Firm Heterogeneity and its Implications for Efficiency Measurement. Antonio Álvarez University of Oviedo & European Centre for Soft Computing

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1 Frm Heterogeney and s Implcatons for Effcency Measurement Antono Álvarez Unversy of Ovedo & European Centre for Soft Computng

2 Frm heterogeney (I) Defnon Characterstcs of the ndvduals (frms, regons, persons, ) that are not measured n the sample Unobserved heterogeney Examples Input qualy n producton functons Genetc level of the herds Land fragmentaton Management

3 Frm heterogeney (II) Consequences of unobserved heterogeney If not accounted for, may cause based estmates Grlches (1957) Dffcult to separate from neffcency Stgler (1966)

4 Frm heterogeney (III) What about heterogeney n the stochastc part? One may beleve that there s heterogeney n the mean or the varance of U u N + 2 ( µ, σ ) Soluton: make them a functon of observed varables = µ exp( q δ ) σ = σ exp( q δ ) µ u Alvarez, Amsler, Orea and Schmdt (2006)

5 Revew of Relevant Lerature

6 Lerature (I) Ths paper examnes several extensons of the stochastc fronter that account for unmeasured heterogeney as well as frm neffcency

7 Lerature (II) The paper proposes a SF model wh random coeffcents to dstngush techncal neffcency from technologcal dfferences across frms

8 Lerature (III) The paper proposes a model to separate techncal neffcency from technologcal dfferences across frms

9 Lerature (IV) Unobserved dfferences n technologes may be napproprately labeled as neffcency f varatons n technology are not taken nto account

10 Lerature (V)

11 Summary of lerature Many estmaton technques to separate frm heterogeney and neffcency Stochastc Fronters wh Fxed Effects Heshmat and Kumbhakar (1994) Greene (2005) Random Coeffcent Models Tsonas (2002), Huang (2004) Alvarez, Aras and Greene (2005) Latent Class Models Orea and Kumbhakar (2004) Local Maxmum Lkelhood Kumbhakar, Smar, Park and Tsonas (2007)

12 Objectves of the Talk Propose a theoretcal framework to understand the relatonshp between unobserved heterogeney and neffcency Revew some technques to deal wh unobserved heterogeney Study the mplcatons for effcency analyss

13 Theoretcal Framework

14 Modellng frm heterogeney Startng pont: there s an unmeasured varable (Z) Two possble effects: ln y = α + β ln x + γz + γ z ln x + x v v N (0, σ 2 v ) If Z =Z, the model becomes ln y = α + β ln x + γz + γ z ln x + v x

15 Specal case: No nteractons If γ x = 0 the unobserved heterogeney can be modelled as an ndvdual effect Fxed Effects ln y = α + β ln x + v α = α + γ z Random Effects ln y = α + β ln x + v + u u = γ z

16 Stochastc Fronter The fronter wll be defned by the frm wh the largest Z (Z*) Average functon ln y = α + β ln x + γz + γ z ln x + x v Fronter ln y = α + β ln x + γz + γ z ln x + * * x * v

17 Effcency and Frm heterogeney Techncal effcency s the rato of observed output to fronter output LnTE * * = ln y ln y = γ ( z z ) + γ x ln x ( z z * ) Implcatons TE s tme-varyng even f Z s tme nvarant If two frms use dfferent nputs wh the same level of TE, an ncrease n TE may requre dfferent ncrease n the level of management for each frm.

18 Separatng Frm Heterogeney from Ineffcency

19 Indvdual effects Fxed Effects ln y = α + β ln x + v Estmaton by OLS wh frm dummes Random Effects ln y = α + β ln x + v + u Estmaton by GLS Heterogeney s confounded wh (tme nvarant) techncal effcency

20 Stochastc Fronter wh Fxed Effects ln y = α + βx + v u Polachek and Yoon (1987) Kumbhakar (1991) Kumbhakar and Hjalmarson (1993) Greene (2005):Estmaton by brute force ML α captures tme-nvarant heterogeney Technologcal dfferences Persstent neffcency U captures tme-varyng heterogeney Tme-varyng neffcency (catch-up) Tme-varyng technologcal dfferences (sector composon)

21 SF Random Coeffcent Models ln y = α + β ln x + v u Tsonas (2002), Huang (2004) Assumpton: the parameters are random varables β = β + ω Estmaton: Bayesan technques

22 SF Random Coeffcent Models (II) ln y = α + β ln x + v u Alvarez, Aras and Greene (2005) Estmaton: Smulated Maxmum Lkelhood (Lmdep 9) ln y = ln y u = α + β ln x + γz + γ z ln * * x * x + v u ln y = ( α + γz ) + ( β + γ z ) ln * x * x + v u ln y = δ + δ ln x x + v u

23 SF Latent Class Models y = α + β j j x + v j u j Orea and Kumbhakar (2004) Alvarez and del Corral (2008) Estmaton by ML Number of classes s unknown

24 Dfferent Groups (Classes) y x

25 Applcaton Separatng frm heterogeney from neffcency n regonal producton functons

26 Data Panel of 50 Spansh provnces ( ) Output: GVA Inputs: Prvate capal (K) Labor (L) Human Capal (HC) Publc Capal (G)

27 Emprcal Model Functonal form: Cobb-Douglas Neutral Techncal Change Stochastc Fronter wh Fxed Effects (SFFE) ln y = α + j β j ln x j + δ t t δ tt t 2 + v u V s assumed to be N(0,σ v ) U s assumed to follow a half-normal dstrbuton: N + (0,σ u )

28 Estmaton Kumbhakar and Hjalmarsson (1993) Estmaton by GLS Greene (2002) Estmaton by ML Maxmzaton of the uncondonal log lkelhood functon can, n fact, be done by brute force even n the presence of possbly thousands of nusance parameters by usng Newton s method and some well known results from matrx algebra

29 Comparng neffcency Mean Ineffcency SFFE (α +V -U ) 0.08 Pooled SF (V -U ) 0.09 Corr (U _SFFE,U _PSF)= 0.50

30 Comparng fxed effects SFFE Whn Mn Max Corr (FE_SFFE,FE_Whn)= 0.19

31 Rankng of Fxed Effects SFFE Cadz Almería Jaén Huelva Valenca Tenerfe Salamanca Baleares Las Palmas Roja Provnce Baleares Sevlla Zaragoza Málaga Alcante Valenca Barcelona Madrd Asturas Vzcaya Whn SFFE Whn Provnce

32 Man fndngs The models wh U yeld smlar results, whch n turn are very dfferent from the FE model The estmated fxed effects n the FE and SFFE models are very dfferent

33 Applcaton Identfyng dfferent technologes: extensve vs ntensve dary farms

34 Dary Farmng n Span Recent trends Large reducton n the number of farms 73% reducton durng Quota System Snce 1991 Farms have grown Average quota almost doubled n last seven years Change n the producton system Many farms have adopted more ntensve systems

35 Intensve vs Extensve Systems Characterstcs of ntensve systems Farms produce more lers of mlk per hectare of land How? More cows per hectare of land Hgher use of concentrates per cow Hgher genetc level of the herds Unobservable!!!

36 Objectves Are there dfferences n technologcal characterstcs between extensve and ntensve farms? H0: Intensve farms have hgher returns to scale They have grown more than extensve farms Are there dfferences n techncal effcency? H0: Intensve farms produce closer to ther fronter We consder that the ntensve system s easer to manage

37 Latent Class Stochastc Fronters Latent Class Stochastc Fronter Model ln Lkelhood functon y = f ( x ) j + v j u j log LF = N log = 1 j= 1 t= 1 J T P j LF jt Probables P = J j= 1 Number of classes j exp( δ q exp( δ q j j ) )

38 Data Panel data set 169 dary farms 6 years ( ) Output Mlk lers Inputs Cows, Feed (kg.), Labor (worker equvalents), Land (hectares), crop expenses (euros)

39 Emprcal Model Translog stochastc producton fronter Control varables Tme dummes Locaton dummes Separatng varables Cows per hectare of land Feed per cow lny 1 L L L t= 2004 z= 6 = β + β l lnx j j l + βlk lnx ln j l xk + λ D j t + 0 l= 1 2 l= 1 k= 1 t= 2000 z= 1 γ DLOC+ v j z j u j

40 Estmaton results Fronter Constant Cows Feed Land Farm$ Pooled Stochastc Fronter *** 0.476*** 0.425*** *** Latent Class Model Extensve Group *** 0.472*** 0.228*** 0.088*** Intensve Group *** 0.684*** 0.325*** *** *, **, *** ndcate sgnfcance at the 10%, 5% and 1% levels

41 Characterstcs of the Systems Farms Mlk (lers) Cows Land (ha.) Mlk per hectare Cows per hectare Mlk per cow Feed per cow Mlk per feed Extensve , , ,522 3, Intensve , , ,130 3,

42 Scale Elastcy n the LCM Extensve Intensve Intensve farms have hgher scale elastcy than extensve farms

43 Techncal Effcency Pooled LCM Extensve Intensve

44 Dscusson The results of the LCM help to explan two emprcal facts Farms grow despe the declne n the prce of mlk Large farms buy quota from small farms The margnal value of quota s prce mnus margnal cost

45 Conclusons It s mportant to model unobserved heterogeney Some new technques provde an nterestng framework to control for frm heterogeney