Threshold effects in price transmission: the case of Brazilian wheat, maize, and soya prices.

The figures in table 3 are the significance values at which noncausality restrictions can be rejected using an F-test within an unrestricted VAR. These should be valid since an F-test or Wald test for noncausality restrictions within the unrestricted VAR has a standard asymptotic distribution, providing the variables are cointegrated. For each price pair, it is evident that the Brazilian price is Granger-caused by the Argentine and U.S. price. However, there is weak evidence of Brazil having a causal influence on either the Argentine or U.S. price. This result would be indicative of the case where the Argentine and U.S. markets dominate the Brazilian market in terms of size, or where the Argentine and U.S. markets react more quickly to international shocks than does the Brazilian market.

Cointegration and the Adjustment and Threshold Parameters

Only the main parameters of interest are presented and discussed in this section. These are the cointegrating equations' [beta], the threshold parameters [lambda] and [theta], along with the adjustment parameters [[pi].sub.i]. Seasonal dummies were included in the ECM equations, but their coefficients and standard errors are not reported here for economy of space.

The results that are perhaps of most interest from the perspective of this article are those presented in tables 4 and 5 corresponding to Model III (equation (8)). Table 4 gives the cointegrating vector estimates for each of the series pairs, their posterior means, and standard deviations derived from the Bayesian approach. For additional information, the standard maximum likelihood estimates that would be obtained using the Johansen procedure are also presented in both tables 4 and 5. (7)

The convergence of the Bayesian algorithms was assessed by observing the "running means" of each of the four independent algorithms. A "burn in phase" (for each independent algorithm) of 50,000 draws was used (this is the number of initial simulations that are then discarded prior to the estimation phase) followed by another 100,000 thousand draws used to simulate the posterior distributions. The maximum difference between the cointegrating parameter estimates (the posterior means) derived from the four algorithms was less than 0.01. All the other parameters had much smaller differences, with the VECM parameters being the same down to three decimal places.

Readers should recall that the cointegrating parameters in table 4 measure the long-run proportionality between the series. Since the variables are in logs, a cointegrating vector of 0.72, as in the ML estimate of the cointegrating vector between Brazil. Argentine wheat prices in table 4, indicates that in the "long-run" the logged Brazilian wheat price should be 0.72 of the logged Argentine wheat price. Therefore, if the Argentine wheat price was to rise by 10% between period t and t + 10, then the Brazilian price for wheat would be expected to be around 7.2% higher than its period t value in year t + 10.

Table 4 includes either standard errors (in the case of the ML nonthreshold model) or standard deviations for the posterior distribution of the cointegrating parameters (in the case of the Bayesian threshold model). As with the parameter estimates, the standard deviations of the posterior distributions of the Bayesian estimates are not universally higher or lower than the standard errors of the ML cointegrating parameter estimates. If 95% confidence intervals, generated using nonthreshold Classical estimation or 95% Bayesian High Density Regions (HDRs), are constructed for the cointegrating parameters, these include unity for both the Bayesian and Classical methods in all of the five cases presented above. In this sense, there is no substantive difference in the results if one were simply testing the LOP that posits a cointegrating coefficient of 1.

The Bayesian techniques used here lend themselves to the production of graphical representations of the p.ds of each model parameter. However, for economy of space these graphical representations of the p.ds are not presented here. It is worth mentioning, however, that the p.ds for the cointegrating parameters for the Brazil-Argentina wheat price pair, and the Brazil-U.S. soya and maize price pairs, did appear to be fairly symmetric. However, for the other price pairs, the posteriors are asymmetric, and rather lumpy.

The posterior means of the threshold parameters [lambda], which describe the distance between the outer threshold boundary and the long-run equilibrium, (2[lambda] being the full threshold bandwidth) for each price pair, are presented in the first column of table 5. The estimated values of these parameters, along side those of [[pi].sub.u], [[pi].sub.l], and [theta] (considered next) are central to the focus of the article. The posterior means for [lambda] (the p.ds of which were also "bell shaped") are all significantly different from zero and suggest that threshold effects are present. However, readers are reminded that in order to identify the model, the distributions for the [lambda] parameters are restricted so as to have all their mass away from zero.

Columns 3 to 6 of table 5 reports the posterior means for [[pi].sub.i,u] and [[pi].sub.i.l], the within- and out-of-threshold speed of adjustment parameters. As discussed earlier, the means of [[pi].sub.i,u]--[[pi].sub.i,l], that lie away from zero (at which the distributions are truncated) support the existence of differential within- and out-of-threshold adjustment and, by implication, the existence of thresholds when [lambda] > 0. Columns 3 and 4 illustrate the asymmetry, or difference in the adjustment speeds, for the Brazilian equation in each VECM while columns 5 and 6 illustrate the asymmetry for the Argentine or U.S. equation, respectively. Three out of the five price pairs have intervals (calculated as [+ or -] one standard deviation from the p.d means) that do not overlap, and therefore provide some support for asymmetric adjustment (in the sense of differing within- and out-of-threshold adjustment speed) in one or both of the equations. These cases are; Brazil-U.S. wheat prices in the Brazilian equation, Brazil-U.S. maize prices in both equations and Brazil-U.S. soya prices in the U.S. equation. Recalling the results in table 3, causality was found to be unidirectional from the United States and Argentina toward Brazil, except in the case of Brazil-U.S. maize prices, where bidirectional causality was found. Accordingly, it is not surprising to find no evidence of asymmetric adjustment in the U.S. or Argentina for the four other cases; Brazil-Argentine wheat (in the direction of Argentina), Brazil-U.S. wheat prices (in both directions), Brazil-Argentine maize prices (in both directions) and Brazil-U.S. soya prices (in the direction of the United States), since those adjustment parameters, [[pi].sub.i,u] and [[pi].sub.i,l], are individually likely to be very close to zero.

The most striking evidence is with regard to the parameter [theta]. Readers should recall that if [theta] = 1, then the Band-TAR (Model II of the theoretical section) is the better representation of the data while [theta] = 0 suggests support for the Eq-TAR (Model I). An investigation of the p.ds of [theta], again not presented here, reveals that, in all cases, the posterior mass of [theta] is weighted toward 1. The Bayesian estimates suggest that the Band-TAR model is the more appropriate representation. Reference to the posterior means of [theta], presented in table 5, for each price pair, which range from 0.68 (Brazil-U.S. wheat) to 0.86 (Brazil-U.S. soya), reveals a slightly less clear picture. The estimated models are clearly neither an unambiguous Eq-TAR nor Band-TAR representation. Moreover, they are a mix of Models I and II suggesting that an "overshooting" Band-TAR model, one in which the outer regime (characterized by [[pi].sub.i,u]) overshoots the threshold boundary [lambda], by 1 - [theta], when prices are returning to equilibrium from outside of the threshold, best characterizes price adjustment in these cases. To put this into context, these results suggest that an overshooting of the threshold limit of between 32% (Brazil-U.S. wheat) to 14% (Brazil-U.S. soya) of the value of [lambda] might be expected when prices are returning to equilibrium from an out of threshold episode. As noted in the theoretical section, one possible reason for this situation could be the existence of a fixed element to transfer costs faced by traders, and provide some indication of the maximum potential share of any fixed element of transfer costs. Alternatively, shipping delays that results in inertia in arbitrage trade may be the cause of overshooting of the thresholds boundary during returning episodes.