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Nowcasting Norway
Matteo Luciani∗ECARES, SBS-EM, Université libre de Bruxelles and F.R.S.-FNRS
Lorenzo RicciECARES, SBS-EM, Université libre de Bruxelles
February 4, 2013
Abstract
We produce predictions of the previous, the current, and the next quarter of Norwe-gian GDP. To this end, we estimate a Bayesian Dynamic Factor model on a panel of 14variables (all followed closely by market operators) ranging from 1990 to 2011. By meansof a real time forecasting exercise we show that the Bayesian Dynamic Factor Model out-performs a standard benchmark model, while it performs equally well than the BloombergSurvey. Additionally, we use our model to produce annual GDP growth rate nowcast. Weshow that our annual nowcast outperform the Norges Bank’s projections of current yearGDP.
Keywords: Real-Time Forecasting, Bayesian Factor model, Nowcasting.JEL classification: C32, C53, E37.
∗Corresponding address: Matteo Luciani, ECARES, Solvay Brussels School of Economics and Management,Université libre de Bruxelles, 50 Av F.D. Roosevelt CP114/04, B1050 Brussels, Belgium. Phone: +3226503366;email: [email protected] are indebted to Daniela Bragoli, Alberto Caruso, Domenico Giannone, Silvia Miranda Agrippina, MicheleModugno and David Veredas for useful suggestions and comments. We also would like to thank Now-CastingEconomics for advice, feedback and access to data. Matteo Luciani is Chargé de Recherches F.R.S.-F.N.R.S.and gratefully acknowledge their financial support. Of course, any errors is our responsibility.
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1 Introduction
Due to publication delays of economic data, institutions are always forced to set their policieswithout knowing the current state of the economy, and, sometimes, even without knowingthe recent past. Institutions have practically solved this problem by producing predictions ofthe current/previous quarter either by judgmental processes, or by simple univariate models.Surprisingly, despite being of great interest for institutions, this problem received almost noattention by the academic literature until recently, when Evans (2005) and Giannone et al.(2008) formalized the problem in statistical models.
In this paper, we produce predictions of the previous, the current, and the next quarter ofNorwegian GDP. 1 To this end, we estimate a Bayesian Dynamic Factor model (D’Agostinoet al., 2012) on a panel of 14 variables (all followed closely by market operators) ranging from1990 to 2011.2
There exists a large literature on nowcasting with Dynamic Factor models (DFM), whichhas shown that DFMs produce nowcasts that outperform standard univariate benchmark suchas random walk models, autoregressive (AR) models, and bridge models, and that performsas well as institutional forecasts. Moreover, this literature has shown that, as more datapertaining the current quarter become available, the nowcasting error decreases monotonically,that is the DFM is able to revise efficiently its prediction as new data are released. A non-exhaustive list of papers that has used DFM for nowcasting is: D’Agostino et al. (2008),Rünstler et al. (2009), Matheson (2010), Marcellino and Schumacher (2010), Barhoumi et al.(2010), Angelini et al. (2011), Bańbura and Rünstler (2011), and Aastveit and Trovik (2012)(see Bańbura et al., 2011, for a review).
A common feature of this literature is the estimation of DFMs on large datasets includingreal, nominal, and financial variables. Unlike this literature, however, we estimate our modelby including only those real variables that market operators consider to be relevant. Actually,the use of DFMs estimated on a small number of variables – either selected with arbitraryjudgmental criteria (Bańbura et al., 2010, 2011) or with statistical procedures (Bai and Ng,2008; Camacho and Perez-Quiros, 2010) – is not novel. The novelty of this paper consistsin the data selection process – as in Bańbura et al. (2012) we include only the data followedclosely by market operators – and in the consideration of real variables only.
Another distinctive feature of this paper is the use of a Bayesian approach. The BDFM,recently introduced by D’Agostino et al. (2012), is an extension to the Bayesian framework ofthe Factor model introduced by Forni et al. (2000) and Stock and Watson (2002a). Comparedto the Factor model, the BDFM is able to better take into account the dynamic heterogeneityof the different variables. This is accomplished by including in the main equation many lagsof each single series and of the factors, and by including many lags in the law of motion ofthe common factors. This is possible because the Bayesian estimation shrinks parametersestimates toward a simple prior model thus limiting estimation uncertainty.
The rest of the paper is organized as follows: in Section 2, we illustrate the econometricframework, while, in Section 3, we describe the database, including the variable selection
1Henceforth, we refer to the prediction of the next quarter as forecast, to the prediction of the currentquarter as nowcast, and to the prediction of the previous quarter as backcast.
2The use of Dynamic Factor models for nowcasting has been pioneered by Giannone et al. (2008) whosuggested to use principal components and the Kalman filter, while recently it has been extended to a fullmaximum likelihood framework by Bańbura and Modugno (2012). The statistical properties of these modelsare studied in Doz et al. (2011, 2012).
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process. Then, in Section 4, we present the results, and finally, in Section 5 we conclude.
2 Econometric framework
In this Section, we present the Bayesian Dynamic Factor Model (BDFM) introduced byD’Agostino et al. (2012). Let xit be the i-th stationary variable in our panel observed atmonth t, with i = 1, . . . , n and t = 1, . . . , T , the BDFM is specified as follows:
ρi(L)xit = λi(L)ft + eit (1)a(L)ft = vt (2)
where ft and vt ∼ N (0, Ir) are r× 1 vectors containing, respectively, the common factors andthe common shocks, eit ∼ N (0, ψi) is the idiosyncratic component, and ρi(L) = (1 − ρi1L −. . . − ρipLp), λi(L) = (λi0 + λi1L + . . . + λipL
p), and a(L) = (1 − a1L − . . . − apLp) are
polynomials of order p.3 Moreover, E(vjt, eis) = 0, for all j, i, t, and s, and E(eit, ejs) = 0,for all i 6= j. Note that, although the model is specified and estimated at monthly frequency,we include also quarterly variables by constructing partially observed monthly counterpartsas explained in Bańbura and Modugno (2012) and Bańbura et al. (2011, 2012).
We estimate the model using the Gibbs Sampler. Suppose that the algorithm was run j−1times, then at the j-th iteration estimation is divided in two steps: in the first step, we drawthe factors f jt conditional on the observations {xit, i = 1, . . . , n; t = 1, . . . , T}, and conditionalon a draw of the parameters ρj−1i (L), λj−1
i (L), and aj−1(L). In the second step, we draw theparameters ρji (L), λ
ji (L), ψ
ji , a
j(L) conditional on the observations and the factors f jt .The first step is done by applying a version of the algorithm proposed by Carter and Kohn
(1994) modified to account for missing data (Bańbura and Modugno, 2012). The second step,since (1) and (2) are two sets of independent linear regressions, is straightforward and itconsists in drawing ρji (L), λ
ji (L), and ψ
ji given xit and f jt , and in drawing aj(L) given f jt .
The algorithm is initialized by principal components, which is equivalent to maximumlikelihood of the model xit = λift + eit, with ft ∼ N (0, Ir) and eit ∼ N (0, ψi) (Doz et al.,2012). That is, we impose λik = aik = 0 for k > 0, and we set f0t = fPC
t , λ0i = λPC
i , andψ0i = var(ξPC
i ), where superscript PC stands for estimated by principal components. Then, forall other iterations, we impose relatively flat priors on the coefficients, that is ψi ∼ IW(1, 3),λik ∼ N (0, τ 1
(k+1)2), and aik ∼ N (0, τ 1
(k+1)2), where τ , the parameter governing the level of
shrinkage, is set to 5.4
Every time a new data is released, the model updates the backcast, the nowcast, and theforecast of the GDP growth rate; that is, in each quarter, the model produces a sequence ofpredictions. The prediction of the GDP growth rate is obtained from the Kalman smootherby assuming that the true data generation process is given by (1) and (2) with parametersequal to the median of the posterior distribution.
Finally, let xgt be the GDP growth rate at time t, and let xvgt be the prediction of theGDP growth rate at time t obtained by using the v-th vintage of data. Then, the revisioninduced by the (v+1)-th vintage (including new data releases) is yv+1
t − yvt . Suppose that the(v + 1)-th vintage contains the release of the i-th variable at time t, xit, then we can define
3In the forecasting exercise, we set r = 1 (see discussion in the next section), and p = 12 thus being able toconsider a whole calendar year when forecasting.
4Robustness analysis for the level of shrinkage can be found in Appendix B.
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the quantity xit− xvit as the news, that is the “unexpected” component from the released data.Let Iv+1 be the set of newly released variables then, as shown in the working paper versionof Bańbura and Modugno (2012), the revision can be decomposed as a weighted average ofthe news in the latest releases:
∑i∈Iv+1
wv+1j (xit − xvit).5 This means, that we are able to
understand why our prediction has changed, and hence we can evaluate the contribution ofeach variable in the dataset in backcasting/nowcasting/forecasting GDP.
3 Data
Factor models are nowadays a common tools for forecasting.6 In addition to their goodforecasting performance, one of the characteristics that made Factor models so popular istheir ability to handle large datasets without suffering from the “curse of dimensionality”problem.
When forecasting, being able to include a large number of variables is particularly appeal-ing since it eliminates the problem of which variables to include in the model. Why includingvariable a and not variable b? Should we also include variable c? These kind of questions arecompletely ruled out when forecasting with Factor models given that these models are usuallyestimated on a hundred, or more, variables, and given that, potentially, one can include asmany variables as she wish.
Some authors have investigated whether it is really worth including a large number of vari-ables when forecasting, and results in Bańbura et al. (2010, 2011) and Barhoumi et al. (2010)show that medium size models (i.e including 10-30 variables) perform equally well than largesize models (about 100 variables). Furthermore, Luciani (2011) shows that aggregate variablesare enough to produce a good forecast of GDP, while when forecasting more disaggregatedvariables, sectoral information matters.
In this paper, we estimate the BDFM on a medium size database. Unlike this literature,however, we estimate the model only on those real variables that market operators considerto be relevant. That is, the novelty of this paper consists in the exclusion of nominal andfinancial variables, and in the data selection process.
The literature on Factor models has shown that for forecasting it suffices to include a smallnumber of factors (Stock and Watson, 2002b; Forni et al., 2003). Often, a few factors meansjust two factors, one “real” factor, and one “nominal” factor (Stock and Watson, 2005). Hence,if we exclude nominal variables, we need just one factor to capture the fluctuations in thereal economy, and that is it. In this way, we completely by-pass the issue of determining thenumber of factors, which often turns out to be controversial.
The literature on medium-size DFMs selects data either with “economic judgment” – which,essentially, amount to include only aggregate variables – (Bańbura et al., 2010, 2011) or withstatistical procedures (Bai and Ng, 2008; Camacho and Perez-Quiros, 2010). In this paper,we follow none of these approaches, but rather we select only those variables that are followedclosely by market operators. The question then is how to identify these variables. The answer
5Both the news and the weights (w) can be retrieved from the Kalman smoother output, see the workingpaper version of Bańbura and Modugno (2012) for details.
6There exists a large literature showing that Factor models outperform standard benchmark when fore-casting. A (non exhaustive) list of papers that use this approach is: Stock and Watson (2002a,b), Forni et al.(2003, 2005), Marcellino et al. (2003), Boivin and Ng (2005, 2006), Artis et al. (2005), Schumacher (2007),Giannone et al. (2008), Bańbura et al. (2011), and D’Agostino and Giannone (2012).
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is: simply by looking at websites like Bloomberg and Forex, or by looking at the websites ofnational statistics offices, and of central banks.
Practically, we proceed as follows: first, we look at the Bloomberg calendar for Norway.Second, we look at the “news” section of both the Statistisk Sentralbyra (SSb), and the NorgesBank, websites. We assume that if a variable is on the Bloomberg calendar, then it is followedclosely by market operators and it is considered to be informative of the Norwegian businesscycle. Similarly, we assume that, since these institutions produce hundreds of series, thefew series that enter the “news” section are those considered the most important by theseinstitutions, and hence likely followed by market operators.
In conclusion, our goal is to select variables with the following characteristics: (i) they arefollowed by market operators; (ii) they are (possibly) more timely than GDP; and, finally,(iii) each series includes sufficient elements for modeling purposes.
By following this strategy, we end-up with a dataset of 14 macroeconomics indicatorsranging from January 1990 to June 2011. The dataset includes indicators representing themain sectors of the real economy including construction, market services, trade and the labormarket. All variables are seasonally adjusted and, where necessary, are transformed to reachstationarity. The dataset was downloaded on May the 2nd 2012 from Haver. The completelist of variables and transformations are available in Table 1.
Table 1: Data Description and Data TreatmentHaver Variable Source F. Unit SA T. Init. Date. Day M.S142VPMI@INTSRVYS PMI NIMA m % 1 0 2-2004 3 1S142R@EUDATA Unemployment Rate EURO m % 1 0 1-1989 23 2NOSD@NORDIC Industrial Production SSb m 2005=100 1 1 1-1960 7 2NOSELE@NORDIC Employment SSb m thousands 1 1 1-1989 23 2NOSTR47C@NORDIC Retail Sales1 SSb m 2005=100 1 1 1-1979 31 1NOSTEN@NORDIC Turnover2 SSb m 2005=100 1 1 1-1998 7 2NOSIX2@NORDIC Merchandise Exports3 SSb m Mil. Kr. 1 1 1-1989 17 1NOSIM2@NORDIC Merchandise Imports3 SSb m Mil. Kr. 1 1 1-1973 17 1S142VZ@INTSRVYS Consumer Confidence TNS q % 1 0 3-1992 6 0S142QFQ@EUDATA Construction Output EURO q 2005=100 1 1 1-1995 17 2NOSNGPMC@NORDIC Gross Domestic Product SSb q † 1 1 1-1978 22 2NOSDU@NORDIC Capacity Utilization SSb q % 1 0 1-1987 29 0NONVNIS@NORDIC Industrial Confidence Indicator4 SSb q % 1 0 1-1990 27 0NONTO@NORDIC New Orders5 SSb q 2005=100 0 1 1-1990 7 2
From left to right: Haver shows the code to retrieve the series from the Haver Database; Variable reports the name of the variable;Source reports the original source of the data; F. specifies whether a variable is monthly (m) or quarterly (q); Unit reports the unitof measure of each variable; SA specifies whether a variable is seasonally adjusted (1) or non-seasonally adjusted (0) by the originalsource; T. specifies whether a variablehas been transformed to growth rates as ∆ log to reach stationarity (1) or it is considered inlevels (0); Init. Date specifies since when a variable is available (the format is either month-year, or quarter-year). Day reports theapproximate day of release of each variables; finally M. indicates after how many month after the end of the reference period thedata is released.Notes: 1Volume: Trade ex Motor Veh & Motorcycles. 2Energy Mining/Manufact/Distrib. 3excl. Ships and Oil Platforms. 4BTS:Mfg/Mining/Quarying. 5All Industries. †Mil.Chn.2009.NOKAbbreviations used for Source: TNS = TNS Gallup; EURO = Statistical Office of the European Communities; SSb = StatistiskSentralbyra; NIMA = Norsk Forbund for Innkjop og Logistikk.
Columns 9 and 10 of Table 1 give information on the publication delay of each series.Column “Day” shows (approximately) in which day of the month the series is released,7 whilecolumn “M” shows after how many months the data is published. For example, PMI is released3 days after the end of the reference month, which means that on February the 3rd we knowthe value of January, while the unemployment rate is published almost three months after thereference month (the 23rd of March we know the value of January).8 As we can see from Table
7Actually, the series are not always released the same day of the month. A series is released, say, the firstTuesday of the month, or the last Friday, or the last day of the month, which, of course, do not occur alwaysthe same day of the month. In our evaluation, we used a stylized data calendar in which each series is alwaysreleased the same day of the month.
8In the case of quarterly series: when “M” = 0, it means that the data is released the last month of thereference quarter (eg. March for the first quarter); when “M” = 1 it means that the data is released the month
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1, there are substantial differences between series in terms of their publication delay. On theone hand, surveys, sometimes labelled soft data, are very timely and are available at the endof the reference period; on the other hand, data on real activity, hard data, are available oneor two months after the reference period, with GDP and labor market indicators experiencingthe longest delay.
Finally, it is worth emphasizing that our target variable is Mainland GDP, to be distin-guished from Total GDP used as the target variable by Aastveit and Trovik (2012).9 Thischoice follows directly from the strategy that we adopt to select the data. Indeed, in the webpage of SSb there is a section named business cycle. From this section, one can clearlyunderstand that for SSb Mainland GDP is the GDP considered most important.10
4 Results
To evaluate the performance of our model we perform a real-time out of sample exercise.Backcasts, nowcasts, and forecasts are produced according to a recursive scheme (describedbelow), where the first sample starts in January 1990 and it ends in December 2005. Morespecifically, starting from January 2006, we construct real-time vintages by replicating thepattern of data availability implied by the stylized calendar. Every time a new data is released,the backcast, the nowcast, and the forecast are updated. The exercise is repeated until theend of June 2011 for a total of 419 backasts/nowcasts/forecasts. Notice that, since data weredownloaded on May 2 2012, we are not able to track data revisions. However, it is well knownthat Factor models are robust to data revisions (Giannone et al., 2008) since revision errors,which by nature are idiosyncratic, do not affect factor estimation. Anyway, we address thispoint in Appendix C.
The model is estimated at the beginning of each year using only information as of Januarythe 1st, and then the parameter are held fixed until the next year. More specifically, for thefirst window we compute the posterior distribution as described in Section 2 by running theGibbs Sampler for 10,000 iterations, by discarding the first 9,000, and by accepting 1 out of 5of the remaining 1,000 for a total of 200 accepted draws. Then, we use the estimated medianfor producing backcasts, nowcasts, and forecasts for the whole year. From the second yearonwards, since the algorithm is initialized with the median from previous year’s estimation,we compute the posterior distribution by running the Gibbs Sampler for 2,000 iterations, bydiscarding the first 1,000, and by accepting 1 out of 5 of the remaining 1,000 for a total of 200accepted draws. We, then, compute predictions using the median estimates.
The evaluation begins by comparing our model with a standard Random Walk (RW)model. We also estimated different AR models but their Mean Squared Errors (MSE) were30% worse than the one of the RW model.
after the end of the reference quarter (eg. April for the first quarter); while, when “M” = 2 the data is releasedtwo months after the end of the reference quarter.
9SSb defines Mainland Norway as consisting “of all domestic production activity except from explorationof crude oil and natural gas, services activities incidental to oil and gas, transport via pipelines and oceantransport” (see SSb website).
10It is also important to emphasize that in the business cycle section there is a link to another page namedEconomic indicators - charts. In this page are plotted 21 variables (16 real and 5 nominal). It is fair toassume that these 21 variables are those that SSb believes to be the relevant ones to describe the Norwegianbusyness cycle. 10 out of the 14 indicators that we selected with our strategy are in the list of the 16 indicatorsselected by SSb.
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Figure 1 shows the MSE of the BDFM and of the benchmark model. Figure 1 is dividedin three sections delimited by a vertical solid line. The first section shows the Mean SquaredForecasting Error (MSFE), the second section the Mean Squared Nowcasting Error (MSNE),and the third section the Mean Squared Backcasting Error (MSBE). The first two sectionsare further divided into three other sections (delimited by a vertical dashed line) representingthe three months within each quarter; while, the third section, representing the backcastingperiod, is divided in just two sections since GDP is released in the second month after the endof the reference period, and once previous quarter GDP is released, there is no more backcastto be estimated.11
Figure 1: Mean Squared ErrorQuarter-on-Quarter GDP Growth Rate
Forecast Nowcast Backcast0
0.2
0.4
0.6
0.8
1
In this plot, the solid line is the MSE of the BDFM. The dashed line is the MSE of the random walk model.The asterisk (∗) is the MSE of the Bloomberg surveys.This figure is divided in three sections delimited by a vertical solid line. The first section shows the MeanSquared Forecasting Error (MSFE), the second section the Mean Squared Nowcasting Error (MSNE), andthe third section the Mean Squared Backcasting Error (MSBE). The first two sections are further dividedinto three other sections (delimited by a vertical dashed line) representing the three months within eachquarter; while, the third section, representing the backcasting period, is divided in just two sections sinceGDP is released in the second month after the end of the reference period, and once the data is released,there is no more backcast to be estimated.
By looking at Figure 1, three main conclusions can be drawn: first, the BDFM outperformsthe benchmark model at all forecasting horizons; second, the major gains are obtained duringthe nowcasting period, as compared to the forecasting and backcasting period; and third, asmore data become available the model is able to revise correctly its prediction with a MSNEsmoothly declining from 0.69 (first nowcast) to 0.51 (last nowcast).
Table 2 analyzes in detail the contribution of each release in nowcasting GDP. In column“MSE”, we report the MSNE, which corresponds to the black line (nowcasting section) ofFigure 1. By subtracting row i to row i + 1 of column “MSE” we can find the contributionof the (i + 1)-th release in reducing the MSNE. In column “Impact”, we report the averagerevision (in absolute value) of the GDP nowcast induced by each release. In column “News”,
11For example, when dealing with the second quarter, in January, February, and March we produce a forecast,than in April, May, and June we produce a nowcast, and, finally, in July, August, and September, we producea backcast. Note however, that on August 22nd the GDP of Q2 is released, hence, in practice, the backcast isproduced only up to August the 21st.
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we report the standard deviation of the news, where, as explained in Section 2, the news isthe “unexpected” component from the released data. Finally, in column “Weight”, we reportthe average estimated weight, where the weight is the coefficient that weights the impact ofthe news on the prediction revision. Note that the average revision (in absolute value) of theGDP nowcast is approximately equal to the standard deviation of the news times its weight.
Table 2: The contribution of data releasesVariable Day MSE Impact News Weight
Mon
th1
PMI 3 0.7952 0.0378 3.2059 0.0112Industrial Production 7 0.7933 0.0091 2.1968 0.0042Turnover 7 0.7933 0.0057 3.5388 0.0011Merchandise Exports 17 0.8115 0.0057 2.6963 0.0019Merchandise Imports 17 0.8115 0.0196 3.7363 0.0052Unemployment Rate 23 0.7958 0.0095 0.0784 0.0748Employment 23 0.7958 0.0522 0.1392 0.3010Retail Sales 30 0.7766 0.0251 0.5971 0.0274
Mon
th2
PMI 3 0.7884 0.0460 3.5675 0.0179Industrial Production 7 0.7935 0.0102 1.2222 0.0055Turnover 7 0.7935 0.0033 3.4111 0.0005New Orders 7 0.7935 0.0096 7.3971 0.0012Merchandise Exports 17 0.7912 0.0481 3.8701 0.0094Merchandise Imports 17 0.7912 0.0143 2.6634 0.0054Construction Output 17 0.7912 0.0115 1.3826 0.0074Gross Domestic Product 22 0.7842 0.0719 0.4788 0.1324Unemployment Rate 23 0.7639 0.0021 0.0998 0.0232Employment 23 0.7639 0.0325 0.0965 0.2281Retail Sales 30 0.7311 0.0383 0.7179 0.0375
Mon
th3
PMI 3 0.7427 0.0536 3.7356 0.0166Consumer Confidence 6 0.6520 0.1149 9.4268 0.0124Industrial Production 7 0.6590 0.0164 1.8958 0.0075Turnover 7 0.6590 0.0087 3.2155 0.0022Merchandise Exports 17 0.6593 0.0139 3.2279 0.0033Merchandise Imports 17 0.6593 0.0203 2.7656 0.0057Unemployment Rate 23 0.6381 0.0095 0.0765 0.0877Employment 23 0.6381 0.0315 0.1140 0.2197Industrial Confidence Indicator 27 0.5864 0.1040 3.9289 0.0208Capacity Utilization 29 0.5721 0.0508 0.4199 0.0732Retail Sales 30 0.5674 0.0188 0.6080 0.0210
Column “Day” indicates which day of the month the data is released. Column “MSE” showsthe average error of the nowcast at each release (this correspond to the black line in figure1). Column “Impact” shows of the average change in GDP nowcast, due to the new datareleased. Column “News” reports the standard deviation of the news, where the news isthe “unexpected” component from the released data. Finally, column “Weight” reports theaverage estimated weight, where the weight is the coefficient that weights the impact of thenews on the revision of the nowcast. Note that the average revision (in absolute value) ofthe GDP nowcast is approximately equal to the standard deviation of the news times itsweight.
From column “MSE” we can see that the variables that contribute the most in decreasingthe MSE are Consumer Confidence, Industrial Confidence Indicator, and Capacity Utilization.All these variables are released in the third month of the quarter and are extremely timelysince they carry information on the current quarter. As expected, the release of the previousquarter GDP helps in improving the prediction. Finally, other relevant variables are the labormarket indicators, and Retail Sales, while surprisingly PMI, which is the first variable releasedwithin the month, has a very low weight and thus leads to tiny revisions.
Many of the variables that contribute the most in decreasing the MSE, are also thoseleading to the most relevant revisions in the GDP nowcast (column “Impact”). In particular,Consumer Confidence and Industrial Confidence Indicator are those that lead to the biggestrevisions, while other soft indicators such as PMI, and Capacity Utilizations leads to importantbut smaller revisions. Hard indicators, instead, do not bring big revisions in the prediction ofcurrent quarter GDP, the only exception being previous quarter GDP, labor market indicators,and Retail Sales.
Finally, from column “News” we can see that there are many variables that produces bignews, i.e. the actual release is different from the prediction of the model. However, withinthese variables, only few of them lead to big GDP nowcast revisions. For example, IndustrialProduction despite producing relevant news brings very small revisions in the nowcast. On
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the other hand, some variables such as previous quarter GDP, labor market indicators, RetailSales, and Capacity Utilization, despite producing small news, have a high weight and hencebring important revisions of the GDP nowcast.
Although widely used in academia as a benchmark model, it is not realistic that a marketoperator (for example an hedge fund, or a government agency) chooses its own strategy onthe basis of the predictions of a RW model. Therefore, we also compare our model with twoother predictions that are much more realistic than those produced by a RW model, namely:the Bloomberg Surveys (BS),12 and the Norges Bank’s projections of the annual GDP growthrate published in the Monetary Policy Report.
In Figure 1, together with the MSE of the BDFM (solid line), we show the MSE of theBloomberg Surveys (asterisk). As we can see, the performance of the BDFM are close to thatof the Bloomberg Surveys. Indeed, at the beginning of the backcasting period the MSE of theBDFM is 12.5% worse than that of the BS, but a few days before the GDP data is releasedthe BDFM’s MSE is 1% better than that of the BS. This is a relevant result since the backcastwith our model can be produced in a few minutes, at zero cost, and at any point in time,while the Bloomberg Survey involves a large community of experts.
As we said earlier in this Section, another natural competitor of our model are the NorgesBank’s (NB) projections of the annual GDP growth rate. The NB updates three times a yearits projection of the annual GDP growth rate for the current year. Since our model producesquarter-on-quarter (QoQ) GDP growth rate predictions, we need to transform these QoQpredictions into annual nowcasts. As it is explained in Appendix A, this can be easily doneby applying the approximation suggested by Mariano and Murasawa (2003).
Figure 2a shows the annual GDP growth rate (grey solid line), the annual BDFM nowcast(black solid line), and NB’s projections (black asterisks). Clearly, the BDFM outperformsthe NB’s projections. This result is also confirmed by Figure 2b, which shows the MSE ofthe two models. More specifically, we can see how the BDFM efficiently exploits the flow ofdata releases throughout the year, thus reducing consistently the nowcasting error. This isanother relevant result, since the goal of the nowcasting literature is to exploit the informationcontained in the new data releases to revise the prediction. In this Section, we have shownthat this happens both when nowcasting QoQ GDP growth rate, and when considering GDPannual growth rate nowcasts.
5 Conclusions
In this paper, by estimating a Bayesian Dynamic Factor model à la D’Agostino et al. (2012)we produce predictions of the previous, the current, and the next quarter growth rate ofNorwegian GDP. The model is estimated on a panel of 14 variables (all followed closely bymarket) ranging from 1990 to 2001.
Our analysis differs from standard nowcasting applications in three aspects. First, we usea Bayesian Dynamic Factor Model. Second, we use a small number of variables chosen becausethey are followed by market operators. Third, we consider real variables only.
12The BS consists of the median GDP prediction provided independently by a number of specialists fewdays before the GDP is released. Both the number of specialists that provide a prediction (13 on average),and the day of released of the survey (six days before GDP is published on average), varies from quarter toquarter. Note that, since the Bloomberg Survey is released few days before previous quarter GDP is released,in our terminology the BS is a backcast.
9
Figure 2: Nowcasting Annual GDP growth rate(a) Nowcast
2006 2007 2008 2009 2010−3
−2
−1
0
1
2
3
4
5
(b) Mean Squared Error
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0
0.5
1
1.5
2
In panel (a), the grey solid line is actual GDP, the black solid line is the nowcast obtained with the BDFM, while the asterisks arethe Norges Bank’s projection. In panel (b), the solid line is the MSE of the BDFM, while the asterisk (∗) is the MSE of the NorgesBank’s Projection.
By means of a real time exercise we show that the Bayesian Dynamic Factor Model out-performs a standard random walk benchmark model, and it performs equally well than theBloomberg Survey, which is the median forecast provided independently by a number of spe-cialists few days before the GDP is released.
Finally, we use our model to produce annual GDP growth rate nowcasts. This is a novelfeature of this paper, since so far the nowcasting literature has concentrated only on quarter-on-quarter GDP growth. We compare our annual nowcast with the Norges Bank’s projectionsof the annual GDP growth rate published in the Monetary Policy Report. Results of thenowcasting exercise show that the Bayesian Dynamic Factor Model clearly outperforms theNorges Bank’s projections. Furthermore, as shown by the strong decrease in the mean squarederror throughout the year, the model efficiently exploits the flow of data releases.
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Appendix A Constructing annual nowcast
As we discussed in Section 4, the Norges Bank (NB) publishes three times a year projectionsof the annual GDP growth rate for the current year. In order to compare our predictions withNB’s projections, we need to transform our quarter-on-quarter (QoQ) predictions in annualvalues. In this Appendix, we explain how we do it.
Let Xyq = 100 × log(GDP y
q ) be the GDP of the q-th quarter of year y, and let Zy =100× log(GDP y) be the GDP of year y. Then, by definition xyq = Xy
q −Xyq−1 is the quarter-
on-quarter growth rate, while zy = Zy − Zy−1 is the annual growth rate.Following Mariano and Murasawa (2003), we make use of the approximation Zy ≈ Xy
1 +Xy
2 +Xy3 +Xy
4 , which allow us to write the annual growth rate as a function of QoQ growthrates:
zy = Zy − Zy−1 ≈ (Xy1 +Xy
2 +Xy3 +Xy
4 )− (Xy−11 +Xy−1
2 +Xy−13 +Xy−1
4 )
= xy4 + 2xy3 + 3xy2 + 4xy1 + 3xy−14 + 2xy−13 + xy−12 . (A1)
Suppose we are in January of year y and that we want to forecast zy with the BDFM, whichproduces QoQ growth rate forecasts. We can do it by using equation (A1). In January of yeary we know only xy−13 and xy−12 , while we need to estimate the other terms of equation (A1).But this is easily done since xy−14 can be estimated with the backcast, xy1 can be estimated withthe nowcast, xy2 can be estimated with the forecast, while xy3 and xy4 can be easily obtainedas two-step, and three-step ahead forecasts. As the time pass by, and more data becomeavailable, the forecast of zy is updated. For example, in February the 22nd the data for xy−14
is released and it is no longer necessary to estimate it. Moreover, as time goes by also xy1, xy2,
and xy3 will be available and hence it will no longer necessary to rely on the three-step aheadforecast, on the two-step ahead forecast and on the forecast (Table A1).
Table A1: Constructing annual nowcast
Day Month xy4 xy3 xy2 xy1 xy−14 xy−13 xy−12
1 January 3s 2s f n b22 February 3s 2s f n1 April 2s f n b22 May 2s f n1 July f n b22 August f n1 October n b22 November n
This table shows how the nowcast of zy is obtained as more GDP data are released. bindicates that that specific qoq growth rate is obtained with the backcast, n with thenowcast, f with the forecast, 2s with the two-step ahead forecast, while 3s with thethree-step ahead forecasts. An empty cell means that the data is available.
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Appendix B Robustness analysis
In this Appendix, we show robustness analysis with respect to τ , the parameter governing thelevel of shrinkage. As we said in Section 2, we choose a relatively flat prior by setting τ = 5. InFigure B1, we show results for three additional level of shrinkage: τ = 1, τ = 2.5, and τ = 10.When τ = 1 we are shrinking towards zero all coefficients of lag higher than 1 (the prior forthe coefficients of lag 2 has a variance of 0.33). However, when τ = 10 we are essentially notshrinking since the prior of the coefficients of lag 12 has a variance of 0.77. Finally, the caseτ = 2.5 is an intermediate case between our benchmark specification, and the hard shrinkagescenario of τ = 1. When τ = 2.5 we are shrinking more than in the benchmark scenario butconsistently less than when τ = 1 (the variance of the prior on the coefficient at lag 4 is still0.5). Results in Figure B1 clearly show that the prediction ability of the BDFM is robust tothe level of shrinkage.
Figure B1: Mean Squared Errorfor different level of shrinkage
Forecast Nowcast Backcast0
0.2
0.4
0.6
0.8
1
In this plot, the black solid line is the MSE of the benchmark model (τ = 5), the black dashed line isthe MSE for τ = 10, the grey dashed line is the MSE for τ = 2.5, and the grey solid line is the MSE forτ = 2.5.
14
Appendix C Accounting for revisions in GDP releases
As it is well known, economic data undergo several revisions after the first estimate is released.In this paper, we use the vintage of data available on May the 2nd 2012 (henceforth the finalrelease), thus not being able to track data revisions. However, we address this point in thisAppendix by studying the robustness of the BDFM to data revisions.
In principle, the correct way of performing this exercise would consist in using historicalvintages of data, that is in using the data available at each point in time the prediction isupdated.13 Unfortunately, to the best of our knowledge, a real time database for Norway isnot available. Therefore, in order to evaluate the robustness of our model to data revisions,we follow Giannone et al. (2008) and we adopt a hybrid approach. This approach consists inevaluating the forecasting performance of our model on a new database including all the seriesconsidered so far, and a new GDP series. This new GDP series is constructed by replacingthe final release with the first release, where the data for the first release are downloaded fromBloomberg.14
Before presenting the result of this exercise, let us emphasize that the fact that we adopta hybrid approach, rather than performing the exercise using historical vintages for all dataseries, has a limited impact in this context. Indeed, it is well known that Factor models arerobust to data revisions (Giannone et al., 2008) since revision errors, which by nature areidiosyncratic, do not affect factor estimation. Therefore, we can safely assume that the factorsare well estimated despite data revisions. What cannot be assumed, instead, is that datarevisions have no impact on the prediction, i.e. on the relation between the factors and thetarget variable. However, the hybrid approach adopted here answers exactly this last question.
We begin this exercise by producing backcasts, nowcasts, and forecasts for the quarter-on-quarter GDP growth rate. To produce these predictions, we use the database modified asexplained above. In Figure C1a, together with the MSE of the BDFM (solid line), and theMSE of the Bloomberg Surveys (asterisk), we show the mean squared error made by the SSb(circle), which gives us a benchmark of how far we are from the best possible prediction. Morespecifically, the solid line in Figure C1a represents the error that we make when forecastingthe final GDP release, using the first release, while the circle represents the mean squareddifference between the first GDP estimate and the final release.
The MSEs reported in Figure C1a shows how the performance of the BDFM just slightlydeteriorates when the prediction is produced by using the GDP first release. Despite that, theperformance of our model is still comparable to (9% worse than) that of the BS (note that theMSE of the BS reported in Figure C1a is the same of that reported in Figure 1). Moreover,our error is not far from the one made by the SSb (26% worse).
We continue this exercise by producing nowcasts of the annual GDP growth rate. Asexplained in Appendix A, to produce these nowcasts we aggregate the QoQ predictions pro-duced by the model with data released by the SSb. Here, the annual nowcast is obtained byusing the final GDP release. Let us give a practical example to clarify. Suppose we want to
13Let us make use of a concrete situation to better explain this point. Suppose we are in February the 3rd
2009, and that we want to nowcast the 2009Q1 GDP growth rate. The best way to perform our evaluationwould be to construct our 2009Q1 GDP nowcast by using the vintage of data available as of February the3rd 2009, whereas, so far, we have used the vintages available as of May the 2nd 2012. The comparison usinghistorical vintages is also more fair since when producing their predictions, both the Bloomberg experts, andthe Norges Bank did not know the revised series.
14Note that Bloomberg data are available only as from 2002Q2, and hence the series that we use in the newevaluation is a combination of the revised GDP and the first release.
15
construct the nowcast of the annual GDP growth rate for 2008, z08. Define x081 the QoQ GDPgrowth rate of the first quarter of 2008, then z08 is computed as (see Appendix A for details):
z08 = x084 + 2x083 + 3x082 + 4x081 + 3x074 + 2x073 + x072 .
Now, suppose we are in July the 10th 2008. Our annual nowcast is computed as
z08 = x084 + 2x083 + 3x082 + 4x081 + 3x074 + 2x073 + x072 ,
where x084 , x083 , and x082 , are respectively the forecast, the nowcast, and the backcast obtainedwith our model, while all the other terms are data released by the SSb. In the exerciseperformed here, x084 , x083 , and x082 are obtained by using the first release of GDP as discussedearlier in this Section, while x081 , x074 , x073 , and x072 are the final GDP release.
In this exercise, our information set is slightly superior than that of the Norges Bank. Onthe one hand, it is true that the NB could not observe the final GDP release, on the otherhand, though, the NB observes the GDP revisions that occurred during the current year. Thealternative would have been to replace x081 , x074 , x073 , and x072 with the first release, which,however, over-penalizes our model since it implies assuming that the first release is neverrevised. Therefore, it is true that our information is superior, but just slightly superior sincethe NB observed the first and second revision of QoQ GDP growth rate before performing itsprojection (in July 2008 x072 , and x073 have already been revised at least twice, while x074 hasalready been revised once).
Figure C1b reports the MSE of the BDFM (solid line) and that of the Norges Bankprojections (black asterisks). As we can see, despite the performance of our model deteriorates,it is still better than that of the Norges Bank.
Figure C1: Accounting for Data Revision(a) Quarter-on-Quarter MSE
Forecast Nowcast Backcast0
0.2
0.4
0.6
0.8
1
(b) Annual MSE
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
In panel (a), the solid line is the MSE of the BDFM, the dashed line is the MSE of the random walk model, the asterisk (∗) is the MSEof the Bloomberg surveys, whereas the circle (◦) is the MSE made by the SSb. More specifically, the solid line is the error that wemake when forecasting the final GDP release, using the first release, while the circle is the mean squared difference between the firstGDP estimate and the final release. The first section of panel (a) shows the Mean Squared Forecasting Error (MSFE), the secondsection the Mean Squared Nowcasting Error (MSNE), and the third section the Mean Squared Backcasting Error (MSBE). The firsttwo sections are further divided into three other sections (delimited by a vertical dashed line) representing the three months withineach quarter; while, the third section, representing the backcasting period, is divided in just two sections since GDP is released inthe second month after the end of the reference period, and once the data is released, there is no more backcast to be estimated.In panel (b), the straight line is the MSE of the BDFM, while the asterisk is the mean squared error of Norges Bank’s Projection.
16
