A computer model is a model in which the implications of the assumptions — that is, the conclusions — are derived by allowing an electronic digital computer to simulate the processes embodied in the assumptions. Computer programs can thus be considered to be a fourth language in which the assumptions of a theory can be expressed and its conclusions derived. Actually, computer models might be viewed as special cases of mathematical models. We shall not pause to debate taxonomic subtleties, however, for it is more important to examine some of the features which characterize computer models.
We have stated above that there are a number of languages that could be used in model building. There are also a number of criteria that might be used to determine which language should be used. It seems obvious, however, that one important criterion is efficiency, as R. G. D. Allen argued. Computer models may be the most efficient approach when the model portrays a dynamic process and numerical answers in the form of time series are desired.
Figure B.1 Reaction curves of A and B.
The notion of a dynamic process can perhaps be made clear by reference to the simple Cournot duopoly model. 6 In , the reaction curves for rivals A and B are given. Each reaction curve shows the optimum output for one firm as a function of the output of its rival. In accordance with the model, the curves are drawn on the assumption that the conjectural variation terms (∂ q A /∂ q B ) and (∂ B /∂ A ) are equal to zero. The dynamic process of the model can be started at any point. Assume that A is producing q A1, then B will produce q B1 In answer to this, A will produce q A2 ; B will then produce q B2, and so forth. If this simple model were analyzed as a computer model, the computer would generate the time series of outputs for each firm. After the model had been run for a large number of periods, it would be clear that the outputs were tending toward equilibrium values where A is producing q A and B is producing q B.
In a model as simple as the Cournot model, we are generally not interested in tracing through the process by which equilibrium is reached but only in deriving the equilibrium values. These values are easy to find by simple mathematical analysis. However, the addition of a few assumptions about the behavior of the two firms can complicate the model sufficiently so that a computer simulation will be the most efficient method for determining the implications of the model. The volume of conclusions derived from a model is within the control of the model builder. However, in complicated computer models there are, generally, a large number of potential implications generated, many of these being time series of particular numerical values.
The fact that conclusions drawn from computer models may consist of a series of numerical values has in itself a number of interesting consequences. Numerical solutions should be contrasted with the analytic solutions usually derived from mathematical models. In terms of our earlier discussion on theory construction, we could say that the conclusions sought from a mathematical model are usually in the form of relations among the variables and parameters (including, frequently, derivatives or differences of the variables or parameters), whereas in computer models the conclusions obtained typically are in the form of time series of specific numerical values. This suggests that computer models are less general than mathematical models, for the reason that the amounts of input for computer models are greater than for the usual mathematical models. The increased input places greater restrictions on the relationships among the variables and parameters and, therefore, produces a less general but more specific model. To economists, one advantage of computer models is that their conclusions are presented in immediately testable form.
It should be emphasized that the above characterization does not imply that computer models are necessarily less general nor mathematical models necessarily less specific. Our considerations are related primarily to questions of convenience and efficiency. It is possible to use a computer model, for example, to gain insight into the effects of rates of change of particular parameters on the results of the model. This end is accomplished by varying the parameters of the model from one simulation run to another and comparing the output time paths that are generated. If the model can be solved analytically, however, such a result could be more easily achieved by mathematical analysis.
1. Comparison of computer models with operations research simulations and econometric models
In order better to understand the nature of computer models and the problems of using them, it is desirable to examine the use of simulation in the burgeoning field of operations research. Additional clarification can be gained by comparing computer and econometric models.
There are two basically different approaches that can be followed in using computer simulation to study a complex system. The actual approach taken, of course, depends on the questions to be answered and the kind of information known at the time of the investigation. The approach generally taken in operations research or management science might be entitled “synthesis.” This approach aims at understanding the operating characteristics of a total system when the behavior of the component units is known with a high degree of accuracy. The basic questions answered by this approach relate to the behavior of the over-all system. In principle, the entire system response is known once the characteristics of the structural relations are specified. If the system is complex, however, it may be difficult or impossible to determine the system behavior by current mathematical techniques. In this situation, simulation by an electronic computer can be utilized to determine the time paths traced by the system.
In social science, generally, the situation is quite the reverse. The behavior of the total system can be observed. The problem is to derive a set of component relations that will lead to a total system exhibiting the observed characteristics of behavior. The usual procedure is to construct a model that specifies the behavior of the components, and then to analyze the model to determine whether or not the behavior of the model corresponds with the observed behavior of the total system. When this model is sufficiently complex, either because of the nature of the underlying functions, the number of variables contained in it, or both, computer simulation may be the most convenient technique for manipulating the model. It is logical to call this approach to simulation “analysis.” The actual output of the model is a set of time paths for the endogenous variables being studied by the model.
Traditional econometric models are essentially one-period-change models. Any lagged values of the endogenous variables are, in effect, treated as exogenous variables. They are assumed to be predetermined by outside forces rather than by earlier applications of the mechanisms specified in the model. Hence the output of econometric models is the determination of the values of the endogenous variables for a given time period. To determine these values for the next period, new values would have to be assigned to the lagged endogenous variables. For this reason, most econometric models should be regarded as determining the changes that take place in the world from one period to another. They should be contrasted with process or evolutionary models, which attempt to exhibit the unfolding of dynamic processes over time.
The mechanisms of a computer process model, together with the observed time paths of the exogenous variables, are treated as a closed, dynamic system. In such a model, the values of the lagged endogenous variables are the values previously generated by the system. Computer models may thus be forced to operate with errors in the values of the endogenous variables made in previous periods, there being no correction at the end of each period to assure correct initial conditions for the next period as in econometric models.
The contrasts between econometric and computer models have not been offered as invidious comparisons. It is clear that economics has benefited and will continue to benefit in the future from work in econometrics. Rather, our analysis is aimed at showing the nature and peculiar attributes of an important new research technique for social science.
Source: Skyttner Lars (2006), General Systems Theory: Problems, Perspectives, Practice, Wspc, 2nd Edition.