58 1. The Determinants of Market Outcomes 5. Multiproduct, multiplant, price-setting monopolist: max p 1 ;:::;p J J X j D1 .p j  c j .D j .p 1 ;:::;p J ///D j .p 1 ;:::;p J /: 6. Multiproduct, multiplant, quantity-setting monopolist: max q 1 ;:::;q J J X j D1 .P j .q 1 ;:::;q J /  c j .q j //q j : Single-product monopolists will act to set marginal revenue equal to marginal cost. In those cases, since the monopoly problem is a single-agent problem in a single product’s price or quantity, our analysis can progress in a relatively straightforward manner. In particular, note that single-agent, single-product problems give us a single equation (first-order condition) to solve. In contrast, even a single agent’s optimiza- tion problem in the more complex multiplant or multiproduct settings generates an optimization problem is multidimensional. In such single-agent problems, we will have as many equations to solve as we have choice variables. In simple cases we can solve these problems analytically, while, more generally, for any given demand and cost specification the monopoly problem is typically relatively straightforward to solve on a computer using optimization routines. Naturally, in general, monopolies may choose strategic variables other than price and quantity. For example, if a single-product monopolist chooses both price and advertising levels, it solves the problem max p;a .p  c/D.p; a/, which yields the usual first-order condition with respect to prices, p c p D  @ ln D.p; a/ @ ln p à 1 ; and a second one with respect to advertising, .p c/ @D.p; a/ @a D 0: A little algebra gives p c p p D.p; a/ a @ ln D.p; a/ @ ln a D 0 and substituting in for .p c/=p using the first-order condition for prices gives the result: a pD.p; a/ D  @ ln D.p; a/ @ ln a Ã  @ ln D.p; a/ @ ln p à ; which states the famous Dorfman and Steiner (1954) result that advertising–sales ratios should equal the ratios of the own-advertising elasticity of demand to the own-price elasticity of demand. 41 41 For an empirical application, see Ward (1975). 1.3. Competitive Environments 59 Quantity Price Dominant firm marginal revenue p * Q dominant Q fringe p 2 Q total p 1 Market demand Residual demand facing dominant firm = D market − S fringe MC of dominant firm Supply from fringe Figure 1.23. Deriving the residual demand curve. 1.3.3.2 The Dominant-Firm Model The dominant-firm model supposes that there is a monopoly (or collection of firms acting as a cartel) which is nonetheless constrained to some extent by a competitive fringe. The central assumption of the model is that the fringe acts in a nonstrategic manner. We follow convention and develop the model within the context of a price- setting, single-product monopoly. Dominant-firm models analogous to each of the cases studied above are similarly easily developed. If firms which are part of the competitive fringe act as price-takers, they will decide how much to supply at any given price p. We will denote the supply from the fringe at any given price p as S fringe .p/. Because of the supply behavior of the fringe, if they are able to supply whomever they so desire at any given price p, the dominant firm will face the residual demand curve: D dominant .p/ D D market .p/  S fringe .p/: Figure 1.23 illustrates the market demand, fringe supply, and resulting dominant- firm demand curve. We have drawn the figure under the assumption that (i) there is a sufficiently high price p 1 such that the fringe is willing to supply the whole market demand at that price leaving zero residual demand for the dominant firm and (ii) there is analogously a sufficiently low price p 2 below which the fringe is entirely unwilling to supply. Given the dominant firm’s residual demand curve, analysis of the dominant-firm model becomes entirely analogous to a monopoly model where the monopolist faces the residual demand curve, D dominant .p/. Thus our dominant firm will set prices so 60 1. The Determinants of Market Outcomes that the quantity supplied will equate the marginal revenue to its marginal cost of supply. That level of output is denoted Q dominant in figure 1.23. The resulting price will be p  and fringe supply at that price is S fringe .p  / D Q fringe so that total supply (and total demand) are Q total D Q dominant C Q fringe D S fringe .p  / C D dominant .p  / D D market .p  /: A little algebra gives us a useful expression for understanding the role of the fringe in this model. Specifically, the dominant firm’s own-price elasticity of demand can be written as 42 Á dominant demand Á @ ln D dominant @ ln p D @ ln.D market  S fringe / @ ln p D 1 D market  S fringe @.D market  S fringe / @ ln p so that we can write Á dominant demand D 1 D market  S fringe Ä D market D market à @D market @ ln p   S fringe S fringe à @S fringe @ ln p  and hence after a little more algebra we have Á dominant demand D  D market D market  S fringe à @ ln D market @ ln p   S fringe =D market .D market  S fringe /=D market à @ ln S fringe @ ln p D 1 Share dom Á market demand   Share fringe Share dom à Á fringe supply ; where Á indicates a price elasticity. That is, the dominant firm’s demand curve—the residual demand curve—depends on (i) the market elasticity of demand, (ii) the fringe elasticity of supply, and also (iii) the market shares of the dominant firm and the fringe. Remembering that demand elasticities are negative and supply elasticities positive, this formula suggests intuitively that the dominant firm will therefore face a relatively elastic demand curve when market demand is elastic or when market demand is inelastic but the supply elasticity of the competitive fringe is large and the fringe is of significant size. 42 Recall from your favorite mathematics textbook that for any suitably differentiable function f.x/ we can write @ ln f.x/ @ ln x D 1 f.x/ @f .x/ @ ln x : 1.4. Conclusions 61 1.4 Conclusions  Empirical analysis is best founded on economic theory. Doing so requires a good understanding of each of the determinants of market outcomes: the nature of demand, technological determinants of production and costs, regulations, and firm’s objectives.  Demand functions are important in empirical analysis in antitrust. The elas- ticity of demand will be an important determinant of the profitability of price increases and the implication of those price increases for both consumer and total welfare.  The nature of technology in an industry, as embodied in production and cost functions, is a second driver of the structure of markets. For example, economies of scale can drive concentration in an industry while economies of scope can encourage firms to produce multiple goods within a single firm. Information about the nature of technology in an industry can be retrieved from input and output data (via production functions) but also from cost, out- put and input price data (via cost functions) or alternatively data on input choices and input prices (via input demand functions.)  To model competitive interaction, one must make a behavioral assumption about firms and an assumption about the nature of equilibrium. Generally, we assume firms wish to maximize their own profits, and we assume Nash equi- librium. The equilibrium assumption resolves the tensions otherwise inherent in a collection of firms each pursuing their own objectives. One must also choose the dimension(s) of competition by which we mean defining the vari- ables that firms choose and respond to. Those variables are generally prices or quantity but can also include, for example, quality, advertising, or investment in research and development.  The two baseline models used in antitrust are quantity- and price-setting mod- els otherwise known as Cournot and (differentiated product) Bertrand models respectively. Quantity-setting competition is normally used to describe indus- tries where firms choose how much of a homogeneous product to produce. Competition where firms set prices in markets with differentiated or branded products is often modeled using the differentiated product Bertrand model. That said, these two models should not be considered as the only models available to fit the facts of an investigation; they are not.  An environment of perfect competition with price-taking firms produces the most efficient outcome both in terms of consumer welfare and production efficiency. However, such models are typically at best a theoretical abstrac- tion and therefore they should be treated cautiously and certainly should not systematically be used as a benchmark for the level of competition that can realistically be implemented in practice. 2 Econometrics Review Throughout this book we discuss the merits of various empirical tools that can be used by competition authorities. This chapter aims to provide important background material for much of that discussion. Our aim in this chapter is not to replicate the content of an econometrics text. Rather we give an informal introduction to the tools most commonly used in competition cases and then go on to discuss the often practi- cal difficulties that arise in the application of econometrics in a competition context. Particular emphasis is given to the issue of identification of causality. Where appro- priate, we refer the reader to more formal treatments in mainstream econometrics textbooks. 1 Multiple regression is increasingly common in reports of competition cases in jurisdictions across the world. Like any single piece of evidence, a regression analy- sis initially performed in an office late at night can easily surge forward and end up becoming the focus of a case. Once under the spotlight of intense scrutiny, regression results are sometimes invalidated. Sometimes, it is the data. Outliers or oddities that are not picked up by an analyst reveal the analysis was performed using incorrect data. Sometimes the econometric methodology used is proven to provide good estimates only under extremely restrictive and unreasonable assump- tions. And sometimes the analysis performed proves—once under the spotlight—to be very sensitive in a way that reveals the evidence is unreliable. An important part of the analyst’s job is therefore to clearly disclose the assumptions and sensitivities at the outset so that the correct amount of weight is placed on that piece of econo- metric evidence by decision makers. Sometimes the appropriate amount of weight will be a great, on other occasions it will be very little. In this chapter we first discuss multiple regression including the techniques known as ordinary least squares and nonlinear least squares. Next we discuss the important issue of identification, particularly in the presence of endogeneity. Specifically, we consider the role of fixed-effects estimators, instrumental variable estimators, and “natural” experiments. The chapter concludes with a discussion of best practice 1 A very nice discussion of basic regression analysis applied to competition policy can be found in Fisher (1980, 1986) and Finkelstein and Levenbach (1983). For more general econometrics texts, see, for example, Greene (2007) and Wooldridge (2007). And for an advanced and more technical but succinct discussion of the econometric theory, see, for example, White (2001). 2.1. Multiple Regression 63 in econometric projects. The aim in doing so is, in particular, to help avoid the disastrous scenario wherein late in an investigation serious flaws in econometric analysis are discovered. 2.1 Multiple Regression Multiple regression is a statistical tool that allows us to quantify the effect of a group of variables on a particular outcome. When we want to explain the effect of a variable on an outcome that is also simultaneously affected by several other factors, multiple regression will let us identify and quantify the particular effect of that variable. Multiple regression is an extremely useful and powerful tool but it is important to understand what it does, or rather what it can and cannot do. We first explain the principles of ordinary least-squares (OLS) regression and the conditions that need to hold for it to be a meaningful tool. We then discuss hypothesis testing and finally we explore a number of common practical problems that are frequently encountered. 2.1.1 The Principle of Ordinary Least-Squares Regressions Multiple regression provides a potentially extremely useful statistical tool that can quantify actual effects of multiple causal factors on outcomes of interest. In an experimental context, a causal effect can sometimes be measured in a precise and scientific way, holding everything else constant. For example, we might measure the effect of heat on water temperature. On the other hand, budget or time constraints might mean we can only use a limited number of experiments so that each experiment must vary more than one causal factor. Multiple regression could then be used to isolate the effects of each variable on the outcomes. Unfortunately, economists in competition authorities cannot typically run experiments in the field. It would of course make our life far easier if we could just persuade firms to increase their prices by 5% and see how many customers they lose; we would be able to learn about their own-price elasticity of demand relatively easily. On the other hand, chief executives and their legal advisors may entirely reasonably suggest that the cost of such an experiment would be overly burdensome on business. More typically, we will have data that have been generated in the normal course of business. On the one hand, such data have a huge advantage: they are real! Firms, for example, will take actions to ameliorate the impact of price increases on demand: they may invest in customer retention strategies, such as marketing efforts aimed at explaining to their customers the cost factors justifying a price increase; they might change some other terms of the offer (e.g., how many weeks of a magazine subscription you get for a given amount) or perform short-term retention advertising targeted at the most price-sensitive group of customers. If we run an experiment in a lab, we will have a “pure” price experiment but it may not tell us about the elasticity of 64 2. Econometrics Review demand in reality, when real consumers are deciding whether to spend their own real money given the firm’s efforts at retaining their business. On the other hand, as this example suggests, a lot will be going on in the real world, and most importantly none of it will be under the control of the analyst while much of it may be under the control of market participants. This means that while multiple regression analysis will be potentially useful in isolating the various causes of demand (prices, advertising, etc.), we will have to be very careful to make sure that the real-world decisions that are generating our data do not violate the assumptions needed to justify using this tool. Multiple regression was, after all, initially designed for understanding data generated in experimental contexts. 2.1.1.1 Data-Generating Processes and Regression Specifications The starting point of a regression analysis is the presumption, or at least the hypoth- esis, that there is a real relationship between two or more variables. For instance, we often believe that there is a relation between price and quantity demanded of a given good. Let us assume that the true population relationship between the price charged, P , and the quantity demanded, Q, of a particular good is given by the following expression: 2 P i D a 0 C b 0 Q i C u i ; where i indicates different possible observations of reality (perhaps time periods or local markets) and the parameters a 0 and b 0 take on particular values, for example 5 and 2 respectively. We will call such an expression our “data-generating process” (DGP). This DGP describes the inverse demand curve as a function of the volume of sales Q and a time- or market-specific element u i , which is unknown to the analyst. Since it is unknown to the analyst, sometimes it is known as a “shock”; we may call u i a demand shock. The shock term includes everything else that may have affected the price in that particular instance, but is unknown and hence appears stochastic to the analyst. Regression analysis is based on the idea that if we have data on enough realizations of .P; Q/, we can learn about the true parameters .a 0 ;b 0 / of the DGP without even observing the u i s. If we plot a data set of sample size N , denoted .P 1 ;Q 1 /; .P 2 ;Q 2 /;:::;.P N ;Q N / or more compactly f.P i ;Q i /I i D 1;:::;Ng, that is generated by our DGP, we will obtain a scatter plot with data spread around the picture. An ideal situation for estimating a demand curve is displayed in figure 2.1. The reason we call it ideal will become clear later in the chapter but for now note that in this case the true DGP, as illustrated by the plotted observations, seems to correspond to a linear relationship 2 It is perhaps easier to motivate a demand equation by considering the equation to describe the price P which generates a level of sales Q.IfQ is stochastic and P is treated as a deterministic “control” variable, then we would write this equation the other way around. For the purposes of illustration and since P is usually placed on the y-axis of a classic demand and supply diagram, we present the analysis this way around, that is, in terms of the “inverse” demand curve. 2.1. Multiple Regression 65 Q . . . . . . . . . . . . . . . . . . (Q i , P i ) Q i P i ‘‘Best-fit’’ line P Figure 2.1. Scatter plot of the data and a “best-fit” line. between the two variables. In the figure, we have also drawn in a “best-fit” line, in this case the line is fit to the data only by examining the data plot and trying to draw a straight line through the plotted data by hand. In an experimental context, our explanatory variable Q would often be non- stochastic—we are able to control it exactly, moving it around to generate the price variable. However, in a typical economics data set the causal variable (here we are supposing Q) is stochastic. A wonderfully useful result from econometric theory tells us that the fact that Q is stochastic does not, of itself, cause enormous problems for our tool kit, though obviously it changes the assumptions we require for our estimators to be valid. More precisely, we will be able to use the technique of OLS regression to estimate the parameters .a 0 ;b 0 / in the DGP provided (i) we consider the DGP to be making a conditional statement that, given a value of the quantity demanded Q i and given a particular “shock” u i , the price P i is generated by the expression above, i.e., the DGP, (ii) we make an assumption about the relationship between the two causal stochastic elements of the model, Q i and u i , namely that given knowledge of Q i the expected value of the shock is zero, EŒu i j Q i  D 0, and (iii) the sequence of pairs .Q i ;u i / for i D 1;:::;ngenerate an independent and identically distributed sequence. 3 The first assumption describes the nature of the DGP. The second assumption requires that, whatever the level of Q, the average value of the shock u i will always be zero. That is, if we see many markets with high sales, say of 1 million units per year, the average demand shock will be zero and similarly if we see many markets with lower sales, say 10,000 units per year, the average demand shock will also be zero. The third assumption ensures that we 3 Note that the technique does not need to assume that Q and u are fully independent of each other, but rather (i) that observations of the pairs .Q 1 ;u 1 /, .Q 2 ;u 2 /, and so on are independent of each other and follow the same joint distribution and (ii) satisfy the conditional mean zero assumption, EŒu i j Q i  D 0. In addition to these three assumptions, there are some more technical “regularity” assumptions that primarily act to make sure all of the quantities needed for our estimator are finite—see your favorite econometrics textbook for the technical details. 66 2. Econometrics Review obtain more information about the process as our sample size gets bigger, which helps, for example, to ensure that sample averages will converge to their population equivalents. 4 We describe the technique of OLS more fully bellow. Other estimators will use different sets of assumptions, in particular, we will see that an alternative estimation technique, instrumental variable (IV) estimation, will allow us to handle some situations in which EŒu i j Q i  ¤ 0. In most if not all cases, there will be a distinction between the true DGP and the model that we will estimate. This is because our model will normally (at best) only approximate the true DGP. Ideally, the model that we estimate includes the true DGP as one possibility. If so, then we can hope to learn the true population parameters given enough data. For example, suppose the true DGP is P i D 10  2Q i C u i and the model specification is P i D a  bQ i CcQ 2 i Ce i . Then we will be able to reproduce the DGP by assigning particular values to our model parameters. In other words, our model is more general than the DGP. If on the other hand the true DGP is P i D 10  5Q i C 2Q 2 i C u i and our model is P i D a  bQ i C e i ; then we will never be able to retrieve the true parameters with our model. In this case, the model is misspecified. This observation motivates those econometricians who favor the general-to-specific modeling approach to model specification (see, for example, Campos et al. 2005). Others argue that the approach of specifying very general models means the estimates of the general model will be very poor and as a result the hypothesis tests used to reduce down to more specific models have an extremely low chance of getting you to the right answer. All agree that the DGP is normally unknown and yet at least some of its properties must be assumed if we are to evaluate the conditions under which our estimators will work. Economists must mainly rely on economic theory, institutional knowledge, and empirical regularities to make assumptions about the likely true relationships between variables. When not enough is known about the form of the DGP, one must be careful to either design a specification that is flexible enough to avoid misspecified regressions or else test systematically for evidence of misspecification surviving in the regression equation. Personally, we have found that there are often only a relatively small number of really important factors driving demand patterns and that knowledge of an industry (and its history) can tell you what those important factors are likely to be. By important factors we mean those which are driving the dominant features of the data. If those factors can be identified, then picking those to begin with and then 4 The third assumption is often stated using the observed data .P i ;Q i / and doing so is equivalent given the DGP. For an introduction to the study of the relationships between the data, DGP, and shocks, see the Annex to this chapter (section 2.5). 2.1. Multiple Regression 67 refining an econometric model in light of specification tests seems to provide a reasonably successful approach, although certainly not one immune to criticism. 5 Whether you use a specific-to-general modeling approach or vice versa, the greater the subtlety in the relationship between demand and its determinants, the better data you are likely to need to use any econometric techniques. 2.1.1.2 The Method of Least Squares Consider the following regression model: y i D a C bx i C e i : The OLS regression estimator attempts to estimate the effect of the variable x on the variable y by selecting the values of the parameters .a; b/. To do so, OLS assigns the maximum possible explanatory power to the variables that we specify as determinants of the outcome and minimizes the effect of the “leftover” component, e i . The value of the “leftover” component depends on our choice of parameters .a; b/ so we can write e i .a; b/ D y i  a  bx i . Formally, OLS will choose the parameters a and b to minimize the sum of squared errors, that is, to solve min a;b n X iD1 e i .a; b/ 2 : The method of least squares is rather general. The model described above is linear in its parameters, but the technique can be more generally applied. For example, we may have a model which is not linear in the parameters which states e i .a; b/ D y i f.x i Ia; b/, where, for example, f.x i Ia; b/ D ax b . The same “least-squares” approach can be used to estimate the parameters by solving the analogous problem min a;b n X iD1 e i .a; b/ 2 : If the model is linear in the parameters, the technique is known as “ordinary” least squares (OLS). If the model is nonlinear in the parameters, the technique is called “nonlinear” least squares (NLLS). In the basic linear-in-parameters and linear-in-variables model, a given absolute change in the explanatory variable x will always produce the same absolute change in the explained variable y. For example, if y i D Q i and x i D P i , where Q i and P i represent the quantity per week and price of a bottle of milk respectively, then an increase in the price of milk by €0.50 might reduce the amount of milk purchased by, say, two bottles a week. The linear-in-parameters and linear-in-variables assumption implies that the same quantity reduction holds whether the initial price is €0.75 or €1.50. Because this assumption may not be realistic in many cases, alternative 5 An example of this approach is examined in more detail in the demand context in chapter 9. [...]... P Supply Demand Q Figure 2.5 Price and quantity data: The intersection of a supply and a demand curve generates our data point (Qi ; Pi ) P S1 S2 S3 D4 D3 D1 D2 Q Figure 2.6 Indicative supply and demand curves shifting and generating a data set points generated if our model of the world is correct by the intersection of the demand and supply curves When we collect price and quantity data and plot them,... are called “reduced-form” equations Estimating a reduced form for market prices and quantities will require data on equilibrium prices and quantities in that market as dependent variables and then observed demand and supply shifters (perhaps GDP and cost data such as input prices respectively) as variables that will explain the market outcomes Note that in estimating the reducedform equations, we are... and Market Equilibria In a classical model of supply and demand both prices and volume of sales (quantity) are determined by the intersection of supply and demand The data we observe are the outcome of a market equilibrium A regression equation attempting to estimate the relationship between price and quantity demanded could therefore be either a demand curve or a supply (i.e., pricing) curve To illustrate... other hand may want to charge higher prices in high demand periods and they know they will face higher demand when they advertise If so, it may appear to us, as analysts, that there was a big positive “shock” u t , and consequently a high demand, in periods when prices P t are high In such a case, we must have information which allows us to distinguish the direct effect of a movement along a demand curve... implications for the probability of those two kinds of errors and both errors can be costly For instance, finding predation when there was none will have the effect of raising prices and may actively impede effective competition that was beneficial for consumers On the other hand, if we find that prices are competitive when in truth there was predation, we may disturb the competitive process by permitting such foreclosure... is higher than 1.96 Since 2 is, for most practical purposes, sufficiently close to 1.96, O as a rule of thumb and for a quick first look, if the estimated coefficient ˇj is more than double its standard error, the null hypothesis that the true value of the parameter O is 0 can be rejected and ˇj is said to be significantly different from 0 In general, small standard errors and/ or a big difference between... parameters, and so the model remains amenable to estimation using OLS We first discuss the single-variable regression to illustrate some useful concepts and results of OLS and then generalize the discussion to the multivariate regression First we introduce some terminology and notation Let a; b/ be estimates of the O O parameters a and b The predicted value of yi given the estimates and a fixed value for xi... causal variable(s) and any variables that are not observed by analysts Further complications arise when the true causal relationships are multidirectional The most famous example of such a situation for economists involves the simultaneous determination of price and quantity by the two causal relationships embodied respectively in demand and supply curves On the demand side, the quantity demanded is usually... do so in the important context of the econometric identification of demand and supply functions We then discuss the most commonly used techniques that aid identification, namely fixedeffects regressions, instrumental variable techniques, and evidence from “natural” experiments Stock market event studies will also be discussed For a semiformal statistical statement of the problem of identification, the reader... annex at the end of this chapter (section 2.5) 2.2.2 Identification of Demand and Supply Much of the empirical work in competition analysis concerns the estimation of demand functions and supply-side relationships (often pricing equations are, in particular circumstances, related to cost functions) Since the basic supply -and- demand model in a competitive market provides a classic identification problem, . in Fisher (1980, 1986) and Finkelstein and Levenbach (19 83) . For more general econometrics texts, see, for example, Greene (2007) and Wooldridge (2007). And for an advanced and more technical but. b 2 x 2i C b 3 x 3i C e i : For given parameter values, the predicted value of y i for given estimates and values of .x 1i ;x 2i ;x 3i / is Oy i DOa C O b 1 x 1i C O b 2 x 2i C O b 3 x 3i and so the. matrix expression 2 6 6 6 6 4 y 1 y 2 : : : y n 3 7 7 7 7 5 D 2 6 6 6 6 4 1x 11 x 21 x 31 1x 12 x 22 x 32 : : : : : : : : : : : : 1x 1n x 2n x 3n 3 7 7 7 7 5 2 6 6 6 4 a b 1 b 2 b 3 3 7 7 7 5 C 2 6 6 6 6 4 e 1 e 2 : : : e n 3 7 7 7 7 5 D 2 6 6 6 6 4 x 0 1 x 0 2 : : : x 0 n 3 7 7 7 7 5 ˇ C 2 6 6 6 6 4 e 1 e 2 : : : e n 3 7 7 7 7 5 ; 2.1.