Is exchange rate pass-through in pork meat export prices constrained by the supply of live hogs?

Data on monthly pork exports from Quebec, Ontario, and Manitoba between January 1988 and November 2003 were collected from Statistics Canada. The two most important export destinations for all three provinces are the United States and Japan. Export prices are proxied by export unit values. Figures 1(A)-(C) present pork export unit values (in Canadian dollars) to each destination from Quebec, Ontario, and Manitoba, respectively. Export unit values differ substantially across destinations, suggesting that the export product mix could be quite different across each destination and thus could be a source of bias in the price indexes (Kravis and Lipsey, 1974). Lavoie and Liu (2007) present Monte Carlo simulations that illustrate the caveats associated with using unit values to proxy export prices when commodities within a product category are significantly differentiated. Nevertheless, pork meat is believed to be a somewhat homogenous commodity and the analysis proceeds with unit values given the absence of a credible alternative to measure export prices.

[FIGURE 1 OMITTED]

Data on monthly average exchange rates between the export market currency and the Canadian dollar and food price indexes were obtained from the U.S. and Japanese Central banks. Each exchange rate series is weighted by the food price index of the importing country to account for foreign firms' pricing strategies (Knetter, 1989). Figure 2 presents a monthly index (January 1988 = 100) of the exchange rate between the currency in each destination and the Canadian dollars, weighted by the consumer food price index in that destination. Finally, live hog prices in all three provinces were obtained from Agriculture and Agri-food Canada.

For further reference, let superscripts QB, MB, and ON indicate the source of exports as Quebec, Manitoba, and Ontario, respectively, and superscripts US and JP indicate the destination markets as the United States and Japan, respectively. The theoretical model suggests estimating the relation between the export price from a province to a specific destination and the price of live hogs, the supply of live hogs available to processors, and the exchange rate in both markets. Hence, the variables used in the study are the export unit values (denoted by [p.sup.j,m]; j = QB, MB, ON and m = US, JP), the exchange rate weighted by the food price index for each destination ([e.sup.m]; m = US, JP), the hog price in each province ([r.sup.j] ; j = QC, MB, ON), and total hogs slaughtered in each province ([Q.sup.j]; j = QC, MB, ON).

At this stage, it is perhaps instructive to discuss the proxy used to measure predetermined hog supplies. There are significant movements in live animals between the three provinces. As such, the supply of live hogs in one province may yield a poor approximation of the total supply of live hogs available to processors in that province because hogs can be transferred from one province to another. Hence, the empirical model uses the total quantity of hogs slaughtered in the province as a proxy to measure if marketing arrangements and production lags have any impact on export pricing decisions. In the case in which these factors have no effects, total hogs slaughtered will not influence export prices as slaughters can be adjusted freely by relying on the spot market.

[FIGURE 2 OMITTED]

The Empirical Model

The first step in the empirical model is to determine the stochastic properties of the data. (4) The Augmented Dickey-Fuller (ADF) unit root test and the Kwiatkowski et al. (KPSS) stationarity test yield conflicting evidence for six out of the fourteen variables in the dataset ([r.sup.QC], [r.sup.MB], [r.sup.ON], [e.sup.US], [e.sup.JP], [p.sup.MB, US]) while the remaining variables can be classified as integrated processes of order one. Carrion-i-Sylvestre, Sanso-i-Rossello, and Ortuno (2001) suggest recognizing the jointness in the distribution of the two tests when carrying out this sort of confirmatory data analysis to alleviate the inconsistency. Their set of critical values only resolved the ambiguity for two variables ([r.sup.QC], [e.sup.US]), which implies that ten out of the fourteen variables can be considered as integrated processes of order one.

Given that the joint null hypothesis of a unit root for most of the variables can not be rejected, we use the DSUR models of Mark, Ogaki, and Sul (2005) and Moon and Perron (2004) to estimate ERPT effects. The DSUR approach admits the possibility that the integrated variables are cointegrated and accounts for potential contemporaneous correlation between each province ERPT equation. Under the hypothesis of cointegration, it corrects endogeneity by adding leads and lags of the independent variables in the regression equation and uses feasible GLS to correct autocorrelation in the error terms. Under certain conditions, the DSUR estimators are normally distributed asymptotically and thus inference can be carried out in the usual way.

The cointegration approach is appealing in the present context for many reasons. It is possible that small variations in the exchange rate can have little or no impacts on pricing decisions in the short run, but would error-correct in the long run because either processors make adjustments to their hog purchases or the exchange rate moves in a different direction and thus cancels out previous disequilibrium pricing strategies. Cointegration between the variables specifically assumes that there exists a stable long-run relationship and admits the possibility that there are deviations from the long-run pricing decision in the short run. (5) Second, the potential endogeneity bias between export unit values and output is explicitly accounted for in the cointegration model.

We illustrate the DSUR approach using the ERPT equations in market m from origins j = QC, MB, ON. The ERPT equations are based on a linear approximation of the solutions defined in (7) and (8). There is one cointegrating regression equation for each origin

(13) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

It is assumed that [u.sup.j.sub.t] is a stationary autoregressive process of order p such that [u.sup.j.sub.t] = [[rho].sup.j][u.sup.j.sub.t - 1] + [[summation].sup.p-1.sub.h=1] [[eta].sup.j,h] [DELTA][u.sup.j.sub.t-h] + [[xi].sup.j.sub.t]. The error terms [[xi].sup.j.sub.t] account for the potential cross-sectional covariance between equations. Potential correlation between the error terms in (13) and the first difference of some regressors (i.e., the endogeneity problem with respect to output) is addressed by augmenting the system in (13) by leads and lags of the independent variables

(14) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

for j = QC, MB, ON and a given m.

Mark, Ogaki and Sul (2005) suggest estimating (14) by first applying OLS to estimate the parameters in (14) and then using the predicted residuals to compute a heteroskedastic and autocorrelation-consistent (HAC) covariance matrix. The problem is that the distribution theory of their estimator depends on the condition that the regressors are not cointegrated. This condition is violated if there are common regressors across equations as in the present case. Moon and Perron (2004) propose a minimum distance estimator (MDE) that is efficient when there are common regressors across equations.

The empirical strategy is carried out in two steps. First, each dependent variable is regressed on all independent variables in the system using the dynamic ordinary least square (DOLS) procedure of Saikkonen (1991). Let [??] denote the vector of stacked estimated parameters for the unrestricted system. The number of leads and lags is determined by using the Schwartz-Bayesian Criterion (SBC) and is equal to one for both the U.S. and Japan systems. In a second step, the parameters of interest stacked in the vector [delta] are obtained by minimizing the objective function ([??]- G[delta])'[??]([??]- G[delta]) where G accounts for the exclusion restrictions on the regressors in each equation and [??] is the HAC covariance matrix. The minimum distance estimate of [delta] is [??] = [(G'[??]G).sup.-1]G'[??][??]. The Newey-West estimator using a Bartlett kernel was applied to the pre-whitened residuals of the unrestricted system to obtain a HAC estimate of W. (6)