Economc Effcency and Factors Explanng Dfferences Between Mnnesota Farm Households Kent Olson and Lnh Vu Professor and Graduate Student Appled Economcs, Unversty of Mnnesota kdolson@umn.edu vuxx0090@umn.edu Selected Paper prepared for presentaton at the Amercan Agrcultural Economcs Assocaton Annual Meetng, Portland, OR, July 29-August 1, 2007 Copyrght 2007 by Kent Olson and Lnh Vu. All rghts reserved. Readers may make verbatm copes of ths document for non-commercal purposes by any means, provded that ths copyrght notce appears on all such copes. 1
Economc Effcency and Factors Explanng Dfferences Between Mnnesota Farm Households Kent Olson and Lnh Vu Economc effcency, especally nter-frm dfferences n effcency, s one of the maor factors explanng dfferences n frm survval and growth and changes n ndustry structure. Thus, factors explanng and determnng dfferences n economc effcency and changes n effcency between frms are of maor nterest to owners, managers, and other stakeholders as they strve to mprove earnngs and mprove the chances of frm survval. Ths current study was undertaken to mprove our understandng of the nter-farm dfferences n and opportuntes to mprove farm household effcency n utlzng ther land, labor, and captal resources to acheve household obectves. Ths study extends current research n several ways. Frst, t uses a true panel dataset versus the pseudo panel used by Morrson Paul et al (2004). To our knowledge, ths study s the frst study estmatng U.S. agrcultural producton effcences to use bootstrappng procedures to correct the bas generated by the determnstc DEA approach. It s the frst to use a weghted Tobt procedure to correct for that same bas. The study s also the frst to extend the results of estmatng effcences and the Tobt dentfcaton of explanatory factors to dentfyng educatonal opportuntes for mprovng effcences. Ths study estmated the techncal, allocatve, and scale effcences of farm households n southern Mnnesota usng a nonparametrc, output-based data envelopment analyss (DEA) of a panel dataset of ndvdual farm and household fnancal records from southern Mnnesota from 1993-2005. Techncal effcency (TE) measures the frm s ablty to 2
use the best avalable practces and technology n the most effectve way. Allocatve effcency (AE) s dependent on prces and measures the frm s ablty to make optmal decsons on product mx and resource allocaton. Combnng measures of techncal and allocatve effcency yelds a measure of economc effcency. Scale effcency (SE) measures the optmalty of the frm s sze, so a change n sze wll not mprove output or revenue. Estmaton of effcency usng nonparametrc lnear programmng has ts orgn wth Farrel (1957). Setz (1970) used lnear programmng technques to calculate measures of Farrel-type effcences for the sngle-output case. However, not untl Charnes, Cooper and Rhodes (1978) has the generalzed lnear programmng method, known as Data Envelopment Analyss (DEA), been appled wdely to estmate techncal effcency, at frst wthn the operatng research and management scence and later, wthn the economcs communty. In US agrculture, Morrson Paul et al. (2004) used survey data collected by the USDA to estmate techncal and scale effcency n US agrculture and found famly farms to be both scale and techncally neffcent. Wu et al. (2003) computed techncal and scale effcency for Idaho sugar beet farms and concluded that mproper scale operaton and nput overutlzaton were the man sources of neffcency. Tauer (1993) calculated techncal and allocatve effcency ndces of 395 dary farms n New York and found that, dary farms n hs sample were more techncally effcent but less allocatvely effcent n the long run than n the short run. Whle most of the studes dd not consder nonfarm ncome and labor n ther study, the fact that nonfarm actvty now accounts for a large percentage of household ncome and resources means that they should be ncorporated n the calculatng of producton fronter. As 3
n Morrson Paul et al. (2004) and Chavas et al. (2005), ths study ncorporated nonfarm ncome as an output and nonfarm labor as an nput n the producton technology. Not many studes usng DEA pay much attenton to ts statstcal propertes. In the context of the mult-output, mult-nput case, the only currently feasble method to establsh the statstcal property for DEA estmators s by bootstrappng (Smar and Wlson 1998, 2000). Smar and Wlson (1998, 2000) proposed a smoothed bootstrappng method to derve the statstcal propertes of techncal effcency. Ths bootstrappng method had been appled emprcally to several studes. In agrculture, Latruffe et al. (2005) used bootstrappng n estmatng the techncal effcency of crop and lvestock farms n Poland. Brümmer (2001) appled t to establsh confdence ntervals for techncal effcency among prvate farms n Slovena. The method was also used n Ortner et al. (2006) for dary farms n Austra. To our knowledge, bootstrappng the DEA estmators has not been used n studes of US agrculture. The specfc obectves of ths study were to (1) estmate techncal, allocatve, and scale effcences of farms usng an output based approach, (2) use bootstrap procedures to correct the bas generated by the determnstc DEA method, (3) dentfy factors that are sgnfcant n explanng dfferences n both levels of effcency and dfferences n effcency among farms and (4) dentfy educatonal opportuntes for helpng farm households mprove ther effcences and, thus, chances for survval. Methods and Models Effcency can be estmated n two ways: parametrc and nonparametrc. The parametrc approach ncludes specfyng and estmatng a parametrc producton fronter (cost or proft functon). In contrast, the nonparametrc approach, or data envelopment analyss (DEA), has 4
the advantage of no pror parametrc restrctons on the technology and thus s less senstve to msspecfcaton. It s also not subect to assumptons on the dstrbuton of the error term. Followng Chavas et al. (2005), Morrson Paul et al. (2004), and others, we frst used nonparametrc (DEA) methods to estmate output-based techncal, allocatve, and scale effcences. Based on the smoothed bootstrap procedure for DEA estmators proposed by Smar and Wlson (2000), the study estmated the bas and the confdence nterval of the DEA estmators for TE, usng the package FEAR developed by Wlson (2005) n the R platform. 1 We then used the estmated effcences to dentfy factors explanng dfferences among farms by standard and weghted Tobt analyss. Techncal Effcency Consder a farm nvolved n both farm and nonfarm actvtes wth nputs X and producng outputs (Y, N) where Y are farm outputs and N s nonfarm ncome. Nonfarm ncome s treated as an output because t generates revenue and uses nput from the farm famly. For the th farm out of n farms, the output-based techncal effcency ndex, TE, s defned as TE ( X, Y, N ) = mn θ (1) θ,λ subect to Y / θ Yλ; N / θ Nλ; X Xλ; λ 0; λ = 1 where θ s a scalar and λ s a n = 1 vector of constant λ (=1,, n). TE measures the dstance between the observed nput-output mx and the producton fronter. In general, 0 TE 1; when TE = 1, the farm s producng on the producton fronter, and hence, techncally effcent. When TE <1, the farm s techncally neffcent. 1 The tme for runnng a bootstrap procedure wth 2000 replcatons for a reference group of 250 farms takes less than one hour for a Pentum IV, 2.8 Ghz computer. 5
The DEA model above s a varable returns to scale (VRS) DEA model, mplyng t permts the producton fronter to have ncreasng, constant or decreasng return to scale. In the case of constant return to scale, one can fnd TE easly by deletng the convexty constrant ( λ = 1). n = 1 Allocatve Effcency The allocatve effcency ndex can be estmated by usng the revenue maxmzaton problem (under VRS): R p, X, Y, N) = max λ ( p' Y + ) (2) ( Y, N, N subect toy n Yλ ; N Nλ; X Xλ; λ 0; λ = 1 where p s a vector of output prces = 1 and other varables are as defned prevously. Equaton (2) only assumes a well-functonng output market and remans vald despte factor market mperfectons. After obtanng maxmal revenue R (p, X, Y, N) from ths problem, we can derve allocatve (AE) and economc effcency (EE) from the equaton: EE ( p, X, Y, N) = ( p' Y + N) / R ( p, X, Y, N) and AE = EE /TE. Thus, EE s the rato of observed output revenue to maxmum revenue for the farm. AE s the economc effcency after takng out the effect of techncal neffcency. In other words, allocatve effcency s the rato of the revenue from the hypothetcal techncal effcent farm to maxmal revenue obtaned by allocatng resources n the rght way. In general, 0 AE 1, where AE=1 represents a farm that s allocatvely effcent n output. 6
Scale Effcency Scale effcency (SE) can be estmated by maxmzng the revenue equaton (2) under both varable returns to scale (VRS) and constant return to scale (CRS) (Chavas et al. 2005). When assumng CRS, the obectve functon s smlar to (2) but wthout the n condton λ = 1: = 1 R C ( Y, N, + N p, X, Y, N) = max λ ( p' Y ) (3) subect to Y Yλ; N Nλ; X Xλ; λ 0 where varables are as defned prevously. The dfference between the two measures s due to scale neffcency. Thus, the scale effcency ndex (SE) can be expressed as the maxmzed revenue under VRS dvded by the maxmzed revenue under CRS or SE ( p, X, Y, N) = R ( p, X, Y, N) / R ( p, X, Y, N). In general, 0 SE 1, wth SE =1 representng effcent economy of scale. SE< 1 mples that the nputs are not effcent n scale, whch can be ether ncreasng returns to scale (IRS) or decreasng returns to scale (DRS). We can decde among farms wth scale neffcency, whch farms are too large (DRS) or too small (IRS) by runnng a DEA problem wth non-ncreasng returns to scale (NIRS) mposed. Ths can be done by replacng n the constrant λ = 1 n equaton (2) wth the constrant λ 1: = 1 R C n = 1 NI ( Y, N, + N p, X, Y, N) = max λ { p' Y ) (4) subect toy Yλ ; N Nλ; X Xλ; λ 0; λ 1. n = 1 7
Then we can compare the NIRS and the VRS effcency scores. For a partcular farm, f the two scores are unequal and SE<1, the farm s ncreasng returns to scale. On the other hand, f they are equal and SE< 1, the farm exhbts decreasng returns to scale. Bootstrappng the DEA estmators Whle DEA methods have been wdely appled, most researchers largely gnored the statstcal propertes n the estmators. Any devaton from the fronter s attrbuted to neffcency. Ignorng the nose n the estmaton can lead to based DEA estmates and msleadng results. Ths paper apples Smar and Wlson s (1998, 2000) smoothed bootstrap procedure to correct the bas n DEA estmators of TE and establsh ther confdence nterval. Bootstrappng s based on the dea that by resamplng the data wth replacement, we can mmc the data-generatng process characterzng the true data generaton. Followng Dong and Featherstone (2004), the procedures are the followng steps:. Frst we calculated the DEA effcency scores for each farm among n farms as n equaton (1) wthout the constrant that the sum of λ s 1, denoted as θˆ for the th farm.. Then a frst, smple bootstrap s made usng θˆ from the frst step. Let smple bootstrap sample fromθ random generator: ˆ1 n β β be a 1,... n,... θˆ. A random sample of sze n s generated for the ~ θ β + hε = 2 β hε f β + hε otherwse 1 where h s the bandwdth of a normal kernel densty, calculated from Smar and Wlson s (2000) method of mnmzng an approxmaton to the mean weghted ntegrated square error, and ε s random devaton. 8
. To obtan the smoothed bootstrap estmates of θ, we now correct the varance of the generated bootstrap sequence snce kernel estmators are used by constructng another 1 ~ sequence: θ = β + ( θ β ) 2 2 1+ h / σˆ θ where N β = (1/N) = 1 β and 1 N 2 σˆ ( ˆ θ = θ N 1 = 1 θ ˆ ) 2. The sequence varance of DEA effcency score. θ has better propertes than the smple bootstrap sequence snce the θ s asymptotcally correct. We obtan a smoothed bootstrap estmate of v. Usng the orgnal estmates of techncal effcency, θˆ, and the smoothed bootstrap estmate of effcency, θ, we construct a pseudo data set of ( x, x and y,b = ( θˆ / θ ),b y,b ) where x,b = y wth x, y the orgnal nput and output vectors of the th farm, respectvely for =1,.., n and b refers to the teratons done n step v. The output vector s modfed (versus the nput vector) snce we are estmatng effcency usng an output-based DEA. v. Now we compute the new DEA score ( x,,b y,b ). θ ˆ for each farm usng the pseudo data set of v. Repeat step () to (v) a suffcently large number of tmes, say B, to yeld B new DEA techncal effcency scores θ ˆ for =1,, n. In our emprcal work, we set B=2000 to ensure the low varablty of the bootstrap confdence ntervals. The number of bootstrap teratons should be more than 1000 f we are nterested n confdence nterval estmaton. A smaller number of teratons would be enough f we 9
only needed estmates for bas and standard devaton (see Efron and Tbshran 1993). v. Calculate the bootstrap bas estmate for the orgnal estmator θˆ as ) bas B ( θˆ ) = B θ B 1 θ ˆ ˆ b= 1. ) The bas-corrected estmator of θˆ can be computed as θˆ = θˆ ( ˆ bas B θ ) The percentle method s nvolved n constructng confdence nterval. The confdence nterval for the true value of θˆ can be establshed by fndng value a, b such that Prob α θˆ ( b θˆ aα ) = 1 α. Snce we do not know the dstrbuton of ( θˆ θˆ ), we can α α use the bootstrap values to fnd aˆ, bˆ such that Prob ˆ θˆ ( b θˆ aˆ ) = 1 α. It α α α α nvolves sortng the value of ( θˆ θˆ ) for b =1,,B n ncreasng order and deletng ( ( α / 2) 100 percent of the elements at ether end of ths sorted array and settng ˆ ˆ ˆ ˆ. aα and b α at the two endponts, wth aα bα Tobt analyss Most authors have used Tobt analyss n the second stage after calculatng the effcency scores to assess the factors nfluencng effcency. The use of the Tobt specfcaton s often motvated by the fact that sometmes many values n the effcency scores are equal to unty. On the other hand, the bas-corrected estmator of techncal effcency generally has hgher mean-square error than the orgnal estmates. Smar and Wlson (2000) suggest that one should avod usng the bas-corrected estmates unless σˆ 1 ( 3 [ ˆ]) 2 2 bas θ n whch 2 σˆ s the sample varance of the bootstrap values and θˆ s the uncorrected estmated effcency score. 10
In our sample, ths only holds for about 5% of the sample, whch could ustfy the use of the orgnal techncal effcency scores n the second stage. However, the nformaton about the standard error and confdence ntervals of the DEA estmator n the frst step s very mportant n ndcatng the senstvty of the DEA estmator. The larger the varance s, the more mprecse the calculaton of effcency score mght be. Therefore, n the second stage, we apply two Tobt specfcatons for techncal effcency. The frst s the conventonal Tobt regresson and the second s the weghted Tobt regresson wth weght equal to the recprocal of standard error n the frst stage. The weghted Tobt regresson uses the nformaton on the varances of techncal effcency scores to mprove the estmaton by prortzng the observatons wth lower standard errors and punshng those wth hgher standard errors. Snce the procedures for estmatng the bas n DEA estmators for scale and allocatve effcency have not been developed, we use the conventonal Tobt analyss for these effcences. Data For ths analyss, we used data from the Southeastern and Southwestern Mnnesota Farm Busness Assocatons collected by the Department of Appled Economcs at the Unversty of Mnnesota. The complete data contans fnancal and farm characterstc records from about 400 farms, whch had been members of ether Assocaton n at least one year from 1993 through 2005, and had records of suffcent qualty to be ncluded n at least one year. The number of records per year averaged 230 and ranged from a hgh of 263 n 1995 and 1999 to a mnmum of 138 n 2005. Membershp n the Assocatons s not stable; farms have dfferng frequences of years n the data. There are 47 farms wth only one year of data and 11
67 farms wth 13 years of data. Eghty percent of the observatons were from the 211 farms (53% of the total) wth 8 to 13 years of data. The model ncludes nne nputs: three labor nputs (famly labor on farm, hred labor on farm, nonfarm labor), three nonlabor varable nputs categorzed nto lvestock-related, crop-related, and operatng-related expendtures, and three nputs for land (rented crop land, owned crop land, and owned pasture land, Table 1). Data for nonlabor and land nputs come drectly from the data base. Labor expenses are not ncluded n these expense categores snce they are accounted for n other nput measures. Income tax expenses are not ncluded n these expenses varables. Famly labor workng on the farm s the total unpad labor hours. Hred labor workng on the farm s the total (pad) hred labor hours. Table 1. Summary Statstcs of Varables for DEA Estmaton Varable Mean Std. Dev. Output Corn producton value a 34.1 (37.8) Soybean producton value a 26.2 (27) Beef producton value a 4.3 (16) Mlk producton value a 14.9 (59.8) Hog producton value a 23.6 (142.6) Nonfarm Income a 21.8 (29.5) Inputs Famly labor b 2.8 (1.8) Hred labor b 1.0 (2.9) Nonfarm labor b 1.0 (1.4) Lvestock-related expendtures a 29.4 (77.6) Crop-related expendtures a 21.9 (21.1) Operatng-related expendtures a 37.5 (42.7) Owned crop land area (acres) 241 287 Rented crop land area (acres) 439 (438) Owned pasture land (acres) 12 (54) Prces Corn prce ($/bu) 2.10 (0.40) Soybean prce ($/bu) 5.64 (0.99) Beef prce ($/cwt) 64.09 (7.29) Mlk prce ($/cwt) 13.88 (1.35) Hog prce ($/cwt) 43.51 (7.10) a thousand $; b thousand hours 12
Snce we dd not have drect nformaton on the hours of nonfarm famly labor (.e., workng hours not on the farm), we estmated these hours from the avalable data on total nonfarm wages and salary. A proxy for nonfarm wages was taken from the average nonfarm wages of the countes where the farms resde. The nonfarm wages based on the weghted average wages of nonfarm sectors, specfcally constructon, manufacturng, and servce wages from 2000 to 2004 (NAICS Industres lst) and of mnng, constructon, manufacturng, transportaton, fnance, servces, publc admnstraton, and trade wages from 1993-1999 (SIC Industres lst). After calculatng the nonfarm wages at the county level, we estmated each farm s nonfarm labor hours as that farm s total nonfarm wages and salary dvded by the approprate county s nonfarm wage rate. The model ncludes sx outputs: two crops (corn and soybean), three lvestock products (beef, mlk, and hog), and nonfarm ncome. Corn and soybean were the most mportant crop outputs n Mnnesota. They were produced n more than 90% of our sample and contrbuted 91% of total crop producton value. Among lvestock, hog and mlk are more mportant than beef n producton value (43%, 40% and 11% of total lvestock producton value, respectvely). Together, these three outputs account for 94% of total lvestock producton value. Nonfarm ncome generates about 16% of total output value generated by the sx outputs n our study. Annual output prce data were taken from Natonal Agrcultural Statstcs Servce, assumng farms n the regon faced the same prces for ther outputs n a gven year. Physcal crop producton for a specfc crop on an ndvdual farm n a specfc year was calculated by dvdng that farm s gross producton value by that year s prce of that 13
crop. Physcal lvestock producton for a specfc lvestock enterprse on an ndvdual farm n a specfc year was calculated by dvdng the total lvestock value by the prce of lvestock. The varables used n the Tobt analyss to determne factors explanng dfferences n farm effcences nclude fnancal condton, farm characterstcs, labor characterstcs, land tenure, and the relatve mportance of dfferent outputs (Table 2). Fnancal condton and farm characterstcs were measured by farm ncome, total asset, debt-asset rato, deprecaton rato, current asset share, farm nvestment rate, captal-labor rato, and land-labor rato. Labor characterstcs were measured by the number of operators, man operator s years farmng, and hred labor rato. Land tenure was measured by the tenancy rato. The relatve mportance of dfferent outputs was measured by the nonfarm ncome rato and the Herfndahl ndex. The Herfndahl ndex measures the degree of output concentraton and s defned as n = 1 s 2 n whch s s the share or rato of each farm s output of the th output to the total of that farm s sx outputs n ths study. Results Effcency estmates obtaned from the DEA analyss are presented wth techncal effcency frst followed by allocatve and then scale effcency. Sgnfcant explanatory factors are then dentfed. Effcences Techncal effcency. Over all years and farms, the ntal estmate of average techncal effcency was 0.87, assumng constant returns to scale (TEC), and 0.90, assumng varable returns to scale (TEV) (Table 3). Over tme, both estmates of average techncal effcency 14
have followed a smlar, varable pattern wth a slght upward trend: from 0.86 n 1993 to 0.90 n 2005 for TEC, and 0.89 to 0.92 for TEV. These ntal estmates showed a maorty of farms beng techncally effcent: 52.8% of farms have an estmated TEC score of 1 and 60.3 % have an estmated TEV score of 1. These estmates of techncal effcency are smlar to Morrson Paul et al. (2004) estmates of techncal effcences for ten corn producng states n the Mdwest (whch ncludes Mnnesota) usng data from USDA s Agrcultural Resources Management Study (ARMS) from 1996-2001. Table 2. Summary Statstcs of Explanatory Varables for Tobt Analyss Descrpton of Varables Varables Mean Standard devaton Gross farm ncome a Farm ncome 397.2 (440.9) Value of farm and nonfarm asset a Asset 1,159 (948.8) Number of operators Number of operators 1.19 (0.65) Years of farmng of the man operator Years of farmng 24.59 (11.28) Rato of nonfarm ncome/ Total ncome Nonfarm rato 0.09 (0.13) Rato of hred hours/ Total labor hours Hred labor rato 0.14 (0.24) Rato of rented land/ Total land Tenancy rato 0.6 (0.33) Debt/Asset Rato Debt/Asset Rato 0.51 (0.23) Current Asset/ Total assets Current asset share 0.25 (0.16) Deprecaton expense rato Deprecaton Rato 0.08 (0.06) Herfndahl Index Herfndahl Index 0.48 (0.14) Captal/Labor rato ($thousand/hour) Captal/Labor rato 4.44 (4.23) Land/Labor rato (acres/hour) Land/Labor rato 2.46 (1.86) Farm nvestment value/ Gross farm ncome Investment rate 0.16 (0.39) Corporate =1 f corporate or partnershp farms; 0 otherwse Corporate 0.16 (0.37) Regon = 1 f Southeast Mnnesota; Regon 0 for Southwest Mnnesota 0.23 (0.42) a thousand dollars 15
Table 3. Average Effcency Estmates, 1993-2005 Techncal Effcency by CRS Allocatve Effcency Scale Effcency Techncal Effcency by VRS Bas corrected TEV Lower bound Hgher bound 1993 0.857 0.696 0.845 0.886 0.749 0.675 0.879 1994 0.827 0.730 0.860 0.869 0.707 0.656 0.859 1995 0.812 0.708 0.867 0.850 0.684 0.636 0.840 1996 0.896 0.715 0.871 0.919 0.817 0.716 0.915 1997 0.891 0.789 0.905 0.916 0.827 0.717 0.914 1998 0.892 0.815 0.898 0.913 0.806 0.712 0.908 1999 0.869 0.804 0.891 0.895 0.775 0.695 0.891 2000 0.872 0.703 0.875 0.901 0.792 0.714 0.896 2001 0.875 0.821 0.899 0.904 0.773 0.694 0.898 2002 0.844 0.789 0.862 0.884 0.754 0.684 0.878 2003 0.886 0.855 0.907 0.916 0.816 0.725 0.911 2004 0.901 0.834 0.933 0.913 0.794 0.711 0.908 2005 0.902 0.851 0.911 0.923 0.801 0.703 0.918 All farms 0.869 0.771 0.884 0.897 0.774 0.694 0.892 Medan 1.000 0.801 0.934 1.000 0.813 0.694 0.892 Std. Dev. 0.185 0.219 0.139 0.165 0.129 0.114 0.164 Skewness -1.281-0.597-1.692-1.580-1.438-1.090-1.580 Kurtoss 3.612 2.279 6.369 4.583 5.095 5.259 4.580 Applyng the bootstrap procedure by Smar and Wlson (2000), we found that the bas was consderable. Whle the average ntal TEV was 0.90, the bas-corrected pont estmate was 0.77, or 86.3% of the ntal, uncorrected estmate. Over tme the bas-corrected TEV followed a trend smlar to, but more accentuated than, that of the ntal TEV estmate. The largest group of farms had a bas-corrected TEV between 0.75 and 0.90 compared to the largest group that had an ntal TEV estmate of 1.0. When farms are ranked by ther bascorrected TEV (from lowest to hghest), the quanttatve dspartes between the ntal and corrected TEV estmates were extremely obvous (Fgure 1). Ths graph also showed that the ntal TEV estmates dd not provde the same rankng of ndvdual farms snce they dd not form a smooth lne followng the corrected TEV. Also vsble s the varablty n the lower and upper bounds of the corrected TEV, even between farms wth smlar expected values of 16
corrected TEV. Ths varablty was greatest for those farms wth ntal TEV estmates of 1.0. The ntal TEV estmate suggested that wth a gven nput, an average farm could expand ts output by about 11.5 % = (((1/0.90)-1)100%) f techncal effcency were mproved to 1.0. The bas-corrected TEV, however, suggested an expected output expanson of 29.2% = (((1/0.77)-1)100%). The lower and upper bounds of the 95% confdence nterval for the bas-corrected TEV were 0.69 and 0.89, respectvely, whch suggested that the amount an average farm could expand ts output by ncreased techncal effcency ranged from 12.1% to 44.1%. 1 0.8 0.6 0.4 0.2 Intal TE estmates Corrected TE estmates Lower bound Hgher bound 0 0 10 20 30 40 50 60 70 80 90 Percent of observartons Fgure 1. Dstrbuton of techncal effcency wth confdence ntervals 17
Allocatve effcency. In terms of allocatve effcency (AE), a maorty of the farms n ths study are not effcent, that s, these farms dd not make the correct allocaton of nputs to produce the correct set of outputs to maxmze revenue based on the prces receved. Over all years, average AE was 0.77 wth 30.8% of the farms havng a score of 1. Thus, the average farm was estmated to potentally have the ablty to ncrease revenue by 29.7% f prce sgnals had been responded to perfectly. Except for one year (.e., 2000), average AE followed a farly stable upward trend over tme. Scale Effcency. Average scale effcency (SE) was 0.88 wth only 19.9% of the farms havng an SE score of 1. However, many farms were near SE: 58.1% of farms had an SE score hgher than 0.90 and 45.1% of farms had an SE score hgher than 0.95. These estmates of scale effcency were smaller than those estmated by Morrson Paul et al. s (2004) estmates of scale effcences usng USDA ARMS data. Smlar to TE and AE, average SE trended upward wth some varablty over tme. Among the farms beng scale neffcent (.e., SE<1), the dstrbuton between farms that are too large (havng decreasng returns to scale (DRS)) and farms that are too small (ncreasng returns to scale (IRS)) are sharply dfferent. Usng the procedures descrbed earler, 61.8 % of farms were found to be too large compared wth 18.3 % beng too small and 19.9% at an optmal scale of operaton. In summary, farms tended to be more techncally effcent (usng the ntal estmates of TEV), followed by scale effcency, and then by allocatve effcency. However, when usng bas-corrected TEV, farms were more scale effcent followed by techncal and allocatve effcency. The overall average for scale effcency s hgher than the average allocatve effcency, but the percentage of farms wth a score of 1 s hgher for allocatve 18
effcency compared to scale effcency. Ths apparent dfference n sgnal can be explaned n the dfferent dstrbutons shown n the skewness and kurtoss statstcs. Factors explanng dfferences n effcences Tobt analyss was used to dentfy sgnfcant factors explanng dfferences n techncal, allocatve, and scale effcences between farms. The estmated effcency scores of farms durng the perod 1993-2005 (presented above) were regressed on the explanatory varables. Techncal Effcency. The Tobt results for explanng techncal effcency (assumng varable returns to scale) are reported n Table 4. A few explanatory varables changed sgnfcance levels but no sgns of coeffcents changed wth the weghted Tobt compared to the standard Tobt. When all years and observatons are analyzed together, explanatory varables for techncal effcency that had a sgnfcant, 2 postve mpact n both models were regon, current asset share, nonfarm rato, captal/labor rato, land/labor rato, Herfndahl ndex, and number of operators. Explanatory varables that had a sgnfcant, negatve mpact n both models were tenancy rato, years of farmng, and the farm s debt/asset rato. The hred labor rato dd not have a sgnfcant effect n the standard model but t had a sgnfcant, postve mpact n the weghted model. Year had a sgnfcant, negatve coeffcent n the weghted Tobt, but t was not sgnfcant n the standard Tobt. Sgnfcant, postve mpacts of the busness organzaton (.e., Corporate) and the deprecaton rato were found n the standard Tobt but were not sgnfcant n the weghted Tobt. Farm ncome, asset, and nvestment rate dd not have a sgnfcant mpact n ether model. 2 Tables ndcate 95% and 99% sgnfcance. When used n the text, sgnfcant refers to a coeffcent wth sgnfcance greater than 95% (.e., p<0.05). To mprove readablty, ths reference s not ncluded at all ponts. 19
Table 4. Tobt Analyss of Techncal Effcency. Standard Tobt Weghted Tobt year 0.00 (-1.63) -0.008 (-3.21) Regon 0.10 (3.8) 0.078 (2.64) Current asset share 0.76 (10.29) 0.854 (9.48) Tenancy rato -0.10 (-3.11) -0.101 (-2.48) Farm ncome 0.03 (0.8) 0.056 (1.15) Asset 0.03 (1.46) 0.048 (1.9) Years of farmng 0.00 (-4.61) -0.005 (-5.15) Nonfarm rato 0.64 (7.85) 0.909 (8.53) Captal/Labor rato 0.02 (3.69) 0.017 (3.07) Land/Labor rato 0.02 (2.41) 0.021 (2.59) Debt/Asset Rato -0.19 (-4.75) -0.271 (-6.03) Hred labor rato 0.07 (1.59) 0.117 (2.31) Herfndahl Index 0.68 (10.74) 0.813 (10.78) Investment rate -0.01 (-0.3) 0.000 (0) Corporate 0.09 (2.14) 0.060 (1.09) Deprecaton Rato 0.29 (2.39) 0.149 (1.08) Number of operators 0.09 (2.59) 0.104 (2.05) Constant 7.64 (1.73) 16.724 (3.26) Number of obs 2503 2436 LR ch2(17) 554.05 498.24 Log lkelhood = -968.22-1105.5 Note: t- statstcs are n parentheses., : sgnfcant at 95% and 99% confdence level respectvely. In the weghted Tobt regresson, whch better accounts for measurement errors as argued above, a hgher current asset share and a lower debt-to-asset rato contrbuted to hgher techncal effcency. Both captal-to-labor and land-to-labor ratos had postve coeffcents, ndcatng that ncreasng captal and land relatve to labor can rase techncal effcency. A hgher hred labor rato (that s, a hgher level of hred labor relatve to operator labor) had a postve effect, ndcatng the mportance of expandng the total amount of avalable labor by addng hred labor to the supply of operator labor. Smlarly, farms wth more operators (.e., a hgher supply of labor and management) had hgher techncal 20
effcency. On the other hand, the land tenancy rato whch measures the amount of rented land relatve to the farm s total land had a negatve effect, smlar to the pattern of farms n Central Europe found by Balcombe et al. (2005). Farms whch were more specalzed, that s, concentrated on a smaller set of outputs, as represented by the Herfndahl ndex, were found to have a hgher techncal effcency than less specalzed farms. Havng a hgher level of nonfarm ncome relatve to total household ncome was also assocated wth hgher techncal effcency. Years of farmng, an ndcaton of both age and experence, had a dampenng effect on techncal effcency. Farm sze (as represented by farm ncome, asset level, and the farm nvestment rato) had no sgnfcant relatonshp wth farm techncal effcency. A slght negatve trend was shown by the sgnfcant negatve coeffcent on year; so the slght postve trend seen n Table 3 must be explaned by trends n other varables, not as a general trend n TE tself. The regon varable ndcated farms n Southeast Mnnesota were more techncally effcent than Southwest farms. Busness organzaton, as ndcated by the dummy varable for partnershp/corporate farms, was not sgnfcant n the weghted Tobt analyss. Nor was the degree of mechanzaton, as ndcated by the deprecaton rato. Allocatve effcency. The Tobt results for explanng allocatve effcency (assumng varable returns to scale) are reported n Table 5. Those explanatory varables wth sgnfcant postve mpacts on allocatve effcences were year, current asset share, tenancy rato, asset, nonfarm rato, captal/labor rato, land/labor rato, hred labor rato, the Herfndahl ndex, corporate, deprecaton rato, and the number of operators. Those explanatory varables whch have sgnfcant, negatve mpacts on allocatve effcency were farm ncome, years of farmng, and debt/asset rato. As wth techncal effcency, a hgher current asset share and a lower debt-to-asset rato were assocated wth better allocatve 21
effcency. Nonfarm ncome opportuntes were agan found to play a postve role n helpng farmers allocate ther resources better. Increasng the amount of captal and land relatve to labor, as well as the amount of hred labor to total labor, also helped mprove allocatve effcency. Hgher levels of specalzaton as measured by the Herfndahl ndex also were assocated wth hgher allocatve effcency. Table 5: Tobt Analyss of Allocatve Effcency and Scale Effcency Allocatve Effcency Scale Effcency All Farms All Farms Farms wth IRS & CRS Farms wth DRS year 0.005 (3.35) 0.002 (2.19) -0.007 (-2.27) 0.005 (5.65) Regon 0.026 (1.49) 0.006-0.61-0.01 (-0.35) 0.016-1.57 Current asset share 0.171 (3.77) 0.113 (4.12) 0.318 (4.33) 0.002 (0.06) Tenancy rato 0.097 (4.35) 0.083 (6.09) 0.093 (2.72) 0.063 (4.65) Farm ncome -0.106 (-4.95) 0.004 (0.3) -0.084 (-1.75) 0.03 (2.74) Asset 0.027 (2.46) -0.032 (-4.99) 0.161 (5.7) -0.057 (-9.66) Years of farmng -0.002 (-3.48) 0 (0.21) 0 (-0.15) 0 (-0.09) Nonfarm rato 0.897 (15.7) 0.305 (9.25) 0.795 (9.51) -0.038 (-1.01) Captal/Labor rato 0.01 (3.66) 0.012 (7.24) 0.004 (0.98) 0.007 (3.32) Land/Labor rato 0.032 (7.14) 0.005 (2.08) 0.019 (2.95) 0 (0.11) Debt/Asset Rato -0.099 (-3.6) -0.073 (-4.39) 0.018 (0.38) -0.088 (-5.65) Hred labor rato 0.138 (4.92) 0.112 (6.62) 0.035 (0.77) 0.092 (5.52) Herfndahl Index 0.796 (18.7) 0.206 (8.13) 0.473 (6.72) 0.066 (2.66) Investment rate 0.016 (1.3) -0.006 (-0.75) 0.003 (0.22) -0.02 (-1.93) Corporate 0.064 (2.44) -0.041 (-2.6) -0.097 (-2.41) -0.022 (-1.43) Deprecaton Rato 0.519 (6.15) 0.105 (2.06) 0.066 (0.5) 0.051 (1.03) Number of operators 0.071 (3.33) 0.013 (1.05) 0.043 (1.33) -0.012 (-0.93) Constant -10.31 (-3.33) -3.497 (-1.84) 13.364 (2.33) -9.001 (-5.16) Number of obs 2503 2503 904 1599 LR ch2(17) 1114.6 525.56 287.6 285.3 Log lkelhood = -442 711.8-168.9 1318.2 Note: t- statstcs are n parentheses.;, : sgnfcant at 95% and 99% confdence level respectvely Notable dfferences n sgnfcance between factors explanng allocatve effcency compared to those explanng techncal effcency nclude the postve effects of land tenancy rato (compared to a negatve effect) and total asset value (compared to no effect). Thus, 22
whle a hgher rented land rato was assocated wth lower techncal effcency, t was assocated wth hgher allocatve effcency, perhaps because land rental expanded the avalable resources for farm producton and allowed for a better mx of enterprses. The level of farm ncome had a sgnfcant, negatve mpact on allocatve effcency compared to no effect on techncal effcency. Scale effcency. The Tobt results for explanng scale effcency are reported n Table 5. When all farmers are grouped together, the explanatory varables that had a sgnfcant postve mpact were year, current asset share, tenancy rato, nonfarm rato, captal/labor rato, land/labor rato, hred labor rato, the Herfndahl ndex, and the deprecaton rato. As wth techncal and allocatve effcency, a hgher current asset share; a lower debt-to-asset rato; hgher levels of captal, land, and hred labor relatve to total labor; and ncreased specalzaton (as measured by the Herfndahl ndex) were assocated wth better scale effcency. Varables that had a sgnfcant negatve mpact were asset, debt/asset rato, and busness organzaton (.e., corporate). Varables whch dd not have any sgnfcant mpact were regon, farm ncome, years of farmng, nvestment rate, and the number of operators. Farms wth scale neffcency (.e., SE < 1) were separated nto farms wth DRS and farms wth ether CRS or IRS usng the NIRS procedure descrbed earler. Weghted Tobt analyss was then done for the two sub-samples. 3 For both types of farms, hgher tenancy ratos and hgher specalzaton (.e., Herfndahl ndex) mproved scale effcency. The current asset share and the land/labor rato had sgnfcant postve mpact for too small farms, but, devatng from the aggregate analyss, they dd not have a sgnfcant mpact on 3 We group farms wth CRS and wth IRS to ncrease the number of observatons. The results are not sgnfcantly dfferent when we run regresson on farms wth IRS only. 23
too large farms. Busness organzaton (.e., corporate) had a negatve mpact on too small farms. For too large farms, farm ncome, captal/labor rato, hred labor rato, and the nvestment rate had sgnfcant postve mpacts, but they dd not have a sgnfcant mpact on too small farms. The debt-to-asset rato had a sgnfcant negatve mpact on too large farms. As should be expected, snce we are analyzng scale, the sze of farm as measured by asset level had dfferent effects: postve for too small farms and negatve for too large farms. Too small farms had a sgnfcant negatve trend n scale effcency over tme ndcatng some concern for the future; whle too large farms had a sgnfcant postve trend n scale effcency. Years of farmng, deprecaton rate, and the number of operators dd not have a sgnfcant mpact on ether group of farms. Conclusons The results of the analyss of techncal, scale and allocatve effcency show the degree of neffcency n Mnnesota farms to be consderable. The farms tend to be more techncally effcent, followed by scale effcency, and then by allocatve effcency. On average, ntal techncal effcency, scale and allocatve effcency are 0.90, 0.88 and 0.77 durng the perod 1993-2005. In general, farm effcency mproved over the perod. The study employed bootstrappng to determne the varablty of DEA techncal effcency estmates and to correct for the bas nherent n the determnstc measurement. The bas-corrected pont estmate of techncal effcency was 0.77. Wth bootstrappng, the wdth of the confdence ntervals was estmated to be about 0.2 on average. These estmates were employed n the second step to evaluate factors nfluencng effcency. Ths Tobt analyss suggested that more specalzed farms (as measured by the 24
Herfndahl ndex) have hgher levels of effcency by all three measures (Table 6). A hgher proporton of rented land (as ndcated by the tenancy rato) s assocated wth hgher allocatve and scale effcency but lower techncal effcency. A hgher current asset share and a lower debt-to-asset rato are postvely assocated wth all three measures of farm effcency, except the current asset share had no effect on scale effcency for too bg farms and the debt-to-asset rato had no effect on scale effcency for too small farms. A hgher proporton of household ncome comng from nonfarm sources and hgher hred labor, captal-to-labor, and land-to-labor ratos had postve effects on all three effcency measures, except the nonfarm and land-to-labor ratos had no effect on scale effcency for too bg farms and the captal-to-labor and hred labor ratos had no effect on scale effcency for too small farms. Table 6. Summary of Sgnfcant Explanatory Varables n Tobt Analyss and ther Impact on Each Effcency Measure Explanatory varable TEV AE SE (wth all farms) SE (for farms wth IRS & CRS) SE (for farms wth DRS) year + + + Regon + Current asset share + + + + Tenancy rato + + + + Farm ncome + Asset + + Years of farmng Nonfarm rato + + + + Captal/Labor rato + + + + Land/Labor rato + + + + Debt/Asset Rato Hred labor rato + + + + Herfndahl Index + + + + + Investment rate Corporate + Deprecaton Rato + + Number of operators + + + and ndcate the sgn of those coeffcents that have a sgnfcance of at least 95%. 25
Several conclusons and suggestons for mprovng farm effcences can be drawn from these results. Frst, whle these results do not show a drect causal relatonshp, a hgher current asset share and a lower debt-to-asset rato are assocated wth hgher effcency levels. Management sklls that mprove these fnancal measures lkely mprove effcency, so mprovement of management sklls n general, through educaton of current and future farmers, appears to be needed. Increasng the amount of rented land relatve to owned land has a postve mpact on allocatve and scale effcency so mproved land markets and the ablty to obtan and hold addtonal land s crtcal. So mprovement n land market negotaton sklls and ntra-personal sklls dealng wth absentee landowners can lead to effcency mprovements. However, snce a hgher tenancy rato was assocated wth lower techncal effcency, mprovements n managng larger operatons and rented propertes appears to be needed. The postve mpact of nonfarm ncome shows the need for farm households to take advantage of nonfarm opportuntes as well as the need for rural communtes to expand and develop those opportuntes. Better access to both debt and nonfarm equty captal can mprove effcences. Ths ncludes the dentfcaton and use of nonfarm captal (such as partnershps and nvestments by nonfarmers) and the dentfcaton and use of lower cost-debt captal for expanson and mprovements as well as the ncreased management ablty to manage hgher debt loads. The postve mpact of hgher captal-tolabor and land-to-labor ratos ndcates the need for more ntensve use of avalable labor through ncreased mechanzaton and expanson of the land base. These steps can be seen as needng to accompany the ablty to access more debt and equty captal. The postve hred labor rato llustrates the mpact of hrng labor and thus, presumably, freeng the farm household to spend more tme on management followng the hghest and best use argument 26
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