How to monitor and forecast public deficit every month. The Case of France. Laurent Moulin , DG ECFIN, European Commission, Matteo Salto , DG COMP , European Commission, Andrea Silvestrini , Universit´ a degli Studi di Perugia, David Veredas , ECARES, Universit´ e Libre de Bruxelles dveredas@ulb.ac.be How to monitor and forecast public deficit every month.The Case of France. – p. 1/3
OVERVIEW Monitor and Forecast State deficit. Use of intra-annual (monthly) information to obtain annual model. Pure time series approach. We use aggregation techniques for ARIMA models. Annual predictions may be updated when new monthly information is released. Our predictions are very accurate and improve, by far, the official ones. How to monitor and forecast public deficit every month.The Case of France. – p. 2/3
Why is intra-annual important? The Stability and Growth Pact (SGP): The budgetary surveillance mechanisms (article 104, SGP) foresee that the Commission and the Council have to take decissions based on budgetary developments Stability programmes are based on annual predictions This increases the need for reliable and frequently updated forecasts for government finances Fiscal policy surveillance of the Council of Ministers Coordination of fiscal policies timely How to monitor and forecast public deficit every month.The Case of France. – p. 3/3
Why State deficit? General government deficit is divided in: Local authorities: No intra annual and no volatile Social Security: No intra annual. Deficit is not very big. Health and unemployment: They could be modelled Pensions: Easy to forecast State deficit: Monthly. It is the most important %GDP 2000 2001 2002 2003 General -1.4 -1.5 -3.2 -4.1 State -2.5 -2.3 -3.8 -3.9 Local authorities 0.2 0.1 0.2 0.1 Social Security 0.5 0.3 -0.3 -0.7 How to monitor and forecast public deficit every month.The Case of France. – p. 4/3
Why State deficit? More evidence: Net lending/borrowing 10 0 −10 State sector −20 billion euros −30 −40 −50 −60 General government sector −70 −80 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002 time Evolutions of the State and general government deficits How to monitor and forecast public deficit every month.The Case of France. – p. 5/3
State deficit: Decomposition State deficit is the balance between revenues and expenditures. In turn they are the sum of several components Revenues: Taxes Other fiscal and non fiscal Expenditures Wages and pensions Debt interest payments Military expenditures Other How to monitor and forecast public deficit every month.The Case of France. – p. 6/3
State deficit: Decomposition Graphically Revenues Expenditures 9% 11% 14% Other fiscal Military 21% Debt interest revenues 5% expenditures Income payments Civilian 10% tax capital Non fiscal expenditures revenues 9% Economic interventions 11% Corporate tax 34% 12% Wages Social and pensions interventions 9% 40% Tax on VAT 9% oil products Other state 6% expenditures Functioning expenditures How to monitor and forecast public deficit every month.The Case of France. – p. 7/3
Our approach Model, via ARIMA, the monthly components. Sample from January 1995 to December 2003. Use econometric techniques of temporal aggregation to infer the annual model from the monthly information Forecast one -step ahead year for all the components. Sum the forecasts to get a forecast of the State deficit Update the models and the predictions as new intra annual information is available. How to monitor and forecast public deficit every month.The Case of France. – p. 8/3
Take a look to graph side of data Revenues Corporate tax Income tax Tax on oil products 12 14 2.3 2.2 10 12 2.1 8 10 2 6 1.9 8 4 1.8 6 1.7 2 1.6 4 0 1.5 2 −2 1.4 −4 0 1.3 1995 1996 1997 1998 1999 2000 2001 2002 2003 1995 1996 1997 1998 1999 2000 2001 2002 2003 1995 1996 1997 1998 1999 2000 2001 2002 2003 years years years Other fiscal revenues Non fiscal revenues VAT 13 5 10 4 8 12 3 6 11 2 4 10 9 1 2 0 0 8 −1 −2 7 −2 −4 6 1995 1996 1997 1998 1999 2000 2001 2002 2003 1995 1996 1997 1998 1999 2000 2001 2002 2003 1995 1996 1997 1998 1999 2000 2001 2002 2003 years years years How to monitor and forecast public deficit every month.The Case of France. – p. 9/3
Take a look to graph side of data Revenues Corporate tax Income tax Tax on oil products 12 14 2.3 2.2 10 12 2.1 8 10 2 6 1.9 8 4 1.8 6 1.7 2 1.6 4 0 1.5 2 −2 1.4 −4 0 1.3 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 months months months Other fiscal revenues Non fiscal revenues VAT 5 10 13 4 8 12 3 6 11 2 4 10 1 2 9 0 0 8 −1 −2 7 −2 −4 6 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 months months months How to monitor and forecast public deficit every month.The Case of France. – p. 10/3
Take a look to graph side of data Expenditures Debt interest payments Military expenditures Wages and pensions Civilian capital expenditures 4.5 9 14 4 12 4 3.5 8.5 10 3 3.5 8 8 2.5 3 7.5 6 2 2.5 7 4 1.5 2 6.5 2 1 1.5 6 0 0.5 1 5.5 −2 0 1995 1996 1997 1998 1999 2000 2001 2002 2003 1995 1996 1997 1998 1999 2000 2001 2002 2003 1995 1996 1997 1998 1999 2000 2001 2002 2003 1995 1996 1997 1998 1999 2000 2001 2002 2003 years years years years Economic interventions Functioning expenditures Social interventions Other interventions 6 2.6 4.5 4.5 2.4 4 4 5 2.2 3.5 3.5 2 4 3 1.8 3 3 1.6 2.5 2.5 1.4 2 2 1.2 2 1.5 1 1 1.5 1 0.8 0.6 0.5 1 0 1995 1996 1997 1998 1999 2000 2001 2002 2003 1995 1996 1997 1998 1999 2000 2001 2002 2003 1995 1996 1997 1998 1999 2000 2001 2002 2003 1995 1996 1997 1998 1999 2000 2001 2002 2003 years years years years How to monitor and forecast public deficit every month.The Case of France. – p. 11/3
Take a look to graph side of data Expenditures Wages and pensions Debt interest payments Military expenditures Civilian capital expenditures 14 9 4.5 4 12 3.5 8.5 4 10 3 8 3.5 8 2.5 7.5 3 6 2 7 2.5 4 1.5 6.5 2 2 1 6 1.5 0 0.5 5.5 −2 1 0 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 months months months months Functioning expenditures Social interventions Other interventions Economic interventions 2.6 4.5 4.5 4 2.4 4 3.5 4 2.2 3.5 3 3.5 2 3 2.5 1.8 3 1.6 2.5 2 2.5 1.4 2 1.5 1.2 2 1.5 1 1 1.5 1 0.5 0.8 0.6 0.5 1 0 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 months months months months How to monitor and forecast public deficit every month.The Case of France. – p. 12/3
Monthly Estimations We use TRAMO (ARIMA + outliers). General results: All series have an unit root in seasonality 12 over 14 have seasonal MA component 2 over 14 do not have outliers (proxy of discretionary measures) How to monitor and forecast public deficit every month.The Case of France. – p. 13/3
Temporal Aggregation Next, we aggregate the monthly observations into annual frequency: � 11 � 11 j =0 L j y t y ∗ T = j =0 y t − j = where y ∗ T is a NON -OVERLAPPING sequence of annual observations How to monitor and forecast public deficit every month.The Case of France. – p. 14/3
Temporal Aggregation We have estimated the monthly model: ARIMA ( p, d, q ) × ( P, D, Q ) 12 � L 12 � � L 12 � φ ( L ) ∆ d ∆ D y t = Θ Φ θ ( L ) ε t , And we are now interested in the annual model: ARIMA ( p ′ , d ′ , q ′ ) ′ α ( B ) ∆ d y ∗ T = η ( B ) ε ∗ T , where B = L 12 because of the non overlapping. How to monitor and forecast public deficit every month.The Case of France. – p. 15/3
Temporal Aggregation The estimated parameters of the annual model are a function of the aggregated observations Is there a way to link both models? Is there a way to infer the parameters of the annual model from the parameters of the monthly model? Is there a way to incorporate all the monthly information into the annual model? How to monitor and forecast public deficit every month.The Case of France. – p. 16/3
Temporal Aggregation The answer is yes. Intuition: How to monitor and forecast public deficit every month.The Case of France. – p. 17/3
Temporal Aggregation ARIMA ( p, d, q ) × ( P, D, Q ) 12 � L 12 � � L 12 � φ ( L ) ∆ d ∆ D y t = Θ Φ θ ( L ) ε t ⇓ ARIMA ( p ′ , d ′ , q ′ ) ′ α ( B ) ∆ d y ∗ T = η ( B ) ε ∗ T There are three things to be solved The orders p ′ , d ′ , q ′ The AR parameters in α ( B ) The MA parameters in η ( B ) How to monitor and forecast public deficit every month.The Case of France. – p. 18/3
Temporal Aggregation The polynomial orders : ′ = p + P p ′ = d + D d ′ = � � 12 − 1 (11 ( p + d + 1) + q + 12 Q ) q , Remember: Monthly model: ARIMA ( p, d, q ) × ( P, D, Q ) 12 Annual model: ARIMA ( p ′ , d ′ , q ′ ) How to monitor and forecast public deficit every month.The Case of France. – p. 19/3
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