The evaluation of public investments in agricultural research has been a topic of special interest to research administrators and others concerned with productivity in agriculture. Tighter research budgets and diminished purchasing power due to inflation have increased concern about research budget allocations. Earlier research evaluation studies have indicated high rates of return to overall agricultural investments. This study is concerned with the evaluation of research investments made at an individual agricultural commodity level. The primary objectives of this study are:

(a) to estimate the marginal product and internal rates of return to research investments in corn, wheat, soybeans, and sorghum.

(b) to estimate separately the internal rate of return to extension investments in these commodities.

(c) to estimate the effect of spillovers from research investments in these commodities by other outside states.

(d) to estimate the impact of these research and extension investments in grain commodities for individual geographical production regions in the U.S.

The theoretical framework of a supply response model with inclusion of a variable to account for aggregate risk by producers was developed as the basis for analyzing research and extension investments in corn, wheat, soybeans, and sorghum. Individual commodity models focusing on the relationship of yield per acre to output prices, land quality differences, weather, aggregate risk, and investments in research and extension were specified. Data were collected for these variables for a cross-section of the major producing states of each commodity for the 1973-1979 crop years. The Park's model, a generalized least squares procedure which includes adjustments for first-order autocorrelation within each state and cross-sectional correlation among states, was used to estimate coefficients of individual commodity models.

Empirical results for the individual commodity models indicate that the prices of output and a substitute commodity, weather, land quality differences, aggregate risk, in-state and outside research investments, and extension investments were significant variables explaining yield per acre of corn, wheat, soybeans, and sorghum. The estimated internal rates of return on research investments indicate very favorable rates of return to both in-state and outside investments in agricultural research. The returns to in-state research investments ranged from 81 percent for wheat to 177 for corn and the returns to outside research investments ranged from 21 percent for wheat to 133 percent for sorghum. The rates of return to outside research expenditures indicate that the benefits of research investments are not confined solely to the state making the investment. The significance of these spillovers suggest that the contribution of federal funds to state research programs is appropriate as a means of compensating states for the externalities. The contributions of extension investment to productivity increases of these grain commodities were estimated separately from the contributions of investments in agricultural research. Based on assumptions of 8 and 12 year "inverted V" distributions of benefits from increased yield per acre, the estimated IRORs for extension investments ranged from 42 percent for sorghum to 96 percent for corn. The estimated IRORs for research and extension investments in the various U.S. production regions were comparable to the rates estimated for the U.S. in total. While the IROR to research investments were higher than for extension investments, these rates are highly sensitive to assumptions made concerning the length and structure of the lag between expenditures and impacts. The measure of benefits based solely on yield increases also may not be appropriate for all types of research and extension expenditures.

Aggregate risk based on past variations in prices has a significant impact on corn and wheat yields. The significant negative coefficients imply risk-averse behavior by corn and wheat producers in the aggregate. Increases in price variability have a depressing effect on yield. The models developed in this study enable price elasticities for grain yields to be estimated. Elasticities estimated at mean levels, using expected nominal prices, ranged from .06 for sorghum to .30 for corn. These elasticities indicate total supply response is 6 to 30 percent greater than estimates based solely on acreage response.