computers as a tool for teaching economics

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Compurmr Ecluc. Vol. 19. No. 112, pp. 61-72. 1992 Printed in Great Britain. All rights reserved 0360~1315192 $5.00 + 0.00 Copyright cc; 1992 Pergamon Press Ltd COMPUTERS AS A TOOL FOR TEACHING ECONOMICS PHIL HOBBS’ and GUY JUDGES ‘CT1 Centre for Computing in Economics, Department of Economics, University of Bristol, 8 Woodland Road, Bristol BS8 ITN and ‘Department of Economics, Portsmouth Polytechnic, Portsmouth, England Abstract-In this paper we discuss the contribution of computer-assisted learning to the teaching of economics in the U.K. Current evidence suggests that, whilst there is a significant investment in computing resources within departments, in the majority of cases their use by students is limited to quantitative methods. econometrics and IT skills training. Few departments have yet to make the computer an integral part of the students’ learning experience across the range of topics taught at undergraduate level. There are, however, a number of departments placing an increasing emphasis on the use of computer-assisted learning and a number of groups exist within the discipline promoting computer-based methods. We argue that, in part, the relative paucity of computer-assisted learning in economics is explained by the priority accorded to the development of econometric modelling packages and the absence of an agreed content for undergraduate teaching. THE NATURE OF ECONOMICS AS AN ACADEMIC DISCIPLINE It is common to characterize economics as a graphical subject. Undergraduate texts are built around X-Y graphs which represent economic behaviour. More advanced work moves beyond two dimensions, looking at multi-good multi-characteristic markets. Economics is not only graphically based, but also dynamic. Undergraduate teaching places great emphasis on the effect of time and changes in tastes, preferences and technology. The use of computers provides lecturing staff with a way of conveying these dynamic images, freeing them to concentrate on description and explanation. It is the area of quantitative methods which has grown most rapidly in economics over the last 20 years. Many of the analytical tools that students now need to be equipped with are based in mathematics and statistics. The increasing sophistication of these quantitative skills contrasts with the purely qualitative and descriptive background that many students joining a degree course have. Indeed, a qualification in mathematics is more frequently an entry requirement for students than one in economics [ 1,2]. Computer packages are frequently used as an integral part of quantitative methods and econometrics courses both for project work and as teaching tools. By tradition economics has not had a prescriptive view of the topics covered within a degree programme. Unlike some disciplines, with professional requirements for certain topics and styles to be adopted, economics staff have retained a degree of personal attachment to what they teach and in what order. As we will discuss later, this tradition has, in part, militated against the widespread adoption of purpose-written packages. A TYPOLOGY OF COMPUTER ASSISTED LEARNING IN ECONOMICS On its own the phrase computer assisted learning provides little information as to how computers are employed in teaching economics. As we discuss later, there are a number of instances where, in what passes for computer assisted learning, the role of the computer is very much secondary to the learning experience. A number of typologies might be used to classify the different ways in which computers are used in teaching economics. For convenience we adapt one based on the focus that the program has. Within this framework the use of computers in teaching economics can be seen as three (overlapping) sets: Computer based tutorials, where students are provided with a computer program that assists in reviewing the key points of a particular topic. Increasingly such programs are being distributed with particular texts or workbooks [3,4]. In other instances the learning material and the tutorial are built 67

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Compurmr Ecluc. Vol. 19. No. 112, pp. 61-72. 1992 Printed in Great Britain. All rights reserved

0360~1315192 $5.00 + 0.00 Copyright cc; 1992 Pergamon Press Ltd

COMPUTERS AS A TOOL FOR TEACHING ECONOMICS

PHIL HOBBS’ and GUY JUDGES

‘CT1 Centre for Computing in Economics, Department of Economics, University of Bristol, 8 Woodland Road, Bristol BS8 ITN and ‘Department of Economics, Portsmouth Polytechnic, Portsmouth, England

Abstract-In this paper we discuss the contribution of computer-assisted learning to the teaching of economics in the U.K. Current evidence suggests that, whilst there is a significant investment in computing resources within departments, in the majority of cases their use by students is limited to quantitative methods. econometrics and IT skills training. Few departments have yet to make the computer an integral part of the students’ learning experience across the range of topics taught at undergraduate level. There are, however, a number of departments placing an increasing emphasis on the use of computer-assisted learning and a number of groups exist within the discipline promoting computer-based methods. We argue that, in part, the relative paucity of computer-assisted learning in economics is explained by the priority accorded to the development of econometric modelling packages and the absence of an agreed content for undergraduate teaching.

THE NATURE OF ECONOMICS AS AN ACADEMIC DISCIPLINE

It is common to characterize economics as a graphical subject. Undergraduate texts are built around X-Y graphs which represent economic behaviour. More advanced work moves beyond two dimensions, looking at multi-good multi-characteristic markets. Economics is not only graphically based, but also dynamic. Undergraduate teaching places great emphasis on the effect of time and changes in tastes, preferences and technology. The use of computers provides lecturing staff with a way of conveying these dynamic images, freeing them to concentrate on description and explanation.

It is the area of quantitative methods which has grown most rapidly in economics over the last 20 years. Many of the analytical tools that students now need to be equipped with are based in mathematics and statistics. The increasing sophistication of these quantitative skills contrasts with the purely qualitative and descriptive background that many students joining a degree course have. Indeed, a qualification in mathematics is more frequently an entry requirement for students than one in economics [ 1,2]. Computer packages are frequently used as an integral part of quantitative methods and econometrics courses both for project work and as teaching tools.

By tradition economics has not had a prescriptive view of the topics covered within a degree programme. Unlike some disciplines, with professional requirements for certain topics and styles to be adopted, economics staff have retained a degree of personal attachment to what they teach and in what order. As we will discuss later, this tradition has, in part, militated against the widespread adoption of purpose-written packages.

A TYPOLOGY OF COMPUTER ASSISTED LEARNING IN ECONOMICS

On its own the phrase computer assisted learning provides little information as to how computers are employed in teaching economics. As we discuss later, there are a number of instances where, in what passes for computer assisted learning, the role of the computer is very much secondary to the learning experience. A number of typologies might be used to classify the different ways in which computers are used in teaching economics. For convenience we adapt one based on the focus that the program has. Within this framework the use of computers in teaching economics can be seen as three (overlapping) sets:

Computer based tutorials, where students are provided with a computer program that assists in reviewing the key points of a particular topic. Increasingly such programs are being distributed with particular texts or workbooks [3,4]. In other instances the learning material and the tutorial are built

67

68 PHIL HOBBS and GUY JUDGE

in to the same program[5]. Tutorial programs, the majority of which address introductory topics, have a valuable role in a subject where students frequently do not require any prior study of economics [ 1,2] and there is a core body of knowledge that all students require before they can move on to more advanced topics. These introductory techniques can, in many instances, be remote from a student’s previous experience. As a consequence. the opportunity to review these topics until they are fully understood is a valuable one[6].

A second group can be summarized as programs that allow students to investigate economic

issues. Here one can include the range of simulation packages, e.g. Macrosolve, Running the British Economy, PC Ready Reckoner, and Chancellor that allow students to explore the effects of changes in parameters on a range of economic variables. For convenience we refer to these as simulations,

although this categorization may not be strictly accurate for some in this group. The final group is a range of programs which are essentially aimed at research users, but which

are incorporated into undergraduate teaching. For the most part these packages are in the area of statistics and econometrics (although there is also a growing interest in the use of algebraic packages). Two distinct streams can be discerned within this group. First, packages that allow students to undertake investigation of data that could otherwise only be dealt with from a theoretical perspective e.g. Microfit, PC-GIVE, Hummer. Second, the use of commercial packages as a vehicle for demonstrating and explaining economic issues, e.g. Lotus l-2-3. Mathcad; this might be described as re-purposing existing software.

Having described a typology for considering the use computer-based applications in economics, it is instructive to consider the way in which computers are actually used within the discipline. It is important to make a distinction between what we term the innozwtizv and the simplistic use of computers within the curriculum. Survey work undertaken by the Centre for Computing in Economics (University of Bristol)[7,8] indicates that whilst there is a generally high level of computer usage across departments both in the university and polytechnic sector, a great deal of this use is in the form of IT skills training (for example spreadsheets, databases and wordprocess- ing) or sophisticated calculators. This is what we describe as simplistic use in that it has very little new to offer to the way that students approach the learning of economics. The innovative use of computers in teaching was much less in evidence. the reasons why this should be the case are discussed below. It is important, however. that simplistic is not confused with ineffective. Students given the opportunity to gain IT skills can improve the effectiveness of their learning in other areas. Similarly many topics in econometrics remain intractable until a student has had the opportunity to apply the theoretical models to real data. Our point is that the simplistic use of computers ignores a significant area of their potential.

THE EVOLUTION OF COMPUTING WITHIN ECONOMICS

A key factor affecting the extent and nature of computer use in economics in the U.K., as elsewhere, has been the dramatic improvement in the priceeperformance ratio[9]. In the recent past the use of computers in economics was confined to researchers writing programs in high-level languages to run on mainframe computers. Today it is common to find a personal computer on all staff member’s desks within a department and suites of computers for use in teaching. However, there remains a core of staff and departments who make little use of computers in either their

research or teaching[7] (see Table 1). It is noticeable that on almost all measures of computer availability and usage within

departments, the polytechnic sector is markedly in advance of the university sector (see Table 2). Perhaps it is no surprise that the most innovative work in the use of computers in teaching economics comes from the polytechnic sector, where the emphasis on quality of teaching has traditionally been stronger[9]. Furthermore, it is argued [7] that the university sector has been handicapped in the provision of stand-alone computing facilities by their commitment to large scale mainframe computing.

One of the earliest attempts to introduce computer-assisted learning to economics teaching stems from the work of Lumsden and Scott [IO, 111. Their investigation of teaching methods in economics led to the development of Running the British Economy, which was launched in 198 1. The program provided students with a stylized representation of the British economy with period by period

Teaching economics 69

Table I. Use of departmental computer facilities

Teaching Individual use

Table 2. Provision of computers for staff

On desk Excl. staff use

UniVersities

Polytechnics

(mean hours/week)

5.9 31.5 (9.2) (49.7)

15.8 32.0 (19.5) (37.9)

IBM PC Apple Mac IBM PC Apple Mac

Umversitles 57.3 5.0 I I.4 0.7 Polytechnics 43.6 6.7 5.0 2.4

Note: figures are the percentage of a computer per member of staff. Data IS for full-time staff onlv. Source: 171.

Note: Four universities and one polytechnic reported that faahties were available 24 hiday. Figures in parentheses are standard deviations. Source: [7].

information on key macroeconomic variables and policy instruments. Users took the role of the Chancellor of the Exchequer attempting to manage the economy over a IO-yr period. The outcome of each year was monitored and the students received a measure of their success in the form of a score determined using a social welfare function. To introduce a degree of reality, the economy

in the game was subject to unanticipated exogenous shocks. As a consequence, students could repeat the game on a number of occasions but would always derive a unique set of results. Despite

the program’s popularity, more than 3000 copies being sold [lo], the main users of the program were in schools and colleges teaching pre-degree-level economics. The relatively poor take-up in the higher education sector has been attributed [l l] to the lack of specification of the underlying structural equations of the economy. In addition, there was concern about the assumptions built-in to the social welfare function which appeared to give a relatively high weight to low inflation compared to low unemployment.

Whilst similar criticisms have been levelled at other equivalent packages, an interesting departure can be seen in the work of Dawson[l3], who has turned the problem around. In his teaching at Staffordshire Polytechnic, Dawson uses the black-box nature of these simulations to provide an innovative exercise for advanced students. They are encouraged to try and estimate the underlying

structural equations of the model by conducting a series of replicable experiments. Although there has been a rolling interest in purpose-written economics teaching software, it has

become evident that the cost of development [lo], limited commercial market, and the perceived inflexibility of the programs for the great variety of topics that are taught, mean that discipline-wide programs are unlikely to be successful[6]. Instead we have witnessed a growing interest in using commercially available software as the vehicle for computer-assisted learning. This approach provides a degree of flexibility, not normally found in teaching packages, to vary the approach of an application either in the light of experience or in response to changes in teaching style. It is interesting to note that, ironically, this approach has gone full circle, with writers creating run-time versions of teaching programs written using commercial software[l4] and in consequence losing the previously mentioned advantages of customisation.

The sharing of experiences of computer-assisted learning in economics has been greatly assisted by the emergence of a number of groups within the discipline keen to promote computer-based methods. The Computers in Economics Unit at Staffordshire Polytechic was an early contributor to the pool of economics teaching software (The Paraffin File, The Energy File) and provided much of the stimulation to lecturing and teaching staff to explore the potential of computer-based methods[l5]. Another key group emerged at Portsmouth Polytechnic in 1987. The Computer Assisted Learning in Economics (CALECO) group developed a philosophy than the most productive way to provide computer-based materials was to make use of commercial packages In particular extensive use has been made of Lotus l-2-3 as a teaching tool. Indeed the current work of the group has transformed this package from a spreadsheet to a sophisticated delivery

system. For example, applications have been developed to explore non-linear dynamics[l6] and duality [ 171.

A final element in the evolution of computing within economics has been the need for specialist econometric modelling packages. Whilst early work in econometric computing made use of packages originally written for statisticians, the growing specialism of econometric theory lead to the development of a number of dedicated packages. These packages represent the cornerstone of most departments computer software. Of packages reported by departments as being used in teaching, Microfit emerges as the most frequently used[7], with similar packages PC-GIVE and

70 PHIL HOBBS and GUY JUDGE

Reg-X also figuring highly in this ranking. It is clear that significant effort has gone into developing these packages which, as a consequence, has not been available for the development of teaching-based programs.

THE USE OF COMPUTERS WITHIN THE ECONOMICS PROFESSION

Within the economics profession, computers are used primarily to run simulations and models of economic systems or to undertake statistical investigations. The models produced vary from relatively simple ones of sectors of the economy or the demand for a particular product to large scale macroeconomic models of the economy.

Whilst professional economists have access to a wide range of tools that are not practically available to undergraduate students, because of their cost and complexity, there is increasing use of versions specially designed for undergraduate teaching. These computer-based simulations provide a variety of learning experiences that would otherwise be unavailable and are the economists equivalent of the laboratory [ 131. They provide students with an opportunity to explore economic systems in a way that would be impossible otherwise. An example of this approach is the PC Ready Reckoner program which allows students to investigate policy changes on three different models of the economy widely used by government and business.

It is the exception for a student graduating in economics to become a professional economistfl]. The majority of graduates go on to take up general management positions or, as is increasingly common, training contracts with accountancy firms [IS]. As a consequence, economics is seldom viewed as a vocational subject and the question of the role of computing amongst professional economists is somewhat misleading. For the most part employers are looking for economics graduates trained in a range of broadly quantitative analytical skills.

THE INCORPORATION OF COMPUTER-ASSISTED LEARNING INTO THE CURRICULUM

The successful utilization of computer-assisted learning relies upon the computer being regarded by the student as a natural tool. A good example can be seen in the economics department at Portsmouth Polytechnic which integrates computer instruction and learning with classes on economic theory under the title of Economics Workshop. Students receive a series of lectures on economic theory and instruction on using a range of commercial computer packages, such as Lotus l-2-3. Seminar work is a mixture of traditional small classes and ones where the students use the commercial packages to explore predesigned economic problems. The emphasis here is on using the exploration of economic problems both to reinforce the material covered in the lecture programme and to provide experience of using the commercial packages. Not only do the students see the computer as a learning tool but they also gain direct experience of using the packages they will be expected to make use of throughout their studies.

Taking a somewhat different approach, staff at Birmingham Polytechnic have made significant effort to give students access to online data, allowing them to undertake real research where in the past they were constrained to datasets available in the department~l9]. As a result, students receive training not only in the appropriate quantitative techniques but also in the associated research skills. In a similar vein, economics students at Oxford University are encouraged to experiment with dynamic modelling using a package written internally. Originally this package was designed for research, but the widespread availability of student computing facilities allows staff to give students access to techniques that would previously be reserved for graduate students.

It is in the area of econometric modelling and forecasting that the effect of computers on teaching has been most marked. Few departments would attempt to tackle these topics without some element of computer-based work. Indeed many of the areas dealt with are inaccessible without the use of computers[20]. However, as has already been mentioned, in many instances the use of computers in quantitative methods could not be regarded as innovative.

Teaching economics 71

IS COMPUTER ASSISTED LEARNING EFFECTIVE?

The effectiveness of computer-assisted learning needs to be seen as a balance between improvements in students levels of comprehension and the costs of achieving that. Given that economics is concerned with the allocation of scarce resources amongst competing uses, one would expect economists to have developed a body of research on this issue. For the most part this is not the case.

The direct, measurable, investment required for introducing computer-assisted learning is relatively modest, certainly when compared to staff costs[21]. There is little evidence that current computer-assisted learning in economics is being constrained by resource availability (although there is a view that there was inadequate provision of suitable software[7]). The real constraints lie in the motivation of staff to change their teaching methods in the light of very little positive reward for doing so. Therefore, whilst the direct cost of investing in computer-assisted learning is relatively low, the indirect costs remain a significant barrier.

Whilst studies of the effectiveness of computers in teaching economics have a long history there is very little substantive knowledge as to its effectiveness. Work by Lumsden[I I] established that there are benefits in terms of improved student performance, but these tend to be marginal and are strongly related to the individuals’ characteristics. Where the topic under instruction is more quantitative the benefits in terms of student performance tend to be more uniformly evident. Levy[22] finds that students studying quantitative methods, where computing was an integral element, performed significantly better than their peers. Others have found that, whilst measureable changes have been less evident, there is a marked change in student attitudes and the maturity of

analysis in assessing problems[23]. There does appear to be a strong link between the use of computers in research by lecturing staff

and the adoption of computer-based methods in the classroom[7]. This trickle-down effect is most marked in the university sector, where the emphasis on scholarly activity tends to lead to a lower emphasis on innovative teaching techniques. Conversely, in the polytechnic sector, where staff have higher teaching loads and where there is a greater emphasis on teaching quality [9] this effect is less marked. This leads us to argue that the effective promotion of computer-assisted learning in the university sector requires either a radical change in the perceptions of the balance between teaching and research or a strategy of promotion that starts with research use.

The research and to a lesser extent the teaching use of computers is increasingly a theme in academic conferences and review sections in scholarly journals. This is a move that has had the active support of the Royal Economic Society. Increasingly, academic journals in economics are sponsoring review articles on the potential of computers in teaching, e.g.[6,24]. Indeed, in these areas the U.K. leads the U.S.A., where there is a growing demand for such topics to be addressed[9]. These developments have coincided with a renewed interest in the economics of education as a research theme. Furthermore, we are beginning to see the emergence of a body of academic work investigating the economic theory of computing and software [25].

CONCLUSION

Whilst there is a great potential for the use of computer-assisted learning in economics, this has yet to be exploited. Although researchers are making increasingly sophisticated use of computers in their work[26], a great deal of the teaching using computers lacks an innovative approach. Computer-assisted learning will not provide a panacea for addressing the questions of increasing student numbers, a growing body of knowledge and declining real resources. However it can contribute in a significant way to providing a variety of learning experiences for economics

students. By this measure many economics lecturers are failing their students. It is, however, too easy to take a doom-laden view of the current situation and infer that nothing

will change. There is much evidence to suggest that we are at a turning point[27]: the increasing interest in computing themes within academic conferences and scholarly journals; the gaining importance of staff training and appraisal of teaching quality[28]. These factors combined with a growing group of enthusiasts who are using computers to produce innovative teaching materials suggests that the future holds great change.

PHIL HOBBS and GUY JUUCE

REFERENCES

72

1. 2.

t b : 5. 6. I

8.

9.

IO.

II.

I?. 13. 14.

IS. 16. 17. ix.

19.

20. 21. 12.

‘3.

24. 25.

26. 27. 28.

Towse R. and Blaug M., The C’urrenf State I?/ the Economics Pr@,wion. The Royal Economic Society, London (I988). Lawson C., Undergraduate economics: some evidence from a survey of universities and polytechnics. Ner+*sl. R. &on, Sot. (June 1990). Blight D. and Shaft0 A.. An i~~r~~~cfj~~n ID ~i~ro~~[~n~~~i~.~. McGraw-Hill. London (1984). Olvey L. D. and Golden J. R., Grffp~~f~n II. Addison-Wesley, Wokin~ham (1988). Attfield C. and Duck N.. Econofnics ill Actiort. McGraw-Hill, London (1985). Welford R., &on. 97, 1075 (1987). Dolton P.. Hobbs P. and Taylor P.. The role and usage of computers in economics. Ro~_t~ul Econc~mic Socirt_v Corz/erenw. Warwick (1991). Dolton P. and Taylor P.. Econometric modeiiing of the use of computers by economists in U.K. Higher Education. Royal Economic So&ry C(mf>rencP on I/W Econamic.v of Nigher Eduwfion. London (September 1991). Judge G. and Hobbs P.. Trends in the use of computers in economics teaching in the United Kingdom. American Economit~ A.wwiu~ion Cor~&wwe. New Orleans ( 1992). Lumsden K. G. and Scott A.. Simulations in economics teaching. Computer Appiicarions in the Sociul Sciences

Cw&wnw. Portsmouth (1989). Lumsden K. G. and Scott A., The dissemination of educational technology in beginning economics courses. Sror. J. ~~~jfj~u~ .&an, 36 (1989). Welford R., Ccmrpzccers Higher Educ. Econ. Rw. 4, 2 (1988). Dawson A., Rr. Rer. Eron. Issues 31, 94 (1991). Jones R. H., A derived model of the interde~ndence of employment. An application of Lotus l-2-3 and Baler to create a stand-alone computer package. Cornpurer Applications in ihe So&i Science.c and 3usines.r Conffrenrc, Portsmouth (1991). Randall K.. .Mic~rc~corr~pu/rr.s and Twching Ewnomic~.s. Longman, London (1984). Judge G.. Conrgurers Higher E&t,. Econ. RFI.. 11, 8 ( 1990). Murphy B... Dncifi/,r I~?I a Sprc~ldsIr~e~. Discussion paper. Department of Economics. P~r~snlou~h Polytechmc (1992). Universities Funding Council. First Destination of Graduates. Ci’niwrsitks Srutivtitrri Record 1989:90 Voi. II. Universities Statistical Record. Cheltenham (1991). Burley T. and Mabbett A.. Making econometrics come alive. C~~?~~pul~,r App/i~~?/if~n.s in rlw Soci& S&nw.s and Bu.sbws,v Confiwnce. Portsmouth (I 99 I ). Mabbctt A.. Computcr.v Higher Edw. Econ. Rw. 13, 8 (1991 ). Dolton P., Economics .b!nirw.ri?,~ Compzc~ing 11, 2 ( 1989). Levy G.. lnt~~rating IT and quantitative methods. Conz~ctfcr ~~~~j~~~i~~~~.s ifr ihe Social Sriencxs C~~}?/~,r~,~~~~. Portsmouth (1990). Hornhy W.. An evaluation of computer-based gaming simulation in economics (Edited by Race P. and Brook D.). In ~~,~.sp~,(,~~~~~~.~ oh Ac&ePflic Gurni~r~~ trtrd Sjn~u~~~i~~~f Vol. V. Kegan Paul, London (1980). Judge G., (‘c>rtipur, Appiic. Bus. So&/ Sri. 2, 33 (1991). Love11 M.. Sponsoring public goods-the case of computer arded instruction and the PC’. .4nwiccrn Econonric~ .I.c.coc~rulron Confiv~ww, Atlanta (I 989). Hammond C., .6?0~2. J. 409, 161 I (1991). Welford R. (Ed.), r~?~~rt7l~l/i~J~? Te~~?~l~l~J~~ ,fnr Socicri Scierriists. European Research Press, Bradford ( 1990). Department of Education and Science. Hi&r Educorirm: A New Frunwrtwrk. Cmd IS4 1~ HMSO. London ( I9Y 1).

APPENDIX

Addison Wesley, .~u~~?C~~. Addison-.Wesley. New York. Rinks M and Jennings A.. ChanceNor: A Mrccmsimularion Package. McGraw-Hill, London (1987) Hall R. E. and Taylor J. B., Mucrofconotnicr. W. W. Norton, London (1991). Hall S., Reg-X. Economics Division, Bank of England, Threadneedle Street, London (lY90). Hendrv D.. PC-GIVE. Institute of Economics and Statistics. Oxford. Lotus -Development Corporation, Lotus l-2-3. Lotus Development Corporation, Cambridge, Mass. Lumsden K. G. and Scott A.. Running the British Econom.v. Longman Micro Software, York (1981). MacDonald G. and Turner D., PC Reudy Reckoner. ESRC Macroeconomic Modelling Bureau. Warwick, CV4 7AL. Pesaran M. H and Pesaran B., Micro$r. Oxford University Press, Oxford (1987). Randah K., Tlte i%crgy File. BP Educational Service, London (1987). Randall K., The Paru@n f&. BP Educational Service, London (1983). Wallace T. D. and Silver J. W., Economerrics, An introduction. Addison-Wesley. New York (1988).