Board of Go vernors of the Federal Reserv e System
In ter na tional Finance Discussion Papers
Number 838
Augu st 2005
General-to-specificModeling:
An Overview and Selected Bibliography
Julia Campos, Neil R. Ericsson, and David F. Hendry
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General-to-specificModeling:
An Overview and Selected Bibliography
JuliaCampos,NeilR.Ericsson,andDavidF.Hendry
∗
Abstract : This paper discusses the econ om etric methodology of general-to-specific
modeling, in wh ich the modeler simplifies an initially general model that adequa tely
c haracterizes the empirical evidence within his or her theoretical framework. Central
aspects of this app roach inclu de the theory of reduction, dynamic specification, model
selection procedures, model selection criteria, model comparison, encompassing, com-
puter automa tion, and empirical implementation. This paper thus reviews the theory
of reduction, summa rizes the appro ach of general-to-specific modeling, and discusses
the econom etr ics of model selection, noting that general-to-specificmodelingisthe
practical em bodiment of reduction. This paper then summ ar izes fift y-s even articles
k e y to the development of general-to-specificmodeling.
Keywor ds: coin tegration, conditional m odels, data min ing, diagnostic testing, dy-
namic specification, econometric methodology, encom passin g, equilibrium correction
models, error correction models, exogeneity, general-to-specific modeling, model com-
parison, model design, model evaluation , model selection, non-nested hypotheses,
PcG ets, PcGive, reduction, specific-to-general modeling.
JEL classifications:C1,C5.
∗
Forthcoming as the editors’ introduction to a two-v olume set of readings entitled General-to-
SpecificModelling, Julia Campos, Neil R. Ericsson, and David F. Hendry (eds.), Edward Elgar
Publishing, Cheltenham, 2005. The first author is a professor of econometrics in the Departamento
de Economía e Historia Económica, Facultad de Economía y Empresa, Universidad de Salamanca,
Salamanca 37008 España (Spain). The second author is a staff economist in the Division of In-
ternational Finance, Board of Governors of the Federal Reserve System, Washington, D.C. 20551
U.S.A. The third author is an ESRC Professorial Researc h Fellow and the head of the Economics
Department at the University of Oxford, Oxford, England. They may be reached on the Internet at
jcampos@usal.es, ericsson@frb.gov, and david.hendry@economics.ox.ac.uk respectively. The views
in this paper are solely the responsibility of the authors and should not be interpreted as reflecting
the views of the Board of Governors of the Federal Reserve System or of any other person associated
with the Federal Reserve System. The authors are indebted to Jonathan Halket, Jaime Marquez,
and Kristian Rogers for helpful comments; and to Nicola Mills for seeing the production of this
work through to completion. Scientific Workplace (MacKich an Soft ware, Inc., Poulsbo, Washing-
ton, U.S.A.) eased the preparation of this paper in L
A
T
E
X. This discussion paper is available from the
authors and at www.federalreserve.gov/pubs/ifdp/2005/838/default.htm on the WorldWide Web.
1 Motiva t ion and Overvie w
This paper focuses on a central method for selecting useful empirical models, called
general-to-specificmodeling. In this method, the m odeler simplifies an initially gene ral
model that adequately characterizes the empirical eviden ce within his or her theo-
retical framew ork. While the methodological, statist ical, and emp irical foun d ations
for general-to-specific modeling ha ve been laid do w n over the last several decades, a
burst of activity has occurred in the last half-dozen ye ars, stimulated in fair part b y
Hoover and Perez’s (1999a) dev elopm ent and analysis of a comp uter algorithm for
general-to-specific modeling. The papers discussed herein detail ho w the subject has
advanced to its presen t stage of success and convey the promise of these dev elopm ents
for future empirical researc h . The remainde r of this o verview mo tivates the in te rest in
general-to-specific modeling and summarizes the structure of the subsequent sections
(Sections 2—5).
Econ omists have long sought to develop quantitative models of economic beha v ior
b y blending economic theory with data evidence. The task has pro ved an arduous
onebecauseofthenatureoftheeconomymodeled,theeconomictheory,andthe
data evidence. The economy is a complicated, dynamic, nonlinear, sim u ltaneous,
high-dimensional, and ev olving en tit y; social systems alter o ver time; law s change;
and tec hnological innovations occur. Thus, the target is not only a moving one; it be-
ha v es in a distinctly nonstationary manner, both evolving over time and being subject
to sudden and unanticipated shifts. Econom ic theories are highly abstract and sim-
plified ; and they also chan ge ov er time, with conflicting rival explanation s sometimes
coexisting. T he data evidence is tarnished: economic magnitud es are inaccurately
measured and subject to substantiv e revisions, and man y important variables are not
even observable. The data themselv es are often time series wher e samples are short,
highly aggregated, heterogeneous, time-dependen t, and in ter-dependen t. Econom et-
ric modeling of econom ic time series has nev e rtheless strived to disco ver sustainab le
and interpreta ble relationships between observed economic variab les. T his paper
focuses on general-to-specific modeling, in wh ich the modeler simplifies an initially
general model that adequately c haracterizes the empirical evidence within his or her
theoretical framework. T h is method has proved useful in practice for selecting em-
pirical economic models.
The difficulties of empirical modeling are well reflected in the slow ness of empirical
progress, providing plen ty of ammunitio n for critics. Howev er , part of the problem
may be internal to the discipline, deriving from inappropriate modeling methods.
The “con ventional” approac h insists on a complete theoretical model of the phe-
nomena of interest prior to data analysis, leaving the empirical evidence as little
more than quantitative clothing. Unfortunately, the com plexity and nonstationar-
it y of economies ma kes it impro b able than an yone–ho wever brilliant–co uld deduce
apriorithe multitude of quantitative equations c haracterizin g the behavior of mil-
lions of disparate and competing agents. Without a radical change in the discipline’s
meth odology, empirical progress seems doomed to remain slo w.
The situation is not as bleak as just described, for two reasons. First, the accu-
mulation of kno w ledge is progressive, implying that one does not need to know all
1
the answers at the start. Otherwise, no science could have advanced. Although the
best empirical model at any given time ma y be supplanted later, it can provide a
springboard for further discovery. Data-b ase d m odel selection need not raise serious
concerns: this im plication is established below and is demonstrated b y the actual
behavior of model selection algorithms.
Second, inconsistencies between the implications of any conjectured model and
the observ ed data are often easy to detect. The ease of model rejection worries some
economists, yet it is also a powerful advantage by helping sort out which models are
empirically adequate and which are not. Constructive progress may still be difficu lt
because “w e don’t know what w e don’t kno w, and so w e cannot know how best to
findoutwhatwedon’tknow”. Thedichotomybetweenmodeldestructionandmodel
construction is an old one in the p hilosop hy of science. Wh ile critical evaluation
of empirical evidence is a destructive use of econometrics, it can also establish a
legitimate basis for empirical models.
To undertake empirical modeling, one m ust begin b y assuming a probabilit y struc-
ture for the data, which is tantamou nt to conjecturing the data generating process.
Because the economic mechanism is itself unkn own, the relevant probability struc-
ture is also unknown, so one must proceed iterativ ely: conjecture the data generation
process (DG P ), develop the associated probabilit y theory, use that theory for model-
ing empirical evidence, and revise the starting point when the results do not match
consistently. The developm ent of economet ric theory highlig hts this iterativ e pro-
gression: from stationarit y assum ptions, through integrated-cointegrated systems, to
general nonstationa ry mixing processes, as empirica l evidence revealed the inadequacy
of each earlier step. Further developmen ts will undoubtedly occur, leading to a still
more useful foundation for empirical modeling. See Hendr y (1995a) for an extensive
treatment of progressive researc h strategies.
Ha ving postulated a reasonable probability basis for the DGP, including the pro-
cedures used for data measurem ent and its collection, the next issue concerns what
classes of model migh t be useful. The theory of reduction (discussed in Section 2)
explains ho w empirical models arise and what their status is, noting that they are
not facsimiles of the DGP. Specifically, empirical models describe the beha v ior of a
relatively small set of variables–often from one to seve ral h und red–and neve r the
many millions of distinct variab les present in most economies.
A k ey concept here is that of the local DG P, which is the probability mec h anism
in the space of those variables under analysis. The theory of reduction shows how
the local DGP arises as a simplification of a vastly more general DGP involving
millions of variables. The usefulness of a given local DGP depends on it capturin g
sustainable links, whic h in turn depends par tly on the theor etica l fram e work and
partly on data accuracy. An econometric model cannot do better than capture the
salien t characteristics of its corresponding local DGP . The extent to wh ich the model
does capture those characteristics depends both on its specification at least embedding
the local DG P and on the goodness of its selection.
Ther e are thu s two distinct conceptual steps in modeling, albeit ones closely re-
lated in practice. First, specify a useful information set for a “well-behaved” local
DGP. Second, select a “good” empirical model of that local DGP.
2
A viable methodology for empirical modeling is an in tegral component of ac hieving
the second step. Despite the controversy surrounding every aspect of econometric
methodology, the “LSE” (or London Sch ool of Economics) approac h has emerged as
a leading me thodology for empirical modeling; see Hend ry (1993) for an o verview.
One of the LSE appro ach’s main tenets is general-to-specific modeling, sometimes
abbreviated as Gets. In general-to-specific modeling, empirical analysis starts with a
general statistical model that captures the essential c ha racteristics of the underlyin g
dataset, i.e., that general model is congruen t. Then , that general model is reduced in
comp lex ity by elimin atin g statistically insignificant variables, checking the va lidity of
the reductions at ev ery stage to ensure congruence of the fin ally selected model.
The papers discussed below articulate many reasons for adopting a genera l-to-
specific approac h. First amongst these reasons is that general-to-specific modeling
implem ents the theory of reduction in an empirical context. Section 2 summar izes
the theory of reduction, and Section 3 discusses general-to-specificmodelingasthe
empirica l analogue of reduction .
General-to -specific modeling also has excellent c ha racteristics for model selection,
as documented in Monte Carlo studies of autom atic general-to -specific modeling al-
gorithms. Hoo ver and Perez (1999a) we re the firsttoevaluatetheperformanceof
general-to-specific modeling as a general approach to econometric model building. To
analyze the general-to-specific approach systematica lly, Hoo ver and Perez mechanized
the dec is ions in gene ral-to - s pecific modeling by coding them in a compu ter algorithm.
In doing so, Hoover and Perez also mad e important advances in practical modeling.
To appreciate Hoover and Perez’s con trib utions to general-to-specific m odeling,
consider the m ost basic steps that such an algorithm follo ws.
1. Ascertain that the general statistical model is congruent.
2. Eliminate a variable (or variab les) that satisfies the selection (i.e., simp lification)
criteria.
3. Chec k that the simplified model remains congruent.
4. Contin u e steps 2 and 3 until none of the rem a inin g variables can be eliminated.
P agan (1987) and other critics have argued that the outcome of general-to-specific
modeling ma y depend on the simplification path chosen– tha t is, on the order in
which var iables are eliminated an d on the data transformations adop ted –and so the
selected m odel might vary with the in vestigator. Many redu ction paths certainly
could be considered from aninitialgeneralmodel.
Hoover and Perez (1999a) turned this potential draw b ack in to a virtue b y explor-
ing man y feasible paths and seeing which models result. When searches do lead to
different model selections, encom passing tests can be used to discrim ina te between
these models, with only the surviving (po ssibly non-nested) specification s retained. If
multiple models are found that are both congruen t and encompassing, a new general
model can be formed from their union, and the simplificationprocessisthenre-
applied. If that union model re-occurs, a final selection am on g the competing models
can be made by using (say) information criteria. Oth erw ise, a unique, congruent,
encom passin g reduction has been loca ted.
3