH0: ∆c ≤ 0vsH1: ∆c (cid:10) 0. A4. Impact of the Releases on the Nowcast TableA3: ImpactoftheReleasesontheNow-cast A B C m1 m2 m3 m1 m2 m3 m1 m2 m3 Merchandiseexports 3.764 3.360 2.365 7.921 5.419 7.741 29.819 18.209 18.308 Merchandiseimports 2.555 2.284 1.623 5.243 6.581 6.511 13.396 15.029 10.571 PMImanufacturing 11.500 9.030 4.210 1.382 2.033 1.889 15.893 18.359 7.952 Industrialproduction 9.797 9.290 8.115 2.035 2.353 1.245 19.940 21.859 10.103 Manufacturingsales 3.806 3.609 3.156 2.277 2.362 2.429 8.664 8.523 7.665 Capacityutilization 25.875 25.075 21.539 0.398 0.351 0.386 10.305 8.814 8.307 Economicactivityindicator 8.210 7.712 6.102 0.582 1.101 0.548 4.778 8.492 3.341 Extendedretailtrade 1.913 1.809 1.393 2.162 2.864 2.749 4.136 5.180 3.829 Retailtrade:volumeofsales 2.205 2.048 1.678 0.973 0.775 0.811 2.146 1.587 1.361 Registeredjobscreated 0.000 0.000 0.000 84,996.848 65,143.536 67,609.663 19.012 11.478 6.313 Formalemployment 92.400 80.040 36.965 0.226 0.140 0.133 20.911 11.209 4.911 Consumerconfidenceindex 0.302 0.198 0.099 4.241 2.566 3.086 1.282 0.507 0.305 MonthlyGDP 5.080 4.430 2.742 1.760 3.168 1.658 8.942 14.032 4.545 RealGDP 20.522 0.592 12.145 Notes.Aistheaverageweight;Bisthenewsstandarddeviation;CistheaverageimpactequaltoA·B. 23