Are piglet prices rational hog price forecasts?

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1 AGRICULTURAL ECONOMICS ELSEVIER Agriultural Eonomis 13 (1995) Are piglet pries rational hog prie foreasts? Ole GjQ)lberg * Department of Eonomis and Soial Sienes, The Agriultural University of Nmway, P.O. Box 5033, N-1432, Aas, Nmway Aepted 4 July 1995 Abstrat In this paper a simple model is developed in whih the piglet prie serves as a foreast for the hog prie 3 months ahead. The model is tested on data from Northern Europe, viz. Norway, Sweden, Denmark and Finland during the period The empirial results lend strong support to the hypothesis that hog produers hold rational expetations when priing the piglets. Thus, the weight adjusted piglet prie typially represents an unbiased (onditional) foreast with unsystemati errors for the hog prie one quarter later. 1. Introdution Piglet pries should embody information about hog pries 3 months into the future. The purpose of this paper is to speify a simple proedure to test whether piglet pries are rational foreasts of subsequent hog pries, i.e. foreasts that are unbiased with unsystemati errors. Suh a test is obviously of great pratial relevane. If piglets are pried rationally, hog prie foreasts are easily available. If hog produers do not hold rational expetations, there should be room for profitable speulation in trading piglets or in offering forward hog pries that are fixed some way or another to the piglet prie. In this paper, we present a simple model in whih the hog prie one quarter into the future is estimated as a funtion of today's weight adjusted piglet prie and today's expeted feed osts and ' Tel.: ; fax: expeted profits. The model is tested on three sub-samples based on monthly prie observations from eah of the Nordi ountries (Norway, Sweden, Finland and Denmark). 2. lntertemporal prie relationships in the hog business The farrowing deision made by the piglet produer (timing and numbers) should be influened by his expetations as to what prie he will get for his piglets some 25 weeks later and by his expeted feeding osts during this time span. However, as he knows that the future piglet prie will depend on the buyer's expetations of what the latter will get paid for his hogs another 3-4 months later, the rational piglet produer should make his farrowing deision based upon his expetations for the hog prie some 9-10 months later j95j$ Elsevier Siene B.V. All rights reserved SSDI (95)

2 Gj lberg j Agriultural Eonomis 13 (1995) One farrowing has taken plae, the subsequent supply of pork is more or less fixed (disregarding the possibility of imports or exports and also the variations in slaughter weight). Hene, both the supply of piglets and the supply of pork are highly inelasti in the short run. Considering the intertemporal sequene of supply and demand deisions, the prie that lears the piglet market should represent a foreast of the hog prie, onditional on the expeted feed osts over the subsequent 2-3 months. However, sine piglets and hogs are qualitatively different entities, the piglet prie annot be used outright as a hog prie foreast. Consequently, for foreasting purposes, the piglet prie should be adjusted in a way that reflets the proportional weight of the piglet osts. The problem aused by the produer's need to foreast two pries simultaneously, (i.e. the hog prie and the feed prie), may be handled by fousing on the expeted profit, i.e. the expeted differene between produt prie and aggregated input osts. Thus, rational expetations should yield piglet pries that are unbiased foreasts of the subsequent margins, with unsystemati errors. Abstrating from apital and labor osts, the hog produer's profit is ( 1) where ph is the prie per kilo pork; pp is the prie per kilo at whih the piglet was bought, whereas pf is the average prie per kilo feed during the feeding period. wh and wp are the weight of hogs (slaughtered) and piglets, respetively and ljj is the feed onversion fator (feed per kilo pork). Profit per kilo finished produt, 7r = IJjwH, is thus given by (2) Letting t - 1 denote the time when the piglets are bought and t the time when the hogs are slaughtered with approximately 3 months between t and t- 1, the expeted profit per kilo is given by where and pp = (wpjwh)pp t-1 t-1 and IL 1 is an error term. Hene, Et-1(Pr) =Et-1(7rt) +Et-1(Pt) +Pt-1 +J.Lt ( 4) Sine expeted profits and expeted feed osts normally are unobservable, these variables will have to be modeled. A ommon proedure to obtain suh data, is to estimate the unknown variables as autoregressions of the observed values or simply to use the observed lagged values as instrumental variables (see Wikens, 1982, for a further disussion). This will be the approah in our empirial analysis. Thus, we speify the time series for the profit and feed osts as first-order autoregressions, i.e. Et-1(Pt) =Ao+"-1Pt-1 +s1,t and Et-1( 1rt) = 8o + 817rt ,1 (5) (6) with error terms that are assumed to be unsystemati. Given rational expetations, Eq. (4) an then be written as Et-1( Pr) = f31pt-1 + f3zet-1( Pt) + f33et-1( 1rt) + ILt (7) where /31 = {32 = {33 = 1 and J.L 1 - IN(O, u 2 ). Assuming that the expeted profit and feed osts an be desribed as a first-order autoregressive proess as in Eqs. (5) and (6), Eq. (7) an be estimated as Pr =A+ f31pt-1 + ljpt-1 + <f>7tt-1 + tt (8) where A is f3 2 A 0 + / ; lj is /3 2 A1; 4> is /3 3 81; gt is ILt + f32s1t + f33s2t- IN(O, u2). Alternatively, one an estimate

0. Gj lberg 1 Agriultural Eonomis 13 (1995) 119-123 121 where * indiates that the values for expeted feed pries and profits are the preditions obtained through Eqs. (5) and (6). Estimating Eq. (9), i.

3 0. Gj lberg 1 Agriultural Eonomis 13 (1995) where * indiates that the values for expeted feed pries and profits are the preditions obtained through Eqs. (5) and (6). Estimating Eq. (9), i.e. using the predited values for expeted profits and feed pries as instruments, gives us diretly parameters that enable us to test the rationality hypothesis ({3; = 1). 3. Empirial results The model above was estimated utilizing monthly prie observations from the Nordi ountries, viz. Norway, Sweden, Denmark and Finland over the period Despite these ountries' quite different institutional harateristis as far as agriultural poliy is onerned, the prie variability in the piglet and hog markets has been of pratially the same magnitude in all four ountries. For the entire period, the monthly SD of absolute pries have been approximately 10-18% of mean absolute pries. The annualized SD of the monthly perent prie hanges has been around 10-14%. As to the variability in relative prie hanges, Finland makes an exeption with a SD of 4-5%. Utilizing monthly observations for testing a 3 month foreast reates the well known overlapping observation problem, ausing serially orrelated foreast errors. Thus, when the foreasting period extends beyond the observation frequeny, the foreast error will follow a moving average proess of degree (k - 1), where k is the number of overlapping periods (Frenkel, 1980). Various ways have been suggested to get around this problem (see, for instane, Sargent, 1979; Hansen and Hodrik, 1980). The simplest solution is, of ourse, to avoid using overlapping observations. In our ase, this would imply using observations from every third month only, the disadvantage being that we may lose relevant information from the intermediate 2 months and hene get large sampling errors. In order to redue this disadvantage, we have divided the series of monthly observations into three sub-samples of 3-monthly observations and then estimated on the basis of eah sub-sample. Consequently, we have tested for rational expetations during the period February 1982-Deember 1992 for the four Nordi ountries using three sets of non-overlapping observations for eah ountry. Data set A inludes observations from January, April, July and Otober, data set B from February, May, August and November, while set C overs the months Marh, June, September and Deember. We have assumed a feed onversion fator (1./J) of 3.0 throughout the period in question, whereas the piglet/hog weight ratio is set at (The feed onversion fator is alulated as the amount of feed onsumed from the time the piglets are bought divided by the slaughter weight. A feed onversion fator of 3.0 is a rough approximation for these ountries during the period in question. A piglet/hog weight ratio of 0.33 reflets the fat that piglets in these ountries are typially kilos, whereas the slaughter weights are normally kilos.) Changing these onstants does not have any signifiant effet on our onlusions. However, any follow-up study to the present paper might onsider a more elaborate treatment of these two fators, as both to some extent may be endogenously influened by expetations. On a few oasions, minor hanges in definitions have ourred as to the way prie data have been registered. We have used dummies tg_ orret for this. However, sine the resulting jumps were both small and infrequent, the inlusion of dummies did not make muh differene to the estimation results. Our assumption that feed osts and profits follow a first-order autoregressive AR(l) pattern is obviously ruial for the tests. Estimating Eq. (5), it was found that feed osts in all samples and ountries are very well desribed by an AR(l) proess. A substantial part of the variane was explained and the errors did not appear to be serially orrelated. In the ase of Norway and Finland, also the profits series were found to follow an AR(l) proess. The first-order parameter was found to be signifiant in a majority of the samples. Still, the explained variane in the profit series through estimation of Eq. (6) was modest for both ountries. For Sweden and Denmark, however, the quarterly profit observations seem to follow a less simplisti proess. The latter fat

4 Gj lberg /Agriultural Eonomis 13 (1995) should be kept in mind when interpreting the results from testing the model in whih, despite the mixed results for Sweden and Denmark, we utilize the autoregressively predited profits and feed pries as proxies for their expeted values. The results from estimating Eq. (9) reported in Table llend strong support to the rational expetation hypothesis. With just a few exeptions, the estimated {3s do not differ signifiantly from unity, and the error terms seem to be unsystemati. The results regarding the foreasting abilities of the (weight adjusted) piglet prie are partiularly strong. Exept for two samples (Sweden in data set C and Finland in data set A), the estimated piglet prie parameter does not differ signifiantly from unity. In many ases, the estimated values are very lose to unity, indeed. Atually, it is for Denmark that we find the largest numerial deviations from 1.0. Still, the rational expetations hypothesis is aepted also in the Danish samples. For Denmark, and in some ases also in the other ountries, the feed parameter, however, differs signifiantly from unity. It is reason to believe that this may be due to our use of simple autoregressive foreasts as instrumental variables for expeted feed osts and profits. Beyond supporting the hypothesis that piglet pries tend to be unbiased foreasts, our simple model predits remarkably well the hog prie 3 months into the future, again with some modifiations for Denmark. Whereas the explained variane for the latter ranges from 0.58 to 0.69, the three other ountries have adj. R 2 s between 0.85 and 0.96! Table 1 Testing for rational expetations, OLS-estimation of P,H =a + /3 1 P,P_ 1 + f3 2(P, *F)+ {33( TT,*) r Data a /31 f3z /33 t-value t-value t-value DW adj.r2 set Ho:/31=1 Ho: f3z = 1 Ho: /33 = 1 Norway A ( -1.60) (6.60) (4.15) (13.18) B ( -1.86) (6.00) (3.77) (11.37) ( -1.60) (4.55) (3.36) (9.69) Sweden A ( -0.23) (9.93) (5.05) (2.39) B ( -0.62) (10.14) (5.90) (1.85) * ( -0.97) (7.27) (6.06) (1.76) Denmark A * ( -1.83) (1.96) (5.85) (1.82) B * ( -2.24) (2.70) (6.82) (1.80) * O.Dl ( -1.54) (2.10) (5.50) (2.15) Finland A * (-1.11) (11.98) (7.28) (6.37) B ( -0.49) (10.02) (4.37) (6.18) ( -0.90) (11.39) (5.16) (6.44) () represent t-values, H 0 : /3i = 0; * signifiantly different from unity at 5% level; n = 43.

0. Gj lberg 1 Agriultural Eonomis 13 (1995) 119-123 123 4. Conlusions The markets for piglets and hogs are in general quite volatile. The Nordi markets make no exeption.

5 0. Gj lberg 1 Agriultural Eonomis 13 (1995) Conlusions The markets for piglets and hogs are in general quite volatile. The Nordi markets make no exeption. Our statistial results support the hypothesis that the Nordi hog produers prie the piglets rationally in the sense that the weight adjusted piglet prie may serve as an unbiased foreast for the hog prie 3 months ahead, onditional on the expeted feed osts and profits. Furthermore, the foreast errors seem to be unsystemati. Our onlusion must be somewhat modified in the ase of Denmark. Although the piglet pries also in the Danish samples were found to be unbiased, the model did not perform as well as for the neighbouring ountries. This may, of ourse, indiate that the produers in the highly ompetitive Danish market are less rational than their Nordi neighbours. An alternative, and more plausible explanation, is that in the ase of Denmark, our model is not well speified. As mentioned above, modeling expeted feed osts and profits as simple AR(l) proesses may be too simplisti in the Danish ase. Despite this modifiation, based on the Nordi data, piglet pries seem to be remarkably good foreasts for hog pries one quarter ahead. Aknowledgments Very useful omments on a previous draft from the Editor and two anonymous reviewers are gratefully aknowledged. The usual dislaimer applies. The omplete data set is available from the author upon request together with information about soures and variable definitions. Referenes Frenkel, J.A., Tests of rational expetations in the forward exhange market. S. Eon. J. 46: Hansen, L.P. and Rodrik, R.J., Forward exhange rates as optimal preditors of future spot rates: an eonometri analysis. J. Polit. Eon. 88: Sargent, T.J., A note on the maximum likelihood estimation of the rational expetations model of the term struture. J. Monetary Eon Wikens, M.R., The effiient estimation of eonometri models with rational expetations. Rev. Eon. Stud. 49:

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