Abstract
The internal rate of return to public investment in agricultural R&D is estimated for each of the continental US states. Theoretically, our contribution provides a way of obtaining the returns to a local public good using Rothbart’s concept of virtual prices. Empirically, a stochastic cost function that includes own knowledge capital stock as well as spillover capital stock variables is estimated. Stochastic spatial dependency among states generated by knowledge spillovers is used to define the ‘appropriate’ jurisdictions. We estimate an average own-state rate of 17% and a social rate of 29% that compare well to the 9 and 12% average returns of the S&P500 and NASDAQ composite indexes during the same period.
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Notes
Khanna et al. (1994) analyzed the optimal allocation of public monies to agricultural R&D in the same 48 US states considered in the present study with a joint production model of public and state-specific benefits. Spillovers were defined as contemporary expenditures on R&D in neighboring states, and state expenditures on R&D were endogenous to their formulation.
The IRR is the rate of return that equals the discounted stream of benefits from an investment with its initial cost.
A virtual price, introduced originally in demand theory by Rothbart (1941), is the price at which the consumer/producer, acting as a price taker, will choose to consume a specified bundle.
As mentioned by a reviewer, there are many examples of knowledge spillovers, like formula-based public research committed to, for example, Michigan’s experiment station to study poultry diseases intended to benefit local poultry producers that benefit producers in Delaware, North Carolina and other poultry producing states as well.
White and Havlicek (1979) showed that failure to take into account geographical spillovers from US regional agricultural research inflated the estimated rate of return to R&D in the Southern region by more than 25%.
Huffman et al. (2002) estimated the own state IRR to public expenditures on agricultural R&D for the “representative” Midwestern state to be 11% per annum, and a social rate of return of 43% per annum. Yee et al. (2002) estimated the social rate of return to public agricultural research to be about 3.5–6.7 times the own state rate of return for the “representative” state in each of the seven regions defined in their study. Huffman and Evenson (2006) estimated regional social IRRs to range from 49 to 62%.
In primal space, Z v ≥ 0 implies that the marginal product of an extra unit of the private fixed factor v is positive when the marginal cost of producing an extra unit of output is positive; i.e., \( Z_{v} = - {{\partial \ell^{*} } \mathord{\left/ {\vphantom {{\partial \ell^{*} } {\partial v}}} \right. \kern-\nulldelimiterspace} {\partial v}} = \left( {{{\partial \ell^{*} } \mathord{\left/ {\vphantom {{\partial \ell^{*} } {\partial y}}} \right. \kern-\nulldelimiterspace} {\partial y}}} \right)\left( {{{\partial y} \mathord{\left/ {\vphantom {{\partial y} {\partial v}}} \right. \kern-\nulldelimiterspace} {\partial v}}} \right) \ge 0 \Leftrightarrow \left( {{{\partial y} \mathord{\left/ {\vphantom {{\partial y} {\partial v}}} \right. \kern-\nulldelimiterspace} {\partial v}}} \right) \ge 0 \); where \( \ell^{*} \) is the Lagrange function corresponding to Eq. (1) evaluated at the optimal x values, \( (\partial \ell^{*} /\partial y) \) is the reciprocal marginal cost of an extra unit of output, and \( (\partial y/\partial v) \) is the marginal product of the private fixed factor v.
Since the second order gradients of the variable cost with respect to private and public fixed inputs (\( \nabla_{vv} c( \cdot ),\nabla_{vV} c( \cdot ) \), and \( \nabla_{VV} c( \cdot ) \)) characterize the rate of change of their shadow values, and no assumption was made on the sign of their shadow values, no assumption is made on the rates of change.
A complete description on construction of G i is given in the following section.
A complete description of S i is given in the following section.
This data set is available at http://www.apec.umn.edu/faculty/ppardey/data.html, and was used in Acquaye et al. (2003). This data set has been revised and extended over 1949–2002 (Pardey et al. 2007), but was not publicly available. Comparing the descriptive statistics of the newer series from Table 1 in Andersen et al. (2007) to the older series, capital seems to have been revised downwards (the mean, the minimum and the maximum values are about 5% lower in the newer data set than in the older one, while the standard deviation is only 1.5% higher). The output series also seems to have suffered significant revision: the minimum value is 24% lower and the standard deviation is 19% higher in the newer data set, while the mean is only 1.6% higher. We did not use the 1960–1993 data set from O'Donnel et al. (1999) because it was revised and modified after 1993. Alternatively we could have used the data developed by ERS (1998) to obtain indexes of productivity by state for 1960–1996 or the revised version used in Ball et al. (2001). But the state-level expenditures on agricultural inputs used in the construction of their quantity indexes needed for our estimation were not available to us.
We obtained the series of expenditures in purchased inputs, capital and labor in constant 1949 dollars by multiplying the Fisher Ideal input quantity indexes (1949 = 100) by the expenditures in each input in 1949. Following standard indexing procedures when quantity indexes take the value of 100 in 1949 the expenditures in that year are used as proxies for prices. According to Acquaye et al. (2003), data for labor comprise 30 farm operator classes (five age and six education characteristics), family labor, and hired labor. Data for purchased inputs involve pesticides, fertilizers, fuel, seed, feed, repairs, machine hire, and miscellaneous expenses. Capital involves buildings and structures, automobiles (units not for personal use), trucks, pickers and balers, mowers and conditioners, tractors, combines, dairy cattle, breeder pigs, sheep and cows, and chickens (not broilers).
Land comprises cropland, irrigated cropland and grassland, pasture, range and grazed forest. Agricultural output aggregates field crops, fruits and nuts, vegetables and livestock.
Evenson (1989), Huffman and Evenson (1989, 1992, 1993, 2001), and Khanna et al. (1994) have constructed and used R&D stocks for US states but these data sets have not been made public. We proceed to build our own for the purpose of this study. The mean of G in our study closely resembles the mean of Huffman and Evenson’s “public agricultural research capital for an originating state”: $1.73 million in 1949 dollars or $10.1 million in 1986 dollars. The mean of S in our study is lower than the mean of Huffman and Evenson’s “public agricultural research capital spillin”: $7.65 million versus $8.86 million in 1949 dollars, or $44.7 million versus $51.8 million in 1986 dollars. We were unable to compare the distribution of our variables to theirs. This is true for variables G and S in our study.
We realize that the marginal effects of public agricultural research expenditure on agricultural productivity might be endogenous to each state and are likely to differ among states. But given that no publicly available study estimates the marginal effects for each state, we use a set of estimated marginal effects at the national aggregate to compute the R&D stocks. While some early studies used 10- or 20-years lags (Evenson 1967; Knutson and Tweeten 1979; White and Havlicek 1979), more recent studies suggest that in order to properly capture the benefits of investment in research on agricultural production, lags of at least 30 years must be used in the construction of the stocks (Pardey and Craig 1989; Schimmelpfennig and Thirtle 1994; Alston et al. 1998; Alston and Pardey 2001).
USDA appropriations for the Forest Service, the Mc Intire-Stennis Act from the CSREES Administered Funds, and all funds for Forestry Schools are excluded. USDA’s intramural research is not included in the current analysis, since it is not possible to assign benefits to particular states, and the focus of this study is to estimate the IRR to agricultural R&D conducted at the state level. Extension is also excluded from the current analysis due to lack of data.
The concept of deflated total public agricultural R&D expenditures in this study resembles that of total public expenditures on agricultural research used by Khanna et al. (1994). The main difference is that forestry funds are excluded from the present study. We have not been able to do a numerical comparison as their data is not publicly available.
We also experimented with another pattern of technological similarity across states by applying cluster analysis techniques to the states’ agricultural output-mix, and the results were highly dependent on the method used (single linkage, average linkage or centroid) and the criteria used to define the optimal number of clusters (hierarchical tree diagram, pseudo F statistic or pseudo Hotteling’s T 2 test statistic).
The McElroy System R2 is a weighted average of the R2 for each equation in the system, and is bounded to the 0–1 interval (Greene 2003, p. 345).
Since private R&D expenditures are embodied in purchased inputs and capital, these effects should account, at least theoretically, for the interaction of public and private research. Our estimates also indicate that, at the mean of the data, land is a substitute for purchased inputs and capital, and a complement for labor in all states.
Price elasticities evaluated at the mean of the data for each state indicate that own-price elasticities are negative, as expected. Cross-price elasticities for all inputs evaluated at the mean are positive, indicating that labor, purchased materials and capital are substitutes in production. Marginal cost elasticities evaluated at the mean of the data show 26 states with increasing returns to scale and 22 states with decreasing returns to scale.
The coefficients of variation are 107, 242 and 51% for California, Maine and Maryland respectively. Coefficient of variation = standard error/|mean|.
For example, Wyoming, South Dakota, Iowa, Missouri, Kansas and Colorado belong to the first “ring” of neighboring states for Nebraska; while New Mexico, Arizona, Utah, Idaho, Montana, North Dakota, Minnesota, Wisconsin, Illinois, Kentucky, Tennessee, Arkansas and Oklahoma form its second “ring” of neighboring states; Texas, California, Nevada, Oregon, Washington, Michigan, Indiana, Ohio, West Virginia, Virginia, North Carolina, Louisiana, Mississippi, Alabama and Georgia form its third “ring” of neighboring states.
We cannot discard the possibility of other variables not included in the model structure, like weather for example, adding to this dependency. In any case IRRs should be corrected if spatial dependency is present no matter what the source.
Plastina and Fulginiti (2007) provide a more detailed description of the GMM estimator of the spatial lags, along with descriptive statistics, elasticity estimates and concavity results by states not included here due to space limitations.
The marginal cost elasticities evaluated at the mean of the variables indicate increasing returns to scale for all states, satisfying one of the necessary conditions for endogenous growth (Onofri and Fulginiti). A second condition, namely that of non-negative returns to public inputs, is also satisfied as the estimates of the shadows for public R&D in Table 4 show.
Land is a substitute for purchased inputs and capital, and a complement of labor.
For all states, the own-price elasticities are negative, as expected, and the cross-price elasticities for all inputs are positive, indicating that labor, purchased materials and capital are substitutes.
The coefficients of variation for California, and Maine are now significantly lower than in Model 1 (55, and 18%, respectively), while the coefficient of variation for Maryland is higher (77%).
Mean difference of 12.8% and a standard deviation of 4.6%.
The 95% confidence interval is [5.98; 21.14%].
The 95% confidence interval is [31.21; 34.91%].
Our estimate of the average elasticity of variable cost with respect to the stock of public R&D in these states is −5%, lower than the −87% estimated in their study.
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Acknowledgments
We thank the support provided by the Nebraska Agricultural Experiment Station in the form of a research assistantship for Dr. Plastina during his graduate work at UNL. In particular, we thank Dr. Darrell Nelson, Dean of Agricultural Research and Director of the Nebraska Agricultural Experiment Station (1988–2005), University of Nebraska-Lincoln, for his personal interest and support on this project. In particular his intervention was crucial in obtaining the data on public R&D expenditures. We also thank the support received from the late Dr. Catherine Morrison-Paul.
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Appendices
Appendix 1: Descriptive statistics
Appendix 2: Model 1, no SAR error structure
Method of estimation: ITSUR.
Parameters in the model: 174.
Linear Restrictions: 55.
Parameters Estimated: 119.
Method: Gauss.
Number of Iterations: 50.
Final Convergence Criteria: CONVERGE = 0.001 Criteria Met.
Observations Processed: 2064.
Equation | DF model | DF error | R2 | Adj. R2 | AIC |
|---|---|---|---|---|---|
ln c | 83.11 | 1,981 | 0.8084 | 0.8004 | 0.24942 |
SH M | 17.94 | 2,046 | 0.9376 | 0.9371 | 0.001031 |
SH K | 17.94 | 2,046 | 0.8034 | 0.8017 | 0.000985 |
2.1 Parameter estimates
Parameter | Estimate | SE | T-value | Parameter | Estimate | SE | T-value |
|---|---|---|---|---|---|---|---|
δ T | 1.661054 | 0.1796 | 9.25 | β KY | −0.03839 | 0.00509 | −7.54 |
δ Y | −1.03266 | 0.2336 | −4.42 | β TY | 0.144139 | 0.0386 | 3.73 |
δ G | 0.439636 | 0.2601 | 1.69 | β MG | 0.009626 | 0.00415 | 2.32 |
β MK | 0.067766 | 0.00568 | 11.93 | β LG | −0.01025 | 0.00386 | −2.65 |
β MT | −0.01813 | 0.00601 | −3.02 | β KG | 0.000619 | 0.00377 | 0.16 |
β MY | 0.124598 | 0.00561 | 22.21 | β TG | 0.014571 | 0.0281 | 0.52 |
β LK | 0.037924 | 0.00415 | 9.14 | β YG | −0.09133 | 0.0463 | −1.97 |
β LT | 0.068861 | 0.00575 | 11.98 | β GS | −0.24097 | 0.021 | −11.46 |
β LY | −0.08621 | 0.0052 | −16.56 | β ML | 0.081212 | 0.00325 | 24.98 |
β LL | −0.11914 | 0.00352 | −33.87 | β MS | 0.034992 | 0.00415 | 8.43 |
β MM | −0.14898 | 0.00501 | −29.71 | β LS | −0.03773 | 0.00387 | −9.75 |
β KK | −0.10569 | 0.00835 | −12.66 | β KS | 0.002742 | 0.00388 | 0.71 |
β TT | −0.19386 | 0.0293 | −6.62 | β TS | −0.16861 | 0.0162 | −10.39 |
β YY | −0.07296 | 0.0644 | −1.13 | β GG | 0.31271 | 0.0374 | 8.35 |
β KT | −0.05074 | 0.00559 | −9.07 | β YS | 0.239682 | 0.0181 | 13.25 |
Appendix 3: Model 2, with SAR error structure
Method of estimation: ITSUR.
Parameters in the model: 174.
Linear Restrictions: 55.
Parameters Estimated: 119.
Method: Gauss.
Number of Iterations: 41.
Final Convergence Criteria: CONVERGE = 0.001 Criteria Met.
Observations Processed: 2064.
Equation | DF model | DF error | R2 | Adj. R2 | AIC |
|---|---|---|---|---|---|
ln c* | 83.11 | 1,981 | 0.9324 | 0.9296 | 0.06615 |
SH M * | 17.94 | 2,046 | 0.926 | 0.9254 | 0.000611 |
SH K * | 17.94 | 2,046 | 0.8904 | 0.8895 | 0.000418 |
Parameter | Estimate | SE | T-value | Parameter | Estimate | SE | T-value |
|---|---|---|---|---|---|---|---|
δ T | 1.007875 | 0.1101 | 9.15 | β KY | −0.05499 | 0.00384 | −14.33 |
δ Y | −0.35228 | 0.1432 | −2.46 | β TY | −0.07576 | 0.0204 | −3.71 |
δ G | −0.40512 | 0.1617 | −2.51 | β MG | 0.013477 | 0.00299 | 4.51 |
β MK | 0.074332 | 0.00888 | 8.37 | β LG | −0.01807 | 0.0026 | −6.95 |
β MT | −0.03649 | 0.00736 | −4.96 | β KG | 0.004589 | 0.0026 | 1.77 |
β MY | 0.135337 | 0.00451 | 30.02 | β TG | 0.035987 | 0.0166 | 2.17 |
β LK | 0.070494 | 0.00739 | 9.54 | β YG | −0.04832 | 0.0268 | −1.80 |
β LT | 0.076869 | 0.00634 | 12.12 | β GS | 0.035599 | 0.0132 | 2.69 |
β LY | −0.08035 | 0.00378 | −21.25 | β ML | 0.058759 | 0.0058 | 10.14 |
β LL | −0.12925 | 0.0072 | −17.95 | β MS | 0.040074 | 0.00347 | 11.54 |
β MM | −0.13309 | 0.00907 | −14.68 | β LS | −0.03284 | 0.00329 | −9.99 |
β KK | −0.14483 | 0.0119 | −12.20 | β KS | −0.00724 | 0.00342 | −2.12 |
β TT | 0.03303 | 0.0156 | 2.12 | β TS | −0.05169 | 0.0096 | −5.39 |
β YY | 0.161682 | 0.0351 | 4.61 | β GG | 0.039228 | 0.0207 | 1.89 |
β KT | −0.04038 | 0.00602 | −6.70 | β YS | 0.020784 | 0.0104 | 2.00 |
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Plastina, A., Fulginiti, L. Rates of return to public agricultural research in 48 US states. J Prod Anal 37, 95–113 (2012). https://doi.org/10.1007/s11123-011-0252-0
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DOI: https://doi.org/10.1007/s11123-011-0252-0
Keywords
- Internal rates of return
- Public R&D
- Spillins
- Spillovers
- Local public goods
- Appropriate jurisdiction
- Spatial