Preliminary, December 2002

Product Diversification, Production Systems, and Economic Performance in U.S. Agricultural Production

Catherine Morrison Paul* and Richard Nehring**

Prepared for the conference on Current Developments in Productivity and Efficiency Measurement, October 24-26 2002, Athens Georgia

*Professor, University of California, Davis, Department of Agricultural and Resource Economics, and Member of the Giannini Foundation, **Economist, Natural Resource Economics Division, Economic Research Service, U.S. Department of Agriculture, Washington D.C. 20005. 202-694-5618, (GA8.doc) 1

Introduction Average farm size in the U.S. Heartland1 rose by 18 percent between 1980 and 2000. Similarly strong growth in farm size also occurred in the Lake (16 percent) and Northern Plains (17 percent) states, although slower growth is evident in other areas (4 percent in the Prairie Gateway).2 Agricultural production is also highly concentrated in large farms, with “large and very large”3 family farms making up only 8 percent of all farms in 1998, but accounting for 53 percent of agricultural production. These farms were “viable economic businesses” in 1998, in the sense that they generated positive profits (revenues exceeded costs), whereas “[m]ost farm typology groups did not report adequate income to cover expenses.” (USDA, 2001a). Such patterns suggest that significant scale economies exist in modern agriculture, and that this technological reality is putting critical pressure on the small family farm. In addition to the apparent importance of scale economies, product diversity or scope economies seem to contribute considerably to farms’ economic performance. The USDA/ERS Family Farm Report (2001a), for example, states that: “…diversification is a significant factor explaining differences in the level and variability of income between higher and lower performing small farms. Financially successful small farms tend to be more diversified” (USDA 2001a). The Report also notes that production of multiple outputs is most prevalent for high-sales farms, and that diversification affects input demand decisions as well as economic performance. Alexander et al. (2001a) support this observation of the importance of product diversity for Iowa farmers. They find that

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As recently defined by the USDA; states for these regions are listed in the Data Appendix. USDA Agricultural Statistics, selected issues, National Agricultural Statistics Service, Washington, D.C. 3 The USDA classifies large farms as those with $250,000-$500,000 farm revenue, and very large farms as those with more than $500,000 revenue; see Appendix Table A1. 2

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94 percent of the respondents to their survey of farmers’ production practices grew both soybeans and corn, and that the balance differed across years. More than half also grew other crops (such as alfalfa and oats), and 60 percent raised livestock. An additional type of “output” – or contribution to revenue – is also notably affecting the economic health (or even viability) of family farms. Off-farm income and business opportunities have become increasingly important in many agricultural areas in the past couple of decades. USDA (2001b) documents that non-farm income sources now dominate net farm income in the U.S.,4 and USDA (2001a) finds that “farm households relied heavily on off-farm jobs,” with 55 percent of all farm households reporting that either the operator, spouse, or both worked off-farm to increase “total operator household income.” Farmers in more rural states are, however, less able to enhance their revenues through off-farm earnings than those in more urban environments (Gardner, 2001).5 The economic performance of U.S. agricultural producers seems also to be increasingly influenced by input jointness or complementarity, as well as embodied technological change. “Production systems” have been recognized as an increasingly important presence in agricultural markets. Alexander and Goodhue (2002), for example, show that recognizing the mounting complementarity of agricultural inputs (such as seeds, pesticides, and labor or machinery devoted to tilling), and substitutability across production systems (rather than individual inputs), is crucial for analysis of transgenic (or

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Income from farming in the U.S., measured by net-farm cash income, was $55.7 billion in 1999, as compared to income from off-farm sources of $124 billion (USDA 2001b). 5 Gardner (2001) shows that the growth of farmers’ income is significantly negatively related to the rural proportion of the state’s population. As he notes, this supports Schultz’s (1950) hypothesis that a more a more urban environment increases farmers’ incomes through enhanced off-farm earnings opportunities, as well as the demand for farm products and services.

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genetically modified, GM) seed demand. Enhanced effectiveness of the inputs used for production, through adoption of new technology – in particular in recent years GM crops – may also have enhanced farm’ performance and competitiveness.6 These output and input (netput) relationships affect the shape and shifts of the production technology for U.S. agricultural producers, and thus how efficiently farmers of different sizes and with different netput composition mixes might be producing. However, farm/farmer characteristics also affect observed productivity. For example, USDA (2001a) documents key dissimilarities in hours worked, age, education, debt, and management methods, that affect both overall agricultural productive performance and the benefits obtained from innovative adoption. If some farms are producing in a technically inefficient manner, or not on their production frontier (given their other measurable characteristics), this will also affect observed economic performance. In this paper we attempt to quantify these types of scale, scope, system, and efficiency effects determining the economic performance of farms in the U.S. Corn Belt. We focus on output and input jointness, and implied complementarities, by measuring scale or size economies (overall relationships between inputs and outputs), scope economies or output jointness (relationships among outputs), and input substitability or complementarity (relationships among inputs). The farms in our data sample produce a variety of outputs (carry out a variety of revenue-generating activities); they produce corn, soybeans, other crops and animal products (dairy, livestock), and generate off-farm income. To accomplish this they rely on a wide variety of inputs, some of which may be relatively fixed or tied together in

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Fernandez-Cornejo and (2000).

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production systems, including labor, fuel, fertilizer, seed, feed, machinery, land, other livestock-specific materials, other crop-specific materials, and other general expenses. The data on these farms, from a farm survey carried out by the USDA (U.S. Department of Agriculture), comprise 20,810 observations across 5 years (1996-2000). These data are summarized or condensed on the basis of cohorts, by averaging similar farms in like areas for each observation, resulting in a balanced pseudo-data panel of 650 observations (130 Per year). Our estimates based on this data therefore represent crossfarm or -cohort-type as well as temporal variations in output and input relationships. We represent the underlying multi-output, multi-input technology of these farms through technological relationships that allow for deviations from the production frontier (technical inefficiency), with alternatively an output- or input-orientation – output and input distance functions. We estimate these functions using stochastic production frontier procedures. Our estimates allow us to compute and evaluate a range of measures capturing the output-input relationships that contribute to economic performance. The alternative perspectives of the output and input distance function frameworks provide useful comparisons for this type of analysis. Homogeneity requirements for these functions imply that production expansion is at least implicitly evaluated holding output composition (for the output distance function) or input composition (for the input distance function) fixed. This implies different “takes” on which relationships are the most crucial for appropriate representation of production processes; input (output) contributions and substitution may better be captured by the output (input) distance function. By contrast, the output and input distance function, respectively, reflect output and input contributions or shadow values in a relative (ratio) form. The different

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perspectives therefore can (and do) provide some quite different implications, although the primary results of our analyses are reasonably consistent. Our findings indicate more complementarity or jointness, and yet less consistent composition, for outputs as compared to inputs. That is, diversification is clearly productive but output composition seems to vary more than input mix across type of farm. Thus, scope as well as scale economies have important implications for economic performance. This in turn suggests that an input distance function, implicitly based on constant input composition but directly allowing for a full range of output relationships, is preferable for representing U.S. agricultural production processes. However, the characterization of scale economies holding input composition constant may result in overestimating the overall impact of returns to scale. Further, off-farm income appears empirically as well as anecdotally to be an important aspect of economic performance and economic viability, especially for small farms. Allowing for this component of farm “output” suggests slightly more efficiency and less returns to scale than for the base farm business model. It also somewhat improves the representation of production processes for the input-oriented model, but exacerbates problems with the output-oriented model. This seems due to the widely varying role of off-farm income across farm types, that augments the variability of output composition when it is included as part of total farm revenue. The Models To explore the roles of scale economies, product diversification, and production systems on farms’ economic performance, we require a multi-output, multi-input specification of the technology that allows us to represent interactions among these netputs. Such a

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specification may be characterized from the output or input perspective, via the output or input sets P(X,R) or L(Y,R). P(X,R) is the set of output vectors Y which can be produced using the input vector X, given the levels of external or shift factors in the vector R, and L(Y,R) is the inverse – the set of all X vectors that can produce Y given R. These relationships can be used to develop estimable distance functions, again with either an output- or input-orientation. The output (O) distance function DO(X,Y,R) identifies the most Y possible to produce given X, and the input (I) distance function DI(X,Y,R) represents the least X necessary to produce Y, defined according to P(X,R) or L(Y,R), respectively. More formally, as developed by Färe (1988), Färe, Grosskopf and Lovell (1994), and Färe and Primont (1995):

(1a)

DO(X,Y,R) = min{Θ: (Y/Θ) ∈ P(X,R)} , and

(1b)

DI(X,Y,R) = max{ρ: (X/ρ) ∈ L(Y,R)} .

DO(X,Y,R) can thus be interpreted as a multi-output production function, and DI(X,Y,R) as a multi-input input-requirement function, with both allowing for deviations (distance) from the frontier, or inefficiency. These functions are primal; they do not represent economic optimization but simply technical (substitution) relationships among and across the inputs and outputs. Thus the deviations from the frontier are interpreted in terms of technical efficiency, TE. To empirically implement these functions, linear homogeneity with respect to outputs (for DO) or inputs (for DI) must be imposed. As described by Lovell et al. (1994), we impose these constraints by normalizing the function by one of the outputs (inputs).

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This procedure is justified by the fact that homogeneity implies DO(X,ωY,R) = ωDO(X,Y,R) for any ω>0, so if ω is set arbitrarily at 1/Y1, DO(X,Y/Y1,R) = DO(X,Y*,R), where Y*=Y/Y1. Analogously such a constraint can be imposed on the input distance function through normalization by one input, based on the definition of linear homogeneity, DI(ωX,Y,R) = ωDI(X,Y,R) for any ω>0; so for ω=1/X1, DI(X,Y,R)/X1 = DI(X/X1,Y,R) = DI(X*,Y,R), where X*=X/X1. Our data, based on a USDA annual survey of farms, allow us to distinguish among a broad range of both outputs and inputs, and thus to evaluate the impacts of product diversification in terms of output jointness, and production systems in terms of input complementarity. The data are for farms in states for which corn is a major component of agricultural output, that produce any combination of crops and animal agricultural products. The farm-level data is used to construct a pseudo panel data set in terms of cohorts, to deal with the problem of intertemporally linking annual cross-section data (explained in more detail in the Data Appendix). For outputs, Y, we distinguish three types of crops – corn, YC, soybean, YS, and “other”, YO. This allows us to separately identify commodities that each provide a large percentage of farm income (see Appendix Table A3), and have been impacted by biotech adoption during this time period (as the planting of insecticide resistant corn and herbicide tolerant soybeans has increased dramatically). We also separate out animal output production (meat or dairy), YA, and off-farm income, YI. Although YI is not, strictly speaking, a farm “output”, it comprises revenue generated from the effort of the farm family, so with YI included one might think of Y as a multi-activity rather than a multi-output vector.

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We also represent a broad variety of inputs, X, including labor, XL, fuel (energy), XE, fertilizer, XF, seed, XSD, feed, XFD, livestock (animal) expenses, XA, custom crop expenses, XC, other expenses, XO, machinery, XK, and (quality-adjusted) land, XLD.7 The materials categories in particular are broken down much more than is often possible, permitting us to explicitly link inputs with their corresponding outputs, and to complementary inputs that might comprise a production system. Note also that the labor input for the off-farm specification is augmented to recognize labor devoted to off-farm activities, based on the opportunity cost of the associated operator or spouse. The farm-level data also allows us to distinguish a number of farm- or farmerspecific characteristics, that we primarily treat as shift factors (along with standard external factors such as year) as components of the R vector. Farmer characteristics include age, AGE, and education, ED. Farm characteristics are a debt-asset ratio, DA, and the proportions of land that are rented, RNT, and planted in GM corn and soybean crops, GMC and GMS. We also include dummy variables for each year, T1996-T2000 (T1996 left out for estimation) and for four size classes or typologies (loosely from small to large), residential farms, RES, small family farms, SM, large family farms, LG, and very large family and corporate operations, CORP (RES left out). The only Rj factors for which we include cross-effects are GMC and GMS, because one would expect these factors to interact with specific inputs or outputs. For the output-oriented specifications that focus on input use, GMC and GMS are “interacted” with XSD and XC, representing seed and (largely) pesticide purchases, because enhanced

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XA includes not only the cost of purchased livestock, but also bedding and litter, and medical expenditures (medical supplies, veterinary and custom services for livestock). XC includes hauling and machine hire, irrigation, and pesticide expenses. XO includes general business expenses that cannot be ascribed specifically to crops or animals, such as interest and insurance.

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embodied technology might be expected to increase the contribution of seeds, and reduce the contribution of pesticides, to total input and thus output. For the input-oriented specifications that target output production for a given amount of inputs, we interact GMC and GMS with YC and YS to directly capture yield or output substitution impacts of genetically modified seeds. Summary statistics for these variables are provided in Appendix Table A3 for the year 2000, in total and distinguished by cohort type. The reported values are averages across all the farms in the sample. Both the levels and balances of inputs and outputs vary by type of farm, with the average farm in the survey generating slightly more than half its farm revenues from crop production, and making about a third of its total revenue from off-farm income.8 One issue that arises for implementing the distance function models is which of the outputs or inputs might be used as normalizing factors. Glossing over the econometric issues associated with a numeraire netput and recognizing that the final results are invariant to this choice (see Coelli and Perelman, 2000), there could still be economic reasons for choosing Y1 or X1. For our output distance function specifications we have chosen Y1=YC; corn is used as the dependent variable because we are focusing on farms in the Corn Belt where this is the primary individual commodity crop. For our input specifications we have chosen X1=XLD; the framework thus specifies all other inputs relative to land. This is consistent with the typical agricultural economics approach to production modeling in terms of “yields”, or inputs and outputs per acre.

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Note that capital and land “services,” as well as wages/prices of the farm operator/livestock, are imputed, so overall input payments in terms of opportunity costs exceed revenues for the average farm.

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This raises another issue to highlight before moving to empirical implementation – the differences embedded in the output as compared to input distance function perspective. As alluded to above, differences arises due not only to the “dual” nature of the output- and input-oriented frameworks, but also to what is “fixed” when one evaluates farm growth or expansion. The “duality” involved is that enhanced economic performance or productivity is represented by the output distance function through overall output expansion given input use, and by the input function through overall input contraction given output production. This expansion or contraction is, however, based on a given output or input composition, respectively; output or input ratios are held constant when measuring output or input elasticities, or scale economies. Thus, in the output distance function model outputs are not as much “choice variables” as are inputs, and vice versa for the input specification. The alternative models therefore provide somewhat different information, and their appropriate use depends on whether one believes production jointness or systems are more fundamental on the output or input side. If inputs are essentially fixed for a farmer, then output composition is the primary economic performance determinant, and an input-oriented function is more appropriate or illustrative. However, if output composition is not as much a “choice” for the farmer – input use is more flexible – the output distance function is more appropriate. Empirical Implementation For empirical implementation of our models, functional forms must be assumed for the distance functions. Assuming they can be approximated by translog functional forms (second order logarithmic functions) limits a priori restrictions on the relationships

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among arguments of the function, allowing us to explore in depth the relationships among the outputs and inputs. However, we do not assume a completely flexible functional form because we treat most of the R factors as fixed effects.9 The resulting functions take the form: 2a) ln DOit/Y1,it= α0 + Σj αj ln Rjit + Σm αm* ln Y*mit + .5 Σm Σn βm*n* ln Y*mit ln Y*nit + Σk αk ln Xkit + Σk(=SD,C)s βks ln Xkit GMs + .5 Σk Σl βkl ln Xkit ln Xlit + Σk Σm βm*k ln Y*mit ln Xkit = TLO(R,Y*,X), and 2b) ln DIit/X1,it = α0 + Σj αj ln Rjit + Σk αk* ln X*kit + .5 Σk Σl βk*l* ln X*kit ln X*lit + Σm αm ln Ymit + Σmj βm(=C,S)s ln Ymit GMs + .5 Σm Σn βmn ln Ymit ln Ynit + Σk Σm βk*m ln X*kit ln Ymit = TLI(R,X*,Y),

where i denotes farm, t time period, m, n the outputs, k, l the inputs, j the external effects, and s the types of GM seeds (C,S). These functions can be rewritten with the distances -ln DOit = -uOit or -ln DIit = -uIit as one-sided error terms, and including standard or random error components vOit or vIit representing factors such as measurement error or unobserved inputs that might generate noise in the data, as: 3a) - ln Y1,it= TLO(R,Y*,X) - uOit + vOit, 3b) - ln X1,it = TLI(R,X*,Y) - uIit + vIit .

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This is done to reduce the number of cross-terms with our specification that is so disaggregated across outputs and inputs.

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The coefficients from these functions will be reversed in terms of sign from the coefficients for a standard production or input requirement function. ∂TLO/∂Xk, for example, represents the overall change in outputs (the change in Y1 with all output ratios, and thus output composition, constant) with a change in Xk. However, from the distance function perspective this “marginal product” will be negative instead of positive. Similarly the “marginal cost” of output Y1 in the input distance function framework, ∂TLI/∂ Y1, representing the overall change in inputs (given input composition) with a change in Y1, will be negative instead of positive. To interpret the measures from (3a,b) more similarly to these more familiar functions, we thus reverse their sign: 4a) ln Y1,it= -TLO(R,Y*,X) + uOit - vOit, 4b) ln X1,it = -TLI(R,X*,Y) + uIit - vIit . These functions are written in standard stochastic production frontier form, allowing for a two-part error term representing deviations from the frontier, that can be estimated econometrically using maximum likelihood techniques. This method10 is based on assuming that vOit or vIit are independently and identically distributed random variables, N(0,σv2), and uOit or uIit are nonpositive random variables independently distributed as truncations at zero of N(0,σu2). For estimation of these equations we have used the error components model of Battese and Coelli (1992), from Tim Coelli’s FRONTIER program, as in Coelli and Perelman (2000) and Paul et al. (2000). From this model we can construct a number of measures, based on first and second order (output or input) elasticities, to summarize production processes and act as performance indicators. For example, we can measure scale economies or returns to 10

As initially developed by Aigner, Lovell and Schmidt (1977) and Meeusen and van den Broeck (1977), and discussed in depth in Coelli et al. (1998).

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scale from either the output or input perspective, to capture the extent to which productivity increases with growth. Such measures provide insights about motivations for farmers to expand their scale of production to enhance their competitiveness, and in turn about the competitive disadvantages potentially faced by small farms. We can also characterize input- or output-specific contributions to these economies, through production complementarities or biases that imply efficiencies from joint production of outputs or use of inputs. And we can identify the productive contributions of other choices or external factors, such as planting GM seeds or the age or education of the farmer, and shifts in the frontier that could arise from any external or unmeasured factors that are specific to a given year or cohort. Finally, we can quantify (residual) indicators of technical inefficiency (TE). That is, we can measure the deviation of a particular observation from the estimated frontier, to establish the remaining apparent technical (in)efficiency after all these factors are taken into account. To develop these measures, we first focus on the overall Y-X relationship that represents the extent of scale economies – typically in elasticity form – from either the output or input perspective. Note again that these measures are asymmetric due to the linear homogeneity of the distance functions, that results in the functions being specified in terms of output or input ratios for the output or input distance function, respectively.11 From an output perspective, or output distance function, the combined output-input relationship representing scale economies captures how much overall output will increase given a 1 percent increase in each input. This is analogous to a returns to scale estimate from a production function, as the sum of the output elasticities for each input. 11

The information on output (input) relationships from the output (input) distance function is thus in the form of relative (to that for the numeraire output or input) shadow values, which are harder to interpret than

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That is, the “output elasticity” for input Xk from the output distance function, εDO,Xk = -∂ln DO/∂ln Xk = ∂ln Y1/∂ln Xk= εY,Xk, represents the percent change in Y1 from a 1 percent change in Xk, holding all output ratios Y* (and thus output composition) constant.12 These elasticities thus represent the “returns” to individual input changes, or the “contribution” to overall scale economies from input Xk, analogous to the output elasticity from a production function. Also, if ∂Y1/∂Xk is interpreted as the marginal product of Xk (an increase in overall output from an increase in Xk, MPk), εY,Xk can be thought of as the output “share” of Xk (with respect to Y1); εY,Xk = MPkXk/Y1. Summing these measures results in an output-oriented distance function-based scale economy measure, as in Färe and Primont (1995): -εDO,X = -Σk∂ln DO/∂ln Xk = Σk∂ln Y1/∂ln Xk= Σk εY,Xk = εY,X. If εY,X > 1, increasing returns to scale are implied; input increases generate a more than proportionate output expansion (with proportional changes in all outputs). From an input perspective, or input distance function, the scale economy relationship reflects how much input use must increase to support one percent increases in all outputs. Similarly to the output-oriented measure, the elasticity representing this relationship is a sum of all the individual input elasticities. This is similar to a cost function-based scale economy measure that captures changes in input use required for output growth, but it is purely a technical measure; it represents just the technological relationship, not input choice. For each output Ym, the required input expansion corresponding to a 1 percent increase in Ym is represented by the elasticity -εDI,Ym = -∂ln DI/∂ln Ym = ∂ln X1/∂ln Ym = absolute measures.

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εX,Ym. Dual to the “output share” notion above, this can be thought of as an input “share” of Ym (with respect to X1) ; ∂ln X1/∂ln Ym = (∂X1/∂Ym)Ym/X1, where ∂X1/∂Ym is the overall input expansion required to increase Ym. In combination, these input elasticities represent scale economies: -εDI,Y = -Σm∂ln DI/∂ln Ym = Σm∂ln X1/∂ln Ym = Σm εX,Ym = εX,Y, similarly to Baumol et al. (1982) for a multiple-output cost model, and consistent with the Färe and Primont (1995) output distance function treatment. The extent of scale or “cost” economies (given proportional changes in all inputs) is therefore implied by the short-fall of εX,Y from 1. The first order elasticities (εYXk, εYX, εXYm, εXY) representing individual and overall input-output or output-input relationships can also be decomposed into their second order effects. These effects reflect changes in input composition (for the output distance function) or output composition (for the input distance function) as scale expands. This information is captured in the form of technological “bias” measures, indicating for the output distance function how the output elasticity or input “share” of output adapts to a change in another input, and the reverse for the input distance function. Such measures therefore contribute to our knowledge of input or output jointness, or production systems. The performance impact of this netput complementarity is represented by a combination of these biases. If overall output (input) relationships are (significantly) complementary or joint, increases in one type of output (input) will enhance the contributions of the other outputs (inputs), and thus productivity. In particular, for inputs (from the output distance function), εYXk,Xl = ∂εY,Xk/∂ln Xl represents the impact on the output-contribution of input Xk from an increase in Xl. If Xk

12

This is analogous to the measure of “returns” to input changes in a basic Cobb-Douglas framework.

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and Xl in some sense “move together” (or are complementary, or act as a system) – an increase in Xl shifts up the output elasticity or share and thus marginal product, of Xk: εYXk,Xl > 0. This measure in the translog context collapses to the cross-input βkl coefficient estimate; with symmetry, εYXk,Xl = βkl = εYXl,Xk. Similarly, εXYm,Yn= ∂εX,Ym/∂ln Yn from the input distance function framework represents the increase in the input share of Ym if Yn also increases. If εXYm,Yn < 0, output jointness (or complementarity or scope economies) is implied; input use does not have to increase as much to expand Ym if the Yn level is higher. This elasticity is represented by the crossoutput coefficient estimate βmn: εXYm,Yn = βmn = εXYn,Ym. In addition to information about input use patterns, some insights about (relative) output contributions may be distilled from the output distance function. Similarly, insights about (relative) input contributions may be derived from the input distance function. From the output perspective, -∂DO/∂Ym = ∂Y1/∂Y*m = r*m represents the (negative of the) shadow value of Ym relative to Y1, or, loosely, the slope of the production possibility frontier.13 εY,Ym = ∂ln Y1/∂ln Y*m = r*mY*m/Y1 therefore represents the “shadow share” or contribution of Ym relative to Y1, and the coefficient βm*n* = ∂εY,Ym/∂ln Y*n represents the change in this share with a change in output (ratio) Y*n. Analogous input relationships may be measured from the input distance function.

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Färe (1988) and Färe and Grosskopf (1990) showed that the distance function duality with the revenue function can be used to define the revenue-deflated shadow price of Ym via a distance-function oriented Shephard’s lemma based on these derivatives. The interpretability of these measures, and their corresponding second order derivatives, is more limited than the other measures focused on above, which have a more direct linkage to standard economic notions of, for example, marginal products or output shares. However, these relationships can be manipulated to obtain some information about substitutability, as illustrated in Paul et al. (2000).

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The information from these measures is not straightforward to interpret, however, because it is relative to the base output (input). That is, rather than identifying “marginal products” or “shadow values” for each output (input), these estimates are in relative terms due to the ratio form of the outputs (inputs) as arguments of the output (input) functions. The productive impacts of the R vector components can be estimated similarly to those for Xk or Ym, based on the (output and input) distance function elasticities -εDO,Rj = -∂ln DO/∂Rj = ∂ln Y1/∂Rj = εY,Rj and -εDI,Rj = -∂ln DI/∂Rj = ∂ln X1/∂Rj = εX,Rj. Thus εY,Rj > 0 (more output is produced for a given input vector given Rj), or εX,Rj < 0 (less input is required to produce a given output vector given Rj), implies greater productivity or enhanced economic performance. Our Rj factors are the farm/farmer characteristic variables AGE, ED, DA, RNT, GMC and GMS, the farm type or “cohort” indicators RES, SM, LG, and CORP, and the dummies representing time-varying environmental or technical factors, T1997-T2000. Most of these characteristics are included only as fixed effects or overall shift factors, so their impacts are represented simply by their associated estimated coefficients (they have only a first order effect and no bias). For example, εX,AGE = ∂ln X1/∂AGE = αAGE reflects to what extent the age of the farmer affects input use for a given output vector and given input composition. An analogous measure, with the opposite expected sign, can be constructed for the output distance function. Similarly, εX,T1998 = ∂ln X1/∂T1998 = α1998, or εX,SM = ∂ln X1/∂SM = αSM, capture the overall contraction or expansion in input requirements in 1998 relative to 1996 (the base or left out year), or for small family farms (SM) relative to residential farms (RES, the base farm type). If εX,T1998 simply captured technical change, technical progress would

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imply εX,T19981 and εX,Y