Miscellaneous Publication 8--1981Minnesota Agricultural Experiment Station

University of Minnesota

Evaluation of Agricultural Research

Proceedings of a Workshop Sponsored by NC-148Minneapolis, Minnesota May 12-13, 1980

INTERREGIONAL SPILLOVER OF AGRICULTURAL RESEARCH RESULTS AND INTERGOVERNHENTAL FINANCE:

SOHE PRELIHINARY RESULTS

Fred C. White and Joseph Havlicek, Jr.*

Introduction

Agricultural research, as with many other gov­ernmental services, can be performed efficientlyat the state level but produces benefits thataccrue to a broader area than just the originatingstate or region. Results from basic research, forexample, would be unrestricted by geographicboundaries. Even applied research which is de­signed to solve specific problems encountered ina particular state may result in spi1lovers--geo­graphically external benefits--to other areas.For example, some research results can readily beapplied over wide geographic areas while otherresults need only additional adaptive researchbefore they are suitable for other areas.

The idea that the benefits of agricultural re­search are not realized solely by the state orregion providing the research expenditures is nota new one. Several researchers have analyzed theinterregional diffusion of a particular technol­ogy (Peterson and Hayami, 1977, pp. 524-526). Inthe study of hybrid corn diffusion, Griliches(1957) found that differences among regions inadoption rates were dependent on such factors asthe size and density of commodity production andprofitability of the new technology. Despite thewidespread concern over the diffusion of a parti­cular technology, the external benefits of agri­cultural research have not received much attentionfrom economists working in the general area ofresearch evaluation and planning.

Attempts at measuring the contribution of agri­cultural research to agricultural production haveoften utilized a production function for a commo­dity or agricultural sector as a whole in such amanner that research was included as a separatevariable (Peterson and Hayami, 1977, pp. 520-521).The majority of studies which have included

*Professor, Department of Agricultural Economics,University of Georgia, and Professor, Departmentsof Agricultural Economics and Statistics,Virginia Polytechnic Institute and State Univer­sity.

60

research as a separate variable in a productionfunction have been aimed at the national levelrather than the regional or state levels.Griliches' (1964) work was one of the first pub­lications in the area and Evenson's (1967) workwas really important because it revealed thenature of the lag between the research input andincreased output. The production functionapproach provides an estimate of the marginalproduct of agricultural research which is parti­cularly useful in guiding decisions about alloca­tion of resources to agricultural research.

Studies directed at the state or regional levelconfront a major problem not encountered in anational analysis: interregional spillovers ofthe benefits from agricultural research results.This problem has been termed pervasiveness, indi­cating the tendency for research results generatedin one region to be incorporated into farm pro­duction functions in other regions (Evenson, 1971,p. 173). Latimer and Paar1berg (1965) and Evenson(1971) recognized the pervasiveness problem.Latimer and Paarlberg were unable to find a sta­tistically significant relationship between re­search expenditures within the state and agricul­tural output. They attributed these findings tothe pervasive nature of agricultural research re­sults (Latimer and Paarlberg, p. 239). Evensonincluded a variable which measured the intensityof commodity research in an attempt to controlfor the pervasiveness of research (1971, p. 177).If research results were completely pervasive,Evenson argued, this variable would dominate thestate research variable. The variable was statis­tically significant indicating that the interre­gional transfer of agricultural research resultsshould be taken into account in cross-sectionalanalyses.

The existence of spillover benefits has abearing on the allocation of research funds bothwithin and between states. One important problemis to determine the appropriate balance betweenfederal and state government in financing agri­cultural research. More specifically, whatportion of the research expenditures should befinanced by the federal government? The federalgovernment initially served as a catalyst

whereQit

in developing the institutional framework toconduct agricultural research. The Morrill LandGrant College Act of 1862 and the Hatch Agricul­tural Experiment Station Act of 1887 reflect theemergence of a dual federal-state approach toagricultural research (Peterson and Fitzharris,1977, pp. 72-73). Under these acts, each statereceived funds for a college of agricultural andmechanical arts and for an agricultural experi­ment station. This institutional framework isstill a dominant force in agricultural research.Federal funds are allocated by a formula whichis based largely on a state's rural and farmpopulation (Peterson and Hayami, 1977, p. 522).Assuming that this system of finance was appro­priate when it was first devised, is it stillequitable after almost a century?

This paper deals with the effects of spill­overs of agricultural research benefits on thefinancing of research by federal and stategovernments. It considers conceptual problemsof financing government services which producespillovers and proposes a model to align aregion's investment in agricultural research withsocial benefits by compensating for spilloverswith funds from the federal government. Inter­regional spillovers of the benefits from agricul­tural research results are empirically measuredin order to determine the appropriate balancebetween federal and state funding of agriculturalresearch.

is the agricultural output in region iand time period t,

X.. is the jth conventional input in region1Jt i and time period t,

R.( ) is agricultural research expenditures1 t-w in region i and time period t-w.

i=1,2,---n is the number of regions,j=1,2,---m is the number of conventional

inputs,t=1,2,---T is the number of time periods and,w=O,1,2,---W is the number of lagged time

periods over which agriculturalresearch affects the output ofthe current time period.

This implicit function, which defines the setof inputs and outputs that may be feasiblyattained is subject to the following conditionsrelated to any regions i and k.

d Q't__1_ > 0 for w=O,l,2,---W() ~(t-w) '-

o for i# k

These conditions state that research in oneregion may affect output in other regions butconventional input usage in one region has noeffect on output in any other region.

The existence of externalities complicatesthe dual problems of optimal provision and finan­cing of agricultural research. First, considersociety's problem in finding the optimum amountof research expenditures subject to the produc­tion constraint. One such procedure is toincrease research expenditures up to the pointwhere its internal rate of return is just equalto returns from alternative social investments(r.) .

1

oW

Iw=o

is the price of the output in region iand time period t,

MP.( ) is the marginal product of research1 t-w in region i and time period t-w, and

r. is the rate of return in region i for the1 best alternative social investments.

(2)

wherep.1t

Conceptual Framework for Financing Externalities

A production externality occurs wheneverresults from agricultural research investmentsin one region affect agricultural production inother regions.ll This phenomenon of interdepen­dence in production can be analyzed through thebasic model of joint production. Consider thecase in which a production possibility schedulefor agricultural output in region i is assumedto be related to the quantity of conventionalinputs employed in region i, as well as researchexpenditures within region i and in other regions.The problem is further complicated by the factthat research expenditures over several yearsmay affect agricultural output. The appropriatemodel of joint production is given by:

The purpose of this section is to investigatethe nature of the divergence between regional andsocial benefits from agricultural research andthe ways in which the federal government can makethem coincide. Particular attention will befocused on the rationale for intergovernmentalgrants from the federal government to financeagricultural research.

---R ) = 0nt-W

61

The partial derivative of the productionfunction with respect to research in the ithregion is:

This condition can also be interpreted as selec­ting the level of research expenditures whosemarginal benefits discounted at the social rateof return is just equal to its marginal cost.Thus, on the margin each dollar of expenditureswill generate benefits equal to one dollar inpresent value.

If the level of expenditures in each regionwas based on benefits to the nation as a wholerather than the benefits to the region, thepotential inefficiency would be resolved. Inthose cases in which only a small number ofdecisionmaking units are involved, voluntaryaction among the interested parties could be usedin such a manner that all benefits are considered(Oates, pp. 67-68). However, attempting to coor­dinate these activities involves costs whichincrease rapidly as larger numbers of partiesare involved. Externalities from agriculturalresearch affect a large number of decisionmakingunits, and therefore the costs and the difficul­ties of effective coordinated action is expectedto be quite large. One feasible solution, shortof transfering the research activity to thefederal government, is for the federal governmentto grant funds to the state to induce it to raisethe level of agricultural research.

dQit

ClR. ( )1 t-wb

wL

w=O

The principal technique used to increasestate expenditures for other governmental ser­vices which create externalities is the matchinggrant, where according to a specified formulathe recipient government is required to matchthe granted funds with funds from its ownsources. While some federal grants for agricul­tural research require matching funds, the fed­eral government does not presently match everystate dollar with a specified amount of support.However, the matching grant program can serve asa standard of evaluation for the current systemof federal grants for agricultural research.

With the matching grant, the formula formatching funding is based on the relative impor­tance of external and internal benefits. Ifthese grant programs are properly designed, theyshould direct regional expenditures towardoptimum levels by financing the cost of externalbenefits or internalizing the externalities.This procedure can best be understood byreferring to Figure 1. The socially optimumlevel of research expenditures is R2 found atthe intersection of r, the social rate of return,and merN, the marginal efficiency of researchinvestment from the national perspective. Sincethe region's decision on research funding isbased on meri' the matching grant program fromthe federal government should reduce the region'seffective cost to r'. The region will thereforechoose R2 as the appropriate level of researchexpenditures by equating marginal regional bene­fits (meri) with marginal regional costs (r').The matching formula in this case will be(r - r')/r' as the appropriate balance betweenfederal and regional funding of agriculturalresearch.

The development of an appropriate matchinggrant program requires identification and quanti­fication of regional benefits and spillovers fromagricultural research. The traditional prescrip­tion to compensate for externalities, as pro­posed by A. C. Pigou (1932), is to provide aunit subsidy equal to the value at the margin ofthe spillovers. This concept is used in thepresent analysis to measure regional benefitsand spillovers. Benefits from agriculturalresearch expenditures in a given region from theregional point of view are measured by the con­tribution of the expenditures to output withinthe region:

(4)

for~ d Qkt

kh dRi(t_w)w=O,1,2,---,W

(3)

This expression indicates that the marginal bene­fits of region i can be separated into two com­ponents, benefits accruing to region i andbenefits accruing to other regions. In selectingthe appropriate level of research expenditures,policy makers in region i will stress those bene­fits which accrue to the region and ignore thosespilling over to other regions. With positivenet spillovers, the level of research expendi­tures is likely to be too small relative to theinterests of the country as a whole if the acti­vity is financed at the regional level. Thissituation is depicted in Figure I by the region'sselection of R as the appropriate level ofresearch expen~itures with the choice based onequating marginal efficiency of research invest­ment from the regional perspective (mer.) withthe social rate of return (r). This de~ision­making process ignores the marginal efficiencyof research investment from the national perspec­tive (mer ), which indicates that the sociallyoptimum l~vel of research expenditures is R2.The externality problem raises the issuesof society's optimal financing of agriculturalresearch.

62

whereBit is the value of the regional benefit in

time period t from agricultural researchexpenditures in region i during the w=0,1,2,---,W previous time periods.

Valuing benefits by this criterion is equivalentto paying resouces according to their marginalproductivities. Similarly, spillovers of agri­cultural research conducted in region i aremeasured by the contribution of the expendituresto output in all other regions:

Total benefits to the nation in time period tresulting from expenditures in region i are thesum of the benefits to the originating region,Bit and spillovers, Sit. The relative import­ance of spillovers to regional benefits in timeperiod t is measured by:

(6)

Figure 1. Adjustment for External Benefits

o

Marginal Efficiency ofResearch Investment

In this study a production function whichincludes variables to reflect conventional inputsas well as agricultural research is estimatedand is the basis for measuring the contributionof research to agricultural production. Variousoutputs are aggregated into a single variableby using relative price weights. Input variablesare similarly aggregated ~nd will thus abstractfrom quality diff~renc€s that are not reflectedin input prices. while this estimation procedurecontrols for the use of other inputs that areexpected to influence agricultural output, weare particularly interested in the effect ofagricultural research on productivity. Theexpected relationship between agriculturalresearch and agricultural output is discussed inthe following paragraphs.

The Model

The impact of federal grants on the level ofresearch expenditures is dependent on the magni­tude of the marginal revenue from grants.However, it is possible to draw some general con­clusions relating to the suitability of federalgrants for achieving particular objectives.First, a matching grant program for agriculturalresearch would tend to increase the level ofthese expenditures by reducing the net price ofagricultural research relative to other publicand private goods. Secondly, the program wouldhelp correct for spillovers so that regionalbenefits would more closely coincide with socialbenefits.

where

Mit is the ratio of spillovers to regionalbenefits in time period t.

In developing a federal grants program, Mit couldbe used as a guide in determining the federalgovernment's share of research expenditures(Musgrave and Musgrave, 1976, p. 630).

merN

mer·,

• R ]i(t-w)= Lk,li

is the value of spillover benefits in timeperiod t from agricultural research expen­ditures in region i during the w=0,1,2,--­W previous time periods.

(5)

rl

I------~----~

where

Sit

r

Research Investment

Ideally, we would like to capture the spill­overs of research results from region i toregion k for every i and k. However, accountingfor such a large number of interregional flowswould be very difficult in a single regressionequation. Furthermore, for purposes of thisstudy it is only necessary to measure the

63

magnitude of spillovers in aggregate and not toidentify the originating region in each case.Thus, the model will contain separate variablesfor research expenditures inside the region andresearch expenditures outside the region. Thespillovers in aggregate (or spillins) into theith region in time period tare:

The time path of output response to increasedexpenditures on research is particularly impor­tant in estimating the benefits from research.If the output response is not forthcoming in thesame year the investment is made, then the esti­mated marginal product overstates the marginalreturns from research investment. Evenson wasperhaps the first to identify the nature of thelag between the research input and increased out­put. He found, that in response to increasedexpenditures on research, agricultural outputfirst increased and then decreased, with theaverage length of lag between six and sevenyears. At the regional level this laggedrelationship is assumed to exist for researchexpenditures both within the region and outsidethe region. Statistical Model and Data

is the research and extension expen­ditures per state inside region i fortime period (t-w),is the research expenditure per stateoutside region i for time period(t-v),

RO. ( )l t-v

S's are regression coefficients,i=1,2,---,n is the number of regions,j=1,2,---,m is the number of conventional

inputs,t=1,2,---,T is the number of time periods,w=0,1,2,---,W is the number of lagged time

periods over which agriculturalresearch and extension expendi­tures within a region affect ag­ricultural output in region iduring time period t, and,

v=O,1,2,---,V is the number of lagged time pe~

iods over which agriculturalresearch expenditures outside ofregion i affect agricultural out­put in region i during time per­iod t.

A production function such as the one presentedabove provides several sets of interrelatedrelationships that are important for economicdecisions on resource use. Considering theunique aspects of the present analysis, attentionwill be focused on factor-product transformationratios for research and extension inside theregion and research outside the region.

whereQit

is the value of agricultural output peracre in region i and time period t,

X.. is the per acre value of the jth conven­lJt tional input in region i and time period

t,

Rli(t_w)

IW ClQ. JI p. I~ . Rk#i It ~=OClRk(t_W) k(t-w) _

is the value of the spillover benefitsinto region i in time period t from agri­cultural research expenditures in theother (n-l) regions during the w=0,1,2,---,W previous time periods.

where

Slit

(7)

The statistical model is a cross-sectionallycorrelated and time-wise autoregressive doublelogarithmic production function with four con­ventional inputs and the research expendituresinside the region and outside of the regionincluded as second order polynomial lags. Thestatistical production function is:

The unit of analysis is an average state foreach of the 10 agricultural production regionsin the United States.2/ Estimates of the contri­bution of agricultural research to agriculturaloutput are obtained from a production functionwhich was estimated using data for the period1949-1972. Data on research expenditures coveredthe period 1929-1972 to account for lagged effectsof the research variables.

Extension investment within the region alsoaffects agricultural output. However, measuringthe influence of extension on agricultural pro­ductivity separate from research has been diffi­cult. If extension's role is distinct from thatof research, then a separate extension variableshould be used in the production function.However, if extension's role can be viewed asimproving labor quality, its effect on productiv­ity can be considered similar to that of research.Consequently, it would be difficult todistinguish between the contribution of researchand extension (Evenson, 1967, p. 1421). Thelatter case is assumed to be the appropriatesituation in the present study. Therefore,research and extension expenditures within theregion are combined into one variable. Extensionis assumed to have no spillover effect to otherregions. (9)

The model used as the basis for empiricalanalysis is:

(8)m Sj W S + V S

Q S ~ X ~ RI m w ~ RO m+W+vit = ° j=l ijt w=O i(t-w)v=O i(t-v)

64

Uit

is assumed to be log normally distributed and

Sit Pi si(t-l) + Uit (autoregression)

S is assumed to be log normally distributedwith the following behavioral attributes:

The parameters of (9) were estimated using ageneralized least squares procedure which esti­mates a serial correlation coefficient for eachregion and adjustments for serial correlationare made in each region using the estimatedregional serial correlation coefficient. Afteradjustment for serial correlation, the variance­covariance matrix for the agricultural productionregions is estimated and the coefficients of themodel are estimated relative to adjustments forheterogeneous variances and non-zero covariancesamong the regions.

Agricultural input and output data wereobtained from Farm Income Estimates, 1949-1972(U.S. Department of Agriculture). Agriculturaloutput was the sum of farmer cash marketing,government payments to farmers, value of horneconsumption of farmers, and net farm inventorychange. Four conventional input-expenditurecategories ",ere used: (1) hired labor, (2) feedand livestock, (3) seed, fertilizer, lime, andmiscellaneous expenses, and (4) capital anddepreciation. Agricultural output and all expen­ditures were recorded in million 1972 dollars.3/

Research and extension expenditures includedonly production-oriented expenditures. Datasources for these expenditures include Budgetof the United States Government; CombinedStatement of Receipts, Expenditures and Balancesof the United States Government (U.S. Departmentof Treasury); Funds for Research at State Agri­cultural Experiment Stations and Other StateInstitutions (U.S. Department of Agriculture,Cooperative State Research Service); and Annual

Report of Cooperative Extension Work in Agriculture (U.S. Department of Agriculture, FederalExtension Service). For a more detailed descrip­tion of data sources see Cline (1975). Researchand extension expenditures were also recordedin million 1972 dollars, with the personnelcomponent of these expenditures deflated with anindex of average salaries of college and univer­sity teachers (AAUP Bulletin) and the remainingexpenditures deflated by the implicit pricedeflator for government purchases of goods andservices.

(mutual correlation)

(heteroskedasticity)o ..II

is the natural logarithm of the valueof agricultural output per acre inregion i and time period t,

In Xilt

is the natural logarithm of the peracre value of hired labor in region iand time period t,

In Xi2t

is the natural logarithm of the peracre value of feed and livestock inregion i and time period t,

In Xi3t

is the natural logarithm of the peracre value of seed, fertilizer, limeand miscellaneous expenses in regioni and time period t,

In Xi4t is the natural logarithm of the peracre value of capital and depreciationin region i and time period t,

In Rlit

is the research and extension expen­diture per state inside productionregion i pertaining to time period tmeasured as a second order polynomialin logarithms covering a II-year lagand having both endpoints constrainedto zero,

In ROit

is the research expenditure per stateoutside region i pertaining to timeperiod t measured as a second orderpolynomial in logarithms covering aII-year lag and having both end pointsconstrained to zero,

SO' Sl,---S6 are parameters and,

Sit is the disturbance term associated withtth observation in region i.

whereIn Q

it

oResults

Empirical Production Function

for i,k=1,2,---,n and t=1,2,---,T.

ment

(variance-covariancematrix after adjust­

for serial correlation)

(t # s),

The statistical results based on the data forthe 10 production regions of the United Statesfor the period 1949-1972 are presented in thissection. Estimated regression coefficients andt-values are shown in Table 1. The sign ofeach coefficient on conventional inputs and edu­cation are consistent with ~ priori knowledge.Each of these coefficients is also different

65

**Statistically significant at the 0.01 level ofsignificance.

Table 1: Empirical Production Function HhichAccounts for Interregional Spilloversof Agricultural Research Results.

Coefficient StandardError

0.153122** 0.018093

0.167828** 0.021168

0.218450** 0.026108

0.467536*~' 0.023348

Research and ResearchExtension Outside

Inside the the RegionRegion

0.000000 0.0000000.003520 0.0000000.006336 0.0000000.008448 0.0061300.009856 0.0110340.010560 0.0147120.010560 0.0171640.009856 0.0183900.008448 0.0183900.006336 0.0171640.003520 0.0147120.000000 0.0110340.000000 0.0061300.000000 0.000000

Variable

Hired LaborFeed and

LivestockSee<l and

FertilizerCapital and

Depreciation

Year

t

t-lt-2t-3t-4t-5t-6t-7t-8t-9t-IOt-11t-12t-13Sum ofResearch andExtensionCoefficients 0.077440~'~' o.134860~'~'

expenditures within the region affected region­al output for 11 years. Research expendituresoutside the region had no effect on regionaloutput for the first two years and then affectedregional output for 11 years. Combini~g thesetwo separate effects from the regional analysisindicates that research and extension expendi­tures affect agricultural output over a l3-yearperiod. These results are consistent withaggregate studies by Evenson (1967) and Cline(1975) which found a l3-year lag. However, thepresent analysis sheds further light on thenature of the lag, indicating the importance ofinterregional flows of research results.

The effect of these expenditures on output ineach year is also sho\vn in Table 1. Researchand extension expenditures inside the region havethe greatest impact on regional output in thefifth and sixth years, while research outsidethe region has the greatest impact in the seventhand eighth years. The sum of the regression coef­ficients on research and extension expendituresinside the region is 0.0695 indicating that a 1%increase in research and extension expendituresincreases output in the region by 0.0695% overits lifetime. These results are similar to esti­mates reported in previous studies.

Harginal Product and Rate of Return

The marginal product and rate of return foragricultural research and extension investmentcan be calculated from the regression results.The regression coefficients on the research andextension expenditure variables are elasticities.However, these elasticities can be converted tomarginal products by the following equation:

sion.

and extensionregion i; bothyear period

Iv

L: p(r ) (Q./RI.)\v=0 .-w l l

TIIPR.l

is the marginal product of research andextension expenditures for region iaggregated over the lifetime of theinvestment,

~WR.( ) is the marginal product of researchl t-\V d . d' ., dan extenslon expen ltures In l an

year (t-\v),Q. is the mean level of agricultural output~ per state in region i, andRI. is mean level of research

l expenditures per state inmeans are based on the 241949-1972 .

The marginal products for research and extensionexpenditures for the 10 regions are presented inTable 2. These estimates reflect the contribu­tion to regional output of research and exten-

\vhe reTHPR.

l

(10)from zero at the 0.01 level of significance.In particular, the elasticity of production issmallest for labor and highest for capital. Itis also interesting to note that the sum of thecoefficients on conventional inputs is approxi­mately one, indicating constant returns to scalewithout the influence of research.

As indicated in equation (9) the model to beestimated in this study contained lags onresearch and extension expenditures \vithin theregion and research expenditures outside theregion. In addition, research expenditures out­side the region would probably not affect theregional output immediately, indicating a morecomplicated lagged structure associated withthese expenditures. Second-degree polynomialexpenditure lagsi/ which were considered appro­priate for this study were chosen from a largenumber of regression equations using differenttime lags with the final choice being on minimummean square error. Research and extension

66

Table 2. Regional Estimates of Benefits and Funding of Production-Oriented Agricultural Researchand Extension: Averages for the 1949-72 Period Expressed in 1972 Dollars.

Ratio ofAverage Spillovers

Regional Annual Average to Ratio ofMarginal Rate Regional Annual Regional Federal-State

Region Product of Return Benefits Spillovers Benefits Expenditures(Dollars) (Percent) --- (Million Dollars)---

Northeast 7.28 43.5 512.86 673.75 1. 31 0.97

Lake States 4.99 32.5 241.17 658.74 2.73 1.10

~~Eg_~~!! §~~Q ~~~~ ~~~~~Q !L~§§~Z~ ~~Q~ !~~~ _Northern Plains 12.27 61.7 536.39 753.59 1.40 1.63

Appalachian 10.30 55.1 610.85 726.62 1.19 1.60

Southeast 5.92 37.2 367.42 513.61 1.40 1.37------------------------------------------------------------------------------------------------------

Delta 4.77 31.3 220.80 548.51 2.48 1.80

Southern Plains 4.78 31.4 215.51 604.48 2.80 2.10

Mountain 7.98 46.4 474.88 758.26 1.60 2.35------------------------------------------------------------------------------------------------------

Pacific 5.13 33.3 370.22 698.33 1.89 0.90------------------------------------------------------------------------------------------------------~~~E~~~!~ ~~~! ~Q~Q ~L!~~~~~ ZL~~~~~Z ~~Z~ ~~~~ _

Since the returns are not forthcoming immedi­ately, it is important to determine the rate ofreturn associated with research and extensioninvestments. The regional rate of return (r.)can be calculated as follows: 1

The Northern Plains and Appalachian Regionshave the highest marginal productivity, reflect­ing relatively low levels of research and exten­sion investments. In contrast, the Lake States,Southern Plains, and Delta Regions have thelowest marginal productivity. The "average"marginal product, which was estimated usingnational averages for agricultural output andresearch and extension expenditures, was $6.51indicating the total returns from $1 invested.

(11)WL: MPR.( )/(1+r.)w -1 =0

w=O 1 t-w 1

that ranged from 30 to 180% for the same 10regions. His average rate of return and averagemarginal product for research and extensioninvestments were more than double the estimatesreported in the present study. This discrepancycan be explained by the fact that Evenson didnot account for the interregional transfer ofresearch results. Furthermore, the rates ofreturn presented in Table 2 are regional ratesof return and not social rates of return whichinclude spillovers of research results.

Evaluation of the rates of return reported inTable 2 indicate that investments in agricul­tural research and extension yield a high rate ofreturn (from 31 to 62%) for the originatingregion. It would appear that the returns fromthis type of investment would compare favorablywith alternative public investments in the regioneven without considering spillovers to otherregions.

Intergovernmental Finance

Regional benefits and spillovers are comparedto develop a mechanism for reallocating costsbetween the federal government and the region onthe basis of benefits realized within eachregion. Empirical estimates of regional benefitscan be calculated as follows:

This procedure explicitly accounts for the lagstructure. The regional rate of return forresearch and extension investments are reportedin Table 2. The average regional rate of returnis 40%, ranging from 31 to 62%. There is adirect relationship between marginal productsand rate of return on investment, since the samelag structure is assumed to exist in everyregion.

The rates of return estimated in this studyare in serious conflict with estimates made inearlier studies. Evenson (1971) reported returns

67

(12) B.1

W

L: B( )(Q./RI.)(RI.)w=0 t-w 1 1 1

Empirical estimates of regional benefits andspillovers as defined by equations (12) and (14),respectively, are shown in Table 2. 21 Thesefigures are annual averages for the 1949-1972period reported in 1972 dollars. Regional bene­fits are highest in the Corn Belt. Four regions

Implications

--the Corn Belt, Appalachian, Northern Plains,and Northeast--generated over $500 millionannually in regional benefits. With regards tospillovers of agricultural research benefits,all 10 regions generated more then $500 millionof spillovers annually. The Corn Belt annuallygenerated over $1.25 billion of spillovers tolead all regions in the amount of spillovers.

The average ratio of spillovers to regionalbenefits is 1.73 (Table 2). The Northeast andthe Appalachian Regions have the lowest ratio ofspillovers to regional benefits. Four regionshave spillover-to-regional benefit ratios higherthan two to one: Lake States, Corn Belt, Deltaand Southern Plains. These differences can beexplained by two factors: (1) the ratio of agri­cultural output to research and extension expen­ditures and (2) the ratio of extension toresearch expenditures. Those regions with lowlevels of research and extension expendituresrelative to agricultural output have high mar­ginal products for research and extension expen­ditures. Extension is assumed to create onlyregional benefits and not spillovers; thus,those regions in which extension is relativelyimportant would have lower ratios of spilloversto regional benefits.

The ratio of federal-to-state expenditures foragricultural research and extension, which arepresented in Table 2, can be compared with theratio of spillovers to regional benefits todetermine \~lether the federal government actuallyfinanced tile spillovers. These results indicatethat the federal government financed all of thespillovers in only three regions, NorthernPlains, Appalachian, and Mountain Regions. Inaggregate, the ratio of federal-to-state expen­ditures is only 1.38 compared to 1.73 for theratio of spillovers to regional benefits. Thusthe federal government's contribution to produc­tion oriented agricultural research and exten­sion expenditures would have to be increased 25%to align regional funding with regional benefits,on the average. However, several regions wouldrequire a greater increase in federal expendi­tures to yield an equitable distribution acrossall regions.

The ratio of spillovers to benefits for anyregion is not a constant but depends on themarginal productivity of research inside theregion, as well as outside the region. A givenunit subsidy would not ensure that the federalgovernment would finance its appropriate shareof agricultural research as determined by therelative importance of spillovers. Maintainingthe proper balance between federal and stategovernment finance would require a variablematching formula, one in which the shares ofthe federal government and the state governmentsvaried with the level of research expenditures.

nITRO. (RO.)1. 1.

V

L: S(t-v) (C)./RO.) RO.v=O 1. 1. 1.

S. = L: SIk

(R.I L: Rl

)1. k#i 1. l#k

S1.1.

is the value of spillover benefits fromagricultural research expenditures inregion i,

R. is the level of research expenditures in1. region i, and

is the level of research expenditures inall regions that generate spillovers intoregion k.

whereS1.1. is spill-ins of agricultural research

benefits in region i,S is a regression coefficient on the

(t-v)variable research expenditures outsidethe region in year (t-v) ,

Q. is mean level of agricultural output per1. state in region i,

RO. is mean level of research expenditures1. outside region i, and

TMPRO. is marginal product of research expen-1. ditures outside of region i.

These spill-ins in region i are allocated amongneighboring regions in proportion to totalresearch expenditures, which provides an estimateof spillovers from region i to region k. Theprocess of calculating spill-ins in every regionand allocating to the originating regions isrepeated until all spill-ins have been accountedfor.

whereB. is regional benefits for region i,S 1.( J is the regression coefficient of

t-w h d . d'esearc an extenS1.on expen 1.turesin year (t-w),

Qi

is mean level of agricultural output perstate in region i,

RI. is mean level of research and extension1. expenditures per state in region i, and

TMPR. is marginal product of research expen-1. ditures in region i.

This condition states that regional benefits arethe product of (a) the level of research andextension expenditures and (b) its value margin­al product. Calculating regional spillovers,which is slightly more complicated, begins withthe calculation of spill-ins (SI) for eachregion.

(13)

whereSi

(14)

68

Determination of the appropriate funding nec­essary to induce efficient behavior is a complexmatter. While this study has shown that matchinggrants can provide a theoretical solution to theexternalities problem, it is not the purpose ofthis study to propose a matching grant programfor agricultural research. Instead, the inter­governmental grant program developed in thispaper was presented as an analytical frameworkfor evaluating the current system of federalsupport for agricultural research.

The limited scope of this analysis resultedin shortcomings that should be taken into con­sideration. First, the spillovers considered inthis analysis were at the regional level ratherthan the state level. Benefits to the origin­ating state would be less than regional benefitsand conversely spillovers outside the statewould be greater than spillovers outside theregion. This study was focused at the regionallevel because previous research had indicatedthat it would be more likely to quantify syste­matic spillovers of agricultural research resultsamong regions than among states. Results ofthis study demonstrate that interregional spill­overs can be empirically measured. However,further research is needed.

Secondly, the production function estimatedin this study can measure only average tenden­cies with respect to interregional spillovers.Thus, greater confidence can be placed on theaggregate estimates of regional benefits andspillovers than on the estimates for a particularregion. Individual studies, region by region,would have to be undertaken in order to pre­cisely measure the interregional flows ofresearch benefits for a particular region. Theauthors have conducted such a study for theSouthern Region, which includes four regions ofthe present study--Appalachian, Southeast,Delta, and Southern Plains. Results of thatstudy indicated an internal rate of return of20% for agricultural research and extensioninvestment in the Southern Region. It is inter­esting to note that if the interregional spill­overs had been ignored in formulating the model,the results would have incorrectly indicated a72% rate of return on regional investment.These figures indicate the magnitude of the biasthat results from failure to account for inter­regional spillovers of agricultural researchresults.

Conclusions

Interregional spillovers of agriculturalresearch results create difficult problemsrelated to the allocation and finance ofresearch expenditures. As a result of thesespillovers, regional benefits diverge fromsocial benefits and therefore action by thefederal government is needed to ensure that thelevel of research investment is optimum.

69

Action by the federal government to deal withthis type of problem has generally been in theform of intergovernmental grants which can beused to ensure that regional and social benefitscoincide.

While the need for intergovernmental grants foragricultural research has been justified in thisstudy primarily on the basis of interregionalspillovers, the existence of spillovers is cer­tainly not the only factor that should be takeninto consideration in determining the federalgovernment's support for agricultural research.Ideally, the returns from agricultural researchinvestment will have to be compared with otherinvestment alternatives. Thus interregionalspillovers of agricultural research results isonly one facet to be considered in determiningthe appropriate balance between federal and stategovernments in financing agricultural research.However, it is hoped that this study has contrib­uted to the general understanding of agricul­tural research finance by identifying and quanti­fying interregional spillovers of agriculturalresearch results.

Footnotes

llFor discussions of externalities see Buchananand Stubblebine (1962), Davis and Whinston (1962),and Mishan (1971).

lIThe 10 production regions correspond to a U.S.Department of Agriculture delineation as reportedin such publications as Farm Real Estate MarketDevelopments (U.S. Department of Agriculture).

llData source for price deflators was Agricul­tural Statustics (U.S. Department of Agriculture).Value of agricultural output was deflated withthe index of prices received by farmers for allfarm products. The labor input for agriculturalhired labor was deflated by the index of pricespaid for hired labor. Total expenditures forfeed and livestock were deflated with the indexof prices paid for feed and livestock, respec­tively. Total expenditures for seed, fertilizer,lime, and miscellaneous expenses were deflatedwith prices paid for seed, fertilizer, and allitems in production, respectively. The capitaland depreciation variable was the farm expendi­tures for repair and operation of capital items,and depreciation and other consumption of farmcapital deflated by the index of prices paid forall items in production.

4/Previous research by Evenson (1967) and Cline(1975) indicated that a second-degree polynomialwas most appropriate from both a theoretical andan empirical perspective.

2/0ne difference between the conceptual modelsof regional benefits and spillovers, equations(4) and (5), and their empirical counterpartsequations (10) and (12) is that no price vari­able is explicitly considered in the latter twoequations. The reason for this difference isthat value rather than quantity is used as thedependent variable in the empirical estimationof the production function. Hence, the deriva­tive of the production function with respect toresearch expenditures is value marginal product.

References

{l} Almon, Shirley. "The distributed lagbetween capital appropriations and expendi­tures." Econometrica 30:178-196 January1965.

{2} American Association of University Profes­sors. AAVP Bulletin. Washington, D.C.,Annual Issues 1950-1972.

{3} Buchanan, James M. and W. C. Stubblebine."Externality." Econometrica 29:371-384November 1962.

{4} Budget of the United States Government.Washington, D.C., Annual Issues 1929-1972.

{5} Cline, Philip Lee. "Sources of ProductivityChange in United States Agriculture." Ph.D.Thesis, Oklahoma State University, May 1975.

{6} Davis, O. A. and A. Whinton. "Externalities,welfare, and the theory of games." Journalof Political Economy 70:241-262 June 1962.

{7} Evenson, Robert E. "The contribution ofagricultural research to production."Journal of Farm Economics 49:1415-1425December 1967.

{8} Evenson, Robert E. "Economic Aspects of theOrganization of Agricultural Research."In Resource Allocation in AgriculturalResearch, Walter L. Fishel (Ed.). Univer­sity of Minnesota Press, Minneapolis, 1971,pp. 163-182.

{9} Griliches, Zvi. "Hybrid corn: An explora­tion in the economics of technologicalchange." Econometrica 25:501-522 October1957.

{10} Griliches, Zvi. "Research expenditures,education, and the aggregate agriculturalproduction function." American EconomicsReview 54:961-974 December 1964.

{ll} Latimer, R. L. and D. Paar1berg. "Geo­graphic distribution of research costs andbenefits." Journal of Farm Economics47:234-241 May 1965.

70

{l2} Mishan, E. J. "The postwar literature onexternalities: An interpretative essay."Journal of Economic Literature 9(1) :1-28March 1971.

{13} Musgrave, Richard A. and Peggy B. Musgrave.Public Finance in Theory and Practice.McGraw-Hill Book Company, New York, 1976.

{14} Peterson, Willis L. and Joseph C. Fitzharris."Organization and Productivity of theFederal-State Research System in the UnitedStates." In Resource Allocation and Produc­tivity in National and International Agri­cultural Research, by Thomas M. Arndt, et a1.(Eds.). University of Minnesota Press,Minneapolis, 1977, pp. 60-85.

{15} Peterson, Willis L. and Yujiro Hayami."Technical Change in Agriculture." In!'=.Survey of Agricultural Economics Literature,Volume I, by Lee R. Martin (Ed.). Univer­sity of Minnesota Press, Minneapolis, 1977,pp. 497-540.

{16} Pigou, A. C. The Economics of Welfare.Fourth edition. Macmillan, London, 1932,part 2.

{17} Oates, Wallace E. Fiscal Federalism.William J. Baumo1 (Ed.). Harcourt BraceJovanovich, Inc., New York, 1972.

{18} U.S. Dept. of Agriculture. AgriculturalStatistics. U.S. Government PrintingOffice, Washington, D.C., Annual Issues.

{19} U.S. Dept. of Agriculture, CooperativeState Research Service. Funds for Researchat State Agricultural Experiment Stationsand Other State Institutions. Washington,D.C., Government Printing Office, AnnualIssues, 1965-1972.

{20} U.S. Dept. of Agriculture, Economic ResearchService. Farm Income State Estimates.Washington, D.C., September 1974.

{21} U.S. Dept. of Agriculture, Federal ExtensionService. Annual Report of Cooperative Ex­tension Work in Agriculture. Washington,D.C., Government Printing Office, AnnualIssues, 1930-1956.

{22} U.S. Dept. of Treasury, Bureau of Accounts.Combined Statement of Receipts, Expenditures,and Balances of the United States Govern­ment. Washington, D.C., Government PrintingOffice, Annual Issues, 1929-1972.