Aggregate Diversion and Market Elasticity

Transcription

1 Aggregate Diversion and Market Elasticity Serge Moresi (CRA) Hans Zenger (European Commission) Disclaimer: The views expressed in this presentation are those of the authors and do not necessarily reflect the views or opinions of the European Commission, other CRA staff or CRA's clients

2 Introduction Most quantitative tools for assessing competitive effects of mergers heavily rely on diversion ratios (DRs) between merging products (e.g., Werden's CMCR, 1996, Farrell & Shapiro's UPP, 2010, Salop & Moresi's GUPPI, 2009). But individual DRs cannot be determined without aggregate diversion ratios (ADRs), which are typically not observable in real-world antitrust procedures. This paper shows how ADRs can be approximated sensibly using their relation to the market elasticity of demand (otherwise: easily 100% off ). This permits implementing quantitative tools for assessing competitive effects when data is limited (based solely on simple, observable parameters such as market shares, profit margins and the market elasticity of demand).

3 The model Consider the standard model of price competition with differentiated products. Diversion ratios are: Aggregate diversion ratios are: δ jk = D k D j δ j = p j p j δ jk k j With proportionality, diversion ratios are: δ jk = s k δ 1 s j j

4 The model With some algebra, we can determine the general relation between ADRs and the market elasticity of demand: ε = t q = j=1 d dt k=1 p j q k=1 D k tp 1,, tp D k p j = j=1 t=1 = p j q k=1 j=1 D k p j p j q D j p j 1 δ jk k j = s j ε j 1 δ j j=1

5 Symmetric ADRs With symmetry, we have ε = 1 δ j=1 s j ε j and since in equilibrium m j = 1 ε j, we obtain δ = 1 mε. Hence: Proposition 1: If aggregate diversion ratios are symmetric, then δ = 1 mε, where m = 1/ j=1 (s j m j ) is the volume-weighted harmonic average mean. This expression solely depends on margins and market shares (which are routinely requested in antitrust investigations) and the market elasticity of demand (for which there are estimates in a multitude of industries). Clements (1998) proposes using an elasticity of -1/2 as a prior absent industry-specific data, as elasticities tend to be scattered around -1/2.

6 Asymmetric ADRs In many cases, symmetric ADRs will be a plausible assumption (e.g., when differentiation is predominantly horizontal and not vertical). In other cases, ADRs will be asymmetric. In particular, this is the case when diversion between inside and outside goods is proportional, in which case: 1 s j δ j = 1 s j + s 0 Since s 0 is not known, we again have to use the relation of ADRs to the market elasticity to substitute for it with observable parameters: s j s 0 ε = j m j 1 + s 0 s j

7 Asymmetric ADRs This system of two equations can be solved numerically in applications, so we have: Proposition 2: If aggregate diversion ratios are proportional to the share of inside and outside goods, then δ j = 1 s j 1 s j + s 0 for all j, where s 0 0 is the unique solution of the equation ε = s j s 0 m j 1 + s 0 s j j. Moreover, comparing the solutions in Propositions 1 and 2 we get: Proposition 3: (i) When ε = 0 or when shares are symmetric, then proportional ADRs are equal to the symmetric ADR (δ j P = δ S ). (ii) Otherwise, δ j P < δ S for products with high share and δ j P > δ S for products with low share.

8 Application 1: Competitive effects of mergers With proportional DRs, for symmetric ADRs, Proposition 1 implies: δ ij = s j 1 mε 1 s i Similarly, for asymmetric ADRs, Proposition 2 implies: s j δ ij = 1 s i + s 0 Two uses: At early stages of an investigation: Ability to implement UPP, CMCR, GUPPI etc. on the basis of minimal information (market shares, margins, market elasticity) provides an estimate of the lower bound of competitive effects when merging products are not remote At later stages of an investigation: Substituting for market shares with estimates of relative diversion (switching data) permits accounting for closeness of substitution

9 Application 2: Market share thresholds A large empirical literature shows a persistent increase in returns to capital/profit margins at the expense of labor (e.g., Karabarbounis & eiman, 2014, Autor et al., 2017, Piketty 2014). Accordingly, there have been calls for more active merger enforcement in a world with higher margins (e.g., Baker & Shapiro, 2008, Stiglitz, 2012). In an application, we apply our model (using Werden's CMCR) to the question whether merger control should be tougher on (market share) concentrations when margins are higher. Direct effect: Higher margins increase anticompetitive effects, since the negative externality of competition on the merging rival is larger.

10 Application 2: Market share thresholds Indirect effect: Higher margins imply less close competition pre-merger (all else equal) and hence lead to less of an anti-competitive effect. The net effect of higher margins on competitive effects is in principle ambiguous. However, we consider the special case of a 50% increase in profit margins and review which concentration level a 50% combined share corresponds to in terms of economic effect once margins have increased. As it turns out, once one takes account of a 50% increase in margins, what used to be a 50% market share threshold corresponds to a 40-45% threshold if margins have increased (holding the anti-competitive effect constant).