Estimating Market Power of Agricultural and Food Industries: An Issue of Data Aggregation

Jungmin Lee and Chanjin Chung1

Selected Poster prepared for presentation at the 2015 Agricultural & Applied Economics Association and Western Agricultural Economics Association Joint Annual Meeting, San Francisco, CA, July 26-28

Copyright 2015 by Jungmin Lee and Chanjin Chung. All rights reserved. Readers may make verbatim copies of this document for non-commercial purposes by any means, provided that this copyright notice appears on all such copies.

1 Jungmin Lee is a graduate research associate, Chanjin Chung is a Professor & Charles Breedlove Professorship in Agribusiness, Department of Agricultural Economics, Oklahoma State University, Stillwater, Oklahoma.

Estimating Market Power of Agricultural and Food Industries: An Issue of Data Aggregation Bias Jungmin Lee1 and Chanjin Chung2

1 Ph.D. Student 2 Professor & Charles Breedlove Professor in Agribusiness , Department of Agricultural Economics, Oklahoma State University

Introduction Methodology • Theil(1971) derived an matrix equation that delineated As agricultural and food industries become increasingly integrated 1. Traditional NEIO model aggregation bias form the linear model based on Let’s suppose that cost function is a trans-log cost function form as and concentrated, there have been numerous studies estimating theoretical finding. We extend Theil’s foundation to 3 3 3 3 1 2 equation (9) and derive different kinds of aggregation bias. market power of these industries. New empirical industrial logc  0  a log wa   y log y  ab log wa log wb  ya log ylog wa   yy (log y)  vi (1) a1 2 a1 b1 a1 where β =β , w is input price, a,b= K, L, M, K is capital input, L is labor input, M is intermediate Y  X  (10) organization (NEIO) models first derive conceptual models from nm mn n profit-maximizing-theory of a single “representative” firm, and then input and y is output. where  x 0 i , x 1 i , x 2 i , x 3 i , x 4 i , x 5 i    1 , y i , w Ki , w Li , w Mi,  1 n 1 n market power parameters are estimated using market- or industry-      X  X  S 2      0 i ,  1 i ,  2 i  3 i ,  4i ,  5 i     yi , 2  yyi ,  y Ki ,  y Li ,  yMi  ,  i  i   x,ig The input demand function can be derived by Shephard’s Lemma when cost is minimized under profit n i1 2n i1 level data due to the lack of firm-level data. However, it is well maximization problem. Y and ε are column vector with T-elements of h known in empirical econometrics that when relations are derived 3  c  p t   and ε , β and vector can be expressed as s     log w   log y (2)  y  t i from microeconomic theory, but are estimated by means of a a  ab ab ya  t b1    0 1 2 3 4    y 2 yy  yK  yL  yM   aggregated data, the aggregation can lead to biased parameter where x a w a , a= K, L, M and s is the industrial cost-share equation. sa  a i  0i 1i 2i 3i 4i i   yi 2 yyi  yKi  yLi  yMi i  estimates. c

The equation (5) can be generated from the first order condition of profit maximization equation. From the equation (10), Take the estimation of market power in the U.S. beef processing n n c    1 1 p  ( )   2 log y   log w   log w   log w 1  (3)     industry as an example. A conceptual model for this analysis may  y yy y K K y L L yM M    b    Wi  I i   Ri  X X  X  (11) y    i1  n  i1 where η is demand elasticity, c is total cost. start from the theory of profit maximization and derive an individual n 1 1 1 1 2 processor’s price equation with a market conduct parameter where Wi  X X  X  X i ,Wi  I, Ri X X  X  Sx,ig  n i1 2n typically represented by a conjectural coefficient or elasticity of the The equation (6) is output demand function and can be written as processor. However, the empirical estimation of the model is ln y  a  ln ( p / S)   ln(q / S) (4) • The second term of right side of equation (11) is usually based on aggregate time-series data at either market or where η is demand elasticity, ρ is income elasticity, q is GNP, S is GNP deflator. aggregation bias from ignoring the parameter industry level, which does not consider the heterogeneity of heterogeneity and third term is the bias caused by using individual processor’s firm behavior. The applied econometrics The equation (7) is total cost linearly aggregated data for nonlinear macro model. literature indicates that ignoring heterogeneity in estimates of c  w x  w x  w x (5) individual firm behavior (represented by conjectural coefficient or K K L L M M elasticity) may result in biased estimation of overall market power Further Studies of U.S. beef processors. Therefore, the issue of aggregation bias 2. Aggregation Bias raises concerns regarding the validity of market power estimated • Aggregation Bias from Cost Share Equation from aggregate data and highlights the need for research • A new procedure that combines aggregate data and Let’s assume that n firms exist, then sum each firm’s cost share equation and divide by n, then the designed to enhance our understanding of aggregation bias in publically available firm-level data will be developed to estimating market power. A proper understanding of the equation is expressed as 1 n 1 n 1 n 3 1 n reduce aggregation bias. aggregation problem and the particular method chosen for the sai  ai  abi log wabi   yai log yi (6) resolution is of the crucial importance for estimating market power n i1 n i1 n i1 b1 n i1 • Empirical analysis will be conducted to demonstrate the 3 n n 1 n 1 n 1 1  log y of agricultural and food industries. Adding and subtracting    abi  log w abi and  yai  i , the equation (6) is aggregation bias and how the aggregation bias can be b1 n i1 n i1 n i1 n i1 3 3 reduced by combining aggregate data and publically s     log w   log y  cov ( ,w )  cov( ,log y ) (7) a a  ab ab ya  i abi abi yai i b1 b1 available firm-level data in the newly developed procedure. 3 n 1 g 2 1 g 2  ab (log wabi  log wab )   ya (log yi  log yab ) 2n b1 i1 2n Objectives • Aggregation Bias from Price Equation References The equation (3) can be showed as equation (8) 4  c      • This paper derives aggregation bias analytically from the p     j log x j  1  (8)    Appelbaum, E. 1982. The Estimation of the Degree of Oligopoly  y  j 0     previous NEIO approach. A statistical procedure is developed Power. Journal of Econometrics 19(2), 287-299. to quantify the degree of bias and conditions under which where i=1,2, …,n and 0i ,1i ,2i3i ,4i    yi ,2 yyi , y Ki , y Li , yMi ,x0i , x1i , x2i , x3i , x4i   1, yi ,wKi ,wLi ,wMi  4 n n 1 1 n 1 n 1 Chung, C., and Harry M. K.2002 "Advertising Evaluation and Cross- 1 1  aggregation bias is likely to occur. Let’s add and subtract  ji log x ji to right sight and also  i  to left side of     n i1 n i1 ki Sectional Data Aggregation." American Journal of Agricultural j0 n i1 n i1 • New procedure is introduced to demonstrate how the equation (8), Economics 800-806. h h 4 4 4 n   Stoker, T. M. 1993. "Empirical Approaches to the Problem of aggregation bias can be reduced or eliminated by combining  c   1 g 2    1  yi   c   p     j log x j  covi ( ji , log x ji )   j log x ji  log x j   1  covi ,     (9) Aggregation over Individuals." Journal of Economic aggregated market-level data with published firm-level data.  y   j 0 j 0 2n j 0 i1      ci   y     Literature 1827-1874. h  c  ci Theil, T. Principles of Econometrics. New York: Wiley, 1971 where   is the harmonic mean of  y  yi