Market Power Effects of the Livestock Mandatory Reporting Act in the U.S. Meat Industry: a Stochastic Frontier Approach Under Uncertainty

Abstract

The present study evaluates changes in market power in the U.S. red meat industry after the implementation of the 1999 Livestock Mandatory Reporting (LMR) Act. It employs the recently developed stochastic frontier approach of market power estimation and accounts for uncertainty in the market, capturing this way the counteractive strategic and risk effects generated by the increased transparency of the Act. The net effect of the LMR Act on market power exerted by packers was estimated. Time series data on the U.S. cattle/beef and hog/pork industries for the period 1970–2010 were employed. The empirical findings suggest that the mandatory reporting program has generated a pro-competitive impact in both livestock markets.

Appendices

Appendix A

Description of the variables and their sources are as follows:

• Source: NBER– CES Manufacturing Industry Database / SIC2011 (meatpacking)

  $$\begin{array}{@{}rcl@{}} L &=& \text{Production worker hours (million hrs)} \\ W_{L} & =& \frac{\text{Production worker wages (million}~\$)} {\text{L}} \\ W_{K} &=& \text{interest rate} + \text{depreciation rate} \\ W_{M} &=& \text{Deflator for MATCOST}~ (1987 = 1.00) \\ W_{E} &=& \text{Deflator for ENERGY}~(1987 = 1.00) \end{array} $$

• Source: United States Department of Agriculture—Economic Research Service

  $$\begin{array}{@{}rcl@{}} Q&=& \text{Commercial beef/pork production (carcass weight, million lbs)}\\ (P-W)&=& \text{Farm--wholesale price spread (cents per retail pound equivalent)} \end{array} $$

Appendix B

According to Eq. 16, the expression for $\frac {dln C_{i}}{dln q_{i}}$ is:

$$\begin{array}{@{}rcl@{}} \frac{dln C_{i} } {dln q_{i}} = \beta_{q}+\beta_{qq}\,\ln q_{i} +\beta_{qT}\,T+\beta_{qK}\,\ln \frac{w_{K}}{w_{M}}+\beta_{qL}\,\ln \frac{w_{L}}{w_{M}}+\beta_{qE}\ln \frac{w_{E}}{w_{M}} \end{array} $$

The expression $\frac {dlnC_{i}} {dlnq_{i}}$ can also be written as:

$$\begin{array}{@{}rcl@{}} \frac{dlnC_{i}} {dlnq_{i}} = \frac{dC_{i}} {dq_{i}} \frac{q_{i}} {C_{i}} \end{array} $$

Hence, the marginal processing cost for the i th meatpacking firm is:

$$\begin{array}{@{}rcl@{}} MC_{i}\,=\, \frac{dC_{i}} {dq_{i}}\,=\, \frac{C_{i}} {q_{i}}\, \left( \beta_{q}+\beta_{qq}\,\ln q_{i} +\beta_{qT}\, T+\beta_{qK}\,\ln \frac{w_{K}}{w_{M}}+\beta_{qL}\,\ln \frac{w_{L}}{w_{M}}+\beta_{qE}\,\ln \frac{w_{E}}{w_{M}}\right) \end{array} $$

Aggregating and deriving Eq. 21 from Eq. 10, we have:

$$\begin{array}{@{}rcl@{}} \frac{dlnC} {dlnQ} = \frac{Q} {C} \,\, MC(Q) =\frac{Q} {C} \sum\limits_{i = 1}^{N} \frac{q_{i}} {Q}\,\, MC_{i} \end{array} $$

Substituting for MC_i and continue with the calculations, we get:

$$\begin{array}{@{}rcl@{}} \frac{Q} {C} \sum\limits_{i = 1}^{N} \frac{q_{i}} {Q}\,\, MC_{i}&=& \frac{Q} {C} \sum\limits_{i = 1}^{N} \frac{q_{i}} {Q}\, \frac{C_{i}} {q_{i}}\, \left( \beta_{q}+\beta_{qq}\, \ln q_{i} +\beta_{qT}\, T+\beta_{qK}\,\ln \frac{w_{K}}{w_{M}}\right.\\&&\qquad\qquad\qquad\,\,\left.+\beta_{qL}\,\ln \frac{w_{L}}{w_{M}}+\beta_{qE}\,\ln \frac{w_{E}}{w_{M}}\right)\\ &=&\beta_{q}+\beta_{qq}\, {\sum}_{i = 1}^{N} \frac{C_{i}} {C}\,\,\ln q_{i} +\beta_{qT}\, T+\beta_{qK}\,\ln \frac{w_{K}}{w_{M}}+\beta_{qL}\,\ln \frac{w_{L}}{w_{M}}\\&&+\beta_{qE}\ln \frac{w_{E}}{w_{M}}\\ \end{array} $$

The second term on the right hand side of the equation above is the cost-share-weighted sum of the logarithm of firms’ quantities. Had data on firm level been available, i.e. observations on each firm’s q_i, we would be able to calculate the terms C_i and C and proceed with our estimation. In the absence of panel data on firm level, an aggregate translog processing cost function is employed. Hence, this study approximates the cost-share-weighted sum of the logarithm of firms’ quantities with the logarithm of the industry’s total quantity. The expression $\frac {dlnC} {dlnQ}$ assumes the following form:

$$\begin{array}{@{}rcl@{}} \frac{dlnC} {dlnQ} \,=\, B_{Q}\,+\,B_{QQ}\,\ln Q +B_{QT}\, T +B_{QK}\, \ln \frac{w_{K}}{w_{M}}+B_{QL}\, \ln \frac{w_{L}}{w_{M}}+B_{QE}\,\ln \frac{w_{E}}{w_{M}} +u+\eta \end{array} $$

The expression above is the relationship on the right hand side of Eq. 25.