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2011 626 - Short-Term GDP Forecasting Using Bridge Models, A Case of Chile - Cobb, Et Al

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  • Banco Central de Chile Documentos de Trabajo

    Central Bank of Chile Working Papers

    N 626

    Mayo 2011

    SHORT TERM GDP FORECASTING USING

    BRIDGE MODELS: A CASE FOR CHILE

    Marcus Cobb Gonzalo Echavarra Pablo Filippi

    Macarena Garca Carolina Godoy Wildo Gonzlez

    Carlos Medel Marcela Urrutia

    La serie de Documentos de Trabajo en versin PDF puede obtenerse gratis en la direccin electrnica: http://www.bcentral.cl/esp/estpub/estudios/dtbc. Existe la posibilidad de solicitar una copia impresa con un costo de $500 si es dentro de Chile y US$12 si es para fuera de Chile. Las solicitudes se pueden hacer por fax: (56-2) 6702231 o a travs de correo electrnico: [email protected]. Working Papers in PDF format can be downloaded free of charge from: http://www.bcentral.cl/eng/stdpub/studies/workingpaper. Printed versions can be ordered individually for US$12 per copy (for orders inside Chile the charge is Ch$500.) Orders can be placed by fax: (56-2) 6702231 or e-mail: [email protected].

  • BANCO CENTRAL DE CHILE

    CENTRAL BANK OF CHILE

    La serie Documentos de Trabajo es una publicacin del Banco Central de Chile que divulga los trabajos de investigacin econmica realizados por profesionales de esta institucin o encargados por ella a terceros. El objetivo de la serie es aportar al debate temas relevantes y presentar nuevos enfoques en el anlisis de los mismos. La difusin de los Documentos de Trabajo slo intenta facilitar el intercambio de ideas y dar a conocer investigaciones, con carcter preliminar, para su discusin y comentarios. La publicacin de los Documentos de Trabajo no est sujeta a la aprobacin previa de los miembros del Consejo del Banco Central de Chile. Tanto el contenido de los Documentos de Trabajo como tambin los anlisis y conclusiones que de ellos se deriven, son de exclusiva responsabilidad de su o sus autores y no reflejan necesariamente la opinin del Banco Central de Chile o de sus Consejeros. The Working Papers series of the Central Bank of Chile disseminates economic research conducted by Central Bank staff or third parties under the sponsorship of the Bank. The purpose of the series is to contribute to the discussion of relevant issues and develop new analytical or empirical approaches in their analyses. The only aim of the Working Papers is to disseminate preliminary research for its discussion and comments. Publication of Working Papers is not subject to previous approval by the members of the Board of the Central Bank. The views and conclusions presented in the papers are exclusively those of the author(s) and do not necessarily reflect the position of the Central Bank of Chile or of the Board members.

    Documentos de Trabajo del Banco Central de Chile Working Papers of the Central Bank of Chile

    Agustinas 1180, Santiago, Chile Telfono: (56-2) 3882475; Fax: (56-2) 3882231

  • Documento de Trabajo Working Paper N 626 N 626

    SHORT TERM GDP FORECASTING USING

    BRIDGE MODELS: A CASE FOR CHILE

    Marcus Cobb Gonzalo Echavarra Pablo Filippi Banco Central de Chile Banco Central de Chile Banco Central de Chile

    Macarena Garca Carolina Godoy Wildo Gonzlez

    Banco Central de Chile Banco Central de Chile Banco Central de Chile

    Carlos Medel Marcela Urrutia Banco Central de Chile Banco Central de Chile

    Abstract The aim of this document is to provide a forecasting tool that facilitates understanding economic developments in a timely manner. This is pursued through the Bridge Model approach by using it to relate a large set of monthly indicators to Chilean GDP and its main components. The outcome is a set of simple equations that characterize reasonably well total GDP and the feasible supply- and demand-side components based on a small set of relevant indicators. The selected equations generally provide better short-term forecasts than simple autoregressive models. However, if needed, the equation selection methodology is straightforward enough to update the equations easily making it an attractive tool for real-time forecasting. Resumen El objetivo de este documento es proveer una herramienta de proyecciones que permita interpretar la informacin coyuntural a travs de una metodologa que relacione indicadores relevantes en frecuencia mensual con los principales componentes de la actividad y la demanda trimestral de Chile. Para esto, se sigue el enfoque de los modelos puente y se recurre a un conjunto importante de informacin. Como resultado se obtienen ecuaciones que permiten caracterizar razonablemente bien el PIB total y sus componentes factibles por el lado de la oferta y de la demanda, a partir de un conjunto acotado de indicadores. En general, estas ecuaciones entregan mejores proyecciones que simples modelos autorregresivos. Sin embargo, de ser necesario, la metodologa de seleccin de ecuaciones es lo suficientemente simple como para que la actualizacin de las ecuaciones sea sencilla, y una herramienta atractiva para las proyecciones en tiempo real.

    We are grateful to an anonymous referee for his or her very helpful comments.

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    22 +'(2.1. Variables of interest

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    Total GDP 33B

    Demand:

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    Primary Equation:

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    Figure 1 Publication and Forecasting Dynamics

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    Annex 1: Data transformation and definitions

    Mnemonic Transf DescriptionPIB d.log Total GDPind d.log Industrycom d.log Commercecons d.log Constructioncp d.log Total private consumption cp_hab d.log Private consumption of non durable goodscp_dur d.log Private consumption of durable goodscgov d.log Government Expendituremye d.log Gross fixed capital formation: machinery and equipmentxbys d.log Export of goods and servicesmbys d.log Import of goods and services

    ext115 d.log Industral prod. U.S., E.U. and Japanact47 d.log Intermediate industrial salesact12 d.log Electricity generationfin23 d.log M3fin37 d.log Chilean Stock Exchangedem10 d.log Retail salesfis5 d.log Government expenditurefin58 d.log Real exchange rateact22 d.log Industrial productionfin48 d Real interest rate: 90 days to 1 yearact2 d.log Served cement ordersact21 d.log Index of real sales of construction material dem40 d.log Housing salesedif01 d.log Building permitsmesagoviv d.log Months to sell housing stockml32 d.log Total employmentcbc d.log Investment surveyipec50 level Economic perspective surveybolsa d.log Real stock exchange Indexact40 d.log Phisical sales manufacturing sectordem1 d.log Supermarket salesdem3 d.log Retail sales of non-durablesfin49 d.log Nominal interest rate: 90 days to 1 yearact42 d.log Industrial salesypd d.log Private disposable incomecoloc d.log Total lending for consumptiondem5 d.log Retail durable salesml38 d.log Employment in non-financial servicesva_per d.log Value Added: personal servicesva_adm d.log Value Added: public administrationext11 d.log Import of capital goodsipe d.log Foreign price indexdef_PIB/MyE d.log GDP deflactor / GFCF M&E deflactorprc8 d.log 5 year Central Bank real bondsact15 d.log IMACECext8 d.log Consumption importsext9 d.log Rest importsact48 d.log Capital goods salesact21 d.log Index of real sales of construction materialext116 d.log U.S. GDPxb_bal d.log Real export of Goods

  • Annex 2a: Supply-side bridge equations

    Total GDPPrimary equation: Supplementary equation:

    Coeff StdError t-value Coeff StdError t-valuePIB(-2) -0.5174 0.1160 -4.46 pib(-2) -0.4903 0.1694 -2.89ext115(-2) 0.2797 0.1158 2.42 ext115(-1) 0.3457 0.0815 4.24act47 0.1663 0.0476 3.49 dem10 0.3255 0.1031 3.16act12 0.3490 0.0996 3.51 act12 0.3305 0.1084 3.05fin23(-1) 0.3126 0.0705 4.43 fin23(-1) 0.2472 0.0928 2.66fin37(-2) 0.0493 0.0169 2.91 cgov(-1) 0.0523 0.0268 1.95RSS 0.0010 Radj 2^ 0.60 RSS 0.0025 Radj 2^ 0.42

    IndustryPrimary equation: Supplementary equation:

    Coeff StdError t-value Coeff StdError t-valuefin58(-1) -0.0928 0.0475 -1.95 fin58(-1) -0.1309 0.0413 -3.17act22 0.0077 0.0009 8.93 fin23(-1) 0.0911 0.0312 2.92

    act22 0.0078 0.0006 13.67RSS 0.0058 Radj 2^ 0.59 RSS 0.0076 Radj 2^ 0.63

    CommercePrimary equation:

    Coeff StdError t-valuedem10 0.3502 0.0934 3.75dem10(-1) 0.2012 0.0858 2.35fin23(-2) 0.2358 0.0562 4.20fin58(-1) -0.1304 0.0451 -2.89act2 0.1646 0.0341 4.83RSS 0.0058 Radj 2^ 0.64

    ConstructionPrimary equation: Supplementary equation:

    Coeff StdError t-value Coeff StdError t-valueact2 0.2714 0.0800 3.39 edif01(-1) 0.0273 0.0128 2.13act21 0.2256 0.1021 2.21 mesagoviv -0.0447 0.0200 -2.24dem40 0.0623 0.0216 2.89 mesagoviv(-1) -0.0491 0.0197 -2.50

    ml32 0.6596 0.1004 6.57act21 0.2207 0.0669 3.30cbc(-2) 0.0637 0.0192 3.32cbc(-3) 0.0471 0.0206 2.29

    RSS 0.0055 Radj 2^ 0.48 RSS 0.0010 Radj 2^ 0.72

  • 2

    Annex 2b: Demand-side bridge equations

    Total private consumption

    Primary equation: Supplementary equation:Coeff StdError t-value Coeff StdError t-value

    cp(-1) 0.3045 0.0820 3.71 Constant 0.0137 0.0016 8.37act40 0.2305 0.0570 4.05 ipec50 0.0004 0.0001 3.95dem1 0.2945 0.0723 4.07 bolsa(-1) 0.0299 0.0168 1.78dem10 0.5215 0.0946 5.51 fin49(-1) -0.0365 0.0135 -2.71fin48 -0.0021 0.0008 -2.85ipec50 0.0002 0.0001 2.75cgov 0.0787 0.0431 1.83dem3 -0.3746 0.0915 -4.09RSS 0.0014 Radj 2^ 0.72 RSS 0.0037 Radj 2^ 0.33

    Private consumption of non durable goodsPrimary equation: Supplementary equation:

    Coeff StdError t-value Coeff StdError t-valueConstant 0.0092 0.0011 8.65 Constant 0.0125 0.0012 10.05fin48 -0.0021 0.0008 -2.70 ipec50(-1) 0.0003 0.0001 3.32fin48(-2) -0.0027 0.0008 -3.50 fin49(-1) -0.0325 0.0104 -3.14ipec50(-2) 0.0002 0.0001 3.50act42 0.2660 0.0486 5.47act42(-2) 0.2103 0.0493 4.27RSS 0.0014 Radj 2^ 0.52 RSS 0.0023 Radj 2^ 0.25

    Private consumption of durable goodsPrimary equation: Supplementary equation:

    Coeff StdError t-value Coeff StdError t-valueypd(-1) 0.2176 0.1679 1.30 Constant 0.0260 0.0079 3.31coloc 0.6839 0.1751 3.91 ipec50 0.0022 0.0005 4.07dem5 0.5354 0.1419 3.77 bolsa(-1) 0.1890 0.0805 2.35

    fin49(-1) -0.1255 0.0648 -1.94RSS 0.0674 Radj 2^ 0.48 RSS 0.0848 Radj 2^ 0.34

    Government ExpenditurePrimary equation: Supplementary equation:

    Coeff StdError t-value Coeff StdError t-valuecgov(-1) 0.3246 0.1073 3.02 cgov(-1) 0.3832 0.1291 2.97ml38(-1) 0.1328 0.0539 2.47 cgov(-2) 0.1716 0.1418 1.21va_per 0.3191 0.1026 3.11 cgov(-3) -0.1889 0.1401 -1.35va_adm 0.6089 0.1987 3.06 cgov(-4) -0.1826 0.1390 -1.31

    ml38(-1) 0.1064 0.0551 1.93va_per 0.3559 0.1066 3.34va_adm 0.8299 0.2391 3.47

    RSS 0.0008 Radj 2^ 0.47 RSS 0.0007 Radj 2^ 0.48

  • =

    Annex 3: Out-of-Sample forecasting evaluation:

    Root mean square forecasting error of the yearly growth rate.

    *233.233-I4

    Primary EquationMean SD. Absolute RMSFE: Abs.RMSFE Relativev12* v12* SARIMA: Eq1(PcGets) (model / SARIMA)

    h=1 h=2 h=3 h=1 h=2 h=3 h=1 h=2 h=3

    SupplyGDP 1.7 3.6 1.7 3.5 4.5 2.1 3.3 3.2 1.2 1.0 0.7Construction 2.2 7.7 4.7 7.4 8.4 4.1 5.8 5.7 0.9 0.8 0.7Commerce 3.5 7.4 3.9 6.5 8.5 2.7 3.7 5.7 0.7 0.6 0.7Industry -2.8 5.3 3.6 5.9 7.0 3.4 4.9 5.2 1.0 0.8 0.7

    DemandPrivate Consumption 4.1 4.1 2.3 3.8 4.7 2.0 2.7 3.5 0.9 0.7 0.7

    Non-durable 3.8 2.0 1.7 2.4 2.9 1.2 1.6 2.0 0.7 0.7 0.7Durable 7.2 21.8 11.4 18.7 23.9 9.7 16.3 20.7 0.8 0.9 0.9

    Gov't Expenditure 3.3 3.2 3.1 5.0 5.6 2.6 3.8 3.5 0.8 0.7 0.6GFCF: Machinery and Equipment 10.4 32.7 17.3 29.2 38.3 13.1 25.1 34.9 0.8 0.9 0.9Import of Goods and Services 4.2 17.7 8.0 14.6 19.3 2.8 9.1 15.7 0.4 0.6 0.8Export of Goods and Services -1.5 4.8 6.0 8.6 9.8 4.5 5.9 5.2 0.7 0.7 0.5

    Supplementary Equation

    Mean SD. Absolute RMSFE: Abs.RMSFE Relativev12* v12* SARIMA: Ec2 (judgment) (model / SARIMA)

    h=1 h=2 h=3 h=1 h=2 h=3 h=1 h=2 h=3

    SupplyGDP 1.7 3.6 1.7 3.5 4.5 1.5 2.4 3.2 0.9 0.7 0.7Construction 2.2 7.7 4.7 7.4 8.4 3.1 5.9 7.5 0.7 0.8 0.9Commerce 3.5 7.4 3.9 6.5 8.5Industry -2.8 5.3 3.6 5.9 7.0 2.8 3.9 4.7 0.8 0.7 0.7

    DemandPrivate Consumption 4.1 4.1 2.3 3.8 4.7 1.8 2.6 2.6 0.8 0.7 0.6

    Non-durable 3.8 2.0 1.7 2.4 2.9 1.3 1.7 1.6 0.8 0.7 0.5Durable 7.2 21.8 11.4 18.7 23.9 8.5 12.7 15.6 0.7 0.7 0.7

    Gov't Expenditure 3.3 3.2 3.1 5.0 5.6 3.0 4.4 4.1 0.9 0.9 0.7GFCF: Machinery and Equipment 10.4 32.7 17.3 29.2 38.3 6.7 15.1 23.8 0.4 0.5 0.6Import of Goods and Services 4.2 17.7 8.0 14.6 19.3 3.4 9.7 16.3 0.4 0.7 0.8Export of Goods and Services -1.5 4.8 6.0 8.6 9.8 3.9 6.3 6.4 0.7 0.7 0.7

    * calculated over de evaluation period only.

    shaded areas mark forecasts that outperform the SARIMA according to a one-sided modified Diebold-Mariano test at a 5% confidence level

  • 6

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