Gerhard Tintner, Econometría (1953)

Gerhard Tintner’s journal article in El Trimestre Económico presents econometrics as the practical conjunction of mathematical economic theory and mathematical statistics. Its central argument is that economic relationships can acquire numerical precision and empirical testability only through explicit theoretical and probabilistic assumptions. Moving from model construction through identification, estimation, and hypothesis testing to policy applications, Tintner repeatedly makes the usefulness of numerical results conditional on the assumptions that produce them.

The exposition begins with maximizing consumers and firms, but immediately distinguishes theoretical restrictions from a fully specified empirical model:

La teoría económica sólo puede darnos algunas propiedades muy generales de esas funciones, pero no su forma específica.

English translation: Economic theory can give us only some very general properties of these functions, but not their specific form.

Different functional forms can express the same broad theoretical relationship while imposing different empirical properties, such as constant elasticities. Two further deficiencies complicate model construction: static theory is frequently applied to dynamic situations, and the transition from individual behavior to aggregate relationships remains unresolved. Better dynamic models, Tintner argues, require confronting the formation of expectations; macroeconomic analysis cannot simply assume that aggregation presents no theoretical difficulty.

The article next explains structural coefficients through estimates of demand elasticities, labor productivity, and the marginal propensity to consume. These examples establish what numerical economic knowledge means: an estimated response under specified conditions, not an unconditional law. Tintner then distinguishes errors in variables, comparable to observational errors, from errors in equations arising when relevant influences are omitted. His own meat-demand estimates illustrate how alternative stochastic specifications can yield similar results without making those specifications dispensable.

Identification is the conceptual hinge between constructing a model and estimating it:

Mediante la investigación de la identificación de las ecuaciones en nuestro modelo queremos determinar si será posible en absoluto el cálculo de esos parámetros estructurales, completamente aparte de todas las complicaciones introducidas por el muestreo.

English translation: By investigating the identification of the equations in our model, we want to determine whether calculating those structural parameters will be possible at all, entirely apart from all the complications introduced by sampling.

Statistical technique cannot recover a structural relationship unless the model first makes that relationship distinguishable. In the agricultural example, income enters demand and costs enter supply as exogenous variables, permitting the two equations to be identified despite equality between observed supply and demand. A dynamic corn-market model introduces lagged prices and stocks as predetermined variables. Such additions enable identification while also creating the harder statistical problems of stochastic difference equations.

Tintner proceeds from maximum-likelihood estimation to confidence limits and significance tests. Numerical estimates extend mathematical economics beyond general functional relationships; uncertainty estimates indicate how precisely their parameters have been measured. Yet neither confidence intervals nor hypothesis tests escape dependence on the model and its stochastic assumptions. Examples involving meat demand, production, and real versus money wages show how statistical inference can provisionally assess economic propositions:

Usando pruebas de significado y pruebas de hipótesis podemos probar ciertas leyes económicas, al menos provisionalmente.

English translation: Using significance tests and hypothesis tests, we can test certain economic laws, at least provisionally.

The qualification matters. Choosing between rival models remains difficult, dynamic theory is inadequate, and the foundations of inference are themselves unsettled. Tintner considers game theory and linear programming possible sources of improved models, discusses Carnap’s probability theory, and notes tensions between Fisher’s and Neyman–Pearson approaches. His skepticism toward Wald’s decision framework reinforces the article’s refusal to treat statistical procedures as a settled foundation.

The conclusion gives this methodological caution a practical purpose:

La econometría no puede, por supuesto, formular los objetivos de la política económica.

English translation: Econometrics cannot, of course, formulate the objectives of economic policy.

Ethical and political considerations supply the ends; econometrics may estimate the consequences of alternative means. Meat-market tax and subsidy calculations illustrate this division, while the closing warning stresses that their assumptions may not hold sufficiently in practice. The article’s enduring relevance lies in this disciplined account of quantitative judgment: structural estimates can guide economic policy, but their apparent precision never abolishes their theoretical, statistical, and historical conditions of validity.