PLACE IN RETURN BOX to remove this checkout from your record. TO AVOID FINES return on or before date due. DATEDUE DATE DUE DATE DUE amiCL 99 LL; MSU Is An Affirmative Action/Equal Opportunity Institution emuna-pJ FINANCING AGRICULTURAL RESEARCH IN A FEDERAL SYSTEM OF GOVERNMENT: OPTIMAL COST-SHARING FOR STATE AND NATIONAL INVESTMENTS Volume I BY David Brian Schweikhardt A DISSERTATION Submitted to Michigan State University in partial fulfillment of the requirements for the degree of DOCTOR OF PHILOSOPHY Department of Agricultural Economics 1989 ABSTRACT FINANCING AGRICULTURAL RESEARCH IN A FEDERAL SYSTEM OF GOVERNMENT: OPTIMAL COST-SHARING FOR STATE AND NATIONAL INVESTMENTS BY David Brian Schweikhardt This dissertation examines the federal-state cost-sharing arrangements necessary to provide a nationally optimal level of state agricultural research investment. Agricultural research is a good that provides benefits that spill across state boundaries. Unless the states are provided compensation for the research.benefits they create, research investment may be sub-optimal from a national perspective. Public finance theory indicates that an open-ended matching grant (i.e., the grantor matches each dollar spent by the recipient on the spillover-generating good with a fixed number of grantor' dollars) is the least-cost. method of financing public goods that create benefit spillovers (such as agricultural research). Each state will provide a nationally optimal level of agricultural research when the federal matching rate is established at a level that (a) equates the share of the marginal benefit of research retained by each state with that state's share of the marginal cost of research and (b) equates the share of the marginal benefit of research that accrues outside the state with the federal government's share of the marginal cost of research. David Brian Schweikhardt To estimate the optimal matching rates for financing agricultural research in the United States, Cobb-Douglas production functions were fitted to state-level cross-section data for' the ‘years 1964, 1969, 1974, 1978, and 1982. Conventional inputs, research investment in the state and other relevant states, state extension investment, and weather were included as the independent variables. Six spillover patterns were used.to examine the sensitivity of the estimated matching rates to the assumed spillover pattern. The marginal benefit of research that accrued inside and outside each state was then estimated, and. the optimal matching rates for financing agricultural research. in each state ‘were then calculated. The average estimated optimal federal matching rates ranged from 0.40 to 1.54 federal dollars per state dollar. These results suggest that the 1.00 matching rate used to allocate Hatch Act funds may be appropriate, but that the closed-ended nature of the Hatch system could be preventing the states from providing a nationally optimal level of research. Since the matching rates of individual states appear sensitive to the spillover specification, future work should focus on improved specification of spillover patterns. Copyright by DAVID BRIAN SCHWEIKHARDT 1989 ACKNOWLEDGMENTS Jim Bonnen served as my major professor during both my M.S. and Ph.D. programs. He suggested the research topic, provided encouragement, and dealt with all the problems that arose. No one could ask for more from a major professor. I have said it elsewhere, but it bears repeating that any student who has worked ‘with Dr. Bonnen knows that the following quote, written about a nineteenth century agricultural educator, describes precisely his contribution to his students' work: His patience in listening to our crude papers and in flooding with light our ignorant discussions was heroic, not to say fairly sublime; while his delicacy and tact in concealing our imperfections from ourselves and stimulating us to higher attainments were as beautiful as they were helpful (Woodward and Waller, p. 17). Warren Samuels, Stan Thompson, and Al Schmid made numerous cements that improved the final product. Their insistence on recognizing the limitations of the analysis resulted in a more complete, coherent, and accurate product. Keith Huston provided important data sources that made this research.possible. The Michigan Agricultural Experiment Station provided generous financial support. Joy Goode handled the details of the final production with speed and accuracy. To my fellow graduate students--especially John and Leslie Ross, Charlie Abdalla, Linda Chase-Wilde, and Bill Knudsen--thanks for everything. Mary Procopio deserves special thanks: never a friend in need, you were always a friend indeed. Finally, thanks must go to my parents, Richard and Emma Schweikhardt, who sent three sons away to college and got back one veterinarian and two economists. Liberty Hyde Bailey knew them well: I think of the father and mother, what it means to them to have sent those boys...away to school. It had not been simple or easy.... I have known them to work for years to the one end, unfalteringly and tirelessly (Dorf, p. 142). As did Alfred Marshall: The heroic sacrifices which some middle-class parents make for the sake of their children's education are instances of the latent romance of modern life (Marshall, volume 2, p. 311). vi TABLE OF CONTENTS LIST OF TABIJES .00.... 0000000000 O ...... CO. ..... O ...... LIST OF FIGURES .......... ............ . ............... CHAPTER I: INTRODUCTION . ............................ Problem Setting ................ ................. The History of Federal-State Relations in Financing Agricultural Research . ........... Research Objectives and Dissertation Organization ..................... ...... . ...... A Preface to Economic Policy Analysis .... ....... CWER II: REVIEWOF LITERAWRE OOOOOOOOOOCOOOOOOOOO Financing Public Goods in a Federal System of Government .................. The Use of Intergovernmental Grants in Achieving Optimal Investment in Public Goods .. The Measurement of Economic Returns from Public Investments in Agricultural Research ..... ..... Measuring Research Benefits: The Economic Surplus Method ........................... Measuring Research Benefits: The Production Function Method ............ .............. Estimates of the Rate of Return on Public Agricultural Research Investments in the United States .............. Benefit Spillovers in Agricultural Research ..... The Role of Intergovernmental Grants in Financing Agricultural Research ............ Summary ............. ...... ........ .............. Notes to Chapter II .................... ......... CHAPTER III: A MODEL OF OPTIMAL COST-SHARING FOR STATE AND FEDERAL INVESTMENTS INAGRICULTUMLRESEARCH .0...‘......... Critical Assumptions of the Model ............... An Optimal Cost-Sharing Model for Agricultural Research with Benefit Spillovers .............. A Model of Agricultural Research Benefit Spillovers ................ ............ Variable Specification .......................... vii xiv 16 21 28 28 38 58 58 64 68 78 86 99 102 113 114 116 118 120 Aggregate Output .............................. Land ........................... ....... ........ Labor ............................... ..... ..... Education ..................................... Fertilizer ............. ......... .............. Machinery ......................... ...... . ..... Livestock ..................................... Other Inputs .................................. Research ......................... ...... ....... Extension ..................................... Weather ....................................... Summary ............................ ............. Notes to Chapter III .................. .......... CHAPTER IV: EMPIRICAL RESULTS ...... ................. Selection of the Observation Set ....... ......... Estimates of the Production Function Model Excluding Research Spillovers ................. Comparison of Observation Sets ............. Assessment of Estimated Equations .......... Estimated Marginal Products and Internal Rates of Return to Research ........ ...... Estimates of the Production Function Model Including Research Spillovers ....... ...... .... Assessment of Estimated Equations ...... .... Estimated Marginal Products and Internal Rates of Return to Research .............. summary 0.00.0000...OOOOOOOOOOOOO0.0....000. 00000 Notes to Chapter IV ............................. CHAPTER V: CALCULATION OF OPTIMAL MATCHING RATES FOR FINANCING AGRICULTURAL RESEARCH ...... Calculation of Optimal Matching Rates ..... ...... Discussion of Results .......................... Comparison to Previous Studies .. ................ Comparison to the Existing Hatch Funding System .............. .................. summary 00.00.000.000...000...... OOOOOOOOOOOOOOO 0 Notes to Chapter V ........... ...... . ........... . CHAPTER VI: CONCLUSION .... ...... ..... ............... summary OOOOOOOOOOOOOOOOOOOO..0...00...... ...... O ResearCh Objectives OOOOOOOOOOOOOOOOOOOOOOOO Research Method ..... ..... . ........ . ........ Research Results ................. ..... ..... Limitations of the Research Method .............. Assumptions of the Public Finance Model .... Assumptions of the Production Function Model ........................... Implications for Agricultural Research Policy in the United States........................... viii 120 122 124 127 129 130 132 133 141 154 156 157 159 165 166 168 171 171 176 186 188 188 194 197 203 204 212 214 216 217 219 220 220 220 221 223 223 224 230 231 A Postscript to Economic Policy Analysis ........ Suggestions for Future Research .......... ....... APPENDIX A: DATA SOURCES AND REGRESSION DATA Aggregate Output .. .............................. Land ......................... ............ . ...... Labor ........................................... Education ....................................... Fertilizer ...................................... Machinery ....................................... Livestock .................. ...... ......... ...... Other Inputs ......................... ........... Research .................................. ...... Extension .............................. ......... Weather ................................. ........ Regression Data ......................... ........ APPENDIX B: BIBLIOGRAPHY CALCULATION OF OPTIMAL MATCHING RATES ... ix 241 244 248 248 249 249 249 250 250 250 251 252 252 253 253 270 304 LIST OF TABLES 1321: 10 11 12 Provisions of Legislation Providing Intergovernmental Support of Agricultural Research .......... ............... Formulas for Calculating the Net Economic Surplus Created by Public Research Investments ..... .......... .... Results of Studies Measuring the Benefits of Agricultural Research in the United States .......................... Estimates of Production Functions Excluding Research Spillovers ................. .......... Estimates of Marginal Products for Production Functions Excluding Research Spillovers ....... Estimates of Marginal Internal Rates of Return on Research for Production Functions Excluding Research Spillovers ... .............. Estimates of Production Functions Including Research Spillovers: 1982 Cross-section .. ..... Estimates of Production Functions Including Research Spillovers: 1978 Cross-section ....... Estimates of Production Functions Including Research Spillovers: 1974 Cross-section ....... Estimates of Production Functions Including Research Spillovers: 1969 Cross-section ....... Estimates of Production Functions Including Research Spillovers: 1964 Cross-section ....... Estimates of Marginal Products of Research and Marginal Internal Rates of Return on Research Under Alternative Spillover Specifications .... 12 61 69 172 178 183 189 190 191 192 193 195 13 14 15 16 17 Optimal Federal Matching Rates for Financing Agricultural Research Under Alternative Specifications of Spillovers, 1982 Cross-section ................ ............ Optimal Federal Matching Rates for Financing Agricultural Research Under Alternative Specifications of Spillovers, 1978 Cross-section ................. ........... Optimal Federal Matching Rates for Financing Agricultural Research Under Alternative Specifications of Spillovers, 1974 Cross-section ....................... ..... Optimal Federal Matching Rates for Financing Agricultural Research Under Alternative Specifications of Spillovers, 1969 Cross-section ................. ........... Optimal Federal Matching Rates for Financing Agricultural Research Under Alternative Specifications of Spillovers, 1964 cross-seetion ......OOOOOOOOOOOO0.00.00... Regression Data, 1982 Cross-section ...... ....... Regression Data, 1978 Cross-section ............. Regression Data, 1974 Cross-section ............. Regression Data, 1969 Cross-section ............. Regression Data, 1964 Cross-section . ............ Calculation of Optimal Matching Rates for Neighboring States Specification (0 = .10), 1982 Cross-section ....................... ..... Calculation of Optimal Matching Rates for Neighboring States Specification (O = .20), 1982 Cross—section ......OOOOOOOOOOOOOOOOO ..... Calculation of Optimal Matching Rates for Neighboring States Specification (0 = .30), 1982 Cross-section .................... ........ Calculation of Optimal Matching Rates for Production Region Specification (Q = .10), 1982 Cross-section .................. .......... xi 207 208 209 210 211 255 258 261 264 267 274 275 276 277 1“ u‘. (Us Calculation of Optimal Matching Rates for Production Region Specification (O = .20), 1982 Cross-section ................ ............ Calculation of Optimal Matching Rates for Production Region Specification (O = .30), 1982 cross-section ......OOOOOOOOOOOOOOOOO ..... Calculation of Optimal Matching Rates for Neighboring States Specification (O = .10), 1978 Cross-section ....... ..... . ............... Calculation of Optimal Matching Rates for Neighboring States Specification (O = .20), 1978 Cross-section ...................... ...... Calculation of Optimal Matching Rates for Neighboring States Specification (O = .30), 1978 Cross-seetion ......OOOOOOOOOOOOOOO ....... Calculation of Optimal Matching Rates for Production Region Specification (O = .10), 1978 Cross-section ......... . ...... . ........... Calculation of Optimal Matching Rates for Production Region Specification (O = .20), 1978 Cross-section .......... ....... . .......... Calculation of Optimal Matching Rates for Production Region Specification (O = .30), 1978 Cross-section ....................... ..... Calculation of Optimal Matching Rates for Neighboring States Specification (O = .10), 1974 Cross-section ............. ...... .... ..... Calculation of Optimal Matching Rates for Neighboring States Specification (O = .20), 1974 Cross-section ............................ Calculation of Optimal Matching Rates for Neighboring States Specification (O = .30), 1974 Cross-section ....... ..... .......... ...... Calculation of Optimal Matching Rates for Production Region Specification (O = .10), 1974 Cross-section ............................ Calculation of Optimal Matching Rates for Production Region Specification (O = .20), 1974 Cross-section ............................ xii 278 279 280 281 282 283 284 285 286 287 288 289 290 but 8.29 B.30 Calculation of Optimal Matching Rates for Production Region Specification (O = .30), 1974 Cross-section ....................... Calculation of Optimal Matching Rates for Neighboring States Specification (O = .10) 1969 Cross-section ....................... Calculation of Optimal Matching Rates for Neighboring States Specification (O = .20) 1969 Cross-section ....................... Calculation of Optimal Matching Rates for Neighboring States Specification (O = .30) 1969 Cross-section ....................... Calculation of Optimal Matching Rates for Production Region Specification (O = .10), 1969 Cross-section ....................... Calculation of Optimal Matching Rates for Production Region Specification (O = .20), 1969 Cross-section ....................... Calculation of Optimal Matching Rates for Production Region Specification (O = .30), 1969 Cross-section ....................... Calculation of Optimal Matching Rates for Neighboring States Specification (O = .10) 1964 Cross-section ....................... Calculation of Optimal Matching Rates for Neighboring States Specification (O = .20) 1964 Cross-section ........... ......... ... Calculation of Optimal Matching Rates for Neighboring States Specification (O = .30) 1964 Cross-section ....................... Calculation of Optimal Matching Rates for Production Region Specification (O = .10), 1964 Cross-section .......... ............. Calculation of Optimal Matching Rates for Production Region Specification (O = .20), 1964 Cross-section ................. ...... Calculation of Optimal Matching Rates for Production Region Specification (O = .30), 1964 Cross-section ....................... xiii I I I ..... I I 291 292 293 294 295 296 297 298 299 300 301 302 303 LIST OF FIGURES Lime 1 Use of a Pigouvian Grant to Achieve a Socially Optimal Level of Investment in a Spillover- GeneratingGOOd ...........O.............O...O. 2 Comparison of an Unconditional Lump-sum Grant and a Conditional Matching Grant .............. 3 Impact of a Closed-Ended Matching Grant on the Budget of the Recipient Jurisdiction .......... 4 Income Effect of Benefit Spillins .... ..... . ..... 5 Economic Surplus Generated by a Public Investment in Agricultural Research ...................... 6 USDA Production Regions ............... .......... 7 Assumed Distribution of Research Benefits over Time ............................ ......... xiv 42 45 49 53 59 148 181 CHAPTER I INTRODUCTION "I am convinced that the plan which we are now discussing, namely, that of joint Federal and State support, is far ahead of any other known system in its possibilities of providing for stable support and proper local appreciation of, and interest in, agricultural research." R.W. Thatcher, Former Director, Minnesota Agricultural Experiment Station (p. 105) "There is and can be no final solution to the allocation of financial resources in a federal system. There can only be adjustments and reallocations in the light of changing conditions. What. a federal government. needs, therefore, is machinery adequate to make these adjustments." Kenneth. C. ‘Wheare, Political Scientist (quoted in Oates, p. 145) We The U.S. agricultural research system is a continually- evolving partnership between the federal government and the states. Over the past century, this evolution has been an ongoing search for balance between the needs expressed in the quotes that preface this chapter. On the one hand, policymakers have sought to maintain a stable federal-state relationship in support of agricultural research. On the other, they have occasionally sought to make adjustments in resource allocations as changing conditions arose. ‘ r d. It. 'A 9o .e ‘A. "n. I“ 2 The U.S. may be approaching the next stage in the evolution of this partnership. Change may be imminent because the existing system suffers from political tensions that.exist both within the system and between the system and the larger scientific community. These tensions involve at least four issues that raise fundamental questions about the responsibilities of the federal government and the states in financing agricultural research. First, some within the system view the Hatch Act formula, which allocates federal agricultural research funds to the states based on their farm and rural populations, as outdated or biased against those states with a predominance of large farms (Hodgson: U.S. Congress, 1986, p. 200). Second, internal tension has arisen because the federal government has failed to maintain its share of the real resources committed to agricultural research. The federal share of the agricultural research funds spent at the state agricultural experiment stations declined from 38% in 1966 to 29% in 1987, leaving an increasing share of the burden of U.S. agricultural research funding on the states (U.S. Office of Technology Assessment, p. 206,‘U.S. Department.of.Agriculture, 1988, p. 117). As a.result, the federal-state partnership that has governed agricultural research for the past century is suffering an erosion of commitment that threatens its capacity to respond to research problems in a coherent manner (Bonnen, 1986, p. 1060). 3 A third source of tension arises from the ongoing debate over the use of formula funds and competitive grants in financing agricultural research. Advocates of competitive grants insist that such a system ensures scientific quality and permits greater flexibility in allocating research resources. Proponents of formula funding contend that a formula system provides a stable system of funding and permits long-term planning of research (Eliot Marshall, 1979a; Strobel: Johnson and.Wittwer, pp. 8-9; Ruttan, 1982a, pp. 215- 236). This debate, conducted both within the agricultural research system and between the system and its critics in the larger scientific community, has thus far been conducted without reference to the economic rationale for either method of financing research. Finally, the system has long been believed to suffer from a persistent problem of underinvestment. The high rates of return on public agricultural research investments, estimated to range from 30 to 70 percent annually, have led economists to suggest that the United States persistently underinvests in public agricultural research (Ruttan, 1982a, pp. 237-59). The most commonly accepted explanation of this problem is that the existence of research benefits that spill across state lines inhibits individual states from providing a nationally optimal level of investment in agricultural research. The existence of spillovers indicates that individual states may underinvest. in. agricultural research. because they’ cannot capture the full benefits of their investment in research 4 (Ruttan, 1982a, p. 254-58: Latimer and Paarlberg; Bredahl and Peterson: Evenson, et al., 1979; Ziemer, et al.: Havlicek and White, 1983a: Lyu and White; Garren and White). The persistence of the underinvestment problem suggests that the present.Hatch.Act formula provides inadequate compensation to the states for the research benefit spillovers they create. Given the tensions that are currently impacting the system, economists, research administrators, and legislators have questioned whether the existing Hatch Act system is the appropriate mechanism for financing agricultural research (Ruttan, 1982a, p. 256: Havlicek and White, 1983a: Hodgson; U.S. Congress, 1984, p. 215; U.S. Congress, 1986, p. 200). The existing system of subsidies, provided as Hatch Act funds, distributes federal agricultural research funds to the states by using a formula.based on each state's share of the national farm and rural population. The Hatch provisions also require that states match federal Hatch funds on a one-to-one basis with state funds. If the present system is inadequate, how should the federal-state agricultural research partnership be redefined? What system of state and federal financing would yield a more optimal level of investment in agricultural research? Within this system, what should be the relative responsibilities of the federal government and the states in financing agricultural research? Similarly, under what conditions are formula funding and competitive grants the appropriate policy tools for financing agricultural research? 5 This research examines these questions within a theoretical framework that, while clearly relevant to the issues at hand, has not yet been applied adequately by economists to the problems associated with public financing of agricultural research. Adopted from a branch of public finance literature, this framework addresses the problem of financing public goods in a federal (i.e. , multi-level) system of government. In particular, this framework--known in the public finance literature as the theory of intergovernmental grants--is intended to identify the conditions under which two levels of government can design an optimal cost-sharing arrangement for financing public goods that create benefits for persons outside the jurisdictional boundaries of the lower level of government. As such, it is particularly relevant to the policy issues facing the agricultural research system. By providing intergovernmental grants to the states, the federal government can compensate the states for the benefit spillovers they create and promote a more efficient allocation of resources to agricultural research, To'do so, however, the subsidies provided by the federal government must be designed to reflect accurately the benefit spillovers generated by agricultural research. This research provides an indication of the system of intergovernmental grants needed to finance an optimal level of agricultural research investment in each state in the presence of research benefit spillovers. In addition, the framework also sheds light on the present institutional barriers to achieving an optimal level of 6 research investment, the adequacy of the existing Hatch Act formula funding system, and the economic rationale for using formula funding or competitive grants in financing agricultural research. The History of Eederai-gtate Reiations in Financing Agriguitural Research The creation and maintenance of economic institutions are fundamental responsibilities of government. .Accordingly, the political structure and philosophy of the government are reflected in the structure of its economic institutions. This is true of the institutions in the United States' federal system of government. To understand the evolution of the institutional structure of the U.S. agricultural research system, it is necessary' to 'understand the philosophical foundations of a federal system of government (Schweikhardt). A federal system of government, according to Riker, has three characteristics. First, "two levels of government rule the same land and people." Second, "each level has at least one area of action in which it is autonomous." And third, "there is some guarantee (even though merely a statement in the constitution) of the autonomy of each government in its own. sphere" (Rikery p. 11). The appropriate areas of responsibility for each level of government in this system have long been a matter of debate in the United States. Elazar has characterized the eighteenth and nineteenth century debate over the proper roles of the national and state governments as a debate over "dualism." In a dual federal 7 system, "the dual sovereignties--federal and state-—were to exist side by side, each virtually independent of the other in its own sphere" (Elazar, 1962, p. 11). On the one hand, Thomas Jefferson envisioned a dual system of government in which the states dominated in the conduct of domestic affairs, including economic development, and the federal government exercised authority in foreign affairs, the supervision of the militia, and a limited number of domestic matters arising between states (Elazar, p. 12). Government, insisted Jefferson, must be based on a "sacred principle, that though the will of the majority is in all cases to prevail, that will, to be rightful, must be reasonable; that the minority possess their equal rights, which equal laws must protect, and to violate which would be oppression" (Koch, p. 54) . The system of government that would best prevent such oppression, according to the Jeffersonian view, is a decentralized system of government that allows political minorities the maximum opportunity to express their preferences and permits the states to fit political decisions to the peculiarities of their regions and citizens. Thus, Jefferson viewed a dual federal system with the maximum power residing with the states as the most appropriate system for guaranteeing both individual and national improvement. A second view of dualism, expressed by Alexander Hamilton, favored a strong national government. The national government, according to Hamilton, "like that of each State, 8 must be able to address itself immediately to the hopes and fears of individuals: and to attract to its support those passions which have the strongest influence upon the human heart" (Hamilton, p. 108). In such a government, the power to address the common interests of the citizens of the states must be held. by the national government. Indeed, the Constitution permitted the national government to establish national copyright laws, a patent system, and postal roads, thereby reflecting the Hamiltonian dualist view that, in the realm of economic development, "Nothing which tends to facilitate the intercourse between the States can be deemed unworthy of the public care" (Madison, p. 293). Reviewing the policies of the nineteenth century, however, Elazar observes that, while the rhetoric of the debate may have focused on the appropriate form of dualism, the political practice was one of cooperative federalism. Under a system of cooperative federalism, the national and state governments of the United States "developed a broadly institutionalized system of collaboration, based on the implicit premise that virtually all functions of government must be shared by virtually all governments in order to fulfill the demands of American democracy for both public service and private access" (Elazar, p. 297). Thus, while dualism implicitly viewed the total amount of political power as a constant, which one level of government could only gain at the expense of the other, cooperative federalism recognizes that government power is a dynamic concept with both levels 9 of government often sharing power in a given area of public policy (Elazar, p. 310: Leach, p. 26). Cooperative federalism often sought to capture the best aspects of both Hamiltonian and Jeffersonian federalism. While the power of the national government was called upon to address the common needs of citizens, administration of that power often resided with state governments, thereby tailoring programs to local needs. This arrangement was used during the nineteenth century to promote the economic development of the United States through the cooperative support of primary and secondary' education, road. construction, railroad development, canal and river development, and forest management (Elazar, pp. 25-30, 102-33; Graves, pp. 932-68). Corwin (p. 19) emphasized the pragmatic nature of such efforts at cooperative federalism: According to this conception, the National Government and the States are mutually complementary parts of a single governmental mechanism all of whose powers are intended to realize the current purposes of government according to their applicability to the problem in hand (italics in original). The land-grant college system was created in this spirit of cooperative federalism. More impressive, perhaps, is that the land-grant college system often provided the prototype for later cooperative efforts such as road construction, health care, and revenue sharing (Graves, pp. 934-68; Walker, pp. 208-209). The land-grant colleges, for example, were established by the Morrill Act of 1862. This legislation, which followed an earlier pattern of providing grants of land I” I: 9 q. 10 to the states to support a specific function, established a precedent by providing the grants uniformly (30,000 acres of land per senator and representative) and simultaneously to all states. Moreover, while this legislation did not require direct matching of the federal effort by the states, it did require the states to fund all building construction at the colleges, thereby establishing the principle that the states should share the burden of providing public services (Elazar, pp. 219-24). The Hatch Act of 1887, which established federal support for agricultural research at the land-grant colleges, was the first modern intergovernmental grant. As such, it abandoned the use of land grants, which had previously been used when land was more plentiful than cash, and introduced the use of cash grants (which were earlier believed to be unconstitutional) that would be provided to the states on a continuing basis (Elazar, p. 230). Moreover, the Hatch Act established the principle that, while the institution would be financed in part by the federal government, administrative control would reside primarily with the states. These innovations signaled the emergence of a new form of cooperative federalism. The historical significance of this step in the evolution of intergovernmental relations was explained by E. W. Allen, Chief of the USDA's Office of Experiment Stations, at the semicentennial celebration of the Connecticut Experiment Station: This nation-wide subsidizing of research in agriculture was evidence of change which had come 11 in the conception of the relationship of the Federal Government and the states. It was a recognition of a joint responsibility in developing the industry of agriculture on a high stage of efficiency, and it was a new expression of what the general Government may do under the Constitution for the promotion of public welfare (True, p. 130). It is important to note, in this regard, the difference between the Merrill Act of 1862 and the Hatch Act of 1887. Being a one—time grant, the Morrill Act shifted control of the colleges of agriculture to the states once the grant was made. Since the Hatch funds were appropriated annually, however, closer federal supervision of the funds was possible. As J. W. Holcombe, Chief Clerk of the U.S. Bureau of Education, observed in 1892: A great and radical step beyond previous legislation must be recognized here. The land-grant of 1862 amounted to an absolute gift. If the institutions established did not teach agriculture or military tactics (and some of them did not do so for years) the President and his Cabinet and the entire judiciary of the United States might whistle to the wind for redress. But this last act establishes, to put it plainly, Federal control and supervision over the use of the fund created. If any dangers, therefore, lurk in the possibility of Federal interference and Federal dictation, the beneficiaries of this last Congressional grant are liable thereto....The cordial acceptance of such a measure by the legislatures indicates that there is no real danger from Federal interference and that jealousy of the Federal power on that score has disappeared (Holcombe, pp. 114-15). Agricultural research continues to be supported cooperatively by the federal government and the states (True: Ball, pp. 4-11; Conover; Knoblauch, et al.; Marcus; Bonnen, 1962: Schweikhardt). Table 1 summarizes the provisions of the legislation.that.has provided federal support.to the state 12 Table 1. Provisions of Legislation Providing Intergovernmental Support of Agricultural Research Legislation Allocation Formula Matching Requirements Hatch Act (1887) Adams Act (1906) Purnell Act (1925) Bankhead-Jones Act (1935) Agricultural Marketing Act (1946) Hatch Consolidation Equal Equal Equal Rural Population 20% equally, 26% by rural population, 26% by farm population, 25% for regional projects, 3% for administration 20% equally, 26% by None None None One state dollar per federal dollar One state dollar per federal dollar None on first Act (1955) rural population, 26% $90,000. One state by farm population, dollar for each 25% for regional additional federal projects, 3% for dollar. administration. Source: Compiled by author from Knoblauch, et al., pp. 219-235. l3 agricultural experiment stations. Under the terms of the original Hatch Act, the federal government provided $15,000 per year for each state to support the newly-created state agricultural experiment stations. While some states did provide additional support for the stations, states were not required to match the federal funding effort. Federal support for the experiment stations was increased by the Adams Act of 1906 and Purnell Act of 1925. The Adams Act provided an additional $30,000 per year for each state, and the Purnell Act added another $60,000 per year for each state. The concept of a formal matching requirement was introduced by the Smith—Lever Act of 1914, the organic legislation of the Cooperative Extension Service. Again, agriculture provided the prototype which many later programs would follow. The Bankhead-Jones Act of 1935 marked the introduction of a state matching requirement for agricultural research funding. To receive Bankhead-Jones funds, each state was required to allocate funds for agricultural research equal to the federal funds provided to the state. The Bankhead-Jones Act also introduced a federal funding formula to allocate federal agricultural research funds among the states based on their share of the total rural population. This formula was adopted "on the assumption that it reflects the need for the service involved, particularly when use has been made of classes of the population to which the aided service is directed" (Key, p. 322). Although a population-based formula has been used in subsequent l4 legislation, it was recognized immediately as discriminating against states with.a highly diversified agriculture that may require relatively more support than those states with a more homogeneous farm sector (Key, pp. 320-21). The Agricultural Marketing Act of 1946 amended the Bankhead-Jones Act to provide a more complex system of funding. TVenty percent of the funds were to be allocated equally among the states. Fifty-two percent were allocated according to a formula based on each state's share of the national farm and rural population. As before, each state was required to match the federal effort with its own funds. Twenty-five percent of the funds were available for the Secretary of Agriculture to allocate to regional research projects, and 3 percent were designated for administrative costs. The present allocation system is the product of the Hatch Consolidation Act of 1955. This legislation consolidated all previous funding and distributes these funds on an equal basis among the states. All additional funding is distributed according to the formula in the 1946 Act (that is, each state is allocated funds based on its share of the national farm and rural population). The states were required to match all but the first $90,000 of their allocation. Attention must.be paid to the political forces that have influenced the evolution of the agricultural research system. The population-based formula used to allocate federal funds for agricultural research originated in the Smith-Lever Act 15 of 1914, the legislation that established the Cooperative Extension Service. During the debate on the Smith-Lever bill, congressmen from the South, who dominated the House and Senate agriculture committees, proposed that extension funds be allocated according to each state's share of the national rural population. Midwestern and western congressmen attempted to amend the bill by allocating the funds according to each state's share of land in farms or value of production, a formula that would have increased funding for western and midwestern states. Arguing that the purpose of extension was to educate people and that the total cost of education was a function of the number of people served, a coalition of southern and eastern congressmen defeated the amendment and established the precedent of a population-based formula (U. 3. Congress, 1914, pp. 2579-83, 2655-58, 2736-44). This precedent, combined with the continuing power of southerners on congressional agriculture committees, may account for the population-based formula used to allocate federal research funds in the Bankhead-Jones Act of 1935. The Agricultural Marketing Act of 1946, which established the present-day formula based on each state's share of national farm population and rural population (where rural population referred to those persons living in towns of 2,500 or less), resulted in a further shift in funding in favor of the southern states, mostly at the expense of eastern and midwestern states (with the notable exceptions of Iowa, Wisconsin, and Minnesota, which gained funds under the new l6 formula) (U. S. Congress, 1946, p. 9027). Again, this may be due in part to the political power exerted by southerners. The history of the federal-state partnership in financing agricultural research may confirm Martin Feldstein's observation, regarding the intergovernmental support of local education, that "the actual development of formula matching grants reflects history, legislative compromise, and accident rather than empirical analysis and economic logic" (Feldstein, p. 80). While such political decisions must also be based on factors other than economic logic, the generally recognized need to consider a revision of the Hatch formula provides an opportunity to apply such logic and analysis to a new and needed area of work. This dissertation is intended to contribute to such policy decisions by applying public finance theory to the problem of financing public agricultural research. e 'e ' s an 'sserta ion Or anization This research has three specific objectives: 1. The development of a public finance model designed to provide the optimal method (expressed as an optimal matching rate) of financing public investments that produce benefit spillovers across governmental boundaries; 2. The development of an econometric model designed to measure the size and geographic distribution of agricultural research. benefit spillovers across state boundaries: l7 3. The calculation of an optimal system of federal agricultural research subsidies (i.e., matching rates for federal payments to each state) based on the results of the models developed under objectives 1 and 2. These objectives will be accomplished in three stages. The first stage of this research, the development of a public finance model to compensate governmental units for benefit spillovers, draws on public finance theory to specify a mathematical model that maximizes national research benefits. It should be noted that this model could be applied to any public investment that produces benefit spillovers and is not limited to agricultural research. The public finance model maximizes national research benefits by compensating states for the marginal research benefits that spill across state lines. National research benefits will be maximized when two conditions are met: (1) when each state equates its share of the marginal benefit that it retains from its own research with its share of the marginal cost of that research, and (2) when the share of the marginal benefit of research that spills outside the investing state equals the federal government's share of the marginal cost of research conducted in that state (i.e. , when the federal matching rate, defined as the number of dollars the federal government provides to a state for each dollar the state spends on agricultural research, compensates each state 18 for the marginal research benefit spillover produced by that state). The second stage of this research, the measurement of agricultural research benefit spillovers, will draw extensively from the existing economic literature on returns to agricultural research. Two methods have been used to measure research spillovers. The first estimates a production function that includes research investment as a production input. The marginal benefit of research can be derived from the estimated equations and, if the equations are properly identified and the data are sufficiently accurate, the research benefit spillovers can be measured. The second method of estimating the returns to agricultural research calculates the producer and consumer welfare gains that result from public investments in agricultural research. By estimating the change in supply that results from agricultural research, changes in the price and quantity of farm products can be estimated and the resulting gains to farmers and consumers can be measured. Again, if the estimated equations are properly specified, benefit spillovers can be measured. While these two :methods have Ibeen used. to measure research benefit spillovers, neither has been used to determine an optimal federal matching rate because the estimates have been made on a regional or national basis and the necessary breakdown of spillovers by states have not been calculated. To make such calculations, state-level estimates 19 of research spillovers must be made. This research will employ the production function method to estimate the state- level research benefit spillovers necessary to make such calculations. Since little is known about the pattern of research spillovers that prevails in the U.S., six assumed spillover patterns will be used to estimate these production functions. The optimal matching rates will then be estimated for each of these six spillover scenarios. The final stage of this research will introduce the research benefit spillover estimates from stage two into the public finance model developed in stage one to determine the optimal federal matching rate for each state. To achieve this, the results of the production function model estimated in the second stage of this research.will be used to calculate (1) the marginal product of research spending that accrues to a given state as a result of agricultural research conducted in that state, and (2) the marginal product of research that accrues to all other states as a result of agricultural research conducted in the given state. These estimates will then be used to calculate the share of the total marginal product of research that spills outside the funding state. This share will be used in the public finance model to estimate the optimal federal matching rate for financing agricultural research in the each state under each of the six spillover scenarios. This dissertation is organized around the three stages of the research. Chapter II reviews the problem of financing 20 public goods in a federal system of government. It then reviews the theory of intergovernmental grants and the use of intergovernmental grants as a means of promoting optimal investments in public goods in the presence of spillovers. Next, the economic literature on the measurement of agricultural research benefits and the measurement of benefit spillovers is reviewed. Finally, the case for a joint system of federal and state investments in agricultural research is considered. Chapter III develops a public finance model of optimal cost-sharing for federal and.state investments in public:goods that create benefit spillovers across state lines. It then presents a production function model designed to measure research benefit spillovers and describes the data used to estimate this function under six assumed spillover patterns. Chapter IV presents the empirical results of the production function models described in Chapter III. Chapter V uses the production. function. estimates reported in Chapter IV ‘to calculate research benefit spillovers. These results are then incorporated into the public finance model to determine an optimal federal matching rate for each state under each spillover scenario. Chapter VI summarizes the research, discusses the limitations of the research method, and examines the policy implications of the results for federal-state relations in funding agricultural research. 9 .41 9! U' ‘- .- ’- en “6 ‘1- ‘b A uh.‘ ‘v 21 o ' ' 1 5'5 This research is an exercise in economic policy analysis. In.order to interpret such analysis correctly, it is necessary to recognize its nature and limitations. It is particularly important to recognize four essential characteristics of economic policy. First, economic policy is concerned with the institutional structure of the economy. An institution, as defined by Commons (p. 69), is collective action in control of individual action. The institutional structure of the economy defines each.persons' rights and responsibilities or, more simply, what persons may do, may not do, and must do (Clark, p. 203; Mitchell, p. 19; Commons, p. 71). All policy, according to Ostrom (p. 126), must "fashion appropriate structures for the allocation, exercise and control of decision-making capabilities among people....Decision structures establish the 'rig' to the games of life. Designing and altering the 'rig' of real-life games is the work of political artisans." He traces this view to Alexander Hamilton, James Madison, and Alexis de Toqueville, who all viewed the political process as a means of biasing selfish human behavior toward politically-chosen ends (Ostrom, p. 7). It must be recognized that economies are always and everywhere an."instituted.process" (Polanyi, p. 248), and that economic policy ultimately deals with the creation, modification, and destruction of institutions (Bonn, p. 337). That is, the choice of an institutional structure determines 22 the production, consumption, and.distribution incentives that exist in the economy (Bonn, p. 333), which in turn determine the distribution of income, wealth, and power in the economy. A change in this incentive structure can lead to a change in individual behavior and a change in the level, composition, or distribution of the output of the economy (Stigler, 1975, p. 33; Samuels, 1978, p. 103). The choice of an institutional structure for the economy is an inevitable duty of government (Bonn, p. 335) . As Brinkmann (p. 331) observed, the problem of determining policy "raises everywhere and at all times the question of as to how economic incentives underlie social behavior," and, furthermore, "it is unrealistic to think of any age or community as exempt from this economic predetermination." The inevitable need to make such choices is also reflected in Knight's observation (1951, pp. 8-15) that all economies must solve five fundamental problems: (1) the fixing of standards of value, (2) the organization of production, (3) the distribution of production, (4) the promotion of economic growth, and (5) the adjustment of consumption to production. This admission of the instituted nature of the economy does not bias policy analysis toward any particular institutional structure (Buchanan, 1964, p. 222: Knight, 1951, pp. 7-14; Robbins, p. 50). Instead, it simply recognizes that the economy is a man-made system, reflecting an "artificial harmony of interests" established by the participants in the 23 system (Mitchell, p. 13: Samuels, 1966, p. 4; Commons, p. 6). Economic policy can only establish this artificial harmony by determining whose interests the economy will serve. The second characteristic of economic policy is that it is necessarily prescriptive in nature. The policy process must organize knowledge in order to guide the evolution of institutions (Mitchell, p. 36). Like any‘ decision, an economic policy decision must be a prescription--a statement of what ought to be done. All prescriptions must be based on two ‘types of knowledge: normative knowledge (about values--i.e., about the goodness or badness of conditions, situations, or things) and positive knowledge (about characteristics other than the goodness or badness of conditions, situations, or things) (Glenn Johnson, 1986b, pp. 16-20). As Glenn.Johnson has also emphasized, decisions require, in addition to knowledge, the use of both decision rules and power. Decision rules (e.g., the maximization of good, minimization of bad, majority voting, etc.) determine the standard by which policy alternatives are judged. Power enters the decision process in at least four ways. First, as Paarlberg (pp. 158-59) observed, the power to place problems and alternative solutions on the political agenda is "the most potent of all powers," since focusing attention on a problem is "an absolutely necessary first step" in the decision process. Second, the possession of knowledge is itself a form of power, since the knowledge that is considered by 24 policymakers will affect the policy alternative chosen (Glenn Johnson, 1986b, p. 230). The ability to provide information in the decision process or to convince policymakers to focus on a certain type of information can be used to influence the outcome of policy decisions (Bartlett, pp. 31-34, 56, 132-37) . Third, the institutional structure of society is only viable when it is enforced by the power of the state, particularly against the challenges of those who disagree with the policy (Bonn, p. 334: Clark, p. 15: Commons, p. 713: Robinson, p. 124: Knight, 1960, p. 113, and 1953, p. 278; Mitchell, p. 19; Robbins, pp. 34-36: Buchanan, 1964, p. 220). Fourth, power is both an input and an output of the policy process. The establishment of an institutional structure produces a power structure 'that. allows individuals to influence (decisions beyond the issue at hand; as mentioned earlier, it grants the power to determine the production, consumption, and distribution patterns in the economy. A third characteristic of economic policy is that it is necessarily predictive in nature. All policy prescriptions must be based on a comparison of the continuation of the existing institutional structure with a modification of that structure. To make such. comparisons, the analyst. must consider the economic incentives under each alternative structure, predict the behavior of individuals under each structure, and assess the success of each policy alternative in achieving the objective chosen (Knight, 1953, p. 282, and 1960, pp. 21, 29, 111, and 146; Tinbergen, pp. 50—53: 25 Lindblom, 1965, p. 138: Ostrom, p. 9). Without such predictions, no economic policy-~including a continuation of the status quo--can be justified. The fourth characteristic of economic policy is that it is necessarily normative in nature on several levels. On the first level, the act of making a policy decision presumes that a problem--defined as a divergence between existing and desired conditions--has been identified and agreed upon as requiring collective action. The assessment of existing and potential conditions involves normative judgments. These judgments must include what conditions do exist, what conditions could exist, the goodness or badness of these conditions, and who benefits or is damaged by current and potential conditions. On the second level, an economic policy decision involves a decision to make a decision. As Dahl and Lindblom (p. 64) have observed, policymakers must first make a rational calculation whether to make a rational policy calculation. Paarlberg (p. 158-59) points out that the resources devoted to political decision-making (in the form of time, capital, and human comprehension) are limited. Thus, he concludes, an agenda is required to provide order in the political process. The decision to place a select number of policy problems and alternatives on the agenda also involves normative judgments. Knight (1960, p. 133) insisted.that the most critical question of the policy process is "What questions are worth discussing?" and called the laws regulating the discussion of 26 this question "the most important of our laws." This level of decision-making, which Paarlberg refers to as the control of the policy agenda, possesses its own distribution of power, its own normative premises, and its own decision rules. On the third level, an economic policy decision involves a choice of ends as well as means. According to Knight, the most important and difficult stage of the policy process is the selection of the economic ends that will be pursued (Knight, 1952, p. 54: 1951, p. 4 and 1960, p. 152). The selection of ends, whether chosen by the economic analyst or imposed on the analyst by the political process, is an indispensible jpart of ‘the policy' process and. of policy analysis, ultimately depending on normative judgments and an assumed or real distribution of power (Rothbard, p. 38: Mitchell, p.35; Myint, p. 230; Lindblom, 1958, p. 533). On the fourth level, any economic policy decision based on a :maximizing or :minimizing‘ calculus must presume an institutional structure for the economy and, therefore, must make normative assumptions about that structure (Rothbard, pp. 36-38: Buchanan, 1962, p. 342, and 1964, p. 216; Clark, p. 108; Knight, 1935, p. 137; Samuels, 1978, pp. 100-113, and 1980, pp. 181-83). Simply put, any policy proposal that intends to maximize or minimize some target measure must first define‘which factors (such.as various benefits and costs) will be included in the optimizing calculus. As emphasized earlier, the institutional structure of the economy defines 27 which benefits and costs will be included in such calculus. Only after these normative judgments have been made can any form of optimization proceed. To summarize, economic policy determines the economic structure of an economy, thereby determining the behavior its participants. All policy--including a continuation of the status quo--is prescriptive and depends on positive knowledge, normative knowledge, numerous decision rules, and a distribution of power. The prescriptive validity of any policy analysis.is determined.by the accuracy of the knowledge upon which it is based. Given the many normative premises involved in policy decisions, accurate policy analysis must make such premises as explicit as possible (Knight, 1953, p. 278: Samuels, 1978, p. 100). Chapter III identifies several such premises underlying this analysis. In Chapter VI, a companion to this section, "A Postscript to Economic Policy Analysis," will examine the implications of these assumptions and the limitations they impose on the results of this research. CHAPTER II REVIEW OF LITERATURE This research applies the principles of public finance theory to the problem of resource allocation in agricultural research. This chapter begins the research by examining the relevant economic literature in ‘three areas. First, the problem of financing public goods is examined, with special emphasis on the problems of providing public goods in a federal system. of government. Second, the use of intergovernmental grants to finance public goods is examined. Third, the measurement of benefit spillovers in agricultural research is examined and the role of intergovernmental grants in financing agricultural research is considered. Financing Public Googs in a Fe e al S stem of Government While earlier authors recognized the existence of public goods, the work of A. C. Pigou provided the foundation of modern public finance theoryfl Pigou differentiated between the marginal private net product of an investment and its marginal social net product. The marginal private net product of an investment, by Pigou's definition, "is that part of the total net.product.of physical things or objective services due to the marginal increment of resources in any given use or place which accrues in the first instance--i.e., prior to 28 29 sale--to the person responsible for investing resources there," while the marginal social net product "is the total net product of physical things or objective services due to the marginal increment of resources inlany'given.use or place, no matter to whom any part of this product may accrue" (Pigou, 1946, pp. 134-35). Private investors, argued Pigou, will allocate their resources in such a manner that, allowing for transaction costs, the money value of the marginal private net products are equal across all investment opportunities. In doing so, investors will contribute to the maximization of national money income (Pigou, 1946, pp. 136-41). This process of equalization will not yield the maximum national welfare, however, if the marginal net private product does not equal the marginal net social product, a condition that occurs when "a part of the product of a unit of resources consists of something, which, instead of coming in the first instance to the person who invests the unit, comes instead, in the first instance (i.e., prior to sale if sale takes place), as a positive or negative item, to other people" (Pigou, 1946, p. 174). Three groups of people were identified by Pigou as potential recipients of these positive or negative effects: 1. "The owners of durable instruments of production, of which the investor is a tenant: 2. Persons who are not producers of the commodity in which the investor is investing: and 30 3. Persons who are producers of the commodity" (Pigou, 1946, p. 174). While Pigou saw all three cases as potentially requiring corrective government action, the concern here is with only the second case. In the second case, according to Pigou, "the essence of the matter is that one person A, in the course of rendering some service, for which payment is made, to a second person B, incidentally also renders services or disservices to other persons (not producers of like services) of such a sort that payment cannot be extracted from the benefited parties or compensation enforced on behalf of the injured parties" (Pigou, 1946, p. 183). Pigou's examples of such disservices included factory smoke, automobile pollution, and added congestion due the erection of high rise buildings in crowded urban areas. His examples of such services included lighthouses, roads, city parks, and, Lastly and most important of all, it is true of resources devoted alike to the fundamental problems of scientific research, out of which, in unexpected ways, discoveries of high practical utility often grow, and also to the perfecting of inventions and improvements in industrial processes. ‘These latter are often of such a nature that they can neither be patented nor kept secret, and, therefore, the whole of the extra reward, which they first bring to their inventor, is very quickly transferred from him to the general public in the form of reduced prices (Pigou, l946,pp. 184-85).2 When such divergences between the marginal private net product and the marginal social net product occur, Pigou argued, the welfare of society could be increased by 31 establishing taxes and subsidies that equate the two. In the case of a disservice, the marginal private net product exceeds the marginal social net product, and overinvestment (as viewed from a social perspective) occurs in the industry producing the disservice. Such overinvestment can be avoided if a tax is imposed on producers that brings their marginal private net product into alignment with the marginal social net product. In the case of a service, the marginal private net product is less than the marginal social net product, and underinvestment (as viewed from a social perspective) occurs in the industry providing the service. A socially optimal level of investment can be reached if the government provides a subsidy to producers equal to the difference between the marginal social net product and the marginal private net product.3 It is notable that Pigou had such subsidies in mind for agricultural research and extension: This type of bounty is also not infrequently given upon the work of spreading information about improved processes of production in occupations where, owing to lack of appreciation on the part of potential beneficiaries, it would be difficult to collect a fee for undertaking that task. Thus the Canadian Government has established a system, "by means of which any farmer can make inquiry, without even the cost of postage, about any matter relating to his business"; and the Department of Interior also sometimes provides, for a time, actual instruction in farming....In the United Kingdom the various Agricultural Organization Societies are voluntary organizations, providing a kindred type of bounty at their subscribers' expense. An important part of their purpose is, in Sir Horace Plunkett's words, to bring freely "to the help of those whose life is passed in the quiet of the field the experience, which belongs to wider opportunities of observation and a larger acquaintance with commercial and industrial affairs." The Development Act of 1909, with its provision for grants towards 32 scientific research, instruction, and.experiment in agricultural science, follows the same lines (Pigou, 1946, pp. 193-94).‘ This Pigouvian view of the public good nature of research was later developed mathematically by McCain (pp. 182-95) and O'Connell (1978; 1982, pp. 96-99). Both demonstrated that profit-maximizing competitive firms would underinvest in research when a portion of the benefits of research investments are captured by firms other than the inventor. Samuelson (1954, 1955, 1958) cast the underinvestment problem in terms of his version of the "new welfare economics." In his version, a pure public good is any good that is common to all consumers in the sense that the consumption of that good by one individual does not reduce the quantity of that good available for consumption by any other individual (Samuelson, 1954, p. 387). Said another way, whatever level of consumption is chosen by one person is also the level available for consumption by all other persons. Given his definition of a public good, which assumes a high cost of excluding users of the good, Samuelson found three conditions that are necessary for optimal investment in private and public goods: (1) each person's marginal rate of substitution.between.each.pair'of private goods in the economy must equal the marginal rate of transformation between those two goods: (2) the marginal utility of each private good must be equal across all consumers of that good; and (3) the sum of all persons' marginal rate of substitution between the public good and each private good in the economy must equal 33 the marginal rate of transformation between those two goods. The last of these conditions leads to what Samuelson called the "impossibility of decentralized spontaneous solution" (1954, pp. 388-89). The third condition implies that each individual receives utility from both the quantity of a public good that he has purchased and from the sum of the quantities of the good purchased by all other individuals. Thus, in this process of summation, each individual.may attempt.to avoid.purchasing the public good in the hope that others will provide a sufficient quantity of the good. If each person adopts such a strategy, however, the net result will be an underinvestment in the public good, since it will be in each person's interest to attempt to "free ride" on the purchases of others. Even if various voting methods are used to determine the level of public goods provided, it will still be in the individual's best interest to hide his true preference for public goods and underinvestment will still result (Samuelson, 1954, pp. 388-89; Bowen). While Samuelson dealt only with public goods that are used for final consumption, Kaizuka extended the Samuelson model to address the problem of public goods that serve as inputs to the production of consumption goods, such as "weather broadcasts for commercial farmers, or research the fruits of which any firm is free to use" (Kaizuka, p. 118). Like Samuelson, Kaizuka concluded that users of such a public good will have an incentive to conceal their demand for the 34 good in hopes of shifting the cost of the good to others and, without some form of government subsidy, underinvestment in the public good may persist.5 Albert Breton (p. 177) redefined the problem as not simply a matter of whether government should provide public goods, but also which unit of government should do so. Economic goods, he argued, can rarely be classified into the polar cases of pure private or public goods. Instead, there are a number of "non-private" goods whose services are available to individuals in unequal amounts (as opposed to a pure public good which must be available to all individuals in an equal amount). The problem of underinvestment in non-private goods is further complicated when such goods are provided by a federal (i.e., multi-level) system of government. In particular, a problem of "imperfect mapping" may arise. If the benefits of a good are perfectly mapped, that is, if the benefits of a good accrue strictly within the boundaries of the unit of government financing the good, then the government of that jurisdiction will provide the optimal quantity of themgood.to its citizens (assuming it has overcome the problem of ascertaining accurately the preferences of its citizens). On.the other hand, if the benefits of the good are imperfectly mapped, or spill across the jurisdictional boundaries of the financing government, the investing government, like the investing individual in Pigou's analysis, will underinvest in the good. A higher level of government 35 could provide a subsidy to the lower level unit of government to induce it to invest in the socially optimal quantity of the good (Breton, pp. 180-82). As Weisbrod (pp. 131-32) would later point out, both spillouts and spillins can lead to underinvestment. The former, as Breton had written, because the investing government cannot capture the full benefits of its investment. The latter, according to Weisbrod, because spilled-in goods can displace internally-financed goods if the recipient of spillins overestimates the benefits it will receive from other jurisdictions. Similarly, McKinney used a Stackelberg model of duopoly behavior to demonstrate that both spillouts and spillins would cause society to suffer welfare losses from underinvestment when units of government attempt to engage in strategic behavior and "free ride" on the purchases of others. Drawing on the welfare economics of Samuelson and the public financeaeconomics of Breton, Oates examined.the problem of underinvestment in public goods when benefits spill across jurisdictional boundaries. Assuming a world of two goods and two jurisdictions (the results can be generalized to many goods and jurisdictions), the optimal allocation for each community in the absence of spillovers can be defined as: (2.1) MRT, = MRS, (2.2) MRT, = MRS“ where: MRT.== the marginal rate of transformation between goods X and Y for community 1: 36 MRS.== the marginal rate of substitution of community i between good X (a private good consumed by the citizens of community i) and good Y (a public good provided by the government of community i), which is, as Samuelson showed earlier, the sum of the marginal rates of substitution of all individuals in community i. Thus, if there are no losses of benefits across jurisdictional boundaries, each community will invest in the level of public good Y that is optimal for its citizens. Again, this assumes the problem of preference revelation has been solved within each community (i.e., each jurisdiction has solved the problems of determining how much of the public good is optimal for its citizens and how the cost of the public good should be shared by its citizens). If some portion of the benefits of good Y spill across the boundaries of the communities, such spillovers must be taken into account when determining the socially optimal level of good Y. The socially optimal level of consumption now becomes: (2.3) MRT, = MRS, + a,*MRS, (2.4) MRT2 = MRS2 + a,*MRS,, where: a,== the increase in consumption of public good Y that occurs in community 1 as a result of a one unit increase in the consumption of Y by community 2: 37 a,== the increase in consumption of public good Y that occurs in community 2 as a result of a one unit increase in the consumption of Y by community 1, and o g a,, a, g 1. It is now'possible to consider a broad range of spillover combinations and their implications for public investment decisions: 1. If a, = a2 = 0, no spillovers will be generated, and each community will provide the socially optimal quantity of Y for its citizens. 2. If a, = a2 = l, the good is a pure Samuelsonian public good and must be provided by a higher level of government than the two community governments if an optimal level of investment is to be reached (this is analogous to Samuelson's "impossibility of decentralized spontaneous solution" for a pair of individuals). 3. If 0 < a” a,<:]q there will be spillovers generated between the communities and, in the absence of a system of compensating subsidies, the quantity of good Y provided by each jurisdiction will less than the socially optimal quantity of Y (Oates, pp. 95-99). To summarize, underinvestment in a good may result when some portion of the benefits of that good accrue to individuals other than the original investor (where, in this 38 case, the investor is a unit of government). A socially optimal level of investment can be obtained through the use of government subsidies. In a federal system of government, a socially optimal level of investment in public goods that create benefit spillovers across jurisdictional boundaries (such as agricultural research) can be achieved through a system of intergovernmental subsidies (e.g., from the federal government to the states). T] H E I ! v ! 1 E ! . ECJ' . gnginni Investnent in Enniig Goods Before considering the use of intergovernmental grants to correct the problem of underinvestment in public goods, it is necessary to examine the use of other policy tools to correct the problem. The first alternative is the reapportionment of jurisdictional boundaries. It is theoretically possible to redefine the boundaries of units of government in such a way that all benefit spillovers would be internalized to the decision process and, as a result, a socially optimal level of investment would be reached (Musgrave and Musgrave, pp. 597-602). Using a spatial model of public goods, McMillan demonstrated that an optimal level of investment could be reached through the use of both grants and reapportionment of jurisdictions” Breton.and Scott (1977) reached a similar result using a transaction cost minimization model. To rely solely’on.reapportionment, however, would.require a unique set of boundaries for each good that creates benefit _ 39 spillovers. This alternative would require a large number of jurisdictions to cover all the. goods that. might create spillovers (Break, 1980a, p. 77). More important, while economists may judge the existing boundaries of government to be inefficient, such boundaries can only be changed at high political cost (Schultze, p. 185). Thus, while changes in jurisdictional boundaries are a possible solution to the underinvestment problem, they are unlikely to succeed if institutional rigidities prove impossible to overcome. A second possible solution to the underinvestment problem would be the granting of taxing authority to the investing jurisdiction, thereby permitting it to tax the recipients of benefit spillovers. Such taxes may either be levied directly on outside citizens by the investing jurisdiction, or the investing jurisdiction may impose taxes on its own firms and citizens which, when the burden is shifted to outside citizens, compensate the jurisdiction for the spillover benefits it has created (Musgrave, p.115; Ellickson). AS'With reapportionment, however, this option may create an large number of taxing authorities and raise the transaction costs of collecting the appropriate taxes. The establishment of taxes, the share of whose burden on outside citizens equals the share of benefits that spill across jurisdictional boundaries, may be an equally difficult and costly task. If this cannot be performed at the lower level of government, a central taxing authority may better serve to correct the underinvestment problem. Finally, as Stigler 40 (1957, p. 214) observed, a central taxing authority may be necessary when the taxed parties can escape their financial obligation by migrating beyond the boundaries of lower level governments. A final option. would simply' be the negotiation of appropriate subsidies between units of government that create and receive benefit spillovers (Coase, pp. 28-42). While such an approach may succeed when the number of units is small, it becomes increasingly'difficult.aS‘the.number’of'units involved in the negotiation process increases, and thus the transaction costs associated with such negotiations rise (Oates, p. 68; Wellisz, p. 361; Regan, p. 436-37; Stigler, 1966, pp. 113-14; Mishan, p. 31: Baumol, 1972, p. 308; Ellickson, pp.97-100). It.must.also be noted that Pigou (1946, pp. 183-84) recognized the self-correcting nature of the small-numbers case and only advocated intervention in those cases where the large number of parties involved makes it "technically difficult to exact payment."‘ If none of the options discussed above will succeed in promoting a socially optimal level of investment in public goods, the use of intergovernmental grants may be the most feasible option. The problem remains, however, to design a system of grants that will encourage an optimal level of investment. As discussed earlier, a simple Pigouvian subsidy will compensate the investing government for the difference between the total marginal benefits received by all citizens 41 and the marginal benefits received by citizens of the investing jurisdiction. Such a subsidy is shown in Figure 1. If jurisdiction i invests in a spillover-generating public good (Y), the optimal quantity for it to provide will be the quantity that equates the marginal cost to jurisdiction i (MC,) and the marginal benefits received by the citizens of i (MEN). Thus, the optimal quantity for jurisdiction 1 to provide for its citizens would be Q" in Figure 1. By providing good Y, jurisdiction i also provides benefits to citizens outside its boundaries. These external benefits are equal to NB, (the marginal social benefit, including all benefits that accrue inside or outside jurisdiction i) minus MB". The socially optimal quantity of good Y is the quantity that equates the marginal social cost (MCJ with the marginal social benefit (MBW), or the quantity On. To achieve this level of investment in Y, jurisdiction i should receive a subsidy (8.) equal to the difference between the marginal social benefit (MEN) and the marginal benefit that accrues to the citizens of jurisdiction i (MBW). As will be discussed, this subsidy may come from either a higher level of government or from the government whose citizens receive benefits from jurisdiction i. Returning to Oates' more general solution, a set of subsidies that encourage an optimal level of investment in the spillover-generating good can be designed (Oates, pp. 99-104). The optimal conditions for each community were 42 Dollars MCY r Si 4 | L_ L .... _ r—" | l I I : MBYi MBYs ! Qyi QYs Quantity of Y Figure 1: Source: Use of a Pigouvian Grant to Achieve a Socially Optimal Investment in a Spillover-Generating Good Oates, p. 67. 43 established in the previous section of this chapter as: (2.3) MRT, (2.4) MRT2 = = MRs,-+en*MRs, MRS,-PEL*MRSH If a, and a2 are both non-zero (i.e., there are reciprocal spillovers), then both governments will receive a subsidy. To find the optimal subsidy for each, a system of equations must be solved: (2.5) MRS, (2.6) MRS, (2.7) MRT (2.8) MRT MRT = a, = S. = MRT-S, =MRT-S2 MRS,-+ay*MRS, = a,*MRS, + MRS“ where the marginal rate of transformation between private good X and a spillover-generating public good Y: the marginal rate of substitution between good X and good Y for jurisdiction i: the increase in the consumption of good Y that occurs in jurisdiction 1 as a result of the consumption of an additional unit of good Y by jurisdiction 2 (0 _<_ a, g l); the increase in the consumption of good Y that occurs in jurisdiction 2 as a result of the consumption of an additional unit of good Y by jurisdiction 1 (0 g a,, 5 1): the subsidy paid to jurisdiction i, expressed in units of good X. ‘n. 'U 4 '. Clue I, H “E I,“ h C: H A \I'V‘V' Jul, ‘11 ‘ ’4'. . 44 The simultaneous solution of equations (2.5) through (2.8) provides the optimal subsidy for each jurisdiction: (2.9) S, = (afiwl - aJ/(l - aunm))* MRT (2.10) 52 = (a,*(1 - a,)/(1 - a,*a,))* MRT. This result suggests some important implications for designing intergovernmental subsidies. As shown by equation (2.9), given an, a larger value fora.2 (i.e., a larger share of benefits that spill from 1 into 2) will yield a larger subsidy paid to jurisdiction 1. Similarly, for a given level of a2 in equation (2.10) , a larger value for a, (i.e. , a larger share of benefits that spill from 2 into 1) will yield a larger subsidy paid to jurisdiction 2. Accepting that intergovernmental grants may be necessary to promote an optimal level of investment.in public goods that create benefit spillovers, the question now turns to what form such grants should take. An analysis of alternative grant forms is shown in Figure 2 (Scott, pp. 377-94; Wilde 1968, pp. 340-57 and 1971, pp. 143-55; Boadway and Wildasin pp. 518-29).’ The jurisdiction is assumed to allocate its resources between the consumption of a public good Y that creates benefit spillovers in other jurisdictions and all other goods. It should be noted that these other goods may be private goods consumed by the citizens of the jurisdiction or public goods that create no benefits outside the funding jurisdiction (Waldauer, p. 215). The jurisdiction can be assumed to have an initial budget AA' that is allocated between the spillover-generating public 45- B Other Goods I3 A I I1 I I I x1 I3 I i | I | I L . 1 Y1 Y2 A' B' Spillover Good Figure 2: Comparison of an Unconditional Lump-Sum Grant and a Conditional Matching Grant Source: Boadway and Wildasin, p. 520. 46 good and all other goods. The community indifference curve IL indicates that community welfare is maximized at point E” and the optimal quantities purchased will be Y, and X,. Assuming that another unit of government (either another unit of government at the same level acting directly--as among two states--or a higher level of government acting on behalf of other lower level governments--as between the federal government and a state government) provides a subsidy to the community to compensate it for the benefits that spill across its boundaries, what form should such a subsidy take? It may take the form of an unconditional, lump-sum grant. Such a grant has no restrictions on its use and may be allocated by the recipient for any purpose. Thus, some of the grant may be allocated to the spillover-generating public good, and some of it may be allocated to private goods (via a reduction in taxes in the recipient community) or to public goods that do not create spillovers. Such a grant is shown in Figure 2 as a shift in the recipient's budget line from AA' to BB'. The recipient's new allocation, located at point E, tangent to the community indifference curve I,, will be Y2 of the spillover-generating good and X, of all other goods. As an alternative to a lump-sum.grant, the grant may take the form of a conditional matching grant. In this case, the grant will only be received if the recipient satisfies two conditions. First, the recipient must use the grant for production of the spillover-generating good. Second, the '3‘! .b Co: ‘In ~w 47 recipient must match the grant at a specified rate with its own funds. Assuming the original slope of the budget line is h and that the matching rate implies that.s is the share of the cost of good Y paid by the grantor, the new budget line will have a slope of h*(1 - s) and will rotate from AA' to AB'. The new allocation of the recipient will be X, and Y,. If Y, is the socially optimal level of the public good, Figure 2 demonstrates that it can be achieved at least cost to the grantor by use of a conditional matching grant. As shown in Figure 2, the grantor's cost of achieving output Y, is DE, if a lump-sum grant is used, but only DE,if'a matching grant is used. This result arises because the lump-sum grant produces only an income effect, while the matching grant reduces the recipient's price of the spillover-generating good, thereby combining the income effect with a price effect to provide a more powerful incentive for the recipient to increase its spending on the spillover-generating good. A number of studies of intergovernmental grant programs have confirmed that recipient jurisdictions do respond to such price effects and, as a result, the recipient's spending on the spillover- generating good is stimulated more by a matching grant than by a lump-sum grant of equal size (Gramlich, pp. 222-35).8 In comparing the cost efficiency of these two types of grants, it should be reiterated that the choice of grant form is determined by the objective of the grant program. This choice of objectives has important distributional consequences 48 for both the grantor and the recipient. While it is true that the recipient would prefer the lump-sum grant (since it would be on the jpreferred indifference curve IQ, it. must. be emphasized that the purpose of the grant is not the maximization of the recipient's welfare. Instead, it is assumed in this analysis that the purpose of the grant is only to compensate the recipient for spillovers and induce the socially optimal level of investment in.the public good at the minimum cost to the grantor. This objective can best be accomplished with a matching grant. If the grantor agrees to provide matching funds for each dollar invested by the recipient, the grant is an open-ended matching grant and will achieve the socially optimal level of investment in the spillover-generating good. Open-ended grants are rarely used, however, since such grants would expose the grantor to an undetermined future budget obligation and would make budget planning difficult for the grantor. To overcome ‘this problem, ‘most. matching' grants are closed-ended grants that impose a limit on the size of the grant provided by the grantor. Such a closed-ended matching grant is shown in Figure 3. Once again, the recipient community has a pre-grant equilibrium at a point along the budget line AA'. If a closed-ended matching grant is offered to it, the budget line will shift to ABC, where point B represents the limit on matching funds imposed.by the grantor. The slope of the budget line is h*(1 - 5) along the segment 49 I4 I3 E4 I4 A' C Spillover Good Figure 3: Impact of a Closed-Ended Matching Grant on the Budget of the Recipient Jurisdiction Source: Boadway and Wildasin, p. 528. 50 AB, reflecting the matching funds provided by the grantor, and returns to h along the segment BC, since matching funds are not provided in this range. A closed-ended matching grant may have three different outcomes, depending on the preferences of the recipient. If the recipient's preferences are such that its indifference curve is tangent to the budget line at a point along the segment.AB (such.as at point E,on the indifference curve In, the recipient is adequately compensated for the spillovers it has created and will provide a socially optimal level of the public good. In this range, the price effect and the income effect are the same as for an open-ended matching grant. There is no price effect in the BC segment of the budget line, however, and while the quantity of the spillover- generating good is greater than in the pre-grant situation, it is still not the socially optimal quantity. That is, because the funds provided to the recipient are limited by the grantor, the recipient still is not compensated fully for the spillovers it has generated and is still underinvesting in. the spillover-generating' good. For example, if the recipient jurisdiction's preferences are represented by the indifference curve I,rether than I“ then the recipient would provide more of the spillover-generating good if an open-ended grant were available. Given the limit imposed by the grantor, however, the recipient still does not have an incentive to provide a socially optimal level of the spillover-generating good. 51 Point B represents an indeterminate corner solution. If the recipient allocates its resources at this point (i.e., if its preferences are represented.by the indifference curve IQ, the allocation may represent a socially optimal allocation (the recipient happens to achieve a socially optimal allocation at the end of the AB segment and would not allocate more resources to the spillover good even if more grantor funds were available), or B may represent a socially sub-optimal allocation (the recipient allocates its resources at the end.of the BC segment and would allocate more resources to the spillover good if the grant was open-ended (Boadway and Wildasin, pp. 518-29). This leads to an.important observation. If the recipient provides less funds than required to receive the maximum matching grant (i.e., it is located along AB on the budget line), then it is providing the socially optimal level of the public good. If it provides more funds than are required to reach the limit (i.e., the recipient is along BC on the budget line), then it is not providing the socially optimal level of the public good. This is particularly relevant for judging the efficiency of the existing system of agricultural research funding in the United States. States have traditionally provided far more funds than are required to receive their matching Hatch Act funds from the federal government (U.S. Office of Technology Assessment, p. 206: U.S. General Accounting Office, 1983, pp. 37-38). In 1987, for example, the states appropriated an average of 5.68 dollars of state 52 agricultural research funds for each dollar of federal Hatch funds (U.S. Department of Agriculture, 1988, p. 117). This suggests the existing system of closed-ended Hatch Act grants fails to provide adequate compensation to the states for the benefit spillovers they create, thereby resulting in a nationally sub-optimal level of investment in agricultural research. A final consideration is the impact of benefit spillins on the provision of public goods. Figure 4 shows a jurisdiction, in the absence of grants and spillins, with an equilibrium position of FL along its budget line AA' (it is, of course, ignoring any benefit spillovers it may be creating). If it receives benefit spillovers because another jurisdiction provides some quantity of the spillover- generating' good, then the budget line of the recipient jurisdiction will shift from AA' to ABB', where A'B' represents the quantity of benefit spillins received. An important result should be noted here: spillovers that are received from another jurisdiction have only an income effect for the recipient, not a price effect. Therefore, receiving spillovers will not induce the recipient jurisdiction to produce the socially optimal level of the spillover-generating good. Thus, even if a jurisdiction produces and receives spillovers, a system of intergovernmental grants may still be required if a socially optimal level of investment in the spillover-generating good is to be achieved (Oates, pp. 97-98). 7w.-.—o- - — Other Goods 53 Figure 4: source : Spillover Good Income Effect of Benefit Spillins Oates, p. 98. 54 If a conditional matching grant is to be used to finance a spillover-generating good, the problem of financing such a good now becomes the determination of the appropriate subsidy to be paid by the higher level government to the recipient government (i.e., the determination of the s in the h*[1 - 5] budget line slope in Figure 2). A model of intergovernmental grants developed by Harford (pp. 99-103) provides a subsidy from each of two higher levels of government (state and national) to a local government that optimizes the quantity of the spillover-generating public good provided by the local government. Although this model introduces the additional complication of two higher levels of government rather than one, it permits some conclusions to be drawn about the optimal shares of the cost of the spillover-generating good that should be paid by the higher levels of government. These shares can then be translated into the optimal matching rates that can be used to finance the spillover-generating good through a conditional matching grant. The Harford model consists of three equations: (2.11) N, = a,*B(Y) - (1 - s, - s,)*C(Y) (2.12) N, = a,*B(Y) - (1 - s,)*C(Y) (2.13) N, = B(Y) - C(Y), where: N, = The local net benefit equation: N, = The state net benefit equation: N, = The national net benefit equation: a, = The share of the benefits of public good Y retained by the local jurisdiction: 55 a, = The share of the benefits of public good Y retained by the state jurisdiction: s,== The share of the cost of public good Y paid by the state government: s,== The share of the cost of public good Y paid by the national government: B(Y) = The benefit function for public good Y; C(Y) = The cost function for public good Y: 05a,$a,51: and o _<_ s,, s, g 1. The necessary conditions for achieving a socially optimal level of investment in Y are reached by equalizing the marginal cost and marginal benefit that accrues within each level of government. Differentiating equations (2.11) to (2.13) and setting them equal to zero yields the optimal conditions for each level of government: (2°14) a1*gfl = (1 " SJ "' 52) *QQ dY dY (2°15) a:*§§ = (1 - 53) *Q3 dY dY (2.16) nn = _Q, where: dY dY nn = The marginal benefit of public good Y: dY d9 = The marginal cost of public good Y. dY Solving equations (2 . 15) and (2. 16) simultaneously yields the optimal share of the cost of good Y paid by the national government: (2.17) s,== 1 - a,. 56 Solving equations (2.14) and (2.15) simultaneously and substituting (2.17) into the result yields the optimal share of the cost of the good paid by the state government: (2.18) s, = a, — a" The results correspond to those discussed in earlier literature (e.g., Oates).° Namely, (2.18) shows that the state government will compensate the local government for those benefits that spill across local boundaries but remain within state boundaries. Equation (2.17) shows that the federal government will compensate the local government for those benefits that spill across state boundaries. These cost shares can now be converted into matching rates that, if used to establish an open-ended conditional matching grant, will yield an optimal investment in the spillover-generating good. These matching rates can be calculated as: (2.19) m, s,/(l - s, - s,) and (2.20) m, = s,/(1 - s, - 5,). Thus, if the federal government grants m, dollars to the local government for each dollar the local government invests in the spillover-generating good, and the state government grants m, dollars to the local government for each dollar the local government invests in the spillover-generating good, a socially optimal level of the good will be provided by the local government. Before turning to a review of the economic literature on the returns to agricultural research, a summary of this 57 section is in order. The provision of public goods is an especially difficult problem when decisions are made within a federal (i.e., multi-level) system of government. When a publicly-provided good yields benefits to residents outside the funding jurisdiction, the jurisdiction providing the good will not have an incentive tijrovide.a socially optimal level of the good. As Pigou suggested should be done with individuals, the producing jurisdiction can be given an incentive to provide the socially optimal quantity of the good by providing it a subsidy equal to the difference between the marginal social benefit obtained from the good (including that portion which accrues to outside residents) and the marginal benefit retained by the funding jurisdiction. In a federal system of government, such a subsidy is typically provided by a higher level government to compensate lower levels of government for the external benefits generated by these jurisdictions. The lowest cost form of such a subsidy is an open-ended matching grant (i.e., a grant of m dollars from the higher level of government for each dollar spent by the lower level government on the spillover- generating good). The matching rate must be established to equate the share of the marginal cost of the good paid by the higher level of government with the share of the marginal benefits of the good that accrue to persons outside the lower level of government. If benefit spillovers are pervasive in agricultural research, matching grants are clearly an appropriate means 58 through which to finance agricultural research in the United States. 'The remainder of this chapter will review the methods of measuring the benefits of agricultural research and the evidence that agricultural research does produce such spillovers. The case for using intergovernmental grants to finance agricultural research will then be considered. The Meeenzenen; of Eeonomie Reeugns fnom Public ves e ts i “cult r Research This section of the chapter reviews the literature on the ex-post measurement of agricultural research benefits, with special consideration of the measurement of benefit spillovers. The two primary methods of measuring the benefits of agricultural research will be reviewed, and the evidence supporting the hypothesis that the U.S. has traditionally underinvested in agricultural research will be considered. The literature on the measurement of benefit spillovers in agricultural research will then be reviewed and the possibility that benefit spillovers are the cause of the underinvestment problem will be discussed. Measuning Research Benefits: The Economic W An extensive number of studies have measured the benefits of agricultural research by using measures of economic surplus. This literature originated with the work of Griliches (1958) and has been refined by a number of authors (Willis Peterson, 1967: Hertford and Schmitz: Lindner and Jarrett, 1978 and 1980: Rose; Wise and Fell; Norton and Davis). The approach of this method is shown in Figure 5. Starting with 59 Price SS. P _ I I P' i. T II I II I I I I I I | A I |I H I I I A I I I D Quantity Figure 5: Economic Surplus Generated by a Public Investment in Agricultural Research Source: Norton and Davis, pp. 686-689. 60 a commodity supply S and demand D, an investment in public research will shift the supply curve to S', producing a net gain of economic surplus (i.e., the combined net gain of producer and consumer surplus) of the area AEE'A'. Reviewing the literature on a number of economic surplus studies, Norton and Davis (pp. 687-90) derived four formulas for estimating the size of the net economic gain that results from public investments in agricultural research. These formulas are shown in Table 2, along with the authors who developed the formulas and the key assumptions behind their development. The evolution of this literature has been marked by a number of attempts to improve the accuracy of the estimates and to provide generalized models for estimating the returns to agricultural research. For instance, Griliches' original studies of hybrid corn estimated the limits of the returns to research by assuming the polar cases of (l) a perfectly elastic supply and a downward supply shift due to research (the upper limit), or (2) a perfectly inelastic supply and a rightward supply shift due to research (the lower limit). Later refinements in the theory showed that Griliches' estimates were simply special cases of the Hertford and Schmitz model (with a perfectly elastic supply) and the Lindner and Jarrett and Rose models (with a perfectly inelastic supply). Thus, the more recent models shown in Table 2 provide less restrictive conditions and more accurate estimates than did earlier versions. 61 Table 2. Formulas for Calculating the Net Economic Surplus Created by Public Research Investments Author Formula Key Assumptions Hertford K*P*Q(l + 1/2(K/n+e)) Demand and supply curves and Schmitz are linear, and the supply shift is parallel. K is a horizontal supply shifter due to research, where K is the horizontal distance from S to S'. Akino K*P'*Q'(l/(l + e) + 1/2(K/(e + n)))Supply elasticity is and Hayami constant, and the supply shift is pivotal. K is a production function shifter due to research equal to the percentage shift from S to S'. Lindner K*P*Q(l + l/2(c*e/(e + n))) Supply and demand curves and Jarrett; are linear, and the Rose supply shift is parallel. K is a vertical supply shifter due to research. Lindner K*P*Q(l/2 + l/2(c*e*n/(e + n))) Supply and demand curves and Jarrett; are linear, and the Rose supply shift is pivotal. K is a vertical supply shifter due to research. Where: P Equilibrium price before the supply shift; Q - Equilibrium quantity before the supply shift; P' - Equilibrium price after the supply shift; 0' - Equilibrium quantity after the supply shift; a - Price elasticity of supply; d - Price elasticity of demand; c - Absolute cost reduction at Q resulting from research, divided by P Source: Norton and Davis. 62 Three factors common to all these models affect the estimated economic benefit generated by agricultural research. First, the elasticities of supply and demand are critical in determining the size and distribution of research benefits. The less elastic are the supply and demand curves, the larger will be the benefits of research, and the larger will be the share of research benefits that accrue to consumers. Second, the total value of the commodity (P*Q in the Hertford and Schmitz, Lindner and.Jarrett, and.Rose models, or P'*Q' in the Akino and Hayami model) also determines the size of the net economic surplus gain that results from research. Commodities with a larger total value of production will, ceteris paribus, produce larger research benefits. Third, the supply shift factor, K, is a major determinant of net economic benefits and, as shown in Table 2, has been specified in a variety of ways. Attention must also be paid to the nature of the supply shift that results from research (i.e., the parallel, divergent, or convergent nature of the supply shift). While Figure 5 shows a parallel shift, care must be taken to determine the appropriate form of the supply shift. Recent research has clarified the importance of such shifts and developed the appropriate formulas for estimating returns to research under each type of shift (Lindner and Jarrett; Wise and Fell: Rose). The choice of the supply shift depends on the nature of the technology resulting from research. If the technology 63 developed is most applicable for those producers with the highest marginal cost and reduces their marginal cost proportionately more than low cost producers, a pivotal or proportional divergent supply shift is most appropriate. On the other hand, if the technology is most applicable to low marginal cost producers, a convergent supply shift should be used. Idndner and Jarrett also recognize that adoption of the technology may be related to farm size, farm specialization, and managerial ability. For these reasons, they argue that biological and chemical innovations will likely produce a divergent shift in supply and that mechanical and organizational innovations will likely produce a convergent shift in supply (Lindner and Jarrett, 1978, pp. 55-57). Thus, it should be noted that the nature of the supply shift is crucial not only to the estimated net economic surplus «generated. by research, but also to the assumed distribution of that surplus among farmers. A final comment is required on the normative underpinnings of all economic surplus studies of the returns to agricultural research. The simple addition of consumer and producer surplus represents a normative assumption that places equal weight on the welfare changes experienced by consumers and producers (Boadway and Bruce, p. 281: Sugden and Williams, p.201: Schmid, 1987, pp. 207-208). Such a weighting scheme is defended by some analysts (Harberger, p. 785), and the purpose here is not question the legitimacy of such an assumption, but simply to identify a crucial normative 64 assumption that underlies all such studies and determines, in part, the empirical results obtained in such studies. Once the net economic surplus arising from research has been calculated, it must.be translated into a form.that allows it to be compared with other investment opportunities. The most common form for such comparisons is the internal rate of return, defined as the interest rate that equates the present value of the benefits and costs of the research investment (Weston and Brigham, p. 225) . In its simplest form, the internal rate of return is the interest rate that solves the equation: 1 * B = 0, where, '=1 (1 + r)t t =The number of years over which the research investment must be discounted; B =The net flow of research benefits over years in which the research investment must be discounted: r = The internal rate of return. The internal rates of return for a number of economic surplus studies will be examined later in this chapter. Meesuging Research Benefins: The Production EBDQEIQH Method A second method of measuring the returns from public investments in research uses a production function to measure the contribution of research to agricultural output. Most such models have taken the form: (2.22) O = f(X, R, e), where: 65 Q = The value of agricultural output: X A set of conventional inputs: R = The public investment in agricultural research; e = A random error term. Like the economic surplus method, the production function method originated with the work of Griliches (1964) and was refined by later authors (Latimer and Paarlberg; Evenson, 1967: Willis Peterson, 1967: Bredahl and Peterson: Norton, 1981). .AS‘with.the economic surplus method, these refinements have attempted to achieve increased sophistication and precision in the estimates of research benefits. Griliches' early work with this method used state-level cross-section data that measured agricultural output and conventional inputs on a per-farm basis and measured research investment as the state's one year lagged expenditure or two year average expenditure. Latimer and Paarlberg used simple 4, 8, and 12 year sums of state research expenditures. Evenson (1967) and Fishelson added more sophisticated lag structures to the research variable. The lag structure of the research variable is a critical component of the production function approach, since four factors can be expected to cause the impact of research on output to vary over time. First, there may be a lag from the time funds are invested in research until the time scientists produce results. Second, there may be a lag from the time scientists produce results until the results can be adapted to the needs of farmers in a given location. Third, there 66 may be a lag from the time usable results are available until the time farmers adopt the results and output is affected. Fourth, there may be a depreciation of the knowledge as ecological factors (such as pests, weeds, or diseases) erode the effectiveness of the knowledge. Given such factors, the effect of research on output (i.e., the benefits of research) would likely be small in the years immediately following the initial investment, would increase as the results are produced by scientists and adopted by farmers, and would begin to decline as the knowledge becomes obsolete. Evenson (1967) developed an "inverted-V" lag structure that estimated a mean time lag of 6 to 7 years between an increase in research expenditures and the maximum effect of research on agricultural output. His results indicated that an agricultural research investment in year t had a positive and increasing effect on agricultural output until the year t+6 or t+7, then decreased until reaching zero in the year t+12 or t+14. Fishelson used an "inverted-U" lag structure that increased the impact of research on output from the year of investment until ten years after the investment, then returned to zero sixteen years after the investment. It should be noted that some studies have used national or regional time-series data rather than state cross-section data to estimate equation (2.22) for aggregate output (Bauer and Hancock: Havlicek and White, 1983a: White and Havlicek, 1979) . Except for Bauer and Hancock (who found that a constant 9-year lag was more appropriate than an "inverted-V" 67 or "inverted-U" lag structure) these studies used some form of an "inverted-V" lag structure (often an Almon lag structure) to measure the effect of past research expenditures on current agricultural output. A second production function approach uses time series data to estimate the equation: (2.23) P = f(W, E, R, e), where: P = A productivity index: W = A weather index: E = A measure of the education level of farmers: R = A measure of the level of research investment: e = A random error term. Two of the most comprehensive studies of agricultural research benefits have used this "productivity decomposition" method. Lu, et al. used a productivity index model to estimate national and regional rates of return. They also used the Almon lag method to estimate an "inverted-U" lag structure for the research variable. Their results showed that a 13 year-lag was most appropriate at the national level and that regional lags ranged from 9 to 14 years. Evenson, et a1. (1979) estimated a number of productivity index models with alternative formulations that measured the effect of research on productivity as well as the interaction between research and extension activities. Once the production function has been estimated, it is again necessary to translate the results into terms that compare the return to agricultural research investments with () 1"” B... (.... Pi LL) 68 other investment opportunities. This is done in two steps (Davis, 1981a). First, the marginal product of research is calculated using the research production coefficient(s) from the estimated production function. Second, this marginal product is converted into a marginal internal rate of return (i.e., the interest rate is found that equates the discounted benefits and costs of research.that accrue over time, as shown in.equation 2.21). The results of several returns to research studies will be examined in the following section. s of t e on ' A r'cu ural e s ' ' ed es As discussed in the previous section, a wide variety of methods have been used to estimate the benefits of agricultural research spending in the United States. The results of several such studies are summarized in Table 3. When viewing these results, the immediate observation is that, despite a series of refinements in the measurement techniques, the rates of return on agricultural research investments have remained high when they are measured over a wide variety of time periods and commodities. A number of criticisms have been leveled at this literature, however, and, to the extent that the critics are correct, the estimated rates of return must be interpreted with caution. First, it has been argued that the returns to research literature has ignored the complementarity between research and.other inputs, thereby exaggerating the returns to research (Pasour and Johnson, p. 305). Glenn Johnson has argued that QI Rhu~ Fe E 1‘4 1 D. an. n. 9 3% Ah. 69 Table 3. Results of Studies Measuring the Benefits of .Agricultural Research Investments in the United States Internal Rate of Author Level Commodity Years Return (Percent) W Griliches (1958) National Corn 1940-1955 35-40 Griliches (1958) National Sorghum 1940-1957 20 Peterson (1967) National Poultry 1915-1960 21-25 Schmitz and National Tomato, with no 1958-1969 37-46 Seckler compensation for displaced workers National Tomato, with 50% 1958-1969 16-28 compensation for displaced workers Peterson and National Aggregate 1937-1942 50 Fitzharris National Aggregate 1947-1952 51 National Aggregate 1957-1962 49 National Aggregate 1957-1972 34 Cooke National Cucumber 1965-1980 55-75 nggnegign Euneeion Studies Griliches (1964) National Aggregate 1949-1959 35-40 Peterson (1967) National Poultry 1915-1960 21 Evenson (1967) National Aggregate 1949-1959 47 Fishelson National, Aggregate 1949-1964 39 Non-South (Continued) Ia II: Ia Table 3 (cont'd.). 70 Internal Rate of Author Level Commodity Years Return (Percent) Bredahl and National Cash Grains 1969 36 Peterson National Poultry 1969 37 National Dairy 1969 43 National Livestock 1969 47 White and Southern Aggregate, not 1949-1972 51 Havliceck (1979) Region accounting for spillins from other regions Aggregate, account- 1949-1972 39 ing for spillins from other regions Lu, Cline and National Aggregate 1939-1972 26 Quance Ten Regions Aggregate 1939-1972 14-44 Evenson, National Aggregate 1868-1926 65 Waggoner, and Ruttan National Aggregate, 1927-1950 95 technology-oriented National Aggregate, 1927-1950 110 science-oriented National Aggregate, 1948-1971 45 science-oriented Southern Aggregate, 1948-1971 130 Region technology-oriented Western Aggregate, 1948-1971 95 Region technology-oriented Northern Aggregate, 1948-1971 93 Region technology-oriented National Farm management 1948-1971 110 and extension (Continued) 71 Table 3 (cont'd.). Internal Rate of Author Level Commodity Years Return (Percent) Sim.and Araji Western Wheat 1939-1974 11-29 Region National Wheat 1939-1974 38-45 Sundquist, 23 states Corn 1977 115 Chang, and Norton 34 states Wheat 1977 97 26 states Soybeans 1977 118 Davis and National Aggregate 1949 100 Peterson National Aggregate 1954 79 National Aggregate 1959 66 National Aggregate 1964 37 National Aggregate 1969 37 National Aggregate 1974 37 Norton (1981) National Cash Grains 1969 31-57 National Cash Grains 1974 44-85 National Dairy 1969 27-50 National Dairy 1974 33-62 National Livestock 1969 56-111 National Livestock 1974 66-132 National Poultry 1969 30-56 White and Ten Aggregate 1949-1972 31-61 Havlicek (1981) regions Havlicek and Ten Aggregate 1977-1981 23-74 White (1983a) regions (Continued) Table 3 (cont'd.). 72 Internal Rate of Author Level Commodity Years Return (Percent) Smith, Norton National Poultry 1978 25-60 and Havlicek National Livestock 1978 22-43 Northeast Dairy 1978 24-38 Region Braha and National Aggregate 1959-1982 41-58 Tweeten Source: Ruttan, 1982a, pp. 242-43, updated by author. 2301 O LRDC \ '7‘, od?‘ lRVE TESE ‘IMH 5k“ 73 productivity growth results from not only from technological innovations, but also from institutional innovations and improvements in human and bio-physical capital, and that investments in all four are required to achieve improvements in productivity (Glenn Johnson, 1986a, pp. 21-27) . The complementarity of institutional and technological change was demonstrated by Ulrich, et al. (1987) , whose results show that the returns to agricultural research investments are reduced when institutional barriers ‘prevent the adoption. of new technologies. Glenn.Johnson's view is also confirmed by the studies of investments in human capital in agriculture, which estimate equally impressive rates of return for public education and extension investments (Welch: Huffman, 1976a; 1978: Evenson, et al., 1979) and for publicly-provided price information on farm commodities (Hayami and Peterson). However, a number of research investment studies (particularly production function studies) have attempted to address this problem by including education and agricultural extension as separate variables or by using the sum of research and extension expenditures as the "research" variable. Evenson, et al. (1979, p. 1105), for example, included an interaction variable for research and extension investments and did find the two had a positive and significant interaction. While care must be taken to consider the complementarity of such investments, the greater problem seems to be in communicating the true results of these SFtudies. While the results of these studies do indicate a 74 strong complementarity between such investments, the results have too often been used to imply that all productivity growth is the result of technological change. The authors of this literature have not reached such conclusions and have often emphasized that other sources of productivity growth are deserving of investigation (Ruttan, 1982a, p. 298-330: Norton and Schuh: Bonnen, 1987, pp. 268-270). A second criticism is that the economic surplus studies are sensitive to the nature of the supply shift that results from investment in research and that both types of studies must account for the lags in the accumulation, dissemination, and obsolescence of knowledge (Pasour and Johnson, pp. 303-307). Again, researchers have sought to address these criticisms. For instance, while the size of the net economic surplus measured is affected by the type of supply shift employed, it must be noted that most studies have used a divergent supply shift which, if inaccurate, would err in the direction of underestimating the rate of return (Ruttan, 1982b, p. 321). Furthermore, Davis (1981b) demonstrated that the use of a Cobb-Douglas production function is the equivalent of estimating a pdvotal divergent supply shift. Since most production function studies have used a Cobb- Douglas specification, any bias introduced by this method of estimation.would be in the direction of an underestimation of the rate of return on agricultural research. Finally, Davis (1981a) also found that most errors that have been made by improper deflation of the research and output variables have 75 resulted in a slight underestimation of the rate of return. While the problem of estimating an appropriate lag between research investment and the affect of research on output is important, the previous section has already shown that numerous methods have been used to estimate the types of lags described by Pasour and Johnson. A third criticism is that past studies have ignored the contributions of private research investments, thereby biasing the rates of return on public research upward (Pasour and Johnson, p. 305). While this is a problem, it has not been ignored by investigators. Two methods have been used to adjust rate of return estimates and account for private research investments. The first method has been to reduce the estimated research benefits by 1/2 (or 2/3 if public extension investments are not included in the model), based on. the assumption. that. private research investments are approximately 1/3 of total public and private research and extension efforts (Bredahl and Peterson). A second method, developed by Evenson, uses a smaller adjustment to reflect the inclusion of the cost of private research in the prices of inputs purchased.by farmers. ZEvenson (1967) estimated that the omission of a private research variable would bias public investment.rate of return estimates upward.by a factor of 1.22 and that such estimates should therefore be adjusted downward lJy this factor. While such adjustments are somewhat crude, ict should be stressed that larger adjustments would make the assumption that private sector research is significantly more 76 productive than public sector research. Even if such an assumption were justified, it should be noted from Table 3 that very large adjustments would be required to reduce the estimated rates of return to the point where the underinvestment hypothesis would no longer be valid. A fourth criticism is that the returns to research literature has focused on a select number of success stories that cannot be used to predict the rate of return on future investments (Pasour and Johnson, p. 307) . If one only considers the original work of Griliches on hybrid seed corn, such criticism might be justified. Considering the large number of commodities that have been studied, however, this criticism loses some of its validity. In addition, if one considers the rate of return estimates for aggregate output (which, by definition, include both research successes and failures) the evidence continues to show a high rate of return on public agricultural research investments (Ruttan, 1982b, p. 320). A fifth criticism of such studies is that they have ignored the social cost of taxation to support public agricultural research, thereby biasing the returns to research upward (Fox, 1985b, 1985c) . Analysis which included such tax costs, however, still reached the conclusion that the U.S. was underinvesting in agricultural research (Fox, 1985a, pp. 46-50) . A sixth criticism of the returns to research literature is that it has failed to account for the social costs created 77 when agricultural research contributes to the excess capacity of the agricultural sector and increases the cost of government commodity programs (Madden, p. 35) . A study by Braha and Tweeten (pp. 24-27) found that public agricultural research was underfunded even after deducting the full social cost of commodity programs. Furthermore, it must be noted that some of the excess capacity in U.S. agriculture must be traced to unstable commodity policies, macroeconomic events, or resource adjustment problems in agriculture (i.e., asset fixity) rather than public research investments. Thus, assigning the full cost of commodity programs to public agricultural research could result in a downward bias in the estimated rate of return on research. A final criticism is that the literature has been based almost exclusively on partial equilibrium analysis and has ignored substantial redistributive effects that result from research investments. This criticism is more serious than many others. Clearly, some of the effects of technological change on farm workers, the environment and the structure of agriculture are factors that must be considered in a full accounting of the returns to research (Pasour and Johnson, p. 305). The study of tomato mechanization research by Schmitz and Seckler, for instance, found that the net social rate of return on such research would have been negative if displaced workers had been compensated for all lost wages (assuming the lowest possible cost reduction due to research). A study of C‘Jl la h be be no an ac 9f in 0f “f 78 cucumber mechanization reached a similar conclusion (Cooke, p. 331). Caution must be exercised, however, in placing the entire burden of labor displacement on mechanization. research. Martin and Olmstead (pp. 602-606) maintain that tomato production would have shifted to Mexico without the development of mechanized harvesters and that the harvester preserved jobs in the tomato input and processing sectors. They also concluded that other research, which lengthened the harvest season for some crops, increased the demand for farm labor. Similarly, a study of cotton mechanization revealed that 79% of the labor that left cotton harvesting operations between 1930 and 1964 could be traced to higher wages in the non-farm sector: only 21% could be traced to a reduced demand for labor arising from cotton mechanization (Willis Peterson and. Kislev, p. 214). As these studies demonstrate, any accounting of the effects of agricultural research on farm labor markets must take care to reflect its labor-displacing effects rather than its labor-replacing effects. Benefit Sniiievers in Agricuituxal Researcn Ruttan (1982a, pp. 254-58) has given two reasons for the continued high rates of return on public agricultural research investments. First, he argues that the decentralized system of state agricultural experiment stations has created fifty "firms" whose supporters, primarily the farmers of the state, (Semand that the station provide research results that keep ‘t:hem competitive with farmers in other states. The station 79 director, facing this competitive pressure, must allocate the state's research funds efficiently or face the displeasure of farmers and legislators. While this may be true, it cannot explain the apparent continuing underinvestment in research since, if legislators were aware of the high rate of return, they would presumably reward the efficiency of the station director with increased funding. A. more likely explanation for' this continuing underinvestment is the spillover of research benefits across state Iboundaries. IRuttan identifies two ‘ways in. which spillovers may occur. First, benefits may spill across state lines in the form of lower food prices for consumers. Second, benefits may spill across state lines as farmers in other states adopt the technology developed in the funding state. As the formulas in Table 2 have shown, the net gain in economic surplus that results from research investments will be larger when the supply and demand for the commodity are inelastic. Most agricultural commodities have such elasticities. When this is true, however, most of the gain in economic surplus will accrue to consumers in the form of lower food prices. The gains that accrue to farmers will often be short-lived and will usually accrue to those astute farmers who adopt the new technology soon after its introduction (Ruttan, 1982a, pp. 257-58). Since many of the gains in consumer welfare will accrue to persons outside the funding state, there will be, to use Breton's phrase, an "imperfect mapping" of the benefits of research. The public 80 finance literature reviewed earlier in this chapter indicates that this condition is a potential source of underinvestment in public goods. The second source of spillovers, the adoption of the new technology by farmers outside the funding state, could also contribute to the underfunding of research. While the results of research may be applicable to the environmental conditions of the funding state, it is unlikely that they could not be used or adapted for use in other states. The early“work:of'Griliches (1957, 1960) found that the percentage of corn acreage planted with. hybrid seed corn took an "S-shape" over time in nearly every state, with some states lagging behind the early-adopting states. The date of introduction of hybrid corn to a state was explained by the profitability of entry into the state (where profitability was measured by the density of production in the state and the cost of research and marketing in the state) (Griliches, 1957, pp. 506-15). The rate of adoption of hybrid corn by farmers in a state (i.e., the slope of the S-curve) was determined by the profitability of switching from open-pollinated corn to hybrid corn (Griliches, 1957, pp. 515-19). Thus, the technology of hybrid corn tended to spill from high density, high profitability states (e.g. , Iowa) into lower density, lower profitability states (e.g., Alabama). A similar pattern of adoption was observed for such mechanical technologies as grain combines, cornpickers, balers, and field forage harvesters (Griliches, 1960, p. 276). 81 More recent studies have also examined the production spillovers created by agricultural research. Araji's survey of scientists and extension specialists indicated that the results of integrated. pest :management research. could. be adopted in many states outside the state in*which.the research was conducted, thereby suggesting the potential for benefit spillovers to arise. On the low end of the estimates, researchers indicated that 16% of the soybean acres in Kansas, Nebraska, and.South Dakota.could adopt.the.results.of research conducted in Indiana. At the high end of the estimates, scientists indicated that research results could be adopted on 100% of other states' acreage for a number of commodities. The results of alfalfa pest management research conducted in Indiana, for example, could be adopted on 100% of the alfalfa acres in Ohio, Michigan, Illinois, Wisconsin, Minnesota, and Nebraska. Research conducted in California on grapes, apples, and pears could be applied to 100% of these crops produced in a large number’ of ‘western, ‘midwestern, and. northeastern states. Peppermint research conducted in Michigan could be applied to 100% of the acreage planted in Indiana, Idaho, Oregon, and Washington (Araji, pp. 124-31). Similarly, a study of wheat research (Dalrymple, p. 63) found that 38% of the 1974 U.S. wheat acreage planted in publicly-developed dwarf varieties was planted.with.varieties developed in other states. The share is even higher for major varieties. For instance, 90% of the acres planted to the Blueboy variety were in twenty states other than the state 82 that developed the variety (North Carolina). Similar spillovers occurred with other wheat varieties: 74% of Caprock acreage (developed in Texas), 71% of TAM W-101 acreage (developed in Texas), and 65% of Twin acreage (developed in Idaho) was planted outside the state that developed the variety. Schultz (1982, p. 182) has also argued that there are likely to be significant spillovers between commodities, such as the 'benefits that accrue. to livestock. producers and consumers from research investments that reduce the price of feed grains. Lyu and White confirmed this by using an economic surplus model to estimate the spillovers from corn research to livestock and poultry markets. Their results indicated that corn research benefits were underestimated by 26% when inter-commodity spillovers results are ignored. The returns to research literature has used various methods to estimate the spillovers of agricultural research benefits. White and Havlicek (1979) estimated a time series production function model that included separate research variables for research conducted inside and outside the southern region of the United States. Their results indicated that the marginal internal rate of return on research conducted in the southern region declined from 50% to 39% when the outside research variable was included. Otto and Havlicek estimated production function models for corn, wheat, and sorghum and included an outside research variable (defined as the total research expenditure of the 83 top five national producers of the commodity) to capture the effect of research spillovers. The spillover variable was significant in only the wheat equation. Sundquist, et al., on the other hand, ran production function models for wheat, corn, and soybeans that did produce significant results for the research spillover variable. In their models, the research spillover variable was defined for soybeans as the research investments in all states at the same latitude, and for corn and wheat as the research investments of all neighboring states. Norton (1981) updated Bredahl's research and also ran production function models for dairy, livestock, poultry, and cash grains that included a research spillover variable based on the research investments in similar geoclimatic regions. The spillover variable was insignificant in each case. Davis (1979, p. 95) used a similar geoclimatic specification in a production function model of aggregate output. Again, the results for the spillover variable were insignificant. Three studies have attempted to examine spillovers on an national aggregate basis. The first, a productivity model estimated by Evenson, et al. (1979: also see Evenson, 1980), used a research spillover variable based on investments in similar geoclimatic regions and subregions. Their research variable for each state was defined as: (2.24) R = A(a,b,c) + s*S(a,b,c) + f*F(a,b,c), where R = Total research investment applicable to agricultural production in state i: A = Research investment made by state i: 84 S = Research investment made in other states in the same geoclimatic subregion as i: F = Research investments made in other states in the same geoclimatic region as i: s and f = "Contiguity parameters" estimated to indicate the share of the research conducted in other states that was applicable to state i: a, b, and c = "Time shapewparameters" estimated to indicate the rising (a), constant (b), and declining (c) impact of research on state i's productivity. Evenson (1980, pp. 200-206) then ran partial correlations between the research variable R and a state productivity index for various values of s, f, a, b, and c to find the highest correlation. The specification of the research. variable ‘was then based on the combination. of contiguity and time shape parameters that provided the highest correlation between productivity and research. Using these parameters, Evenson ran a time-series productivity index model similar to that shown in equation (2.23). His results indicated that 67% of the marginal benefit of research accrued inside the funding state in the southern and western regions, and 44% of the marginal benefit accrued inside the funding state in the northern region (Evenson, et al., 1979, p. 1105: Evenson, 1980, p. 211). 85 The second national study (Ziemer, et al.) used an economic surplus model to estimate the total national net gain from.a 10% increase in research spending. Ten regional supply and demand equations were derived using each region's share of total agricultural production and population, respectively. These regional equations were then used to determine the economic surplus that accrued inside and outside each region from research conducted in that region. As expected, their results showed that substantial portion of research benefits spill across regions. At one extreme, the Northeastern region retained 68% of the average benefit of its research: at the other, the Northern Plains region retained only 2% of the average benefit of research conducted in the region. Comparing these estimates to the share of research funded by the federal government in each region, they conclude that insufficient compensation for spillovers is an important cause of underinvestment in agricultural research. The final national study estimated a production function using pooled time-series/cross-section regional data that included variables for research inside and outside each of the ten USDA production regions (Havlicek and White, 1983a). After calculating the total benefit spillovers that resulted from research, these spillovers were allocated among the regions based on each region's share of the total national research investment. Their results indicated that, at one extreme, the Nbrtheastern region retained 23% of the total benefits produced by its research investment. At the other 86 extreme, the Corn Belt region retained 58% of the total benefits generated by its research. Comparing each region's share of spillovers with the share of its research funded by the federal government, Havlicek and White concluded that only the Corn Belt was compensated adequately for the benefit spillovers it created. Comparing these results to those of their earlier research (White and Havlicek, 1980), they concluded that the undercompensation problem had worsened since 1972. While the results of the latter two studies do suggest that the federal government is not providing adequate compensation for research benefit spillovers, their results were not appropriate for use in a public finance framework. As emphasized by the public finance literature, the appropriate criterion for judging the adequacy of the existing research funding system must be the share of the marginal benefit of research that spills across state lines and the share of the marginal cost of research paid by the federal government. Neither of these studies provided the results necessary to make such a comparison. Evenson's study (1980) does provide such results on a regional basis, but does not incorporate the results in a public finance framework to determine an optimal system for financing research. o te v e Ga c' r' a1 Resea ch Should agricultural research be financed through a system of intergovernmental grants from the federal government to the states? This section will address this question in two parts. 87 First, the general case for public support of scientific research will be examined. Second, the unique character of agricultural research will be examined and the case for intergovernmental support of agricultural research will be considered. Arrow (pp. 609-15) cited three reasons why a perfectly competitive market may not lead to a socially optimal allocation of resources. First, uncertainty may exist in production relationships of some goods. Second, the consumption of some goods may be indivisible. Finally, the producers of some goods may not be able to appropriate the market price of their products because they cannot prevent non-paying users from consuming the goods. Arrow argued that all three of these conditions apply to scientific research. Uncertainty poses two deterrents to obtaining a socially optimal level of research investment in a competitive market. First, since the outcome of research is unknown, inventors may underinvest in research if they cannot shift some of the risk associated with research to those persons willing to assume such risk. Arrow discusses an idealized system of "commodity options" in which inventors wishing to shift risk and investors wishing to assume risk can reach an optimal allocation of risk-bearing, but contends that such arrangements rarely exist in a real economy. While institutions such as insurance policies and stock markets exist to promote risk sharing, they may be inadequate in the case of research, which, according to Arrow, involves a unique 88 moral hazard. Since the success of research is related to "an inextricable tangle of objective uncertainties and decisions of the entrepreneurs," it is almost "certainly uninsurable" (Arrow, p. 613).‘0 The second deterrent posed by uncertainty is that the demand for research may be reduced by the uncertainty of buyers as to the usefulness of the knowledge. Buyers cannot know the value of the research until they have the information. but then the users will have acquired the knowledge and will have little incentive to provide adequate compensation to the inventor. As a result, the demand for research may, according to Arrow (p. 617) , be less than socially optimal. Thus, Arrow concludes that uncertainty on both the demand side and the supply side may prevent research investments from reaching a socially optimal level. A second problem is that the results of research may be indivisible. That is, once the research is conducted and results produced, the cost of transmitting the knowledge to an additional user is very low. Thus, from a social perspective, the knowledge should be made as widely available as possible, since the marginal social benefit will nearly always exceed the marginal social cost of its distribution. To make knowledge this widely available, however, gives rise to the problem of inappropriability and raises the problem of equitable cost-sharing among users. If an inventor has a monopoly on his knowledge, he may indeed seek.to extract a price for sharing that knowledge with 89 buyers. In doing do, however, he must reveal the knowledge to buyers who may then refuse to compensate the seller or may who pass the information on to other buyers (either intentionally or simply by having other buyers observe the initial buyer's use of the knowledge). The spread of information may break the monopoly and prevent the inventor from appropriating a return from many users of his results. Legally imposed property rights, such as patents, can only partially solve this problem, since there may be difficulties in determining the exact source of a piece of knowledge (Arrow, p. 614-15). Thus, Arrow concludes that a perfectly competitive market will underinvest in research because of the product's risky nature, because of the increasing returns to its use, and because producers may not be able to protect their monopoly over the knowledge produced. Because of these conditions, he concludes that public provision of scientific research may be justified. Some economists do not share Arrow's view that research has the characteristics of a public good. Hirshleifer, for instance, argues that Arrow's analysis omits the possibility of speculative gain by inventors and, as a result, Arrow underestimates the returns available to private inventors and overstates the case for publicly-funded research. As an example, Hirshleifer (p. 571) argues that Eli Whitney, who fought to protect his patent on the cotton gin, would have been better served by speculating in the pecuniary effects of his invention on the prices of cotton, slaves, land, and 90 warehousing and transportation facilities. Had he done so, Hirshleifer contends, Whitney would have been compensated adequately for his invention. Hirshleifer then concedes, however, that such speculation may be difficult since: (1) the limited wealth of the inventor may prevent him from engaging in such speculation; (2) the cost of establishing markets for such speculation may be large when large numbers of parties are involved: (3) by engaging in speculation, the inventor' may reveal his knowledge to other’ speculators, thereby reducing his speculative profits: and ( 4) the inventor may not.be able to insure himself against other risks that may negate the pecuniary effects of his invention. Given these constraints on the inventor's speculative gains, Hirshleifer concludes, public support of research may be justified. Demsetz is critical of all three of Arrow's arguments in favor of public support of research. First, Demsetz (pp. 2-14) argues that we cannot conclude that the absence of risk-bearing institutions in the economy implies that inefficiency exists, because their absence may result from the cost of insurance exceeding its benefits. Second, the problem of indivisibility arises "only when the costs of contracting are relatively large" (but. he concedes that indivisibility will lead to underinvestment when contracting costs are large). ‘Third, he argues that the inappropriability of research is a problem.of poorly designed and enforced legal arrangements.” 91 Similarly, Pasour and Johnson argue that agricultural research does not qualify as a public good. While they concede ‘that research. is indivisible, they contend ‘that research is not inappropriable, since patents and copyrights can be used to protect the inventor's interest (Pasour and Johnson, p. 310). This view of industrial research is shared by Scitovsky (1954, pp. 144-45). It must be noted, however, that Scitovsky believed agricultural research was a special case that did require public funding (presumably because of the atomistic nature of farming). This solution to the underinvestment problem is best expressed by von Mises (p. 658), who viewed the problem of inappropriability as a "consequence of loopholes left in the system" of public property that can be corrected "by rescinding the institutional barriers preventing the full operation of private ownership." This view ignores the fact that the establishment of a patent system involves a trade-off of benefits and costs (Hirshleifer and Riley, p. 1404). Namely, a patent system provides the benefit. of’ greater research investment (by providing a means of appropriating the benefits of research) at the cost of worsening the underutilization problem (by pricing information at a level above its marginal cost of zero, a patent system imposes a loss of welfare on society). Machlup (1968, pp. 470-71) examines a broad set of benefits and costs arising from a patent system. The benefits of a patent system include the development or early 92 introduction of inventions that would not have been introduced or would have been delayed if the patent system had not existed. The costs include: (1) the increased research and development costs incurred by the inventor: (2) the loss of output due to limited use of the patented invention: (3) the loss of output that may result if the patent owner uses the power granted by the patent monopoly to strengthen its market power in other areas: (4) the loss of output that may result if the patent owner uses patents of associated inventions to extend the power granted by the original patent, thereby delaying entry by other firms beyond the life of the original patent: (5) the cost of resource reallocation that may result when new inventions cause accelerated obsolescence of existing physical and human capital; and (6) the administrative and legal costs that result from granting and defending patents. Nordhaus (1969, pp. 76-89 and 1972: Scherer, 1972) considers a narrower set of costs and benefits associated with a patent system and develops a model of optimal patent life length which equates the marginal cost of the patent system (measured as the consumer surplus loss that occurs due to the restriction of output during the life of the patent plus the cost of research) with the marginal benefit of the patent system.(measured as the producer and consumer surplus created by the cost reductions resulting from the additional research stimulated by lengthening the patent life). His results indicate that a fixed-life patent system may impose welfare losses on society by providing excessively long patent 93 protection for most inventions. To avoid such losses, he prescribes a variable-life patent system that would base each invention's patent life on its research costs, riskiness, cost-reducing effect, imitation costs, and market structure (Nordhaus, 1972, pp. 430-31). It should be noted, however, that such a patent system would increase the cost of administering the system. More relevant for this research, however, is the question of whether a patent system is capable of providing a socially optimal level of agricultural research investment. Villard (p. 488) argues that, even with a patent system, predicting the private benefits of some research, including some applied research, is so difficult that private firms will be unwilling to accept the risk.of investing in research. Even abstracting from the risk of research, however, underinvestment in research may still persist under a patent system. Usher used production-possibility curves and indifference curves to demonstrate that underinvestment will persist when the benefits of research are shared by consumers. Arrow (pp. 619-22) used a model of private profit maximization to arrive at a similar result, or, at the very least, to conclude that a patent system will bias private research efforts toward those activities that are easily appropriable. This implies that a patent system may be effective at stimulating investment in minor innovations that provide small cost savings to producers without affecting total output, but may be ineffective at promoting optimal investment in research for 94 those major innovations that.provide substantial cost savings and increased total output (i.e. , a patent system may not provide optimal investment when a large share of the benefits of research accrue to consumers rather than the inventor).'2 This view of the patent system has been confirmed by estimates of the divergence between the private and social rates of return for several industrial innovations (Mansfield, et al., 1977a, pp. 221-40: Mansfield, et al., 1977b, pp. 144-89: Willis Peterson, 1976: Bresnahan: Jaffe: Ulrich, et al., 1986: Martinez and Norton).‘3 The work of Mansfield, et al., for example, shows not only that the median social rate of return exceeded the median private rate of return for the seventeen innovations studied (56% to 25%, respectively), but that this divergence was positively and significantly related to the "importance" of the innovation (measured as the annual net social benefit of the innovation three years after its introduction). This result suggests that the divergence between social and private rates of return will be the greatest and, therefore, the problem of underinvestment most severe, for those inventions that provide a large share of their benefits to consumers rather than to inventors.“ While Demsetz and Pasour and Johnson do force a clarification of the issues at hand, the conclusion can still reached that there is a role for public support of research. They may be correct that the problem of inappropriability can be overcome by a fully enforced set of patents, but they fail to recognize that the correct comparison is between the costs 95 and benefits of such a patent system and the costs and benefits of a publicly-funded research system. As Machlup (1984, pp. 133-34) has observed, the proper role for public and private sector research can only be determined by comparing the relative inefficiencies of the tax burden of public research with those of the monopoly burden.of private research (i.e., the inefficiency created by pricing knowledge above its marginal user cost of zero). When one considers the transaction costs of enforcing a patent system that identifies the source of each piece of knowledge, the beneficiaries (including consumers) of that knowledge, and the correct compensation due to its owner, the case for publicly-funded research is strengthened. This is particularly true as the number of users and producers of knowledge increases and. the transaction costs of patent enforcement increase. A final word on the justification of publicly-funded research is offered.by Nelson (1959). He raises the question: Is it possible that the total public and private research investment exceeds the socially optimal level? Assuming that (1) research results are homogeneous, hence users of research are indifferent between the results of public and private laboratories: (2) the marginal cost of research is equal in public and.private laboratories; and (3) private laboratories operate where their marginal cost equals their marginal benefit, then the fact that industry laboratories perform any research is evidence that there is underinvestment in 96 research. If this were not true, there would be no incentive for the private sector to conduct research: it would merely use the results of public research (Nelson, 1959, p. 304). If there is a case for public funding in some areas of research, what evidence is there that agricultural research should be funded jointly by the federal government and the states? The answer to this question relies mainly on the unique nature of agricultural research. Unlike some types of research, agricultural research, particularly at the applied end of the research spectrum, is often "soil specific, crop and plant specific, animal production specific, market specific, and location specific" (Schultz, 1985, p. 15). For instance, theiclimatic conditions conducive to cherry production are significantly different from those conducive to corn or cotton production. Thus, there is often a need to do commodity-specific research in the same climate where the commodity is grown. This is particularly true when researchers are dealing with such factors as weeds, pests, and diseases or are adapting plants to the growing seasons of specific regions. While it is conceivable that such conditions could be approximated at locations far removed from the production region (say, in greenhouses) such efforts would only come at a high cost of facilities and a high risk of error.‘5 There may also be other advantages to a decentralized system of research that places researchers in contact with farmers and keeps researchers informed of the problems faced 97 by producers of particular commodities. Gershinowitz (pp. 149-50) contends that such a decentralized system will speed the adoption of innovations, while Harry Johnson (1965, p. 138) contends that such a research system will respond more rapidly to the changing needs of research users. As Stigler (1957, p. 213) has noted, a federal system of government provides a greater capacity to adapt public goods to local needs and to "allow legitimate variations of types and scales of governmental activity to correspond.with variations in the preferences of different groups of citizens".” There is some empirical evidence that the decentralized U.S. system of agricultural research does indeed operate as suggested by Gershinowitz, Stigler, and Harry Johnson. First, the available evidence indicates that the demand for agricultural research comes primarily from farmers and, in particular, from. those farmers most likely to be early adopters of the research results (Willis Peterson, 1969: Guttman, 1978: Huffman and Miranowski, 1981: Rose-Ackerman and Evenson, 1985: Merrill, pp. 429-33; Hadwiger, p. 148). Despite the evidence that a large share of the benefits of research accrue to consumers, the general public may be indifferent to the need for public investments in agricultural research. This is not surprising, however, when one considers that such benefits are diffuse and difficult for consumers to identify, and that benefits are often spillovers resulting from research conducted in other states (Olson, 1965, p. 48). Finally, while research may be location specific, the 98 ecosystems to which a technology is applicable may not conform to state lines. As noted earlier, spillovers are often generated across state lines as farmers outside the funding state adopt the technology. As a result, consumers may not recognize the source of benefits created by such technology transfers." Second, the results of the study by Evenson, et al. (1979) show that there is a significant positive relationship between agricultural productivity and the decentralization of research from the station to the substation level in each state. Commenting on these results, Bonnen observed, "The logic of diminishing returns suggests that national-to-state decentralization, if one could measure it, would have an even stronger impact on productivity" (Bonnen, 1987, p. 295) . These results indicate that the location specificity of research can best be addressed by a decentralized system of research. Third, the location specificity of research should also be evident in the estimated returns from agricultural research. If it is true that research is location specific, then the problem of underinvestment should be greater for those commodities that are produced most widely (i.e., for those commodities that are likely to produce the largest share of marginal benefit spillovers relative to the marginal benefit retained by the funding state). The results of Bredahl and Peterson's and Norton's (1981) research support this hypothesis. In both studies, the rate of return on 99 livestock. research (which. is less location specific and should, therefore, produce a greater share of spillovers) was higher than the rate of return on cash grains research, thereby indicating a greater degree of underinvestment in those commodities that produce the greatest share of spillovers (Ruttan, 1982a, p. 256). These two reasons--the location specificity of agricultural research and the spillover of research benefits to farmers and consumers outside the funding state--provide the justification for the use of intergovernmental grants in financing public agricultural research. As suggested by public finance theory, the existence of benefit spillovers may discourage states from.providing a socially optimal level of investment in a spillover-generating good. This appears to be true for agricultural research. If so, a system of matching grants would be the least-cost method for inducing a.nationally optimal levei.of state investment.in.agricultural research.“ Sunnaty How should agricultural research be financed in the United States? This chapter has reviewed two branches of economic literature that. are relevant 'to this question. First, the theory of public goods was reviewed, with special concern for the problems of financing public goods in a federal (i.e., multi-level) system of government. Second, the economic literature on the returns to agricultural 100 research was reviewed, with special emphasis on the measurement of research benefit spillovers among states. The problem of financing public goods is especially difficult in a federal system of government. When a public good provided by one jurisdiction of government yields benefits to citizens in other jurisdictions, the funding government will not have sufficient incentive to provide a socially optimal level of the spillover-generating good. This jurisdiction can be provided a Pigouvian subsidy that will compensate it for the benefit spillovers it has created. Such subsidies are typically provided by a higher level of government to a lower level of government. The least-cost method of providing such subsidies is through the use of a conditional matching grant. Under such a system, the grantor provides the recipient with a given number of dollars for each dollar that the recipient spends on the spillover-generating good. Such a grant decreases the recipient's price of the spillover-generating good and biases the recipient's budget allocation toward a socially optimal level of investment in that good. Such a system of matching grants appears to be especially appropriate for financing U.S. agricultural research. Agricultural research is a location-specific enterprise. That is, it must be conducted in a given ecosystem if it is to be applicable to the conditions within that ecosystem. Since such ecosystems do not coincide with state boundaries, research benefit spillovers will be created as farmers outside 101 the funding state adopt the new technology generated by research. In.addition, the inelastic nature of the supply and demand for many farm commodities, along with the atomistic nature of farming, suggests that a preponderance of the benefits of agricultural research will accrue to consumers in the form of lower prices. Since the majority of these consumers will reside outside the funding state, spillovers will again be created. As a result, federal matching grants may be required if a nationally optimal level of investment in agricultural research is to be achieved. To determine the matching rates needed to finance agricultural research, the marginal product of research that accrues inside and outside the funding state must be estimated. These estimates must then be incorporated into a public finance model to determine the optimal matching rate for financing agricultural research. Chapter III will use the literature reviewed.here to provide (1) a model of optimal matching grants that can be used to finance public goods that generate benefit spillovers and (2) a production function model that provides estimates of the marginal product of research that accrues inside and outside each state from research funded by that state. The empirical results of the second model, when combined with the theoretical results of the first model, will yield ‘the optimal matching' rates necessary to finance agricultural research. 1. 102 No e t I Adam Smith, for example, cited as a legitimate function of government the support of those public institutions and those public works, which, though they may be in the highest degree advantageous to a great society, are, however, of such a nature, that the profit could never repay the expence [eie] to any individual or small number of individuals, and which it therefore cannot be expected that any individual or small number of individuals should erect or maintain (Smith, p. 681). Alfred Marshall (pp. 208-16), Sidgwick (pp. 464-67), Bastable (pp. 86-100), Say (pp. 283-84, 373-400), and Adams (pp. 26-36) also discussed the public nature of some goods. Several early essays on public goods and public finance are also published in Musgrave and Peacock. Sidgwick had earlier used similar terms to justify the public support of research: A modern university, however, is not merely an institution for imparting special kinds of knowledge for professional purposes; it.has also the function of advancing knowledge generally and facilitating its acquisition by students whose aims are purely scientific. This speculative pursuit of knowledge is to a large extent--and to an extent incapable at any given time of being definitely determined--indirectly useful to industry; and since, as was before noticed, its results cannot usually be appropriated and sold, there is an obvious reason for remunerating the labor required to produce these results, and defraying the expenses incidental to the work, out of public funds--at any rate if a provision adequate for the purpose is not available from private sources (Sidgwick, pp. 466-67). While Pigouvian taxes and subsidies can internalize external costs and. benefits, such. claims of social optimality must also be considered "narrow and selective" (Samuels, 1976b, p. 413). For’ while a subsidy may solve the "free rider" problem (i.e., it compensates the producer for the benefits provided to those persons who use the service but who did not contribute to its cost) the use of subsidies also raises the problem of the "unwilling rider" who must pay taxes to provide a subsidy for a good he does not want. To 103 prescribe the use of subsidies to correct the free rider problem, while ignoring the unwilling rider, requires a normative assumption that places high value on the welfare of free riders and low value on the welfare of unwilling riders (Schmid, 1978, pp. 44-48, 52, 56, 86). Bastable (p. 99) had earlier cited "model institutions, such as agricultural schools" as an appropriate function of government. Earlier authors identified the indivisible nature of public goods, but were divided on whether it was possible to assess taxes in such a manner that each person would contribute to the supply of such goods based on his share of the total marginal utility derived from such goods. Mazzola (pp. 42-44) and Sax (pp. 180-83) argued such taxes could be levied, while Wicksell (p. 81) and Barrone (pp. 165-67) argued, like Samuelson, that self-interested individuals would not make such contributions and that underinvestment in such goods would result. Any argument in favor of the use of intergovernmental grants must recognize the interpersonal welfare comparisons that are required in determining the "optimal" level of investment in a public good. Some economists reject the possibility of such comparisons on the grounds that (a) all costs are subjective and known only to individual decision makers at the time decisions are made: (b) market prices do not reflect subjective costs accurately since nonmonetary factors may affect the individual's true costs: and (c) central decision makers cannot ascertain the true costs (including all relevant.production relationships and utility functions) of all individuals as accurately or quickly as such costs can be expressed in the market. Thus, collective decision-making cannot hope to make the economic calculations necessary'to allocate resources efficiently (von. Mises, 1935: 1963, pp. 698-715: Hayek, 1935a: 1935b: 1937: 1945: Vaughn). Adopting the subjective theory of cost, Buchanan argues that only a collective system that uses a unanimous decision rule can produce Pareto optimal decisions that approximate the decentralized decisions of the market (an argument made originally by Wicksell) . Under certain conditions, however, Buchanan concedes that collective action under a less-than-unanimous voting rule may be preferable to individual transactions or unanimous voting. First, he recognizes that individual negotiations may break down when (a) the number of persons involved is sufficiently large that transaction costs prevent the negotiation and enforcement of private exchanges or (b) the number of persons involved is sufficiently large that individuals will not recognize or will ignore the effects of their 8. 104 decisions on others and will choose to "free ride" on the collective activities of other parties. Second, when collective action is required, Buchanan concedes that less-than-unanimous voting rules may be necessary, since unanimous rules will become prohibitively expensive in the legislative process and will provide an opportunity for strategic behavior by some parties. Thus, Buchanan provides conditions under which less-than-unanimous collective action is preferable to individual exchange or unanimous voting (Buchanan, 1965, pp. 1-13: 1969, pp. 12-13, 27-41; 1968, 87-95: 1972, pp. 439-52: Wicksell, pp. 87-97). These are the conditions (i.e., large numbers of participants and widely dispersed benefits) under which agricultural research policy is made. A variety of views have developed on what the community indifference curves used in this grant analysis represent. One view is that the indifference curves are those of a "representative citizen." This view may not hold true, however, if the grants will produce a redistribution of income through the provision of selected goods, thereby changing the identity of the representative citizen. A second view is that the indifference curves represent those of the median voter (since this is the voter who will cast the decisive vote in allocating resources between private and.public goods under a majority-vote decision rule). As with the "representative citizen" case, this view can only be true if the same person is the median voter before and after the grant is given (Goetz and McKnew). The third and perhaps most acceptable view is that the indifference curves are those of the recipient legislature. This view can only hold true, however, if it is assumed that the preferences of the citizenry are reflected accurately in the legislature or that the legislature is authorized to make judgments on the social welfare of its citizens (Scott, pp. 381-94). This view is supported by Bradford and Oates' demonstration that under certain conditions (fixed tax shares in the jurisdiction, majority rule in the legislature, and standard assumptions about the shape of individuals' indifference curves) a grant to the legislature is equivalent to a grant to each individual in the jurisdiction (Bradford and Oates, 1971a, pp. 416-39 and 1971b, pp. 440-48). Such indifference curves are also consistent with the view of social indifference curves developed by Samuelson (1956). A noteworthy example of the price effect of matching grants ‘may have occurred after' the passage. of the Smith-Lever Act of 1914, which.provided.matching federal grants in support of state agricultural extension activities. As the theory of intergovernmental grants 105 would predict, when the Smith-Lever Act made the cost of extension activities less expensive relative to the cost of research activities (which did not have matching grant support), growth in state appropriations for research declined and growth in state appropriations for extension increased. This represented a substantial shift from prior funding patterns: The record shows that with 1914 the States ceased adding to [ experiment ] station appropriations, in marked contrast to the practice up to that time. In each of the three five-year periods immediately preceding 1914 the total State appropriation practically doubled, or increased in an even greater ratio (Allen, p. 2). This decline in research funding soon led to calls by experiment station directors for new legislation that provided matching grants for research: The Smith-Lever and the Smith-Hughes Acts, in which the Federal government offers to match dollars with the State government to promote agricultural extension and vocational education, place the experiment station under a handicap in securing appropriations from the State legislature, unless the same system is used for all. Members of the legislature unfamiliar with the purposes of different agricultural activities and interested mainly in other questions are not likely to discriminate between various lines of agricultural work. If they match dollars with.the Federal government in one and not in the other they are likely to give most support to activities in which one dollar will do the work of two. It is necessary, therefore, to secure new Federal legislation placing the experiment stations upon the same basis as the extension service before we can expect. adequate: support from. 'the States (Burnett, p. 99). It was also recognized that matching grants were required to address the problem of benefit spillovers: First, there is the fundamental reason that the results of agricultural research are of nation-wide application and benefit and lead to increased wealth and happiness for all the people. Agricultural products are grown for interstate or international use. The people of many of our States are largely dependent upon the products of the farms of other States for 10. 106 their food, clothing, etc. Hence, it is right that Federal funds should be available for the support of this work. In the second place, agricultural research is peculiarly long-time and continuous in character and provision for its support ought to be such as will secure it from frequent temporary fluctuations in popular whims or legislative emergencies. The Federal Congress has established the principle of continuing long-time appropriations which (while they may, of course, be modified by Congress at any time, by repeal or amendment of the original act) have all the moral force and effect of permanent endowments for agricultural research and permit constructive planning of such research....Next, I think the principle of making' the increased. appropriation available only to those States which provide out of State funds an equivalent sum to be expended for the same purpose, is sound in principle and feasible in practice. It insures that those States which need, and recognize the need for, additional support for agricultural research may get it. While there can be no doubt of the nation-wide, or international, benefits from appropriation of Federal funds for its support, the success in getting these results promptly into practice in actual farm operations depends largely upon local understanding of and interest in the work of the State experiment station. Hence, the local State agencies ought to participate in the support and understanding of the administration of the experiment station research work....The suggestion that the individual States be permitted to determine whether they will accept the whole or only part of the funds to be made available under the proposed plan, seems to be a wise one. This would involve no serious difficulty of administration, either nationally or locally, and.would provide a plan which would adequately adapt the principle of joint Federal and State support to the varying needs and possibilities of the several States (Thatcher, pp. 103-04). It should be noted that the Harford model is a model of one-way spillovers, while the Oates model is a model of reciprocal spillovers. In.a world of one-way spillovers (i.e., if a, equals 0 in equation 2.9 or a, equals 0 in equation 2.10) the Oates model yields the same results as the Harford model. While most of the early authors cited in endnote 1 emphasized the inappropriability of research, Adams, 11. 12. 107 like Arrow, stressed that the state could better support research because its ability to bear risk gave it a lower discount rate: It is certain that every true discovery and every talent developed.will sooner or later find their place in the economy of industry and react upon the life and aims of the people. Such a view is, from the nature of the case, foreign to the individual who, conscious that life is fleeting, is constrained to judge every investment on.the basis of proximate rather than ultimate results (Adams, p. 30). This view was expressed by Frank Knight (1924) in his response to Pigou. In Knight's view, any divergence in private and social costs or benefits is due to the failure of government to fulfill its role in defining property rights. Harry Johnson (1976) used a graphical model of firm behavior under a patent system to arrive at the following propositions: (a) Any innovation that is profitable to the innovator will be socially beneficial, regardless of whether the welfare of the innovator is included in the welfare of society. (b) The reverse is not true. An innovation might be socially profitable to invest in, but not privately profitable to develop: consequently the patent and license system will not make all of the socially desirable investments in research. This proposition is supported by studies that indicate private sector researchers will prefer to participate in joint public-private research projects that maximize the private benefits of the firm rather than social benefits (Ulrich, et al., 1986). (c) Where an innovation is profitable to introduce, it will be under-utilized from a social point of view. (d) Where there is a choice between a cheaper but less productive and a more expensive but more productive innovation, the patent system. biases innovative investment towards the less productive but cheaper alternative. (e) Research investment will be biased towards "applied" research and away from "basic" research whose benefits are likely to be more dispersed. (f) Innovative investment will tend to be wasteful in two respects. First, excessive resources will be devoted to certain kinds of innovation, in the form of duplication of effort. Second, some innovations will be introduced too rapidly from a societal perspective (Harry Johnson, 1976, pp. 31-36). Other 13. 14. 108 economists have developed this proposition in more detail (see endnote 14 below). This view is also consistent with the early history of research at the land-grant colleges. Consider, for example, the (difference in. the development of agricultural research and engineering research. While agricultural research was supported by the public sector, historian Edward Eddy notes that engineering research was poorly supported at the land-grant colleges. While each state had an agricultural experiment station in 1888 (or as soon thereafter as the state became eligible) the first engineering experiment station did not come into existence until 1903. By 1940 there were 46 engineering stations, but, despite occasional efforts to secure federal funds, engineering research did not gain substantial funding until general research appropriations began to increase after World War II. Eddy explains this lack of engineering support as the result of (a) the lack of an effective political organization, such as the Association of American Agricultural Colleges and Experiment Stations, to present the political case for public support of engineering research, and (b) the presence of an effective patent system that allowed private firms to capture sufficient returns to support industrial research, thereby lessening the demand for public support of engineering research. Whether the unequal development of engineering and agricultural research at the land-grant colleges was due to political or economic factors remains a question for historians and economists to address, but it must be noted that much of the early engineering research was in areas that private firms could not support--e.g., the development of industrial tests, grades, and standards or the lessening of industrial pollution (Eddy, pp. 100, 127-129, 172-174, 233-35). Thus, it must be concluded that early research at the land-grant colleges developed along the lines suggested by economic theory (i.e., in areas of atomistic competition, such as agriculture, or in areas where industrial firms could not justify research investments given the limitations of the patent system). It should also be noted that there are some theoretical reasons why a patent system may lead to overinvestment in research. Eads (pp. 5-6) concludes that overinvestment in research (i.e., the private rate of return on research. will exceed the social rate of return) will result when firms compete on the basis of product differentiation rather than price. Similarly, Schmid (1985, p. 132) has argued that a patent system may lead to excessive investment in "cosmetic" innovations in some areas of plant breeding. Plant (p. 51) has argued that research overinvestment may arise 15. 109 when the social costs of obsolete physical and human capital caused by new inventions are considered. Usher (p. 287) has argued that a patent system may cause overinvestment in research, since inventors must race to be the first to apply for a patent, thereby resulting in a wasteful duplication of research efforts. Usher's argument has been formalized by other economists (Barzel: Kitti: Brian Wright, pp. 49-51). These models reach the common conclusion that the race to attain a patent may cause firms to overinvest in research and introduce the invention at the privately optimal date (the date when the private return from the research equals zero, since all inventors introducing the invention after that date will be denied a patent and will suffer a loss due to the wasted research investment) rather than the later socially optimal date (defined as the date upon which the private return to the research investment is maximized). However, such models assume that the entire benefit of research is captured by the inventor. If a share of the research benefits accrue to consumers, underinvestment may still persist under a patent system (Barzel, p. 354). The problem of location specificity was well understood at the time of the writing of the Hatch Act of 1887. The regionalization of production that was occurring at the time led historian Margaret Rossiter (p. 157) to observe: Connecticut with its relatively poor land for grain and corn was rapidly losing its remaining markets to western competition. Economic pressures forced Connecticut agriculture back on its comparative geographical advantage in supplying eastern cities. After 1860 those farms that were not abandoned turned increasingly to such perishable food products as fruits, eggs, and dairy products and to other crops, such as hay, which would not pay the long cost of transportation. The rise of such a specialized commercial agriculture required a more precise knowledge of crops, costs, and methods of cultivation and was a great spur to agricultural reform in Connecticut in the late 1860's [including the establishment of the first agricultural experiment station in the United States]. Congress also understood the need for a geographically decentralized research system, as shown by the report of the House Committee on Agriculture on the Hatch bill: Experiments in the Agricultural Department at Washington are reliable only for such portions 16. 110 of the country as present the same conditions of temperature, moisture, soil, etc.... Agriculture is so variable in the different States that it is impracticable for one station to cover the field of needed investigation. The cotton and rice States have their climate, their peculiar crops, their insect enemies, and their special problems. The great prairie States have their peculiar wants and difficulties, and so of the several sections. Experiments that are at all reliable can only be performed in the several localities and under their varying conditions.... When we consider the vast area of our country it will not be seriously contended that one station in each state would be too many (U. 8. Congress, 1887, Appendix, p. 121). W. B. Kemp, Director of the Maryland Agricultural Experiment Station, would later describe the varying conditions in his state: The problems on which information is asked are doubly complicated.because of varying conditions even within a single State. In one as small as Maryland with less than 10,000 square miles of land area there are.4 different geological zones with more than 300 distinct soil types and classes named to date, with mean precipitation varying from 20 to 30 inches during the growing season and with the period between killing frost varying from 120 days in one section to 210 days in another. No one fertilizer practice: no one seeding mixture: no one set of variety recommendations can apply over such a range of conditions (U. S. Congress, 1946b, p. 55). Three additional benefits that accrue from a decentralized research system should also be noted. First, Nelson (1961) developed a cost minimization model that showed a decentralized research system may be the most efficient system possible when several promising opportunities exist for solving a scientific problem. The long run cost of research may be reduced as the information 'produced by parallel research efforts improves the ability of research managers to select the most promising solution. Second, Hardin (pp. 27-29) surveyed the history of federal-state relations in funding agricultural research and concluded that the joint responsibility of funding research has helped protect the experiment stations from political manipulation. By seeking to protect its investment in the stations, each level of government acts as a countervailing balance to prevent the political interference of the other in experiment station affairs. 17. 18. 111 Third, a federal system of government can provide a laboratory in which local jurisdictions experiment with public services before they are funded by the federal government. Such experimentation often provides a test of the desirability of public services and the administrative tools necessary for successful execution of new programs (Maxwell, p. 117). Indeed, many services (including agricultural research) now provided jointly by the federal government and the states were originally provided solely by the states (Maxwell, p. 117: Key, pp. 1-7: True). Tiebout developed a model of local government finance that indicates that consumers of public services register their preferences by "voting with their feet" (i.e., by moving to the jurisdiction that provides them with the combination of services and taxes that maximizes their utility). However, agricultural research violates two key assumptions of the Tiebout model, namely, the free mobility of citizens and the absence of spillover benefits. Clearly, farmers are limited in their ability to register their demand for more agricultural research by the high cost of disinvesting at their present location and moving to another state, and individual food consumers cannot capture a greater share of research benefits simply by moving to another state. When such spillovers and high relocation costs exist, Tiebout concludes, a system of intergovernmental grants may be justified. Indeed, Stiglitz (1983, p. 48) cited scientific research as a classic example of a public good whose provision cannot be assured by' the. Tiebout model and that must be provided exclusively or jointly by the national government. Further development of the Tiebout model has also revealed that it may be of limited use in providing an optimal quantity of public goods (Pestieau: Bewley: Stahl and‘Varaiya: Zodrow: Stiglitz, 1977, 1983: Rose-Ackerman). Any discussion of investment in publicly-provided goods must consider the political structure in which public resource allocation decisions are made, since this structure may contribute to either an underinvestment or overinvestment in public goods. The diffuse and uncertain nature of public good benefits, combined with the high cost of gathering information on such benefits and the low cost of assessing the tax costs of such goods, may worsen the underinvestment problem by distorting the perceived costs and benefits of publicly-provided goods (Downs, pp. 546-54: Harry Johnson, 1968, p. 12: Margolis, 1964, pp. 237-38: Olson, 1965, pp. 43-52). Margolis (1961, p. 270) hypothesizes that the local control of intergovernmental grants may overcome the resistance of local taxpayers more easily 112 than would shifting the function to a higher level of government. If so, intergovernmental grants may be especially useful in correcting the information bias of taxpayers. Similarly, Douglas (1920a, p. 257) observed that the organizational costs of collective action may be reduced by passing legislation in the national legislature rather than each of the state legislatures. If so, intergovernmental grants may the most appropriate tool for both maintaining local control of a program and overcoming the political transaction costs of establishing the program. The underinvestment problem may also persist because advertising creates a bias in favor of private goods (Galbraith, pp. 221-38: Olson, 1964, p. 250). Overinvestment in publicly-provided goods may result when decisions are based on bureaucratic self-interest rather than social welfare. That is, bureaucrats may have an incentive to maximize their own welfare, and therefore their budgets, rather than any democratically- determined notion.of public welfare (McKean, pp. 247-48: Niskanen, 1968, 1971: Harry Johnson, 1968, p. 12: DeAlessi: Shapiro: Orzechowski: Staaf). The possibility of overinvestment in public goods also arises when voters suffer from "fiscal illusion" (i.e., when voters underestimate the true cost of public goods because part of the cost. of such. goods is imposed indirectly). Fiscal illusion.may arise when public goods are financed by indirect taxation, public ownership of income-generating property, inflation, public«debt, gift or luxury taxes, and. taxes on specific classes of individuals (Buchanan, 1960, pp. 59-64: Goetz, pp. 176-85). Fiscal illusion. may also occur' when the benefits or costs of a publicly-provided good are unevenly distributed among voters (Downs, pp. 556-59: Buchanan and Tullock, p. 169: Buchanan, 1961, 1967, pp. 126-43). This version of the overinvestment hypothesis views intergovernmental grants as a means of shifting the cost of local public goods to outside taxpayers, thereby creating an illusion of inexpensive local public goods and leading to overinvestment in such goods (Brennan and Buchanan, pp. 179-186). Overinvestment.may also result when the political structure permits the use of logrolling to reach decisions that provide mutual benefits to the logrollers at the expense of third parties (Davis and Meyer: Tullock, 1959). Overinvestment may also be encouraged by the use of a representative legislature for allocation decisions. Such a structure may permit a minority of voters to pass legislation which a majority of voters oppose when the minority is a majority of voters in a majority of represented jurisdictions (Tullock, 1970, p. 423). CHAPTER III A MODEL OF OPTIMAL COST-SHARING FOR STATE AND FEDERAL INVESTMENTS IN AGRICULTURAL RESEARCH This chapter presents a model for determining the optimal cost-sharing arrangements for investments in public agricultural research in the United States. First, the critical assumptions of the model are identified. Second, a public finance model for financing an optimal level of investment in agricultural research in the presence of benefit spillovers is specified. The model employed here is a simplified version of the Harford model presented in Chapter II. This model yields the optimal federal matching rate for financing agricultural research (i.e., the rate at which the federal government should. match state spending for agricultural research in order to achieve a nationally optimal level of research investment). To make this public finance model operational, the share of the marginal product of research that accrues outside the funding state must be estimated. Thus, the third section of this chapter presents a production function model capable of estimating agricultural research benefit spillovers. Finally, the data used to estimate the production function model will be presented. 113 114 C ' t o e Any analysis of economic policy is conditioned by the positive and normative assumptions implicit in the analysis. Only by identifying such assumptions can the limitations of policy analysis be known. This section.presents the critical assumptions underlying this study. These assumptions are drawn from both the public finance literature on intergovernmental grants and the literature on the returns to agricultural research. The assumptions of this analysis include: 1. The objective of publicly-funded agricultural research is the maximization of the net monetary benefit of research: 2. The resources displaced by technology resulting from public investments in agricultural research have no value and receive no compensation: 3. The results produced by public investments in agricultural research have value in use but no value in consumption (i.e. , the value arising from research results from its application, not from the mastery of knowledge for its own sake): 4. Legislators at each level of government act with perfect, costless knowledge in a rational, maximizing manner within their jurisdiction, or (a) state legislators ignore benefits that accrue to other states when making state-level research investment decisions, and (b) national legislators ignore 115 benefits that accrue to other nations when making national-level research investment decisions: The marginal cost of an additional dollar of public research investment is constant and equal to one dollar (i.e. , the marginal burden of taxation is zero and the supply of research inputs purchased with public funds is perfectly elastic): The full incidence of all taxes falls on the jurisdiction imposing the tax (i.e., the full incidence of each state's taxes falls within the state and the full incidence of national taxes falls within the United States): The taxes imposed by state and national governments in support of agricultural research do not have a significant effect in reducing income in the taxing jurisdiction and do not distort the prices of private and public goods in the economy (i.e. , the total size of the public agricultural research budget is insignificant when compared to the total income of each state and the nation): Except for the changes in the federal matching rate for state agricultural research investments, the institutional structure of the economy remains fixed: The same spillover pattern (i.e., the share of research benefits retained by each state) will exist in the future as existed during the period for which such spillovers are estimated in the model: 116 10. The market prices of inputs used in agricultural production reflect the social value of those inputs (i.e. , there are no externalities associated with any input).‘ Chapter VI will review these assumptions and examine the limitations they impose on the results of this research and on the prescriptive validity of this research. 0 s -S ' M r A 'cultural Reeeazen witn Benefit Spillovets Chapter II reviewed the public finance literature on the economics of intergovernmental grants and concluded (1) that the least-cost method of financing public goods that generate benefit spillovers across governmental jurisdictions is through the use of a matching grant from a higher level of government.to the lower level unit of government, and (2) that the matching rate of such a grant should reflect the share of the total marginal benefit that accrues tijersons outside the jurisdictional boundaries of the lower level of government. In the case of agricultural research, the federal government would provide a matching grant to each state that is based on the share of the marginal benefit of research that accrues outside the funding state. The model of optimal public investment used in this research is a modified version of the Harford model. More specifically, it is a simplified version of the Harford model, since the Harford model deals with three levels of government, 117 while the model used here deals with only two levels of government (the national government and the states). This model maximizes total national research.benefits by providing federal subsidies to the states based on the share of research benefits that spill across state lines. For each state, the model has two equations: (3.1) B(X) - C(X) (The National Net Benefit Equation) (3.2)¢n*B(X) - (1 - sJ*C(X) (The State Net Benefit Equation). Where: B(X) = The benefit function of agricultural research: C(X) = The cost function of agricultural research: in = The share of research benefits that accrue to state i as a result of research conducted in state i: s. == The share of the cost of research conducted in state i paid by the federal government: X = Funds spent on agricultural research in state i. The optimal share of the.cost of research in state.i that would be paid by the federal government can be determined by maximizing the state and national net benefit equations. Differentiating equations (3.1) and (3.2) provides: (3-3) Q3131 - _QIXI = 0 dX dX (3.4) esteem) - (1 - some“) = o. dX dX 118 Solving (3.3) and (3.4) simultaneously and rearranging provides the optimal share of the cost of research in state i that would be paid by the federal government: (3.5) s. = l - 0.. Thus, the share of the cost of research paid by the federal government varies directly with the proportion of marginal research benefits that spill out of state i. This result is consistent with the literature on intergovernmental grants reviewed in Chapter II. Since the intergovernmental grant used here is a matching grant, equation ( 3.5) should be expressed as a matching rate. The optimal federal matching rate implied by equation (3.5) is: (3.6) m. = (l - a.)/a.. Thus, to achieve the nationally optimal level of investment in agricultural research, the federal government should provide m. dollars to state i for every dollar of agricultural research funding provided by state i. A Mode; of Agrieuitutal Research Benefit Spillovers The major task of this investigation now becomes the measurement of the share of the marginal product of agricultural research that is retained by the funding state (i.e., the estimation of ‘the = . 10, .20, or .30). Column 3 shows the share of the total marginal product of research that is retained by the state 1 (ad. This share was calculated as Column 1/(Co1umn 1 + Column 2) from equation (5.3): (5.3) a. = MPR,/MPR,. 272 The optimal matching rate (Column 4) is then calculated as (1 - Column 3)/Column 3 as shown in equation (5.4): (5.4) m. = (1 - a,)/a.. To provide clarity, the discussion of one sample calculation that was presented in Chapter V will be repeated here. Using the 1982 cross-section data, the optimal matching rate for the state of Alabama will be calculated using the assumptions that (1) the pervasiveness weight is .10, and (2) the states neighboring Alabama (Florida, Georgia, Mississippi, and Tennessee) are the states in which Alabama's research is relevant (shown in Table 8.1). Equation.(5.1) yielded a marginal product of research of $24.82 for Alabama. This indicates that an additional dollar of research spending in Alabama would have yielded a marginal product of $24.82 within Alabama. The pervasiveness weight of .10, it should.be recalled, assumed.that.the additional dollar of research spending in Alabama also provided 10 cents worth of research spending that was relevant in Florida, Georgia, Mississippi, and Tennessee, whose marginal products were calculated (using equation 5.1) to be $20.36, $23.13, $27.22, and $20.24, respectively. Thus, the additional dollar of research spending in Alabama also yielded marginal products of $2.03 in Florida, $2.31 in Georgia, $2.72 in Mississippi, and $2.02 in Tennessee (calculated as the .10 pervasiveness weight times the marginal product in these states from the second term.on the right hand side of equation 5.2 above), for 273 a total marginal product of research spending in Alabama of $33.90 (calculated as $24.82 + 2.03 + 2.31 + 2.72 + 2.02 from equation 5.2). The share of marginal research benefits retained by Alabama ((2,) equals .73 (calculated as $24.82/$33.90 from equation 5.3). This indicates that the optimal matching rate for Alabama under this scenario is .37 (calculated as [1-.73]/.73 from equation 5.4). 274 Table B.1: Calculation of Optimal Matching Rates for Neighboring States Specification (0 = 0.10), 1982 Cross-section Matching State MPR, MPR, a, Rate Alabama 24.83 9.10 0.73 0.37 Arizona 17.35 7.05 0.71 0.41 Arkansas 31.90 18.80 0.63 0.59 California 39.57 3.58 0.92 0.09 Colorado 20.25 16.45 0.55 0.81 Florida 20.36 4.80 0.81 0.24 Georgia 23.14 8.26 0.74 0.36 Idaho 32.32 9.73 0.77 0.30 Illinois 78.21 23.04 0.77 0.29 Indiana 37.81 17.58 0.68 0.47 Iowa 87.77 29.37 0.75 0.33 Kansas 45.36 13.73 0.77 0.30 Kentucky 32.46 23.14 0.58 0.71 Louisiana 16.17 11.49 0.58 0.71 Maryland 26.77 5.67 0.83 0.21 Michigan 26.68 11.25 0.70 0.42 Minnesota 53.01 20.15 0.72 0.38 Mississippi 27.23 9.31 0.75 0.34 Missouri 36.16 28.91 0.56 0.80 Montana 27.42 12.09 0.69 0.44 Nebraska 48.56 15.44 0.76 0.32 Nevada 3.81 11.36 0.25 2.98 New Jersey 9.10 5.16 0.64 0.57 New Mexico 17.37 12.58 0.58 0.72 New York 15.38 4.53 0.77 0.29 North Carolina 25.69 7.58 0.77 0.29 North Dakota 35.97 12.20 0.75 0.34 Ohio 38.49 13.84 0.74 0.36 Oklahoma 32.37 20.68 0.61 0.64 Oregon 14.59 10.63 0.58 0.73 Pennsylvania 36.20 9.50 0.79 0.26 South Carolina 17.14 4.88 0.78 0.28 South Dakota 41.59 17.60 0.70 0.42 Tennessee 20.25 21.67 0.48 1.07 Texas 55.79 9.78 0.85 0.18 Utah 9.75 8.48 0.53 0.87 Virginia 15.25 11.04 0.58 0.72 Washington 30.63 4.69 0.87 0.15 West Virginia 5.28 14.92 0.26 2.83 Wisconsin 36.16 24.57 0.60 0.68 WYoming 11.06 13.13 0.46 1.19 Source: Author. 275 Table 8.2: Calculation of Optimal Matching Rates for Neighboring States Specification (0 = 0.20), 1982 Cross-section Matching State MPR, MPRo a. Rate Alabama 20.51 16.48 0.55 0.80 Arizona 14.99 13.32 0.53 0.89 Arkansas 26.22 33.22 0.44 1.27 California 43.23 6.00 0.88 0.14 Colorado 18.97 28.36 0.40 1.50 Florida 21.39 8.28 0.72 0.39 Georgia 20.89 14.37 0.59 0.69 Idaho 27.63 17.53 0.61 0.63 Illinois 68.15 41.91 0.62 0.61 Indiana 36.71 30.88 0.54 0.84 Iowa 83.51 51.70 0.62 0.62 Kansas 42.76 23.63 0.64 0.55 Kentucky 26.05 40.36 0.39 1.55 Louisiana 15.29 21.57 0.41 1.41 Maryland 23.14 9.96 0.70 0.43 Michigan 24.96 21.29 0.54 0.85 Minnesota 50.88 36.74 0.58 0.72 Mississippi 24.93 15.45 0.62 0.62 Missouri 28.79 49.76 0.37 1.73 Montana 25.21 20.21 0.56 0.80 Nebraska 45.20 25.85 0.64 0.57 Nevada 2.49 21.32 0.10 8.57 New Jersey 8.07 9.70 0.45 1.20 New Mexico 12.62 23.17 0.35 1.84 New York 16.41 8.03 0.67 0.49 North Carolina 26.59 12.96 0.67 0.49 North Dakota 34.67 21.42 0.62 0.62 Ohio 35.23 24.72 0.59 0.70 Oklahoma 25.22 37.21 0.40 1.48 Oregon 12.50 20.96 0.37 1.68 Pennsylvania 32.08 17.33 0.65 0.54 South Carolina 14.73 9.50 0.61 0.64 South Dakota 31.00 32.74 0.49 1.06 Tennessee 15.22 37.58 0.29 2.47 Texas 56.68 15.87 0.78 0.28 Utah 8.24 14.37 0.36 1.74 Virginia 13.94 18.95 0.42 1.36 Washington 31.46 8.03 0.80 0.26 West Virginia 3.77 26.09 0.13 6.92 Wisconsin 34.50 45.50 0.43 1.32 Wyoming 7.75 22.21 0.26 2.86 Source: Author. 276 Table 8.3: Calculation of Optimal Matching Rates for Neighboring States Specification (4 = 0.30), 1982 Cross-section Matching State MPR, MPRo a. Rate Alabama 16.78 21.71 0.44 1.29 Arizona 12.60 18.52 0.40 1.47 Arkansas 21.39 43.12 0.33 2.02 California 43.44 7.46 0.85 0.17 Colorado 16.81 36.08 0.32 2.15 Florida 20.74 10.45 0.67 0.50 Georgia 18.05 18.51 0.49 1.03 Idaho 23.07 23.08 0.50 1.00 Illinois 57.58 54.99 0.51 0.96 Indiana 33.40 39.42 0.46 1.18 Iowa 74.87 66.44 0.53 0.89 Kansas 38.07 29.93 0.56 0.79 Kentucky 20.97 51.49 0.29 2.46 Louisiana 13.65 28.98 0.32 2.12 Maryland 19.46 12.72 0.60 0.65 Michigan 22.11 28.54 0.44 1.29 Minnesota 45.91 48.38 0.49 1.05 Mississippi 21.75 19.10 0.53 0.88 Missouri 23.07 62.92 0.27 2.73 Montana 22.07 25.29 0.47 1.15 Nebraska 39.90 32.34 0.55 0.81 Nevada 1.82 28.92 0.06 15.91 New Jersey 6.89 13.06 0.35 1.90 New Mexico 9.66 30.85 0.24 3.19 New York 16.13 10.29 0.61 0.64 North Carolina 25.46 16.32 0.61 0.64 North Dakota 31.38 27.60 0.53 0.88 Ohio 30.74 32.03 0.49 1.04 Oklahoma 19.97 48.74 0.29 2.44 Oregon 10.45 29.48 0.26 2.82 Pennsylvania 27.40 22.83 0.55 0.83 South Carolina 12.35 13.05 0.49 1.06 South Dakota 24.01 43.53 0.36 1.81 Tennessee 11.84 47.89 0.20 4.05 Texas 53.45 19.40 0.73 0.36 Utah 6.83 18.04 0.27 2.64 Virginia 12.15 24.18 0.33 1.99 Washington 29.94 10.06 0.75 0.34 West Virginia 2.86 33.22 0.08 11.61 Wisconsin 31.00 60.14 0.34 1.94 Wyoming 5.84 27.84 0.17 4.77 Source: Author. 277 Table 8.4: Calculation of Optimal Matching Rates for Production Region Specification (0 = 0.10), 1982 Cross-section Matching State MPR. MPRo a. Rate Alabama 26.90 6.15 0.81 0.23 Arizona 19.12 12.18 0.61 0.64 Arkansas 41.58 4.80 0.90 0.12 California 39.51 3.99 0.91 0.10 Colorado 21.68 11.93 0.65 0.55 Florida 19.97 6.84 0.74 0.34 Georgia 25.89 6.25 0.81 0.24 Idaho 31.61 10.94 0.74 0.35 Illinois 83.40 20.55 0.80 0.25 Indiana 37.51 25.14 0.60 0.67 Iowa 85.33 20.36 0.81 0.24 Kansas 48.41 13.64 0.78 0.28 Kentucky 37.63 7.41 0.84 0.20 Louisiana 17.91 7.17 0.71 0.40 Maryland 21.08 5.91 0.78 0.28 Michigan 28.48 9.64 0.75 0.34 Minnesota 56.78 6.81 0.89 0.12 Mississippi 30.07 5.95 0.83 0.20 Missouri 44.59 24.43 0.65 0.55 Montana 23.37 11.76 0.67 0.50 Nebraska 53.55 13.12 0.80 0.25 Nevada 5.34 13.56 0.28 2.54 New Jersey 7.97 7.22 0.52 0.91 New Mexico 19.07 12.19 0.61 0.64 New York 14.86 6.53 0.69 0.44 North Carolina 25.45 8.63 0.75 0.34 North Dakota 33.27 15.15 0.69 0.46 Ohio 38.05 25.08 0.60 0.66 Oklahoma 47.07 6.13 0.88 0.13 Oregon 15.19 6.42 0.70 0.42 Pennsylvania 36.30 4.39 0.89 0.12 South Carolina 15.67 7.27 0.68 0.46 South Dakota 49.56 13.52 0.79 0.27 Tennessee 28.36 8.34 0.77 0.29 Texas 61.30 4.71 0.93 0.08 Utah 8.80 13.22 0.40 1.50 Virginia 15.58 9.61 0.62 0.62 Washington 24.73 5.47 0.82 0.22 West Virginia 4.70 10.70 0.31 2.28 Wisconsin 39.61 8.53 0.82 0.22 Wyoming 11.98 12.90 0.48 1.08 Source: Author. 278 Table 8.5: Calculation of Optimal Matching Rates for Production Region Specification (0 = 0.20), 1982 Cross-section Matching State MPRI MPRo a. Rate Alabama 25.77 13.09 0.66 0.51 Arizona 19.48 22.60 0.46 1.16 Arkansas 44.22 10.64 0.81 0.24 California 48.08 7.86 0.86 0.16 Colorado 23.75 21.75 0.52 0.92 Florida 23.01 13.64 0.63 0.59 Georgia 28.05 12.63 0.69 0.45 Idaho 29.80 20.54 0.59 0.69 Illinois 84.07 42.32 0.67 0.50 Indiana 40.40 51.06 0.44 1.26 Iowa 88.86 41.36 0.68 0.47 Kansas 53.28 27.48 0.66 0.52 Kentucky 36.09 15.26 0.70 0.42 Louisiana 20.37 15.41 0.57 0.76 Maryland 18.27 12.09 0.60 0.66 Michigan 31.10 21.81 0.59 0.70 Minnesota 63.96 15.24 0.81 0.24 Mississippi 32.33 12.92 0.72 0.39 Missouri 43.77 50.38 0.46 1.15 Montana 21.94 22.11 0.50 1.01 Nebraska 59.55 26.23 0.69 0.44 Nevada 4.15 25.67 0.14 6.19 New Jersey 7.36 14.28 0.34 1.94 New Mexico 15.90 23.32 0.41 1.47 New York 17.17 12.31 0.58 0.72 North Carolina 29.16 16.65 0.64 0.57 North Dakota 33.97 31.34 0.52 0.92 Ohio 38.58 51.42 0.43 1.33 Oklahoma 49.38 15.08 0.77 0.31 Oregon 14.83 14.51 0.51 0.98 Pennsylvania 35.94 8.56 0.81 0.24 South Carolina 14.38 15.36 0.48 1.07 South Dakota 43.89 29.36 0.60 0.67 Tennessee 27.39 17.00 0.62 0.62 Texas 75.41 9.88 0.88 0.13 Utah 7.92 24.92 0.24 3.15 Virginia 16.10 19.26 0.46 1.20 Washington 24.47 12.58 0.66 0.51 West Virginia 3.64 21.75 0.14 5.97 Wisconsin 45.10 19.01 0.70 0.42 Wyoming 9.56 24.59 0.28 2.57 Source: Author. 279 Table 8.6: Calculation of Optimal Matching Rates for Production Region Specification (0 = 0.30), 1982 Cross-section Matching State MPRl MPRo a. Rate Alabama 24.36 20.08 0.55 0.82 Arizona 19.16 31.76 0.38 1.66 Arkansas 44.82 16.70 0.73 0.37 California 54.47 11.34 0.83 0.21 Colorado 24.62 30.12 0.45 1.22 Florida 24.83 19.93 0.55 0.80 Georgia 28.83 18.73 0.61 0.65 Idaho 27.90 29.14 0.49 1.04 Illinois 82.11 62.97 0.57 0.77 Indiana 41.33 75.20 0.35 1.82 Iowa 88.74 60.98 0.59 0.69 Kansas 55.43 40.67 0.58 0.73 Kentucky 34.15 22.93 0.60 0.67 Louisiana 21.75 23.63 0.48 1.09 Maryland 16.32 18.02 0.48 1.10 Michigan 32.16 34.79 0.48 1.08 Minnesota 67.77 24.11 0.74 0.36 Mississippi 33.93 19.97 0.63 0.59 Missouri 42.01 75.00 0.36 1.79 Montana 20.49 31.36 0.40 1.53 Nebraska 62.46 38.56 0.62 0.62 Nevada 3.52 36.45 0.09 10.37 New Jersey 6.81 20.87 0.25 3.07 New Mexico 13.93 33.33 0.29 2.39 New York 18.57 17.34 0.52 0.93 North Carolina 31.32 23.78 0.57 0.76 North Dakota 33.46 47.26 0.41 1.41 Ohio 37.83 76.25 0.33 2.02 Oklahoma 49.57 25.89 0.66 0.52 Oregon 14.18 23.42 0.38 1.65 Pennsylvania 34.69 12.51 0.73 0.36 South Carolina 13.26 23.41 0.36 1.77 South Dakota 39.65 45.41 0.47 1.15 Tennessee 26.03 25.36 0.51 0.97 Texas 86.31 14.87 0.85 0.17 Utah 7.21 35.34 0.17 4.90 Virginia 16.00 28.37 0.36 1.77 Washington 23.61 20.59 0.53 0.87 West Virginia 3.08 32.25 0.09 10.47 Wisconsin 48.21 29.98 0.62 0.62 Wyoming 8.20 35.05 0.19 4.27 Source: Author. 280 Table 8.7: Calculation of Optimal Matching Rates for Neighboring States Specification (0 = 0.10), 1978 Cross-section Matching State MPR, MPR, a. Rate Alabama 8.39 3.14 0.73 0.37 Arizona 7.26 2.66 0.73 0.37 Arkansas 14.38 6.59 0.69 0.46 California 13.31 1.33 0.91 0.10 Colorado 9.74 6.06 0.62 0.62 Florida 7.28 1.70 0.81 0.23 Georgia [8.59 2.73 0.76 0.32 Idaho 12.80 3.50 0.79 0.27 Illinois 27.65 8.50 0.76 0.31 Indiana 13.57 5.91 0.70 0.44 Iowa 32.92 9.89 0.77 0.30 Kansas 17.46 4.92 0.78 0.28 Kentucky 12.65 8.00 0.61 0.63 Louisiana 5.61 4.48 0.56 0.80 Maryland 8.53 1.90 0.82 0.22 Michigan 7.65 3.68 0.68 0.48 Minnesota 16.59 7.24 0.70 0.44 Mississippi 9.60 3.43 0.74 0.36 Missouri 13.80 10.37 0.57 0.75 Montana 9.65 4.57 0.68 0.47 Nebraska 15.43 5.99 0.72 0.39 Nevada 1.32 4.18 0.24 3.17 New Jersey 2.49 1.58 0.61 0.64 New Mexico 8.19 4.80 0.63 0.59 New York 4.79 1.35 0.78 0.28 North Carolina 6.24 2.62 0.70 0.42 North Dakota 14.05 3.97 0.78 0.28 Ohio 11.18 4.69 0.70 0.42 Oklahoma 10.26 8.43 0.55 0.82 Oregon 4.67 3.76 0.55 0.80 Pennsylvania 11.02 2.90 0.79 0.26 South Carolina 5.77 1.48 0.80 0.26 South Dakota 13.45 6.12 0.69 0.45 Tennessee 5.89 7.95 0.43 1.35 Texas 20.79 3.84 0.84 0.18 Utah 3.81 3.66 0.51 0.96 Virginia 5.92 3.53 0.63 0.60 Washington 10.15 1.75 0.85 0.17 West Virginia 2.02 4.93 0.29 2.45 Wisconsin 12.01 8.48 0.59 0.71 Wyoming 5.44 4.94 0.52 0.91 Source: Author. 281 Table 8.8: Calculation of Optimal Matching Rates for Neighboring States Specification (0 = 0.20), 1978 Cross-section Matching State MPR, MPRo a. Rate Alabama 7.81 6.30 0.55 0.81 Arizona 6.90 5.45 0.56 0.79 Arkansas 13.13 13.06 0.50 0.99 California 16.08 2.47 0.87 0.15 Colorado 9.93 11.59 0.46 1.17 Florida 8.49 3.22 0.73 0.38 Georgia 8.28 5.42 0.60 0.65 Idaho 11.97 6.99 0.63 0.58 Illinois 26.97 17.01 0.61 0.63 Indiana 14.31 11.61 0.55 0.81 Iowa 34.78 19.46 0.64 0.56 Kansas 18.11 9.53 0.66 0.53 Kentucky 11.17 15.59 0.42 1.40 Louisiana 5.86 9.20 0.39 1.57 Maryland 8.39 3.66 0.70 0.44 Michigan 8.13 7.73 0.51 0.95 Minnesota 18.07 14.62 0.55 0.81 Mississippi 9.60 6.38 0.60 0.67 Missouri 12.27 19.99 0.38 1.63 Montana 10.08 8.39 0.55 0.83 Nebraska 16.27 11.15 0.59 0.69 Nevada 0.97 8.62 0.10 8.85 New Jersey 2.54 3.29 0.44 1.30 New Mexico 6.55 9.86 0.40 1.51 New York 5.67 2.67 0.68 0.47 North Carolina 7.11 4.99 0.59 0.70 North Dakota 14.57 7.88 0.65 0.54 Ohio 11.80 9.21 0.56 0.78 Oklahoma 9.17 16.65 0.36 1.82 Oregon 4.49 8.12 0.36 1.81 Pennsylvania 10.80 6.01 0.64 0.56 South Carolina 5.68 3.08 0.65 0.54 South Dakota 11.22 12.64 0.47 1.13 Tennessee 5.12 15.04 0.25 2.94 Texas 23.28 6.94 0.77 0.30 Utah 3.64 6.80 0.35 1.86 Virginia 5.86 6.68 0.47 1.14 Washington 11.57 3.29 0.78 0.28 West Virginia 1.62 9.60 0.14 5.92 Wisconsin 12.51 17.59 0.42 1.41 Wyoming 4.20 9.37 0.31 2.23 Source: Author. 282 Table 8.9: Calculation of Optimal Matching Rates for Neighboring States Specification (0 = 0.30), 1978 Cross-section Matching State MPR, MPRo a. Rate Alabama 7.47 9.58 0.44 1.28 Arizona 6.68 8.65 0.44 1.30 Arkansas 12.41 19.69 0.39 1.59 California 18.69 3.57 0.84 0.19 Colorado 10.07 17.10 0.37 1.70 Florida 9.55 4.67 0.67 0.49 Georgia 8.09 8.21 0.50 1.01 Idaho 11.48 10.66 0.52 0.93 Illinois 26.54 25.69 0.51 0.97 Indiana 14.85 17.29 0.46 1.16 Iowa 36.13 29.11 0.55 0.81 Kansas 18.58 14.08 0.57 0.76 Kentucky 10.37 23.11 0.31 2.23 Louisiana 6.03 14.19 0.30 2.35 Maryland 8.30 5.37 0.61 0.65 Michigan 8.48 11.99 0.41 1.41 Minnesota 19.22 22.21 0.46 1.16 Mississippi 9.59 9.19 0.51 0.96 Missouri 11.43 29.42 0.28 2.57 Montana 10.39 12.05 0.46 1.16 Nebraska 16.89 16.15 0.51 0.96 Nevada 0.83 13.43 0.06 16.22 New Jersey 2.58 5.14 0.33 1.99 New Mexico 5.78 15.18 0.28 2.63 New York 6.47 3.97 0.62 0.61 North Carolina 7.84 7.27 0.52 0.93 North Dakota 14.94 11.92 0.56 0.80 Ohio 12.25 13.74 0.47 1.12 Oklahoma 8.56 25.07 0.25 2.93 Oregon 4.38 13.13 0.25 3.00 Pennsylvania 10.65 9.31 0.53 0.87 South Carolina 5.62 4.78 0.54 0.85 South Dakota 10.11 19.52 0.34 1.93 Tennessee 4.71 21.90 0.18 4.65 Texas 25.30 9.83 0.72 0.39 Utah 3.54 9.81 0.27 2.77 Virginia 5.81 9.80 0.37 1.68 Washington 12.76 4.76 0.73 0.37 West Virginia 1.43 14.22 0.09 9.92 Wisconsin 12.87 27.11 0.32 2.11 Wyoming 3.64 13.68 0.21 3.75 Source: Author. 283 Table 8.10: Calculation of Optimal Matching Rates for Production Region Specification (0 = 0.10), 1978 Cross-section Matching State MPR. MPRo a. Rate Alabama 5.45 1.34 0.80 0.25 Arizona 4.91 3.12 0.61 0.64 Arkansas 11.23 1.02 0.92 0.09 California 7.96 0.79 0.91 0.10 Colorado 6.25 2.99 0.68 0.48 Florida 4.26 1.46 0.74 0.34 Georgia 5.93 1.29 0.82 0.22 Idaho 7.80 2.83 0.73 0.36 Illinois 17.41 4.44 0.80 0.25 Indiana 8.10 5.37 0.60 0.66 Iowa 19.42 4.24 0.82 0.22 Kansas 11.22 2.82 0.80 0.25 Kentucky 8.72 1.31 0.87 0.15 Louisiana 3.72 1.77 0.68 0.48 Maryland 4.04 1.09 0.79 0.27 Michigan 4.78 1.83 0.72 0.38 Minnesota 10.41 1.27 0.89 0.12 Mississippi 6.45 1.49 0.81 0.23 Missouri 10.16 5.16 0.66 0.51 Montana 5.00 3.11 0.62 0.62 Nebraska 10.17 2.93 0.78 0.29 Nevada 1.15 3.50 0.25 3.03 New Jersey 1.35 1.36 0.50 1.01 New Mexico 5.31 3.08 0.63 0.58 New York 2.79 1.22 0.70 0.44 North Carolina 3.73 1.81 0.67 0.49 North Dakota 8.00 3.14 0.72 0.39 Ohio 6.70 5.51 0.55 0.82 Oklahoma 8.46 1.38 0.86 0.16 Oregon 2.92 1.29 0.69 0.44 Pennsylvania 6.79 0.82 0.89 0.12 South Carolina 3.22 1.56 0.67 0.49 South Dakota 10.04 2.94 0.77 0.29 Tennessee 4.67 1.72 0.73 0.37 Texas 13.79 0.85 0.94 0.06 Utah 2.08 3.40 0.38 1.64 Virginia 3.64 1.82 0.67 0.50 Washington 4.98 1.09 0.82 0.22 West Virginia 1.09 2.08 0.34 1.90 Wisconsin 7.89 1.52 0.84 0.19 Wyoming 3.61 3.25 0.53 0.90 Source: Author. 284 Table 8.11: Calculation of Optimal Matching Rates for Production Region Specification (4 = 0.20), 1978 Cross-section Matching State MPR. MPRo a. Rate Alabama 4.23 2.26 0.65 0.54 Arizona 3.99 4.61 0.46 1.15 Arkansas 9.53 1.78 0.84 0.19 California 7.68 1.25 0.86 0.16 Colorado 5.33 4.34 0.55 0.81 Florida 3.89 2.33 0.63 0.60 Georgia 4.98 2.11 0.70 0.42 Idaho 5.88 4.23 0.58 0.72 Illinois 13.97 7.34 0.66 0.53 Indiana 6.81 8.77 0.44 1.29 Iowa 16.23 6.89 0.70 0.42 Kansas 9.78 4.58 0.68 0.47 Kentucky 6.56 2.14 0.75 0.33 Louisiana 3.34 3.02 0.53 0.90 Maryland 2.84 1.80 0.61 0.64 Michigan 4.19 3.28 0.56 0.78 Minnesota 9.39 2.24 0.81 0.24 Mississippi 5.56 2.57 0.68 0.46 Missouri 8.00 8.53 0.48 1.07 Montana 3.83 4.64 0.45 1.21 Nebraska 9.20 4.70 0.66 0.51 Nevada 0.74 5.26 0.12 7.13 New Jersey 1.04 2.16 0.32 2.08 New Mexico 3.47 4.72 0.42 1.36 New York 2.57 1.85 0.58 0.72 North Carolina 3.39 2.78 0.55 0.82 North Dakota 6.43 5.26 0.55 0.82 Ohio 5.65 9.00 0.39 1.59 Oklahoma 7.20 2.69 0.73 0.37 Oregon 2.29 2.33 0.50 1.02 Pennsylvania 5.40 1.29 0.81 0.24 South Carolina 2.44 2.62 0.48 1.07 South Dakota 7.30 5.08 0.59 0.70 Tennessee 3.72 2.71 0.58 0.73 Texas 13.47 1.44 0.90 0.11 Utah 1.52 5.11 0.23 3.36 Virginia 2.93 2.87 0.50 0.98 Washington 3.95 2.00 0.66 0.51 West Virginia 0.68 3.32 0.17 4.87 Wisconsin 7.02 2.72 0.72 0.39 Wyoming 2.28 4.95 0.32 2.17 Source: Author. 285 Table 8.12: Calculation of Optimal Matching Rates for Production Region Specification (6 = 0.30), 1978 Cross-section Matching State MPR. MPRo a. Rate Alabama 3.31 2.83 0.54 0.85 Arizona 3.23 5.31 0.38 1.65 Arkansas 7.94 2.28 0.78 0.29 California 7.11 1.48 0.83 0.21 Colorado 4.46 4.94 0.47 1.11 Florida 3.44 2.79 0.55 0.81 Georgia 4.12 2.59 0.61 0.63 Idaho 4.52 4.92 0.48 1.09 Illinois 11.18 8.99 0.55 0.80 Indiana 5.63 10.66 0.35 1.89 Iowa 13.35 8.34 0.62 0.62 Kansas 8.30 5.61 0.60 0.68 Kentucky 5.04 2.63 0.66 0.52 Louisiana 2.90 3.78 0.43 1.30 Maryland 2.09 2.22 0.49 1.06 Michigan 3.57 4.28 0.45 1.20 Minnesota 8.20 2.89 0.74 0.35 Mississippi 4.68 3.25 0.59 0.69 Missouri 6.32 10.45 0.38 1.65 Montana 2.98 5.38 0.36 1.81 Nebraska 8.05 5.68 0.59 0.71 Nevada 0.52 6.12 0.08 11.76 New Jersey 0.81 2.60 0.24 3.22 New Mexico 2.47 5.54 0.31 2.24 New York 2.28 2.16 0.51 0.95 North Carolina 2.97 3.25 0.48 1.09 North Dakota 5.14 6.55 0.44 1.27 Ohio 4.68 10.94 0.30 2.34 Oklahoma 6.01 3.78 0.61 0.63 Oregon 1.81 3.08 0.37 1.70 Pennsylvania 4.30 1.56 0.73 0.36 South Carolina 1.88 3.26 0.37 1.73 South Dakota 5.49 6.45 0.46 1.17 Tennessee 2.96 3.25 0.48 1.10 Texas 12.62 1.80 0.87 0.14 Utah 1.15 5.93 0.16 5.17 Virginia 2.34 3.44 0.41 1.47 Washington 3.14 2.68 0.54 0.85 West Virginia 0.48 4.00 0.11 8.41 Wisconsin 6.06 3.53 0.63 0.58 Wyoming 1.60 5.80 0.22 3.62 Source: Author. 286 Table 8.13: Calculation of Optimal Matching Rates for Neighboring States Specification (0 = 0.10), 1974 Cross-section Matching State MPR, MPRo a. Rate Alabama 11.33 4.95 0.70 0.44 Arizona 12.46 4.39 0.74 0.35 Arkansas 17.58 9.78 0.64 0.56 California 22.54 2.27 0.91 0.10 Colorado 27.17 8.96 0.75 0.33 Florida 11.14 2.58 0.81 0.23 Georgia 14.47 4.35 0.77 0.30 Idaho 24.79 5.49 0.82 0.22 Illinois 36.36 11.79 0.76 0.32 Indiana 19.04 8.55 0.69 0.45 Iowa 46.84 14.65 0.76 0.31 Kansas 25.15 8.30 0.75 0.33 Kentucky 16.25 11.64 0.58 0.72 Louisiana 10.16 6.04 0.63 0.59 Maryland 11.66 2.77 0.81 0.24 Michigan 12.19 5.75 0.68 0.47 Minnesota 30.32 11.09 0.73 0.37 Mississippi 14.26 4.87 0.75 0.34 Missouri 18.03 14.28 0.56 0.79 Montana 14.43 7.84 0.65 0.54 Nebraska 20.72 10.09 0.67 0.49 Nevada 1.99 7.49 0.21 3.77 New Jersey 3.61 2.42 0.60 0.67 New Mexico 12.46 8.53 0.59 0.68 New York 9.06 1.87 0.83 0.21 North Carolina 15.90 4.46 0.78 0.28 North Dakota 23.02 6.80 0.77 0.30 Ohio 20.67 6.61 0.76 0.32 Oklahoma 17.08 12.90 0.57 0.76 Oregon 8.21 6.54 0.56 0.80 Pennsylvania 15.10 4.85 0.76 0.32 South Carolina 11.34 3.04 0.79 0.27 South Dakota 23.29 9.58 0.71 0.41 Tennessee 9.64 11.69 0.45 1.21 Texas 28.61 5.73 0.83 0.20 Utah 6.90 7.37 0.48 1.07 Virginia 9.12 5.70 0.62 0.62 Washington 16.09 3.30 0.83 0.21 West Virginia 3.53 7.28 0.33 2.07 Wisconsin 17.77 12.57 0.59 0.71 Wyoming 7.31 9.66 0.43 1.32 Source: Author. 287 Table 8.14: Calculation of Optimal Matching Rates for Neighboring States Specification (0 = 0.20), 1974 Cross-section Matching State MPR. MPRo a. Rate Alabama 8.58 7.98 0.52 0.93 Arizona 9.35 7.40 0.56 0.79 Arkansas 13.03 15.53 0.46 1.19 California 21.96 3.36 0.87 0.15 Colorado 19.28 13.91 0.58 0.72 Florida 10.37 4.00 0.72 0.39 Georgia 11.44 6.88 0.62 0.60 Idaho 18.18 8.97 0.67 0.49 Illinois 28.83 19.37 0.60 0.67 Indiana 16.15 13.62 0.54 0.84 Iowa 40.67 23.33 0.64 0.57 Kansas 20.73 12.50 0.62 0.60 Kentucky 11.77 18.30 0.39 1.55 Louisiana 8.44 10.01 0.46 1.19 Maryland 9.25 4.36 0.68 0.47 Michigan 10.47 9.66 0.52 0.92 Minnesota 25.89 18.29 0.59 0.71 Mississippi 11.51 7.32 0.61 0.64 Missouri 13.13 22.20 0.37 1.69 Montana 12.22 11.73 0.51 0.96 Nebraska 17.57 14.82 0.54 0.84 Nevada 1.18 12.24 0.09 10.38 New Jersey 3.04 4.08 0.43 1.34 New Mexico 8.41 13.33 0.39 1.58 New York 8.42 3.01 0.74 0.36 North Carolina 14.64 6.87 0.68 0.47 North Dakota 19.53 10.84 0.64 0.56 Ohio 17.02 10.55 0.62 0.62 Oklahoma 12.51 20.01 0.38 1.60 Oregon 6.27 11.24 0.36 1.79 Pennsylvania 12.01 8.02 0.60 0.67 South Carolina 8.90 5.22 0.63 0.59 South Dakota 16.09 16.01 0.50 1.00 Tennessee 6.56 18.31 0.26 2.79 Texas 25.49 8.48 0.75 0.33 Utah 5.46 10.57 0.34 1.94 Virginia 7.46 8.91 0.46 1.19 Washington 14.87 4.89 0.75 0.33 West Virginia 2.35 11.50 0.17 4.90 Wisconsin 15.14 21.17 0.42 1.40 wyoming 4.87 14.25 0.25 2.93 Source: Author. 288 Table 8.15: Calculation of Optimal Matching Rates for Neighboring States Specification (0 = 0.30), 1974 Cross-section Matching State MPR. MPRo a. Rate Alabama 6.33 9.29 0.41 1.47 Arizona 6.86 9.11 0.43 1.33 Arkansas 9.49 17.88 0.35 1.88 California 19.63 3.68 0.84 0.19 Colorado 13.70 15.74 0.47 1.15 Florida 8.89 4.50 0.66 0.51 Georgia 8.66 7.95 0.52 0.92 Idaho 13.16 10.59 0.55 0.80 Illinois 21.89 22.74 0.49 1.04 Indiana 12.85 15.60 0.45 1.21 Iowa 32.94 26.82 0.55 0.81 Kansas 16.16 13.86 0.54 0.86 Kentucky 8.46 20.83 0.29 2.46 Louisiana 6.62 11.82 0.36 1.79 Maryland 7.03 4.96 0.59 0.71 Michigan 8.41 11.46 0.42 1.36 Minnesota 20.71 21.55 0.49 1.04 Mississippi 8.85 8.10 0.52 0.92 Missouri 9.47 25.07 0.27 2.65 Montana 9.71 12.99 0.43 1.34 Nebraska 13.98 16.18 0.46 1.16 Nevada 0.77 14.53 0.05 18.92 New Jersey 2.41 4.90 0.33 2.04 New Mexico 5.82 15.20 0.28 2.61 New York 7.20 3.46 0.68 0.48 North Carolina 12.44 7.72 0.62 0.62 North Dakota 15.54 12.51 0.55 0.80 Ohio 13.26 12.14 0.52 0.92 Oklahoma 9.05 22.71 0.28 2.51 Oregon 4.64 13.87 0.25 2.99 Pennsylvania 9.14 9.45 0.49 1.03 South Carolina 6.71 6.33 0.51 0.94 South Dakota 11.26 18.98 0.37 1.69 Tennessee 4.55 20.85 0.18 4.58 Texas 21.07 9.29 0.69 0.44 Utah 4.14 11.35 0.27 2.74 Virginia 5.79 10.23 0.36 1.77 Washington 12.68 5.34 0.70 0.42 West Virginia 1.61 13.10 0.11 8.13 Wisconsin 12.09 25.18 0.32 2.08 Wyoming 3.34 15.59 0.18 4.67 Source: Author. 289 Table 8.16: Calculation of Optimal Matching Rates for Production Region Specification (0 = 0.10), 1974 Cross-section Matching State MPR. MPRo a. Rate Alabama 13.27 4.07 0.77 0.31 Arizona 16.03 11.06 0.59 0.69 Arkansas 24.67 2.93 0.89 0.12 California 24.32 2.33 0.91 0.10 Colorado 34.57 9.20 0.79 0.27 Florida 11.87 4.21 0.74 0.35 Georgia 17.64 3.63 0.83 0.21 Idaho 28.21 9.84 0.74 0.35 Illinois 40.91 11.34 0.78 0.28 Indiana 20.11 13.42 0.60 0.67 Iowa 47.93 10.64 0.82 0.22 Kansas 29.47 7.68 0.79 0.26 Kentucky 20.58 4.55 0.82 0.22 Louisiana 12.13 4.19 0.74 0.35 Maryland 9.57 2.93 0.77 0.31 Michigan 14.14 5.57 0.72 0.39 Minnesota 34.53 3.53 0.91 0.10 Mississippi 17.19 3.68 0.82 0.21 Missouri 23.53 13.08 0.64 0.56 Montana 14.03 11.26 0.55 0.80 Nebraska 24.66 8.16 0.75 0.33 Nevada 3.32 12.33 0.21 3.71 New Jersey 3.54 3.53 0.50 1.00 New Mexico 14.94 11.17 0.57 0.75 New York 9.47 2.94 0.76 0.31 North Carolina 17.11 4.90 0.78 0.29 North Dakota 22.27 8.40 0.73 0.38 Ohio 21.86 13.25 0.62 0.61 Oklahoma 24.76 3.42 0.88 0.14 Oregon 9.19 3.84 0.71 0.42 Pennsylvania 16.28 2.26 0.88 0.14 South Carolina 11.17 4.28 0.72 0.38 South Dakota 29.88 7.64 0.80 0.26 Tennessee 14.59 5.15 0.74 0.35 Texas 34.22 2.48 0.93 0.07 Utah 6.64 12.00 0.36 1.81 Virginia 10.15 5.59 0.64 0.55 Washington 14.11 3.35 0.81 0.24 West Virginia 3.66 6.24 0.37 1.70 Wisconsin 21.13 4.87 0.81 0.23 Wyoming 8.86 11.77 0.43 1.33 Source: Author. 290 Table 8.17: Calculation of Optimal Matching Rates for Production Region Specification (6 = 0.20), 1974 Cross—section Matching State MPR, MPRo a. Rate Alabama 11.30 7.38 0.60 0.65 Arizona 14.30 17.77 0.45 1.24 Arkansas 22.97 5.54 0.81 0.24 California 25.43 3.96 0.87 0.16 Colorado 28.52 14.93 0.66 0.52 Florida 11.73 7.29 0.62 0.62 Georgia 16.19 6.40 0.72 0.40 Idaho 22.82 16.06 0.59 0.70 Illinois 35.74 20.11 0.64 0.56 Indiana 18.05 23.65 0.43 1.31 Iowa 43.05 18.65 0.70 0.43 Kansas 27.61 13.40 0.67 0.49 Kentucky 17.37 8.21 0.68 0.47 Louisiana 11.63 7.81 0.60 0.67 Maryland 7.16 5.22 0.58 0.73 Michigan 13.77 10.75 0.56 0.78 Minnesota 32.95 6.92 0.83 0.21 Mississippi 16.07 6.92 0.70 0.43 Missouri 20.37 23.19 0.47 1.14 Montana 11.94 18.24 0.40 1.53 Nebraska 24.18 14.09 0.63 0.58 Nevada 2.36 20.16 0.10 8.55 New Jersey 3.01 6.05 0.33 2.01 New Mexico 11.28 18.37 0.38 1.63 New York 9.19 4.82 0.66 0.52 North Carolina 16.88 8.31 0.67 0.49 North Dakota 18.93 15.14 0.56 0.80 Ohio 19.10 23.44 0.45 1.23 Oklahoma 23.16 7.15 0.76 0.31 Oregon 7.69 7.50 0.51 0.98 Pennsylvania 13.90 3.87 0.78 0.28 South Carolina 8.98 7.84 0.53 0.87 South Dakota 23.91 14.14 0.63 0.59 Tennessee 12.48 9.19 0.58 0.74 Texas 35.74 4.63 0.89 0.13 Utah 5.31 19.57 0.21 3.69 Virginia 9.09 9.86 0.48 1.08 Washington 12.09 6.62 0.65 0.55 west Virginia 2.59 11.16 0.19 4.31 Wisconsin 20.82 9.34 0.69 0.45 Wyoming 6.61 19.31 0.26 2.92 Source: Author. 291 Table 8.18: Calculation of Optimal Matching Rates for Production Region Specification (O = 0.30), 1974 Cross-section Matching State MPR, MPRo a. Rate Alabama 9.34 7.38 0.56 0.79 Arizona 12.21 17.77 0.41 1.46 Arkansas 20.23 5.54 0.79 0.27 California 24.71 3.96 0.86 0.16 Colorado 23.11 14.93 0.61 0.65 Florida 10.83 7.29 0.60 0.67 Georgia 14.11 6.40 0.69 0.45 Idaho 18.28 16.06 0.53 0.88 Illinois 30.06 20.11 0.60 0.67 Indiana 15.47 23.65 0.40 1.53 Iowa 36.93 18.65 0.66 0.51 Kansas 24.44 13.40 0.65 0.55 Kentucky 14.28 8.21 0.64 0.57 Louisiana 10.49 7.81 0.57 0.74 Maryland 5.48 5.22 0.51 0.95 Michigan 12.56 10.75 0.54 0.86 Minnesota 29.57 6.92 0.81 0.23 Mississippi 14.19 6.92 0.67 0.49 Missouri 17.03 23.19 0.42 1.36 Montana 9.88 18.24 0.35 1.85 Nebraska 22.19 14.09 0.61 0.63 Nevada 1.76 20.16 0.08 11.47 New Jersey 2.49 6.05 0.29 2.43 New Mexico 8.69 18.37 0.32 2.12 New York 8.36 4.82 0.63 0.58 North Carolina 15.56 8.31 0.65 0.53 North Dakota 15.64 15.14 0.51 0.97 Ohio 16.06 23.44 0.41 1.46 Oklahoma 20.47 7.15 0.74 0.35 Oregon 6.28 7.50 0.46 1.19 Pennsylvania 11.52 3.87 0.75 0.34 South Carolina 7.16 7.84 0.48 1.10 South Dakota 19.02 14.14 0.57 0.74 Tennessee 10.35 9.19 0.53 0.89 Texas 34.70 4.63 0.88 0.13 Utah 4.22 19.57 0.18 4.64 Virginia 7.79 9.86 0.44 1.27 Washington 10.04 6.62 0.60 0.66 West Virginia 1.93 11.16 0.15 5.79 Wisconsin 19.18 9.34 0.67 0.49 Wyoming 5.06 19.31 0.21 3.82 Source: Author. 292 Table 8.19: Calculation of Optimal Matching Rates for Neighboring States Specification (4 = 0.10), 1969 Cross-section Matching State MPR| MPRo a. Rate Alabama 9.17 4.08 0.69 0.44 Arizona 8.60 2.97 0.74 0.35 Arkansas 14.58 8.09 0.64 0.56 California 12.90 1.51 0.90 0.12 Colorado 16.66 6.51 0.72 0.39 Florida 8.66 1.88 0.82 0.22 Georgia 9.66 3.57 0.73 0.37 Idaho 14.12 3.85 0.79 0.27 Illinois 26.32 8.44 0.76 0.32 Indiana 14.49 5.76 0.72 0.40 Iowa 33.33 11.04 0.75 0.33 Kansas 16.00 5.78 0.73 0.36 Kentucky 9.60 8.65 0.53 0.90 Louisiana 7.24 5.62 0.56 0.78 Maryland 7.48 2.20 0.77 0.29 Michigan 7.68 4.28 0.64 0.56 Minnesota 25.93 8.21 0.76 0.32 Mississippi 15.27 3.82 0.80 0.25 Missouri 12.75 10.21 0.56 0.80 Montana 11.82 5.40 0.69 0.46 Nebraska 16.32 6.56 0.71 0.40 Nevada 1.47 4.59 0.24 3.13 New Jersey 2.95 1.78 0.62 0.60 New Mexico 10.01 6.38 0.61 0.64 New York 7.56 1.31 0.85 0.17 North Carolina 11.67 3.70 0.76 0.32 North Dakota 19.73 5.26 0.79 0.27 Ohio 14.03 4.43 0.76 0.32 Oklahoma 12.12 9.64 0.56 0.80 Oregon 4.98 3.80 0.57 0.76 Pennsylvania 10.19 3.44 0.75 0.34 South Carolina 10.72 2.13 0.83 0.20 South Dakota 14.82 7.92 0.65 0.53 Tennessee 7.19 9.21 0.44 1.28 Texas 26.38 4.40 0.86 0.17 Utah 5.30 4.62 0.53 0.87 Virginia 9.42 3.83 0.71 0.41 Washington 9.54 1.91 0.83 0.20 West Virginia 2.34 5.07 0.32 2.17 Wisconsin 14.25 9.33 0.60 0.65 Wyoming 5.36 6.27 0.46 1.17 Source: Author. 293 Table 8.20: Calculation of Optimal Matching Rates for .Neighboring States Specification.(¢ = 0.20), 1969 Cross-section Matching State MPR. MPRo a. Rate Alabama 7.45 6.82 0.52 0.92 Arizona 6.71 5.09 0.57 0.76 Arkansas 10.97 13.56 0.45 1.24 California 13.07 2.32 0.85 0.18 Colorado 12.58 10.60 0.54 0.84 Florida 8.43 3.09 0.73 0.37 Georgia 8.01 5.94 0.57 0.74 Idaho 10.90 6.52 0.63 0.60 Illinois 22.02 14.57 0.60 0.66 Indiana 12.80 9.64 0.57 0.75 Iowa 30.52 18.33 0.62 0.60 Kansas 14.17 9.22 0.61 0.65 Kentucky 7.29 14.20 0.34 1.95 Louisiana 6.44 9.52 0.40 1.48 Maryland 6.32 3.49 0.64 0.55 Michigan 6.98 7.39 0.49 1.06 Minnesota 22.12 14.22 0.61 0.64 Mississippi 12.29 6.05 0.67 0.49 Missouri 9.99 16.68 0.37 1.67 Montana 10.36 8.59 0.55 0.83 Nebraska 14.20 10.32 0.58 0.73 Nevada 0.90 7.80 0.10 8.65 New Jersey 2.59 3.15 0.45 1.22 New Mexico 7.17 10.59 0.40 1.48 New York 7.19 2.22 0.76 0.31 North Carolina 11.05 5.82 0.65 0.53 North Dakota 17.22 8.71 0.66 0.51 Ohio 11.91 7.45 0.62 0.63 Oklahoma 9.36 15.84 0.37 1.69 Oregon 4.01 6.82 0.37 1.70 Pennsylvania 8.53 5.93 0.59 0.69 South Carolina 8.46 3.81 0.69 0.45 South Dakota 11.08 13.54 0.45 1.22 Tennessee 5.39 14.87 0.27 2.76 Texas 24.32 6.79 0.78 0.28 Utah 4.32 6.97 0.38 1.61 Virginia 7.27 6.34 0.53 0.87 Washington 9.25 2.98 0.76 0.32 West Virginia 1.63 8.26 0.16 5.07 Wisconsin 12.26 16.33 0.43 1.33 Wyoming 3.77 9.85 0.28 2.61 Source: Author. 294 Table 8.21: Calculation of Optimal Matching Rates for Neighboring States Specification.(¢ = 0.30), 1969 Cross-section Matching State MPR, MPRo a. Rate Alabama 5.96 8.44 0.41 1.41 Arizona 5.24 6.56 0.44 1.25 Arkansas 8.39 16.73 0.33 1.99 California 12.43 2.72 0.82 0.22 Colorado 9.63 12.84 0.43 1.33 Florida 7.73 3.74 0.67 0.48 Georgia 6.50 7.33 0.47 1.13 Idaho 8.46 8.17 0.51 0.97 Illinois 17.97 18.32 0.50 1.02 Indiana 10.85 11.83 0.48 1.09 Iowa 26.61 22.39 0.54 0.84 Kansas 12.05 10.99 0.52 0.91 Kentucky 5.60 17.22 0.25 3.08 Louisiana 5.50 11.85 0.32 2.16 Maryland 5.20 4.14 0.56 0.80 Michigan 6.04 9.26 0.39 1.53 Minnesota 18.30 17.91 0.51 0.98 Mississippi 9.79 7.19 0.58 0.73 Missouri 7.82 20.18 0.28 2.58 Montana 8.73 10.24 0.46 1.17 Nebraska 11.92 12.21 0.49 1.02 Nevada 0.63 9.83 0.06 15.73 New Jersey 2.18 4.03 0.35 1.85 New Mexico 5.34 13.03 0.29 2.44 New York 6.47 2.74 0.70 0.42 North Carolina 9.89 6.87 0.59 0.69 North Dakota 14.47 10.64 0.58 0.74 Ohio 9.81 9.20 0.52 0.94 Oklahoma 7.26 19.36 0.27 2.67 Oregon 3.19 8.99 0.26 2.82 Pennsylvania 6.97 7.46 0.48 1.07 South Carolina 6.64 4.92 0.57 0.74 South Dakota 8.43 16.86 0.33 2.00 Tennessee 4.11 17.88 0.19 4.35 Texas 21.32 7.94 0.73 0.37 Utah 3.46 8.02 0.30 2.32 Virginia 5.64 7.80 0.42 1.38 Washington 8.45 3.49 0.71 0.41 West Virginia 1.20 9.96 0.11 8.33 Wisconsin 10.19 20.67 0.33 2.03 wyoming 2.78 11.62 0.19 4.18 Source: Author. 295 Table 8.22: Calculation of Optimal Matching Rates for Production Region Specification (0 = 0.10), 1969 Cross-section Matching State MPR, MPRo a. Rate Alabama 9.18 2.69 0.77 0.29 Arizona 9.85 6.46 0.60 0.66 Arkansas 18.60 2.38 0.89 0.13 California 12.03 1.20 0.91 0.10 Colorado 18.12 5.64 0.76 0.31 Florida 7.96 2.81 0.74 0.35 Georgia 10.15 2.59 0.80 0.26 Idaho 13.86 6.06 0.70 0.44 Illinois 25.43 6.90 0.79 0.27 Indiana 13.24 8.12 0.62 0.61 Iowa 29.00 6.55 0.82 0.23 Kansas 15.95 4.88 0.77 0.31 Kentucky 10.73 3.08 0.78 0.29 Louisiana 7.40 3.50 0.68 0.47 Maryland 5.40 1.86 0.74 0.34 Michigan 7.68 4.08 0.65 0.53 Minnesota 25.85 2.26 0.92 0.09 Mississippi 16.40 2.60 0.86 0.16 Missouri 13.96 8.05 0.63 0.58 Montana 10.10 6.44 0.61 0.64 Nebraska 16.93 4.78 0.78 0.28 Nevada 2.24 7.22 0.24 3.22 New Jersey 2.46 2.15 0.53 0.88 New Mexico 10.21 6.43 0.61 0.63 New York 6.74 1.72 0.80 0.26 North Carolina 10.74 3.08 0.78 0.29 North Dakota 16.01 4.88 0.77 0.30 Ohio 12.83 8.16 0.61 0.64 Oklahoma 15.05 2.73 0.85 0.18 Oregon 4.79 1.92 0.71 0.40 Pennsylvania 9.39 1.46 0.87 0.16 South Carolina 8.79 2.73 0.76 0.31 South Dakota 15.88 4.89 0.76 0.31 Tennessee 8.63 3.29 0.72 0.38 Texas 27.30 1.50 0.95 0.06 Utah 4.49 7.00 0.39 1.56 Virginia 9.29 3.23 0.74 0.35 Washington 7.16 1.68 0.81 0.23 West Virginia 2.18 3.94 0.36 1.80 Wisconsin 14.97 3.35 0.82 0.22 Wyoming 5.61 6.89 0.45 1.23 Source: Author. 296 Table 8.23: Calculation of Optimal Matching Rates for Production Region Specification (0 = 0.20), 1969 Cross-section Matching State MPR. MPRo a. Rate Alabama 7.78 4.66 0.63 0.60 Arizona 8.69 10.19 0.46 1.17 Arkansas 16.77 4.30 0.80 0.26 California 12.19 1.97 0.86 0.16 Colorado 14.81 8.97 0.62 0.61 Florida 7.66 4.69 0.62 0.61 Georgia 9.12 4.40 0.67 0.48 Idaho 11.00 9.73 0.53 0.88 Illinois 21.78 11.92 0.65 0.55 Indiana 11.53 13.97 0.45 1.21 Iowa 25.29 11.22 0.69 0.44 Kansas 14.86 8.30 0.64 0.56 Kentucky 8.97 5.28 0.63 0.59 Louisiana 7.08 6.24 0.53 0.88 Maryland 4.00 3.20 0.56 0.80 Michigan 7.37 7.43 0.50 1.01 Minnesota 23.10 4.28 0.84 0.19 Mississippi 14.43 4.77 0.75 0.33 Missouri 12.00 13.87 0.46 1.16 Montana 8.38 10.25 0.45 1.22 Nebraska 15.95 8.08 0.66 0.51 Nevada 1.57 11.62 0.12 7.39 New Jersey 2.01 3.60 0.36 1.79 New Mexico 7.60 10.41 0.42 1.37 New York 6.19 2.76 0.69 0.45 North Carolina 10.06 5.06 0.67 0.50 North Dakota 12.85 8.70 0.60 0.68 Ohio 10.77 14.12 0.43 1.31 Oklahoma 13.86 5.50 0.72 0.40 Oregon 3.92 3.63 0.52 0.92 Pennsylvania 7.81 2.44 0.76 0.31 South Carolina 6.53 4.91 0.57 0.75 South Dakota 12.71 8.73 0.59 0.69 Tennessee 7.41 5.59 0.57 0.75 Texas 27.52 2.77 0.91 0.10 Utah 3.48 11.23 0.24 3.23 Virginia 7.39 5.59 0.57 0.76 Washington 5.95 3.22 0.65 0.54 West Virginia 1.52 6.77 0.18 4.44 Wisconsin 14.03 6.09 0.70 0.43 Wyoming 4.13 11.10 0.27 2.69 Source: Author. 297 Table 8.24: Calculation of Optimal Matching Rates for Production Region Specification (0 = 0.30), 1969 Cross-section Matching State MPR. MPRo a. Rate Alabama 6.30 5.82 0.52 0.92 Arizona 7.23 11.83 0.38 1.64 Arkansas 14.20 5.48 0.72 0.39 California 11.39 2.36 0.83 0.21 Colorado 11.70 10.49 0.53 0.90 Florida 6.84 5.66 0.55 0.83 Georgia 7.70 5.40 0.59 0.70 Idaho 8.53 11.44 0.43 1.34 Illinois 17.75 14.66 0.55 0.83 Indiana 9.51 17.13 0.36 1.80 Iowa 20.88 13.72 0.60 0.66 Kansas 12.90 10.18 0.56 0.79 Kentucky 7.19 6.50 0.53 0.90 Louisiana 6.28 7.85 0.44 1.25 Maryland 2.98 3.94 0.43 1.32 Michigan 6.56 9.50 0.41 1.45 Minnesota 19.42 5.64 0.77 0.29 Mississippi 11.98 6.14 0.66 0.51 Missouri 9.81 17.04 0.37 1.74 Montana 6.68 12.00 0.36 1.80 Nebraska 13.98 9.85 0.59 0.70 Nevada 1.14 13.66 0.08 12.03 New Jersey 1.59 4.36 0.27 2.75 New Mexico 5.67 12.30 0.32 2.17 New York 5.31 3.24 0.62 0.61 North Carolina 8.78 6.02 0.59 0.69 North Dakota 10.03 11.04 0.48 1.10 Ohio 8.65 17.39 0.33 2.01 Oklahoma 11.92 7.68 0.61 0.64 Oregon 3.10 4.84 0.39 1.56 Pennsylvania 6.24 2.96 0.68 0.47 South Carolina 4.87 6.25 0.44 1.28 South Dakota 9.91 11.07 0.47 1.12 Tennessee 6.05 6.84 0.47 1.13 Texas 25.59 3.58 0.88 0.14 Utah 2.66 13.20 0.17 4.96 Virginia 5.73 6.94 0.45 1.21 Washington 4.75 4.35 0.52 0.92 West Virginia 1.10 8.33 0.12 7.57 Wisconsin 12.25 7.79 0.61 0.64 wyoming 3.06 13.08 0.19 4.27 Source: Author. 298 Table 8.25: Calculation of Optimal Matching Rates for Neighboring States Specification (0 = 0.10), 1964 Cross-section Matching State MPR. MPRo a. Rate Alabama 10.93 4.88 0.69 0.45 Arizona 9.50 3.49 0.73 0.37 Arkansas 15.31 10.03 0.60 0.66 California 15.86 1.64 0.91 0.10 Colorado 17.52 8.57 0.67 0.49 Florida 9.74 2.31 0.81 0.24 Georgia 12.21 4.37 0.74 0.36 Idaho 14.41 4.57 0.76 0.32 Illinois 30.83 10.99 0.74 0.36 Indiana 20.27 7.60 0.73 0.38 Iowa 42.24 12.98 0.76 0.31 Kansas 23.68 7.41 0.76 0.31 Kentucky 11.75 11.51 0.51 0.98 Louisiana 7.66 6.40 0.54 0.84 Maryland 9.43 2.92 0.76 0.31 Michigan 13.69 5.66 0.71 0.41 Minnesota 21.59 9.70 0.69 0.45 Mississippi 15.96 4.48 0.78 0.28 Missouri 19.05 13.00 0.59 0.68 Montana 14.67 5.94 0.71 0.40 Nebraska 23.57 8.53 0.73 0.36 Nevada 1.49 5.22 0.22 3.50 New Jersey 4.68 2.33 0.67 0.50 New Mexico 10.62 7.38 0.59 0.69 New York 8.36 1.96 0.81 0.23 North Carolina 19.40 4.59 0.81 0.24 North Dakota 19.94 5.44 0.79 0.27 Ohio 19.74 6.42 0.75 0.33 Oklahoma 13.96 11.90 0.54 0.85 Oregon 5.46 4.20 0.56 0.77 Pennsylvania 14.90 4.58 0.76 0.31 South Carolina 12.12 3.16 0.79 0.26 South Dakota 18.16 8.66 0.68 0.48 Tennessee 10.92 11.53 0.49 1.06 Texas 32.77 4.76 0.87 0.15 Utah 6.97 4.98 0.58 0.71 Virginia 10.69 5.51 0.66 0.51 Washington 10.25 1.99 0.84 0.19 West Virginia 3.58 6.65 0.35 1.86 Wisconsin 16.62 10.84 0.61 0.65 Wyoming 6.86 7.17 0.49 1.05 Source: Author. 299 Table 8.26: Calculation of Optimal Matching Rates for Neighboring States Specification (0 = 0.20), 1964 Cross-section Matching State MPRl MPRo a. Rate Alabama 8.25 7.41 0.53 0.90 Arizona 6.71 5.50 0.55 0.82 Arkansas 10.96 15.13 0.42 1.38 California 14.65 2.32 0.86 0.16 Colorado 12.74 12.74 0.50 1.00 Florida 8.63 3.50 0.71 0.41 Georgia 9.24 6.68 0.58 0.72 Idaho 10.28 7.02 0.59 0.68 Illinois 23.90 17.03 0.58 0.71. Indiana 15.97 11.73 0.58 0.73 Iowa 34.32 19.74 0.63 0.58 Kansas 18.84 10.84 0.63 0.58 Kentucky 8.31 17.24 0.33 2.07 Louisiana 6.24 9.99 0.38 1.60 Maryland 7.02 4.31 0.62 0.61 Michigan 10.98 8.96 0.55 0.82 Minnesota 17.66 15.10 0.54 0.86 Mississippi 12.02 6.52 0.65 0.54 Missouri 13.21 19.48 0.40 1.47 Montana 11.50 8.54 0.57 0.74 Nebraska 18.22 12.34 0.60 0.68 Nevada 0.82 8.16 0.09 9.94 New Jersey 3.64 3.69 0.50 1.01 New Mexico 6.91 11.29 0.38 1.63 New York 7.41 2.94 0.72 0.40 North Carolina 16.16 6.80 0.70 0.42 North Dakota 15.48 8.30 0.65 0.54 Ohio 15.48 9.72 0.61 0.63 Oklahoma 10.04 17.93 0.36 1.79 Oregon 4.08 6.95 0.37 1.70 Pennsylvania 11.05 7.16 0.61 0.65 South Carolina 9.37 5.08 0.65 0.54 South Dakota 12.35 13.49 0.48 1.09 Tennessee 7.15 17.28 0.29 2.42 Texas 26.97 6.83 0.80 0.25 Utah 5.10 7.02 0.42 1.38 Virginia 8.23 8.18 0.50 0.99 Washington 9.00 2.87 0.76 0.32 West Virginia 2.28 10.02 0.19 4.40 Wisconsin 13.35 17.37 0.43 1.30 wyoming 4.57 10.39 0.31 2.27 Source: Author. 300 Table 8.27: Calculation of Optimal Matching Rates for Neighboring States Specification (0 = 0.30), 1964 Cross-section Matching State MPR. MPRo a. Rate Alabama 6.18 8.44 0.42 1.37 Arizona 4.82 6.56 0.42 1.36 Arkansas 7.93 17.09 0.32 2.16 California 12.87 2.51 0.84 0.20 Colorado 9.31 14.23 0.40 1.53 Florida 7.29 3.93 0.65 0.54 Georgia 6.93 7.65 0.48 1.10 Idaho 7.42 8.06 0.48 1.09 Illinois 18.21 19.55 0.48 1.07 Indiana 12.32 13.39 0.48 1.09 Iowa 27.05 22.37 0.55 0.83 Kansas 14.63 11.95 0.55 0.82 Kentucky 5.97 19.35 0.24 3.24 Louisiana 4.93 11.52 0.30 2.34 Maryland 5.21 4.79 0.52 0.92 Michigan 8.57 10.39 0.45 1.21 Minnesota 13.99 17.39 0.45 1.24 Mississippi 8.99 7.19 0.56 0.80 Missouri 9.39 21.84 0.30 2.33 Montana 8.84 9.33 0.49 1.06 Nebraska 13.86 13.55 0.51 0.98 Nevada 0.52 9.57 0.05 18.35 New Jersey 2.78 4.33 0.39 1.56 New Mexico 4.74 12.86 0.27 2.71 New York 6.26 3.29 0.66 0.53 North Carolina 12.99 7.56 0.63 0.58 North Dakota 11.81 9.45 0.56 0.80 Ohio 11.89 10.97 0.52 0.92 Oklahoma 7.28 20.24 0.26 2.78 Oregon 3.04 8.51 0.26 2.80 Pennsylvania 8.18 8.31 0.50 1.02 South Carolina 7.12 5.97 0.54 0.84 South Dakota 8.68 15.50 0.36 1.79 Tennessee 4.92 19.38 0.20 3.94 Texas 21.47 7.47 0.74 0.35 Utah 3.75 7.57 0.33 2.02 Virginia 6.24 9.19 0.40 1.47 Washington 7.54 3.14 0.71 0.42 West Virginia 1.54 11.25 0.12 7.29 Wisconsin 10.43 20.35 0.34 1.95 Wyoming 3.18 11.40 0.22 3.59 301 Table 8.28: Calculation of Optimal Matching Rates for Production Region Specification (0 = 0.10), 1964 Cross-section Matching State MPR, MPRo a. Rate Alabama 11.98 3.51 0.77 0.29 Arizona 12.18 7.84 0.61 0.64 Arkansas 20.16 2.71 0.88 0.13 California 16.47 1.44 0.92 0.09 Colorado 19.88 7.07 0.74 0.36 Florida 9.91 3.71 0.73 0.37 Georgia 14.07 3.30 0.81 0.23 Idaho 15.88 7.47 0.68 0.47 Illinois 33.73 10.76 0.76 0.32 Indiana 20.58 12.07 0.63 0.59 Iowa 43.40 9.79 0.82 0.23 Kansas 26.48 7.13 0.79 0.27 Kentucky 14.29 5.05 0.74 0.35 Louisiana 8.58 3.87 0.69 0.45 Maryland 7.54 2.79 0.73 0.37 Michigan 14.87 4.29 0.78 0.29 Minnesota 23.79 3.40 0.88 0.14 Mississippi 18.55 2.87 0.87 0.15 Missouri 23.61 11.77 0.67 0.50 Montana 13.93 7.66 0.65 0.55 Nebraska 27.82 7.00 0.80 0.25 Nevada 2.65 8.79 0.23 3.32 New Jersey 4.33 3.11 0.58 0.72 New Mexico 11.80 7.88 0.60 0.67 New York 8.39 2.70 0.76 0.32 North Carolina 19.93 4.48 0.82 0.22 North Dakota 20.16 7.76 0.72 0.39 Ohio 20.00 12.13 0.62 0.61 Oklahoma 18.90 3.87 0.83 0.20 Oregon 5.83 2.50 0.70 0.43 Pennsylvania 15.18 2.03 0.88 0.13 South Carolina 11.09 3.60 0.76 0.32 South Dakota 23.34 7.45 0.76 0.32 Tennessee 15.10 4.97 0.75 0.33 Texas 38.70 1.89 0.95 0.05 Utah 6.61 8.39 0.44 1.27 Virginia 11.57 5.32 0.69 0.46 Washington 8.57 2.23 0.79 0.26 West Virginia 3.86 6.09 0.39 1.58 Wisconsin 19.09 3.87 0.83 0.20 Wyoming 7.62 8.29 0.48 1.09 Source: Author. 302 Table 8.29: Calculation of Optimal Matching Rates for Production Region Specification (0 = 0.20), 1964 Cross-section Matching State MPR. MPRo a. Rate Alabama 9.85 5.89 0.63 0.60 Arizona 10.23 11.93 0.46 1.17 Arkansas 17.59 4.73 0.79 0.27 California 15.99 2.29 0.87 0.14 Colorado 16.01 10.77 0.60 0.67 Florida 9.07 6.05 0.60 0.67 Georgia 11.99 5.46 0.69 0.46 Idaho 12.30 11.51 0.52 0.94 Illinois 28.49 17.77 0.62 0.62 Indiana 16.83 20.10 0.46 1.19 Iowa 36.84 16.10 0.70 0.44 Kansas 23.40 11.92 0.66 0.51 Kentucky 11.62 8.30 0.58 0.71 Louisiana 7.80 6.68 0.54 0.86 Maryland 5.23 4.53 0.54 0.87 Michigan 12.96 7.77 0.63 0.60 Minnesota 21.43 6.07 0.78 0.28 Mississippi 15.83 5.08 0.76 0.32 Missouri 18.93 19.68 0.49 1.04 Montana 10.90 11.79 0.48 1.08 Nebraska 24.77 11.65 0.68 0.47 Nevada 1.74 13.62 0.11 7.84 New Jersey 3.31 4.91 0.40 1.48 New Mexico 8.31 12.31 0.40 1.48 New York 7.59 4.05 0.65 0.53 North'Carolina 17.33 7.16 0.71 0.41 North Dakota 16.21 13.36 0.55 0.82 Ohio 16.26 20.22 0.45 1.24 Oklahoma 16.95 7.45 0.69 0.44 Oregon 4.68 4.56 0.51 0.97 Pennsylvania 11.73 3.23 0.78 0.28 South Carolina 8.40 6.18 0.58 0.74 South Dakota 18.64 12.88 0.59 0.69 Tennessee 11.92 8.24 0.59 0.69 Texas 37.26 3.39 0.92 0.09 Utah 4.88 13.00 0.27 2.67 Virginia 9.63 8.70 0.53 0.90 Washington 6.79 4.13 0.62 0.61 West Virginia 2.62 10.10 0.21 3.85 Wisconsin 17.41 6.88 0.72 0.40 Wyoming 5.50 12.87 0.30 2.34 Source: Author. 303 Table 8.30: Calculation of Optimal Matching Rates for Production Region Specification (0 = 0.30), 1964 Cross-section Matching State MPR. MPRo a. Rate Alabama 7.61 6.98 0.52 0.92 Arizona 8.02 13.17 0.38 1.64 Arkansas 14.20 5.72 0.71 0.40 California 14.15 2.60 0.84 0.18 Colorado 12.19 11.92 0.51 0.98 Florida 7.61 6.98 0.52 0.92 Georgia 9.50 6.41 0.60 0.67 Idaho 9.14 12.84 0.42 1.41 Illinois 22.44 20.67 0.52 0.92 Indiana 12.96 23.52 0.36 1.82 Iowa 29.12 18.67 0.61 0.64 Kansas 19.08 14.03 0.58 0.74 Kentucky 8.91 9.67 0.48 1.09 Louisiana 6.51 8.03 0.45 1.23 Maryland 3.64 5.23 0.41 1.44 Michigan 10.46 9.69 0.52 0.93 Minnesota 17.74 7.50 0.70 0.42 Mississippi 12.56 6.21 0.67 0.49 Missouri 14.38 23.09 0.38 1.61 Montana 8.14 13.14 0.38 1.61 Nebraska 20.31 13.66 0.60 0.67 Nevada 1.18 15.23 0.07 12.95 New Jersey 2.44 5.60 0.30 2.29 New Mexico 5.83 13.83 0.30 2.37 New York 6.31 4.44 0.59 0.70 North Carolina 13.96 8.15 0.63 0.58 North Dakota 12.33 16.05 0.43 1.30 Ohio 12.46 23.67 0.34 1.90 Oklahoma 13.99 9.81 0.59 0.70 Oregon 3.55 5.78 0.38 1.63 Pennsylvania 8.70 3.72 0.70 0.43 South Carolina 6.15 7.41 0.45 1.20 South Dakota 14.12 15.52 0.48 1.10 Tennessee 8.95 9.65 0.48 1.08 Texas 32.69 4.20 0.89 0.13 Utah 3.51 14.53 0.19 4.14 Virginia 7.50 10.09 0.43 1.34 Washington 5.11 5.31 0.49 1.04 West Virginia 1.81 11.80 0.13 6.53 Wisconsin 14.55 8.46 0.63 0.58 Wyoming 3.92 14.40 0.21 3.67 Source: Author. 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