constructing Coincident and Leading Indeces of Economic Activity for the Brazilian Economy

8/10/2019 constructing Coincident and Leading Indeces of Economic Activity for the Brazilian Economy

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Ensaios Econmicos

Escola de

Ps-Graduao

em Economia

da Fundao

Getulio Vargas

N 730 ISSN 0104-8910

Constructing Coincident and Leading Indices

of Economic Activity for the Brazilian Econ-

omy

Issler, Joo Victor, Notini, Hilton Hostalacio, Rodrigues, Claudia Fontoura

Maro de 2012


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Os artigos publicados so de inteira responsabilidade de seus autores. Asopinies neles emitidas no exprimem, necessariamente, o ponto de vista daFundao Getulio Vargas.

ESCOLA DE PS-GRADUAO EM ECONOMIADiretor Geral: Rubens Penha CysneVice-Diretor: Aloisio AraujoDiretor de Ensino: Carlos Eugnio da CostaDiretor de Pesquisa: Luis Henrique Bertolino BraidoDireo de Controle e Planejamento: Humberto MoreiraVice-Diretor de Graduao: Andr Arruda Villela

Joo Victor, Issler,

Constructing Coincident and Leading Indices of Economic

Activity for the Brazilian Economy/ Issler, Joo Victor, Notini,

Hilton Hostalacio, Rodrigues, Claudia Fontoura Rio de Janeiro

: FGV,EPGE, 201230p. - (Ensaios Econmicos; 730)

Inclui bibliografia.

CDD-330


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Constructing Coincident and Leading Indices ofEconomic Activity for the Brazilian Economy

Joo Victor Isslery Hilton Hostalacio NotiniClaudia Fontoura Rodrigues

March 14, 2012

Abstract

This paper has three original contributions. The rst is the reconstructioneort of the series of employment and income to allow the creation of a newcoincident index for the Brazilian economic activity. The second is the con-struction of a coincident index of the economic activity for Brazil, and fromit, (re) establish a chronology of recessions in the recent past of the Brazil-ian economy. The coincident index follows the methodology proposed by TheConference Board (TCB) and it covers the period 1980:1 to 2007:11. The thirdis the construction and evaluation of many leading indicators of economic ac-tivity for Brazil which lls an important gap in the Brazilian Business-Cycle

literature.Keywords: Coincident and Leading Indicators, Business Cycles, CommonFeatures, Latent Factor Analysis

J.E.L. Codes: C32, E32.

We gratefully acknowledge the comments and suggestions of Marcelle Chauvet, Kajal Lahiri,Paulo Picchetti, the Editor in Charge (Michael Gra), two anonymous referees, and participantsof CIRET 2008 in Santiago, Chile. All errors are ours. We thank Marcia Waleria Machado andRafael Burjack for excellent research assistance and thank CNPq-Brazil, FAPERJ and INCT fornancial support.

yCorrresponding author: Graduate School of Economics EPGE, Getulio Vargas Foundation,Praia de Botafogo 190, s. 1100, Rio de Janeiro, RJ 22250-900, Brazil.

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1 Introduction

An important concern of any modern society is: what is the current state of econ-omy and what should be the state of the economy in the near future? Entrepreneursand individuals are interested in the question because their prots and welfare are afunction of it. Governments also have an interest in the subject for budgetary andwelfare issues. Unfortunately, no one possesses a series that represents the state ofthe economy because it is a latent variable, or rather, it is unobservable.

Since Burns and Mitchell (1946), there has been a great deal of interest in makinginferences about the state of the economy from sets of monthly variables thatare believed to be either concurrent or to lead the economys business cycles (theso called coincident and leading indicators, respectively). The most educatedestimate of U.S. turning points is embodied in the binary variable announced by theNBER Business Cycle Dating Committee. These announcements are based on the

consensus of a panel of experts, and they are made some time (usually six monthsto one year) after the time of a turning point in the business cycle. The NBERsummarizes its deliberations as follows:

The NBER does not dene a recession in terms of two consecutive quar-ters of decline in real GNP. Rather, a recession is a recurring period ofdecline in total output, income, employment, and trade, usually last-ing from six months to a year, and marked by widespread contractions inmany sectors of the economy. (Quoted from http://www.nber.org/cycles.html)

The time it takes for the NBER committee to deliberate and decide that a turning

point has occurred is often too long to make these announcements practically useful.This gives importance to two constructed indices, namely the coincident index andthe leading indicator index. The traditional coincident index constructed by theDepartment of Commerce is a combination of four representative monthly variableson total industrial production, income, employment and sales. TCB uses a simpleaverage of the standardized dierenced (logged) series, which is a way of treatingequally the uctuations of all four series in computing the index. TCB approach issomewhat heuristic, since it requires no estimation of a formal econometric model.Despite that, it works surprisingly well in practice for the U.S.; see the comparisonin Issler and Vahid (2006) using the TCB index and alternative econometric-basedindices in trying to replicate the NBER dating decisions1.

1 Regarding Brazilian data, the evidence in Duarte, Issler and Spacov (2004) and in Hollauer,Issler and Notini (2009) concurs with this positive assessment for TCB index.

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As an alternative to heuristic methods such as TCBs, several authors have pro-posed methods of building indices supported by sophisticated econometric and statis-tic techniques. Stock and Watson (1998a, 1998b, 1989, 1993a, 1993b) were the rst

to apply the tools of modern time-series econometrics to build an approach able toconstruct leading and coincident indices, detect turning points of economic activity,and to predict the probability of a recession.

An important empirical drawback of Stock and Watsons approach was its failureto detect the U.S. recession in 1990-1991. Many papers tried to improve on Stockand Watsons method, while keeping the formal building block of a structural econo-metric model (see e.g., Chauvet (1998) and Mariano and Murasawa (2003)). Morerecently, Giannone, Reichlin and Small (2008) have developed a framework for real-time nowcasting (and forecasting) on the basis of a large and unbalanced dataset.Their model provided a timely and up to date estimation of the state of the econ-omy. Prior to that, and using a dierent approach, Evans (2005) incorporated daily

information to update the real-time estimates of GDP and ination in a nowcastingexercise.

In Brazil, with the exception to the work of Contador (1977) and Contador andFerraz (1999), research on coincident and leading indices of economic activity isfairly young and most of the literature dates from the 2000s. Chauvet (2001) andPicchetti and Toledo (2002) use common-factor models to generate a monthly coinci-dent indicator of economic activity. Chauvet (2002) uses a two-state Markov Chaincharacterizing a recession or an expansion to propose a chronology for Brazilian busi-ness cycles. On a broader study, Duarte, Issler and Spacov (2004) evaluated threecandidates for composite coincident indices: The Conference Boards (TCBs) index;Spacovs (2000) index, and Issler and Vahids (2006) index. Using quadratic loss, thedating of these three indices was compared with that of a monthly proxy of BrazilianGDP, suggesting that the Brazilian coincident index should use the methodologyput forth by TCB. Similarly, Hollauer, Issler and Notini (2009) found that the TCBindex perform best when compared to the methods of Mariano and Murasawa (2003)and of Stock and Watson (1989, 1993) when industrial-sector coincident indicatorswere evaluated.

Unfortunately, part of this recent research eort in Brazil came to a halt be-cause of the recent redesign of the ocial employment survey conducted by IBGE Monthly Employment Survey (Pesquisa Mensal do Emprego) which providesmonthly Brazilian data on employment and labor income. Indeed, the change in

the survey design in 2002 was so drastic that it eliminates long-span time-series onemployment and income, which are crucial series for business-cycle research usingTCB and NBER oriented methods.

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The rst goal of this paper is to resume business-cycle research in Brazil usingthese methods, which proved to be valuable after the empirical results of Duarte,Issler and Spacov (2004) and Hollauer, Issler and Notini (2009). Indeed, one of

the main challenges of Brazilian business-cycle research is to back-cast currentlyavailable income and employment series to be able to form a long enough coincidentindex using TCBs method which component series are industrial production, sales,income and employment. Here, we devote a great deal of eort to reconstruct theemployment and income series using a novel State-Space representation, which isexplained at some length. Our proposed back-casting approach is based on theinterpolation method originally proposed by Bernanke, Gertler and Watson (1997)and later improved by Mnch and Uhlig (2005). It is a very exible setup that allowsthe estimation of a wide range of models in the time-series literature. As usual,estimation of the unobserved components in these models is performed employingthe Kalman lter.

Once we obtain a long enough span of the usual series used in TCBs method, wecompute a new composite coincident index of Brazilian economic activity. Its datingof recessions is compared with those of Duarte, Issler and Spacov (2004) and withthose implied by the monthly GDP estimate computed by Issler and Notini (2008).It is also compared with the dating properties of alternative techniques deliveringa long-span coincident index like chaining new and old employment and incomeseries, for example. This comparison shows that not only our proposed technique hassuperior results to chaining old and new series but also that our dating of recessionsis in line with past experience.

Our last contribution is regarding the construction of leading indices of economicactivity to track the composite coincident index proposed here. Although coincidentindices have been relatively well studied in Brazil, leading indices have not. Inconstructing leading indices we take into account three interesting and novel featuresin Brazilian business-cycle research: (i) we compare leading and coincident indicesin sample and out-of-sample, where recursive methods are used to mimic the actualtracking problem encountered in practice; (ii) we consider using Granger (1969)causality tests, as well as novel alternative criteria in choosing candidate series to beincluded in leading composite indices; (iii) we investigate the ability of survey-basedtime series to lead our composite index.

Although comparisons are based on a variety of features of the dating propertiesof these dierent indices, our decision to validate the current composite index is

mostly based on a variant of the Quadratic Probability Score (QP S)quadratic-lossstatistic proposed for that purpose by Diebold and Rudebusch (1989).Empirical results obtained here are compared with the previous literature on

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Brazil. In evaluating dierent results and techniques used in constructing coincidentand leading indices, we borrow from the almost century-long debate on this issue thathas been present in the U.S. economy, and a similar half-century or older debate in

Europe.One of the aspects of the methodology employed in this paper is the heavy use ofstatistical and econometric tools in devising dierent measures of economic activity.This is done in detriment of the use of a theoretical-based approach. Indeed, there isan old macroeconomics debate which started after Koopmans (1947) critique of thelack of theory behind the NBER business cycle methodology labelled measurementwithout theory2. As stressed by Auerbach (1981), if the success of a specic approachto economic analysis can be measured by its longevity and continued use under avariety of environments, then the use ofmeasurementof economic activity must beparamount.

Still, Koopmans compares the early empirical NBER methodology to the "Kepler

stage" of science, whereas the "Newton stage" develops theoretical models explainingthese measured phenomena. He seems to prefer the latter as if nothing is gained bythe former. We disagree with this view. Measurement establishes stylized facts ifdone properly, which then establishes what theoretical models should aim to explain.Indeed, the main paragraph in the classic book by Burns and Mitchell is subsequentlycited by most modern theoretical work in economics, e.g., Lucas (1977). Also, gener-ating the business-cycle regularities found by Burns and Mitchell and their followersnow constitutes a basic goal of the recent theory of business cycles. The core of thisliterature and its main shortcomings is surveyed in Kocherlakota (2010), for example.Indeed, science benets from both measurement and theory, since they complementeach other in giving a broad view of a specic phenomenon. This shows that themotivation to use statistical methods is neither an end on itself nor because they areavailable, but simply because they will nally help in uncovering and/or answeringan interesting economic question.

This article is organized as follows: section 2 contains a brief review of the Confer-ence Board method. Section 3 presents the Kalman lter model. Section 4 presentsthe data and the main results. Section 5 concludes.

2 The Methodology of TCB

The ideas behind TCBs method are twofold: simplicity and robustness. Simplicity isused because they weight information in coincident and leading indices equally, once

2 See also Hoover (1988), Biddle (1994), and Simkins (1999).

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one controls for the fact that dierent signals carry dierent information dependingon their variance. One simple way to treat every series equally in this context is tostandardize them, treating the standardized series equally. Robustness comes into

play here, since standardizing is a way to robustify the series used in the econometricanalysis.The coincident series is an equally-weighted linear combination of four coincident

series (income (It), output (Yt), employment (Nt), and sales (St)), once we controlfor the fact that the growth rate of these series have dierent variances. Hence, inits bear essentials3, the coincident indicator uses weights constructed as:

ln(CIt) =1

4

ln(It)

ln(I)+

ln (Yt)

ln(Y)+

ln(Nt)

ln(N)+

l n (St)

ln(S)

; (1)

where ln(I), ln(Y), ln(N), and ln(S)are respectively the standard deviationsof income, output, employment, and sales growth. It is straightforward to construct

the level series ln (CIt)or CIt once we possess ln(CIt).The leading series are usually chosen because they have turning points that hap-pen before those of the level series ln (CIt)or CIt. To determine that, we rst needa denition of turning points and of before. In this literature, turning points areusually determined using an accepted algorithm for turning points or local minimaand maxima of a time series the Bry-Boschan algorithm, Bry and Boschan (1971).With turning points of the target variable and of the potential leading series in hand,all we have to determine is whether those of the potential leading series precede thoseof the target series. Leading series are those that, on average, downturn or upturnprior to the target series. Once we determine the candidates of leading series, all wehave to do is to combine them. Again, the TCBs methodology uses simplicity androbustness: all leading series are combined using a procedure similar to (1).

3 Back-Casting Using the Kalman Filter

In this section, we give a brief review of the Kalman lter model applied to back-casttwo of our coincident series employment and income. A detailed description ofthis technique can be found in Harvey (1989) or in Hamilton (1994). After that, wediscuss how to back-cast series using a novel state-space representation.

Our starting point in using the Kalman lter to back-cast employment and in-come is the interpolation technique of Bernanke, Gertler and Watson (1997) and the

3 As is well known, TCBs coincident series is computed recursively. Also, it does not use in-stantaneous growth rates of the coincident series in it. Equation (1) serves merely to illustrate themethod in a simplistic way.

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extensions made by Mnch and Uhlig (2005). In both papers, the Kalman lter isused to interpolate GDP from quarterly to monthly frequency, where monthly auxil-iary series help in estimating monthly GDP. It is assumed that unobserved monthly

GDP (labelled asy+

t here) follows anAR

(p

)process explained by pre-determinedregressors xt and an AR (1) error term. The term xt contains co-variates, whichshould have a high correlation with the series being interpolated: much of the con-temporaneous behavior of the interpolated series comes from them. Also in xt aredeterministic series such as a constant and/or seasonal dummies, which, togetherwith these co-variates, explain the behavior ofy+t . The model for y

+t is:

1 1L pLp

y+t = xt+ ut

ut = ut1+ "t: (2)

Observed quarterly GDP (labelled as yt here) is:

yt =2X

i=0

y+ti, t= 3; 6; 9; 12; : : : (3)

yt = 0, otherwise. (4)

Hence, quarterly GDP, which we can only observe on months t= 3; 6; 9; 12, etc.,is the sum of the corresponding monthly GDPs in that quarter4. Otherwise, it isjust set to a ctional value of zero. Notice that setting yt = 0 for the months wedo not observe GDP is a way of making quarterly GDP observable at the monthlyfrequency; see Mnch and Uhlig, Appendix, just above equation (1). In the Kalman-lter literature for mixed frequency models (see, for example, Giannone, Reichlinand Small, 2008) a ctional value is usually assumed for missing observations (zerois the most frequent choice). The crucial step is to impose that the ctional observeddata has a very large variance, so that the zero value is discounted and overwrittenby the Kalman-lter technique. This is exactly how Mnch and Uhlig proceed.

A second issue is how to initialize the values of,, and the variance ofutin theKalman-lter procedure. Mnch and Uhlig aggregate the covariates in xt from high(monthly) to low (quarterly) frequency, and run an OLS regression ofyt on its lagsandxt(regression (2)) at the quarterly frequency. This yields estimates ofand thes, as well as an estimate for the variance ofut. With the latter, an estimate of isobtained from an OLS regression ofutonut1.

4 Note that the aggregation of monthly GDP can also be made averaging the y+t s, i.e., as

yt = 1

3

2Xi=0

y+ti.

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If we assume that the polynomial

1 1L pLp

is of order one, i.e.,p= 1, with coecient , the state-space form of Mnch and Uhligs problem is thefollowing:

t =

0BB@y+t

y+t1y+t2

ut

1CCA =0BB@

0 0 1 0 0 00 1 0 00 0 0

1CCA0BB@

y+t1y+t2y+t3ut1

1CCA+0BB@

xt

000

1CCA+0BB@

"t00"t

1CCA (5)

yt = H0tt, (6)

where (5) and (6) are respectively the state and the observation equations and thematrix H0tis time-varying, with the following format:

H0t = 8


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GDP, and bydutjTthe same estimate of the error term ut, they consider:R2

level =

VARdy+tjT

VARdy+tjT+VAR dutjT , and,

R2di =VAR

\y+

tjT

VAR

\y+

tjT

+VAR

\utjT

:Bernanke, Gertler, and Watson and Mnch and Uhlig claim that it is more informa-tive to report the R2 in rst dierences since the same statistic in levels will alwaysbe close to unity.

We now adapt the state-space representation in (5) and (6) to the problem ofback-casting a series for which we observe part of its realizations but not all, andwhere both the target variable as well as the covariates are in the same frequency(monthly, in our case). In some sense, this is very close to the problem worked outin Bernanke, Gertler and Watson and Mnch and Uhlig. There, they only observequarterly GDP for some but not all months of the year. Their solution was to setto zero the missing observations and to impose that the ctional observed data hasa very large variance, so that this zero value is discounted and overwritten by theKalman-lter technique. We follow their solution here, setting to zero all the missingobservations to be back-cast. We also impose that the ctional data has a very largevariance. Also, we initialize the values of,, and the variance ofutin the Kalman-lter procedure by means of an OLS regression for the overlapping period, where we

observe the variable being back-cast as well as the covariates used in back-casting it.Dierently from Bernanke, Gertler and Watson, and Mnch and Uhlig, here thereis no need to aggregate from high to low frequency. We explain further our methodbelow.

Suppose we possess a total of t = 1; 2; ; T; ; T, observations on xt. How-ever, for series y+t , we only possess data from t = T

+ 1; ; T, with missing valuesfrom t= 1; 2; ; T. This is exactly our setup for income and employment in thispaper. If we set the order of the polynomial

1 1L pL

p

to unity, i.e.,p= 1, with coecient, recalling that now we need not impose the time-aggregationrestriction in (7), the state-space form of our problem collapses to the following:

t = y+tut = 0 y+t1ut1 + xt0 + "t"t (8)yt = H

0tt, (9)

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where (8) and (9) are respectively the state and the observation equations and thematrix H0tis time-varying, with the following format:

H0t = 8


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4.2 The Coincident Series

As stressed above, one of the original contributions of this paper is to back-cast two ofthe coincident series for the Brazilian economy income and employment. We used

the techniques described in the previous section to back-cast them. In the currentMonthly Employment Survey, income is available from 2002:2 on, while employmentis available from 2002:3 on.

Back-casting was conducted in two steps. First we selected the co-variate series,which could potentially explain the variations of income or employment. These co-variates were then used in the state-space regression, which was estimated using theframework described above based on the algorithm by Mnch and Uhlig (2005).Our setup allows for several dierent dynamic models to be estimated, all describedin Table 1, depending on dierent values for the parameters and .

We tested seven series as auxiliary regressors in the back-casting procedure, allavailable for the period 1980:1 to 2007:11. They are: industrial production, output inthe process industry, corrugated paper production, car production, steel production,cement production, energy production, and the monthly real GDP series estimatedby Issler and Notini (2008). The dependent variables and all co-variates entered inlevels in the state space representation, which is estimated in all the six dierentversions described in Table 1. In addition to the co-variates listed above, our modelsalso include eleven seasonal dummies. Therefore, there is no seasonal adjustmentprior to back-casting.

In Table 2, we present theR2dimeasure of t for each model described in Table1.

Table 2 Employment and Income Resulting R2

difor each ModelModel Employment IncomeStatic model in levels with IID residuals 0:4979 0:1134Static model in levels with AR(1)residuals 0:4729 0:0425Static model in 1st dierences with IID residuals 0:0072 0:0000Dynamic model in levels with IID residuals 0:0597 0:0827Dynamic model in 1st dierences with IID residuals 0:0000 0:0000Dynamic model in levels with AR(1)residuals 0:0000 0:0048

Our nal choice of auxiliary variables and models were as follows. For employment(in logarithms) we choose only the monthly GDP series and energy production (inlogarithms) as co-variates. For income (in logarithms), we selected only the paper

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production series and cement production (in logarithms) as auxiliary variables. Inboth cases, the model with the highest R2leveland R

2diwas the static model with i.i.d.

errors.

Once the back-casting procedure was implemented, all coincident series were sea-sonally adjusted using the X-12 procedure5. The results are plotted below includingthe results of the back-cast series. For income and employment, the shaded areas inthe graphs below depict the actual sample in which we observe them.

Industrial Production Sales

1.76

1.80

1.84

1.88

1.92

1.96

2.00

2.04

2.08

2.12

80 82 84 86 88 90 92 94 96 98 00 02 04 06

4.6

4.7

4.8

4.9

5.0

5.1

5.2

5.3

80 82 84 86 88 90 92 94 96 98 00 02 04 06

Income Employment

2.7

2.8

2.9

3.0

3.1

3.2

1980 1985 1990 1995 2000 2005

3.90

3.95

4.00

4.05

4.10

4.15

4.20

4.25

80 82 84 86 88 90 92 94 96 98 00 02 04 06

Figures 1-4: Coincident Series - In log and Seasonally Adjusted (Shaded areas arethe actual sample)

5 The seasonal adjustment method adopted was the X-12 Reg-ARIMA 0.3 method (U.S. CensusBureau, 2007). Indeed, changing the seasonal adjustment method changes very little the nalresults in this paper.

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All four coincident series were tested for unit roots. We used three dierenttests. On a preliminary basis, we used the Augmented Dickey-Fuller (ADF) test.Initial results were later examined in light of the results of the Phillips and Perron

(1988) test and the stationarity test proposed by Kwiatkowski et al. (1992). All fourcoincident series showed signs of unit roots in testing and therefore were transformedinto rst dierences (logs) prior to combination into a composite index.

4.3 TCBs Coincident Index T CB CIt

Using (1), we constructed a coincident index consistent with TCBs method, labelledT CB C It, and plotted in Figure 5 below. Next, we compare the turning-pointdating of this index with that of two other indices: a monthly estimate of BrazilianGDP computed by Issler and Notini (2008) and the composite index previouslyproposed by Duarte, Issler and Spacov (2004), available until 2002:11. The latter

also uses TCBs technique.

96

100

104

108

112

116

120

1980 1985 1990 1995 2000 2005

Figure 5: Coincident Index Shaded Bry-Boschan TurningPoints

The turning points of these three composite indices were then compared usingthe Bry and Boschan (1971) and the Mnch and Uhlig (2005) dating algorithm, thelatter being a slightly modied version of the former. Results in Table 3 show that

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the current dating using TCBs method yields results closer to the dating in Duarte,Issler and Spacov than to the dating of Brazilian monthly GDP. The most strikingdierences appear in the dating of the 1991 recession. The dating of Duarte, Issler

and Spacov and of GDP encompass two recession episodes into one as comparedto the dating of T CB C It. It is also noteworthy that GDP misses the two lastrecessions as dated by T CB CIt and by Duarte, Issler and Spacov6.

Table 3 Turning-Point Comparisons Using Bry-Boschan DatingPeak Dates Through Dates

T CB CIt Duarte et al. Brazilian GDP T CB CIt Duarte et al. Brazilian GDP1980:10 NA 1981:09 NA 1981:111982:07 1982:6 1983:02 1983:10 1983:021987:02 1987:04 1988:3 1988:10 1989:02 1988:101989:06 1989:08 1989:6 1990:041991:07 1991:12 1991:03 1991:12

1994:12 1995:03 1994:12 1995:07 1995:09 1995:071997:10 1997:10 1997:10 1999:02 1999:02 1999:012000:12 2001:092002:10 2002:4 2003:06

Notes: The analysis in Duarte et al. (2004) starts in 1982:05, therefore could not have dated the recession of 1980.Brazilian GDP dating uses the monthly series constructed by Issler and Notini (2008).

Given the results in Table 3, we can compute how frequent Brazilian recessionsare. From 1980-2007:11 we have a total of 9 recessions. On average, we observein this period one recession at approximately every 3 years and 3 months, which issubstantially more frequent than the U.S. historical average of one recession aboutevery 5 years. Recessions in Brazil also last longer than U.S. recessions: while ourslast about 12 months, on average, U.S. recessions last typically from 6 months toone year, on average (in our sample period here 1980:1 to 2007:11 U.S. recessionslasted, on average, 9 months). Indeed, Duarte, Issler and Spacov make the pointthat this behavior may be due to hardships that the Brazilian economy has enduredin the post-1980 era, where GDP growth declined form about 7% a year in real termsprior to 1980 to about 2.2% a year after 1980.

Table 4 below lists Brazilian recessions from 1980:1 to 2007:11 when the datingof turning points is made using the modied Bry and Boschan technique proposedby Mnch and Uhlig (2005). The latter takes into account asymmetry dierences in

peak and through dating, which may be at work to explain the dierence in dating6 This behavior GDP missing the last two recessions vanishes if one uses the modied Bry-

Boschan dating method proposed in Mnch and Uhlig (2005) to date all three indices.

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between the Bry and Boschan and the Mnch and Uhlig method. Here, the datingof peaks in T CB CIt is identical to that in Brazilian GDP, whereas the dating ofthroughs is almost identical.

Table 4 Turning-Point Comparisons Using Mnch and Uhlig DatingPeak Dates Through Dates

T CB CIt Duarte et al. Brazilian GDP T CB CIt Duarte et al. Brazilian GDP1980:10 NA 1980:10 1981:09 NA 1981:111982:07 1982:07 1983:02 1983:021987:02 1987:04 1987:02 1988:10 1989:02 1988:101989:06 1989:08 1989:06 1990:04 1990:041991:07 1991:07 1991:12 1991:12 1991:121994:12 1994:12 1994:12 1995:07 1995:9 1995:071997:10 1997:10 1997:10 1999:02 1999:02 1999:012000:12 2000:12 2000:12 2001:09 2001:9 2001:092002:10 2002:10 2003:06 2003:03

Notes: The analysis in Duarte et al. (2004) starts in 1982:05, therefore could not have dated the recession of 1980.Brazilian GDP dating uses the monthly series constructed by Issler and Notini (2008).

Taking into account the overall results of the dating exercise shows that theback-casting of income and employment proposed in this paper has the followingproperties: (i) generates sensible results for those series in the back-cast period; (ii)generates a sensible composite coincident index of economic activity. The latter isable to approximate reasonably well the turning points of monthly GDP and thoseof the TCB index using the retired income and employment series in Duarte, Isslerand Spacov (2004). Of course, there are more similarities in turning-point dating

when dating uses the technique proposed by Mnch and Uhlig.Because of these results, we believe that the strategy we chose in this paperto construct a long span time-series for the Brazilian coincident indicator was thebest possible. Despite of our belief, we have also considered an alternative exercise:chaining the current employment and income series with their respective series retiredby IBGE. The results of the latter, in terms of dating Brazilian cycles, were inferiorto that of the back-cast series. For example, in terms of the Quadratic ProbabilityScore(QP S), which measures the in-sample frequency of erroneous dating, when wetake the GDP dating as a benchmark, our technique produced QP S = 0:26, whilethe chained series produced QP S = 0:34. Similar results were obtained when weconsider only recession periods as dated by monthly GDP. What probably explains

the superior dating of our chosen technique was that the redesign of the MonthlyEmployment Surveywas drastic. Hence, chaining was done using two completely

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dierent series7. Indeed, we observe also an increase in "incorrect" dating whenchained-series coincident indicators are evaluated vis--vis the dating in Duarte, Isslerand Spacov.

Finally, we link our dating of Brazilian recessions with economic episodes in Braziland/or abroad, trying also to identify in each recession, the most important factor forits occurrence and the transmission mechanism from factor to the four series in thecoincident index. The recession in 1980-81 can be linked to the increase in interestrates by the FED in the early 1980s which was later responsible for the emerging-market (mostly Latin America) debt crisis. The 1982-83 recession is related to theLatin American debt crisis, where international credit to these economies came to ahalt after the Mexican moratorium in 1982. In these two recessions, there was anexternal factor at work. In 1980-81, this external factor was the increase of foreigninterest rates, which reduced domestic demand and economic activity. In 1982-83,due to the Mexican Moratorium, there was a halt to international lending to Brazil

as well as capital ight abroad, both working towards reducing economic activitydomestically.

The next three recession were "home made": 1987, 1989, 1991. In them, theBrazilian government could not curb high ination with many unsuccessful economicplans, which had in common the absence of long-term scal discipline. In all of them,a sudden transitory contraction of the money supply was observed, which could notbe sustained in the long run due to the lack of scal discipline.

After the Real Plan, in July 1994, ination nally gets under control and mostrecessions are again related to events abroad, which generated capital ight andthus prompted a sudden rise in domestic interest rates as a reaction to keep foreigncapital in domestic markets. The Mexican crisis in 1994 aected Brazil and otheremerging markets. In 1997-98, the Asian, the Russian, and the Brazilian crises hadsimilar eects here and in other emerging markets. On these three occasions domesticinterest rates risen to very high levels, leading to a reduction in domestic economicactivity. In 2000-01 our local energy-supply crisis (electrical energy) was responsibleto an economy-wide crisis, while in 2002-03 international markets were nervous withBrazilian high indebtness and a newly elected "left-wing" president.

7 Another alternative would be to only use industrial production and sales to construct thecomposite index up to 2002:2, and then use the four usual series from 2002:3 onwards. Thisprocedure would probably induce structural changes in mean and variance of the composite indexafter 2002:3.

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4.4 The Composite Leading Indicator

Here we propose and evaluate the tracking performance of ten dierent leading in-dices vis--vis the coincident index proposed in the previous section. This is done

for two dierent ways. The rst is a typical in-sample analysis and comprises thewhole period 1980:1 to 2007:11. Such an exercise is of limited practical importance,since it does not take into account the usual lags in data releases and the fact thatdating algorithms, such as Bry-Boschan, requires at least six months ahead of data todetect a recession today. In order to track closely their future use as leading indica-tors, we also devised an out-of-sample exercise where leading indices were recursivelycomputed using the most recent observations available and were forecast six monthsahead in order to date the current state of the economy (recession vs. expansion).The latter is then confronted to the realizations of the future coincident index usingtheQP Sstatistic. In this second exercise, we use the period 1980:1 to 1994:12 as astarting point to compute weights of the series in the leading indices. From 1995:1to 2007:11, these leading indices have their tracking performance evaluated vis--visthe coincident index.

4.4.1 Data Properties and Evaluation Methods

The selection of a leading indicator index involves three steps: (i) select an appropri-ate indicator as a measure of economic activity to be targeted, also called a referenceseries; (ii) select appropriate economic and nancial indicators as predictors of theturning points of the reference series; (iii) combine the selected leading series in orderto construct a composite leading index. We search for series to be in the leading in-

dices that satisfy the following conditions: (a) are observable at a monthly frequencyfor the period 1980-2007:11; (b) which have timely data releases and small revisionsregarding nal data gures.

Recent research has shown that business-tendency survey data are particularlysuitable for business cycle monitoring and forecasting. Business tendency surveysare conducted in all OECD member countries and have proved to be a cost-eectivemeans of generating timely information on short-term economic uctuations. InBrazil, Getulio Vargas Foundation (FGV) is a pioneering institution that computessurveys of economic activity. These include a survey of consumer expectations andanother on business expectations on industrial production and related series: inowof new orders, level of book orders, stocks of nished goods, etc8.

8 FGVs survey series are computed on a quarterly frequency up to September 2005. From thenon, surveys were then conducted on a monthly basis. Therefore, there is the need to interpolate thedata on quarterly frequency to have a homogeneous series on a monthly basis. Our interpolation

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From FGVs survey series and other Brazilian databases (IBGE, IPEADATA, andthe Central Banks), we selected 44 series that are candidates of being leading seriesin leading indices. Our choice was guided by the international experience (Stock

and Watson (1989, 1993)) and also by local experience (Duarte, Issler and Spacov(2004)).All leading nominal series were deated to reect their purchasing power as of

March, 2008. The deator used was the Brazilian General Price Index IGP-DI calculated by FGV. All series denominated in foreign currency were converted intoBrazilian Reais at the prevailing exchange rate and subsequently deated. All serieswere logged, unless logs could not be taken of the original series (potentially zero ornegative gures). All series were also seasonally adjusted prior to the analysis usingthe X-12 procedure, whenever a seasonal pattern in them was detected.

With the exception of the survey-tendency series, all leading series were tested forunit roots. Survey series are bounded series by construction, which is theoretically

inconsistent with the presence of unit roots in them. To test for unit roots we usedthe Augmented Dickey-Fuller (ADF) test, the Phillips and Perron (1988) test, andthe stationarity test proposed by Kwiatkowski et al. (1992). All series with a unitroot were transformed into rst dierences (logs) prior to forming a composite index9.

In order to measure the quality with which a leading series correctly anticipatethe state of the economy implied by the coincident series (recession or expansion),we use a criterion originally proposed by Diebold and Rudebusch (1990), and lateremployed by Zhang and Zhuang (2002) and Gallardo and Pedersen (2007). TheQuadratic Probability Score, labelled as QP S(h), is given by:

QP S(h) =

T

Xt=1

(Pt Rt)2

T (11)

where Ptdenotes the predicted state outcomes from a candidate leading indicator andRtdenotes the observed state outcome of the reference series. Both are equal to onefor a turning point and zero otherwise;Tis the total number of sample observations,while h is the horizon in which the leading series potentially predicts the referenceseries. By construction, the value ofQP S(h)ranges between zero and one, with zeroindicating a perfect t for the the state of the economy of the reference series hperiods in advance.

Next, we describe the basic criteria used to select the leading series that will

method was, again, Mnch and Uhligs (2005).9 ADF unit-root test results other test results are available upon request.

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compose our index. First, for each series, we calculate the optimum (minimum)QP S(h)value, denoted by QP S(h), where h is the resulting optimum lag. To bea leading series candidate, the series must have h >0in QP S(h). This means that

the series is leading not lagging or coincident to the reference series. Second, weapply Granger (1969) causality tests in order to examine whether the leading seriesprecedes the reference series. We expect that a leading series Granger-causes thereference series but is not Granger-caused by it.

In the Appendix, Table A1 shows the QP S(h), h, and Granger-causality testresults. The majority of the potential leading series do not Granger cause the coin-cident series. The exceptions are some FGVs survey series, in addition to SELIC Central Banks basic interest rate and IBOVESPA Brazilian Stock MarketIndex. From them, IBOVESPA shows promise, since its QP S(h) = 24:5%, andh = 5. This means that, when we take the IBOVESPA index, with a lag of 5months vis--vis period t, it correctly predicts 75:5%of the state of the economy

as measured by the peak and through behavior of our composite index. A slightlyworse result in observed to the survey series on the production of real-estate inputs QP S(h) = 25:1%, and h = 1.

The QP S()statistic has only three series with values between 10%and20%intermediate-good production, consumer-good production, and inventories, and a fewbetween20and30%. The intersection of the two criteria above Granger causalityand low QP S(h) only has the IBOVESPA index and the production of real-estate inputs. Across all potential leading series the mean lag is 3, but the medianand modal lag are 1. There are several interesting series which have h > 1 and arelatively low QP S(h): FGVs survey series on inventories (QP S(h) = 17:6%),the IBOVESPA index (QP S(h) = 24:5%), as well as a myriad of other FGVssurvey series.

4.4.2 In-Sample Analysis

Next, we present 10 ad-hoccriteria to select series to be in a leading index. Thebasic idea is that we want h to be high, QP S(h) to be low, and that a leadingseries Granger-causes the reference series but is not Granger-caused by it. We alsoinvestigate whether a series that has low h, with low QP S(h), would also have arelatively low QP S(h) for higher values of h. The 10 criteria we chose are listedbelow:

1. Select all series possessing QP S(h)less than0:4and positive optimum lag;

2. Select all series possessing QP S(h)less than0:4;

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3. Select all series that satised the Granger causality test criterion;

4. Select all series in the intersection between the rst and third criterion;

5. Select all series in the intersection between the second and third criterion;6. Select all Survey series that satised the Granger causality test criterion;

7. Select the ve series in Table A1 that have the lowest QP S(h)value;

8. Select the series for which h is between two and seven months and QP S(h)0 and QPS 0 and QP S


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the composite index has a QP S(h) = 10:15% lower than the smallest QP S(h)of the series in it. Although the QP S(h) statistic shows that LI7;t appropriatelydates the state of the economy about 90% of the time, its optimalh is rather small

just one month, on average. If we compute by how many months the leading seriesLI7;t leads T CB C It in peaks and throughs we get the following results: by2:5months for peaks and by 0:37months for throughs. Thus it does a much better jobin anticipating peaks.

There are other leading indices with a higher h in Table 5, but they all havea QP S(h) statistic that is at least two and a half times those of that ofLI7;t. Ifwe constrain the QP S(h)statistic to be below 20%, there are two other compositeindices that also fare relatively well: indicesLI2;tand LI1;t, which can be consideredas an alternative to LI7;t, especially if we take into account the fact that LI7;t doesnot perform well in terms of through prediction. For example, while LI7;t predictsthroughs with a very small average lead of0:37months, LI1;t leads T CB C It by

2:25months on average.

4.4.3 Out-of-Sample Analysis

In the out-of-sample exercise, we used the period 1980:1 to 1995:1 as a starting pointto compute weights of the series in the leading indices. For 1995:1, and each candi-date leading index, we estimated an AR(1) model to forecast all leading indices sixmonths ahead in order to date whether 1995:1 was either a recession or an expansionperiod11. We re-balanced the weights for 1995:2 using data until then, and repeatedthe forecasting exercise dating whether 1995:2 was a recession or an expansion pe-riod. This recursion ended in 2007:11. As a result, for each leading index, we have

a sample of states for the economy dated from 1995:1 to 2007:11. These were con-fronted to the realizations (observed states of the economy) of the coincident indexcomputed in the previous section. The distance between each leading index and thecoincident index was computed using the QP S statistic, h periods ahead. Table 6contains the QP S(h)results for the 10 candidate leading indices of this exercise.

In Table 6, using the AR(1) model as a benchmark to forecast leading indicesout of sample, we nd QP S(h) statistics which are higher than those in Table 5(in-sample exercise). This is expected, since in the previous exercise there was noforecasting uncertainty in predicting the state of the economy. Also, the sampleis not the same in both exercises: 1980:1-2007:11 versus 1995:1-2007:11. Trying to

11 We have done the same procedure with a ARMA (1,1) model and the with the best ARMA(p,q)model chosen by the AIC. Results using the AR(1) are superior in almost all cases and dierencesin results are of no practical importance.

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25/32

the time. Second, with much smaller weight, we also took into account its relativelygood results for the in-sample analysis in the previous section.

The performance of LI1;t can be attributed to some of its components: series

highly correlated to the international economic activity (e.g., terms of trade, exportsquantum and prices, etc.), which we previously identied as key factors determiningmany recessions in Brazil. Moreover, it also contains some key nancial variables suchas stock-market index in Brazil (IBOVESPA) and M1, as well as some importantcredit variables (SPC).

Finally, an alternative to use LI1;tas a leading index could be the use ofLI6;t, orLI2;t orLI8;t. The rst includes only series that Granger cause the coincident indexbut are not caused by it, which perhaps suggests that we should pay more attentionto Granger-causality tests in choosing series to be in a composite leading index.

5 ConclusionThis paper has three original contributions. First, by back-casting current employ-ment and income series for Brazil, we allow business-cycle research in Brazil to resumeusing methods inspired in TCBs and NBERs, which proved valuable after the com-parison made by Duarte, Issler and Spacov (2004). Indeed, the main challenge ofBrazilian business-cycle research was to be able to form a long enough coincidentindex with the usual series used in TCBs method industrial production, sales,income and employment. Here, we devoted a great deal of eort in reconstructingemployment and income using a novel exible state-space representation based onthe interpolation method of Bernanke, Gertler and Watson (1997) and Mnch and

Uhlig (2005).Once we obtained a long enough span of the usual series used in TCBs method,

we compute a new composite coincident index of Brazilian economic activity. Itsdating of recessions is compared with those in Duarte, Issler and Spacov and withthose implied by the monthly GDP estimate computed by Issler and Notini (2008).

Our last contribution is to propose a composite leading index of economic activ-ity to track our composite coincident index. This is an important topic here, sinceBrazilian research had focused mainly on the construction of coincident indices. Af-ter a wide empirical search, we settled for a composite index (LI1;t) that predictscorrectly the state of the economy (expansion vs. recession) about 70% of the time.This is achieved in a recursive exercise, where we forecast the next 6 months of theleading index in order to date whether or not the economy was in recession today.

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6 Appendix

Table A1: Leading Series QP S(h)and Granger CausalityLeading Optimum h Min QPS-QP S(h) Granger-Causes

BASE_R 1 0.4567 BDEMGLOB 3 0.2806 BDEMPREV 4 0.2866 BEXP_R 7 0.3642 NEXP_QUANTUM 12 0.3104 NHPP 1 0.4299 BHTP 1 0.3940 NIMP_R 1 0.3761 NIPA_R 11 0.5164 NM1_R 1 0.3373 CNUCI_BC 1 0.3463 CNUCI_BK 1 0.3134 CNUCI_MC 1 0.2507 CPO 1 0.4090 NPRODAUTO 1 0.2149 BPROD_BC 1 0.1254 BPROD_BCND 1 0.2328 NPROD_BI 1 0.1104 NPROD_BK 1 0.3463 NPRODINDT 1 0.3104 NESTOQUES 2 0.1761 BIBOV_R 5 0.2448 CICMS_R 1 0.3134 BINPC_R 5 0.4776 NNUCI_BR 1 0.2746 BNUCIFIESP 1 0.2478 BPROD_BCD 1 0.2746 NPROD_CAM 1 0.2627 NPRODONI 1 0.4179 NPRODPREV 3 0.2507 NPRODVEI 1 0.3224 NSAL_R 1 0.3761 NNUCI_BI 1 0.3224 B

CAMBIO_R 12 0.6000 BEXP_PRECOS 3 0.3881 NIMP_PRECOS 10 0.5045 NSELIC_R 11 0.5821 CTTROCA 2 0.3642 NDEMEXT 6 0.3164 NDEMINT 2 0.2746 BDEMPREVEXT 4 0.3463 NDEMPREVINT 4 0.2716 BIMP_QUANTUM 1 0.3343 NSPC 1 0.2537 B

Notes: i) Statistics QPS(h)and h are computed in accordance with the description of theequation (11) in the text. (ii) in the Granger causality test, the symbol C means that theleading series Granger-cause at least three out of four series that make up the coincidentindex with the reciprocal is not true. The symbol B means bi-directional causality in theGranger causality test. The symbol N indicates that the leading series not Granger causethe coincident series. The level of signicance was set at 5% in these tests and the number oflags tested was set at 3, 6, 12. To compute the results of the Granger test it was consideredthe existence of causality in at least one of these lags.

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TableA2:LeadingSeries

Seriesname

Description

Source

SeriesNam

e

Description

Source

BASE

_R

Monetarybase

Bacen

NUCI_BR

SurveyofManufacturingIndustry

FGV

SELIC

_R

Selicinterestrate

Bacen

NUCI_BC

SurveyofConsumerGoodsIndustry

FGV

M1_

R

M1moneystock

Bacen

NUCI_BK

SurveyofCapitalGoodsIndustry

FGV

IBOV

_R

Ibovespaindex

Bovespa

NUCI_MC

SurveyofConstructionMaterialsIndustry

FGV

EXP_

PR

ECOS

Exportsprices

Funcex

NUCI_BI

SurveyofIntermediariesGoodsIndustry

FGV

EXP_

QUANTUM

Quantum

ofexports

Funcex

DEMINT

SurveyofIndustry-LevelofInternalD

emand

FGV

EXP_

R

Exports(FOB)

Funcex

DEMEXT

SurveyofIndustry-LevelofExternalDemand

FGV

TTRO

CA

Termsoftrade

Funcex

DEMPREVINT

SurveyofIndustry-InternalDemandForecast

FGV

IMP_

PR

ECOS

Importsprices

Funcex

DEMPREVE

XT

SurveyofIndustry-ExternalDemand

Forecast

FGV

IMP_

QUANTUM

Quantum

ofimports

Funcex

DEMGLOB

SurveyofIndustry-LevelofGlobalDemand

FGV

IMP_

R

Imports(FOB)

Funcex

DEMPREV

SurveyofIndustry-GlobalDemandForecast

FGV

CAMBIO_

R

ExchangeRate

Bacen

EMPPREV

SurveyofIndustry-Employmentforec

ast

FGV

NUCIF

IESP

ManufacturingIndustry

Fiesp

ESTOQUE

S

SurveyofIndustry-LevelofInventories

FGV

PROD_

BC

Production-ConsumerGoods

IBGE/PIM

PRODPRE

V

SurveyofIndustry-ProductionForeca

st

FGV

PROD_

BCD

Production-ConsumerDurable

IBGE/PIM

FALENCIA

S

Bankruptcy-SaoPauloCapital

SPState

PROD_BCND

Production-ConsumptionandNonDurable

IBGE/PIM

IPA_

R

Ratio:PPItoGeneralPriceIndex

FGV

PROD

_BI

Production-IntermediateGoods

IBGE/PIM

SPC

Creditratingchecks

ACSP

PROD_

BK

Production-CapitalGoods

IBGE/PIM

INPC_

R

NationalConsumerPriceIndex

IBGE

PRODI

NDT

Industrialproduction-processing

industry

IBGE/PIM

ICMS_R

ICMSTaxes

Confaz

PROD

ONI

Production-buses

IBGE/PIM

HTP

Hoursworkedinproduction-industry

Fiesp

PROD

VEI

Production-vehicles

Anfavea

HPP

Hourspaid-industry

Fiesp

PRODA

UTO

Production-motors

Anfavea

PO

Staemployed-industry

Fiesp

PRODCAM

Production-trucks

Anfavea

SAL_

R

NominalSalary-industry

Fiesp

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Table A3 - Leading series in Leading Indices 1-10

LI1: DEMGLOB, DEMPREV, EXP_R, EXP_QUANTUM, IMP_R, M1_R,PRODAUTO, PROD_BC, PROD_BCND, PROD_BI, PROD_BK, PRODINDT,ESTOQUES, IBOV_R, ICMS_R, PROD_BCD, PRODPREV, EXP_PRECOS,TTROCA, DEMEXT, DEMINT, DEMPREVEXT, DEMPREVINT, SPC.

LI2: DEMGLOB, DEMPREV, EXP_R, EXP_QUANTUM, IMP_R, M1_R,NUCI_BC, NUCI_BK, NUCI_MC, PRODAUTO, PROD_BC, PROD_BCND,PROD_BI, PROD_BK, PRODINDT, ESTOQUES, IBOV_R, ICMS_R, NUCI_BR,NUCI_BI, EXP_PRECOS, TTROCA, DEMEXT, DEMINT, DEMPREVEXT,DEMPREVINT, IMP_QUANTUM, SPC.

LI3: BASE_R, M1_R, NUCI_BC, NUCI_BK, NUCI_MC, IBOV_R, NUCI_BI,CAMBIO_R, SELIC_R, DEMEXT.

LI4: M1_R, IBOV_R, DEMEXT.

LI5: M1_R, NUCI_BC, NUCI_BK, NUCI_MC, IBOV_R, NUCI_BI, DE-MEXT.

LI6: DEMGLOB, DEMPREV, IBOV_R, PRODPREV, DEMPREVINT.

LI7: PROD_BI, PROD_BC, ESTOQUES, PRODAUTO, PROD_BCND.

LI8:DEMGLOB, DEMPREV, IBOV_R, PRODPREV, DEMEXT, DEMPREVINT.

LI9: DEMGLOB, DEMPREV, PRODPREV, DEMEXT, DEMPREVINT, DEM-PREVEXT.

LI10: DEMGLOB, DEMPREV, ESTOQUES, NUCI_MC, PRODPREV, DEMINT,DEMPREVINT, NUCI_BR.

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constructing Coincident and Leading Indeces of Economic Activity for the Brazilian Economy