Gerhard Tintner and O. H. Brownlee, Production Functions Derived from Farm Records (1944)

Tintner and Brownlee’s research note investigates how farm business records can be used to estimate production functions and guide decisions about agricultural investment. Its evidence consists of records from 468 Iowa farms for 1939, grouped into dairy, hog, beef-feeding, crop, and general farming. The article moves from the construction of input measures and the choice of regression model through statistical results to their economic interpretation. Its central contribution is to distinguish the responsiveness of output to individual inputs, returns to scale, and the marginal returns on additional expenditure. These estimates suggest that the sampled farms could often gain more from operating expenditures and productive assets than from further improvements, but the authors restrict that conclusion to a particular population and year.

The records belong to members of Iowa Farm Business Associations, whose farms had larger assets and higher incomes than the Iowa average. Gross profits serve as the measure of total product. Six inputs are distinguished: land, labor, improvements, liquid assets, working assets, and cash operating expenses. Acres and labor-months measure the first two; the remaining categories encompass buildings and fences, livestock and supplies, machinery and breeding stock, and expenditures such as repairs, fuel, and purchased feed. The translation of accounting records into productive factors is deliberately provisional:

The productive agent management has been excluded since there is no satisfactory index of inputs of this factor.

This omission matters both to measurement and to interpretation. Acreage disregards land quality, labor-months disregard differences in intensity and skill, and improvement values depend substantially on appraisal. The authors consider valuations sufficiently consistent within the associations, while acknowledging that the categories are not entirely clear-cut. Their procedure therefore establishes an empirical approximation, not an exhaustive account of the determinants of production.

The chosen function is linear in logarithms, following the approach associated with Paul Douglas. Its coefficients directly express elasticities: the average percentage change in product associated with a one-percent increase in an input. The form permits substitution among productive agents and diminishing marginal returns without the additional parameters required by a quadratic specification. The authors also invoke the statistical advantages of logarithmic transformation, but qualify the reliability of inference:

Even though the errors are not independent and are not normally distributed, one still obtains the best linear estimate of the regression coefficients by using the method of least squares, although tests of significance are no longer reliable.

Statistical fit and trustworthy significance tests thus remain distinct considerations. For the pooled sample, the included inputs account for approximately 74 percent of variation in gross profits. Explanatory power varies across farm types, reaching its highest level for general farms and its lowest for beef feeders. The elasticities also differentiate production systems: crop farms show the strongest responses to land and labor, while liquid assets are particularly important in hog production. Several estimated coefficients are negative, but none of those negative estimates is statistically significant. The authors consequently decline to treat them as evidence that additional inputs actually reduce production.

A central conceptual distinction separates diminishing marginal returns to an individual input from returns to scale when all measured inputs increase together. The authors interpret elasticities below unity as indicating diminishing marginal returns with other factors held constant. They then sum the elasticities to characterize scale effects. These sums are below one for every group except crop farms; the pooled estimate is 0.9871, close to unity. Yet this finding is conditional on the specification: if management could be included, they suggest, estimated returns to scale might become constant or increasing. The apparent scale disadvantage is therefore not presented as an unconditional property of farming.

The next step converts elasticities into estimated marginal productivities per dollar of input. These calculations use the geometric means of the observed inputs, valuing land at $79 per acre and annual labor at $600. Their interpretation is explicitly local:

It should be again emphasized that these apply only to changes in the inputs of the various factors at the geometric means.

The estimates and their reported uncertainty limits support comparisons at a representative input combination, rather than universal investment rules. In the pooled results, cash operating expenses have the highest estimated marginal productivity, followed by liquid assets, while improvements have the lowest. Land and labor yield approximately equivalent marginal returns. From this pattern the authors infer that the farms are, on average, over-improved. More spending on supplies, repairs, fuel, and feed may produce greater returns than additional buildings or related improvements. The higher return to operating expenses than to working assets also suggests that machinery may be replaced prematurely: maintaining older equipment could be more economical than purchasing replacements.

The article’s practical relevance lies in connecting fitted production relationships to the allocation of farm resources. Its recommendations nevertheless remain tentative. Some estimates are imprecise, asset values can fluctuate within a year, and the discussion contains inconsistencies with the tabulated rankings—for example, its claim of high labor productivity on dairy farms is not supported by Table 3. The strongest conclusions concern broad investment patterns rather than every comparison among farm types. The closing qualification fixes the scope of the entire exercise:

It should be remembered that these results are not typical for Iowa farms and that they apply only to one year.

These unusually prosperous record-keeping farms may represent the upper portion of a broader Iowa production function, but they cannot establish that function for the whole state. The note’s achievement is a qualified demonstration of how business records can inform production analysis and investment decisions while exposing the consequences of imperfect measurements, omitted management, and limited representativeness.