BANCO DE PORTUGAL Economic Research Department Nonlinearities over the Business Cycle: An Application of the Smooth Transition Autoregressive Model to Characterize GDP Dynamics for the Euro-area and Portugal Francisco Craveiro Dias WP 9-03 July 2003 The analyses, opinions and findings of these papers represent the views of the authors, they are not necessarily those of the Banco de Portugal. Please address correspondence to Francisco Craveiro Dias, Economic Research Department, Banco de Portugal, Av. Almirante Reis nº 71, 1150-165 Lisboa, Portugal, Tel.#351-213128327; Fax#351-213107804; email:[email protected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y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ortugal 0.10 D4lgdp 0.08 0.06 0.04 0.02 2002-1 2000-1 1998-1 1996-1 1994-1 1992-1 1990-1 1988-1 1986-1 1984-1 1982-1 1980-1 -0.02 1978-1 0.00 -0.04 + - + + " ! + + + - - & & + A + " 5 - - " ! + - " A 0$=* A 5 + / + 0 - 78 C - C " $76* ! " &' # " $ &' ! " ! " - ( + - " > & & > 9 3 &% ! / & , @9 - 0! 3 - %# &' ! " - $ &- C C & % / ! & ! 0 L$/* 2& 9 0 L 4 /" ) - - - &+ !A - 4 " A + + ! , - + ! " C A , + 3 - " - " - R ES ID U ALS OF LIN EAR MOD E L 0.05 0.04 A R(9) 0.03 0.02 0.01 -0.03 -0.04 -0.05 7? 2002.3 2000.3 1998.3 1996.3 1994.3 1992.3 1990.3 1988.3 1986.3 1984.3 1982.3 -0.02 1980.3 0 -0.01 " " - + A , ! ! ! / & 92 - " & - *+, - , - A + " C + - - + -! - " 9 + 0$=* A ! ( ("(7'' ("((88 ("((;F ("?=68 (")(86 ("'))7 7 ' ) F 8 ? ( ! ("'F68 ("'6); ! ! ! ( ! ("((7= ("(==7 ! ! ! 2 0 9 0 - / ( ! ("'(;8 ("((F? ! ! ! J' " 9 0 + - J) " L - &- 0 " 7 , 3 + , - - 0 & + ! / + " + " - 4- " A &9 0 + A - - / $7;* . ! " ! " &# " . " . 23 . - $ %# ! " &# " / 3 $ ! " 7 .. # " &# "$'(('* " 0 - 76 - + - & - C - 3 - + , & 9 " / / " + D $7==F*" - 2 + " - & , & " , + ; " @ ! + & - ! ! ! , + , A 92 , - & A ! - - - " , RESIDUALS 0.05 STAR model AR(9) 0.04 0.03 0.02 0.01 2002.3 2000.3 1998.3 1996.3 1994.3 1992.3 1990.3 1988.3 1986.3 1984.3 -0.02 1982.3 -0.01 1980.3 0 -0.03 -0.04 -0.05 # - - - A 7=;) '!7=;8 F& 7==' )!7==F 7 - 7==6 '!7==; F" - ! - A - ! - E ,+ - 5 - 5- " + + - - - " + ! 7; + Transition function versus time Transition function versus y(t-3) 1.2 1.2 1 1 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 # / , - A 5 - 5 + & / ("67 / & + - - + 2002.1 " / / - , - , " / - " $#J(*& + - - 4 + / 2000.1 - + - 1998.1 1996.1 1994.1 1992.1 1990.1 0.075 1988.1 0.025 1986.1 -0.025 1984.1 -0.075 1982.1 1980.1 0 0 - 5 / 5 / - 7"(? / ("=F& ("=( / & / ("6F& - - " - - 3 + - : - & ! " @ ! - + , 5 5 - 3" + - - , - " " / + ("()= $)"=P )"FP" + & @+ + *!+ - 2 53 4 2 + , " - 3 - + - 5 , " & - , ," G & 7= 2 E - , ! $#"('"F*& , ! 5 5& + - 3 " # ! / + 3 & + & - - + ! / - !- A, + & , & - ! 0 A, ! + ! / $7;*" - ! ! & " Obs F.84.2 F.93.1 F.90.4 F.87.3 F.95.4 F.98.4 F.00.4 F.02.4 "FORECASTS" (for 8 periods horizon) 0.10 0.08 0.06 0.04 0.02 2002.2 2000.2 1998.2 1996.2 1994.2 1992.2 1990.2 1988.2 1986.2 1984.2 -0.02 1982.2 0.00 -0.04 4 +2 & - , , - - ! ! , 3 - " " ! + " - - - / ! 3 !7";P& - A =")P - A - '(('OF 3 ! + + A - A - / + - 7==)O7 ! - 3" - + : 7==(OF $ *& - $Q("8P* - - 0123 4 - A '( " C ! -41 4 1 " + " 1993Q1-Lower Regime 1990Q4-Upper Regime 0.04 0.04 0.03 +2*SER +2*SER 0.03 -2*SER -2*SER 0.02 sum sum 0.02 0.01 0.01 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1 -0.01 -0.01 -0.02 -0.02 -0.03 -0.03 -0.04 -0.04 2 3 2000Q4-Near Threshold 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 GIR(+2*SER) 0.04 0.04 +2*SER 0.03 0.02 -2*SER 0.03 sum 0.03 Threshold Lower Upper 0.02 0.01 0.02 0 0.01 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.01 0.01 -0.02 0.00 -0.03 -0.01 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 -0.01 -0.04 + - 3 5 + - + 5" C $=")P* + 5 " 3 A A - 7==(OF A &5 + - 4 + & " % % , - - - + + 3" ! - , & " !- " '((' '7 " L # 2 - , , 4 ! !$ F &- " + *" G D P -E u ro a re a 0 .0 7 D4 lg d p e 0 .0 6 0 .0 5 0 .0 4 0 .0 3 0 .0 2 0 .0 1 2000.4 1997.4 1994.4 1991.4 1988.4 1985.4 1982.4 1979.4 1976.4 - 0 .0 2 1973.4 - 0 .0 1 1970.4 0 - 0 .0 3 , & + - ! - - & " A " & + 3 + + C A C - $7=* ! " # " %# $ &' &' $ &' ! " ! " ! " - ( ! A " ! , A A A - + + / 2 + + + A " L - - - " 3 , " '' " C " R E S ID U AL S OF L IN E AR M OD E L 0.020 A R(5) 0.015 0.010 0.005 2002-1 2000-1 1998-1 1996-1 1994-1 1992-1 1990-1 1988-1 1986-1 1984-1 1982-1 1980-1 1978-1 1976-1 1974-1 -0.005 1972-1 0.000 -0.010 -0.015 -0.020 -0.025 - A - 9 + + + + 0$8* A ! 7 ' ) F 8 ( ("'?)? (")F)8 ("7'7' ("()=F ("')?; ( ! ! ! ("767= ! ( ! ! ! ("(?FF ! ( ! ! ! ("(6(? ! " C 2 - A ( 2 *+, 0 / 0 ! " L - 9 / 9 0 - " A - 8P 0 9 + A 0 + - ') " 0 " ! $'(* . ! " # " %# $ $ ! " ! " ! " &# &# &# ,! ? " G A , , + + & " & ! ! + " + - & - - " ! , R ES ID U ALS 0.020 STAR model AR(5) 0.015 0.010 0.005 2002-1 2000-1 1998-1 1996-1 1994-1 1992-1 1990-1 1988-1 1986-1 1984-1 1982-1 1980-1 1978-1 1976-1 1974-1 -0.005 1972-1 0.000 -0.010 -0.015 -0.020 -0.025 - + + 3 ! - + 5 " - 7=;7 7" 2 - 7=;7 )!7=;) )& 7=;F '!7=;? ' A 5 7=;8 7" 'F - - 2 7=6' '! - - E A ! A + - ! A " ! , " Transition function versus y(t-4) 1.2 ! Transition function versus time 1.2 1.0 0.9 0.8 0.6 0.6 0.4 0.3 0.2 # - ! + ! A , " L - - ! " C / ! + 5 - / - - 5 7")P - 7"(F + A - ("8' A / 5 - ! / / / + / / 5 2 '( + ("=7& ("6=& ! + + - ! + " C , : + ! ! + $#J7* ! ("('? $'"?P + + 4 ! / ! 5+ 7"(P - - - 3 5 - 5 - - / ! ! + , / / + - + / 5 " - $#J(* 2002.1 , & ! / 1999.1 + / , 1996.1 1993.1 1990.1 0.055 1987.1 0.035 1984.1 0.015 1981.1 -0.005 1978.1 -0.025 1975.1 1972.1 0.0 0.0 " &- + / *& " " '8 - + - - " @ - 3 + - 2 - , " & - ! - " A - 3 A, / ! " 0.07 "FORECASTS" (for 8 periods horizon) Obs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— John T. Addison, Pedro Portugal 2/00 THE ESTIMATION OF RISK PREMIUM IMPLICIT IN OIL PRICES — Jorge Barros Luís 3/00 EVALUATING CORE INFLATION INDICATORS — Carlos Robalo Marques, Pedro Duarte Neves, Luís Morais Sarmento 4/00 LABOR MARKETS AND KALEIDOSCOPIC COMPARATIVE ADVANTAGE — Daniel A. Traça 5/00 WHY SHOULD CENTRAL BANKS AVOID THE USE OF THE UNDERLYING INFLATION INDICATOR? — Carlos Robalo Marques, Pedro Duarte Neves, Afonso Gonçalves da Silva 6/00 USING THE ASYMMETRIC TRIMMED MEAN AS A CORE INFLATION INDICATOR — Carlos Robalo Marques, João Machado Mota 2001 1/01 THE SURVIVAL OF NEW DOMESTIC AND FOREIGN OWNED FIRMS — José Mata, Pedro Portugal 2/01 GAPS AND TRIANGLES — Bernardino Adão, Isabel Correia, Pedro Teles 3/01 A NEW REPRESENTATION FOR THE FOREIGN CURRENCY RISK PREMIUM — Bernardino Adão, Fátima Silva 4/01 ENTRY MISTAKES WITH STRATEGIC PRICING — Bernardino Adão 5/01 FINANCING IN THE EUROSYSTEM: FIXED VERSUS VARIABLE RATE TENDERS — Margarida Catalão-Lopes 6/01 AGGREGATION, PERSISTENCE AND VOLATILITY IN A MACROMODEL — Karim Abadir, Gabriel Talmain 7/01 SOME FACTS ABOUT THE CYCLICAL CONVERGENCE IN THE EURO ZONE — Frederico Belo 8/01 TENURE, BUSINESS CYCLE AND THE WAGE-SETTING PROCESS — Leandro Arozamena, Mário Centeno 9/01 USING THE FIRST PRINCIPAL COMPONENT AS A CORE INFLATION INDICATOR — José Ferreira Machado, Carlos Robalo Marques, Pedro Duarte Neves, Afonso Gonçalves da Silva 10/01 IDENTIFICATION WITH AVERAGED DATA AND IMPLICATIONS FOR HEDONIC REGRESSION STUDIES — José A.F. Machado, João M.C. Santos Silva 2002 1/02 QUANTILE REGRESSION ANALYSIS OF TRANSITION DATA — José A.F. Machado, Pedro Portugal Banco de Portugal / Working papers I 2/02 SHOULD WE DISTINGUISH BETWEEN STATIC AND DYNAMIC LONG RUN EQUILIBRIUM IN ERROR CORRECTION MODELS? — Susana Botas, Carlos Robalo Marques 3/02 MODELLING TAYLOR RULE UNCERTAINTY — Fernando Martins, José A. F. Machado, Paulo Soares Esteves 4/02 PATTERNS OF ENTRY, POST-ENTRY GROWTH AND SURVIVAL: A COMPARISON BETWEEN DOMESTIC AND FOREIGN OWNED FIRMS — José Mata, Pedro Portugal 5/02 BUSINESS CYCLES: CYCLICAL COMOVEMENT WITHIN THE EUROPEAN UNION IN THE PERIOD 1960-1999. A FREQUENCY DOMAIN APPROACH — João Valle e Azevedo 6/02 AN “ART”, NOT A “SCIENCE”? CENTRAL BANK MANAGEMENT IN PORTUGAL UNDER THE GOLD STANDARD, 1854-1891 — Jaime Reis 7/02 MERGE OR CONCENTRATE? SOME INSIGHTS FOR ANTITRUST POLICY — Margarida Catalão-Lopes 8/02 DISENTANGLING THE MINIMUM WAGE PUZZLE: ANALYSIS OF WORKER ACCESSIONS AND SEPARATIONS FROM A LONGITUDINAL MATCHED EMPLOYER-EMPLOYEE DATA SET — Pedro Portugal, Ana Rute Cardoso 9/02 THE MATCH QUALITY GAINS FROM UNEMPLOYMENT INSURANCE — Mário Centeno 10/02 HEDONIC PRICES INDEXES FOR NEW PASSENGER CARS IN PORTUGAL (1997-2001) — Hugo J. Reis, J.M.C. Santos Silva 11/02 THE ANALYSIS OF SEASONAL RETURN ANOMALIES IN THE PORTUGUESE STOCK MARKET — Miguel Balbina, Nuno C. Martins 12/02 DOES MONEY GRANGER CAUSE INFLATION IN THE EURO AREA? — Carlos Robalo Marques, Joaquim Pina 13/02 INSTITUTIONS AND ECONOMIC DEVELOPMENT: HOW STRONG IS THE RELATION? — Tiago V. de V. Cavalcanti, Álvaro A. Novo 2003 1/03 FOUNDING CONDITIONS AND THE SURVIVAL OF NEW FIRMS — P.A. Geroski, José Mata, Pedro Portugal 2/03 THE TIMING AND PROBABILITY OF FDI: An Application to the United States Multinational Enterprises — José Brandão de Brito, Felipa de Mello Sampayo 3/03 OPTIMAL FISCAL AND MONETARY POLICY: EQUIVALENCE RESULTS — Isabel Correia, Juan Pablo Nicolini, Pedro Teles 4/03 FORECASTING EURO AREA AGGREGATES WITH BAYESIAN VAR AND VECM MODELS — Ricardo Mourinho Félix, Luís C. Nunes 5/03 CONTAGIOUS CURRENCY CRISES: A SPATIAL PROBIT APPROACH — Álvaro Novo 6/03 THE DISTRIBUTION OF LIQUIDITY IN A MONETARY UNION WITH DIFFERENT PORTFOLIO RIGIDITIES — Nuno Alves Banco de Portugal / Working papers II 7/03 COINCIDENT AND LEADING INDICATORS FOR THE EURO AREA: A FREQUENCY BAND APPROACH — António Rua, Luís C. Nunes 8/03 WHY DO FIRMS USE FIXED-TERM CONTRACTS? — José Varejão, Pedro Portugal 9/03 NONLINEARITIES OVER THE BUSINESS CYCLE: AN APPLICATION OF THE SMOOTH TRANSITION AUTOREGRESSIVE MODEL TO CHARACTERIZE GDP DYNAMICS FOR THE EURO-AREA AND PORTUGAL — Francisco Craveiro Dias Banco de Portugal / Working papers III
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