农业无形资产的评估27020437

Valuationof IntangibleCapitalin AgricultureFred C,White*AbstractThis study examines the valuation of research as intangible capital in agriculture usingTobinsqtheory.The market value of public research capital is estimated to be 8.6 times higherthan conventional assets.Private research capital is valued 5.2 times higher than conventionalassets.The estimated valuation multiplier for all farm assets dropped 1/3 over the last decade.Inrecent years the valuation multiplier has dropped below a dollar,which indicates the market isundervaluing farm assets.Key Words:farmasseta,flexible interceptmodel,principal components,research evaluation,ridge regression,Tobins q theoryAgricultural economists have for a longtime been interested in the valuation of farm assets,especiallyland.Considerableeffort has beenfocused on analyzing the impact of commodityprices and government programs on land values(Alston;BurG Harris).Valuation of governmentquotas has also been addressed(Vantreese,Reed,andSkees).However,marketvaluationofintangibleassets such as the stock of researchcapital has not been addressed in agriculture.In determining the valuation of intangibleassets in agriculture,it is important to distinguishthe impacts of research on society in general and onagriculturein particular.The empirical studieswhich have measured the impacts of agriculturalresearch typically measure the rates of return fromthe perspective of overall society.Huffman andEvenson recently cited 40 different estimates fromthe literature,which averaged 51 percent rate ofreturn to society,In comparison,the rate of returnon tangible assets in agriculture,including currentincome and real capital gains,averaged 4,9 percentfor the period 1950-91(USDA,Economic Indicatorsof tfie Farm Sector).Thus the social rate of returnon public research as an intangible asset was 10times the rate of return on tangible assets.Many of the benefits of public agriculturalresearchaccruetoconsumersbecauseoftheinelastic demand for agricultural products in theshort-run.The high benefit-cost ratios to society asreported in the literature do not necessarily implyhigh benefit-cost ratios to farmers.The returnsfrom public research to farmers would be expectedto be lower than the returns to society.Someeconomists argue that farmersneed commodityprice support programs to compensate them forpossible welfare losses resulting from agriculturalresearch.Valuation of intangible public researchcapital takes into account the direct benefits ofresearch to farmers and the indirect benefits of pricesupport programs which help ameliorate the impactsof productivity increases with an inelastic demand.Valuation of intangible private researchcapital must distinguishthe benefitsto privateagribusiness firms and to farmers.Some of thebenefits from private research are captured by thefums conducting the research.Patents and other*D.W.Brooks Distinguished Professor.Department of Agricultural and Applied Economics,The University ofGeorgia,Athens,GA.JAgr.and Applied Econ,27(2),December,1995:437-445Copyright 1995 Southern Agricultural Economics AssociationJ.Agr and Applied Econ.,Decenzber1995438forms of protection for intellectual property rightsincrease appropriability and curtail the spillover ofbenefits to other fm.If the agribusiness firmscaptured all the benefits of private research therewould be no incentive for adoption.Empiricalevidence indicates that some of the benefits ofprivate agricultural research accrue to consumersand farmers.Huffmanand Evenson measuredpublic returns from private research in agriculture.They estimated a rate of return of 46.3 percent onprivateresearchandreportedfourpreviousestimates ranging from 25,5 percent to 90 percent.The average of these 5 estimates was 63 percent,For the nonagricultural sector,valuation ofintangiblecapital can be examined through theappreciationin the stock markets valuation offm,Since agricultural firms are not traded on thestock market,USDA estimates are generally used tomeasure changes in asset values in agriculture.Valuation of intangible capital in agriculture can bemeasured by quantiing the impact of research onchanges in asset values.With land being the majorasset in agriculture,the benefits of research wouldbe expected to be capitalized into land values.However,other asset values may also be influencedby research.Valuationofintangibleassetscanbedetermined using Tobinsqtheory.This theoryallows for deviations between the market value andthe book value of assets.Such deviations could beattributed to unmeasured sources of rent which drivea wedge between the market value and the bookvalueof assets(Halo.WithTobinsq,theunmeasuredsources of rent can be explained interms of intangible assets.Griliches considered a sample of 457 largefirms over the period 1968-74.His results indicatedthat the long-run effect of a dollar of research anddevelopment(R&D)added about$2 to the marketvalueofthefirm,CockburnandGrilichesexamined 722 manufacturing firms with 1980 dataand reported estimated shadow prices of researchcapital ranging from 0.34 to 1,44.The impacts ofresearch were higher than these prices in somecases,becauseinteractiontermswithresearchcapital were also included in the models,Hallanalyzed 2,480 manufacturing firms from 1973 to1991.Hereported a shadow price of researchcapital stock of 0.48,which is relative to 1 fortangible capital.These shadow prices for researchcapital are quite different from the results to beexpectedin the currentstudy,Thesestudiesconsidered the effect of private research by a firmon the valuation of that firm,The present studyexamines the effects of public reseamh on thevaluation ofthe agricultural sector.It also examinesthe public effects(those not captured by privatenon-farmfws)ofprivateresearchonthevaltitionof the agricultural sector.The objective of this paper is to examinemarket valuations of public and private reseamhcapital for U.S.agriculture.A model of firmvaluation based on Tobinsqtheory is developedandappliedtotheU.S,agriculturalsector.Particular attention is focused on the valuationmultiplier,which is the market value relative to thereplacement cost of total assets.It shows themarket value of each dollar of assets.Although thevaluation multiplier is not observed directly,it isestimated for each year.Theoretical FrameworkFollowingHayashiandWildasin,thetheoretical framework is based on the maximizationof an individual firms discountedflow of netincome,The firm receives income from the sale ofoutputandhasexpensesforvariableinputs,investment,andadjustmentcosts,Inthisdiscussion,time subscripts are suppressed whereeverpossible,Productionisassumedtobegenerated according to a production technology Fwhich is a linear homogeneous fmction over capital(andthevectorofvariableinputs(L).Adjustment costs are assumed to take the form oflostoutputand/orwasteofinvestmentgoods(Wildasin).Hence two adjustment cost fimctionsare considered.First,the loss in output resultingfrom investment(1)is assumed to be a linearhomogeneous fimction G(z,K).Secondly,the loss ininvestmentgoodsresultingfrominvestmentisassumed to be a linearhomogeneousfunctionH(Z,K).Net income(n)is given byn(t)=poF(K,L)-G(I,K)-WL-plI+H(I,K),(1)439White:ValuationofIntangibleCapital in AgriculturewherepOis the price of output,w is the vector ofvariableinputprices,andplisthepriceofinvestment goods,The discounted value of net income,isgiven byV(0)=j%(t)(t)dt,(2)0where r(t)=exp(-tp(s)ds),and p is the discountrate.0Maximization of the objective function issubject to a capital constraint,The net change incapital stock(K)is composed of investment incapital and depreciation of existing capital goods.K=I-yK,(3)where y is the depreciation rate,Substituting(1)into(2)and using an auxiliary variable L for theconstraint yieldsV(0)=(pOIF(K,L)-G(I,K)-WL-pIII0+H(I,K)+LK-(I-yK)dt.(4)First order conditions for maximization for all timeperiods arev(o)=L(0)K(O).(6)Defining TobinsqasV/K gives an observablemeasure of k,Alternatively,Griliches empiricallyestimated a relationship that is a direct extension of(6),althoughhisworkprecededHayashisderivation.Griliches used two forms of capital-conventional inputs and the firms intangible stockof knowledge,which was estimated as a distributedlag measure of past researchand development(R&D),Following the notation used by Cochburnand GrilichesV=bA+Z8JQ,(7)where V is the market value of the firm,b is theaverage multiplier of market value relative to thereplacementcost of total assets,A is tangiblecapital,K is intangible capital,and 6 is the relativeshadow price for intangible capital,The estimationequation is derived by adding a multiplicative errorterm,dividing through by A and taking logarithmsof both sides of equation(7).When ZKJA isrelatively small,log(l+ZKA,Jcan be approximatedbyZK/A.TheestimationequationusedbyCockburn and Griliches is given bylog(q)=log(b)+MJQA+e,(8)where q=VIA,K,is an intangible asset,and e isthe error term.pp.-w=o;(5a)Flexible Intercept Modelk-pOGI+p!(l+H1)T=O;(5b)-?L=po(F-GJ-pIHJ-l.y;and(5C)lim?u(K(t,)=O,t+ca(5d)where subscripts on F,G,and H denote partialderivatives.Previous literature has emphasized equation(5b)inempiricallyestimatinganinvestmentequation.This equation involves an unobsemablevariableL,butHayashiprovedthatwithhomogeneityof F and G and the application ofEulers theorem:Previousstudiesofvaluationmodels,including Griliches and Hall,have dealt with bothtime-series and cross-sectional data,Hence it waspossible in these earlier studies to use year-specificdummies,While only time-series data are used inthepresentstudy,variableinterceptswillbeaccounted for with a flexible intercept regressionmodel,which is a special case of a time-varyingparametermodel.Aflexibleinterceptisparticularity important in the current study,becausethe intercept of equation(8)reflects the valuationmultiplier,which may have changed over time.A time-varying parameter model can beformulated as follows:J.Ag and Applied Econ.,Decembe1995Y,=Xt B,+&l,t=1,2,.T(9)where y,is the h observation of the dependentvariable,Xjis a K component vector of explanatovariables,B,is a K component vector of parameterssubjecttosequentialvariation,andet istheprediction error.Kalaba and Tesfatsion proposedthat the parameters in the model change only asmallamountfrom periodto periodwith thefollowing pattern of variation:B,=B,.,+V,(lo)where v,is the dynamic error.In a traditional constant parameters modelthe parameters would be estimated by minimizingTW=EE:(11)t=lwhereW is thesum of thesquaredresidualpredictionerrors,In Kalaba and Tesfatsionsgeneral model,which is called flexible least squares,theparametersareestimatedbytakingbothprediction and dynamic errors into account,Againthesum of the squared errorsare minimized,normalizing on the sum of the squared predictionerrors by giving these errors a weight of one andgiving the sum of the squared dynamic errors anarbitrary weight of p.The flexible least squaresestimator minimizes440TTW(jf)=pxv;v,+zs:(12)t=2t=lwhereW(p)is the p-weightedsum of squaredresidu prediction and,dynarnic errors,and Vj=B,-B,.,Recall that v,is a K component vector and S,is a scalar.Large values of#will penalize dynamicerrorsheavily,causingthedynamicerrorstodiminish.If there are no dynamic errors,the modelbecomesanordinary.leastsquaresmodel.Alternatively,small values of p penalize predictionerrors heavily,causing prediction eors to diminish,As p approaches zero,the model approaches arandom coefficient model.Estimation ProcedureUsing matrix notation,the flexible interceptmodel can be estimated as follows:B=A-)Xj(13)where B is the coefficient vector with the first Tcoefllcientsbeingyear-specificinterceptsB=ll,.,B=B+l,.B+JJ and y is the(Tx f)vector ofendogenous variables.The A and X matrices aredefined below,A=+1-po(1.()x,./YK,-2+1-po.0X,2.XK2o-JJ2+1-poii:“.%.;:.0-2+1-o.0-p+1X,r.-.XKTx,X12.x,X(xl*“”J(XK*j%.XK,XK2.xK,x;,“;K.Where X,is a vector of exogenous variables(X,X,2.X,!(14)441x=1 0 0.0 x,./YK,o1 0,.0 X,2XK2001!Ii“.010001 X,T.XKZ(15)Let the variance from the model be givenby az.The covariance of the flexible interceptmodel with independently and identically distributedel is as follows:COV(13)=02A-X X4,(16)Since 02 is unknown,its estimateis used inequation(16).Multicolinearity was a problem with thedata,so a ridge regression model with flexibleintercepts was used.The ridge regression estimatorisb,=A+rD-X y,(17)whereD isa diagonalmatrixcontainingthediagonal elements of A and r is an arbitrary scalar,The variable r was incremented from.01 to 1.0 by.01 with the appropriate r chosen on the basis of theb,coefficients being stable.When the absolutevalue of changes in all coefficients averaged lessthan one percent,that was the value of r chosen,Forcomparisonpurposes,severalregressionmodels will be used,including leastsquares,principal components,and ridge regressionwith constant intercepts.The latter two approachesare used to deal with multicolinearityproblemswhich are evident in the data.These procedures arewidelyreportedin econometrictexts,includingGreene.However,these models with constantintercepts do not report how the valuation multiplierchanges over time,White:ValuationofIntangibleCapital in AgricultureDataThe penocl of analysis covers 1950 through1991.Data for the farm variables were mainlyfrom EconomicIndicatorsof the FarmSector(USDAC).Thesumoftotalliabilitiesandproprietors equity for the farm sector,excludinghouseholds,was used to reflect total value of farmassets.Dataforpublicandprivateresearchexpendituresandapriceindexforresearchexpenditureswere from Huffmanand Evenson.Their time series covered 1888 to 1990,but only1915-90 was used in the present study,Privateresearch was reported only as decade averages priorto 1956,Interpolation between decade averages wasused for annual estimates prior to 1956.FollowingCockburn and Griliches and Hall,research capitalwas calculated as a stock variable from previousresearch expenditures under the assumption of a 15percentdepreciationrate.Expendituresweredeflated using the Huffman and Evenson researchprice index to calculate the stock variable.Then thestock variablewas reflatedtocurrentdollars.Separate capital variables were calculated for publicresearch and private research.Two cash flow variables-governmentpayments and value of agricultural exports-wereincluded in the analysis.The government paymentsvariable was from Economic Indicators qfthe FarmSector(USDAC)and the valueof agriculturalexports variable was from AgriculturalStatistics(USDAb),In both cases,lagged variables were usedin the analysis.The tangible capital stock included grosscapital expendituresin farm structures and landimprovement,motor vehicles,and machinery.Datafor these variables were from Economic Indicatorsof the Farm Sector(USDAC).The 1945 level ofassets in real estate,motor vehicles,and machinerywas taken as the base level of capital.Annualadditions to the base were derived from investments.Annualreductionsincapitalwerebasedondepreciation and loss of farmland.Depreciationrates were calculated as the ratio of depreciationexpenditures to the beginning values of assets ineach year for each category,Data used to calculatedepreciation rates were from Economic Indicators ofJ.Agr and Applied Econ.,DecembeC 1995442the Farm Sector(USDAC),Depreciation rates were0.22 for automobiles,0.21 for trucks,0.12 fortractors,0.14 for machinery and 0,03 for buildings.The capital stocks were constructed with deflatedvariables,After depreciation was accounted for,thevariables were reflated to current dollars,Indexesof prices paid by farmers for automobiles,tractors,machinery and buildings and fences were obtainedfrom Agricultural Prices(USDAa),Livestock andcropinventories,whichwereobtainedfromEconomic indicators of the Farm Sector(USDAC),were also includedin the measure of tangiblecapital.The tangible capital variable is the sum ofcapital in automobiles,trucks,tractors,machinery,buildings,land,livestock,and crops.ResultsRegression models of equation(8)wereestimated to explain q,which is the ratio of marketvalue to book value,for US.agricultural assets.The explanatoryvariables include capitalstockvariables for public research and private research,Two cash flow variables-government paymentsand agricultural exports-were also included in theregression models,All four explanatory variableswere divided by book value of assets.Fouralternativesestimationprocedureswere used.These procedures were least squareswith a correction for autocorrelation(AR1),principalcomponentsregression(PCR),andtworidgeregression models.One of the ridge regressionmodels had a constant intercept and the other hadflexible intercepts which varied from year to year.Regression results are reported in table 1.The ARI model explains91 percent of the variationin the model,but the standard errors are quite high,which is indicative of a multicolinearity problem.In fact,none of the explanatoryvariablesarestatistically significant in the AR1 model.Sincethese coefficients are not measured with adequateprecision,twotraditionalmodelstoaddressmulticolinearity problems are estimated.The resultsfromPCRandridgeregressionwith constantintercepts are similar,and all the coefficients arestatistically significant at the 0.01 level.From thesetwo models,the shadow prices for a dollar of publicresearch capital are$7.20 and$7.79.The shadowprices for a dollar of private research capital are$3.63 and$5.42.The coefficients for the ridge regressionmodelwithflexibleinterceptsaresimilarinmagnitudetotheresultsforPCRandridgeregressionwithconstantintercepts.Allthecoefficients in the ridge regression with flexibleintercepts are statistically significant at the 0,01level.Its shadow prices are$8.59 for publicresearch capital and$5,22 for privateresearchcapital,These shadow prices are relative to tangibleassets,Hence each dollar of public research capitalis valued 8,59 times as much as a dollar of tangiblecapital.Likewise,each dollar of private researchcapital is valued 5.22 times as much as a doilar oftangible capital.Conglomerate results from all four modelsare reported in table 2,For each model,99%confidenceintervalswerecalculatedforthecoefficientsof the explanatoryvariables.Theoverlapping porhons of these confidence intervalsare reported in table 2.The shadow price for publicresearch capital could fall within the range from$7,69 to$8.07and bewithintheconfidenceintervals of all four models.For private researchcapital,there was no value that would fall withinthe confidence intervals of all four models.Table2 also reports 99 percent confidence intervals forthe ridge regression model with flexible intercepts.Its coefficientfor public research capital couldrangefrom$7,69to$9.48asa99percentconfidence interval.Likewise,its coefficient forprivate research capital could range from$4,63 to$5.81,The exponential of each intercept in theridge regressionwith flexibleinterceptsis themarket valuation multiplier of agricultural assets.These multipliers for the period 1950-91 are shownin figure 1.In one sense the multiplier might bethought of as rather stable over the period 1950-80,followed by a dramatic reduction from 1980-91.Analternative interpretation might be that the multiplierbegantodeclineafter1960,However,theprosperity experienced by agriculture m the 1970scaused a departure from the long-term decline in thevaluation multiplier.After the 1980 peak,themultiplier reverted back to its long-term downwardtrend.443White:ValuationofIntangibleCapital in AgricultureTable 1.Selected Regression Models of Tobins q for US,Agriculture,1950-91,PrincipalRidge RegressionAutoregressionComponentsConstantFlexibleMeans(ARl)RegressionInterceptInteiceptIntercept1.022*0.2030,406$(0.123)a(0.037)(0,028)Public ResearcMAssets,0269.4397,790”7,196*8.587*(14,262)(1,416)(0,339)(0,348)Prwate ResearchJAsset.s,036-7.9115.422*3.626*5.219*(8,245)(O986)(o 307)(0.230)Government Payments/Assets.0221,0307.119*2.839*5 469*(0.902)(1.294)(1.035)(0.594)Value of Exports/Assets.5290,1850.349”0,258*0.349”(0,I14)(0,06