Gerhard Tintner, Stochastische Elemente in der Ökonomie (1971)

Gerhard Tintner’s short methodological book argues that uncertainty belongs within the conceptual foundations of economics, not merely among the errors attached to deterministic equations. Its three sections move from an introduction to stochastic processes, through a critique of economics’ inherited models, to empirical applications and unresolved statistical problems. Seven examples connect the methodological argument to growth, agricultural policy, industrial development, and investment planning. The central proposal is to understand economic quantities as random variables generated by processes whose probability distributions can change over time.

Tintner begins by distinguishing the relatively static treatment of probability in conventional statistics from the study of changing distributions:

Ein stochastischer Prozeß ist eine Familie von zufälligen Größen, deren Wahrscheinlichkeitsverteilung von einem Parameter abhängt.

English translation: A stochastic process is a family of random quantities whose probability distribution depends on a parameter.

That parameter is often time. The distinction matters because economic development may alter both expected outcomes and their dispersion. Tintner illustrates this with a Poisson model of Indian national income, lognormal diffusion models of Chilean income and Indian agricultural production, and a regime-changing model of British industrial production. Government expenditure enters several models, making forecasts conditional on future policy. The British example also shows how estimated development stages depend on the number of regimes assumed: stochastic modelling supplies an empirical framework, not a uniquely determined historical periodization.

The methodological section places deterministic economics within the history of scientific borrowing. Classical and neoclassical theory followed the example of Newtonian physics, while modern physics subsequently incorporated probability at a fundamental level. Tintner does not regard borrowing itself as discrediting economics; he recalls that Malthus also influenced Darwin. His objection concerns the continued authority of an older scientific model and the narrow economic circumstances under which its abstractions appear plausible.

Game theory occupies an ambivalent position. Tintner praises its originality, its treatment of choice under uncertainty, and its equilibrium-existence results, but judges that it has not fulfilled its promise of explaining oligopoly and related market forms. Meanwhile, the highly abstract conditions supporting perfect competition contrast with the concentrated markets emphasized by Galbraith. Tintner therefore questions both the empirical reach of neoclassical models and their tendency to make competitive equilibrium the privileged object of theory.

His positive alternative also addresses Hayek’s objection to treating historical economic observations as samples from an unchanging population:

Hayek behauptet mit Recht, daß wirtschaftliche Größen nicht als Stichproben aus einer Grundgesamtheit betrachtet werden können, die zwar unbekannt aber statisch und für alle Zeiten unveränderlich ist.

English translation: Hayek rightly maintains that economic quantities cannot be regarded as samples from a population that, although unknown, is static and unchanging for all time.

Stochastic processes offer a response because distributions themselves can evolve. Adding random disturbances drawn from a fixed distribution is consequently insufficient. Yet Tintner also rejects an easy identification of stochastic economics with the better-developed theory of stationary processes:

Wenn wir uns auf die stationären stochastischen Prozesse beschränken, haben wir keine Möglichkeit, Erscheinungen zu behandeln, welche mit der Theorie des Wirtschaftswachstums zusammenhängen.

English translation: If we restrict ourselves to stationary stochastic processes, we have no possibility of treating phenomena connected with the theory of economic growth.

The requirement to explain trends thus generates a demanding research programme. Nonstationary processes remain mathematically difficult, and methods of estimation and hypothesis testing are especially inadequate for the small samples available to economists. Distributional assumptions introduce further difficulties. Since quantities such as prices and output cannot be negative, Tintner considers lognormal distributions attractive; nevertheless, evidence discussed by Mandelbrot raises the possibility of heavy-tailed distributions with infinite variance.

This possibility threatens familiar statistical assurances. With a Cauchy distribution, averaging observations produces no gain in precision of the usual kind. Tintner also draws on Basmann’s finite-sample results to argue that troublesome estimator distributions can arise even when underlying disturbances are Gaussian. Normality assumptions and asymptotic theory therefore cannot automatically guarantee reliable econometric inference. His advocacy of stochastic economics simultaneously becomes a critique of complacency about existing statistical techniques.

The applications show why these issues matter for decisions. Operations research, inventory management, control theory, and stochastic programming already incorporate probabilistic reasoning. In Tintner’s agricultural example, public expenditure becomes a control variable in policy optimization. More pointedly, a stochastic extension of Mahalanobis’s Indian planning model yields different investment recommendations depending on the criterion chosen. Allocating one-third of new investment to capital-goods production performs best by expected income or the mode; allocating two-thirds gives the stronger lower-tail outcome. A policy judged by protection against disappointing results need not coincide with one judged by its average payoff.

Tintner closes with a qualified preservation of deterministic theory:

Wir müssen nur in der Interpretation dieser Ergebnisse etwas Vorsicht walten lassen und unsere Theoreme so interpretieren, daß sie sich auf die mathematischen Erwartungen (Mittelwerte) unserer empirischen wirtschaftlichen Variablen beziehen.

English translation: We must simply exercise some caution in interpreting these results and interpret our theorems as referring to the mathematical expectations (means) of our empirical economic variables.

Deterministic results may remain useful approximations, but they should not be mistaken for complete descriptions of economic reality. The book’s contribution is this conjunction of conceptual ambition and statistical caution: growth, uncertainty, and policy require attention to changing distributions, while the tools needed to study them remain unfinished.