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.

本研究从一个新的视角考察了公共农业研究与开发(R&D)在美国农业知识生产和生产力增长过程中的作用。Griliches(1967)的开创性工作建立了研发投资、知识生产过程和它们所创造的提高生产率的利益之间的关系。在关于估计知识生产函数的文献中，多因素生产率(MFP)的度量对知识库存的度量进行了回归，从而使研究者能够量化投资支出流和它们产生的提高生产率的效益之间的关系。这项研究的一个关键方面涉及如何处理跨期研究溢出，或换句话说，如何将当前和以往的研发支出总和为最能代表当前知识存量的措施。本研究扩展了Alston等人(2010)最近发表的一项研究，该研究利用来自明尼苏达大学国际科学技术实践与政策(InSTePP)中心的数据，对汇总研发投资的理想滞后结构进行了估计。我们重现了Alston等人(2010)研究中关于估计知识生产函数的一些分析，但在分析中替代了MFP的另一种度量。具体地说，我们重新估计知识生产函数使用对偶，而不是原始的生产力的衡量。本研究的作者还没有在文献中看到这种方法的使用，我们相信这种新颖的方法将为知识生产和生产力增长的过程提供额外的有价值的见解。Griliches和Jorgenson(1967)形式化了MFP的对位和原始测度之间的关系。通常，MFP的原始度量被定义为总产出除以总投入的度量。双重指标可以定义为总投入价格与总产出价格的比率。我们概述了MFP的原始措施和双重措施之间可能存在差异的理论原因。此外，我们还比较了InSTePP数据库中原始MFP和双MFP的经验度量，并确定了这些度量随时间的差异。文献中考虑了许多不同的估计知识储备的滞后结构，包括几何分布、伽马分布和梯形分布，以及分布的形状和长度都是重要的。伽马分布具有几个有利特征:1)由函数确定的滞后权值均非负的;2)隐含的形状相对光滑;3)伽马分布是单峰的;4)分布可能会发生倾斜，使较近或较远的时滞得到更大的权重;和5)可以用两个参数来表征分布。基于35年和50年的研究滞后，我们构建了64伽马分布的两个网格。可以通过改变两个参数来表示分布。其目的是检视最佳的滞后结构，以表示研发支出、知识生产和由此产生的生产力提升效益之间的关系。我们通过估计不同滞后规范下的知识生产函数来做到这一点，并选择在回归中产生最小平方和误差(SSE)的规范。主要的目标是比较和对比回归分析的结果与首选的滞后结构使用双重而不是原始的衡量MFP。原始和双重方法的结果是否支持研发支出总和的类似滞后结构，或者它们相互矛盾?本研究方法完备，研究结果对农业经济学的一个重要领域具有直接意义，引发讨论和辩论的可能性很大。