AJAE Appendix for: Induced Innovation In U.S. Agriculture: Time-series, Direct Econometric, and Nonparametric Tests. Yucan Liu. C.

Transcription

1 AJAE Appendix for: Induced Innovaion In U.S. Agriculure: Time-series Direc Economeric and Nonparameric Tess Yucan Liu C. Richard Shumway March

2 Appendix A: Srucure of he Direc Economeric Model Le A M L K represen he quaniies of land maerials labor and capial respecively E A E M E L and E K represen heir facor augmenaions. Suppose oupu (Y) is produced wih a land inpu index X A (E A A E F M) and a labor inpu index X L (E L LE K K) according o a wo-level producion echnology: Y= F[ X ( E A E M ) X ( E L E K )] (A1) A A M L L K where F ( ) is assumed o vary across ime. We assume he producion echnology can be approximaed by a wo-level CES funcional form (e.g. de Janvry e al. 1989; Thirle e al. 00): (A) Y=[ γx + (1 γ ) X ] ρ ρ 1/ ρ A L 1 1 1/ 1 (A3) X [ ( E A) ρ α (1 α)( E M ) ρ = + ] ρ A A M 1/ (A4) X [ ( E L ) ρ β (1 β)( E K ) ρ = + ] ρ L L K whereα βγρρ 1 ρ are parameers and ρ ρ1 ρ > 1. The logarihms of he firs-order condiions of profi maximizaion can be rearranged o give: (A5) A M + ρ1 α α + ρ1 PA PM ρ1 + ρ 1 EA/ M ln( / )=[1/(1 )]ln[ /(1 )] [1/(1 )]ln( / ) [ /(1 )]ln( ) ln( L / K )=[1/(1 + ρ )]ln[ β /(1 β)] [1/(1 + ρ )]ln( P / P ) [ ρ /(1 + ρ )]ln( E ) (A6) L K L/ K where P A P M P L and P K are he prices of land maerials labor and capial respecively; EA/ M = EA / EM and EL/ K= EL / EK. Following Armanville and Funk (003) and using noaion (E i ) o represen he

3 efficiency variables (facor augmenaions) we define he IPF as he following se of insananeous raes of facor augmenaion ( ( Eˆ ˆ ˆ ˆ A EM )( EL E K ) ) ha producers can choose: 1 {( Eˆ Eˆ ) ( Eˆ Eˆ ) : Eˆ φ ( Eˆ ); Eˆ φ ( Eˆ )} (A7) A M L K M 1 A K L where he circumflexes ( Λ ) denoe relaive raes of change i.e. E ˆ ( )/ i = Ei Ei 1 Ei 1; φ () and 1 φ () are he firs-level innovaion possibiliy froniers which are assumed o be differeniable decreasing sricly concave and ellipses cenered a (-1-1) i.e. (A8) φ () : ˆ ˆ 1 ( E +1) + n ( E + 1) = m A 1 M 1 (A9) φ () : ˆ ˆ ( E +1) + n ( E + 1) = m L K where n is a slope parameer and m is a level parameer. The parameers n and m measure he augmenaion rade-off rae beween facors. The slopes of φ () and φ () wih 1 respec o E A and E L respecively a given ( Eˆ ˆ A E M ) and ( Eˆ ˆ L E K ) are: (A10) (A11) φ = de de = ( Eˆ + 1)/[ n ( Eˆ + 1)] 1 M A A 1 M φ = de de = ( Eˆ + 1)/[ n ( Eˆ + 1)]. K L L K Generally innovaions can be viewed as aciviies ha reallocae resources among facor augmenaions for he purpose of profi maximizaion. The hypohesis of induced innovaion is ha a firm chooses a feasible se of facor augmenaions on he IPF o maximize profi given he amoun of employed facors (Funk 00; Armanville and Funk 003). Leing π denoe profi he firms innovaive decisions are made as follows:

4 Max { ˆ : ˆ ( ˆ ); ˆ ( ˆ )} (A1) π ˆ ˆ ˆ ˆ EM φ1 EA EK φ EL E A E M E L E K given M A K L and echnology as defined in equaion (A1). Since he consrain is always binding a he opimum he firs-order condiions of he maximizaion problem wih respec o facor augmenaions are: ˆ ˆ = ( ˆ )[ / ( ˆ )] + λφ = 0 (A13a) π EA F X A X A EA A A 1 1 (A13b) ˆ π ˆ ˆ ˆ EM = ( F XM )[ XM / ( EM M)] M λ1 = 0 ˆ π ˆ = ( ˆ )[ / ( ˆ )] + λφ = 0 (A13c) EL F XL XL EL L L (A13d) ˆ π ˆ ˆ ˆ EK = ( F XK )[ XK / ( EK K)] K λ = 0 Since he facor s marginal produciviy is equal o is normalized price a insananeous equilibrium (A13a-d) yield: (A14a) 1 ( PA A)/( PM M) 1 φ = =Φ (A14b) ( PL L)/( PK K) φ = =Φ. Equaions (A14a-b) specify he firs-order curvaure properies of he IPF required o saisfy he hypohesis of induced innovaion. In his specificaion he profi maximizer will choose he se of facor augmenaions such ha he slope of he IPF equals he relaive inpu shares. As demonsraed by Funk (00) he hypohesis of induced innovaion can be derived from a microeconomic model wih fully raional firms. Suppose firms can make profis wih an innovaion chosen from heir perceived IPF unil his innovaion is imiaed by oher firms. Wih he aggregae echnology defined in (A) he IPF defined

5 in (A7) and profi-maximizing choice of innovaions in a coninuous-ime seing 3 he slopes of he IPF are: 4 σ1 1 (A15) [ /(1 )] [( P / E ) /( P / E )] 1 σ φ = α α 1 A A M M σ 1 σ (A16) φ = [ β /(1 β)] [( P / E ) /( P / E )] L L K K where σ = /(1 + ) is he elasiciy of subsiuion beween land (A) and maerials (M) 1 1 ρ1 and σ = /(1 + ) is he elasiciy of subsiuion beween labor (L) and capial (K). 1 ρ Equaions (A15-16) imply ha when he elasiciy of subsiuion is greaer (less) han one an increase in efficiency-adjused relaive prices induces much (lile) subsiuion beween he facors given any echnology. Thus we ge he surprising resul ha afer he subsiuion i is more profiable o augmen he inensively-used facor even if i is relaive cheaper when he elasiciy of subsiuion is greaer han one (Armanville and Funk 003). If he elasiciy of subsiuion is less han one we ge he well-known resul ha i is more profiable o augmen he relaively more expensive facor. Consequenly one es for he IIH in his framework is o deermine wheher he bias of echnical change is posiively (negaively) correlaed wih relaive prices in efficiency unis (i.e. relaive inpu shares) when he elasiciy of subsiuion is greaer (less) han one. For example if he elasiciy of subsiuion is less han one he null hypohesis for esing he IIH in land (A) and maerials (M) can be expressed as: H 0 : corr( Eˆ ˆ A EM ( PA / EA )/( PM / EM )) > 0 or H 0 : corr( Eˆ ˆ A EM Φ 1 ) > 0 where corr denoes he correlaion operaor. Failure o rejec he null hypohesis implies ha he direcion of producers innovaive decisions are guided by efficiency-adjused

6 relaive prices as prediced by he IIH. Armanville and Funk (003) labeled his direcional es as a weak es of he IIH. A srong es would deermine wheher quaniaive innovaion choices correspond o hose prediced by he hypohesis i.e. wheher innovaive behavior fully saisfies equaions (A14a-b). Following Armanville and Funk (003) a srong es can be developed from (A14a-b) by deermining wheher γ 1 and γ equal 1 in he following specificaion of he slopes of he firs-level innovaion possibiliy froniers: γ1 (A17) φ =Φ 1 1 γ (A18) φ =Φ Tha is for he IIH o be srongly suppored he elasiciy of he slopes of φ () and φ () 1 wih respec o relaive inpu shares mus be 1. From equaions (A10-11) and (A17-18) we derive he following relaionships: 5 1 (A19) E / E ( E / E ) γ = Πn Φ A M A0 M0 1 s 1 s s= 1 (A0) E / E ( E / E ) γ = Πn Φ L K L0 K0 s s s= 1 Inuiively he relaive facor produciviies a ime depend on pas values of he slope parameer n i pas values of he relaive inpu shares and he relaive produciviies a he saring period. By subsiuing (A19-0) ino (A5) and (A6) respecively we obain: (A1) A 1 α 1 PA ρ E 1 A0 ln = ln ln γ1 ln Φ 1 s + lnn1 s + ln M 1 ρ1 1 α 1 ρ1 PM 1 ρ s= 1 s= 1 E M0

7 (A) L 1 β 1 PL ρ E L0 ln = ln ln γ ln Φ s + lnn s + ln K 1 ρ 1 β 1 ρ PK 1 ρ s= 1 s= 1 E K0 Since daa are available for facor prices and he relaive inpu shares ( Φ 1 and Φ ) he relaive demand equaions (A1-) can be esimaed if slope parameers n 1 and n are specified. Insead of following Armanville and Funk (003) in making he n s a funcion only of ime we rea hem as funcions of innovaion invesmens including public research R pub privae research R pri and exension Ex: ln( ) = ln( ) + ln( ) + ln( ) ( j = 1 ) (A3) nj δ j1 Rpri δ j Rpub δ j3 Ex where δ ji (j = 1 ; i = 1 3) is a consan. Assuming ha innovaion invesmens are allocaed evenly for facor augmenaion a he saring period i.e. EA0 / E M0 = 1 and EL0 / E K0 = 1 rewriing equaions (A1-) gives equaion (3.3) in he paper.

8 Appendix B: Nonparameric Tess Under he ranslaing hypohesis i.e. X i = xi + B i he weak axiom of profi maximizaion (WAPM) is equivalenly wrien as: (B1) Px Px s s T or (B) P ( ) X B P( Xs B s) s T where x x s X and X s are effecive and acual nepu vecors a observaions and s and B and B s are he augmenaion vecors a he respecive observaions. If he daa saisfy he WAPM here exiss a closed convex and negaive monoonic producion possibiliies se ha raionalizes he daa in T and here exiss a profi-maximizing oupu supply and inpu demand soluion. The WAPM specified in equaion (B) also allows us o recover he echnology in he presence of echnical change given he daa observaions. If i > is B B for an inpu echnical change beween s and is ih-inpu saving. In anoher words o achieve he same level of effecive inpu a ime as in ime s requires a smaller quaniy of he ih-inpu. If Bi > B is for oupus echnical change beween s and is oupu augmening. For he same acual level of all inpus more oupu is produced a ime han in ime s. We follow Chavas e al. (1997) in specifying hree augmenaion resricions needed o conduc nonparameric esing of he IIH. The firs resricion specified in equaion (3.5) in he ex reas he echnology indices as funcions of a consan erm and a weighed sum of a finie lag of pas innovaion invesmens. The idea for his model specificaion is ha R&D invesmens can generae echnical progress and he process of

9 echnical change akes ime. Also he Hicksian IIH emphasizes he crucial role of relaive price changes in deermining he direcion of research invesmens owards augmening paricular facors which suggess ha he marginal impac of R&D depends on relaive prices. Thus i provides an approach o direcly invesigae he Hicksian IIH. The second resricion smoohing resricion on he oupu augmenaion variables has he following expression: c (B3) By ( By j)/ c j= 1 This resricion requires oupu augmenaion o be a leas as large as a moving average of previous values so augmenaion is no permied o rend downward over ime. The moving average allows for weaher o dampen oupu augmenaion in individual years. Following Chavas e al. (1997) we used a 5-year moving average. The hird resricion assumes nonnegaiviy of he marginal effec of innovaion aciviies on augmenaion indices: (B4) Bi / R j i j ( Pi j 1) i j 0 i A M L K j 1 ri = β + γ = = and (B5) By / R j = β y j 0 j = 1 ry. In he las sep hese parameers are esimaed by solving a quadraic programming problem. The inuiion is o make he augmenaion indices and he impac of exogenous shifers as close o he daa as possible while saisfying he WAPM. Based on he esimaes of hese parameers he induced innovaion hypohesis and he naure of echnical change in U.S. agriculure are examined.

10 Appendix C: Consrucion of Inpu Price Proxies for he Period Using prices for machinery and ferilizer from he Thirle e al. (00) daa se o represen prices of capial and maerials respecively we indexed boh Ball s and Thirle e al. s U.S.-level daa ses o Ball s (004) sae-level series in he following way: Firs we compued averages of Ball s and Thirle e al. s U.S. prices for each inpu caegory for he firs five years in he Ball series Second we merged Thirle e al. s prices for each inpu caegory ino Ball s U.S. series by muliplying Thirle e al. s U.S. prices series for by he raio of Ball s and Thirle e al s U.S. average prices for and denoe i he Ball-TST daa se. Third we compued averages of each sae-level price series and of Ball s U.S. prices for he firs five years of he sae-level series Lasly we spliced he Ball-TST U.S. prices wih he sae-level series by muliplying he Ball-TST daa for by he raio of he sae average o he U.S. average price in for each sae and inpu.

11 Appendix D: Addiional Empirical Resuls Table D.1. Reverse Causaliy Tes Resuls a LnP A/M LnR pri LnR pub LnEx Number Causal Esimaed Sandard Esimaed Sandard Esimaed Sandard Esimaed Sandard of lags variable Coefficien Coefficien Coefficien Coefficien 1 LnR A/M * * * LnR A/M * * LnR A/M * LnR A/M * * LnR A/M * LnR A/M * LnP L/K LnR pri LnR pub LnEx Number Causal Esimaed Sandard Esimaed Sandard Esimaed Sandard Esimaed Sandard of lags variable Coefficien Coefficien Coefficien Coefficien 1 LnR L/K * LnR L/K * LnR L/K * * LnR L/K * LnR L/K * LnR L/K a The opimal lag seleced by he AIC was 1 in all equaions. The criical -values for hese -ailed ess are 1.96 a he 0.05 significance level. Significan coefficiens are idenified by an aserisk.

12 Table D.. Esimaed Direc Economeric Model wih Innovaion Sock Variables a Land-Maerials Equaion Labor-Capial Equaion Variable Coefficien Sandard Variable Coefficien Sandard Consan * Consan * LnP A/M * LnP L/K * F * F * ln R pri 0.049* ln R pri ln R pub * ln R pub ln Ex ln Ex R b R Hypohesis Tesed Null Saisic Hypohesis Tesed Null Saisic Weak Tes γ A/M >0 γ A/M Weak Tes γ L/K > 0 γ L/K * Srong Tes γ A/M = 1 γ A/M = * Srong Tes γ L/K = 1 γ L/K = * a Criical values a he 0.05 significance level are 1.96 for he -ailed -raios on he coefficiens 1.65 for he 1-ailed sandard normal saisics for he weak es and 3.84 for he 1-ailed Wald chi-square saisics for he srong es. Significan coefficiens are idenified by an aserisk. b R is an average of sae-specific adjused R-square values.

13 Appendix E: Marginal Cos of Developing and Implemening Inpu-Saving Technologies All ess of he IIH conduced o dae have only esed he demand side of he hypohesis. Tha includes ours. Alhough boh Binswanger (1974) and Olmsead and Rhode (1993) acknowledged he demand-side naure of he hypohesis ess mos ohers who have esed he IIH have been silen abou his imporan limiaion (Coxhead 1997 is an excepion). 6 All ess of he hypohesis have implicily mainained he hypohesis ha he marginal cos of developing and implemening echnologies ha save one inpu is he same as he marginal cos of saving an equal percen of any oher inpu. Since i is highly unlikely ha innovaion possibiliies are his neural i is possible ha he IIH is in fac a valid explanaion and ye producers augmen cheaper facors because he marginal coss of developing and implemening inpu-saving echnologies for he relaively expensive inpus are greaer han for he relaively cheap ones. Tha is echnical change may no bias oward saving a paricular inpu even when i ends o be relaively expensive. Unforunaely daa on he developmen and implemenaion coss of various inpu-saving echnologies are lacking. Having failed o find suppor for he IIH relying exclusively on he demand for innovaion and lacking essenial daa o disinguish differences in innovaion supply we calculaed relaive differences in he marginal coss of developing and implemening saving echnologies for he various inpus o be consisen wih he hypohesis. The qualiaive pairwise resuls of hese nonparameric compuaions are repored for nine represenaive saes in Table E.1. For differences in marginal coss of echnology developmen and implemenaion

14 o have rendered he daa consisen wih he IIH sufficien condiions included higher marginal coss of land- and capial-saving echnologies han of maerial-saving echnologies in nearly all saes. 7 This finding was robus across he various ypes of inpu-saving innovaion invesmen. If hese marginal cos differences acually exised hen he higher cos of developing and implemening land- or capial-saving echnologies could have induced profi-maximizing echnical change ha was biased oward augmening maerials raher han land or capial even when land and capial were he relaively more expensive inpus. For consisency wih he IIH anoher condiion included a higher marginal cos of developing and implemening land-saving echnology han of labor-saving echnology in mos saes for all ypes of innovaion invesmen. Anoher condiion was a higher marginal cos of land-saving echnology han of capial-saving echnology in all saes for research invesmens and in a majoriy of saes for exension invesmens. This same observaion also applies in nearly all saes for labor vs. maerial-saving echnologies. However he order ranking of sufficien marginal cos differences for labor and capial was less clear. For privae research invesmens higher marginal coss for labor-saving echnology han for capial-saving echnology were implied in /3 of he saes. Nearly he reverse was found for exension invesmens and neiher dominaed for public research invesmens.

15 Table E.1. Nonparameric Esimaes of Relaive Marginal Cos of Developing and Implemening Inpu-Saving Technology Required for Consisency wih he Induced Innovaion Hypohesis a Inpu Pair Marginal Cos Inpu-Saving Innovaion Invesmens Relaionship R pri R pub Ex CA FL IA CA FL IA KS CA FL IA KS Land vs. maerials MC A > MC M KS MI NC MI NC NY MI NC NY NY TX WA TX WA TX WA MC L > MC K CA FL KS NY TX WA CA FL KS TX WA CA KS WA Labor vs. capial MC L = MC K FL MC L < MC K IA MI NC IA MI NC NY IA MI NC NY TX Land vs. capial MC A > MC K CA FL IA KS MI NC NY TX WA CA FL IA KS MI NC NY TX WA CA KS NC NY WA MC A = MC K FL IA MITX Labor vs. maerials MC L > MC M CA FL IA KS NC NY TX WA CA FL IA KS NC TX WA CA FL IA KS WA MC L < MC M MI MC NY MI NC NY TX

16 Land vs. labor MC A > MC L CA IA KS MI NC NY TX WA IA MI NC NY WA IA MI NC NY TX WA MC A = MC L FL FL FL KS Capial vs. maerials MC A < MC L CA KS TX CA MC K > MC M CA FL IA KS NC TX WA CA FL IA KS MI NC NY TX WA MC K < MC M MI NY NY CA FL IS KS MI NC TX WA a Codes: R pri is privae research invesmens R pub is public research invesmens Ex is exension invesmens. MC i represens marginal cos of developing and implemening inpu-saving echnologies for inpu i.

17 Foonoes 1 When he producers simulaneously choose all four facors o maximize profi he IPF {( ˆ ˆ ˆ ˆ ) ˆ ( ˆ ˆ ˆ )}. should be defined as he following se: E E E E E φ E E E A M L K A M L K However his four-dimensional innovaion possibiliy fronier proves o be inracable for empirical applicaion. By mainaining weak separabiliy beween (A M) and (K L) he wo-level producion echnology faciliaes empirical esing of he IIH. The assumpion ha he IPF is cenered a (-1-1) is imposed o assure ha he slope of he IPF a he axis poins is finie and nonzero (Armanville and Funk 003). 3 In his case he lengh of he period beween innovaion and imiaion ends o zero. 4 See Funk (00) for deails and discussion of he derivaion. 5 Combining equaion (B10-11) and (B17-18) and noing ha K L) gives: E ˆ i + 1 = i / i 1 E E (i = M A ( E / E )/( E / E ) n γ = Φ and ( EL / EL 1 )/( EK / EK 1) = n Φ. By subsiuing γ1 A A 1 M M backward unil = 1 we obain equaion (B19-0). 6 Binswanger (1974 p. 975) wroe Bu despie ha price rise echnical change was machinery-using no saving. Had innovaion possibiliies been neural his could no occur. From Olmsead and Rhode (1993 p. 110) he evolving srucure of American agriculure canno be explained simply in erms of he relaive supplies and prices of a

18 few facors. The induced innovaion hypohesis pus oo many eggs in he demand-side baske. 7 The cos shares averaged across saes and years for maerials (45%) is greaer han for labor (3%) which in urn is greaer han for capial. Among he 4 inpus he average cos share for land is he smalles (13%).

19 Addiional References Coxhead I Induced Innovaion and Land Degradaion in Developing Counry Agriculure. The Ausralian Journal of Agriculural and Resource Economics 41():305-3.