**Classroom context**

Faced with ever larger class sizes and dwindling resources in higher education, there is increasing pressure to move away from traditional lectures, tutorials and seminars, towards new modes of delivery, especially computer-based learning materials. Most of the initiatives to introduce computers into education have focused on the development of hypertext-based courseware (McAlpin, 1992). Despite the interactivity of courseware, there is a tendency for students to become rather passive in front of the technology, and in practice we are still a long way from "replacing" traditional lecturing and tutoring systems (Shackleford, 1990). In part, this is because the learning environment was developed by someone else, and its responses pre-defined. The students have not "constructed" their own learning environment.

For several years, spreadsheets have
been used to teach second and final year units on the undergraduate
course in Business Mathematics at South Bank University, London.
More recently, the System Dynamics (SD) package *Stella*
has been introduced into the undergraduate syllabus. This paper
uses the specific example of how SD tools can be used to teach
the difficult topic of expectations motivated behaviour in economic
modelling to illustrate a more general point about how SD can
be used to enhance student learning.

The aims of the *Economic Modelling*
unit include: (1) to provide students with a firm theoretical
basis in modern micro- and macroeconomic theory, and in particular
the central role played by theories of expectations formation;
(2) to refine students' skills in using mathematical methods to
formulate and solve economic problems. A specific Learning Outcome
is that by the end of the course, students should be able to*
use computer applications to model and solve a variety of economic
problems*.

**A leap of understanding**

Expectations formation plays a central
role in modern theories of economic behaviour. Rational, adaptive
and extrapolative expectations hypotheses are introduced at an
early stage in the undergraduate syllabus (Begg *et al*,
1994). Expectations motivated behaviour is taken to be the bridge
between observed macro-scale phenomena and the aggregated behaviour
of representative individual micro-economic agents. But from
a student's perspective, there is a considerable leap of understanding
required from the static equilibrium models of intersecting supply
and demand curves to dynamic behavioural models.

A good example is the macroeconomic consumption function. The Keynesian consumption function model introduced in first year undergraduate courses assumes that consumption is a fixed proportion of income (the marginal propensity to consume) plus "autonomous expenditure". This leads to the simple multiplier model, a linear simultaneous equations model with an explicit solution. In the second year, students are taught the permanent income hypothesis (PIH), in which consumption is a fixed proportion of "permanent income", an unobserved variable which does not respond to temporary fluctuations in income caused by external factors. The model of economic behaviour then hinges on how consumers form expectations of their long run income.

As a teacher, one is faced with trying to explain the implications of different expectations formation processes whilst at the same time making the models realistic enough to be compared with real economic data, which, after all, was the reason for developing the PIH in the first place.

**Voyages of discovery**

It is not only students who embark
on a journey of discovery at the start of a new course. If students
face the challenge of learning new material, teachers face the
challenge of finding new ways of communicating unfamiliar concepts,
stimulating understanding and developing skills. Over the past
three years, the authors have been through an odyssey of methods
for teaching expectations formation, moving away from the blackboard
and into the computer lab. Starting from traditional methods of
chalk'n'talk using difference equations and sketch graphs, the
first innovation was to get students using spreadsheets. Spreadsheets
helped students develop modelling skills and allowed them to investigate
the impact of different parameter values on dynamic behaviour,
but it was hard to build models with a realistic level of complexity.
Students were also presented with a ready-made Microworld, the
Keynesian macroeconomic model supplied with Stella. The aim of
the exercise was to achieve economic growth and lower unemployment
using a mix of monetary and fiscal policies (Sosa *et al*,
1996). However, feedback from students at the end of the unit
revealed that they felt frustrated merely running the model in
flight simulator mode. They wanted to learn how to use the package.

**Flying in a new world or building
your own?**

The appropriate teaching method must depend on the intended learning outcomes. There are several initiatives underway to use and evaluate Microworlds as environments for building understanding of complex business and economic systems (Langley & Morecroft, 1996). If learning outcomes are primarily about developing understanding, such as the response of an economy to different policies, then goal centred exploration in a simulation environment is a useful approach. But when the learning outcomes include developing modelling skills, a different approach is needed. SD modelling environments can be used to construct extremely simple models of the expectations formation process and then explore the dynamic implications. Once that understanding has been forged, students are equiped to criticise an existing model and suggest and implement improvements.

**Top down … bottom up …
or both?**

Figure 1. Example of an adaptive expectations model

To build their own models, students firstly need to be taught how to use the package. This is done by giving step-by-step instructions in building simple generic structures for alternative expectations formation processes which are kept as simple as possible to make the dynamics of adjustment processes transparent, an example is shown in Figure 1. The structural differences between models of alternative expectations formation hypotheses are emphasised. Sensitivity analysis is used to contrast structural changes with changes to parameter values.

Students are then given an in-depth assignment based on an existing macroeconomic model to (1) give a critique of the model; (2) propose and implement improvements; and (3) compare their model with real economic data for key variables.

**Lessons learned**

SD packages are becoming increasingly established as teaching tools on undergraduate and post-graduate University courses. The Microworlds approach is readily accepted by students who have grown up in the age of computer games. The approach enhances students understanding of the link between structure and behaviour for complex dynamic systems and allows them to explore relationships amongst decision variables. But a further stage in understanding is to be able to question existing models and eventually build your own.

In many socio-economic systems, the key to understanding behavioural dynamics is the way in which economic agents update expectations based on new information. The authors experiences suggest that SD tools offer considerable advantages in helping students make the leap of understanding from the comparative statics of simultaneous linear model systems to the dynamics of expectations and feedback. By using the combined bottom-up and top-down approach described in this paper students gain the confidence to first criticise and then attempt to improve on existing models with a realistic level of complexity. Additionally, providing historic data for key variables encourages students to contrast models with reality.

**References**

Begg D K H, Dornbusch R and Fischer S, 1994. Economics. McGraw Hill, London, UK.

Langley P and Morecroft J, 1996. Learning from Microworld Environments: a Summary of the Research Issues. Proc 1996 Int. System Dynamics Conference, Cambridge Massachusetts.

McAlpin A, 1992. The computers in teaching initiative. Proc. Conference on Developments in the Teaching of Computer Science, April 1992, University of Kent, pp152-157.

Shackleford R L, 1990. Educational
computing: myths versus methods - why computers haven't helped
us and what we can do about it __in__ Proc. of Conf. on Computers
and the Quality of Life 1990, Washington DC, pp139-146.

Sosa H H A, Castro J D M, Vivas R V J and Mantilla J A P, 1996. Microworlds: A System Dynamics Application in Learning Keynesian Macroeconomics. Proc. of the 1996 International System Dynamics Conference, Cambridge Massachusetts, July 1996, pp28-31.