Abstract
Abstract The aggregate Lerner index is a popular composite measure of multi-product banks’ market power, based on total assets as the single aggregate output factor. We show that the aggregate Lerner index only qualifies as a consistently aggregated Lerner index if three conditions hold. Under these conditions, the aggregate Lerner index reduces to a weighted-average of the product-specific Lerner indices. We test the three conditions for a sample of U.S. banks covering the years 2011–2017. All three conditions are rejected and we show that they may cause an economically relevant bias to the aggregate Lerner index, depending on the economic context. As a general solution, we propose using the always consistently aggregated weighted-average Lerner index whenever a composite Lerner index is needed.
Highlights
The Lerner index is a widely used measure of market power in the economic literature, whose historical and theoretical foundations have been extensively discussed in the literature (Amoroso, 1933; Lerner, 1934; Amoroso, 1938; 1954; Landes and Posner, 1981; Elzinga and Mills, 2011; Giocoli, 2012; Shaffer and Spierdijk, 2017)
We find that all three conditions are statistically rejected, which means that the aggregate Lerner index is not consistently aggregated for our sample of banks
Aggregate Lerner index In line with the literature about consistent aggregation, we find a strong relation between separability in total output of the multi-product cost function and consistent aggregation of the aggregate Lerner index
Summary
The Lerner index is a widely used measure of market power in the economic literature, whose historical and theoretical foundations have been extensively discussed in the literature (Amoroso, 1933; Lerner, 1934; Amoroso, 1938; 1954; Landes and Posner, 1981; Elzinga and Mills, 2011; Giocoli, 2012; Shaffer and Spierdijk, 2017). Despite the multi-product character of banks, the ‘aggregate’ Lerner index has remained popular in the empirical banking literature This Lerner index is based on total assets as the single aggregate output factor. Notes: This non-exhaustive table lists some recent studies (published since 2013) using aggregate, product-specific and weighted-average Lerner indices. If any of these conditions is rejected, the aggregate Lerner index is no longer consistently aggregated Because the weighted-average Lerner index is always consistently aggregated regardless of the underlying cost function, this index can be based on a cost function that fits the data well without further concerns about this cost function’s separability properties.
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