"This book will be eminently helpful to both the practitioner with an undergraduate background in economics and to the academic economist. It offers the practitioner a clear and concise rendering of the techniques used in antitrust analysis. It offers the academic an explanation of the issues that arise in antitrust cases and the institutional setting in which they are analyzed."Ariel Pakes, Harvard University
"An excellent and wide-ranging introduction to the new econometric literature that has played an increasingly important role in competition policy over the past decade."John Sutton, London School of Economics and Political Science
"Davis and Garcés have filled a longstanding gap in the market with their detailed overview of modern empirical research in industrial organization. Their book would be an excellent text for a graduate class in empirical industrial organization. More generally, the authors provide a comprehensive introduction to the field."Robert Porter, Northwestern University
"There is no other book like this on the market. The authors provide essential guidance for skilled antitrust practitioners who want to learn up-to-date empirical methods. The comprehensive body of material, skillfully explained, will also be of great use to graduate students and academics who want to explore the intersections of policy and econometric practice."Steven Berry, Yale University
"This book provides a comprehensive overview of quantitative techniques used in competition analysis, ranging from very simple methods when limited data are available to the most advanced and state-of-the-art techniques. It fills important gaps because no other recent book combines insights from empirical industrial organization and quantitative competition policy analysis. There is also a very good mix between discussion of techniques and cases. Although its primary audience is practitioners at competition policy authorities, it will also interest academics and consultants and can serve as a textbook for advanced masters and PhD courses."Frank Verboven, Katholieke Universiteit Leuven
"This very useful book is a great addition to the discipline. Applied industrial organization is a rapidly developing field, with many open areas and problems, but practitioners are often forced to work with what is available to make antitrust decisions. A good user's manual like this one is important to have. I am sure practitioners will find this a handy toolbox."Maarten Pieter Schinkel, University of Amsterdam
The book consistently evaluates empirical techniques in light of the challenge faced by competition analysts and academicsto provide evidence that can stand up to the review of experts and judges. The book's integrated approach will help analysts clarify the assumptions underlying pieces of empirical work, evaluate those assumptions in light of industry knowledge, and guide future work aimed at understanding whether the assumptions are valid. Throughout, Davis and Garcés work to expand the common ground between practitioners and academics.
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Quantitative Techniques for Competition and Antitrust Analysis
By Peter Davis Eliana Garcis
Princeton University PressCopyright © 2010 Peter Davis and Eliana Garcis
All right reserved.
Chapter OneThe Determinants of Market Outcomes
A solid knowledge of both econometric and economic theory is crucial when designing and implementing empirical work in economics. Econometric theory provides a framework for evaluating whether data can distinguish between hypotheses of interest. Economic theory provides guidance and discipline in empirical investigations. In this chapter, we first review the basic principles underlying the analysis of demand, supply, and pricing functions, as well as the concept and application of Nash equilibrium. We then review elementary oligopoly theory, which is the foundation of many of the empirical strategies discussed in this book. Continuing to develop the foundations for high-quality empirical work, in chapter 2 we review the important elements of econometrics for investigations. Following these first two review chapters, chapters 3-10 develop the core of the material in the book. The concepts reviewed in these first two introductory chapters will be familiar to all competition economists, but it is worthwhile reviewing them since understanding these key elements of economic analysis is crucial for an appropriate use of quantitative techniques.
1.1 Demand Functions and Demand Elasticities
The analysis of demand is probably the single most important component of most empirical exercises in antitrust investigations. It is impossible to quantify the likelihood or the effect of a change in firm behavior if we do not have information about the potential response of its customers. Although every economist is familiar with the shape and meaning of the demand function, we will take the time to briefly review the derivation of the demand and its main properties since basic conceptual errors in its handling are not uncommon in practice. In subsequent chapters we will see that demand functions are critical for many results in empirical work undertaken in the competition arena.
1.1.1 Demand Functions
We begin this chapter by reviewing the basic characteristics of individual demand and the derivation of aggregate demand functions.
188.8.131.52 The Anatomy of a Demand Function
An individual's demand function describes the amount of a good that a consumer would buy as a function of variables that are thought to affect this decision such as price [P.sub.i] and often income y. Figure 1.1 presents an example of an individual linear demand function for a homogeneous product: [Q.sub.i] = 50 - 0.5 [P.sub.i] or rather for the inverse demand function, [P.sub.i] = 100 - 2[Q.sub.i]. More generally, we may write [Q.sub.i] = D([P.sub.i], y). Inverting the demand curve to express price as a function of quantity demanded and other variables yields the "inverse demand curve" [P.sub.i] = P([Q.sub.i], y). Standard graphs of an individual's demand curve plot the quantity demanded of the good at each level of its own price and take as a given the level of income and the level of the prices of products that could be substitutes or complements. This means that along a given plotted demand curve, those variables are fixed. The slope of the demand curve therefore indicates at any particular point by how much a consumer would reduce (increase) the quantity purchased if the price increased (decreased) while income and any other demand drivers stayed fixed.
In the example in figure 1.1, an increase in price, [delta]P, of [member of]10 will decrease the demand for the product by 5 units shown as [delta]Q. The consumer will not purchase any units if the price is above 100 because at that point the price is higher than the value that the customer assigns to the first unit of the good.
One interpretation of the inverse demand curve is that it shows the maximum price that a consumer is willing to pay if she wants to buy [Q.sub.i] units of the good. While a consumer may value the first unit of the good highly, her valuation of, say, the one hundredth unit will typically be lower and it is this diminishing marginal valuation which ensures that demand curves typically slope downward. If our consumer buys a unit only if her marginal valuation is greater than the price she must pay, then the inverse demand curve describes our consumer's marginal valuation curve.
Given this interpretation, the inverse demand curve describes the difference between the customer's valuation of each unit and the actual price paid for each unit. We call the difference between what the consumer is willing to pay for each unit and what he or she actually pays the consumer's surplus available from that unit. For concreteness, I might be willing to pay a maximum of 10 for an umbrella if it's raining, but may nonetheless only have to pay 5 for it, leaving me with a measure of my benefit from buying the umbrella and avoiding getting wet, a surplus of 5. At any price [P.sub.i], we can add up the consumer surplus available on all of the units consumed (those with marginal valuations above [P.sub.i]) and doing so provides an estimate of the total consumer surplus if the price is [P.sub.i].
In a market with homogeneous products, all products are identical and perfectly substitutable. In theory this results in all products having the same price, which is the only price that determines the demand. In a market with differentiated products, products are not perfectly substitutable and prices will vary across products sold in the market. In those markets, the demand for any given product is determined by its price and the prices of potential substitutes. In practice, markets which look homogeneous from a distance will in fact be differentiated to at least some degree when examined closely. Homogeneity may nonetheless be a reasonable modeling approximation in many such situations.
184.108.40.206 The Contribution of Consumer Theory: Deriving Demand
Demand functions are classically derived by using the behavioral assumption that consumers make choices in a way that can be modeled as though they have an objective, to maximize their utility, which they do subject to the constraint that they cannot spend more than they earn. As is well-known to all students of microeconomic theory, the existence of such a utility function describing underlying preferences may in turn be established under some nontrivial conditions (see, for example, Mas-Colell et al. 1995, chapter 1). Maximizing utility is equivalent to choosing the most preferred bundle of goods that a consumer can buy given her wealth.
More specifically, economists have modeled a customer of type ([y.sub.i], [[theta].sub.i]) as choosing to maximize her utility subject to the budget constraint that her total expenditure cannot be higher than her income:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where [p.sub.j] and [q.sub.j] are prices and quantities of good j, [u.sub.i] ([q.sub.1]; [q.sub.2], ..., [q.sub.j]; [[theta].sub.i]) is the utility of individual i associated with consuming this vector of quantities, [y.sub.i] is the disposable income of individual i, and [[theta].sub.i] describes the individual's preference type. In many empirical models using this framework, the "i" subscripts on the V and u functions will be dropped so that all differences between consumers are captured by their type ([y.sub.i], [[theta].sub.i]).
Setting up this problem by using a Lagrangian provides the first-order conditions
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
together with the budget constraint which must also be satisfied. We have a total of J + 1 equations in J + 1 unknowns: the J quantities and the value of the Lagrange multiplier, [lambda].
At the optimum, the first-order conditions describe that the Lagrange multiplier is equal to the marginal utility of income. In some cases it will be appropriate to assume a constant marginal utility of income. If so, we assume behavior is described by a utility function with an additively separable good [q.sub.1], the price of which is normalized to 1, so that [u.sub.i] ([q.sub.1], [q.sub.2], ..., [q.sub.j]; [[theta].sub.i]) = [u.sub.i] ([q.sub.2], ..., [q.sub.j]; [[theta].sub.i]) + [q.sub.1] and [p.sub.1] = 1. This numeraire good q1 is normally termed "money" and its inclusion provides an intuitive interpretation of the first-order conditions. In such circumstances a utilitymaximizing consumer will choose a basket of products so that the marginal utility provided by the last euro spent on each product is the same and equal to the marginal utility of money, i.e., 1.
More generally, the solution to the maximization problem describes the individual's demand for each good as a function of the prices of all the goods being sold and also the consumers' income. Indexing goods by j, we can write the individual's demands as
[q.sub.ij] = [d.sub.ij]([p.sub.1], [p.sub.2], ..., [p.sub.j]; [y.sub.i]; [[theta].sub.i]), j = 1, 2, ..., J.
A demand function for product j incorporates not only the effect of the own price of j on the quantity demanded but also the effect of disposable income and the price of other products whose supply can affect the quantity of good j purchased. In figure 1.1, a change in the price of j represents a movement along the curve while a change in income or in the price of other related goods will result in a shift or rotation of the demand curve.
The utility generated by consumption is described by the (direct) utility function, [u.sub.i], which relates the level of utility to the goods purchased and is not observed. We know that not all levels of consumption are possible because of the budget constraint and that the consumer will choose the bundle of goods that maximizes her utility. The indirect utility function [V.sub.i](p, [y.sub.i]; [[theta].sub.i], where p = ([p.sub.1], [p.sub.2], ..., [p.sub.j]), describes the maximum utility a consumer can feasibly obtain at any level of the prices and income. It turns out that the direct and indirect utility functions each can be used to fully describe the other.
In particular, the following result will turn out to be important for writing down demand systems that we estimate.
For every indirect utility function [V.sub.i](p, [y.sub.i]; [[theta].sub.i]) there is a direct utility function [u.sub.i] ([q.sub.1], [q.sub.2], ..., [q.sub.j]; [[theta].sub.i]) that represents the same preferences over goods provided the indirect utility function satisfies some properties, namely that [V.sub.i](p, [y.sub.i]; [[theta].sub.i] is continuous in prices and income, nonincreasing in price, nondecreasing in income, quasi-convex in (p, [y.sub.i]) with any one element normalized to 1 and homogeneous degree zero in (p, [y.sub.i]).
This result sounds like a purely theoretical one, but it will actually turn out to be very useful in practice. In particular, it will allow us to retrieve the demand function [q.sub.i](p; [y.sub.i]; [[theta].sub.i]) without actually explicitly solving the utility-maximization problem. Computationally, this is an important simplification.
220.127.116.11 Aggregation and Total Market Size
Individual consumers' demand can be aggregated to form the market aggregate demand by adding the individual quantities demanded by each customer at any given price. If [q.sub.ij] = [d.sub.ij]([p.sub.1], [p.sub.2], ..., [p.sub.j]; [y.sub.i]; [[theta].sub.i]) describes the demand for product j by individual i, then aggregate (total) demand is simply the sum across individuals:
[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]
where I is the total number of people who might want to buy the good. Many potential customers will set [q.sub.ij] = 0 at least for some sets of prices [p.sub.1], [p.sub.2], ..., [p.sub.j] even though they will have positive purchases at lower prices of some products. In some cases, known as single "discrete choice" models, each individual will only buy at most one unit of the good and so [d.sub.ij] ([p.sub.1], [p.sub.2], ..., [p.sub.j], [y.sub.i]; [[theta].sub.i]) will be an indicator variable taking on the value either zero or one depending on whether individual i buys the good or not at those prices. In such models, the total number of people who may want to buy the good is also the total potential market size. (We will discuss discrete choice models in more detail in chapter 9.) On the other hand, when individuals can buy more than one unit of the good, to establish the total potential market size we need to evaluate both the total potential number of consumers and also the total number of goods they might buy. Often the total potential number of consumers will be very large-perhaps many millions-and so in many econometric demand models we will approximate the summation with an integral.
In general, total demand for product j will depend on the full distribution of income and consumer tastes in the population. However, under very special assumptions, we will be able to write the aggregate market demand as a function of aggregate income and a limited set of taste parameters only:
[Q.sub.j] = [D.sub.j] ([p.sub.1], [p.sub.2], ..., [p.sub.j], Y; [theta]),
where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].
For example, suppose for simplicity that [[theta].sub.i] = [mu] for all individuals and every individual's demand function is "additively separable" in the income variable so that an individual's demand function can be written
[d.sub.ij] ([p.sub.1], [p.sub.2], ..., [p.sub.j], [y.sub.i]; [[theta].sub.i]) = [d.sup.*.sub.ij]([p.sub.1], [p.sub.2], ..., [p.sub.j]; [mu]) + [[alpha].sub.j][y.sub.i],
where [[alpha].sub.j] is a parameter common to all individuals, then aggregate demand for product j will clearly only depend on aggregate income. Such a demand function implies that, given the prices of goods, an increase in income will have an effect on demand that is exactly the same no matter what the level of the prices of all of the goods in the market. Vice versa, an increase in the prices will have the same effect whatever the level of income.
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