R000234954

Modelling Cointegrated ProcessesFinal Report

Principal Investigators: John N. J. Muellbauer and David F. HendryResearch Officers: Jurgen A. Doornik and Gavin Cameron

1 Background

Distributions of estimators, tests, and empirical modelling strategies are greatly affected by data beingintegrated-cointegrated processes, which seems a common phenomenon in macro-economics. Long-run equilibria such as consumption-income relations; purchasing power parity, etc., create cointegratedrelations. Multivariate cointegration modelling has developed rapidly over the last decade, with manyimportant advances: seeinter alia Banerjee, Dolado, Galbraith and Hendry (1993), Hamilton (1994),Hendry (1995), Johansen (1995), Hatanaka (1996), and Hansen and Johansen, 1998. Nevertheless,important modelling difficulties include:

• determining the cointegration rank;• identifying cointegration vectors;• checking weak exogeneity violations from multiple vectors (so conditioning to create ‘partial’

systems must be done with care);• the presence or absence of deterministic terms (constants and trends) in the process and/or the

model can greatly alter limiting distributions;• (asymptotic) similarity of key test statistics to nuisance parameters can be lost by inappropriate

formulations;• finite-sample critical values may differ notably from asymptotic equivalents;• the use of indicator variables can alter critical values; and• the data may beI(2) rather thanI(1), altering the relevant reference limiting distributions.

These problems are compounded by structural breaks ‘mimicking’ integrated processes, and incorrectfunctional form inducing parameter non-constancy. Finally, data measurement errors can camouflage orlose cointegration, even across revision vintages, and seasonality can exacerbate non-stationarity.

Section 2 records the objectives,§3 and§4 the outputs and activities, and§5 the impacts of theresearch. The main methods and results are in§6.1–6.5. Section 6.1 records work on system analysesand weak exogeneity, and§6.2 considers inference inI(1) processes, allowing for other forms of non-stationarity (such as structural breaks). Modelling strategies are discussed in§6.3. Empirical resultson aggregate and regional consumption and housing, money, and productivity and competitiveness arediscussed in§6.4. Developments on the computing front, and the Monte Carlo simulation ‘experimentalengine’ (PcNaive for Windows) based on the high-level language Ox, are reviewed in§6.5.1

2 Objectives

Our research concernedmodelling strategies for cointegrated systems, required because distributions ofestimators and tests are affected by data being integrated (denotedI(1)) and cointegrated. Its five main

1DFH’s publications under L116251015 onThe Econometrics of Economic Forecastingare marked by†, and listedseparately.

1

2

aims were to:

1. develop system analyses, with weak exogeneity tests, for small samples ofI(1) data;2. study inference problems inI(1) systems, tabulating or approximating critical-values;3. develop congruent, theory consistent, and encompassing approaches to cointegratedI(1) pro-

cesses;4. empirically apply these to housing, consumption, portfolio behaviour, productivity and competit-

iveness;5. develop a powerful software system for Monte Carlo simulation of the approach.

All five mains aims of the research were successfully achieved as sections 6.2–6.5 describe. We haveinvestigated all these issues both theoretically and computationally, and applied the resulting develop-ments to a range of macroeconomic time series. Many of our papers involve both theory and empiricalmodelling, and this is reflected in the detailed report ([·] refer to our publications).

3 Outputs

As usual, we devoted considerable time and effort to dissemination. In addition to the10 books, oneedited volume and30 papers published during the course of the award under this grant, another11papers are forthcoming.2 The very acceptance by so many international journals of the output of ourprogram demonstrates the interest in this research. Moreover, a remarkable16 earlier papers by teammembers were reprinted by other scholars over the four-year period. Publications appeared in (interalia) Business Economist; Econometric Reviews; Econometric Theory (2); Economic Journal (2); J.Econometrics (2); OxBull ; andOxReP (3). Two papers were awarded the highest ANBAR Citation ofExcellence (http://www.anbar.co.uk/anbar/excellence/authors.htm).

JAD’s Web site (http://www.nuff.ox.ac.uk/users/doornik/) was a popular source of information andsoftware, with the number of hits nearly50,000in 1997 alone. His page is cross-referenced by manyinformation lists, and was selected by the Scout Report for Business and Economics as a valuableresource for research. The MS-DOS version of Ox is freely downloadable, as is a version of the PcGivesystem, limited only by the database size.

4 Activities

We also presented some30 seminars abroad,11 invited special lectures, a further33 seminars in theUK, and gave61conference papers (of which33were abroad). This comprises more than135presenta-tions in total, across25 countries worldwide, as well as representing the international perspective at theCopenhagen UniversityCity of CultureConference on Cointegration.

5 Impacts

Interest from non-academics and public bodies included Memoranda for the House of Commons; invitedtalks at the Central Banks of Norway (2), Portugal (2), Spain, New Zealand, South Africa, and theBank of England, as well as HM Treasury, DTI, Royal Institute of Chartered Surveyors, GovernmentEconomic Service, Chemical Bank, the European Commission, and the Board of Governors of theFederal Reserve System. The annex provides details.

2These numbers donotcount the further edited volume and13papers published by a principal under the forecasting project,with a further2 books and5 papers forthcoming.

3

6 Methods and results

6.1 System analyses

6.1.1 Modelling dynamic systems

Econometric modelling of cointegrated dynamic systems was considered in the light of general-to-simple modelling of the joint data density[36]. Ten interrelated, reasons for commencing from the jointdensity were proposed:

• the economy is a system;• simultaneous relations may exist;• to test marginalization;• to investigate weak exogeneity;• to check identification;• to analyze cointegration;• to test cross-equation dependencies,• to test super exogeneity;• to check invariance; and• to conduct multistep forecasts.

To offset the modelling burden due to large numbers of variables, equations and parameters, we pro-posed PcFiml[1] (and[11]) as a modelling tool, using graphics to allow large amounts of informationto be appraised at a glance ([4]), and developed a practical strategy for linear small systems. A modeland system typology was proposed[22].

6.1.2 Weak exogeneity

Estimation and inference on individual cointegrated linear relationships in unit-root processes dependscrucially on the presence of weak or strong exogeneity of conditioning variables for the parametersof interest [31]. In I(1) systems, parameters of interest cannot simply be redefined to obtain weakexogeneity: common equilibrium-correction mechanisms (EqCMs) distort inference, and may induceserious over- or under-rejection. Thus, empirical analyses should commence from the joint density totest for long-run weak exogeneity first (§6.5 describes the computer implementation).

6.2 Inference problems inI(1) processes

Paper[52] addresses all the issues noted in§1.

6.2.1 Testing general restrictions on the cointegrating space

We developed and implemented a new switching algorithm for general (possibly non-linear) restrictionson the cointegrating space, to test a wide class of hypotheses, especially weak exogeneity[1]. Thisanalysis was conducted in conjunction with the identification of cointegration vectors. Standard errorsof identified cointegration and feedback parameters were derived and computed.

6.2.2 Structural breaks and unit roots

Using recursive Monte Carlo techniques, we investigated cointegration tests when a marginal processin the cointegrating relationship is stationary around a structural break[23]. The break has little effect

4

on the tests’ sizes, but tests based on estimated equilibrium-correction mechanisms (EqCMs) are morepowerful than the two-step procedure in Engle and Granger (1987) when the DGP does not have acommon factor.

6.2.3 Log versus linear models inI(1) processes

Using the actual values of economic variables, rather than their logs, can induce apparent non-constancyin non-stationary processes. Encompassing tests between these choices were developed, and their finite-sample properties examined using Ox. This revealed both good size and power despite the untreatedheteroscedasticity under the linear specification. Mis-specification tests also had high power, particu-larly the heteroscedasticity test in White (1980).

6.2.4 Data revisions inI(1) processes

When raw series areI(1), revisions are likely to be so as well: sinceI(1) measurement errors pose seriousproblems for modelling (see[8]), a test for which data vintage is the more accurate was developed(compare[41]). Model choice may switch between vintages of data when measurement errors in thefirst vintage yield a congruent model ofy on x even thoughy on z (say) is the DGP. Revision to moreaccurate data can later reveal the correct choice[39].

6.3 Modelling strategies and methodology

A complete overview of econometric modelling was provided in[8]. We also developed a system-modelling strategy for cointegrated data, and applied it to a small monetary model of the UK[36].

6.3.1 General to specific modelling

General-to-specific methods now play a major role in econometric modelling: Hoover and Perez (1996)find exceptionally good behaviour for a modified data-based model-selection procedure by exploringseveral paths, then testing encompassing between them. More generally, such methods avoid direc-tionless strategies and potential contradictions (including thenon sequiturof accepting the alternativehypothesis when the null is rejected), as against commencing from a congruent model[3], [10].

6.3.2 Encompassing and specificity

We proposed a general notion of encompassing, covering both classical and Bayesian viewpoints, as aconcept of sufficiency among models. The parent notion of specificity measures lack of encompassing.Tests for encompassing were discussed and compared to Bayesian posterior odds[21].

6.3.3 On congruent econometric relations

We responded to the claimed criticisms in Faust and Whiteman (1997) of the ‘LSE’ approach to empir-ical macro-econometrics[46], building on[38] Their attempt to inter-relate ‘alternative methodologies’is undone by misconceptions which lead them to seriously incorrect conclusions. To clarify the analysis,the notion of structure was reviewed to underpin sustainable econometric relations, then identificationand exogeneity were reconsidered. The results rebut their claims, and confirm the need for a progressiveresearch strategy which combines the best of both theory and evidence.

5

6.3.4 Econometrics and business cycle empirics

Economic theory and empirical evidence play very different roles in alternative approaches to macroe-conomic modelling[29]. Since relations which are invariant over extensions of the information set intime, interventions, or variables are needed to determine structure, some approaches fail to offer a vi-able route for structural econometrics. Our analysis focused on the problem of theory dependence versussample dependence when modelling data by econometric methods. Six aspects of the determination ofstructure in practice were related to business-cycle modelling practice. Paper[13] overviews businesscycles.

6.3.5 History of econometrics

The major book[7] was completed, establishing the record for how modern econometrics evolved.Earlier work was placed in context, including replicating most of the reported empirical research, andevaluating it using the modern techniques embedded in PcGive. We also reviewed the contributions ofH. Wold and J. Tinbergen[40], [26].

6.3.6 Vector tests

Vector normality (JAD with H. Hansen) and error autocorrelation tests (using Rao’sF-approximation)were developed and simulated for VARs and SEMs, showing the tests to have good size and powerproperties ([1]). Experiments on uncorrected vector heteroscedasticity tests showed the test does notwork well, because it is hard to control size as the dimension of the system grows.

6.3.7 Encompassing in stationary linear dynamic models

A modelM1 encompasses a rival modelM2 if M1 can explainM2’s results[37]. A Wald encompassingtest (WET) checks if a statistic of interest toM2 coincides with an estimator of its predicted value underM1. We proposed techniques for evaluating WETs in conditional equations, extending results for strongexogeneity. The completing system plays a fundamental role in determining the test outcomes, so a sys-tem approach is essential. Dynamics can constrainM1’s predictions ofM2’s findings, so encompassingtests can differ from existing tests, as examples illustrated. The asymptotic power functions comparedwell with the outcomes in a small Monte Carlo, and support the use of parsimonious-encompassingtests. The testing of rational expectations was also considered[48].

6.3.8 Implications for econometric modelling of forecast failure

To reconcile forecast failure (relative to fit) with congruent empirical modelling, we analyzed the sourcesof mis-prediction[14]. This revealed thatex anteforecast failure was primarily a function of forecast-period events, not determinable from in-sample information. The primary causes are unmodelled shiftsin deterministic factors, rather than model mis-specification, collinearity, or a lack of parsimony. We ex-amined the effects of deterministic breaks on EqCMs using Monte Carlo simulations based on PcNaive,and empirical models, to illustrate the analysis.

6.4 Empirical applications

The areas investigated included consumers’ expenditure, house prices, financial liberalization, mortgagearrears and possessions, aggregate income determination, productivity change, trade and competitive-ness, and money demand.

6

6.4.1 Modelling consumption

The failures of economic management and econometric modelling in the UK in the 1980s and early1990s reveal that the behaviour of aggregate consumption was not well understood. Modellers failedto forecast the consumer boom of the 1980s and, to a degree, the fall in consumption in the early1990s. There are other empirical consumption puzzles. One is the secular decline in US personal sectorsaving rates between the mid 1970s and the mid 1980s. Furthermore, standard life-cycle/permanent-income theory seems to be contradicted by empirical evidence: the old save too much; in cross-sections,consumption follows income too closely; and consumption growth, in theory unpredictable, respondssignificantly to anticipated income growth. A third is the ‘excess-smoothness’ puzzle.

Two survey articles addressed these issues as well as comparing the Euler equation approach tomodelling consumption with the solved-out approach[28], [32]. The former, popular since Hall (1978),claims theoretical advantages, but throws away long-run cointegrating information preserved by thelatter. The articles show how, to an approximation, realistic economic theory implications of behaviourunder uncertainty, not fully rational income expectations, credit constraints, habits and durability, thedistinctions between liquid and illiquid assets, and aggregation when lives are finite, can all be built intoaggregate consumption functions of the solved-out kind.

The omission from pre-existing consumption functions of realistic wealth effects, financial liber-alization, income uncertainty and income expectations hold much of the key to underestimating bothboom and bust in UK consumption in the last 15 years. These conclusions are supported in work byJNJM (with A. Murphy) on regional consumption functions for the 11 standard regions of the UK. Theyaddress the Lucas (1976) critique explicitly, by building in parameter shifts in consumption behaviourcaused by financial liberalization and shifts in macropolicy feedback rules affecting income expecta-tions. Among the substantive conclusions for policy makers studying the UK economy are:

• Financial liberalization tended to increase both the spendability of illiquid wealth and the drag onspending from debt.

• Changes in illiquid assets, such as housing and shares, had an increasing impact on consumptionover the eighties, and now have almost1/2 the effect of changes in net liquid assets.

• Every£ of debt now decreases spending two to three times as much as every£ of housing or otherilliquid wealth increases it.

• There is evidence of increased responsiveness of consumption to real interest rates and incomegrowth expectations after financial deregulation.

The shifts in behaviour in the UK over time parallel important differences in behaviour across countrieswith different credit, financial and housing systems. The UK has a high owner-occupancy rate, a smallmarket rental sector, wide credit availability, low transactions costs in housing, and largely floating ratemortgages. The situation in Germany is almost diametrically opposed: changes in interest rates havetheir main effects on consumption via asset prices and income-growth expectations. Thus, a commoninterest rate policy under EMU is likely to have very different consequences in the UK than Germany.If the UK joins EMU, it will be important to develop new policy instruments operating on credit growthand asset values to compensate for the interest rate instrument which is being given up.

Work with J. Aron on South African savings behaviour using quarterly macro-data finds that similarshifts took place in the spendability of illiquid assets there as a result of extensive domestic financialliberalization in the second half of the 1980s and the 1990s. Although there was no overall boom inasset values, the personal sector saving rate still declined. This has significant policy implications forSouth Africa, where the decline in personal saving, in the context of declining government saving, is ofconsiderable concern to policy makers.

7

A further study by DFH reconsidered the HUS model on a recent data vintage[39]. The data wereextensively revised since that study, such that their model no longer held even over the same sampleperiod. Issues of aggregation, seasonality, liquidity, uncertainty, dynamics, cointegration, structuralchange, financial deregulation, inflation and relative prices were considered. A revised specificationwas proposed which seemed congruent with the data evidence and was constant over the sample.

6.4.2 House prices

The paper on booms and busts in UK house prices parallels the consumption research, and supports thepolicy conclusions discussed above[12]. The theory of housing demand is examined in an intertemporalcontext, taking into account expectations, credit constraints, lumpy transactions costs, and uncertainty.The resulting equation for real house prices is an inverted housing-demand function. The theory predictsseveral shifts in parameters as a result of the financial liberalization of the 1980s. One of these concernsshifts in wealth effects, already analyzed in work on UK consumer spending at a national and regionallevel. The empirical evidence supports similar shifts in the housing demand function. Furthermore, thetheory predicts an increased role for income growth expectations and real interest rates in the 1980s,strongly borne out by the empirical evidence.

The presence of lumpy transactions costs results in important nonlinearities, or threshold effects,in the aggregate demand for housing. These arise from the extensive margin of housing demand: thegreater is appreciation of house prices, actual and prospective, the more households are pulled over thetransactions-cost hurdle to engage in trade. At these times of heightened activity or ‘frenzy’, sharplyincreased demand feeds back into higher prices. Such ‘frenzy’ effects were first included in house priceequations in Hendry (1984). The resulting volatility of UK house prices contrasts strongly with theirrelative stability in countries such as Germany, Italy and France (outside Paris).

Their research on regional house prices throws further light on house price dynamics. Among thesubstantive conclusions are that movements in regional house prices tend to be self-reinforcing (interalia) because expectations of the financial gains or losses from changing house values tend to extrapolatepast capital gains or losses.3

6.4.3 Financial liberalization

Increased consumer credit availability has important repercussions for consumer behaviour, and hencefor macroeconomic fluctuations as demonstrated in our papers on consumption and house prices. JNJMdeveloped an index of mortgage credit conditions that captures the financial deregulation of the 1980s,together with more recent changes in mortgage markets. Previously proposed measures, includingcredit/GDP ratios, interest rate differentials between borrowing and lending rates and loan-to-value andloan-to-income ratios, are defective: they depend also on interest rates, income, wealth, expectationsof income, of inflation and of asset prices and on consumer uncertainty. His paper analyses a panelof UK regional data on loan-to-value ratios for first-time buyers for 1971–1995. Time effects uniformacross regions for the 1980s and 1990s are used to estimate a credit-conditions index, after controllingfor economic variables. This index shows a sharp jump in the early 1980s and reaches a peak in the late1980s. In turn, this index is used in[12], [28] and[39].

3This research received partial support from the Joseph Rowntree Trust.

8

6.4.4 Arrears and possessions

Earlier work on data up to 1990 suggested that aggregate rates of arrears and possession are cointegrated(together with interest rates and perhaps other variables), see Breedon and Joyce (1992), Allen and Milne(1994) and Brookes, Dicks and Pradhan (1994).

Post-1990 data reject this finding – a classic case of a structural break. A series of papers by JNJMwith GC and DFH brings to bear a variety of data sets to analyze the nature of this break. JNJM and GCanalyze regional county-court data on mortgage possessions actions, orders and suspended orders to tryto separate the differencing influences of policy shifts by the courts and by the mortgage lenders[15].JNJM and DFH analyzed aggregate data on rates of arrears and possession from the Council of MortgageLenders, and for one particular mortgage lender, and find strong confirmation that a temporary softeningof policy both reduced rates of possession below, and increased ratios of arrears above, where theywould otherwise have been. It appears that the courts reverted to normal procedures more quickly thanthe mortgage lenders. The longer duration of the policy shift for the latter is probably associated withNovember 1991 decision to pay DSS mortgage support for unemployment benefit claimants directly tomortgage lenders rather than to households. Further confirmation of a policy shift comes from analyzinga set of data on possessions by vintage of original loan from one mortgage lender, JNJM with GC andDFH. These data allow more precise links to be made between a precarious debt/equity position and theprobability of possession than is possible for more aggregate data. They also provide confirmation that,in addition to the debt/equity position, there are important cash flow causes of possession.

JNJM also investigated the well-known measurement biases in the published mortgage arrears data(the number of mortgages 6-months or more in arrears) to check that these are not responsible for thestructural break in the possessions/arrears relationship.

6.4.5 Aggregate income determination and policy feedback rules

[18] analyzed and forecast annual time series of aggregate real income per head in the US. The approachintegrates elements from recent univariate time-series analyses with multi-equation macromodels inwhich policy feedback rules have been endogenized. The main conclusions were:

First, aggregate real per capita income is subject to significant trend reversion. This conclusioncomes through clearly by examining the data at an annual rather, than the more usual quarterly, fre-quency and by incorporating multivariate economic content in the income process. Split time trends, ora low varianceI(2) stochastic trend, model the underlying trends in income. Secondly, there is signific-ant evidence for the Lucas (1976) or Haavelmo (1944) critique: in the US, there appears to have been ashift in the structural macropolicy reaction function causing a corresponding shift in the reduced-formincome forecasting equation, associated with increased concern in the late 1980s over the size of USbudget deficits. Thirdly, useful real income forecasts can be made three years ahead. Finally, the em-pirical evidence shows the effectiveness of monetary policy on real output or income: a change in theshort-term interest rate is highly significant in forecasting income growth up to three years later.

The paper estimated a structured, parsimonious VAR of fourI(1) variables and threeI(0) variables:log real income, the unemployment rate, the government surplus to GDP ratio and the trade surplus toGDP ratio in theI(1) set, and the change in the nominal interest rate, the change in competitiveness andthe change in the log real stock price index in theI(0) set. A separate cointegration analysis suggestedthat, for 1951–1988 when tests for parameter stability are broadly acceptable, there are 3 cointegratingvectors (even more conclusively when conditioning on theI(0) variables). The long-run coefficients inthe parsimonious income forecasting equation correspond approximately to those obtained from a linearcombination of the 3 cointegrating vectors.

9

6.4.6 Productivity change

Recent developments in the theory of economic growth emphasize the roles of human capital andprofit seeking R&D activities of firms: see[6], [19], [20], and [43]. The four principal issues con-cern: spillovers in the innovation process; the relationship between R&D spending and innovation; andthe causal and temporal links between innovation and physical investment; the relationship betweeninternational openness and economic growth: see[42], [44] and [45]. This last concern tests whetheropenness affects (a) the rate of domestic innovation or the fraction of knowledge that can be transferred,versus (b) the rate of technology transfer. The main empirical results provide a body of evidence notonly to support the claim that openness and productivity growth are closely associated, but also that isconsistent with the hypothesis that openness increases the rate of adoption of technology developed inmore advanced economies[16].

The overall main conclusions that emerged were[33]–[35]:Most of the growth in aggregate UK manufacturing productivity is due to growth within sectors,

rather than switches in factor resources between sectors. Thus, the impact of openness on growth workslargely through its effects on the incentives to innovate or adopt technology relative to engaging in cur-rent production within sectors, rather than through the reallocation of resources across sectors resultingfrom changes in comparative advantage[27].

Labour productivity in the UK is correlated with a number of measures of openness. This correl-ation is explained by an association between openness and Total Factor Productivity but not capitalaccumulation. This is consistent with the hypothesis that openness affects growth through the rate oftechnological change rather than through investment. Indeed, within UK manufacturing, open sectorshave recorded significantly higher TFP growth than closed sectors.

The rate of productivity growth in UK manufacturing is associated with differences in the initiallevel of total factor productivity between the UK and the US. From 1970 to 1992, some 15% of theinitial gap in levels of TFP between the two countries was closed. The rate at which the gap was closedwas fastest in sectors with the lowest initial levels of relative TFP. This is consistent with the hypothesisthat the adoption of technology is an important determinant of productivity growth.

The rate at which a manufacturing sectors productivity converges to the US level depends uponthe level of international openness - as measured by the flow of goods and the flow of ideas, but notthe flow of capital. That is, trade in goods and the spillover of ideas accelerate the rate at which UKproductivity converges to US levels. This finding remains true even when we allow for changes incapacity utilization, the degree of unionization, the intensity of domestic R&D and the level of humancapital.4

6.4.7 Modelling linear dynamic econometric systems

The demand for M1 in the UK was modelled as a system using the approach described in§6.1 and§6.2, to establish a congruent model[36]. We showed that inflation, the interest rate and output interactclosely but are weakly exogenous in the money demand equation, which closely reproduces in a systemearlier findings in single equations[41].

6.4.8 UK broad money

The extended annual model of the demand for broad money in the UK over a sample1875 − 1993takes account of changed data definitions, and appropriate measures of opportunity cost and credit

4GC was awarded a DPhil for his research on innovation and economic growth.

10

deregulation[47]. The model’s parameters are empirically constant over the extended sample, whichwas economically rather turbulent. It encompasses the phase-average model[49].

6.4.9 Constancy

Parameter constancy is a fundamental requirement for empirical models to be useful for forecasting,analyzing economic policy, or testing economic theories[25]. However, constant-parameter modelscan have time-varying coefficients, and expanded parameterizations over time . A comparison of twomodels of UK money demand illustrates the analysis empirically: one suffers predictive failure but theother does not, despite being identical in-sample.

6.4.10 Cointegration analysis of UK inflation

The history of cointegration and related notions were illustrated (live at theCity of Culture Conference)in the context of long-run inflation, which has been the centre of much economic policy, and manytheoretical and empirical analyses[17]. Most extant theories of inflation have elements of truth as manyeffects matter empirically, including: excess demands for goods and services, factors of production, andfinancial assets; direct external shocks (exchange rates and imported inflation); unfunded deficits; andspecial factors such as wars, commodity-price shocks, and price controls.

6.4.11 Demand for food in the USA

A ‘general-to-specific’ modelling approach was applied to the US annual food expenditure time seriesin Magnus and Morgan (1995), using updated data from Tobin (1950). The analysis demonstrates thevalue of multivariate cointegration analysis and weak exogeneity reductions to develop a congruentmodel over 1931–1989, despite important structural changes[51].

6.5 Computational aspects of cointegration analysis

Most computational aspects of cointegration analysis were investigated. A numerically stable solutionto the general cointegration algorithm was found using singular-value decompositions,which workedwhen the traditional implementation failed.5

An important advance was solving the identification problem when imposing restrictions on thecointegrating space[1]. Counting parameter restrictions does not yield the degrees of freedom of thelikelihood-ratio test statistic. This problem had been solved under linear within equation restrictionsonly. We derived and implemented a general solution, which verifies identification prior to estimatingrestricted cointegrating vectors, using a sophisticated switching algorithm for testing restrictions on thecointegrating space, where restrictions are rewritten, and scale restrictions temporarily removed, duringmaximization.

Approximations to the asymptotic distributions of cointegration tests were developed (inI(1) andI(2) models) using the Gamma distribution[52]. Formulae for the parameters of the Gamma distribu-tions were derived from response surfaces. The resulting approximations are easy to implement andwork well enough to replace standard tables. Ox code is available from JAD’s web page.

5JAD was awarded a DPhil for his work on Computational Econometrics.

11

6.5.1 Simulation software

Object-oriented and visual programming have shaped PcNaive. There is a ‘front end’ (an intelligent,user-friendly interface, PcNaive) and a ‘back end’ (powerful computational engine, Ox:[5]). The frontend allows the user to design experiments (formulate DGPs, models, estimators and tests within thePcFiml class), then writes a computer program run by the back end. Previous runs provide a basis forfurther simulations. A vast range of experiments can be done recursively, graphed in ‘real time’ andeasily analyzed. The object-oriented matrix language Ox (designed and written by JAD, and closelyresembling C++) has a Pcnaive class (to generate observations), a simulation class (to replicate experi-ments and accumulate information), and a Pcfiml class (to formulate and estimate models, and computetest statistics), used in§6.2.3 and§6.3.6, as well as by other researchers. Ox provides asymptoticanalyses, structural break tests, custom transformations, and plotting facilities. The new PcNaive is avaluable aid in teaching econometrics, and with the flexibility of Ox, is a powerful research tool. Workon the accompanying book is well advanced.

6.5.2 The evolution of econometric modelling software

[50] discussed the evolution of our software, and its influence on econometrics. The main trends arefrom ‘techniques’ to graphical tools; a formalization of the econometric modelling methodology; andan emphasis on the user interface. Software has enabled previously infeasible calculations, allowedgraphical presentation of an otherwise incomprehensible mass of output, and altered how econometricmodelling is practiced, substantially improving the quality of empirical research.

6.5.3 A window on econometrics

[24] illustrates how econometricians practice their subject, but using primarily graphical tools basedon software which shows data, results, reports, and graphics simultaneously on screen[4]. It seeks tocapture the learning process involved in econometric modelling. The main concepts of modern time-series econometrics are illustrated, avoiding technical derivations, for a model of UK inflation over thepast century, finding an important role for excess demand.

6.5.4 PcGive

Several releases of the PcGive system provided major updates to econometric modelling software withextended data bases, improved graphics, precision, speed, and flexibility, including programming non-linear procedures ([1], [3], [4], [10], and [11]). The system modelling provides a complete cointeg-ration analysis, offers the full range of system estimators recursively (including constrained models),and implements a model reduction strategy from general to specific. Two extensive books documentthe econometric methods and the software, with extensive tutorials to facilitate teaching and learningeconometrics while working at the computer. Detailed, context-sensitive, hypertext help is always avail-able.

6.5.5 Other programs

ARFIMA Work on the fractionally integrated ARMA model (with M. Ooms) resulted in a reductionof the storage requirement fromO(T 2) to O(T ), making application of MLE to larger samples feasible.An ARFIMA class in Ox was made available over the internet.

12

Dynamic forecast standard errors A more elegant derivation was obtained of the formula for thevariance of dynamic forecast standard errors in open systems with non-modelled variables. These stand-ard errors have been implemented in software, and can be graphed easily[1].

7 Future research priorities

Our work has generated a large number of new directions for future research, documented in our recentlysuccessful ESRC application for a general investigation of non-stationarity in econometrics.

References

Allen, C., and Milne, A. (1994). Mismatch in the housing market.Urban Studies, 31, 1451–1463.

Banerjee, A., Dolado, J. J., Galbraith, J. W., and Hendry, D. F. (1993).Co-integration, Error Correctionand the Econometric Analysis of Non-Stationary Data. Oxford: Oxford University Press.

Breedon, F. J., and Joyce, M. A. (1992). House prices, arrears and repossessions: A three equationmodel for the UK.Bank of England Quarterly Bulletin, May, 173–179.

Brookes, M., Dicks, M., and Pradhan, M. (1994). An empirical modelof mortgage arrears and repos-sessions.Economic Modelling, 2, 134–144.

Engle, R. F., and Granger, C. W. J. (1987). Cointegration and error correction: Representation, estima-tion and testing.Econometrica, 55, 251–276.

Faust, J., and Whiteman, C. H. (1997). General-to-specific procedures for fitting a data-admissible,theory-inspired, congruent, parsimonious, encompassing, weakly-exogenous, identified, struc-tural model of the DGP: A translation and critique. mimeo, Federal Reserve Board, Washington.Forthcoming, Carnegie–Rochester Conference Series on Public Policy.

Haavelmo, T. (1944). The probability approach in econometrics.Econometrica, 12, 1–118. Supplement.

Hall, R. E. (1978). Stochastic implications of the life cycle-permanent income hypothesis: Evidence.Journal of Political Economy, 86, 971–987.

Hamilton, J. D. (1994).Time Series Analysis. Princeton: Princeton University Press.

Hansen, P. R., and Johansen, S. (1998).Workbook on Cointegration. Oxford: Oxford University Press.

Hatanaka, M. (1996).Time-Series-Based Econometrics: Unit Roots and Cointegration. Oxford: OxfordUniversity Press.

Hendry, D. F. (1984). Econometric modelling of house prices in the United Kingdom. In Hendry, D. F.,and Wallis, K. F. (eds.),Econometrics and Quantitative Economics, pp. 135–172. Oxford: BasilBlackwell.

Hendry, D. F. (1995).Dynamic Econometrics. Oxford: Oxford University Press.

Hoover, K. D., and Perez, S. J. (1996). Data mining reconsidered: Encompassing and the general-to-specific approach to specification search. Mimeo, Economics department, University of Califor-nia, Davis.

Johansen, S. (1995).Likelihood-based inference in cointegrated vector autoregressive models. Oxford:Oxford University Press.

Lucas, R. E. (1976). Econometric policy evaluation: A critique. In Brunner, K., and Meltzer, A. (eds.),The Phillips Curve and Labor Markets, Vol. 1 of Carnegie-Rochester Conferences on PublicPolicy, pp. 19–46. Amsterdam: North-Holland Publishing Company.

13

Magnus, J. R., and Morgan, M. S. (1995). The experiment in applied econometrics. Discussion paper,London School of Economics, London.

Tobin, J. (1950). A statistical demand function for food in the U.S.A..Journal of the Royal StatisticalSociety, A, 113(2), 113–141.

White, H. (1980). Non-linear regression on cross-section data.Econometrica, 48, 721–746.

14

Annex: Publications and disseminationBooks

[1] Modelling Dynamic Systems using PcFiml. International Thomson Business Press, 1997. (DFHwith JAD).

[2] Co-integration and Dynamics in Economics, Journal of Econometrics, Special Issue, 80, 1997.(DFH edited with N. Shephard).

[3] Empirical Econometric Modelling using PcGive. International Thomson Business Press, 1996.(DFH with JAD).

[4] GiveWin: An Interface to Empirical Modelling. International Thomson Business Press, 1996.(DFH with JAD).

[5] Ox: An Object-oriented Matrix Programming Language. International Thomson Business Press,1996. (JAD).

[6] Options for Britain – A Strategic Policy Review, Dartmouth, 1996. (GC edited with D. Halpern,S. Wood and S. White).

[7] The Foundations of Econometric Analysis. Cambridge University Press, 1995. (DFH edited withM.S. Morgan).

[8] Dynamic Econometrics. Oxford University Press, 1995. (DFH)[9] Structural Time Series Modelling Manual, Chapman and Hall, 1995. (JAD with A.C. Harvey, S.J.

Koopman and N. Shephard).6

[10] PcGive 8: An Interactive Econometric Modelling System. Chapman and Hall & Duxbury Press,1994. (DFH with JAD).

[11] PcFiml 8: Interactive Econometric Modelling of Dynamic Systems. Chapman and Hall, 1994.(DFH with JAD).

Papers

[12] ‘Booms and Busts in the UK Housing Market’,Economic Journal, 107, 1701–1727, 1997. (JNJMwith A. Murphy)

[13] ‘The Assessment: Business Cycles’,Oxford Review of Economic Policy, 13, 1–18, 1997. (JNJM)[14] ‘The Implications for Econometric Modelling of Forecast Failure’,Scottish Journal of Political

Economy, Centenary Issue, 44, 437–61, 1997. (DFH with JAD).[15] ‘A Regional Analysis of Mortgage Possessions: Causes, Trends and Future Prospects’,Housing

Finance, 34, pp. 25–34, 1997. (GC and JNJM). A longer version was published asCouncil ofMortgage Lenders Discussion Paper, No. 2, September.

[16] ‘Deconstructing Growth in UK Manufacturing’, Bank of England Discussion Paper no. 73, 1997.(GC with J. Proudman and S. Redding).

[17] ‘Cointegration Analysis: An International Enterprise’,Centre-of-Excellence Conference Proceed-ings, 190–208, 1997. Copenhagen University. (DFH).

[18] ‘Income Persistence and Macropolicy Feedbacks in the US’,Oxford Bulletin of Economics andStatistics, 58, 703–733, 1996. (JNJM)

[19] ‘On the Measurement of Real R&D: Divisia Price Indices for UK Business Enterprise R&D’,Research Evaluation, 6, 215-219, 1996. (GC)

[20] ‘Innovation and Economic Growth’, Centre for Economic Performance, LSE, Discussion PaperNo. 277, 1996. (GC).

6A reduced version was published as well, consisting of the first part only.

15

[21] ‘Encompassing and Specificity’,Econometric Theory, 12, 620–56, 1996. (DFH with J-P. Florensand J-F. Richard).

[22] ‘Typologies of Linear Dynamic Systems and Models’,Journal of Statistical Planning and Infer-ence, 49, 177–201, 1996. (DFH)

[23] ‘Cointegration Tests in the Presence of Structural Breaks’,Journal of Econometrics, 70, 187–220,1996. (DFH with J. Campos and N.R. Ericsson).

[24] ‘A Window on Econometrics’,Cyprus Journal of Economics,8, 77–104, 1996. (DFH with JAD).[25] ‘On the Constancy of Time-Series Econometric Equations’,Economic and Social Review, 27,

401–22, 1996. (DFH)[26] ‘Jan Tinbergen: 1903–1994’,Journal of the Royal Statistical Society, A, 159. 614–6, 1996. (DFH

with M.S. Morgan).[27] ‘Knowledge and Increasing Returns in the UK Production Function’, in M. Lansbury and D.

Mayes, (eds.),Sources of Productivity Growth in the 1980s, London: Simon & Schuster, 1995.(GC and JNJM).

[28] ‘The Consumption Function: A Theoretical and Empirical Overview’, in M.H. Pesaran and M.Wickens, (eds),Handbook of Applied Econometrics, Oxford: Basil Blackwell, 1995. (JNJM withR. Lattimore).

[29] ‘Econometrics and Business Cycle Empirics’,Economic Journal (Controversies), 105, 1622–36,1995. (DFH) (ANBAR Citation of Excellence)

[30] ‘The Role of Econometrics in Scientific Economics’, 172–196 in A. d’Autume and J. Cartelier(eds.)L’Economie Devient-elle une Science Dure?Paris: Economica (in French), 1995. (DFH)

[31] ‘On the Interactions of Unit Roots and Exogeneity’,Econometric Reviews, 14, 383–419, 1995.(DFH).

[32] ‘The Assessment: Consumer Expenditure’,Oxford Review of Economic Policy, 1–41, 1994.(JNJM)

[33] ‘Productivity and Innovation in UK Manufacturing’,Memorandum for the House of CommonsSelect Committee on Science and Technology, 1994. (JNJM and GC).

[34] ‘Innovation, Productivity and the Case for a UK R&D Tax Credit’,Memorandum for the Houseof Commons Select Committee on Science and Technology, 1994. (GC)

[35] ‘Innovation in UK Manufacturing’,The Business Economist, 25, 3, 1994. (GC)[36] ‘Modelling Linear Dynamic Econometric Systems’,Scottish Journal of Political Economy, 41,

1–33, 1994. (DFH with JAD).[37] ‘Encompassing in Stationary Linear Dynamic Models’Journal of Econometrics, 63, 245–70,

1994. (DFH with B. Govaerts and J-F. Richard).[38] ‘The Theory of Reduction in Econometrics’ inIdealization in Economics (Poznan Studies in the

Philosophy of the Sciences and the Humanities), 38, 71–100, 1994. (DFH with S. Cook).[39] ‘HUS Revisited’,Oxford Review of Economic Policy, 10, 86–106, 1994. (DFH)[40] ‘The ET Interview: Professor H.O.A. Wold, 1908–1992’,Econometric Theory, 10, 419–33, 1994.

(DFH with M.S. Morgan).[41] ‘Cointegration, Seasonality, Encompassing and the Demand for Money in the United Kingdom’,

179–224 in C. Hargreaves (ed.),Non-stationary Time-Series Analyses and Cointegration. OxfordUniversity Press, 1994. (DFH with N.R. Ericsson and H-A. Tran).

16

Forthcoming

[42] ‘Productivity Growth in an Open Economy: The Experience of the UK’ (GC with J. Proudmanand S. Redding), in Barrell, R. (ed.)Productivity and Competitiveness, Cambridge: CUP, 1998.

[43] ‘Economic Growth in the Information Age: From Physical Capital to Weightless Economy’,Journal of International Affairs, 51, no. 2, 1998. (GC)

[44] ‘Productivity Convergence and International Openness’, Bank of England Discussion Paper,1998. (GC with J. Proudman and S. Redding).

[45] ‘Openness and its Association with Productivity Growth in UK Manufacturing’, Bank of EnglandDiscussion Paper, 1998. (GC with J. Proudman and S. Redding).

[46] ‘On Congruent Econometric Relations’,Journal of Money, Credit and Banking, 1998. (DFH)[47] ‘The UK Demand for Broad Money over the Long Run’,Scandinavian Journal of Economics,

Centenary Issue, 100, 1998. (DFH with N.R. Ericsson and K.M. Prestwich).[48] ‘Encompassing and Rational Expectations’,Empirical Economics, 1998. (DFH with N.R. Eric-

sson).[49] ‘Friedman and Schwartz (1982) Revisited: Assessing Annual and Phase-Average Models of

Money Demand in the United Kingdom’,Empirical Economics, Special Issue on Money Demandin Europe, 1998. (DFH with N.R. Ericsson and K. Prestwich).

[50] ‘The Impact of Computational Tools on Time-series Econometrics’,British Academy, 1998.(DFH with JAD).

[51] ‘An Econometric Analysis of US Food Expenditure, 1931–1989’, in J.R. Magnus and M.S. Mor-gan, (eds.)Two Experiments in Applied Econometrics, John Wiley, 1998. (DFH).

[52] ‘Inference in Cointegrated Models: UK M1 Revisited’,Journal of Economic Surveys, SpecialIssue on Cointegration, 1998. (JAD and DFH with B. Nielsen)

Reprints

[53] ‘On the Formulation of Empirical Models in Dynamic Econometrics’, in P.F. Whiteley (ed.)Eco-nomic Policy, Edward Elgar, 1998. (DFH with J-F. Richard).

[54] ‘An Econometric Analysis of UK Money Demand inMonetary Trends in the United States andthe United Kingdomby Milton Friedman and Anna J. Schwartz’, in P.F. Whiteley (ed.)op. cit.(DFH with N.R. Ericsson), 1998.

[55] ‘Econometrics: Alchemy or Science?’, in P.F. Whiteley (ed.),op. cit. (DFH).[56] ‘An Econometric Analysis of UK Money Demand inMonetary Trends in the United States and

the United Kingdomby Milton Friedman and Anna J. Schwartz’, 256–86 in O.F. Hamouda andJ.C.R. Rowley (eds.)The Reappraisal of Econometrics, Edward Elgar, 1997. (DFH with N.R.Ericsson).

[57] ‘The Encompassing Implications of Feedback versus Feedforward Mechanisms in Econometrics’,238–55 in O.F. Hamouda and J.C.R. Rowley (eds.),op. cit. (DFH)

[58] ‘The Econometric Analysis of Economic Time Series (with Discussion)’, 448–500 in O.F.Hamouda and J.C.R. Rowleyop. cit. (DFH with J-F. Richard).

[59] ‘The Role of Econometrics in Scientific Economics’, (originally in French), in English inIs Eco-nomics Becoming a Hard Science? by Edward Elgar, 1997. (DFH).

[60] ‘The Assessment: Consumer Expenditure’, inOxford Review of Economic Policy, 1994, 1–41.Reprinted in T. Jenkinson (ed.),Readings in Macroeconomics, 92–126. Oxford University Press,1996. (JNJM).

17

[61] ‘Productivity and Competitiveness: Economic Policy in the 1980s’,Oxford Review of EconomicPolicy, Autumn 1991, 99–113. Reprinted in T. Jenkinson (ed.),op. cit., 219–235. (JNJM).

[62] ‘An Econometric Analysis of TV Advertising Expenditure in the United Kingdom’, 275–307 inN.R. Ericsson and J.S. Irons (eds.),Testing Exogeneity, Oxford: Oxford University Press, 1995.(DFH)

[63] ‘Exogeneity’, 39–70 in N.R. Ericsson and J.S. Irons (eds.),op. cit. (DFH with R.F. Engle and J-F.Richard).

[64] ‘The Encompassing Implications of Feedback versus Feedforward Mechanisms in Econometrics’,71–92 in N.R. Ericsson and J.S. Irons (eds.),op. cit. (DFH)

[65] ‘Testing Super Exogeneity and Invariance in Regression Equations’, 93–119 in N.R. Ericsson andJ.S. Irons (eds.),op. cit. (DFH with R.F. Engle).

[66] ‘On the Formulation of Empirical Models in Dynamic Econometrics’, 223–53 in D.J. Poirier(ed.),The Methodology of Econometrics, Edward Elgar, 1994. (DFH with J-F. Richard).

[67] ‘The ET Dialogue: A Conversation on Econometric Methodology’, in D.J. Poirier (ed.),op. cit.,345–435, 1994. (with E.E. Leamer and D.J. Poirier). (DFH)

[68] ‘The Theory of Reduction in Econometrics’, in Spanish, inCarnueros Economicos de ICE, 1994.(DFH with S. Cook).

Forecasting PublicationsBooks

[69] The Econometric Analysis of Economic Policy. Oxford: Blackwell Publishers. Also publishedasOxford Bulletin of Economics and Statistics, Special Issue, 58, 1997. (DFH edited with A.Banerjee and G.E. Mizon).†

Forthcoming

[70] Forecasting Economic Time Series. Cambridge University Press. (DFH with M.P. Clements): inPress, 1998.(Marshall Lectures).†

[71] The Zeuthen Lectures on Economic Forecasting. MIT Press, 1998. (DFH with M.P. Clements).†

Papers

[72] ‘An Empirical Study of Seasonal Unit Roots in Forecasting’,International Journal of Forecasting,13, 341–55, 1997. (DFH with M.P. Clements).†

[73] ‘The Econometrics of Macroeconomic Forecasting ’,Economic Journal, 107, 1330–57, 1997.(DFH)†

[74] ‘The Econometric Analysis of Economic Policy’,Oxford Bulletin of Economics and Statistics,Special Issue, 58, 573–600, 1996. (DFH with A. Banerjee and G.E. Mizon).†

[75] ‘Multi-step Estimation for Forecasting’,Oxford Bulletin of Economics and Statistics,58, 657–84,1996. (DFH with M.P. Clements).†

[76] ‘An Evaluation of Forecasting using Leading Indicators’,Journal of Forecasting, 15, 271–91,1996. (DFH with R.A. Emerson).†(ANBAR Citation of Excellence)

[77] ‘Intercept Corrections and Structural Breaks’,Journal of Applied Econometrics, 11, 475–94,1996. (DFH with M.P. Clements).†

[78] ‘Forecasting in Macro-Economics’, 101–41 in D.R. Cox, D.V. Hinkley and O.E. Barndorff–Nielsen (eds.),Time Series Models in Econometrics, Finance and Other Fields. Chapman and

18

Hall, 1996. (DFH with M.P. Clements). Also published in a Russian Translation. Moscow:TVP-Interkniga.†

[79] ‘Macro-Economic Forecasting and Modelling’,Economic Journal (Policy Forum), 105, 1001–13,1995. (DFH with M.P. Clements).†

[80] ‘A Reply to Armstrong and Fildes’,Journal of Forecasting, 14, 73–76, 1995. (DFH with M.P.Clements).†

[81] ‘Forecasting in Cointegrated Systems’,Journal of Applied Econometrics, 10, 127–46, 1995.(DFH with M.P. Clements).†

[82] ‘Towards a Theory of Economic Forecasting’, 9–52 in C. Hargreaves (ed.),Non-stationary Time-Series Analyses and Cointegration. Oxford University Press, 1994. (DFH with M.P. Clements).†

[83] ‘On a Theory of Intercept Corrections in Macro-Econometric Forecasting’, 160–80 in S. Holly(ed.),Money, Inflation and Employment: Essays in Honour of James Ball. Edward Elgar, 1994.(DFH with M.P. Clements).†

[84] ‘How can Econometrics Improve Economic Forecasting?’,Swiss Journal of Economics and Stat-istics, 130, 267–98, 1994. (DFH with M.P. Clements).†

Forthcoming

[85] ‘Forecasting Economic Processes (with Discussion)’,International Journal of Forecasting, 1998.(DFH with M.P. Clements).†

[86] ‘The Influence of A.W.H. Phillips on Econometrics’, in R. Leeson (ed.),A.W.H. Phillips: Col-lected Works in Contemporary Perspective, 1998. Cambridge University Press. (DFH with G.E.Mizon).†

[87] ‘Exogeneity, Causality, and Co-breaking in Economic Policy Analysis of a Small EconometricModel of Money in the UK’,Empirical Economics, 1998. (DFH with G.E. Mizon).†

[88] ‘Forecasting Non-Stationary Economic Time Series’, in S. Holly and M. Weale (eds.)Economet-ric Modelling: Techniques and Applications, Cambridge University Press, 1998. (DFH with M.P.Clements).†

[89] ‘Econometric Issues in Economic Policy Analysis’,Journal of Business and Economic Statistics,1998. (DFH with N.R. Ericsson and G.E. Mizon).†

Papers in Progress

‘Economic Fundamentals vs. Policy Shifts in the UK’s Mortgage Possessions Crisis’ (JNJM with GC).‘Modelling Mortgage Arrears and Possessions in the UK’, (JNJM and DFH).‘Modelling Vintage Mortgage Possessions Data’ (JNJM with GC and DFH).‘Measurement Biases in UK Mortgage Arrears Data’. (submitted toOxford Bulletin of Economics andStatistics). (JNJM).‘Consumption, Wealth and Income Expectations: Evidence from a UK Regional Panel’, (JNJM with A.Murphy).‘Forecasting Regional Incomes in the UK’ (JNJM with A. Murphy).‘Saving in South Africa’ (JNJM with J. Aron).‘Testing General Restrictions on the Cointegrating Space’ (JAD).‘Testing Vector Autocorrelation and Hetersocedasticity in Dynamic Models’ (JAD)‘Identifiability of Cointegrated Systems’ (JAD with H.P. Boswijk).‘Explaining Regional House Prices in the UK’, (JNJM with A. Murphy).

19

‘Log Income versus Linear Income: an Application of the Encompassing Principle’. (DFH with L.Ermini).‘A Practical Test for Univariate and Multivariate Normality’. (JAD with H. Hansen).‘Testing Vector Autocorrelation in Dynamic Models’. (JAD).‘Model Selection when Forecasting’, (DFH with M.P. Clements).†

‘A Convenient Approximation to the Asymptotic Distribution of Cointegration tests’. (JAD).‘Dynamic panel data estimation using DPD for Ox’. (JAD with M. Arellano and S. Bond), 1997-W7 inNuffield Economics Research via WWW.Introduction to Ox(2nd version) (with G. Draisma and M. Ooms) 1997-W8 in Nuffield EconomicsResearch via WWW. JAD‘A Package for Estimating, Forecasting and Simulating Arfima Models’ (JAD with M. Ooms).‘Monte Carlo Experimentation in Econometrics using PcNaive’ (JAD and DFH)‘The Roles of Economic Theory and Econometrics in Time-series Economics’. (DFH)

8 Seminar and Conference Presentations

JNJM7

Overseas: ESEM, Maastricht; EEA, Prague; Conference onThe Econometrics of Economic Policyat EUI, Florence; IFS/Bank of Portugal Conference onMicroeconomics of Saving and ConsumptionGrowth, Estoril; Bank of Spain, Madrid∗; CEMFI, Madrid; University College, Dublin; European Net-work of Housing Economists Conference, Vienna; International Conference of the American Real Es-tate and Urban Economics Association, Berkeley, California; ESEM, Toulouse; Reserve Bank of SouthAfrica, Pretoria; University of Capetown+.UK: European Network of Housing Research, Glasgow; Nuffield College; Royal Institute of CharteredSurveyors, Bristol; Council of Mortgage Lenders Conference; Royal Economic Society Conferences atExeter, Swansea, and Stoke; Glasgow; UCL; LBS; Oxford; Exeter; Manchester.

GCOverseas: Foundation for Advanced Information and Research, Tokyo: EEA, Istanbul.UK: Fulbright Colloquium, NIESR, Oxford; Royal Economic Society Conferences at Kent andSwansea; R&D, Innovation & Productivity Conference, IFS; Queen Mary & Westfield College, London;Department of Trade & Industry; Centre for Economic Performance, LSE; Bank of England.

JADOverseas: European University Institute, Florence (2); ESEM, Maastricht; Nordic Cointegration Con-ference, Ebeltoft; Econometric Society World Congress, Tokyo; Computing in Economics and Finance,Geneva∗; Department of Economics, Aarhus; (EC)2, Florence∗; University of Sydney; University ofEichstaett.UK: Warwick; Royal Economic Society Conferences at Exeter and Stoke-on-Trent; ESRC EconometricStudy Group Conference, Bristol (2); Manchester; Oxford; Glasgow; Exeter; Reading; Bristol (Caleco).

DFHOverseas: Bonn; Board of Governors of the Federal Reserve System; Cointegration Conference, Stock-holm; CIDE Teaching Meeting, Bertinoro∗; Bank of Portugal; European University Institute, Florence(2)∗; Bergen; EC2, Berlin; (EC)2 Non-linear Econometrics Conference Round Table, Aarhus∗; Coin-tegration Conference, Aarhus; Finnish Doctoral Program on Cointegration, Helsinki+; EEA Confer-ence, Prague; Econometrics of Economic Policy Conference, Florence; Humbold University, Berlin;

7∗ denotes an invited or special lecture and+ a week’s visit or longer.

20

CORE, Louvain-La-Neuve; Copenhagen: Stockholm School of Economics (2); Norges Bank (2); Re-serve Bank of New Zealand; Canterbury+; Dunedin; Bilkent Forecasting Workshop+; IFS Round Table,Istanbul; Dutch Doctoral Program on Economic Forecasting+; Pittsburgh; Carnegie-Rochester Con-ference, Pittsburgh; NBER Time Series Conference, Rotterdam: Berlin Money-Demand Conference;IFS, Barbados+; Toulouse; Carlos III, Madrid+; CEMFI, Madrid; UC, San Diego+; Instituto di Tella,Buenos Aires; ESEM, Toulouse; DGII of the European Union Commission.UK: Oxford (3); Royal Economic Society Conferences at Exeter, Swansea, Kent and Stoke; Macro-Modelling Bureau Conference (2); LSE (2); Chemical Bank Forecasting Conference; SEMSTAT,Oxford: Quincentenary Lecture in Economics, University of Aberdeen∗; Liverpool Macroeconom-ics Workshop; Econometric Study Group Conference, Bristol; CTI Course on PcGive (2); LBS; HMTreasury Macro-Modelling Panel; Exeter; Manchester; Birmingham; UCL; RES/ESRC Easter School+;Bank of England; Government Economic Service Conference, Oxford∗; Dundee; St. Andrews; Notting-ham; Oxford (Economic History); Warwick; Oxford Forecasting Workshop.

Special Invited LecturesThe Zeuthen Lectures on Economic Forecasting, Copenhagen University, 1997.European Union Economists Course, Brussels, 1997.Econometric Society Latin American Conference, Santiago de Chile, 1997.Featured Address, International Forecasting Symposium, Barbados, 1997.Econometrics Lecture, Centenary Conference of theScandinavian Journal of Economics, 1997.Invited Lecture, Copenhagen University City-of-Culture Conference, 1996.Keynote Address, International Forecasting Symposium, Istanbul, 1996.Guest Lecture, Irish Economic Association, Limerick, 1996.Science Prestige Lecture, University of Canterbury, New Zealand, 1996.Annual Lecture, Cyprus Economic Society, 1995.Swiss National Economics and Statistics Meeting, Neuchatel, 1994.

9 Summary of Proposal

Cointegration captures long-run statistical relations. Our research concernsmodelling strategiesforcointegrated systems. First, cointegration requires system analysis as weak exogeneity is lost whencointegrating vectors also appear in marginal densities, entailing that hypothesis tests will not rejectcorrectly on integrated [I(1)] data. Structural cointegration relations must be identified by prior eco-nomic analysis. Weak exogeneity tests need studied for small samples ofI(1) data. The invariance ofcointegration under extensions of the information set needs analysis.

Second, we will study inference problems which arise inI(1) systems. These include not know-ing the degree of integration; the best ordering of hypothesis tests; non-linearity; and robustness tomis-specification. Many limiting distributions are new, incompletely tabulated, and may not be goodapproximations to finite sample behaviour. Many tests need extensions to multivariate models, andrequire critical-value response surfaces and finite sample investigations.

Third, modelling strategies must be developed forI(1) systems. Conditional encompassing requiresa completing system, so a system approach is essential to check if conditioning is valid. Model design,pre-testing, and sample selection entail a key role for economic theory in locating permanent relations.We aim to develop congruent, theory consistent, and encompassing approaches relevant to analysingpotentially cointegratedI(1) processes.

Fourth, modelling strategies must be tested by empirical application. We will study housing mar-kets; productivity, innovation, employment and investment; consumption and portfolio behaviour; com-petitiveness and the balance of payments. Problems of measurement errors, data revisions, seasonaladjustment, time aggregation, and pooling across frequencies will be analysed forI(1) data.

Fifth, we propose to develop a powerful software system by interfacing PC-NAIVE with PcGiveand PcFiml for Monte Carlo simulation of sequential testing strategies; recursive FIML estimation,cointegration and encompassing tests; system mis-specification; non-linearities; system constancy tests;lag length selection; critical values of new tests; and conditionalversusunconditional inference.

Theory research, data collection and analysis, and programming will all commence immediately andproceed in tandem throughout the grant. Empirical modelling and Monte Carlo studies will start oncetheory and data analysis are sufficiently advanced (at about 3 months). Thereafter, exact times dependon progress along each front, and on how fruitful each research avenue proves. Intermediate results willbe written up as we proceed, and the main findings and reports will be produced during the final year.

During the award, DFH was elected an Honorary Vice-president of the Royal Economic Societyand served on its Executive Committee and Council; he acted as Chairman for the Research Assess-ment Exercise in Economics, and served on the Editorial Boards ofOxford Review of Economic Policy,Empirica, andOxford Economic Papers. JNJM served on the Council of the Royal Economic Societyand on the Editorial Board ofOxford Review of Economic Policy. Both JAD and GC remained in postthroughout, and both obtained their Doctorates. JAD was awarded a Research Fellowship by Nuffield.