The need for high frequency data:

estimating monthly GDP

MSc student George Constantinescu

Supervisor PhD. Professor Moisa Altar

The Academy of Economic StudiesThe Faculty of Finance, Insurance, Banking and Stock Exchange

Doctoral School of Finance and Banking

July 2009, Bucharest

Page 2

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

Content

Page 3

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;

Motivation

Page 4

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).

Literature Review

Page 5

The Kalman filter

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.

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Page 6

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 7

Monthly estimation without related series

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Observation equation

Page 8

Graphs

Standard deviation depending on teta

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Page 9

Monthly estimation with related series

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Page 10

Describing the relates series

Correlations GDP Industrial

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GDP 1.0000 0.8916 0.9009 0.9788

Industrial production 1.0000 0.9015 0.9235

Construction index 1.0000 0.9565

Services index 1.0000

Pairwize correlations between GDP and related series

The high correlation is partly explained by the non-stationary data series, which is not an impediment for the Kalman filter

Romanian GDP production approach was employed in choosing the related series

Page 11

Economic data release

The disaggregation of GDP in monthly observations allows quarterly estimations by about 30 days in advance of the official figures.

Page 12

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.

The related series also bring some noise into the model:

Std. dev. : 0.02686 for entire series 0.01619 for the second half

Note: the model was tested for Q1_2009 : estimation -5.84% vs. real -6.19%.

Page 13

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

Output gap in a state space approach:Model of Clarcke (1987)

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Page 14

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

Summary statistics

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

Cycle period (years) 1.67 2.07 1.98 1.81 5.20

Probability of T-test

Level 0.0000 0.0000 0.0000 0.0000 0.0000

Slope 0.0632 - 0.1515 0.0567 0.0000

Page 15

Graphic results

The model illustrates a relatively short cyclical (1.98 years) component, stochstic slope and the error term

Page 16

Hodrick – Prescott filter

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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).

Page 17

Testing Taylor Rule model at a monthly level

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:

1.175 vs. 1.198

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Page 18

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

Czech Republic 0.2281 1.9963 ↑ 2.8455 ↑

Hungary 0.4204 0.5073 ↑ 0.5936 ↑

Poland 0.4950 0.5669 ↑ 0.5035 ↓

Unrestricted models

Czech Republic 1.6607 2.6099 ↑ 6.4155 ↑

Hungary 0.1806 1.3358 ↑ 1.1452 ↓

Poland 2.7669 3.1848 ↑ 3.5463 ↑

Page 19

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 monthly growth y/y

-5%

-4%

-3%-2%

-1%

0%

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Jan_2007 Jul_2007 Jan_2008 Jul_2008 Jan_2009

USA GDP quarterly evolution

-4%

-2%

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2%

4%

6%

8%

10%

1977 1979 1981 1983 1985

Estimates on GDP are published each month in USA, allowing a close watch of the current economic evolution (www.e-forecasting.com)

Page 20

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 21

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).

Conclusions

Page 22

References

Altar M., L. L. Albu, I. Dumitru and C. Necula (2005) – “Estimation of equilibrium real exchange rate and of deviations for Romania”, study no. 2 within CEEX Program.

Andrei, T. and R. Bourbonnais (2007) – “Econometrie”, ed. Economica, 335 – 365.

Astolfi R., D. Ladiray, G.L. Mazzi, F. Sartori and R. Soares (2001) – “A monthly indicator of GDP for the Euro-zone”, Luxembourg.

Barro, R. J. and X. Sala-i-Martin (2003) – “Economic Growth”, second edition, The MIT Press.

Castelnuovo, E., L. Greco and D. Raggi (2008) – “Estimating regime-switching Taylor Rules with trend inflation”, Bank of Finland Research, Working Paper 20.

Cerra, V. and S. C. Saxena (2000) – “Alternative methods of estimating Potential GDP and the Output Gap: an application to Sweeden”, IMF WP 59/2000.

Chow, G. C. and A. Lin (1971) – “Best Linear Unbiased Interpolation, Distribution and Extrapolation of Time Series by Related Series”, Review of Economics and Statistics 53, 372-375.

Christou, C., M. Goretti, L. Moulin and R. Atoyan (June 2008) – “Romania: Selected issues”, IMF Country Report.

Cuche N. A. and M. K. Hess (Winter 2000) – “Estimating monthly GDP in a general Kalman filter framework: Evidence from Switzerland”, Economic & Financial Modeling

Dobrescu, E. (2006) – “Macromodels of the Romanian Market Economy”, Economica Press, Bucharest.

Dornbusch, R., S. Fisher and R. Startz (2004) – “Macroeconomics”, 9th edition, McGraw Hill Press.

Enders, W. (2004) – “Applied Econometric Time Series”, second edition, Wiley Series in Probability and Statistics, USA, 301-305

Faal, E. (2005) – “GDP Growth, Potential Output and Output Gaps in Mexico”, IMF WP 93/2005.

Friedman, M. (1962) – “The interpolation of time series by related series”, Journal of American Statistical, Association, 57(300), 729-757.

Galatescu, A, B. Radulescu and M. Copaciu (April 2007) – “Estimating the potential GDP in Romania”, Working Paper no. 20, National Bank of Romania.

Gourieroux, C. and A. Monfort (1997) – “Time Series and Dynamic Models”, Cambridge University Press, UK.

Gujarati D. N. (2004) – “Basic Econometrics”, 4th edition, Mc-Graw Hill Press.

Harvey, A. C. (2001) – “Forecasting, structural time series models and the Kalman Filter”, Cambridge University Press, Cambridge, UK.

Konuky, T. (2008) – “Estimating Potential Output and the Output Gap in Slovakia”, IMF WP 275/2008.

Koopman, G. J., I. P. Szekely, A. Hobza, K. Mc Morrow and G. Mourre (June 2009) – “Impact of the current economic and financial crisis on potential output”, Occasional paper 49, Directorate-General for Economic and Financial Affairs, European Commission.

Lanning, S. G. (1986) – “Missing Observations: A simultaneous Approach versus Interpolation by Related Series”, Journal of Economic and Social Measurement 14, 155-163.

Mishkin, F. S. (2007) – “The Economics of money, banking and Financial Markets”, Alternative edition, 8th edition, Pearson Education, 179 - 218, 465 – 500

Mishkin, F. S. (2007) – “Monetary Policy Strategy”, MIT Press, Cambridge, chapters : Rethinking the Role of NAIRU in Monetary Policy: Implications of Model Formulation and Uncertainty / Why the Federal Reserve Should Adopt Inflation Targeting

Orphanides, A. and S. Van Norden (1999) – “The Reliability of Output Gap Estimates in Real Time”, Board of Governors of the Federal Reserve System and Economics Discussion Series, No. 38.

Sarikaya, C., F. Ogunc, D. Ece, H. Kara and U. Ozlale (April 2005) – “Estimating output gap for emerging market economies”.

Stanica, C. (2004) – “Aplicatii privind estimarea PIB-ului potential trimestrial / Empirical study on estimating the quarterly potential GDP ”, Economic Prognosis Institute, Bucharest.Hamilton, J. D. (1994) – “Time Series Analysis”, Princeton University Press, New Jersey, USA.

Welch, G. and G. Bishop (2003) – “An introduction to Kalman Filter”