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The Academy of Economic Studies
The Faculty of Finance, Insurance, Banking and Stock Exchange
Doctoral School of Finance and Banking
The need for high frequency data:
estimating monthly GDP
MSc student George Constantinescu
Supervisor PhD. Professor Moisa Altar
July 2009, Bucharest
Content
 Motivation
 Literature review
 The model
 Estimating output gap (Kalman and HP filters)
 Testing a possible Taylor Rule model at a monthly level
 Shape of recession & long run effects
 Conclusions
 References
Page  2
Motivation
 Decision makers often use models containing monthly variables,
while GDP only comes in quarterly series;
 For emerging countries (such as Romania) there is a limited
availability of compatible and relevant number of observations; By
estimating a monthly GDP we tripled their number;
 It allows quite accurate GDP forecasts with more than 30 days in
advance;
 No such study has been performed for the Romanian economy so
far;
 Higher frequency GDP can help identify the evolution of the
economic cycle and moreover the current recession pattern for
different countries;
Page  3
Literature Review
 Chow and Lin (1971, 1976) built the first coherent econometric procedure for
interpolation of stock and flow variables, improving the work of Friedman (1962);
 Denton (1971), Fernandez (1981) and Litterman (1983) who suggest a
approach based on regression to minimize the loss function on the difference
between the series to be estimates and a linear combination of the observed
related series.
 Bernanke, Getler and Watson (1997) use the state space framework to
interpolate real GDP for USA, by employing the Kalman filter.
A notable contribution is represented by the refinement of modeling, estimation
and inference of structural or unobserved components, time series models,
starting from Harvey (1989) and proceeding to Durbin and Koopman (2001).
Lanning suggests (1986) that missing observations is better to be obtained
independently, than to be considered as common variables along with other data.
Obtaining higher frequency data from lower frequency ones is called temporal
disaggregation, in its 2 forms: interpolation (for stock variables) and
distribution (for flow variables).
Page  4
The Kalman filter
Representation of a state space model:
xt 1  Ft  xt  Ct  zt 1  Rt  vt 1
State equation
yt  At  xt*  H t  xt  N t  wt
Observation (measurement) equation
R. E. Kalman (1960) develops a filter based on adaptive system and
recurrent calculus, which solved the existing limitation of working only with
stationary variables. Kalman filter relies less on initial data input.
Page  5
The data
 This study uses as input values the Romanian quarterly GDP, current
prices (mn. RON), published by the National Institute of Statistics, for
period Q1_2000 : Q1_2009 (37 observations).
 Based on the corresponding deflators, initial data is transformed into real
quarterly GDP (year 2000).
 By using the Census X12 procedure, the time series is seasonally
adjusted to provide comparability between consecutive observations.
 Further on we use the natural logarithm to introduce the data into the
models.
Page  6
Monthly estimation without related series
 yt 
xt   yt 1    yt
 yt 1 
 yt 1  1  
 y  1
 t  
 yt 1   0
yt 1

0
1

yt 2 
0  yt  1 0 0 ut 1 
0   yt 1   0 0 0   ut 
0  yt  2  0 0 0 ut 1 
yt  (1   )  yt 1    yt  2  ut
yt  ht  xt
Page  7
State equation
Observation equation
ht  0 0 0 ,
for t = 1, 2, 4, 5, 7, 8, ....., T-1
ht  1 1 1,
for t = 3, 6, 9, 12, ....., T
GDP is a AR(2)
Graphs
Standard deviation depending on teta
0.99
0.96
0.94
0.92
0.91
0.90
0.89
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
Page
0.008 8
By minimizing the standard deviation of
errors, according to several values for θ , we
obtain a value of 0.008290, corresponding
to θ = 0.902
0.009
0.01
0.011
0.012
Monthly estimation with related series

yt  xt  c  ut
Vector containing the related series
 y  x  c 
t
 t


zt   yt 1  xt 1  c 



 yt 1  xt  2  c 


 ut 1 


zt 1  I 3   ut 
u 
 t 1 


yt  at  xt*  ht  zt
x 
*
t
State equation
Measurement equation




x
,
h

0
0
0
,
a
 j t
t  0, t  1,2,4,5,7,...
t
j t  2


ht  1 1 1,a t  c, t  3,6,9,.....
Page  9
State vector
ut ~ NID (0,  u )
c  0.055 0.300 1.100
Describing the relates series
Romanian GDP production approach was employed in choosing the related series
Pairwize correlations between GDP and related series
Correlations
GDP
GDP
1.0000
Industrial production
Construction index
Services index
Page  10
Industrial
production
Construction
index
Services
index
0.8916
0.9009
0.9788
1.0000
0.9015
0.9235
1.0000
0.9565
1.0000
The high correlation is partly
explained by the nonstationary data series, which
is not an impediment for the
Kalman filter
Economic data release
The disaggregation of GDP in monthly observations allows quarterly
estimations by about 30 days in advance of the official figures.
Page  11
Related series model (2)
By running the application with related
series recently released for May, we
see monthly GDP falling by 6.9% y/y,
as compared to 5.7% at April.
Note: the model was tested for Q1_2009 :
estimation -5.84% vs. real -6.19%.
The related series also bring some
noise into the model:
Std. dev. : 0.02686 for entire series
0.01619 for the second half
Page  12
Output gap in a state space approach:
Model of Clarcke (1987)
yt  ytp  zt
ytp  ytp1  t   ty
t  t 1   t
zt  1  zt 1  2  zt  2   tz
 yt  1 0 0
 z  0  
1
2
 t 
 zt 1  0 1 0
  
  t  0 0 0
1  yt 1   ty 
 
0  zt 1   tz 


0  zt  2   0 
  
 
1  t 1   t 
 The log of the quarterly GDP is the sum of log real potential output and a
log cyclical component.
 This cyclical component is assumed to be stationary second order
autoregressive process
 The trend is assumed to follow a random walk with drift. The drift, in turn,
is also assumed to follow a random walk
Other models include local level model, local linear trend model,
Watson model (1986), Harvey and Jaeger (1993) – with a seasonal
component
Page  13
Statistics of several models with related series
Monthly series
Level
stochastic
stochastic
fixed
fixed
fixed
Slope
stochastic
no
stochastic
stochastic
fixed
Cycle
yes, 20
yes, 20
yes, 20
yes, 50
yes, 20
Seasonal
no
no
no
No
no
Irregular
yes
yes
yes
Yes
yes
AR
no
no
no
No
no
Std.Error
0.0048
0.0051
0.0048
0.0048
0.0046
Normality
4.7415
5.7185
5.3757
5.2355
7.1194
H( 28)
0.5416
0.5167
0.5232
0.5536
0.5498
DW
1.8596
1.9568
1.8631
1.8451
1.9040
Q(9, 6)
33.2590
51.3060
32.0130
31.5160
35.6980
Rd^2
0.1679
0.9807
0.1915
0.1731
0.2395
1.67
2.07
1.98
1.81
5.20
Level
0.0000
0.0000
0.0000
0.0000
0.0000
Slope
0.0632
-
0.1515
0.0567
0.0000
Summary statistics
Cycle period (years)
Probability of T-test
Page  14
Graphic results
 The model illustrates
a relatively short
cyclical (1.98 years)
component, stochstic
slope and the error
term
Page  15
Hodrick – Prescott filter
T 1
T
min

2
(
y

y
)



[(
y

y
)

(
y

y
)]
 t t
 t 1 t
t
t 1
2
t 1
t 2
= 100, annual data
= 1.600, quarterly data
= 14.400, monthly data
HP filter was used in order to provide comparison for the Kalman filter technique,
revealing some of its limitations in being consistent for both quarterly and monthly
data (different signals).
3.48
GDP
HP_14.400
3.46
0.6%
HP_50.000
HP_14.400
HP_50.000
HP_5.000
0.4%
3.44
HP_5.000
0.2%
3.42
0.0%
-0.2%
3.4
-0.4%
3.38
-0.6%
3.36
3.34
2002
2003
Page  16
-0.8%
2002
2004
2005
2006
2007
2008
2009
2003
2004
2005
2006
2007
2008
2009
Testing Taylor Rule model at a monthly level
it  2   t 
1
1
 ( t  2)   ( yt  yt )
2
2
it   t  rt*  a  ( t   t* )  ay  ( yt  yt )
Classic form
Generalized form
it  1.0000   t  0.9803  rt*  0.1919  ( t   t* )  0.8544  ( yt  yt )  0.7509
 We find prove of Taylor rule (1993)
monetary policy existence during
2006_01 : 2009_04;
 Coefficients for 2007_01 : 2009_04:
1.347 vs. 0.619
for 2006_01 : 2008_11:
Page  17
1.175 vs. 1.198
Case of Czech Rep, Hungary, Poland
 Despite the fact that we lacked in finding consistent evidence, there
are short periods of time for which the rule is obeyed.
 Nevertheless, we note a rise in the ratio between coefficients
corresponding to deviation from the inflation target and output gap.
 This means that the Central Banks key rates were even more
impacted by changes in inflation rate deviation, rather than output
gap.
 More or less surprisingly the model fails for USA.
2001:01 – 2008:04
2001:01 – 2008:10
2001:01 – 2009:04
Restricted models
↑
2.8455
↑
0.5073
↑
0.5936
↑
0.4950
0.5669
↑
0.5035
↓
Czech Republic
1.6607
2.6099
↑
6.4155
↑
Hungary
0.1806
1.3358
↑
1.1452
↓
Poland
2.7669
3.1848
↑
3.5463
↑
Czech Republic
0.2281
Hungary
0.4204
Poland
1.9963
Unrestricted models
Page  18
What‘s the shape of recession ?
 By observing the monthly
estimations of GDP it is less facile
to identify a pattern of recession as
early classified to replicate the
letters J, L, W, V or most the
common U.
USA GDP quarterly evolution
10%
8%
6%
4%
2%
0%
-2%
-4%
1977
1979
1981
1983
USA monthly growth y/y
Estimates on GDP are published
each month in USA, allowing a
close watch of the current economic
evolution (www.e-forecasting.com)
Page  19
4%
3%
2%
1%
0%
-1%
-2%
-3%
-4%
-5%
Jan_2007
Jul_2007
Jan_2008
Jul_2008
Jan_2009
1985
Effects of economic crisis on LT potential GDP growth rates
History has shown that recessions
often leave their marks on the long
term economic growth evolution, as
restructuring process is slower,
investors take lower risks, R&D
expenses drop and NAIRU
increases during recession.
Page  20
Conclusions
The main goal of obtaining a monthly estimate of the Romanian GDP was finally
achieved.
By including some related series into the model, its economic relevancy is improved,
but with the trade-off consisting in higher noise.
Figures at monthly level can be used now to integrate into macroeconomic models,
make anticipated estimates on quarterly GDP, increase the number of
observations by three times, and thus improving the quality of the model.
We partially failed in observing prove of a Taylor Rule monetary policy existence at a
monthly level. Best results seemed to be obtained in the case of National Bank of
Romania. The empirical result is that the real-economy component becomes less
valuable during recessions, in the favor of inflation adjusting to its target.
Limits:
It is not possible to include the effect of agriculture (highly volatile in Romania), due
to lack of corresponding related series, perhaps use some confidence indicator as
a soft variable.
The standard deviation of errors in the related series model can be further improved
by better choosing the related series (perhaps a different approach that
production).
Page  21
References
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Page  22
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