This paper investigates the rationality and price responsiveness of sugar cane and coffee farmers in Jamaica for the period 1960-1980. The output supplied by these farmers is modeled to incorporate anticipation by farmers of commodity board actions. The structure of constraints imposed by the rationality of these anticipated responses 1s derived and tested by means of a likelihood ratio test statistic. The results support the joint hypothesis of rationality and price responsiveness. Policy implications of the anticipated response function are also identifies

Graham, Douglas H.

Pollard, Stephen K.

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Economics and Sociology Occasional Paper No. 1260 Rational Expectations and output supply Evidence from the Sugar cane and Coffee Industries in Jamaica stephen K. Pollard* Douglas H. Graham C/9?6] * Associate Professor of Economics and statistics, California state University, Los Angeles and Professor of Agricultural Economics and Rural sociology, The Ohio state University. ABSTRACT This paper investigates the rationality and price responsive-ness of sugar cane and coffee farmers in Jamaica for the period 1960-1980. The output supplied by these farmers is modeled to incorporate anticipation by farmers of commodity board actions. The structure of constraints imposed by the rationality of these anticipated responses is derived and tested by means of a like-lihood ratio test statistic. The results support the joint hypothesis of rationality and price responsiveness. Policy impli-cations of the anticipated response function are also identifies. RATIONAL EXPECTATIONS AND OUTPUT SUPPLY: EVIDENCE FROM THE SUGAR CANE AND COFFEE INDUSTRIES IN JAMAICA Economists have long agreed that farmers in Less Developed countries {LDC's) are responsive to price incentives. This consensus has developed out of the growing evidence of the last twenty-five years, ably summarized in the seminal work of Askari and cummings [3], as well as Schultz [11] and Krishna [7]. These results reveal that farmers respond to the expected price they will receive, where the expected price is formulated as an adap-tively formed function of past prices received. An expected price variable is used since the prevailing price of the crop at planting time may not be the same as the price received at harvest. Whether farmers' expectations are indeed adaptive is an important question that has not been addressed by past researchers, with the exception of Shonkwiler and Emerson [12] and Eckstein [4 1 5]. Finally, from the point of view of marketing board policy, it is important to determine if farmers in fact do respond to prices and the way farmers form their price expectations before setting farmgate prices and establishing board objectives in such areas as gross rnarketi~g margins and foreign exchange target earnings. These latter goals are decidedly influenced by the output response of farmers to prices. - 2 -In this paper, we directly test whether Jamaican farmers respond to the expected price received and whether price expec-tations are formed rationally. The rational expectations hypo-thesis (REH} assumes that farmers use all information available to them when making forecasts about the expected price received (Muth) [8]. The Jamaican agricultural subsectors of sugar cane and coffee provide a unique opportunity for testing the REH, since prices are determined by a set of marketing boards for each of these crops and the information used in making these pricing decisions, such as world prices and exchange rates, is published and distributed to farmers at annual meetings. The REH theoretical model and methodology is presented in the next section. A full information maximum likelihood tech-nique is utilized as the REH implies highly non-linear restric-tions across the derived set of equations (Sargent) [10]. The statistical results are presented and discussed in the third section of the paper. The final section presents the conclusions and implications of our study. we conclude that farmers formu-late expectations rationally and they do respond to the expected price. These findings create important implications for market-ing board policies in a small, open economy like Jamaica. Analytical Framework Consider the general form of the output supply function found in the literature (Askari and cummings) [3]: ( l ) ( 2 ) ( 3 ) - 3 -e Qt = ao + alPt + a2Qt-l + ut where Q is the quantity supplied; P~ is the expected farm-gate price: u is a normally distributed random variable with zero mean, constant variance, and serial independence. P~ is unobserved but its expectation, if formed rationally by farmers, is based on an information set Q that can be expressed as: e Pt = E(Pt IQt-1) Pt, the observed farmgate price can then be decomposed into an expectational component (P~) and an error component (vt} e Pt : Pt + vt where E(P~vt) = 0 E(utut-i) = a~ for i=O 0 for i~O E(vtut-i) = a~ for 0 for i~O 0 for i;O i=O Eqs. (1) and (3} represent the structural model describing output supplied by farmers. These equations cannot be estimated di-rectly due to the unobservability of P~ and lack of knowledge of the variables that make up Q. This can be overcome by specifi-cation of a subset of Q so that P~ can be stated as an expression of exogenous and lagged endogenous variables. The expression for P~ can then be substituted into eqs. (1) and (3) and a set of estimable reduced form equations derived. The variables - 4 -incorporated into the informational subset of Q are drawn from the pricing data utilized in setting farmgate prices that mar-keting board officials have published in interviews, newspaper articles and annual reports. This information is readily avail-able to all farmers. For example, in the coffee sector, the Coffee Industry Board (CIB) announces a price at the beginning of the crop season with the final price the farmer receives, i.e. the announced price plus a "bonus" payment determined by the board at the end of the season. The bonus payment can vary from zero to any amount the board wishes to pay and therefore the farmer does not know the final price to be paid. We can specify this price setting behav-ior in the coffee sector in the following manner: (4) e DPt = b 0 + b1EWPt + b 2EERt + b3ELMt Substituting eq. (4) into eqs. (1) and {3) gives the following set of equations: (6) DPt = b 0+ b1EWPt + b 2EERt + b3ELMt + vt where Q is the quantity of coffee in boxes (10 lbs. of coffee per box) delivered by farmers to the BoardJ DP is the difference between the announced price and the final price received by farmers; WP is the nominal F.O.B. price of coffee received by the Board in u.s. dollars~ LM is the percentage share of coffee sold by the Board to domestic coffee brewers; ER is the exchange rate ($J/$US) deflated by the GDP deflatorrl/ and E is the conditional expec-tation operator. - 5 -Economic theory suggests that a 1 , b1 , b 2, b 3 should all be positive. For sugar cane, specification of the information subset yields: (7) P~ = b 0 + b1EWPt + b 2EERt + b 3ECSRt where WP is the nominal F.O.B. price of sugar received by the board in u.s. dollars; ER is the exchange rate ($J/$US) deflated by the GDP deflator;~/ CSR is the cane sugar ratio which defines how much cane is required to make a ton of sugar; E is the expected value operator. Again economic theory suggests that the signs of a1, b1, b2 are positive. The sign of b3 is expected to be negative because the more sugar cane that is required to produce one ton of sugar, the less the value and price of the crop. substituting eq. (7) into eqs. (1) - (3) yields: (8) Qt = a 0 + a 1b 0 + a 1b 1EWPt + a 1b 2EERt + a 1b 3ECSRt + a 2Qt-l + et where Q is the quantity of sugar cane in tons. (9) Pt = b0 + b1EWPt + b 2EERt + b 3ECSRt + zt Eqs. (5) - (6) and (8) - (9) represent the reduced form equations, with the REH imposed, of the "structural" model for output supply in the coffee and sugar cane sectors. This is termed the restricted reduced form model as the coeffi-cients of the output equation are in the price equation.l/ The output and price reduced form equations without the rationality of farmers' expectations imposed are written as follows (using coffee as our example): (10) Qt = k0 + k1EWPt + k2EERt + k 3ELMt + kyQt-l + Ut - 6 -(11) Pt = b 0 + b1EWPt + b2EERt+ b 3 ELMt + vt A test of the REH is then a test of the equality of the following cross equation restrictions: (12) ko = ao + albo (13) kl = albl (14) k2 = alb2 (15) k3 = alb3 These restrictions imposed by the REH are highly nonlinear and hence, eqs. (5) and (6) are jointly estimated as are eqs. (10) and (11) by a Full Information Maximum Likelihood (FIML) technique. The validity of the restrictions in eqs. (12) - (15) are then tested by means of a likelihood ratio test statistic (LRTS). The LRTS is equal to -(2 log l) where \ = Lr/Lu and Lr is the value of the log of the maximum likelihood of the restricted model and Lu is the value of the log of the maximum likelihood of the unrestricted model. The LRTS is distributed as a x2 with 2 degrees of freedom. A similar procedure is utilized for sugar cane. Empirical Results The restricted and unrestricted reduced form equations were estimated using annual data over the period 1960-1980. We handle the problem of the expected exogenous variables by utilizing the actual values lagged one period as the expectations of these variables are determined outside the model. The estimated para-meters and related statistics of the reduced form equations are presented in Table 1 and the estimated structural parameters are - 7 -presented in Table 2. The LRTS is equal to 2.278 with a marginal significance level of .3202. The marginal significance level is equal to the area in the upper tail of a x2 distribution with two degrees of freedom marked off by the LRTS. Given this mar-ginal significance level, the restrictions of the REH cannot be rejected. Coffee farmers are responsive to the expected bonus payment received and form such expectations rationally. The results for sugar cane can be interpreted in a similar fashion. The signs of the estimated coefficients in the restricted model, have the expected signs and are significantly different from zero except for b1. The LRTS is equal to 2.862 with a marginal signi-ficance level of .2391 indicating that the REH cannot be rejected. A more relevant measure to evaluate the impact of the ex-pected price and the variables in the information subset on out-put supplied are the elasticities rather than the estimated co-efficients themselves. The elasticities, reported in Table 3, are all derived at the point of sample means. The values for ope and pe are the predicted values derived from eqs. (4) and (7) respectively. The elasticity of supply with respect to expected price is .205 for coffee and .629 for sugar cane. That is, an expected 10% increase in the bonus payment will raise the output of coffee supplied to the CIB by 2.05% and a correctly antici-pated 10% increase in sugar cane price will raise sugar cane output supplied by 6.29%. The calculated elasticity for coffee supply is much less thar. the value of .82 reported by Williams - 8 -£13] for the supply elasticity of Jamaican coffee over the period 1953-1969, however, he used an adaptive expectations approach and the actual final price received. Elasticities for the other variables can be interpreted in the same way. For sugar cane, a change in the cane sugar ratio has a strong impact on the supply response of sugar cane producers. This is not surprising as technological improvement in sugar mills in Jamaica has not been undertaken and the cane-sugar ratio has been increasing over time (Annual Report of AICFA, 1983). The insignificance of the coefficient for the nominal world price of sugar implies that farmers do not consider this piece of information when formulating their price expectation and suggests that changes in world sugar prices are not transmitted to farmers by the board. sugar cane farmers are then "protected" from some uncertainty due to world price fluctuations.!/ The significance of the positive coefficient for the real exchange rate implies that changes in macroeconomic and trade policies have a direct influence on output supplied. The implication of these findings is that the sugar Industry Authority can improve incentives for sugar cane farmers only if the government will enhance incentives faced by all exporters (i.e. a devaluation of the exchange rate). A different picture emerges in the coffee industry. The coefficient of the nominal world price of coffee is significant, while the coefficient of the exchange rate is insignificant. The Coffee Industry Board does pass on world price increases to farmers, thereby improving incentives faced by farmers, while an - 9 -improvement of generalized incentives for all exporters (i.e. exchange evaluation) has no impact on increasing output supply. Coffee farmers appear to realize that higher world prices are translated into higher bonus payments regardless of general macro-economic conditions. However, world price fluctuations are ap-parently passed through to the farmer who is consequently subject to some uncertainty.~/ Conclusions The major finding of this paper is that farmers do respond to the expected price received and that farmers use available information to formulate this expectation. Rational expectations of price formation by sugar cane and coffee farmers implies that farmers correctly anticipate board pricing decisions over time and adjust output supplied accordingly. However, extensive interviews with marketing board officials by the authors indicate that the positive price responsiveness of these farmers has not been recognized by these officials. The sugar and coffee marketing boards in Jamaica should consider the behavior of their respective farmer constituencies when setting farm level prices if desired foreign exchange target earnings are to be attained. The marketing boards cannot set farmgate prices independent of the farmers output response to such prices since farmers respond to the boards' actions.~/ These results indicate there is ample room for improvement in the pricing policy of these Boards.l/ !I 1/ ll !/ ~I ~I 21 - 10 -FOOTNOTES Following Hertford, for an export crop farmer the important relationship is the domestic cost of producing his export crop compared to the value of his output valued in the domes-tic currency. As the price (and value) of foreign exchange rises relative to the domestic price level, incentives to produce export crops are enhanced. See footnote 1. DPt-i and Pt-i are not included in the information subsets for sugar and coffee respectively, because these variables represent price expectation formation under the adaptive ex-pectations hypothesis which cannot be nested within a model incorporating the rational expectations hypothesis. A re-jection of the null hypothesis that the restrictions of the REH hold: cannot lead one to conclude that the adaptive ex-pectations hypothesis or any other hypothesis is "correct". This is consistent with findings reported by Pollard and Graham [9] on price stabilization policy of marketing boards in Jamaica. See footnote 4. This point is exemplified in statements made by the head of the AICFA, after the writing of this article, which lambasted the current government for ignoring the sugar cane farmers in sugar industry policy decisions (The Daily Gleaner, December 21, 1985 p. 3). Recognition of this statement has come from the current government (again after completion of this article) which has reorganized the Coffee Industry Board to improve policy coordination throughout the coffee industry beginning in 1986. - 11 -REFERENCES [1] Annual Report of the All Island cane Farmers Association, Kingston, Jamaica, various years. [2] Annual Report of the Coffee Industry Board, Kingston, Jamaica, various years. [3] Askari, Hossein and cummings, John T., Agricultural supply Response--A survey of the Econometric Evidence, Praeger Publishers, New York, 1976. [4] Eckstein, Zri, "A Rational Expectations Model of Agricul-tural supply," Journal of Political Economy, February 1984. [5] Eckstein, Zvi, "The Dynamics of Agricultural supply: A Reconsideration," American Journal of Agricultural Econo-mics, May 1985. [ 6] Hertford, Reed, ''Government Price Policy in Colombia," in T.W. Schultz (ed.), Distortions of Agricultural Incentives (Bloomington: Indiana University Press, 1978). [7) Krishna, Raj, "Farm supply Response in India-Pakistan: A case study of the Punjab Region," Economic Journal, Vol. 73, No. 291, Sept. 1963, pp. 477-87. [8] Muth, J.F., "Rational Expectations and the Theory of Price Movements," Econometrica, Vol. 29, 1961, pp. 315-35. [9] Pollard, stephen K. and Douglas H. Graham, "Price Policy and Agricultural Export Performance in Jamaica," world Development, Vol. 13, No. 9, 1985, pp. 1067-1075. [10) sargent, Thomas J., Macroeconomic Theory, Academic Press, New York, 1979. [11) Schultz, T.w. (ed.), Distortions of Agricultural Incentives, Indiana University Press, Bloomington, Indiana, 1978. [12] Shonkwiler, J. Scott and Robert D. Emerson, "Imports and the supply of Winter Tomatoes: An Application of Rational Expectations," American Journal of Agricultural Economics, Vol. 64, No. 4, 1982, pp. 634-641. [13] Williams, R.L., "Jamaican Coffee Supply, 1953-1968: An Exploratory study," social and Economic studies, June, 1972. - 12 -Table 1. FIML Estimates of the Reduced Form Equations for Jamaican Coffee and Sugar cane Supply, 1960-1980. sugar cane Coffee output Equation Restricted Unrestricted Restricted Unrestricted constant EWPt EERt ECSRt ELMt Ot-1 Price Equation Constant EWPt EERt ECSRt ELMt L LRTS 1759440 ( 776751) 443.473 (378.647) 300360 ( 155308) -108889 (46696.6) n.a. .4039 ( .2379) 19.4638 ( 5.8777) .0048 ( .0054) 3.2571 ( 1.9212) -1.1806 ( .5519) n.a. -303.833 1498900 (1593170) 227.384 (1266.96) 348766 ( 296609) -76404.8 (91569.0) n.a. .3567 ( .2578) 26.5620 (26.0848} .0085 ( .0157) 2.5438 ( 5.7443) -1.8558 ( 1.7280) n.a. -302.392 2.862 [.2391] 417994 (93712.2) 25.1082 (11.7384) -1689.85 (14854.2) n.a. 653.863 (513.144) -.9839 ( .2059) -.8525 ( 1.0907) .0010 ( .00018) -.0678 ( .6125) n.a. .0262 ( .0110) -247.986 518579 ( 205471) 7.960 ( 22.657) -61561.9 ( 105305) n.a. 1041.08 (1437.73) -1.013 ( .2534) -1.967 ( 2.564) .j)Ol2 ( .0003) .6640 ( 1.2670) n.a. .0208 ( .0345) -246.847 2.278 [ .3202] Notes: Asymptotic standard errors in parentheses. Marginal significance in brackets. - 13 -Table 2. FIML Estimates of the structural Models for Jamaican Coffee and Sugar cane supply, 1960-1980 Parameter sugar cane ao -335575.6 ( 50588.9 ) a1 92254.4 ( 58827.0 } a2 .4039 ( .2379 ) bo 19.4638 ( 5.8777 ) bl .0048 ( .0054 b2 3.2571 ( 1. 9212 b3 -1.1806 ( .5519 Note: Asymptotic standard errors in parentheses. Coffee 439310 ( 76433 ) 24997.4 ( 13326 ) -.9839 ( .2059 -.8525 ( 1. 0907 .0010 ( .00018) -.0678 ( .6125 .0262 ( .0110 - 14 -Table 3. Derived Elasticies of output supply with Respect to Expected variables--Restricted Model Elasticity of Supply with Respect to: sugar cane .629 n.a. n.s • • 206 -.577 n.a. Note: Calculated at the point of sample means Coffee n.a • . 205 .182 n.s. n.a • • 114 

Rational Expectations and Output Supply: Evidence from the Sugar Cane and Coffee Industries in Jamaica

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Rational Expectations and Output Supply: Evidence from the Sugar Cane and Coffee Industries in Jamaica

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