A Brief History of General‐to‐specific Modelling*
| Published date | 01 February 2024 |
| Author | David F. Hendry |
| Date | 01 February 2024 |
| DOI | http://doi.org/10.1111/obes.12578 |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 86, 1 (2024) 0305-9049
doi: 10.1111/obes.12578
A Brief History of General-to-specific Modelling*
DAVID F. HENDRY
Climate Econometrics, Nuffield College, University of Oxford, Oxford, UK
(e-mail: david.hendry@nuffield.ox.ac.uk)
Abstract
We review key stages in the development of general-to-specific modelling (Gets).
Selecting a simplified model from a more general specification was initially implemented
manually, then through computer programs to its present automated machine learning
role to discover a viable empirical model. Throughout, Gets applications faced many
criticisms, especially from accusations of ‘data mining’— no longer pejorative— with
other criticisms based on misunderstandings of the methodology, all now rebutted. A prior
theoretical formulation can be retained unaltered while searching over more variables
than the available sample size from non-stationary data to select congruent, encompassing
relations with invariant parameters on valid conditioning variables.
I. Introduction
General-to-specific modelling, Gets, has a long history of important methodological devel-
opments, but has faced many criticisms, especially as being mindless ‘data mining’, now no
longer pejorative, and other criticisms often based on misunderstandings of its properties.
The key stages in Gets development are reviewed, leading to its present automated
machine learning role. Gets can search over more variables than the available sample
size from wide-sense non-stationary data to select congruent, encompassing relations
with invariant parameters on valid conditioning variables. This brief history draws
on many sources where more detailed discussions of various aspects can be found
(see Morgan, 1990, and Qin, 1993,2013, for histories of econometrics and Klein, 1997,
for a history of time series analysis). In particular, Ericsson (2004,2021) discusses the
writing of Dynamic Econometrics (Hendry, 1995) and the backgrounds to automated
Gets, indicator saturation estimation, and the development of the implementing software
(see Klein, 1987, Doornik and Hendry, 1999, and Renfro, 2009, for histories of
econometric computing). Ericsson also reviews a number of my empirical modelling
JEL Classification numbers: C5, C18.
*Financial support from Nuffield College is gratefully acknowledged as are valuable comments on the paper
by Anindya Banerjee, Jennie Castle, Jurgen Doornik, Neil Ericsson and Andrew Martinez. Many important
contributions to research on Gets were made by (inter alia) Julia Campos, Jennifer Castle, Jurgen Doornik, Rob
Engle, Neil Ericsson, Kevin Hoover, Søren Johansen, Katarina Juselius, Hans-Martin Krolzig, Grayham Mizon,
Bent Nielsen, Peter Phillips, Felix Pretis, Jean Franc¸ois Richard and Aris Spanos. All calculations and graphs use
PcGive and OxMetrics.
1
©2023 The Authors. Oxford Bulletin of Economics and Statistics published by Oxford University and John Wiley & Sons Ltd.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and
reproduction in any medium, provided the original work is properly cited.
2Bulletin
studies of housing and mortgage markets, consumers’ expenditure, money demand,
television advertising, and climate change, most jointly with co-authors, and provides
an extensive bibliography. Even so, there is too large a number of important empirical
applications by others to record here, hence the title ‘brief’.
The structure of the paper is as follows. Section II discusses developments till the
late 1970s of model selection by general-to-specific modelling (also known as the LSE
approach). Section III links Gets to encompassing and the theory of reduction as its
methodological basis. Section IV describes some of the important later developments
of Gets, then section Vconsiders the extensions of Gets to contracting and expanding
multiple-path searches needed once the number of variables (n) to be searched over
exceeds the available sample size (T). In particular, this extension is required for indicator
saturation estimators. Section VI notes the essential contributions of computer software,
and section VII concludes. Throughout, the main criticisms of ‘data mining’, as data-
based model selection was often called, are addressed, as are counter criticisms of simply
estimating a theory-specified model.
II. Early developments of Gets
This section focuses on three key aspects in the early development of Gets: its comparison
with specific-to-general approaches, selection criteria and distinguishing endogenous
dynamics from error autocorrelation (COMFAC).
General-to-specific versus specific-to-general
To date, model selection by a general-to-specific approach has been mainly time
series focused, especially macroeconomics: see Hendry (2020). Much of the structure
of econometrics was formalized by Haavelmo (1944), essentially assuming a viable
economic theory context (see Moene and Rødseth, 1991, Spanos, 1989, and Hendry,
Spanos and Ericsson, 1989).1Although Koopmans (1937) had noted the need for ‘a
reductionist approach of proceeding from general to simple’ as discussed by Hendry
and Morgan (1995), the Gets story really begins with Sargan (1957), who emphasized
the dangers of over-simplification when model building.2Sargan was concerned that
economic theory was too abstract given the complexities of data, so that large numbers of
estimated regression equations excluded relevant variables, as well as misinterpreting tests
that had been applied to many hypotheses. Nevertheless, Sargan was a lone voice against a
deluge of existing criticisms of anything other than estimating a theory-based specification,
facing the early 1940s John Maynard Keynes– Jan Tinbergen debate and ‘measurement
without theory’ by Koopmans (1947) (on both, see Hendry and Morgan, 1995).
However, Anderson (1962) demonstrated that general-to-specific (Gets) dominated
simple-to-general (Sig) when selecting the degree of a polynomial regression, and
in Anderson (1971) showed the same conclusion applied to selecting the lag length
1However, in Haavelmo (1958), he complained about ‘‘the shortcomings of basic economic theory’’, p. 355.
2Denis Sargan was discussing a paper by Fisher (1956)intheOxford Bulletin, also discussed by Albert Ando,
Franco Modigliani, Milton Friedman, Trygve Haavelmo, Lawrence Klein and James Tobin, all six later Economics
Nobel Laureates.
©2023 The Authors. Oxford Bulletin of Economics and Statistics published by Oxford University and John Wiley & Sons Ltd.
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