Journal of Productivity Analysis, 22, 185–205, 2004© 2004 Kluwer Academic Publishers. Manufactured in The Netherlands.

Scale Economies and Efficiency in U.S. Agriculture:Are Traditional Farms History?

CATHERINE MORRISON PAUL∗ cjmpaul@primal.ucdavis.eduDepartment of Agricultural and Resource Economics, and Member of the Giannini Foundation, Universityof California, Davis, U.S.A.

RICHARD NEHRINGU.S. Department of Agriculture, Resource Economics Division, Economic Research Service, WashingtonDC 20005, U.S.A.

DAVID BANKERU.S. Department of Agriculture, Resource Economics Division, Economic Research Service, WashingtonDC 20005, U.S.A.

AGAPI SOMWARUU.S. Department of Agriculture, Resource Economics Division, Economic Research Service, WashingtonDC 20005, U.S.A.

Abstract

The structural transformation of agriculture in recent decades has raised seriousconcerns about the future of the family farm. This study examines the economicperformance of U.S. farms, to explore the potential of smaller farms to competewith larger entities, and ultimately to survive in this rapidly changing environment.We use deterministic and stochastic frontier methods and survey data to mea-sure and evaluate factors underlying scale economies (SEC) and efficiency (SEF)of corn-belt farms for 1996–2001. Our results suggest that family farms are bothscale and technically inefficient. Potential for the exploitation of significant scaleand scope economies, and some greater technical efficiency, seem to be drivingtrends toward increased farm size and dwindling competitiveness of the small fam-ily farm.

JEL Classification: O3, O13

Keywords: DEA, Stochastic frontier, efficiency, agriculture, scale efficiencies, scale economies

1. Introduction

In the past few decades, unprecedented changes in technological and market forcesand urbanization pressures have arguably changed forever the structure of U.S.

∗ Corresponding author.

186 MORRISON PAUL ET AL.

agriculture. Serious concerns about the impacts of this structural transformationon the economic health of family farms have emerged as traditional farming com-munities have experienced conspicuous declines in profitability and competitiveness(National Commission on Small Farms, 1998; Harl, 2000; USDA, 2001a). In par-ticular, an increasingly strong move toward larger farms has long been a perceivedthreat to the long-term economic viability of the small family farm. Associatedrecent trends toward greater farm (especially livestock) concentration, and corpo-rate industrialization and contracting out of production, also have raised seriousquestions about the future survival of remaining small independent operations thatface increasingly unfamiliar and powerful markets.

Observed production patterns in the U.S. agricultural sector suggest that thesetechnological and structural changes are likely associated with economies fromboth scale of production and output composition, so that larger and more diver-sified farms are increasingly more productive or efficient than small farms. Kum-bhakar et al. (1989, for dairy farms), Heshmati and Kumbhakar (1997, for grainfarms) and Sharma et al. (1999, for hog farms) provide evidence that this hypoth-esis may be true in the context of technical efficiency. These findings suggest theimportance of efficiency impacts from scale and composition changes, and thepotential to enhance our understanding of farms’ performance patterns by furtherevaluation of these productivity drivers.

To facilitate such an evaluation of farms’ competitive possibilities, in this arti-cle we assess the performance of small and large farms in terms of scale econ-omies, and scale and technical efficiency. We measure these key efficiency factorsusing a farm-level dataset for agricultural producers in the corn states, recogniz-ing a broad range of outputs, inputs, and farm characteristics, for 1996–2001. Weevaluate these performance indicators across time, space, and farm typology,1 andassess the distribution of performance patterns across farmer and farm characteris-tics, including farmers’ education and age, financial circumstances, and innovation(biotech adoption).

We use an input distance function approach to represent farms’ technologicalstructure in terms of minimum input (resource) use to produce given output lev-els, because farmers typically have more short-term control over their input thanoutput decisions.2 The resulting theoretical framework represents input contribu-tions per land mass unit, which is consistent with analysis of yields in traditionalagricultural studies but stems theoretically from the homogeneity properties ofthe distance function. To estimate our model we use and compare two methods,deterministic data envelopment analysis (DEA) and stochastic production frontier(SPF) procedures. Assessing the consistency of results across estimating methods isparticularly useful since questions arise about the lack of statistical inference forDEA analysis, and about the stochastic specification with pseudo data for SPFanalysis.

Our data are from an annual U.S. Department of Agriculture (USDA) survey offarms, in Heartland and Northern Crescent states for which corn is a major com-ponent of agricultural output, that produce any combination of crops and animalagricultural products. The farm-level data is used to construct a pseudo panel data

SCALE ECONOMIES AND EFFICIENCY IN U.S. AGRICULTURE 187

set in terms of cohorts, to deal with the problem of intertemporally linking annualcross-section data. We distinguish crop (corn, soy, “other”) and livestock outputs,and labor, capital, fuel, fertilizer (chemicals), materials (feed and seed), specificcrop and animal inputs, “other” materials, and (quality-adjusted) land inputs. Wealso recognize off-farm income as a key source of revenue for farm families.3

We find strong evidence of the potential to exploit scale economies (especiallyfrom the SPF framework), which are particularly great for smaller farms, andwhich seem largely attributable to output diversification or scope economies. Esti-mated efficiency levels are also lower for small farms (and in the DEA relative tothe SPF framework). Temporal effects are less definitive, and differ more acrossspecification—although both technical efficiency (especially for SPF) and scale effi-ciency (especially for DEA) generally seem be increasing over time. Specifically,the SPF model suggests that technical efficiency, and to some extent scale anddiversification economies, have been increasing over time, but that technical andenvironmental changes are repressing productivity increases. In reverse, the DEAframework reveals little increase in technical efficiency, but reduced scale econo-mies and shifts out in the production frontier over time. Little variation in perfor-mance, or consistency across estimation models, is apparent across region, or otherfarm and farmer characteristics (when cohort, year, and region are held constant).

Growth thus appears to enhance both scale and technical efficiency; scale econ-omies in particular, with associated output composition adjustments, seem to bethe primary driving factor for economic performance of these farms. Increasingcompetitiveness will require small family farms to move toward producing morediversified output at a larger scale, as well as improving efficiency toward the levelsexhibited by larger farms.

2. The Model and Estimating Methods

2.1. The Modeling Framework

Analyzing production structure and performance requires representing the under-lying multi-dimensional (-input and -output) production technology. This may beaccomplished by specifying a transformation function, T(X,Y,R)=0, which sum-marizes the production frontier in terms of an input vector X, an output vectorY, and a vector of external production determinants R. This information on theproduction technology can equivalently be characterized by an input set, L(Y, R),representing the set of all X vectors that can produce Y, given R.

An input distance function (denoted by superscript I ) identifies the minimumpossible input levels for producing a given output vector, defined according toL(Y,R):

DI (X,Y,R)=max{ρ : (X/ρ)∈L(Y,R)}. (1)

It is therefore essentially a multi-input input-requirement function, allowing fordeviations from the frontier. Although it is a primal function with no economic

188 MORRISON PAUL ET AL.

optimization implied, it is also conceptually analogous to a cost function if allo-cative efficiency is assumed, since in this case the lowest possible input use impliesminimized costs for production of Y.

The deterministic and stochastic efficiency models used for our analysis char-acterize the input distance function alternatively using programming and econo-metric methods. Estimation of (1) by either method is designed to represent thedistance of an observation from the frontier, or technical inefficiency, assuming aradial contraction of inputs to the frontier (constant input composition). The ratioof estimated efficient input use to actual use, computed by programming methods(DEA) as the distance from a piece-wise linear frontier, and by econometric meth-ods (SPF) as a one-sided error term, is denoted TE (technical efficiency).

Characterizing scale economies (SEC) and efficiency (SEF), and imputing therole of output diversification or scope in these economies, differs across estimationmethods. For both DEA and SPF models variable returns to scale must of coursebe allowed for in order to measure scale effects. For SPF the scale elasticity rep-resenting SEC may then be computed parametrically as the proportionate changein output(s) producible from a small proportional change in each input quantity.However, SEF, or the (ray) average productivity at the observed input scale relativeto that attainable where the scale elasticity equals unity, is not as straightforwardto compute. The reverse is true for DEA. These measures both provide informa-tion about scale effects, although they are not equivalent except at the point whereboth the scale elasticity and efficiency measures equal one (see Ray, 1998, for morediscussion), so they provide somewhat different perspectives on scale effects.

In addition, the scale elasticity (scale economy measure) implicitly containsinformation about output jointness, and thus scope economies. In a parametriccontext, such jointness may be inferred from the cross-effects among the inputs.That is, specific constraints may be used to impose non-jointness of the outputs,resulting in a “net” scale economy measure (SECN).

Another potential contributor to economic performance is technical progress(commonly denoted TP), reflected by shifts in the technological frontier over time.However, for our empirical application productive differences across time may arisefrom a variety of both environmental and technological factors (such as weather,regulations, or varying input and output quality) that do not necessarily causeoutward shifts of the frontier—particularly in the short time frame of our anal-ysis. We can infer the yearly performance impacts of such technical and environ-mental change (TEC) from the measurement of the DEA frontier over time, orfrom time dummies in SPF estimation, although this is not a primary focus of ouranalysis.

Such efficiency, scale, and shift measures are often characterized as componentsof overall total factor productivity (TFP), through the computation of Malmquistindexes that represent these separate contributors to technical (and economic) per-formance in terms of their growth rates over time. However, for our purposes weare less interested in temporal changes in these indicators than in their compara-tive levels over time, space, and size, so we measure them directly and then sum-marize their patterns across these dimensions. We also assess differences in these

SCALE ECONOMIES AND EFFICIENCY IN U.S. AGRICULTURE 189

performance indicators across farm and farmer characteristics, through regressionanalysis, to summarize their distribution across these factors.

2.2. Nonparametric (DEA) Estimation

Functional relationships representing production processes, such as the distancefunction discussed above, provide only a loose foundation for deterministic pro-gramming-based DEA procedures. The DEA input-oriented linear programmingproblem is formally written as

min θ,λθit s.t.−Yit +Yλ≥0, θXit −Xλ≥0, N1′λ=1, (2)

where θit is a scalar representing the efficiency score for the ith firm in time t, λ

is an N × 1 vector of constants, N1 is a N × 1 vector of ones, and the N1′λ = 1convexity constraint allows for variable returns to scale (VRS).4 For our empiri-cal implementation, the solutions to this problem were developed and computedin General Algebraic Modeling Systems (GAMS), (Brooke et al., 1988).

The results from estimation of this framework can directly be used to measureTE; TE = θit indicates the proportion by which inputs could contract and main-tain the same output level, or the proportional deviation from full technical effi-ciency (TE) in that time period. To measure SEF we can compare the TE estimatesfrom this framework (TEVRS) with those from a constant returns to scale (CRS)model that does not include the N1′λ = 1 constraint (TECRS).5 Such a measure,TECRS/TEVRS, will fall short of 1 if either increasing (IRS) or decreasing (DRS)returns to scale exist, since the CRS frontier will always envelope the VRS frontier.Further, the TEC index capturing technical and environmental changes betweenadjacent periods t and s, may be computed from these estimates as

TEC=[

TEs(Yt ,Xt ,Rt )

TEt (Yt ,Xt ,Rt )• TEs(Ys,Xs,Rs)

TEt (Ys,Xs,Rs)

]1/2

. (3)

Computing SEC (often denoted ε) from DEA estimates is less straightforward,because SEC apply only to efficient points. Thus, inefficient observations mustfirst be represented by their efficient counterparts using input- and output-orientedreference points (radial projections). This may be accomplished, as developed byForsund and Hjalmarsson (2002), based on the Lagrangian of equation (1)

L= θit −υit (Yλ−Yit )−νit (θXit −Xλ)−uit (N1′λ), (4)

where υit , νit , and uit are the shadow prices of the output, input, and equalityconstraints on the sum of the λs, respectively. The uit values are unique forinefficient units, and can be used to calculate the scale elasticity as SEC =minθz,λ /(minθz,λ −uit ). The radial projected observation to the DEA frontierexhibits IRS if uit >0, CRS if uit =0, and DRS if uit <0.

190 MORRISON PAUL ET AL.

2.3. Parametric (SPF) Estimation

The SPF measurement involves econometric estimation of the input distance func-tion DI (X, Y, R). This requires first imposing the condition that DI (X, Y, R) behomogeneous of degree one in the inputs. Analogous to the output distance func-tion case (Lovell et al., 1994), this can be accomplished through normalization.By definition, linear homogeneity implies that DI (ωX,Y,R) = ωDI (X,Y,R) forany ω > 0; so if ω is set arbitrarily at 1/X1, DI (X,Y,R)/X 1 = DI (X/X1,Y,R) =DI (X*,Y,R) (where X* is a vector of input ratios normalized by X1). Approxi-mating this function by a translog functional form to limit a priori restrictions onthe relationships among its arguments results in:

ln DIit /X1,it =α0 +

∑m

αm ln X∗mit (4a)

+0.5∑m

∑n

αmn ln X∗mit ln X∗

nit +∑

k

βkln Ykit

+0.5∑

k

∑l

βkl ln Ykit ln Ylit

+∑q

δqRqit +∑

k

∑m

γkm ln Ykit ln X∗mit

=TL(X∗,Y,R),or (4b)

− ln X1,it =TL(X∗,Y,R)− ln DIit , (4c)

where i denotes farm, t time period, k, l, outputs, and m, n, inputs.6 If X1 is land,for example, the function is essentially specified on a per-acre basis, which is con-sistent with much of the literature on farm production and productivity in termsof yields.

Estimation of this equation by SPF methods, as initially developed by Aigneret al. (1977) and Meeusen and van den Broeck (1977), involves characterizing thedistance from the frontier, − ln DI

it , as a technical inefficiency error, −uit . Thiserror is then combined with a random error component νit , representing factorsthat might generate noise in the data that is attributed to technical inefficiencyin deterministic models (such as measurement error and unobserved inputs). Theνit are assumed to be independently and identically distributed random variables,N(0, σ 2

ν ), and the −uit to be non-negative random variables independently distrib-uted as truncations at zero of N(0, σ 2

u ).The resulting − ln X1 = TL(X*,Y,R)+ ν −u equation (with the sub-scripts sup-

pressed for notational simplicity) may be estimated by maximum likelihood (ML)methods. We used Tim Coelli’s FRONTIER program, based on the error compo-nents model of Battese and Coelli (1992), for this purpose; the resulting technicalefficiency scores are measured as TE = exp−u. Shifts in the frontier for each yearcan be computed, if time dummies are included as components of the R vector, asTEC= εDIt = ∂ ln DI (X,Y,R)/∂t .7

SCALE ECONOMIES AND EFFICIENCY IN U.S. AGRICULTURE 191

The SEC can also be computed from the estimated model as the scale elastic-ity SEC = −εDIY = −∑

k ∂ ln DI (X,Y,R)/∂ ln Yk = εX1Y for K outputs Yk. Thismeasure is consistent with the output distance function formula in Fare and Pri-mont (1995), but is also similar and conceptually more comparable to the multiple-output cost-function-based elasticity in Baumol et al. (1982) (although it does notallow for input choice). The extent of SEC is implied by the short-fall of SECfrom 1.

The SEC measure embodies scope as well as scale economies through the cross-terms among the outputs. As shown by Denny and Pinto (1978), scope economiesexist in the translog function if −βkβl <βkl . Thus, testing the constraint −βkβl =βkl

allows us to determine whether scope economies exist, and evaluating the functionwith this constraint imposed (resulting in the net measure SECN), indicates the extentof such economies. SEF may also be assessed in the SPF framework, following Ray(1998), who shows for a translog functional form that SEF = (1-SEC)2/2β, whereβ =∑

k

∑l

∑βkl .

8 This provides additional information on the potential to reduceinput use per unit of output by moving to the point where SEC = 1.

Finally, note that the individual −εDIYk = −∂ ln DI (X,Y,R)/∂ ln Yk elastici-ties underlying the −εDIY scale elasticity, and the analogous −εDIX*m = −∂ lnDI (X,Y,R)/∂ ln X∗

m elasticities representing relative input shadow shares (Fare andGrosskopf, 1990), may be examined to evaluate the appropriateness of the assumedtechnological form. The output measures indicating the increase in input use whenoutput expands should be positive (like a marginal cost measure), and the inputmeasures indicating the shadow value of the mth input relative to X1 should benegative (like the slope of an isoquant).

3. The U.S. Agriculture Panel Data

The U.S. farm level data used to construct our panel data set are from the1996–2001 Agricultural Resources Management Study (ARMS) Phase-III survey.This is an annual survey covering U.S. farms in the 48 contiguous states, con-ducted by the National Agricultural Statistics Service (NASS), USDA, in cooper-ation with the Economic Research Service (ERS). Our data cover the ten primarycorn-producing states, from the Heartland (HL) and the Northern Crescent (NC).9

For empirical production studies using such panel data, the temporal pattern ofa given farm’s production behavior must be established. In the absence of genuinepanel data, repeated cross-sections of data across farm typologies may be used toconstruct pseudo panel data (see Deaton, 1985; Heshmati and Kumbhakar, 1997;Verbeek and Nijman, 1992). Such a panel is created by grouping the individualobservations into homogeneous cohorts, distinguished according to time-invariantcharacteristics such as fixed assets, geographic location, or land quality or acreage.The empirical analysis is then based on the cohort means rather than the individ-ual farm-level observations.

For our analysis we assigned the farm-level data to cohorts, based on the ERSfarm typology (TYP) groups summarized in Appendix Table A1.10 The data in

192 MORRISON PAUL ET AL.

TYP1-3 (limited resource, retirement, and residential) is relatively limited com-pared to the traditional farm data, so they were further grouped into three cohortsby level of agricultural sales. Three cohorts each were similarly defined for TYP4-6, and two each were distinguished for TYP5-7. The definitions of the resulting 13cohorts (COH1-13) are outlined in Table A1.

The pseudo-panel data we use for estimation are the weighted mean values ofthe variables to be analyzed, by cohort, state, and year. In total we thus have abalanced panel of 780 annual observations (130 per year, for our 10-state sam-ple),11 summarizing the activities of 2,127 farms in 1996, 4,305 in 1997, 2,479 in1998, 3,593 in 1999, 2,714 in 2000, and 1,372 in 2001.12 To present our resultsbelow, we group these cohorts into (i) residential farms (RES, COH1-3); (ii) smallfamily farms (SM, COH4-6); (iii) larger family farms (LG, COH7-10); and (d) verylarge family and non-family farms (VLG, COH11-13).

For our analysis the Y vector contains YC = corn, YS = soybean, YO = other crops,YA = livestock, and YI = off-farm income. Off-farm income is treated as an “out-put” because it is a revenue-generating activity that uses measured inputs andaffects farm family economic performance.13 The components of the X vector aredefined as XLD = land, XL = labor, XK = capital, XE = energy (fuel), XF = fertilizer(including lime and other chemicals), XFD = feed, XSD = seed, XC = other crop-spe-cific materials, XA = other animal specific materials, and XO = all other operatingexpenses. Time dummies, t1997–t2001, are the only R components.14 This treatmentrecognizes that yearly variations may not follow a smooth trend, due to variousshort-term exogenous factors in addition to technical change;15 these shifters thuscapture a combination of various technical and environmental changes that differby year.

Agricultural outputs are measured in terms of dollars per farm, calculated as thesum of the value of sales for each type of farm product distinguished. The variableinputs are annual per-farm expenditures on each input category. Capital machineryis measured as the annualized flow of capital services from assets (excluding land).Land is measured as an annualized flow of services from land, valued at the qual-ity-adjusted price of land.16 To translate these nominal values into real terms, allvariables are deflated by the estimated increase or decrease in cost of productionin 1997–2001 compared to 1996 (in terms of agricultural prices).

Our data on farm and farm operator characteristics include the age and educa-tion of the farmer, the percent of acres rented rather than owned, debt/asset ratios,and the percent of acres in biotech corn and soybeans.

A summary of the sample data for 2001 is presented in Appendix Table A2. Ingeneral, the data for 2001 are representative of those for 1996–2000 except thatthe percent of biotech corn and soybean acres greatly increased during this timeperiod.

4. Empirical Results

The ML parameter estimates for our SPF model are presented in Appendix TableA3; the γkm and most αmn parameters were set to zero due to individual and joint

SCALE ECONOMIES AND EFFICIENCY IN U.S. AGRICULTURE 193

statistical insignificance, but the remaining parameters are quite significant over-all. The first order distance function elasticities (and standard errors) representingeach output and input’s contribution to production and summarizing the techno-logical structure, are presented in Appendix Table A4 for the whole data sampleand each combined cohort.17 All have the appropriate sign, except −εDIX∗A for theRES and −εDIX∗C and −εDIX∗O for the LG and VLG combined cohorts (whichare also statistically indistinguishable from zero). These sign discrepancies appearto result from the small contribution of the animal-oriented inputs in the relativelycrop- (and labor-) intensive cohorts, and of the crop-oriented inputs in the rela-tively livestock- (and capital-) intensive cohorts.

Estimates of the scale and efficiency performance indicators outlined above forthe DEA and SPF models, based on the parameter estimates in Table A3 for theSPF model, are reported in Table 1. These measures are computed for each obser-vation and then averaged over the whole sample, and for each combined cohort,year, and region.18

The SEC measures for both the DEA and SPF specification reveal scale econ-omies (IRS),19 that are generally greater for the smaller-farm cohorts (RES andSM). The estimated SEC for the SPF model are also considerably larger, and havea stronger tendency toward lower economies for the larger cohorts, than those forthe DEA model.20

Consideration of the SECN measures for the SPF model suggests why this mightbe the case. These elasticities purge the output jointness underlying scope econo-mies by imposing the restriction of no output-cross-effects on the model estimatedwith such cross-terms. They are much larger in magnitude, and in fact (exceptfor the RES cohort group) indicate mild to strong diseconomies if growth doesnot take advantage of output complementarities by adapting output composition,implying a key role of scope economies in measured scale effects.

Table 1. DEA and SPF performance measures, averages.

DEA SPF

SEC SEF TE TEC SEC SECN TE TEC

Total 0.929 0.937 0.895 1.036 0.696 1.202 0.935 0.957RES 0.944 0.909 0.835 0.544 0.919 0.936SM 0.905 0.927 0.812 0.595 1.022 0.916LG 0.917 0.948 0.946 0.778 1.355 0.945VLG 0.955 0.963 0.970 0.839 1.463 0.942

1996 0.854 0.896 0.892 0.000 0.679 1.170 0.895 0.0001997 0.964 0.957 0.892 1.040 0.715 1.238 0.917 1.0331998 0.954 0.879 0.926 0.975 0.706 1.221 0.934 0.9841999 0.930 0.941 0.885 1.078 0.709 1.225 0.948 0.9022000 0.900 0.875 0.879 1.076 0.700 1.210 0.959 0.9412001 0.973 1.075 0.897 1.011 0.667 1.150 0.959 0.889

HL 0.932 0.944 0.905 0.689 1.191 0.932NC 0.925 0.927 0.880 0.707 1.219 0.941

194 MORRISON PAUL ET AL.

Some insights about the relative contributions (or “shadow shares”) of individ-ual outputs and inputs, embodied in the SPF SEC elasticities, may be gained fromthe first order elasticity measures in Table A4. The “marginal cost”, in terms ofoverall input increases as outputs expand, is lower for each output for smallerfarms, except off-farm income for RES farms. That is, the greater SEC for thesmaller cohorts is driven by relative (to larger farms) input savings for expansionof any farm business outputs, but not off-farm income (which requires more laborand energy input use).

The SEF measures for the DEA model show that farms in the RES cohortshave a greater potential to reduce costs by moving to a scale efficient point thanimplied by the SEC estimates, and than those in other cohorts (consistent with theSPF SEC estimates). For all other cohorts somewhat lower input savings per unitof output are evident from the SEF than the SEC measures, which is even morestrongly implied by the SPF model. The SPF SEF measures in fact suggest that,for existing input and output composition and evaluated from the projected effi-cient point on the frontier (Ray, 2003), virtually no input savings may be gener-ated by movement toward a scale efficient point; SEF is always negligibly differ-ent than 1.0 (so it is not presented separately in the table). These results supportthe conclusion from the SEC estimates that performance differences across cohortsarise largely from netput (output and input) composition changes accompanyinggrowth; simply expanding the scale of operations, while maintaining current pro-duction practices, is not input-saving.

The temporal patterns of the scale economy and efficiency measures do not seemdefinitive for either specification, although more fluctuations are implied by the DEAestimates. Roughly speaking, the DEA measures suggest falling SEC over time, andthe SPF estimates fairly constant levels—but a tendency for potential economies todrop in 1997–1999 and then rise again is also evident for both models. Further, littlevariation in scale effects is apparent in the spatial (regional) dimension.

The TE estimates also exhibit differing levels but comparable patterns acrossthe DEA and SPF models. The DEA model indicates greater technical inefficiencythan the SPF model (as expected for a deterministic as compared to stochasticspecification) but also much more variation across farm-type; estimated efficiencylevels are much lower for the smaller cohorts, and higher for the VLG cohorts.For both models, however, the lowest efficiency levels are attained by farms inthe SM combined cohort, with RES slightly above. Over time the SPF TE resultsshow steadily rising efficiency levels, although for DEA TE increases in 1998, andthen drops below 1996 levels in 1999–2000. In turn, little regional TE variation isapparent, although somewhat less efficiency is evident for the Northern farms forthe DEA model, and the reverse is true for the SPF model.

The TEC measures also in Table 1 suggest that some temporal variation betweenthe estimated DEA and SPF TE patterns may stem from differing decompositionsof shifts in the function versus movements toward the frontier. Although bothmodels indicate a shift out in the frontier in 1997 and back in 1998, the DEAmodel shows further outward shifts whereas the SPF model implies contractions.This results in overall “technological regress” for the SPF model if these shifts

SCALE ECONOMIES AND EFFICIENCY IN U.S. AGRICULTURE 195

are interpreted as technical change rather than as stemming from a combinationof unmeasured technical and environmental factors (although only for 2001 is theunderlying time dummy coefficient statistically different from zero).

However, these TEC patterns for the second half of our time period coincidewith increasing estimated TE for the SPF model, but declining TE for the DEAmodel. Thus, the DEA model suggests that over time the technological frontier isshifting out but farms are getting further from the frontier (and scale economiesare dropping), and vice versa for the SPF model (for which SEC seem roughlyconstant). More yearly fluctuations in the scale and efficiency indicators are alsoimplied by the DEA model. On balance, therefore, temporal performance patternsare not definitive from these estimates, as might be expected due to the variety ofshort-term external factors affecting agricultural production, and the likely domi-nance of the farm type and regional dimensions of the panel data over technolog-ical changes, during the short-time frame of our data sample.

The regressions of the estimated performance indicators presented in Table 2provide a somewhat different perspective on the distribution of performance indi-cators across time, space, and cohort, as well as other farm/farmer characteristics.Note that the unit represented by the constant term is the RES cohort in 1996 inthe HL; other cohort, time, and regional differences are compared from this base,holding other factors constant.

Few clear insights may be gained from these estimates across the farm type, tem-poral, and spatial dimensions, except additional support for the variations in pat-terns across performance indicator and estimating method suggested above. Forexample, for the scale effects the DEA and SPF cohort patterns are quite consis-tent; less SEC are found for the larger cohorts (except for the distinction betweenRES and SM for DEA SEC), especially for the SPF specification. Over time theDEA measures more definitively suggest decreasing and the SPF measure increas-ing SEC (particularly from 1999 to 2001), holding all else constant, than is impliedfrom the averages in Table 1. Regional differences in scale effects also seem statis-tically different (but small) according to the SPF but not DEA specification, withless SEC in the North.

The technical efficiency estimates underscore the inference from the averages (inTable 1) that small farms are the least efficient; they are significantly less efficienteven than RES according to the SPF specification, and the larger cohorts (LG andVLG) more efficient (although only significantly so for the DEA model, holding allelse constant). The DEA estimates also confirm rising TE over time (significantlyfor 1998 and 2001), although the increments are small; for SPF the increase is bothlarger and more significant. In turn, although regional variations—as per the aver-age elasticities—are not large in magnitude (particularly for the SPF model), theDEA estimates suggest that Northern farms have (statistically) significantly lowerTE, and the reverse is found by the SPF estimates.

Holding cohort, year, and region constant, the remaining coefficient estimatesprovide somewhat inconsistent indications of how farm and farmer characteristicsaffect the performance measures. For example, education seems to have little sig-nificant(or consistent) impact, but greater age is associated with lower efficiency for

196 MORRISON PAUL ET AL.

Tab

le2.

DE

Aan

dSP

Fre

gres

sion

s.

DE

ASP

F

SEC

SEF

TE

SEC

SEC

NT

E

C0.

930

22.1

80.

579

4.80

0.97

415

.70

0.50

913

.47

0.86

012

.36

0.94

245

.63

1997

0.11

88.

290.

073

1.78

0.03

61.

70−0

.016

−1.2

6−0

.030

−1.2

60.

028

4.00

1998

0.10

07.

87−0

.016

−0.4

50.

039

2.06

0.02

01.

780.

036

1.74

0.04

16.

5619

990.

085

5.48

0.06

31.

420.

039

1.72

−0.0

37−2

.64

−0.0

71−2

.77

0.06

28.

1820

000.

057

3.53

0.00

40.

090.

039

1.62

−0.0

59−4

.08

−0.1

11−4

.13

0.07

49.

2920

010.

130

8.04

0.20

54.

410.

057

2.36

−0.0

92−6

.31

−0.1

71−6

.39

0.07

49.

29SM

−0.0

41−3

.47

−0.0

11−0

.33

−0.0

08−0

.47

0.07

26.

690.

140

7.10

−0.0

12−2

.02

LG

0.00

20.

170.

033

0.94

0.12

16.

730.

139

12.6

80.

259

12.8

70.

002

0.41

VL

G0.

048

3.47

0.04

71.

200.

150

7.36

0.18

214

.72

0.33

714

.76

−0.0

01−0

.10

NC

−0.0

14−1

.77

0.00

010.

01−0

.032

−2.6

60.

041

5.71

0.07

15.

330.

008

1.96

AG

E−0

.001

−0.4

70.

005

2.42

−0.0

02−1

.80

−0.0

01−2

.11

−0.0

02−2

.16

−0.0

01−2

.81

ED

UC

0.00

20.

700.

008

1.05

−0.0

01−0

.18

−0.0

03−1

.25

−0.0

05−1

.12

−0.0

03−2

.22

Deb

t/E

quit

y−0

.001

−2.0

10.

001

0.68

−0.0

01−0

.99

0.00

11.

890.

001

1.48

0.00

00.

50R

EN

T−0

.001

−3.1

60.

001

0.97

0.00

00.

080.

003

12.7

90.

005

12.9

60.

000

1.26

BIO

CO

RN

0.00

0−1

.48

−0.0

02−2

.02

−0.0

01−1

.61

0.00

13.

840.

002

3.81

0.00

00.

48B

IOSO

Y0.

000

−0.2

90.

000

0.05

−0.0

01−2

.69

0.00

16.

690.

002

6.80

0.00

0−2

.01

SCALE ECONOMIES AND EFFICIENCY IN U.S. AGRICULTURE 197

both specifications (although less significantly for the DEA model). Age also seems(significantly) associated with greater potentially exploitable SEC based on the SPFmodel, but greater SEF according to the DEA estimates. In reverse, higher propor-tions of rented acres (and to some extent debt/equity levels) seem associated withless SEC, consistent with the USDA (2001b) suggestion that renting is a “key strat-egy to expanding the size of business and capturing size economies”, according tothe SPF but not the DEA model. Finally, larger proportions of GM corn produc-tion seem from the SPF specification to be consistent with lower SEC, but not forDEA, and more GM soybeans seem from both specifications to be associated withlower TE.

5. Concluding Remarks

In this study we generated and summarized scale- and efficiency-oriented mea-sures of economic performance for U.S. farms across farm type, time, region, andfarm/farmer characteristics. These measures provide insights about productivitypatterns underlying the structural transformation of the U.S. agricultural sectorthat has increasingly generated apprehension about the economic health of thefamily farm. Although some differences emerge from the DEA and SPF models,our findings are generally consistent with the suggestions in USDA (2001b) thatthe inability of small farms to improve cost efficiency by expanding their scale ofoperations and diversity is a primary factor inhibiting their competitiveness.

We find that small family farms are generally less efficient in terms of both theirscale of operations and technical aspects of production than are large farms. Inparticular, they face significant unexploited SEC, which our SPF estimates stronglysuggest are much greater when output composition or scope effects are taken intoaccount; increasing both the scale and scope (diversity) of operations has signifi-cant potential to enhance small farms’ competitiveness. This puts them at a disad-vantage relative to farms that have taken advantage of such opportunities. Smallerfamily farms also seem somewhat less technically efficient than larger, or even res-idential, farms.

Temporal and spatial (regional) patterns, and the impacts of other farm andfarmer characteristics, are less definitive. Fluctuations in performance indicatorsappear over time (particularly for the DEA model), but little trend is evident,and what is apparent is attributed more to movements toward the technical fron-tier by the SPF estimates and to shifts in the frontier by the DEA estimates.Little productivity difference, in terms of magnitude or consistency of our per-formance indicators across estimating methods, is captured by region or farmcharacteristics.

More specifically, in terms of levels the SPF measures suggest more scaleeconomies and technical efficiency, and the DEA measures more “technicalprogress”, or shifts out in the technological frontier over time. Although bothspecifications identify lower SEF and TE levels for the smaller farms, the SPFframework suggests greater decreases in SEC and lesser increases in TE from the

198 MORRISON PAUL ET AL.

smaller to larger cohorts than is implied by the DEA measures. The DEA frame-work also finds a decline in SEC and little increase in TE over time, contrary tothe SPF model.

Overall, our empirical results support the USDA (2001b) assertion that largefarms have gained a cost advantage by taking advantage of scale and diver-sification economies, and thus the strong and rising concerns about the threatto the small family farm from increasing competitiveness of larger enterprises.Small family farms, which make up close to one-quarter of all farms and one-half of all non-residential farms, are “high-cost” operations; they have beenunable to improve cost efficiency sufficiently to compete effectively. Increasingthe ability of these farms to expand and diversify is fundamental to enhancetheir competitiveness, and thus long term viability, in the new U.S. agriculturalarena.

Appendix

Table A1. The farm typology groups and cohort definitions.

Typology USDA definition Sales ($)

TYP1 Limited resource <100,000 (assets <150,000, income <2,000)TYP2 Retirement <250,000TYP3 Residential (other major occupation) <250,000TYP4 Farm/lower sales <100,000TYP5 Farm/higher sales <250,000TYP6 Large family farms 250,000–499,999TYP7 Very large farms 500,000+

Cohort Typology GV Sales

COH1 TYP1-3 <2,499COH2 TYP1-3 2,500–29,999COH3 TYP1-3 >30,000COH4 TYP4 <10,000COH5 TYP4 10,000–29,999COH6 TYP4 30,000–99,999COH7 TYP5 100,000–174,999COH8 TYP5 175,000–249,999COH9 TYP6 250,000–329,999COH10 TYP6 330,000–409,999COH11 TYP6 >500,000COH12 TYP7 <1000,000COH13 TYP7 >1000,000

SCALE ECONOMIES AND EFFICIENCY IN U.S. AGRICULTURE 199

Tab

leA

2.Su

mm

ary

stat

isti

cs,

2001

.

Ful

lR

esSm

Lg

Cor

p

Far

ms

1372

380

261

345

386

Out

put

shar

eC

orn

0.09

30.

031

0.08

00.

172

0.09

1So

ybea

n0.

081

0.04

70.

083

0.15

20.

061

Oth

ercr

op0.

122

0.03

20.

103

0.13

10.

185

Ani

mal

0.41

20.

092

0.26

50.

461

0.65

1O

ff-f

arm

0.29

20.

798

0.46

90.

084

0.01

2

Inpu

tsh

are

Lab

or0.

178

0.25

70.

268

0.18

20.

104

Fue

l0.

022

0.02

00.

024

0.02

60.

019

Fer

tiliz

er0.

054

0.04

40.

050

0.07

40.

046

Seed

0.02

90.

019

0.02

20.

040

0.02

8F

eed

0.09

20.

033

0.02

90.

063

0.16

2A

nim

alin

puts

0.12

60.

019

0.01

50.

044

0.27

3C

rop

inpu

ts0.

039

0.02

60.

032

0.04

70.

041

Oth

erin

puts

0.07

80.

090

0.08

30.

089

0.06

2C

apit

al0.

088

0.09

50.

096

0.09

70.

075

Lan

d0.

296

0.39

50.

381

0.34

00.

189

Age

Yea

rs53

.15

51.5

959

.84

51.3

148

.46

Ed

Inde

x*2.

552.

652.

32.

582.

52D

ebt/

asse

t13

.47

10.4

78.

1717

.83

18.6

2A

cres

(%)

Ren

ted

land

42.0

632

.43

38.0

757

.15

35.4

2G

Mco

rn29

.77

12.8

421

.53

29.6

137

.08

GM

soy

71.0

771

.49

66.9

169

.43

75.5

5

*ED

:1:

nohi

ghsc

hool

;2:

high

scho

ol/e

quiv

alen

t;3:

som

eco

llege

;4:

four

year

degr

ee;

5:gr

adua

tesc

hool

.

200 MORRISON PAUL ET AL.

Tab

leA

3.P

aram

eter

esti

mat

es,

SPF

spec

ifica

tion

.

Coe

ffici

ent

Est

imat

et-

Stat

isti

cC

oeffi

cien

tE

stim

ate

t-St

atis

tic

α0

6.07

422

.21

αF

L−0

.014

−0.7

8δ 1

997

−0.0

33−1

.22

αF

E−0

.015

−0.5

1δ 1

998

−0.0

16−0

.59

αF

S−0

.017

−1.8

6δ 1

999

0.05

51.

57α

FF

D−0

.031

−3.7

4δ 2

000

0.06

61.

78α

FA0.

033

3.82

δ 200

10.

190

4.61

αF

C−0

.016

−2.4

7α

F−0

.148

−2.2

6α

FO

−0.0

32−1

.08

αL

−0.1

46−2

.46

αF

K0.

032

1.49

αE

0.10

32.

18α

LE

0.01

70.

67α

SD−0

.075

−1.6

4α

LS

0.05

93.

40α

FD

−0.0

17−0

.48

αL

FD

0.01

51.

20α

A−0

.160

−6.3

4α

LA

0.01

21.

39α

C−0

.053

−0.9

3α

LC

−0.0

73−3

.69

αO

−0.0

22−0

.27

αL

O−0

.008

−0.4

1α

K−0

.083

−1.4

2α

LK

0.08

23.

60β

C0.

003

0.08

αE

S0.

078

3.74

βS

0.05

01.

25α

EF

D0.

030

1.67

βO

−0.0

29−0

.82

αE

A−0

.032

−2.3

2β

A0.

031

0.84

αE

C−0

.044

−1.8

5β

I−0

.016

−0.7

1α

EO

−0.0

63−1

.58

SCALE ECONOMIES AND EFFICIENCY IN U.S. AGRICULTURE 201

Tab

leA

3.C

onti

nued

..

αF

DF

D0.

000

−0.0

5α

EK

0.09

73.

42β

CC

0.01

211

.63

αSF

D0.

034

3.71

βSS

0.01

311

.62

αSA

−0.0

17−3

.88

βO

O0.

010

11.0

0α

SC−0

.006

−0.6

7β

AA

0.01

914

.36

αSO

0.01

60.

74β

II0.

006

5.36

αSK

−0.0

95−6

.62

βC

S−0

.003

−3.6

1α

FD

A−0

.011

−2.1

7β

CO

−0.0

04−3

.58

αF

DC

0.01

42.

25β

CA

−0.0

04−2

.68

αF

DO

0.01

10.

56β

CI

0.00

20.

50α

FD

K−0

.029

−2.0

7β

SO−0

.003

−2.7

3α

AC

−0.0

17−2

.81

βSA

−0.0

04−2

.73

αA

O0.

017

1.36

βSI

−0.0

04−1

.23

αA

K−0

.017

−3.8

0β

OA

−0.0

04−2

.25

αC

O0.

078

2.94

βO

I0.

004

1.23

αC

K0.

053

3.49

βA

I−0

.004

−1.5

4α

OK

−0.0

46−1

.55

202 MORRISON PAUL ET AL.

Tab

leA

4.F

irst

orde

rel

asti

citi

es,

SPF

mod

el.

Ful

lsa

mpl

eSt

anda

rder

ror

RE

SSt

anda

rder

ror

SMSt

anda

rder

ror

LG

Stan

dard

erro

rV

LG

Stan

dard

erro

r

εD

IY0.

708

0.01

60.

557

0.01

80.

601

0.01

60.

792

0.01

80.

854

0.02

0ε

DIY

C0.

122

0.01

20.

087

0.00

80.

084

0.00

90.

153

0.01

60.

154

0.01

7ε

DIY

S0.

151

0.01

30.

085

0.00

90.

134

0.01

00.

186

0.01

60.

186

0.01

7ε

DIY

O0.

099

0.00

60.

087

0.00

70.

083

0.00

60.

103

0.00

70.

121

0.00

9ε

DIY

A0.

273

0.01

40.

218

0.01

20.

246

0.01

20.

289

0.01

60.

334

0.01

9ε

DIY

I0.

063

0.01

20.

079

0.01

50.

054

0.01

30.

061

0.01

20.

059

0.01

2ε

DIX

F−0

.080

0.02

6−0

.078

0.02

5−0

.083

0.02

3−0

.078

0.03

2−0

.082

0.03

6ε

DIX

L−0

.317

0.02

4−0

.366

0.02

6−0

.348

0.02

4−0

.311

0.02

6−0

.248

0.03

0ε

DIX

E−0

.018

0.03

0−0

.045

0.03

2−0

.024

0.03

2−0

.010

0.03

70.

006

0.03

9ε

DIX

SD−0

.181

0.02

1−0

.164

0.02

3−0

.189

0.02

0−0

.195

0.02

9−0

.170

0.03

3ε

DIX

FD

−0.1

160.

015

−0.1

170.

017

−0.1

110.

014

−0.1

210.

017

−0.1

140.

021

εD

IXA

−0.0

280.

008

0.01

10.

009

−0.0

050.

008

−0.0

410.

009

−0.0

720.

012

εD

IXC

−0.0

120.

025

−0.0

500.

020

−0.0

330.

021

0.01

00.

032

0.02

00.

037

εD

IXO

−0.0

110.

029

−0.0

560.

029

−0.0

710.

028

0.02

30.

036

0.05

00.

041

εD

IXK

−0.0

840.

028

−0.0

170.

025

−0.0

190.

026

−0.1

170.

036

−0.1

730.

040

SCALE ECONOMIES AND EFFICIENCY IN U.S. AGRICULTURE 203

Notes

1. Farm typologies are distinguished by sales, operator occupation, assets, and total household incomeof the farm, as summarized in Appendix Table A1 (Hoppe, et al., 1999).

2. For example, corn-belt farmers typically do corn/soybean rotations hinged on maintaining theircorn base, whereas the timing and level of input use is quite varied. The appropriateness of aninput specification for analysis of farm production and performance is supported by Williams andShumway (1998), and Paul and Nehring (2003).

3. Paul and Nehring (2003) compared parametric scale economy estimates for a farm business-only modeland a model including off-farm income, and found that the off-farm specification yielded importantinsights about the role of off-farm opportunities in maintaining the competitiveness of small farms.

4. See Coelli et al. (1998) for an overview of these procedures and many references to more rigoroustreatments.

5. In the CRS case, therefore, a firm can be benchmarked against larger or smaller firms rather thanjust firms of a similar size (Coelli et al., 1998)

6. We include no cross terms with the R terms because our only R components are time dummies;attempts to do so resulted in overall insignificance of the input- and output-specific shifts.

7. We computed these measures as well as all other elasticity measures and regressions using PC-TSP.8. This was developed for a production function, but shown to apply also to the input distance func-

tion in Ray (2003).9. The Heartland States include all or parts of Illinois, Indiana, Iowa, Missouri, Ohio, Nebraska, and

South Dakota. Northern Crescent states include Michigan, Minnesota, and Wisconsin.10. Although state and (generally) farm type are time-invariant for a particular farm, the sub-typol-

ogies also depend on sales brackets, a fundamental indicator of economic activity that may notbe time-invariant for a particular farm. Although some exit and entry of farms may occur overtime, different farms are sampled each year of the survey, and the definitions of the typologies byare themselves time invariant. An alternative to sales for defining cohorts might be land, or moregenerally assets, although this raises issues of quality variations. As reported in Paul and Neh-ring (2003), our technological estimates are robust to such cohort redefinitions, suggesting that thecohorts are also stable.

11. Although each of these cohorts represents many individual farms, we can interpret each observa-tion as an aggregate in the same sense that state data are aggregates, and thus present statisticalresults using classical methods rather than the bootstrapping or jackknifing techniques suggestedby Dubman (2000).

12. The sample size was particularly high in 1997 because it was a census year, and dropped in 2001due to USDA budget pressures and resulting cuts in data efforts.

13. Comparisons with and without off-farm income are presented in Paul and Nehring (2003). Theresults for the two output specifications are similar, but are more robust and suggest even moreSEC for the model including off-farm income, which is an important revenue component particu-lar for small family farms.

14. Initial estimation was carried out using a time trend instead of time dummies, with cross termsfor the inputs and outputs. However, in response to the suggestion of an anonymous referee wechanged our specification to one with time fixed effects, to make the specification somewhat moreconsistent with the DEA model. The patterns of the primary performance estimates were not sub-stantively affected by the temporal treatment.

15. We wish to establish patterns of measured productivity growth across space, size and farm/farmercharacteristics, rather than attempt to “explain” such variation by including these potential deter-minants of production processes in the functional specification. We thus do not include otherpotential “explanatory” variables, such as regional dummies, in our representation of the produc-tion structure.

16. In earlier versions of this paper we compared estimates for land data that were not qualityadjusted, which did not result in substantive differences in the estimated performance patterns. An

204 MORRISON PAUL ET AL.

Appendix discussing the hedonic model used for these quality adjustments is available from theauthors.

17. These measures were computed by evaluating the measures for average values of the data for eachof these sample and sub-samples using the delta method, implemented using the ANALYZ com-mand in TSP.

18. These averages were computed by regressing each indicator on a full set of the yearly, state,regional, or cohort dummies, respectively, to estimate the means for each group. Note that theSEC estimates presented for the SPF model differ somewhat from the εDIY estimates presented inAppendix Table A4, because the SEC measures are computed for each observation and then aver-aged, whereas the elasticities are evaluated based on the estimated parameters and averaged data,in order to compute standard errors.

19. To assess the sensitivity of these estimates to the cohort definitions, we did experiments definingthe “cohorts” for estimation in terms of the 8 typologies instead of the 13 cohorts in Table A1, byusing asset- instead of sales-based divisions, and by estimating the model for the entire farm-leveldata set by year. The typology- and asset-based specifications yielded comparable overall patterns,including significant SEC that declined for the larger typologies, and similar relative output andinput “shares” and efficiency scores, although the scale elasticities were somewhat larger in magni-tude for the typology data, and exhibited little difference across cohort for the asset-based model.The specification with individual farm data suggested even greater SEC, but the estimated laborcontribution was implausibly high (which may be due to problems imputing total labor input forthe cross-section analogous to that for the cohorts).

20. The SEC measure for RES for DEA indicates less potential SEC than for SM and even LG farms.This is consistent with the one real difference if the SPF model is estimated separately by year.(The pooled model was chosen as our preferred model because such estimation generated insignifi-cant parameter estimates.)

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