III. Research Opportunities

• A. Econometrics
  • 1. Estimation of dynamic programming (DP) models
  • 2. Estimation by simulation
  • 3. Global optimization algorithms
  • 4. Interactive graphical data analysis
  • 5. Estimation of models of economic equilibrium
  • 6. Application of artificial intelligence methods to econometrics
  • 7. Bayesian econometrics
• B. Environmental Change
• C. Microeconomics
  • 1. Simulation Methods
  • 2. Mathematical Programming Methods
  • 3. Artificial Intelligence Methods
  • 4. Computable Dynamic Heterogenous Agent Models
• D. Sectoral Economics
• E. Growth and Development
• F. Macroeconomics
• G. International Trade
• H. Economic Databases
• I. Economic Theory
  • 1. Numerical Solutions of Rational Expectations Equilibrium
  • 2. Asymptotic Methods of Approximation
  • 3. Hybrid methods
  • 4. Substantive areas
  • 5. Convergence Problems
• J. Optimization Methods
• K. Computational General Equilibrium
• L. Game Theory and Mechanism Design
• M. Economic Institutions
• N. Qualitative Economics
• O. Theory of Computation
• P. Resource Allocation in Computer Networks
• Q. Transitions to Market Economies

Recent theoretical breakthroughs by McFadden (1989) and Pakes and Pollard (1989) have suggested ways to estimate econometric models that were previously thought to be computationally intractable due to the fact that they required evaluation of multiple integrals with no closed-form solution. An example is the standard probit model of discrete choice which requires evaluation of multiple integrals of the the multivariate standard normal distribution in order to compute the choice probabilities entering the likelihood function. Previously the probit model was thought to be intractable for problems with choice sets of more than 3 or 4 elements. The new simulation approaches allow one to completely avoid explicit evaluation of such multiple integrals (which amount to "integrating out" unobservables), and, instead, take Monte Carlo draws of the unobservables to yield simulated choices which are unbiased (i.e. the expectation of the simulated choices is identical to the choice probability as computed by explicit numerical integration, for example). This approach provides great potential speed-ups by allowing estimation algorithms to avoid complicated multi-dimensional integrations. However, we are now starting to find out that the simulation approach does not come without its costs. First, the standard simulation approach yields a statistical objective function (likelihood function) that is typically non-differentiable and even discontinuous as a function of the unknown parameters. This makes it much more difficult to use nonlinear hill-climbing algorithms to compute the likelihood function, since numerical derivatives must be computed, and the discontinuities often yield a large number of local optima that make finding globally optimal parameter estimates very difficult. Second, we are starting to realize that simulation itself can be very time-consuming in more complex models. For example, recent work by Hotz, Miller, Sanders and Smith (1990) has applied the simulation approach to the estimation of DP models. The approach requires simulations over a set of possible paths an agent could follow in the future. The set of all such paths is a very high- dimensional object, and sufficient simulations must be done to guarantee reliable parameter estimates. In these cases simulation can require large amounts of computation. Thus, while simulation approaches offer the hope of allowing econometricians to significantly weaken the maintained distributional assumptions underlying their models (such as the distribution of unobserved heterogeneity, for example), these approaches will nonetheless require significant amounts of computation. We expect that simulation estimators will be another "growth industry" in econometrics in the 1990's and beyond. Evidence is the recent work on "smooth simulators" by Stern (1988), Keane (1990) and Hajivassiliou and McFadden (1990).

3. Global optimization algorithms

The new interactive programming languages now come bundled with superior full-screen editors, built-in advanced publication graphics, and extensive and efficiently pre-coded numerical libraries. This allows researchers great flexibility in the kinds of questions they can pose and answer, without annoying constraints of the old mainframe environment such as maintaining funding for accounts, reacting to unpredictable systems/software changes, and disk and cpu-time allocation problems. But the most important feature is the interactivity of these languages, allowing researchers to keep large data arrays in memory and perform complex data transformations by executing memory-resident procedures with simple key-strokes. However, there are two areas where further improvement is needed. One ambitious area is the development of artificial intelligence voice-recognition software to allow researchers to literally "talk" to their computers, allowing their minds to freely conceptualize the problem at hand, rather than worry about the unnecessary syntactical details of a particular programming language. We expect that by the end of the decade such software will begin to appear, freeing researchers from the tedium of programming, a task better left to computers (they will essentially "self-program" with only high-level verbal guidance from humans).

In the meantime, perhaps more realistic goals are to 1) make high- performance workstations available to all empirical researchers, 2) improve network communications to allow researchers to communicate with each other easily and rapidly, using "machine transparent" protocols for interchange of data and programs, 3) develop a common high-level language syntax to eliminate the necessity of knowing the myriad of competing programming languages (or alternatively, to develop translation programs that allow code of one language to be easily converted into other code, similar to the way Mathematica programs can be automatically translated into Fortran or C "pseudo-code"), and 4) promote an incentive structure which provides higher rewards to basic measurement and data analysis rather than implicitly treating it as dirty work to be relegated to graduate students.

Given the great expense of data collection in the social sciences, it is paradoxical how cavalier many current econometric analyses are with the data. Basic quantities, such as wealth and consumption, are notoriously badly measured, yet there is very little research directed toward constructing improved measures. The current reward structure in econometrics places much more value on inventing new estimators and proving their asymptotic statistical properties rather than applying one of the large number of methods we already have at our disposal.

We see advanced computing as a way of bridging the gap between theory and practice of econometrics. We think that previously the complexity and sheer awkwardness of the traditional computing languages provided a strong deterrent for theoretically-oriented researchers to use computers. It helped create the current schism which has divided the profession into "applied econometricians," who are essentially computer specialists who know the data but do not have time to fully understand econometric theory, and econometric theorists, who know the theory but have little time and/or concern for the data. We see in the coming decade a new era where computers become sufficiently advanced that one does not have to be a specialist to use them effectively. This will encourage more theorists to actually look at data on their own, and to see how the methods they are proposing really work. At the same time, advanced computers will also free-up time of applied researchers so they can keep up with recent developments in economic and econometric theory.

Given the increasingly large size of data-archives, it is going to be important to have institutional structure for recording problems with the data and the results of data analyses. Currently researchers exchange "recoded" data sets that apply various transformations that "correct" problems in the original survey data. However, it is rare that researchers will also provide the source code that produced the recoded data set. Without knowing the exact transformations that have been applied, these recoded data sets are often of little value to subsequent researchers, who may not trust the original transformations and are therefore forced to "re-invent the wheel" and rediscover all the problems that the original researcher found. The NSF's recent initiative to require all empirical researchers funded by NSF to turn over their data and programs is very important. However, as yet there is no institution responsible for archiving and disseminating these data and programs. In addition, current professional reward structure places little value on writing computer code: one's curriculum vita counts publications in English, not computer programs written in C, Gauss, or Pascal. We need to take steps to increase professional awareness of new journals such as "Computer Science in Economics and Management" and "Economics and Financial Computing" that provide a forum for publishing algorithmic and computer-science oriented research that is not offered in the "traditional journals." We would also encourage efforts to improve professional awareness and attitudes towards existing applied journals such as the Review of Economics and Statistics or the Review of Income and Wealth that publish articles concerned with measurement of economic variables, and to even consider the creation of new journals such as "Communications on Economic Data and Measurement" to fill the void left by similar journals that became defunct in the 1980's (an example is the Annals of Economic and Social Measurement). Our impression is that there currently is no journal that serves as a "clearinghouse" for articles on problems with variable measurements in major commonly used datasets, nor a good outlet for publishing innovations in recording and defining improved measures of economic variables. It is a sad commentary that even basic economic variables such as income, consumption and wealth that are cornerstones of economic theory are currently so poorly measured that they have seriously compromised many empirical studies to date. The challenge will be to find some sort of "universal" computer syntax to enable effective and appealing communication of these results in journal form.

5. Estimation of models of economic equilibrium

Understanding the implications of an AI-based theory of economics is going to require computers: there is no easy way to study a collection of AI algorithms analytically. For example, see the articles by Pau and others in Pau, Motiwalla, Pao and Teh (1989). We predict that enhanced computer resources will allow the development of a wide array of detailed, interesting, and realistic economic models based on AI principles that will allow us to draw conclusions about topics that traditional economic methods offer little hope of analyzing. We think this will be another growth area in the 1990's and beyond, one that could benefit from an NSF computer initiative.

It is clear that an important source of innovations in economic theory is computational technologies imported from other disciplines. For example, one could reasonably argue that the last twenty years in macroeconomics and applied econometrics have involved a profitable translation of prior work in electrical engineering on control and filtering, with significant modifications such as the Lucas emphasis on the mutual interdependence of perception and action that is unique to human (as opposed to physical) events. Some of the most interesting recent work in economics has been imported from other information sciences, ranging from cognitive psychology to the theory of computer algorithms. Although some "new wave" computational techniques, such as simulated annealing, are explored by groups such as the Santa Fe Institute, one field that may be relatively under-examined in economics is that of computational learning. From the perspective of agent learning, for example, work on classifying learning algorithms that can and cannot be solved in polynomial time may suggest reasonable restrictions on real-time agent learning, see Spear (1989). If markets may further be characterized by parallel learning by nearly-independent processors (agents), it would be useful to know which algorithms in the computable set can be parallelized. Also, work on algorithmic performance guarantees, see Garey and Johnson (1979), which establish bounds on worst-case or average departures from optimal solutions by heuristic solution methods, seems in line with work in economics on satisficing.

7. Bayesian econometrics

1. Laplace expansions (Tierney and Kadane (1986)) provide an approximation that converges a half-order of magnitude faster (in sample size) than traditional expansions of the likelihood function. Moreover, compute time is very fast.
2. Monte Carlo integration with importance sampling (Geweke (1989)) provides a more flexible approach that has now been used in a wide variety of applications and has been incorporated in some commercially produced software. Unlike expansion methods, it can provide an arbitrarily good approximation of the requisite multiple integrals, but computation times can be much longer.
3. Gibbs sampling (Gelfand and Smith (1990)) and data augmentation (Tanner and Wong (1987)) have been developed for statistical applications only quite recently. They are based in part on methods developed for image reconstruction (Geman and Geman (1984)). For many econometric problems they appear to be much more stable than Monte Carlo integration, and typically the person-hour requirement for implementing this solution is an order of magnitude smaller than is the case with Laplace expansions or Monte Carlo integration with importance sampling.

Computing platforms and software are essential to these lines of research, for they define the environments in which solutions can be implemented. The best work is invariably done by individuals or groups who confront actual applied problems, and can iterate between machines, algorithms, and productive formulations of the problem itself.

B. Environmental Change

The problem can be analyzed both at a national and at an international level. Analysis at the national level focuses on the effects of carbon emission taxes. One of the questions posed is how high these taxes must be to bring about a certain reduction in carbon emission. Also, these taxes cause substitution between fuels and between energy and other inputs. For example, coal has a high carbon content relative to natural gas so these models analyze the extent to which natural gas will be substituted for coal in the production of electric power. Both econometric models (Jorgenson and Wilcoxen (1990)) and mathematical programming models (Manne and Richels (1990)) have been developed along these lines.

However, analysis of this problem at the national level is not sufficient. The global warming problem is essentially an international problem, cf. Nordhaus (1990). The developing countries can be expected to increase their carbon emissions and thus there will be substantial tensions between developed and developing countries over who will emit how much carbon dioxide in the effort to prevent global temperatures from rising. The modeling effort at the international level is at an early stage of development. These models will involve many countries and also will require a small grid area in order to obtain acceptable levels of accuracy, thus they will require large computer resources to solve.

C. Microeconomics

Markowitz and Manne (1957) laid the foundation for the inclusion of economies of scale in dynamic investment models using mixed- integer programming techniques. This foundation was built on with a series of studies for steel, pulp and paper, fertilizers, and other industries done at the World Bank in the 70's and 80's, viz Choksi, Meeraus and Stoutjesdijk (1980). High-speed microcomputers and workstations, along with modeling languages like GAMS (Brooke, Kendrick and Meeraus (1988)), have opened the door to modeling firms and collections of plants and markets with linear and nonlinear programming techniques.

Recently, this work has moved into expert system methods using Prolog (Krishnan (1988)) and into graphical interfaces which hold great promise for making it easier to develop models of firms and industries (Kendrick (1991)). These graphical interfaces permit the user to work with a number of windows on a computer screen which display different representations of the same model. For example, a linear programming production and transportation problem may be represented in various windows as: (1) a map or graph showing the location of plants and markets in space, (2) a mathematical model with constraints and an objective function, (3) a modeling language such as GAMS or Structured Modeling, (4) various spreadsheets which display transportation costs between plants and markets or input-output data for alternative production processes, and (5) databases which provide organizations for the data and/or expert system code to describe the model. Any one of these representations may be used to update a portion of the model. For example, the addition of another plant to the model may be done in the graphical view, the mathematical modeling view or the expert system database. The user can use whichever view is most natural or most effective and then see the model immediately updated in all parallel views.

Progress in microeconomic modeling of firms has been slowed by the difficulty of building computer representations. The advent first of modeling languages and secondly of graphical interfaces will free this area for rapid development.

Another promising area in the application of mathematical programming methods to economic problems is that of variational inequality algorithms for the computation of equilibrium problems (Dafermos (1983)). Since the variational inequality problem contains, as special cases, nonlinear equation systems, optimization problems, complementarity problems, min/max problems, and fixed-point problems, the framework is a powerful and unifying one.

Variational inequality theory was originally developed in the late 60's and the 70's for the study of partial differential equations arising in mechanics. Recently, the variational inequality problem, in the finite-dimensional form, has been used to formulate and solve a variety of problems in economics, governed by distinct equilibrium conditions. Examples include: oligopolistic market equilibrium problems, in which the producers and consumers are spatially separated and a cost of transporting the commodity is incurred (Dafermos and Nagurney (1987), Nagurney (1988)), and spatial price equilibrium problems, which can treat multiple commodities and are not limited to the case of "symmetric" Jacobians of the supply price, demand price, and transportation cost functions, as in the classical Samuelson, Takayama-Judge models (Nagurney (1987)). General economic equilibrium problems have also been recently solved via a variational inequality decomposition algorithm (Zhao and Dafermos (1990)), with the numerical results suggesting that the algorithms are very suitable for large-scale problems.

Variational inequality algorithms are relatively simple to implement, allowing for the exploitation of problem structure, thus yielding efficient algorithms for large-scale problems. Such algorithms are needed since certain fixed-point algorithms do not perform efficiently on large-scale problems. Further, alternative variational inequality formulations of a given problem may suggest alternative serial and parallel decomposition algorithms, the latter being amenable to implementation of parallel architectures. Research along these lines has yielded a parallel decomposition algorithm by commodity which has been applied to multi- commodity market equilibrium problems on an IBM 3090 in Nagurney and Kim (1989) and a parallel decomposition algorithm by time period for the solution of dynamic market equilibrium problems, again implemented on an IBM 3090, in Nagurney and Kim (1991). Ongoing research in designing decomposition algorithms by markets is suggesting that equilibrium problems will soon be solvable on massively parallel architectures.

Finally, variational inequality-based algorithms have been developed for the solution of policy models. One example is the work of Nagurney and Zhao (1991) in modeling price controls in the form of price floors and ceilings in multi-commodity trade models which shows that such models are not much harder to solve than models without such policies. Another example is the generalization of goal programming in a variational inequality framework to determine taxes in a model with negative economic externalities and with production and transportation targets by Nagurney, Thore, and Pan (1991).

3. Artificial Intelligence Methods

The methodology is relatively new (viz. Axelrod (1987), Miller, (1989), Marimon and Miller (1989), Marimon, McGrattan and Sargent (1990) and Andreoni and Miller (1990)). Although novel, we feel that this methodology not only complements both the existing theoretical and experimental methods, but also offers a number of new opportunities for productive economic analysis.

Solutions based on optimization approaches often require technically demanding derivations. Thus, these solutions may be criticized on the basis that typical agents lack the analytic sophistication necessary to derive them. By analyzing simple adaptive learning systems, one can explore whether or not these systems will converge to the optimization prediction. The analysis can extend beyond questions of simple convergence, and encompass a search for the necessary preconditions on the problem as well as the adaptive process which will facilitate such convergence (e.g., the structure of the basins of attraction of the theoretical solutions, the complexity of the solution space, etc.). Even though adaptive forces may encourage convergence to optimizing solutions, coevolutionary forces may demonstrate very different dynamics. Moreover, if adaptive systems do tend to converge towards optimal solutions, they may provide a technique for deriving numerical solutions to problems that do not currently have analytical ones (for an example of this, see Marimon and Miller (1989)).

The use of artificial intelligence techniques also produces a rather unique experimental environment. These techniques provide an enormous degree of control over the entire experiment. The information, knowledge, experience and expectations of every player can be fully controlled. Each subject's motivation can be explicitly formulated, and difficulties caused by differing levels of education, attention span, income, risk aversion and non- pecuniary utility (e.g., gaining utility from winning an auction, etc.) can be avoided (or encouraged). A subject's knowledge of the game and level of learning can be reset to any previous level. By "resetting" subjects to a given initial condition, subtle variations of the game can be explored (e.g., how robust is the game to slight changes in valuations, are there path dependencies which will lead to very different outcomes based on small events, etc.). Furthermore, any conceivable a posteriori analysis is feasible since the state of the system is fully recoverable. These experiments also have relatively low cost and time requirements. Obviously, no monetary payments are necessary to motivate subjects. Initial programming effort is comparable to setting up a well-designed human experiment. Once programmed, literally thousands of extremely intensive (e.g., 100,000 auctions) variations of the game can be produced in a relatively short time. Finally, in human experiments, one can only observe players' behaviors; in these experiments, one can observe players' strategies. At any point in time the actual strategic components which produced a given move are available for in-depth study. Early work with machine-learning techniques has shown that they may provide an important bridge between current theoretical and experimental work (see, for example, Andreoni and Miller (1990)).

Obviously, the relevance of artificial intelligence techniques to the analysis of human experiments depends on their ability to give insights into current experimental results. An understanding of the behavior of artificial adaptive systems may highlight those environments that are either difficult or easy for humans. Perhaps the adaptive properties of different market institutions might explain the patterns of their actual real-world use. If the above techniques are found to correlate well with human behavior, then a variety of applications arise. Using these techniques, one could derive a set of useful benchmarks for human experiments. One could also search a large space of new games and designate those which appear to have potentially interesting behavior (given some set of objectives) for further analysis.

The artificial intelligence approach also offers a variety of other opportunities. The methodology creates an easily manipulated model world in which one can generate and test theoretical hypotheses. It also suggests a new direction for economic theory whereby theoretically plausible models of cognition (many of which incorporate ideas of bounded rationality, etc.) are placed in an easily implemented empirical framework. Holland and Miller (1991) provide a general overview of these issues.

4. Computable Dynamic Heterogenous Agent Models

The more one thinks about the relationship between the issues typically analyzed and the data, the more one becomes convinced that little can be done without first coming to some understanding of the factors underlying these differences among firms. This is true for more than one reason. First, without some knowledge of how these differences evolve, it will be impossible to develop estimation strategies for those primitives of the model that can reasonably be assumed to be constant across agents. For example, to control for the selection induced by exit behavior, we need a model of when exit occurs. The exit decision is determined by the firm's perceptions of the future market conditions, and its own state variables. The latter are precisely those variables which are causing heterogeneity in responses or in efficiencies of firms, so we cannot analyze responses or efficiency without first accounting for the fact that by selecting on survival we are throwing out one tail of the distribution of outcomes. Note also that the actual exit rule, precisely which firms exit when, is an integral part of the market's equilibrating forces, and to get precise estimates of it we will have to solve for the entire equilibrium. However, sometimes we will be able to use qualitative characteristics of the exit rule together with semiparametric estimating techniques to account for the selection induced by exit in the estimating process, e.g. Olley and Pakes (1991).

Second, as noted earlier, the evolution of the sources of heterogeneity is both endogenous and of fundamental importance to the issues we want to analyze. If the price of energy rises, we expect firms that chose energy-intensive technology to shrink, while the firms which chose technologies which were more, say, labor-intensive, might actually grow. If the price of energy stayed high for some time, we would expect the whole distribution to shift towards less energy-intensive firms, and we would want to pick this shift up in our analysis. It would occur partly through entry and exit, partly through the investment patterns of the existing firms in currently available technology, and partly through the development of new technology. Note that once we sink funds in new firms or new technologies, a return to the pre-energy shock prices will not generally cause the new entrants or the new technologies to exit (see Dixit (1989), for a discussion). Indeed, an explicit analysis of how the market directs these adjustments will require a solution to the sequential interrelated investment problems - a solution for the form of the dynamic equilibrium among the heterogeneous agents.

This is an example where we need to be able to compute the equilibrium just in order to get the aggregate response to the change. There are many areas in economics where more detailed characteristics of the distribution of equilibrium responses are central to the analysis. The analysis of the link between default probabilities and the market for finance capital, and of the effects of various regulatory change on market structure, are examples that occur repeatedly in the finance and industrial organization literature. More recently, the finding that almost all of the variance in gross job creation and gross job destruction is within time- period, within-industry variance (see Davis and Haltwinger (1989)) makes any analysis of the causes or the effects of job turnover highly dependent on the detailed characteristics of the equilibrium from dynamic heterogeneous agent models (see Hoppenhayn and Rogerson (1990) for a start at such an analysis).

What we would like to stress here is that though we may be able to estimate all, or almost all, of the parameters of interest without ever computing the equilibrium for the model that guides the analysis, we are going to have to compute the equilibrium to do the subsequent policy analysis. Computing it once or twice does not require as fast an algorithm as the algorithm that would be needed if we were to nest the fixed point calculation needed for the equilibrium into an iterative maximum likelihood (or minimum distance) estimation subroutine. On the other hand, as our models grow to encompass say, foreign sectors, with the associated possibilities of tariffs, orderly marketing agreements, exchange rate fluctuations, and the like, the computation will become quite demanding. For those who have worked in this area there is little doubt that to make full use of the estimates that should be obtainable from the newly available panel data sets we will need significant progress on the computational front.

D. Sectoral Economics

Duloy and Norton's (1973) model of agriculture in Mexico provides a good example. The model considers inputs such as labor, land, water and fertilizer into the production of ten or so different crops which have different growing seasons and sharply varying labor requirements in different months of the year. They consider the acreage of land of different types available in different regions of the country and the amount of farm labor which exist in the regions. Thus, the model can capture labor migration patterns as well as study the income distribution effects of various agricultural policies such as the reduction of price supports and the freeing of controlled prices of inputs such as fertilizers and crops such as wheat and cotton. Because of the combinatorics of the number of crops, inputs, regions, and seasons, these models quickly grow in size and require fast workstations to solve and analyze. A recent book on this type of model is Kutcher, Meeraus and O'Mara (1986).

Pindyck's (1978) model of OPEC provides an example from industry. This dynamic nonlinear model of the oil industry pits OPEC against the fringe producers in the determination of the world oil price. OPEC can raise its price and increase its revenues in the short run but this higher price causes the fringe producers such as Norway, England, the U.S. and others to increase their production over time. This, in turn, results in lower future prices for OPEC. Also, consumers respond over time to the higher oil prices and adapt their behavior, thereby increasing the trend toward lower prices. This model is a nonlinear programming problem which was relatively difficult to solve when it was developed but can now be solved on microcomputers. Models of this type should continue to be developed and updated to help in the analysis of U.S. energy policy.

Linear programming models have been a staple for many years in the oil refining business and these models are now evolving into large nonlinear programming models. They began as single refinery models and have now become company wide, national and international. This tendency toward the development of international models of an industry was also pushed forward by the World Bank with studies of the aluminum and copper industries, viz. Brown, Dammert, Meeraus and Stoutjesdijk (1983) and Dammert and Palaniappan (1985), respectively. The aluminum model includes the principal mines for several types of bauxite located in the major producing countries such as Australia, Brazil, Surinam, etc. It also includes production facilities for alumina and aluminum in a number of countries and the cost of transporting bauxite and alumina between mines and plants and of transporting aluminum to markets. Market areas are scattered around the world in the leading industrial countries. The cost of electricity is included since the transformation of alumina to aluminum requires large amounts of electric power so that plants near hydroelectric sites are favored. Finally, investment cost is characterized by economies of scale so that the model is nonconvex and must be solved with mixed-integer programming methods. Thus the model is expensive to solve but it captures much of the essential economics of this worldwide industry. We foresee that similar models of most of the world's globe-straddling industries will be constructed in the years to come.

At the time many of the models discussed in this section were built, they could only be solved on large mainframes; however, they can now be solved quickly on workstations in a much more friendly and accessible atmosphere. A priority area of work here is to provide graphical interfaces for these modeling systems and expert systems software which can be used in conjunction with the models, as discussed above in the microeconomics section.

E. Growth and Development

There are several promising new areas of nonlinear modeling and optimization, including the neural network models of learning reviewed in Hinton (1989), and new techniques of large-scale numerical analysis, discussed in a review of automatic differentiation by Dixon, Maany and Mohseninia (1990). In addition, there is renewed interest in older techniques of analysis that are now rendered more computationally feasible on modern high-speed chips and disk drives.

A rich area of prospective work in macroeconomic modeling is associated with the revival of earlier work on nonlinear control, filtering and dynamic programming. In the case of macroeconomic policy design framed as a single-agent optimization, early work began with the small, linear model illustration by Pindyck (1973). Applications were readily extended to large-scale, nonlinear macroeconomic models using open-loop optimizations, vis. Tinsley, Craine and Havenner (1974); feedback optimizations with filtering of incomplete observations, vis. Shupp (1976) and Kalchbrener and Tinsley (1976); and dual control learning methods which combined both estimation and optimization, viz. Kendrick (1981). Work on single-agent stochastic control with active learning, slowed by prohibitive computational requirements that outstripped the capacities of conventional mainframes, has resumed with supercomputers, Amman and Kendrick (1991).

Although modeling of intertemporal optimizations was also readily extended to single-agent characterizations of firms, such as Tinsley (1971) and Sargent (1978), estimation and solution of multiple-agent models where all private and public agents exhibit rational or model-consistent expectations, was computationally confined to illustrative small-scale linear models. Using recent- generation computers and low-order difference equation approximations of Euler conditions, applications of policy design analysis with forward-looking agents have been extended to nonlinear macroeconomic models of moderate complexity, as illustrated in Bryant et. al. (1991), usually employing a variant of the certainty-equivalent algorithm suggested by Fair and Taylor (1983).

The accessibility of high-speed drives and inexpensive disk storage has also reduced the "curse of dimensionality" computational barrier associated with dynamic programming, as developed by Bellman (1957, 1971). Characterization of rational intertemporal planning by a representative agent through stochastic dynamic programming is the analytical core of "equilibrium" macroeconomics; references to work in this burgeoning area of research into growth and business cycle mechanisms may be found in Stokey and Lucas (1989) and Hansen and Prescott (1991).

Of particular interest to computational macroeconomists interested in "bottom up" modeling of macroeconomic systems based on optimizing agents is recent work on simulation estimators of systems that do not admit closed-form solutions of endogenous state variables. A highly-simplified analogy to the familiar filtering and estimation cycles in the EM estimator of Dempster, Laird and Rubin (1977) is used. The "filter" cycle consists of solving the intertemporal optimization problem of agents, given "deep" parameter characterizations of taste and technology. The "estimation" cycle consists of maximum likelihood or method-of- moments estimation of deep parameters, given the state variable predictions of the simulated "filter" cycles. In contrast to the closed-form predictions based on conventional linear, quadratic, Gaussian (LQG) specifications, the simulation approach may accommodate numerical dynamic programming solutions of general nonlinear problems, such as absorbing boundary or inequality constraints, or unusual selection problems with sample observations. Useful references include Rust (1987), McFadden (1989), and Lee and Ingram (1991). Applications of this estimation technology to even small-scale macroeconomic models will be extremely demanding of advanced computer hardware but should provide useful insights into the macroeconomic importance of realistic conditions that are difficult to accommodate in standard modeling procedures, such as rationing, bankruptcy exits and asymmetric adjustment costs. These techniques should also be useful in pursuing empirical models of the large nonlinear impacts of small transaction costs on the distributions of asset prices or durable expenditures, as in the work on impulse control of Brownian motion by Dixit (1989) and by Bertola and Caballero (1990).

A fundamental aim of macroeconomic theories of business cycles is to interpret why producers respond to unfavorable "news" by rapid adjustments of production and employment rather than by adjustments of prices. Greenwald and Stiglitz (1989) recently suggested that the rigidity of nominal prices may be due to producers' perceptions of lower risks associated with quantity reductions of production costs rather than with price manipulations of demand revenue. Optimization under "instrument uncertainty" can be analyzed in the context of approximate LQG systems with stochastic coefficient state equations, viz. Norman and Tinsley (1983). Estimation of stochastic coefficient or state-dependent systems is well-established, viz. Priestley (1980) and Swamy and Tinsley (1980), and encompasses a wide class of commonly- encountered error structures, e.g. Nelson and Kim (1988). Empirical applications have been confined largely to single- equation applications, in part due to the high dimensionality of stochastic coefficient specifications, and access to high-speed and large-memory computer systems should make this a more tractable method of modeling state-dependent systems.

Macroeconomists are also turning to panel data to obtain sharper empirical resolutions of macroeconomic issues. In addition, characteristics of macroeconomic systems are often attributed to complex dynamic aggregations, such as Blanchard's (1987) cumulative lag interpretation of sticky price aggregates or Hall's (1989) suggestions regarding thick-market externalities. Nevertheless, aggregation of estimated micro-behavior of heterogeneous agents is a topic that has been badly neglected in computational economics since the early work by Green (1964), Klein, and Theil on exact, static aggregations. See Lippi (1988) for a recent discussion of problems associated with aggregations of micro error-corrections and Balasko's (1984) discussion of the related problem of approximate small models. Along with improvements in computing equipment, increased public access to disaggregated panel databases is likely to encourage work needed to resolve some marked discrepancies between time series models and cross-section models of macroeconomic behavior. In addition to more recent work on aggregation by superlative indexes and neural networks, early theoretical work on computational techniques that should be useful in this arena include Zellner's (1969) motivation of stochastic coefficient modeling, Luenberger (1971) on low-order system observers, and Chipman (1976) on generalized inverse aggregations.

G. International Trade

One way to capture the economics of intermediate products is to build programming models which include capacity, not at the plant level, but rather at the level of the productive unit. Thus a model of the automobile industry would not have just plants, but would rather go inside the plants and have productive units and assembly lines for key components such as engines and transmissions.

While it was difficult at an earlier stage to construct worldwide models even at the plant disaggregation level, we need to press forward to improve our capabilities to analyze industries at the level of key productive units, and thereby to model the tremendous potential increase in trade in intermediate products.

H. Economic Databases

Thus, the first need is for a theoretical framework rich enough to allow for estimation of basic structural relationships among economic agents, establishments, firms, individuals and households. The models developed must be rich enough to provide for stochastic outcomes, incorporate equilibrium concepts that enable researchers to evaluate the impacts of spillovers on behavior, and provide for efficient use of both cross-section and time-series variations in agents behavior. In order to make progress on answering basic policy questions, these models must be parameterized and "experiments" with different policy instruments undertaken. This requires microdata panels. Such panels are possible to create, but they require substantial matching across existing databases, extensive editing, and long term commitments of resources, including mechanisms for feedback between the entities collecting data and the information developed from the matched database(s). In addition, since the data involved will be subject to confidentiality restrictions, methods for researcher access will need to be a part of any plan.

Until recently, information on economic agents were accessible to scientific inquiry only at relatively high levels of aggregation. Thus, the richness of human behavior was not reflected in the volume of data available. This situation has changed rapidly over the last decade in a number of areas of inquiry, among them industrial organization, environmental economics, productivity, labor and demographic analysis. Nonetheless, the availability of rich micro-databases in economics is in its infancy. Newly emerging models require substantial bodies of data organized into large and dynamic databases to support ongoing economic research. Indeed, most aspects of modern economics are now utterly dependent upon database and computer technology. However, in many cases current data collections are not well organized for ease of retrieval. Nonetheless, many new microdata databases such as Survey of Income and Program and Program Preparation (SIPP), Longitudinal Research Database (LRD) and National Panel on Income and Aging are central to large bodies of work. As a result of these recent advances in models and data it is possible for people to devote their careers to data management and computational analysis in economic areas.

This "explosion" of data is large in a quantitative sense, but is equally daunting in terms of its diversity and the interrelationships that must be represented, organized and maintained. The data are generated by a statistical system and researchers that are widely dispersed both geographically and organizationally with relatively little standardization. Taken together, these problems pose transdisciplinary challenges for database design.

The report of the Lagunita Workshop on database systems (Silberschatz, Stonebraker and Ullman (1990)) clearly recognizes these problems. They speak of "1. Efficiency in the access to and modification of very large amounts of data" and "4. Persistence, the maintenance of data over long periods of time independent of any programs that access the data." Both have historically been bottlenecks for scientific economic discoveries (David (1991)). To the extent that their concern is integration of distributed heterogeneous databases the interests of computer scientists are identical to those of economists. To the extent that they are concerned with systems that incorporate rules as part of particular applications, they will open up the possibility of embedding logic in scientific databases that is now undocumented.

The current generation of databases is surely limited. As M. Stonebreaker himself confesses, one-dimensional optimization of storage is feasible. Multi-dimensional optimization is still a difficult problem. Yet it is precisely the capacity for optimal storage of dated, spatially referenced and entity-indexed data that is required for economic applications -- particularly applications that involve physical environment, local labor markets, and minimization of transport cost.

Also obvious in the economics community is the fact that research databases will need to be designed to work with virtual storage and storage on optical media. That is, only a small part of the research database need be on-line and most of the database will be read-only and should be treated accordingly. Lack of such capability in the present limits the development of databases. Lastly, attention must be given to versions, since the process of scientific discovery is inevitably a process of iterative discovery of error, and no adequate system exists at this time to deal with dated versions and their dissemination at appropriate marginal costs.

The critical issue for economists is the organization of disparately developed data structures relevant to common problems. Software technology has undergone rapid changes in the last 10 years with the development of, for example, relational databases. While it is important to note that it is now possible to adequately serve many design needs, databases for much of the economics of the next decade may not yet be in hand. It is still difficult to process data in environments where the underlying relationships are defined differently and the linking of new data structures to old is not part of the database development design. Despite significant and robust efforts in the last 10 years, the present generation of economic databases may fail in the next decade because they are not designed to deal with the volume, complexity and diversity of the data which will need to be accessible for economic research.

In both French, Jones and Pfaltz (1990) and Silberschatz, Stonebreaker and Ullman (1990), the writers are naive as to the complexity of the information that must be integrated with economic measurements to specify models of real world behavior. In the tax field, for example, the logic of the entire Internal Revenue Code and instances of interpretation need to be added to a database on corporate financing and investment to arrive at a model of investment behavior. The conceptual structure for such metadata exists (David (1991)); the implementation does not.

What is needed are paradigms and technology to represent and organize economic information, particularly in areas where economic information will need to be linked. For example, in accessing environmental regulations and policies, the cost of which are standard fodder for economic modeling and analysis, the benefits of such regulations must of necessity come from biological science in the form of predications about the effects of emissions on health. It is imperative that we bring together establishment and firm information on outputs (products and services), inputs (capital, labor, R&D, materials, purchase services), financial and management characteristics, and demographic information on workers (work histories, education, training, etc.) in an efficient computational environment if economic research is to proceed.

Evolution of scientific discovery will be enhanced by increased use of databases for economic data. The consistency of nomenclature, the portability of the relational database schema across computing platforms, and the capacity for dynamic independence (Codd (1985a and 1985b)) all promise economies of scale in research that have not yet been realized. The obverse of this proposition is that scientific support for economic computation must include maintenance of such databases.

The linkage of economic databases which are under the jurisdiction of different governmental offices is a matter of substantial importance in computational economics. There are four or five data merges that would open frontiers for research on topics of substantial current interest.

The first three merges discussed here would, together, generate a discrete jump in our ability to analyze environmental issues. They involve linking different data bases to the Longitudinal Research Database (LRD). The LRD is a plant-level panel of manufacturing firms that contains information on the "traditional" inputs and outputs that appear (in an aggregated way) in the annual survey of manufacturers (as well as some more detailed plant-level characteristics such as ownership, location, etc.). The three data sets which should be linked to it are: the Manufacturing Energy Consumption Survey (MECS) data set, the National Science Foundation Research and Development (NSF-R&D) panel data set, and the Environmental Protection Agency (EPA) data sets on emissions of pollutants. The MECS data set contains information on different forms of energy consumption by establishments: the NSF-R&D panel data set contains information on R&D expenditures by manufacturing firms broken down into about 30 product categories; and the EPA data sets track establishment- level water and air emissions of various pollutants.

Any analysis of the effects of policy on pollutant (or, for that matter on greenhouse gas) emissions is going to require estimates of the distribution of responses of the plants in the manufacturing sector to the alternative possible policy scenarios (taxes and subsidies that lead to relative price changes; quantity constraints on emissions; subsidies to "directed" R&D; etc.). These responses are likely to be dynamic. Initial responses will be augmented by (1) the exit of the firms that are most adversely affected by the change and (2) changes of technology among continuing firms. The fact that the LRD is a panel should allow us to follow this process quite closely (at least when we combine it with other relevant information as is discussed below). On the other hand, the fact that the policy change itself will induce a restructuring of the industry makes empirical work particularly hazardous. For example, the analysis will have to be careful to account for the selection biases generated by exit, to take account of the responses not only of incumbents but also of potential entrants, and to account for the spillovers generated by the R&D induced by the policy change. We will argue below that the way of accounting for these phenomena is to set out a logically coherent structure that is both appropriate for the data at hand and allows for these phenomena, and then insure that the estimation algorithm is consistent with it. Though we may not need to actually compute the equilibrium that results from the model to estimate its parameters, we will need to do the relevant computations to do subsequent policy analysis.

The EPA data sets follow plant-level emissions of pollutants over a period which includes the imposition of state regulation in the late 1960's, and of federal regulations in the early 1970's. In themselves, these data sets would allow us to get some idea of the immediate quantitative impacts of the regulations on emissions. However, in order to evaluate the costs and benefits of the alternative possible policy scenarios (and their distribution across various subsectors of the economy), we need more than just the impact of the regulation on emissions. We would also want their impacts on productivity, job displacement patterns, etc. For an analysis of these phenomena we need to link the EPA data sets to the LRD. Moreover, if we could use the match to estimate a structural model of the industry's equilibrium response to the change, we could then turn around and use the parameters estimated from that structural model to investigate what the impacts of alternative policy scenarios would be.

A related set of "natural experiments" are embodied in the sharp swings in the price of energy since 1973. These ought to be helpful in obtaining estimates of how industries restructure in response to price changes (and recall that this is what we can expect from a tax or a subsidy program). Indeed, the reason we want to link the MECS data set to the LRD is to enable more detailed analysis of the effects of the energy price changes on demand for energy both in the short and the longer run, and some of the impacts of those changes on the structure of manufacturing.

Finally, if we also linked the NSF R&D panel to the LRD we could attempt to get direct estimates of the effects of the various policy scenarios on the inducement to engage in research activity, and perhaps to a lesser extent, on the research efficiency or technology response function. The latter is a more delicate issue since we are opening up incentives to do research in relatively unexplored territory, and the outcomes of the research processes of the different firms are likely to be highly correlated. On the other hand, there can be no doubt that policy-induced changes in the environment can generate large research responses. As a simple example, consider Pakes (1989). In this study he analyzed the impact of water and air emissions regulations on the 43 patent (IPC) categories that seemed directly related to reducing air and water pollutants. The definitions of the first few IPC classes were: combating harmful chemical agents, purification of smoke, and preventing escape of dirt fumes. Recall that the federal regulations on emissions were instituted in the early 1970's but state regulations date from at least the mid-1960's. The annual average number of successful patents applied for in these 43 "pollution abatement" categories increased by 196 percent between the 1959/1969 and 1970/1980 decade. This is twelve times as large as the 16 percent increase in the average number of successful patent applications in all categories.

There is another important reason to merge the NSF R&D panel with the LRD. It would allow us to analyze the effects of research activities (or the lack thereof) on the increase in the import component of many manufacturing industries over the last decade and a half (relevant industries here include autos, steel, radio and TV receiving equipment, and telecommunications equipment). Indeed, we would argue that largely because of lack of available data and models, there has been little comprehensive econometric analysis done on the causes or the effects of the massive restructuring of the manufacturing economy that has occurred over the last two decades, or of the impacts of alternative policies (e.g. orderly marketing agreements) on that phenomena. This is a topic we should be analyzing with at least as much vigor as our analysis of the environment.

There are two other data linkages which we think could lead to a significant increase in our ability to do empirical work on issues of major importance. The first is a merge of the Decennial Census of Population (both the 1980 and the 1990 censuses) with the Census of Manufacturing, and then if possible, with the Censuses of Retail, Wholesale, Services, and Transportation. Studies in labor economics to date have had to suffice with empirical information on either the supply or demand side of the market, never being able put them both together to do a more complete "equilibrium" analysis. Part of the literature studied, say labor supply or the determination of wages, as a function of individual characteristics with no, or very little, information on the characteristics of the work environment. Another part used data on firms to study, say labor demand or the average wages of a plant, as a function of the characteristics of the the plant, with little or no information on the detailed characteristics of its labor force. The former studies are unable to account for the influence of demand factors (layoffs, plant closings, slowdowns or the need for overtime) on hours worked and participation, and they are unable to take account of the role of the characteristics of the plant on wages (e.g. shutdown probabilities, characteristics associated with labor contracts of different duration, etc.). The studies based on firm-level data suffer from an inability to partial out the effects of worker characteristics on wages, or on the sunk costs of hiring and firing decisions. By integrating the Current Population Survey (CPS) with the Census of Manufacturing we could match information on characteristics of workplaces with information on the characteristics of laborers, and try to separate out the effects of demand and supply factors on hours and wages.

Finally, some attempt should be made to line up the quintennial Censuses of Wholesale, Retail, Transportation, and Services into panels. These are sectors which have grown relative to manufacturing over the past decade, and we have very little information on precisely how that growth occurred. For example, are there really such things as agglomeration economies and how would we pick them up in data? Also, we have little information on the relationship of this sector to various deregulation and environmental changes, such as developments in information- processing technology and inventory systems.

I. Economic Theory

However, it is surely the case that once we bring to the analysis the idiosyncratic structure of an economic problem, there will be ways in which specially designed algorithms will be able to use that structure to speed computations. Therefore, a second effort should be development of new numerical methods which are designed to do well on economic problems.

The use of standard methods and the development of these methods will be of little interest if they do not advance our knowledge of economic problems. Therefore, a third priority should be special support of researchers who exploit the state of the art in numerical techniques to make their economic analyses more realistic, more believable and better adapted for data analysis.

These points can be illustrated with a number of examples.

1. Numerical Solutions of Rational Expectations Equilibrium

More recently, some have begun working on these problems with a focus on comparing the speed and accuracy of various methods (see Taylor and Uhlig (1990), and the accompanying papers). A weakness of this literature is that there has been little use of formal numerical analysis in developing these methods. In fact, most of the methods discussed in Taylor and Uhlig are, in reality, standard Minimum Weighted Residual methods (Fletcher (1984)), and in recognizing this fact and using standard methods from the numerical analysis literature, one can develop methods which will solve simple optimal growth models far faster and more accurately than any method discussed in Taylor and Uhlig.

Further exploitation of standard numerical solution techniques for evolution equations in Banach spaces will provide methods which will solve more elaborate stochastic optimal growth models, models with tax and externality distortions, and models with imperfect competition. An elaboration on these applications is given below.

2. Asymptotic Methods of Approximation

Econometricians will feel at home with these methods since the basic idea is similar to asymptotic methods in statistics. They have been used in some dynamic economic contexts. Examples include starting with the steady state of a deterministic growth model and using asymptotic methods to approximate what happens for nearby capital stocks when there are random shocks to output, Magill (1977). Recently, these methods have been applied to dynamic games in Judd (1985) and in Budd, Harris and Vickers (1990).

Research is needed on several issues. First, there is a need to develop more general methods for showing that these expansions are valid. Bensoussan (1988) has summarized the literature for dynamic control models, but outside of some special cases, there has been little done on dynamic games or economies with distortions. The work surveyed by Bensoussan was for finite- time horizon problems. Some mathematical work will be needed to prove the validity of asymptotic methods for the infinite-horizon models we use in economics, as in Magill (1977) for example. Second, the algebraic manipulations associated with these methods is very tedious but can be performed on computers using symbolic languages such as MACSYMA, MAPLE, REDUCE, or Mathematica. Development of generally useful software for economic problems would be important for disseminating these techniques and realizing their potential.

3. Hybrid methods

a. Dynamic Fiscal Policy

Recent work by Kehoe and Levine (verbal communication) indicates that economists can make real contributions to numerical methods. The problem with shooting methods in economic models is that they are shooting for a saddlepoint stable point, implying that if they get off the true path the errors explode. In fact, standard numerical analysts suggest not using shooting methods for such systems. Kehoe and Levine have developed an algorithm which exploits the Stable Manifold theorem and shoots forward in the stable subspace and shoots backward in the unstable subspace, resulting in a stable method. This is a good example of where researchers exploited the special structure of an economic problem to develop an efficient solution method for an important economic problem.

This and further improvements in the Auerbach-Kotlikoff framework would allow for many consumption and capital goods as well as diverse tastes and productivities among individuals. This would allow for a richer analysis of the distributional and sectoral impacts of macroeconomic and tax policy shocks. Combinations of asymptotic, Galerkin, and hybrid approaches will allow us to add uncertainty to the model, making it possible to examine business cycle fluctuations and asset pricing, among other important stochastic features of equilibrium.

Such a stochastic model would also allow econometricians to develop and evaluate relevant empirical tests. Monte Carlo studies of estimators are used systematically in econometrics. This, however, requires that one be able to solve the equilibrium of models in order to generate the synthetic data necessary for the Monte Carlo studies. In this regard, solutions of dynamic models have been very useful.

The importance of this was illustrated by Auerbach and Kotlikoff (1983b), who showed that standard empirical methods for analyzing the economic impact of Social Security were totally unreliable when using data generated by their model, strongly indicating that this empirical literature is devoid of any actual meaning. In general, we can use these numerical models and samples generated by them to test the reliability and robustness of empirical methods.

Ultimately, we will even want to use these methods within a maximum likelihood estimation framework. Fair and Taylor (1983) is an initial attempt to do this using a certainty equivalent approach. Further work on nonlinear solution techniques will make it possible to implement maximum likelihood estimation without invoking certainty equivalence, an assumption known to be false in most nonlinear models.

b. Financial Equilibrium

Recent developments in empirical finance indicate that financial markets are much more complicated than the usual simple theories assume. A large amount of the empirical analysis of financial markets relies on the Unanimity Principle, that is, all shareholders share a common value for their shares. Recent work has shown that this description of shareholder values is substantially inaccurate and that frictions in real-world financial markets reduce the applicability of the Unanimity Principle. Therefore, realistic analyses of financial markets must consider these frictions, a task better suited for computational approaches than pure theory.

Theoretical finance has spent much effort studying how information asymmetries affect equilibrium. Unfortunately, their studies almost always make assumptions on tastes and returns which are certainly not compelling and have very special properties, many of which Jordan showed were not robust. Numerical methods will allow us to examine these issues more robustly.

c. Savings and Taxation

The only way to rigorously analyze investor behavior faced with these tax rules is numerically. Formally, these problems are high- dimension dynamic programming problems. With solutions to these problems, we can provide a full and rigorous analysis of the economic impact of these tax issues. Furthermore, it will provide a badly needed sound theoretical basis for interpretation of the data.

For a discussion of computational methods for solving models of taxed stochastic economies, see Bizer and Judd (1989).

d. Dynamic Incentive Problems

Related issues include tacit collusion in dynamic oligopoly. This problem can also be reduced to a dynamic programming problem (Abreu, Pearce and Stacchetti (1986, 1990)), making computational techniques applicable. With numerical solutions, we could determine just how likely tacit collusion is under realistic conditions of uncertainty and imperfect monitoring -- issues which are currently examined only in simple frameworks giving no sense as their quantitative importance.

5. Convergence Problems

Johansen (1960) developed general equilibrium models which were linearized in rates of growth and which could be solved as systems of simultaneous linear equations. This idea gave birth to a whole family of models. Three of the groups which have pushed this work forward are (1) Irma Adelman and Sherman Robinson (1978); (2) Lance Taylor and his associates, viz. Taylor, Bacha, Cardoso and Lysy (1980); and (3) Peter Dixon and his colleagues in Australia, viz. Dixon, Parmenter, Sutton and Vincent (1982). The Australian models have played an important role in the analysis of tariff reform. They have thousands of equations and were difficult to understand and check when they were first developed. However, they can now be solved in very short periods of time so that the teams working with them can use them to analyze a broad variety of policies.

Recently, CGE models have played a role in the economics analysis which was done for the U.S.-Canada trade agreement. Moreover, this work is now being extended to include Mexico for the coming three-way negotiations.

The Canada-Mexico-U.S. trade negotiations represent one fairly typical situation in economic modeling. The models are sufficiently difficult to build that the events under study can transpire more rapidly than the models can be developed. Economists need to be able to respond more quickly. One avenue for increasing the speed of our response is to develop expert system and graphical interfaces for our software. One example is Drud's (1989) work on expert system software which can be used to aid in the construction of CGE's. The user need only provide the data and indicate the sectors and functional forms for the components of the model, and the system will construct and solve the model. Work of this type should be one of the high-priority areas in computational economics.

Although historically some equilibrium problems were solved using fixed-point algorithms, simplicial algorithms have not performed well on large-scale problems. More recently, complementarity algorithms and variational inequality algorithms have been proposed for the computation of equilibria. Complementarity algorithms, which have performed well in practice for the computation of general economic equilibria, have not been fully verified theoretically, whereas variational inequality algorithms have been theoretically analyzed but still need to be compared with the other algorithms. Computational research (both theoretical and experimental) needs to be conducted to determine the relative efficiencies, effectiveness, and level of generality of existing algorithms, as well as to suggest entirely new decomposition algorithms.

Further, although research has begun in the use and application of parallel processing systems for the computation of equilibria, these investigations are presently in the very early phases. Many problems in economics have a naturally decomposable structure, be it by agent, commodity, location or time period, and hence, suggest new algorithms which can be viewed as tatonnement processes and simulated on parallel architectures. Such problems with decomposable structures lend themselves not only to explorations via coarse grain parallelism, but fine grain parallelism as well. The availability of high-level parallel languages makes these challenges tractable.

L. Game Theory and Mechanism Design

Modern game theory has really begun to clearly lay out and analyze these issues in its formulation of games of incomplete information, a construct due to Harsanyi (1967-8), which extended the concept of equilibrium due to Nash (1950). We will not provide a history of modern game theory here, except to mention a few significant contributions that we think will have lasting significance. This includes the concept of sequential equilibrium of Kreps and Wilson (1982), the theory of sequential bargaining of Rubinstein (1982) (and extensions to incomplete information by Cramton (1984), Fudenberg, Levine, and Tirole (1985), Grossman-Perry (1986) and others), the theory of auctions by Vickrey (1961), Milgrom and Weber (1982), Myerson (1981) and others, and the multilateral bargaining models of Wilson (1985) and Satterthwaite and Williams (1989) et al.

However, from the standpoint of practical applications, we think the theory of mechanism design of Harris and Raviv (1981), Maskin and Laffont (1982), Myerson (1982), Townsend (1989), et al. will turn out to be the most important contribution. This literature describes a method ("the revelation principle") for designing games that achieve desirable outcomes despite the presence of information asymmetries that lead to problems of "moral hazard" and "adverse selection." Myerson showed that use of probabilistic payoff schemes (which includes deterministic schemes as a special case) allows one to reduce the general (one- shot) mechanism design problem to the solution of a linear programming problem. Subsequent work by Spear and Srivastava (1987) and Phelan and Townsend (1988) has shown how to apply the revelation principle in multiperiod contexts where an efficient mechanism cannot be easily formulated as a one-shot problem (or reduces to a repeated sequence of one-shot contracts). In this case, the mechanism design problem reduces to a recursive sequence of linear programming problems.

We believe that this methodology, when combined with recent work on estimation of dynamic programming models, may lead to some important new ways of evaluating and designing policy. An example of such a strategy can be found in a recent paper by Phelan and Rust (1991). One can imagine there are many private firms that are facing huge pension liabilities and problems of figuring out "how to retire unproductive older workers." These firms might benefit from a technology to design efficient retirement policies that recognize that workers have private information about health or productivity (and that many older workers are productive).

Recent empirical work on auctions and bidding procedures by Paarsch (1990), Hendricks and Porter (1988), and the recent game-theoretic analyses of "revolving door" relationships of Che (1991), may ultimately result in more efficient procurement procedures and bidding systems for the military and government. It is obvious that we need good procurement, bidding and wage incentive systems to attract and retain good people if we want to keep a strong military.

However, it is not yet clear that the mechanism design approach will produce policies which are robust to variations in the assumed form of technology and preferences. If efficient policies depend critically on certain parameters of taste and technology that are difficult to estimate, the ultimate value of the approach will be more limited. Yet here again, a computational approach will be invaluable to gauging robustness, since it allows us to solve for efficient programs corresponding to various assumptions about technology and preferences. Existing analytical approaches to mechanism design (e.g. Harris and Raviv (1981), Myerson (1982)) have yielded brilliant insights, but by in large they have been limited to a small number of problems with very restrictive specifications of taste and technology in order to produce analytically tractable solutions.

Given the success of more traditional approaches to policy design in the literature on military and firm retirement plans (Gotz and McCall (1984), Daula and Moffitt (1991), and Lumsdaine, Stock and Wise (1991)), it is likely that these types of economic models will be important inputs to designing efficient policies in the future.

M. Economic Institutions

1. What will be the impact of eventual conversion to a system of 100 percent electronic money (credit and debit cards) from the current system of predominantly paper money (bills and checks)? Why hasn't this conversion proceeded more rapidly than it has? What are the implications for profitability and competitiveness of private banking firms and the ability of the government to control inflation and real economic activity?
2. What will be the impact of the rapid movement to electronic and computerized trading systems in exchanges around the world? Will the changes stabilize or destabilize world financial and commodity markets? What types of trading institutions (e.g. rules for market access and execution priority) will lead to more efficient and stable outcomes?
3. How much of the total capital stock is "informational capital" and "human capital," as opposed to "physical capital"? How do we measure or quantify informational capital, and how do we make sensible investment decisions in the production of informational capital at both the public and private level? Also, how do we assign "property rights" or otherwise control informational capital, given that information has many aspects of a "public good," including transmission at near zero marginal cost?
4. How will the computer and communications revolution affect the structure of economic activity? Will it promote decentralization and a trend to "de-urbanization" as people begin to move away from cities when they realize that many economic activities can be performed remotely over high-speed computer links (e.g. doing financial consulting while located on a Greek island)?

We are particularly surprised that economists have done so little to understand the events surrounding and possible causes of the stock market crash of 1987. (Notable exceptions are Kleidon (1990) and Miller (1990)). The SEC has recently adopted some significant changes in response to the crash, including setting restrictions on computerized trading activities and creating market "tripwires" that suspend trading for various lengths of time in response to various size movements in stock indices. These are significant institutional changes that could have a major impact on market efficiency, yet we have seen very little formal analysis from economists indicating whether the changes are good, bad or irrelevant.

These are just a few of a rich set of research topics in economic institutions that have been spawned by the rapid development of computer and communications technology. We believe that NSF should encourage proposals in some of these areas.

N. Qualitative Economics

Qualitative specification and analysis of a model can be viewed as an alternative to an econometric approach. The main idea is to assume that the functional relations describing the system are known to fall into various classes of functions. Using the knowledge of the mathematical properties of the classes, it is possible to derive the qualitative behavior of the system. Bendsen and Daniels (1991) illustrate some recent qualitative techniques with an application to a Keynesian model. There is no need to use statistical techniques, although at some point there may be ways of integrating the statistical and qualitative approaches.

O. Theory of Computation

This ends our discussion of some of the leading research opportunities in computational economics. Next we turn our attention to the infrastructure that is necessary required by the economics community if we are to perform efficient research using computational economics methods.