Quantitative tools for market definition: an overview

Lorenzo Ciari, consultant

Plan of the talk 1.  Price tests

  Price correlation tests   Stationarity test

2.  Natural experiments

3.  Estimating diversion ratios

4.  Use of shipment data for geographic market definition

Price tests for market definition   Examining price differences and correlations is

perhaps the most common empirical method for market definition

  Analysis simple to perform, not data demanding   It is based on the intuition that the prices of goods

that are substitutes should move together   Despite this simple intuition, applying correlation

analysis is not always straightforward (and it can bring to false conclusions)

  In the course of the lecture, we will see a price test that moves from the same intuition, but applies time series econometrics tools (stationarity test)

  Application to an Italian case (merger)

Price correlation   The law of one price states that active sellers of

identical goods must sell them at identical prices   Formally, if goods 1 and 2 are perfect substitutes, the

demand schedule for firm 1 is

  The law of one price applies only to goods that are perfect substitutes, at least once transported to the same location (if goods are in different location they would differ only for their transport cost).

  However, goods may be close enough substitutes to ensure that demand schedules hence prices are correlated

Price correlation   The intuition from the law of one price is that

similarities in the levels of price can indicate that goods are substitute

  Taking this idea one step further, price correlation analysis is based on the idea that prices of close substitutes will co-move (demand substitution forces the prices to move together)

  An example of application of price correlation analysis: the Nestlé/Perrier case.

  In the proposed merger between the two companies, the key issue was whether the relevant market was the market for still water, the market for water, or the market for non-alcoholic drinks

Price correlation: Nestlé/Perrier   Below I report the correlation pattern:

  The results suggest that the market is that for water, including both sparkling and still water.

  Other non-alcoholic drinks should be excluded   Obviously, other evidence could outweigh the corr.

analysis

Price correlation: the salmon debate   The Salmon debate: in the UK it became relevant to

understand whether Scottish farmed salmon was in the same market of Norwegian farmed salmon

  Both Atlantic salmons   Correlation between the two weekly price series

(1997-2000) : 0.67   More difficult to interpret that a 0.9   What approach? The consultants choose to compare

the correlation coefficient with the correlation of products clearly in the same market (salmon of different weights)

  This appears a sensible approach

Price correlation   In order to understand what lies behind price

correlation analysis, the starting point is what drives price variations:

  Cost factors   Demand factors   Availability and prices of substitutes

  When we use price correlation analysis, we are assuming that what drives the co-movements is mainly the influence of good’s prices on consumers’ behaviour (consumer’s substitution)

  However, there might be other factors that determine the co movement not related to substitutability

Price correlation   Consider a simple model of price setting firms with

two differentiated products.   Suppose firms are not related form a demand side.

That is: demands are defined

  b12 = b21=0. Then,

  We can already have an intuition of where “false positives” can come from

Price correlation   False positives: correlated inputs or demand shocks   If two products use the same inputs and its price

varies, we will generate a positive correlation (think of oil based products)

  This implies that cov(c1, c2)≠0   In the salmon case, the potential common input was

salmon feed (sold in a global market)   However, the CC found that there was a negative

correlation between the price of salmon feed in Norway and the UK.

  Another cause of false positive is cov(a1, a2)≠0, that is the correlation of demand shocks

  Income is a major driver of common demand shocks

Price correlation   Another potential problem is the existence of spurious

correlation   Two series appear correlated but only because each of

them has a trend   The correlation is thus a pure coincidence   Formal way to approach the problem is to verify

whether the series are stationary   A series is stationary when, eventually, shocks to the

series no longer affect the value of the series.   As the simplest example, suppose the series at each

point in time is entirely independent of the points in any other period

  In this case, if we know the value of the variable yesterday or the day before, this carries absolutely no information for predicting the value of the variable today.

  And, if a shock occurs, it is not at all persistent.   This archetype of stationary series is a white noise   Suppose concretely we draw observations randomly from a

uniform (-1;1) distribution.   The expected value of the distribution is zero   So, observations are independent from one another.

Price correlation

Price correlation   This is how a white noise series might look (on the left):

  Now consider a price series generated by an autoregressive DGP (of order 1)

  Prices today are determined by price yesterday plus a white noise shock

Price correlation   The series can be expanded to see how that prices today are

actually determined by the price at the beginning of the series, and all the shocks that followed

  If ρ<1, the effect of both the initial condition and P0 and also of all the old shocks die out with time

  When this happens, we say that the series is stationary   If ρ=1 the series is a random walk and is non stationary or

integrated series (see the graph, left)

Price correlation   In essence (we will go later on more in the detail of

stationarity), a series is stationary when it exhibits a mean reverting behaviour

  It turns out that if we have two series generated with ρ=1, even if the shocks are completely independent, the long run covariance will tend to 1.

  So, let’s say it again: in the presence of integrated series we face a danger when look at correlation

  This is an issue that was present in the salmon debate (series were non stationary for a part of the sample). Solution, split the sample and see what happens in the stationary part

  Another possibility is to look at the behaviour of the series defined as the ratio of the two prices.

Natural experiments   The use of natural experiments (shock analysis) for

market definition follows a similar logic of price correlation analysis.

  However, it is a method that is far more rigorous in controlling the source of price variation in the data

  Shock analysis looks at the reaction of the prices of other goods following an exogenous shock on the price of the good which is the center of the investigation

  Shock analysis is the simplest way to get a feel of the magnitude of price elasticity without being involved in a complex exercise of demand estimation

  However, the investigator needs to be careful to ensure that the shock causing the initial price variation is exogenous, i.e. not determined by market conditions affecting consumers or competitors

Natural experiments   To see the logic of natural experiments, assume a

sudden unanticipated exogenous shocks in the price of good A, Pa

  Imagine it is a designed experiment of the firm   Such change impacts on the quantity of good A, the

price of good B and the quantity of good B   Once the shock occurs, we simply look at what

happens to quantities to have a feel of elasticities   The key factor for the success of the methodology is

that the shock is exogenous and not related to the demand of good A or B.

  An interesting example is provided by Davis (2002)   The example refers to a reduction in prices by a

cinema in New Haven, Connecticut

Natural experiments   The reduction in price was a marketing experiment, it

was an unusual and unanticipated move   There were five cinemas around that in New Haven   The exam of what were the reduction of the prices of the

cinemas around could shed light on which cinemas belong to the same market (product and geographic)

  If cinemas compete for customers, there is an incentive for competing cinemas to also reduce their prices.

  The exercise shows that the two more distant cinemas did not change their price while the closest ones did (actually they more than matched the price reduction)

  One close cinema did not change the price   Conclusions can be taken both for the geographic and

product market definition

Natural experiments   The case is certainly interesting: the problem is that it is

very difficult to identify such purely exogenous price changes in one product

  However, even in the absence of such controlled experiments, we may find “exogenous” movements in factors that affect demand or supply of one product

  Such events may be related to entry, regulatory changes, or input cost movements

  Let’s see the use of natural experiments within the context of a regression framework.

  We use again an example from Davis (2010).   He looks at geographic market definition for theatres, he

uses entry as source of variation and he wants to see up to what distance entry matters on pricing

Natural experiments   Consider the following regression for each theatre h:

  where x are counts of own and rivals’ screens within a given number of miles at time t in market m.

  We can use different distances   We wish to learn about how market structure affects

prices and we want to use the within theatre data variation

  To ensure we use this type of variation the regression uses theatre fixed effects (time and market fixed effects are also introduced)

  The results suggest that the presence of other movie screens within a range of ten miles has a negative effect on a given theatre’s price

 

Natural experiments   This example is useful to say a word on endogeneity   To attribute a value to this regression for geographic

market definition, we must claim that market structure, as measured by x is exogenous

  We need to argue that a higher density of cinemas is not correlated with factors that generate particularly high prices for reasons we cannot control for

  Another classical example of endogeneity in similar context relates to pharmaceutical prices (the impact of entry after a drug goes off patent)

Diversion ratios   Directly estimating the substitution effect is another

way to proceed for market definition.   We need to have consumer level data on the set of

possible choices that consumers face and the actual choice that they made (or the aggregate data on sales of each good)

  We will also need data on prices and possibly on other characteristics of the product being sold

  We will see a part of the immense literature on demand estimation

  Here we look at simpler ways to gauge substitution effects, beginning with a discussion on diversion ratios

Diversion ratios   A diversion ratio tries to answer the following

question: if the price of good 1 increases, what fraction of lost sales goes to good 2?

  An easy way is to look at market shares of competing products and interpreting their share of the total sales as the likelihood of being chosen by the average consumer

  However, market shares can be a misleading proxy for substitution effects.

Diversion ratios   The picture shows four shops with their catchment

areas (areas within which they can attract customers)   We can see that stores 1 and 2 compete only for a

subset of customers, while store 3 does not face any competitive constraint

  If we only computed market shares for the whole town, we would have a clearly bad representation of substitution effects

  The critique is then very clear for geographic markets’ definition, but it also applies to product market definition.

  There are products markets in which products differ in many dimensions in the eyes of consumers.

Diversion ratios   The relationship between the diversion ration and the

demand curve.   Let’s consider the demand for two differentiated

products

  b11 is the loss of sales of good 1 for a price increase of good 1, while b21 is the increase in sales of good 2. The diversion ratio is then:

  When p1 goes up, some sales will be lost to an outside good, that’s why even with two goods diversion ratio is less than 1

Diversion ratios   Now, if we want to estimate diversion ratios we need

information about how customers would react to a price change

  There are two ways: using revealed preferences, and using stated preferences

  Using revealed preferences involves demand estimation (see later)

  Using stated preferences implies that we rely on surveys

  We might have a separate discussion on the use of surveys for market definition (in particular on the use of discrete choice surveys), but here we introduce it

Diversion ratios   What we need to do is to select a representative

sample and ask customers about what they would in hypothetical circumstances

  Examples of questions:   I notice you have bought brand A. Suppose it costs 50

cents more, would you switch and buy brand B or C instead?

  Would you travel to the next big town if tomatoes cost 10 cents per kilo less than here?

  How high would the price of yellow paint have to be in order to induce you to switch your red paint machines to start producing yellow paint?

  The discussion on the quality of surveys is never-ending

Diversion ratios   What is agreed is that no room should be left for

subjective interpretation of questions   Also, there should not be too much information being

asked for (the possible alternatives should be clear)   Care should be taken in expressing probabilities or

percentages   An interesting case for the estimation of diversion

ratios through surveys is contained in Somerfield and Morrisons merger, approved with remedies by the CC

  Crucially, the CC decided not to ask for the reaction to price increases, as this would be too vague a concept for groceries

  The question asked was: if chain A was not present, what chain would you have chosen?

Diversion ratios   This is an interesting, though controversial approach.   What we are actually measuring here is reaction to

infinite price changes (and this is not what we look for in order to define relevant markets!!)

  The diversion ratio should measure the behaviour of marginal consumers, those who switch from A to B for a 5% increase in prices

  So it captures the behaviour of consumers who are close to being indifferent

  Instead, the CC question is geared to finding what happens if A goes away entirely (what is the next best option)

Elzinger and Hogarty   We now turn to the discussion about the use of

shipment data to define geographic markets   In particular, we look at the two stage test proposed

by Helzinger and Hogarty   The two stages are known as the LIFO and the LOFI   Basically the test amounts to verifying how much

flows of imports and exports there are in a given area   The overall idea is to expand the candidate market

until both dimensions of the test are satisfied   To operationalize the test, we need to define what is

“little”   The authors suggest to use a benchmark of 25% for

the LOFI

Elzinger and Hogarty   This implies to find an area where:

  Notice that increasing the size of the area might imply that new firms are involved in the computation

  The second criterion to be met is that:

  The test has been traditionally accepted by Antitrust authorities

  It came under scrutiny in the 1990s. Many mergers objected by US antitrust authorities were approved using the test

Elzinger and Hogarty   This happened in particular in relation with hospital

mergers   Several critiques can be moved to the test (in the

hospital merger case)   First: existing flows of supply or demand need not

be informative about market power (the fact that some consumers travel does not say that those who are currently not travelling are price sensitive)

  the second critique is that if the test fails, and you increase the market, this implies that you increase both the number of patients and hospitals

  Bottom line is clear: as for any other techniques, it must be used with caution.

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Obrigado!

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