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## Chilean journal of agricultural research

##
*versión On-line* ISSN 0718-5839

### Chilean J. Agric. Res. v.68 n.2 Chillán jun. 2008

#### http://dx.doi.org/10.4067/S0718-58392008000200006

Chilean Journal of Agricultural Research 68:166-174 (April-June 2008)
Implicancias del Cambio Estructural en el Mercado de Productos Lácteos Sobre el Precio de Leche Pagado a Productor en Chile.
^{1*} and Laura Nahuelhual^{2 }^{1} Universidad de Talca, Facultad de Ciencias Agrarias, Casilla 747, Talca, Chile. E-mail: mengler@utalca.cl * Corresponding author. ^{2} Universidad Austral de Chile, Facultad de Ciencias Agrarias, Casilla 567, Valdivia, Chile. E-mail: lauranahuel@uach.cl Key words: milk market, international trade, vector error correction, persistence profiles.
Desde 1990 la producción de leche ha experimentado un rápido incremento, pasando de 890 millones de litros en 1990 a 1.818 millones de litros en 2006. El exceso de producción de leche ha permitido la expansión comercial, transformando a Chile en exportador neto a partir del año 2001. En este nuevo escenario de mercado, una pregunta relevante es cómo este cambio estructural puede afectar el precio de leche pagado a productor. En este estudio se aborda esta interrogante, utilizando un Modelo de Corrección de Error (VEC) y análisis de cointegración. Los resultados demuestran que el precio doméstico, y los precios CIF (Cost, Insurance, Freight) y FOB (Free On Board) están cointegrados, lo que implica que fluctuaciones en los precios de importación y exportación son transmitidos al mercado doméstico. Antes de 2001 el precio CIF era la referencia relevante para los movimientos del precio doméstico, mientras que a partir de 2001 el precio FOB se transformó en la referencia y CIF dejó de ser significativo. Los parámetros del modelo sugieren que la relación de cointegración entre CIF y el precio doméstico para el primer período de análisis (1990-2000) es más robusta que la relación entre FOB y el precio doméstico para el segundo período (2001-2007/3). El coeficiente de elasticidad precio para el vector FOB-precio doméstico tiene un intervalo de confianza amplio, lo cual no permite concluir de manera robusta la dirección y magnitud del efecto del precio FOB sobre el precio pagado a productor en Chile a partir del año 2001. Palabras clave: mercado de la leche, comercio internacional, vector de corrección de error, perfiles de persistencia.
The excess production has allowed for the expansion of the export sector toward new markets overseas. Exports of dairy products started at the beginning of the 90s and have increased rapidly since then (Figure 1), converting Chile into a net exporter in 2001, as recognized by public authorities and the private sector. Between 1990 and 2000, the exported volume represented 2.6% of total production, while between 2001 and 2006 this participation went up to 10.2%. On the other hand, the imported volume decreased from 6.9% to 5.6% of the total production from the first to the second period (elaborated using information from ODEPA 2007b). According to ODEPA (2007a), during the first trimester of 2007, dairy exports continued to show a significant increase, which is expected to persist due to favorable international prices of most dairy products.
Chilean exports are concentrated in certain countries and products. The main importers are Latin American countries, Mexico being the most important. In the first trimester of 2007, 47% of total exports went to Mexico, while Venezuela, Guatemala, Peru and Honduras represented 24%. The main dairy products exported to these markets were cheese, whole fat milk and condensed milk, with a participation of 30.5, 30.4 and 22.7%, respectively (FEDELECHE, 2007).
The use of the vector error correction model (VEC) allows for the rigorous study of long run and short run price relationships simultaneously. The short run elements describe the dynamics of moving toward a new equilibrium. The long run relationships provide insights of how equilibrium relationships are restored and how new equilibrium levels can be obtained after a shock to the cointegrated system has occurred (Mohanty et al. (1997). In this trade model, the domestic price within a country is influenced by import prices and the exchange rate when the country exhibits an excess demand. In turn, when there is excess supply in the domestic market, the domestic price will be influenced by export (FOB) prices and the exchange rate. The variables selected for this case study were the domestic price of milk (the price paid to producers in Chile), the price of dairy exports (FOB), and the price of dairy imports (CIF). The FOB price was calculated as the weighted average of the ratio between export values and quantities of the three main exported products, namely condensed milk, whole fat milk, and cheese. The CIF price was calculated as the weighted average of the ratio between import value and quantity of the five most relevant imported products, namely whole dry milk, non-fat dry milk, cheese, butter, and whey. The nominal exchange rate of each year was used to transform international prices from US dollars into Chilean pesos. All variables were transformed into natural logarithms for the estimation of the VEC model, which allows for interpreting vector coefficients as price elasticities. All price series corresponded to monthly data from January 1990 to March 2007, obtained from the ODEPA (2007b) and the Central Bank of Chile (2007). To asses the impact of the structural change on the domestic price of milk, the VEC model was estimated separately for two distinct periods: period 1, from 1990 to 2000, during which Chile was a net importer of dairy products, and period 2, from 2001 to March of 2007, during which Chile was a net exporter. Description of the VEC model Vector autoregressive (VAR) models, error correction models and cointegration are related concepts in time series analysis, used to characterize the relationships between the series being studied. In essence, it can be shown that, with re-parameterization, the error correction model is a standard VAR in first differences augmented by error correction terms. Moreover, according to the Granger Representation theorem, a VEC representation for a set of variables that are integrated of order one (I(1)), implies cointegration among variables and vice versa (Engel and Granger, 1987). The characterization of the finite-order underlying a VAR system of variables can be represented as follows: P_{t} = A_{0} + A_{1}P_{t-1} + ...+ A_{p}P_{t-p} + ε [1] _{t}where P is a (_{t}nx1) vector containing each of the n variables included in the VAR, which in this case are the domestic, CIF and FOB prices expressed in natural logarithms; P _{t - }_{1} y P are vectors of prices for periods t-1 and t-p_{t – p} ; A is an (_{0}nx1) vector of intercept terms; A_{1} is (nxn) matrices of unknown coefficients with p equal to the lag length; and ε is an (_{t}nx1) vector of error terms. A main result of the Granger Representation Theorem is that a cointegrated system can be written as a VEC model (Johansen, 1991). Thus, the error correction representation of the VAR system in equation [1] is: ∆P is now the vector of prices in first differences. The term П_{t}P is the error correction term and contains information on the long run equilibrium relationship of the variables in _{t-p}P. The matrix П contains cointegrating relationships and has a deficient rank _{t}r, which represents the maximum number of cointegrating vectors. If cointegration holds, it implies that a long term economic relationship exists such that none of the series can wander too far away for any extended period after a shock to the system has occurred. If the rank r of the matrix П, which is the long run impact matrix, in the term ПP of Equation [2] is equal to zero, a stationary linear combination among the variables in the system does not exist and the model reduces to a VAR in differences (Enders, 1995). To the contrary, if the rank of the matrix П is deficient, there will be two _{t-p}k × r matrices defined as α and β, such that П can be written as П = αβ, where β is the matrix that contains the r cointegrating vectors and α is the matrix of speed of adjustment coefficients. The magnitude of the speed of adjustment indicates the velocity at which the price variables will react to a shock in the system and return to long run equilibrium. Furthermore, the significance of these parameters allows for identifying the variables responsible for the adjustment after a shock has occurred. Finally, the persistence profiles for the vectors were derived. Persistence profiles show the time it takes for the long run relationships, represented in the VEC by the error correction terms, to return to equilibrium following a system-wide shock (Pesaran and Shin, 1996; Pesaran and Pesaran, 1997), providing information on the speed of convergence of the system of variables. The faster the long run equilibrium is regained, the stronger is the integration of the market. For a detailed derivation of persistence profiles see Pesaran and Shin (1996). The cointegrating VAR was estimated on the levels of the natural logarithms of the three price series with n lags. The number of lags was determined using three selection criteria, namely the Akaike Information Criterion (AIC), the Schwarz Bayesian Criterion (SBC), and the likelihood ratio test (LRT) (Pesaran and Pesaran, 1997). Following lag selection, the cointegrating VAR was specified and estimated. The existence of cointegration was determined based on the maximal eigenvalue statistic and trace statistic. Given the existence of a cointegrating relationship, Johansens procedure exactly identified cointegrating vectors, and from them the VEC model was estimated. Treatment of seasonality Milk production and supply are characterized by a clear seasonal behavior, which arises mainly from deterministic factors, such as weather. In time series analysis, seasonal fluctuations are treated differently: i) they can be removed from the series by means of a seasonal adjustment procedure; ii) they can be ignored, in which case raw data are used; iii) or seasonality can be explicitly modeled (Ghysels et al., 1993; Canova and Hansen, 1995; Franses, 1996; Ghysels and Osborn, 2001). As pointed out by Franses and McAleer (1998), although the treatment of seasonality is still subject of debate, there is agreement on the belief that seasonally adjusted data would lead to inferences that are different from the results obtained using unadjusted data. In cointegrating models, the assumptions made about seasonal patterns may be relevant for both, the long run relationship among the variables, as well as the short run dynamics of the cointegrated system. In the case at hand, whereas domestic milk price exhibits a clear seasonal behaviour, CIF and FOB prices displayed almost no seasonal patterns. To verify the features of the seasonal pattern of the domestic milk price series, the Miron (1996) test was applied, which is based on a regression of a first differenced time series on seasonal dummy variables. The results of the test showed that the domestic price exhibited a large deterministic seasonal component, with seasonal dummies, accounting for 64.8% of the price variation as reflected in a R ^{2} equal to 0.648. Based on this result, seasonality was treated as deterministic and addressed by the inclusion of a dichotomous variable equal to 1 for the period January-August and 0 otherwise. While we recognize that the rest of the behavior of the domestic price could be explained by stochastic seasonal components, addressing such components is beyond the scope of this study. RESULTS AND DISCUSSION Unit roots and lag structure of the VEC model The order of integration of the price series was tested based on the augmented Dickey-Fuller (ADF) test (Engle and Granger, 1987). The results indicated that all three price series in levels had unit roots and therefore the log-transformed series LPP (log-domestic price), LCIF (log-CIF price), and LFOB (log-FOB price) were integrated of degree one or I(1). These results are available from the authors upon request. After confirming that the price series were I(1), the next step was to determine the proper lag length for the VEC. Testing for this implies pair-wise comparisons between two standard VARs, each having a different lag length. As Pesaran and Pesaran (1997) pointed out, since the aim is to select an optimal order for the VAR, it is important to select a number of lags high enough such that the optimal order will not exceed it. Following this criterion, the selection processes started with a number of 12 lags. The final decision was based on the Schwarz Bayesian Criterion (SBC), Akaike Information Criterion (AIC), and the adjusted likelihood ratio test (LRT). The three selection criteria consistently indicated a number of two lags. Table 1 shows the test results using six lags.
Equations [3] and [4] show the restricted cointegrating vectors for periods 1 and 2, respectively; standard deviations are indicated below the coefficients. For period 1, the coefficient on the log-transformed FOB price was not significant and therefore it was restricted to 0. This result implies that prior to 2001 the relevant reference for the domestic price was clearly the price of imports as found by Nahuelhual and Engler (2004). The coefficient of LCIF was equal to 0.71 implying that a 10% change in CIF prices will cause a 7.1% change in the same direction in domestic prices, which suggests an inelastic response. For period 2, the cointegrating vector was restricted by setting the coefficient on LCIF equal to 0 as the variable was not significant. After the restriction was imposed, the coefficient on LFOB became significant at 10%. This result has two implications. First, after 2001 import prices (CIF) are no longer the reference for domestic price, and export price (FOB) becomes the one that dictates the movements of domestic price; and second, the domestic price becomes more responsive to fluctuations in the international market as indicated by an elasticity coefficient equal to 1.47. However, it is important to note that this parameter has a large confidence interval at 10% probability [0.27; 2.67]. This implies that it is more difficult to predict how export price fluctuations will be transmitted to the domestic price of milk.
During period 1, the speed of adjustment coefficient on the export price (-0.005) was not significant, indicating that LFOB does not respond to disequilibriums in the LCIF-LPP vector. Only LCIF and LPP variables respond to bring the system back to equilibrium after an exogenous shock occurs, as indicated by the significance of their speed of adjustment coefficients. The magnitude of the parameters indicates a fast adjustment to disequilibrium by the two variables, being faster in the case of the CIF price (0.36) (Table 2).
In period 2, the speed of adjustment coefficients is significant only for export and domestic prices (Table 3), as only these two variables conform the cointegrating vector after 2001. This result implies that only LFOB and LPP will react to bring the system back to equilibrium. The coefficient in the domestic price equation is much smaller (0.03, as compared to 0.14) indicating that after 2001 domestic prices adjust more slowly to disequilibrium. The lagged coefficients in each equation indicate the variables that react to bring the system to a new equilibrium in each period. In period 1, the coefficient on LFOB is significant in the equation of export price, as expected. The same is true for the coefficient on LCIF in the import price equation. In the equation of domestic price, the lagged coefficient on LCIF (-0.07) was found to be significant. This corroborates that domestic price responds to movements in import price during period 1, but not to movements in the export price as indicated by a statistically non-significant coefficient (-0.02). During the second period the results were also consistent. In the domestic price equation, only the coefficient on LFOB was significant (-0.03), while the LCIF coefficient was statistically non-significant (-0.02) (Table 3). Figure 3. Persistence profiles of a wide shock to the cointegrating vectors for periods 1 and 2.
The persistence profiles for the two periods had in common that effects of shocks were rapidly reduced with almost all of the adjustment (80%) occurring within the first month, which indicates strong market integration (Figure 3). In other words, when there is a system-wide shock that affects the long run equilibrium between the price series, most of the adjustment will occur within the first month. The main implication of this result is that the structural change in international trade, and consequently the price reference from CIF to FOB price, did not change the pattern of adjustment of the total system. This in turn implies that, as expected, the structural change that occurred in 2001 only affects the dynamics of domestic price. After a shock, both profiles converge to their asymptotic values (zero) within four months. As pointed out by Pesaran and Pesaran (1997), the value of the profile must converge to zero as the time horizon tends to infinity if the identified vectors are indeed cointegrating vectors. CONCLUSIONS The results indicated that domestic CIF and FOB prices were cointegrated, implying that a price change in the international market is transmitted to the related domestic market. This co-movement of related price series ensures that when shocks to the cointegrated system occur, prices will adjust to restore their long run equilibrium relationship. However, due to the structural change in the market, the results indicated that there has been a change in the reference for the domestic milk price. Prior to 2001, CIF was clearly the relevant price, dictating the movements of domestic price. After that year, CIF was no longer relevant and FOB became the reference affecting the movements of domestic price. However, it is important to mention that the cointegration relation between CIF and domestic price for the first period under analysis (1990-2000) was clearer than the relation between FOB and domestic price for the second period (2001-2007/3). Price elasticity for the FOB-PP vector had a large confidence interval, which is why it was difficult to make strong conclusions regarding the impact of future FOB fluctuations on the domestic milk market. Despite the price reference, the results indicated that exogenous demand or supply shocks affecting the system are absorbed quickly in both periods, suggesting strong market integration. The persistence profiles in both periods show that the effects of these shocks are quickly reduced with 80% of the adjustment occurring within the first month, which suggests that the change in the structure of international trade and price reference after 2001 did not change the pattern of adjustment of the total system. 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