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Data revisions to German national accounts: Are initial releases good nowcasts?
International Journal of Forecasting xxx (xxxx) xxx
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Data revisions to German national accounts: Are initial releases good nowcasts?✩ ∗
Till Strohsal a,b , , Elias Wolf b a b
Macroeconomic Projections, German Federal Ministry for Economic Affairs and Energy, Germany Department of Economics, Freie Universität Berlin, Germany
article
info
Keywords: Revisions Real-time data German national accounts Nowcasting News Noise
a b s t r a c t Data revisions to national accounts pose a serious challenge to policy decision making. Well-behaved revisions should be unbiased, small, and unpredictable. This article shows that revisions to German national accounts are biased, large, and predictable. Moreover, with use of filtering techniques designed to process data subject to revisions, the realtime forecasting performance of initial releases can be increased by up to 23%. For total real GDP growth, however, the initial release is an optimal forecast. Yet, given the results for disaggregated variables, the averaging out of biases and inefficiencies at the aggregate GDP level appears to be good luck rather than good forecasting. © 2020 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.
1. Introduction Economic policy decisions have to be made on the basis of the latest official statistics on the current economic situation. In business cycle policy, assessing the current state of the economy as weak may result in stimulating policy measures. In financial policy, tax revenue estimation as well as budgetary planning build on the latest data on GDP, private consumption, wages and salaries, and ✩ This article has benefited from valuable comments and suggestions from Dieter Nautz, Helmut Lütkepohl, Charlotte Senftleben, Mathias Kesting, Lars Winkelmann, Salmai Qari, two anonymous referees, one anonymous associate editor and the editor Michael McCracken as well as from participants of the research seminar ‘‘Quantitative Economic Research" at the University of Hamburg, the 38th International Symposium on Forecasting (Boulder, Colorado), the Freie Universität Berlin’s School of Business & Economics faculty council meeting during the presentation of Till Strohsal’s habilitation, and the German Federal Ministry for Economic Affairs and Energy Brown Bag Lunch Seminar. The opinions in this article are those of the authors and do not necessarily reflect the views of the German Federal Ministry for Economic Affairs and Energy. ∗ Correspondence to: Federal Ministry for Economic Affairs and Energy, 10115 Berlin, Germany. E-mail addresses: [email protected], [email protected] (T. Strohsal), [email protected] (E. Wolf).
further variables from the national accounts. Similarly, interest rate decisions by monetary policymakers depend on the current rate of inflation and the current output gap estimate. In all of these areas, it is crucial to have data that reflect the current economic situation as precisely as possible. Therefore, the ideal state would be knowing the final data values, or, in other words, the truth. Unfortunately, this is not realistic. Instead, the latest national accounts data represent only a first estimate of the final value. In subsequent releases, the data are necessarily revised and sometimes substantially so. The reasons for revisions include lagged deliveries of source data that enter the national accounts or the fact that the source data themselves are revised. Existing literature on US data documents that revisions can matter for policy decisions; see, for example, the survey by Croushore (2011). Orphanides (2001) shows that the optimal interest rate implied by a Taylor rule varies drastically with different data vintages of inflation and real activity.1 Ghysels, Horan, and Moench (2018) 1 A contrasting result is given by Croushore and Stark (2001), who show that the identification of monetary policy shocks in structural vector autoregressions is quite robust with respect to different data vintages.
https://doi.org/10.1016/j.ijforecast.2019.12.006 0169-2070/© 2020 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
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find that the forecasting power of macroeconomic variables for returns declines strongly when their unrevised, real-time values are used instead of the latest-vintage data. Similarly, Diebold and Rudebusch (1991) show that the US composite leading index’s forecasting performance for industrial production substantially deteriorates when real-time data are used. A comprehensive study of revisions to US national accounts is provided by Aruoba (2008). The results indicate that revisions do not satisfy simple desirable statistical properties. Significant biases and predictability of revisions imply that initial releases are not rational forecasts of the final values. Given that revisions are predictable, various econometric approaches have been developed to forecast the final values of macroeconomic data; see Clements and Galvão (2019). This article makes two contributions. The first one is to test whether revisions to German national accounts are well behaved. In line with Aruoba’s results for US data, it turns out that revisions are often biased, are fairly large, and are significantly correlated with information available at the time when the initial release was published. The correlation with time-t information implies predictability. Therefore, the second contribution is to go one step further by analyzing whether the real-time forecasting performance of initial releases can be improved empirically. This requires models that are designed to process data that are subject to revisions. With use of the filtering approach of Kishor and Koenig (2012) and a number of restricted versions of it, the root-mean-square forecast error is reduced by up to 23% relative to the initial release. However, for some cases, notably real GDP growth, the initial release is found to be an optimal forecast. The rest of this article is structured as follows. In Section 2, data revisions are defined and their desirable statistical properties are discussed. Section 3 briefly reviews the econometric models used to forecast the final data values. The real-time data are introduced in Section 4. Section 5 provides the main empirical results, and the conclusions are presented in Section 6. 2. Defining final revisions and their desirable statistical properties 2.1. Final revisions The German Federal Statistical Office distinguishes between two types of revisions: ongoing revisions and benchmark revisions. Ongoing revisions are data-driven and can occur every quarter. Typical reasons for ongoing revisions include late data deliveries or revisions to the data delivered. For instance, industrial production figures are first published about 35 days after the reference period and are usually revised in the subsequent months. Another example is tax revenue statistics, which in some cases become available to the statistical office only after several years. A specific characteristic of ongoing revisions to quarterly national accounts is that the final revision is undertaken 4 years after the initial release, usually in August. Hence, the four quarterly growth rates of GDP in 2014 will undergo final revision in August 2018. Beyond
4 years, only benchmark revisions are undertaken. Benchmark revisions occur about every 5 years and, in contrast to ongoing revisions, are not data-driven. Instead, benchmark revisions include redefinitions of variables or the implementation of new calculation methods. Therefore, benchmark revisions can be interpreted as a redefinition of the truth, while ongoing revisions are an attempt to get closer to a given definition of the truth. Benchmark revisions cannot be anticipated and should not be considered when one is judging revisions. To limit the influence of benchmark revisions, we follow Aruoba (2008) and consider national accounts data as final after the last ongoing revision. In the empirical analysis we also consider some monthly indicators. In contrast to the quarterly data, the final ongoing revision is often undertaken after a period of less than 4 years. In particular, the CPI undergoes final revision as early as 15 days after the initial release, industrial production undergoes final revision in May of the next year, and retail sales undergo final revision after 25 months and 15 days.2 Throughout this article, we will limit our attention to the properties of final revisions. The initial and final releases are denoted by xinitial and xfinal , respectively. For t t quarterly national accounts data, xinitial is available 45 t days after the reference quarter (‘‘t + 45 announcement’’). 3 Accordingly, final revisions are defined as rtfinal = xfinal − xinitial . t t
(1)
Being aware of the existence of revisions is one thing. But do revisions actually matter? A first impression is provided in Fig. 1, which documents the history of values assigned to the quarterly growth rate of real German GDP in the second quarter of 2005. The first vintage is the initial release in the third quarter of 2005, and the latest vintage is February 14, 2018. To attach some meaning to the magnitudes, the German economy is currently growing at a yearly rate of around 2%. Therefore, a typical quarterly growth rate may be around 0.5%. The first release suggested that the German economy was stagnating during the second quarter of 2005. However, the rate was substantially revised in subsequent periods. After about 4 years, the initial assessment has changed drastically from stagnation to very strong growth of around 0.7%. This example highlights the economic significance that revisions to national accounts can have. Fig. 1 also shows that after around 4 years, revisions become very small and the time series somewhat converges to its true (final) value. 2.2. Three properties revision should have The first desirable statistical characteristic of revisions is unbiasedness. Second, revisions should not be too large in terms of their variance. Third, revisions should be unpredictable when information that was available at 2 More details on the data are provided in Section 4. 3 As of the second quarter of 2020, German GDP will be officially published 30 days after the end of the reference quarter (‘‘t + 30 announcement’’).
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
T. Strohsal and E. Wolf / International Journal of Forecasting xxx (xxxx) xxx
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Fig. 1. Quarterly growth rate of real GDP. This figure shows historical data vintages for the German real quarterly GDP growth rate in the second quarter of 2005 (2005Q2). The initial release was published in the third quarter of 2005, and the latest vintage included is February 14, 2018.
the time when the initial release was published (Iinitial ) is used. If revisions were predictable, the initial release would not be an optimal forecast of the final value. In that case, a more precise forecast must exist that has a smaller root-mean-square error (RMSE). Formally, the three properties can be summarized as follows: P1: Unbiasedness: E[rtfinal ] = 0. P2: Variance: V[rtfinal ] should be small. P3: Unpredictability: E[rtfinal |Iinitial ] = 0. There are several possibilities for empirically measuring the properties of revisions, particularly with respect to P2 and P3. Regarding P1, for revisions to be unbiased, the sum of the upward and downward revisions of the statistical agency should amount to zero. This null hypothesis can be tested, if necessary, using robust standard error estimates. The desire to have a small variance is more difficult to formalize and needs a reference value to judge what small actually means. In the following analysis, we therefore consider the ratio of the variance of revisions to the variance of the underlying time series, termed noise-to-signal ratio. A value of 1, for instance, can be reasonably considered as large and economically relevant since it implies that the revisions vary by the same size as the actual time series. Unpredictability can be analyzed by the correlation between the revisions and the initial releases. The idea is that the initial release is a proxy for the information available at the time when the data were published, even though the information may have not been optimally exploited. 2.3. Noise versus news The concept of news and noise is an important element of studies on data revisions; see Aruoba (2008), Kishor and Koenig (2012) and Mankiw and Shapiro (1986). It is closely related to property P3 above. The noise hypothesis defines the initial data release as the truth plus measurement error and assumes that the error will eventually disappear in the revision process. Thus, the final revision is correlated with information available at the time of the initial announcement, implying predictability of rtfinal .
Hence, under the noise hypothesis, P3 is not satisfied. Conversely, under the news hypothesis, the initial release is an efficient estimate of the truth, and revisions are unpredictable. Therefore, the initial announcement should be uncorrelated with information available at t, and P3 holds. The distinction between news and noise also has implications for the variance of the underlying series. The news hypothesis implies that the variance increases as more and more revisions are made. The noise hypothesis implies that later revisions decrease the variance of the series as estimations become more accurate. Whether revisions are news or noise can be tested empirically. The models presented in the next section assume that revisions are noise that can be filtered out to better predict the final value. The Mincer–Zarnowitz regressions presented in Section 5 are formal tests of the news hypothesis. To check whether first releases provide a good picture of the current economic situation, the performance of alternative forecasts of the final value needs to be evaluated. It is more accurate to term an initial release a nowcast than to call it a forecast. Therefore, we will often refer to nowcasts in the remainder of this article. 3. Models for nowcasting German national accounts There are a number of approaches that are designed to process data that are subject to revisions; see Kishor and Koenig (2012). Many of them have a similar basic framework. Suppose the true, or final, value of the time series is generated by an AR(1) process: xt = β xt −1 + νt .
(2)
The statistical agency observes the true value only with measurement error ηt :
wt = xt + ηt .
(3)
The statistical agency may now use its experience, expert knowledge, and possibly also a model to evaluate wt . Thereafter, the value yt is published.
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
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3.1. Naive nowcast
3.4. Kishor-Koenig nowcast
For now, it is assumed that the statistical agency publishes the observed value of a variable without further data processing; that is, yT = wT . For the users of the official data, the first option is to ignore the possible occurrence of revisions and to naively set the published initial release at T equal to the nowcast xˆ T of the final value:
Kishor and Koenig (2012) propose an encompassing model that includes the Howrey model and the Sargent model as special cases. In contrast to the situation above (naive, Kalman, and Howrey nowcasts), Sargent (1989) assumes that the statistical agency itself filters its noisy observation wt before publishing the data. Sargent also allows for a white noise filtering error ξt (‘‘typo’’). The revision process is defined as
xˆ T = yT .
yt − xt = h(yt −1 − xt −1 ) + ϵt − (1 − g)νt ,
(4)
where ϵt equation
3.2. Kalman nowcast The alternative is to explicitly model data revisions, being aware that the published value represents a noisy signal. Keeping the assumption that the statistical agency provides just the value that it has observed itself, we have yt = xt + ηt .
= (ξt + g ηt ) and the nowcast follows the
ˆ T −1 − xT −1 ) − βˆ xT −1 ]. xˆ T = βˆ xT −1 + γˆK [yT − k(y
(10)
For g = 1, the model becomes the Howrey approach. Consistent estimates of the true parameter γK ≡ g σν2 /(g 2 σν2 + σϵ2 ) can be obtained in a similar way as in the Howrey model. However, efficiency requires application of the seemingly unrelated regression (SUR) estimator.
(5) 3.5. The generalized Kishor-Koenig model
If a forecaster receives a surprisingly large yT at the current edge of the sample, it is unclear how to interpret that value. Either the economic variable of interest, xT , has actually taken on a high value due to a large shock νT in (2) or the large yT is only a result of a sizable measurement error ηT in (5). Therefore, forecasters optimally update their expectations: xˆ T = βˆ xT −1 . If we define Eqs. (2) and (5) as the measurement and state equations of a state space system, the optimal updating rule is given by the Kalman filter as xˆ T = βˆ xT −1 + γˆK (yT − βˆ xT −1 ).
(9)
(6)
The idea of (6) is that the forecasters incorporate only a fraction of the surprise that they experience. The parameter γK is given by γˆK = σˆ ν2 /(σˆ ν2 + σˆ η2 ) and can be estimated from the data.4 The estimate is optimal in the sense that it minimizes
The above models assume that the second release is an efficient estimate of the final value. However, this might not be the case in empirical applications. Kishor and Koenig (2012) extend their encompassing model in that direction and propose a general filtering procedure. The procedure is based on the assumption that there exists an efficient estimate xet of the final release that becomes available e periods after the initial release xinitial . t Assuming that eth revision data follow an AR(1) process, the generalized state space system of (2) and (9) is given by the state equation xt = Fxt −1 + νt
(11)
and the observation equation y t = (I − G)Fy t −1 + Gxt + ϵt .
(12)
The vectors xt , y t , νt , and ϵt are defined as x′t ≡ [xet−e , xet−e+1 , . . . , xet ]′ ,
E[(xT − {β xT −1 + γN (yT − β xT −1 )})2 ].
−1 intial ′ y ′t ≡ [xet−e , xet − ], e+1 , . . . , xt
ν′t ≡ [0, 0, . . . , 0, ν0,t ]′ , ϵ′t ≡ [0, ϵe−1,t , . . . , ϵ1,t , ϵ0,t ]′ .
3.3. Howrey nowcast A common empirical property of revisions is that they are autocorrelated; see Aruoba (2008) for US data. As an extension of (6), Howrey (1978) proposes yt − xt = h(yt −1 − xt −1 ) + υt .
(7)
0 ⎢0
1 0
0 1
F ≡⎢ ⎢0 ⎣0 0
0 0 0
0 0 0
⎡ ⎢
Similarly to the Kalman model, the nowcast is
ˆ T −1 − xT −1 ) − βˆ xT −1 ]. xˆ T = βˆ xT −1 + γˆH [yT − h(y
The matrices F and G determine the dynamics of the revisions process and have the following forms:
(8)
In the Howrey model, γH is estimated as γˆH = σˆ ν2 /(σˆ ν2 + σˆ υ2 ). 4 σˆ 2 , σˆ 2 , and σˆ 2 refer to the empirical estimates of the variances ν η υ of νt , ηt , and υt , respectively.
⎡
1
⎢Ge−1,e ⎢G e−2,e G≡⎢ ⎢ . ⎣
... ... .. .
... ... 0
Ge−1,e−1 Ge−2,e−1
..
.. .
G0,e
G0,e−1
0 0⎥
⎤ ⎥ ⎥
0⎥ ⎦ 1 F0 (e+1×e+1)
... ... ... .. .
...
0
and
⎤
Ge−1,0 ⎥ Ge−2,0 ⎥ ⎥
.. .
G0,0
⎥ ⎦
.
(e+1×e+1)
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
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Table 1 Economic indicators in real time. Variable
Sample period
Frequency
Unit
SA
CA
Publication lag (days)
Real GDP Private consumption Public consumption Investment Exports CPI Production Retail sales Employment
1995Q2–2017Q4 1995Q2–2017Q4 1995Q2–2017Q4 1995Q2–2017Q4 1995Q2–2017Q4 2004M10–2018M2 1995M2–2017M12 2005M9–2017M12 1995M5–2018M1
Quarterly Quarterly Quarterly Quarterly Quarterly Monthly Monthly Monthly Monthly
QonQ growth QonQ growth QonQ growth QonQ growth QonQ growth YonY growth MonM growth MonM growth MonM absolute changes
Yes Yes Yes Yes Yes No Yes Yes Yes
Yes Yes Yes Yes Yes No Yes Yes Yes
45 55 55 55 55 No lag ≈35 ≈30 ≈66
The sample period is predefined by the Bundesbank’s real-time database. Publication lags reflect the institutional conventions of the German Federal Statistical Office. The seasonal adjustment is performed by X-12-ARIMA. The calendar adjustment accounts for differences in working days. CA, calendar adjustment; M, month, MonM, month on month; Q, quarter; QonQ, quarter on quarter; SA, seasonal adjustment; YonY, year on year.
The entries of both matrices can be estimated consistently by SUR using observable (revised) data. Once the state space system has been specified and the coefficients have been estimated, optimal predictions of the efficient release xet at time t that are given by the eth element of the state vector xt can be obtained by applying the Kalman filter to (11) and (12). Note that the Kishor-Koenig model includes the other models as special cases. Imposing the restriction G = I yields the Kalman model. Setting the entries Ge−i,0 = 0 for i = 1, . . . , e − 1 and G0,0 = 1 results in the Howrey model. 4. Data: Deutsche Bundesbank’s real-time database To compare alternative nowcast models, real-time data are needed. The Bundesbank provides a comprehensive database with vintages from 1995 onward for quarterly data. For monthly economic indicators, data are available from 2005 onward. We have selected a number of variables that receive particular attention in the business cycle analysis of the German government, which is executed by the Federal Ministry for Economic Affairs and Energy. Specifically, we investigate the nine variables in Table 1. GDP, private consumption, public consumption, investment in equipment and machinery, and exports are analyzed as real quarter-on-quarter growth rates. The German CPI, measured at a monthly frequency, is commonly analyzed as the yearly growth rate. Industrial production and retail sales are analyzed as month-on-month growth rates. Employment refers to the monthly absolute change in the number of people employed. All variables except the CPI are seasonally adjusted and most of the series are calendar adjusted. 5. Results 5.1. Actual properties of revisions Unbiasedness, small size, and unpredictability are desirable properties of revisions. Yet, if we take a closer look at the data, Table 2 shows that in many cases these properties are not satisfied. While quarterly national accounts data appear unbiased, the bias of the monthly economic indicators is statistically significant. This is shown in column 3, where bold numbers indicate significance at least
at the 10% level. With the exception of the CPI, the biases are also of economic significance. For instance, the monthly growth rate of German industrial production is usually 0.14 percentage points greater than the first release suggests. What about the size of revisions? The noise-to-signal ratio, depicted in column 7 in Table 2, documents that revisions are large. Other than for the CPI, the noiseto-signal ratio ranges from about 0.5 to more than 1, implying that in some cases the variation of revisions is as large as the variation of the underlying time series. Generally, sizable revisions may well be unpredictable. If this were the case, they should be uncorrelated with the information available at the time when the initial value was released. Using the initial release itself as a proxy for this information, one can see from column 8 in Table 2 that for many variables the null hypothesis of unpredictability is significantly rejected. The negative sign of the correlations is in line with the noise interpretation of revisions; see Mankiw and Shapiro (1986). If the true value of a data point is observed only with noise, the revision will subtract the noise from the initial release and thereby induce the negative correlation. 5.2. Nowcasting versus initial data release: Real-time exercise Evidence-based economic and financial policy needs a precise idea of the current economic situation. The results for the statistical properties of revisions suggested that there may be some room to improve on the initial releases. To verify this conjecture, we start the empirical analysis by identifying the efficient eth release and run the following set of Mincer–Zarnowitz regressions for each variable: xfinal = α + β xit + ut , t
(13)
where i = 0, 1, 2, . . . denotes the ith release. The initial release is obtained for i = 0. For each regression, an F test of the joint null hypothesis that α = 0 and β = 1 is performed. The null hypothesis implies that xi is an efficient release since the forecast errors would be purely random and therefore unpredictable. Thus, the Mincer–Zarnowitz regressions are formal tests to check from which release onward revisions can be considered news instead of noise.
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
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Table 2 Revision properties: Unbiasedness, size, and predictability. Variable
No. of observations
Mean
Min
Max
SD
Noise/signal
Correlation
Real GDP Private consumption Public consumption Investment Exports CPI Production Retail sales Employment
75 75 75 75 75 147 263 123 224
0.03 0.08 −0.01 0.02 −0.01 0.01 0.14 0.30 9.56
−0.91 −1.48 −3.58 −5.18 −2.12 −0.30 −2.78 −4.32 −91
1.02 1.36 2.60 4.72 2.48 0.64 2.22 6.57 166
0.36 0.51 1.02 2.01 1.09 0.08 0.80 1.47 33.42
0.44 0.74 1.24 0.60 0.43 0.09 0.56 1.09 0.78
−0.07 −0.22 −0.65 −0.12 −0.32 0.04
−0.57 −0.66 −0.18
This table shows estimated statistics of final revisions. Numbers in bold indicate statistical significance at least at the 10% level. The term noise/signal is defined as the variance of the revisions divided by the variance of the underlying time series and is thus a relative measure of the size of revisions. Correlation measures the correlation of the revisions with the initial release, the latter being a proxy for the information available at the time of the initial release. SD, standard deviation.
Table 3 Optimality tests of releases: Mincer–Zarnowitz regressions. Variable Real GDP Private consumption Public consumption Investment Exports CPI Production Retail sales Employment
No. of revisions e
Unbiasedness
Efficiency
Optimal forecast
α
β
α = 0, β = 1
0 3 6 0 0 0 6 2 7
0.04 0.12 0.08 0.17 0.25 0.01 −0.02 0.01 6.41
0.96 0.82 0.82 0.90 0.85 1.00 0.98 0.86 0.87
0.62 0.09 0.14 0.65 0.08 0.07 0.06 0.21 0.06
This table shows parameter estimates of α and β and corresponding p values for joint hypotheses of the Mincer–Zarnowitz regression with the release that provides an optimal forecast based on a 5% confidence level. Inference is based on heteroskedasticity and autocorrelation-consistent standard errors.
Unbiasedness is given if α = 0 and an efficient forecast satisfies β = 1. Given the predictability and bias of revisions in many cases, the results in Table 3 do not come as a great surprise. At the 5% significance level, for more than 50% of the variables the first release is not efficient. Moreover, according to the p values of the F test reported in the last column in Table 3, for many variables the releases become efficient only after a number of revisions. Retail sales, for example, become efficient only with the third release (e = 2). Concluding that the first release is often not an optimal prediction of the final value cannot be the end of the story. The more important question is whether superior alternative nowcasts can be found empirically. This exercise requires the use of real-time data and models that are able to handle data revisions. The approach we consider is the generalized Kishor-Koenig model described by Eqs. (11) and (12) in Section 3 as well as two restricted versions of it: the Kalman nowcast and the Howrey nowcast. We apply these three models to all variables where the evidence from the Mincer–Zarnowitz regressions suggests that the initial release is not efficient. The estimated parameter e ranges between 0 and 7 (see Table 3). The performance of the competing nowcast models is measured by the root-mean-square forecast errors. The forecast errors are defined as xˆ t − xfinal . The precision t is analyzed in relative terms where the naive nowcast,
the initial release of the German Federal Statistical Office, serves as the benchmark model. Table 4 summarizes the results. Values below 1 imply that the RMSE of the alternative model is smaller than that of the naive nowcast. Values above 1 indicate that the initial release has a higher precision. For each of the five variables, all of the alternative nowcast models outperform the initial release. The reduction in the RMSE is up to 23%, which is comparable to the gains in precision reported in Aruoba (2008) for US data. The Howrey model and the Kishor-Koenig model seem to be more suitable for German national accounts data than the standard textbook Kalman nowcast. This is in line with autocorrelation in the revisions and with not perfectly filtered releases by the German Federal Statistical Office. 5.3. Robustness: The role of benchmark revisions The results have shown that the alternative models could improve the nowcasts of German national accounts. Yet, the performance comparison requires a specific definition of the forecast errors and hence of xfinal . Up to now, t xfinal was considered to be the release for which the last t ongoing revision was undertaken. For quarterly data, for example, that date lies 4 years in the future. During such a long period, it might well be the case that a benchmark revision was undertaken between the first release and the
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
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Table 4 Nowcasting the truth in real time: Initial release versus alternative models. Final release defined as final ongoing revision Variable
Nowcast sample
e
Naive
Kalman
Howrey
Kishor-Koenig
Real GDP Private consumption Public consumption Investment Exports CPI Production Retail sales Employment
2006Q1–2013Q4 2006Q1–2013Q4 2006Q1–2013Q4 2000Q1–2013Q4 2000Q1–2013Q4 2007M11–2017M1 2000M1–2016M12 2007M2–2015M11 2003M1–2013M12
0 3 6 0 0 0 6 2 7
1 1 1 1 1 1 1 1 1
– 0.92 0.92 – – – 0.82 0.81 0.97
– 0.92 0.89 – – – 0.81 0.77 0.97
– 0.92 0.97 – – – 0.81 0.79 0.95
This table shows root-mean-square errors (RMSEs) of alternative nowcast models relative to the initial release of the German Federal Statistical Office (naive nowcast), which serves as the benchmark model. If the alternative model has a smaller RMSE than the benchmark model, the relative RMSE is below 1. Similarly, if the benchmark model performs better, the relative RMSE is above 1. The forecast error is defined as xˆ t − xfinal . The t parameter e indicates the eth release, which, according to pretesting in Table 3, is efficient. M, month; Q, quarter. Table 5 Robustness to benchmark revisions: Alternative definitions of the truth. Final release as final ongoing revision—excluding benchmark revisions Variable
Period
e
Naive
Kalman
Howrey
Kishor-Koenig
Real GDP Private consumption Public consumption Investment Exports CPI Production Retail sales Employment
2006Q1–2013Q4 2006Q1–2013Q4 2006Q1–2013Q4 2000Q1–2013Q4 2000Q1–2013Q4 2007M11–2017M1 2000M1–2016M12 2007M2–2015M11 2003M1–2013M12
1 0 6 0 0 0 5 2 10
1 1 1 1 1 1 1 1 1
0.98 – 0.90 – – – 0.83 0.80 0.97
0.99 – 0.88 – – – 0.82 0.76 0.99
0.96 – 0.93 – – – 0.82 0.77 0.94
Final release defined as the latest vintage Variable
Period
e
Naive
Kalman
Howrey
Kishor-Koenig
Real GDP Private consumption Public consumption Investment Exports CPI Production Retail sales Employment
2006Q1–2013Q4 2006Q1–2013Q4 2006Q1–2013Q4 2000Q1–2013Q4 2000Q1–2013Q4 2007M11–2017M1 2000M1–2016M12 2007M2–2015M11 2003M1–2013M12
0 3 7 0 0 0 8 2 22
1 1 1 1 1 1 1 1 1
– 0.92 0.91 – – – 0.85 0.81 1.06
– 0.92 0.87 – – – 0.87 0.77 0.99
– 0.92 0.86 – – – 0.87 0.78 0.85
This table shows root-mean-square errors (RMSEs) of alternative nowcast models relative to the initial release of the German Federal Statistical Office (naive nowcast), which serves as the benchmark model. If the alternative model has a smaller RMSE than the benchmark model, the relative RMSE is below 1. Similarly, if the benchmark model performs better, the relative RMSE is above 1. The forecast error is defined as xˆ t − xfinal . The t parameter e indicates the eth release, which, according to pretesting in Table 3, is efficient. M, month; Q, quarter.
final release.5 Benchmark revisions can, however, have a large impact on the forecasting results; see Knetsch and Reimers (2009). To investigate the effect of benchmark revisions, we consider two alternative definitions of the final release. First, to exclude benchmark revisions completely, we use the last ongoing revision as the final release only if no benchmark revision occurred between the first release and the final release. If a benchmark revision was actually undertaken, we take the last release before that benchmark revision as the final value. Second, to include all benchmark revisions, we use the latest vintage, February
5 In our forecasting sample, three benchmark revisions occurred, in 2005, 2011, and 2014.
14, 2018, as the final value. The outcome of the nowcast competition with alternative definitions of xfinal is t provided in Table 5. A number of results stand out. First, the parameter e, indicating the efficient release, varies only slightly when benchmark revisions are excluded. In contrast, when the latest vintage is used as the final value, e increases. This is intuitive, since including benchmark revisions introduces larger differences between the first and final values. Second, the finding from the previous section that all alternative models beat the naive nowcast survives the robustness test. Third, changes in the RMSEs are limited. The gains in forecast performance are mostly somewhat lower when the latest vintage is considered as the final release. Including all benchmark revisions, which are not datadriven by definition, appears to add additional complexity to the data and makes nowcasting more difficult.
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
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6. Conclusions
References
Data revisions arise as a matter of course when official data are produced. One reason is that not all data needed to calculate a data point of a variable are available to the statistical office at the date of the initial release. These gaps have to be filled by estimated values in one way or another. Moreover, the data delivered to the statistical office by third parties are usually revised too. Also, statistical offices produce large amounts of different data and have to operate under budget restrictions. However, official data are used for policy decision making. Therefore, initial releases should be unbiased and unpredictable. In this article, we have provided evidence that revisions to German official data are often biased and predictable. Using a number of simple multivariate models designed for data revisions, we showed that the forecasting power of the initial release can be increased. The effort of estimating these models is limited and reasonable. Future research may well find more powerful models that can improve the forecasting performance further. The models of Cunningham, Eklund, Jeffery, Kapetanios, and Labhard (2012) and Jacobs and Van Norden (2011), for example, are promising alternatives. Additionally, Clements and Galvão (2013) propose using autoregressive distributed lag (ADL) models that take into account the number of revisions. They show that their approach works well when the sample size is small and provide evidence for more precise forecasts compared with the Kishor-Koenig model. At least two policy conclusions emerge from the current article. First, the users of data should consider simple filtering of the initial release. On average, they will have a better idea of the actual situation for many important economic variables. Second, the providers of data may want to consider eliminating the predictability of revisions. Since this might require extensive institutional reform efforts, there is an alternative: the data production process could be left unchanged. Instead, just a second before the data point is released, the time series should be put through a simple filter.
Aruoba, S. B. (2008). Data revisions are not well behaved. Journal of Money, Credit and Banking, 40(2–3), 319–340. Clements, M. P., & Galvão, A. B. (2013). Real-time forecasting of inflation and output growth with autoregressive models in the presence of data revisions. Journal of Applied Econometrics, 28(3), 458–477. Clements, M. P., & Galvão, A. B. (2019). Data revisions and real-time forecasting. In The Oxford research encyclopedia of economics and finance. Oxford University Press. Croushore, D. (2011). Frontiers of real-time data analysis. Journal of Economic Literature, 49(1), 72–100. Croushore,
D.,
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(2001).
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macroeconomists. Journal of Econometrics, 105(1), 111–130. Cunningham, A., Eklund, J., Jeffery, C., Kapetanios, G., & Labhard, V. (2012). A state space approach to extracting the signal from uncertain data. Journal of Business & Economic Statistics, 30(2), 173–180. Diebold, F. X., & Rudebusch, G. D. (1991). Forecasting output with the composite leading index: A real-time analysis. Journal of the American Statistical Association, 86(415), 603–610. Ghysels, E., Horan, C., & Moench, E. (2018). Forecasting through the rearview mirror: Data revisions and bond return predictability. Review of Financial Studies, 31(2), 678–714. Howrey, E. P. (1978). The use of preliminary data in econometric forecasting. The Review of Economics and Statistics, 60(2), 193–200. Jacobs, J. P. A. M., & Van Norden, S. (2011). Modeling data revisions: Measurement error and dynamics of ‘‘true’’ values. Journal of Econometrics, 161(2), 101–109. Kishor, N. K., & Koenig, E. F. (2012). VAR estimation and forecasting when data are subject to revision. Journal of Business & Economic Statistics, 30(2), 181–190. Knetsch, T. A., & Reimers, H.-E. (2009). Dealing with benchmark revisions in real-time data: The case of german production and orders statistics. Oxford Bulletin of Economics and Statistics, 71(2), 209–235. Mankiw, N. G., & Shapiro, M. D. (1986). News or noise: An analysis of GNP revisions. Survey of Current Business, 66, 20–25. Orphanides, A. (2001). Monetary policy rules based on real-time data. American Economic Review, 91(4), 964–985. Sargent, T. J. (1989). Two models of measurements and the investment accelerator. Journal of Political Economy, 97(2), 251–287.
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
Contents lists available at ScienceDirect
International Journal of Forecasting journal homepage: www.elsevier.com/locate/ijforecast
Data revisions to German national accounts: Are initial releases good nowcasts?✩ ∗
Till Strohsal a,b , , Elias Wolf b a b
Macroeconomic Projections, German Federal Ministry for Economic Affairs and Energy, Germany Department of Economics, Freie Universität Berlin, Germany
article
info
Keywords: Revisions Real-time data German national accounts Nowcasting News Noise
a b s t r a c t Data revisions to national accounts pose a serious challenge to policy decision making. Well-behaved revisions should be unbiased, small, and unpredictable. This article shows that revisions to German national accounts are biased, large, and predictable. Moreover, with use of filtering techniques designed to process data subject to revisions, the realtime forecasting performance of initial releases can be increased by up to 23%. For total real GDP growth, however, the initial release is an optimal forecast. Yet, given the results for disaggregated variables, the averaging out of biases and inefficiencies at the aggregate GDP level appears to be good luck rather than good forecasting. © 2020 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.
1. Introduction Economic policy decisions have to be made on the basis of the latest official statistics on the current economic situation. In business cycle policy, assessing the current state of the economy as weak may result in stimulating policy measures. In financial policy, tax revenue estimation as well as budgetary planning build on the latest data on GDP, private consumption, wages and salaries, and ✩ This article has benefited from valuable comments and suggestions from Dieter Nautz, Helmut Lütkepohl, Charlotte Senftleben, Mathias Kesting, Lars Winkelmann, Salmai Qari, two anonymous referees, one anonymous associate editor and the editor Michael McCracken as well as from participants of the research seminar ‘‘Quantitative Economic Research" at the University of Hamburg, the 38th International Symposium on Forecasting (Boulder, Colorado), the Freie Universität Berlin’s School of Business & Economics faculty council meeting during the presentation of Till Strohsal’s habilitation, and the German Federal Ministry for Economic Affairs and Energy Brown Bag Lunch Seminar. The opinions in this article are those of the authors and do not necessarily reflect the views of the German Federal Ministry for Economic Affairs and Energy. ∗ Correspondence to: Federal Ministry for Economic Affairs and Energy, 10115 Berlin, Germany. E-mail addresses: [email protected], [email protected] (T. Strohsal), [email protected] (E. Wolf).
further variables from the national accounts. Similarly, interest rate decisions by monetary policymakers depend on the current rate of inflation and the current output gap estimate. In all of these areas, it is crucial to have data that reflect the current economic situation as precisely as possible. Therefore, the ideal state would be knowing the final data values, or, in other words, the truth. Unfortunately, this is not realistic. Instead, the latest national accounts data represent only a first estimate of the final value. In subsequent releases, the data are necessarily revised and sometimes substantially so. The reasons for revisions include lagged deliveries of source data that enter the national accounts or the fact that the source data themselves are revised. Existing literature on US data documents that revisions can matter for policy decisions; see, for example, the survey by Croushore (2011). Orphanides (2001) shows that the optimal interest rate implied by a Taylor rule varies drastically with different data vintages of inflation and real activity.1 Ghysels, Horan, and Moench (2018) 1 A contrasting result is given by Croushore and Stark (2001), who show that the identification of monetary policy shocks in structural vector autoregressions is quite robust with respect to different data vintages.
https://doi.org/10.1016/j.ijforecast.2019.12.006 0169-2070/© 2020 International Institute of Forecasters. Published by Elsevier B.V. All rights reserved.
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find that the forecasting power of macroeconomic variables for returns declines strongly when their unrevised, real-time values are used instead of the latest-vintage data. Similarly, Diebold and Rudebusch (1991) show that the US composite leading index’s forecasting performance for industrial production substantially deteriorates when real-time data are used. A comprehensive study of revisions to US national accounts is provided by Aruoba (2008). The results indicate that revisions do not satisfy simple desirable statistical properties. Significant biases and predictability of revisions imply that initial releases are not rational forecasts of the final values. Given that revisions are predictable, various econometric approaches have been developed to forecast the final values of macroeconomic data; see Clements and Galvão (2019). This article makes two contributions. The first one is to test whether revisions to German national accounts are well behaved. In line with Aruoba’s results for US data, it turns out that revisions are often biased, are fairly large, and are significantly correlated with information available at the time when the initial release was published. The correlation with time-t information implies predictability. Therefore, the second contribution is to go one step further by analyzing whether the real-time forecasting performance of initial releases can be improved empirically. This requires models that are designed to process data that are subject to revisions. With use of the filtering approach of Kishor and Koenig (2012) and a number of restricted versions of it, the root-mean-square forecast error is reduced by up to 23% relative to the initial release. However, for some cases, notably real GDP growth, the initial release is found to be an optimal forecast. The rest of this article is structured as follows. In Section 2, data revisions are defined and their desirable statistical properties are discussed. Section 3 briefly reviews the econometric models used to forecast the final data values. The real-time data are introduced in Section 4. Section 5 provides the main empirical results, and the conclusions are presented in Section 6. 2. Defining final revisions and their desirable statistical properties 2.1. Final revisions The German Federal Statistical Office distinguishes between two types of revisions: ongoing revisions and benchmark revisions. Ongoing revisions are data-driven and can occur every quarter. Typical reasons for ongoing revisions include late data deliveries or revisions to the data delivered. For instance, industrial production figures are first published about 35 days after the reference period and are usually revised in the subsequent months. Another example is tax revenue statistics, which in some cases become available to the statistical office only after several years. A specific characteristic of ongoing revisions to quarterly national accounts is that the final revision is undertaken 4 years after the initial release, usually in August. Hence, the four quarterly growth rates of GDP in 2014 will undergo final revision in August 2018. Beyond
4 years, only benchmark revisions are undertaken. Benchmark revisions occur about every 5 years and, in contrast to ongoing revisions, are not data-driven. Instead, benchmark revisions include redefinitions of variables or the implementation of new calculation methods. Therefore, benchmark revisions can be interpreted as a redefinition of the truth, while ongoing revisions are an attempt to get closer to a given definition of the truth. Benchmark revisions cannot be anticipated and should not be considered when one is judging revisions. To limit the influence of benchmark revisions, we follow Aruoba (2008) and consider national accounts data as final after the last ongoing revision. In the empirical analysis we also consider some monthly indicators. In contrast to the quarterly data, the final ongoing revision is often undertaken after a period of less than 4 years. In particular, the CPI undergoes final revision as early as 15 days after the initial release, industrial production undergoes final revision in May of the next year, and retail sales undergo final revision after 25 months and 15 days.2 Throughout this article, we will limit our attention to the properties of final revisions. The initial and final releases are denoted by xinitial and xfinal , respectively. For t t quarterly national accounts data, xinitial is available 45 t days after the reference quarter (‘‘t + 45 announcement’’). 3 Accordingly, final revisions are defined as rtfinal = xfinal − xinitial . t t
(1)
Being aware of the existence of revisions is one thing. But do revisions actually matter? A first impression is provided in Fig. 1, which documents the history of values assigned to the quarterly growth rate of real German GDP in the second quarter of 2005. The first vintage is the initial release in the third quarter of 2005, and the latest vintage is February 14, 2018. To attach some meaning to the magnitudes, the German economy is currently growing at a yearly rate of around 2%. Therefore, a typical quarterly growth rate may be around 0.5%. The first release suggested that the German economy was stagnating during the second quarter of 2005. However, the rate was substantially revised in subsequent periods. After about 4 years, the initial assessment has changed drastically from stagnation to very strong growth of around 0.7%. This example highlights the economic significance that revisions to national accounts can have. Fig. 1 also shows that after around 4 years, revisions become very small and the time series somewhat converges to its true (final) value. 2.2. Three properties revision should have The first desirable statistical characteristic of revisions is unbiasedness. Second, revisions should not be too large in terms of their variance. Third, revisions should be unpredictable when information that was available at 2 More details on the data are provided in Section 4. 3 As of the second quarter of 2020, German GDP will be officially published 30 days after the end of the reference quarter (‘‘t + 30 announcement’’).
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
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Fig. 1. Quarterly growth rate of real GDP. This figure shows historical data vintages for the German real quarterly GDP growth rate in the second quarter of 2005 (2005Q2). The initial release was published in the third quarter of 2005, and the latest vintage included is February 14, 2018.
the time when the initial release was published (Iinitial ) is used. If revisions were predictable, the initial release would not be an optimal forecast of the final value. In that case, a more precise forecast must exist that has a smaller root-mean-square error (RMSE). Formally, the three properties can be summarized as follows: P1: Unbiasedness: E[rtfinal ] = 0. P2: Variance: V[rtfinal ] should be small. P3: Unpredictability: E[rtfinal |Iinitial ] = 0. There are several possibilities for empirically measuring the properties of revisions, particularly with respect to P2 and P3. Regarding P1, for revisions to be unbiased, the sum of the upward and downward revisions of the statistical agency should amount to zero. This null hypothesis can be tested, if necessary, using robust standard error estimates. The desire to have a small variance is more difficult to formalize and needs a reference value to judge what small actually means. In the following analysis, we therefore consider the ratio of the variance of revisions to the variance of the underlying time series, termed noise-to-signal ratio. A value of 1, for instance, can be reasonably considered as large and economically relevant since it implies that the revisions vary by the same size as the actual time series. Unpredictability can be analyzed by the correlation between the revisions and the initial releases. The idea is that the initial release is a proxy for the information available at the time when the data were published, even though the information may have not been optimally exploited. 2.3. Noise versus news The concept of news and noise is an important element of studies on data revisions; see Aruoba (2008), Kishor and Koenig (2012) and Mankiw and Shapiro (1986). It is closely related to property P3 above. The noise hypothesis defines the initial data release as the truth plus measurement error and assumes that the error will eventually disappear in the revision process. Thus, the final revision is correlated with information available at the time of the initial announcement, implying predictability of rtfinal .
Hence, under the noise hypothesis, P3 is not satisfied. Conversely, under the news hypothesis, the initial release is an efficient estimate of the truth, and revisions are unpredictable. Therefore, the initial announcement should be uncorrelated with information available at t, and P3 holds. The distinction between news and noise also has implications for the variance of the underlying series. The news hypothesis implies that the variance increases as more and more revisions are made. The noise hypothesis implies that later revisions decrease the variance of the series as estimations become more accurate. Whether revisions are news or noise can be tested empirically. The models presented in the next section assume that revisions are noise that can be filtered out to better predict the final value. The Mincer–Zarnowitz regressions presented in Section 5 are formal tests of the news hypothesis. To check whether first releases provide a good picture of the current economic situation, the performance of alternative forecasts of the final value needs to be evaluated. It is more accurate to term an initial release a nowcast than to call it a forecast. Therefore, we will often refer to nowcasts in the remainder of this article. 3. Models for nowcasting German national accounts There are a number of approaches that are designed to process data that are subject to revisions; see Kishor and Koenig (2012). Many of them have a similar basic framework. Suppose the true, or final, value of the time series is generated by an AR(1) process: xt = β xt −1 + νt .
(2)
The statistical agency observes the true value only with measurement error ηt :
wt = xt + ηt .
(3)
The statistical agency may now use its experience, expert knowledge, and possibly also a model to evaluate wt . Thereafter, the value yt is published.
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
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3.1. Naive nowcast
3.4. Kishor-Koenig nowcast
For now, it is assumed that the statistical agency publishes the observed value of a variable without further data processing; that is, yT = wT . For the users of the official data, the first option is to ignore the possible occurrence of revisions and to naively set the published initial release at T equal to the nowcast xˆ T of the final value:
Kishor and Koenig (2012) propose an encompassing model that includes the Howrey model and the Sargent model as special cases. In contrast to the situation above (naive, Kalman, and Howrey nowcasts), Sargent (1989) assumes that the statistical agency itself filters its noisy observation wt before publishing the data. Sargent also allows for a white noise filtering error ξt (‘‘typo’’). The revision process is defined as
xˆ T = yT .
yt − xt = h(yt −1 − xt −1 ) + ϵt − (1 − g)νt ,
(4)
where ϵt equation
3.2. Kalman nowcast The alternative is to explicitly model data revisions, being aware that the published value represents a noisy signal. Keeping the assumption that the statistical agency provides just the value that it has observed itself, we have yt = xt + ηt .
= (ξt + g ηt ) and the nowcast follows the
ˆ T −1 − xT −1 ) − βˆ xT −1 ]. xˆ T = βˆ xT −1 + γˆK [yT − k(y
(10)
For g = 1, the model becomes the Howrey approach. Consistent estimates of the true parameter γK ≡ g σν2 /(g 2 σν2 + σϵ2 ) can be obtained in a similar way as in the Howrey model. However, efficiency requires application of the seemingly unrelated regression (SUR) estimator.
(5) 3.5. The generalized Kishor-Koenig model
If a forecaster receives a surprisingly large yT at the current edge of the sample, it is unclear how to interpret that value. Either the economic variable of interest, xT , has actually taken on a high value due to a large shock νT in (2) or the large yT is only a result of a sizable measurement error ηT in (5). Therefore, forecasters optimally update their expectations: xˆ T = βˆ xT −1 . If we define Eqs. (2) and (5) as the measurement and state equations of a state space system, the optimal updating rule is given by the Kalman filter as xˆ T = βˆ xT −1 + γˆK (yT − βˆ xT −1 ).
(9)
(6)
The idea of (6) is that the forecasters incorporate only a fraction of the surprise that they experience. The parameter γK is given by γˆK = σˆ ν2 /(σˆ ν2 + σˆ η2 ) and can be estimated from the data.4 The estimate is optimal in the sense that it minimizes
The above models assume that the second release is an efficient estimate of the final value. However, this might not be the case in empirical applications. Kishor and Koenig (2012) extend their encompassing model in that direction and propose a general filtering procedure. The procedure is based on the assumption that there exists an efficient estimate xet of the final release that becomes available e periods after the initial release xinitial . t Assuming that eth revision data follow an AR(1) process, the generalized state space system of (2) and (9) is given by the state equation xt = Fxt −1 + νt
(11)
and the observation equation y t = (I − G)Fy t −1 + Gxt + ϵt .
(12)
The vectors xt , y t , νt , and ϵt are defined as x′t ≡ [xet−e , xet−e+1 , . . . , xet ]′ ,
E[(xT − {β xT −1 + γN (yT − β xT −1 )})2 ].
−1 intial ′ y ′t ≡ [xet−e , xet − ], e+1 , . . . , xt
ν′t ≡ [0, 0, . . . , 0, ν0,t ]′ , ϵ′t ≡ [0, ϵe−1,t , . . . , ϵ1,t , ϵ0,t ]′ .
3.3. Howrey nowcast A common empirical property of revisions is that they are autocorrelated; see Aruoba (2008) for US data. As an extension of (6), Howrey (1978) proposes yt − xt = h(yt −1 − xt −1 ) + υt .
(7)
0 ⎢0
1 0
0 1
F ≡⎢ ⎢0 ⎣0 0
0 0 0
0 0 0
⎡ ⎢
Similarly to the Kalman model, the nowcast is
ˆ T −1 − xT −1 ) − βˆ xT −1 ]. xˆ T = βˆ xT −1 + γˆH [yT − h(y
The matrices F and G determine the dynamics of the revisions process and have the following forms:
(8)
In the Howrey model, γH is estimated as γˆH = σˆ ν2 /(σˆ ν2 + σˆ υ2 ). 4 σˆ 2 , σˆ 2 , and σˆ 2 refer to the empirical estimates of the variances ν η υ of νt , ηt , and υt , respectively.
⎡
1
⎢Ge−1,e ⎢G e−2,e G≡⎢ ⎢ . ⎣
... ... .. .
... ... 0
Ge−1,e−1 Ge−2,e−1
..
.. .
G0,e
G0,e−1
0 0⎥
⎤ ⎥ ⎥
0⎥ ⎦ 1 F0 (e+1×e+1)
... ... ... .. .
...
0
and
⎤
Ge−1,0 ⎥ Ge−2,0 ⎥ ⎥
.. .
G0,0
⎥ ⎦
.
(e+1×e+1)
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
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5
Table 1 Economic indicators in real time. Variable
Sample period
Frequency
Unit
SA
CA
Publication lag (days)
Real GDP Private consumption Public consumption Investment Exports CPI Production Retail sales Employment
1995Q2–2017Q4 1995Q2–2017Q4 1995Q2–2017Q4 1995Q2–2017Q4 1995Q2–2017Q4 2004M10–2018M2 1995M2–2017M12 2005M9–2017M12 1995M5–2018M1
Quarterly Quarterly Quarterly Quarterly Quarterly Monthly Monthly Monthly Monthly
QonQ growth QonQ growth QonQ growth QonQ growth QonQ growth YonY growth MonM growth MonM growth MonM absolute changes
Yes Yes Yes Yes Yes No Yes Yes Yes
Yes Yes Yes Yes Yes No Yes Yes Yes
45 55 55 55 55 No lag ≈35 ≈30 ≈66
The sample period is predefined by the Bundesbank’s real-time database. Publication lags reflect the institutional conventions of the German Federal Statistical Office. The seasonal adjustment is performed by X-12-ARIMA. The calendar adjustment accounts for differences in working days. CA, calendar adjustment; M, month, MonM, month on month; Q, quarter; QonQ, quarter on quarter; SA, seasonal adjustment; YonY, year on year.
The entries of both matrices can be estimated consistently by SUR using observable (revised) data. Once the state space system has been specified and the coefficients have been estimated, optimal predictions of the efficient release xet at time t that are given by the eth element of the state vector xt can be obtained by applying the Kalman filter to (11) and (12). Note that the Kishor-Koenig model includes the other models as special cases. Imposing the restriction G = I yields the Kalman model. Setting the entries Ge−i,0 = 0 for i = 1, . . . , e − 1 and G0,0 = 1 results in the Howrey model. 4. Data: Deutsche Bundesbank’s real-time database To compare alternative nowcast models, real-time data are needed. The Bundesbank provides a comprehensive database with vintages from 1995 onward for quarterly data. For monthly economic indicators, data are available from 2005 onward. We have selected a number of variables that receive particular attention in the business cycle analysis of the German government, which is executed by the Federal Ministry for Economic Affairs and Energy. Specifically, we investigate the nine variables in Table 1. GDP, private consumption, public consumption, investment in equipment and machinery, and exports are analyzed as real quarter-on-quarter growth rates. The German CPI, measured at a monthly frequency, is commonly analyzed as the yearly growth rate. Industrial production and retail sales are analyzed as month-on-month growth rates. Employment refers to the monthly absolute change in the number of people employed. All variables except the CPI are seasonally adjusted and most of the series are calendar adjusted. 5. Results 5.1. Actual properties of revisions Unbiasedness, small size, and unpredictability are desirable properties of revisions. Yet, if we take a closer look at the data, Table 2 shows that in many cases these properties are not satisfied. While quarterly national accounts data appear unbiased, the bias of the monthly economic indicators is statistically significant. This is shown in column 3, where bold numbers indicate significance at least
at the 10% level. With the exception of the CPI, the biases are also of economic significance. For instance, the monthly growth rate of German industrial production is usually 0.14 percentage points greater than the first release suggests. What about the size of revisions? The noise-to-signal ratio, depicted in column 7 in Table 2, documents that revisions are large. Other than for the CPI, the noiseto-signal ratio ranges from about 0.5 to more than 1, implying that in some cases the variation of revisions is as large as the variation of the underlying time series. Generally, sizable revisions may well be unpredictable. If this were the case, they should be uncorrelated with the information available at the time when the initial value was released. Using the initial release itself as a proxy for this information, one can see from column 8 in Table 2 that for many variables the null hypothesis of unpredictability is significantly rejected. The negative sign of the correlations is in line with the noise interpretation of revisions; see Mankiw and Shapiro (1986). If the true value of a data point is observed only with noise, the revision will subtract the noise from the initial release and thereby induce the negative correlation. 5.2. Nowcasting versus initial data release: Real-time exercise Evidence-based economic and financial policy needs a precise idea of the current economic situation. The results for the statistical properties of revisions suggested that there may be some room to improve on the initial releases. To verify this conjecture, we start the empirical analysis by identifying the efficient eth release and run the following set of Mincer–Zarnowitz regressions for each variable: xfinal = α + β xit + ut , t
(13)
where i = 0, 1, 2, . . . denotes the ith release. The initial release is obtained for i = 0. For each regression, an F test of the joint null hypothesis that α = 0 and β = 1 is performed. The null hypothesis implies that xi is an efficient release since the forecast errors would be purely random and therefore unpredictable. Thus, the Mincer–Zarnowitz regressions are formal tests to check from which release onward revisions can be considered news instead of noise.
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
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Table 2 Revision properties: Unbiasedness, size, and predictability. Variable
No. of observations
Mean
Min
Max
SD
Noise/signal
Correlation
Real GDP Private consumption Public consumption Investment Exports CPI Production Retail sales Employment
75 75 75 75 75 147 263 123 224
0.03 0.08 −0.01 0.02 −0.01 0.01 0.14 0.30 9.56
−0.91 −1.48 −3.58 −5.18 −2.12 −0.30 −2.78 −4.32 −91
1.02 1.36 2.60 4.72 2.48 0.64 2.22 6.57 166
0.36 0.51 1.02 2.01 1.09 0.08 0.80 1.47 33.42
0.44 0.74 1.24 0.60 0.43 0.09 0.56 1.09 0.78
−0.07 −0.22 −0.65 −0.12 −0.32 0.04
−0.57 −0.66 −0.18
This table shows estimated statistics of final revisions. Numbers in bold indicate statistical significance at least at the 10% level. The term noise/signal is defined as the variance of the revisions divided by the variance of the underlying time series and is thus a relative measure of the size of revisions. Correlation measures the correlation of the revisions with the initial release, the latter being a proxy for the information available at the time of the initial release. SD, standard deviation.
Table 3 Optimality tests of releases: Mincer–Zarnowitz regressions. Variable Real GDP Private consumption Public consumption Investment Exports CPI Production Retail sales Employment
No. of revisions e
Unbiasedness
Efficiency
Optimal forecast
α
β
α = 0, β = 1
0 3 6 0 0 0 6 2 7
0.04 0.12 0.08 0.17 0.25 0.01 −0.02 0.01 6.41
0.96 0.82 0.82 0.90 0.85 1.00 0.98 0.86 0.87
0.62 0.09 0.14 0.65 0.08 0.07 0.06 0.21 0.06
This table shows parameter estimates of α and β and corresponding p values for joint hypotheses of the Mincer–Zarnowitz regression with the release that provides an optimal forecast based on a 5% confidence level. Inference is based on heteroskedasticity and autocorrelation-consistent standard errors.
Unbiasedness is given if α = 0 and an efficient forecast satisfies β = 1. Given the predictability and bias of revisions in many cases, the results in Table 3 do not come as a great surprise. At the 5% significance level, for more than 50% of the variables the first release is not efficient. Moreover, according to the p values of the F test reported in the last column in Table 3, for many variables the releases become efficient only after a number of revisions. Retail sales, for example, become efficient only with the third release (e = 2). Concluding that the first release is often not an optimal prediction of the final value cannot be the end of the story. The more important question is whether superior alternative nowcasts can be found empirically. This exercise requires the use of real-time data and models that are able to handle data revisions. The approach we consider is the generalized Kishor-Koenig model described by Eqs. (11) and (12) in Section 3 as well as two restricted versions of it: the Kalman nowcast and the Howrey nowcast. We apply these three models to all variables where the evidence from the Mincer–Zarnowitz regressions suggests that the initial release is not efficient. The estimated parameter e ranges between 0 and 7 (see Table 3). The performance of the competing nowcast models is measured by the root-mean-square forecast errors. The forecast errors are defined as xˆ t − xfinal . The precision t is analyzed in relative terms where the naive nowcast,
the initial release of the German Federal Statistical Office, serves as the benchmark model. Table 4 summarizes the results. Values below 1 imply that the RMSE of the alternative model is smaller than that of the naive nowcast. Values above 1 indicate that the initial release has a higher precision. For each of the five variables, all of the alternative nowcast models outperform the initial release. The reduction in the RMSE is up to 23%, which is comparable to the gains in precision reported in Aruoba (2008) for US data. The Howrey model and the Kishor-Koenig model seem to be more suitable for German national accounts data than the standard textbook Kalman nowcast. This is in line with autocorrelation in the revisions and with not perfectly filtered releases by the German Federal Statistical Office. 5.3. Robustness: The role of benchmark revisions The results have shown that the alternative models could improve the nowcasts of German national accounts. Yet, the performance comparison requires a specific definition of the forecast errors and hence of xfinal . Up to now, t xfinal was considered to be the release for which the last t ongoing revision was undertaken. For quarterly data, for example, that date lies 4 years in the future. During such a long period, it might well be the case that a benchmark revision was undertaken between the first release and the
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
T. Strohsal and E. Wolf / International Journal of Forecasting xxx (xxxx) xxx
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Table 4 Nowcasting the truth in real time: Initial release versus alternative models. Final release defined as final ongoing revision Variable
Nowcast sample
e
Naive
Kalman
Howrey
Kishor-Koenig
Real GDP Private consumption Public consumption Investment Exports CPI Production Retail sales Employment
2006Q1–2013Q4 2006Q1–2013Q4 2006Q1–2013Q4 2000Q1–2013Q4 2000Q1–2013Q4 2007M11–2017M1 2000M1–2016M12 2007M2–2015M11 2003M1–2013M12
0 3 6 0 0 0 6 2 7
1 1 1 1 1 1 1 1 1
– 0.92 0.92 – – – 0.82 0.81 0.97
– 0.92 0.89 – – – 0.81 0.77 0.97
– 0.92 0.97 – – – 0.81 0.79 0.95
This table shows root-mean-square errors (RMSEs) of alternative nowcast models relative to the initial release of the German Federal Statistical Office (naive nowcast), which serves as the benchmark model. If the alternative model has a smaller RMSE than the benchmark model, the relative RMSE is below 1. Similarly, if the benchmark model performs better, the relative RMSE is above 1. The forecast error is defined as xˆ t − xfinal . The t parameter e indicates the eth release, which, according to pretesting in Table 3, is efficient. M, month; Q, quarter. Table 5 Robustness to benchmark revisions: Alternative definitions of the truth. Final release as final ongoing revision—excluding benchmark revisions Variable
Period
e
Naive
Kalman
Howrey
Kishor-Koenig
Real GDP Private consumption Public consumption Investment Exports CPI Production Retail sales Employment
2006Q1–2013Q4 2006Q1–2013Q4 2006Q1–2013Q4 2000Q1–2013Q4 2000Q1–2013Q4 2007M11–2017M1 2000M1–2016M12 2007M2–2015M11 2003M1–2013M12
1 0 6 0 0 0 5 2 10
1 1 1 1 1 1 1 1 1
0.98 – 0.90 – – – 0.83 0.80 0.97
0.99 – 0.88 – – – 0.82 0.76 0.99
0.96 – 0.93 – – – 0.82 0.77 0.94
Final release defined as the latest vintage Variable
Period
e
Naive
Kalman
Howrey
Kishor-Koenig
Real GDP Private consumption Public consumption Investment Exports CPI Production Retail sales Employment
2006Q1–2013Q4 2006Q1–2013Q4 2006Q1–2013Q4 2000Q1–2013Q4 2000Q1–2013Q4 2007M11–2017M1 2000M1–2016M12 2007M2–2015M11 2003M1–2013M12
0 3 7 0 0 0 8 2 22
1 1 1 1 1 1 1 1 1
– 0.92 0.91 – – – 0.85 0.81 1.06
– 0.92 0.87 – – – 0.87 0.77 0.99
– 0.92 0.86 – – – 0.87 0.78 0.85
This table shows root-mean-square errors (RMSEs) of alternative nowcast models relative to the initial release of the German Federal Statistical Office (naive nowcast), which serves as the benchmark model. If the alternative model has a smaller RMSE than the benchmark model, the relative RMSE is below 1. Similarly, if the benchmark model performs better, the relative RMSE is above 1. The forecast error is defined as xˆ t − xfinal . The t parameter e indicates the eth release, which, according to pretesting in Table 3, is efficient. M, month; Q, quarter.
final release.5 Benchmark revisions can, however, have a large impact on the forecasting results; see Knetsch and Reimers (2009). To investigate the effect of benchmark revisions, we consider two alternative definitions of the final release. First, to exclude benchmark revisions completely, we use the last ongoing revision as the final release only if no benchmark revision occurred between the first release and the final release. If a benchmark revision was actually undertaken, we take the last release before that benchmark revision as the final value. Second, to include all benchmark revisions, we use the latest vintage, February
5 In our forecasting sample, three benchmark revisions occurred, in 2005, 2011, and 2014.
14, 2018, as the final value. The outcome of the nowcast competition with alternative definitions of xfinal is t provided in Table 5. A number of results stand out. First, the parameter e, indicating the efficient release, varies only slightly when benchmark revisions are excluded. In contrast, when the latest vintage is used as the final value, e increases. This is intuitive, since including benchmark revisions introduces larger differences between the first and final values. Second, the finding from the previous section that all alternative models beat the naive nowcast survives the robustness test. Third, changes in the RMSEs are limited. The gains in forecast performance are mostly somewhat lower when the latest vintage is considered as the final release. Including all benchmark revisions, which are not datadriven by definition, appears to add additional complexity to the data and makes nowcasting more difficult.
Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.
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T. Strohsal and E. Wolf / International Journal of Forecasting xxx (xxxx) xxx
6. Conclusions
References
Data revisions arise as a matter of course when official data are produced. One reason is that not all data needed to calculate a data point of a variable are available to the statistical office at the date of the initial release. These gaps have to be filled by estimated values in one way or another. Moreover, the data delivered to the statistical office by third parties are usually revised too. Also, statistical offices produce large amounts of different data and have to operate under budget restrictions. However, official data are used for policy decision making. Therefore, initial releases should be unbiased and unpredictable. In this article, we have provided evidence that revisions to German official data are often biased and predictable. Using a number of simple multivariate models designed for data revisions, we showed that the forecasting power of the initial release can be increased. The effort of estimating these models is limited and reasonable. Future research may well find more powerful models that can improve the forecasting performance further. The models of Cunningham, Eklund, Jeffery, Kapetanios, and Labhard (2012) and Jacobs and Van Norden (2011), for example, are promising alternatives. Additionally, Clements and Galvão (2013) propose using autoregressive distributed lag (ADL) models that take into account the number of revisions. They show that their approach works well when the sample size is small and provide evidence for more precise forecasts compared with the Kishor-Koenig model. At least two policy conclusions emerge from the current article. First, the users of data should consider simple filtering of the initial release. On average, they will have a better idea of the actual situation for many important economic variables. Second, the providers of data may want to consider eliminating the predictability of revisions. Since this might require extensive institutional reform efforts, there is an alternative: the data production process could be left unchanged. Instead, just a second before the data point is released, the time series should be put through a simple filter.
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Please cite this article as: T. Strohsal and E. Wolf, Data revisions to German national accounts: Are initial releases good nowcasts?. International Journal of Forecasting (2020), https://doi.org/10.1016/j.ijforecast.2019.12.006.