Decomposition of Total Factor Productivity Change in the U.S. Hog Industry

Transcription

1 Journal of Agrcultural and Appled Economcs, 40,1(Aprl 2008): # 2008 Southern Agrcultural Economcs Assocaton Decomposton of Total Factor Productvty Change n the U.S. Hog Industry Ngel Key, Wllam McBrde, and Roberto Moshem The U.S. hog ndustry has experenced dramatc structural changes and rapd ncreases n farm productvty. A stochastc fronter analyss s used to measure hog enterprse total factor productvty (TFP) growth between 1992 and 2004 and to decompose ths growth nto techncal change and changes n techncal effcency, scale effcency, and allocatve effcency. Productvty gans over the 12-year perod are found to be explaned almost entrely by techncal progress and by mprovements n scale effcency. Dfferences n TFP growth rates n the Southeast and Heartland regons were found to be explaned prmarly by dfferences n farm sze growth rates. Key Words: hog producton, scale effcency, stochastc fronter, techncal change, total factor productvty growth JEL Classfcatons: D24, Q12 In recent years, the U.S. hog ndustry has undergone substantal structural changes. Between 1992 and 2004, the share of hogs produced on farms wth at least 2,000 head ncreasedfromabout30% to 80% (USDA NASS). Over the same perod, the total number of hog operatons fell by more than 70%, from over 240,000 to less than 70,000 (USDA NASS). Hog farmng has become ncreasngly specalzed, wth most phases of producton (gestaton, farrowng, fnshng) now occurrng on separate operatons (Key and McBrde). Ths ncreasng specalzaton has been facltated by a rapd growth n contract arrangements between ntegrators and growers. Between 1992 and 2004, the share of market hogs Ngel Key, Wllam McBrde, and Roberto Moshem are agrcultural economsts at the Economc Research Servce n the U.S. Department of Agrculture, Washngton, DC. The vews expressed are those of the authors and do not necessarly correspond to the vews or polces of ERS or those of the U.S. Department of Agrculture. produced under a producton contract ncreased from 5% to 67% (Key and McBrde). Recent years have also been a perod of rapd technologcal nnovaton n hog genetcs, nutrton, equpment, and veternary medcne. These technologcal advances and the structural changes n the hog ndustry have resulted n substantal ncreases n farm productvty. Between 1992 and 2004, the average cost of producton declned over 40% for feeder pgto-fnsh operatons, n real terms. The ncreases n productvty have exerted a downward pressure on hog prces pad by packers, whch has contrbuted to a hgh ext rate for less effcent hog farmers (USDA ERS). Structural changes n the hog sector partcularly the shft n producton to large operatons have precptated controverses over water and ar qualty, odor nusances, anmal welfare, the ntegrty of rural communtes, and the vablty of small- and medumscale famly hog farms. Ths analyss seeks nsghts nto the future drecton of structural change through an examnaton of the causes of recent productvty growth n the hog sector.

2 138 Journal of Agrcultural and Appled Economcs, Aprl 2008 Specfcally, ths study uses a stochastc fronter analyss to decompose hog farm total factor productvty growth between 1992 and 2004 nto four components: 1) techncal change, whch s the ncrease n the maxmum output that can be produced from a gven level of nputs (a shft n the producton fronter); 2) techncal effcency change, whch s the change n a frm s ablty to acheve maxmum output gven ts set of nputs (how close t s to the producton fronter); 3) scale effcency change, whch s the change n the degree to whch a frm s optmzng the scale of ts operatons; and 4) allocatve effcency change, whch s the change n a frm s ablty to select a level of nputs so as to ensure that the nput prce ratos equal the ratos of the correspondng margnal products. Results provde estmates of how economes of scale vary by farm sze, how much observed ncreases n scale contrbuted to the observed growth n productvty, and whether scale economes have ncreased over tme. The analyss also dsaggregates productvty change n three regons to gan nsght nto regonal dfferences n productvty change. Durng the last two decades, the hog ndustry has undergone sgnfcant geographcal shfts n producton (Onal, Unnevehr, and Bekrc; Roe, Irwn, and Sharp). In the early and mddle 1990s, producton expanded rapdly n the Southeast as large contract operatons ntated producton. Begnnng n the late 1990s, growth n the sze of hog farms n the Southeast slowed, lkely n part because of a moratorum on hog farm expanson n North Carolna that was enacted n In contrast, farms n the Heartland grew relatvely slowly n the early and mddle 1990s but grew relatvely rapdly after that. We examne the extent to whch dfferences n productvty between regons can be explaned by dfferences n the scale of producton. The results of the regonal analyss provde nsghts nto the consequences of polces that would drectly or ndrectly lmt the scale of farm operatons. For the total factor productvty decomposton we use the methodology proposed by Orea, whch assumes that technology can be represented by a translog producton functon. We employ the tme-varyng model for techncal neffcency proposed by Battese and Coell. Frm neffcency s assumed to be dstrbuted as a generalzed truncated normal random varable whch s dstrbuted ndependently of the normally dstrbuted random errors. Data for the study are drawn from three natonally representatve surveys of the hog sector conducted n 1992, 1998, and The farm-level USDA-ARMS data permt a detaled analyss of productvty change by farm sze category and regon. Data nclude quantty and expendture nformaton on labor (operator and hred), captal (detaled nformaton based on deprecaton of productve assets), feed, and other nputs (e.g., veternary servces and energy). Some past studes have examned effcency n hog producton n cross-sectonal samples. Sharma, Lueng, and Zalensk examned the scale and techncal effcency of swne producers n Hawa usng a stochastc fronter producton functon and an output-orented data envelopment analyss (DEA) model. Rowland et al. used a DEA approach to determne the relatve measure of techncal, allocatve, scale, and economc and overall effcency for a sample of 43 Kansas hog farms. Ther study used three consecutve years of data, but the short tme frame and small sample sze dd not permt a decomposton of effcency change over tme. Tonsor and Featherstone also used a DEA model to evaluate the components of effcency by hog farm specalzaton type usng a 1998 survey of the hog sector. Unlke past studes that explaned dfferences n effcency across hog farms at a sngle pont n tme, ths study s the frst that we are aware of to decompose the change n hog farm productvty over tme. The next secton revews the theoretcal framework for decomposng changes n total factor productvty over tme. The thrd secton provdes a detaled descrpton of the data. The fourth secton dscusses the results of the total factor decomposton and the regonal analyss. The fnal secton concludes. Theoretcal Framework Ths study uses a stochastc fronter analyss to decompose total factor productvty (TFP)

3 Key, McBrde, and Moshem: Decomposton of Productvty Change 139 growth nto four components: techncal change, techncal effcency change, scale effcency change, and allocatve effcency change. 1 Orea shows that f frm s technology n tme t can be represented by the translog output-orented dstance functon D O (q t, x t, t), where q s output, x t, a K-dmensonal nput vector wth elements (x t1... x tk... x tk ), then the logarthm of a generalzed output-orented Malmqust productvty ndex ln M O can be decomposed nto changes n techncal effcency (EC), techncal change (TC), and scale effcency change (SC), between tme perods r and s: ð1þ where lnm O ~EC rs ztc rs zsc rs, ð2þ ~lnd O ðq s,x s,sþ{lnd O ðq r,x r,rþ ð3þ TC rs ~{ 1 LlnD O ðq s,x s,sþ z LlnD Oðq r,x r,rþ 2 Lt Lt ð4þ SC rs ~ 1 X K e s {1 e sk z e r{1 e rk : x sk ln, 2 e s e r x rk EC rs where for t 5 (r, s), e t ~S K e tk s the scale elastcty such that e tk 5 q ln D O (q t, x t, t)/ q ln x tk. Wth one output, a translog dstance functon can be defned: ð5þ lnd O ðq t,x t,tþ~lnq t {f ðb,x t,tþ{v t, where b s a vector of parameters, v t s a normally dstrbuted random error wth mean zero and estmate a stochastc producton functon model of the form ð7þ lnq t ~f ðb,x t,tþzv t {u t, where u t, a nonnegatve random varable assocated wth techncal neffcency, s drawn from a truncated normal dstrbuton (Battese and Coell). An output-orented measure of techncal effcency s the rato of observed output to the correspondng stochastc fronter output: ð8þ q t TE t ~ expðf ðb,x t,tþzv t Þ ~ exp ð f ð b,x t,tþzv t {u t Þ expðf ðb,x t,tþzv t Þ ~exp ð{u t Þ: By usng Equaton (7), t can be shown that the techncal effcency factor n Equaton (8) equals the dstance functon n Equaton (5): ð9þ exp ð{u t Þ~expðlnq t {f ðb,x t,tþ{v t Þ ~D 0 ðq t,x t,tþ: The techncal effcency measure n Equaton (8) can be estmated condtonal on e t 5 v t 2 u t. It follows from Equatons (2) and (8) that the effcency change can be estmated ð10þ or ð11þ EC rs ~E ð{u s je s Þ{E ð{u r je r Þ exp EC rs ~E ð exp ð {us je s ÞÞ 7Eðexp ð{u r je r ÞÞ, ð6þ f ðb,x t,tþ~b 0 z XK z 1 2 z XK X K j~1 b k lnx tk X K b kj lnx tk lnx tj b tk tlnx tk zb t tz 1 2 b ttt 2 : where the numerator and denomnator n Equaton (11) are the estmated techncal effcency scores n perods s and r, respectvely, whch have values between zero and one. By usng Equatons (3), (5), and (6), the techncal change ndex can be derved: To account for techncal neffcency, we 1 Ths secton s based prmarly on Coell et al. (2005), pp ; Coell et al. (2003), pp ; and Orea. ð12þ TC rs ~ 1 2 " X K z XK b tk lnx sk # b tk lnx rk z2b t z2b tt ðrzsþ :

4 140 Journal of Agrcultural and Appled Economcs, Aprl 2008 From Equaton (6), the scale elastcty s: ð13þ e t ~ X K e tk, where e tk ~b k z 1 2 X K j~1 b kj lnx tj zb tk t: Ths can be used to compute the scale effcency change ndex shown n Equaton (4). To estmate allocatve effcency change, we compare the Malmqust TFP ndex (1) to the logarthm of the Tornqvst TFP change ndex (wth one output): lntfp rs ~lnq s {lnq r ð14þ { 1 X K ½ðs sk zs rk Þ 2 : ðlnx sk {lnx rk ÞŠ where s tk are the nput cost shares. Any dfference between the Tornqvst TFP change calculated n Equaton (14) and the Malmqust TFP ndex calculated n Equaton (1) must be due to allocatve effcency change. Hence, t can be shown that the allocatve effcency change s ð15þ ACrs Data ~ 1 2 X K e sk {s sk z e rk {s rk e sk e rk ðlnx sk {lnx rk ÞŠ: Data used n ths study are from the 1992, 1998, and 2004 USDA Agrcultural Resource Management Survey (ARMS) of the hog sector. Because of broad dfferences n producton technques among varous types of hog operatons, we lmt the sample to feeder pg-to-fnsh hog operatons. 2 Over the perod of ths study, hog operatons have become more specalzed, wth producton shftng from farrow-to-fnsh operatons to separate farrowng, nursery, and fnshng operatons. Ths study does not capture effcency gans resultng from ths specalzaton, but nstead 2 Feeder-to-fnsh operatons are those on whch feeder pgs (weghng pounds) are purchased or placed, fnshed, and then sold or removed for slaughter (weghng pounds). captures gans n effcency wthn the feederto-fnsh product cycle. The analyss focuses on two major hog producng regons: the Heartland (Iowa, Illnos, Indana, Kentucky, Mssour, and Oho) and the Southeast (Alabama, Arkansas, Georga, North Carolna, South Carolna, and Vrgna). Producers located n the remanng surveyed states (Colorado, Kansas, Mchgan, Mnnesota, Nebraska, Oklahoma, Pennsylvana, South Dakota, Tennessee, Texas, Utah, and Wsconsn) were placed n the Other category. Table 1 lsts the dstrbuton of observatons, farms, and output by regon and farm sze for the three survey years. The 1992 to 1998 perod s characterzed by a shft n producton from the Heartland to the Southeast and Other regons. Over ths perod, the share of output produced by farms n the Southeast ncreased by 12.2 percentage ponts, even though the share of feeder-to-fnsh operatons located n ths regon declned by 5.6 percentage ponts. Ths ncrease n output despte a relatve declne n farm numbers s explaned by a large ncrease n scale of producton: average farm sze n the Southeast ncreased almost tenfold. 3 Farms n the Heartland, whle representng roughly half of all feeder-to-fnsh hog farms n both 1992 and 1998, experenced a relatvely small proportonal ncrease n average farm output over ths perod, and consequently suffered a 22.5 percentage ponts declne n output share. The 1998 to 2004 perod s characterzed by a rebound of output share n the Heartland regon and a declne n output share n the Southeast. From 1998 to 2004, Heartland farms doubled n sze whle farms n the Southeast experenced a much smaller pro- 3 Output s measured n hundredweght gan (cwt.) the weght added to purchased/placed hogs and exstng hog nventory n the calendar year. Each head produced represents approxmately 2 cwt. (250 pounds for a typcal fnshed market hog mnus 50 pounds for a typcal feeder pg). Hence, gnorng losses due to anmal mortalty, a farm wth an output of 6,000 cwt. produces approxmately 3,000 head per year. Assumng three hog cycles per year, annual producton of 6,000 cwt. could be produced by an operaton wth an nventory of 1,000 head.

5 Key, McBrde, and Moshem: Decomposton of Productvty Change 141 Table 1. Descrptve Statstcs by Regon and Farm Sze Share of feeder-to-fnsh farms (%) Heartland Southeast Other Share of feeder-to-fnsh output (%) Heartland Southeast Other Mean farm output (cwt. gan) Heartland 1,649 3,763 9,671 Southeast 2,062 20,050 24,216 Other 1,142 5,563 7,767 Share of feeder-to-fnsh output (%) Output, 1, ,000 # Output, 2, ,500 # Output, 10, ,000 # Output, 25, ,000 # Output Observatons Heartland Southeast Other Source: 1992, 1998, and 2004 USDA ARMS. portonal ncrease (though startng from a larger average sze). As a result, farms n the Heartland ncreased ther share of output by 10.2 percentage ponts over ths perod, and the share of output produced n Southeast declned by 7.6 percentage ponts. The relatve declne n output and growth n average farm sze n the Southeast durng lkely resulted n part from the moratorum n North Carolna on new hog farm constructon. In the ARMS surveys, feeder to fnsh farms n North Carolna accounted for 78%, 92%, and 93% of fnshed hog output n the Southeast regon n 1992, 1998, and 2004, respectvely. In 1997, North Carolna passed House Bll 515, The Clean Water Responsblty and Envronmentally Sound Polcy Act, whch mposed a moratorum on the constructon of new and expanded hog operatons wth 250 or more hogs. There were several exceptons to ths moratorum, ncludng for new constructon usng nnovatve anmal waste management systems that do not employ an anaerobc lagoon. 4 The moratorum, whch was orgnally to expre n 1999, was extended several tmes n modfed form through Table 2 provdes summary statstcs for the output and nput varables by regon. Output s defned as hog weght gan the weght added to purchased/placed hogs and exstng hog nventory n the calendar year pror to the year of the survey. Hog weght gan, unlke the alternatve measures of output such as number of head removed, accounts for changes n nventory and for varaton n the weght of feeder and fnshed pgs. Feed s defned as the total weght of feed appled. 5 The labor nput s a Tornqvst quantty ndex comprsed of 4 For full text of the bll see: dockets/99bscblls/2499b01nchb515cleanswne.html 5 It s not possble to dsaggregate feed nto components because many operatons, partcularly those that contract, dd not report the composton of feed used.

6 142 Journal of Agrcultural and Appled Economcs, Aprl 2008 Table 2. Summary Statstcs for Producton Varables by Regon Heartland Southeast Other Output (cwt. gan) 4,557 12,853 4,925 (63,650) (93,909) (116,737) Feed (cwt.) 12,174 27,106 13,780 (163,170) (193,659) (316,029) Labor (Tornqvst ndex a ) (59.2) (61.9) (34.2) Captal (dollar b ) 29,597 70,934 29,124 (284,255) (422,608) (1,099,257) Other nputs (dollar c ) 12,856 37,256 12,261 (169,263) (481,801) (262,583) Observatons Note: Standard devatons are n parentheses. Source: 1992, 1998, and 2004 USDA ARMS. a The Tornqvst ndex combnes pad labor plus unpad farm household labor used n the hog enterprse. Labor expendture shares for pad and unpad labor are used as weghts, and expendtures for unpad labor are mputed. b Captal s the captal recovery cost the estmated cost of replacng the exstng captal equpment (barns, feedng equpment, etc.). c Other nputs are defned as expendtures on veternary servces, beddng, marketng, custom work, energy, and repars. pad labor and unpad farm household labor usng the labor expendture shares for pad and unpad labor as weghts. 6 Captal s the captal recovery cost the estmated cost of replacng the exstng captal equpment (e.g., barns and feedng equpment). Other nputs s defned as expendtures on veternary servces, beddng, marketng, custom work, energy, and repars. Labor wages are deflated usng the Bureau of Labor Statstcs (BLS) Blue Collar Total Compensaton ndex; feed prces are deflated usng a weghted average of the BLS corn and soybean Producer Prce Index (PPI); Captal s deflated usng the BLS farm machnery PPI, and other nputs are deflated usng the CPI. In the estmaton we rescale all logged values of the varables as devatons from the sample mean to facltate nterpretaton of the coeffcents. Table 3 provdes an overvew of the advances n factor productvty durng the study perod for the three regons. Except for other nputs n the Southeast, all partal factor productvty measures ncreased at roughly the same annual rates between 1992 and However, ths pattern masks 6 The labor expendtures for pad labor are observed. Labor expendtures for unpad labor are estmated usng an mputed wage for unpad labor. substantal dfferences between the Heartland and the Southeast durng the two ntervenng perods. Whle all regons began n 1992 wth approxmately the same levels of factor productvty, from 1992 to 1998 farms n the Southeast experenced much larger ncreases n feed, labor, and captal productvty than dd farms n the Heartland. Between 1998 and 2004, ths pattern s reversed, wth farms n the Heartland ncreasng ther feed, labor, and captal productvty at a much more rapd rate than farms n the Southeast. The next secton examnes whether these shfts n productvty were caused manly by changes n the scale of producton, whch was llustrated n Table 1, or whether the shfts were caused by dfferences n rates of technologcal change, allocatve effcency change, or techncal effcency change. Emprcal Results Table 4 presents the estmated coeffcents of the stochastc producton functon. Because the varables are expressed as devatons from ther means, the frst-order parameters of the translog functon can be drectly nterpreted as estmates of producton elastctes evaluated at the sample means. The producton elastc-

7 Key, McBrde, and Moshem: Decomposton of Productvty Change 143 Table 3. Partal Factor Productvty by Regon and Year Partal Factor Productvty Average Annual Growth Rate Feed productvty (cwt. gan per cwt. feed) Heartland Southeast Other Labor productvty (cwt. gan per unt a ) Heartland Southeast Other Captal productvty (cwt. gan per dollar b ) Heartland Southeast Other Other nputs productvty (cwt. gan per dollar c ) Heartland Southeast Other Source: 1992, 1998, and 2004 USDA ARMS. a Hog enterprse labor s measured usng a Tornqvst ndex that aggregates pad labor and unpad farm household labor usng labor expendture shares as weghts. Expendtures for unpad labor are mputed. b Captal s the captal recovery cost the estmated cost of replacng the exstng captal equpment (e.g., barns and feedng equpment). c Other nputs are defned expendtures on veternary servces, beddng, marketng, custom work, energy, and repars. tes wth respect to feed, captal, and other nputs have plausble values and are statstcally sgnfcant. The estmated elastcty of output wth respect to labor s qute low, but ths fndng s consstent wth other studes that also found low labor elastctes (e.g., Brummer, Glauben, and Thjssen). Labor, partcularly unpad famly labor, s dffcult to quantfy and value usng a survey nstrument and the resultng low elastcty and relatvely low statstcal sgnfcance level for labor could reflect these emprcal challenges. Techncal effcency scores are dsaggregated by regon and farm sze n Table 5. Techncal effcency measures the extent to whch farms are able to combne nputs n an effcent manner to acheve the maxmum possble output (.e., proxmty to the producton fronter). Because a common producton functon s estmated for all three regons, effcency scores can be nterpreted as an estmate of the productve effcency n each regon assumng all farms had access to the same technology. It s possble that regonal dfferences n clmate and geology mpose some dfference n hog farm technology (allowng for dfferent lvestock facltes, feed, and manure management practces). Unfortunately, estmatng a model that allows for technologcal dfferences across producton regons s lmted by the number of observatons n the sample. Table 5 shows lmted varaton n average techncal effcency across regons and over tme. However, there s a subtle pattern that seems consstent wth our earler observatons about factor productvty: techncal effcency declnes n the Heartland between 1992 and 1998 and then rebounds by In the Southeast, techncal effcency ncreases slghtly between 1992 and 1998 and then declnes between 1998 and The table shows a

8 144 Journal of Agrcultural and Appled Economcs, Aprl 2008 Table 4. Stochastc Producton Functon Parameter Estmates Parameter Coeffcent SE t-statstc b 0 constant b 1 feed b 2 labor b 3 captal b 4 other nputs b b b b b b b b b b b t tme b tt tme-squared b t b t b t b t s 2 ~s 2 v zs u c ~su 2 s 2 v zs u Observatons 1,181 Source: Authors calculatons usng data from the 1992, 1998, and 2004 USDA ARMS. stronger relatonshp between effcency and farm output wth larger operatons beng, on average, more techncally effcent than smaller ones. Ths result suggests greater scope for mprovng techncal effcency through enhanced adopton of best practce technques for smaller scale operatons. Decomposng TFP Change Table 6 presents the average results of the TFP decomposton for every regon and for all farms. In aggregate, TFP ncreased at an average rate of 6.3% per year. The overwhelmng porton of ths growth resulted from techncal progress (expandng at an average rate of 3.0% per year) and ncreases n scale effcency (3.4% per year). The rate of change n TFP appears to be relatvely constant over the two perods ncreasng by 45.1% from and by 44.1% from Interestngly, the contrbuton of technologcal change to ncreasng productvty appears to have ncreased substantally over the two perods techncal change contrbuted to a 13.5% ncrease n productvty between 1992 and 1998, and a 25.6% ncrease between 1998 and In contrast, the scale effect appears to have dmnshed: whle changes n scale effcency contrbuted to a 30.6% ncrease n productvty between 1992 and 1998, scale effects only rased productvty by 13.8% between 1998 and Snce, as we dscuss later, scale elastcty ncreased somewhat between the two perods (holdng farm sze constant) as the producton technology Table 5. Techncal Effcency by Farm Output Category, Regon, and Year Techncal Effcency Index Regon Heartland Southeast Other Fnshed hog output (cwt. gan) Output, 1, ,000 # Output, 2, ,500 # Output, 10, ,000 # Output, 25, ,000 # Output NA All farms Source: Authors calculatons usng data from the 1992, 1998, and 2004 USDA ARMS.

9 Key, McBrde, and Moshem: Decomposton of Productvty Change 145 Table 6. Decomposton of Total Factor Productvty Change, Percent Change Average Annual Growth Rate Heartland Techncal effcency change Techncal change Scale effcency change Allocatve effcency change Total factor productvty change Southeast Techncal effcency change Techncal change Scale effcency change Allocatve effcency change Total factor productvty change Other Techncal effcency change Techncal change Scale effcency change Allocatve effcency change Total factor productvty change All farms Techncal effcency change Techncal change Scale effcency change Allocatve effcency change Total factor productvty change Source: Authors calculatons usng data from the 1992, 1998, and 2004 USDA ARMS. evolved, the reducton n the contrbuton of the scale effcency to TFP can be attrbuted to a slowdown n the growth of average farm output (whch was shown n Table 1). Over tme, some farmers may have mproved ther allocatve effcency that s, they may have become better at selectng nput quanttes to equate nput prce ratos wth the ratos of the correspondng margnal products. However, allocatve effcency change appears to have played a relatvely small role n TFP change ncreasng at an annual rate of only 0.5%. Wth constantly changng factor prces and turnover n the sample of farmers, t s possble that mprovements n allocatve effcency were mnmal for the same reasons that changes n techncal effcency were mnmal. The regonal changes n TFP are consstent wth changes n partal factor productvty shown n Table 3 and dscussed prevously. Between 1992 and 1998, TFP almost doubled n the Southeast. In contrast, productvty ncreased by only about a thrd n the Heartland over the same sx-year perod. Between 1992 and 1998, techncal progress contrbuted roughly equal amounts to the growth n TFP for farms n both the Heartland and Southeast regons. However, the contrbuton of scale effcency to TFP was much greater n the Southeast than the Heartland (67.7% versus 19.9%). The large ncrease n scale effcency n the Southeast resulted from the regon s rapd ncrease n the scale of producton (see Table 1), gven the ncreasng returns to scale of the producton technology (whch we dscuss later). In the perod, productvty n the Heartland rebounded ncreasng by al-

10 146 Journal of Agrcultural and Appled Economcs, Aprl 2008 Table 7. Scale Elastcty by Farm Output Category, Regon, and Year Scale Elastcty Regon Heartland Southeast Other regons Fnshed hog output (cwt. gan) Output, 1, ,000 # Output, 2, ,500 # Output, 10, ,000 # Output, 25, ,000 # Output NA All farms Source: Authors calculatons usng data from the 1992, 1998, and 2004 USDA ARMS. most 60%, compared wth only 36% n the Southeast. Ths catchng up n the Heartland n the second perod was also drven by ncreases n scale effcency n the Heartland, scale effcency contrbuted to a 29.3% ncrease n TFP compared to only a 13.8% ncrease n TFP n the Southeast. The Heartland actually lagged slghtly behnd the Southeast n technologcal progress durng ths perod. Snce ncreases n scale effcency played such an mportant role n contrbutng to productvty gans over the twelve-year perod and seem to have been mportant n determnng productvty growth at the regonal level wthn the two subperods, t s worth examnng n more detal. Table 7 dsplays the average scale elastcty by regon and scale category for the three survey years. The average scale elastcty for all farms, rangng between 1.12 and 1.16, ndcates substantal returns to scale n the producton technology n all perods. Snce the producton technology s assumed to be the same across regons, regonal dfferences n scale effcency can be attrbuted to dfferences n sze: returns to scale are greater for smaller operatons, and farms n the Heartland (and Other regon) are smaller, on average, than farms n the Southeast. Table 7 shows that for all output categores, returns to scale ncreased between 1992 and 1998 and between 1998 and Ths mples that holdng output constant (output s approxmately constant wthn each scale category) returns to scale ncreased steadly over the study perod. However, because the scale elastcty declnes wth farm sze and average farm sze ncreased substantally over the study perod (as shown n Table 1), the average scale elastcty showed lttle change over tme. Whle the potental for effcency gans from further ncreases n scale may be lmted for large farms (farms producng more than 25,000 cwt had an average scale elastcty of 1.05) there remans a substantal scope for effcency gans n the sector as a whole from further ncreases n scale. Ths s partcularly true n the Heartland (and the Other regon), where the average farm output s substantally smaller than t s n the Southeast. Lmtatons of the Analyss There are some lmtatons n the methodologcal approach that are worth hghlghtng. Frst, ths study dd not account for the fact that manure s an output produced jontly wth hogs. Manure s an unusual output n

11 Key, McBrde, and Moshem: Decomposton of Productvty Change 147 that t can have ether a postve or negatve value, dependng on a number of factors. In general, manure s more valuable n regons where the demand for manure nutrents s relatvely hgh (n regons wth abundant cropland, where envronmental regulatons are less strngent, and where hog producton s less concentrated). By not consderng manure as an output, the study underestmates hog farm output n regons where manure has postve value and overestmates output n regons where manure has negatve value. As a consequence, the analyss lkely underestmates productvty n the Heartland and overestmates productvty n the Southeast. 7 In addton, for many farms, t s lkely that the shadow value of manure declned between 1992 and 2004, as nutrent applcaton lmts and other regulatons became more strngent and bndng. If so, the analyss overestmates the ncreases n farm productvty between 1992 and Hence, not ncludng manure as an output bases to some degree the estmates of the changes n total factor productvty, scale effcency, techncal effcency, techncal change, and allocatve effcency. To account for manure as an output n a TFP decomposton would requre nformaton about the quantty of manure produced (and ts nutrent content) and the shadow value of the manure (or ts nutrents). The ARMS survey provdes no drect nformaton about the quantty of manure produced, or ts value to the farmer. 8 Estmatng the quantty and shadow prce of manure or manure nutrents wth the data avalable would requre makng a set of assumptons that would lkely ntroduce substantal error nto the analyss. Consequently, an accountng of hog farm output that ncludes manure s left for future research. A second lmtaton of ths study s that t dd not account for output qualty. Hog (pork) qualty has changed over tme to reflect consumer preferences. For example, hogs have generally become leaner durng the perod of ths study. It s plausble that a typcal hog produced n 2004 would command a hgher prce per pound than a typcal hog produced n 1992, f they were both sold n In other words, hogs produced n 2004 probably better reflect consumer preferences and are therefore hgher qualty. Because hgherqualty hogs command a hgher prce, ths study underestmates output, and therefore productvty, for operatons producng hgherqualty lvestock. To the extent that contract operatons are better able to rase hgh-qualty hogs, the study could have underestmated productvty gans n the Southeast, where contractng s more prevalent. In addton, t s lkely that the study underestmated productvty gans over tme as qualty mproved. Because the surveys used n ths study dd not provde any nformaton about hog qualty attrbutes, efforts to control for product qualty are left for future research. 7 In the Southeast, the demand for manure nutrents s generally lower because there s relatvely less land avalable for spreadng manure and there s a denser concentraton of anmal feedng operatons (Kellogg et al.). Envronmental regulatons lmt the allowable nutrent applcaton on land, so many farmers n the Southeast have an ncentve to treat manure n lagoons n order to lower the nutrent content of the manure (Allery et al.; Kaplan, Johansson, and Peters; Rbaudo et al.). In contrast, n the Heartland, the value of manure s greater because there s relatvely more land avalable on whch to apply the manure, so fewer farmers use storage facltes desgned to lower the nutrent content of the manure. 8 The ARMS survey provdes no drect nformaton about the quantty and prce of manure sold. Estmatng the shadow prce of manure would requre detaled nformaton about how much manure s produced and ts nutrent content (both of whch may have changed substantally over tme, wth mprovements n feed effcency). It would also requre nformaton about how the manure s used whether t s appled on farm or off farm, the rate at whch t s appled, the rate chemcal fertlzers are appled along wth the manure, the yelds on the crops on whch manure s appled, and the costs assocated wth transportng and applyng the manure. Most of ths nformaton s not avalable from the ARMS survey.

12 148 Journal of Agrcultural and Appled Economcs, Aprl 2008 Conclusons There have been pronounced structural changes n the hog ndustry n the last two decades: farms have ncreased n scale and become more specalzed, the use of producton contracts has ncreased, and producton has shfted regonally. These changes have concded wth a substantal ncrease n productvty TFP ncreased at an average annual rate of over 6% between 1992 and Ths study used a stochastc fronter analyss to decompose the TFP growth nto four components: techncal change and changes n techncal effcency, scale effcency, and allocatve effcency. The study found that the productvty gans n the 12-year study perod were explaned almost entrely by techncal progress and mprovements n scale effcency. There were mnmal changes n average allocatve or techncal effcency, though estmates of techncal effcency ndcate substantal scope for mprovement, especally for smaller-scale operatons. Between 1992 and 1998, farms n the Southeast (manly n North Carolna) ncreased ther share of fnshed hog output whle farms n the Heartland (manly Iowa, Illnos, and Oho) decreased ther share. Lkely n part as a result of a state moratorum on large hog farm constructon n North Carolna, ths trend was later reversed between 1998 and 2004: average farm sze and output share grew faster n the Heartland relatve to the Southeast. The trends n output were mrrored by the trend n productvty: TFP ncreased more n the Southeast between 1992 and 1998, and later ncreased more n the Heartland between 1998 and Average farm sze growth and the resultng mprovements n scale effcency appear to explan most of the dfferences n productvty growth between the Heartland and Southeast snce Farms n both regons had smlar rates of techncal advance over the study perod. However, n the Southeast, relatvely rapd growth n average farm output durng resulted n relatvely large gans n scale effcency n that perod. From 1998 to 2004, farms grew faster n the Heartland, leadng to greater productvty growth n that regon. Results of ths study suggest there could be substantal economc costs to polces that lmt the sze or growth of hog farm enterprses. To the extent that the moratorum on hog farm expanson n North Carolna lmted the growth n farm sze n the Southeast regon, farm productvty was lower than t would have been wthout the moratorum. Decsonmakers wll have to wegh these effcency costs aganst envronmental and other benefts to socety from sze-restrctng polces. The North Carolna moratorum had the objectve of temporarly slowng the growth of hog producton n the state to allow for studes and legslaton to address envronmental problems assocated wth nutrent runoff from lagoons and felds. 9 In addton to provdng tme for studes and legslaton, the moratorum lkely had the effect of lmtng the growth of hog output and thereby lmtng the amount of manure produced n the state. Wth less manure producton there was lkely a lower rsk of nutrent runoff from lagoons nto surface water, a reducton n ntrogen and phosphorus loads n nutrent-senstve waterways, and reductons n odor and ammona emssons. 10 Estmatng the value of these or other potental benefts s beyond the scope of ths study. The study also found that despte the large ncreases n the scale of producton that have occurred over the past decades, there remans substantal scope for further scale effcency gans, partcularly n the Heartland, where farms operate at a smaller average scale than do farms n the Southeast. Ths fndng suggests we are lkely to observe further ncreases n the scale of hog producton n the comng decade. [Receved Aprl 2007; Accepted September 2007.] 9 See Secton 1.1, Part I of the Clean Water Responsblty and Envronmentally Sound Polcy Act, referenced n Footnote Allery et al. dscusses some of the envronmental mpacts assocated wth lvestock producton, and provdes some emprcal research relatng lvestock producton to envronmental outcomes.

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