Market definition: the stationarity test and the Granarolo/CLV case

Brasilia, March 2010

Lorenzo Ciari Lear

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Granarolo (a major milk and diary producer) planned the acquisition of Centrale del Latte di Vicenza (CLV), a locally owned diary firm

CLV was one of the strongest remaining competitors of Granarolo in the Veneto region (Italy)

The Italian Competition Authority (AGCM) prohibited the acquisition, proving that the concentration would have created a joint dominant position

Granarolo - Ground

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The AGCM defined the relevant product market with reference to:

•  differences in perishability rates and •  taste and nutritional qualities…

…between the fresh milk and the long-life (UHT) milk

These fresh milk characteristics also influences the definition of the relevant geographic markets

The relevant market

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To ensure an adequate shelf-life of the fresh milk, producers distributed the product within a few hours of bottling

Moreover the legislative framework mandated a sell-by date of no more than 4 days from the date of bottling

These factors obliged producers to distribute fresh milk within a few hundred kilometres from the different production sites

The geographic markets were found to be regional in scope

The relevant geographic market

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The AGCM also found that the companies rely on an trademarks which were renowned locally

This was confirmed by the largest competitors’ strategies:

producers operating on a national basis preferred to acquire local producers (and to adopt a co-brand strategy, using their own brand in combination with the local one) rather than competing against them using their own, nationwide, trademarks

The relevant geographic market (2)

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The AGCM found that the acquisition would have created a joint dominant position involving Granarolo and Parmalat (the other major national player) in the Veneto fresh milk market

Granarolo would have increased its 15-18% market share to 25-28%, close to that of Parmalat (33-35%)

Thus the combine market share of the two main players on the Veneto fresh milk market could have been nearly 60%

Granarolo and Parmalat could have been able to act independently of their competitors

The joint dominant position

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The joint dominant position (2)

Has Bean Steve

The market was also characterized by:

•  stagnating milk consumption (low likelihood of market grow); •  product homogeneity; •  no significant improvement in technology; •  producers share the same cost structures; •  high barriers to market entry; and •  transparent prices

Such circumstance considered alongside the economic ties between Granarolo and Parmalat would have created a joint dominance such to enable them to tacitly adopt parallel pricing policies

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Definition of the relevant market

Has Bean Steve

The AGCM used a stationarity test to define the dimension of the relevant geographic market: Dickey-Fuller test (DF) and the Augmented Dickey-Fuller test (ADF)

The idea behind this approach is that if two products or geographic areas belong in the same market, their price will not move indefinitely far from each other in the long-run (price comovement), so their relative price must be stationary

If the products are very close substitutes (on the demand or on the supply side) their prices cannot move too far apart, since consumer/producers will shift between them

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Stationarity test

Has Bean Steve

A necessary condition for two products being in the same antitrust market is then that the log of the price ratio is stationary

A property of stationary series is that they frequently cross the mean line and exhibit a tendency to revert to it

The shocks affecting stationary series have only temporary effects. The long-run prediction of the series is equal to the mean

Same relevant market

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Stationarity test (2)

Has Bean Steve

By contrast, a property of difference-stationary (DS) series is that they do not necessarily have a constant mean and do not frequently cross any horizontal line

The variance of a DS series grows over time without limit, and the shocks affecting it are permanent

If the difference between two log prices is DS, the log prices can move far from each other without limit as time goes on

Separate market

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Excursus: Stationarity and the Dickey-Fuller test

Has Bean Steve

Let us briefly remind the definition of stationarity: a time series is (weakly) stationary if:

In order to understand the logic of the ADF test, consider a random walk, which is a clearly non stationary series

where ε is a stationary error term. Yt is an I(1) series, which means that the first difference is stationary.

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Excursus: Stationarity and the Dickey-Fuller test

Has Bean Steve

This relationship can be expressed in a slightly more general form, as

Expressed in this way, we see that Yt is non stationary if |α|=1. If |α|<1 the series is stationary. Thus, formal tests of unit root are tests on the hypothesis that |α|=1.

Notice two things: first, the test implies the comparison between an I(0) and an I(1) series. Second, the test is one sided, as we rule out the hypothesis of |α|>1. It is unreasonable as the series would explode in that case.

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Excursus: Stationarity and the Dickey-Fuller test

Has Bean Steve

Given the intuition, let us be slightly more formal. The random walk series

can be written as

from which it can be seen that the impact of an error in a I(1) series does not die out. It is permanent. On the other hand, the series

can be expressed as

we can see that the error (the shock) has a transitory effect if |α|<1

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Excursus: Stationarity and the Dickey-Fuller test

Has Bean Steve

We have outlined the logic of the test. Formally the Dickey-Fuller test is a test of |α-1|=0 in the reparametrized model

Using OLS on the above model, you could retrieve the usual t-statistic to reject the null of unit root

Unfortunately it can be shown that the t-statistic under the null of unit root is not distributed as a standard t-statistic (in particular, it is not asymptotically normally distributed), so that special critical values have to be computed (the contribution of Dickey and Fuller)

Moreover, you might want to include in the model an intercept and/or a trend. Again the critical values will depend on the specification

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Excursus: Stationarity and the Dickey-Fuller test

Has Bean Steve

Finally, if the DGP has more than one lagged value of y on the right hand side (so it is autoregressive of an order greater than k), the ADF test is employed

In this case, the auxiliary regression is augmented for the appropriate number of lagged Δy’s to become

Where θ is the sum of all coefficients on the lagged dependent variables. The ADF test is used to protect against possible serial correlation in the error term.

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Excursus: Stationarity and the Dickey-Fuller test

Has Bean Steve

Indeed, a pth order autocorrelated error in the original specification gives rise to estimating an equation with p lagged values of y serving as regressors.

To see where the auxiliary regression comes from in ADF, start from :

subtract yt-1 on each side and add and subtract on both sides, in order to get

Hence this is the logic of the ADF tests. Other completely different tests have been proposed (not go in details)

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The application to the Italian Milk Market

Has Bean Steve

The AGCM analyzes prices of the one-litre brick of fresh milk of the kind “intero normale”, for all brands sold in supermarkets in several Italian regions

The Authority has 105 weekly data points between March 13, 1999 and March 10, 2001

For each couple of region the AGCM compute the difference of the logs of prices (log price in Veneto - log price in Piemonte, and so on) using the DF test and the ADF of orders 1, 2 and 3 (ADF1, ADF2, ADF3)

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The application to the Italian Milk Market

Has Bean Steve

First, the test was conducted on retail prices of one-litre brick of fresh milk. The test proved that the Veneto region is a separate geographical market

Second, considering that the promotions can be a disturbing element in the average price, the analysis was repeated using the prices adjusted for sales promotions

The test confirms that the results do not change!

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The application to the Italian Milk Market

Has Bean Steve

Results for the DF and ADF Test (promotions excluded)

DF ADF1 ADF2 ADF3

Piemonte 0,67 -1,57 -1,04 -1,24

Liguria -1,24 -2,31 -1,8 -0,89

Lombardia -1,08 -2,77 -1,32 -1,17

Trentino A.A. -2,07 -3,93 -1,81 -1,25

Emilia Romagnia -2,44 -3,52 -3,27 -2,59

Toscana -1,99 -1,92 -1,8 -2,13

Marche -1,77 -2,81 -2,4 -1,21

Lazio -1,57 -3,03 -2,81 -2,08

Campania -0,97 -1,12 -0,62 -1,06

Puglia -1,4 -2,09 -1,5 -0,9

Calabria -2,11 -2,52 -2,18 -1,83

Sicilia -1,84 -1,18 -0,66 -1,06 Significant at the 95% confidence level (-2.98)

For the majority of the regions the value of the test is inferior to the critical values. The only regions that present superior values are Trentino A.A., Emilia Romagna and Lazio. As for the three regions at most two tests out of four reject the null of non stationarity, the AGCM concluded in favour of separate markets between Veneto and the other Italian regions

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The application to the Italian Milk Market

Has Bean Steve

Granarolo has tried to demonstrate the non reliability of the AGCM analysis showing that the test, applied to the time series of prices for different brands within the same regions, gave counterintuitive results.

That is, the log of the difference between Granarolo and Parmalat prices in Veneto was non stationary.

The AGCM responded to that criticism suggesting that the parties have confronted average prices and prices of single references.

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The application to the Italian Milk Market

Has Bean Steve

Replicating the test using a single reference, Granarolo and Parmalat appeared to be in the same market.

At a 5% significance level (critical value -2.98) only three tests shoe results below the critical value, still above -2.63, critical value for 10% significance

DF ADF1 ADF2 ADF3

Agica -3.20 -2.86* -3.34 -2.95*

Ala -3.68 -3.79 -3.43 -2.29*

Lattebusche -3.31 -3.08 -3.56 -3.07

CLV -3.27 -3.43 -3.90 -3.50

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The application to the Italian Milk Market

Has Bean Steve

The criticism to the application by the AGCM might have been deeper.

First of all, there is a lot of approximation in the application of the test.

  There is no discussion on the specification (inclusion of a deterministic component for example)   There is no motivation for the order of autoregression of the estimated model (Pantula principle, other information criteria?)

More in general, there are criticisms that can be made to the very logic of the test.

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The application to the Italian Milk Market

Has Bean Steve

The claim that the ratio of two goods should be stationary when the goods are substitutes appears plausible but it is indeed very strong

Suppose we have two differentiated products nash equilibrium prices

The ratio can be expressed as:

Note that the ratio can be stationary, but only under very stringent conditions.

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The application to the Italian Milk Market

Has Bean Steve

In particular, note that even if products are substitutes, the relative costs of the two products need to remain broadly constant, as will the relative demand intercepts and the own and cross price elasticities

If, for example, we have a persistent shock in the cost of producing one product, this will determine a non stationary behaviour of the series

On the other hand, even if the products are not demand substitutes, we could potentially wrongly find stationarity if cost and demand shocks are correlated.

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The application to the Italian Milk Market

Has Bean Steve

The criticism to the application by the AGCM might have been deeper.

First of all, there is a lot of approximation in the application of the test.

  There is no discussion on the specification (inclusion of a deterministic component for example)   There is no motivation for the order of autoregression of the estimated model (Pantula principle, other information criteria?)

More in general, there are criticisms that can be made to the very logic of the test.

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Obrigado!

www.planejamento.gov.br/gestao/dialogos

dialogos.setoriais@planejamento.gov.br

Departamento de Cooperação Internacional Secretaria de Gestão – SEGES Ministério do Planejamento, Orçamento e Gestão Esplanada, Bloco K, 4° andar (61) 2020- 4906