Efficiency: A Dual Approach

Transcription

1 Educaton, Experence, and AIlocatve Effcency: A Dual Approach Spro E. Stefanou and Swat Saxena A generalzaton of the dual, non-fronter proft functon approach to evaluatng allocatve effcency s deveoped that allows for tranng (human captal) varables to nfluence the effcency level drectly. An applcaton to Pennsylvana dary ndcates that educatonand experenceare substtutes and playasgnfcant role n the level of effcency. Whle these operatorsare not allocatngthervarable nputs n an absolutely effcent manner, relatve effcency can be acheved for four of sx possble nput combnatons for prescrbed levels of educaton and experence. Furthermore, the estmatesof the effcency measures suggest that these operators are maxmzng producton rather than short-run profts. Key words: allocatve effcency, human captal. Varous types of tranng can help the farm operator to enhance proftablty. When ths tranng nfluences producton decson makng' t s relevant to consder allocatve effcency (Welch, Huffman 1977). Ths paper focuses on the mpact of tranng on operator decson makng and develops an mplementable theoretcal framework that lnks tranng varables to allocatve effcency. Two examples oftranng are years offormal educaton and years of management experence. The former can be vewed as formal tranng, whle the latter s nformal tranng. Welch vews educaton as a factor of producton and focuses on the educaton-usng bas of technologcal change; Fane measures the productve value of educaton and the role of educaton n allocatve effcency. Lke Fane, Huffman (1985) characterzes educaton as a tranng process that promotes the learnng and nformaton-processng ablty necessary for decson makng n a changng economc and physcal envronment. However, confuson sets n about whether years of educaton s lke other physcal factors of producton such that elastctes of substtuton of Spro E. Stefanou and Swat Saxena are an assstant professor and a graduate assstant, respectvely, Department of Agrcultural Economcs and Rural Socology, Pennsylvana State Unversty. The helpful comments of Chng-Cheng Chang and James W. Dunn are greatly apprecated. The authors are also grateful to Wllam Grsley for provdng access to the data set. Journal Seres Artcle No. 76m ofthe Pennsylvana Agrcultural Experment Staton. educaton for another factor of producton can be calculated (Welch, Fane), or whether the level of educaton serves as an endowment that the operator cannot sgnfcantly alter durng the producton perod. In short, the queston s whether educaton s a flow or a stock. It has also been argued n the "learnng by dong" lterature that management experence can lead to gans n effcency through better organzaton and knowledge of the results of expermentng wth alternatve producton technques (Arrow, Rosen). Hence, an ncrease n effcency may result from more management experence. The non-fronter approach to modelng effcency, poneered by Lau and Yotopoulos, nvestgates effcency ssues wthout the explct use of models wth one-sded error terms-the fronter functon approach-that attempt to estmate the outer boundary of the producton, cost, or proft functon. Examples of the latter approach to assessng effcency nclude Schmdt and Lovell and Fersund and Hjalmars son. The non-fronter models ntroduce neffcency va varyng coeffcents or asymmetry. Investgatons nto allocatve effcency have been conducted by Toda and by Atknson and Halvorson for sngle product dual cost and proft functons, respectvely. Lovell and Sckles parametrcally ntroduce techncal and allocatve neffcency n a dual multproduct proft functon. However, all of the dualty analyses gnore the drect mpact of Copyrght 1988 Amercan Agrcultural Economcs Assocaton

2 Stejanou and Saxena tranng varables on measurng effcency levels. When educaton s ncluded as an explanatory varable, t s typcally appended as a fxed factor of producton. Educaton's mpact on supply and nput demands s then evaluated just as any other fxed factors of producton (e.g., Sdhu and Baanante, Lopez). The prncpal goal of ths paper s to develop and mplement a methodology to evaluate how the stock of human captal nfluences shortrun varable nput allocaton decsons. An neffcency functon s ntroduced that depends on the level of the tranng varables. Whle the tranng varables are stll consdered to be condtonng arguments ofthe dual proft functon, these varables enter the specfcaton dfferently than the physcal, fxed factors of producton. These tranng varables are explctly assumed to nfluence the producton decson-makng process va the degree of allocatve neffcency. Therefore, a dual proft functon framework allowng for an effcency functon s developed and presented as a flexble functonal form specfcaton. Ths model s then appled to Pennsylvana dary farm operators, and the mpact of the tranng varables on allocatve effcency s evaluated. Actual and Behavoral Dual Proft Functons The frm s assumed to maxmze profts subject to perfectly compettve nput and output markets and a sngle output technology that s quas-concave n the (n x 1) vector of varable nputs, v, and the (m x 1) vector of fxed factors, X. Two operators wth dfferent human captal endowments may have dfferent perceptons of the producton process. As long as each'operator attempts to produce at hs/her perceved producton fronter, he/she s techncallyeffcent. Hence, the relevant effcency ssue concerns the nput allocaton process. The actual normalzed proft functon s expressed as Educaton, Experence, and Effcency 339 (2) aq/avj = kp = 1,..., n. The term kj, whch represents the devaton from the effcent allocaton of nput, tradtonally has been modeled as a constant n both prmal-based models (Lau and Yotopoulos, Yotopoulos and Lau, Sdhu, Khan and Mak) and dualty-based models (Toda, Atknson and Halvorson, Lovell and Sckles). Expandng upon ths approach, the tranng varables, S, are assumed to nfluence effcency through the nput allocaton process. Thus, k, s consdered a functon of the tranng varables, k, = k(s). Relatve prce effcency between varable nputs andj (for =1= j) exsts f k(s) = kj(s), and absolute effcency exsts f kj(s) = 1 for all. Snce S s fxed n a gven perod, one may consder k(s)p the effectve normalzed prce of the th nput. The behavoral normalzed proft functon s defned as (3) where kp s the vector (k1(s)pl'..., kn(s)pn). Applyng Hotellng's lemma, the nput demands and output supply functons are (4) V = -a1tb(kp, X)/ak(S)P = - k(s)-l[a1tb/ap], (5) Q = 1Tb(kp, X) - L k(s)p[a1tb/a(k(s)p)], = 1Tb(kp, X) - L P[cJ1Tb/apl. Here, V and Qare the actual quanttes of nputs demanded and output suppled, respectvely. The actual normalzed proft functon s clearly related to,the behavoral normalzed proft functon. Usng (4) and (5) n (1) results n where the astersk denotes optmzed values; Q( ) s the producton functon; andp = w/p, where P s the output prce and P s the normalzed prce ofnput. Allocatve neffcency enters the calculus va the alteraton of the frst-order proft-maxmzng condtons as - I PE-k(S)-l(a1To/ap)] = 1Tb( ) + L [k(s)-l

3 340 May 1988 Specfcaton As (6) ndcates, n the presence of absolute allocatve effcency, the actual and behavoral proft functons are equvalent. The generalzed leontefflexble functonal form s specfed for the behavoral proft functon as n n (7) 7Tt,( ) = I I aj[k(s)p][ks)p;] ; m m + I I J3lk(X I)l(Xk)l I k n m + 2I L 'Yk[k(5)P]Xm 1 wth the restrctons of aj = a and,elk =,ekl. The effcency functon s assumed to be nonnegatve and nonstochastc n addton to beng nonlnear n S as follows: (8) where 8 s a vector of coeffcents assocated wth S. Varable factor demands are (4').\ = -{t a,,[k,(s)p.j-[k;(s)pjj k + ~ y,.[k,(s)p,j-x.} Output supply s obtaned by substtutng (4') and (7) nto (5) yeldng (5') 111 m Q=IIJ3lk(X I)l(Xk)l I k n m + I I. 'Yk[k(5)P]Xk Imbeddng (8) nto (7), (4'), and (5'), the parameters of these equatons can be estmated jontly once an addtve error s appended to each equaton to allow for errors n the observaton of proft-maxmzng behavor. An Applcaton to Pennsylvana Dary Farm Operators The model developed n the prevous secton s appled to operators of dary farms n Pennsylvana. Observatons for 131 farms are used for 1982 by mergng a cross secton of farms common to three surveys. The Dary Herd Improvement Assocaton data provde nformaton on the quanttes and cost offeed; k Amer. J. Agr. Econ. the latter are the value of the feed produced on the farm as well as purchased feed. No assessment of dfferences n feed qualty s avalable. The Pennsylvana Farmers Assocaton (PFA) survey provdes data on the cost and quantty of hred labor, the quantty of famly labor, the value of captal, the herd sze of mlkng cows, the quantty of mlk sold, and the prce of mlk. The value of captal s defned as the value of machnery, equpment, and buldngs. Herd sze s defned as the average number of mlkng cows n the herd durng the year. A thrd survey of PFA farmers was conducted to obtan data on the operator's years of formal educaton and years of management experence. Detals of the last survey are found n Grsley. The varable factors ofproducton are gran and supplements (G), hereafter referred to as gran; the quantty of pasture and slage (F), hereafter referred to as forage; hay (ll); and hred labor (L). The fxed factors ofproducton are the herd sze (Xl), the value of captal (X 2 ) and famly labor (Xa). The tranng varables are educaton (51) and years of management experence (52). Management experence can be vewed as a composte varable reflectng the mpact of learnng by expermentaton on the operator's own farm, conversatons wth other operators regardng ther own producton experences, consultatons wth agrcultural nput sales and feld persons, contact wth extenson personnel, and exposure to ther educaton programs, etc. The dstrbuton of 51 ranges from 8 to 18 years wth a mean of 12.3years. For ths sample 12%,65%, and 23% of the observatons take on values less than 12, 12, and greater than 12, respectvely. Gven the lmted dsperson n ths varable a dummy s ntroduced, I where DE = 1 f SI ::5 12 o otherwse. The dstrbuton of52 ranges from 1to 48 years wth a mean of 20.8 years and exhbts no sgnfcant clusterng. I To use the nterval varable of years of educaton s analytcally msleadng. The change n effcency or supply and nput demand arsng from a change n educaton s not a smooth process but, rather, subject to dscrete jumps. Whle one can expect a sgnfcant response to a change n educaton to occur between operators wth 11and 12years of educaton, there s no sgnfcant dfference between operators wth 9 and 10 years of educaton (Carter). The hgh concentraton of observatons at 12 or more years of schoolng does not allow enough varaton to use a polychotomous transformaton of the educaton varable. When educaton s splt nto three categores (8-11 years, 12years, 13+ years), the model would not converge.

4 Stefanou and Saxena Educaton, Experence, and Effcency 341 The effcency functon for the th varable factor demand s (9) k, = (OO + SlDE + 02S2)2. To avod a sngular covarance matrx, the output supply and varable factor demand equatons are jontly estmated usng the nonlnear teratve Zellner procedure. All estmated coeffcents but one have asymptotc t-values sgnfcant at less than the 0.01 level (see table 1). Table 2 presents the pont estmates of the supply and factor demand elastctes for the categores of educaton." The mlk supply elastcty s postve but of neglgble magntude for both educaton levels. 2 The absence of standard errors for the elastctes was a pont noted by an anonymous revewer. The usual way for dervng standard errors for functons of parameters s the frst-order Taylor-seres approxmaton known as the delta method. However, these standard error estmates are of questonable accuracy n small samples. Green et al. fnd that 7 of 12 bootstrap estmates for the elastcty standard errors exhbt a dfference of more than 80% when compared to the lnearly approxmated standard error estmates. Thus, standard error estmates were not calculated n ths study. Table 1. Coeffcent Estmates The pont estmates are substantally less than the short-run supply elastcty estmates for Pennsylvana reported by Hallberg et al. (approxmately 0.20). Ths result s due to the fact that mlk prce does not vary much over the sample wth a coeffcent of varaton of4.2%. The responses of supply wth respect to all nput prces are of neglgble magntudes wth correct sgns reported for nearly all operators. The excepton s the supply elastcty wth respect to hay prce for operators wth postsecondary educaton. Wrong sgns on the own-nput demand elastctes are obtaned for forage for operators of both educaton categores and for hay for operators n the lower educaton category. Gran s relatvely more elastc wth respect to ts own prce than the other factors. The cross-prce elastctes ndcate that gran and hred labor are substtutes for the lower educaton level. However, wth the hgher educaton level, substtuton relatons exst among gran and hay, gran and hred labor, hay and forage, and hred labor and hay. Coeffcent Estmate Coeffcent Estmate Coeffcent Estmate CtGG {3XlX 'YLX (45.60)3 (35.31) (3.02) CtPP {3XlX 'YLX (124.94) (0.28) (3.02) CtHH {3X.X a OG (146.14) (23.11) (3.03) Ct LL 'YGXl a op (181.38) (3.03) (3.03) CtGP 'YPX aoh (98.08) (3.02) (2.99) Ct GH 'YHX aol (19.99) (2.87) (3.02) CtGL 'YGX G (42.59) (3.01) (3.03) CtPH 'YGX F (0.018) (19.83) (2.95) (3.03) Ctn 'YPXl alh (48.08) (3.03) (2.99) CtHL 'YFX e; os.z» (3.02) (3.02) {3XlX 'YHXl G (74.23) (2.93) (3.03) {3X.X 'YHX P (23.55) (2.73) (3.03) {3X3X 'YLXl H (22.19) (3.02) (2.99) a 2L (3.02) a Absolute value of asymptotc r-rato n parentheses.

5 342 May 1988 Amer, J. Agr. Econ. Table 2. Own- and Cross-Prce Elastcty Pont Estmates For Dfferent Levels of Educaton Quanttes Hred Mlk Gran Forage Hay Labor Prce of Mlk (0.004)b (1.177) (0.896) (0.192) (0.089) Gran (-0.002) (-0.859) (-0.594) (-0.128) (0.018) Forage (-0.001) (-0.319) (0.243) (-0.053) (-0.061) Hay ( ) (-0.082) (-0.(64) (0.008) (-0.003) Hred labor (-0.001) (0.075) (-0.481) (-0.019) (-0.044) Fxed Factors Herd sze (0.455) (0.997) (0.989) (0.099) (0.118) Captal (0.049) (0.126) (0.123) (0.050) (0.049) Famly labor (-0.003) (0.054) (-0.216) (0.043) (-0.077) Experence ( ) (1.077) (-4.50) (-1.460) (0.625) Note: Elastctes are evaluated at sample means. Reflects educaton level of greater than 12 years. b Reflects educaton level of less than or equal to 12 years. Whle the educaton level does not nfluence the elastcty of supply, the demand elastctes for the varable factors of gran, forage, and hred labor wth respect to the fxed factors of producton are consderably more elastc for less-educated operators. The demand elastcty for hay wth respect to herd sze, captal, and famly labor changes sgns wth changes n the educaton category. It s nterestng to note that the demand elastcty of hred labor wth respect to famly labor s negatve but very small for operators of both educaton categores. Three not necessarly mutually exclusve possbltes may explan ths result: (a) a surplus of famly labor exsts, (b) famly labor s not vewed as an effectve alternatve to hred labor, or (c) changes n famly labor (relatve to hred labor) may occur n dscrete (or lumpy) unts resultng n lower elastcty estmates due to the nfntesmal change assumpton n the elastcty defnton. The supply elastctyof experence, whch s unaffected by the educaton level, s negatve and of neglgble magntude. Addtonal experence has more educated operators usng less gran and forage and more hay and hred labor. Less-educated operators use less forage and hay and more gran and hred labor as they accumulate experence. The hred labor demand elastcty of experence s postve and over twce as elastc for less educated operators. The results of table 2 suggest that operators wth post-secondary educaton demonstrate a greater degree n flexblty n the allocaton of ther varable nputs as ndcated by the greater number of substtuton relatons. All of the sgn changes n the cross-nput prce elastctes that are a result of a change n the educaton level ndcate how the change n hay prce nfluences the demand for gran, forage, and hred labor and how the hay demand s nfluenced by the prce changes n the other varable nputs. Ths suggests that operators wth post-secondary educaton vew hay as a substtute n the mlk producton process, whle operators wth less educaton vew hay as a complementary nput. The fact that more hghly educated operators have a smaller response of varable factors to changes n herd sze and captal s related to the flexblty of the producton process for operators wth post-secondary educaton.

6 Stefanou and Saxena Educaton, Experence, and Effcency 343 Allocatve Effcency and Dary Producton The estmated effcency functons are (10.1) (10.2) (10.3) (l0.4) kg = ( DE + O.OO4Sz)Z k F = ( DE - 0.OO3S z )Z k H = ( DE Sz)Z k L = ( O.OllDE - O.OOO1S z )Z, where all coeffcents are asymptotcally dfferent from zero at probablty level less than The forage and hay effcency functons ndcate that addtonal educaton (DE = 0) leads to lower effcency and addtonal management experence leads to less effcency. The remanng effcency functons ndcate addtonal educaton and experence lead to ncreased effcency. The null hypothess of absolute effcency for factor (Ro : k; = 1) s rejected for nearly all possble combnatons of educaton and experence." Hay s the excepton. The null hypothess of the absolutely effcent allocaton ofhay s accepted at the.01 sgnfcance level when the operator has four or fewer years of management experence regardless of the educaton level. Hence, educaton has lttle nfluence on the absolute effcent allocaton of hay. In fact, the effcency functons for gran, forage, and hred labor are close to zero for reasonable values of Sz. In lght of the frstorder proft-maxmzng condtons n (2), these dary operators are applyng these nputs to maxmze producton. Two possble explanatons for ths result may suggest these operators are behavng ratonally. The frst concerns the fact that the data are not adjusted for nput qualty. As the varaton n nput qualty ncreases, operators may appear to apply more than the proft-maxmzng levels. The second explanaton focuses on the ntertemporal allocaton of resources. In the presence ofadjustment costs on quas-fxed factors of producton, the maxmzaton ofproducton n a partcular perod may be an ntertemporally consstent response to prce changes for J The null hypothess of absolute effcency for factor s Ho: (tl o)2 = 1, where tl o = (B OI + BuDE + B 2152 ) and Tj = tl ovar(tlot1 s asymptotcally dstrbuted t wth n-3 degrees of freedom. Under the null hypothess Tf s a noncentral F random varable wth 1 and n-3 degrees offreedom and noncentralty parameter [var(tijj-l (Rao, pp ). the frm maxmzng profts over tme (Treadway)." Relatve effcency between nputs and j requres that kdk j = 1. Ths mples (8 O + 8 l DE + 8ZSZ)Z = (8 oj + 8t1JE + 82jSz)Z, or (11) as~ + bs z + c = 0, where a = 8~ - 8~j, b = 2(8 0 8z DE - 8 oj82j - 8lj82PE), c = DE - 8~j - 8tDE. Solvng the quadratc n Sz for DE = 0, 1 provdes the years of management experence necessary for the exstence of relatve effcency between nputs andj. Table 3 presents the educaton and experence levels requred to meet relatve effcency. Relatve effcency s possble for four nput combnatons: gran/forage, gran/hay, forage/hay, and hred labor/hay. Only the values of years of management experence that correspond to the observed range are reported. The substtuton relatonshp between educaton and experence s evdent. To acheve relatve effcency n the applcaton of the possble combnatons, the operator n the lower educaton category requres over twenty years of management experence. However, 4 A dynamc smulaton of alternatve dary prce scenaros ndcates that Pennsylvana dary operators may ncrease producton n response to prce decreases for some perods as they adjust ther producton practces (Chang). Table 3. Educaton and Experence Necessary for Relatve Effcency Factor Combnatons 1. Gran/forage Educaton :S 12 years Educaton > 12 years 2. Gran/hay Educaton :S 12 years Educaton > 12 years 3. Forage/hay Educaton :S 12 years Educaton > 12 years 4. Hay/hred labor Educaton ~12 years Educaton>12 years Years of Management Experence Necessary for ktlk j = Note: Only the mnmum soluton to the quadratc equaton n (11) s reported.

7 344 May 1988 the operator wth a post-secondary educaton requres between 45% and 75% less management experence to acheve a relatvely effcent applcaton of these nput combnatons. Acqurng a post-secondary educaton can be vewed as an nvestment that provdes the operator wth a learnng and nformatonprocessng framework that he/she can explot n order to assmlate and respond to new developments n the marketng and techncal producton envronment. Concludng Comments A generalzaton of the dual, non-fronter approach to evaluatng the allocatve effcency of nputs s developed allowng the tranng varables of educaton and management experence to nfluence the effcency level drectly. The applcaton to Pennsylvana dary farms ndcates that these operators are not allocatng ther varable nputs n an absolutely effcent manner. In fact, the results suggest that these operators are applyng ther varable nputs n order to maxmze producton rather than proft. However, relatve effcency can be acheved for four of sx possble nput combnatons. Educaton and experence are found to be substtutes and playa sgnfcant role n the level of effcency. These tranng varables enter the calculus as an endowment or, alternatvely, as the operator's state of nature. Thus, educaton and experence levels are representatve of the operator's ablty to learn but are not ndcators of the flow of learnng undertaken by the operator. Furthermore, operators wth post-secondary educaton are found to engage n more factor substtuton and may be closer to ther optmal long-run equlbrum fxed factor levels. [Receved June /987; fnal revson receved September 1987.] References Arrow, K. J. "The Economc Implcatons of Learnng by Dong." Rev. Econ. Stud. 29(1962): Atknson, S. E., and R. Halvorson. "A Test of Relatve and Absolute Prce Effcency n Regulated Industres." Rev. Econ. and Statst. 62(1980): Amer. J. Agr. Econ. Carter, L. F. "Inadvertent Socologcal Theory." Socal Forces 50(1971): Chang, C. C. "Asset Fxty, Non-Reversbltes and Dynamc Structure of Producton: A Mcro-Applcaton to Pennsylvana Dary Farms." Ph.D. thess, Pennsylvana State Unversty, Fane, G. "Educaton and the Manageral Effcency of Farmers." Rev. Econ. and Statst. 57(1975): Fersund, F.R., and L. Hjalmarsson. "Fronter Producton Functons and Techncal Progress: A Study of General Mlk Processng n Swedsh Dary Plants." Econometrca 47(1979): Green, R., W. Hahn, and D. Rocke. "Standard Errors for Elastctes: A Comparson of Bootstrap and Asymptotc Standard Errors." J. Bus. and Econ. Statst. 5(1987): Grsley, W. Dary Management Practces and Pennsylvana Dary Farm Incomes, Agr. Econ. and Rural Soc. Rep. No. 179, Pennsylvana State Unversty, Aprl Hallberg, M. C., D. E. Hahn, R. W. Stammer, G. J. Elterch, and C. E. Ffe. Impact ofalternatve Federal Mlk Marketng Order Prcng Polces on the Unted States Dary Industry. Pennsylvana State Unversty Agr. Exp. Sta. Bull. No. 818, May Huffman, W. E. "Allocatve Effcency: The Role of Human Captal." Quart. J. Econ. 91(1977): "Human Captal, Adaptve Ablty, and the Dstrbutonal Implcatons of Agrcultural Polcy. " Amer. J. Agr. Econ. 67(1985): Khan, M. H., and D. Mak. "The Effects of Farm Sze on Economc Effcency: The Case ofpakstan." Amer. J. Agr. Econ. 61(1979): Lau, L. J., and P. A. Yotopoulos. "A Test for Relatve Effcency and Applcaton to Indan Agrculture." Amer. Econ. Rev. 61(1971): Lopez, R. E. "Estmatng Substtuton and Expanson Effects Usng a Proft Functon Framework." Amer. J. Agr. Econ. 66(1984): Lovell, C. A. K., and R. C. Sckles. "Testng Effcency Hypotheses n Jont Producton: A Parametrc Approach." Rev. Econ. and Statst. 65(1983): Roo, C. R. Lnear Statstcal Inference and Its Applcatons, 2nd ed. New York: John Wley & Sons, Rosen, S. "Learnng By Experence as Jont Producton." Quart. J. Econ. 86(1972): Schmdt, P., and C. A. K. Lovell. "Estmatng Techncal and Allocatve Effcency Relatve to Stochastc Producton and Cost Fronters." J. Econometrcs 9(1979): Sdhu, S. S. "Relatve Effcency n Wheat Producton n the Indan Punjab." Amer. Econ. Rev. 64(1974): Sdhu, S., and C. Baanante. "EstmatngFarm-LevelInput Demand and Wheat Supply n the Indan Punjab Usng a Translog Proft Functon." Amer. J. Agr. Econ. 63(1982): Toda, Y. "Estmaton of a Cost Functon When Cost Is Not a Mnmum: The Case of Sovet Manufacturng

8 Stefanou and Saxena Industres, Rev. Econ. and Statst. 58(1976): Treadway, A. B. "Adjustment Costs and Varable Inputs n the Theory of the Compettve Frm." J. Econ. Theory 2(1970): Educaton, Experence, and Effcency 345 Welch, F. "Educaton n Producton." J. Polto Econ. 78(1970): Yotopoulos, P. A., and L. Lau. "A Test for Relatve Economc Effcency: Some Further Results." Amer. Econ. Rev. 63(1973):