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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 ytp1 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 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. Page 22 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. 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