Introduction to Econometrics

Description
Econometrics is a rapidly developing branch of economics which, broadly speaking, aims to give empirical content to economic relations.

econometrics
1 What is Econometrics?
Econometrics is a rapidly developing branch of economics which, broadly speaking, aims to give
empirical content to economic relations. The term ‘econometrics’ appears to have been first sed by
!awel "iompa as early as 1#1$% althogh it is &agnar 'risch, one of the fonders of the Econometric
(ociety, who shold be given the credit for coining the term, and for establishing it as a sb)ect in the
sense in which it is known today *see 'risch, 1#+,, p. #-.. Econometrics can be defined generally as
‘the application of mathematics and statistical methods to the analysis of economic data’, or more
precisely in the words of (amelson, /oopmans and (tone *1#-0.,
... as the 1antitative analysis of actal economic phenomena based on the concrrent development of
theory and observation, related by appropriate methods of inference *p. 102..
3ther similar descriptions of what econometrics entails can be fond in the preface or the
introdction to most te4ts in econometrics. 5alinvad *1#,,., for e4ample, interprets econometrics
broadly to inclde ‘every application of mathematics or of statistical methods to the stdy of economic
phenomena’. "hrist *1#,,. takes the ob)ective of econometrics to be ‘the prodction of 1antitative
economic statements that either explain the behavior of variables we have already seen, or forecast
*i.e. predict. behavior that we have not yet seen, or both’. "how *1#6+. in a more recent te4tbook
sccinctly defines econometrics ‘as the art and science of sing statistical methods for the
measrement of economic relations’.
7y emphasi8ing the 1antitative aspects of economic problems, econometrics calls for a ‘nification’
of measrement and theory in economics. Theory withot measrement, being primarily a branch of
logic, can only have limited relevance for the analysis of actal economic problems. While
measrement withot theory, being devoid of a framework necessary for the interpretation of the
statistical observations, is nlikely to reslt in a satisfactory e4planation of the way economic forces
interact with each other. 9either ‘theory’ nor ‘measrement’ on their own is sfficient to frther or
nderstanding of economic phenomena. 'risch was flly aware of the importance of sch a
nification for the ftre development of economics as a whole, and it is the recognition of this fact
that lies at the heart of econometrics. This view of econometrics is e4ponded most elo1ently by
'risch *1#++a. in his editorial statement and is worth 1oting in fll:
... econometrics is by no means the same as economic statistics. 9or is it identical with what we call
general economic theory, althogh a considerable portion of this theory has a definitely 1antitative
character. 9or shold econometrics be taken as synonymos with the application of mathematics to
economics. E4perience has shown that each of these three view;points, that of statistics, economic
theory, and mathematics, is a necessary, bt not by itself a sfficient, condition for a real
nderstanding of the 1antitative relations in modern economic life. <t is the unification of all three
that is powerfl. =nd it is this nification that constittes econometrics.
This nification is more necessary today than at any previos stage in economics. (tatistical
information is crrently accmlating at an nprecedented rate. 7t no amont of statistical
information, however complete and e4act, can by itself e4plain economic phenomena. <f we are not to
get lost in the overwhelming, bewildering mass of statistical data that are now becoming available, we
need the gidance and help of a powerfl theoretical framework. Withot this no significant
interpretation and coordination of or observations will be possible.
The theoretical strctre that shall help s ot in this sitation mst, however, be more precise,
more realistic, and, in many respects, more comple4, than any heretofore available. Theory, in
formlating its abstract 1antitative nations, mst be inspired to a larger e4tent by the techni1e of
observation. =nd fresh statistical and other factal stdies mst be the healthy element of distrbance
that constantly threatens and dis1iets the theorist and prevents him from coming to rest on some
inherited, obsolete set of assmptions.
This mtal penetration of 1antitative economic theory and statistical observation is the essence
of econometrics *p. 2..
Whether other fonding members of the Econometric (ociety shared 'risch’s viewpoint with the same
degree of conviction is, however, debatable, and even today there are no dobt economists who regard
sch a viewpoint as either ill;conceived or impractical. 9evertheless, in this srvey < shall follow
'risch and consider the evoltion of econometrics from the nification viewpoint.
2 Early =ttempts at >antitative &esearch in Economics
Empirical analysis in economics has had a long and fertile history, the origins of which can be traced
at least as far back as the work of the 1,th;centry !olitical =rithmeticians sch as William !etty,
?regory /ing and "harles @avenant. The political arithmeticians, led by (ir William !etty, were the
first grop to make systematic se of facts and figres in their stdies. *(ee, for e4ample, (tone *1#60.
on the origins of national income acconting.. They were primarily interested in the practical isses of
their time, ranging from problems of ta4ation and money to those of international trade and finance.
The hallmark of their approach was ndobtedly 1antitative and it was this which distingished
them from the rest of their contemporaries. !olitical arithmetic, according to @avenant *1,#6, !art <,
p. 2. was ‘the art of reasoning, by figres, pon things relating to government’, which has a striking
resemblance to what might be offered today as a description of econometric policy analysis. =lthogh
the political arithmeticians were primarily and nderstandably preoccpied with statistical
measrement of economic phenomena, the work of !etty, and that of /ing in particlar, represented
perhaps the first e4amples of a nified 1antitativeAtheoretical approach to economics. <ndeed
(chmpeter in his History of Economic Analysis *1#-0. goes as far as to say that the works of the
political arithmeticians ‘illstrate to perfection, what Econometrics is and what Econometricians are
trying to do’ *p. 2$#..
The first attempt at 1antitative economic analysis is attribted to ?regory /ing, who is credited with
a price;1antity schedle representing the relationship between deficiencies in the corn harvest and
the associated changes in corn prices. This demand schedle, commonly known as ‘?regory /ing’s
law’, was pblished by "harles @avenant in 1,##. The /ing data are remarkable not only becase they
are the first of their kind, bt also becase they yield a perfectly fitting cbic regression of price
changes on 1antity changes, as was sbse1ently discovered independently by Whewell *16-$.,
Wicksteed *166#. and by Ble *1#1-.. =n interesting accont of the origins and natre of ‘/ing’s law’
is given in "reedy *1#6,..
3ne important consideration in the empirical work of /ing and others in this early period seems to
have been the discovery of ‘laws’ in economics, very mch like those in physics and other natral
sciences. This 1est for economic laws was, and to a large e4tent still is, rooted in the desire to give
economics the stats that 9ewton had achieved for physics. This was in trn reflected in the conscios
adoption of the method of the physical sciences as the dominant mode of empirical en1iry in
economics. The 9ewtonian revoltion in physics, and the philosophy of ‘physical determinism’ that
came to be generally accepted in its aftermath, had far;reaching conse1ences for the method as well
as the ob)ectives of research in economics. The ncertain natre of economic relations only began to
be flly appreciated with the birth of modern statistics in the late 1#th centry and as more statistical
observations on economic variables started to become available. /ing’s law, for e4ample, was viewed
favorably for almost two centries before it was 1estioned by Ernest Engel in 16,1 in his stdy of
the demand for rye in !rssia *see (tigler, 1#-0, p. 1$0..
The development of statistical theory at the hands of ?alton, Edgeworth and !earson was taken p in
economics with speed and diligence. The earliest applications of simple correlation analysis in
economics appear to have been carried ot by Ble *16#-, 16#,. on the relationship between
paperism and the method of providing relief, and by Cooker *1#$1. on the relationship between the
marriage;rate and the general level of prosperity in the Dnited /ingdom, measred by a variety of
economic indicators sch as imports, e4ports, and the movement in corn prices. <n his applications
Cooker is clearly aware of the limitations of the method of correlation analysis, especially when
economic time series are involved, and begins his contribtion by an important warning which
contines to have direct bearing on the way econometrics is practised today:
The application of the theory of correlation to economic phenomena fre1ently presents many
difficlties, more especially where the element of time is involved% and it by no means follows as a
matter of corse that a high correlation coefficient is a proof of casal connection between any two
variables, or that a low coefficient is to be interpreted as demonstrating the absence of sch
connection *p. 06-..
<t is also worth noting that Cooker seems to have been the first to se time lags and de;trending
methods in economics for the specific prpose of avoiding the time;series problems of sprios or
hidden correlation that were later emphasi8ed and discssed formally by Ble *1#2,..
7enini *1#$E., the <talian statistician, according to (tigler *1#-0. was the first to make se of the
method of mltiple regression in economics. Ce estimated a demand fnction for coffee in <taly as a
fnction of coffee and sgar prices. 7t as arged in (tigler *1#-0, 1#,2. and more recently detailed in
"hrist *1#6-., it is Cenry 5oore *1#10, 1#1E. who was the first to place the statistical estimation of
economic relations at the centre of 1antitative analysis in economics. Throgh his relentless efforts,
and those of his disciples and followers !al @oglas, Cenry (chlt8, Colbrook Working, 'red Wagh
and others, 5oore in effect laid the fondations of ‘statistical economics’, the precrsor of
econometrics. 5oore’s own work was, however, marred by his rather cavalier treatment of the
theoretical basis of his regressions, and it was therefore left to others to provide a more satisfactory
theoretical and statistical framework for the analysis of economic data. The monmental work of
(chlt8, The Theory and the Measurement of Demand *1#+6., in the Dnited (tates and that of =llen
and 7owley, Family Expenditure *1#+-., in the Dnited /ingdom, and the pioneering works of Fenoir
*1#1+., Wright *1#1-, 1#26., Working *1#2E., Tinbergen *1#+$. and 'risch *1#++b. on the problem of
‘identification’ represented ma)or steps towards this ob)ective. The work of (chlt8 was e4emplary in
the way it attempted a nification of theory and measrement in demand analysis% whilst the work on
identification highlighted the importance of ‘strctral estimation’ in econometrics and was a crcial
factor in the sbse1ent developments of econometric methods nder the aspices of the "owles
"ommission for &esearch in Economics.
Early empirical research in economics was by no means confined to demand analysis. =nother
important area was research on bsiness cycles, which in effect provided the basis of the later
development in time;series analysis and macroeconometric model bilding and forecasting.
=lthogh, throgh the work of (ir William !etty and other early writers, economists had been aware
of the e4istence of cycles in economic time series, it was not ntil the early 1#th centry that the
phenomenon of bsiness cycles began to attract the attention that it deserved. *=n interesting accont
of the early developments in the analysis of economic time series is given in 9erlove and others,
1#E#.. "lement Gglar *161#H1#$-., the 'rench physician trned economist, was the first to make
systematic se of time;series data for the specific prpose of stdying bsiness cycles, and is credited
with the discovery of an investment cycle of abot EH11 years dration, commonly known as the
Gglar cycle. 3ther economists sch as /itchin, /8nets and /ondratieff followed Gglar’s lead and
discovered the inventory cycle *+H- years dration., the bilding cycle *1-H2- years dration. and the
long wave *0-H,$ years dration., respectively. The emphasis of this early research was on the
morphology of cycles and the identification of periodicities. Fittle attention was paid to the
1antification of the relationships that may have nderlain the cycles. <ndeed, economists working in
the 9ational 7rea of Economic &esearch nder the direction of Wesley 5itchell regarded each
bsiness cycle as a ni1e phenomenon and were therefore relctant to se statistical methods e4cept
in a non;parametric manner and for prely descriptive prposes *see, for e4ample, 5itchell, 1#26 and
7rns and 5itchell, 1#0E.. This view of bsiness cycle research stood in sharp contrast to the
econometric approach of 'risch and Tinbergen and clminated in the famos methodological
interchange between T)alling /oopmans and &tledge Iining abot the roles of theory and
measrement in applied economics in general and bsiness cycle research in particlar. *This
interchange appeared in the =gst 1#0E and 5ay 1#0# isses of The Review of Economics and
Statistics..
+ The 7irth of Econometrics
=lthogh, as < have arged above, 1antitative economic analysis is a good three centries old,
econometrics as a recogni8ed branch of economics only began to emerge in the 1#+$s and the 1#0$s
with the fondation of the Econometric (ociety, the "owles "ommission in the Dnited (tates, and the
@epartment of =pplied Economics *@=E. nder the directorship of &ichard (tone in the Dnited
/ingdom. *= highly readable blow;by;blow accont of the fonding of the first two organi8ations can
be fond in "hrist *1#-2, 1#6+., while the history of the @=E is covered in (tone, 1#E6.. The reasons
for the lapse of more than two centries between the pioneering work of !etty and the recognition of
econometrics as a branch of economics are comple4, and are best nderstood in con)nction with, and
in the light of, histories of the development of theoretical economics, national income acconting,
mathematical statistics, and compting. (ch a task is clearly beyond the scope of the present paper.
Cowever, one thing is clear: given the mlti;disciplinary natre of econometrics, it wold have been
e4tremely nlikely that it wold have emerged as a serios branch of economics had it not been for
the almost synchronos development of mathematical economics and the theories of estimation and
statistical inference in the late 1#th centry and the early part of the 2$th centry. *=n interesting
accont of the history of statistical methods can be fond in /endall, 1#,6..
3f the for components of econometrics, namely, a priori theory, data, econometric methods and
compting techni1es, it was, and to a large e4tent still is, the problem of econometric method which
has attracted most attention. The first ma)or debate over econometric method concerned the
applicability of the probability calcls and the newly developed sampling theory of &.=. 'isher to the
analysis of economic data. =s 5organ *1#6,. arges in some detail, prior to the 1#+$s the application
of mathematical theories of probability to economic data was re)ected by the ma)ority in the
profession, irrespective of whether they were involved in research on demand analysis or on bsiness
cycles. Even 'risch was highly sceptical of the vale of sampling theory and significance tests in
econometrics. Cis ob)ection to the se of significance tests was not, however, based on the
epistemological reasons that lay behind &obbins’s and /eynes’s criticisms of econometrics. Ce was
more concerned with the problems of mlticollinearity and measrement errors which he believed,
along with many others, afflicted all economic variables observed nder non;controlled e4perimental
conditions. 7y drawing attention to the fictitious determinateness created by random errors of
observations, 'risch *1#+0. lanched a severe attack on regression and correlation analysis which
remains as valid now as it was then. With characteristic clarity and boldness 'risch stated:
=s a matter of fact < believe that a sbstantial part of the regression and correlation analyses which
have been made on economic data in recent years is nonsense for this very reason Jthe random errors
of measrementK *1#+0, p. ,..
<n order to deal with the measrement error problem 'risch developed his conflence analysis and
the method of ‘bnch maps’. =lthogh his method was sed by some econometricians, notably
Tinbergen *1#+#. and (tone *1#0-., it did not find mch favor with the profession at large. This was
de, firstly, to the indeterminate natre of conflence analysis and, secondly, to the alternative
probabilistic rationali8ations of regression analysis which were advanced by /oopmans *1#+E. and
Caavelmo *1#00.. /oopmans proposed a synthesis of the two approaches to the estimation of
economic relations, namely the error;in;variables approach of 'risch and the error;in;e1ation
approach of 'isher, sing the likelihood framework% ths re)ecting the view prevalent at the time that
the presence of measrement errors per se invalidates the application of the ‘sampling theory’ to the
analysis of economic data. <n his words <t is the conviction of the athor that the essentials of 'risch’s
criticism of the se of 'isher’s specification in economic analysis may also be formlated and
illstrated from the conceptal scheme and in the terminology of the sampling theory, and the
present investigation is an attempt to do so *p. +$..
The formlation of the error;in;variables model in terms of a probability model did not, however,
mean that 'risch’s criticisms of regression analysis were nimportant, or that they cold be ignored.
Gst the opposite was the case. The probabilistic formlation helped to focs attention on the reasons
for the indeterminacy of 'risch’s proposed soltion to the problem. <t showed also that withot some
a priori information, for e4ample, on the relative importance of the measrement errors in different
variables, a determinate soltion to the estimation problem wold not be possible. What was
important, and with hindsight path;breaking, abot /oopmans’s contribtion was the fact that it
demonstrated the possibility of the probabilistic characteri8ation of economic relations, even in
circmstances where important deviations from the classical regression framework were necessitated
by the natre of the economic data.
/oopmans did not, however, emphasi8e the wider isse of the se of stochastic models in
econometrics. <t was Caavelmo who e4ploited the idea to the fll, and arged forceflly for an e4plicit
probability approach to the estimation and testing of economic relations. <n his classic paper
pblished as a spplement to Econometrica in 1#00, Caavelmo defended the probability approach on
two gronds: firstly, he arged that the se of statistical measres sch as means, standard errors and
correlation coefficients for inferential prposes is )stified only if the process generating the data can
be cast in terms of a probability model: ‘'or no tool developed in the theory of statistics has any
meanin ; e4cept, perhaps, for descriptive prposes ; without bein referred to some stochastic
scheme’ *p. iii.. (econdly, he arged that the probability approach, far from being limited in its
application to economic data, becase of its generality is in fact particlarly sited for the analysis of
‘dependent’ and ‘non;homogeneos’ observations often encontered in economic research. Ce
believed what is needed is to assme that the whole set of, say n, observations may be considered as
one observation of n variables *or a ‘sample point’. following an n;dimensional !oint probability law,
the ‘e4istence’ of which may be prely hypothetical. Then, one can test hypotheses regarding this )oint
probability law, and draw inference as to its possible form, by means of one sample point *in n
dimensions. *p. iii..
Cere Caavelmo ses the concept of )oint probability distribtion as a tool of analysis and not
necessarily as a characteri8ation of ‘reality’. The probability model is seen as a convenient abstraction
for the prpose of nderstanding, or e4plaining or predicting events in the real world. 7t it is not
claimed that the model represents reality in all its minte details. To proceed with 1antitative
research in any sb)ect, economics inclded, some degree of formali8ation is inevitable, and the
probability model is one sch formali8ation. This view, of corse, does not avoid many of the
epistemological problems that srrond the concept of ‘probability’ in all the varios senses
*sb)ective, fre1entist, logical, etc.. in which the term has been sed, nor is it intended to do so. =s
Caavelmo himself pt it:
The 1estion is not whether probabilities exist or not, bt whether ; if we proceed as if they e4isted ;
we are able to make statements abot real phenomena that are ‘correct for practical prposes’ *1#00,
p. 0+..
The attraction of the probability model as a method of abstraction derives from its generality and
fle4ibility, and the fact that no viable alternative seems to be available.
Caavelmo’s contribtion was also important as it constitted the first systematic defence against
/eynes’s *1#+#. inflential criticisms of Tinbergen’s pioneering research on bsiness cycles and
macroeconometric modelling. The ob)ective of Tinbergen’s research was twofold. 'irstly, to show how
a macroeconometric model may be constrcted and then sed for simlation and policy analysis
*Tinbergen, 1#+E.. (econdly, ‘to sbmit to statistical test some of the theories which have been pt
forward regarding the character and cases of cyclical flctations in bsiness activity’ *Tinbergen,
1#+#, p. 11.. Tinbergen assmed a rather limited role for the econometrician in the process of testing
economic theories, and arged that it was the responsibility of the ‘economist’ to specify the theories
to be tested. Ce saw the role of the econometrician as a passive one of estimating the parameters of an
economic relation already specified on a priori gronds by an economist. =s far as statistical methods
were concerned he employed the regression method and 'risch’s method of conflence analysis in a
complementary fashion. =lthogh Tinbergen discssed the problems of the determination of time
lags, trends, strctral stability and the choice of fnctional forms, he did not propose any systematic
methodology for dealing with them. <n short, Tinbergen approached the problem of testing theories
from a rather weak methodological position. /eynes saw these weaknesses and attacked them with
characteristic insight */eynes, 1#+#.. = large part of /eynes’s review was in fact concerned with
technical difficlties associated with the application of statistical methods to economic data. =part
from the problems of the ‘dependent’ and ‘non;homogeneos’ observations mentioned above, /eynes
also emphasi8ed the problems of misspecification, mlti;collinearity, fnctional form, dynamic
specification, strctral stability, and the difficlties associated with the measrement of theoretical
variables. <n view of these technical difficlties and /eynes’s earlier warnings against ‘indctive
generalisation’ in his Treatise on "robability *1#21., it was not srprising that he focssed his attack
on Tinbergen’s attempt at testin economic theories of bsiness cycles, and almost totally ignored the
practical significance of Tinbergen’s work on econometric model bilding and policy analysis *for
more details, see !esaran and (mith, 1#6-a..
<n his own review of Tinbergen’s work, Caavelmo *1#0+. recogni8ed the main brden of the criticisms
of Tinbergen’s work by /eynes and others, and arged the need for a general statistical framework to
deal with these criticisms. =s we have seen, Caavelmo’s response, despite the views e4pressed by
/eynes and others, was to rely more, rather than less, on the probability model as the basis of
econometric methodology. The technical problems raised by /eynes and others cold now be dealt
with in a systematic manner by means of formal probabilistic models. 3nce the probability model was
specified, a soltion to the problems of estimation and inference cold be obtained by means of either
classical or of 7ayesian methods. There was little that cold now stand in the way of a rapid
development of econometric methods.
0 Early =dvances in Econometric 5ethods
Caavelmo’s contribtion marked the beginning of a new era in econometrics, and paved the way for
the rapid development of econometrics on both sides of the =tlantic. The likelihood method soon
became an important tool of estimation and inference, althogh initially it was sed primarily at the
"owles "ommission where Caavelmo himself had spent a short period as a research associate.
The first important breakthrough came with a formal solution to the identification problem which had been
formulated earlier by E. Working (1927. !y defining the concept of "structure# in terms of the $oint probability
distribution of obser%ations& 'aa%elmo (19(( presented a %ery general concept of identification and deri%ed the
necessary and sufficient conditions for identification of the entire system of e)uations& including the parameters
of the probability distribution of the disturbances. 'is solution& although general& was rather difficult to apply in
practice. *oopmans& +ubin and ,eipnik& in a paper presented at a conference organi-ed by the .owles
.ommission in 19(/ and published later in 19/0& used the term "identification# for the first time in
econometrics& and ga%e the now familiar rank and order conditions for the identification of a single e)uation in
a system of simultaneous linear e)uations. The solution of the identification problem by *oopmans (19(9 and
*oopmans& +ubin and ,eipnik (19/0& was obtained in the case where there are a priori linear restrictions on
the structural parameters. They deri%ed rank and order conditions for identifiability of a single e)uation from a
complete system of e)uations without reference to how the %ariables of the model are classified as endogenous
or e1ogenous. 2ther solutions to the identification problem& also allowing for restrictions on the elements of the
%ariance3co%ariance matri1 of the structural disturbances& were later offered by Wegge (194/ and 5isher
(1944. 6 comprehensi%e sur%ey of some of the more recent de%elopments of the sub$ect can be found in 'siao
(1978.
7roadly speaking, a model is said to be identified if all its strctral parameters can be obtained from
the knowledge of its nderlying )oint probability distribtion. <n the case of simltaneos e1ations
models prevalent in econometrics the soltion to the identification problem depends on whether
there e4ists a sfficient nmber of a priori restrictions for the derivative of the strctral parameters
from the redced;form parameters. =lthogh the prpose of the model and the focs of the analysis
on e4plaining the variations of some variables in terms of the ne4plained variations of other
variables is an important consideration, in the final analysis the specification of a minimm nmber
of identifying restrictions was seen by researchers at the "owles "ommission to be the fnction and
the responsibility of ‘economic theory’. This attitde was very mch reminiscent of the approach
adopted earlier by Tinbergen in his bsiness cycle research: the fnction of economic theory was to
provide the specification of the econometric model, and that of econometrics to frnish statistically
optimal methods of estimation and inference. 5ore specifically, at the "owles "ommission the
primary task of econometrics was seen to be the development of statistically efficient methods for the
estimation of strctral parameters of an a priori specified system of simltaneos stochastic
e1ations.
<nitially, nder the inflence of Caavelmo’s contribtion, the ma4imm likelihood *5F. estimation
method was emphasi8ed as it yielded consistent estimates. /oopmans and others *1#-$. proposed the
‘information;preserving ma4imm;likelihood method’, more commonly known as the 'll
<nformation 5a4imm Fikelihood *'<5F. method, and =nderson and &bin *1#0#., on a sggestion
by 5.=. ?irshick, developed the Fimited <nformation 5a4imm Fikelihood *F<5F. method. 7oth
methods are based on the )oint probability distribtion of the endogenos variables and yield
consistent estimates, with the former tili8ing all the available a priori restrictions and the latter only
those which related to the e1ation being estimated. (oon other comptationally less demanding
estimation methods followed, both for a flly efficient estimation of an entire system of e1ations and
for a consistent estimation of a single e1ation from a system of e1ations. The Two;(tage Feast
(1ares *2(F(. procedre, which involves a similar order of magnitde of comptations as the least
s1ares method, was independently proposed by Theil *1#-0, 1#-6. and 7asmann *1#-E.. =t abot the
same time the instrmental variable *<I. method, which had been developed over a decade earlier by
&eiersol *1#01, 1#0-., and ?eary *1#0#. for the estimation of errors;in;variables models, was applied
by (argan *1#-6. to the estimation of simltaneos e1ation models. (argan’s main contribtion
consisted in providing an asymptotically efficient techni1e for sing srpls instrments in the
application of the <I method to econometric problems. = related class of estimators, known as k;class
estimators, was also proposed by Theil *1#,1.. 5ethods of estimating the entire system of e1ations
which were comptationally less demanding than the '<5F method also started to emerge in the
literatre. These inclded the Three;(tage Feast (1ares method de to Lellner and Theil *1#,2., the
iterated instrmental variables method based on the work of Fyttkens *1#E$., 7rndy and Gorgenson
*1#E1., @hrymes *1#E1.% and the system k;class estimators de to (rivastava *1#E1. and (avin *1#E+..
=n interesting synthesis of different estimators of the simltaneos e1ations model is given by
Cendry *1#E,.. The literatre on estimation of simltaneos e1ation models is vast and is still
growing. <mportant contribtions have been made in the areas of estimation of simltaneos non;
linear models, the seemingly nrelated regression model proposed by Lellner *1#,2., and the
simltaneos rational e4pectations models which will be discssed in more detail below. &ecent
stdies have also focsed on the finite sample properties of the alternative estimators in the
simltaneos e1ation model. <nterested readers shold conslt the relevant entries in this
@ictionary, or refer to the e4cellent srvey articles by Casman *1#6+., by =memiya *1#6+. and by
!hillips *1#6+..
While the initiative taken at the "owles "ommission led to a rapid e4pansion of econometric
techni1es, the application of these techni1es to economic problems was rather slow. This was partly
de to a lack of ade1ate compting facilities at the time. = more fndamental reason was the
emphasis of all the "owles "ommission on the simltaneity problem almost to the e4clsion of other
problems that were known to afflict regression analysis. (ince the early applications of the correlation
analysis to economic data by Ble and Cooker, the serial dependence of economic time series and the
problem of sprios correlation that it cold give rise to had been the single most important factor
e4plaining the profession’s scepticism concerning the vale of regression analysis in economics. =
satisfactory soltion to the sprios correlation problem was therefore needed before regression
analysis of economic time series cold be taken seriosly. &esearch on this important topic began in
the midH1#0$s nder the direction of &ichard (tone at the @epartment of =pplied Economics *@=E.
in "ambridge, England, as a part of a ma)or investigation into the measrement and analysis of
consmers’ e4penditre in the Dnited /ingdom *see (tone and others, 1#-0a.. (tone had started this
work dring the 1#+#H0- war at the 9ational <nstitte of Economic and (ocial &esearch. =lthogh the
first steps towards the resoltion of the sprios correlation problem had been taken by =itken
*1#+0A+-. and "hampernowne *1#06., the research in the @=E introdced the problem and its
possible soltion to the attention of applied economists. 3rctt *1#06. stdied the atocorrelation
pattern of economic time series and showed that most economic time series can be represented by
simple atoregressive processes with similar atoregressive coefficients, a reslt which was an
important precrsor to the work of Lellner and !alm *1#E0. discssed below. (bse1ently in their
classic paper, "ochrane and 3rctt *1#0#. made the important point that the ma)or consideration in
the analysis of stationary time series was the atocorrelation of the error term in the regression
e1ation and not the atocorrelation of the economic time series themselves. <n this way they shifted
the focs of attention to the atocorrelation of distrbances as the main sorce of concern. (econdly,
they pt forward their well;known iterative method for the comptation of regression coefficients
nder the assmption that the errors followed a first order atoregressive process.
=nother important and related development at the @=E was the work of @rbin and Watson *1#-$,
1#-1. on the method of testing for residal atocorrelation in the classical regression model. The
inferential breakthrogh for testing serial correlation in the case of observed time;series data had
already been achieved by von 9emann *1#01, 1#02., and by Cart and von 9emann *1#02.. The
contribtion of @rbin and Watson was, however, important from a practical viewpoint as it led to a
bonds test for residal atocorrelation which cold be applied irrespective of the actal vales of the
regressors. The independence of the critical bonds of the @rbin;Watson statistic from the matri4 of
the regressors allowed the application of the statistic as a general diagnostic test, the first of its type in
econometrics. The contribtions of "ochrane and 3rctt and of @rbin and Watson nder the
leadership of (tone marked the beginning of a new era in the analysis of economic time;series data
and laid down the basis of what is now known as the ‘time;series econometrics’ approach.
The significance of the research at the @=E was not confined to the development of econometric
methods. The work of (tone on linear e4penditre systems represented one of the first attempts to se
theory directly and explicitly in applied econometric research. This was an important breakthrogh.
!reviosly, economic theory had by and large been sed in applied research only indirectly and as a
general method for deciding on the list of the variables to be inclded in the regression model and,
occasionally, for assigning signs to the parameters of the model. *'or an important e4ception, see
5arschak and =ndrews, 1#00.. <n his seminal paper in the Economic #ournal, (tone *1#-0b. made a
significant break with this tradition and sed theory not as a sbstitte for common sense, bt as a
formal framework for deriving ‘testable’ restrictions on the parameters of the empirical model. This
was an important move towards the formal nification of theory and measrement that 'risch had
called for and (chlt8 earlier had striven towards.
- "onsolidation and 'rther @evelopments
The work at the "owles "ommission on identification and estimation of the simltaneos e1ation
model and the development of appropriate techni1es in dealing with the problem of sprios
regression at the @=E paved the way for its widespread application to economic problems. This was
helped significantly by the rapid e4pansion of compting facilities, the general acceptance of
/eynesian theory and the increased availability of time;series data on national income acconts. =s
/lein *1#E1. pt it, ‘The /eynesian theory was simply MaskingM to be cast in an empirical mold’ *p.
01,.. The <(;F5 version of the /eynesian theory provided a convenient and fle4ible framework for
the constrction of macroeconomic models for a variety of prposes ranging from pedagogic to short;
and medim;term forecasting and policy analysis. <n view of /eynes’s criticisms of econometrics, it is
perhaps ironic that his macroeconomic theory came to play sch a central role in the advancement of
econometrics in general and that of macroeconometric modelling in particlar.
<nspired by the /eynesian theory and the pioneering work of Tinbergen, /lein *1#0E, 1#-$. was the
first to constrct a macroeconometric model in the tradition of the "owles "ommission. (oon others
followed /lein’s lead: prominent e4amples of early macroeconometric models inclded the /lein;
?oldberger and the 7rookings;((&" models of the D( economy, and the Fondon 7siness (chool and
the "ambridge ?rowth !ro)ect models of the D/ economy. 3ver a short space of time
macroeconometric models were bilt for almost every indstriali8ed contry, and even for some
developing and centrally planned economies. 5acroeconometric models became an important tool of
ex ante forecasting and economic policy analysis, and started to grow both in si8e and sophistication.
The relatively stable economic environment of the 1#-$s and 1#,$s was an important factor in the
initial sccess en)oyed by macroeconometric models. Whether the se of macroeconometric models in
policy formlation contribted towards the economic stability over this period is, of corse, a
different matter.
The constrction and se of large;scale models presented a nmber of important comptational
problems, the soltion of which was of fndamental significance not only for the development of
macroeconometric modelling, bt also for econometric practice in general. <n this respect advances in
compter technology were clearly instrmental, and withot them it is difficlt to imagine how the
complicated comptational problems involved in the estimation and simlation of large;scale models
cold have been solved. The increasing availability of better and faster compters was also
instrmental as far as the types of problems stdied and the types of soltions offered in the literatre
were concerned. 'or e4ample, recent developments in the area of microeconometrics *see section ,.+
below. cold hardly have been possible if it were not for the very important recent advances in
compting facilities.
The development of economic models for policy analysis, however, was not confined to
macroeconometric models. The inter;indstry inpt;otpt models originating from the seminal
work of Feontief *1#+,, 1#01, 1#-1., and the microanalytic simlation models pioneered by 3rctt and
his colleages *1#,1., were amongst the other inflential approaches which shold be mentioned here.
7t it was the srge of interest in macroeconometric modelling which provided the single most
important impets to the frther development of econometric methods. < have already mentioned
some of the advances that took place in the field of estimation of the simltaneos e1ation model.
3ther areas where econometrics witnessed significant developments inclded dynamic specification,
latent variables, e4pectations formation, limited dependent variables, discrete choice models, random
coefficient models, dise1ilibrim models, and non;linear estimation. The 7ayesian approach to
econometrics was also developed more vigorosly, thanks to the relentless efforts of Lellner, @rN8e
and their colleages. *(ee @rN8e and &ichard *1#6+., and Lellner *1#60, 1#6-. for the relevant
references to theoretical and applied 7ayesian econometric stdies.. <t was, however, the problem of
dynamic specification that initially received the greatest attention. <n an important paper, 7rown
*1#-2. modelled the hypothesis of habit persistence in consmer behavior by introdcing lagged
vales of consmption e4penditres into an otherwise static /eynesian consmption fnction. This
was a significant step towards the incorporation of dynamics in applied econometric research and
allowed the important distinction to be made between the short;rn and the long;rn impacts of
changes in income on consmption. (oon other researchers followed 7rown’s lead and employed his
atoregressive specification in their empirical work.
The ne4t notable development in the area of dynamic specification was the distribted lag model.
=lthogh the idea of distribted lags had been familiar to economists throgh the pioneering work of
<rving 'isher *1#+$. on the relationship between the nominal interest rate and the e4pected inflation
rate, its application in econometrics was not seriosly considered ntil the mid 1#-$s. The geometric
distribted lag model was sed for the first time by /oyck *1#-0. in a stdy of investment. /oyck
arrived at the geometric distribted lag model via the adaptive e4pectations hypothesis. This same
hypothesis was employed later by "agan *1#-,. in a stdy of demand for money in conditions of
hyperinflation, by 'riedman *1#-E. in a stdy of consmption behavior and by 9erlove *1#-6a. in a
stdy of the cobweb phenomenon. The geometric distribted lag model was sbse1ently generali8ed
by (olow *1#,$., Gorgenson *1#,,. and others, and was e4tensively applied in empirical stdies of
investment and consmption behavior. =t abot the same time =lmon *1#,-. provided a polynomial
generali8ation of 'isher’s *1#+E. arithmetic lag distribtion which was later e4tended frther by
(hiller *1#E+.. 3ther forms of dynamic specification considered in the literatre inclded the partial
ad)stment model *9erlove, 1#-6b% Eisner and (trot8, 1#,+. and the mltivariate fle4ible accelerator
model *Treadway, 1#E1. and (argan’s *1#,0. work on econometric time series analysis which we
discss below in more detail. =n e4cellent srvey of this early literatre on distribted lag and partial
ad)stment models is given in ?riliches *1#,E..
"oncrrent with the development of dynamic modelling in econometrics there was also a resrgence
of interest in time;series methods, sed primarily in short;term bsiness forecasting. The dominant
work in this field was that of 7o4 and Genkins *1#E$., who, bilding on the pioneering works of Ble
*1#21, 1#2,., (ltsky *1#2E., Wold *1#+6., Whittle *1#,+.and others, proposed comptationally
manageable and asymptotically efficient methods for the estimation and forecasting of nivariate
atoregressive;moving average *=&5=. processes. Time;series models provided an important and
relatively cheap benchmark for the evalation of the forecasting accracy of econometric models, and
frther highlighted the significance of dynamic specification in the constrction of time;series
econometric models. <nitially nivariate time;series models were viewed as mechanical ‘black bo4’
models with little or no basis in economic theory. Their se was seen primarily to be in short;term
forecasting. The potential vale of modern time;series methods in econometric research was,
however, nderlined in the work of "ooper *1#E2. and 9elson *1#E2. who demonstrated the good
forecasting performance of nivariate 7o4;Genkins models relative to that of large econometric
models. These reslts raised an important 1estion mark over the ade1acy of large econometric
models for forecasting as well as for policy analysis. <t was arged that a properly specified strctral
econometric model shold, at least in theory, yield more accrate forecasts than a nivariate time;
series model. Theoretical )stification for this view was provided by Lellner and !alm *1#E0.,
followed by Trivedi *1#E-., !rothero and Wallis *1#E,., Wallis *1#EE. and others. These stdies
showed that 7o4;Genkins models cold in fact be derived as nivariate final form soltions of linear
strctral econometric models so long as the latter were allowed to have a rich enogh dynamic
specification. <n theory, the pre time;series model cold always be embodied within the strctre of
an econometric model and in this sense it did not present a ‘rival’ alternative to econometric
modelling. This literatre frther highlighted the importance of dynamic specification in econometric
models and in particlar showed that econometric models that are ot;performed by simple
nivariate time;series models most probably sffer from serios specification errors.
The response of the econometrics profession to this time;series criti1e was rather mi4ed and has
taken different forms. 3n the one hand a fll integration of time;series methods and traditional
econometric analysis has been advocated by Lellner and !alm, Wallis and others. This blending of the
econometric methods which Lellner has called the (E5T(= *strctral econometric modelling times;
series analysis. approach is discssed in some detail in Lellner *1#E#.. The (E5T(= approach
emphasi8es that dynamic linear strctral econometric models are a special case of mltivariate time;
series processes, and arges that time;series methods shold be tili8ed to check the empirical
ade1acy of the final e1ation forms and the distribted lag *or transfer fnction. forms implicit in
the assmed strctral model. The modelling process is contined ntil the implicit estimates of the
final e1ation forms and the distribted lag forms of the strctral model are empirically compatible
with the direct time;series estimates of these e1ations.
=n alternative ‘marriage’ of econometric and time;series techni1es has been developed by (argan,
Cendry and others largely at the Fondon (chool of Economics *F(E.. This marriage is based on the
following two premises:
*i. Theoretical economic considerations can at best provide the specification of e1ilibrim or long;
rn relationships between variables. Fittle can be inferred from a priori reasoning abot the time lags
and dynamic specification of econometric relations.
*ii. The best approach to identification of lags in econometric models lies in the tili8ation of time;
series methods, appropriately modified to allow for the e4istence of long;rn relations among
economic variables implied by economic theory.
=lthogh the approach is general and in principle can be applied to systems of e1ations, in practice it
has been primarily applied to modelling one variable at a time. The origins of this approach can be
fond in the two highly inflential papers by (argan *1#,0. on the modelling of money wages, and by
@avidson and others *1#E6. on the modelling of non;drable consmption e4penditres. 7y focsing
on the modelling of one endogenos variable at a time, the F(E approach represents a partial break
with the strctral approach advocated by the "owles "ommission. 7t in an important sense the F(E
approach contines to share with the "owles "ommission the emphasis it places on a priori economic
reasoning, albeit in the form of e1ilibrim or long;period relationships.
, &ecent @evelopments
With the significant changes taking place in the world economic environment in the 1#E$s, arising
largely from the breakdown of the 7retton Woods system and the 1adrpling of oil prices,
econometrics entered a new phase of its development. 5ainsteam macroeconometric models bilt
dring the 1#-$s and 1#,$s, in an era of relative economic stability with stable energy prices and fi4ed
e4change rates, were no longer capable of ade1ately captring the economic realities of the 1#E$s. =s
a reslt, not srprisingly, macroeconometric models and the /eynesian theory that nderlay them
came nder severe attack from theoretical as well as from practical viewpoints. While criticisms of
Tinbergen’s pioneering attempt at macroeconometric modelling were received with great optimism
and led to the development of new and sophisticated estimation techni1es and larger and more
complicated models, the more recent bot of disenchantment with macroeconometric models
prompted a mch more fndamental reappraisal of 1antitive modelling as a tool of forecasting and
policy analysis. =t a theoretical level it is arged that econometric relations invariably lack the
necessary ‘microfondations’, in the sense that they cannot be consistently derived from the
optimi8ing behavior of economic agents. =t a practical level the "owles "ommission approach to the
identification and estimation of simltaneos macroeconometric models has been 1estioned by
Fcas and (argent and by (ims, althogh from different viewpoints. There has also been a move away
from macroeconometric models and towards microeconometric research where it is hoped that some
of the pitfalls of the macroeconometric time;series analysis can be avoided. The response of the
econometric profession as a whole to the recent criticism has been to emphasi8e the development of
more appropriate techni1es, to se new data sets and to call for a better 1ality control of
econometric research with special emphasis on model validation and diagnostic testing.
What follows is a brief overview of some of the important developments of the past two decades.
?iven space limitations and my own interests there are inevitably significant gaps. These inclde the
important contribtions of ?ranger *1#,#., (ims *1#E2. and Engle and others *1#6+. on different
concepts of ‘casality’ and ‘e4ogeneity’, and the vast literatre on dise1ilibrim models *>andt,
1#62% 5addala, 1#6+, 1#6,., random coefficient models *"how, 1#60., continos time models
*7ergstrom, 1#60., non;stationary time series and testing for nit roots *@ickey and 'ller, 1#E#,
1#61% Evans and (avin, 1#61, 1#60% !hillips, 1#6,, 1#6E% !hillips and @rlaf, 1#6,. and small sample
theory *!hillips, 1#6+% &othenberg, 1#60., not to mention the developments in the area of policy
analysis and the application of control theory of econometric models *"how, 1#E-, 1#61% =oki, 1#E,..
,.1 &ational E4pectations and the Fcas "riti1e
=lthogh the &ational E4pectations Cypothesis *&EC. was advanced by 5th in 1#,1, it was not ntil
the early 1#E$s that it started to have a significant impact on time;series econometrics and on
dynamic economic theory in general. What broght the &EC into prominence was the work of Fcas
*1#E2, 1#E+., (argent *1#E+., (argent and Wallace *1#E-. and others on the new classical e4planation
of the apparent breakdown of the !hillips crve. The message of the &EC for econometrics was clear.
7y postlating that economic agents form their e4pectations endoenously on the basis of the true
model of the economy and a correct nderstanding of the processes generating e4ogenos variables of
the model, inclding government policy, the &EC raised serios dobts abot the invariance of the
strctral parameters of the mainstream macroeconometric models in the face of changes in
government policy. This was highlighted in Fcas’s criti1e of macroeconometric policy evalation.
7y means of simple e4amples Fcas *1#E,. showed that in models with rational e4pectations the
parameters of the decision rles of economic agents, sch as consmption or investment fnctions,
are sally a mi4tre of the parameters of the agents’ ob)ective fnctions and of the stochastic
processes they face as historically given. Therefore, Fcas arged, there is no reason to believe that
the ‘strctre’ of the decision rles *or economic relations. wold remain invariant nder a policy
intervention. The implication of the Fcas criti1e for econometric research was not, however, that
policy evalation cold not be done, bt rather than the traditional econometric models and methods
were not sitable for this prpose. What was re1ired was a separation of the parameters of the policy
rle from those of the economic model. 3nly when these parameters cold be identified separately
given the knowledge of the )oint probability distribtion of the variables *both policy and non;policy
variables., wold it be possible to carry ot an econometric analysis of alternative policy options.
There have been a nmber of reactions to the advent of the rational e4pectations hypothesis and the
Fcas criti1e that accompanied it. The least controversial has been the adoption of the &EC as one of
several possible e4pectations formation hypotheses in an otherwise conventional macroeconometric
model containing e4pectational variables. <n this conte4t the &EC, by imposing the appropriate cross;
e1ation parametric restrictions, ensres that ‘e4pectations’ and ‘forecasts’ generated by the model
are consistent. The nderlying economic model is in no way constrained to have particlar /eynesian
or monetarist featres, nor are there any presmptions that the relations of the economic model
shold necessarily correspond to the decision rles of economic agents. <n this approach the &EC is
regarded as a convenient and effective method of imposing cross;e1ation parametric restrictions on
time series econometric models, and is best viewed as the ‘model;consistent’ e4pectations hypothesis.
The econometric implications of sch a model;consistent e4pectations mechanism have been
e4tensively analysed in the literatre. The problems of identification and estimation of linear &E
models have been discssed in detail, for e4ample, by Wallis *1#6$., Wickens *1#62. and !esaran
*1#6E.. These stdies show how the standard econometric methods can in principle be adapted to the
econometric analysis of rational *or consistent. e4pectations models.
=nother reaction to the Fcas criti1e has been to treat the problem of ‘strctral change’ emphasi8ed
by Fcas as one more potential econometric ‘problem’ *on this see Fawson, 1#61.. <t is arged that the
problem of strctral change reslting from intended or e4pected changes in policy is not new and
had been known to the economists at the "owles "ommission *5arschak, 1#-+., and can be readily
dealt with by a more carefl monitoring of econometric models for possible changes in their strctre.
This view is, however, re)ected by Fcas and (argent and other proponents of the rational
e4pectations school who arge for a more fndamental break with the traditional approach to
macroeconometric modelling.
The optimi8ation approach of Fcas and (argent is based on the premise that the ‘tre’ strctral
relations contained in the economic model and the policy rles of the government can be obtained
directly as soltions to well;defined dynamic optimi8ation problems faced by economic agents and by
the government. The task of the econometrician is then seen to be the disentanglement of the
parameters of the stochastic processes that agents face from the parameters of their ob)ective
fnctions. =s Cansen and (argent *1#6$. pt it,
=ccomplishing this task Jthe separate identification of parameters of the e4ogenos process and those
of taste and technology fnctionsK is an absolte prere1isite of reliable econometric policy
evalation. The e4ection of this strategy involves estimating agents’ decision rles )ointly with
models for the stochastic processes they face, sb)ect to the cross;e1ation restrictions implied by the
hypothesis of rational e4pectations *p. 6..
(o far this approach has been applied only to relatively simple set;ps involving aggregate data at the
level of a ‘representive’ firm or a ‘representive’ hosehold. 3ne important reason for this lies in the
rather restrictive and infle4ible econometric models which emerge from the strict adherence to the
optimi8ation framework and the &EC. 'or analytical tractability it has often been necessary to confine
the econometric analysis to 1adratic ob)ective fnctions and linear stochastic processes. This
problem to some e4tent has been mitigated by recent developments in the area of the estimation of
the Eler e1ations *see Cansen and (ingleton, 1#62.. 7t there are still important technical
difficlties that have to be resolved before the optimi8ation approach can be employed in
econometrics in a fle4ible manner. <n addition to these technical difficlties, there are fndamental
isses concerning the problem of aggregation across agents, information heterogeneity, the learning
process, and the effect that these complications have for the implementation of the Fcas;(argent
research programme *cf. !esaran, 1#6E..
,.2 =theoretical 5acroeconometrics
The Fcas criti1e of mainstream macroeconometric modelling has also led some econometricians,
notably (ims *1#6$, 1#62., to dobt the validity of the "owles "ommission style of achieving
identification in econometric models. The view that economic theory cannot be relied on to yield
identification of strctral models is not new and has been emphasi8ed in the past, for e4ample, by
Fi *1#,$.. The more recent disenchantment with the "owles "ommission’s approach has its origins
in the &EC, and the nease with a priori restrictions on lag lengths that are needed if rational
e4pectations models are to be identified *see !esaran, 1#61.. (ims *1#6$, p. E. writes: ‘<t is my view,
however, that rational e4pectations is more deeply sbversive of identification than has yet been
recogni8ed.’ Ce then goes on to say that ‘<n the presence of e4pectations, it trns ot that the crtch of
a priori knowledge of lag lengths is indispensable, even when we have distinct strictly e4ogenos
variables shifting spply and demand schedles’ *p. E.. While it is tre that the &EC complicates the
necessary conditions for the identification of strctral models, the basic isse in the debate over
identification still centres on the validity of the classical dichotomy between e4ogenos and
endogenos variables. Whether it is possible to test the ‘e4ogeneity’ assmptions of
macroeconometric models is a controversial matter and is very mch bond p with what is in fact
meant by e4ogeneity. <n certain applications e4ogeneity is viewed as a property of a proposed model
*O la /oopmans, 1#-$., and in other sitations it is defined in terms of a grop of variables for
prposes of inference abot ‘parameters of interest’ *Engle and others, 1#6+.. <n the "owles
"ommission approach e4ogeneity was assmed to be the property of the strctral model, obtained
from a priori theory and testable only in the presence of maintained restrictions. Ths it was not
possible to test the identifying restrictions themselves. They had to be assmed a priori and accepted
as a matter of belief or on the basis of knowledge e4traneos to the model nder consideration.
The approach advocated by (ims and his co;researchers departs from the "owles "ommission
methodology in two important respects. <t denies that a priori theory can ever yield the restrictions
necessary for identification of strctral models, and arges that for forecasting and policy analysis,
strctral identification is not needed *(ims, 1#6$, p. 11.. =ccordingly, this approach, termed by
"ooley and Fe&oy *1#6-. ‘atheoretical macroeconometrics’, maintains that only nrestricted vector;
atoregressive *I=&. systems which do not allow for a priori classification of the variables into
endogenos and e4ogenos are admissible for macroeconometric analysis. The I=& approach
represents an important alternative to conventional large;scale macroeconometric models and has
been employed with some sccess in the area of forecasting *Fitterman, 1#6-.. Whether sch
nrestricted I=& systems can also be sed in policy evalation and policy formlation e4ercises
remains a controversial matter. "ooley and Fe&oy *1#6-. in their criti1e of this literatre arge that
even if it can be sccessflly implemented, it will still be of limited relevance e4cept as a tool for ex
ante forecasting and data description *on this also see Feamer, 1#6-a.. They arge that it does not
permit direct testing of economic theories, it is of little se for policy analysis and, above all, it does
not provide a strctral nderstanding of the economic system it prports to represent. (ims and
others *@oan, Fitterman and (ims, 1#60% (ims, 1#6,., however, maintain that I=& models can be
sed for policy analysis, and the type of identifying assmptions needed for this prpose are no less
credible than those assmed in conventional or &E macroeconometric models.
,.+ 5icroeconometrics
Emphasis on the se of micro;data in the analysis of economic problems is not, of corse, new and
dates back to the pioneering work of &ggles and &ggles *1#-,. on the development of a micro;
based social acconting framework and the work of 3rctt and his colleages already referred to
above, and the inflential contribtion of !rais and Cothakker *1#--. on the analysis of family
e4penditre srveys. 7t it is only recently, partly as a response to the dissatisfaction with
macroeconometric time;series research and partly in view of the increasing availability of micro;data
and compting facilities, that the analysis of micro;data has started to be considered seriosly in the
econometric literatre. <mportant micro;data sets have become available especially in the Dnited
(tates in sch areas as hosing, transportation, labor markets and energy. These data sets inclde
varios longitdinal srveys *e.g. Dniversity of 5ichigan !anel (tdy of <ncome @ynamics and 3hio
(tate 9F( (rveys., cross;sectional srveys of family e4penditres, and the poplation and labor
force srveys. This increasing availability of micro;data, while opening p new possibilities for
analysis, has also raised a nmber of new and interesting econometric isses primarily originating
from the natre of the data. The errors of measrement are more likely to be serios in the case of
micro; than macro;data. The problem of the heterogeneity of economic agents at the micro level
cannot be assmed away as readily as is sally done in the case of macro;data by appealing to the
idea of a ‘representive’ firm or a ‘representive’ hosehold. =s ?riliches *1#6,. pt it
Iariables sch as age, land 1ality, or the occpational strctre of an enterprise, are mch less
variable in the aggregate. <gnoring them at the micro level can be 1ite costly, however. (imilarly,
measrement errors which tend to cancel ot when averaged over thosands or even millions of
respondents, loom mch larger when the individal is the nit of analysis *p. 10,#..
The natre of micro;data, often being 1alitative or limited to a particlar range of variation, has also
called for new econometric models and techni1es. The models and isses considered in the micro;
econometric literatre are wideranging and inclde fi4ed and random effect models *e.g. 5ndlak,
1#,1, 1#E6., discrete choice or 1antal response models *5anski and 5c'adden, 1#61., continos
time dration models *Ceckman and (inger, 1#60., and micro;econometric models of cont data
*Casman and others, 1#60 and "ameron and Trivedi, 1#6,.. The fi4ed or random effect models
provide the basic statistical framework. @iscrete choice models are based on an e4plicit
characteri8ation of the choice process and arise when individal decision makers are faced with a
finite nmber of alternatives to choose from. E4amples of discrete choice models inclde
transportation mode choice *@omenich and 5c'adden, 1#E-., labor force participation *Ceckman
and Willis, 1#EE., occpation choice *7oskin, 1#E0., )ob or firm location *@ncan 1#6$., etc. Fimited;
dependent variables models are commonly encontered in the analysis of srvey data and are sally
categori8ed into trncated regression models and censored regression models. <f all observations on
the dependent as well as on the e4ogenos variables are lost when the dependent variable falls otside
a specified range, the model is called truncated, and, if only observations on the dependent variable
are lost, it is called censored. The literatre on censored and trncated regression models is vast and
overlaps with developments in other disciplines, particlarly in biometrics and engineering. The
censored regression model was first introdced into economics by Tobin *1#-6. in his pioneering
stdy of hosehold e4penditre on drable goods where he e4plicitly allowed for the fact that the
dependent variable, namely the e4penditre on drables, cannot be negative. The model sggested by
Tobin and its varios generali8ations are known in economics as Tobit models and are srveyed in
detail by =memiya *1#60..
"ontinos time dration models, also known as srvival models, have been sed in analysis of
nemployment dration, the period of time spent between )obs, drability of marriage, etc.
=pplication of srvival models to analyse economic data raises a nmber of important isses reslting
primarily from the non;controlled e4perimental natre of economic observations, limited sample
si8es *i.e. time periods., and the heterogeneos natre of the economic environment within which
agents operate. These isses are clearly not confined to dration models and are also present in the
case of other microeconometric investigations that are based on time series or cross section or panel
data. *'or early literatre on the analysis of panel data, see the error components model developed by
/h, 1#-# and 7alestra and 9erlove, 1#,,.. = satisfactory resoltion of these problems is of crcial
importance for the sccess of the microeconometric research programme. =s aptly pt by Csiao
*1#6-. in his recent review of the literatre:
=lthogh panel data has opened p avenes of research that simply cold not have been prsed
otherwise, it is not a panacea for econometric researchers. The power of panel data depends on the
e4tent and reliability of the information it contains as well as on the validity of the restrictions pon
which the statistical methods have been bilt *p. 1,+..
!artly in response to the ncertainties inherent in econometric reslts based on non;e4perimental
data, there has also been a significant move towards ‘social e4perimentation’, especially in the Dnited
(tates, as a possible method of redcing these ncertainties. This has led to a considerable literatre
analysing ‘e4perimental’ data, some of which has been recently reviewed in Casman and Wise
*1#6-.. =lthogh it is still too early to arrive at a definite )dgement abot the vale of social
e4perimentation as a whole, from an econometric viewpoint the reslts have not been all that
encoraging. Evalation of the &esidential Electricity Time;of;Dse E4periments *=igner, 1#6-., the
Cosing;=llowance !rogram E4periments *&osen, 1#6-., and the 9egative;<ncome;Ta4 E4periments
*(tafford, 1#6-. all point to the fact that the e4perimental reslts cold have been e1ally predicted by
the earlier econometric estimates. The advent of social e4perimentation in economics has
nevertheless posed a nmber of interesting problems in the areas of e4perimental design, statistical
methods *e.g. see Casman and Wise *1#E#. on the problem of attrition bias., and policy analysis that
are likely to have important conse1ences for the ftre development of micro;econometrics. *=
highly readable accont of social e4perimentation in economics is given by 'erber and Cirsch, 1#62..
=nother important aspect of recent developments in microeconometric literatre relates to the se of
microanalytic simlation models for policy analysis and evalation to reform packages in areas sch
as health care, ta4ation, social secrity systems, and transportation networks. (ome of this literatre
is covered in 3rctt and others *1#6,..
,.0 5odel Evalation
While in the 1#-$s and 1#,$s research in econometrics was primarily concerned with the
identification and estimation of econometric models, the dissatisfaction with econometrics dring the
1#E$s cased a shift of focs from problems of estimation to those of model evalation and testing.
This shift has been part of a concerted effort to restore confidence in econometrics, and has received
attention from 7ayesian as well as classical viewpoints. 7oth these views re)ect the ‘a4iom of correct
specification’ which lies at the basis of most traditional econometric practices, bt differ markedly as
how best to proceed.
7ayesians, like Feamer *1#E6., point to the wide disparity that e4ists between econometric method
and the econometric practice that it is spposed to nderlie, and advocate the se of ‘informal’
7ayesian procedres sch as the ‘e4treme bonds analysis’ *E7=., or more generally, the ‘global
sensitivity analysis’. The basic idea behind the E7= is spelt ot in Feamer and Feonard *1#6+. and
Feamer *1#6+. and has been the sb)ect of critical analysis in 5c=leer, !agan and Iolker *1#6-.. <n
its most general form, the research strategy pt forward by Feamer involves a kind of grand 7ayesian
sensitivity analysis. The empirical reslts, or in 7ayesian terminology the posterior distribtions, are
evalated for ‘fragility’ or ‘strdiness’ by checking how sensitive the reslts are to changes in prior
distribtions. =s Feamer *1#6-b. e4plains:
7ecase no prior distribtion can be taken to be an e4act representation of opinion, a global
sensitivity analysis is carried ot to determine which inferences are fragile and which are strdy *p.
+11..
The aim of the sensitivity analysis in Feamer’s approach is, in his words, ‘to combat the arbitrariness
associated with the choice of prior distribtion’ *Feamer, 1#6,, p. E0..
<t is generally agreed, by 7ayesians as well as by non;7ayesians, that model evalation involves
considerations other than the e4amination of the statistical properties of the models, and personal
)dgements inevitably enter the evalation process. 5odels mst meet mltiple criteria which are
often in conflict. They shold be relevant in the sense that they oght to be capable of answering the
1estions for which they are constrcted. They shold be consistent with the acconting andAor
theoretical strctre within which they operate. 'inally, they shold provide ade1ate representations
of the aspects of reality with which they are concerned. These criteria and their interaction are
discssed in !esaran and (mith *1#6-b.. 5ore detailed breakdowns of the criteria of model
evalation can be fond in Cendry and &ichard *1#62. and 5c=leer and others *1#6-.. <n
econometrics it is, however, the criterion of ‘ade1acy’ which is emphasi8ed, often at the e4pense of
relevance and consistency.
The isse of model ade1acy in mainstream econometrics is approached either as a model selection
problem or as a problem in statistical inference whereby the hypothesis of interest is tested against
general or specific alternatives. The se of absolte criteria sch as measres of fitAparsimony or
formal 7ayesian analysis based on posterior odds are notable e4amples of model selection procedres,
while likelihood ratio, Wald and Fagrange mltiplier tests of nested hypotheses and "o4’s centred log;
likelihood ratio tests of non;nested hypotheses are e4amples of the latter approach. The distinction
between these two general approaches basically stems from the way alternative models are treated. <n
the case of model selection *or model discrimination. all the models nder consideration en)oy the
same stats and the investigator is not committed a priori to any one of the alternatives. The aim is to
choose the model which is likely to perform best with respect to a particlar loss fnction. 7y contrast,
in the hypothesis;testing framework the nll hypothesis *or the maintained model. is treated
differently from the remaining hypotheses *or models.. 3ne important featre of the model;selection
strategy is that its application always leads to one model being chosen in preference to other models.
7t in the case of hypothesis testing, re)ection of all the models nder consideration is not rled ot
when the models are non;nested. = more detailed discssion of this point is given in !esaran and
@eaton *1#E6..
While the model;selection approach has received some attention in the literatre, it is the hypothesis;
testing framework which has been primarily relied on to derive sitable statistical procedres for
)dging the ade1acy of an estimated model. <n this latter framework, broadly speaking, three
different strands can be identified, depending on how specific the alternative hypotheses are. These
are the eneral specification tests, the dianostic tests, and the non$nested tests. The first of these,
introdced in econometrics by &amsey *1#,#. and Casman *1#E6., and more recently developed by
White *1#61, 1#62. and Cansen *1#62., are designed for circmstances where the natre of the
alternative hypothesis is kept *sometimes intentionally. rather vage, the prpose being to test the
nll against a broad class of alternatives. <mportant e4amples of general specification tests are
&amsey’s regression specification error test *&E(ET. for omitted variables andAor misspecified
fnctional forms, and the Casman;W test of misspecification in the conte4t of measrement error
models, andAor simltaneos e1ation models. (ch general specification tests are particlarly sefl
in the preliminary stages of the modelling e4ercise.
<n the case of diagnostic tests, the model nder consideration *viewed as the nll hypothesis. is tested
against more specific alternatives by embedding it within a general model. @iagnostic tests can then
be constrcted sing the likelihood ratio, Wald or Fagrange mltiplier *F5. principles to test for
parametric restrictions imposed on the general model. The application of the F5 principle to
econometric problems is reviewed in the papers by 7resch and !agan *1#6$., ?odfrey and Wickens
*1#62. and Engle *1#60.. E4amples of the restrictions that may be of interest as diagnostic checks of
model ade1acy inclde 8ero restrictions, parameter stability, serial correlation, heteroskedasticity,
fnctional forms, and normality of errors. =s shown in !agan and Call *1#6+., most e4isting
diagnostic tests can be compted by means of a4iliary regressions involving the estimated residals.
<n this sense diagnostic tests can also be viewed as a kind of residal analysis where residals
compted nder the nll are checked to see whether they can be e4plained frther in terms of the
hypothesi8ed sorces of misspecification. The distinction made here between diagnostic tests and
general specification tests is more apparent than real. <n practice some diagnostic tests sch as tests
for serial correlation can also be viewed as a general test of specification. 9evertheless, the distinction
helps to focs attention on the prpose behind the tests and the direction along which high power is
soght.
The need for non;nested tests arises when the models nder consideration belong to separate
parametric families in the sense that no single model can be obtained from the others by means of a
sitable limiting process. This sitation, which is particlarly prevalent in econometric research, may
arise when models differ with respect to their theoretical nderpinnings andAor their a4iliary
assmptions. Dnlike the general specification tests and diagnostic tests, the application of non;nested
tests is appropriate when specific bt rival hypotheses for the e4planation of the same economic
phenomenon have been advanced. =lthogh non;nested tests can also be sed as general specification
tests, they are designed primarily to have high power against specific models that are seriosly
entertained in the literatre. 7ilding on the pioneering work of "o4 *1#,1, 1#,2., a nmber of sch
tests for single e1ation models and systems of simltaneos e1ations have been proposed *see the
entry on 939;9E(TE@ CB!3TCE(<( in this @ictionary for frther details and references..
The se of statistical tests in econometrics, however, is not a straightforward matter and in most
applications does not admit of a clear;ct interpretation. This is especially so in circmstances where
test statistics are sed not only for checking the ade1acy of a iven model bt also as gides to model
constrction. (ch a process of model constrction involves specification searches of the type
emphasi8ed by Feamer and presents insrmontable pre;test problems which in general tend to
prodce econometric models whose ‘ade1acy’ is more apparent than real. =s a reslt, in evalating
econometric models less reliance shold be placed on those indices of model ade1acy that are sed
as gides to model constrction, and more emphasis shold be given to the performance of models
over other data sets and against rival models. The evalation of econometric models is a complicated
process involving practical, theoretical and econometric considerations. Econometric methods clearly
have an important contribtion to make to this process. 7t they shold not be confsed with the
whole activity of econometric modelling which, in addition to econometric and compting skills,
re1ires data, considerable intition, instittional knowledge and, above all, economic
nderstanding.
E =ppraisals and 'tre !rospects
Econometrics has come a long way over a relatively short period. <mportant advances have been made
in the compilation of economic data and in the development of concepts, theories and tools for the
constrction and evalation of a wide variety of econometric models. =pplications of econometric
methods can be fond in almost every field of economics. Econometric models have been sed
e4tensively by government agencies, international organi8ations and commercial enterprises.
5acroeconometric models of differing comple4ity and si8e have been constrcted for almost every
contry in the world. 7oth in theory and practice econometrics has already gone well beyond what its
fonders envisaged. Time and e4perience, however, have broght ot a nmber of difficlties that
were not apparent at the start.
Econometrics emerged in the 1#+$s and 1#0$s in a climate of optimism, in the belief that economic
theory cold be relied on to identify most, if not all, of the important factors involved in modelling
economic reality, and that methods of classical statistical inference cold be adapted readily for the
prpose of giving empirical content to the received economic theory. This early view of the interaction
of theory and measrement in econometrics, however, proved rather illsory. Economic theory, be it
neoclassical, /eynesian or 5ar4ian, is invariably formlated with ceteris paribus clases, and
involves nobservable latent variables and general fnctional forms% it has little to say abot
ad)stment processes and lag lengths. Even in the choice of variables to be inclded in econometric
relations, the role of economic theory is far more limited than was at first recogni8ed. <n a Walrasian
general e1ilibrim model, for e4ample, where everything depends on everything else, there is very
little scope for a priori e4clsion of variables from e1ations in an econometric model. There are also
instittional featres and acconting conventions that have to be allowed for in econometric models
bt which are either ignored or are only partially dealt with at the theoretical level. =ll this means
that the specification of econometric models inevitably involves important a4iliary assmptions
abot fnctional forms, dynamic specifications, latent variables, etc. with respect to which economic
theory is silent or gives only an incomplete gide.
The recognition that economic theory on its own cannot be e4pected to provide a complete model
specification has important conse1ences both for testing economic theories and for the evalation of
econometric models. The incompleteness of economic theories makes the task of testing them a
formidable ndertaking. <n general it will not be possible to say whether the reslts of the statistical
tests have a bearing on the economic theory or the a4iliary assmptions. This ambigity in testing
theories, known as the @hem;>ine thesis, is not confined to econometrics and arises whenever
theories are con)nctions of hypotheses *on this, see for e4ample "ross, 1#62.. The problem is,
however, especially serios in econometrics becase theory is far less developed in economics than it
is in the natral sciences. There are, of corse, other difficlties that srrond the se of econometric
methods for the prpose of testing economic theories. =s a rle economic statistics are not the reslts
of designed e4periments, bt are obtained as by;prodcts of bsiness and government activities often
with legal rather than economic considerations in mind. The statistical methods available are
generally sitable for large samples while the economic data *especially economic time;series. have a
rather limited coverage. There are also problems of aggregation over time, commodities and
individals that frther complicate the testing of economic theories that are micro;based.
The incompleteness of economic theories also introdces an important and navoidable element of
data;instigated searches into the process of model constrction, which creates important
methodological difficlties for the established econometric methods of model evalation. "learly, this
whole area of specification searches deserves far greater attention, especially from non;7ayesians,
than it has so far attracted.
There is no dobt that econometrics is sb)ect to important limitations, which stem largely from the
incompleteness of the economic theory and the non;e4perimental natre of economic data. 7t these
limitations shold not distract s from recogni8ing the fndamental role that econometrics has come
to play in the development of economics as a scientific discipline. <t may not be possible conclsively
to re)ect economic theories by means of econometric methods, bt it does not mean that nothing
sefl can be learned from attempts at testing particlar formlations of a given theory against
*possible. rival alternatives. (imilarly, the fact that econometric modelling is inevitably sb)ect to the
problem of specification searches does not mean that the whole activity is pointless. Econometric
models are important tools of forecasting and policy analysis, and it is nlikely that they will be
discarded in the ftre. The challenge is to recogni8e their limitations and to work towards trning
them into more reliable and effective tools. There seem to be no viable alternatives.
5. Cashem !esaran
(ee also estimation; hypothesis testing; macroeconometric models; specification
problems in econometrics; time series analysis.
7ibliography
=igner, @.G. 1#6-. The residential electricity time;of;se pricing e4periments: what have we learned?
<n Social Experimentation, ed. G.=. Casman and @.=. Wise, "hicago: Dniversity of "hicago !ress.
=itken, =.". 1#+0H-. 3n least s1ares and linear combinations of observations. "roceedins of the
Royal Society of Edinbunh --, 02H6.
=llen, &.?.@. and 7owley, =.F. 1#+-. Family Expenditure. Fondon: !.(. /ing.
=lmon, (. 1#,-. The distribted lag between capital appropriations and net e4penditres.
Econometrica ++, 1E6H#,.
=memiya, T. 1#6+. 9onlinear regression models. <n Handboo% of Econometrics, ed. L. ?riliches and
5.@. <ntriligator, Iol. 1, =msterdam: 9orth;Colland.
=memiya, T. 1#60. Tobit models: a srvey. #ournal of Econometrics 20, +H,1.
=nderson, T.W. and &bin, C. 1#0#. Estimation of the parameters of a single e1ation in a complete
system of stochastic e1ations. Annals of Mathematical Statistics 2$, 0,H,+.
=oki, 5. 1#E,. Dynamic Economic Theory and &ontrol in Economics. 9ew Bork: =merican Elsevier.
7alestra, !. and 9erlove, 5. 1#,,. !ooling cross section and time series data in the estimation of a
dynamic model: the demand for natral gas. Econometrica +0, -6-H,12.
7asmann, &.F. 1#-E. = generali8ed classical method of linear estimation of coefficients in a strctral
e1ation. Econometrica 2-, EEH6+.
7enini, &. 1#$E. (ll’so delle formole empiriche a nell’economia applicata. 'iornale deli
economisti, 2nd series, +-, 1$-+H,+.
7ergstrom, =.&. 1#60. "ontinos time stochastic models and isses of aggregation over time. <n
Handboo% of Econometrics, ed. L. ?riliches and 5.@. <ntriligator, Iol. 2, =msterdam: 9orth;
Colland.
7oskin, 5.G. 1#E0. = conditional logit model of occpational choice. #ournal of "olitical Economy 62,
+6#H#6.
7o4, ?.E.!. and Genkins, ?.5. 1#E$. Time Series Analysis( Forecastin and &ontrol. (an 'rancisco:
Colden;@ay.
7resch, T.(. and !agan, =.&. 1#6$. The Fagrange mltiplier test and its applications to model
specification in econometrics. Review of Economic Studies 0E, 2+#H-+.
7rown, T.5. 1#-2. Cabit persistence and lags in consmer behavior. Econometrica 2$, +--HE1.
7rndy, G.5. and Gorgenson, @.9. 1#E1. Efficient estimation of simltaneos e1ations by
instrmental variables. Review of Economics and Statistics -+, 2$EH20.
7rns, =.'. and 5itchell, W.". 1#0E. Measurin )usiness &ycles. 9ew Bork: "olmbia Dniversity
!ress for the 9ational 7rea of Economic &esearch.
"agan, !. 1#-,. The monetary dynamics of hyperinflation. <n Studies in the *uantity Theory of
Money, ed. 5. 'riedman, "hicago: Dniversity of "hicago !ress.
"ameron, =.". and Trivedi, !./. 1#6,. Econometric models based on cont data: comparisons and
applications of some estimators and tests. #ournal of Applied Econometrics 1, 2#H-+.
"hampernowne, @.?. 1#06. (ampling theory applied to atoregressive se1ences. #ournal of the
Royal Statistical Society (eries 7, 1$, 2$0H+1.
"how, ?.". 1#E-. Analysis and &ontrol of Dynamic Economic Economic Systems. 9ew Bork: Gohn
Wiley.
"how, ?.". 1#61. Econometric Analysis by &ontrol Methods. 9ew Bork: Gohn Wiley.
"how, ?.". 1#6+. Econometrics. 9ew Bork: 5c?raw;Cill.
"how, ?.". 1#60. &andom and changing coefficient models. <n Handboo% of Econometrics, ed. L.
?riliches and 5.@. <ntriligator, Iol. 2, =msterdam: 9orth;Colland.
"hrist, ".'. 1#-2. Economic Theory and Measurement( a twenty year research report+ ,-./01/.
"hicago: "owles "ommission for &esearch in Economics.
"hrist, ".'. 1#,,. Econometric Models and Methods. 9ew Bork: Gohn Wiley.
"hrist, ".'. 1#6+. The fonding of the Econometric (ociety and Econometrica. Econometrica -1, +H,.
"hrist, ".'. 1#6-. Early progress in estimating 1antitative economic relations in =merica. American
Economic Review, @ecember, +#H-2 *spplementary information and statistical smmaries..
"ochrane, !. and 3rctt, ?.C. 1#0#. =pplication of least s1ares regression to relationships
containing atocorrelated error terms. #ournal of the American Statistical Association 00, +2H,1.
"ooley, T.'. and Feroy, (.'. 1#6-. =theoretical macroeconometrics: a criti1e. #ournal of Monetary
Economics 1,, 26+H+,6.
"ooper, &.F. 1#E2. The predictive performance of 1arterly econometric models of the Dnited (tates.
<n Econometric Models of &yclical )ehaviour, ed. 7.?. Cickman, (tdies in <ncome and Wealth +,,
Iol. 2, 61+H#2-.
"o4, @.&. 1#,1. Tests of separate families of hypotheses. "roceedins of the Fourth )er%eley
Symposium on Mathematical Statistics and "robability, Iol. 1, 7erkeley: Dniversity of "alifornia
!ress, 1$-H2+.
"o4, @.&. 1#,2. 'rther reslts of tests of separate families of hypotheses. #ournal of the Royal
Statistical Society, (eries 7, 20, 0$,H20.
"reedy, G. 1#6,. 3n the /ing;@avenant ‘law’ of demand. Scottish #ournal of "olitical Economy ++,
=gst, 1#+H212.
"ross, &. 1#62. The @hem;>ine thesis, Fakatos and the appraisal of theories in macroeconomics.
Economic #ournal #2, +2$H0$.
@avenant, ". 1,#6. Discourses on the "ublic% Revenues and on the Trade of Enland, Iol. 1. Fondon.
@avidson, G.E.C., Cendry, @.'., (rba, '. and Beo, (. 1#E6. Econometric modelling of the aggregate
time;series relationship between consmers’ e4penditre and income in the Dnited /ingdom.
Economic #ournal 66, ,,1H#2.
@hrymes, !. 1#E1. = simplified estimator for large;scale econometric models. Australian #ournal of
Statistics 1+, 1,6HE-.
@ickey, @.=. and 'ller, W.=. 1#E#. @istribtion of the estimators for atoregressive time series with a
nit root. #ournal of the American Statistical Association E0, 02EH+1.
@ickey, @.=. and 'ller, W.=. 1#61. The likelihood ratio statistics for atoregressive time series with a
nit root. Econometrica 0#, 1$-EHE2.
@oan, T., Fitterman, &. and (ims, ".=. 1#60. 'orecasting and conditional pro)ection sing realistic
prior distribtions. Econometric Reviews +, 1H1$$.
@omenich, T. and 5c'adden, @. 1#E-. 2rban Travel Demand( A )ehavioural Analysis. =msterdam:
9orth;Colland.
@rN8e, G.C. and &ichard, G;'. 1#6+. 7ayesian analysis of simltaneos e1ation systems. <n
Handboo% of Econometrics, ed. L. ?riliches and 5.@. <ntriligator, Iol. 1 =msterdam: 9orth;Colland.
@ncan, ?. 1#6$. 'ormlation and statistical analysis of the mi4ed continosAdiscrete variable
model in classical prodction theory. Econometrica 06, 6+#H-2.
@rbin, G. and Watson, ?.(. 1#-$. Testing for serial correlation in least s1ares regression <.
)iometri%a +E, 0$#H26.
@rbin, G. and Watson, ?.(. 1#-1. Testing for serial correlation in least s1ares regression <<.
)iometri%a +6, 1-#HE6.
Eisner, &. and (trot8, &.C. *1#,+.. @eterminants of bsiness investment. <n "ommission on 5oney
and "redit, 3mpacts of Monetary "olicy, Englewood "liffs, 9G: !rentice;Call, -#H++E.
Engle, &.'. 1#60. Wald likelihood ratio and Fagrange mltiplier tests in econometrics. <n Handboo%
of Econometrics, Iol. 2, ed. L. ?riliches and 5.@. <ntriligator, =msterdam: 9orth;Colland.
Engle, &.'., Cendry, @.'. and &ichard, G.;'. 1#6+. E4ogeneity. Econometrica -1, 2EEH+$0.
Evans, ?.7.=. and (avin, 9.E. 1#61. Testing for nit roots <. Econometrica 0#, E-+HEE.
Evans, ?.7.=. and (avin, 9.E. 1#60. Testing for nit roots <<. Econometrica -2, 1201HE$.
'erber, &. and Cirsch, W.L. 1#62. Social Experimentation and Economic "olicy4 "ambridge:
"ambridge Dniversity !ress.
'isher, '.5. 1#,,. The 3dentification "roblem in Econometrics4 9ew Bork: 5c?raw;Cill.
'isher, <. 1#+$. The Theory of 3nterest4 9ew Bork: 5acmillan. &eprinted, !hiladelphia: !orcpine
!ress, 1#EE.
'isher, <. 1#+E. 9ote on a short;ct method for calclating distribted lags. )ulletin de l53nstitut
3nternational de Statisti6ue 2#, +2+HE.
'riedman, 5. 1#-E. A Theory of the &onsumption Function4 !rinceton: !rinceton Dniversity !ress.
'risch, &. 1#++a. Editorial. Econometrica 1, 1H0.
'risch, &. 1#++b. "itfalls in the Statistical &onstruction of Demand and Supply &urves4 Feip8ig: Cans
7ske Ierlag.
'risch, &. 1#+0. Statistical &onfluence Analysis by Means of &omplete Reression Systems4 3slo:
Dniversity <nstitte of Economics.
'risch, &. 1#+,. 9ote on the term ‘Econometrics’. Econometrica 0, #-.
?eary, &.". 1#0#. (tdies in relations between economic time series. #ournal of the Royal Statistical
Society, (eries 7 1$, 10$H-6.
?odfrey, F.?. and Wickens, 5.&. 1#62. Tests of misspecification sing locally e1ivalent alternative
models. <n Evaluation and Reliability of Macro$economic Models, ed ?.". "how and !. "orsi, 9ew
Bork: Gohn Wiley.
?ranger, ".W.G. 1#,#. <nvestigating casal relations by econometric models and cross;spectral
methods. Econometrica +E, 020H+6.
?riliches, L. 1#,E. @istribted lags: a srvey. Econometrica +-, 1,H0#.
?riliches, L. 1#6,. Economic data isses. <n Handboo% of Econometrics, ed. L. ?riliches and 5.@.
<ntriligator, Iol. +, =msterdam: 9orth;Colland.
Caavelmo, T. 1#0+. (tatistical testing of bsiness cycle theories. Review of Economics and Statistics
2-, 1+H16.
Caavelmo, T. 1#00. The probability approach in econometrics. Econometrica 12, (pplement, 1H116.
Cansen, F.!. 1#62. Farge sample properties of generali8ed method of moments. Econometrica -$,
1$2#H-0.
Cansen, F.!. and (argent, T.G. 1#6$. 'ormlating and estimating dynamic linear rational
e4pectations models. #ournal of Economic Dynamics and &ontrol 2, EH0,.
Cansen, F.!. and (ingleton, /.G. 1#62. ?enerali8ed instrmental variables estimation of non;linear
rational e4pectations models. Econometrica -$, 12,#H6,.
Cart, 7.(. and von 9emann, G. 1#02. Tablation of the probabilities for the ratio of mean s1are
sccessive difference to the variance. Annals of Mathematical Statistics 1+, 2$EH10.
Casman, G.=. 1#E6. (pecification tests in econometrics. Econometrica 0,, 12-1HE2.
Casman, G.=. 1#6+. (pecification and estimation of simltaneos e1ation models. <n Handboo% of
Econometrics, Iol. 1, ed. L. ?riliches and 5.@. <ntriligator, =msterdam: 9orth;Colland.
Casman, G. and Wise, @.=. 1#E#. =ttrition bias in e4perimental and panel data: the ?ary income
maintenance e4periment. Econometrica 0E, 0--HE+.
Casman, G.=. and Wise, @.=. 1#6-. Social Experimentation. "hicago: Dniversity of "hicago !ress for
the 9ational 7rea of Economic &esearch.
Casman, G.=., Call, 7.C. and ?riliches, L. 1#60. Econometric models for cont data with application
to the patents ; & P @ relationship. Econometrica -2, #$#H1$+6.
Ceckman, G.G. and (inger, 7. 1#60. Econometric dration analysis. #ournal of Econometrics 20, ,+H
1+2.
Ceckman, G.G. and Willis, &. 1#EE. = beta;logistic model for the analysis of se1ential labor force
participation by married women. #ournal of "olitical Economy 6-, 2EH-6.
Cendry, @.'. 1#E,. The strctre of simltaneos e1ations estimators. #ournal of Econometrics 0,
-1H66.
Cendry, @.'. and &ichard, G;'. 1#62. 3n the formlation of empirical models in dynamic
econometrics. #ournal of Econometrics 2$, +H++.
Cooker, &.C. 1#$1. "orrelation of the marriage rate with trade. #ournal of the Royal Statistical
Society 00, 06-H#2.
Csiao, ". 1#6+. <dentification. <n Handboo% of Econometrics, Iol. 1, ed. L. ?riliches and 5.@.
<ntriligator, =msterdam: 9orth;Colland.
Csiao, ". 1#6-. 7enefits and limitations of panel data. Econometric Reviews 0, 121HE0.
Gorgenson, @.W. 1#,,. &ational distribted lag fnctions. Econometrica +0, 1+-H0#.
/endall, 5.?. 1#,6. The history of statistical methods. <n 3nternational Encyclopedia of the Social
Sciences, ed. @.F. (ills, Iol. 1-, 9ew Bork: 5acmillan and The 'ree !ress, 220H+2.
/eynes, G.5. 1#21. A Treatise on "robability4 Fondon: 5acmillan.
/eynes, G.5. 1#+#. The statistical testing of bsiness cycle theories. Economic #ournal 0#, --6H,6.
/lein, F.&. 1#0E. The se of econometric models as a gide to economic policy. Econometrica 1-, 111H
-1.
/lein, F.&. 1#-$. Economic Fluctuations in the 2nited States ,-/,0,-7,4 "owles "ommission
5onograph 9o. 11, 9ew Bork: Gohn Wiley.
/lein, F.&. 1#E1. Whither econometrics? #ournal of the American Statistical Society ,,, 01-H21.
/lein, F.&. and ?oldberger, =.(. 1#--. An Econometric Model of the 2nited States+ ,-/-0,-1/4
=msterdam: 9orth;Colland.
/oopmans, T.". 1#+E. 8inear Reression Analysis of Economic Time Series. Caarlem: @e Erven '.
7ohn for the 9etherlands Economic <nstitte.
/oopmans, T.". 1#0#. <dentification problems in economic model constrction. Econometrica 1E,
12-H00.
/oopmans, T.". 1#-$. When is an e1ation system complete for statistical prposes? <n Statistical
3nference in Dynamic Economic Models, ed. T.". /oopmans, "owles "ommission 5onograph 9o. 1$,
9ew Bork: Gohn Wiley.
/oopmans, T."., &bin, C. and Feipnik, &.7. 1#-$. 5easring the e1ation systems of dynamic
economics. <n Statistical 3nference in Dynamic Economic Models, ed. T.". /oopmans, "owles
"ommission 5onograph 9o. 1$, 9ew Bork: Gohn Wiley.
/oyck, F.5. 1#-0. Distributed 8as and 3nvestment Analysis4 =msterdam: 9orth;Colland.
/h, E. 1#-#. The validity of cross;sectionally estimated behavior e1ations in time series
applications. Econometrica 2E, 1#EH210.
Fawson, T. 1#61. /eynesian model bilding and the rational e4pectations criti1e. &ambride
#ournal of Economics -, +11H2,.
Feamer, E.E. 1#E6. Specification Searches( Ad Hoc 3nference with 9on$experimental Data4 9ew
Bork: Gohn Wiley.
Feamer, E.E. 1#6+. Fet’s take the con ot of Econometrics. American Economic Review E+, +1H0+.
Feamer, E.E. 1#6-a. Iector atoregressions for casal inference. <n &arneie$Rochester &onference
Series on "ublic "olicy 22, ed. /. 7rnner and =.C. 5elt8er, =msterdam: 9orth;Colland, 2--H+$0.
Feamer, E.E. 1#6-b. (ensitivity analyses wold help. American Economic Review 6-, +$6H1+.
Feamer, E.E. 1#6,. = 7ayesian analysis of the determinants of inflation. <n Model Reliability, ed. @.=.
7elsley and E. /h, "ambridge, 5ass: 5<T !ress.
Feamer, E.E. and Feonard, C. 1#6+. &eporting the fragility of regression estimates. Review of
Economics and Statistics ,-, +$,H1E.
Fenoir, 5. 1#1+. Etudes sur la formation et le mouvement des prix4 !aris: ?iard et 7riNre.
Feontief, W.W. 1#+,. >antitative inpt;otpt relations in the economic system of the Dnited (tates.
Review of Economic Statistics 16, 1$-H2-.
Feontief, W.W. 1#01. The Structure of American Economy+ ,-,-0,-/-4 "ambridge, 5ass: Carvard
Dniversity !ress.
Feontief, W.W. 1#-1. The Structure of American Economy+ ,-,-0,-.-4 2nd edn, 34ford: 34ford
Dniversity !ress.
Fitterman, &.7. 1#6-. 'orecasting with 7ayesian vector atoregressions: five years of e4perience.
#ournal of )usiness and Economic Statistics 0, 2-H+6.
Fi, T.". 1#,$. Dnderidentification, strctral estimation and forecasting. Econometrica 26, 6--H,-.
Fcas, &.E. 1#E2. E4pectations and the netrality of money. #ournal of Economic Theory 0, 1$+H20.
Fcas, &.E. 1#E+. (ome international evidence on otpt;inflation tradeoffs. American Economic
Review ,+, +2,H+0.
Fcas, &.E. 1#E,. Econometric policy evalation: a criti1e. <n The "hillips &urve and 8abor Mar%ets,
ed. /. 7rnner and =.5. 5elt8er, "arnegie;&ochester "onferences on !blic !olicy, Iol. 1,
=msterdam: 9orth;Colland, 1#H0,.
Fyttkens, E. 1#E$. (ymmetric and asymmetric estimation methods. <n 3nterdependent Systems, ed. E.
5osback and C. Wold, =msterdam: 9orth;Colland.
5c=leer, 5., !agan, =.&. and Iolker, !.=. 1#6-. What will take the con ot of econometrics?
American Economic Review E-, 2#+H+$E.
5addala, ?.(. 1#6+. 8imited Dependent and *ualitative :ariables in Econometrics4 "ambridge:
"ambridge Dniversity !ress.
5addala, ?.(. 1#6,. @ise1ilibrim, self;selection, and switching models. <n Handboo% of
Econometrics, Iol. +, ed. L. ?riliches and 5.@. <ntriligator, =msterdam: 9orth;Colland.
5alinvad, E. 1#,,. Statistical Methods of Econometrics4 =msterdam: 9orth;Colland.
5anski, ".'. and 5c'adden, @. 1#61. Structural Analysis of Discrete Data with Econometric
Applications4 "ambridge, 5ass: 5<T !ress.
5arschak, G. 1#-+. Economic measrements for policy and prediction. <n Studies in Econometric
Method, ed. W.". Cood and T.". /oopmans, "owles "ommission for &esearch in Economics
5onograph 9o. 10, 9ew Bork: Gohn Wiley.
5arschak, G. and =ndrews, W.C. 1#00. &andom simltaneos e1ations and the theory of
prodction. Econometrica 12, 10+H2$-.
5itchell, W.". 1#26. )usiness &ycles( the "roblem in its Settin4 9ew Bork: 9ational 7rea of
Economic &esearch.
5oore, C.F. 1#10. Economic &ycles( Their 8aw and &ause4 9ew Bork: 5acmillan !ress.
5oore, C.F. 1#1E. Forecastin the ;ield and the "rice of &otton4 9ew Bork: 5acmillan !ress.
5organ, 5.(. 1#6,. (tatistics withot probability and Caavelmo’s revoltion in econometrics. <n The
"robabilistic Revolution( 3deas in the Social Sciences, ed. F. /rger, ?. ?igeren8er and 5. 5organ,
"ambridge, 5ass: 5<T !ress.
5ndlak, B. 1#,1. Empirical prodction fnction free of management bias. #ournal of Farm
Economics 0+, 00H-,.
5ndlak, B. 1#E6. 3n the pooling of time series and cross section data. Econometrica 0,, ,#H6-.
5th, G.'. 1#,1. &ational e4pectations and the theory of price movements. Econometrica 2#, +1-H+-.
9elson, ".&. 1#E2. The prediction performance of the '&7;5<T;!enn model of the D( economy.
American Economic Review ,2, #$2H1E.
9erlove, 5. 1#-6a. =daptive e4pectations and the cobweb phenomena. *uarterly #ournal of
Economics E2, 22EH0$.
9erlove, 5. 1#-6b. Distributed 8as and Demand Analysis4 D(@=, =gricltre Candbook 9o. 101,
Washington, @".
9erlove, 5., ?rether, @.5. and "arvalho, G.F. 1#E#. Analysis of Economic Time Series( A Synthesis4
9ew Bork: =cademic !ress.
9emann, G. von. 1#01. @istribtion of the ratio of the mean s1are sccessive difference to the
variance. Annals of Mathematical Statistics 12, +,EH#-.
9emann, G. von. 1#02. = frther remark on the distribtion of the ratio of the mean s1are
sccessive difference to the variance. Annals of Mathematical Statistics 1+, 6,H6.
3rctt, ?.C. 1#06. = stdy of the atoregressive natre of the time series sed for Tinbergen’s model
of the economic system of the Dnited (tates, 1#1#H1#+2. #ournal of the Royal Statistical Society+
(eries 7 1$, 1H0- *@iscssion, 0,H-+..
3rctt, ?.C., ?reenberger, 5., /orbel, G. and &ivlin, =.5. 1#,1. Microanalysis of Socioeconomic
Systems( A Simulation Study4 9ew Bork: Carper P &ow.
3rctt, ?.C., 5er8, G. and >inke, C. *eds. 1#6,. Microanalytic Simulation Models to Support Social
and Financial "olicy4 =msterdam: 9orth;Colland.
!agan, =.&. and Call, =.@. 1#6+. @iagnostic tests as residal analysis. Econometric Reviews 2, 1-#H
216.
!aris, (.G. and Cothakker, C.(. 1#--. The Analysis of Family )udets4 "ambridge: "ambridge
Dniversity !ress.
!esaran, 5.C. 1#61. <dentification of rational e4pectations models. #ournal of Econometrics 1,, +E-H
#6.
!esaran, 5.C. 1#6E. The 8imits to Rational Expectations4 34ford: 7asil 7lackwell.
!esaran, 5.C. and @eaton, =.(. 1#E6. Testing non;nested nonlinear regression models. Econometrica
0,, ,EEH#0.
!esaran, 5.C. and (mith, &.!. 1#6-a. /eynes on econometrics. <n <eynes5 Economics(
methodoloical issues+ ed. T. Fawson and 5.C. !esaran, Fondon: "room Celm.
!esaran, 5.C. and (mith, &.!. 1#6-b. Evalation of macroeconometric models. Economic Modellin,
=pril, 12-H+0.
!hillips, !.".7. 1#6+. E4act small sample theory in the simltaneos e1ations model. <n Handboo%
of Econometrics, ed. L. ?riliches and 5.@. <ntrilgator, Iol. 1, =msterdam: 9orth;Colland.
!hillips, !.".7. 1#6,. Dnderstanding sprios regressions in econometrics. #ournal of Econometrics
++, +11H0$.
!hillips, !.".7. and @rlaf, (.9. 1#6,. 5ltiple time series regression with integrated processes.
Review of Economic Studies -+, 0E+H#-.
!hillips, !.".7. 1#6E. Time series regression with nit roots. Econometrica *forthcoming..
!rothero, @.F. and Wallis, /.'. 1#E,. 5odelling macroeconomic time series. #ournal of the Royal
Statistical Society, (eries = 1+#, 0,6H6,.
>andt, &.E. 1#62. Econometric dise1ilibrim models. Econometric Reviews 1, 1H,+.
&amsey, G.7. 1#,#. Tests for specification errors in classical linear least s1ares regression analysis.
#ournal of the Royal Statistical Society+ (eries 7 +1, +-$HE1.
&eiersol, 3. 1#01. "onflence analysis by means of lag moments and other methods of conflence
analysis. Econometrica #, 1H20.
&eiersol, 3. 1#0-. &onfluence Analysis by Means of 3nstrumental Sets of :ariables4 (tockholm.
&osen, C.(. 1#6-. Cosing behavior and the e4perimental hosingallowance program: what have we
learned? <n Social Experimentation, ed. G.=. Casman and @.=. Wise, "hicago: Dniversity of "hicago
!ress.
&othenberg, T.G. 1#60. =ppro4imating the distribtions of econometric estimators and test statistics.
<n Handboo% of Econometrics, ed. L ?riliches and 5.@. <ntriligator, Iol. 2, =msterdam: 9orth;
Colland.
&ggles, &. and &ggles, 9. 1#-,. 9ational 3ncome Account and 3ncome Analysis4 2nd edn, 9ew
Bork: 5c?raw;Cill.
(amelson, !.=., /oopmans, T.". and (tone, G.&.9. 1#-0. &eport of the evalative committee for
Econometrica. Econometrica 22, 101H,.
(argan, G.@. 1#-6. The estimation of economic relationships sing instrmental variables.
Econometrica 2,, +#+H01-.
(argan, G.@. 1#,0. Wages and prices in the Dnited /ingdom: a stdy in econometric methodology. <n
Econometric Analysis for 9ational Economic "lannin, ed. !.E. Cart, ?. 5ills and G./. Whitaker,
Fondon: 7tterworths.
(argent, T.G. 1#E+. &ational e4pectations, the real rate of interest and the natral rate of
nemployment. )roo%ins "apers on Economic Activity 9o. 2, 02#HE2.
(argent, T.G. and Wallace, 9. 1#E,. &ational e4pectations and the theory of economic policy. #ournal
of Monetary Economics 2, 1,#H60.
(avin, 9.E. 1#E+. (ystems k;class estimators. Econometrica 01, 112-H+,.
(chlt8, 5. 1#+6. The Theory and Measurement of Demand4 "hicago: Dniversity of "hicago !ress.
(chmpeter, G.=. 1#-0. History of Economic Analysis4 Fondon: ?eorge =llen P Dnwin.
(hiller, &.G. 1#E+. = distribted lag estimator derived from smoothness priors. Econometrica 01, EE-H
66.
(ims, ".=. 1#E2. 5oney, income and casality. American Economic Review ,2, -0$H-2.
(ims, ".=. 1#6$. 5acroeconomics and reality. Econometrica 06, 1H06.
(ims, ".=. 1#62. !olicy analysis with econometric models. )roo%ins "apers on Economic Activity
9o. 1, 1$EH,0.
(ims, ".=. 1#6,. =re forecasting models sable for policy analysis? Federal Reserve )an% of
Minneapolis Review 1$, 2H1,.
(ltsky, E. 1#2E. The smmation of random cases as the sorce of cyclic processes. <n "roblems of
Economic &onditions, Iol. +, 5oscow. English trans. in Econometrica -, *1#+E., 1$-H0,.
(olow, &.5. 1#,$. 3n a family of lag distribtions. Econometrica 26, +#+H0$,.
(rivastava, I./. 1#E1. Three;stage least;s1ares and generali8ed doble k;class estimators: a
mathematical relationship. 3nternational Economic Review 12, +12H1,.
(tafford, '.!. 1#6-. <ncome;maintenance policy and work effort: learning from e4periments and
labor;market stdies. <n Social Experimentation, ed. G.=. Casman and @.=. Wise, "hicago:
Dniversity of "hicago !ress.
(tigler, ?.G. 1#-0. The early history of empirical stdies of consmer behavior. #ournal of "olitical
Economy ,2, #-H11+.
(tigler, ?.G. 1#,2. Cenry F. 5oore and statistical economics. Econometrica +$, 1H21.
(tone, G.&.9. 1#0-. The analysis of market demand. #ournal of the Royal Statistical Society (eries =
1$6, 26,H+62.
(tone, G.&.9. et al. 1#-0a. Measurement of &onsumers5 Expenditures and )ehaviour in the 2nited
<indom+ ,-/=0.>, Iols 1 and 2. Fondon: "ambridge Dniversity !ress.
(tone, G.&.9. 1#-0b. Finear e4penditre systems and demand analysis: an application to the pattern
of 7ritish demand. Economic #ournal ,0, -11H2E.
(tone, G.&.9. 1#E6. /eynes, political arithmetic and econometrics. 7ritish =cademy, (eventh /eynes
Fectre in Economics.
(tone, G.&.9. 1#60. The acconts of society. 9obel 5emorial lectre. &eprinted in #ournal of Applied
Econometrics 1, *1#6,., -H26.
Theil, C. 1#-0. Estimation of parameters of econometric models. )ulletin of 3nternational Statistics
3nstitute +0, 122H6.
Theil, C. 1#-6. Economic Forecasts and "olicy4 =msterdam: 9orth;Colland% 2nd edn, 1#,1.
Tinbergen, G. 1#2#H+$. 7estimmng nd @etng von =ngebotskrven: ein 7eispiel. ?eitschrift f@r
9ationalQ%onomie 1, ,,#HE#.
Tinbergen, G. 1#+E. An Econometric Approach to )usiness &ycle "roblems4 !aris: Cerman P "ie
Editers.
Tinbergen, G. 1#+#. Statistical Testin of )usiness &ycle Theories4 Iol. 1: A Method and its
Application to 3nvestment activityA Iol. 2: )usiness &ycles in the 2nited States of America+ ,-,-0
,-./4 ?eneva: Feage of 9ations.
Tobin, G. 1#-6. Estimation of relationships for limited dependent variables. Econometrica 2,, 20H+,.
Treadway, =.7. 1#E1. 3n the mltivariate fle4ible accelerator. Econometrica +#, 60-H--.
Trivedi, !./. 1#E-. Time series analysis verss strctral models: a case stdy of "anadian
manfactring behavior. 3nternational Economic Review 1,, -6EH,$6
Wallis, /.'. 1#EE. 5ltiple time series analysis and the final form of econometric models.
Econometrica 0-, 1061H#E.
Wallis, /. 1#6$. Econometric implications of the &ational E4pectations Cypothesis. Econometrica 06,
0#HE+.
Wegge, F.F. 1#,-. <dentifiability criteria for a system of e1ations as a whole. Australian #ournal of
Statistics +, ,EHEE.
Whewell, W. 16-$. Mathematical Exposition of some Doctrines of "olitical Economy( Second
Memoir4 "ambridge: "ambridge !hilosophical (ociety, 16-,, Transaction #, !t. <. "hilosophical
Society4
White, C. 1#61. "onse1ences and detection of misspecified nonlinear regression models. #ournal of
the American Statistical Association E,, 01#H++.
White, C. 1#62. 5a4imm likelihood estimation of misspecified models. Econometrica -$, 1H2,.
Whittle, !. 1#,+. "rediction and Reulation by 8inear 8east$s6uares Methods4 Fondon: English
Dniversities !ress.
Wickens, 5. 1#62. The efficient estimation of econometric models with rational e4pectations. Review
of Economic Studies 0#, --H,6.
Wicksteed, !.C. 166#. 3n certain passages in Gevons’s theory of political economy. The *uarterly
#ournal of Economics +, 2#+H+10.
Wold, C. 1#+6. A Study in the Analysis of Stationary Time Series4 (tockholm: =lm1vist and Wiksell.
Working, E.G. 1#2E. What do statistical ‘demand crves’ show? *uarterly #ournal of Economics 01,
212H+-.
Wright, !.?. 1#1-. &eview of economic cycles by Cenry 5oore. *uarterly #ournal of Economics 2#,
,+1H01.
Wright, !.?. 1#26. The Tariff on Animal and :eetable Bils4 Fondon: 5acmillan for the <nstitte of
Economics.
Ble, ?.D. 16#-, 16#,. 3n the correlation of total paperism with proportion of ot;relief. Economic
#ournal -, ,$+H11% ,, ,1+H2+.
Ble, ?.D. 1#1-. "rop prodction and price: a note on ?regory /ing’s law. #ournal of the Royal
Statistical Society E6, 5arch, 2#,H6.
Ble, ?.D. 1#21. 3n the time;correlation problem, with special reference to the variate;difference
correlation method. #ournal of the Royal Statistical Society 60, 0#EH-2,.
Ble, ?.D. 1#2,. Why do we sometimes get nonsense correlations between time;series? = stdy in
sampling and the natre of time;series. #ournal of the Royal Statistical Society 6#, 1H,0.
Lellner, =. 1#,2. =n efficient method of estimating seemingly nrelated regressions and tests for
aggregation bias. #ournal of the American Statistical Association -E, +06H,6.
Lellner, =. 1#E#. (tatistical analysis of econometric models. #ournal of the American Statistical
Association E0, ,26H0+.
Lellner, =. 1#60. )asic 3ssues in Econometrics4 "hicago: Dniversity of "hicago !ress.
Lellner, =. 1#6-. 7ayesian econometrics. Econometrica -+, 2-+HE$.
Lellner, =. and !alm, '. 1#E0. Time series analysis and simltaneos e1ation econometric models.
#ournal of Econometrics 2, 1EH-0.
Lellner, =. and Theil, C. 1#,2. Three;stage least s1ares: simltaneos estimation of simltaneos
e1ations. Econometrica +$, -0HE6.

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