FADS VERSUS FUNDAMENTALS IN FARMLAND PRICES

Transcription

1 FADS VERSUS FUNDAMENTALS IN FARMLAND PRICES Barry Falk* Associae Professor of Economics Deparmen of Economics Iowa Sae Universiy Ames, IA and Bong-Soo Lee Assisan Professor of Finance Deparmen of Finance Universiy of Houson Houson, TX Saff Paper No. 281 Augus 1996 *271 Heady Hall/ISU/Ames IA ABSTRACT: This paper develops an approach o decompose farmland price ime series ino hree componens: permanen fundamenal componen, emporary fundamenal componen, and nonfundamenal componen. This decomposiion is useful for sudying he imporance of fundamenal versus nonfundamenal facors in explaining farmland price behavior and he dynamic response of farmland price o shocks o each of hese componens, among oher issues. The approach is applied o annual Iowa farmland prices over he sample period. Copyrigh 1996 by Barry Falk and Bong-Soo Lee. All righs reserved. Readers may make verbaim copies of his documen for non-commercial purposes by any means, provided his copyrigh noice appears on all such copies. IOWA STATE IS AN EQUAL OPPORTUNITY EMPLOYER

2 2 1. Inroducion A consensus appears o be forming ha farmland price movemens are no well-explained by he presen value model wih raional expecaions. See, for example, Bur (1986), Feahersone and Baker (1987), Falk (1991,1992), and Hanson and Meyers (1995). Alhough he specific mehods and daa ses differ across hese papers, each one formally or informally rejecs he presen value model as an explanaion of farmland prices. The reasons for he empirical failure of he presen value model are no clear. Bur (1986) concludes ha deviaions of farmland price from is fundamenal pah can be explained in erms of overreacion o ren movemens. Feahersone and Baker (1987), on he oher hand, conclude ha hese deviaions are largely deermined by purely speculaive forces, i.e., by fads. No one, however, has aemped o quanify he fad componen o help resolve his basic issue. The purpose of his paper is o sugges and apply an empirical sraegy o decompose farmland price movemens ino a componen driven by fundamenal forces and a componen driven by fad forces. This decomposiion will provide measures ha will help resolve he issue of he relaive imporance of hese wo componens in explaining overall farmland price movemens. In addiion, we will esimae and compare he dynamic responses of farmland prices o nonfundamenal shocks and wo ypes of fundamenal shocks. The basic framework is a rivariae vecor auoregression (VAR) formulaed in erms of (funcions of) farmland price,

3 3 farmland ren, and a ime-varying discoun rae. In his respec, he paper is closely relaed o Feahersone and Baker (1987). They applied innovaion accouning and impulse response analysis o an unresriced VAR represenaion of price, ren, and he discoun rae, under he assumpion ha hese series are rend saionary. In conras, we assume ha prices and rens are differencesaionary. This enables us o apply generic properies of uni roo and coinegraed processes o formulae resricions on he VAR ha provide us wih he means o, among oher hings, idenify he fad componen of he price series. The remainder of he paper is organized as follows. The model is developed in Secion 2, he daa are described in Secion 3, and he empirical resuls are presened in Secion 4. A summary of he paper and is main conclusions are conained in Secion Model Le p denoe he log of he real price per acre of farmland in period, le d denoe he log of he real ren per acre of farmland in period, and le r denoe he real ineres rae in period. Assume ha p and d are difference-saionary processes, while r is a saionary process. Define he spread, s, according o p - d (i.e., he log of he price-ren raio) and assume ha i is saionary, which implies ha p and d are coinegraed wih coinegraing vecor [1-1]. Campbell and Shiller (1988) used a log-linear approximae asse pricing framework o show ha he VAR represenaion of he

4 bivariae saionary process [)d -r s ]' is characerized by a r paricular se of cross-equaion resricions if p is deermined by curren and expeced fuure values of d and r according o he presen value model of asse pricing. Falk (1992) used heir framework o es (and rejec) he ime-varying discoun rae version of he presen value model as an explanaion of Iowa farmland prices. We begin under he premise ha he presen value model does no provide an adequae explanaion of farmland prices and so we mus work wih a more general VAR ha can accoun for he nonfundamenal shocks ha are no admied ino he Campbell- Shiller seup. Specifically, we consider he VAR represenaion of 4 he rivariae saionary process [)d )d-r s]'. 1/ Assume ha price, ren, and he ineres rae are subjec o hree ypes of orhogonal innovaions: permanen fundamenal innovaions, emporary fundamenal innovaions, and nonfundamenal innovaions. Fundamenal shocks are defined o be shocks ha influence he ime pahs of ren and/or he ineres rae. Permanen fundamenal shocks, e.g., echnology shocks, aler he s- sep ahead forecas of fuure rens by a nonnegligible amoun for arbirarily large s. The effec of a emporary fundamenal shock, e.g., a weaher shock, on he s-sep ahead forecas of d and r is arbirarily small for sufficienly large s. The assumpion ha fundamenal innovaions can be decomposed ino orhogonal permanen and emporary innovaions is compleely general so long as d is an 2/ I(1) process, as we have assumed. Nonfundamenal shocks are

5 defined o be shocks ha influence he ime pah of price bu no he ime pah of ren or he ineres rae. The Wold represenaion heorem and he assumpions made regarding he saionariy of )d, )p, r and p - d guaranee he exisence of a rivariae moving-average represenaion (TMAR) of [)d )d-r s]': z / [)d )d -r s ]' = C(L), (1) n where L is he lag operaor (i.e., L x =x ); C(L)=[C (L)], -n ij 2 C ij (L) = c ij,0 + cij,1 L + cij,2l +... for i,j = 1,2,3; and, = [,,, ] is he vecor of (linear) innovaions in z, which implies ha, is a zero-mean and serially uncorrelaed process. For convenience, we choose o normalize he variance of each elemen of, o be equal o one, raher han resricing he coefficiens c o be equal o one. ii,0 5 We idenify, as he permanen fundamenal innovaion,, 1 2 as he emporary fundamenal innovaion, and, as he nonfundamenal 3 innovaion, by imposing he following addiional resricions on (1). Firs, we assume ha he elemens of, are conemporaneously uncorrelaed, i.e., E(,,') = I (2.a) where I is he 3x3 ideniy marix. Second, we assume ha, does 2 no have a permanen effec on d, i.e., C (1) = 0 12 (2.b) where C (1) = c + c + c +... Finally, we assume ha, 12 12,0 12,1 12,2 3

6 6 does no affec he ime pahs of d or r and, herefore, C (L) = C (L) = (2.c) Since c measures he k-period ahead effec of a sandardij,k deviaion j shock on variable i, knowledge of he free parameers of he TMAR can be applied in a variey of commonly used ways o sudy how prices, rens, and ineres raes are deermined. For example, forecas error variance decomposiions can be used o address our main concern, which is o measure he relaive imporance of fundamenal vs. nonfundamenal shocks in deerminining he ime pah of farmland price. Hisorical decomposiions can also be used for his purpose and o isolae paricular periods of ime for which a paricular ype of shock seems o have been especially imporan in deermining unusual movemens in farmland prices (e.g., boom and bus periods). Of course he TMAR canno be esimaed direcly from he daa since he innovaions ha appear in (1) are unobservable. However, assume ha z has he following VAR(p) represenaion: z = A(L)z + u (3) -1 p-1 where A(L) = [A ij (L)], A ij (L) = a ij,0 + aij,1 L aij,p-1l for i,j = 1,2,3 and u = [u 1 u 2 u 3]' is he innovaion vecor, which is a zero-mean, serially uncorrelaed process. Le E denoe he variance-covariance marix of u, i.e., E = E(u u '). Proposiion: The parameers in he TMAR (1), C(L), are overidenified by he VAR parameers in (3), A(L) and G, when resricions (2.a)-(2.c) are imposed.

7 The proof of his proposiion is given in he Appendix and i provides he sraegy for esimaion of he TMAR (1) from 7 esimaes of he VAR parameers, provided he over-idenifying resricions are saisfied. This approach o idenificaion follows along he pah developed by Blanchard and Quah (1989) and Lee (1995a, 1995b, 1996). 3. Daa Nominal farmland price and ren daa are updaed versions of he annual Iowa price and ren daa used by Falk (1991, 1992), covering he sample period This daa se is appealing because of is lengh and he homogeneiy of he asse being priced. The price series measures he average price per acre of whole farms sold in Iowa and he ren series measures he average 3/ cash ren per acre for he renal of whole farms in Iowa. The January producer price index is used o deflae he daa, January 1967 PPI = 100. Naural logs of he deflaed price and ren series measure he variables p and d, respecively. The six-monh commercial paper rae is used o measure he nominal ineres rae. Feahersone and Baker (1987) and Hanson and Myers (1995) also used he commercial paper rae o measure he discoun rae. Falk (1992) used Treasury bill raes bu was forced o hrow away several observaions of price and ren since T-bill rae daa are only available from The real ineres rae, r, was measured as he difference beween he period nominal ineres rae and he inflaion rae, log PPI - log PPI. -1

8 The heoreical model developed in he preceding secion began wih he assumpion ha p and d are difference-saionary processes, while r and p - d are saionary processes. Augmened Dickey-Fuller and Phillips-Perron uni roo ess were applied o es hese resricions. The resuls are summarized here and in Table I. The null hypohesis ha p (d ) is difference-saionary canno be rejeced a he 10-percen level agains he alernaive of rend-saionariy or he alernaive of saionariy using eiher es procedure. However, he null hypohesis ha )p ()d) is difference-saionary can be rejeced a he five-percen level agains he alernaive of saionariy using eiher es procedure. The null hypohesis ha r (p -d ) is difference saionary is rejeced agains he saionary alernaive a he five-percen level. Thus, uni roo es resuls are consisen wih he assumpions made abou he basic ime series properies of p, d, and r Empirical Resuls The daa series p, d, and r were ransformed ino he series )d, )d -r, and s ( = p - d ) and hen fi o a second-order VAR. The lag lengh of wo was implied by boh he Akaike (1974) and Schwarz (1978) crieria. Our main ineres in his VAR is o use i o idenify he TMAR of [)d )d - r s ]' in erms of permanen fundamenal innovaions, emporary fundamenal innovaions, and nonfundamenal innovaions.

9 I is shown in he Appendix ha he TMAR resricions imply he following over-idenifying resricions on he VAR: A (L) = 13 A 23 (L) = 0, i.e., he spread does no Granger-cause he bivariae [)d )d -r ]' process. This se of resricions can be viewed as anoher preliminary es of he compaibiliy of he daa wih he heoreical model developed in Secion 2. A quasi-log-likelihood es was applied o es hese resricions wih he resul ha hey canno be rejeced a he 10-percen significance level. 4/ The esimaed resriced VAR and resricions (2.a)-(2.c) were used o esimae he TMAR parameers according o he procedure described in he Appendix. The remainder of his secion presens he resuls of several applicaions of he TMAR Forecas Error Variance Decomposiions The firs applicaion measures he relaive imporance of fundamenal versus nonfundamenal shocks in explaining farmland price movemens over various ime horizons. More precisely, we compue he proporion of he variance of he k-sep-ahead forecas error in p aribuable o each of he hree ypes of shocks: permanen fundamenal shocks (, ), emporary fundamenal shocks (, ), 1 2 and nonfundamenal shocks (, ). This is accomplished in wo seps. 3 Firs, he ime pahs of )d, )d -r, and s are simulaed according o he esimaed TMAR in response o represenaive,,,, and, shocks in he sandard manner o decompose he k-sep-ahead forecas error variances for hese hree variables. The resuls of

10 his exercise are presened in he op panel (Panel A) of Table II, alhough hey are no of direc ineres for our purposes. Second, for each represenaive shock he simulaed ime pahs of )d, )d r, and s are ransformed ino simulaed ime pahs of d, r, and p, which are used o obain he forecas error variance decomposiions presened in he lower panel (Panel B) of Table II. According o Panel B, nonfundamenal shocks accoun for fify percen of he year-o-year volailiy in (logged real) farmland price. Tha is, half of he year-o-year volailiy in farmland prices canno be explained by facors ha influence rens or ineres raes. The relaive imporance of hese nonfundamenal forces declines monononically over ime, accouning for abou 25- percen of he six-year-ahead forecas error variance and 11- percen of he 24-year-ahead forecas-error variance. Thus, alhough half of he year-o-year volailiy in farmland prices canno be explained by facors ha influence rens or ineres raes, abou 90-percen of he long-run volailiy in farmland prices can be explained in erms of fundamenal forces. Temporary fundamenal shocks are nearly as imporan as nonfundamenal shocks in accouning for shor-run forecas uncerainy in price. Their imporance also falls monoonically as he forecas horizon increases, alhough he decline occurs much more rapidly han i does wih respec o nonfundamenal shocks: emporary fundamenal shocks accoun for only abou en percen of he six-year-ahead forecas error variance in price and only abou six percen of he 24-year-ahead forecas error variance. As he 10

11 11 forecas horizon is exended furher, his percenage would decline furher since, by consrucion, is limi mus be zero as forecas horizon goes o infiniy. Permanen fundamenal shocks explain nearly 85-percen of he 24-year-ahead forecas error variance in price, playing a more imporan role as he forecas horizon increases. Ineresingly, permanen fundamenal shocks are far less imporan han emporary fundamenal shocks in explaining annual variaion in price. By he wo-year horizon hey are abou of equal imporance and subsequenly permanen fundamenal shocks become increasingly imporan. In summary, year-o-year movemens in farmland prices are deermined mosly by emporary fundmenal shocks and nonfundamenal shocks, hese wo ypes of shocks being abou equally imporan in his regard. In he long-run, however, farmland prices are mosly explained by permanen fundamenal shocks. Thus, purely speculaive forces do seem o be imporan in explaining shor-run price volailiy in he Iowa farmland marke, where he shor-run can be inerpreed as long as abou five years. Bu he effecs of hese speculaive forces evenually dissipae, as one would expec. To conclude he analysis of Table II, noice ha permanen fundamenal shocks appear o be much more imporan relaive o emporary fundamenal shocks in explaining ren uncerainy han in explaining price uncerainy a all horizons, bu especially a shorer horizons. Permanen fundamenal shocks appear o be much less imporan relaive o emporary fundamenal shocks in

12 explaining real ineres rae uncerainy han in explaining price uncerainy, excep for he one-year ahead horizon. Nonfundamenal shocks do no affec he ime pahs of d or r by consrucion Impulse Response Funcions Nex we urn o Figure 1, which graphically illusraes he impulse response funcions. Panels A and B illusrae he dynamic responses of d and r, respecively, o a posiive one-uni permanen fundamenal shock and o a posiive one-uni emporary fundamenal shock. Panel C illusraes he dynamic response of p o a posiive, one-uni permanen fundamenal shock, a posiive, one-uni emporary fundamenal shock, and a posiive, one-uni nonfundamenal shock. In response o a one-uni posiive permanen fundamenal shock (log) ren increases iniially by abou.05 unis, hen gradually increases over abou he nex en years oward a new long-run value, which is abou.075 unis greaer han he iniial value. The real ineres rae, which is assumed o be a saionary process, iniially decreases by abou.02, hen gradually increases back oward is iniial level, which i reaches in abou six o eigh years. Thus, during he firs six o eigh years following a posiive permanen fundamenal shock curren and expeced fuure discoun raes and rens are increasing, which increases he fundamenal value of farmland. Afer his inerval, expeced fuure rens remain higher bu he discoun rae has reurned o is normal level. So he fundamenal value should decline a bi afer

13 13 he iniial run-up, bu remain a a permanenly higher level. This is exacly he paern of response of (logged) farmland price (Panel C) o his shock, indicaing ha he responses of farmland price o permanen fundamenal shocks are consisen wih he predicions of he presen value model. Posiive, emporary fundamenal shocks emporarily increase ren and he ineres rae according o Panels A and B of Figure 1. Ren and he ineres rae iniially increase by abou.05 and decline monoonically oward zero, dissapaing in abou six o seven years. Thus, over he six o seven year period curren and expeced fuure rens will be higher bu curren and expeced discoun facors will be lower. A he end of he period, curren and expeced rens and discoun facors will be a heir iniial values. If he farmland marke responds o hese shocks according o he presen value model, he impac on farmland price over he firs six o seven years will be ambiguous, bu here should be no effec on farmland price afer his inerval. According o Panel C, however, farmland price increases above is iniial value immediaely afer he shock hen decreases monoonically over he nex six o seven years, falling below is iniial value afer he firs four years, and hen slowly increases back oward he iniial value. The naure of he response and lengh of he response period indicae ha farmland price overreacs o emporary fundamenal shocks. Panel C also illusraes he reacion of farmland price o a posiive, one-uni nonfundamenal shock. The iniial and long-run

14 14 effecs are abou he same as he effec of a emporary fundamenal shock. However, farmland price remains above is iniial value over he enire adjusmen process. 4.3 Hisorical Decomposion The esimaed VAR and TMAR are used o decompose he acual (logged) real farmland price series ino hree componens: he permanen fundamenal componen, he emporary fundamenal componen, and he nonfundamenal componen. The esimaed VAR and TMAR and he relaionship beween he u 's and, 's enable us o esimae he, ime series. The esimaed, 's (, 's,, 's) are used o simulae he ime pah of p and derive he permanen fundamenal componen (emporary fundamenal componen, nonfundamenal 5/ componen) of price. This decomposiion is illusraed in Figure 2. Firs consider he permanen fundamenal componen of farmland price, illusraed in Panel A. This componen of farmland price appears o be a smoohed version of he acual price series, capuring he overall long-run behavior of price, bu missing many of he shor-run cycles in price. Noice, however, ha he upward rend in acual price from abou 1950 unil abou 1980 and he subsequen rapid fall in price during he 1980's is largely explained by he permanen fundamenal componen. The sample correlaion beween price and he permanen fundamenal componen is The (saionary) emporary fundamenal and nonfundamenal

15 15 componens are of relaively minor significance in explaining he overall behavior of he (nonsaionary) price series, which can be seen from he differences in he verical scales of Panels B and C relaive o Panel A. However, hese wo componens in price explain he shor-run volailiy ha he permanen fundamenal componen does no capure. So, for example, he shor-run flucuaions in price prior o he early 1950's and he shor-run decline in farmland prices around 1972 can be explained by movemens in he emporary fundamenal componen of price. Tha par of he major boom and bus of he 1970's and 1980's no explained by he permanen fundamenal componen can be explained by he nonfundamenal componen. In paricular, he very rapid growh in price during he lae 1970's and he seep decline following he peak several years laer, seem o be accouned for by he behavior of he nonfundamenal componen. 4.4 Furher Discussion The empirical resuls presened in his secion indicae ha here is an imporan nonfundamenal (or fad) componen o Iowa farmland price movemens. This is indicaed by he forecas error variance decomposiion and he hisorical decomposiion. The forecas error variance decomposiion of price implies ha abou one-half of he year-o-year variaion in farmland price is driven by nonfundamenal shocks. Even over a six-year forecas horizon approximaely one-quarer of he forecas error variance in price is aribuable o nonfundamenal shocks. The hisorical

16 16 decomposion provides an esimae of he nonfundamenal componen of he acual farmland price series and alhough his componen generally is very small relaive o he acual price, i has occasionally played an imporan role in he shor-run dynamics of price, paricularly in he several years before and afer Fads provide one explanaion of he failure of price o move according o he predicions of he presen value model. Anoher par of he sory migh be ha prices overreac o fundamenal shocks, i.e., marke paricipans pu more weigh on news abou rens and ineres raes han he news deserves. The impulse response analysis provided some suppor o he overreacion hypohesis. In paricular, he response of price o a emporary fundamenal shock displayed in Figure 1, Panel C appears o be consisen wih overreacion for reasons discussed earlier. Falk (1991) characerized he failure of Iowa farmland price o saisfy he saisical resricions implied by he presen value model using he ime series relaionship among he real price, real ren, and he ex-ane raional price (i.e., he price implied by he presen value model) o help make his poin. 6/ Specifically, he showed ha he ex-ane raional price ypically moves less han proporionally wih respec o changes in ren, while acual price moves more han proporionally wih respec o changes in ren. In his seup, however, here was no room for a nonfundamenal componen in price and he discoun rae was assumed o be consan. In Figure 3 we illusrae he ime series relaionship among

17 he real price, real ren, and he fundamenal componen of price, where he fundamenal componen is he sum of he permanen and 17 emporary fundamenal componens described in Figure 2. 7/ The fundamenal componen and he acual price series end o fall on he same side of weighed ren, indicaing ha hey boh end o move more han proporionally wih respec o ren movemens. This is in conras o he behavior of Falk's ex-ane raional price, which moves less han proporionally wih respec o ren movemens. On his basis i appears ha he fundamenal componen of price is no equivalen o he fundamenal value of land implied by he presen value heory: price appears o overreac o fundamenal shocks. However, in Figure 3, he fundamenal componen ends o fall beween acual price and weighed ren, indicaing in ye anoher way ha here is a fad componen in farmland price. 5. Summary and Conclusions The main purpose of his sudy was o propose and apply a procedure o decompose farmland price movemens ino movemens aribuable o fundamenal facors (i.e., facors ha influence he ime pahs of rens and ineres raes) and movemens aribuable o nonfundamenal facors. We assume ha he real ineres rae is a saionary process and ha he bivariae log real price and log real ren process is a coinegraed process. Then we can formulae a rivariae moving average represenaion (TMAR) of he growh rae of real ren, he growh rae of real ren minus he real ineres rae, and he log of he real price-

18 18 ren raio. The innovaions in his TMAR can be inerpreed as permanen fundamenal shocks, emporary fundamenal shocks, and nonfundamenal shocks. Knowledge of he parameers of he TMAR can be used in a variey of ways (e.g., impulse response analysis, forecas error variance decomposiions, and hisorical decomposiions) o sudy he influence of fundamenal shocks and nonfundamenal shocks on he ime pah of farmland prices. We prove ha he parameers of he TMAR are overidenified by he parameers of a finie-order rivariae vecor auoregression and so can easily be esimaed from price, ren, and ineres rae daa. The procedure is applied o sudy Iowa annual farmland prices and rens over he sample period, using he six-monh commercial paper rae (adjused for inflaion) o measure he real ineres rae. Uni roo ess indicae ha he behavior of he daa is consisen wih he ime series resricions ha he model imposes on price, ren, and he ineres rae. Furher, he overidenifying resricions he model imposes on he VAR are no rejeced. Therefore, we esimae a resriced VAR and apply i o idenify he TMAR of ineres o us. Based upon he esimaed TMAR, our wo main conclusions abou he behavior of Iowa farmland prices are as follows. Firs, nonfundamenal shocks appear o play an imporan role in explaining he shor-run behavior of farmland prices. In paricular, shor-run movemens in farmland prices are mosly deermined by emporary fundamenal shocks and nonfundamenal

19 19 shocks, wih hese wo ypes of shocks being of roughly equal imporance in his regard. In he long-run, however, farmland prices are mosly explained by permanen fundamenal shocks. Second, he dynamic responses of ren, he ineres rae, and price o permanen fundamenal shocks seem o be consisen wih he predicions of he presen value model of asse pricing. However, heir dynamic responses o emporary fundamenal shocks sugges ha farmland prices overreac o emporary fundamenal shocks. Thus, we conclude ha deviaions of farmland price from he predicions of he presen value model are imporan in he shorrun bu no in he long-run. The shor-run deviaions appear o be a combinaion of overreacions o emporary fundamenal shocks and reacions o nonfundamenal facors.

20 20 NOTES 1. The VAR represenaion of he rivariae process [)d )d-r s] can be formally derived from he asse pricing model applied by Campbell (1991) and Campbell and Ammer (1993), alhough i exiss more generally. The Campbell-Ammer model exends he log-linear approximae asse pricing framework developed by Campbell and Shiller (1988) by allowing for excess reurns (due o overreacion o fundamenals or reacions o nonfundamenals). Noe ha we canno work direcly wih he [ )p )d r ] process because he assumpion ha p and d are coinegraed means ha his rivariae process does no have a finie-order VAR represenaion. 2. See, for example, Quah (1992). 3. The price and ren daa are acually available since However, we followed Falk (1991,1992) in pushing each price daa poin up a year since he published prices (a leas since 1950) are end-of-he-year prices. Thus, land purchased a he beginning of year a a price per acre of P is assumed o generae per acre ren D during year. Furher discussion of hese daa and heir sources can be found in Falk's papers. The daa we use here are available upon reques. 4. Under he null hypohesis, he saisic T(ln*V r*-ln*v u*) is

21 2 asympoically disribued as a i (4), where T is he effecive sample size for esimaion of he VAR, ln*v * is he naural log of r he deerminan of he sample second momen marix of he residual vecor from he resriced VAR, and ln*v * is he naural log of he u deerminan of he sample second momen marix of he residual 21 vecor from he unresriced VAR. The realized value of he saisic was 6.19 implying a p-value of Since u and C 0, are boh he innovaion vecor in z, C 0, = u. Thus, given he VAR esimaes of u and he esimaed C, esimaes 0-1 of, can be obained according o, = C u. Consruc a new u 0 sequence according o u = C 0 1 [, 0 0]'. Use he esimaed VAR o simulae he behavior of )d, )d - r, and s from he iniial condiions and his innovaion sequence. This yields he permanen fundamenal componens of d, r, and, p. The emporary fundamenal componen and he nonfundamenal componen are consruced analogously. 6. See Figure 3 in Falk (1991). 7. Ren is weighed by he consan 14.92, which is he reciprocal of he sample mean real rae of reurn in his marke.

22 22 APPENDIX In his Appendix, we prove ha he moving average represenaion of z saisfying resricions (2.a)-(2.c) is over idenified by is vecor auoregressive represenaion. We also characerize he over-idenifying resricions. Le C denoe he coefficien marix associaed wih he 0 conemporaneous innovaion erm, in (1), he MA represenaion of z. Comparing (1) and (3), he VAR represenaion of z, noe ha C, and u are boh defined o be he innovaion in z and so 0 C, = u. o (A.1) Furher, (1) and (3) imply C(L), = [I - A(L)L] u, -1 (A.2) which, in ligh of (A.1), requires ha C(L) = [I - A(L)L] C (A.3) From (A.3) i is clear ha given A(L), C(L) can be deermined once C is deermined. To deermine C 's nine elemens, firs noe 0 0 from (2.c) ha c = 0 and c = 0. (A.4) 13,0 23,0 Second, from (A.1) and he normalizaion resricions (2.a), we obain he condiion CC' = E 0 0 u (A.5) where G u is he conemporaneous covariance marix of u, imposing six addiional resricions on C. Third, seing L = 1 in (A.3) 0

23 23 and using he long-run resricion (2.b), {[I - A(1)] C } = Thus, (A.3), (A.4), and (A.5) impose nine resricions on C ha 0 idenify ha marix given he VAR parameers A(L) and G. u Resricions (2.c) impose addiional condiions on C(L) beyond hose in (A.4). These are overidenifying resricions which imply ha in he VAR represenaion of z A (L) = 0 and A (L) = 0, (A.6) ha is z 3 does no Granger-cause he [z 1 z 2] process.

24 24 REFERENCES Akaike, H. (1974), A new look a he saisical model idenificaion, IEEE Transacions on Auomaic Conrol, AC- 19, Blanchard, O. and D. Quah (1989), The dynamic effecs of aggregae demand and supply disurbances, American Economic Review, 79, Bur, O.R. (1986), Economeric modeling of he capializaion formula for farmland prices, American Journal of Agriculural Economics, 68, Campbell, J.Y. (1991), A variance decomposiion for sock reurns, Economic Journal, 101, and J. Ammer (1993), Wha moves he sock and bond markes? A variance decomposiion for long-erm asse reurns, Journal of Finance, 48, and R.J. Shiller (1988), The dividend-price raio and expecaions of fuure dividends and discoun facors, Review of Financial Sudies, 1, Falk, B. (1991), Formally esing he presen value model of farmland prices, American Journal of Agriculural Economics, 73, (1992), Predicable excess reurns in real esae markes: A sudy of Iowa farmland values, Journal of Housing Economics, 2, Feahersone, A.M. and T.G. Baker (1987), An examinaion of farm secor real asse dynamics, American Journal of Agriculural Economics, 69, Fuller, W.A. (1996), Inroducion o Saisical Time Series, Wiley: New York. Hanson, S.D. and R.J. Meyers (1995), Tesing for a ime-varying risk premium in he reurns o U.S. farmland, Journal of Empirical Finance, 2, Lee, B.S. (1995a), The response of sock prices o permanen and emporary shocks o dividends, Journal of Financial and Quaniaive Analysis, 30, 1-22.

25 25 (1995b), Permanen, emporary, and nonfundamenal componens of sock price, unpublished manuscrip, Deparmen of Finance, Universiy of Houson. (1996), Time series implicaions of aggregae dividend behavior, Review of Financial Sudies, 9, Phillips, P.C.B. and P. Perron (1988), Tesing for a uni roo in ime series regression, Biomerika, 75, Quah, D. (1992), The relaive imporance of permanen and ransiory componens: idenificaion and some heoreical bounds, Economerica, 60, Schwarz, G. (1978), Esimaing he dimension of a model, Annals of Saisics, 6,

26 26 Tables and Figures: Table 1 - Uni Roo Tes Resuls Table 2 - Forecas Error Variance Decomposiions Figure 1 - Impulse Respons Graphs Figure 2 - Hisorical Decomposiions Figure 3 - Price, Weighed Ren, Fundamenal Componen