SUPPLY RESPONSE WITHIN THE FARMING SYSTEM CONTEXT. by Colin Thirtle and Robert Townsend, University of Reading and University of Pretoria

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SUPPLY RESPONSE WITHIN THE FARMING SYSTEM CONTEXT WEEK 2: DAY 5 DYNAMIC SUPPLY RESPONSE ESTIMATION b Colin Thirle and Rober Townsend, Universi of Reading and Universi of Preoria CONTENTS INTRODUCTION 1.
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SUPPLY RESPONSE WITHIN THE FARMING SYSTEM CONTEXT WEEK 2: DAY 5 DYNAMIC SUPPLY RESPONSE ESTIMATION b Colin Thirle and Rober Townsend, Universi of Reading and Universi of Preoria CONTENTS INTRODUCTION 1. THE BASIC THEORY OF PRODUCTION AND SUPPLY RESPONSE 1.1. The Producion Funcion 1.2. Feaures of Agriculural Producion in LDCs Farmers as Producers and Consumers Risk and Uncerain Expecaions, Disequilibria and Adjusmen 1.3. The Marke Suppl Curve Suppl curve shifs 1.4. Elasiciies of Suppl Own-Price Elasici of Suppl Cross-price Elasici Oupu Elasiciies wih Respec o Inpu Prices 1.5. Esimaion of he Parameers of Suppl Funcions Basic Suppl Funcion Esimaion 2. TIME SERIES ANALYSIS 2.1. Saionari 2.2. Coinegraion 2.3. Uni Roo Tess for Saionari The Dicke-Fuller Tes The Durbin Wason Tes 2.4. Tess for Coinegraion Engle and Granger Single Equaion Approach The Coinegraing Regression Durbin Wason Tes 2.5. Problems wih he Single Equaion Approach Coinegraion wih Muliple Equaions: The Johansen Mehod 3. APPLYING TIME SERIES ANALYSIS TO SUPPLY RESPONSE: THREE MODELS 3.1. The Auoregresive Disribued Lag Model 3.2. The Error Correcion Model 3.3. The Parial Adjusmen Model An Example and Commens 3.4. Concluding Commens REFERENCES 1 APPENDIX LIST OF TABLES Table 1. Shifing he Suppl Curve Table 2. Tesing procedure using he DF/ADF ess Table 3. Shor and long run price elasiciies of agriculural oupu LIST OF FIGURES Figure 1. The Producion Funcion and he Suppl Curve Figure 2. The Suppl Curve: Quani as a Funcion of Price Figure 3. A Difference Saionar Process Figure 4. A Trend Saionar Process 2 INTRODUCTION This sud sars b explaining he heoreical framework of suppl response analsis. I begins wih a brief derivaion of suppl from he producion funcion. Facors affecing he shifs in he suppl curve are hen discussed afer which suppl elasiciies are derived and esimaion of he hese parameers is discussed. The second secion offers a brief review of ime series analsis, leading o he concep of coinegraion. The hird secion deals wih he more popular suppl response models, which are he disribued lag, error correcion and parial adjusmen models. This leads o a case sud of suppl response esimaion, using he error correcion model, which will form he basis of da 2 of week 4. 3 1. THE BASIC THEORY OF PRODUCTION AND SUPPLY RESPONSE 1.1 The Producion Funcion The producion funcion defines he relaionship beween inpus and oupus, describing he rae a which resources (several inpus, X i ) are ransformed ino producs (a single oupu, Q Y ). The equaion in is general form is: Q = F(X ), where i = 1,...,N Y i where all he variables are measured in homogeneous phsical unis, such as ons of oupu, acres of land and hours of labour. If we assume ha he inpus are land (X A ) which is fixed in he shor run, and labour, (X L ), which is variable, we can derive he shor run suppl curve. The upper par of figure 1 shows he oupu of Y, Q Y, measured in phsical erms, increasing bu a a diminishing rae, as increasing amouns of labour are combined wih a fixed area of land. This can be viewed as he shor run siuaion, in which he size of he farm canno be increased. There will alwas be diminishing reurns o he variable facor if he oher facor is fixed. Wih onl one variable facor, he producion funcion 0,B,C is he oal phsical produc (TPP) curve of labour. The relaionship beween oal phsical produc (TPP), average phsical produc (APP) and marginal phsical produc (MPP) can be saed explicil as: 1 TPP L = Q Y = F(X A, X L) 2 APPL = Q / X = TPP / X 3 Y L L L MPP = Q / X = TPP / X 4 L Y L L L For oupu level Q Y0, he APP L is 0Q Y0 /0L 0 in he figure, which is he slope of he line 0B, from he origin o he poin B. The MPP L is he slope of he line AB in he figure. Thus, he APP of he facor is jus he TPP divided b he amoun of he inpu and he MPP is he slope of he TPP curve a a given poin. [Figure 1: The Producion Funcion and he Suppl Curve] If we assume ha he farmer is a profi maximiser, we can deermine he opimal amoun of inpu used. Profi can be defined as oal revenue less oal cos (variable coss + fixed coss) which can be wrien as: Profi = P Q Y - PL X L - P A X A where P Y is he price of he oupu, Q Y is he quani of oupu produced, P L is he price of he variable inpu, labour, X L is he quani of labour, P A is he price of he fixed inpu, land, and X A is he quani. Differeniaing wih respec o X L we ge: 5 4 Profi X L = P Q X Y L - P = 0 L = P MPP - P = 0 L L 6 Equaion (6) can be rearranged o give: MPP L = P L/ P The MPP is he slope of he TPP curve, and a oupu level Q Y0 he slope of P L /P Y is AB. Thus, profi is maximised a poin B where he relaive price line is angenial o he slope of he TPP curve. So a B, MPP L = P L /P Y0, or rearranging, P Y0 (MPP L ) = P L. Thus, he value of he marginal produc of labour (VMP L ) is equal o he mone wage and he farm will be maximising he value of oupu for he inpu and oupu prices i faces. If he oupu price is increased o P Y1, hen he relaive price line will be P L /P Y1 and he MPP L is equal o he price raio a poin C. Labour inpu will increase from L 0 o L 1 and oupu from Q Y0 o Q Y1. The lower par of he diagram is obained b ploing he original price of he oupu, P Y0, and he higher price, P Y1, on he verical axis and using he 45 o line o ransfer he oupu levels, Q Y0 and Q Y1 ono he horizonal axis. This gives he relaionship beween he level of oupu and oupu price, which is of course he suppl curve. For convenience, we assume ha he suppl curve is a sraigh line, so ha he wo poins ploed are sufficien o define i. Then, he suppl curve is he line DEF. In he shor run, he suppl curve will be upward sloping because land is fixed and we ge diminishing reurns o he variable facor. Even in he long run, where all inpus are variable, in an case where an inpu canno be increased a a consan cos (perfecl elasic suppl), he suppl curve will rise, as shown. Noice ha i is he price of he oupu relaive o he inpu price ha maers; he same increase in oupu could equall well have been obained b reducing he wage rae. This means ha in esimaing suppl relaionships, he inpu prices maer jus as much as he oupu prices. In erms of polic, reducing inpu prices will have similar effecs o increasing he oupu price, bu he wo will no be he same 1. This is no surprising, since he suppl curve is he marginal cos curve of he firm. These suppl parameers mus be esimaed, so we can quanif our polic opions, and his mus be done wih poor daa and no informaion a all on some imporan variables. Again, our ineres in heor is no for is own sake, bu because knowledge of he heoreical relaionships can allow us o calculae he values of unknown parameers from hose we do know. For example, if here is no rural labour marke, here will be no informaion on wages. In a labour surplus econom, like Egp, i ma be possible o assume ha he social cos of labour is zero and use his as a shadow price. Bu for some African counries, seasonal labour shorages are a serious consrain on agriculural oupu and a wage would have o be calculaed. Indeed, if he MPP L and he oupu price were known, he fac ha P Y (MPP L ) = P L could be used o esimae he unknown inpu price. 1 The wo changes appear o have idenical effecs in his diagram, and Tweeen (1989, Ch.5)shows ha he elasici of inpu demand funcion wih respec o aggregae inpu price will be he same as he elasic of inpu demand wih respec o oupu price, bu wih he opposie sign. However, we will soon face up o he fac ha subsisence farmers sell onl a small proporion of heir oupu, so for hem a decrease in he price of purchased inpus, like ferilizer, ma well be a more powerful polic insrumen han increases in oupu price. 5 7 1.2. Feaures of Agriculural Producion in LDCs Farmers as Producers and Consumers An imporan feaure of LDC agriculure ha makes suppl response difficul o calculae is ha peasan farmers are onl pariall inegraed ino he goods markes. The farm households are boh producers and consumers of agriculural oupu, much of which never leaves he farm (see Week 3, Da 2, on household models). The firs priori for he peasan is o feed he household, and onl he surplus over and above he needs of he famil is markeed. In recen ears, sophisicaed models of household producion and consumpion have been developed (see Ellis 1988, for an inroducion) ha make i clear ha response will no be as sraighforward as in commercial agriculure Risk and Uncerain All farmers face risk which can be divided ino oupu uncerain and price uncerain 2. The commercial farmer has some advanages here, in ha a poor crop will carr a high price, bu he peasan ma be forced o sell land or animals o avoid sarvaion. A hese high sakes, risk aversion mus be expeced, and he response of peasan farmers o opporuniies ha increase uncerain ma be exreme cauion. Thus, when new echnologies, such as high ielding seed varieies are inroduced, small farmers ma onl be able o respond if here are supporing policies like cheap credi and feriliser subsidies ²Expecaions, Disequilibria and Adjusmen One paricular elemen in he heor of producion will be deal wih more full. So far, he analsis has concenraed on equilibrium posiions, bu in reali, he farmer will be in a consan sae of adjusmen, reacing o changing prices and oher condiions. This can be included in he analsis b inroducing disequilibria and price expecaions and b making a disincion beween shor and long run responses The Marke Suppl Curve The analsis so far has deal wih he behaviour of he individual producer, whereas aenion now urns o he aggregae oupus of all farmers ogeher. The whole is made up of he sum of he pars, so he earlier work gives a good basis for his analsis. In paricular, he marke suppl curve is derived b summing he individual suppl curves, so he same relaionships hold in general. However, here are also differences; if one farm increases is oupu, i will no affec he price of inpus or he price of oupus, bu when all farms respond ogeher, inpu prices will end o rise, and unless demand is perfecl elasic, an increase in he oupu of he indusr will drive oupu prices downwards Suppl curve shifs We have esablished ha he suppl curve is upward sloping in he previous secion. How seepl he suppl curve rises, will depend on he elasici of suppl of inpus. If some facors, such as land are relaivel fixed in suppl, hen aemps o increase oupu will drive up heir prices rapidl, and he suppl curve will have a seep slope. If here are few relaivel fixed 2 For sudies on risk see Behrman (1968), Ran (1977), Baile and Womack (1985), Brorsen e al (1985), Jus (1974), Hur and Garcia (1982) and Traill (1978). 6 inpus, he suppl curve will rise more slowl and a price will cause a greaer quani response. The relaionship will be measured as an elasici. Suppl response also depends on he price of oher crops ha compee for resources, he price of inpus, weaher, insiuions and echnolog. Some of hese will be discussed. In case of join producs like coon and coonseed, or wool and muon, one canno be produced wihou he oher, so boh prices will maer. Technical joinness for oupus like hese ma be a special case, bu in Africa agriculural monocropping is relaivel rare. The relaionship beween he suppl of one produc and he price of anoher requires careful analsis based on local knowledge. Mos small farmers inercrop a wide varie of plan species, so ha here ma be a complex agronomic inerdependence beween crops ha will onl be known o local expers. For insance, coffee or bananas ma be grown wih maize for shade, and beans or peas ma be planed beween he rows for ground cover. Thus, here ma be a degree of agronomic complemenari or subsiuabili beween crops. Once seasonali is aken ino accoun, a furher form of inerdependence arises. If a crop has a growing season ha fis convenienl beween maize crops, i ma be grown because i does no compee wih maize for land or labour. Anoher crop ma require planing or harvesing a he same ime as maize, and herefore, be compeiive wih maize. The common presumpion ha crops compee for land ma be rue of some producs and no ohers. Whea and maize ma be compeiive, bu neiher are likel o compee for land wih swamp rice. Weaher is obviousl ver imporan wih respec o shifing he suppl curve. If he monsoon fails in Asia, he effec can be caasrophic. African weaher paerns are more variable and difficul o deal wih, bu canno be ignored, as he devasaing effecs of periodic droughs in he Sahel, Ehiopia, he Sudan and Souhern Africa have shown. Ofen he bes we can do is o consruc a weaher index from rainfall and emperaure daa and include his in he analsis o a leas pick up he effecs a a broad level of aggregaion. Insiuions consiue anoher imporan facor. The include, he sae of he infrasrucure, credi, exension and irrigaion as well as he efficienc of he markeing boards and he rules governing maers like land enure. Technolog is clearl ver imporan and has been a favourie opic of agriculural developmen economiss in recen ears. The assumpion is ha improved echnolog is generaed b agriculural research ssems and is spread o farmers b he exension services - alhough i has been recognised ha on-farm experimenaion, b farmers, is also criical. The effec on he suppl curve of changes in hese variables is summarised in Table 1. A negaive shif means a movemen of he suppl curve (in he lower par of figure 1) upwards and o he lef. A plus sign means a movemen downwards and o he righ. 7 Table 1: Shifing he Suppl Curve Increase of improvemen in: Effec on suppl Price of an alernaive produc (-) Price of a join produc (+) Price of inpus (-) Sae of echnolog (+) Naural environmen (+) Economic environmen (insiuions and organisaions) (+) 1.4. Elasiciies of Suppl Tpicall, we wan o know elasiciies which ell us he proporional change in quani ha resuls form a proporional change in price. Noe ha, alhough he exbooks picall pu price on he verical axis, as in figure 1, elasiciies rea quaniies as he dependen variable, which should be on he verical axis. To preven confusion, figure 1 is re-drawn wih quani on he verical axis; hus, figure 2 maches he expressions for he elasiciies which follow. [Figure 2: The Suppl Curve: Quani as a Funcion of Price ] Own-Price Elasici of Suppl This is he relaionship shown in figure 2; i is he proporional change in he quani supplied of a good in response o a proporional change in is price. I can be defined as: s ε p = ( Q - Q )/ Q ( P 1 -P 0)/ P0 where ε p is he price elasici, he Qs are oupu quaniies and he Ps are oupu prices. Again, he elasici is calculaed for a single poin on he suppl curve - for ver small changes. Equaion (8) can be rearranged b collecing ogeher he changes and he saring values, o show ha an elasici is alwas a relaionship beween a marginal and an average value (see equaions (2) - (4) and figure 1 and 2): ε = (Q - Q )/Q ( P - P )/ P = s p Q - Q P - P Q / P The raio (Q 1 - Q 0 )/(P 1 - P 0 ) is he slope of he suppl curve (DGS in figure 2), and he raio (Q 0 /P 0 ) or (0,Q 0 /0,P 0 ) defines he slope of a line from he origin o a poin on he curve (0G in figure 2). Then (δq/δp)/(q/p) is he marginal relaionship beween Q and P a an poin such as G - he slope of he curve - divided b he average relaionship a he same poin. The las erm shows ha he elasici can be convenienl expressed as he raio of he changes in he logarihms of he variables. Thus, we will find ha if we ransform our daa ino logarihms 8 = δq/ δp Q/ P = δlnq δ ln P 8 9 before esimaion, he parameers we esimae will be he elasiciies we require, wihou furher calculaions being required. In figure 2, he marginal relaionship is posiive and consan, while Q/P is posiive and increasing as we move ou along he suppl curve from G o S. A S, i is greaer han a G, so he elasici (marginal over average) will be lower. So, he elasici will be considerabl greaer han uni, for low levels of oupu like Q Y0, and will approach one as oupu becomes ver large. This is no a general proposiion, bu i is rue of all sraigh line suppl curves wih posiive inerceps on he price axis. If he value is less han uni, suppl is said o be inelasic and if i is greaer han one, i is described as elasic. Unless here is a ver special reason o expec oherwise, own-price elasiciies should be posiive. The size of he elasici should depend o a considerable exen on he period allowed for adjusmen. If he price increases afer planing ime, more work on he crop can sill raise ields, bu here will be no response in erms of greaer acreage being planed. Over a long period of ime farmers will have he chance o full adjus o changes, bu his can be expeced o ake a few ears for annual crops. For ree crops, ha ield lile or nohing for some ears afer planing, he adjusmen ma be a decade or more. So in general, long-run elasiciies should be noiceabl greaer han shor run responses. As a general rule, responses are larger for minor crops, clearl i is no hard o double he oupu of a crop ha accouns for a couple of percen of he value of oupu, bu i is quie anoher maer o double he oupu of he main foodgrain crops Cross-price Elasici This is he proporional change in he quani of one good due o he change in he price of anoher good. Le he firs good be Y and he second good be Z. Then he cross price elasici can be defined as: ε pz The expecaion is ha major crops will be subsiues, because he compee for land and labour. When he price of whea rises, he quani produced increases a he expense of rice. So, here should be a negaive relaionship beween oupu of he good and he price of an alernaive. Bu, as noed above, some crops will be unrelaed and join producs and oher forms of complemenari are possible. So, he possibiliies are; if ε pz 0, hen Y and Z are compeiive (subsiues) if ε pz = 0, hen Y and Z are no relaed if ε pz 0, hen Y and Z are complemens/join producs. = Q - Q P z - P Q / P z 1 0 z = δq / δ Pz δ lnq = Q / Pz δ ln P z 10 9 Oupu Elasiciies wih Respec o Inpu Prices The elasiciies of oupu wih respec o inpu prices, P i are defined as: ε pi where he P i s now refer o inpu prices. These should usuall be negaive, meaning ha a fall in he inpu price should increase oupu. However, if he oal change is spli ino a subsiuion effec and an oupu effec, he oupu effec can be negaive Esimaion of he Parameers of Suppl Funcions = Q - Q Y P i - P Q / P i 1 0 i Our objecive is o derive esimaes of he parameers of he suppl funcions, usuall for paricular crops, in order o be able o consruc suppl projecions. These allow us o compare he effecs of changes and inpu prices, hence faciliaing he analsis of polic alernaives, which is our goal. Wih limied daa, usuall ime series, a he naional aggregae level, our resuls should be reaed as useful indicaors of he rue sae of he world, raher han as an solid conribuion o knowledge Basic Suppl Funcion Esimaion A number of approaches have been adoped in modelling agriculural suppl. The approaches range from he fairl ad hoc single equaion models o more heoreicall rigorous duali models. This paper will no deal wih he duali models, which is lef o he nex chaper. Following he discussion above, he suppl funcion of good Y is made dependen on is own price, he price of oher producs (including join producs), inpu prices, echnolog, he environmen, insiuional facors and he weaher. A funcional form for he suppl response relaionship mus be chosen, and i is convenien o begin wih he hpohesis ha he suppl curve is linear. If onl he own-price of he good changes, he suppl curve can be described b he linear equaion: Q = α + βp where α is he inercep and β is he slope of he suppl curve. However, since he oher variables in he suppl funcion will change over ime, he mus also be included, giving he suppl funcion: Q i = a 0 + ap 1 i + a2p j + a3p k + a4i + a5 + a6w = where Q i is he phsical quani of he good, P i is is price, P j is he price of alernaive producs (an index of aggregae producer prices, or several separae prices), P k is he price of he inpus (an aggregae index, or several separae inpus), I represens infrasrucure (perhaps he proporion of he acreage irrigaed, alhough here could be several separae variables), is ime, which is a prox for echnical c
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