Assessing the role of futures position substitutability in a monthly slaughtered pork factor demand by US processors: a cointegrated VAR model approach

ABSTRACT

This article combines cointegrated VAR modelling with basic neoclassical production microeconomics in a new way that tests for, and illuminates the empirical nature of, the monthly US pork processing sector’s factor demand for slaughtered pork. Statistical evidence strongly suggests that the US pork processing sector has a Hicksian Cobb–Douglas slaughtered pork demand that arises from applying Shephard’s lemma to the sector’s cost function and that US pork processors treat slaughtered pork and related futures positions as close factor substitutes. In the wake of major and ongoing futures market events and trends, this study establishes and statistically tests a theoretical link between futures price movements and impacts on the underlying slaughtered pork market through monthly formation of US pork processors’ factor demand for slaughtered pork. Evidence suggests that demand agents shift between demands for the two substitutes based on movements in the slaughter/futures price ratio that results in a market-stabilizing cushion against sharp pork price movements such as those observed in the late-1990s. Statistical and diagnostic evidence suggests that our modelled non-experimental data and estimated Hicksian demand that arose from the cointegrated VAR model’s cointegration space met Haavelmo’s setting of passive variables and associated ceteris paribus conditions.

KEYWORDS:

• Commodity markets
• pork prices
• input factor demand
• cointegrated VAR

JEL CLASSIFICATION:

• Q11
• C32
• D20

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ For reasons explained later, throughout this article, ‘slaughtered pork’ refers to US commercial pork slaughter published monthly by the U.S. Department of Agriculture, Economic Research Service (USDA, ERS 2013). Futures positions and prices of such positions are for the CMEGroup’s lean hog futures contract.

² Silberberg (1978, 196) notes that the sign is ambiguous: γ > 0 when the Hicksian factor demand is normal; and γ < 0, when the factor demand is not normal. He further notes that γ must be positive at some level of output, or the factor would not ever be employed in the first place. In our case of factor demand for pork as a productive factor, is a normal one.

³ We realize that our modelled system does not include a variable for US pork processor output that would serve as an output constraint for US pork processors that minimize production costs. Data for quantities for major US processed pork products are not available on a monthly, or even quarterly, basis as such data are considered by private processors as confidential business information and are precluded from the public domain. Certain government sources of output data compiled by the U.S. Department of Commerce are available for some US processed pork products but on an annual basis and not on a monthly basis as needed to conduct our study. We relegate to future research efforts the tasks of generating and using such data that would serve as the ‘Y’ argument in Equations (4) and (5). We note that in spite of our data availability constraints that precluded our inclusion of a monthly pork processor output level (Y), our efforts are valid for two reasons. First, we meet accepted standards of statistical and diagnostic adequacy for our cointegrated VAR model. Second, our ‘… inclusion of cointegrating relationships enhances structure in that they remain invariant to expansions in the information set’ (Bardsen, Fischer, and Nymoen 1998, 506). So future research could build off of our cointegration results which should remain invariant and valid, as more data and information become available in the future.

⁴ See the following link accessed on 4 August 2013: www.bloomberg.com. Ticker: LH1 Comdty. The roll methodology was chosen as the front month contract with roll into the next nearest contract on the first business day of the front month contract’s expiration month. Further, the futures contracts used in PFUTURES have a final settlement price that is based on the information obtained from the ‘National Daily Direct Hog Prior Day Report-Slaughtered Swine’ released by the U.S. Department of Agriculture for the 2-day period ending on the contract’s last day of trading. The settlement price is derived from data concerning all producer-sold negotiated and swine or pork market formula barrows and gilts purchased on a lean value direct basis for which the head count, average net price and average carcass weight are reported in the above report. See CME Rule book at the following link: http://www.cmegroup.com/rulebook/CME/II/150/152/152. Note further that the CMEGroup changed from what was a live hog futures contract to a lean hog (carcass) contract in 1997. The transition began with the February 1997 contract. In order to provide historical perspective on lean hogs, the CMEGroup converted prices actually traded in live hog futures to lean hog equivalent prices. All of our futures prices reflect lean hogs after the contract’s 1997 conversion and lean hog price equivalents before the contract’s 1997 conversion (see CMEGroup 2008).

⁵ The estimate that PFUTURES prices unprocessed product at/near the slaughter point at an average forward time-stamp of 70 days arises from consideration of a number of factors. First, as close as could be obtained, PSLAUGHT provides a current national price for unprocessed slaughtered pork. And second, the 70-day average estimate uses the assumptions that (i) a monthly average price presents approximately half a month (15 days), (ii) the contract will have 1 or 2 months until the delivery month and (iii) average settlement occurs about 15 days into the delivery month so as to realize the following summation: 15 + (30 or 60) + 15. Since PFUTURES is based on futures contracts that are more often a single month out, rather than two, the 70-day period of futures being forwardly priced from the current pricing point of PSLAUGHT emerged.

⁶ This section draws heavily on Johansen and Juselius (1990) and Juselius (2006).

⁷ In following Juselius’ (2006) methods in estimating the final cointegrated model, space considerations precluded the reporting of the full array of statistical results that included both the long-run component that is focused on here and the short-run component that is not addressed here. The fairly voluminous full output of the finally estimated cointegrated VAR model is available from the authors on request.

⁸ A month-specific event was considered as potentially ‘extraordinary’ if its standardized residual exceeded 3.0 in absolute value. This rule was designed based on the effective size of T = 289 observations using the Bonferoni criterion programmed by Estima (RATS, version 8.2): INVNORMAL(1–1.025)^T. INVNORMAL is a function for the normal distribution that returns the variable for the cumulative density function as a standard normal distribution and suggested that the absolute Bonferoni value was 3.75. Having realized that there were some month-specific events with potentially extraordinary effects with absolute standardized residual values of about 3.0, we followed recent cointegrated VAR modelling work and chose a more conservative Bonferoni absolute value criterion of 3.0 rather than 3.75 (Babula and Rothenberg 2012). Observations with absolute standardized residual values of 3.0 or more were considered potential outliers and appropriately defined binaries were specified for such observations for the above-cited sequential estimation procedure. Four outlier binaries were included. Because of space considerations, we do not analyse these binaries as they lie in the cointegrated VAR model’s short-run component that is not a focus of this study on long-run US slaughtered pork market relationships.

⁹ Due to space considerations, we have summarized and have not reported the full results of the unit root patterns, root values and other relevant information under r = 1 and 2. These results and matrices are available from the authors on request.

¹⁰ An α-estimate is taken as statistically nonzero at the 5% significance level if its absolute pseudo-t value is 2.6 or more (Juselius 2006, 142). The pseudo-t values generated by the statistically significant α-estimates are as follows: −5.43 on α(QSLAUGHT) and 4.11 on α(PSLAUGHT) in CV1 and −4.80 on α(PFUTURES) in CV2.

¹¹ The p1 equals 9: it is the sum of p = 3 endogenous variables plus the 6 previously discussed deterministic variables that were restricted to lie in the cointegration space.

¹² More specifically, Equation (9) is re-written as β^c = [b,φ], where β^c is a p1 × r or 9 × 1 matrix with one of the variable’s levels restricted to a unit vector and b is a p1 × 1 or 9 × 1 vector with a unity value corresponding to the variable the stationarity of which is being tested. The φ is a p1 × (r – 1) matrix that vanishes under r = 1 since (r – 1) is zero. Given the rank of 1, the test values and parenthetical p-values for the three stationarity tests are as follows with the null of stationarity rejected for p-values below 0.05: 31.65 (p = 0.00011) for QSLAUGHT; 30.52 (p = 0.00017) for PSLAUGHT; and 26.45 (p = 0.00088) for PFUTURES.

¹³ The χ² value (five degrees of freedom) was 6.81 with a p-value of 0.24. Evidence was insufficient to reject these five restrictions.

¹⁴ Pseudo-t test statistics are in parentheses.

¹⁵ A colleague insightfully inquired about the issue of storage costs. Our demand in Equation (11), as stated, is a Hicksian US processor demand for slaughtered pork as a productive factor. This demand arises from applying Shephard’s lemma to the indirect cost function in an output-constrained cost minimization optimization model of US pork processors. Two-factor demands could theoretically arise in our ‘n = 2’ factor setting. First would be taking the cost function’s first partial derivative with respect to slaughtered pork price which renders our Equation (11), the factor demand for currently priced slaughtered pork in which futures price serves as a substitute price argument. The second would be the cost function’s first partial derivative with respect to futures price which would render pork processors’ factor demand for futures positions. In this theoretical model, storage costs would more likely be an argument in the factor demand for futures positions than in Equation (11) depicting a factor demand for slaughtered pork.

¹⁶ This discussion uses the same observed historical data collected and analysed for the same time frame that coincides with the noted price volatility episode noted and summarized by Babula and Rothenberg (2012, 16–8). And so our analysis of these observed pork price trends is similar to that provided in the prior study.

¹⁷ This information on the causes of this US pork price volatility was discussed in Babula and Lund (2008, 202).

¹⁸ This analysis of the PSLAUGHT and PFUTURES price declines’ coincidence with the 8.4% decrease in US processed pork price arose from consideration of the data over the relevant late-1998/early-1999 periods for the US PPI for pork, processed or cured, not canned or made into sausage, series no. PCU3116123116121. The data were obtained from the following site accessed by the authors on 4 August 2013: http://data.bls.gov. Also see Babula and Rothenberg (2012, 17).

¹⁹ This analysis of the PSLAUGHT and PFUTURES price increases’ coincidence with the 12.5% increase in US processed pork price arose from consideration of the data over the relevant 1998–1999 periods for the US PPI for pork, processed or cured, not canned or made into sausage, series no. PCU3116123116121. The data were obtained from the following site accessed by the authors on 4 August 2013: http://data.bls.gov.