The Portuguese Business Cycle: Chronology and … · The Portuguese Business Cycle: Chronology and Duration ... Employing a duration dependent Markov-switching vector ... Ignore that

MotivationLiterature

MethodologyEmpirical Results

Conclusions

The Portuguese Business Cycle:Chronology and Duration Dependence

Vítor Castro

University of Coimbra and NIPE, Portugal

Presentation at the5th Annual Meeting of the Portuguese Economic Journal

University of Aveiro, Portugal8-9 July, 2011

Vítor Castro The Portuguese Business Cycle



Conclusions

Outline

1 Motivation

2 Literature

3 Methodology

4 Empirical Results

5 Conclusions




Conclusions

Motivation

The NBER has been publishing a business cycle chronologyfor the United States since 1929.

The ECRI and the CEPR have recently started to producesimilar chronologies for some market oriented economies andthe Euro Area, respectively.

However, to our knowledge, no national or internationalorganization or scienti�c study has produced, so far, abusiness cycle chronology for Portugal.




Conclusions

Motivation







Conclusions

Motivation







Conclusions

Motivation

This study intends to identify a chronology for thePortuguese business cycle, and...

At the same time, to test for the presence of durationdependence in expansions and contractions.

Employing a duration dependent Markov-switching vectorautoregressive model (DDMSVAR).

This model alows: (i) to date the business cycle; (ii) andcontrol for the presence of duration dependence in its phases.




Conclusions

Motivation








Conclusions

Motivation








Conclusions

Motivation








Conclusions

Outline

1 Motivation

2 Literature

3 Methodology

4 Empirical Results

5 Conclusions




Conclusions

Literature: (i) business cycle chronology available

No need to date the business cycle => traditional durationanalysis can be employed to test for duration dependence.

Great attention to the US business cycle because its turningpoint dates are well documented by the NBER.

ECRI and CEPR chronologies => other countries under thescope of other studies.

Do business cycles exhibit positive duration dependence?

Are expansions and contractions in economic activity morelikely to end as they become older?




Conclusions










Conclusions










Conclusions










Conclusions


Parametric duration models:Sichel (1991), Diebold et al. (1993), Zuehlke (2003) andDavig (2007): evidence of positive duration dependence forpre-WWII expansions and post-WWII contractions in the US.

Diebold et al. (1990): reach a similar conclusion for France,Germany and the UK in the pre-WWII period.

Abderrezak (1998): evidence of positive duration dependencein the whole growth cycles and growth phases (upswings anddownswings) for a group of 11 countries.

Castro (2010): evidence of positive duration dependence forboth expansions and contractions (using a discrete-timeduration model over a panel of 13 industrial countries). Healso notices that the probability of a contraction endingincreases more quickly with its age than an expansion.




Conclusions

Literature: (ii) chronology not needed or unavailable

Other approaches regard the business cycle as an unobservedstochastic process.

The business cycle is seen as the outcome of a Markov processthat switches between the states of expansion and contraction(Hamilton, 1989).

Turning point dates identi�ed by the NBER, ECRI or CEPRare not necessary.

Very useful to identify the business cycle chronology when it isnot available at all.




Conclusions









Conclusions









Conclusions









Conclusions


Markov-switching models:

Hamilton (1989): �rst to implement this kind of analysis tothe US business cycle.

Krolzig (1997), Krolzig (2001), Artis et al. (2004) andKrolzig & Toro (2005): apply some variants of these modelsto identify the European business cycle.

Schirwitz (2009): also employs them to identify a chronologyfor the German business cycle.

Ignore that the switching process can be a¤ected by theduration of each state.




Conclusions


Markov-switching models:

Hamilton (1989): �rst to implement this kind of analysis tothe US business cycle.

Krolzig (1997), Krolzig (2001), Artis et al. (2004) andKrolzig & Toro (2005): apply some variants of these modelsto identify the European business cycle.

Schirwitz (2009): also employs them to identify a chronologyfor the German business cycle.

Ignore that the switching process can be a¤ected by theduration of each state.




Conclusions


Duration dependent Markov-switching models:

Allow for state transition probabilities to be durationdependent.

Durland & McCurdy (1994), Kim & Nelson (1998) andPelagatti (2001, 2002): evidence of duration dependence forthe US contractions but not for expansions after WWII.

Perruchoud (2008): similar conclusion for the Swiss businesscycle.

Kim (1996) and Iiboshi (2007): evidence of positiveduration dependence for, respectively, Korean and Japaneseexpansions and contractions.




Conclusions


Duration dependent Markov-switching models:

Allow for state transition probabilities to be durationdependent.

Durland & McCurdy (1994), Kim & Nelson (1998) andPelagatti (2001, 2002): evidence of duration dependence forthe US contractions but not for expansions after WWII.

Perruchoud (2008): similar conclusion for the Swiss businesscycle.

Kim (1996) and Iiboshi (2007): evidence of positiveduration dependence for, respectively, Korean and Japaneseexpansions and contractions.




Conclusions

Literature: (iii) additional remarks

Advantages of Pelagatti�s (2001, 2002) DDMSVAR:

Applies a Bayesian approach => inference does not depend onthe sample size and it is not conditional on the estimatedparameters.

Considers a multivariate speci�cation => inference using amulti-move Gibbs sampler => faster convergence to theinvariant distribution.

Chen & Shen (2006) and Ozun & Turk (2009) employ thismodel to identify the Taiwanese and Turkish business cycles,respectively, and �nd evidence of positive duration dependence.




Conclusions

Literature: (iii) additional remarks

Advantages of Pelagatti�s (2001, 2002) DDMSVAR:

Applies a Bayesian approach => inference does not depend onthe sample size and it is not conditional on the estimatedparameters.

Considers a multivariate speci�cation => inference using amulti-move Gibbs sampler => faster convergence to theinvariant distribution.

Chen & Shen (2006) and Ozun & Turk (2009) employ thismodel to identify the Taiwanese and Turkish business cycles,respectively, and �nd evidence of positive duration dependence.




Conclusions

Outline

1 Motivation

2 Literature

3 Methodology

4 Empirical Results

5 Conclusions




Conclusions

The DDMSVAR model

yt = µ0+µ1St+A1(yt-1-µ0-µ1St-1)+...+Ap(yt-p-µ0-µ1St-p)+εt

� yt � vector of observable variables;

� A1, ...,Ap � coe¢ cient matrices of a stable VAR process;

� εt � gaussian white noise vector with covariance matrix Σ;� St � binary unobservable random variable following a Markov chain

with varying transition probabilities (1=expans.; 0=contr.);

� µ0, µ0 + µ1 �average growth rates of yt in state 0 (contraction)and state 1 (expansion), respectively.




Conclusions

The DDMSVAR model

A Markov chain is built for the pair (St ;Dt)

The probability of St being in a particular state is assumed tobe dependent on the previous state St�1 and on the durationdependent variable Dt�1, where:

Dt =

(Dt�1 + 1

1

if

if

St = St�1St 6= St�1

Duration dependent transition probabilities:

pi jj (d) = Pr(St = i jSt�1 = j ;Dt�1 = d), i , j = 0, 1

� probability of the economy moving to or staying in state i giventhat in the previous period it was in state j with duration d .




Conclusions

The DDMSVAR model

A Markov chain is built for the pair (St ;Dt)

The probability of St being in a particular state is assumed tobe dependent on the previous state St�1 and on the durationdependent variable Dt�1, where:

Dt =

(Dt�1 + 1

1

if

if

St = St�1St 6= St�1

Duration dependent transition probabilities:

pi jj (d) = Pr(St = i jSt�1 = j ;Dt�1 = d), i , j = 0, 1

� probability of the economy moving to or staying in state i giventhat in the previous period it was in state j with duration d .




Conclusions

The DDMSVAR model

Hence, the vector of observable variables yt is dependentupon the unobserved states from St to St�p , and the durationdependent variable Dt�1.

Implies an extended state variable

S�t = (Dt ,St ,St�1, ...,St�p)

that includes all combinations of states in the last p periods.

A probit speci�cation is used to model the transitionprobabilities and to characterize the duration dependence inthe business cycle.




Conclusions

The DDMSVAR model



S�t = (Dt ,St ,St�1, ...,St�p)






Conclusions

The DDMSVAR model



S�t = (Dt ,St ,St�1, ...,St�p)






Conclusions

The DDMSVAR model

# A latent variable, S�t , can then be expressed as:

S�t =(β1+β2Dt-1) St-1+(β3+β4Dt-1) (1-St-1)+εt , εt � N(0, 1)Pr(S�t � 0jSt�1;Dt�1) = Pr(St = 1jSt�1;Dt�1)Pr(S�t < 0jSt�1;Dt�1) = Pr(St = 0jSt�1;Dt�1)

# Transition probabilities for expansions (1) and contractions (0):

p1j1(d) = Pr(S�t � 0jSt�1 = 1;Dt�1 = d) = 1�Φ(�β1 � β2d)

p0j0(d) = Pr(S�t < 0jSt�1 = 0;Dt�1 = d) = Φ(�β3 � β4d)

where d = 1, ..., τ, and Φ(�) is the standard normal CDF.- Transition probabilities de�ned by β = (β1, β2, β3, β4).- If β2 = β4 = 0) no business cycle duration dependence.




Conclusions

The DDMSVAR model

# A latent variable, S�t , can then be expressed as:

S�t =(β1+β2Dt-1) St-1+(β3+β4Dt-1) (1-St-1)+εt , εt � N(0, 1)Pr(S�t � 0jSt�1;Dt�1) = Pr(St = 1jSt�1;Dt�1)Pr(S�t < 0jSt�1;Dt�1) = Pr(St = 0jSt�1;Dt�1)

# Transition probabilities for expansions (1) and contractions (0):

p1j1(d) = Pr(S�t � 0jSt�1 = 1;Dt�1 = d) = 1�Φ(�β1 � β2d)

p0j0(d) = Pr(S�t < 0jSt�1 = 0;Dt�1 = d) = Φ(�β3 � β4d)

where d = 1, ..., τ, and Φ(�) is the standard normal CDF.- Transition probabilities de�ned by β = (β1, β2, β3, β4).- If β2 = β4 = 0) no business cycle duration dependence.




Conclusions

The DDMSVAR model: Gibbs sampling

To obtain parameter estimates from the DDMSVAR model,we employ a Bayesian (Gibbs sampler) approach.

� Parameters: θ =�θ01, θ

02, θ

03, θ

04

�0θ01=(A

0,Σ0)0, θ02=(µ00, µ

01)0, θ03=β0, θ04=(f(St ,Dt )gTt=1)

0

� Prior distribution:

p (µ,A,Σ, β,S�0 ) = p(µ).p(A).p(Σ).p(β).p(S0,D0)

� Conditional distribution of θk :

p�θk jY, θ�k

�, k=1,...,4; Y=(y1,...,yT ); θ-k : set without θk .




Conclusions


Bayesian inference using Markov chain Monte Carlo:

� From arbitrary initial values θ(0) =�

θ(0)01 , θ

(0)02 , θ

(0)03 , θ

(0)04

�0,

(1) draw θ(i )1 from p

�θ1jY, θ(i�1)2 , θ

(i�1)3 , θ

(i�1)4

�(2) draw θ

(i )2 from p

�θ2jY, θ(i )1 , θ

(i�1)3 , θ

(i�1)4

�(3) draw θ

(i )3 from p

�θ3jY, θ(i )1 , θ

(i )2 , θ

(i�1)4

�(4) draw θ

(i )4 from p

�θ4jY, θ(i )1 , θ

(i )2 , θ

(i )3

�� The i th realization of θ is then θ(i ) =

�θ(i )01 , θ

(i )02 , θ

(i )03 , θ

(i )04

�0.

� Repeating steps (1) to (4) I times, we get the Gibbs sequenceθ(1), θ(2), θ(3), ..., θ(I ) that will converge to the distribution of θ,

i.e θ(I )d�! p(θjY) (true posterior distribution).




Conclusions




θ(0)01 , θ

(0)02 , θ

(0)03 , θ

(0)04

�0,


�θ1jY, θ(i�1)2 , θ

(i�1)3 , θ

(i�1)4

�


�θ2jY, θ(i )1 , θ

(i�1)3 , θ

(i�1)4

�(3) draw θ

(i )3 from p

�θ3jY, θ(i )1 , θ

(i )2 , θ

(i�1)4

�(4) draw θ

(i )4 from p

�θ4jY, θ(i )1 , θ

(i )2 , θ

(i )3


�θ(i )01 , θ

(i )02 , θ

(i )03 , θ

(i )04

�0.






Conclusions




θ(0)01 , θ

(0)02 , θ

(0)03 , θ

(0)04

�0,


�θ1jY, θ(i�1)2 , θ

(i�1)3 , θ

(i�1)4

�(2) draw θ

(i )2 from p

�θ2jY, θ(i )1 , θ

(i�1)3 , θ

(i�1)4

�


�θ3jY, θ(i )1 , θ

(i )2 , θ

(i�1)4

�(4) draw θ

(i )4 from p

�θ4jY, θ(i )1 , θ

(i )2 , θ

(i )3


�θ(i )01 , θ

(i )02 , θ

(i )03 , θ

(i )04

�0.






Conclusions




θ(0)01 , θ

(0)02 , θ

(0)03 , θ

(0)04

�0,


�θ1jY, θ(i�1)2 , θ

(i�1)3 , θ

(i�1)4

�(2) draw θ

(i )2 from p

�θ2jY, θ(i )1 , θ

(i�1)3 , θ

(i�1)4

�(3) draw θ

(i )3 from p

�θ3jY, θ(i )1 , θ

(i )2 , θ

(i�1)4

�


�θ4jY, θ(i )1 , θ

(i )2 , θ

(i )3


�θ(i )01 , θ

(i )02 , θ

(i )03 , θ

(i )04

�0.






Conclusions




θ(0)01 , θ

(0)02 , θ

(0)03 , θ

(0)04

�0,


�θ1jY, θ(i�1)2 , θ

(i�1)3 , θ

(i�1)4

�(2) draw θ

(i )2 from p

�θ2jY, θ(i )1 , θ

(i�1)3 , θ

(i�1)4

�(3) draw θ

(i )3 from p

�θ3jY, θ(i )1 , θ

(i )2 , θ

(i�1)4

�(4) draw θ

(i )4 from p

�θ4jY, θ(i )1 , θ

(i )2 , θ

(i )3

�

� The i th realization of θ is then θ(i ) =�

θ(i )01 , θ

(i )02 , θ

(i )03 , θ

(i )04

�0.






Conclusions




θ(0)01 , θ

(0)02 , θ

(0)03 , θ

(0)04

�0,


�θ1jY, θ(i�1)2 , θ

(i�1)3 , θ

(i�1)4

�(2) draw θ

(i )2 from p

�θ2jY, θ(i )1 , θ

(i�1)3 , θ

(i�1)4

�(3) draw θ

(i )3 from p

�θ3jY, θ(i )1 , θ

(i )2 , θ

(i�1)4

�(4) draw θ

(i )4 from p

�θ4jY, θ(i )1 , θ

(i )2 , θ

(i )3


�θ(i )01 , θ

(i )02 , θ

(i )03 , θ

(i )04

�0.






Conclusions




θ(0)01 , θ

(0)02 , θ

(0)03 , θ

(0)04

�0,


�θ1jY, θ(i�1)2 , θ

(i�1)3 , θ

(i�1)4

�(2) draw θ

(i )2 from p

�θ2jY, θ(i )1 , θ

(i�1)3 , θ

(i�1)4

�(3) draw θ

(i )3 from p

�θ3jY, θ(i )1 , θ

(i )2 , θ

(i�1)4

�(4) draw θ

(i )4 from p

�θ4jY, θ(i )1 , θ

(i )2 , θ

(i )3


�θ(i )01 , θ

(i )02 , θ

(i )03 , θ

(i )04

�0.






Conclusions

Outline

1 Motivation

2 Literature

3 Methodology

4 Empirical Results

5 Conclusions




Conclusions

Data

growth rate of the Industrial Production index (IP)

growth rate of a Composite Leading Indicator (CLI )

growth rate of civilian Employment (Emp)

monthly and year-on-year (monthly) growth rates

January 1978 - October 2010

Sources: OECD, MEI & http://www.oecd.org/std/cli

- NBER & ECRI monthly indicators: industrial production, personalincome, sales, employment, monthly estimates of GDP.




Conclusions

Table 3 - DDMSVAR estimates: monthly growth rates (Jan1978-Oct2010)

Prior PosteriorParameter mean var. mean st.dev. 2.5% 50.0% 97.5%µ0dlIP1 -0.2 1.0 -0.212 0.242 -0.709 -0.208 0.233µ0dlCLI 1 -0.2 1.0 -0.416 0.055 -0.527 -0.415 -0.309µ1dlIP1 0.5 1.0 0.511 0.275 0.044 0.497 1.078µ1dlCLI 1 0.5 1.0 0.818 0.047 0.727 0.818 0.912β1 1.0 2.0 1.747 0.261 1.270 1.729 2.303β2 0.0 2.0 0.003 0.008 -0.013 0.004 0.018β3 -1.0 2.0 -1.692 0.328 -2.376 -1.676 -1.092β4 0.0 2.0 0.026 0.025 -0.020 0.026 0.077

� Evidence of positive duration dependence for contractions (β4);

� No duration dependence for expansions (β2).Vítor Castro The Portuguese Business Cycle



Conclusions

Figure 1a - Transition probabilities for contractions: monthly growth rates

Pr(S t = 1 |S t 1= 0,D t 1= d )

0.00.10.20.30.40.50.60.70.80.91.0

0 5 10 15 20 25 30 35 40 45 50 55 60

mean 2.5% median 97.5%




Conclusions

Figure 1b - Transition probabilities for expansions: monthly growth rates

Pr(S t = 0 |S t 1= 1,D t 1= d )

0.00.10.20.30.40.50.60.70.80.91.0

0 5 10 15 20 25 30 35 40 45 50 55 60





Conclusions

Figure 2 - Probability of expansion: monthly growth rates

Pr(St =1)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1978 1982 1986 1990 1994 1998 2002 2006 2010

� monthly rates => higher volatility => y-o-y (monthly) growth ratesVítor Castro The Portuguese Business Cycle



Conclusions

Figure 3 - Annual growth rate of real GDP (%), 1971-2010

6.0

5.0

4.0

3.0

2.0

1.0

0.0

1.0

2.03.0

4.0

5.0

6.0

7.0

8.0

9.0

10.0

11.0

12.0

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

2004

2005

2006

2007

2008

2009

2010




Conclusions

Table 5 - DDMSVAR estimates: y-o-y growth rates (Jan1978-Oct2010)

Prior PosteriorParameter mean var. mean st.dev. 2.5% 50.0% 97.5%µ0dlIP12 -2.0 4.0 -2.490 0.374 -3.226 -2.489 -1.752µ0dlCLI 12 -2.0 4.0 -2.876 0.319 -3.506 -2.872 -2.263µ1dlIP12 5.0 4.0 6.678 0.437 5.814 6.679 7.534µ1dlCLI 12 5.0 4.0 7.315 0.359 6.602 7.319 8.029β1 1.0 5.0 2.568 0.517 1.641 2.543 3.679β2 0.0 5.0 -0.009 0.010 -0.030 -0.008 0.012β3 -1.0 5.0 -2.495 0.521 -3.649 -2.458 -1.588β4 0.0 5.0 0.026 0.023 -0.008 0.023 0.089

� Some evidence of pos. dur. dep. for contr. but not for expans.




Conclusions

Figure 5 - Probability of expansion: y-o-y growth rates

Pr(St =1)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1978 1982 1986 1990 1994 1998 2002 2006 2010




Conclusions

Table 6 - Portuguese business cycle chronology

Business cycle reference dates Duration (in months)Peak Trough Contr. Expans. Cycle(P) (T) P-T T-P T-T P-P

� December 1977+ � � � �

October 1983 June 1984 8 70+ 78+ �March 1991 November 1993 32 81 113 89May 2001 February 2006 57 90 147 122May 2007 November 2009 30 15 45 72October 2010

+ � � 11+ � 41+

Average (4 cycles) 32 62 102 94

� Using Hamilton�s (1989) 0.5-rule to determine the states.




Conclusions

Table 7 - DDMSVAR estimates: y-o-y rates with dlEmp12Prior Posterior

Parameter mean var. mean st.dev. 2.5% 50.0% 97.5%µ0dlIP12 -2.0 4.0 -2.085 0.954 -3.803 -1.908 -0.544µ0dlCLI 12 -2.0 4.0 -3.911 0.685 -5.336 -3.867 -2.739µ0dlEmp12 -2.0 4.0 -1.095 0.287 -1.692 -1.082 -0.566µ1dlIP12 5.0 4.0 4.898 1.266 2.956 4.571 7.128µ1dlCLI 12 5.0 4.0 7.702 0.543 6.713 7.688 8.799µ1dlEmp12 5.0 4.0 2.598 0.305 2.011 2.595 3.188β1 1.0 5.0 2.584 0.655 1.542 2.499 4.263β2 0.0 5.0 -0.011 0.014 -0.042 -0.010 0.013β3 -1.0 5.0 -3.311 1.026 -5.833 -3.130 -1.833β4 0.0 5.0 0.088 0.056 0.008 0.079 0.224

� Shorter time period: June 1984 - October 2010.� Stong evidence of positive duration dependence for contractions (β4).




Conclusions

Figure 6a - Transition probabilities for contractions: y-o-y with dlEmp12Pr(S t = 1 |S t 1= 0,D t 1= d )

0.00.10.20.30.40.50.60.70.80.91.0

0 5 10 15 20 25 30 35 40 45 50 55 60





Conclusions

Figure 6b - Transition probabilities for expansions: y-o-y with dlEmp12Pr(S t = 0 |S t 1= 1,D t 1= d )

0.00.10.20.30.40.50.60.70.80.91.0

0 5 10 15 20 25 30 35 40 45 50 55 60





Conclusions

Figure 7 - Probability of expansion: y-o-y with dlEmp12

Pr(St =1)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1984 1988 1992 1996 2000 2004 2008

� "Weak" contraction in 1995-1996 (very close to the 0.5-rule).� Early 2000s contraction seems to die out sooner.




Conclusions

Outline

1 Motivation

2 Literature

3 Methodology

4 Empirical Results

5 Conclusions




Conclusions

Conclusions

The DDMSVAR model with year-on-year (monthly) growthrates of IP, CLI and Emp (Jun1983-Oct2010) together withthe model without Emp (Jan1978-Oct2010) provide:

a reasonable picture of the Portuguese business cyclechronology over the last 33 years,

and indicate the presence of positive duration dependencein contractions but not in expansions.

Four important periods of contraction are identi�ed:

October 1983 - June 1984;March 1991 - November 1993;May 2001 - February 2006;May 2007 - November 2009.




Conclusions

Conclusions

The DDMSVAR model with year-on-year (monthly) growthrates of IP, CLI and Emp (Jun1983-Oct2010) together withthe model without Emp (Jan1978-Oct2010) provide:

a reasonable picture of the Portuguese business cyclechronology over the last 33 years,

and indicate the presence of positive duration dependencein contractions but not in expansions.

Four important periods of contraction are identi�ed:

October 1983 - June 1984;March 1991 - November 1993;May 2001 - February 2006;May 2007 - November 2009.




Conclusions

The model is quite successful in identifying the contraction inthe Portuguese economy caused by the recent �nancial crisis.

The model shows that the 2000s can be seen as a "lostdecade" for Portugal in terms of economic expansion.

Big concern for the next years since economic expansion isneeded to serve private and public debt that was accumulatedover the last decade.

The likelihood of a contraction ending increases over time,but for expansions it remains constant.

These results are similar to others obtained for the US:contractions are duration dependent, while expansions are not.




Conclusions









Conclusions









Conclusions









Conclusions









Conclusions

Extensions

This analysis can be extended to the study of the businesscycle in other countries for which no organization is datingtheir business cycle turning points.

The model employed here may also be useful to test for thepresence of duration dependence in the phases of their cycles.

The DDMSVAR model can also be used to detect thepresence of duration dependence in other areas where cyclesmight be present, like in the stock or housing markets.




Conclusions

Extensions







Conclusions

Extensions







Conclusions

THE END

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Documents

The Portuguese Business Cycle: Chronology and … · The Portuguese Business Cycle: Chronology and Duration ... Employing a duration dependent Markov-switching vector ... Ignore that