Endogenous risk and long run effects of liberalisation in a global analysis framework

E n d o g e n o u s r i s k a n d l o n g r u n e f f e c t s o f l i b e r a l i s a t i o n i n a g l o b a l a n a l y s i s f r a m e w o r k B y

Jean -M ar c B O U S S AR D 1_{, Fr an ç o ise G E R AR D} 2_{, M ar ie G ab r iel l e P IK E T T Y} 3_,

M o ur ad AY O U Z 2 an d T an c r è d e V O IT U R IE Z 2

P a p e r s u b m i t t e d t o t h e S e v e n t h A n n u a l C o n f e r e n c e on G l o b a l E c o n o m i c A n a l y s i s

1 _{INRA-M ona, 4 5 bi s Avenue de la B elle G abri elle, 9 4 7 3 6 Nog ent sur M arne, F ranc e} 2 _{C IRAD -E c opol, 4 5 bi s Avenue de la B elle G abri elle, 9 4 7 3 6 Nog ent sur M arne, F ranc e} 3_{U S B , S ao P aulo , B rasi l}

A b s t r a c t

In a classical Walrassian framework of smoothly functioning markets and comparative static analysis, the b eneficial effects of trade lib eralisation are well known. In the real world, production decisions develop along time. T hey are fringed with uncertainty, and sub j ect to unfulfilled ex pectations. D epending upon demand elasticity, such phenomena lead to converging or diverging cob web s. Y et, even if demand is inelastic, diverging cob web s are rarely ob served, b ecause there ex ist also many return strings which call systems b ack in the vicinity of ( unstab le) eq uilib rium. A mong the latter, as already noticed b y K nut Wicksell in the 1 9 3 0 ’ s, attitudes toward risk and investment functions play a large role. In effect, introducing such mechanisms into a dynamic market eq uilib rium leads to “ chaotic motion” , a now well documented mathematical b eing, with very specific characteristics.

In this contex t, market price fluctuations no longer occur b ecause of the “ hand of G od” , from completely ex ternal sources, such as climatic events. T hey are endogenous, generated b y the market itself. While ex ternal risk is sub j ect to the “ law of large numb er” , thus allowing for the b enefit of risk pooling through insurance mechanisms, endogenous is not. In particular, any effort to lower individual decision maker ex position to risk affects the values of the key model parameters, such as supply elasticity, thus changing the risk regime itself. N ow, while many studies ( especially b y H ertel et al) have b een undertaken in order to elicit the conseq uences of ex ternal risk for the magnitude and distrib ution of the trade lib eralisation b enefits, the endogenous risk case has generally b een b enignly ignored b y the world research community. T he present paper aims at filling this gap.

T o this end, a G T A P model along that line is developed, with and without agricultural lib eralisation. It is shown that, after a while, the tendency to divergence is smoothed out b y risk considerations. Y et, b ecause of a greater price uncertainty, over 6 0 years, long run world growth is significantly affected b y lib eralisation. Increased price volatility plays the role of a negative technical progress, which offset the b enefits from a more efficient use of comparative advantage. D istrib utional effects are discussed, b oth b etween regions and within. R esults suggest that lib eralisation is not likely to reduce poverty, q uite the contrary, b ecause rich are less risk averse than poor, and thus, can accumulate more reinsvestib le b enefits. H owever, richest nations do not b enefit in the whole, b ecause of the investment slowing down mechanism outlined ab ove.

E fforts have b een done to test the model, taking opportunity of its dynamic character, which allows for the comparison b etween “ predicted” and “ actual” series. A lthough results in this respect can still b e very much improved, price regimes from this model are compared with a few actual long run ob served series, and found to b e similar. T he paper b riefly discuss the difficulty of such comparisons, which, b ecause of the “ sensitivity to initial condition” , cannot b e reduced to the simple point per point measurement of the discrepancy b etween “ predicted” and “ ob served” . S eries must b e characteriz ed b y glob al indices, such as moments or F ourrier spectrums.

M ost of these results very much contradict common wisdom. T his is why they are interesting. M ore research is thus needed to specify the deep sources of this outcome and their political significance.

Table of c on t en t

I n t r o d u c t i o n : F r o m t h e W a l r a s s i a n t o t h e W i c k s e l l i a n f r a m e w o r k . I - T h e t h e o r y o f c h a o t i c m a r k e t s :

A) T he essen c e o f c hao t ic mo t io n an d t he l o c al d y n amic in st ab il it y t heo r y B ) Ho w c an c hao s o c c ur in mar ket s ?

C ) W id en in g t he sc o pe: r isk in G en er al E q uil ib r ium M o d el s I I - A G e n e r a l D i s e q u i l i b r i u m M o d e l

A) T ime an d r isk in C G E M ’ s

B ) P r ac t ic al impl emen t at io n : eq uil ib r ium eq uat io n s C ) P r ac t ic al impl emen t at io n : r ec ur r en c e eq uat io n s D ) D at a an d o t her set t in g s

E ) S ust ain ab il it y an d c o mput in g c o n sid er at io n s P a r t 3 : R e s u l t s

A) W il l t r ad e l ib er al izat io n in c r ease wel f ar e ? B ) Is t hat c r ed ib l e ?

I n t r o d u c t i o n : F r o m t h e W a l r a s s i a n t o t h e W i c k s e l l i a n f r a m e w o r k

Al t ho ug h en o r mo us r ec en t pr o g r esses have b een mad e in d at a c o l l ec t io n an d c o mput in g , f r o m an an al y t ic al po in t o f view, t he g en er al eq uil ib r ium mo d el s pr esen t l y in use ar e c o n c ept ual l y an d ec o n o mic al l y st il l ver y simil ar t o t he o r ig in al c o n c ept d evel o ped b y L é o n W al r as mo r e t han o n e c en t ur y ag o ( W al r as, 1874). Y et , just as ec o n o mic t heo r y as a who l e, t hey d o have muc h l ar g er po t en t ial t han t he st r ic t W al r assian f r amewo r k, so g en ial an d in ad van c e o n his t ime as it mig ht have b een .

A whit e st o n e in po st W al r assian an al y sis is c er t ain l y t he wo r ks b y K n ut W ic ksel l ( 1898) ( see B l an c har d , 20 0 1) who in t r o d uc ed t he id ea o f c umul at ive pr o c esses an d d iseq uil ib r ia, st r essin g t he impo r t an c e o f expec t at io n s, an d o pen in g t he way f o r t he K ey n esian an al y sis. C an W ic ksel l ’ s id eas in t hese mat t er b e in t r o d uc ed in t o a C G E mo d el , just as was t he c ase wit h W al r as’ s ? T he pr esen t paper is an at t empt in t hat d ir ec t io n .

In ef f ec t , t he t hr ee key po in t s in W ic ksel l an al y sis ar e t hat :

a) A smal l d epar t ur e f r o m eq uil ib r ium may t r ig g er a “ c umul at ive pr o c ess” , b y whic h t he sy st em mo ve c o n t in uo usl y away f r o m “ o pt imum” , eit her shr in kin g o r expan d in g in d ef in it el y ( in val ue if n o t in “ r eal ” t er ms).

b ) T her e ar e n ever t hel ess l imit s t o t his pr o c ess, b ec ause a t o o l ar g e d isc r epan c y b et ween expec t at io n an d r eal it y is n o t sust ain ab l e. Al t ho ug h he sug g est ed sever al mec han isms b y whic h t hese l imit s c an mat er ial ize, o n e par t ic ul ar l y in t er est in g is t he f ac t t hat b an ks mig ht b e “ af r aid ” o f l o an s expan d in g c o n t in uo usl y .

c ) Ad just men t s o c c ur t hr o ug h “ un f ul f il l ed expec t at io n s” an d “ in vo l un t ar y ” savin g s in st o c ks, wit h t he f amo us d ist in c t io n o per at ed b et ween t he ex ante an d t he ex post eq uil ib r iums.

N o wad ay s, t he ab o ve c o n sid er at io n s ar e t he b asic in g r ed ien t s o f d y n amic c hao t ic mo d el s. W e shal l t hus f ir st r ec al l t he t heo r y r eg ar d in g suc h mo d el s, pr esen t l y at t he exac t o ppo sit e o f t he g en er al eq uil ib r ium an al y sis main st r eam. W e shal l t hen sho w why may suc h t heo r y b e n ever t hel ess r el evan t , espec ial l y when ag r ic ul t ur al t r ad e l ib er al isat io n is un d er examin at io n . W e shal l pr esen t t he r esul t s o f an empir ic al mo d el b uil t al o n g t hat l in e. An d we shal l en d wit h pr ac t ic al po l ic y impl ic at io n s o f suc h an appr o ac h, as wel l as wit h q uest io n s r eg ar d in g t he val id it y o f al t er n at ive mo d el s.

I - T h e t h e o r y o f c h a o t i c m a r k e t s A ) T h e e s s e n c e o f c h a o t i c m o t i o n

Fr o m a mat hemat ic al po in t o f view, a c hao t ic mo t io n is just a spec if ic kin d o f so l ut io n f o r a d y n amic d if f er en t ial eq uat io n . E ver y b o d y kn o ws t hat a d if f er en t ial eq uat io n f &(x&&,x,x,t)=0, ( wher e x&& an d x& st an d f o r t he sec o n d an d f ir st d er ivat ive o f x( t ) wit h r espec t t o t ime t ) may have “ expl o d in g ” so l ut io n s ( t hat is, x( t ) g r o wt hs in d ef in it el y wit h t ime), o r so l ut io n s c o n ver g in g t o a l imit , o r “ per io d ic ” so l ut io n s, x= f [ sin ( 2πωt )] , impl y in g t hat x( t ) c o mes o ut t o b e eq ual t o it sel f at r eg ul ar in t er val s. Y et , t hese pat t er n s d o n o t exhaust po ssib il it ies. T her e is al so a po ssib il it y t hat x( t ) is n ever per io d ic , whil e n o t g r o win g t o in f in it y , n o r r eac hin g a l imit . T his sit uat io n is c al l ed a “ c hao t ic so l ut io n ” t o t he d y n amic eq uat io n . In g en er al , it is n o t

po ssib l e t o expr ess a c hao t ic mo t io n al g eb r aic al l y whic h d o es n o t mean s t hat it d o es n o t exist4_.

W hat is per haps mo r e c o un t er in t uit ive is t hat t he same d y n amic eq uat io n may l ead t o d if f er en t r eg imes, d epen d in g upo n t he val ue o f spec if ic par amet er s ( r ef er en c es ? ). T hus, t he mer e spec if ic at io n o f a t heo r et ic al mo d el is n o t suf f ic ien t t o war r an t a q ual it at ive so l ut io n : an o r d er o f mag n it ud e must b e spec if ied f o r t he par amet er s. E ven so , in t he par amet er spac e, t he d o main f o r whic h so l ut io n s ar e c hao t ic may n o t b e a st an d ar d “ vo l ume” c l ear l y d el imit ed b y l in es o r pl an es o r hy per pl an es t he eq uat io n s o f whic h c o ul d b e so ug ht f o r . M o st o f t he t ime, suc h d o main s ar e “ f r ac t al s” , t hat ar e c o mpl ic at ed g eo met r ic f ig ur es. Fo r t hese r easo n s, c hao t ic mo t io n r ar el y c an b e t he sub jec t o f pur el y an al y t ic al t r eat men t . P r ac t ic al mo d el l in g an d exper ien c es ar e n ec essar y .

Y et , t her e ar e c o n st an c ies in po t en t ial l y c hao g en ic sit uat io n s. An essen t ial c o n d it io n f o r c hao s is t hat at l east o n e eq uil ib r ium po in t b e in st ab l e ( o r “ r epel l in g ” , o r “ a wel l ” ). O t her wise, if t he eq uil ib r ium is an at t r ac t o r , o f c o ur se, t r ajec t o r ies have a t en d en c y t o c o n ver g e t o war d t hat po in t ( it is t hen “ at t r ac t in g ” , o r “ a sin k” ) . B ut a r epel l in g eq uil ib r ium po in t is n o t suf f ic ien t t o g en er at e a c hao t ic d y n amic s. An o t her c o n d it io n is t hat when t hey ar e f ar away , t r ajec t o r ies ar e at t r ac t ed b ac k t o war d eq uil ib r ium. O t her wise, if an y po in t o f t he phase spac e is r epel l in g , t r ajec t o r ies mo ve away t o in f in it y . If t hese t wo c o n d it io n s ( l o c al l y un st ab l e eq uil ib r ium po in t and a “ r et ur n spr in g ” mo vin g b ac k t o war d it ) ar e f ul f il l ed , o n e o f t he n at ur al o ut c o mes is a per io d ic mo t io n , as wit h a f r ic t io n l ess pen d ul um, b ut c hao s c an o c c ur as wel l .

B ) H o w c a n c h a o s o c c u r i n m a r k e t s .

C an suc h sit uat io n s o c c ur in mar ket s ? T he b asic r ef er en c e o n t his issue is c er t ain l y E zekiel ( 1938) , wit h it f amo us “ c o b web t heo r em” . It sho ws t hat wit h “ n aï ve expec t at io n s” , a mar ket eq uil ib r ium po in t may b e r epel l in g , if d eman d is r ig id .

In d eed , wit h n aï ve expec t at io n s, assumin g l in ear suppl y an d d eman d c ur ves ( o r “ l in ear ized ” ) pt an d q t st an d in g f o r t ime t q uan t it y an d pr ic e, an d t b ein g d isc r et e, t hen :

( 1) pt=α_apt−1+aβ_a−b

wit h ( α,β) b ein g t he d eman d c ur ve sl o pe an d in t er c ept , an d ( a,b ), t he suppl y c ur ve sl o pe an d in t er c ept . If α_a ≥1, t hen t her e is n o l imit f o r pt whic h g r o wt hs t o in f in it y ( b y al t er n at e

val ues, sin c e α is n o r mal l y n eg at ive) as t ime passes.

Y et , t he c o b web mo d el is c l ear l y in suf f ic ien t , sin c e n o b o d y n ever saw an y pr ic e g r o win g t o in f in it y ( espec ial l y min us in f in it y ). T hus so met hin g must b e c al l in g b ac k t he sy st em t o war d eq uil ib r ium when it c o mes t o st ay t o o f ar away . M an y suc h d evic es c an b e imag in ed , b ut t he simpl est is pr o b ab l y pr o vid ed b y r isk c o n sid er at io n s, as al r ead y n o t ic ed b y W ic ksel l when he was seekin g exac t l y t he same kin d o f mec han ism t o pr even t t hat b usin ess c y c l e r eac h in f in it y . B o ussar d ( 1996) sug g est ed t o in t r o d uc e r isk c o n sid er at io n s in t o t he c o b web mo d el . L et us suppo se t hat pr o d uc er s maximize t he pr o f it c er t ain t y eq uival en t ( in V o n N euman sen se) , g iven expec t ed pr ic e pˆt , expec t ed pr ic e var ian c e σˆt2an d a,b ,α,β as ab o ve. T hen , A

4_{Af ter all, i t i s not possi ble to express e}x _{or L og ( x) alg ebrai c ally , w h i c h does not prevent th ese f unc ti ons to be} f am i li ar to ec onom i sts.

b ein g t he pr o d uc er ab so l ut e r isk aver sio n , t he expec t ed pr ic e assumed c o n st an t p~ , an d t he var ian c e expec t at io n b ein g “ n aï ve” , t hus 2

1 1

2 (ˆ )

ˆt=pt− −pt−

σ _{. O n t he o t her han d , l et us assume}

t hat t he suppl y c ur ve is id en t ic al t o mar g in al c o st , t he pr o d uc er o pt imal it y c o n d it io n is : ( 2) pˆt−σˆétqt=aqt+b

In t r o d uc in g t hese c han g es in t o t he t r ad it io n al c o b web mo d el , o n e g et t he f o l l o win g expr essio n f o r q t = f ( q t-1) : ( 1b is) ₂ 1 ) ~ ( ~ β α − − + − = − t t _{a Ap}p _qb q

T his is a ver y in t r ic at e f o r mul a, d espit e t he mo d el simpl ic it y . N o w, f o r so me par amet er val ues, it pr o d uc es even mo r e c o mpl ic at ed o ut c o mes, as pl o t t ed o n f ig ur e 1 .

Figure 1 : Constant mean expectation risk y cob w eb

There is nothing random in this graph… The red and blue curves are with the same parameters, and start at about the same point. They part one f rom each other, j ust as two

ex ponential do.

O t her “ r et ur n spr in g s” c an b e imag in ed . E spec ial l y , t he c apit al st o c k, whic h ac t s as a memo r y in an y ec o n o mic sy st em, c an b e in vo l ved in suc h mec han isms. As f ar as c apit al is un d er empl o y ed , t he suppl y c ur ve may b e el ast ic . It b ec o mes ext r emel y r ig id as so o n t he c apit al st o c k is f ul l y empl o y ed , if n ew mac hin es c an n o t b e pur c hased at o n c e. Ag ain , t his kin d o f sit uat io n is l ikel y t o d r ive b ac k mar ket s t o war d eq uil ib r ium, even if t he l at t er ar e in st ab l e. T hus, as so o n as:

i - expec t at io n s may n o t b e exac t l y f ul f il l ed , an d ,

a mar ket may n o t n ec essar il y c o n ver g e. In st ead , it may r o c k up an d d o wn , b o t h in q uan t it y an d in pr ic e. B ec ause suc h d y n amic is sen sit ive t o in it ial c o n d it io n s, it is t hen un pr ed ic t ab l e, even if n o t sub mit t ed t o an y r an d o m c o n t in g en c y ( b ut f o r t he in it ial c o n d it io n s).

C) W id ening th e scope : risk into general eq uil ib rium mod el s

W hat has just b een said , wit h o n e pr o d uc t , o n e pr o d uc er an d o n e c o n sumer , is pr o b ab l y even mo r e r el evan t f o r r eal wo r l d mar ket s, wit h man y c o mmo d it ies an d mul t ipl e eq uil ib r iums. E spec ial l y , in t he mul t id imen sio n al c ase, t wo spec ial l y pr eo c c upy in g pr o b l ems ar ise.

a) In a mul t id imen sio n al sy st em, an eq uil ib r ium po in t may n o t b e in st ab l e in al l d ir ec t io n s. M o st o f t he t ime, it st an d s as a “ sad d l e po in t ” , wit h o n e ( o r mo r e) d ir ec t io n ( s) l o o kin g l ike an at t r ac t in g sin k, an d o n e ( o r mo r e) o t her d ir ec t io n ( s) l ike a wel l . Ho wever , in suc h a c ase, as so o n as t he t r ajec t o r y o f t he who l e sy st em c o mes c l o se t o t he eq uil ib r ium, it is pushed away in t he r epel l in g d ir ec t io n . T hus, even if a sub sy st em may l o o k st ab l e, t he simpl e c o n sid er at io n o f t he un st ab l e po r t io n o f t he who l e may make n ec essar y r ec o n sid er in g t his c o n c l usio n 5 _{In pr ac t ic e, a g en uin el y st ab l e mar ket , f o r in st an c e a l uxur y g o o d , wit h a l ar g e}

d eman d el ast ic it y , may ver y wel l b e “ po l l ut ed ” b y a f o o d c o mmo d it y mar ket , t he in st ab il it y o f whic h d er ives f r o m t he c o r r espo n d in g d eman d in el ast ic it y .

b ) As f ar as t wo suc h c hao t ic sy st ems ar e iso l at ed o n e f r o m eac h o t her , t hey may l o o k “ c o mpl emen t ar y ” , in t he sen se t hat a peak in o n e o f t hem may c o r r espo n d t o a ho l l o w in t he o t her . In suc h a c ase, it is ver y t empt in g t o st ab il ise mar ket s b y mer g in g t he t wo in o n e. Ac t ual l y , t his r easo n in g is t he c o r e o f a ver y st r o n g ar g umen t f o r t r ad e, wit ho ut c o mpar at ive ad van t ag es ( B al e an d L ut z, 1979). It wo ul d b e per f ec t l y val id if t he so ur c e o f in st ab il it y wer e t o b e f o un d in t o c o mpl et el y exo g en o us c ir c umst an c es, suc h as c l imat ic even t s. B ut t his is n o t t r ue an y mo r e her e, wit h t he en d o g en o us in st ab il it y un d er d isc ussio n . O n t he c o n t r ar y , t her e may b e a ver y per ver se ef f ec t o f mer g in g t wo pr evio usl y iso l at ed c hao t ic mar ket s: in st ead o f f l uc t uat in g in d epen d en t l y o n e o f eac h o t her , t hey may t hen f l uc t uat e “ in phase” , just as t wo r ad io set s c o r r ec t l y t un ed .

T he q uest io n whic h ar ises at t his po in t is t hen : al l t hat is pur el y t heo r et ic al . W hat ab o ut r eal mar ket s ? T his is t he q uest io n we t r ied t o l o o k at , b y b uil d in g up a mo d el whic h pr esen t s mo st o f t he c har ac t er ist ic s o f a C o mput ab l e G en er al E q uil ib r ium ( C G E ) mo d el , exc ept t hat , in st ead o f assumin g eq uil ib r ium is r eac hed ever y t ime wit ho ut pr o b l ems, we sy st emat ic al l y al l o w f o r sit uat io n s wit h a l ag b et ween t he d ec isio n s t o pr o d uc e an d t he d ec isio n t o c o n sume, in t he spir it o f t he c o b web mo d el . Y et , un l ike t he c o b web mo d el , we al so sy st emat ic al l y pr o vid e a set o f r easo n ab l e “ r et ur n spr in g s” , in t he spir it d esc r ib ed ab o ve, t hus en sur in g t hat t he sy st em, in st ead o f mo vin g away at inf initum, wil l b e kept wit hin a “ pipe” . As we wil l se, r isk pl ay an impo r t an t r o l e in d ef in in g t his “ pipe” .

5 _{A very f am ous anec dote i n th i s respec t i s th e « th ree body problem » parti ally solved by P oi nc aré at th e end of} th e 1 9 th _{c entury : C onsi deri ng a sy stem i n R}2 _{w i th one sun, one planet and one asteroi d, h e c onc luded to stabi li ty} and reg ular elli pti c orbi ts. In R3_{, th ere i s th e possi bi li ty of an unstable si tuati on, w i th th e asteroi d roc k i ng} betw een i nc om plete orbi ts around th e planet and around th e sun. E ventually , suc h si tuati ons w ere ac tually observed.

I I - A general d iseq uil ib rium mod el A ) - T ime and risk in CG E ’ s

T he n o t io n o f eq uil ib r ium is essen t ial l y st at ic : ear l y C G E ’ s wer e c o n sid er ed as a pic t ur e o f a l o n g r un per man en t sit uat io n , “ af t er al l ad just men t s have b een mad e” . Y et , t he exist en c e o f c apit al makes t his sit uat io n un r eal ist ic : if savin g s exist , it must in c r ease c apit al st o c k. T hus, ver y q uic kl y , mo st G G E ’ s wer e g iven a t ime d imen sio n . T wo po ssib il it ies exist in t his r espec t :

i- O n e is t o t r an sl at e t he st an d ar d mul t iper io d t heo r et ic al Ar r o w-D eb r eu mo d el in t o a c o mput ab l e mo d el , just ad d in g a t ime sub sc r ipt t o al l pr ic es an d q uan t it ies, as d o n e b y suc h aut ho r s as D evar ad jan ( 1995 ). A main ad van t ag e o f t his appr o ac h is t hat savin g s is t hen per f ec t l y c o n sist en t wit h t he n eo c l assic al t heo r y o f savin g s, even in pr esen c e o f r isk( whic h, in t his c ase, may b ec o me o n e o f t he d et er min an t o f t he d ic o un t r at e6_{). C o n c ept ual l y , it is n o t}

ver y d if f ic ul t . P r ac t ic al l y , even wit h t he mo st po wer f ul c o mput er s, t his is a har d t ask.

ii- An o t her po ssib il it y is t o set up a “ r ec ur sive mo d el ” , t hat is a mo d el whic h is so l ved f o r eq uil ib r ium eac h “ y ear ” , t he “ y ear t st o c k o f c apit al ” b ein g r el at ed wit h “ y ear t -1” t hr o ug h savin g s an d d epr ec iat io n . A d if f ic ul t y her e is wit h t he f ac t t hat savin g s may n o t b e “ o pt imal ” , al t ho ug h t hat a vag ue r ef er en c e t o a st r an g e mix o f K ey n es an d Fr ied man al l o ws mo st aut ho r s t o d ef in e it as a c o n st an t f r ac t io n o f in c o me. E ven so , a d if f ic ul t y st il l exist s, b ec ause eac h y ear , t he n ew c apit al must b e al l o c at ed t o o n e o r an o t her sec t o r . T he q uest io n t hen ar ise o f t he n at ur e o f c apit al , “ put t y -put t y ” , “ c l ay -c l ay ” , an d so o n … . M o st o f t he t ime, C G E ’ s aut ho r s assume t hat o l d c apit al is spec if ic f o r eac h sec t o r o f t he ec o n o my ( t hus, a c o mb in e har vest er c an n o t b e used t o pr o d uc e el ec t r ic it y ) whil e n ew c apit al is al l o c at ed b et ween sec t o r s t han ks t o a pr o f it d r iven in vest men t f un c t io n .

T he r ec ur sive appr o ac h is o f t en viewed as a pr o xy f o r t he “ b et t er , b ut mo r e d if f ic ul t ” mul t iper io d appr o ac h7_{. Y et , it mig ht have it s o wn just if ic at io n , pr ec isel y if r isk an d imper f ec t}

f o r esig ht ar e c o n sid er ed .

In ef f ec t , t he r isk c o n sid er at io n s pr esen t in t he t heo r et ic al appr o ac hes q uo t ed ab o ve is q uit e d if f er en t f r o m what we had in min d in t he f ir st sec t io n o f t his paper . T he n eo c l assic al r isk is exo g en o us. It o r ig in at es in “ t he han d o f G o d ” . N o l in ks exist b et ween ag en t s b ehavio ur an d t he r isk man g n it ud e. It d o es n o t mean t hat ag en t s c an n o t c ho o se t heir r isk expo sit io n l evel s – o n t he c o n t r ar y , mo st o f t he mo d el s in t r ic ac ies ar e c o n seq uen c es o f t he way s suc h c ho ic es ar e mad e. B ut t hese b ehavio ur al assumpt io n s have n o c o n seq uen c es upo n t he r isk g en er at io n mec han ism it sel f .

O n t he c o n t r ar y , t he r isk d esc r ib ed ab o ve is t he c o n seq uen c e, n o t o f exo g en o us sho c ks, b ut o f expec t at io n s er r o r s. N o t hin g , in t he mo d el , is r an d o m. R isk an d in st ab il it y ar e pur el y en d o g en o us, an d pr o d uc ed b y t he mar ket it sel f , un d er so me c ir c umst an c es d epen d in g o n t he par amet er s val ues. T hus, er r o r s must b e pr esen t , whic h c o n t r ad ic t s t he “ r at io n al expec t at io n hy po t hesis” . W e shal l see t hat l eavin g t he r at io n al expec t at io n hy po t hesis o ut , r at her t han an

6 _{O f c ourse, th e num ber of w ri ters on th i s poi nt i s m uc h too larg e f or th at w e c an q uote any of th em . Y et, let us} m enti on H ertz ler ( 1 9 9 7 ) , as one outstandi ng rec ent c ontri buti on on th i s i ntri c ate q uesti on of th e relati on betw een di sc ount and i nterest rates and ri sk aversi on, as w ell as th e basi c ref erenc es, th e tw o papers, one by G randm ond and one by Radner in H i ldenbrand and S onnensc h ei n( 1 9 9 1 ) . .

7 _{T h i s poi nt w as c entral i n D ay ’ s analy si s of f arm ers dec i si on m ak i ng . It led h i m to bec om e a pi oneer i n c h aoti c} dy nam i c studi es. S ee D ay ( 1 9 6 3 , 1 9 8 2 )

d epar t ur e f r o m, mig ht b e a pr o g r ess t o war d r eal ism. In t his c o n t ext , a r ec ur sive sc heme, n o r mal l y sub jec t t o er r o r s, is just a l o g ic al c o n seq uen c e o f a r eal ist ic appr o ac h o f t he wo r l d . B ut if we c o n sid er t he “ r ec ur sive l o g ic ” at l east as a pr o misin g appr o ac h, we sho ul d n o t r est r ic t it t o t he o n l y pr o b l em o f c apit al . In par t ic ul ar , o n e o f t he spec if ic it y o f C G E ’ s mo d el sho ul d t hen b e q uest io n ed : t he simul t an eit y b et ween suppl y an d d eman d d ec isio n . In ef f ec t , in a “ st an d ar d ” C G E , at an y po in t o f t ime, g iven f ac t o r s, pr o d uc er s an d c o n sumer s pl an s ar e d r iven b y eq uil ib r ium pr ic e. T his is a c o n seq uen c e o f t he “ r at io n al expec t at io n ” assumpt io n 8. B ut o f c o ur se, suc h an assumpt io n is hig hl y d isc ussib l e. If we ad mit t he po ssib il it y o f expec t at io n er r o r s in c apit al d ec isio n s, t hen why sho ul d we n o t assume t hat t hey mat t er al so in so me pr o d uc er s b ehavio ur , espec ial l y when a sig n if ic an t d el ay exist s b et ween t he d ec isio n t o pr o d uc e an d t he d ec isio n t o sel l . .

T his, o f c o ur se, impl ies a d r amat ic r eappr aisal o f t he b asic phil o so phy o f C G E mo d el s. It wil l n o t b e easil y ac c ept ed b y ever y b o d y . Y et , t his appr o ac h st ay al o n g t he g en er al d evel o pmen t l in e o f t hese t o o l s t o war d mo r e r eal ist ic mo d el s. In t his n ew f r amewo r k, simul t an eo us eq uat io n s wil l n o t ser ve in c o mput in g a f ul l eq uil ib r ium b et ween pr o d uc t io n an d c o n sumpt io n , b ut o n l y b et ween c o n sumpt io n an d suppl y . T he suppl y it sel f wil l b e g en er at ed o n t he b asis o f expec t ed , in st ead o f eq uil ib r ium pr ic es– exac t l y as it d o es in t he o n e c o mmo d it y c o b web mo d el . O f c o ur se, wit h t he po ssib il it y o f er r o n eo us expec t at io n , in t r o d uc in g r isk is q uit e n at ur al , even in t he ab sen c e o f exo g en o us sho c ks ( whic h d o es n o t mean t he l at t er d o n o t exist ). T his is t he essen c e o f t he K n ut W ic ksel l messag e, a messag e whic h was seized up b y K ey n es l at er o n , an d un just l y f o r g o t t en sin c e9_.

B ) P ractical impl ementation : eq uil ib rium eq uations

T he pr ac t ic al impl emen t at io n o f t he pr in c ipl es set o ut ab o ve is n o t d if f ic ul t , an d d o es n o t r eq uir e an y mo r e d at a n o r c o mput at io n al skil l t han st an d ar d C G E mo d el .

In ef f ec t , r ed uc ed t o skel et o n , a st an d ar d r ec ur sive10 C G E c an b e d esc r ib ed wit h t he f o l l o win g eq uat io n s:

( 1) Fj ( . . . xi jt. . ) =

∑

h zhjt + i

∑

∈ JI_, xji t +

∑

_h vhjt , j∈J ( suppl y eq uat es d eman d )

( 2) φjt = pjt Fj ( . . . xi j. . ) -

∑

∈J i pi t xi jt -

∑

i_∈I πi t xi jt, j∈J ; ( pr o d uc er ’ s ut il it y ) ( 3)

∑

j xi jt =

∑

h ehi t ∈ ∀i I ( f ac t o r s avail ab il it y ) ( 4) uht = U ( . . . zhjt. . , sht), h∈H ; ( c o n sumer ’ s ut il it y ) ( 5)

∑

j pjt zhjt =

∑

i∈I ei ht πi t + sh, t h∈H ( c o n sumer ’ s b ud g et c o n st r ain t )

8 _{O r rath er, of a som ew h at naï ve versi on of th e rati onal expec tati on assum pti on. O f c ourse, nobody c an deny th e} relevanc e of assum i ng dec i si on m ak ers are rati onal i n proc essi ng th e i nf orm ati on avai lable to th em at a spec i f i c ti m e. B ut assum i ng rati onali ty does not i m ply i nf orm ati on i s perf ec tly relevant, and c annot g enerate errors or “ surpri se” .

9 _{At th i s poi nt, th at i s w h y , one sh ould th eref ore speak of di seq ui li bri um rath er on eq ui li bri um m odels.} 10 _{“ Rec ursi ve” h ere m eans th at plans x}

t m ade at ti m e t f or ti m e DEdepend on observed past values xt-1. H ow ever, xt m ay be eventually revi sed, i n suc h a w ay th at xt+ 1, 1 m ay be di f f erent f rom xt, 2 . T h us, i n th i s f ram ew ork , a m odel m ay be both rec ursi ve and m ulti peri odi c , alth oug h th e planni ng h ori z on i s only one i n all appli c ati ons below .

( 6)

∑

h sht =

∑

h

∑

j pjt vhjt h∈H ( val ue f o r savin g s)

( 7) ehi t = ehi t-1( 1 - δh i) + G ( . . vhjt… ) h∈H, i∈I ( r ec ur r en c e eq uat io n )

W it h t he set s I f o r f ac t o r s , J f o r c o mmo d it y , H f o r in st it ut io n , t f o r t ime; Fj ( . ) a pr o d uc t io n

f un c t io n , U ht ( . ) t he ut il it y f un c t io n o f c o n sumer h, an d G ( . ) t he in vest men t f un c t io n whic h

t r an sf o r ms in put s in t o f ac t o r s – main l y c apit al , b ut man po wer as wel l ; zhjt t he f in al

c o n sumpt io n o f c o mmo d it y j b y c o n sumer h; xi j t he q uan t it y o f c o mmo d it y o r f ac t o r i used as

in put f o r c o mmo d it y j ; vk jt t he d eman d o f c o mmo d it y j b y c o n sumer k f o r in vest men t , ehi ,

t he q uan t it y o f f ac t o r I b el o n g in g t o in st it ut io n h ; φjt , t hepr o f it o f in d ust r y j ; sht t he savin g s

b y in st it ut io n h , δhi a d epr ec iat io n r at e; pjt f o r c o mmo d it y pr ic es, πi t f o r f ac t o r s pr ic es.

T he mo d el is so l ved b y wr it in g t he f ir st -o r d er c o n d it io n s f o r pr o d uc er ’ s an d c o n sumer ’ s o pt ima, t hat ar e t he d er ivat ives wit h r espec t t o xi jt o f eq uat io n ( 2) sub jec t t o ( 3), an d t he

d er ivat ives wit h r espec t t o zhjt an d sht o f eq uat io n ( 4) sub jec t t o ( 5). It is t o b e n o t ic ed t hat ,

her e, t he o n l y in t er t empo r al eq uat io n is ( 7), whic h, appl ied t o c apit al , is t he b asic d y n amic al eq uat io n . O ur W ic ksel l ian ID 3 _{mo d el is d er ived f r o m t hese eq uat io n s, wit h t he f o l l o win g}

mo d if ic at io n s:

a) . A l ag b etw een prod uction and consumption d ecisions:

Fir st , a l ag is in t r o d uc ed b et ween t he pr o d uc t io n an d t he c o n sumpt io n d ec isio n s. E q uat io n ( 1) must b e r ewr it t en as:

( 1b is) Fj ( . . . xi jt-1. . ) =

∑

h zhjt + i

∑

∈ JI_, xji t-1 +

∑

_h vhjt , j∈J

T hus, t he mar ket eq uil ib r ium o c c ur s b y t he c o n f r o n t at io n o f l ast y ear ( g iven ) pr o d uc t io n , an d c ur r en t c o n sumpt io n . B ut t his mean s t hat pr o d uc t io n d ec isio n s must n o t b e t aken o n t he b asis o f eq uil ib r ium pr ic es. R at her , expec t ed pr ic es pˆjt must b e used . Hen c e eq uat io n ( 2) is

mo d if ied : (2b is) φjt = pˆ Fjt _j ( . . . x_{i j}. . ) -

∑

∈J i pi t xi jt -

∑

i∈I πi t xi jt j ∈ ∀iJ ; In ad d it io n , an expec t at io n f un c t io n E m( . ) must b e d ef in ed t o d et er min e pˆjt .

It is c l ear t hat d if f er en t expec t at io n sc hemes c an ( an d sho ul d ) b e en visag ed . In t he r un s pr esen t ed in t his paper , a N er l o vian ad apt at ive expec t at io n s sc heme wit h a 5% r evisio n c o ef f ic ien t has b een c ho sen 11_:

jt

pˆ = pˆjt-1 + 0 . 0 5* ( pjt-1 - pˆjt-1)

N o t ic e t hat ac t ual eq uil ib r ium pr ic es ar e used f o r in put s, so t hat expec t at io n s ar e impo r t an t o n l y f o r n ext y ear pr o d uc t io n . At t he same t ime, sin c e in c o mes ar e d ist r ib ut ed immed iat el y , in c o mes f o r y ear t d epen d heavil y o n expec t at io n s f o r y ear t + 1, whic h impl ies t hat f ir ms may suf f er l o sses o r pr o f it g ain s. T hey hen c e b ear r isks : t his is t he l ast an d mo st impo r t an t aspec t o f t he mo d el . In f ac t , r isk pl ay s a key r o l e in t wo d if f er en t way s: in t he pr o d uc er ’ s ut il it y f un c t io n ( 2b is), an d in t he r ec ur r en c e eq uat io n ( 7).

b ) A risk sensitiv e prod ucer util ity f unction

In t he pr o d uc er ’ s ut il it y f un c t io n , f o l l o win g t he r emar ks ab o ve, it was d eemed r el evan t t o in t r o d uc e so me so r t o f r isk pr emium. Al t ho ug h t her e ar e a var iet y o f po ssib il it ies in t his r espec t , t he simpl er M ar ko wit z ut il it y f un c t io n was o pt ed f o r . T hus, ( 2t er ) r epl ac es ( 2b is): ( 2t er ) φjt = pˆjt Fj (. . . xi j. . ) -

∑

∈J

i pi t xi jt -

∑

i∈I

πi t xi jt - 2 A jt σˆ2jtF2jt(. . . xi j. . )

wher e σˆ2_jt is t he expec t ed var ian c e o f p_jt, an d A_jt so me r isk aver sio n c o ef f ic ien t .

O f c o ur se, t his impl ies an expec t at io n f un c t io n E v( . ) is d ef in ed f o r var ian c e. W it h n aï ve

expec t at io n s, E m,, it seems l o g ic al t o t ake σˆ2jt= ( pˆjt-1 - pjt-1)2, al t ho ug h mo r e c o mpl ic at ed

expec t at io n sc hemes c o ul d b e en visag ed . T he o r d er o f mag n it ud e o f Ajt ( t he ab so l ut e r isk

aver sio n c o ef f ic ien t ) is impo r t an t . It sho ul d b e c o mmen sur ab l e wit h 1/ w, wher e w is t he aver ag e weal t h o f t he d ec isio n -maker . T his r emar k o pen s t he way f o r in t r o d uc in g weal t h an d weal t h d ist r ib ut io n ( in ad d it io n t o in c o me) c o n sid er at io n s in t o C G E ’ s – an d t his n o t t he l east in t er est o f t his appr o ac h.

O f c o ur se, d at a r eg ar d in g weal t h ar e n o t c o mmo n pl ac e. T ho se mad e use o f used in o ur mo d el have b een t he sub jec t o f r o ug h g uesses. T he pr o b l em her e is t he c al ib r at io n o f t he mo d el , whic h sho ul d r epr o d uc e t he S AM mat r ix at t he st ar t in g po in t o f t he simul at io n . It has b een d o n e b y ad just in g c o ef f ic ien t s in a “ maximum l ikel iho o d “ l o g ic , al t ho ug h, o f c o ur se, n o f o r mal use o f an y st at ist ic al in st r umen t has b een mad e.

c) P rof its d istrib uted as capital income

Fin al l y , t he l ast t er m o f eq uat io n ( 2t er ), 2Ajt σˆ2jtF2jt( . . . xi j. . ), is an expec t ed pr o f it . It sho ul d b e

d ist r ib ut ed o n e way o r an o t her . W e d ec id ed t o d ist r ib ut e it just as t he in c o me f r o m c apit al , o n t he ( f r ag il e12_{) g r o un d t hat pr o f it is t he r ewar d f o r t akin g r isk, an d t hat pr o f it ac c r ue in g en er al}

t o c apit al ho l d er s.

C) P ractical impl ementation : recurrence eq uations

( 2t er ) is n o t t he o n l y eq uat io n f o r whic h r isk mat t er s. As f ar as g r o wt h an d ac c umul at io n ar e c o n c er n ed , eq uat io n ( 7) an d t he f un c t io n G ( . . vhjt… ) ar e o f t he ut mo st impo r t an c e. In t he f ir st

C G E ver sio n , f un c t io n G was st r aig ht f o r war d : c han g es in t o t al l ab o r f o r c e wer e d r iven b y d emo g r aphy , whil e c apit al was easil y shif t ed f r o m o n e sec t o r t o an o t her , so t hat it was “ n at ur al l y ” in vest ed in t he mo st pr o d uc t ive pl ac es. Y et , suc h assumpt io n s impl y t hat a n uc l ear po wer pl an t c an b e used t o har vest g r ain , o r t hat a b us d r iver c an b e empl o y ed immed iat el y as a t eac her in mat hemat ic s. It n o t ver y r eal ist ic . M an y mo d el s have b een set up wit h sec t o r -spec if ic l ab o r f o r c e an d c apit al . T he d if f ic ul t y , in t hat c ase, is t hat n eit her c apit al n o r l ab o r ar e o b vio usl y st uc k wit h an y sec t o r f o r ever . S o me f l exib il it y must b e ad d ed .

In t he pr esen t mo d el , n o spec ial c ar e has b een t aken f o r l ab o r : it shif t s f r eel y wit hin g r o ups o f sec t o r s ( ag r ic ul t ur e, man uf ac t ur es, et c . . ). In ad d it io n , t he t o t al l ab o r f o r c e is d r iven b y simpl e d emo g r aphic c o n sid er at io n s. B y c o n t r ast , an o r ig in al sub mo d el has b een d evel o ped f o r c apit al . T he o l d c apit al is f ixed b y sec t o r , just d ec ay in g at a c o n st an t r at e. B ut t he “ n ew” c apit al o wn ed b y eac h in st it ut io n is al l o c at ed b et ween sec t o r s ac c o r d in g t o a M ar ko wit z ( 1970 ) mean / var ian c e po r t f o l io sel ec t io n mo d el . L et b e :

12_{W ithout q uoting the whole enormous literature pertaining to distrib ution theory and the soc iolog y of lab or, it}

is well k nown that work ers may b enefit from the profits of a suc c essful firm, espec ially if the latter enj oy s some monopoly power, and even if this k ind of advantag e is vanishing nowaday s under the pressure of c ompetition.

kjt : c apit al o f b r an c h j, t ime t S t : t o t al savin g per io d t jt πˆ : expec t ed pr o f it ab il it y o f c apit al in b r an c h j ) ( ˆ _jt

V _{π : expec t ed var ian c e o f πjt}

Ak : r isk aver sio n par amet er f o r in vest o r k

P kjt : pr ic e o f t he c apit al g o o d f o r b r an c h j jt

k

Pˆ : expec t ed val ue o f P _{k jt}

Ijt : c apit al g o o d b o ug ht f o r b r an c h j, t ime t

T hen , Ijt is c ho sen b y in vest o r s t hr o ug h t he maximizat io n o f :

( 8) jt jt k j jt A I Pk ₋

∑

πˆ Vˆ(πjt)Ijt2 sub jec t t o : ( 9) jt jt t j S I Pk _≤

∑

wit h a n aï ve expec t at io n sc heme :

( 10 ) πˆ = jt πjt−1

( 11) Pˆ = P kk_{jt jt-1}

( 12) Vˆ(πjt)= (πˆjt−1−πˆjt−2)2

In ad d it io n , sin c e Pˆ ≠ P kk_{jt jt, so me savin g may l ast o r b e c r eat ed o n t ime t . It is t hen c r ed it ed} t o o r sub t r ac t ed f r o m savin g y ear t + 1.

T he c apit al avail ab l e f o r eac h b r an c h j is upd at ed in t he r ec ur sive l o o p o ver t ime: ( 13) kjt+ 1= kjt ( 1-δ) + Ijt

Al t ho ug h exc han g e r at e var iab il it y has n o t b een t aken in t o ac c o un t , suc h a mo d el c o ul d b e easil y ext en d ed t o c o pe wit h t his impo r t an t so ur c e o f vo l at il it y .

d) Data and other settings

T he G t ap d at a b ase ( ver sio n 5) has b een used t o r epr esen t t he wo r l d t hr o ug h 13 r eg io n s, 5 pr o d uc t io n f ac t o r s an d 17 sec t o r s, in c l ud in g 8 f o r ag r ic ul t ur al pr o d uc t io n an d 4 f o r ag r i-b usin ess ( see T ai-b l e 1).

T wo t y pes o f ho useho l d s ar e c o n sid er ed , spl it t in g t he po pul at io n ar o un d t he in c o me med ian , an d d ef in in g mid d l e-l o w in c o me an d mid d l e-hig h in c o me g r o up, in o r d er t o b e ab l e t o in c l ud e eq uit y c o n sid er at io n s when an al y zin g t he r esul t s.

P r o d uc t io n is d esc r ib ed b y emb ed d ed C E S pr o d uc t io n f un c t io n s. At t he f ir st l evel , ag g r eg at e ad d ed val ue an d ag g r eg at e var iab l e in put s ar e c o n sid er ed . T hese ar e d isag g r eg at ed at t he sec o n d l evel , wher e t wo o t her C E S ar e used , o n e f o r t he f ive pr o d uc t io n f ac t o r an d an o t her f o r in put s. P ar amet er s ar e t aken f r o m t he G T AP d at a b ase13_.

D eman d is a l in ear expen d it ur e sy st em, est imat ed b y usin g G T AP in c o me el ast ic it ies as wel l as c o n sumpt io n an d pr ic e l evel s.

E xc han g e r at es ar e exo g en o us. In vest men t is d et er min ed b y savin g s an d f o r eig n c apit al f l o ws, c al c ul at ed t o b al an c e t he ext er n al t r ad e. G o ver n men t b ud g et is b al an c ed t hr o ug h pub l ic c o n sumpt io n ad just men t . T he t wo ver sio n s o f t he mo d el ar e d y n amic , usin g t empo r ar y eq uil ib r ia. B ec ause o f un c er t ain t y o n ag r ic ul t ur al pr ic es, t he expec t ed pr o f it ab il it y o f ag r ic ul t ur al ac t ivit y , whic h d et er min es r eso ur c es al l o c at io n t o t he var io us ag r ic ul t ur al ac t ivit ies, may d if f er f r o m t he r eal o n es, c al c ul at ed o n e y ear l at er . T her ef o r e, at l east o n e pr o d uc t io n f ac t o r has r et ur n s d ist r ib ut ed wit h t he same l ag , so as t o al l o w t he ad just men t b et ween expec t ed an d r eal r esul t s. C apit al r et ur n s ar e c al c ul at ed ex-po st , in o r d er t o al l o w t his ad just men t .

Ar min g t o n assumpt io n o f imper f ec t sub st it ut es o f pr o d uc t s f r o m d if f er en t c o un t r ies ho l d s. P ar amet er s as wel l as t r an spo r t c o st s ar e t aken f r o m t he G T AP d at a b ase.

T ab l e 1 : G T A P datab ase desegregation f or I D3 m odel

Re g i o n s S e c t o r s P r o d u c t i o n f a c t o r s

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W heat O thers g rains L iv estock

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2 . 3 . A gric u l tu ral P ol ic ies

A l ast o r ig in al f eat ur e o f t he mo d el c o n c er n s ag r ic ul t ur al po l ic ies in t he E ur o pean U n io n an d U n it ed S t at es, espec ial l y mar ket pr ic e suppo r t po l ic ies as t her e ar e t ho se t hat sho ul d b e d isman t l ed wit h t r ad e l ib er al izat io n . In ear l ier ver sio n , t he t r ue po l ic ies had b een r epl ac ed b y P r ic e S uppo r t E q uival en t ( P S E ) f r o m O E C D , as it is c o mmo n l y f o un d in t he l it er at ur e. Ho wever , suc h simpl if ic at io n b ec o mes har d l y ac c ept ab l e, o n c e o n e assumes t hat imper f ec t in f o r mat io n an d r isk mat t er in pr o d uc er s b ehavio ur . In d eed , o n e o f t he main ad van t ag es o f g uar an t eed pr ic e t hr o ug h pub l ic st o r ag e in E ur o pe o r in t er ven t io n pr ic e in U n it ed S t at es is t hat suc h po l ic ies er ase pr ic e f l uc t uat io n s an d r isk f o r ag r ic ul t ur al pr o d uc er s c o n c er n ed . As it has b een sho wn ab o ve, r isk an d pr ic e f l uc t uat io n s mat t er a l o t in t he suppl y f un c t io n s in t he imper f ec t in f o r mat io n ver sio n , so t hat r emo vin g suc h po l ic ies c an n o t o n l y b e c o n sid er ed as t he r emo val o f a simpl e pr o d uc er s sub sid y .

Fo r g uar an t eed pr ic es in E ur o pe, t he eq uat io n f o r pr o d uc er suppl y r emain s ( 2) wher e o ut put pr ic e, pjt is n o w t he d o mest ic mar ket pr ic e, at l east eq ual t o t he g uar an t eed pr ic e. In o r d er t o

a c h i e ve t h i s l e ve l f o r d o m e s t i c m a r k e t pr i c e b e , t h e g o ve r n m e n t s t o r i n g t h e e xc e s s o f s u ppl y . A s t o c k , s t o r jt i s t h u s a d d e d t o E q u a t i o n ( 1 b i s ) : ( 1 t e r ) Fj ( . . . xi jt-1. . ) =

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_h vh jt + s t o r e jt, j∈J a n d a n e q u a t i o n i s a d d e d t o d e t e r m i n e t h e s t o c k l e ve l , c o n s i d e r i n g pg jt, t h e c o r r e s po n d i n g g u a r a n t e e d pr i c e f o r j pr o d u c t : ( 1 4 ) pjt ≥ pg jt W e a s s u m e d h e r e t h a t pu b l i c s t o c k c a n b e s o l d o n t h e m a r k e t o n e y e a r l a t e r . T h e d i f f e r e n c e b e t w e e n t h e m a r k e t pr i c e a n d t h e g u a r a n t e e d pr i c e i s a n e w e xpe n d i t u r e i n g o ve r n m e n t b u d g e t . Fo r i n t e r ve n t i o n po l i c y i n t h e U n i t e d S t a t e s , t h e s c h e m e i s d i f f e r e n t s i n c e s u c h po l i c y i s m o r e s i m i l a r t o a pr o d u c e r s u b s i d y t h a t d o e s n o t a f f e c t d o m e s t i c c o n s u m e r s , c o n t r a r y t o t h e E u r o pe a n c a s e . T h u s ( 1 b i s ) s t a y s t h e s a m e , b u t e q u a t i o n ( 2 ) b e c o m e s , w i t h i n t e r jt t h e l e ve l o f i n t e r ve n t i o n : ( 2 q u a r ) φjt = (pjt +interjt) Fj ( . . . xi j. . ) -

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i∈I πi t xi jt j ∈ ∀iJ ; a n d a n o t h e r e q u a t i o n i s a l s o a d d e d t o d e t e r m i n e t h e i n t e r ve n t i o n l e ve l , c o n s i d e r i n g pi n t e r v jt, t h e i n t e r ve n t i o n pr i c e s e t e a c h y e a r b y t h e U S g o ve r n m e n t : ( 1 5 ) pjt + i n t e r j ≥ pi n t e r v jt A g a i n , a n e w e xpe n d i t u r e i s t h u s a d d e d i n U S pu b l i c b u d g e t t o t a k e a c c o u n t f o r t h i s po l i c y c o s t . e) S u s t a i n a b i l i t y a n d c o m p u t i n g c o n s i d er a t i o n s S o l u t i o n s f r o m t h i s s e t o f e q u a t i o n s a r e t i m e s e r i e s o f pr i c e s , q u a n t i t i e s a n d i n c o m e s . I n pr i n c i pl e , t h e w h o l e s e r i e s o f S o c i a l A c c o u n t M a t r i c e s f o r e a c h r e g i o n s , t o g e t h e r w i t h a t r a d e f l o w m a t r i x s h o u l d b e pr o d u c e d o ve r a n u n s pe c i f i e d l e n g t h o f t i m e . I n t h e c a s e o f a pe r f e c t n e o c l a s s i c a l m o d e l ( a l o n g t h e l i n e d e ve l o pe d b y D e va r a ja n a n d G o 1 9 9 5 ) , u n l e s s t e c h n o l o g y d o e s n o t a l l o w f o r g r o w t h , t h e o n l y l i m i t t o t h e n u m b e r o f “ y e a r s ” t o b e c o n s i d e r e d i s t h e s i ze o f c o m pu t e r s m e m o r i e s . I n e f f e c t , i n t h i s c a s e , y e a r l y s o l u t i o n s s h o u l d c o n ve r g e t o w a r d e i t h e r a V o n N e u m a n n “ t u r n pi k e ” g r o w t h pa t h ( i f all f a c t o r s a r e va r i a b l e ) o r a l i m i t s o l u t i o n ( i f s o m e u l t i m a t e f i xe d f a c t o r – s u c h a s m a n po w e r o r n a t u r a l r e s o u r c e s – d o e s e xi s t ) . A s s o o n a s e xpe c t a t i o n s a r e n o t pe r f e c t , t h e r e i s a po s s i b i l i t y f o r t h e s y s t e m b e i n g l o c k e d i n t o a t r a p, w i t h o u t f e a s i b l e s o l u t i o n s : f o r i n s t a n c e , u n d e r i n ve s t m e n t c r e a t e s a s i t u a t i o n w h e r e e ve n c a pi t a l r e n e w a l i s n o t po s s i b l e . T h i s i s t r u e o f m o s t s t a n d a r d m o d e l s , w i t h pe r f e c t f o r e s i g h t f o r c a pi t a l a n d pr o d u c t i ve r e s o u r c e s a l l o c a t i o n s , b u t “ i n c o n s i s t e n t ” s a vi n g s . Y e t , m o s t o f t h e t i m e , s u c h m o d e l s d o n o t r e s u l t i n t o t a l i n f e a s i b i l i t y , b e c a u s e s a vi n g s a f f e c t s o n l y a s m a l l s h a r e o f t o t a l d e m a n d , t h u s l e a vi n g r o o m f o r a d a pt a t i o n s . I n t h e c a s e o f t h e pr e s e n t m o d e l , pr i c e s m a y b e ve r y m u c h i n c o n s i s t e n t , e s pe c i a l l y t h o s e o f a g r i c u l t u r a l a n d ,

m o r e g e n e r a l l y , l o w d e m a n d e l a s t i c i t y pr o d u c t s . T h e r e f o r e , c o m pu t a t i o n a l pr o b l e m s a r e t o b e e xpe c t e d . I n e f f e c t , m o s t o f m o d e l r u n s s t o p a f t e r a f e w “ y e a r s ” , b e c a u s e G A M S / P A T H d o e s n o t f i n d a n y s o l u t i o n f r o m t h e c u r r e n t s t a r t i n g po i n t ( a n d a l t h o u g h a f e a s i b l e s o l u t i o n m a y s t i l l e xi s t ) . W e n e ve r t h e l e s s pr e s e n t h e r e s o m e o f t h e “ l o n g e r l a s t i n g ” s o l u t i o n w e c o u l d f i n d – s o l u t i o n s w h i c h , f o r f o r t u i t o u s r e a s o n s ( m a i n l y , a ppa r e n t l y s e c o n d a r y pa r a m e t e r s va l u e s ) , c o u l d b e o pe r a t e d o ve r 6 0 y e a r s . T h e r e a r e a t l e a s t t w o r e a s o n s f o r t h a t : a ) m a n y y e a r s a r e n e c e s s a r y f o r t h a t t h e e f f e c t s o f m o s t o f t h e a b o ve d e s c r i b e d m e c h a n i s m s c a n b e o b s e r va b l e 14 _. b ) A s t a t i s t i c a l a n a l y s i s o f r e s u l t s – n e c e s s a r y f o r va l i d a t i o n pu r po s e – r e q u i r e s a “ l a r g e ” n u m b e r o f o b s e r va t i o n s . T h u s , s e r i e s pr e s e n t e d h e r e a r e o n l y i n s t r u m e n t a l i n va l i d a t i n g t h e i n t u i t i o n s a t t h e o r i g i n o f t h e m o d e l , a n d c h e c k i n g e s s e n t i a l m e c h a n i s m s o f m a r k e t i m pe r f e c t i o n h a ve b e e n c a pt u r e d . O f c o u r s e , t h e y d o n o t i m pl y a n y i d e a o f pr e d i c t i n g t h e f u t u r e f o r 6 0 y e a r s a h e a d . I I I – R es u l t s , p o l i t i c a l c o n s eq u en c es a n d v a l i d a t i o n A ) – W i l l t r a d e l i b er a l i z a t i o n i n c r ea s e w el f a r e ? T h e m a i n r e s u l t i s t h a t ve r y s t r a n g e c o n c l u s i o n s c a n b e d e r i ve d f r o m a m o d e l a l o n g t h a t l i n e . A s f o r m o s t o f pr e s e n t l y e xi s t i n g w o r l d C G E ’ s m o d e l s , t h e m o d e l o u t l i n e d a b o ve h a s b e e n u s e d t o a s s e s s t h e c o n s e q u e n c e o f a g r i c u l t u r a l t r a d e l i b e r a l i za t i o n . W h i l e m o s t e xi s t i n g m o d e l s c o n c l u d e t h a t l i b e r a l i za t i o n w i l l i n c r e a s e g l o b a l w e l f a r e b y a n a m o u n t w h i c h , a l t h o u g h m o d e s t ( a f e w pe r c e n t ) i n t e r m s pe r c e n t a g e o ve r e xi s t i n g w e l f a r e , r e pr e s e n t n e ve r t h e l e s s a ve r y l a r g e n u m b e r o f b i l l i o n d o l l a r s , t h e I D 3 m o d e l pr e s e n t e d h e r e i s m u c h m o r e c a u t i o u s . I n e f f e c t , t w o ve r s i o n s o f t h e m o d e l h a ve b e e n r u n : o n e i s t h e s t a n d a r d g e n e r a l e q u i l i b r i u m m o d e l , w i t h r a t i o n a l e xpe c t a t i o n s a n d n o r i s k . T h e s e c o n d i s t h e d i s e q u i l i b r i u m m o d e l d e s c r i b e d a b o ve . D a t a a r e t h e s a m e , a s w e l l a s t h e g e n e r a l s e t t i n g ( s e e B o u s s a r d , G e r a r d e t al. , 2 0 0 1 )

14 _{For instance, in a standard model, EU and US subsidies to agricultural exports increase welfare in food} importing countries, by prov iding urban poor with ch eap food. Y et, th is is sh ort sigh ed a v iew: th e maj or perv erse effect of such subsidies are th at, because agricultural prices are depressed in th e importing countries, th e latter are unable to dev elop any food producing industry by th emselv es, wh atev er th eir comparativ e adv antage for such production. I n th at case, for th e beneficial effect of remov ing subsidies to be apparent in th e importing counties, it is necessary to wait until th e beneficial effect of inv estment can be observ ed. N ow, in th e present framework , th is will req uire th at entrepreneurs be reasonably sure th at th e subsidy policy is remov ed for long, and th at th ey can gath er th e necessary resources to significantly increase domestic food production: it may necessitate sev eral y ears for th ese conditions to be fulfilled.

F i g u r e 2 S t a n d a r d m o d el l i b er a l i z a t i o n ef f ec t s o n r i c h a n d p o o r : D i f f e r e n c e b e t w e e n “ li b e r ali z at i o n ” an d “ r e f e r e n c e ” , i n % o f r e f e r e n c e 0 10 20 30 40 50 60 70 -1 0 1 2 3 4 5 6 7 8x 10 -3 time (C u rr en t re fe re n ce )/r ef er en ce %

Rich households utility index Whole World LIBNOLAG 0 10 20 30 40 50 60 70 -1 0 1 2 3 4 5 6x 10 -3 time (C ur re nt - re fe re nc e) /re fe re nc e %

Poor households utility index Whole World LIBNOLAG T h e s t a n d a r d e q u i l i b r i u m m o d e l pr o d u c e s t h e s a m e r e s u l t s a s m a n y s i m i l a r m o d e l s pr e s e n t e d i n t h i s o r a pr e c e d i n g c o n f e r e n c e ( f i g u r e 2 ) : l i b e r a l i za t i o n 15 _{i n c r e a s e s t h e g r o w t h r a t e , a n d i s} g l o b a l l y b e n e f i c i a l . Fo r va r i o u s r e a s o n s , b e n e f i t s 16 _{a c c r u e t o t h e po o r a s w e l l a s t o t h e r i c h :} B e c a u s e f o o d i m po r t s a r e n o w d e pr i ve d o f s u b s i d i e s , u r b a n po o r – e s pe c i a l l y i n f o o d i m po r t i n g d e ve l o pi n g c o u n t r i e s – a r e h a r m e d b y a r i s e i n f o o d pr i c e s . B u t r i s e s i n a g r i c u l t u r a l pr i c e s b e n e f i t s r u r a l po o r . I n t h e w h o l e , t h e i n c r e a s e o f e f f i c i e n c y , a n d t h e e xpl o i t a t i o n o f c o m pa r a t i ve a d va n t a g e b e n e f i t s e ve r y b o d y , a t l e a s t a t t h e b e g i n n i n g o f t h e pr o c e s s . A s t i m e pr o g r e s s e s , b e n e f i t g r a d u a l l y va n i s h , a n d vi r t u a l l y d i s a ppe a r a f t e r a b o u t 3 0 y e a r s . T h i s i s s u r pr i s i n g : a pu r e l y r a t i o n a l g r o w t h m o d e l s h o u l d d i s pl a y a c e r t a i n “ s e n s i t i vi t y t o i n i t i a l c o n d i t i o n s ” , pr e c l u d i n g t h e po s s i b i l i t y o f t w o t r a je c t o r i e s m e r g i n g t o g e t h e r a f t e r h a vi n g b e e n r e m o t e f o r a w h i l e . T h i s i s b e c a u s e e ve n w i t h “ r a t i o n a l e xpe c t a t i o n s ” t h i s m o d e l i s n o t “ pu r e g r o w t h ” : e xpe c t a t i o n s ( a n d r i s k , a s s e e n a b o ve ) pl a y a r o l e i n d e c i d i n g s a vi n g s a l l o c a t i o n t o c a pi t a l g r o w t h . A s a c o n s e q u e n c e , m i s t a k e n i n ve s t m e n t s c a n o c c u r , l e a d i n g t h e g r o w t h pa t h t o w a r d a q u a s i c h a o t i c t r a je c t o r y . Y e t , t h e c o n s e q u e n c e s o f s u c h e r r o r s a r e s m a l l , b e c a u s e t h e b e t t e r e f f i c i e n c y o f t h e w h o l e s y s t e m a l l o w s f o r r e c o ve r y . T h u s , a f t e r t h e “ t h i r t y y e a r c r i s i s ” , l i b e r a l i za t i o n b e n e f i t s c o m e b a c k a g a i n .

15 _{H ere, “ liberaliz ation” means remov ing all export and import taxes and subsidies, as defined in th e G T A P} database.

16 _{T h ese effects are measured in terms of “ utility ” – th at is, in practice, with a linear expenditure sy stem, as th e} amount of expenses in excess of th e minimum lev el . Utility is assumed to be additiv e across h ouseh olds – obv iously , somewh at h eroic an assumption. Unfortunately , v ery few easily computed welfare indexes are av ailable. T h is one is freq uently made use of in th e literature. I t is fully consistent with th e v ery logic of models, as soon as th e L ES consumption function is assumed ruling consumption decisions. I f certainly not th e best, it is at least not th e worse.

F i g u r e 3 R ec u r s i v e m o d el l i b er a l i z a t i o n ef f ec t s o n r i c h a n d p o o r D i f f e r e n c e b e t w e e n “ li b e r ali z at i o n ” an d “ r e f e r e n c e ” , i n % o f r e f e r e n c e 0 10 20 30 40 50 60 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 time (C u rr en t re fe re nc e) /r ef er en ce %

Rich households utility index Whole World LIBtot 0 10 20 30 40 50 60 -0.04 -0.02 0 0.02 0.04 0.06 0.08 0.1 time (C ur re n t re fe re n ce )/r ef er en ce %

Poor households utility index Whole World LIBtot I n t h e c a s e o f t h e I D 3 “ r e c u r s i ve m o d e l ” ( f i g u r e 3 ) , s i m i l a r ph e n o m e n a d o o c c u r . Fo r t h a t r e a s o n , l i b e r a l i za t i o n i s f a r f r o m b e i n g c o m pl e t e l y n e g a t i ve , a n d m a y pr o d u c e a f e w b e n e f i t s . Y e t , t h e l a t t e r a r e e ve n s m a l l e r t h a n w i t h t h e s t a n d a r d m o d e l . W o r s e , i n s o m e o c c a s i o n s , b e n e f i t s a r e f r a n k l y n e g a t i ve , a n d s u c h s i t u a t i o n s c a n l a s t f o r l o n g . I n t h e w h o l e , w i t h i n t h i s f r a m e w o r k , l i b e r a l i za t i o n s e e m s m o r e b e n e f i c i a l f o r t h e po o r t h a n f o r t h e r i c h , a l t h o u g h o n l y a f t e r a ve r y l o n g t i m e . O n t h e o t h e r h a n d , l o s s e s m a t e r i a l i ze e a r l i e r t o t h e po o r , w h i l e t h e r i c h m a y b e n e f i t a l i t t l e a t l e a s t f o r s o m e y e a r s a t t h e b e g i n n i n g . T h e w o r l d l e ve l s u m m a t i o n m a s k s d i s c r e pa n c i e s b e t w e e n r e g i o n s a n d c o u n t r i e s . I t i s s t r i k i n g t o l o o k a t t h e d i f f e r e n t c o n c l u s i o n s t o b e d e r i ve d f r o m t h e m o d e l f o r t h e s a m e r e g i o n , w i t h o r w i t h o u t pe r f e c t f o r e c a s t s . Fi g u r e 4 i l l u s t r a t e s t h i s s t a t e m e n t i n t h e c a s e o f A u s t r a l i a / n e w Z e a l a n d : o n t h e g r o u n d o f a c u r s o r y i n s pe c t i o n o f t h e l e f t pa r t o f f i g u r e 4 , a n a ï ve a n a l y s t w o u l d h a ve c o n c l u d e d t h a t l i b e r a l i s a t i o n , i n t h e s e c o u n t r i e s , w i l l , a t t h e b e g i n n i n g , b e r a t h e r d e t r i m e n t a l t o r i c h pe o pl e , a n d s l i g h t l y b e n e f i c i a l a f t e r a ve r y l o n g t i m e . B u t i f t h e r i g h t s i d e o f t h e s a m e d r a w i n g s h o w s t h e s a m e k i n d o f “ s t a r t i n g ” s c e n a r i o – e f f e c t s a r e e ve n s t r o n g e r , b e c a u s e t h e s c a l e i s n o t t h e s a m e o n t h e t w o g r a ph s , ( o b s e r ve t h e m a xi m u m y s c a l e i s 0 . 1 % o n t h e l e f t s i d e g r a ph , w h i c h i s d i vi d e d b y 1 E -3 , a n d a m o u n t t o 1 0 % o n t h e r i g h t s i d e g r a ph ) f o l l o w e d a f t e r a f e w y e a r s b y a ve r y s t r o n g d e c r e a s e o f u t i l i t y , u p t o –3 0 % . S i m i l a r f i g u r e s c a n b e f o u n d i n a b u n d a n c e i n t h e w h o l e s e t o f g r a ph s d e r i ve d f r o m t h i s s t u d y .

F i g u r e 4 : A u t r a l i a -N ew Z ea l a n d E v a l u a t i o n o f r i c h h o u s eh o l d s u t i l i t y i n d ex , a c c o r d i n g t o t y p e o f m o d el S t a n d a r d m o d e l 0 10 20 30 40 50 60 70 -8 -6 -4 -2 0 2 4 6 8 10x 10 -3 time % : (C ur re n t r ef er en ce )/r ef er en ce

Rich households utility index Australia new Zealand

LIBNOLAG I D 3 m o d e l T h e r e a s o n s f o r t h e s e s u r pr i s i n g r e s u l t s a r e o f c o u r s e t h o s e d e ve l o pe d a b o ve : b e c a u s e m a r k e t s d o n o t o pe r a t e pr o pe r l y , e s pe c i a l l y i n t h e c a s e o f r i g i d d e m a n d f u n c t i o n , t h e y t r a n s m i t s c r a m b l e d i n f o r m a t i o n t o pr o d u c e r s . A s a c o n s e q u e n c e , t h e l a t t e r t a k e d e c i s i o n s w h i c h a r e f i n a l l y e ve n w o r s e t h a n t h o s e – c e r t a i n l y n o t o pt i m a l – d e r i ve d f r o m g o ve r n m e n t i n t e r ve n t i o n s a n d m o r e o r l e s s i n e f f i c i e n t a g r i c u l t u r a l po l i c i e s . Fi g u r e s 5 i l l u s t r a t e t h i s s t a t e m e n t . F i g u r e 5 P r i c es o f s u g a r a n d m a n u f a c t u r es w i t h f o u r s c en a r i o s L I B N O L A G an d L I B t o t ar e li b e r ali s at i o n w i t h an d w i t h o u t p e r f e c t i n f o r m at i o n . R E F n o lag an d R E F 6 0 ar e c o r r e s p o n d i n g r e f e r e n c e r u n s S u g a r M a n u f a c t u r es W e s e e f r o m Fi g u r e 5 ( r e l a t i ve t o “ s u g a r ” a n d “ m a n u f a c t u r e s ” i n t h e “ r e s t o f t h e w o r l d ’ , b u t s i m i l a r g r a ph s c o u l d h a ve b e e n d r a w n f o r a l m o s t a l l c o u n t r i e s a n d c o m m o d i t i e s ) t h a t pr i c e s a r e m u c h m o r e vo l a t i l e i n t h e I D 3 m o d e l r e s u l t s t h a n w i t h t h e c o r r e s po n d i n g s t a n d a r d s i m u l a t i o n s . A g a i n s c a l e s a r e n o t t h e s a m e i n b o t h g r a ph s : o n t h e r i g h t pa n e l , pr i c e i n d e xe s va r y f r o m 0 . t o 3 – w h i c h i s r a t h e r r e a l i s t i c f o r t h e f r e e s u g a r m a r k e t - , w h i l e t h e y va r y f r o m 0 . 8 t o 1 . 3 o n l y i n t h e c a s e o f “ m a n u f a c t u r e s ” . I t r e f l e c t s t h e m u c h l a r g e r pr i c e d e m a n d e l a s t i c i t y i n t h e c a s e o f m a n u f a c t u r e s a s c o m pa r e d w i t h s u g a r . Y e t , s u g a r ( a n d o t h e r

a g r i c u l t u r a l c o m m o d i t i e s ) vo l a t i l i t y i s s o m e h o w c o n t a g i o u s , s i n c e , o t h e r w i s e , g i ve n a l a r g e d e m a n d e l a s t i c i t y , m a n u f a c t u r e pr i c e s s h o u l d c o n ve r g e t o w a r d e q u i l i b r i u m i n t h e I D 3 a s t h e y d o i n t h e s t a n d a r d m o d e l . B ) I s t h i s c r ed i b l e ? A t t h i s s t a g e , t h e q u e s t i o n w h i c h a r i s e s i s t h a t o f t h e c r e d i b i l i t y o f t h e a n a l y s i s u n d e r l y i n g t h e I D 3 m o d e l . I s t h i s m o d e l t e l l i n g a f a i r y t a l e , o r s o m e t h i n g l o o k i n g l i k e r e a l i t y ? I t i s d i f f i c u l t t o a n s w e r . H o w e ve r , s o m e c l u e s c a n b e f o u n d i n t h e s t a t i s t i c a l pr o pe r t i e s o f t h e s e r i e s – e s pe c i a l l y pr i c e s e r i e s – d e r i ve d f r o m b o t h m o d e l s . E a r l y e c o n o m e t r i c i a n s u s e d t o c h e c k m o d e l s b y c o m pu t i n g s o m e s o r t o f d i s t a n c e – o f t e n , t h e s u m o f s q u a r e d d i f f e r e n c e s - b e t w e e n “ a c t u a l ” a n d “ pr e d i c t e d ” s e r i e s . I t w o u l d n o t w o r k h e r e , f o r m a n y r e a s o n s : f i r s t , w e d o n o t h a ve m a n y o b s e r va t i o n s o f s i t u a t i o n s “ w i t h ” a n d “ w i t h o u t ” s u c h o r s u c h po l i c y – w h a t e ve r “ l i b e r a l ” o r n o t . S e c o n d , i f w e a d m i t t h e i d e a t h a t pr i c e s e r i e s a r e e i t h e r r a n d o m w a l k o r c h a o t i c m o t i o n , t h e y a r e s u b je c t t o “ s e n s i t i vi t y t o i n i t i a l c o n d i t i o n s ” , w h i c h m e a n s t h a t o n l y a ve r y m o d e s t h e l p c a n b e e xpe c t e d f r o m a n y c l a s s i c a l s t a t i s t i c a l t e s t . R a t h e r t h a n a d i r e c t t e s t o f t h e m o d e l , t h e r e f o r e , w e s h a l l t r y t o d e t e r m i n e t o w h a t e xt e n t t h e “ g e n e r a l s h a pe ” o f t h e s e r i e s pr o d u c e d b y I D 3 ( o r b y t h e a l t e r n a t i ve “ r a t i o n a l e xpe c t a t i o n m o d e l ” ) r e s e m b l e o r n o t t o t h e g e n e r a l s h a pe o f pr i c e s e r i e s t h a t c a n b e o b s e r ve d i n r e a l i t y - e s pe c i a l l y f o r a g r i c u l t u r a l c o m m o d i t i e s . T o t h a t e n d w e c o m pa r e t h e d y n a m i c pr o pe r t i e s o f s i m u l a t e d pr i c e s w i t h pr o pe r t i e s o b s e r ve d o n r e a l s e r i e s . A m o n g t h e i n d i c a t o r s a va i l a b l e , w e pa r t i c u l a r l y l o o k f o r t h o s e d e s c r i b i n g t h e vo l a t i l i t y pa t t e r n s o f pr i c e s , e . g . t h e r i s k t h a t pr i c e c h a n g e s m i g h t i n f l i c t t o m a r k e t o pe r a t o r s . W e d e r i ve f r o m t h e l i t e r a t u r e t h r e e m a i n pr o pe r t i e s : a g r i c u l t u r a l pr i c e s a r e n o n n o r m a l - t h e i r d i s t r i b u t i o n i s f a t -t a i l e d a n d m i d d l e -pe a k e d , t h e y e xh i b i t a u n i t r o o t ( i n n o m i n a l t e r m s ) w h i c h m a k e s t h e m n o n s t a t i o n a r y , a n d l a s t l y , t h e y d i s pl a y n o n l i n e a r i t i e s , e i t h e r i n a s t o c h a s t i c ( c o n d i t i o n a l h e t e r o s k e d a s t i c i t y o r “ A r c h ” e f f e c t ) o r d e t e r m i n i s t i c f o r m ( c h a o s )17 _{. T h e t a b l e 1} s u m m a r i s e s t h e pr o pe r t i e s s e t a n d t h e s t a t i s t i c a l t e s t s a s s o c i a t e d . T h e s t a n d a r d d e vi a t i o n va l u e o f l o g pr i c e c h a n g e s h a s b e e n a d d e d t o pr o vi d e d i r e c t c o m pa r i s o n o f i n s t a b i l i t y b e t w e e n pr o d u c t s a m o n g d i f f e r e n t s c e n a r i o s . B e c a u s e o f d a t a c o n s t r a i n t s , t e s t s a n d m e a s u r e s o f c h a o s ( B D S t e s t , G r a s s b e r g e r a n d P r o c a c c i a a t t r a c t o r ’ s d i m e n s i o n ) a r e o m i t t e d : t h e y w o u l d n o t pr o vi d e r o b u s t r e s u l t s o n s e r i e s w h o s e l e n g t h i s 6 0 . W e pr o c e e d i n t h r e e s t e ps : I n t h e f i r s t s t e p, i n d i c a t o r s va l u e i s a s s e s s e d o n r e a l m a r k e t pr i c e s o f a r e pr e s e n t a t i ve s e t o f c o m m o d i t i e s . T e s t va l u e s c o n f i r m t h e t h r e e m a i n pr o pe r t i e s d e s c r i b e d a b o ve ( a n n e x 1 ) . T h e n w e a s s e s s t h e s i m u l a t e d pr i c e pr o pe r t i e s pr o vi d e d b y t h e r a t i o n a l e xpe c t a t i o n ( vi z. w i t h n o t i m e l a g ) ve r s i o n o f t h e m o d e l , w i t h a n d w i t h o u t l i b e r a l i s a t i o n . W e r e s t r i c t t o t h e a g r i c u l t u r a l pr o d u c t o f t h e r e s t o f t h e w o r l d ( R O W ) , f o r i t b e i n g l i k e l y t o b e m u c h l e s s a f f e c t e d b y d o m e s t i c po l i c y c h a n g e s o ve r t h e l o n g r u n ( l i b e r a l i s a t i o n i s pa r t l y a c h i e ve d n o w ) . L a s t , w e d u pl i c a t e t h e pr e vi o u s s t e p o n t h e pr i c e s g e n e r a t e d b y t h e r e c u r s i ve m o d e l ve r s i o n w i t h r i s k . R e s u l t s c a n b e s u m m a r i s e d a s f o l l o w s ( d e t a i l s a r e pr o vi d e d i n a n n e x 2 ) : R es u l t 1 : pr i c e s a r e m u c h m o r e i n s t a b l e w h e n g e n e r a t e d b y t h e m o d e l w i t h t i m e l a g a n d r i s k t h a n w i t h t h e r a t i o n a l e xpe c t a t i o n m o d e l w i t h o u t l a g . B e i t m e a s u r e d t h r o u g h t h e c o e f f i c i e n t o f va r i a t i o n ( C V ) o f n o m i n a l pr i c e s o r w i t h t h e s t a n d a r d d e vi a t i o n o f t h e l o g d i f f e r e n c e o f

17 _{A mong th e v ast literature body , one can refer to A y ouz , D av iron, V oituriez ( 2 0 0 3 ) for a surv ey of price} properties and th eir implication on policies.