Guillermo L. Gómez M. and Gerhard Tintner, Aplicación de los procesos de difusión a la planificación del desarrollo económico (1977)

Gómez and Tintner’s journal article develops a stochastic framework for economic-development planning and applies it to Colombia’s national accounts for 1950–1972. Its central proposal is to model development as a multivariate diffusion process: economic variables follow continuous, uncertain trajectories whose expected movement can be estimated and made responsive to policy instruments. The argument proceeds from systems theory and stochastic estimation to a lognormal growth model, then introduces government expenditure and private investment as determinants of its drift. A final, explicitly provisional section outlines optimal control. Three appendices explain systems concepts, derive maximum-likelihood estimation, and report parameter estimates and their variances.

The opening situates mathematical planning within postwar reconstruction, international economic dependence, resource politics, and increasingly complex administrative systems. The authors present their contribution as preliminary and connect technical expertise to the struggle against underdevelopment, hunger, unemployment, and inadequate public health. This practical ambition informs their treatment of economic trajectories as susceptible to intervention:

El comportamiento humano juega, por esta razón, un papel decisivo en la modelación del camino del progreso.

English translation: Human behavior therefore plays a decisive role in shaping the path of progress.

Uncertainty does not negate this agency. The model distinguishes the economy’s underlying state from imperfect observations of it, allowing disturbances both in economic movement and in measurement. The authors identify omitted variables, the quantification of qualitative characteristics, observational errors, and simplified empirical relationships as reasons for a probabilistic approach. Stochastic initial conditions and subsequent disturbances also allow structurally similar economies to develop differently. Development planning must therefore concern distributions of possible trajectories, not merely a uniquely determined path.

The mathematical exposition introduces Wiener processes, white noise, and the Itô integral before characterizing continuous-path Markov diffusion through transition probabilities. Two objects organize the analysis: the drift vector describes average local movement, while the diffusion matrix measures fluctuations around it and their interdependence. Under suitable regularity conditions, these coefficients determine transition probabilities. This supplies the conceptual bridge between a tractable statistical specification and a probabilistic account of economic change.

For the empirical model, drift is proportional to each variable’s level, while diffusion terms are proportional to products of the relevant levels. The authors make the substantive implication explicit:

Esto significa que las variaciones esperadas en x(t) y en la matriz de varianzas-covarianzas son supuestas proporcionales a los valores reales de x(t).

English translation: This means that the expected changes in x(t) and in the variance-covariance matrix are assumed to be proportional to the actual values of x(t).

The resulting multivariate lognormal process produces exponential expected trajectories and associated variances, covariances, and correlations. Rather than directly solving individual stochastic paths, the authors work through transition densities and maximum-likelihood estimation. Their four Colombian variables are real national product, real private consumption, real private investment, and real government expenditure. Nominal national-account data are deflated using the consumer-price index, which they acknowledge was the only price index available to them. The initial specification estimates constant drift coefficients and projects time-dependent trends for 1973–1982. It supplies a forecasting baseline, but does not yet explain how policy changes could redirect growth.

The decisive extension introduces instruments into the drift while retaining the proportional diffusion specification:

Las variables instrumento, también llamadas controles, son elementos, que por su naturaleza se dejan manipular con objetivos económico-políticos.

English translation: Instrument variables, also called controls, are elements that by their nature can be manipulated for economic-policy purposes.

Government expenditure and private investment now enter through their relative changes. Expected development consequently depends on accumulated changes in these instruments as well as elapsed time. The article compares observed and fitted historical values and generates three conditional projections: continuation of average 1950–1972 growth rates, continuation of the rates recorded in 1972, and sustained growth at the historical maximum rates. The scenarios show why a single extrapolated trend is insufficient for planning. Maintaining the negative investment and expenditure changes of 1972 produces declining paths for those variables, whereas the maximum-rate scenario yields much faster expansion. These are consequences of stipulated instrument paths, not demonstrated future outcomes.

The transition from forecasting to policy choice nevertheless remains incomplete. The authors distinguish a rapidly growing trajectory from an economically achievable intervention:

Una combinación óptima significa que las variaciones induzcan mayores tasas de crecimiento en las variables dependientes y permanezcan en un dominio realizable.

English translation: An optimal combination means that the changes induce higher growth rates in the dependent variables and remain within a feasible domain.

The final section, marked as research in progress, introduces admissible feedback controls and an expected cost functional incorporating running and terminal costs. It seeks a control minimizing that functional, but does not calculate an optimal Colombian policy or specify a fully operational welfare criterion and feasible set. Its significance lies in connecting estimated stochastic dynamics to a prospective decision framework. The article thus establishes a methodological progression—from uncertain economic movement, through conditional forecasting, to constrained intervention—while leaving actual optimization for further investigation. Some equations and fit-statistic entries in the supplied transcription contain visible inconsistencies, so their exact numerical interpretation requires checking; the distinction between the estimated diffusion model and the unfinished control programme remains clear.