Brand-level diversion ratios from product-level data

ABSTRACT

The diversion ratio is a key ingredient for merger analysis, as mentioned in the new Horizontal Merger Guidelines (2010) in the US and similar documents abroad. It is a measure of substitutability between merging goods, which determines the potential for price increase post-merger. This paper derives ready-to-use expressions for brand-level aggregated elasticities and diversion ratios, to be used with product-level data. I use the nested logit model and consider three different ways that nested products are grouped into brands, because most brands contain many individual goods, some of which form nests of higher similarity. While rich high-frequency data on the product level become increasingly available, a lot of relevant antitrust analyses, such as merger price effects, are conducted at the brand level. This paper fills a gap in the practitioner's toolkit, valuing ease of use without sacrificing richness of micro-data.

KEYWORDS:

• Horizontal merger
• unilateral price effect
• differentiated products
• upward pricing pressure
• diversion ratio
• product aggregates

Acknowledgments

I thank seminar participants at the third ATE (Applied and Theoretical Economics) Symposium in University of Auckland.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. For a detailed overview on the latest guidelines and its predecessors, see Shapiro (2010).

2. https://www.ftc.gov/enforcement/cases-proceedings/0210174/nestle-holdings-inc-dreyers-grand-ice-cream-holdings-inc. Accessed on 13 April 2016.

3. https://www.ftc.gov/news-events/press-releases/2015/05/ftc-requires-reynolds-lorillard-divest-four-cigarette-brands. Accessed on 13 April 2016.

4. http://www.comcom.govt.nz/the-commission/media-centre/media-releases/2015/commerce-commission-declines-reckitt-benckiser-lubricant-merger/. Accessed on 13 April 2016.

5. Consider this example of a simple market with two brands: m, n, and four products: m1, m2, n1, n2. Their observed prices are p_m1, p_m2, p_n1, p_n2. They are given weights w_m1, w_m2, w_n1, w_n2. Then, brand-level prices are given by p_m = w_m1p_m1 + w_m2p_m2 and p_n = w_n1p_n1 + w_n2p_n2. The brand-level demand function for brand m is Q_m = Q_m(p_m, p_n), which can be further written as Q_m(p_m(w_m1, w_m2), p_n(w_n1, w_n2)) to highlight the role of weights. Estimation of brand-level elasticity is a thought experiment on changing the brand-level price by, say, one percent. There are many ways to change p_m to, say, 1.01p_m, but the most straightforward way to do so, while keeping all weights constant, is to multiply both p_m1 and p_m2 by 1.01. (There are infinitely many other ways to achieve a one percent increase in p_m through p_m1 and p_m2, for example, by a larger-than-one percent increase in p_m1 and a smaller-than-one percent increase in p_m2. However, these respective percentage changes will depend on values of p_m1, p_m2, w_m1, w_m2, and will have to be calculated in an ad hoc manner. We do not entertain the idea of changing weights w_m1 and w_m2 to accommodate ad hoc percentage changes because this would alter the brand-level demand function, as highlighted above.) The brand-level elasticity or capture ratio that we want to measure is then the aggregation of all product-level changes from these one percent increases in p_m1 and p_m2.

6. The volume capture ratio from good mj to good nk is given by . The value capture ratio from good mj to good nk is given by . I present both of these capture ratios in Section 2.2.