Euro-MIND: A Monthly INDicator of the Economic Activity in the Euro Area

Euro-MIND: A Monthly INDicator of the Economic Activity in the Euro Area C. Frale, M. Marcellino, G.L. Mazzi and T. Proietti 9 Brown Bag Lunch Meeting-MEF Rome, 9th December 2008

Motivation Gross domestic product (GDP) is perhaps the most relevant coincident economic indicator, as it provides a comprehensive measure of the level of economic activity. Currently, its estimation requires a relevant flow of information and yet monthly estimates are not made available officially. What motivates this research project is the awareness that we may go beyond the quarterly GDP estimates due to the availability of timely and reliable statistical information on related indicators at the monthly frequency.

Introduction We carry out the disaggregation of the chain-linked quarterly value added from the output side (Agriculture, Industry, Construction, Trade, Financial services,other services) and from the expenditure side (Final consumption,gross capital formation, Exports, Imports). We adopt a parametric dynamic factor model at the monthly level, taking the temporal aggregation constraint into account. The multivariate models are cast in the state space form and computational efficiency is achieved by implementing univariate filtering and smoothing procedures. The chained-linked total GDP results via a multistep procedure that exploits the additivity of the volume measures expressed at the prices of the previous year. The final estimate is obtained by combining the two estimates (output side and expenditure side) with weights reflecting their relative precision.

Outline Introduction and Motivation Univariate Regression based methods Multivariate Dynamic Factor Model: Model formalization and specification Estimation and time constraint procedure Chain link Empirical application: Output side Expenditure side Final result Performance and benchmarks

Regression based models State space representation: y t = z α t + x tβ, t = 1,...,n, α t = Tα t 1 + W t β + Hε t, t = 2,...,n α 1 = a 1 + W 1 β + H 1 ε 1, ε t NID(0,σ 2 ), β N(b,σ 2 V). Chow-Lin: y t can be represented by a linear regression model with AR(1) errors: y t = α t + x t β, α t = φα t 1 + ε t, ε t NID(0,σ 2 ), Litterman (1983) model is formulated as regression model with ARIMA(1,1,0) disturbances: y t = x t β + u t, u t = φ u t 1 + ε t. The Fernández (1981) model arises in the particular case when φ = 0 (u t is a random walk).

Two main related sources of criticism on the regression based model assumptions. 1 Exogeneity: In general there is no causal relationship between, say, the monthly (deflated) turnover of the retail sector and its value added. 2 Indicators are measured without error. The consequence is that the information on the indicators is transmitted to the disaggregated series by a single regression coefficient and thus any outlying and purely idiosyncratic feature, such as trading day variation, is automatically attributed to the estimated series. A multivariate framework is more realistic.

The Stock and Watson dynamic factor model The vector of N 1 time series, y t, supposed I(1), is decomposed into a common cyclical trend,µ t, and an idiosyncratic component specific for each variables, µ t. Both the components are difference stationary and subject to autoregressive dynamics: y t = ϑ 0 µ t + ϑ 1 µ t 1 + µ t + X tβ, t = 1,...,n, φ(l) µ t = η t, η t NID(0,ση), 2 D(L) µ t = δ + ξ t, ξ t NID(0,Σ ξ ), φ(l) is an autoregressive polynomials of order p with stationary roots. The matrix polynomial D(L) is diagonal and Σ ξ = diag(σ 2 1,...,σ2 N ). The disturbances are mutually uncorrelated at all leads and lags. X t contains regression effects and intervention variables, e. g. outliers, working days dummies...

Advantages of the dynamic factor model It rationalises the practice of statistical offices of summarizing the available indicators in a unique common indicator that is then smoothed and corrected for outliers and structural breaks. In our approach all these operations are carried out simultaneously in a model based framework, and the common factor extracts the dynamics that are common to the indicators and that are relevant for the disaggregation of the quarterly flows, while in the regression approach these operations are carried out as preliminary corrections, which makes the disaggregation exercise more elaborate and less internally consistent. Furthermore, the approach allows easily for extensions to include more factors and/or variables.

Model specification issues Our previous experience, dealing with the temporal disaggregation of the Italian national accounts and with the the dynamic factor model for the U.S. and Euro area economy (reported in Istat, 2005, Proietti, 2006, and Proietti and Moauro, 2006), is that it is usually safer to assume that cointegration is not present. The logarithmic transformation was found to be most suitable when a long time series is available and the growth rate of the series is sustained and homoscedastic, as it occurs in the U.S. case. For the Euro area the time series are short and growth is not sustained, so that disaggregating the time series on the original scale is usually appropriate. These a priori information is reinforced by the empirical evidence originating from a rolling forecast experiment for the Industrial sector documented in the final research Report 2006.

Estimation and time constraint procedure The model involves mixed frequency data, e.g. monthly indicators and quarterly GDP. Following Harvey (1989) and Proietti(2006), the time constraint is traslated into a problem of missing observations. more The model is cast in State Space Form and, under Gaussian distribution of the errors, the unknown parameters can be estimated by maximum likelihood, using the prediction error decomposition, performed by the Kalman filter. Filter and Smoother are based on the Univariate statistical treatment of multivariate models by Koopman and Durbin (2000): very flexible and convenient device for handling missing values in multivariate models and reduce the time of convergence. The multivariate vectors y t, t = 1,...,n, where some elements can be missing, are stacked one on top of the other to yield a univariate time series {y t,i,i = 1,...,N,t = 1,...,n}, whose elements are processed sequentially.

Chain-linking and temporal disaggregation The MS chain-link the quarterly data on an annual basis: manly by the annual overlap (compiling estimates for each quarter at the weighted annual average prices of the previous year). Quarterly volume estimates add up to the corresponding annual aggregate, but cross-sectional additivity is lost. Multistep procedure advocated by the IMF manual: 1 Transform the monthly estimates into Laspayres quantity indices (volumes evaluated at reference year b = 2000 average prices), 2 Change the reference year to the second year of the series (e.g. 2001) 3 Compute the series at the average prices of the previous year 4 Aggregation step: the values for the i-th component series are additive and can be summed up, 5 Chain-linking (annual overlap): Chain-link the indices using a recursive formula If b > 1 then change the reference year to year b Compute the chain-linked volume series with reference year b

Disaggregation from the Output side

NA Label Monthly Indicators Delay A B Agriculture, hunting and fishing C D E Industry, incl. Energy Monthly production index (CDE) 45 Number of persons employed 70 Volume of work done (hours worked) 60 Industrial Confidence Indicator (Dg Ecfin) 15 Production trend in recent months (Dg Ecfin) 15 Assessment of order-book levels (Dg Ecfin) 15 F Construction Monthly production index (F) 70 Building permits 70 Number of persons employed 70 Volume of work done (hours worked) 70 Construction Confidence Indicator (Dg Ecfin) 15 Trend of activity over recent months (Dg Ecfin) 15 G H I Trade, transport and Monthly IP for consumption goods 45 communic. serv. Index of deflated turnover 35 Number of persons employed 90 Car registrations 15 Retail trade Confidence Indicator (Dg Ecfin) 15 Business activity over recent months (Dg Ecfin) 15 Assessment of stocks (Dg Ecfin) 15 J K Financial serv. Monetary aggregate M3, M1, M2 (deflated) 27 and business activities Loans of MFI (deflated) 27 Monthly production index (CDE) 45 Unemployment rate 45 L P Other services Debt securities government (defl.) 27 Monthly production index (CDE) 45 Unemployment rate 45 Total Gross Value Added (A6) Taxes less subsidies on products Monthly production index (CDE) 45 Index of deflated turnover 35

Industry Sector (CDE): Quarterly Value Added and Euro-MIND 375 Quarterly Value Added Industry 130000 Euro MIND Industry in Level 350 120000 325 110000 300 100000 1995 1997 1999 2001 2003 2005 2007 2009 1995 1997 1999 2001 2003 2005 2007 2009 1.50 Euro MIND Industry (YoY) Estimated 15 November Estimated 15 October 7.5 1.25 6.0 1.00 4.5 0.75 0.50 3.0 0.25 1.5 0.00 0.0 0.25 1.5 0.50 Euro MIND QoQ 1996 1998 2000 2002 2004 2006 2008 2006 2007 2008 2009

Construction Sector (F): Quarterly Value Added and Euro-MIND 95 Quarterly Value Added Construction 32500 Euro MIND Construction in Level 90 30000 85 27500 80 1995 1997 1999 2001 2003 2005 2007 2009 10 Euro MIND Construction (YoY) 5 0 5 1995 1997 1999 2001 2003 2005 2007 2009 3 Estimated 15 November Estimated 15 October 2 1 0 10 1996 1998 2000 2002 2004 2006 2008 1 Euro MIND QoQ 2006 2007 2008 2009

Trade and Communication Sector (GHI): Quarterly Value Added and Euro-MIND 375 Quarterly Value Added Trade and Communication Euro MIND Trade and Communication in Level 350 120000 325 110000 300 100000 275 90000 1995 1997 1999 2001 2003 2005 2007 2009 1995 1997 1999 2001 2003 2005 2007 2009 Euro MIND Trade and Communication (YoY) 1.6 Estimated 15 November Estimated 15 October 6 1.4 5 1.2 4 1.0 0.8 3 0.6 2 0.4 1 0.2 0 0.0 0.2 1 Euro MIND QoQ 0.4 1996 1998 2000 2002 2004 2006 2008 2006 2007 2008 2009

Financial Services and Business Activities Sector (JK): Quarterly Value Added and Euro-MIND 450 Quarterly Value Added Financial Services 160000 Euro MIND Financial Services in Level 400 140000 350 120000 1995 1997 1999 2001 2003 2005 2007 2009 1995 1997 1999 2001 2003 2005 2007 2009 6 Euro MIND Financial Services (YoY) Estimated 15 November Estimated 15 October 1.25 5 4 3 2 1.00 0.75 1 1996 1998 2000 2002 2004 2006 2008 Euro MIND QoQ 2006 2007 2008 2009

Other Services Sector (LP): Quarterly Value Added and Euro-MIND 360 340 320 Quarterly Value Added Other Services 125000 120000 115000 110000 105000 Euro MIND Other Services in Level 1995 1997 1999 2001 2003 2005 2007 2009 2.5 Euro MIND Other Services (YoY) 2.0 1.5 0.6 0.4 1995 1997 1999 2001 2003 2005 2007 2009 Estimated 15 November Estimated 15 October 1.0 1996 1998 2000 2002 2004 2006 2008 0.2 0.0 Euro MIND QoQ 2006 2007 2008 2009

Disaggregation from the Expenditure side

Quarterly Aggregate Monthly Indicators Delay Final consumption expenditure Monthly production index for consumption goods 45 Car registrations 15 Index of deflated turnover retail 35 Consumer Confidence Indicator (Dg Ecfin) 15 Financial situation (Dg Ecfin) 15 General Economic situation(dg Ecfin) 15 Price trends (Dg Ecfin) 15 Gross capital formation Monthly production index (CDE) 45 Monthly production index (F) 70 Monthly production index for capital goods 45 Building permits 70 Construction Confidence Indicator (Dg Ecfin) 15 Assessment of order in construction (Dg Ecfin) 15 Industrial Confidence Indicator (Dg Ecfin) 15 Production trend observed in recent months (Dg Ecfin) 15 Assessment of order-book levels (Dg Ecfin) 15 Exports of goods and services Monthly Export volume index 42 Monthly production index for intermediate goods 45 Real Effective Exchange Rate 30 Assessment of export order-book levels (CDE) (Dg Ecfin) 15 Imports of goods and services Monthly Import volume index 42 Monthly production index for intermediate goods 45 Real Effective Exchange Rate 30 Assessment of export order-book levels (CDE) (Dg Ecfin) 15

Final Consumption Expenditure: Quarterly values and Euro-MIND Quarterly Expenditure in Consumption 500000 Euro MIND Consumption in Level 1400 1300 1200 475000 450000 425000 400000 1995 1997 1999 2001 2003 2005 2007 2009 1995 1997 1999 2001 2003 2005 2007 2009 4 Euro MIND Consumption (YoY) 0.8 Estimated 15 November Estimated 15 October 3 0.6 2 0.4 1 0 1996 1998 2000 2002 2004 2006 2008 0.2 0.0 Euro MIND QoQ 2006 2007 2008 2009

Gross Capital Formation Expenditure: Quarterly values and Euro-MIND 400 350 Quarterly Expenditure in Investment 150000 140000 130000 120000 110000 Euro MIND Investment in Level 300 100000 1995 1997 1999 2001 2003 2005 2007 2009 1995 1997 1999 2001 2003 2005 2007 2009 Euro MIND Investment (YoY) Estimated 15 November Estimated 15 October 10 4 Euro MIND QoQ 3 5 2 0 5 1 0 1 1996 1998 2000 2002 2004 2006 2008 2 2006 2007 2008 2009

Exports of Goods and Services: Quarterly values and Euro-MIND 900 800 700 600 500 Quarterly Expenditure in Exports 300000 Euro MIND Exports in Level 250000 200000 150000 1995 1997 1999 2001 2003 2005 2007 2009 1995 1997 1999 2001 2003 2005 2007 2009 15 Euro MIND Exports (YoY) 3.5 Estimated 15 November Estimated 15 October 3.0 10 2.5 2.0 5 1.5 1.0 0 0.5 0.0 Euro MIND QoQ 1996 1998 2000 2002 2004 2006 2008 2006 2007 2008 2009

Imports of Goods and Services: Quarterly values and Euro-MIND 800 Quarterly Expenditure in Imports 300000 Euro MIND Imports in Level 700 250000 600 500 200000 400 150000 1995 1997 1999 2001 2003 2005 2007 2009 1995 1997 1999 2001 2003 2005 2007 2009 15 Euro MIND Imports (YoY) 2.5 Estimated 15 November Estimated 15 October 2.0 10 1.5 5 1.0 0 5 1996 1998 2000 2002 2004 2006 2008 0.5 0.0 0.5 Euro MIND QoQ 2006 2007 2008 2009

Euro MIND-Total GDP by combined estimates 650000 GDP_exp GDP_output 3000 650000 Euro MIND combined in level 600000 2000 600000 1000 550000 0 550000 500000 GDP_output GDP_exp 1996 1998 2000 2002 2004 2006 2008 Euro MIND combined YoY 5 1000 500000 1996 1998 2000 2002 2004 2006 2008 1.2 Euro MIND combined QoQ 4 3 2 1 1.0 0.8 0.6 0.4 0.2 0.0 1996 1998 2000 2002 2004 2006 2008 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

One year of estimation... Our estimates are subject to revisions... 600000 jan07 may07 set07 595000 feb07 jun07 oct07 mar07 jul07 nov07 apr07 aug07 dec07 590000 585000 580000 575000 570000 565000 560000 2005 2006 2007 2008

...mostly because Value Added and indicators are revised rather than because parameters vary in time 0.050 0.025 0.000 0.025 0.050 0.075 Dec 07 Oct 07 Aug 07 Jun 07 Apr 07 Jan 07 Nov 07 Sep 07 Jul 07 May 07 Mar 07 2005 2006 2007 2008 Figure: Relative differences (in %) between the real time estimates and the estimates with constant parameters

2006 2007 2008 I II III IV I II III IV I II III Dec-06 0.83 0.99 0.52 0.47 NA Dec-06 0.83 0.99 0.52 Jan-07 0.83 0.99 0.52 0.52 Feb-07 0.86 0.96 0.53 0.82 0.58 Mar-07 0.82 0.97 0.57 0.89 0.68 NA Mar-07 0.82 0.97 0.57 0.89 Apr-07 0.83 0.99 0.58 0.89 0.65 May-07 0.83 0.99 0.58 0.89 0.74 0.55 Jun-07 0.88 0.93 0.59 0.86 0.60 0.40 NA Jun-07 0.88 0.93 0.59 0.86 0.60 Jul-07 0.92 0.90 0.58 0.92 0.68 0.39 Aug-07 0.92 0.91 0.58 0.89 0.70 0.35 0.34 Sep-07 0.88 0.98 0.57 0.87 0.70 0.35 0.38 NA Sep-07 0.88 0.98 0.57 0.87 0.70 0.35 Oct-07 0.89 0.96 0.60 0.80 0.76 0.31 0.52 Nov-07 0.89 0.96 0.60 0.80 0.76 0.31 0.52 0.54 Dec-07 0.89 0.96 0.60 0.80 0.76 0.31 0.74 0.50 NA Dec-07 0.89 0.96 0.57 0.82 0.77 0.31 0.71 Jan-08 0.89 0.96 0.60 0.80 0.76 0.31 0.74 0.50 Feb-08 0.86 0.96 0.57 0.80 0.80 0.31 0.76 0.28 0.36 Mar-08 0.87 0.96 0.55 0.77 0.79 0.27 0.75 0.38 0.53 NA Mar-08 0.87 0.96 0.55 0.77 0.79 0.27 0.75 0.38 Apr-08 0.81 1.00 0.54 0.83 0.74 0.33 0.72 0.35 0.61 May-08 0.81 1.00 0.54 0.83 0.74 0.33 0.72 0.35 0.61 0.43 Jun-08 0.82 0.98 0.57 0.83 0.78 0.37 0.66 0.31 0.80 0.39 NA Jun-08 0.82 0.98 0.57 0.83 0.78 0.37 0.66 0.31 0.80 Jul-08 0.82 0.98 0.57 0.83 0.78 0.37 0.66 0.31 0.80 0.20 Aug-08 0.83 0.99 0.55 0.84 0.81 0.34 0.63 0.36 0.72 0.08 0.35 Sep-08 0.81 1.07 0.54 0.83 0.73 0.45 0.57 0.36 0.66-0.20 0.12 NA Sep-08 0.81 1.07 0.54 0.83 0.73 0.45 0.57 0.36 0.66-0.20 Oct-08 0.82 1.09 0.52 0.82 0.72 0.47 0.55 0.35 0.66-0.18 0.21

Standard errors by sectors and expenditure components are stable in time (exercise for 2007) 600 Output side 500 400 300 200 100 jan cde GDP_output Expenditure side 1500 feb mar apr may jun jul aug set f ghi jk lp tls oct nov dec 1000 500 0 jan feb mar apr may jun jul aug cons inv imp exp GDP_exp set oct nov dec

Some alternative Monthly Indicators 1 Euro-coin (Bankitalia & CEPR 2007) different reference: medium term growth; huge dataset of indicators; unbalanced sample not treated 2 Euro-Sting (Perez-Quiros, Camacho 2008)(cont.)

Euro-MIND versus Euro-Sting Euro-sting direct estimate of GDP with forecasting purpose Euro-MIND GDP estimation from expenditure and output side and chain link selected by fore- Few indicators, casts experts indicators selected by statistical signif.; specific for components/sectors GDP growth rate in log GDP level (from which YoY and MoM) flash,first, second GDP first or second GDP in real time disaggregation as in Mariano and Murasawa(2001) cumulator function as in Harvey(1989) (easier) Standard Smoother and Filter Multivariate Smoother by Koopman

Conclusions The methodology proposed for the estimation of Euro-MIND, the Monthly Indicator of the Economic activity, is based prominently on the Stock and Watson (1991) dynamic factor model of coincident indicators. The model is defined at the monthly level, taking the temporal aggregation constraint into account. The disaggregation exercise was conducted on the output side and expenditure side. The combination of the estimates obtained from the two approaches, with weights reflecting their relative precision, yielded a more accurate combined precision. The chain-linked estimates are obtain by a multistep procedure One of the benefits of the approach is that measures of reliability concerning the estimated levels and growth rates of the indicator of the monthly economic activity available.

The set of coincident indicators y t is partitioned into two groups, y t = [y 1t,y 2t ], where the second block gathers the flows subject to temporal aggregation (sum of three consecutive months=quarterly NA) Harvey (1989): augmenting the state vector in the State Space form using a cumulator variable ψ t such that: { 0 t = δ(τ 1)+1, τ = 1,...,[n/δ] ψ t = 1 otherwise. The cumulator at times t = δτ coincides with the (observed) aggregated series, oth. contains the partial cumulative value of the aggregate.(e.g. M1=J=., M2=J+F=., M3=J+F+M=Q1) A new augmented SSF is defined in terms of a new state and observation vectors based on that cumulator