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This study examines the role of public agricultural research and development (R&D) in the process of knowledge production and productivity growth in U.S. agriculture from a new perspective. The seminal work of Griliches (1967) established the relationship between investments in R&D, the process of knowledge production, and the productivity enhancing benefits they create. In the literature on estimating knowledge production functions measures of multi-factor productivity (MFP) are regressed against measures of knowledge stocks, thereby enabling the researcher to quantify the relationship between the stream of investment expenditures and the productivity enhancing benefits they produce. A critical aspect of this research involves how to handle inter-temporal research spillovers, or in other words how to sum current and previous R&D expenditures into a measure that best represents the current stock of knowledge. This research expands on recently published work by Alston et al (2010) related to estimating the ideal lag structure for summing R&D investments, using data from the International Science and Technology Practice and Policy (InSTePP) Center at the University of Minnesota. We reproduce some of the analysis in the Alston et al (2010) research related to estimating knowledge production functions, but substitute an alternative measure of MFP in the analysis. Specifically, we re-estimate the knowledge production functions using a dual as opposed to a primal measure of productivity. The authors of this study have not seen this approach utilized in the literature, and we believe this novel approach will provide additional valuable insight on the process of knowledge production and productivity growth. Griliches and Jorgenson (1967) formalized the relationship between a dual and a primal measure of MFP. Commonly, a primal measure of MFP is defined as a measure of aggregate output divided by aggregate input. A dual measure can be defined as the ratio aggregate input to output prices. We outline the theoretical reasons why there may differences between the primal and dual measures of MFP. Furthermore, we compare the empirical measures of primal and dual MFP from the InSTePP database and identify differences in these measures over time. Many different lag structures for estimating knowledge stocks have been considered in the literature, including geometric, gamma, and trapezoidal distributions to name a few, and both the shape as well as the length of the distribution are important. The gamma distribution embodies several favorable characteristics: 1) all lag weights determined by the function are non-negative; 2) the shape implied is relatively smooth; 3) the gamma distribution is unimodal; 4) the distribution can be skewed to give more weight to more recent or more distant lags; and 5) the distribution can be characterized by only two parameters. We construct two grids of 64 gamma distributions based on a research lags of 35 and 50 years. The distributions can be represented by altering two parameters. The goal is to examine the best lag structure to represent the relationship between R&D expenditures, knowledge production, and the resulting productivity enhancing benefits. We do this by estimating knowledge production functions under the different lag specifications, and choose the specification that produces the lowest Sum-of-Squared Errors (SSE) in the regressions. The primary objective is to compare and contrast the results of the regression analysis with regards to the preferred lag structure using the dual as opposed to primal measure of MFP. Do the results from a primal and dual approach support a similar lag structure for summing R&D expenditures or do they contradict one another? The methodology of this study is well established, the results have direct significance to an important field of agricultural economics, and the potential to generate discussion and debate is high.


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