Discovering Specific Common Trends in a Large Set of Disaggregates: Statistical Procedures, their Properties and an Empirical Application*
| Published date | 01 June 2021 |
| Author | Guillermo Carlomagno,Antoni Espasa |
| Date | 01 June 2021 |
| DOI | http://doi.org/10.1111/obes.12412 |
641
©2020 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 83, 3 (2021) 0305–9049
doi: 10.1111/obes.12412
Discovering Specific CommonTrends in a Large Set of
Disaggregates: Statistical Procedures, their Properties
and an EmpiricalApplication*
Guillermo Carlomagno† and Antoni Espasa‡
†Central Bank of Chile,Agustinas 1180Santiago, Chile 8340454, (e-mail:
gcarlomagno@bcentral.cl)
‡Department of Statistics and Instituto Flores de Lemus, University Carlos III of Madrid,
(e-mail: antoni.espasa@uc3m.es)
Abstract
Macroeconomic variables are weighted averages of a large number of components. Our
objective is to model and forecast all of the Ncomponents of a macro variable.The main
feature of our proposal consists of discovering subsets of components that share single
common trends while neither assuming pervasiveness nor imposing special restrictions on
the serial or cross-sectional idiosyncratic correlation. We adopt a pairwise approach and
study its statistical properties. Our asymptotic theory works both with fixed Nand T→∞
and with [T,N]→∞. We show that the pairwise approach can be implemented using
three alternative strategies, which take into account alternative characteristics of the data
generating process. The paper includes an application to the US CPI broken downinto 159
components.
I. Introduction
Macroeconomic variables are weighted averages of a large number of components; thus
the usual focus on the aggregate alone implies neglecting a large amount of information.
The objective of this paper is to develop a procedure to model and forecast all of the
components of a macro or business variable at the maximum level of disaggregation. Our
strategy consists of identifying and estimating relevant relationships between the compo-
nents (disaggregates), then exploiting those relationships in single-equation models for the
components. This strategy’s value is twofold: (i) it might provide relatively precise models
and accurate forecasts of the components, which is our main interest, and (ii) it might
generate an improved indirect forecast for the aggregate, in the sense that, at least, it is
JEL Classification numbers: C01, C22, C32, C53.
*Both authors gratefully acknowledge financial support from the Spanish Ministry of Economy and Competitive-
ness research projects ECO2012-32401 and ECO2015-70331-C2-2. The first author also acknowledgessupport from
the Uruguayan Agencia Nacional de Investigaci´on e Innovaci´on research project FMV 3 2016 1 126200.
642 Bulletin
not significantly worse than direct forecasts.Achieving the latter aim would be an indirect
validation of the strategy for achieving the former.
When deciding whether and how much to dissagrgate, we confront a trade-off between
informational losses and estimation uncertainty. A possible way to deal with this is by
considering the restrictions derived from the existence of common features (such as trends
and cycles) between the components, as proposed by Espasa and Mayo-Burgos (2013).
They argue that when analysing the components of a macro variable, it is usual to observe
that while some components share features, others do not; this is probably because they
incorporate changes in technology or in agents’ preferences in different ways. Hence, a
valid hypothesis maybe that while specific subsets of components share common features,
others do not.1
In this paper, we adopt the strategy of Espasa and Mayo-Burgos (2013) and focus
only on common trends. We generalize the approach in several dimensions and provide
all theoretical results to support the strategy.An important contribution in this regard is
showing that subsets of components that share single common stochastic trends, which we
denote as fully cointegrated, can be discovered bypairwise methods using three alter native
strategies for testing cointegration.
The problem of how to discover unknown restrictions in multivariate models is also
present in the dynamic factors models (DFM) literature. Several authors have shown that
if the data contain non-pervasive factors (i.e. factors that are common only to a reduced
subset of series), the results are more accurate when factors are extracted from data that
are informative about them (see e.g. Boivin and Ng, 2006; Beck, Hubrich and Marcellino,
2015). Proposals to deal with non-pervasive factors can be found in Karadimitropoulou and
Le´on-Ledesma (2013), Moench, Ng and Potter (2013), Breitung and Eickmeier (2015),
Bailey, Kapetanios and Pesaran (2015) (BKP hereafter), Bailey, Holly and Pesaran (2015)
(BHP hereafter) and Ando and Bai (2015).
The closest approaches to ours are those of Ando and Bai (2015), BKP and BHP. In
these cases, the authors restrict their attention to stationary series, assume that the cross-
sectional dimension goes to infinity, and require the usual restrictions of DFM on the serial
and cross-correlation of idiosyncratic components (see e.g. assumption C in Bai and Ng,
2002). All of these assumptions do not fit our framework of interest.
We face the problem of identifying subsets (possibly small) of components that share
only one common trend. Apart from dealing with I(1) variables, our strategy has three
additional advantages, which derive from the fact that it does not rely on any type of
cross-sectional averaging method. First, we do not need the trends to be pervasive to the
whole set of disaggregates. Second, the cross-sectional dimension of the subsets that have
a common trend does not need to go to infinity (our theory works with both fixed Nand
T→∞and with [T,N]→∞). Third, since we do not need idiosyncrasies to average out,
we do not need to impose special restrictions on idiosyncratic serial or cross-correlation
of the components.
The rest of the paper is organized as follows. In section II, we describe our proposal
and three implementation strategies. In section III, we study their asymptotic properties
1Citing a working paper version of Espasa and Mayo-Burgos(2013), Castle and Hendry (2010) also highlight the
importance of including long- and short-run restrictions in individual models for the components.
©2020 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
Get this document and AI-powered insights with a free trial of vLex and Vincent AI
Get Started for FreeStart Your 3-day Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
Start Your 3-day Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
Start Your 3-day Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
Start Your 3-day Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting
Start Your 3-day Free Trial of vLex and Vincent AI, Your Precision-Engineered Legal Assistant
-
Access comprehensive legal content with no limitations across vLex's unparalleled global legal database
-
Build stronger arguments with verified citations and CERT citator that tracks case history and precedential strength
-
Transform your legal research from hours to minutes with Vincent AI's intelligent search and analysis capabilities
-
Elevate your practice by focusing your expertise where it matters most while Vincent handles the heavy lifting