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

Broad globalization pressures and increased concentration in downstream levels of agri-food supply chains have spurred a keen interest in the relationship between competition, export prices, and exchange rates. Exchange Rate Pass-Through (ERPT) can be broadly defined as the export price movement following changes in exchange rates (Bowen, Hollander and Viaene, 1998). Some notable ERPT studies include Pick and Carter's (1994) wheat study, Griffith and Mullen's (2001) analysis about Australia's rice exports, Brown's (2001) analysis of Canadian canola exporters and Miljkovic, Brester, and Marsh's (2003) analysis of U.S. meat exports. Incomplete ERPT implies some form of market power because export prices in different markets are not equal to firms' marginal cost. It does not imply that markets are segmented, however, because imperfect competition is not inconsistent with integrated markets.

One issue that has been neglected in the literature is whether firms have unlimited capacity when adjusting export prices following changes in the exchange rate. Knetter (1994) suggested that export price adjustments were likely to be linked to whether firms face capacity constraints in distribution networks or quantitative restrictions in export markets. In his framework, bottlenecks at the border are revealed through asymmetric adjustment in export prices. Bughin (1996) used panel data from Belgian manufactures to estimate a cost function under potential capacity constraints. He finds that the degree of mark-up adjustment following currency movements is significantly linked to each firm's capacity constraint.

In the context of agricultural supply chains, capacity constraints in downstream agri-food markets can stem from the usual short-run fixity of an input (e.g., stock of capital) or lengthy lags between production and marketing of primary agricultural goods. These lags are especially lengthy in livestock and grain industries whose production decisions precede marketing decisions by several months. For example, currency depreciation may not trigger immediate increases in exports of processed commodities because the supply of upstream producers may be perfectly inelastic in the short run. Moreover, processing firms and agricultural producers have developed different marketing strategies (e.g., contracts) that often include binding commitments with respect to price and output. Hence, even though a processing firm is faced with unexpected and unfavorable movement in the exchange rate, it may sell more output than it would otherwise choose due to binding marketing agreements.

The objectives of the article are twofold. First, a theoretical model that accounts for production and marketing lags is used to explain the pricing decisions of a firm that exports a processed good to two markets. At the marketing stage, the downstream firm's capacity may be predetermined due to the inelastic supply of the primary agricultural commodity or because of committed purchases of the primary input. We refer to these scenarios as a capacity constraint from the processing firm's perspective. If the capacity constraint is not binding and there are constant returns to scale in processing, the mark-up of the firm in a given export market reduces to the standard monopoly pricing rule. If the capacity constraint is binding, the destination-specific mark-up of the firm is a function not only of the exchange rate in that particular market, but also of the exchange rate in the other export market.

The second objective is to measure ERPT in pork meat export prices from three Canadian provinces (Ontario, Quebec, and Manitoba) to two destinations (United States and Japan) over the 1988-2003 period. The empirical model of Knetter (1989, 1993) is modified to test the theoretical finding that if export prices of processed pork meat are constrained by the supply of live hogs, the number of hogs slaughtered and the exchange rate in the other market should explain export pricing decisions. The idea is to use an empirical model that can identify long-run effects of predetermined supplies from short-term effects due to bottlenecks and/or frictions in supply chains that error correct in the long run.

There are two main empirical challenges when estimating ERPT in Canadian pork export prices. First, it is not unusual to find that export prices and exchange rates possess a unit root (see, for example, Carew and Florkowski 2003; Choudhri, Faruqee, and Hakura 2005). As such, the empirical model must account for the potential nonstationarity in the data when estimating the model. Second, efficiency gains in the estimation can be captured by estimating the ERPT equation of each province to a given market simultaneously. These two issues are addressed by using the Dynamic Seemingly Unrelated Regression (DSUR) model proposed by Mark, Ogaki and Sul (2005) and Moon and Perron (2004). The estimation procedure involves two steps. First, leads and lags of the independent variables and a generalized least squares (GLS) estimator are used to correct, respectively, for potential endogeneity bias and autocorrelation in the residuals. In the second stage, restrictions on the cointegrating vectors are accounted for using the minimum distance estimation method proposed by Moon and Perron (2004).

The results suggest that pork packers' volumes in Quebec and Ontario have significant impacts on export prices while there is no evidence of this being the case for Manitoba. The empirical model also reveals significant differences between estimates of ERPT accounting for lags in production and marketing decisions and the ones obtained using a standard specification that implicitly assumes instantaneous adjustment in output. The ERPT elasticities are statistically different than zero and thus suggest that Canadian pork exporters adjust their margin in response to fluctuations in the relative value of currencies.

The remainder of the article is structured as follows. The next section presents a theoretical model that explains pricing decisions in a framework that accounts for marketing lags in agri-food supply chains. The section titled "Data" investigates the statistical properties of the variables used in the empirical model. The section titled "The Empirical Model" presents the econometric procedures and discusses the estimation results. Concluding remarks are presented in the last section.

The Theoretical Model

Consider a processing firm that exports pork meat to two segmented foreign markets, identified by a and b. The demand in each market for the domestic firm's output is: [D.sup.a]([e.sup.a] [p.sup.a], [[bar.p].sup.a]) and [D.sup.b]([e.sup.b] [p.sup.b], [[bar.p].sup.b]), where [[bar.p].sup.j] is the price set in market j by the domestic firm (in domestic currency) and [e.sup.j] is the exchange rate defined as the value of country j's currency per unit of domestic currency. The variable [[bar.p].sup.j] is the price level of foreign substitute products in market j. The model uses the Armington assumption and purposely avoids modeling the interaction between the domestic and foreign firms) This assumption is made for analytical convenience but does not qualify the result, given that the emphasis of the article is not to relate the degree of ERPT to market structure.

The processing firm maximizes profits defined as

(1) [pi] = ([p.sup.a] - [t.sup.a])[D.sup.a]([e.sup.a] [p.sup.a], [[bar].sup.a]) + ([p.sup.b] - [t.sup.b])[D.sup.b]([e.sup.b][p.sup.b], [[bar].sup.b]) - [r.sup.p][Q.sup.p],

where [t.sup.j] measures the transportation cost between the domestic market and destination j, [r.sup.p] is the price of live hogs paid to domestic hog producers, and [Q.sup.p] represents live hogs that are purchased by the firm. Processing marginal costs are assumed constant and normalized to zero.

There are many ways to secure a desired supply of live hogs for the processing firm. The current analysis will focus on two hog marketing mechanisms: (1) the processor relies on the spot market to purchase hogs; and (2) contracts between the processor and individual hog suppliers specify quantities to be delivered and the price that will be paid upon delivery. Additional assumptions about hog marketing arrangements are that (1) live hogs are homogenous products (unlike the processed commodity); (2) hog producers are price takers in the world market; and (3) the domestic firm has monopsony power in the domestic market when purchasing live hogs.

The above assumptions are not unrealistic in the context of the Canadian hog/pork industry (Larue, Gervais, and Lapan 2004), but also apply to numerous other sectors that experienced increased concentration in downstream market levels. Assume that market a is closer to the domestic country than market b such that [t.sup.a] < [t.sup.b]. If the processing firm relies on the spot market to buy live hogs, it can capture all of the available domestic output (denoted by [Q.sup.r]) at a price of [e.sup.a][r.sup.a] - [mu][t.sup.a], where [r.sup.a] is the price of live hogs in country a's currency and [mu] is an adjustment factor between transportation costs of the processed and primary commodities. As Larue, Gervais, and Lapan (2004) argue, the possibility of a hold-up by the processing firm is constrained by the existence of an export market for the primary commodity. There is the possibility, however, that not enough hogs are produced from the processor's perspective because rational hog producers anticipate that the best price they will receive is the price in market a adjusted for transportation costs.

One option would be for the processing firm to commit its price (to a level higher than the expected value of [e.sup.a][r.sup.a] - [mu][t.sup.a]) before hog producers make their decision and thus effectively setting the quantity of hogs available in the marketing period. Even when contracting is possible, the processor's ex ante demand for live hogs may not necessarily coincide with his ex post optimal capacity choice once exchange rates are known. Under price commitment, capacity is sunk at the marketing stage unless hog producers anticipate exporting hogs to market a in the marketing period. In the spot market scenario, the processing firm can simply wait until the hogs attain market-ready weight to secure its supply of live hogs. It faces the possibility that its desired demand be higher than the available domestic supply.

The various hog-marketing mechanisms in Canada provide us with a rich and diversified economic environment to test the theoretical predictions of the model. For example, hog marketing mechanisms in Quebec address coordination issues between packers and producers by relying on some hybrid marketing schemes. In short, a marketing board has exclusive rights to market hogs to processors. An important share of all hogs available in any given period is allocated to processors at a predetermined price based on their historical market shares while the others are auctioned off (Larue et al. 2000). Hog marketing mechanisms in other provinces involve contracts between individual packers and hog producers as well as spot market transactions.

Going back to the profit maximization problem defined in (1), suppose that prior to export pricing decisions, the firm committed to buy a quantity [Q.sup.p] of live hogs. The processing firm makes pricing decisions in the foreign market subject to the constraint that [Q.sup.p] = [D.sup.a] + [D.sup.b]. Given the foreign price level of substitute goods (denoted [[bar].sup.a] and [[bar].sup.b]), the first-order conditions are

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [lambda] is the Lagrange multiplier associated with the capacity constraint. Equations (2) and (3) define the domestic firm's export prices [p.sup.a]([e.sup.a], [e.sup.b], [Q.sup.p]; [[bar].sup.a], [[bar].sup.b]) and [p.sup.b]([e.sup.a], [e.sup.b], [Q.sup.p]; [[bar].sup.a], [[bar].sup.b]), which can be substituted back into (1) to yield

(4) [pi](x) = TR([e.sup.a], [e.sup.b], [Q.sup.p]; [[bar].sup.a], [[bar].sup.b]) - [r.sup.p][Q.sup.p]

where TR(x) denotes total export revenues.

In the first scenario, the price commitment of the processing firm is made before hog producers make their sunk investment decisions. In the first stage, we assume that hog producers' supply is [Q.sup.r]([r.sup.p]) with [Q.sup.r,] > 0. (2) Because of its monopsony position in the purchase of domestic hogs, a risk-neutral processing firm maximizes

(5) E[[pi](x)] = E[TR([e.sup.a], [e.sup.b], [Q.sup.r]([r.sup.p]); [[bar].sup.a], [[bar].sup.b])] - [r.sup.p][Q.sup.r]([r.sup.p]).

The first-order condition to the optimization problem in (5) yields the optimal live hog price [r.sup.p*] = [phi]([e.sup.a], [e.sup.b]; [[bar].sup.a], [[bar].sup.b]), which is a function of the various moments of the distribution of the exchange rates and the foreign firms' prices. (3)

In the second case, the domestic firm uses the spot market to purchase live hogs and [r.sup.p] is chosen when uncertainty about the exchange rates is resolved. However, the hog supply is perfectly inelastic at that point, and the processor knows it can buy as many hogs as there are available ([Q.sup.r]) as long as it offers at least [e.sup.a][r.sup.a] - [mu][t.sup.a]. Let the parameter [theta] be the Lagrange multiplier associated with the inequality [Q.sup.p] [less than or equal to] [Q.sup.r]. If [Q.sup.r] > [Q.sup.p] ([theta] = 0), the processor does not face any constraint ex post when setting export prices ([D.sup.a] + [D.sup.b] = [Q.sup.p] < [Q.sup.r]) and (1) becomes

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

The processing firm maximizes (6) subject to the constraint [r.sup.p] = [e.sup.a][r.sup.a] - [mu][t.sup.a]. The first-order conditions are

(7) [partial derivative][pi]/[partial derivative[p.sup.a] = [D.sup.a]([e.sup.a] [p.sup.a], [[bar].sup.a]) + [e.sup.a]([p.sup.a] - [t.sup.a] - [r.sup.p]) x (partial derivative][D.sup.a]/[partial derivative]([e.sup.a][p.sup.a])) = 0

(8) [partial derivative][pi]/[partial derivative][p.sup.b] = [D.sup.b]([e.sup.b] [p.sup.b], [[bar].sup.b]) + [e.sup.b]([p.sup.b], [[bar].sup.b]) + [e.sup.b]([p.sup.b] - [t.sup.b] - [r.sup.p]) x ([partial derivative][D.sup.b]/[partial derivative]([e.sup.b][p.sup.b])) = 0.

The first-order conditions in (7) and (8) can be manipulated to yield the standard elasticity pricing formula of Knetter (1989). The equilibrium prices defined by (7) and (8) are pa([e.sup.a]; [[bar].sup.a], [r.sup.p]) and [p.sup.b]([e.sup.b]; [[bar].sup.b], [r.sup.p]).

However, if the processors' demand for live hogs is equal to the (perfectly inelastic) supply of hogs ([Q.sup.p] = [Q.sup.r]), the optimization problem of the processor when selecting export prices reduces to (2) and (3). As Larue, Gervais, and Lapan (2004) argued, if the processor does not commit its output price, it has no incentive to raise prices above the net marginal revenue that hog producers can obtain in the export market once hogs attain ready-to-market weight. Producers are rational and fully anticipate that outcome, thus leading to a potential "low-price, low-capacity trap."

Based on the previous theoretical set-up, the empirical model needs to distinguish between two general cases. In the first instance, production of live hogs will impact ERPT because hog supplies are predetermined (i.e., inelastic hog supply). For example, consider a favourable movement in the exchange rate that was unexpected when the processor's price commitment was made. The variation would normally induce additional sales in the export market but additional purchases on the spot market may not be possible due to the inelasticity of the short-run hog supply. Similarly, commitments made in the first stage can also influence ERPT when there are unfavorable movements in the exchange rate because the domestic firm's purchases of live hogs are sunk at this stage. In the second general situation, the domestic firm relies exclusively on the spot market and the supply of live hogs does not constrain the domestic firm's behavior; i.e., there exists an excess supply of live hogs at the observed domestic price.

Comparative static exercises can be carried out on the set of first-order conditions in (2) and (3) or (7) and (8), which define the equilibrium price. The latter first-order conditions are independent of each other and, provided that the export demand in country j is negatively sloped and not too convex, it can be shown that

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Equation (9) illustrates the standard result that depreciation (appreciation) of the domestic currency will increase (decrease) the export price, albeit in a lesser proportion. In the linear case, manipulating (9) shows that the pass-through impact is equal to -(1 + 1/[[epsilon].sup.j])/2 where [[epsilon].sup.j] is the export demand price elasticity. Zero pass-through occurs when the demand elasticity is -1.

The comparative static exercise for case of a binding capacity constraint is a little more involved. Assume for simplicity that the demand in each market is linear in its arguments. Totally differentiate the set of first-order conditions in (2) and (3) and the constraint to obtain

(10) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(11) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The system in (10), (11), and (12) can be solved using Cramer's rule to obtain [partial derivative][p.sup.j]/[partial derivate][e.sup.j] < 0 and [partial derivative][p.sup.j]/[partial derivative][e.sup.i] < 0; i [not equal to] j. A depreciation (appreciation) of the domestic currency with respect to country a's currency will increase (decrease) the export price in market a. Incomplete pass-through will increase (decrease) sales in market a and will decrease (increase) sales in market b because supply is sunk at this stage. The decrease (increase) in sales to market b must necessarily be induced by an increase (decrease) in the export price in market b. It is, however, difficult to directly compare the pass-through coefficients under the standard elasticity pricing formula and the case of predetermined supplies because, in the latter case, the demand elasticity of both markets affects the degree of exchange rate pass-through.

Data

Hog marketings, slaughters, and exports from January 1988 to November 2003 in Manitoba, Ontario, and Quebec were obtained from the Red meat market division of Agriculture and Agri-food Canada. The three provinces accounted for more than 75% of all hogs marketed in Canada in 2003. There are in some instances some significant differences between total hog marketings and hog slaughterings within a province. Processors in Quebec almost always slaughter all available hogs in the province while a significant portion of total hog production in Ontario is sold to Canadian packers outside Ontario. The relationship between slaughterings and production in Manitoba is less stable over the sample, but Manitoba can generally be considered a net exporter 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)

Before investigating the economic implications of the statistical model, it is important to test cointegration and homogeneity restrictions in the system. The Phillips-Ouliaris [Z.sub.[tau]], and [Z.sub.[alpha]] residual-based tests reject the null hypothesis of no cointegration for each equation and thus the dependent and independent variables are considered cointegrated. (7) Homogeneity restrictions are particularly important from an efficiency perspective because a homogenous system implies that the three equations in (14) could be pooled to proceed with the panel DOLS estimator of Mark and Sul (2003). The MDE has the advantage of being asymptotically normally distributed and linear restrictions can be tested using a Wald test. The homogeneity restriction for the ERPT coefficients of the U.S. system ([[beta].sup.QC,US] = [[beta].sup.MB, US] = [[beta].sup.ON, US]) in table 1 is strongly rejected as the joint restrictions [[beta].sup.QC,JP] = [[beta].sup.MB,JP] = [[beta].sup.ON,JP]). The two other homogeneity restrictions also yield p-values lower than 0.01. Hence, it is not surprising that the Wald test for the joint restrictions of homogenous coefficients throughout the system yields a very low p-value. Similarly, the exchange rate coefficients seem to be different across provinces for the Japan export price equations. The only homogeneity restriction that is not rejected by the data is the joint restrictions that the coefficients of the hog price are all equal (p-value of 0.421). The joint restrictions leading to pooling the three export price equations is strongly rejected for Japan.

Table 2 presents the estimation results for the ERPT equations in the U.S. market. The coefficients of the lead and lagged first differences are not reported out of concern for space. The adjusted coefficient of determination ([R.sup.2]) of each equation is large, suggesting that the model explains well the variability in the export price. The Jarque-Bera (JB) statistic (Greene 2003) indicates that the null hypothesis of normally distributed residuals cannot be rejected for the Quebec and Manitoba export price equations at conventional levels of significance. (8) The large value of the JB statistic of the Manitoba equation is due to excess kurtosis in the distribution of the residuals. (9)

The ERPT coefficients in table 2 for each of the three provinces have the expected sign and are statistically different than zero at the 5% significance level in all three provinces. The coefficient of the hog price is positive and significant (p-value less than 0.01) as well. The coefficient for hog slaughters is statistically significant in Quebec and Ontario and has the expected sign. However, the p-value of the null hypothesis [[beta].sup.MB,US] = 0 is larger than 0.10; thus suggesting that output in Manitoba does not impact the export price. The coefficient of the yen exchange rate is statistically significant in Quebec and Ontario ERPT cointegrating equations. The yen exchange rate has a positive coefficient in the Manitoba equation but is not statistically significant.

Based on the theoretical framework, when (predetermined) hog supplies have no impact on pricing, the export price in a given market is independent of the exchange rate in the other destination. Hence, testing the nonsignificance of hog production on pork meat pricing decisions in province ] is a test of the null hypothesis: [[beta].sup.j,JP] = [[lambda].sup.j] = 0. When the joint null hypothesis of zero coefficients on the yen exchange rate and the capacity variable is tested, the p-value is 0.308 for Manitoba but less than 0.01 in Quebec and Ontario. The latter results provide additional evidence that the supply of live hogs impacts Quebec and Ontario pork export prices in the United States.

The results in table 2 are consistent with anecdotal evidence in the Canadian hog/pork industry. Quebec packers historically processed all hogs that were marketed by Quebec hog producers while Manitoba has been known to produce and export large volumes of live hogs. While exports of live hogs from Ontario were also significant from time to time over the sample period, Ontario has run a positive inter-provincial trade balance for live hogs with other Canadian provinces (AAFC 2006) suggesting that there is stronger competition for the local supply of live hogs in Ontario than in Manitoba, which has had a negative inter-provincial trade balance. Hog marketing arrangements in Ontario and Manitoba rely heavily on private contracts between producers and packers while it is mandatory for Quebec hog marketings to go through the producers' marketing board. These differences in marketing institutions combined with different domestic competitive forces in the market for live hogs can explain the different results with respect to the effect of hog supplies on pork meat export prices.

Table 3 presents the estimation results for the Japanese market. (10) The adjusted coefficients of determination in the regressions are all lower than in the U.S. case. Once again, it is highly unlikely that the empirical distribution of the residuals in the Manitoba equation is normal. (11) The ERPT coefficient in the Japanese market is negative and statistically significant for the Quebec and Manitoba provinces, but it is positive (and significant) in the Ontario export price equation. The latter finding is puzzling because a depreciation of the Canadian dollar with respect to the Japanese yen is expected to increase the export price in Canadian dollars, albeit in a smaller proportion. A positive ERPT coefficient is usually termed perverse pass-through (Bowen, Hollander, and Viaene 1998) and similar results have been reported in the literature (e.g., Webber 1999). (12)

The price of live hogs is insignificant in Quebec and Manitoba. As in the U.S. case, the coefficients of the number of hogs slaughtered within the province are strongly significant in Quebec and Ontario (and have the correct sign), but the number of hogs slaughtered in Manitoba is not significant at the 99% confidence level and has the wrong sign under the assumption of constant returns to scale in processing. The Wald test of the joint null hypothesis [[beta].sup.j, US] = [[lambda].sup.j] = 0 is strongly significant (p-value less than 0.001) for Ontario and Quebec, which indicates hog supplies have an important impact on the export price response. It is also significant (13) for Manitoba despite the large standard error associated with the coefficient on hogs slaughtered because the coefficient for the exchange rate in the U.S. market is strongly significant (t-statistic is--13.96).

The Manitoba result for the Japan system is not a rejection of the hypothesis that production lags have an impact on export pricing decisions. The number of hogs slaughtered could capture some factor other than the existence of lags in production and marketing. For example, a positive (or even a small negative) coefficient could indicate that there exist decreasing returns to scale in pork meat processing. In that case, the output coefficient could capture two opposing effects: production lags and increasing marginal cost. While a negative coefficient provides evidence that marketing lags and hog production impact pork meat export pricing decisions, the converse is not true; a positive or insignificant coefficient could still be consistent with significant marketing lags if there exist decreasing returns to scale.

It is useful at this point to investigate pass-through coefficients using standard empirical techniques that do not account for lags between hog production and marketing decisions. The existence of lags can introduce some significant bias in ERPT coefficients if output and other currency exchange rates are omitted from the ERPT equations. The framework of Knetter (1989, 1993) is used to investigate potential misspecification problems associated with "traditional" ERPT equations. It is adapted to account for unit roots and cointegration, and uses a somewhat different specification to proxy firms' costs. Knetter's ERPT equation assumes that marginal cost is exclusively a function of time while processors' marginal costs in the current model are proxied by hog prices. Moreover, his analyses usually employ the first difference of the variables to address nonstationarity in the data.

Table 4 reports the ERPT coefficients as well as the constant and marginal cost coefficients for export prices in one province to each market, as well as the t-statistic of the null hypothesis that the coefficient is not statistically different than zero. The only ERPT coefficient in the U.S. system substantially different from the estimates in table 2 is for the Ontario equation. However, the ERPT coefficients in the Japanese market reported in table 4 are strikingly different than the coefficients in table 3. When potential marketing lags are not considered, the empirical framework finds little evidence of significant exchange rate pass-through in the export price in Japan. The coefficients for Ontario and Manitoba are definitely not significant while the magnitude (in absolute value) of the ERPT coefficients for Quebec has decreased compared to the results in table 3. Hence, the failure to account for lags in production and marketing activities in agri-food supply chains can create substantial biases in the estimation of ERPT effects. In the current application, the standard Knetter ERPT equation underestimates the ability of Ontario firms to exercise some market power in the U.S. market.

Concluding Remarks

Exchange Rate Pass-Through is broadly defined as the export price response following a movement in the relative price of the domestic currency over the currency in the export market. The analysis investigated how ERPT for processed agri-food commodities can be impacted by predetermined supplies of primary agricultural goods. It has been customary in the literature to assume constant returns to scale (e.g., Knetter 1989) in order to separate out the firms' pricing decisions across export markets. The current framework assumed that there exist significant lags between production and marketing decisions for goods such as grains and livestock. Under the assumption that processing firms commit to purchase agricultural products before marketing decisions occur, export pricing decisions in all markets for processed commodities are tied together. Even in the case when a processor relies on the spot market to purchase agricultural goods, there may be an excess demand at the prevailing hog price due to the inelastic supply of primary commodities. The theoretical model leads to simple testable predictions about the impact of the predetermined hog supply on pork meat export prices and on ERPT behavior.

Canadian pork meat export prices from three provinces to two destinations (United States and Japan) were collected to investigate ERPT. The empirical model tested the ERPT implications of predetermined supplies by regressing the export price in a given market on the exchange rate, the price of live hogs, total processed output, and the other export market's exchange rate. Potential nonstationary in the data and endogeneity bias were addressed using the DSUR framework proposed by Mark, Ogaki, and Sul (2005) and Moon and Perron (2004) as well as the MDE of the latter authors. The DSUR procedure uses generalized least squares to account for potential autocorrelation in the residuals and it corrects the endogeneity bias by introducing leads and lags of the independent variables in the equations. The MDE was used to account for cointegration between the independent variables because identical regressors appear across the three export price equations.

The estimation results strongly support the hypothesis that predetermined supplies have a significant impact on export prices for two out of three Canadian provinces. ERPT elasticity for Canadian exports to the United States is approximately in the range of -0.2 to -0.7. In the case of exports to Japan, the degree of misspecification involved with the standard ERPT equation that only includes the Canadian dollar to yen exchange rate as well as a marginal cost proxy is quite large. The standard specification yields ERPT coefficients that are much smaller in absolute value than the ERPT coefficients found in the full system approach that includes predetermined hog supplies. Hence, failure to account for the dynamic nature of agricultural supply chains may result in significantly biased estimates of ERPT.

One interesting extension to the current framework would involve using predetermined supplies to investigate the selection of export markets. In some periods, exports to particular destinations are zero and thus no export unit values are available. This seriously impedes the ability to analyze ERPT behavior in emerging markets. Zero-trade flows are not uncommon in the empirical trade literature but researchers have struggled to properly address the issue (Helpman, Melitz, and Rubinstein 2007). A promising research avenue would perhaps involve using a two-stage estimation procedure in which (1) trade flows are first explained by a set of independent variables (as in gravity models) and (2) the first-stage results are used to correct the selection bias related to missing values when estimating the ERPT equation. The existence of production and marketing lags in agri-food supply chains is likely to influence the selection rule.

[Received November 2005; accepted January 2007.]