Matteo Luciani. Lorenzo Ricci

Transcription

1 Nowcasting Norway Matteo Luciani SBS EM, ECARES, Université Libre de Bruxelless and FNRS Lorenzo Ricci SBS EM, ECARES,, Université Libre de Bruxelles ECARES working paper ECARES ULB - CP 4/ /04 50, F.D. Roosevelt Ave., B-0500 Brussels BELGIUM B

2 Nowcasting Norway Matteo Luciani ECARES, SBS-EM, Université libre de Bruxelles and F.R.S.-FNRS Lorenzo Ricci ECARES, SBS-EM, Université libre de Bruxelles February 4, 203 Abstract We produce predictions of the previous, the current, and the next quarter of Norwegian GDP. To this end, we estimate a Bayesian Dynamic Factor model on a panel of 4 variables (all followed closely by market operators) ranging from 990 to 20. By means of a real time forecasting exercise we show that the Bayesian Dynamic Factor Model outperforms a standard benchmark model, while it performs equally well than the Bloomberg Survey. Additionally, we use our model to produce annual GDP growth rate nowcast. We show that our annual nowcast outperform the Norges Bank s projections of current year GDP. 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 CP4/04, B050 Brussels, Belgium. Phone: ; matteo.luciani@ulb.ac.be. We are indebted to Daniela Bragoli, Alberto Caruso, Domenico Giannone, Silvia Miranda Agrippina, Michele Modugno and David Veredas for useful suggestions and comments. We also would like to thank Now-Casting Economics 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.

3 Introduction Due to publication delays of economic data, institutions are always forced to set their policies without knowing the current state of the economy, and, sometimes, even without knowing the recent past. Institutions have practically solved this problem by producing predictions of the current/previous quarter either by judgmental processes, or by simple univariate models. Surprisingly, despite being of great interest for institutions, this problem received almost no attention 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 of Norwegian GDP. To this end, we estimate a Bayesian Dynamic Factor model (D Agostino et al., 202) on a panel of 4 variables (all followed closely by market operators) ranging from 990 to There exists a large literature on nowcasting with Dynamic Factor models (DFM), which has shown that DFMs produce nowcasts that outperform standard univariate benchmark such as random walk models, autoregressive (AR) models, and bridge models, and that performs as well as institutional forecasts. Moreover, this literature has shown that, as more data pertaining 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 nonexhaustive list of papers that has used DFM for nowcasting is: D Agostino et al. (2008), Rünstler et al. (2009), Matheson (200), Marcellino and Schumacher (200), Barhoumi et al. (200), Angelini et al. (20), Bańbura and Rünstler (20), and Aastveit and Trovik (202) (see Bańbura et al., 20, for a review). A common feature of this literature is the estimation of DFMs on large datasets including real, nominal, and financial variables. Unlike this literature, however, we estimate our model by 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 arbitrary judgmental criteria (Bańbura et al., 200, 20) or with statistical procedures (Bai and Ng, 2008; Camacho and Perez-Quiros, 200) is not novel. The novelty of this paper consists in the data selection process as in Bańbura et al. (202) we include only the data followed closely 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. (202), is an extension to the Bayesian framework of the Factor model introduced by Forni et al. (2000) and Stock and Watson (2002a). Compared to the Factor model, the BDFM is able to better take into account the dynamic heterogeneity of the different variables. This is accomplished by including in the main equation many lags of each single series and of the factors, and by including many lags in the law of motion of the common factors. This is possible because the Bayesian estimation shrinks parameters estimates toward a simple prior model thus limiting estimation uncertainty. The rest of the paper is organized as follows: in Section 2, we illustrate the econometric framework, while, in Section 3, we describe the database, including the variable selection Henceforth, we refer to the prediction of the next quarter as forecast, to the prediction of the current quarter as nowcast, and to the prediction of the previous quarter as backcast. 2 The use of Dynamic Factor models for nowcasting has been pioneered by Giannone et al. (2008) who suggested to use principal components and the Kalman filter, while recently it has been extended to a full maximum likelihood framework by Bańbura and Modugno (202). The statistical properties of these models are studied in Doz et al. (20, 202). 2

4 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 by D Agostino et al. (202). Let x it be the i-th stationary variable in our panel observed at month t, with i =,..., n and t =,..., T, the BDFM is specified as follows: ρ i (L)x it = λ i (L)f t + e it () a(l)f t = v t (2) where f t and v t N (0, I r ) are r vectors containing, respectively, the common factors and the common shocks, e it N (0, ψ i ) is the idiosyncratic component, and ρ i (L) = ( ρ i L... ρ ip L p ), λ i (L) = (λ i0 + λ i L λ ip L p ), and a(l) = ( a L... a p L p ) are polynomials of order p. 3 Moreover, E(v jt, e is ) = 0, for all j, i, t, and s, and E(e it, e js ) = 0, for all i j. Note that, although the model is specified and estimated at monthly frequency, we include also quarterly variables by constructing partially observed monthly counterparts as explained in Bańbura and Modugno (202) and Bańbura et al. (20, 202). We estimate the model using the Gibbs Sampler. Suppose that the algorithm was run j times, then at the j-th iteration estimation is divided in two steps: in the first step, we draw the factors f j t conditional on the observations {x it, i =,..., n; t =,..., T }, and conditional on a draw of the parameters ρ j i (L), λ j i (L), and a j (L). In the second step, we draw the parameters ρ j i (L), λj i (L), ψj i, aj (L) conditional on the observations and the factors f j t. The first step is done by applying a version of the algorithm proposed by Carter and Kohn (994) modified to account for missing data (Bańbura and Modugno, 202). The second step, since () and (2) are two sets of independent linear regressions, is straightforward and it consists in drawing ρ j i (L), λj i (L), and ψj i given x it and f j t, and in drawing aj (L) given f j t. The algorithm is initialized by principal components, which is equivalent to maximum likelihood of the model x it = λ i f t + e it, with f t N (0, I r ) and e it N (0, ψ i ) (Doz et al., 202). That is, we impose λ ik = a ik = 0 for k > 0, and we set ft 0 = ˆf t P C, λ 0 i = ˆλ P i C, and ψi 0 = var(ˆξ i P C ), where superscript P C stands for estimated by principal components. Then, for all other iterations, we impose relatively flat priors on the coefficients, that is ψ i IW(, 3), λ ik N (0, τ ), and a (k+) 2 ik N (0, τ ), where τ, the parameter governing the level of (k+) 2 shrinkage, is set to 5. 4 Every time a new data is released, the model updates the backcast, the nowcast, and the forecast of the GDP growth rate; that is, in each quarter, the model produces a sequence of predictions. The prediction of the GDP growth rate is obtained from the Kalman smoother by assuming that the true data generation process is given by () and (2) with parameters equal to the median of the posterior distribution. Finally, let x gt be the GDP growth rate at time t, and let ˆx v gt be the prediction of the GDP growth rate at time t obtained by using the v-th vintage of data. Then, the revision induced by the (v + )-th vintage (including new data releases) is ŷt v+ ŷt v. Suppose that the (v + )-th vintage contains the release of the i-th variable at time t, x it, then we can define 3 In the forecasting exercise, we set r = (see discussion in the next section), and p = 2 thus being able to consider a whole calendar year when forecasting. 4 Robustness analysis for the level of shrinkage can be found in Appendix B. 3

5 the quantity x it ˆx v it as the news, that is the unexpected component from the released data. Let I v+ be the set of newly released variables then, as shown in the working paper version of Bańbura and Modugno (202), the revision can be decomposed as a weighted average of i I v+ w v+ j (x it ˆx v it ).5 This means, that we are able to the news in the latest releases: understand why our prediction has changed, and hence we can evaluate the contribution of each 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 good forecasting performance, one of the characteristics that made Factor models so popular is their 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 appealing since it eliminates the problem of which variables to include in the model. Why including variable a and not variable b? Should we also include variable c? These kind of questions are completely ruled out when forecasting with Factor models given that these models are usually estimated on a hundred, or more, variables, and given that, potentially, one can include as many variables as she wish. Some authors have investigated whether it is really worth including a large number of variables when forecasting, and results in Bańbura et al. (200, 20) and Barhoumi et al. (200) show that medium size models (i.e including 0-30 variables) perform equally well than large size models (about 00 variables). Furthermore, Luciani (20) shows that aggregate variables are enough to produce a good forecast of GDP, while when forecasting more disaggregated variables, 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 consider to be relevant. That is, the novelty of this paper consists in the exclusion of nominal and financial variables, and in the data selection process. The literature on Factor models has shown that for forecasting it suffices to include a small number of factors (Stock and Watson, 2002b; Forni et al., 2003). Often, a few factors means just 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 the real economy, and that is it. In this way, we completely by-pass the issue of determining the number 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., 200, 20) or with statistical procedures (Bai and Ng, 2008; Camacho and Perez-Quiros, 200). In this paper, we follow none of these approaches, but rather we select only those variables that are followed closely by market operators. The question then is how to identify these variables. The answer 5 Both the news and the weights (w) can be retrieved from the Kalman smoother output, see the working paper version of Bańbura and Modugno (202) for details. 6 There exists a large literature showing that Factor models outperform standard benchmark when forecasting. 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. (20), and D Agostino and Giannone (202). 4

6 is: simply by looking at websites like Bloomberg and Forex, or by looking at the websites of national 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 Norges Bank, websites. We assume that if a variable is on the Bloomberg calendar, then it is followed closely by market operators and it is considered to be informative of the Norwegian business cycle. Similarly, we assume that, since these institutions produce hundreds of series, the few series that enter the news section are those considered the most important by these institutions, and hence likely followed by market operators. In conclusion, our goal is to select variables with the following characteristics: (i) they are followed 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 4 macroeconomics indicators ranging from January 990 to June 20. The dataset includes indicators representing the main sectors of the real economy including construction, market services, trade and the labor market. All variables are seasonally adjusted and, where necessary, are transformed to reach stationarity. The dataset was downloaded on May the 2 nd 202 from Haver. The complete list of variables and transformations are available in Table. Table : Data Description and Data Treatment Haver Variable Source F. Unit SA T. Init. Date. Day M. S42VPMI@INTSRVYS PMI NIMA m % S42R@EUDATA Unemployment Rate EURO m % NOSD@NORDIC Industrial Production SSb m 2005= NOSELE@NORDIC Employment SSb m thousands NOSTR47C@NORDIC Retail Sales SSb m 2005= NOSTEN@NORDIC Turnover 2 SSb m 2005= NOSIX2@NORDIC Merchandise Exports 3 SSb m Mil. Kr NOSIM2@NORDIC Merchandise Imports 3 SSb m Mil. Kr S42VZ@INTSRVYS Consumer Confidence TNS q % S42QFQ@EUDATA Construction Output EURO q 2005= NOSNGPMC@NORDIC Gross Domestic Product SSb q NOSDU@NORDIC Capacity Utilization SSb q % NONVNIS@NORDIC Industrial Confidence Indicator 4 SSb q % NONTO@NORDIC New Orders 5 SSb q 2005= 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 unit of measure of each variable; SA specifies whether a variable is seasonally adjusted () or non-seasonally adjusted (0) by the original source; T. specifies whether a variablehas been transformed to growth rates as log to reach stationarity () or it is considered in levels (0); Init. Date specifies since when a variable is available (the format is either month-year, or quarter-year). Day reports the approximate day of release of each variables; finally M. indicates after how many month after the end of the reference period the data is released. Notes: 2 Volume: Trade ex Motor Veh & Motorcycles. Energy Mining/Manufact/Distrib. 3 excl. Ships and Oil Platforms. 4 BTS: Mfg/Mining/Quarying. 5 All Industries. Mil.Chn.2009.NOK Abbreviations used for Source: TNS = TNS Gallup; EURO = Statistical Office of the European Communities; SSb = Statistisk Sentralbyra; NIMA = Norsk Forbund for Innkjop og Logistikk. Columns 9 and 0 of Table give information on the publication delay of each series. Column Day shows (approximately) in which day of the month the series is released, 7 while column M shows after how many months the data is published. For example, PMI is released 3 days after the end of the reference month, which means that on February the 3 rd we know the value of January, while the unemployment rate is published almost three months after the reference month (the 23 rd of March we know the value of January). 8 As we can see from Table 7 Actually, the series are not always released the same day of the month. A series is released, say, the first Tuesday of the month, or the last Friday, or the last day of the month, which, of course, do not occur always the same day of the month. In our evaluation, we used a stylized data calendar in which each series is always released the same day of the month. 8 In the case of quarterly series: when M = 0, it means that the data is released the last month of the reference quarter (eg. March for the first quarter); when M = it means that the data is released the month 5

7 , there are substantial differences between series in terms of their publication delay. On the one hand, surveys, sometimes labelled soft data, are very timely and are available at the end of the reference period; on the other hand, data on real activity, hard data, are available one or two months after the reference period, with GDP and labor market indicators experiencing the longest delay. Finally, it is worth emphasizing that our target variable is Mainland GDP, to be distinguished from Total GDP used as the target variable by Aastveit and Trovik (202). 9 This choice follows directly from the strategy that we adopt to select the data. Indeed, in the web page of SSb there is a section named business cycle. From this section, one can clearly understand that for SSb Mainland GDP is the GDP considered most important. 0 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 (described below), where the first sample starts in January 990 and it ends in December More specifically, starting from January 2006, we construct real-time vintages by replicating the pattern 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 the end of June 20 for a total of 49 backasts/nowcasts/forecasts. Notice that, since data were downloaded on May 2 202, we are not able to track data revisions. However, it is well known that 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 this point in Appendix C. The model is estimated at the beginning of each year using only information as of January the st, and then the parameter are held fixed until the next year. More specifically, for the first window we compute the posterior distribution as described in Section 2 by running the Gibbs Sampler for 0,000 iterations, by discarding the first 9,000, and by accepting out of 5 of the remaining,000 for a total of 200 accepted draws. Then, we use the estimated median for producing backcasts, nowcasts, and forecasts for the whole year. From the second year onwards, 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, by discarding the first,000, and by accepting out of 5 of the remaining,000 for a total of 200 accepted 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) were 30% 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 released two months after the end of the reference quarter. 9 SSb defines Mainland Norway as consisting of all domestic production activity except from exploration of crude oil and natural gas, services activities incidental to oil and gas, transport via pipelines and ocean transport (see SSb website). 0 It is also important to emphasize that in the business cycle section there is a link to another page named Economic indicators - charts. In this page are plotted 2 variables (6 real and 5 nominal). It is fair to assume that these 2 variables are those that SSb believes to be the relevant ones to describe the Norwegian busyness cycle. 0 out of the 4 indicators that we selected with our strategy are in the list of the 6 indicators selected by SSb. 6

8 Figure shows the MSE of the BDFM and of the benchmark model. Figure is divided in three sections delimited by a vertical solid line. The first section shows the Mean Squared Forecasting Error (MSFE), the second section the Mean Squared Nowcasting Error (MSNE), and the third section the Mean Squared Backcasting Error (MSBE). The first two sections are further divided into three other sections (delimited by a vertical dashed line) representing the three months within each quarter; while, the third section, representing the backcasting period, is divided in just two sections since GDP is released in the second month after the end of the reference period, and once previous quarter GDP is released, there is no more backcast to be estimated. Figure : Mean Squared Error Quarter-on-Quarter GDP Growth Rate Forecast Nowcast Backcast 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 Mean Squared Forecasting Error (MSFE), the second section the Mean Squared Nowcasting Error (MSNE), and the third section the Mean Squared Backcasting Error (MSBE). The first two sections are further divided into three other sections (delimited by a vertical dashed line) representing the three months within each quarter; while, the third section, representing the backcasting period, is divided in just two sections since GDP 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, three main conclusions can be drawn: first, the BDFM outperforms the benchmark model at all forecasting horizons; second, the major gains are obtained during the nowcasting period, as compared to the forecasting and backcasting period; and third, as more data become available the model is able to revise correctly its prediction with a MSNE smoothly declining from 0.69 (first nowcast) to 0.5 (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) of Figure. By subtracting row i to row i + of column MSE we can find the contribution of the (i + )-th release in reducing the MSNE. In column Impact, we report the average revision (in absolute value) of the GDP nowcast induced by each release. In column News, For 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 produce a backcast. Note however, that on August 22 nd the GDP of Q2 is released, hence, in practice, the backcast is produced only up to August the 2 st. 7

9 we report the standard deviation of the news, where, as explained in Section 2, the news is the unexpected component from the released data. Finally, in column Weight, we report the average estimated weight, where the weight is the coefficient that weights the impact of the news on the prediction revision. Note that the average revision (in absolute value) of the GDP nowcast is approximately equal to the standard deviation of the news times its weight. Month Month 2 Month 3 Table 2: The contribution of data releases Variable Day MSE Impact News Weight PMI Industrial Production Turnover Merchandise Exports Merchandise Imports Unemployment Rate Employment Retail Sales PMI Industrial Production Turnover New Orders Merchandise Exports Merchandise Imports Construction Output Gross Domestic Product Unemployment Rate Employment Retail Sales PMI Consumer Confidence Industrial Production Turnover Merchandise Exports Merchandise Imports Unemployment Rate Employment Industrial Confidence Indicator Capacity Utilization Retail Sales Column Day indicates which day of the month the data is released. Column MSE shows the average error of the nowcast at each release (this correspond to the black line in figure ). Column Impact shows of the average change in GDP nowcast, due to the new data released. Column News reports the standard deviation of the news, where the news is the unexpected component from the released data. Finally, column Weight reports the average estimated weight, where the weight is the coefficient that weights the impact of the news on the revision of the nowcast. Note that the average revision (in absolute value) of the GDP nowcast is approximately equal to the standard deviation of the news times its weight. From column MSE we can see that the variables that contribute the most in decreasing the 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 timely since they carry information on the current quarter. As expected, the release of the previous quarter GDP helps in improving the prediction. Finally, other relevant variables are the labor market indicators, and Retail Sales, while surprisingly PMI, which is the first variable released within 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 those leading 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 biggest revisions, while other soft indicators such as PMI, and Capacity Utilizations leads to important but smaller revisions. Hard indicators, instead, do not bring big revisions in the prediction of current 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 big news, i.e. the actual release is different from the prediction of the model. However, within these variables, only few of them lead to big GDP nowcast revisions. For example, Industrial Production despite producing relevant news brings very small revisions in the nowcast. On 8

10 the other hand, some variables such as previous quarter GDP, labor market indicators, Retail Sales, and Capacity Utilization, despite producing small news, have a high weight and hence bring important revisions of the GDP nowcast. Although widely used in academia as a benchmark model, it is not realistic that a market operator (for example an hedge fund, or a government agency) chooses its own strategy on the basis of the predictions of a RW model. Therefore, we also compare our model with two other predictions that are much more realistic than those produced by a RW model, namely: the Bloomberg Surveys (BS), 2 and the Norges Bank s projections of the annual GDP growth rate published in the Monetary Policy Report. In Figure, together with the MSE of the BDFM (solid line), we show the MSE of the Bloomberg Surveys (asterisk). As we can see, the performance of the BDFM are close to that of the Bloomberg Surveys. Indeed, at the beginning of the backcasting period the MSE of the BDFM is 2.5% worse than that of the BS, but a few days before the GDP data is released the BDFM s MSE is % better than that of the BS. This is a relevant result since the backcast with 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 Norges Bank s (NB) projections of the annual GDP growth rate. The NB updates three times a year its projection of the annual GDP growth rate for the current year. Since our model produces quarter-on-quarter (QoQ) GDP growth rate predictions, we need to transform these QoQ predictions into annual nowcasts. As it is explained in Appendix A, this can be easily done by 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 outperforms the NB s projections. This result is also confirmed by Figure 2b, which shows the MSE of the two models. More specifically, we can see how the BDFM efficiently exploits the flow of data releases throughout the year, thus reducing consistently the nowcasting error. This is another relevant result, since the goal of the nowcasting literature is to exploit the information contained in the new data releases to revise the prediction. In this Section, we have shown that this happens both when nowcasting QoQ GDP growth rate, and when considering GDP annual growth rate nowcasts. 5 Conclusions In this paper, by estimating a Bayesian Dynamic Factor model à la D Agostino et al. (202) we produce predictions of the previous, the current, and the next quarter growth rate of Norwegian GDP. The model is estimated on a panel of 4 variables (all followed closely by market) ranging from 990 to 200. Our analysis differs from standard nowcasting applications in three aspects. First, we use a Bayesian Dynamic Factor Model. Second, we use a small number of variables chosen because they are followed by market operators. Third, we consider real variables only. 2 The BS consists of the median GDP prediction provided independently by a number of specialists few days before the GDP is released. Both the number of specialists that provide a prediction (3 on average), and the day of released of the survey (six days before GDP is published on average), varies from quarter to quarter. 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

11 Figure 2: Nowcasting Annual GDP growth rate (a) Nowcast (b) Mean Squared Error Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec In panel (a), the grey solid line is actual GDP, the black solid line is the nowcast obtained with the BDFM, while the asterisks are the Norges Bank s projection. In panel (b), the solid line is the MSE of the BDFM, while the asterisk ( ) is the MSE of the Norges Bank s Projection. By means of a real time exercise we show that the Bayesian Dynamic Factor Model outperforms a standard random walk benchmark model, and it performs equally well than the Bloomberg Survey, which is the median forecast provided independently by a number of specialists few days before the GDP is released. Finally, we use our model to produce annual GDP growth rate nowcasts. This is a novel feature of this paper, since so far the nowcasting literature has concentrated only on quarteron-quarter GDP growth. We compare our annual nowcast with the Norges Bank s projections of the annual GDP growth rate published in the Monetary Policy Report. Results of the nowcasting exercise show that the Bayesian Dynamic Factor Model clearly outperforms the Norges Bank s projections. Furthermore, as shown by the strong decrease in the mean squared error throughout the year, the model efficiently exploits the flow of data releases. References Aastveit, K. A. and T. Trovik (202). Nowcasting norwegian GDP: the role of asset prices in a small open economy. Empirical Economics 42, Angelini, E., G. Camba-Mendez, D. Giannone, L. Reichlin, and G. Rünstler (20). Shortterm forecasts of euro area gdp growth. Econometrics Journal 4, C25 C44. Artis, M. J., A. Banerjee, and M. Marcellino (2005). Factor forecasts for the UK. Journal of Forecasting 24, Bai, J. and S. Ng (2008). Forecasting economic time series using targeted predictors. Journal of Econometrics 46 (2), Bańbura, M., D. Giannone, M. Modugno, and L. Reichlin (202). Now-casting and the realtime data-flow. In G. Elliott and A. Timmermann (Eds.), Handbook of Economic Forecasting. Amsterdam: Elsevier-North Holland. forthcoming. Bańbura, M., D. Giannone, and L. Reichlin (200). Large bayesian vector auto regressions. Journal of Applied Econometrics 25,

12 Bańbura, M., D. Giannone, and L. Reichlin (20). Nowcasting. In M. P. Clements and D. F. Hendry (Eds.), Oxford Handbook on Economic Forecasting. New York: Oxford University Press. Bańbura, M. and M. Modugno (202). Maximum likelihood estimation of factor models on data sets with arbitrary pattern of missing data. Journal of Applied Econometrics. Forthcoming. Bańbura, M. and G. Rünstler (20). A look into the factor model black box: Publication lags and the role of hard and soft data in forecasting GDP. International Journal of Forecasting 27, Barhoumi, K., O. Darné, and L. Ferrara (200). Are disaggregate data useful for factor analysis in forecasting French GDP? Journal of Forecasting 29, Boivin, J. and S. Ng (2005). Understanding and Comparing Factor-Based Forecasts. International Journal of Central Banking, 7 5. Boivin, J. and S. Ng (2006). Are more data always better for factor analysis? Econometrics 27, Journal of Camacho, M. and G. Perez-Quiros (200). Introducing the euro-sting: Short-term indicator of euro area growth. Journal of Applied Econometrics 25, Carter, C. K. and R. Kohn (994). On gibbs sampling for state space models. Biometrika 8, D Agostino, A. and D. Giannone (202). Comparing alternative predictors based on largepanel factor models. Oxford Bulletin of Economics and Statistics 74, D Agostino, A., D. Giannone, and M. Lenza (202). Université libre de Bruxelles. The bayesian dynamic factor model. D Agostino, A., K. McQuinn, and D. O Brien (2008). Now-casting irish GDP. Research Technical Papers 9/RT/08, Central Bank of Ireland. Doz, C., D. Giannone, and L. Reichlin (20). A two-step estimator for large approximate dynamic factor models based on kalman filtering. Journal of Econometrics 64, Doz, C., D. Giannone, and L. Reichlin (202). A quasi maximum likelihood approach for large approximate dynamic factor models. Review of Economics and Statistics 94, Evans, M. D. D. (2005). Where are we now? real-time estimates of the macroeconomy. International Journal of Central Banking, Forni, M., M. Hallin, M. Lippi, and L. Reichlin (2000). The Generalized Dynamic Factor Model: Identification and Estimation. The Review of Economics and Statistics 82, Forni, M., M. Hallin, M. Lippi, and L. Reichlin (2003). Do financial variables help forecasting inflation and real activity in the Euro Area? Journal of Monetary Economics 50,

13 Forni, M., M. Hallin, M. Lippi, and L. Reichlin (2005). The Generalized Dynamic Factor Model: One Sided Estimation and Forecasting. Journal of the American Statistical Association 00, Giannone, D., L. Reichlin, and D. Small (2008). Nowcasting: The real-time informational content of macroeconomic data. Journal of Monetary Economics 55, Luciani, M. (20). Forecasting with approximate dynamic factor models: the role of nonpervasive shocks. Ecares Working Paper 22, Université libre de Bruxelles. Marcellino, M. and C. Schumacher (200). Factor MIDAS for nowcasting and forecasting with ragged-edge data: A model comparison for German GDP. Oxford Bulletin of Economics and Statistics 72, Marcellino, M., J. H. Stock, and M. W. Watson (2003). Macroeconomic forecasting in the Euro Area: Country specific versus area-wide information. European Economic Review 47, 8. Mariano, R. S. and Y. Murasawa (2003). A new coincident index of business cycles based on monthly and quarterly series. Journal of Applied Econometrics 8 (4), Matheson, T. D. (200). An analysis of the informational content of new zealand data releases: The importance of business opinion surveys. Economic Modelling 27, Rünstler, G., K. Barhoumi, S. Benk, R. Cristadoro, A. Den Reijer, A. Jakaitiene, P. Jelonek, A. Rua, K. Ruth, and C. Van Nieuwenhuyze (2009). Short-term forecasting of GDP using large datasets: a pseudo real-time forecast evaluation exercise. Journal of Forecasting 28, Schumacher, C. (2007). Forecasting German GDP using alternative factor models based on large datasets. Journal of Forecasting 26 (4), Stock, J. H. and M. W. Watson (2002a). Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association 97, Stock, J. H. and M. W. Watson (2002b). Macroeconomic forecasting using diffusion indexes. Journal of Business and Economic Statistics 20, Stock, J. H. and M. W. Watson (2005). analysis. Working Paper 467, NBER. Implications of dynamic factor models for VAR 2

14 Appendix A Constructing annual nowcast As we discussed in Section 4, the Norges Bank (NB) publishes three times a year projections of the annual GDP growth rate for the current year. In order to compare our predictions with NB s projections, we need to transform our quarter-on-quarter (QoQ) predictions in annual values. In this Appendix, we explain how we do it. Let Xq y = 00 log(gdpq y ) be the GDP of the q-th quarter of year y, and let Z y = 00 log(gdp y ) be the GDP of year y. Then, by definition x y q = Xq y X y q is the quarteron-quarter growth rate, while z y = Z y Z y is the annual growth rate. Following Mariano and Murasawa (2003), we make use of the approximation Z y X y + X y 2 + Xy 3 + Xy 4, which allow us to write the annual growth rate as a function of QoQ growth rates: z y = Z y Z y (X y + Xy 2 + Xy 3 + Xy 4 ) (Xy + X y 2 + X y 3 + X y 4 ) = x y 4 + 2xy 3 + 3xy 2 + 4xy + 3xy 4 + 2x y 3 + x y 2. (A) Suppose we are in January of year y and that we want to forecast z y with the BDFM, which produces QoQ growth rate forecasts. We can do it by using equation (A). In January of year y we know only x y 3 and x y 2, while we need to estimate the other terms of equation (A). But this is easily done since x y 4 can be estimated with the backcast, x y can be estimated with the nowcast, x y 2 can be estimated with the forecast, while xy 3 and xy 4 can be easily obtained as two-step, and three-step ahead forecasts. As the time pass by, and more data become available, the forecast of z y is updated. For example, in February the 22 nd the data for x y 4 is released and it is no longer necessary to estimate it. Moreover, as time goes by also x y, xy 2, and x y 3 will be available and hence it will no longer necessary to rely on the three-step ahead forecast, on the two-step ahead forecast and on the forecast (Table A). Table A: Constructing annual nowcast Day Month x y 4 x y 3 x y 2 x y x y 4 x y 3 x y 2 January 3s 2s f n b 22 February 3s 2s f n April 2s f n b 22 May 2s f n July f n b 22 August f n October n b 22 November n This table shows how the nowcast of z y is obtained as more GDP data are released. b indicates that that specific qoq growth rate is obtained with the backcast, n with the nowcast, f with the forecast, 2s with the two-step ahead forecast, while 3s with the three-step ahead forecasts. An empty cell means that the data is available. 3

15 Appendix B Robustness analysis In this Appendix, we show robustness analysis with respect to τ, the parameter governing the level of shrinkage. As we said in Section 2, we choose a relatively flat prior by setting τ = 5. In Figure B, we show results for three additional level of shrinkage: τ =, τ = 2.5, and τ = 0. When τ = we are shrinking towards zero all coefficients of lag higher than (the prior for the coefficients of lag 2 has a variance of 0.33). However, when τ = 0 we are essentially not shrinking since the prior of the coefficients of lag 2 has a variance of Finally, the case τ = 2.5 is an intermediate case between our benchmark specification, and the hard shrinkage scenario of τ =. When τ = 2.5 we are shrinking more than in the benchmark scenario but consistently less than when τ = (the variance of the prior on the coefficient at lag 4 is still 0.5). Results in Figure B clearly show that the prediction ability of the BDFM is robust to the level of shrinkage. Figure B: Mean Squared Error for different level of shrinkage Forecast Nowcast Backcast In this plot, the black solid line is the MSE of the benchmark model (τ = 5), the black dashed line is the MSE for τ = 0, the grey dashed line is the MSE for τ = 2.5, and the grey solid line is the MSE for τ =

16 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 2 nd 202 (henceforth the final release), thus not being able to track data revisions. However, we address this point in this Appendix by studying the robustness of the BDFM to data revisions. In principle, the correct way of performing this exercise would consist in using historical vintages of data, that is in using the data available at each point in time the prediction is updated. 3 Unfortunately, to the best of our knowledge, a real time database for Norway is not 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 in evaluating the forecasting performance of our model on a new database including all the series considered so far, and a new GDP series. This new GDP series is constructed by replacing the final release with the first release, where the data for the first release are downloaded from Bloomberg. 4 Before presenting the result of this exercise, let us emphasize that the fact that we adopt a hybrid approach, rather than performing the exercise using historical vintages for all data series, has a limited impact in this context. Indeed, it is well known that Factor models are robust to data revisions (Giannone et al., 2008) since revision errors, which by nature are idiosyncratic, do not affect factor estimation. Therefore, we can safely assume that the factors are well estimated despite data revisions. What cannot be assumed, instead, is that data revisions have no impact on the prediction, i.e. on the relation between the factors and the target 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-onquarter GDP growth rate. To produce these predictions, we use the database modified as explained above. In Figure Ca, together with the MSE of the BDFM (solid line), and the MSE 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. More specifically, the solid line in Figure Ca represents the error that we make when forecasting the final GDP release, using the first release, while the circle represents the mean squared difference between the first GDP estimate and the final release. The MSEs reported in Figure Ca shows how the performance of the BDFM just slightly deteriorates when the prediction is produced by using the GDP first release. Despite that, the performance of our model is still comparable to (9% worse than) that of the BS (note that the MSE of the BS reported in Figure Ca is the same of that reported in Figure ). 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. As explained in Appendix A, to produce these nowcasts we aggregate the QoQ predictions produced by the model with data released by the SSb. Here, the annual nowcast is obtained by using the final GDP release. Let us give a practical example to clarify. Suppose we want to 3 Let us make use of a concrete situation to better explain this point. Suppose we are in February the 3 rd 2009, and that we want to nowcast the 2009Q GDP growth rate. The best way to perform our evaluation would be to construct our 2009Q GDP nowcast by using the vintage of data available as of February the 3 rd 2009, whereas, so far, we have used the vintages available as of May the 2 nd 202. The comparison using historical vintages is also more fair since when producing their predictions, both the Bloomberg experts, and the Norges Bank did not know the revised series. 4 Note that Bloomberg data are available only as from 2002Q2, and hence the series that we use in the new evaluation is a combination of the revised GDP and the first release. 5

17 construct the nowcast of the annual GDP growth rate for 2008, z 08. Define x 08 the QoQ GDP growth rate of the first quarter of 2008, then z 08 is computed as (see Appendix A for details): z 08 = x x x x x x x Now, suppose we are in July the 0 th Our annual nowcast is computed as ẑ 08 = ˆx ˆx ˆx x x x x 07 2, where ˆx 08 4, ˆx08 3, and ˆx08 2, are respectively the forecast, the nowcast, and the backcast obtained with our model, while all the other terms are data released by the SSb. In the exercise performed here, ˆx 08 4, ˆx08 3, and ˆx08 2 are obtained by using the first release of GDP as discussed earlier in this Section, while x 08, x07 4, x07 3, and x07 2 are the final GDP release. In this exercise, our information set is slightly superior than that of the Norges Bank. On the one hand, it is true that the NB could not observe the final GDP release, on the other hand, though, the NB observes the GDP revisions that occurred during the current year. The alternative would have been to replace x 08, x07 4, x07 3, and x07 2 with the first release, which, however, over-penalizes our model since it implies assuming that the first release is never revised. Therefore, it is true that our information is superior, but just slightly superior since the NB observed the first and second revision of QoQ GDP growth rate before performing its projection (in July 2008 x 07 2, and x07 3 have already been revised at least twice, while x 07 4 has already been revised once). Figure Cb reports the MSE of the BDFM (solid line) and that of the Norges Bank projections (black asterisks). As we can see, despite the performance of our model deteriorates, it is still better than that of the Norges Bank. Figure C: Accounting for Data Revision (a) Quarter-on-Quarter MSE (b) Annual MSE Forecast Nowcast Backcast 0 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 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 MSE of the Bloomberg surveys, whereas the circle ( ) is the MSE made by the SSb. More specifically, the solid line is the error that we make when forecasting the final GDP release, using the first release, while the circle is the mean squared difference between the first GDP estimate and the final release. The first section of panel (a) shows the Mean Squared Forecasting Error (MSFE), the second section the Mean Squared Nowcasting Error (MSNE), and the third section the Mean Squared Backcasting Error (MSBE). The first two sections are further divided into three other sections (delimited by a vertical dashed line) representing the three months within each quarter; while, the third section, representing the backcasting period, is divided in just two sections since GDP 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. 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. 6