Short-Term GDP Forecasting Using Bridge Models: a Case for Chile

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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 Echavarría Pablo Filippi

Macarena García Carolina Godoy Wildo González

Carlos Medel Marcela Urrutia



La serie de Documentos de Trabajo en versión PDF puede obtenerse gratis en la dirección electrónica:

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 través de correo electrónico: [email protected].

Working Papers in PDF format can be downloaded free of charge from:

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BANCO CENTRAL DE CHILE

CENTRAL BANK OF CHILE

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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.

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

Agustinas 1180, Santiago, Chile

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Documento de Trabajo

Working Paper

N° 626

SHORT – TERM GDP FORECASTING USING

BRIDGE MODELS: A CASE FOR CHILE

‡

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

Macarena García Carolina Godoy Wildo González 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 información coyuntural a través de una metodología 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 información. 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 metodología de selección de ecuaciones es lo suficientemente simple como para que la actualización de las ecuaciones sea sencilla, y una herramienta atractiva para las proyecciones en tiempo real.

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2.1. Variables of interest

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2.2. Procedure for the selection of bridge equations

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3.1. Data

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3.2. Selection of final bridge equations

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3.2.2. Demand-side components.

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Annex 1: Data transformation and definitions

Mnemonic Transf Description

PIB d.log Total GDP

ind d.log Industry

com d.log Commerce

cons d.log Construction

cp d.log Total private consumption

cp_hab d.log Private consumption of non durable goods

cp_dur d.log Private consumption of durable goods

cgov d.log Government Expenditure

mye d.log Gross fixed capital formation: machinery and equipment

xbys d.log Export of goods and services

mbys d.log Import of goods and services

ext115 d.log Industral prod. U.S., E.U. and Japan

act47 d.log Intermediate industrial sales

act12 d.log Electricity generation

fin23 d.log M3

fin37 d.log Chilean Stock Exchange

dem10 d.log Retail sales

fis5 d.log Government expenditure

fin58 d.log Real exchange rate

act22 d.log Industrial production

fin48 d Real interest rate: 90 days to 1 year

act2 d.log Served cement orders

act21 d.log Index of real sales of construction material

dem40 d.log Housing sales

edif01 d.log Building permits

mesagoviv d.log Months to sell housing stock

ml32 d.log Total employment

cbc d.log Investment survey

ipec50 level Economic perspective survey

bolsa d.log Real stock exchange Index

act40 d.log Phisical sales manufacturing sector

dem1 d.log Supermarket sales

dem3 d.log Retail sales of non-durables

fin49 d.log Nominal interest rate: 90 days to 1 year

act42 d.log Industrial sales

ypd d.log Private disposable income

coloc d.log Total lending for consumption

dem5 d.log Retail durable sales

ml38 d.log Employment in non-financial services

va_per d.log Value Added: personal services

va_adm d.log Value Added: public administration

ext11 d.log Import of capital goods

ipe d.log Foreign price index

def_PIB/MyE d.log GDP deflactor / GFCF M&E deflactor

prc8 d.log 5 year Central Bank real bonds

act15 d.log IMACEC

ext8 d.log Consumption imports

ext9 d.log Rest imports

act48 d.log Capital goods sales

act21 d.log Index of real sales of construction material

ext116 d.log U.S. GDP

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Annex 2a: Supply-side bridge equations

Total GDP

Primary equation: Supplementary equation:

Coeff StdError t-value Coeff StdError t-value

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

fin58(-1) -0.0928 0.0475 -1.95 fin58(-1) -0.1309 0.0413 -3.17 act22 0.0077 0.0009 8.93 fin23(-1) 0.0911 0.0312 2.92 act22 0.0078 0.0006 13.67 RSS 0.0058 Radj^2 0.59 RSS 0.0076 Radj^2 0.63 Commerce Primary equation:

Coeff StdError t-value

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

act2 0.2714 0.0800 3.39 edif01(-1) 0.0273 0.0128 2.13 act21 0.2256 0.1021 2.21 mesagoviv -0.0447 0.0200 -2.24 dem40 0.0623 0.0216 2.89 mesagoviv(-1) -0.0491 0.0197 -2.50 ml32 0.6596 0.1004 6.57 act21 0.2207 0.0669 3.30 cbc(-2) 0.0637 0.0192 3.32 cbc(-3) 0.0471 0.0206 2.29 RSS 0.0055 Radj^2 0.48 RSS 0.0010 Radj^2 0.72

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Annex 2b: Demand-side bridge equations

Total private consumption

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

Private consumption of non durable goods

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

Private consumption of durable goods

ypd(-1) 0.2176 0.1679 1.30 Constant 0.0260 0.0079 3.31 coloc 0.6839 0.1751 3.91 ipec50 0.0022 0.0005 4.07 dem5 0.5354 0.1419 3.77 bolsa(-1) 0.1890 0.0805 2.35 fin49(-1) -0.1255 0.0648 -1.94 RSS 0.0674 Radj^2 0.48 RSS 0.0848 Radj^2 0.34 Government Expenditure

cgov(-1) 0.3246 0.1073 3.02 cgov(-1) 0.3832 0.1291 2.97 ml38(-1) 0.1328 0.0539 2.47 cgov(-2) 0.1716 0.1418 1.21 va_per 0.3191 0.1026 3.11 cgov(-3) -0.1889 0.1401 -1.35 va_adm 0.6089 0.1987 3.06 cgov(-4) -0.1826 0.1390 -1.31 ml38(-1) 0.1064 0.0551 1.93 va_per 0.3559 0.1066 3.34 va_adm 0.8299 0.2391 3.47 RSS 0.0008 Radj^2 0.47 RSS 0.0007 Radj^2 0.48

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Annex 2b (continued): Demand-side bridge equations

Gross fixed capital formation: machinery and equipment

ext11 - ipe 0.6492 0.0579 11.20 Constant 0.0577 0.1256 0.46

def_PIB/MyE 0.4247 0.1290 3.29 log(mye/PIB)(-1)* -0.1101 0.0411 -2.68 fin58(-1) -0.0028 0.0015 -1.81 prc8(-1) -0.0184 0.0085 -2.17 ext11 0.5632 0.0640 8.80 act15(-1) 1.2112 0.5730 2.11 RSS 0.0683 Radj^2 0.74 RSS 0.0591 Radj^2 0.75

(*) cointegrating relation of the levels of the variables

Export of goods and services

xbys(-1) -0.4128 0.1324 -3.12 xbys(-1) -0.1585 0.0822 -1.93

act40 0.7656 0.2826 2.71 ext116(-1) 1.4937 0.3601 4.15

ext116(-1) 2.1345 0.5938 3.59 xb_bal 0.4714 0.0564 8.36

fin58 0.0666 0.0673 0.99

RSS 0.0157 Radj^2 0.39 RSS 0.0052 Radj^2 0.79

Import of goods and services

ext11 - ipe 0.1213 0.0397 3.31 Constant 0.0121 0.0034 3.54

ext8 0.1476 0.0529 2.79 ext11 0.1529 0.0390 3.92

ext9 0.1874 0.0786 2.39 ext8 0.2075 0.0502 4.13

act48 0.0483 0.0195 2.47 ext9 0.1820 0.0855 2.13

act21 0.2623 0.0990 2.65

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Annex 3: Out-of-Sample forecasting evaluation:

Root mean square forecasting error of the yearly growth rate.

,D,9SHULRG

Primary Equation

Mean SD. Absolute RMSFE: Abs.RMSFE Relative

v12* v12* SARIMA: Eq1(PcGets) (model / SARIMA)

h=1 h=2 h=3 h=1 h=2 h=3 h=1 h=2 h=3 Supply GDP 1.7 3.6 1.7 3.5 4.5 2.1 3.3 3.2 1.2 1.0 0.7 Construction 2.2 7.7 4.7 7.4 8.4 4.1 5.8 5.7 0.9 0.8 0.7 Commerce 3.5 7.4 3.9 6.5 8.5 2.7 3.7 5.7 0.7 0.6 0.7 Industry -2.8 5.3 3.6 5.9 7.0 3.4 4.9 5.2 1.0 0.8 0.7 Demand Private 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 0.7 Durable 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 0.6

GFCF: Machinery and Equipment 10.4 32.7 17.3 29.2 38.3 13.1 25.1 34.9 0.8 0.9 0.9

Import of Goods and Services 4.2 17.7 8.0 14.6 19.3 2.8 9.1 15.7 0.4 0.6 0.8

Export 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 Relative

v12* v12* SARIMA: Ec2 (judgment) (model / SARIMA)

h=1 h=2 h=3 h=1 h=2 h=3 h=1 h=2 h=3 Supply GDP 1.7 3.6 1.7 3.5 4.5 1.5 2.4 3.2 0.9 0.7 0.7 Construction 2.2 7.7 4.7 7.4 8.4 3.1 5.9 7.5 0.7 0.8 0.9 Commerce 3.5 7.4 3.9 6.5 8.5 Industry -2.8 5.3 3.6 5.9 7.0 2.8 3.9 4.7 0.8 0.7 0.7 Demand Private 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 0.5 Durable 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 0.7

GFCF: Machinery and Equipment 10.4 32.7 17.3 29.2 38.3 6.7 15.1 23.8 0.4 0.5 0.6

Import of Goods and Services 4.2 17.7 8.0 14.6 19.3 3.4 9.7 16.3 0.4 0.7 0.8

Export 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

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Documentos de Trabajo

Banco Central de Chile

Working Papers

Central Bank of Chile

NÚMEROS ANTERIORES PAST ISSUES



La serie de Documentos de Trabajo en versión PDF puede obtenerse gratis en la dirección electrónica:

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DTBC – 625

Introducing Financial Assets into Structural Models

Jorge Fornero

Mayo 2011

DTBC – 624

Procyclicality of Fiscal Policy in Emerging Countries: the Cycle is the Trend

Michel Strawczynski y Joseph Zeira

Mayo 2011

DTBC – 623

Taxes and the Labor Market

Tommaso Monacelli, Roberto Perotti y Antonella Trigari

Mayo 2011

DTBC – 622

Valorización de Fondos mutuos monetarios y su impacto sobre la estabilidad financiera

Luis Antonio Ahumada, Nicolás Álvarez y Diego Saravia

Abril 2011

DTBC – 621

Sobre el nivel de Reservas Internacionales de Chile: Análisis a Partir de Enfoques Complementarios

Gabriela Contreras, Alejandro Jara, Eduardo Olaberría y Diego Saravia

Abril 2011

DTBC – 620

Un Test Conjunto de Superioridad Predictiva para los Pronósticos de Inflación Chilena

Pablo Pincheira Brown

(21)

DTBC – 619

The Optimal Inflation Tax in the Presence of Imperfect Deposit – Currency Substitution

Eduardo Olaberría

Marzo 2011

DTBC – 618

El Índice de Cartera Vencida como Medida de Riesgo de Crédito: Análisis y Aplicación al caso de Chile

Andrés Sagner

Marzo 2011

DTBC – 617

Estimación del Premio por Riesgo en Chile

Francisca Lira y Claudia Sotz

Marzo 2011

DTBC – 616

Uso de la aproximación TIR/Duración en la estructura de tasas: resultados cuantitativos bajo Nelson – Siegel

Rodrigo Alfaro y Juan Sebastián Becerra

Marzo 2011

DTBC – 615

Chilean Export Performance: the Rol of Intensive and Extensive Margins

Matías Berthelom

Marzo 2011

DTBC – 614

Does Lineariry of the Dynamics of Inflation Gap and Unemployment Rate Matter?

Roque Montero

Febrero 2011

DTBC – 613

Modeling Copper Price: Regime Switching Approach

Javier García – Cicco y Roque Montero

Febrero 2011

DTBC – 612

Riding the Roller Coaster: Fiscal Policies of Non-renewable Resources Exporters in Latin America and the Caribbean.

Mauricio Villafuerte Pablo López-Murphy y Rolando Ossowski