Stata Technical Bulletin
21
coefficient,” “conductance coefficient,” and so on (Ferrari 1978). TC relates to the well-known “half-life time” and “doubling
time” concepts by the relations:
half-life time = log(1∕2) × TC
doubling time = log(2) × TC
6. Auxiliary variables: Rates can be also functions of “auxiliary variables.” Using them, the formulation of the rate equations
becomes simpler, also permitting the linking of state variables with different measurement units. An auxiliary variable is a
function of state or exogenous variables that relates fluxes of different materials, or transforms state variables in some way.
C) Model coding and simulation
To obtain simulations of real (or hypothetical) systems, it is necessary to code the mathematical model in a computer
language, to perform the numerical integration and to obtain the evolution of the system states with time. The system simulation
is, in effect, a method for the numerical solution of the state equations.
Many programs are available for this task. For example, DINAMO (Forrester 1968; Richardson and Pugh 1981), CSMP (IBM
1972), ACSL (ACSL 1987) and PCSMP (Jansen et al. 1988) are the most known. The equations can also be solved by using
routines coded in a lower level language (as FORTRAN, C, PASCAL, BASIC, etc.).
A useful feature of models coded for specific languages (ex: DYNAMO, CSMP, and simula, too) is the possibility to represent
all the system aspects in a conceptual rather than computational order. This makes the code more readable and errors easier to
detect.
The author has implemented some of the simulation possibilities of the specific languages in a program (simula) that,
being a Stata ado-file, looks like a real Stata command. This command works as a small simulation language, interpreting
lists of statements written following a few syntax rules. Simulations are then performed. Modification of parameters and initial
values is allowed. Moreover, the simulation results obtained with simula can be treated with all the other Stata commands. The
simulation with the simula command is not very fast when compared with dedicated or low level languages. However, for not
large models and for didactic purposes these do not seem big problems, at least when one takes into account its ease of use.
simula could also be useful to evaluate small models before linking them to larger models.
D) Parameters and initial values
The adopted parameter values determine, in addition to the model structure and equations, the model behavior. Parameters
are constant (or so considered) for the entire simulation period. Changing the parameter values also changes the model response.
This allows fitting of the model to different situations by the calibration. Parameter values can be obtained by experience,
by literature review, or by experiments. Also, initial conditions of the state variables are specified in the model. Sometimes,
depending on the model structure, these values can be important for the model’s dynamics. For a more detailed and complete
description of system analysis and modeling see, for example, Forrester (1968), Ferrari (1978) and Richardson and Pugh (1981).
Procedure for system simulation with Stata
The overall procedure can be divided into four steps:
1. Development of equations governing the model (state, rate and auxiliary) and identification of the parameters and initial
values.
2. Model coding into a .dta file. In this phase, it is possible also to state parameter and initial values.
3. Preparing of a .dta file containing the exogenous variables, if necessary.
4. Using the simula command. The command permits specification of the time solution step, the initial time, the simulation
duration, the required exogenous variable’s file name, the parameter values, the initial conditions and the graphic options
for the results.