Real-time versus revised Czech data: a DSGE analysis
Jan ˇCapek1
Abstract. The paper investigates the effects of using real-time data instead of revised
ﬁnal data within Dynamic Stochastic General Equilibrium (DSGE) framework. Theoretically,
using most recent, updated historical data for ex-post analyses for a historical
time-sample may be misleading, because revised data were not available at that time.
The contribution uses a small-scale monetary macroeconomic DSGE model to analyze
the importance of real-time data compared to most-recent revised data with a focus on
the differences in decision-making of the monetary authority. The analysis proceeds
from Bayesian estimation of model parameters in a model with real-time data and in
a model with the most recent revised data.
Keywords: real-time data, data revision, recursive estimate, DSGE model
JEL classiﬁcation: C11, C32, C52, C54, E52, F41
AMS classiﬁcation: 91B51, 91B64, 91B84, 62P20
1 Introduction
The paper investigates the effects of using real-time data instead of revised ﬁnal data within Dynamic Stochastic
General Equilibrium (DSGE) framework. Theoretically, using most recent, updated historical data for ex-post
analyses for a historical time-sample may be misleading, because revised data were not available at that time. In
case of e.g. monetary macroeconomic models with the usage of revised data, the monetary authority would be
expected to make decisions based on then-unknown data. The contribution uses a small-scale monetary macroeconomic
DSGE model to analyze the importance of real-time data compared to most-recent revised data with a focus
on the differences in decision-making of the monetary authority. The analysis proceeds from Bayesian estimation
of model parameters in a model with real-time data and in a model with the most recent revised data. Statistical
signiﬁcance of the differences in the Bayesian estimates is presented.
Following section introduces the reader to real-time data literature. Literature review focuses on papers that
are relevant for this paper’s aim. Section 3 presents analysis of the data itself with descriptive statistic. Section
4 presents results of recursive estimation on a SOE DSGE model with real-time and revised data. Final section
concludes.
The term “real-time data” addresses data that become available right after collection. In accordance with the
literature on similar topics, this paper understands “real-time data” as data that are available 3-4 months after the
end of a quarter and are typically the ﬁrst estimates published for that quarter.
A “vintage” is a quarter at which the data becomes available, or, the time of publishing. For example, if Czech
statistical ofﬁce releases during April of 2013 an estimate of GDP growth for last quarter of 2012, it is said that the
data for fourth quarter of 2012 are in vintage of April of 2013.
2 Literature review
The issue of data revising and properties of real-time versus revised data has been investigated in the literature for
a long time and until now, it is still a topic for scientiﬁc discussion.
The orientation of various literature and methodology differs. Some articles focus on the data itself and investigate
properties of real-time data in comparison with revised data. There is also a group of articles that focus on the
inﬂuence of real-time data on model results, e.g. for forecasting or reactions of monetary policy. This contribution
follows both of these lines of research.
1Masaryk University, Faculty of Economics and Administration, Department of Economics, Lipov´a 41a, 600 02 Brno, capek@econ.muni.cz
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Croushore and Stark [2] investigate properties of a real-time dataset and show that data vintages matter in comparison
to revised data. Taylor [8] focuses on forecast quality when real-time data are used for its construction.
He shows that forecasting models that use timely data have higher forecasting power. Business cycle analysis in
real-time data environment is done e.g. by Lee et al. [4], who construct real-time macroeconomic database for
Australia. The database exposes the difﬁculties in drawing inferences and decision-making based on macroeconomic
data that is subsequently revised. Molodtsova et al [6] estimate Taylor rule with revised data and real-time
data. There is a difference between the two estimates in Germany but not so much in the USA. Orphanides and van
Norden [7] examine the reliability of alternative output detrending methods with special attention to the accuracy
of real-time estimates of the output gap. They ﬁnd out that the revision of published data is not the primary source
of revisions in measured output gaps; the bulk of the problem is due to the pervasive unreliability of end-of-sample
estimates of the trend in output. Boivin [1] searches for the differences in drifting parameters with real-time data.
The ﬁndings suggest important but gradual changes in the Taylor rule coefﬁcients, not adequately captured by the
usual split-sample estimation.
This contribution follows the trends in literature and it presents analysis on the data itself by descriptive statistics
in section 3 and it also calculates model results with recursive estimates in section 4.
3 Data analysis
There is a number of sources of uncertainty concerning the data and its model implementation. This contribution
addresses three of them: (i) the differences in the data by source, (ii) the magnitude of data revisions and (iii) the
differences in detrended data due to data availability at time of detrending.
3.1 Differences in the data by source
Figure 1 depicts the differences between the data from two widely used databases: OECD and Eurostat. The data
should be the same with the exception of inﬂation, which is only available as CPI in OECD real-time database
and HICP in Eurostat database. In most cases, the differences are small or none at all, which is the case of both
domestic and foreign interest rates with no error and EuroArea growth with only 0.02 percentage points of average
absolute error. On the other hand, average absolute difference in data series for Czech inﬂation differs by a half of
a percentage point, which is not negligible. As the errorbars display, there are no systematic patterns in differences
between Eurostat and OECD data.
2000 2005 2010
−4
−2
0
2
4
6
8
depreciation, avg. abs. err. = 0.14 p.p.
2000 2005 2010
−10
−5
0
5
Czech GDP growth, avg. abs. err. = 0.21 p.p.
2000 2005 2010
−10
−5
0
5
EA12 GDP growth, avg. abs. err. = 0.02 p.p.
2000 2005 2010
0
5
10
15
Czech inflation, avg. abs. err. = 0.51 p.p.
2000 2005 2010
−2
0
2
4
EA12 inflation, avg. abs. err. = 0.17 p.p.
2000 2005 2010
0
5
10
15
Czech 3M rate, avg. abs. err. = 0.00 p.p.
Eurostat
OECD
errorbar
2000 2005 2010
0
2
4
EA 3M rate, avg. abs. err. = 0.00 p.p.
Figure 1 Eurostat and OECD data, Note: (error)bar plot around zero = difference between Eurostat and OECD
data, “avg. abs. err.” = average absolute error in percentage points
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3.2 Magnitude of data revisions
Figure 2 displays the series of real-time data and most-recent updated data, all from OECD database. The differences
in the series are not insigniﬁcant and the errorbars in cases of GDP growths show that the deviations
are also non-random. Real-time data tend to underestimate the actual development. For example, in periods of
expansion, real-time data underestimate positive growth in the Czech Republic in 2004/2005 and also in EuroArea
in 2007/2008. As for recessions, both real-time values for domestic and EuroArea economy underestimate the
severity of the crisis of 2009. The average absolute error tops at 1.34 percentage poins (quarterly, per annum) for
Czech GDP growth, which means that the average value of the error is approximately 56% of average GDP growth
over the sample. Average error-to-average value is also very high for EuroArea growth with 39%.
1998 2000 2002 2004 2006 2008 2010 2012
−10
−5
0
5
Czech GDP growth, avg. = 2.38, avg. abs. err. = 1.34 p.p.
1998 2000 2002 2004 2006 2008 2010 2012
−10
−5
0
5
EA12 GDP growth, avg. = 1.52, avg. abs. err. = 0.59 p.p.
1998 2000 2002 2004 2006 2008 2010 2012
0
5
10
15
Czech inflation, avg. = 3.48, avg. abs. err. = 0.45 p.p.
real−time data
final data
errorbar
1998 2000 2002 2004 2006 2008 2010 2012
−2
0
2
4
EA12 inflation, avg. = 2.00, avg. abs. err. = 0.39 p.p.
Figure 2 Real-time and ﬁnal (revised) data, Note: (error)bar plot around zero = difference between ﬁnal and revised
data, “avg.” = simple average of ﬁnal data over the sample, “avg. abs. err.” = average absolute error in percentage
points
3.3 Differences in detrended data due to data availability at time of detrending
This section offers a depiction of a source of uncertainty which is not in the data itself but stems from the need to
detrend the time series prior to modeling. In the model used, EuroArea interest rate is detrended with a linear trend
and since Czech interest rates display even more curvature, Hodrick Prescott trend is used.
This type of analysis uses only revised data series. At ﬁrst, the trend is computed on time series truncated to
30 observations. Then, the truncation moves one-by-one to more observations and the trend is recomputed each
time. This procedure results in a number of time series of different length, each one detrended on its sample. Such
results depict changes in the time series stemming only from the recomputation of the trend.
Figure 3 displays all vintages of detrended data with a solid line and ﬁnal data with a circled line for comparison.
The last values of each vintage form a real-time data in the second row panels. Time series formed this way
will be addressed “detrend real-time” data in the remainder of the paper. Note that the difference between “detrend
real-time” data and ﬁnal revised detrended data stems only from the fact that detrending is calculated repeatedly
for each length of the series. The third row in Figure 3 displays errorbars that are expectedly systematic.
4 Estimation
4.1 Model and Identiﬁcation
This paper uses a New Keynesian (NK) Dynamic Stochastic General Equilibrium (DSGE) model. The model is
derived from microeconomic behavior of particular economic agents. These include domestic and foreign households,
domestic and foreign producers, domestic importers and domestic and foreign monetary authority. The
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1998 2000 2002 2004 2006 2008 2010 2012
−2
0
2
4
CZ 3m rate, vintages of detrended data
final data
1998 2000 2002 2004 2006 2008 2010 2012
−2
0
2
4
CZ 3m rate, avg. abs. err. = 0.53 p.p.
detrend real−time data
1998 2000 2002 2004 2006 2008 2010 2012
−1
0
1
CZ 3m rate, errorbar
1998 2000 2002 2004 2006 2008 2010 2012
−1
0
1
2
EA 3m rate, vintages of detrended data
1998 2000 2002 2004 2006 2008 2010 2012
−1
0
1
2
EA 3m rate, avg. abs. err. = 0.27 p.p.
1998 2000 2002 2004 2006 2008 2010 2012
−0.5
0
0.5
EA 3m rate, errorbar
Figure 3 Differences in detrended data due to data availability
model is in small open economy (SOE) setting, so that it presumes two countries - small open economy that is
inﬂuenced by a big closed economy. The small open economy is the home Czech economy, the big large economy
is the foreign EuroArea economy. Most of the model assumptions are adopted from Lubik and Schorfheide [5].
The model is estimated by Bayesian methods in Dynare package1 on a dataset with 7 variables. All the estimates
share the same prior setting. Convergence of each estimate is checked by Brooks and Gelman convergence
diagnostics.
4.2 Recursive estimates
Recursive estimates are constructed so that as a new data point is added to the existing set, the model is re-estimated.
New values of parameter estimates are then reported. One can argue that if parameters estimates change, it reﬂects
the information in the newly-added data.
Recursive analysis is regularly done by policy institutions if newly-data becomes available to actualize the
model for a new round of predictions or forecasting. Recursive analysis is also done on historical sample to
analyze the evolution of policy. The former inevitably uses real-time data, the latter mostly uses updated ﬁnal
data, because the estimation is easier to implement and older vintages of real-time data may not be available. This
sections shows two examples where the choice of real-time versus ﬁnal data does matter.
Figures in this section present four estimates to compare. Estimates based on Eurostat and OECD data are
standard recursive estimates – only the time series of most updated ﬁnal data is used, detrended on the whole
sample and the detrended series is then truncated to mimic shorter sample. Note that the detrended series do not
change at all in this type of estimation, there is just one new data point added in each longer time-frame.
Another approach is a genuine real-time estimate. This sequence of estimates use only data available at the
vintage in question. Each time series may undergo revisions and therefore may be different. Also, detrending is
made on these potentially different series with different number of observations. Although this approach mimics
the historical possibilities of analysis best, it has a drawback that the inﬂuence of the data revisions and the inﬂuence
of potentially changing trends cannot be distinguished.
To address this problem, another recursive estimate is introduced. The original data series for estimation are
revised ﬁnal series, but the truncation of the series is done prior to detrending. This estimation therefore does not
reﬂect any issues of data revisions but it captures the inﬂuence of re-detrending in each quarter. It is then possible
1www.dynare.org
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to infer the relevance of data revisions by comparing the genuine real-time estimate and the estimate that covers
the problems arising from consecutive detrending. Note that this type of results was earlier addressed to as based
on “detrend real-time” data. In order to easily see the signiﬁcance of the results, a 90 % probability band of the
“detrend real-time” estimate is drawn.
The estimates start in second quarter of 1996 and have at least 30 observations. The last observation is third or
fourth quarter of 2012 which makes 66 or 67 observations in the most-recent estimates.
Estimates based on Eurostat and OECD data usually behave similarly, although there may be some vertical
difference between the series of the estimates. However, on the two presented cases, the “detrend real-time”
estimate that covers only the problem of consecutive detrending is different than the former two. This means that
knowledge of the trend is signiﬁcant and not knowing future trend leads to different estimates. Also, the real-time
estimates differs from “detrend real-time” estimates, which again means that also the nature of the changes in the
data itself due to revisions are signiﬁcant.
2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
0
0.5
1
1.5
2
Time (end−of−period) / Last observation
psi2, mean out of HPDi @ alpha<0.06
prior
recursive EUROSTAT
recursive OECD
recursive real−time
recursive detrend real−time
Figure 4 Recursive estimates of the weight on output growth in a domestic Talyor rule
Figure 4 displays the evolution of recursive estimates of a parameter that is the weight on output growth in a
domestic Talyor rule. It is therefore a preference parameter of domestic monetary authority. The higher it is, the
more important is output growth for the central bank when it set its policy interest rates.
All of the estimates display a tendency of a decline. The tendency is gradual in standard recursive estimates.
On the other hand, the real-time estimate shows no gradual tendency but there is a great drop in the estimate in
fourth quarter of 2008 (denoted as 2009 in the ﬁgure).2 Since the evolution of the real-time estimate is outside
of 90 % probability bands of “detrend real-time” estimate, the difference is statistically signiﬁcant. Such result
may be interpreted intuitivelly – from the point of view of real-time data, the oncoming crisis was a shock that
is captured by a major change in the estimate in the quarter in question. Other estimates display gradual decline,
because the information may have been included in revised data and the future trend was known.
Figure 5 displays estimation results for the persistence of domestic interest rate and it displays rather different
development. Both standard recursive estimates calculated on ﬁnal revised data tend upwards from 0.6 to ﬁnal 0.7.
However, both remaining estimates also show a decline in years 2006 and 2007 before converging upwards. This
results may mean that 2006/2007 period is consistent with lower interest rate smoothing that would seem from the
estimates on revised data. Since the evolution of real-time and “detrend real-time” data is similar, the differences
are probably mainly due to re-estimation of the trend rather than in data revision itself. Note also that the results
are not signiﬁcant at conventional levels so that we can only discuss tendencies.
5 Conclusion
Data from OECD and Eurostat are very similar and the use in a DSGE model does not make much difference.
Comparing revised and real-time data shows that the differences are not insigniﬁcant and also with systematic
patterns. Also, if the preparation of the data for a model use means detrending (other than demeaning), this makes
rise to a problem of trend recomputation, which can also be signiﬁcant.
2Note that missing values of the estimates are due to missing real-time data at respective quarters.
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2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013
0.45
0.5
0.55
0.6
0.65
0.7
0.75
Time (end−of−period) / Last observation
rhoR, mean out of HPDi @ alpha<0.59
prior
recursive EUROSTAT
recursive OECD
recursive real−time
recursive detrend real−time
Figure 5 Recursive estimates of the persistence of domestic interest rate
Analysis on a DSGE model shows results where the re-detrending is signiﬁcant and also where the nature of
real-time data in comparison to revised data is signiﬁcant.
Paper’s results are in line with existing literature that ﬁnds the use of real-time data signiﬁcant in various
estimation or forecasting exercises. This contribution conﬁrms the results on Czech data.
Acknowledgements
The access to computing and storage facilities owned by parties and projects contributing to the National Grid
Infrastructure MetaCentrum, provided under the programme ”Projects of Large Infrastructure for Research, Development,
and Innovations” (LM2010005) is highly appreciated.
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