Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

THE BRAZILIAN QUARTERLY REAL

GDP:TEMPORAL DISAGGREGATION AND

NOWCASTING.

André Nunes Maranhão - University of Brasília and Bank of BrazilAndré Minella - Central Bank of Brazil

Cleomar Gomes da Silva - Federal University of Uberlandia.

II Seminário em Macroeconomia Aplicada - EESP-FGV

19 - October - 2017andrenmaranhao@gmail.com

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Presentation

1 IntroductionMonitoring of Economic Activity

2 Temporal Disaggregation MethodsInternational ReviewAggregation and Disaggregation Methods

3 Model Selection Criteria and Data DescriptionModel Selection CriteriaData Description and Variable Selection

4 ResultsResults of Model SelectionNowcasting Exercises

5 ConclusionConclusion and Research Agenda

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Monitoring of Economic Activity

Nowcasting Problem

Economic variables and diferent frequencies:industrial production (PIM), retail survey (PMC) Monthly, 2months lag (t +2);Average Electric Energy Consumption Monthly, 1 month lag(t +1);

GDP frequency: Quarterly with Lag;IBC-Br: The Central Bank of Brazil Economic ActivityIndex;IBC-Br frequency: Monthly, 2 months lag (t +2);IBC-Br : Weaknesses and questions;Is there any room for advancement and improvement?

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

International Review

Literature

Article ThemeBoot, Feibes & Lisma (1965) Interpolation methods

Denton (1971) Interpolation methodsChow & Lin (1971) Parametric modelFernandez (1981) Unit root case

Gregoir (1995) Dynamic modelSalazar et al. (1997, 1998) Dynamic model

Santos, Silva & Cardoso (2001) Dynamic modelMonch & Uhlig (2005) State-Space (SS) model

Cardoso (1981) Fisrt brazilian caseNotini et alli. (2012) SS Coincident index for brazilian GDP

Table : Time evolution of the disaggregation models

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Aggregation and Disaggregation Methods

Concepts and Definitions

yl,t =s∑

i=1

ciyh,i

Yl = CYh

Yh = AYl

Ct×3t =13

1 1 1 0 0 0 0 · · · 00 0 0 1 1 1 0 · · · 0...

......

......

......

. . ....

0 0 0 0 0 0 0 · · · 1

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Aggregation and Disaggregation Methods

First Model

Chow & Lin (1971):

Yl = X ′l β + ul ul ∼ N(0,Vl)

Yh = X ′hβ + uh uh ∼ N(0,Vh)

uh,t = ρuh,t−1 + εt

ε ∼ N(0, σ2ε )

Yh = A(X ′l β + ul)⇔ Yh = AYl

minβ,ρ

COV (Yh − Yl)

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Aggregation and Disaggregation Methods

A Disaggregation Model using Kalman Filter

Monch & Uhlig (2005):

y+ = (0 0 y3 0 0 y6 0 0 y9...)

y+l,t =

13

2∑i=0

yh,t−i , t=3,6,9,...

0, otherwise

y+l,t = Htξt

Ht =

{[1/3 1/3 1/3 0], para, t = 3,6,9, ...

[0 0 0 0], otherwise

ξt =

yh,t

yh,t−1yh,t−2uh.t

=

φ 0 0 ρ1 0 0 00 1 0 00 0 0 ρ

×

yh,t−1yh,t−2yh,t−3uh,t−1

+

X ′h,tβ

000

+

εt00εt

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Aggregation and Disaggregation Methods

State-Space Models for Disaggregation

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Model Selection Criteria

Methods of Evaluation

In-Sample CriteriaMonch & Uhlig (2005):

R2diff =

Var(∆y+t |T )

Var(∆y+t |T ) + Var(∆ut |T )

Out-of-Sample CriteriaProietti (2006):

MAPE =1T

T∑t=1

∣∣∣∣∣ y+t − y+

t

y+t

∣∣∣∣∣RMSE =

√√√√ 1T

T∑t=1

(y+t − y+

t )2

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Data Description and Variable Selection

Variable Selection

1st quarter of 2003 to the 2rd quarter of 2017 (Real GDP);54 variables were tested;Unit root tests: ADF, MADFgls, with and without structuralbreaks - Perron (1989), determinist trend with structuralbreaks;Cross correlation in first difference: Monch & Uhlig (2005),Notini & Issler (2008) and Notini et alli. (2012);Causality tests;Principal Component Analysis in time series context;

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Data Description and Variable Selection

Selected Variables

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Results of Model Selection

Models Selected

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Nowcasting Exercises

Model t+1

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Nowcasting Exercises

Model t+2 without IBC-Br

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Nowcasting Exercises

Model t+2

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Nowcasting Exercises

Predictive Ability

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Conclusion and Research Agenda

Final Considerations

Main Contribuitions1 Model (t+1) and GDP disaggregation;

Same predictive capacity of the IBC-Br, however withvariables t + 1;The quarterly average coincides with the values of realGDP, in this sense it is literally a coincident indicator.

2 Model (t+2) without IBC-Br and Model (t+2);Both models have a better predictive performance than theIBC-Br;The quarterly average coincides with the values of realGDP.In all models of the nowcasting exercise, we have themonthly estimate of real GDP for the periods prior tonowcasting. (Temporal disaggregation of real GDP).

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Conclusion and Research Agenda

Final Considerations

Research Agenda1 Possibility of testing variables from the big data context;2 Use of high-dimensional time series models;3 Extended temporal sample for the purpose of using

predictability tests as presented by Giacomini and White(2006);

4 Study of turning points and economic cycles.

Introduction Temporal Disaggregation Methods Model Selection Criteria and Data Description Results Conclusion

Conclusion and Research Agenda

Article Presented:

THE BRAZILIAN QUARTERLY REAL GDP:TEMPORAL

DISAGGREGATION AND NOWCASTING.

André Nunes Maranhão.

THANK YOU ALL.