Citation |

- Permanent Link:
- https://ufdc.ufl.edu/UF00047745/00001
## Material Information- Title:
- An analysis of weekly F.O.B. prices for fresh limes
- Series Title:
- Technical report Florida Agricultural Market Research Center
- Creator:
- Shonkwiler, J. S ( John Scott )
Degner, Robert L Florida Agricultural Market Research Center - Place of Publication:
- Gainesville Fla
- Publisher:
- University of Florida, IFAS, Food and Resource Economics Dept.
- Publication Date:
- [1980]
- Language:
- English
- Physical Description:
- iv, 30 p. : ill. ; 28 cm.
## Subjects- Subjects / Keywords:
- Limes -- Prices -- Florida ( lcsh )
Lime fruit industry -- Prices -- Florida ( lcsh ) - Genre:
- bibliography ( marcgt )
non-fiction ( marcgt )
## Notes- Bibliography:
- Includes bibliographical references (p. 29-30).
- General Note:
- "December 1980"--Cover.
- Funding:
- Technical report (Florida Agricultural Market Research Center) ;
- Statement of Responsibility:
- J. Scott Shonkwiler and Robert L. Degner.
## Record Information- Source Institution:
- University of Florida
- Holding Location:
- University of Florida
- Rights Management:
- All applicable rights reserved by the source institution and holding location.
- Resource Identifier:
- 027808755 ( ALEPH )
26812824 ( OCLC ) AJG5563 ( NOTIS )
## UFDC Membership |

Full Text |

HISTORIC NOTE The publications in this collection do not reflect current scientific knowledge or recommendations. These texts represent the historic publishing record of the Institute for Food and Agricultural Sciences and should be used only to trace the historic work of the Institute and its staff. Current IFAS research may be found on the Electronic Data Information Source (EDIS) site maintained by the Florida Cooperative Extension Service. Copyright 2005, Board of Trustees, University of Florida DECEMBER 1980 TECHNICAL REPORT 80-2 - An Analysis of Weekly F.O.B. Prices for Fresh Limes (Jo AN ANALYSIS OF WEEKLY F.O.B. PRICES FOR FRESH LIMES J. Scott Shonkwiler and Robert Assistant Professors L. Degner Y:-: A.a.... .. : r University of Florida IFAS, Food and Resource Economics Department Gainesville, Florida 32611 The Florida Agricultural Market Research Center is a service of The Food and Resource Economics Department of the Institute of Food and Agricultural Sciences The purpose of this Center is to provide timely, applied research on current and emerging marketing problems affecting Florida's agri- cultural and marine industries. The Center seeks to provide research and information to production, marketing, and processing firms, groups and organizations concerned with improving and expanding markets for Florida agricultural and marine products. The Center is staffed by a basic group of economists trained in agriculture and marketing. In addition, cooperating personnel from other IFAS units provide a wide range of expertise which can be applied as determined by the requirements of individual projects. ^-a) LT 1 TABLE OF CONTENTS LIST OF TABLES . . . . . LIST OF FIGURES . . . . . INTRODUCTION . . . . . The Florida Lime Market . . . Causal Analysis an Transfer Function Identifi Seasonality of the Lime Price Equation . SUMMARY . . . . . FOOTNOTES . . . . . REFERENCES . . . ... . . . . catii . . LIST OF TABLES Table 1 Filter models . . 2 Residual cross correlations 3 Causality tests . . 4 Estimated transfer function 5 Florida lime price equation . . . . . . . . . . . . . . . model . . ... . . . . . . Page ii iv 1 3 4 15 25 26 27 Page 7 9 10 14 18 LIST OF FIGURES Figure Page 1 Average weekly F.O.B. lime prices and shipments 1976/77 through 1979/80 seasons . . . . 2 2 Seasonal variation of FLSt parameter and 95 percent confidence interval . . . . . 19 3 Seasonal variation of FLSt-1 parameter and 95 percent confidence interval . . . . ... 20 4 Seasonal variation of FLSt-2 parameter and 95 percent confidence interval . . . . . 21 5 Seasonal variation of FLSt-3 parameter and 95 percent confidence interval . . . . 22 6 Seasonal. variation of sum of parameters forFLS FLS. I, FLS_ 2and FLSt 3 and 95 percent confidence interval for thi sum . . . . . 24 AN ANALYSIS OF WEEKLY F.O.B. PRICES FOR FRESH LIMES J. Scott Shonkwiler and Robert L. Degner INTRODUCTION Many recent studies have analyzed the supply and marketing of fresh Florida limes (Degner and Mathis; Mathis; Degner and Rooks; Ward and De; Degner, Shonkwiler and Cubenas [A, B],; Pagoulatos, Shonkwiler and Degner). A concern common to most of these studies is that of depressed prices resulting from large seasonal supplies during the summer months. Another concern focuses on the effect of Mexican lime exports to the U.S. and corresponding effects on Florida fresh lime prices and future production. To date, however, no study has integrated these two concerns so that a single model can address them simultaneously. The objective of this study is to provide a systematic means for testing causal relationships and for specifying distributed lag formulations within the context of a model for weekly lime prices. Our discussion pro- ceeds as follows: We first review the general market forces affecting Florida's F.O.B. lime prices and state our hypotheses. Next, causal relationships are investigated via the transfer function approach. The magnitude and statistical significance of seasonal parameters are then investigated, and finally, we discuss the implications of our analysis. J. SCOTT SHONKWILER and ROBERT L. DEGNER are assistant professors of food and resource economics, University of Florida. The Florida Lime Market Weekly fresh lime prices typically exhibit substantial variation during the annual April through March marketing season (Figure 1). The lime production cycle explains much of the volatility. Very few limes are produced during the winter and early spring, but large quantities are available during late spring and most of the summer. Thus, it is hypothesized that lime quantities, or shipments, significantly affect weekly prices. Because the shelf life of limes is of sufficient duration, we postu- late that inventories in the marketing channel probably affect weekly prices. Unfortunately there are no data available on the volume of unsold limes held by wholesalers and retailers. Therefore previous levels of lime shipments are used as a proxy. Lime imports, primarily 'Persian' limes from Mexico, have increased dramatically in the past five years. These imports are indistinguishable from limes produced in Florida and are essentially perfect substitutes. Thus, they are hypothesized to have a significant, adverse affect on Florida lime prices. There is a widespread belief in the industry that consumer demand for fresh limes varies seasonally, and is affected by special holidays. Seasonal demand parameters, explored by Ward and De, are further investi- gated and refined. Models specifying no seasonality and models with seasonality are estimated. Other domestically produced limes and lemons are commonly believed to have significant negative effects on Florida fresh lime prices, but the preponderance of evidence indicates otherwise. Ward and De obtained a weak relationship between lime prices and lemon supplies and other FIGURE 1 AVERAGE WEEKLY F.O.B. LIME PRICES AND SHIPMENTS 1976/77 THROUGH 1979/80 SEASONS $10 Lime Prices ($/10 lb. carton) ( .. ) Lime Revenues ($100,000) ( ..) I .11 / ~I .. 'I 'I I *s= ~ 'I I' ~1 35 1000 cartons Lime Shipments 30 (50 lb. units) ( ) 40 Week of Season 30 studies have found only a marginal relationship (Degner, Shonkwiler and Cubenas; Pagoulatos, Shonkwiler and Degner). Although fresh limes are also produced commercially in California, their lime production is pri-:. marily comprised of the seeded 'Mexican' variety which is viewed by many retailers as inferior to the 'Persian' variety because of its tendency to quickly turn yellow, resulting in decreased marketability (Degner and Mathis). Finally factors such as population, consumer disposable income, and long term advertising and promotion programs, while important in an extended analysis, are subsumed under a trend term over the four year period studied. Thus we focus our attention on how Florida fresh lime prices are related to Florida and Mexico lime shipments, seasonal factors, and a secular trend term. Causal Analysis and Transfer Function Identification Four years of weekly data on lime prices and shipments were analyzed for the 1976-77 through 1979-80 April to March seasons (Federal-State Market News Service). First differences of the logarithms of the variables of interest were used to provide stationary series for the Mexican imports (MLS) and Florida F.O.B. price (FPR) and shipments (FLS) variables.1 For a traditional economic analysis, prior information and/or experimen- tation is used to discriminate between endogenous and exogenous variables as well as to specify the form and length of lagged responses. While theory: and observation can suggest the general nature of such relationships, the exact nature and timing of causal relationships may be unknown in an emoirical study (Bessler aniSchrader). The transfer function approach proposes that the data be given the opportunity to provide this information. The transfer function approach can employ the Granger notion of causality to discern interrelationships between two series, Specifically Granger says that"Yt is causing Xt if we are better able to predict Xt using all available information than if the information apart from Yt had been used." (p.428). This prediction oriented definition of causality is conceptually straightforward, but it is subject to the major deficiency that rarely is it possible to include all relevant information in predicting Xt. A simpler definition is proposed which states that Yt causes Xt when it can improve the prediction of Xt compared to the prediction of Xt taking into account the past history of Xt alone, Causality may be unidirectional or have feedback, and maybe instan- taneous or delayed. To indicate unidirectional causality we write Xt_j Yt for j > 0 (j = .0 implies an instantaneous relationship). Feedback occurs when current, lagged, and future Y causes and is caused by current, lagged and future X. Haugh has suggested a method to elicit the existence of Granger causality between two time series. Assume that the two stationary series may be represented by the univariate models: (1) G(L)Xt =ut (2) H(L)Yt = vt where G(L) and H(L), the filters, are invertible polynomials in the lag operator L, and ut, vt are white noise processes (innovations) having 2 2 2 variances 0 v, respectively By construction. each individual noise process is not autocorrelated and represents that part of the series which cannot be explained by past information. To assess Granger causality in a systematic manner, Haugh suggests examining the cross correlations between the two residual series. To implement this technique for eliciting causality univariate models were identified and fitted to the three time series. Using the Box-Jenkins approach auto regressive models of order five (AR5) were fitted to the Mexican imports (MLS) and Florida shipments (FLS) series, and a first order auto regressive model (ARI) was used to filter the Florida lime price series (FPR). The estimated models are presented in Table 1. The chi-squared statistics were calculated under the null hy- pothesis that the residuals from these models are mutually uncorrelated. The associated a-levels indicate that the null hypothesis cannot be re- jected at a reasonable level of significance for any of the estimated filter models. It is assumed that each residual series is white noise. This assumption then implies that the cross correlations between the. series are not confounded by the effects of autocorrelation in the in- dividual series. The cross correlation between the residuals is denoted at lag K as (3) uv(K) = E(ut-k,') [E(ut)2E(v)2] 1/2 If for a positive value of k the cross correlation is significantly different than zero we say that Xt leads (causes) Yt' and conversely for a negative value of k we say that Yt leads (causes) Xt. Of course, u and v are not observed but are replaced by their estimated values form (1) and (2). The sample counterpart to the lefthand side of (4) then is ruv(k). Under the null hypothesis that X and Y are independent series, Haugh has shown that the r(k) are asympototically normally and independently distributed with mean zero and standard deviation T -1/2, where T is the sample size. Once the residual cross correlation estimates have been calculated, statistical tests of significance for individual Table 1.--Filter Models Florida Lime Shipments (1 + .355B + .08882 (.069) (.073) - .011B3 - (.073) U2 = .108 .1584 - (.073) .176B)FLSt = a (.070) X2(19) = 16.24 Florida Lime Price (1 .392B)FPRt = a2t (.064) 32 = .023 X2(19) = 15.7 Mexican Lime Shipments (1 + .742B + .476B2 + .443B3 + .412B4 + .236B5)MLSt = a3t (.068) (.081) (.082) (.081) (.069) o2 = .260 X (19) = 24.3 a = .641 a = .677 a = .185 estimates are obtained by the criterion that sample cross correlations exceed their approximate standard deviations by a factor of two. That is (4) r^(k) 1 2T-1/2 indicates a significant cross correlation. Individual significant cross correlations may then be used to detect causal directions at specific lags. Overall tests of unidirectional causality have been suggested (Pierce) using the following statistics m (5) Q = T [r^^(k)]2 indicates X leads Y at the a level k=l 2 of significance if it exceeds X m, and -m 2 (6) Q = T 2 [r^(k)] indicates Y leads X at the a level y*x uv k=-1 of significance if it exceeds x2, m. The calculated residual cross correlations are presented in Table 2. Table 3 summarizes the results of the statistical tests which follow from the proceeding discussion. The null hypothesis of no instantaneous causality between the series may be rejected with high degrees of confidence for the Florida lime shipment-Florida lime price relationship and the Florida lime shipment-Mexican import relationship. On the other hand there appears to be no instantaneous relationship between Florida lime prices and Mexican shipments. The unidirectional causality tests show that the null hypothesis of one series not causing the other may be strongly rejected in one case and marginally rejected in another. The clear rejection implies that Mexican imports lead (or cause ) Florida lime prices. Additionally at the .112 level we can reject the hypothesis that Florida lime prices do not cause Table 2.--Residual cross correlations Current residuals Current and Florida lime Florida lime Mexican lime Lagged Residuals shipments (alt) price (a2t) shipments (a2t) -.184 -.179 -.032 -.017 -.060 -.110 -.022 alt alt-I alt-2 alt-3 al t-4 alt-5 alt-6 a2t a2t-'1 a2t-2 a2t-3 a2t-4 a2t-5 a2t-6 a3t a3t-1 a3t-2 a3t-3 a3t-4 a3t-5 a3t-6 -.184 -.106 -.012 -.093 -.013 -.022 -.019 .268 -.041 -.007 -.033 .106 .041 .068 .268 .010 -.082 -.019 -.031 -.012 .001 .023 .145 .051 .013 .027 -.092 -.060 .023 -.099 -.215 -.169 -.060 .039 .005 Table 3.--Causality tests. Instantaneous Causality Hypothesis alt a2t a1t i a3t a2t / a3t Unidirectional Causality Hypothesis alt a2t alt Aa3t a2t /-alit a2t / a3t a3t /+alt a3t /*a2t a 208 observations. b 6 degrees of freedom. Calculated correlation -.184 .268 .023 Calculated X2b 10.30 1.72 4.38 7.72 4.24 18.64 a-level .008 .001 .746 a-level .112 .944 .625 .259 .645 .005 Florida lime prices. However from Table 2, the cross correlation between alt-land a2t reveals that we may reject at the .01 level the hypothesis that lime shipments lagged one period do not cause current Florida lime prices. Thus these results indicate instantaneous and unidirectional! causality from the two shipment series to the price series. Further instantaneous causality exists between the two shipment series, but it appears that neither series leads the other. It should be noted that several difficulties with this method of identifying causal relationships have been noted. It has been shown by Sims (1977) that the chi-square tests for unidirectional causality are biased toward acceptance of the null hypothesis. Additionally, Feige and Pearce have pointed out that the causality tests may be highly con- ditioned by the filters used to obtain the whitened noise processes u and v. Nevertheless, this procedure provides a systematic means for permitting the data themselves to suggest patterns of interrelationship and generates the major results necessary for specifying the transfer function. The causal relationships detected via cross-correlating the residuals of the filtered series readily lend themselves to transfer function analysis. Suppose that Xt leads Yt, but not conversely, then as Sims (1972) has noted we can properly write Yt as a distributed lag on Xt. Mathematically (7) Yt = V(L)Xt + nt where nt is some (complex) noise process. The weights VO, VIL, V2L2... are called the impulse response parameters of the system. As noted by Zeller and Palm, this expression has as its counterpart the final form representation of a dynamic econometric model. In determining the order of V(L) the residual cross correlations of the filtered series are analyzed to suggest the so-called dynamic shock model which is of the form (8) vt = W(L)ut + Y(L)at where ut and vt are the previously defined noise process, 'F(L) is a polynomial in the lag operator L of the same degree as W(L) and at is the dynamic shock model error process (Haugh and Box). By construction, Cov (ut, us) = 0 for all t f s; i.e., the ut are orthogonal to each other. Thus, each individual W. represents the (bivariate) regression coefficient relating vt to ut-k, i.e. -a1 (9) Wi p uv(1) . Once the order of the dynamic shock model is determined and the appropriate elements of W(L) estimated, the impulse response model is obtained by replacing the observed error processes by the filtered series: (10) H(L)Yt = W(L)G(L)Xt + Y(L)at or (11) Yt = H(L)-1W(L)G(L)Xt + H(L)-1Y(L)at which may in general be estimated by a non-linear least squares or maximum likelihood algorithm. Given the nature of the cross correlations between a2t and alt, a3t the general form of the dynamic shock model is hypothesized to be (12) a2t = (W0 W1B) alt + (-W2B2 W3B3)a3t + nt. The estimated parameters are calculated to be W0 = -.0849 W1 = Wi = W2 = W3 = .0826 .0639 .0503 The noise processes in the dynamic shock model may be replaced by their associated filter models which were presented in Table 1. This substitution yields (13) (1 .392B)FPRt By carrying out the indicated the resulting remainders, the (14) FPRt = (-.085 - .122B3 - = (-.0849- .0826B)(1 + .355B + .088B2 .011B3 .158B4 .176B5)FLSt + (-.0639B2 - .0503B3)(1 + .742B + .476B2 + .443B3 + .412B4 + .236B5)MLSt + nt. multiplications and divisions and truncating impulse response function is identified as .146B .094B2 .043B3)FLSt + (-.064B2 .106B4 .097B5 .087B6 .070B7 .039B8)MLSt + nt. where nt is some (complex) noise process. The noise component may be ignored at the expense of incurring some inefficiency in estimation. Thus the sample data was used to estimate the model given by expression (14) yielding the results in Table 4. There is substantial agreement between the identified transfer function model (expression 14) and the estimated model (Table 4). In fact 95 percent confidence intervals on the estimated parameters include each of the point estimates of the corresponding identified transfer function's parameters. Table* 4.--Estimated transfer function model. Standard error .030 ,032 .033 .031 .021 .025 .026 .026 .026 .024 .020 Variable FLSt FLSt-1 FLSt-2 FLSt-3 MLSt-2 MLSt_3 MLSt-4 MLSt-5 MLSt-6 MLSt-7 MLSt-8 Parameter -.133 -.187 -.108 -.034 -.071 -.134 -.148 -.116 -.093 -.062 -.034 = .0203 = 1.61 Before attempting to correct for the error process on the hypothesized transfer or dynamic regression model, we consider ways of accommodating possible seasonal influences in the following section. Seasonality of the Lime Price Equation There is evidence of strong seasonal effects associated with the Florida lime price- quantity relationship (Ward and De). Seasonal influences may be ascribed to varying levels of consumer demand as affected by weather patterns or holidays, changes in marketing methods as production levels vary, or changes in size or quality of the fruit during the season. In particular we are concerned with identifying whether these changes shift the price-quantity curve or alter its slope, or both. To investigate such seasonal effects a flexible technique is required. Ward and De incorporate seasonality via slope and intercept interaction by using a sine wave having a 52 week period. While this may be justified by the strong annual lime production cycle, this technique appears unneces- sarily restrictive because it requires the seasonal effects to be smooth, continuous and symmetric. An alternative approach is to assume that seasonal effects may be captured by piecewise linear segments termed splines. By making the linear segments small enough, even highly curvilinear re- lationships may be closely approximated. The method used in this study is outlined below. Let s represent the seasonal unit of observation and S represent the length of season so that s = 1, ..., S. Those points or values of s where the slopes of the splines may change will be termed nodes and designated by ni with i = 1, ..., k. The general form of the seasonal linear spline function may be written (Robb) B(s) = a0 + b0s + (a1 + bl(s n1))d1 + (a2 + b2(s n2))d2 + ... where an individual d. = 1 if s > ni, otherwise d. = 0. By imposing the constraint that the piecewise linear sections be connected at the node points the following expression can be derived k B(s) = a0 + Z bi Z(s)i i=l where Z(s)i = (s n )di s(S ni) S Let Z(s)t represent the vector (1, Z(s)1t, ..., Z(s)kt) and note that s = t when t < S. Partition the design matrix X into [X1 !X2} where X, is the T x I submatrix of variables to be investigated for seasonal effects. Then the T x k matrix Z which incorporates the seasonal splines has as its tth element Xlt 8 Z(s)t. Estimation proceeds via the model Y = [Z :X2] 1 + 2 and each of S seasonal parameters for the variables in X1, say the first, is recovered as B(s)1 = Z(s) "11 l1k and the variance of B(s), is given as V[B(s)1] = Z(s)Cov(11... 3lk)Z'(s). To implement this technique, decisions must be made concerning the number and placement of the nodes. It was decided that four nodes placed evenly apart and corresponding to spring, summer, fall and winter quarters should be detailed enough to investigate seasonal changes. Both intercept and slope shifters for the Florida shipments variable were included in the full model. However the intercept splines Sl-S3 were dropped from this model due to their high level of insignificance (F3,179 = .0105). The estimated model's residuals were then analyzed and an autoregressive error structure of first and fifth orders AR(1,5) was imposed to whiten the residual series. This estimated model appears in Table 5. Despite the large number of regressors in the estimatedmodel note that its calculated variance is substantially below that of the filter model presented in Table 1. Although a number of coefficients on the Florida shipments variables and their transformations are not different than zero at customary levels of significance, the total effect of all seasonal forces may result in an individual seasonal coefficient being significant during certain parts of the season. The seasonal patterns of the calculated parameters are presented in Figures 2 through 5 along with their corresponding 95 percent confidence intervals. Examination of Figures 2 through 5 points out the relative insensitivity of Florida price to current and lagged Florida lime shipments. Note-that from the 24th week no coefficient is significant at the .05 level. The seasonal coefficients on FLSt and FLSt_1 follow nearly the same pattern and depict a significant inverse relationship between price and quantity during a 20 week interval near the first of the season. The seasonal coefficient on FLSt_2 is negative and significant for two short periods during the first half of the season. Table 5.--Florida lime price equation. Variable Intercept FLSt FLSt*S1 FLSt*S2 FLSt*S3 FLSt-l1 FLSt-1*S1 FLSt- *S2 FLStI*S3 FLSt-2 FLSt-2*Sl FLSt-2*S2 FLSt-2*S3 FLSt-3 FLSt_3*S1 FLSt-3*S2 FLSt-3*S3 MLSt-2 MLSt- 3 MLSt-4 MLSt-5 MLSt-6 MLSt-7 MLSt-8 S Parameter -.0365 -.03536 .0457 -.0375 .0107 -.0594 .0571 -.0323 .00127 -.09.11 -.00856 .0229 -.0234 -.069.7 -,042 .0327 -.0109 -.0589 -.119 -.118 -.0788 -.0584 -.0366 -.0244 .00183 Standard error .026 .055 .017 .020 .016 .069 .020 .022 .019 .075 .020 .022 .021 .072 .020 .020 .018 .020 .026 .029 .030 ,029 .026 .019 '2 .2 .00078 = .0171 19) = 20.5 a=.364 FIGURE 2 SEASONAL VARIATION OF FLSt PARAMETER AND 95 PERCENT CONFIDENCE INTERVAL 20 25 35 40 Parameter Value .2. -.3 -.4 -.5 I I I I 1 - 5 10 45 Week _~'LL''-L FIGURE 3 SEASONAL VARIATION OF FLSt_ PARAMETER AND 95 PERCENT CONFIDENCE INTERVAL 40 45 50 Week Parameter Value .2 .1 , 0 . -.1. -.2. -.3 . -.4 -.5. 5 10 15 20 5 10 15 20 g I m - - FIGURE 4 SEASONAL VARIATION OF FLSt-2 PARAMETER AND 95 PERCENT CONFIDENCE INTERVAL - -Y - S S I 30 35 40 45 50 Week Parameter Value .2- .1 - 0. -.1 - -.2 . -.4 -.5 _`LL''I ,..~r . * FIGURE 5 SEASONAL VARIATION OF FLSt-3 PARAMETER AND 95 PERCENT CONFIDENCE INTERVAL 4' *. . 5 10 15 20 25 30 35 40 45 50 Week Parameter Value 0 1- -.1 . -.2 -.3 -.5 o Figure 5 shows that the seasonal coefficient on FLS t-3 is not significantly different than zero at the .05 level over the entire season. Note that a larger alpha level would reveal a significant positive effect centered around the 13th week. Clearly these results show that the effects of current and lagged Florida shipments on current price are highly variable and not subject to straightforward interpretation. Because the price-quantity model is hypothesized to be neither a supply or demand curve, there was no a priori expectation as to the pattern of the seasonal coefficients. Indeed we can conclude that with 95 percent confidence there is an inverse relation- ship between price and some quantity variables only during the first half of the year, otherwise there is no significant (a= .05) effect. The total effect of current and lagged Florida shipments can be found by summing the seasonal coefficients found in Figures 2 through 5. These results are presented in Figure 6. Again the same general pattern of a significantly negative long run response to Florida shipments is seen during the first half of the season, and no significant relationship appears thereafter. Additional characteristics of the estimated model stem from the other estimated coefficients. The lagged Mexican shipments variables are generally significantly negative at the .05 level. The cumulative effect of lagged Mexican shipments yields a .494 coefficient. This suggests that a 10 percent increase in Mexican shipments at all lags reduces Florida price by almost 5 percent. Clearly this is a much stronger effect than that of cumulative Florida shipments for all but about 10 weeks during the season. In completing the discussion of the estimated model, it is seen that the intercept term is negative. Because all variables are specified as first differences, this coefficient represents a secular trend effect and FIGURE 6 SEASONAL VARIATION OF SUM OF PARAMETERS FOR FLSt, FLSt-1, FLSt2 AND FLSt-3 and 95 PERCENT CONFIDENCE INTERVAL FOR THIS SUM Sum of Parameters 0 -.2 -.4 -.6 -.8 -1.0 -1.2 5 10 15 20 25 30 35 40 45 50 Week _ __ suggests (ceteris paribus) prices have been trending downward. On the other hand, the coefficient for the variable denoting week (s) is signifi- cantly positive. This suggests (ceteris paribus) that over the season fresh lime prices tend to increase. Finally the calculated-X2 statistic for the regression model implies that there is no pattern to the rcesilduals at any conventional level of significance. Implications The previous discussion has quantified the relationship of fresh Florida lime prices to current and lagged Florida lime shipments and lagged Mexican lime shipments. Mention of price flexibilities or implied demand elasticities has been avoided for several reasons. First the hypothesized model does not follow closely the theoretical constructs which guide specification of demand curves. Secondly, the market is not fully modeled because the demand for processing limes has not been accounted for. Un- fortunately, weekly data on processing lime use is proorietory and un- available. Thirdly, some of the seasonal coefficients on current Florida shipments show a (weakly) positive magnitude. This may suggest that over part of the season a demand curve has not been identified, but rather a hybrid supply/demand curve has been estimated. These apparent shortcomings in the analysis presented do not preclude meaningful interpretation of the results, however. An immediate consequence of this study is the implication that the Ward and DE findings may be misleading. During the period they analyzed, 52 percent of limes harvested went to processing use, yet no mention of this important outlet is made. Further, their calculation of tremendouly high implied elasticites of demand during much of the season appears unrealistic given the nature of the product and the weekly observation units. Finally, their demand model is incomplete because it does not take into account Mexican lime imports as important substitutes. Our results imply that during the May to August peak harvest season prices are significantly, inversely related toFlorida fresh lime shipments Because the total effect of these increased shipments depresses price by a less than proportionate amount, we agree with Ward and De that iprorating is not an economically acceptable solution to the relatively low prices which occur during this period. If some of this production could be spread more evenly across the season, however, revenues would be increased. A major implication of this study stems from the analysis of lagged Mexican lime shipments. Florida lime producers apparently face a strong competitor. The estimated distributed lag on Mexican shipments shows that shipments three and four weeks prior have a substantial impact on Florida lime prices. By monitoring Mexican lime shipments, Florida producers may be able to avoid some price erosion by either accelerating or delaying marketing when a particularly large Mexican shipment enters the United States. Additionally, the case against prorating is further strengthened in light of the fact that reduced Florida supplies may cause it to lose marketing share or market channels. SUMMARY This study investigated the response of Florida lime prices to levels of Florida and Mexican lime shipments. The lag structures on the lime shipments variables were discerned using a transfer function or dynamic regression approach. The analysis offered a systematic way of relating prices and quantities. Further a flexible transformation was introduced which permitted the coefficients on the Florida shipments variables to vary seasonally. The estimated model then yieled seasonal effects which either depicted a significant ( a= .05 ) inverse relationship between Florida shipments and price, or no significant relationship at all during a large part of the season. The effects of Mexican lime shipments on Florida lime prices are inverse and substantial. This study represents an extension of the Ward and De report by incorporating the Mexican data. Further the use of unrestricted lag patterns, less severely restricted seasonal components., and presentation of statistics on the reliability of the seasonal coefficients make the results more general and complete. FOOTNOTES 1 Stationarity implies that the series possesses a finite, time invariant mean and variance. 2 For example, if G(L) is of degree k then the left hand side of expression 1 may be written (1 GIL G2L2 GkLk)X = Xt GXt_1 G2Xt2 - ... GkXt-k where G. is the coefficient on the i lag of X . 1 t REFERENCES Bessler, David A. and Lee F. Schrader. "Measuring Leads and Lags Among Prices: Turkey Products." Agricultural Economics Research (July 1980) 1-7. Box, George E. P. and G. M. Jenkins. Time Series Analysis. San Francisco, CA.: Holden-Day, 1976. Degner, Robert L. and Kary Mathis. "Marketing Florida Limes: A Wholesale and Retail Analysis." Research Report, Florida Agricultural Market Research Center, University of Florida (November 1976). Degner, Robert L. and Michael G. Rooks. "Lime Production in Florida Projections and Economic Implications for 1981-82." Proceedings of the Florida State Horticultural Society (1978) 194-197. Degner, Robert L., J. Scott Shonkwiler and Gervasio J. Cubenas. "Grower Prices for Limes: Projections through 1981-82." Proceedings of the Florida State Horticultural Society (1979)A 291-294. "Economic Outlook for Lime Production in Florida." Staff Report 8, Florida Agricultural Market Research Center, University of Florida (December 1979)B. 00o Federal-State Makert News. "Marketing Florida Tropical Fruits and Vegetables." Winter Park, Florida. Various issues. Feige, Edgar L. and Douglas K. Pearce. "The Causal Relationship Between Money and Income: Some Caveats for Time Series Analysis." Review of Economics and Statistics (November 1979) 521-533. Granger, C. W. J. "Investigating Causal Relationships by Econometric Models and Cross Spectral Methods". Econometrica (July 1969) 424-438. "____Relationships-and the Lack Thereof-Between Economic Time Series, with special Reference to Money and Interest Rates: Comment." Journal of the American Statistical Association (March 1977) 22-23. Haugh, Larry D. 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