Genetically Modified Crops An Input Distance Function Approach 1

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1 Genetically Modified Crops An Input Distance Function Approach Selected Paper 28 Southern Agricultural Econoics Association Annual Meeting Dallas, TX February 3-5 Keywords/Subject Areas: Production Econoics, Genetically Modified Crops, Distance Function, Stochastic Frontier Analysis By Justin G. Gardner 2 (Middle Tennessee State University), Richard F. Nehring (ERS) and Carl H. Nelson (University of Illinois at Urbana-Chapaign) Abstract: GM crops have been widely adopted by U.S. Farers. The welfare ipact of this technology is not always clear cut, Fernandez-Cornejo et al (25) for exaple found that the adoption of GM soybeans lead to increased off-far incoe. In light of these findings it is necessary to estiate the ipacts of GM crops using a whole-far approach. Our initial findings indicate that GM crops do not contribute to the decline of traditional faily fars. In addition we ake a significant ethodological ipact by using the within transforation to reove unobserved individual effects (Mundlak, 996) and estiate a distance function that is free of anageent bias. We show that the within transforation results in ML estiates that are identical to OLS estiates. Disclaier: The views expressed are the authors and do not necessarily represent policies or views of ERS, USDA, Middle Tennessee State University or The University of Illinois. Introduction Genetically odified organiss (GMOs) have been used in crop production for over a decade. According to Brookes and Barfoot (25) the first genetically odified (GM) crop was the toato in 994, followed by GM soybeans. Currently the ost coon GMOs in agriculture crops can be classified into two groups: herbicide tolerant (HT) and insect resistant varieties of corn, cotton and soybeans. This technology was not developed via conventional crop breeding ethods. Instead, a trait that is foreign to the organis was inserted into its genoe. Roundup Ready soybeans are resistant to the herbicide glyphosate, which Monsanto arkets under the brand nae Roundup. Monsanto developed the Roundup Ready HT trait to serve as a copleentary input to Roundup (Just and Hueth, 993). Glyphosate resistance has also been inserted into corn and cotton. Insect resistance is achieved by inserting a gene fro the bacteria Bacillus thuringiensis (Bt), which creates a toxin that affects Lepidoptera larvae. Currently the Bt trait has been inserted into corn and cotton to control the European Corn Borer, the Corn Rootwor, the Cotton Bollwor, the Pink Bollwor, the Asian Bollwor and the Tobacco Budwor. Working paper, please do not cite or circulate without perission for the authors. 2 Contact author (jggardne@tsu.edu)

2 GMOs are controversial. With the eergence of glyphosate resistant weeds (Gardner and Nelson, 27) and recent accidental release of unapproved GM rice (Endres and Gardner, 26) the debate over GM crops is not over. Therefore, it is prudent to continually re-assess the econoic, environental and regulatory issues regarding GM crops. There have been any studies on the welfare ipacts of GM crops in US agriculture. In their review of the econoics literature, Marra et al.(22), broadly concluded that GM crops are profitable for U.S. farers. However, soe evidence suggests that GM crops ay not be profitable (Bullock and Nitsi, 2, Fernandez- Cornejo, et al., 22). Our objective is to investigate the welfare ipacts of GM crops with the goal of deterining if GM crops are in fact profitable for US farers and if not then why would farers adopt a crop that is not profitable. Furtherore we seek to understand which fars have gained, or lost, the ost fro GM technology. A priory we suspect that far-specific conditions such as location, far size and pest pressure will have an effect on the profitability of adopting a GM crop. Specific farer attributes such as education, off-far eployent and age ay also have an effect. My idea is that these factors ight help to identify which farer types gain fro adoption, and how econoic gain varies by farer type. Using 23 data, Hoppe and Banker (26), classified 67.8% of US fars as liited resource, retireent, or lifestyle fars. These fars hold 44.4% of US far assets and produce 8.% of the US far output. They tend to specialize in beef production, and the household of the principal operators do not rely on far incoe. Sall to ediu size faily fars (23.6% of all fars accounting for 8.9% of output) rely heavily on far incoe, and large fars (8.8% of all fars accounting for 72.8% of output) rely alost exclusively on far incoe. Understanding how eerging technology changes the distribution of fars is iportant, as far distribution has iportant iplications for far policy. For exaple, Hoppe and Banker (26) report that large fars tend to receive coodity-based support, while sall fars tend to receive conservation-based support. If GM crops are only profitable for sall and ediu sized faily fars, how will this change the cost of coodity progras? Thus, it is iportant to know how the technology ipacts different types of fars. Theory Consider two fars (see Figure 2..), where one uses a high cost production ethod (denoted by H), while the other uses a low cost production ethod (denoted by L). In the initial equilibriu (Indexed by ) GM inputs are not available. In the final equilibriu (Indexed by ) both fars realize a decrease in costs relative to the initial conditions and both fars are assued to adopt the technology. The arket supply curve is the horizontal 2

3 su of the arginal costs curves of all the fars in the arket. Thus, if far costs decrease, the supply curve ust shift out, lowering the arket price (p). In Figure, after the introduction of the GM input, profits for both types of fars are about the sae. As drawn the low-cost farer has realized an increase in profit while the high-cost farer s change in profit is sall in absolute value. This is just one possibility; our objective is to devise a ethod to distinguish between low and high cost farers, and then copare their welfare changes. If production relationships, differentiated by farer type, can be estiated, the research proble becoes a testable hypothesis. Consider a change in arket price as illustrated in Figure, and copare the price change to the change in Average Total Cost (ATC). As shown by equation (), the null hypothesis is that the changes to the arket price and the average cost changes are equal. If the null is true then no farer has gained; adoption does not guarantee a welfare increase. The alternative is that changes in average costs and price are not the sae; only one type ight gain. H () : Δ ATC ( ) ( ) H q =Δ ATCL q = Δp. H : ΔATC ( q) ΔATC ( q) Δp a H L Figure : High-Cost vs. Low-Cost Farers p AC,MC AC,MC MC H S (p,w t,w c,w g,w h,w l,w,w a,w k ) π H ATC H MTC L p MC H π L AC L S (p,w t,w c,w g,w h,w l,w,w a,w k ) MTC L p ATC H π H π L ATC L D(p) q H q H q H q L q L q L q q q 3

4 However, the proble is uch ore coplex. Fars produce ultiple outputs using ultiple inputs. Consider an alternative way to express far type, the elasticity of scale for a fir with K outputs. ln C( ywg,, ) ln yk (2) ε =, ( k =,2,, K) s k Where y is a vector of K outputs, w is a vector of input M prices and g is a vector of I GM crop variables. The elasticity of scale is the inverse of the elasticity of cost. (3) ε = ( k = K) c k ln C( ywg,, ),,2,, ln y k The elasticity of cost is the percentage change in cost arising fro a percent increase in output. If ε c is less than one ( ε is greater than one) then the fir exhibits increasing returns to scale iplying that average costs will s decrease if the fir expands output. A far that produces at iniu average cost is said to exhibit constant returns to scale and by differentiating ε c with respect to the i th GM crop variable, (4) ε 2 c ln C( ywg,, ) = g ln y i k k g i one can investigate how ε c changes when firs adopt GM crops 3. If the derivative of ε c with respect to the i th GM crop variable in equation (4) is positive, then the percentage change in cost for a one percent increase in output increases as the GM adoption rate increases. Iplying that the GM input akes output expansion ore expensive thus favoring sall fars; in other words, the optial far size would decrease. Alternatively, if the derivative were negative then the GM input would ake output expansion less expensive. If far size, easured by output, is used to differentiate far type then the hypothesis that far size has an influence on the returns to GM adoption can be phrased as: (5) : ε c, : ε c H = Ha g g If the alternative is true then GM crops will have an ipact on the optial far size. i i 3 In general, it is not possible to take this derivative, as GM adoption is not a continuous variable. This will be addressed below when we discuss pseudo-panel data. 4

5 Literature Review To date the ost coprehensive literature review of the welfare ipacts of GM crops can be found in Marra (2) and Marra et al. (22). The authors reached several broad conclusions regarding the literature on the current generation of GM field crops, Bt cotton is likely to be profitable in the cotton belt and reduces pesticide use, adopting Bt corn should provide a sall yield increase, and in soe cases adoption leads to significant increases in profit. For HT soybeans they conclude that cost savings should offset any revenue loss due to yield drag. These conclusions see plausible as there are several effects that could induce a welfare gain. Bullock and Nitsi (22) and Carpenter and Gianessi (2) list four advantages of HT crops: ) HT technology leads the farer to substitute relatively less-expensive glyphosate for other herbicides;. 2) farers realize a change in the shadow price of labor and anageent 4 ; 3) due to glyphosate s effectiveness at killing larger weeds, weather induced spraying delays do not significantly affect weed control; 4) when farers switch to HT technology substitution effects lead to a decrease in the price of alternative herbicides. The widespread adoption of GM crops ay be evidence of a welfare gain. In 25 Herbicide tolerant crops ade up 87% and 6%, of U.S. soybean and cotton acreage respectively, while 35% of the corn acreage and 6% of cotton acres were insect resistant (Fernandez-Cornejo and Caswell, 25). Bernard et al. (24) found that fars in Delaware had yield increases and decreases in weed control costs when they adopted HT soybeans. So it would see that adopting this technology results in a welfare gain for farers. But, as noted above, soe studies do not support this conclusion. The literature requires ore exaination before one can draw a conclusion fro it. Marra (2) and Marra s et al s. (22) evidence concerning the profitability of Bt cotton sees overwheling. All of the 47 studies that were copiled indicated that Bt cotton is profitable. Only two HT cotton studies were copiled, both indicated that the technology was profitable, as did two studies where these two traits were stacked. However, the GM corn and soybean evidence lacks the depth to be conclusive; the author(s) drew conclusions based on two studies for each GM crop. Studies using the United States Departent of Agriculture s (USDA s) Agricultural Resource Manageent Survey (ARMS) were excluded fro the analysis based on the arguent that field level data, such as that collected in ARMS phase II, could not capture within-far effects leading to an anti-gm bias. 4 Far labor and anageent has no arket price, the price of a non-arket good is its shadow price. 5

6 Fernandez-Cornejo et al. (22) used ARMS data and concluded that HT soybean adoption did not have a statistically significant effect on farer profit. The Fernandez-Cornejo et al. study ade use of a flexible functional for to estiate a profit function and corrected for endogeneity using an instruental variables ethod. Even though the study did not find a profit ipact they did find a sall positive yield ipact. Bullock and Nitisi s (2) study, which used a cost-iniizing siulation, found that GM soybean farers are less profitable than their conventional counterparts. However, they did not take into account the labor and anageent savings that arise fro convenience and tiing factors, as these were not observable variables. This leads to a puzzling conclusion; it is uncertain whether or not HT soybeans are ore profitable than conventional soybeans, but alost every farer uses the technology. Perhaps the research counity has been unable to easure an iportant coponent of farers welfare. Bernard et al. (24), as entioned before did find a positive ipact in Delaware. However, they pointed out that Delaware soybean fars are larger then the national average, which ay have biased their results. Fernandez-Cornejo et al. (25) ade an iportant advanceent by explaining high adoption rates for roundup ready soybeans in spite of the technology s inability to increase far profits. Using a household production fraework they found a positive relationship between HT soybean adoption and off far incoe. Their result suggests that adopting HT soybeans can free up resources for alternative uses. In addition the result highlights the iportance of properly odeling far production; fars are ulti-output producers that generate off-far incoe as well as coodity-derived on-far incoe. Data We used data collected via the USDA s ARMS Cost and Returns Report (CRR) survey. CRR data are collected at the far level and contain inforation on far revenue, by crop and on input expenditures. This data also includes classification variables such as USDA far typologies (Hoppe, et al., 2) which have been used to create cohort classifications, thus allowing the annual cross sections to be treated as if they were panel data (Nehring, et al., 25, Paul and Nehring, 25, Paul, et al., 24). Starting in 998 the CRR surveys began asking respondents about GMO usage. However, this inforation was collected in the 996 and 997 Production Practices Report (PPR) surveys, and therefore it is possible to use survey-based iputation to infer the specifics of GMO adoption (Nehring, et al., 25, Paul, et al., 24). In addition to pooling ARMS cross sections fro 996 to 25 we also create a pseudo-panel using the cohort definitions shown in table. These cohorts have been used extensively with ARMS data and the data has 6

7 been shown to be robust to cohort specification (Paul, et al., 24). One of the objectives of this study is to copare all three of the priary GM crops, thus the geographic scope has been widened beyond the Corn Belt that is traditionally studied to include cotton-growing regions. This presents a proble with respect to cohort size. The nuber of individuals in each cohort ust be large to prevent a easureent error bias (Verbeek and Nijan, 992), and any states outside of the corn belt have low sapling rates. To overcoe this proble, under-sapled states were cobined with their geographic neighbors. The states that stand alone are Illinois, Indiana, Iowa, Kansas, Michigan, Minnesota, Missouri, Nebraska, North Carolina, Ohio, South Dakota, Texas and Wisconsin. The reainder of the states were grouped into one of six regions, Southeast (Alabaa, Georgia, South Carolina), Delta (Arkansas, Louisiana, Mississippi), Mid-South (Kentucky, Tennessee, Virginia), Northeast (Maine, New Hapshire, Veront, New York, Massachusetts, Connecticut, Rhode Island, Delaware, Pennsylvania, West Virginia, New Jersey ), Southwest (California, Nevada, Arizona, New Mexico, Colorado, Utah), and Northwest (Washington, Oregon, Idaho, Montana, Wyoing). The pseudo panel covers years, and twenty geographic regions with 3 cohorts in each region. The pseudo saple size is 26. The sallest annual average cohort size is 2.66, in 2, while the largest is in 24. Table : Cohort Definitions Cohort USDA Far Typology Gross Value of Sales ,5-29, >29, ,-29, >29, 7 5 <75, 8 5 >74, ,-329, ,-49,999 6 >49, , >999,999 Estiation 7

8 In order to estiate the ipact of genetically odified crops in a ulti-output ulti-input setting, if one cannot observe the allocation of inputs aong crops, it is necessary to use either an input or an output distance function; we choose the forer. The derivation of the input distance function and its properties can be found in any sources (Coelli, et al., 998, Fare and Priont, 995, Irz and Thirtle, 24, Kubhakar and Lovell, 2, Lovell, et al., 994, Nehring, et al., 25, Paul and Nehring, 25, Paul, et al., 24, Shephard, 953, Shephard, 97). Let L ( y ) denote the input requireent set, which is the set of all inputs that can feasibly produce output y, or (6) L ( y ) = {( x, y) : x can be used to produce y }. The input distance function is defined as 5 : x (7) D( yx, ) = ax λ > : st Ly ( ) λ λ. It is the axiu aount by which the input bundle can be scaled down and still produce y. The input distance function is nondecreasing and concave in x, and nonincreasing in y. It is hoogenous of degree one, also known as linear hoogenous, in inputs. (8) D( y, ρ x) ρd( y, x ), ρ > We will exploit this fact when we paraeterize an estiable functional for. If the underlying production technology exhibits constant returns to scale then the distance function is also hoogenous of degree one in outputs. (9) D( ρ yx, ) = ρd( yx, ), ρ > The ost significant proble associated with estiating a distance function is that distance is not an observable quantity. Therefore, one can not siply specify a functional for and estiate the odel. Lovell et al. (994) deonstrated how one can use the distance function s hoogeneity property and the fact that distance functions are always greater than one to estiate the distance function using stochastic frontier analysis (SFA). In ters of a single-input single-output production odel a SFA odel is expressed as follows: () y = α + xβ + v u, 5 Typically, the literature uses a subscript or superscript i to denote the input distance function, and an o to denote the output distance function. As we are only using an input distance function the notation is not necessary and has been dropped. 8

9 where the error ter has two coponents, v is the standard identically and independently distributed regression error ter with ean zero, and u is a one-sided error ter. The purpose of the one-sided error ter is to shift the regression estiate fro the iddle of the dataset to the edge of the dataset, allowing one to estiate a frontier. A SFA odel allows for two effects that ight cause an individual to deviate fro the ost efficient input-output cobination. The stochastic effect, arising fro rando shocks due to things like weather, is captured by the standard regression error ter. The inefficiency effect, resulting fro non-rando effects such as location or anagerial ability, is captured by the one-sided error ter. Following Lovell et al. (994) one can use linear hoogeneity in inputs, D( ρ x, y) = ρd ( x, y ), setting ρ = x, where x is any arbitrary input. So that () D x * ( x, y) = D( x, y ) where an asterisk (*) denotes a noralized input. Recalling that D( x, y ), equation () can be partially paraeterized by setting D ( x, y) = and including an error ter that is always positive. (2) * ε D( x, y ) = e, ε. x Rearranging (2) yields: (3) x * ε = D( x, y ) e, ε. Taking the natural logarith of (3) the partially paraeterized odel can be expressed as a linear odel. (4) = x y ε ε x * ln ln D(, ), The error ter can then be decoposed into a standard ter and a one-sided ter, ln ln D, v u, u x = x y + * (5) ( ) After assuing a functional for, equation (5) takes the sae for as equation () and a distance function can be estiated using SFA. 9

10 The literature (Coelli and Perelan, 2, Irz and Thirtle, 24, Nehring, et al., 25, Paul and Nehring, 25, Paul, et al., 24) has adopted a translog functional for in favor of a sipler Cobb-Douglas functional for. Coelli and Perlan (2), who estiate an output distance function, argue that the translog functional for is superior to the Cobb-Douglas because it is flexible and it is easy to ipose hoogeneity restrictions. The Cobb- Douglas does have drawbacks, unlike the translog it will not allow for the calculation of scope econoies, which are based on second order interaction ters (Paul, et al., 24). The priary disadvantage of the translog odel is the large nuber of estiated paraeters, it is thus plagued by ulticollinearity probles and a large nuber of insignificant paraeters. Pervious studies (Irz and Thirtle 24) have shown that the translog is preferable to the Cobb-Douglas although it ay not ake a significant difference when answering the research question. Augenting the noralized distance function with a vector g of GM crop variables equation (5) becoes ln ln D,, v u, x = x y g + u * (6) ( ) The Cobb-Douglas functional for with GM interaction ters is: * ln D( yxg,, ) = α + α ln x + β ln y + γ g k k r r k r (7),. * +.5 γ g ln x +.5 γ g ln y + v u r r rk r k r r k According to Irz and Thirtle (24) the log derivative of the input distance function with respect to the th input is that input s cost share, (8) ε ln D( yxg,, ) wx = = S ln x C( ywg,, ) =, which can be interpreted as the th input s relative iportance in the production process. A cost share is by definition positive. Alternatively, the negative of the input cost share is the shadow value of the th input relative to the noralizing input, x (Paul et al. 24). The log derivative of the input distance function with respect to the k th output, (9) ln D( yxg,, ) ln C( ywg,, ) ε k = = ln y ln y k k

11 is the negative cost elasticity of that output. It is expected to be negative for all desirable outputs and, in absolute value, reflects the relative iportance of each output. One can also copute the elasticity of costs (SEC) (Paul et al. 24), which is the su of the individual cost elasticities. (2) ln D( x, y, g) ln C( y, w, g ) SEC = ε = εk = =. ln y ln y k k k k k The derivative of the distance function with respect to the GM variables, (2) ln D( yxg,, ) εi =, ln g i can be used to deterine if GM crops increase efficiency, if (2) is negative then increasing the GM adoption rate decreases the distance to the efficiency frontier. One drawback of using the distance function to estiate the elasticity of cost is that doing so requires a behavioral assuption, cost iniization, or the equivalent assuption that the firs are price efficient. Rather than using the elasticity of cost one can calculate the elasticity of scale. Following Fare and Priont (995) one can specify a distance function where the inputs and outputs are scaled by the fixed factors ρ and θ. (22) D( ρ x, θ y ) = The elasticity of scale is the percentage change in θ for a percentage change in ρ. In other words it answers the question, if producers increase all inputs by soe fixed aount how uch will outputs increase? (23) lnθ ε s = ln ρ ρ = θ = By applying the Iplicit Function Theore, invoking Euler s Theore and recalling that the distance function is equal to one when the fir is operating optially Fare and Priont (995) show that the elasticity of scale can be calculated as follows: (24) D( x, y) xn n xn D( x, y) D( x, y) ε s = = y D( x, y) D( x, y) = y y y y y. Note that the elasticity of scale is the inverse of the elasticity of cost. The proble with using the elasticity of scale is that it assues firs are able to scale all inputs. This is not realistic in agriculture as fars ay not be able to

12 increase ites like land and capital equipent. Therefore, we propose to use a odified version of equation (24) where only the variable inputs, denoted by a v subscript, are scaled. (25) ε = s v D( x, y) x xv D( x, y) y y v. Because the nuerator in (25) will always be less than or equal to one, the odified scale easure will always be less than or equal to the elasticity of scale, ε s ε s. We can take the derivative of equation (25) with respect to GM crops in order to deterine if GM crops increase the elasticity of scale. D( x, y, g) y y ε s gi (26) = 2 gi D( x, y, g) y y If equation (26) is positive then we can conclude that the i th GM technology favors large fars. A ajor pitfall when estiating a production function is endogeneity. To illustrate this point Mundlak (2, 996) used a single input Cobb-Douglas odel, and assued that panel data are available, to show the source of endogeneity. Equation (3) illustrates Mundlak s (2, 996) odel: β + u it i (27) Y it = AX e it This odel has an individual fixed effect,, that does not vary over tie, it is unobservable and correlated with the input X. As the individual fixed effect is not observed it anifests itself in the error ter. The errors are thus correlated with the independent variable, giving rise to endogeneity. When panel data are available endogeneity can be eliinated by using the within estiator. This is done by averaging the variables for the i th individual over tie and ean differencing the data. Thus any endogeneity arising fro unobserved anageent ability disappears fro the odel. The priary otivation for building the pseudo panel is to correct for endogeneity. Consider a distance function, which could take on any arbitrary functional for, expressed as an estiable odel: x = D x y g + + v u. * (28), (,, ) ct ct ct ct ct ct ct 2

13 Unlike the distance function in equation (6), this odel includes an additional error ter, ct. This error ter, described by Mundlak (996; 2), is an individual fixed effect that is assued to be constant over tie, (29) ct = c it is unobservable by the researcher and correlated with the inputs x. (3) Cov( x, ),. ct ct As the individual fixed effect is not observed, it anifests itself in the error ter. The errors are thus correlated with the independent variables, giving rise to endogeneity. The odel also includes the traditional error ter, v ct, which is not correlated with the inputs and is assued to be identically and independently distributed with ean zero. (3) cov( x, v ) =, v ~ N(, iid) ct ct ct Further coplicating atters, Lovell et al. s (994) exposition deonstrated that one could use SFA to estiate a distance function. Lovell et al. s (994) ethod leads to the third error ter in equation (28). Conceptually, this error ter will shift a line fitted by OLS fro the center of the data so that the fitted line sits on the edge, or frontier of the data. The only assuption about u ct is that it is always positive. (32) u ct > As shown by Mundlak (996; 2) we can correct for endogeneity by using the within transforation. In addition Verbeek and Nijan (992) deonstrated that, when n c is large, it is safe to assue that the cohort fixed effect, ct, would reain constant through tie and hence the within estiator will reove ct fro the error ter because ct (33) t ct T =. In this case the within transforation also has an ipact on the one-sided error ter. (34) v v ct t ct = φct T. The one-sided error ter, which was added to the odel in order to shift the fitted odel to the frontier of the data, is absorbed into the traditional error ter. In effect, the fitted odel is shifted back to the iddle of the data and frontier estiates converge to OLS estiates. Therefore, a distance function can be estiated via OLS when panel 3

14 data is available. By analogy, if a researcher is using panel data to estiate a frontier production function, correcting for endogeneity using the within transforation will result in the sae paraeter estiates as a traditional production function that has been corrected for endogeneity using the within transforation. Results A pseudo-panel ay be rendered invalid if cohort ebers are able to switch cohorts. In a footnote Paul et a l. (24) suggest that a pseudo-panel can be validated by perforing a regression using the pooled observations. Hence we will proceed by estiating a pooled distance function odel using SFA ethods, and then copare the results to a pseudo-panel that has been ean-differenced so as to estiate a within odel. In addition we will copare the results of OLS and SFA versions of a within odel. Outputs and inputs are expressed in natural logariths, inputs have been noralized by the natural logarith of the dependant variable, land. Variable definitions can be found in table 2. The estiated odels can be found in table 3. Inputs are the total expenditure on the input, and outputs are total revenues fro the output. All inputs are noralized using the dependant variable, land. Land and capital were converted fro stocks to annualized flows. In a pseudo-panel, duy variables are interpreted as the percentage of individuals in the cohort for which the variable is equal to one. i.e an education duy variable in the pooled data becoe the percentage of farers within a cohort that has at least a high school education. The pooled odel was estiated using the survey weights supplied with the ARMS data, and variances were estiated using Huber-White Standard errors. We copare OLS and SFA versions of the within-transfored input distance function to deonstrate that, given the within transforation, stochastic frontier and OLS estiates are identical. Stochastic frontier and OLS odels were estiated using Stata s frontier and regress coands respectively. When using robust or cluster standard errors Stata s frontier coand will not provide a χ 2 statistic in order to test the null hypothesis that u =, therefore, to illustrate this test, we also include a frontier within estiate with non-robust standard errors. If the null is rejected then the one-sided error ter is statistically significant and the odel cannot be estiated via OLS. For the SFA odel using the within transforation we fail to reject the null, iplying that we can use OLS. When a robust variance estiator is used the estiated value of u is zero. The reader will notice that the paraeter estiates for the OLS and SFA within odels are identical. This is because the 4

15 likelihood function for SFA within is just the noral likelihood function where β is obtained by iniizing the su of squared errors. For the within odel with the exception of off-far incoe (E), all of the output coefficients are statistically significant. All of the output coefficients are negative and all of the input coefficients are positive, which is a arked iproveent over the pooled and the pseudo-panel estiates. When a non-robust variance estiator is used fuel, (f) is the only output that is not statistically significant at the five percent level. For the robust variance odels fertilizer (n) is statistically significant at the ten percent level and off far eployent (j) is statistically significant in the OLS cluster-variance odel. These results highlight the true value of creating a pseudo-panel. The input and output cost shares, coputed using Stata s linco coand, are reported in table 5. Table 2: Variable Definitions, Input Distance Function Outputs Inputs M Corn s Seed C Cotton n Fertilizer L Livestock l Labor O Other Crops c Other Crop Expenses E Off-Far Incoe o Other Miscellaneous Expenses a Feed and Anial Expenses f Fuel and Electricity e Capital Equipent j Off-far Eployent Other Variables s-s9 State or Region Duy Variables Mbt Corn*Bt Corn interaction ter y-y9 Year Duy Variables Mht Corn*HT Corn interaction ter abtcorn Acres of Bt Corn Cbtc Cotton*Bt Cotton interaction ter abtcotton Acres of Bt Cotton Chtc Cotton*HT Cotton interaction ter ahtcorn Acres of HT Corn Shts Soybean*HT Soybean interaction ter ahtcotton Acres of HT Cotton OP_AGE Age of the Priary Opertor ahtsoy Acres of HT Cotton vsall Very Sall Far Duy Variable hs Copleted High School sall Duy Variable Sall Far Duy Variable crop Crop Far Duy Variable large Large Far Duy Variable All of the input shares have the hypothesized sign; fertilizer is the only input share that is not statistically significant. Following Irz and Thirtle, it is possible to calculate an input share for the noralizing input, labor. Unlike Irz and Thirtle we are able to report a significance level for the noralizing input. The results show that the ost iportant inputs, the ones with the largest cost shares, are labor and land, which together ake up 5 percent of all input costs, this is a predictable result. However, the next largest cost share is other iscellaneous expenses 5

16 Table 3: Input Distance Function Results 3 Dependant Variable: land Pooled SFA Huber-White Robust Standard Errors OLS 2 Within SFA Within OLS 2 Cluster Standard Errors SFA Cluster Standard Errors SFA Robust Standard Errors M (4.2)*** (6.89)*** (6.94)*** (6.85)*** (6.9)*** (4.88)*** C (5.6)*** (3.4)*** (3.6)*** (2.3)** (2.33)** (2.55)** L (8.7)*** (8.59)*** (8.65)*** (2.42)** (2.43)** (3.5)*** O (22.62)*** (9.65)*** (9.72)*** (4.3)*** (4.6)*** (5.52)*** S (5.6)*** (4.99)*** (5.2)*** (6.3)*** (6.36)*** (3.)*** E (32.4)*** (.94) (.94) (.59) (.6) (.67) s (3.93)*** (4.25)*** (4.28)*** (4.8)*** (4.2)*** (2.98)*** n (.28) (3.5)*** (3.8)*** (.84)* (.85)* (.76)* p (.3)*** (6.44)*** (6.49)*** (2.82)** (2.84)*** (3.29)*** l (7.93)*** (7.9)*** (8.4)*** (3.4)*** (3.43)*** (8.6)*** c (3.67)*** (3.3)*** (3.34)*** (2.46)** (2.48)** (2.4)** o (6.52)*** (8.2)*** (8.8)*** (6.2)*** (6.24)*** (5.37)*** a (.7)*** (8.29)*** (8.35)*** (2.47)** (2.49)** (3.94)*** f (6.84)*** (.8) (.8) (.63) (.63) (.74) e (2.6)*** (8.5)*** (8.57)*** (2.7)** (2.72)*** (3.55)*** j (53.26)*** (2.99)*** (3.)*** (2.6)* (2.7)** (3.4)*** abtcorn (3.87)*** (5.7)*** (5.75)*** (6.39)*** (6.43)*** (3.25)*** abtcotton (.77) (.82) (.83) (.6) (.6) (.74) ahtcorn (.5) (.39) (.4) (.37) (.38) (.48) * significant at %; ** significant at 5%; *** significant at %. z-statistics in parenthesis 2. t-statistics in parenthesis 3. Year and state duy variables have been oitted fro the pooled odel due to space considerations. 6

17 Table 3, Continued 3 Dependant Variable: land Pooled SFA Huber-White Robust Standard Errors OLS 2 Within SFA Within OLS 2 Cluster Standard Errors SFA Cluster Standard Errors SFA Robust Standard Errors ahtcotton (.34) (2.2)** (2.3)** (.22) (.23) (.52) ahtsoy (.56) (.67) (.67) (.6) (.6) (.6) hs (7.)*** (.59) (.6) (.44) (.44) (.5) crop (4.9)*** (.9) (.9) (.4) (.4) (.9) OP_AGE (.77)*** (3.5)*** (3.54)*** (2.92)** (2.94)*** (3.24)*** Mbt (3.89)*** (.95)* (.96)** (3.3)** (3.5)*** (.85)* Mht (.24) (.5) (.5) (.5) (.5) (.6) Cbtc (.7) (.27) (.27) (.25) (.25) (.22) Chtc (2.9)** (.52) (.52) (.47) (.47) (.45) Shts (.59) (3.5)*** (3.8)*** (.89)* (.9)* (2.57)** vsall.278 (3.8)*** sall -.22 (.4) large -.36 (5.4)*** Constant N/A N/A N/A N/A N/A (44.48)*** N/A N/A N/A N/A N/A Observations R-squared N/A.74 N/A.74 N/A N/A Overall F N/A N/A N/A N/A N/A P>F N/A N/A. N/A N/A N/A Overall Chi N/A N/A N/A N/A P>Chi2.. N/A N/A N/A N/A sigav N/A N/A.23 N/A sigau N/A N/A. N/A.. χ2 N/A N/A. N/A N/A N/A P>Chi2 N/A N/A. N/A N/A N/A * significant at %; ** significant at 5%; *** significant at %. z-statistics in parenthesis 2. t-statistics in parenthesis 3. Year and state duy variables have been oitted fro the pooled odel due to space considerations. 7

18 Table 4: Output and Input Shares, Within Model Outputs Inputs M -.23 s.3 a.47 (4.7)*** (4.2)*** (2.49)** C -.9 n.28 f.2 (2.57)*** (.85)* (.63) L -.46 p.56 e.27 (2.42)** (2.84)*** (2.72)*** O -.38 l.3 j.3 (4.3)*** (3.43)*** (2.7)** S -.9 c.4 land.27 (3.52)*** (2.48)** (9.84)*** E -.4 o.54 (.59) (6.24)*** followed by capital equipent. Copared to those four inputs seed, fertilizer, pesticides fuel and anial specific inputs ake up a very sall percentage of a far s total cost. The adjusted elasticity of scale is surprisingly sall at.75. Paul et al. (24) calculated cost elasticities using a translog input distance function, using ARMS data fro 996-2, which were between.554 for lifestyle fars and.839 for very large fars. When inverted this would result in an elasticity of scale of.88 and.9 respectively. This difference could be due to the functional for, the Paul et al. (24) paper used a translog odel which could have lead to differences due to econoies of scope. The Paul et al. (24) paper focused specifically on fars in the Corn Belt, our data include fars outside of the Corn Belt that are believed to be less efficient than Corn Belt fars. These factors could explain the differences between y odel and Paul et al. s odel. The output*gm interaction coefficients in table 2 deonstrate how the elasticity of scale changes as the GM adoption increases. Recalling that the coefficients ust be inverted and ultiplied by - to deterine the ipact on the elasticity of scale (see equation Error! Reference source not found.), we know that if an interaction coefficient is positive then the GM technology in question is biased in favor of large fars. For HT soybeans the interaction coefficient (Sht) is negative and significant for the within odel. In the pooled odel the coefficient is not statistically significant. The within estiate iplies that the output level that iniizes average costs has increased, thus larger fars will realize an efficiency gain. One ight also conclude that the within estiate iplies that HT soybeans will put upward pressure on far size. The Bt corn interaction ter is statistically significant and positive in both the within odel and the pooled odel. The iplication is that adopting Bt corn decreases the elasticity of scale. The GM*Cotton interaction coefficients are not statistically significant 8

19 The estiated odels can also be used to deterine if GM crops increase efficiency. According to the pooled odel results, increasing the nuber of acres planted with Bt corn will increase efficiency, as evidenced by a statistically significant negative coefficient for the pooled odel. The within odel reports that Bt corn increases efficiency and the result is statistically significant regardless of the ethod used to copute variances. For the within odel, when robust variance estiates are not used the HT cotton variable is negative and statistically significant, which would indicate that HT cotton increases efficiency. The reainders of the GM variables are not significant. These results strongly suggest that planting Bt corn increases efficiency, while the reainder of the GM crops do not. Conclusion In this paper we present two versions of an input distance function; a pooled odel using ARMS data fro 996 through 25, and a pseudo-panel odel that has been first-differenced to reove unobserved cohort-level endogeneity. Both odels have siilar results. In the context of ARMS, where the data are collected by a stratified rando saple, it is difficult to argue that a pseudo-panel odel is superior to cross-section odels or a odel where repeated cross sections are pooled. However, the advantage to using a pseudo-panel lies in the fact that it allows researchers to use panel data ethods that are not available in a pooled cross-section odel. One can eandifference the data and estiate a within odel that is free of unobserved anageent bias. Furtherore, when using SFA to estiate a distance function using panel data that has been ean-differenced we can see that the OLS and the SFA estiation ethods provide the exact sae results. In this exaple, the within odel results are siilar to the pooled odel, but any tie-invariant unobserved cohort-level heterogeneity has been reoved fro the data. All of the input coefficients are of the correct sign, and only off-far incoe is not statistically significant. Likewise all of the output coefficients have the correct sign and only fuel is insignificant. The within odel shows that Bt corn increases efficiency, while decreasing the elasticity of scale and HT soybeans increase the elasticity of scale. References Bernard, J. C., J. D. Pesek, Jr., and C. Fan. "Perforance Results and Characteristics of Adopters of genetically Engineered Soybeans in Delaware." Agricultural and Resource Econoics Review 33, no. 2(24): Brookes, G., and P. Barfoot. "GM Crops: The Global Econoic and Environental Ipact â The first Nine Years " AgBioForu 8, no. 2(25): 87. 9

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