Quantitative tools for market definition: an overview

Lorenzo Ciari, consultant

1.  Price tests

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Plan of the talk

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Price correlation tests

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Stationarity test

Natural experiments

3.  Estimating diversion ratios 4.

Use of shipment data for geographic market definition

Price tests for market definition 

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Examining price differences and correlations is perhaps the most common empirical method for market definition Analysis simple to perform, not data demanding

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It is based on the intuition that the prices of goods that are substitutes should move together

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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)

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Application to an Italian case (merger)

Price correlation

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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

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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:

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The results suggest that the market is that for water, including both sparkling and still water. Other non-alcoholic drinks should be excluded

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Obviously, other evidence could outweigh the corr. analysis

Price correlation: the salmon debate 

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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

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Correlation between the two weekly price series (1997-2000) : 0.67

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More difficult to interpret that a 0.9

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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

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Price correlation

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In order to understand what lies behind price correlation analysis, the starting point is what drives price variations: 

Cost factors

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Demand factors

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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

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b12 = b21=0. Then,

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

Price correlation

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False positives: correlated inputs or demand shocks

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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

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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

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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

Price correlation 

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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.

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This archetype of stationary series is a white noise

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Suppose concretely we draw observations randomly from a uniform (-1;1) distribution.

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The expected value of the distribution is zero

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So, observations are independent from one another.

Price correlation 

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

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

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

Price correlation

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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

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

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When this happens, we say that the series is stationary

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If ρ=1 the series is a random walk and is non stationary or integrated series (see the graph, left)

Price correlation

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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

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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

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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

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Such change impacts on the quantity of good A, the price of good B and the quantity of good B

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Once the shock occurs, we simply look at what happens to quantities to have a feel of elasticities

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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)

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The example refers to a reduction in prices by a cinema in New Haven, Connecticut

Natural experiments

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The reduction in price was a marketing experiment, it was an unusual and unanticipated move

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There were five cinemas around that in New Haven

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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)

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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)

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One close cinema did not change the price

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Conclusions can be taken both for the geographic and product market definition

Natural experiments

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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.

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We use again an example from Davis (2010).

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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.

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We can use different distances

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We wish to learn about how market structure affects prices and we want to use the within theatre data variation

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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

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This example is useful to say a word on endogeneity

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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)

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Diversion ratios

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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

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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

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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

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

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

Diversion ratios

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The relationship between the diversion ration and the demand curve. Let’s consider the demand for two differentiated products

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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:

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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

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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

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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?

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

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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 neverending

Diversion ratios

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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

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This is an interesting, though controversial approach.

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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)

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Elzinger and Hogarty

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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

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This implies to find an area where:

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

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The second criterion to be met is that:

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The test has been traditionally accepted by Antitrust authorities

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

Elzinger and Hogarty

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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) 

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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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Marketdefquantitative

Quantitative tools for market definition: an overview Lorenzo Ciari, consultant 2.  Natural experiments 3.  Estimating diversion ratios 1....

Marketdefquantitative

Quantitative tools for market definition: an overview Lorenzo Ciari, consultant 2.  Natural experiments 3.  Estimating diversion ratios 1....