Hendry Busniss Cycles Empirics 2235123

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Econometrics and Business Cycle Empirics

Author(s): David F. Hendry

Source: The Economic Journal , Vol. 105, No. 433 (Nov., 1995), pp. 1622-1636

Published by: Wiley on behalf of the Royal Economic Society

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The Economic Journal, 105 (November), I622-I636. ) Royal Economic Society I995. Published by Blackwell

Publishers, io8 Cowley Road, Oxford OX4 iJF, UK and 238 Main Street, Cambridge, MA 02I42, USA.

ECONOMETRICS AND BUSINESS CYCLE

EMPIRICS*

David F. Hendry

Business cycle empirics have long been a central arena for the debate about the

roles of economic theory and econometrics in modelling economic time-series

data: some famous historical examples are Moore (I9I4), Keynes (I939) and

Koopmans (I947). Sources for potential disagreements include that the entire

economic system is involved, and unobservable stochastic 'forces' seem more

than usually prominent in determining the outcome. Not only do these

constitute two aspects about which it is hard to theorise, they are equally

difficult to model empirically. There are both positive arguments for and

negative arguments against according a dominant role to either 'theory' or

'evidence', not least because it is unclear what constitutes admissible instances

of either in the absence of the other. We first review what precludes a purely

theoretical approach, what prevents a purely empirical approach, and hence

why an interactive approach is imperative. Even so, both the relative

importance of the two ingredients and their substantive contents are likely to

remain, at issue.

First, concerning the economy, considerable empirical evidence suggests that

it is a dynamic, non-linear, high dimensional, and evolving entity, so studying

it is difficult. Society and social systems alter over time, laws change, and

technological innovations occur, so establishing any invariants of an economic

system is not easy. Such difficulties adversely afflict both theory and empirical

modelling.

Secondly, concerning the observations, time-series data in economics are

heterogeneous, non-stationary, time dependent, and interdependent, so it is

difficult to acquire knowledge from the available empirical information. Again,

such factors also make it hard to theorise about the properties of the underlying

system. A more direct critique of the empirical enterprise is that samples are

short and highly aggregated, economic magnitudes are inaccurately measured,

are subject to considerable revision, and important variables are not measured

or are unobservable, so inferences are both imprecise and tentative. Combined

with the simultaneity, non-constancy, and high dimensionality of economic

data, a purely empirical approach seems to many to be precluded. Other

criticisms of econometric approaches include worries about 'data mining', pre-

test biases, a lack of genuine identifiability, and 'collinearity'- sometimes

combined with a belief that theory can compensate. An overemphasis on a

* This research was financed in part by grants Rooo233447 and Boo2200I2 from the United Kingdom

Economic and Social Research Council. Helpful comments from Mike Clements, Jurgen Doornik, Neil

Ericsson, Bronwyn Hall, Grayham Mizon, John Muellbauer, Danny Quah and an anonymous referee are

gratefully acknowledged. The paper is closely based on Hendry (I 993) and draws heavily on Hendry (I 995)

as background, and Hendry and Morgan (I995) for historical context.

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data-based methodology induces sample dependence of models, namely, results

which vary across different samples.

Thirdly, concerning economic theory, it can deliver important insights into

how an economic system might function, enhanced by the fact that we are also

agents. This should not be extrapolated to the belief that theory is 'correct'

since in practice, economic theories are seriously incomplete, highly aggregate,

make demanding assumptions about economic agents, rely on an unstated

multitude of ceteris paribus assumptions, change over time, and co-exist with

rival explanations. Thus, no firm theoretical basis exists either: that arm-chair

theoretical deduction could be claimed to tell us more about reality than

empirical study is a relic of a failed scholasticism. No matter how good

economic theory may be, it is manifestly inadequate to characterise many

salient aspects of real-world economies. An overemphasis on theory, which at

the extreme involves imposing the theory model on data, leads to the theory

dependence of results, where the very relevance of empirical evidence changes as

theory progresses.

All models - theory or empirical - are not born equal, and economics needs

those which are useful for understanding economic behaviour, for testing

economic theories, for forecasting, and for analysing economic policy. All four

objectives involve discovering sustainable empirical relationships between

observed economic magnitudes, and rejecting models which lack desirable

characteristics. This viewpoint directs the subsequent analysis. Since the

economy is too large and complicated to sustain 'true' models, empirical

models are invariably simplifications and, in that sense, inevitably false.

Consequently, we require other criteria than truth to judge empirical models.

This formulation and its related concepts are discussed in Hendry (I995). The

two main concepts used below are congruence and encompassing. The former

denotes that the empirical model matches the available evidence in all

measured attributes (e.g. is consistent with the theory from which it was

ostensibly derived, with unexplained components that are innovations against

available information, and parameters that are constant when assumed so,

etc.). The latter denotes that the model of interest can account for the results

of rival models of the same phenomena (see Mizon and Richard, I986).

Congruent, encompassing models need not be 'true' in any sense.

My experience is that economic theory and econometrics combine fruitfully

and produce more than either individually, highlighting the advantages of a

joint approach. Either could be used in isolation, but if used alone is shown

below to have drawbacks as part of a process of accumulating knowledge about

economic behaviour: substantive progress only seems likely from a combined

approach. That conclusion, however, does not resolve the issues of what theory,

what evidence, and how they are to be combined.

The structure of the paper is as follows. We first comment on the potential

role of economic theory, then consider any likely precedence of theory or

evidence in general. Since structure is central to the sustainability of economic

relations, Section III defines it as invariance under extensions of the

information set over time, across regimes, and for new sources. The main result

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is that partial knowledge of structure can be acquired empirically without prior

omniscience, whereas theory alone cannot deliver structure in principle.

Section IV considers the problems of theory dependence and sample

dependence when data modelling by econometric methods, against the

background that empirical evidence is essential to distinguish between rival

theoretical views. Finally, Section V examines the extent to which alternative

modelling approaches are likely to lead to the discovery of structure. It shows

that some approaches fail to determine structure on one or more of its

requirements, so they cannot offer a viable route for structural econometrics.

In particular, calibration may lose insights gleaned from the theory, and is

subject to potentially serious problems of both theory dependence and sample

dependence. However, other econometric approaches could yield aspects of

economic structure.

I. ECONOMC THEORY

The positive arguments for basing empirical research on economic analysis are

powerful. First, the principles of economic theory are nearly independent of the

specific phenomena to be explained as they rely on assumptions about latent

propensities of economic agents (e.g. individualistic utility maximisers). What

could have been a weakness has proved to be a strength, since ad hoc arguments

infrequently hold sway, and most economic analyses are recognisably similar in

broad outline, have clear commonalties, and rarely represent a sequence of

disparate analyses. Although the same principles apply to many empirical

problems, crucial details differ including what function is maximised, what its

arguments are, what constraints operate, and what information is used.

Further, institutional frameworks can play a key role. Whether economic

incentives operate is not contentious, but the 'detailed' issues are precisely why

empirical evidence is essential to make our science operational. For example,

tastes and technology may not prove to be a useful basis for 'structural' analysis

due to their endogenous responses to other economic factors.

Secondly, 'explanations' by economic theory could apply despite there

being no quantitative laws (see Robbins, I932), although the absence of any

evidence may render the concept of 'explanation' empty. Even so, one could

imagine a world where price and quantity were never reliably related, yet

'laws' of supply and demand operated. However, this positive argument for

theory only becomes a negative one for econometrics with the unsubstantiated

claim that useful empirical regularities do not exist.

Thirdly, economic analysis has a perceived general success in explaining

economic behaviour, from why the postman delivers our mail, through why

health care is hard to deliver effectively, to why the 'Oil crisis' would not end

economic growth. However, some issues have not yielded, one of the most

salient being high levels of unemployment in OECD countries. Moreover, the

success is a 'broad sweep' explanation, not always accompanied by precise and

accurate quantitative statements about magnitudes, speeds of adjustment to

change etc. This is exactly the basis on which econometrics was founded.

Finally, economic concepts and models are an essential component of our




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cognitive structure, and it is difficult to think about economic events without

invoking aspects of existing theory. The consistency and generality of economic

theory endow it with considerable power as a first-order description of

individual economic behaviour in relatively static circumstances. However,

theories are drastic abstractions which focus on only a few phenomena in

isolation from other potential influences. Even at their best, they are incomplete

and idealised descriptions. Notwithstanding the rhetoric of the real business

cycle (RBC) literature, there is a large gap between an abstract theory of an

unrationed, inter-temporal optimising agent and an empirical model of

aggregate behaviour. Other sources of information and forms of reasoning than

just economic theory are obviously admissible in formulating and analysing

parameters of interest: theory needs to be used flexibly to guide an analysis

rather than be simply imposed on data.

II. PRECEDENCE OF THEORY OR EVDENCE

Whether theoretical advances lead or follow empirical discoveries depends

partly on the quality of, and pre-eminence accorded to, theory: both orderings

occur in practice. Since new contributions can affect all existing knowledge in

an empirical science, neither can claim logical precedence. Substantive

reconstructions of any aspect can overturn the existing edifice. Nevertheless,

granted an insistence on progression, neither contradictory empirical evidence,

nor new theories, alone will reject the status quo. Empirical anomalies may act

as prompts for discovery, but the only available theory will almost never be

rejected by adverse evidence alone: a better alternative is needed to sustain the

scientific goal of progressive understanding. Similarly, new theories may lead

to questioning the status of previous evidence, and often stimulate a search for

new findings, but 'protection' strategies also exist, so haphazard progress, or

even degeneration, can result. In any case, the rejection of an empirical model

does not entail rejecting the theory from which it was derived, nor does

corroborating the model entail the validity of the theory (Section V considers

testing rival theories in econometrics).

Further, theory is neither necessary nor sufficient for successful policy

intervention. Necessity is refuted by a counter example from biochemistry:

aspirin is perhaps the most common scientific intervention in everyday life as

a pain killer, but until recently there was no rigorous theory as to how it

worked. This did not stop aspirin from working (the initial use of aspirin -

acetylsalicylic acid - arose as a folklore remedy for hangovers, based on

brewing willow-tree bark, of which it is a natural constituent: see Weissmann,

I99I). Sufficiency falls on the example of a theory that is violently false, such

as that a huge dose of arsenic will cure a cold with no side effects.

Three famous earlier debates concerned with whether to acquire economic

knowledge from directly analysing phenomena or from 'fundamental theory'

in the context of business cycle analysis are extensively discussed in Hendry and

Morgan (I995) (see Moore, I9I4, versus Wright, I9I5; Keynes, I939, versus

Tinbergen, I940; and Koopmans, I947, versus Vining, I949). The outcomes




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served to emphasise the dangers of relying on either theory or evidence in

isolation. Even though the third debate ended as one of research priority, rather

than of the principle of using economic theory and statistical methods in

analysing economic data, a dominant theme of econometrics since then has

been studying empirical models through pre-specified theoretical models. The

RBC literature is an extreme example thereof.

III. STRUCTURE

Structure has many meanings in econometrics (see, inter alia, the different

notions in Frisch (I 934), Haavelmo (I 944), Wold and Jureen (I 953), Bardsen

and Fisher (I 993), and Juselius (I 993), as well as connoting 'being derived

from inter-temporal optimisation by economic agents ). Here, we define

structure as the set of invariant features of the economic mechanism. This

captures the idea of permanence in a framework which is hidden from direct

view and needs to be uncovered. The parameters of an economic structure may

include those of agents' decision rules, but there is no presumption that these

must be derived by inter-temporal optimisation (particularly by a so-called

'representative agent'). Then, e0 defines a structure if it is invariant and

directly characterises the relations of the economy under analysis. Thus,

structure need not be identifiable, and correspondences between model and

reality are not fully testable. However, an immediate consequence of the

definition is that a parameter can be structural only if it is invariant to an

extension of the sample period (constant), invariant to changes elsewhere in the

economy (regime shifts), and invariant to extensions of the information set

(adding more variables): all three of these aspects are open to empirical

scrutiny, so necessary attributes of structure are testable even if sufficient ones

are not.

IV THEORY DEPENDENCE VERSUS SAMPLE DEPENDENCE

There are many extant approaches in empirical economics and we consider a

caricature of three of these. Theory dependence is construed as the problem

that the 'empirical' results are merely a quantified theory model and are

therefore no more or less valid than the initial theory; sample dependence is the

opposite extreme that the results are subject to important sampling vagaries.

A. Theory-driven Approaches

The RBC approach starts with a theoretical model and estimates (or

calibrates) its parameters; deliberately little testing is done on any one

occasion, and little is learnt from the data. Between occasions, however, the

theory is revised in the light of manifest failures, then reapplied to (essentially)

the same data, inducing a sophisticated data-mining problem. Such 'theory-

driven' approaches, where a model is derived from a priori theory and calibrated

from data evidence, suffer from theory dependence. Their credibility depends

on the credibility of the theory from which they arose, and when that theory

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is discarded, so is the associated evidence (see Kydland and Prescott, I 99 I). Since

economic theory is progressing rapidly, theory dependence is likely to induce

transient and non-structural evidence.

If an empirical implementation is discarded when it is inconsistent with the

theory, the theory loses credibility, whereas if the implementation is not

discarded, the theory must be altered to avoid maintaining contradictory

propositions. Of course, the phenomena that induced rejection may be

unrelated to the ostensible nature of the problem: for example, the

measurement process may be at fault. Evidence that this is so must be adduced

to rescue the theory model. In practice, the empirical model, the

measurement instruments, and the theory may be revised till consistency is

achieved. Depending on how model design is implemented, the result may or

may not lack credibility. But postulating an endless sequence of theories that

get rejected in turn fails to incorporate learning from the evidence. My

proposed solution is to conduct research in a progressive framework of

successively encompassing, congruent models consolidated by empirically

relevant theories.

As an aside, so-called 'stylised facts' seem to denote abstracted summary

statistics of aspects of marginal distributions. A set of stylised facts may be a

reasonable summary of the salient features of each element of the data taken in

isolation (e.g. an output growth rate of 2-5%, a savings rate of io%, a real

interest rate of 400, and an unemployment rate of 80 ), yet jointly can be

inconsistent with the evidence in that there is a negligible probability of

observing the vector of claimed stylised facts, given the joint distribution of the

original data. There seem no good reasons for eschewing internally consistent

multivariate estimates- and avoiding rejection of poor empirical models is a

bad reason. However, recent work suggests some convergence of 'estimation'

approaches, and indeed models: see Burnside and Eichenbaum (I 994) and

Watson (I 993) .

By ignoring the possibility that the claimed 'parameters' of RBC models

may not in fact be constant, existing calibration approaches, matching a subset

of data moments, induce a perverse sample-dependence problem - for the very

models that apparently strive to avoid this difficulty. If any of the parameters

are non-constant, then the values used are dependent on the particular sample

or historical epoch chosen, and will vary as the period changes: the estimated

model then suffers from both theory dependence and sample dependence.

B. Data-driven Approaches

An alternative approach abandons structural modelling, and estimates data-

descriptive models such as ARIMAs or VARs. 'Data-driven' approaches,

where models are developed to closely describe the data, may suffer from

sample dependence in that accidental and transient data features are embodied

as tightly in the model as permanent aspects, so that extensions of the data set

may reveal predictive failure. Restrictions are sometimes imposed to offset this

problem. These could be data-based as in Box and Jenkins (I976) modelling

with its 'identification' procedures, or claim an extraneous source as in the

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'Minnesota prior' which shrinks lagged dependent variable parameters to

unity and others to zero (see Doan et al. I984). However, such restrictions will

deliver structure only if the resulting parameters chance to coincide with

invariant aspects of the underlying relations (even so, such restrictions could

improve forecasting: see Clements and Hendry, I994).

Empirical models which are not quantitative facsimiles of theory models are

sometimes dismissed as the outcome of 'data mining'. This phrase connotes a

prejudiced search for corroborative evidence (see Leamer, I978), and may

even be believed to vitiate any substantive role for empirical evidence in

economics. Since models can be designed to satisfy selection criteria, we must

distinguish that legitimate productive activity from one of 'torturing data till

a false confession is obtained'. Following Gilbert (1 986), distinguish weak data

mining, whereby corroboration is sought for a prior belief, from strong data

mining, in which conflicting evidence is either camouflaged or not reported. A

model-search process which deliberately camouflages conflicting results is

unscientific, but is open to adversarial scrutiny by seeing how well the resulting

model accounts for the findings of rival studies. Thus, the resolution of potential

data-mining criticisms is to explain the Gestalt of empirical evidence: strong

data mining fails when there is already conflicting evidence; weak data mining

fails when other models cannot be emcompassed.

C. Data Modelling Using Economic Theory Guidelines

A further approach attempts to merge inference from data with guidelines from

economic theory, emphasising empirical models as reductions which can be

designed to be congruent. Cointegration analysis, seeking to establish robust

conclusions about long-run relations between integrated (usually I ( i))

variables, has been extensively adopted in this approach, but is by no means

restricted to it. Relative to the previous extremes, this approach seeks to

characterise data parsimoniously in a general economic theoretical framework,

as well as providing a statistical baseline against,which other models can be

evaluated (see Spanos, I990).

Simplification procedures are often used in data modelling, and these could

attenuate or exacerbate sample dependence: the former by eliminating

irrelevant factors, the latter if the influences of accidental aspects are captured

more 'significantly'. This last difficulty may be offset by reference to a theory

model, but is a transient problem since an extended data sample will reveal the

accidental nature of the earlier effects by their becoming less significant.

Such an approach also often relies on multiple tests. A misplaced objection

to statistical testing is that test statistics can be made insignificant by

construction. Selecting an empirical model to ensure that a test criterion is

insignificant guarantees such a outcome - independently of the correctness of

the solution. Some of the worries about 'data mining' may arise because tests

can be made insignificant by iteratively revising models in the light of adverse

data evidence. Certainly, model design strategies can lead to the mis-

interpretation of diagnostic tests, so a clear reporting distinction is needed

between tests which are used as within-sample model-design criteria (reflecting

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the exploitation of data evidence), and genuine tests in the Neyman-Pearson

sense (using previously unavailable evidence). Even so, rejection on any test

entails model invalidity or a type I error. While multiple testing may raise

worries about 'pre-test' problems, not doing so ignores the opposite problem

of never discovering that the model class is incorrect (see Mayo, I98I). The

analysis in White (I990) shows that testing provides one strategy for ensuring

the selection of an acceptable data representation, providing the significance

level of the complete testing process is controlled and declines as the sample

grows.

Rejecting a null hypothesis against a specific hypothesis provides no

information about an appropriate alternative model. This is a minor variant of

the Duhem-Quine thesis (see Cross, I982), which also reveals that rejecting an

empirical model does not entail rejecting the theory from which it was derived,

nor does accepting .the model entail the validity of the theory: mutually

incompatible congruent empirical models can be designed to match in-

consistent theories (see Mizon, I993). Although most empirical testing is to

ascertain the status of assumptions behind empirical models, not to test

theories, the latter is feasible since incompatible congruent empirical models

cannot mutually encompass each other.

D. Overview

All three approaches base their conclusions on a mixture of theory and

evidence, but accord very different weights to the components, and often have

very different constructions of admissible theory. These major differences in

approach reflect genuine difficulties in empirical economics and are not merely

fads. There are obvious dangers in trying to learn more from a relatively short,

autocorrelated, non-homogeneous, non-stationary, imprecise and inaccurate

data sample than it can reasonably yield. The problem of sample dependence

of findings is especially acute in practice because all aspects of an empirical

model may be designed to satisfy pre-assigned criteria, even parameter

constancy (highlighting the distinction between explanation and prediction:

see Hendry and Starr, I993). Conversely, the ability of pure theory to deliver

ideas about permanent relationships is far from established. Since congruent

and invariant models depend on the identification of structural relations, the

major issue remains the respective weight to be accorded to avoiding theory

dependence and sample dependence of econometric evidence. Good empirical

modelling helps mitigate the sample dependence of findings while linking

evidence to theory.

V DETERMNNG STRUCTURE INPRACTCE

Economies are subject to regime shifts as well as technological and financial

innovations which force adaptation and learning by economic agents, and

induce different forms of non-stationarity. Empirical studies in econometrics

are limited in scope over time and information sets, comprising a small set of

variables relative to the potentially important determinants of any economic




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phenomena. Thus, it is unsurprising that our evidence is less secure than in

natural sciences, a difficulty exacerbated by the minuscule resources allocated

to data collection in economics.

Important and unresolved issues of principle in econometrics are whether

structure exists, and if so, whether it can be 'identified' in any sense. As implied

by our framework, when structure exists it could be determined in a progressive

research strategy: partial knowledge of structure may be acquired without

complete knowledge in advance of what structure comprises. Without such a

result, structural knowledge could not be acquired till everything was known,

contradicting the realised progress of science. However, identification has three

other attributes: 'uniqueness', 'correspondence to the desired entity' and

'satisfying the assumed interpretation'. For example, a regression of quantity

on price delivers a unique function of the data second moments, but need not

correspond to any underlying demand behaviour, and may be incorrectly

interpreted as a supply schedule. Koopmans et al. (I950) formalised conditions

for the uniqueness of coefficients in simultaneous systems, often the sense

intended in econometrics, but conditions for the correspondence of model

parameters to those of DGPs, or for the correct interpretation of parameters,

are not easily specified. In practice, the meaning of 'identified' can be

ambiguous as in 'Have you identified the parameters of the money demand

function?'.

The logic of our analysis is perhaps best seen by applying it to five aspects

of econometric modelling. Each of these either offers what I deem to be

achievable conditions for structure to be determined, or highlights the

drawbacks of approaches that seem unlikely to achieve structural knowledge.

A. Identified Cointegration Vectors

Given an information set {xt}, where xt is n x i, consider the cointegrated VAR:

h-1

Axt = Ai Axt-i + al}Xt_h + ut where ut - IN. [o, ], (I)

where oc and P are n x r matrices of feedback and cointegrating coefficients

respectively (see Johansen, I 988, Phillips, i 99 i, and Banerjee et al., I 993). Even

assuming that (i) captures the long-run dependencies, any coordinate system

is acceptable for the cointegration space without further restrictions, since

e4i' _ aPP-l,' = e*p*'. Unless sufficient valid identifying restrictions are

imposed, the set of cointegrating vectors will not correspond to a structural

relation, and need not be interpretable in the light of theory. When the

empirical analysis yields oc*p*' instead of o4p', let the first vector be *' xt_ =

ft1 Xl + P2 xt-1. This has two consequences. First, by using PI* xt-, rather than

pj xt_, the unwanted I(o) combination Pjxt_ makes the resulting equation

non-structural. Secondly, if PJ xt_ enters any other equation, weak exogeneity

will be violated with adverse implications for inference (see Engle et al. I983,

and Hendry, I 994) .

Conversely, consider the cointegrating matrix P once sufficient valid

restrictions have been imposed to ensure unique identification, such that the

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resulting characterisation of the long run matches that of the DGP and is

constant over prolonged periods of time. Then , would constitute structural

knowledge. To identify the structural cointegration vectors J8 certainly

necessitates both careful formulation of the long-run economic analysis and

thorough testing of the requisite restrictions. Johansen and Juselius (I992)

show the latter aspect in operation, and Hendry and Mizon (I993) investigate

the former. However, once an identifiable , is determined, it is unique under

expansions of the information set. This follows because I'xt is I(o), so once J is

identifiable then that is not affected by the presence of additional variables,

whether these are I(o) or I(i) (cointegrated or not).

In a linear system, , is an invariant, and cointegration could be defined by

that property. Premultiply (i) by any non-singular n x n matrix Q:

h-1

QAAxt = -i At Ax + QxP'Xt-h + tu*

i=l

The adjustment coefficients are altered to Qx, whereas J'xt remain the

cointegrating vectors. This result extends to 1(2) processes, and to conditional

models of yt given zt when xt = (Yt: zt) (the transformation E12 21 only affects

a). As Ericsson et al. (I994) show, P is also invariant to seasonal adjustment

filters like XI I. We conclude that identified P represent one aspect of structure

that may be determinable without omniscience.

B. Orthogonal Parameters

A second example is a linear conditional model with parameters which are

super exogenous on variables which are both mutually orthogonal and are

orthogonal to excluded functions of information. Extending the information set

over time, across regime shifts or by additional variables will not alter the

knowledge achieved: being invariant and constant, such parameters satisfy all

the testable attributes of structurality. This situation may arise when economic

agents orthogonalise information in their decision rules, in which case, the

entailed model could capture structural information. Meta-considerations

would be needed to decide whether the parameters in fact correspond to the

actual hidden structure. I do not claim that the world must satisfy the

assumptions needed to sustain the existence of such a structure, merely that

when it does so, a suitable progressive research strategy may acquire empirical

knowledge without complete prior information as to the nature of that

structure. The point is one of principle: regression parameters could embody

structure. In practice, conditional models with nearly orthogonal parameters

have proved surprisingly durable and robust. An example is provided by the

long sequence of studies on the UK consumption function from Davidson et al.

(I 978) through Hendry et al. (I990) to Muellbauer and Murphy (I 993) and

Harvey and Scott (I 993): the original dynamic and 'error-correction'

parameters recur in greatly extended information sets and over longer time

periods, despite considerable regime shifts. This is one answer to Eichenbaum's

question about the importance of such parameters. Another answer is that a




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value of zero for the error-correction term may entail non-stationarity,

affecting inference, as well as the presence of cointegrating structure.

By way of contrast, other features sometimes emphasised in modelling seem

to need an additional assumption of omniscience to justify a claim to

structurality. We consider two examples.

C. Inappropriate Estimation

Perhaps the greatest worry from using 'inconsistent' estimators is that they

deliver different parameters in the empirical model from those which would

have been obtained by more appropriate methods. Consequently, structure

could be lost despite a clever prior analysis. For example, as Campos et al.

(I996) show, if the two-step method in Engle and Granger (I987) is used when

the imposed common factor restrictions are invalid (see Kremers et al., I992),

breaks in marginal distributions are carried into the procedure, so structurality

can be lost in the model despite its presence in reality. Thus, the operating

characteristics of our tools merit careful analysis to ensure that econometric

procedures do not lose hard-earned insights.

Since so-called 'calibration' methods have been subjected to little formal

analysis, and what exists is rather critical (see Canova et al., I992, Kim and

Pagan, I993, and Hoover, I995), one must be concerned that implementations

of the resulting models could be non-structural even when the theory happened

to capture some structural aspects of reality. Worse still, present intertemporal

optimisation theory seems ineffective without arbitrary assumptions about

stochastic forcing functions (such as technical progress) which do not themselves

have a theory basis as yet.

D. Residual Analysis

A similar difficulty plagues attempts to interpret residuals on econometric

equations, such as for impulse-response analysis (see Sims, I 980), or for

correspondence of residuals to 'supply' or 'demand' shocks (see Blanchard and

Quah, I989). A model could embody (partial) structure in its parameters yet

have non-structural errors: Section B provided an example. Focusing on the

unmodelled component in an analysis seems unlikely to be as productive as

seeking to interpret what has been explicitly modelled.

A more mixed possibility arises in a fifth example.

E. Expectations and Structure

A theory, or class of models (rather than just a single exemplar), could be

rejected by testing against a class of encompassing contenders which are mutual

counter examples: see Favero and Hendry (I 992) who use an idea proposed in

Boland (i 989). For example, the Lucas (I 976) critique leads to an expectations'

based counter example to any claimed invariant conditional model. However,

the converse also holds, so a 'crucial' test between them is feasible: there

are automatically two mutually inconsistent theories when expectations are

involved (namely, feedback and feedforward models: see Hendry, I 988). When

no member of one class can encompass a congruent representative of the other,




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I995] ECONOMETRCS AND BUNESS CYCLE 633

then that class is in grave doubt. If agents form expectations about zt when

planning Yt, then behavioural parameters +1 will depend on the expectations

parameters +2 of the zt process, and should alter when +2 changes. This is a

testable hypothesis, with the implication that the failure of +1 to change when

+2 changes is inconsistent with the critique.

Since both conditional and expectational models can be derived from the

sequential joint density of (Yt: zt), and all sensible forms of expectations should

be cointegrated with outcomes, aspects of the Lucas critique are testable in a

framework of cointegration where some of the expectations variables are

subject to regime shifts (see Hendry and Neale, I988). The constancy of a

conditional model in the face of a changing marginal process entails that agents

do not use expectations models to predict future values of relevant decision

variables. A possible explanation is that contingent planning dominates

forward-looking behaviour in practice. Another possibility is that agents form

expectations without using models, but use data-based predictors, perhaps

because of high costs of information collection and processing (especially the

difficulty of discovering a usable approximation to the DGP when it is subject

to intermittent regime shifts ). The detailed analysis in Ericsson and Irons

(I996) suggests that almost no test of the critique has ever rejected the

conditional model, whereas several results are inconsistent with the critique.

We conclude that the possible role of expectations in agent behaviour does

not preclude learning about structure from data evidence.

V. CONCLUSION

The development of congruent, theory-consistent, and encompassing models

remains a viable route in econometrics, even with non-stationary data. When

structure represents an invariant feature of reality, progressive research can

discover it in part without prior knowledge of the whole: Keynes's worry about

the prior necessity of a complete specification is misplaced. Tests for necessary

attributes of structure exist, especially its invariance to extensions of the

information over longer time periods (constancy), regime changes (parameter

invariance, or super exogeneity in conditional models), or additional sources of

variation (added variables). Even though empirical models are perforce

reductions of the data generation process, and can be explicitly designed to

satisfy various criteria, they can embody structure. Conversely, an emphasis on

interpreting the unmodelled component in a model seems misplaced, as

'errors ' could be structural only with the additional assumption of omniscience.

A key property of economic analysis is to delineate the economic structure,

but by itself, it cannot endow a parameter with structurality since the mapping

involved is between a theory and a model, whereas structure concerns a

mapping between a model and reality. The best is that theory delivers a model

which happens to capture structure after appropriate estimation. Since

structure must be invariant under extensions of the information set, it cannot

be learnt from theory alone without an assumption of omniscience. However,




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I634 THE ECONOMCJOURNAL NOVEMBER

structure potentially can be learned from empirical evidence without prior

knowledge as to what exists to be discovered. Hence, economic theory is neither

necessary nor sufficient for determining structure, although it remains one of

several useful tools for the econometrician.

Nevertheless, economic theory is likely to prove a productive companion in

empirical econometric research, by suggesting directions for discovering

structure, excluding unlikely contenders, helping identify structure (in all three

senses of uniqueness, correspondence and interpretation), and consolidating

empirical findings. Theoretical reasoning is of considerable help in determining

parameters of interest, although how one discovers useful knowledge remains

an art rather than a science. But good econometric modelling practice is also

important if structure is not to be lost from inappropriate procedures. The

negative reasons for using economic theory have less force than is sometimes

argued, in that best practice does not fall foul of them, even if there remain

potential problems due to moral hazard (selecting only a favourable subset of

results to report, etc.). The positive aspects of theory provide a much stronger

case without resolving what are the precise theories of relevance and how best

to use them. Finally, the two-way interaction between evidence and theory

would benefit from being strengthened in practice.

Nuffield College, Oxford

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