Estimating Excess Product Variety in the Swedish Beer Market

Transcription

1 Estimating Excess Product Variety in the Swedish Beer Market André Romahn August 22, 2013 Preliminary and Incomplete Comments Welcome! Abstract Using a modified nested logit model, I find strong evidence for excess variety in the Swedish beer market. While the actual market carries between 230 and 300 products, counterfactual simulations indicate that consumer welfare is flat beyond a number of 135 beers. This result is driven by product space congestion. As more and more varieties enter the market, consumers willingness to pay for a further increase in choice diminishes and products become more substitutable. This also drives down market power. Raising the number of products from 50 to 350, more than doubles the magnitude of own-price elasticities and increases cross-price elasticities almost five-fold. In contrast, for the same counterfactual scenario, the standard nested logit model predicts that welfare can be raised further by introducting more than 350 varieties. Moreover, entry attenuates competition, because the magnitude of ownand cross-price elasticities decreases by 15 and 83 percent, respectively. Methodologically, I show how to use tests of parameter instability to determine whether or not congestion effects are present in a particular data set. JEL Classification: L11, L13, L66 Keywords: demand estimation, entry, competition, welfare, congestion 1 Introduction Using structural models of demand, I investigate how substantial variation in the number of products in the Swedish beer market affects consumer welfare and competition. Building on the work of Ackerberg and Rysman (2005), I compare the implications of the standard nested logit model with those of a modified version that allows for product space congestion. I find strong evidence for substantial congestion effects in the data. The actually observed number of products varies between 230 and 300 varieties. With the estimates of the congestion model and the standard nested logit model, I conduct counterfactual simulations for a wider range of products (50 to 350). The congestion model implies that consumer welfare is flat beyond 135 IESE Business School, Public-Private-Sector Research Center, Avenida de Pearson 21, Barcelona, Spain; aromahn@iese.edu 1

2 beers, whereas the standard nested logit model predicts that welfare can be raised further by having more than 350 varieties in the market. With regard to competition, the congestion model s predictions are economically intuitive. Moving from 50 to 350 beers more than doubles the magnitude of own-price elasticities and raises the magnitude of cross-price elasticities five-fold. The standard nested logit model, however, implies that for the same counterfactual scenario the respective changes in own- and cross-price elasticities are decreases of 15 and 83 percent. Thus, in terms of the effect of entry on competition, the two models point in opposite directions. This also has a substantial impact on the predictions for relative markups over price. In the congestion model markups fall from close to 30 percent to 15 percent. Markups in the standard nested logit model, however, are hardly affected. They fall from roughly 27 percent to 25.4 percent as the number of products increases seven-fold. The main driver for this divergence in model predictions is that the congestion model has a flexible distribution for the logit errors that can be tied to the data. Markets with higher numbers of products are estimated to have lower logit error variances. This reduces the welfare benefits from additional varieties and raises product substitutability. In the standard nested logit model, the variance of the logit errors is constant across all markets. Bajari and Benkard (2003) derive the implications of this model restriction for a wide range of logit models. My empirical findings are in line with their theoretical results. The standard logit assumption imposes economically counterintuitive patterns on the data, both with regard to consumer welfare and competition. Several papers take this into account when assessing the welfare effects of product entry. Petrin (2002) limits the role of the logit errors by matching simulated market shares with their empirical counterparts that are observed for different demographics. Goolsbee and Petrin (2004) avoid the potential pitfalls of standard logit models by using a probit specification. This is feasible in their application, due to the low number of products. As an alternative for markets with more products, Berry and Pakes (2007) and Bajari and Benkard (2005) develop logit-type models where the variance of the logit errors is zero. These pure hedonic or pure characteristics models can be difficult to estimate because of their computational and data requirements. Moreover, these models do not allow for a love-for-variety. In some markets, as for example the beer market, this assumption could prove to be too harsh. The framework of Ackerberg and Rysman (2005), on the other hand, also allows for intermediate cases, where consumers are willing to pay for more variety, but less so than in standard logit models. Moreover, their approach can be implemented quite easily. 1 Even though these alternative models can remedy the shortcomings of the standard logit models, the question remains as to when a particular market is best modeled in a product space congestion framework. I tackle this issue by explicitly testing for the presence of congestion effects in a given data set. For the nested logit model, a necessary condition for product space congestion is the identification of one or more structural breaks in the nesting coefficient, ρ. Such a break implies that the variance of the logit errors statistically significantly differs be- 1 In principle, the framework of Ackerberg and Rysman (2005) could also be used for markets with no love-forvariety. This is a corner solution case for the model, however. A similar approach in Berry and Pakes (2007) indicates that the corner case still behaves quite differently than the pure characteristics model, so that it would be preferable to implement the latter directly. 2

3 tween sub-samples. For the Swedish beer data, I find that the sub-samples with higher numbers of products are consistently estimated to have lower logit error variances. This clearly points to product space congestion effects. I use the statistical test procedures developed by Bai and Perron (1998), to identify multiple structural breaks in the nesting coefficient. To the best of my knowledge, there is only one existing paper that applies the framework of Ackerberg and Rysman (2005). Mariuzzo et al. (2010), however, take a narow stance on product space congestion. They only allow for congestion effects stemming from differences in store coverage. As more and more varieties enter the market, stores do not necessarily create more shelf space, so that some varieties have incomplete store coverage. Even though this effect is certainly relevant for product space congestion, it is unnecessarily restrictive. It is unlikely that the econometrician observes every relevant characteristic, except for each product s store coverage. As the number of products grows large, entering varieties might differentiate into new dimensions, which consumers attribute relatively little value to, for example package design. Moreover, in the Swedish beer market the majority of sales are generated in stores that carry all available products. Thus, only looking at store coverage effects would be inappropriate. Song (2007) estimates a pure characteristics model for the Central Processing Unit (CPU) industry. He finds substantial welfare gains for consumers stemming from the rapid technological improvement of CPU capabilities. CPUs can generally be described in terms of few characteristics: processing speed, energy consumption and price. Given this and the fact that there are relatively few (current) products available in the market, the pure characteristics model is a good fit for this industry. For the Swedish beer market, with more than 200 varieties on offer, the assumption that consumers have no love-for-variety is likely to be too stringent, however. The remainder of the paper is structured as follows. In the next section, I describe the data and provide details about the Swedish beer market. In Section 3, I present the demand model and show how product space congestion is incorporated in an otherwise standard nested logit model. I move on to explicitly testing for the presence of congestion effects in the data by identifying structural breaks in the nesting coefficient. This is followed by the estimation of demand, where I discuss the instruments and the estimation results for the two models. With the estimated parameters in hand, I conduct counterfactual simulations in the following section. I trace out the effects of moving from 50 to 350 beer varieties on consumer welfare and price elasticities. The final section concludes. 2 The Swedish Beer Market I use nationwide monthly retail sales data at the bar-code level provided by Systembolaget, the Swedish retail monopoly for alcoholic beverages. The sample covers the six-year period from January 1996 to December Systembolaget owns the retail monopoly for all beverages with an alcohol content of at least 3.5 percent of volume. Beers with a lower alcohol content can be purchased in regular supermarkets. I only observe the sales of beers in the stores of the retail monopoly, however. For each beer, the data reports the liters sold and price in any given month for all the stores in Sweden. Thus, sales are aggregated at the national level. The data also distinguishes between 3

4 Table 1: Observable product characteristics, X Column Characteristic Mean [Min,Max] Std. Dev. X 1 Price Per Liter (SEK) [19.4,95.8] 9.08 X 2 Richness 5.78 [1,11] 1.82 X 3 Sweetness 2.27 [1,9] 1.37 X 4 Bitterness 6.24 [1,12] 2.11 X 4 Alcohol (% of Vol.) 5.41 [4,12] 1.02 X 5 Advertising (mln SEK).11 [0,10.69].66 X 6 Foreign.44 [0,1] - X 7 Ale.12 [0,1] - X 8 Dark Lager.04 [0,1] - X 10 Stout.03 [0,1] - X 11 Wheat Beer.02 [0,1] - X 12 Bottle (.33 Liter).38 [0,1] - X 13 Bottle (.5 Liter).30 [0,1] - X 14 Can (.33 Liter).05 [0,1] - - Light Lager.78 [0,1] - - Can (.5 Liter).27 [0,1] - Note: The possible range for the taste characteristics, richness, sweetness and bitterness is from 1 to 12. For all dummy variables, such as the packaging dummies for example, the mean is simply the fraction of all observations for which the dummy is 1. Light lager is the base category for beer type and the half liter can is base category for packaging. the different types of packaging. For example, Heineken in a.33 liter can and Heineken in a.33 liter bottle are different products. Table (1) lists all the observable product characteristics other than price and packaging covered by the data. This information stems from the retail monopoly s catalogs that are available free of charge in its stores. These catalogs also contain information regarding the taste of the different beers, which is characterized along three dimensions: richness, sweetness and bitterness. All of these characteristics can have values in the range from 1 to 12, where higher values indicate a more intense taste. Moreover, five different types of beer are available: ales, dark and light lagers, stouts and wheat beer. As can be seen from the table, light lagers account for the bulk of beer sales in Sweden, followed by ales. The retail monopoly imposes uniform pricing across all stores in Sweden and it does not engage in temporary price cuts in the form of sales. 2.1 Institutional Setting Before the beginning of 1995, the Swedish market for alcohol was characterized by two monopolies. Vin & Sprit owned the monopoly for the production, import and export of alcohol, while Systembolaget owned the retail monopoly and the monopoly for sales of alcohol to restaurants. On the first of January 1995, however, Sweden joined the European Union (EU) and its common 4

5 Figure 1: The Number of Beers Varieties Year market. The European Commission ruled that the monopolies owned by Vin & Sprit and Systembolaget are not compatible with the common market and must be abandoned upon Sweden s entry into the EU. For public health reasons, the Swedish government managed to preserve the retail monopoly of Systembolaget. All other monopolies had to be abandoned. Consequently, Vin & Sprit lost control over which product is allowed to enter the market. This led to a substantial rise in the number of available varieties in the retail outlets of Systembolaget until the beginning of In this period, the number of available beers increased from 230 to 300, a more than 30 percent increase. Subsequently, more and more beers exit the market and the total number of varieties falls to 270 at the end of the sample period, which is a reduction of 10 percent relative to the maximum. Thus, the data contains substantial changes in the number of products, making the Swedish beer market an appropriate testing ground for product space congestion. Figure (1) graphs the number of available beers over the sample period. Before moving on, I have to mention that Systembolaget only allows firms to change prices and the number of products on offer when it issues a new catalog. Thus, for periods in-between catalog issues there are no observed changes in prices and the number of varieties. These periods contain no useful variation to identify my parameters of interest, which is confirmed by estimating a standard logit model on the full and reduced sample. The resulting coefficients are virtually identical. I therefore drop the periods in-between catalog issues. This reduces the total number of months in the sample from 72 to Demand Model I estimate a nested logit specification to model demand for beer in Sweden. As nests, I define the different types of beer: ales, dark lagers, light lagers, stouts and wheat beer. The indirect 5

6 utility that agent i derives from purchasing beer j in market t is given as follows. u ijt = δ jt + ζ igt + (1 ρ t )ɛ ijt δ jt = x jt β αp jt + ξ jt (1) There are two sources of product differentiation in this model: the mean utility, δ jt, and the total idiosyncratic taste shock, ζ igt + ɛ ijt, where the former is a nest-consumer-specific and the latter a product-consumer-specific taste shock. Cardell (1997) shows that the distribution of ζ igt is such that ζ igt + (1 ρ t )ɛ ijt has a Gumbel distribution. ρ t controls the correlation of utilities within each nest and is bounded on the unit interval. As ρ t 1, the within-nest correlation of utilities also tends to 1 and the market is completely segmented at the nest-level. If ρ t = 0, the model collapses to the standard logit model. In what follows, the correlation coefficient can vary across markets. As I detail further below, this modifies the nested logit model to allow for product space congestion. The mean utility of each beer variety is a preference-weighted linear combination of each variety s observable product characteristics, x jt, price, p jt, and unobservable product characteristics, ξ jt. δ jt therefore measures each beer s location in characteristics space. The second source of differentiation is each product s location in product space. This space is spanned by the idiosyncratic taste shocks, ɛ ijt. 2 With a total of N consumers and J varieties, the space has dimension (N J). With the entry of a new variety the dimension expands to (N (J + 1)). New products differentiate into new dimensions. This holds irrespective of how many beers are already in the market. Consequently, product space never fills up. Bajari and Benkard (2003) prove the following result holds for logit models that do not allow for product space congestion. ɛ ijt lim 1 (2) J u ijt As more and more products enter the market, each product s location in characteristics space becomes less and less important for explaining consumer utility derived from purchasing the product. This is highly problematic, because characteristics space can fill up, as is for example the case in Salop s circular city model, while product space does not. Thus, as J, price and all other characteristics become irrelevant as a determinant for consumer purchasing decisions. This implies that logit models tend to understimate the competitive effect of entry and overestimate the beneficial effect of entry on consumer welfare. To explicity allow for product space congestion and thereby avoid this effect, I follow the multiplicative approach of Ackerberg and Rysman (2005). 3 The idea is the following. Suppose that the variance of the idiosyncratic taste shocks is a decreasing function of the number of available varieties. σɛ 2 (J) < 0 (3) J If the variance of the taste shocks decreases sufficiently fast as additional varieties enter the market, (2) no longer applies. In the limit, i.e. σ 2 ɛ = 0, a variety s location in product space becomes irrelevant for the indirect utility it provides to consumers and consumers will not be 2 ζ igt also affects the dimension of product space, but I do not observe the entry of new nests in the data as for example in Petrin (2002). Therefore, for the data at hand, I am only interested in how the idiosyncratic taste shocks affect the dimension of product space. 3 The multiplicative approach is described in detail in the Appendix to Ackerberg and Rysman (2005). 6

7 willing to pay for variety as such (no love-for-variety). Every product has the same draw for the idiosyncratic taste shock. All products are therefore located in the same point in product space, shutting down this source of differentiation. This is the case for the pure characteristics model of Berry and Pakes (2007) and the hedonic approach of Bajari and Benkard (2005), who impose that ɛ ijt = 0 i, j, t. For cases in-between the extremes of these latter models and the standard logit model, Ackerberg and Rysman (2005) show that having σɛ 2 decrease with the number of products can be linked to an adress model in which new varieties differentiate into dimensions that consumers are less willing to pay for. In this way, product space can effectively become crowded as products enter the market. With characteristics space filling up as well, entry causes products to become better substitutes, driving up the intensity of competition and attenuating the benefits from entry on consumer welfare. 3.1 Functional Form Assumptions for Product Space Congestion As I explain in more detail in Section 4, to allow for product space congestion in the nested logit model, ρ t must be a function of the number of varieties. I compare the implications of a nested logit model allowing for product space congestion against those of the standard nested logit model. ρ (I) t = ρ, t ρ (II) t = µ γ/jt, µ (0, 1), γ > 0 µ is the base for the power function approach in specification (II). It can be set to any value inside the unit interval. 4 The functional form of the power function guarantees that the withinnest correlation is always consistent with random utility maximization, i.e. ρ t [0, 1). In what follows, I refer to specifications (I) and (II) as the benchmark or standard and congestion models, respectively. (4) 3.2 The Additive Versus the Multiplicative Approach Ackerberg and Rysman (2005) consider two approaches to make the distribution of the logit errors more flexible. In the additive approach, the mean of the logit errors is tied to the number of varieties in a market. If there is congestion in product space, the mean of the logit shocks is lower for markets with a large number of varieties than for markets with relatively few products. This limits the welfare gains from adding new products, because consumers willingness to pay for more choice decreases. In fact, this is equivalent to stating that, ceteris paribus, substantial entry diminishes consumers overall liking for this type of product. Even though this is somewhat counterintuitive, the model s implications are comparable to those of the multiplicative approach. The main drawback of the additive approach is that it can be more easily confounded with 4 µ is therefore a free parameter and does not reduce the degrees of freedom in the estimation. Given two values for the base inside the unit interval, the corresponding exponents are related by γ 1 = γ 2(ln(µ 2)/ ln(µ 1)). 7

8 market-specific shocks. To see this, consider the simplest implementation of the additive approach for the standard logit model. ln(s jt ) ln(s ot ) = δ jt + γ ln(j t ) (5) γ is the congestion parameter, where γ = 1 corresponds to full congestion (no love-for-variety) and γ = 0 yields the standard logit outcomes. J t is the number of products available in market t. It is obvious that the congestion term would be perfectly collinear with market fixed effects, because within market, there is no variation in the number of products. 5 This implies that the congestion term not only picks up congestion effects in the data, but all other unobserved market-specific shocks, as well. A prime candidate for such shocks is measurement error in the sales of the outside good. The left-hand side of (5) can be re-written as ln(q j,t ) ln((1 + ɛ o,t)q o,t), where q j,t denotes the true sales of product j and q0,t are the true sales of the outside good. The econometrician only observes the sales of the outside good after it is shifted by measurement error (1 + ɛ o,t ). In the estimation of the additive approach, the congestion term γ ln(j t ) picks up both actual congestion effects and measurement error. To credibly identify product space congestion in this setting, it would be preferable to estimate the standard logit model with market fixed effects. Then, ln(j t ) can be regressed on the series of market fixed effects to decompose these estimates into congestion and measurement error terms. Identification would be further aided, if in addition shifters for the sales of the outside good are available. I opt for the multiplicative approach and let the variance of the logit errors adjust in response to changes in the number of products in the market. This adjustment enters the regression equation non-linearly, which should weaken the relationship between unobserved market-specific shocks and the estimated congestion parameter. In the data, the share of the outside good exhibits a slight downward trend over the sample period and in each year beer sales peak in Summer and Winter, while they reach a trough in Spring. I capture these patterns by including a linear trend and seasonal dummies. 6 Moreover, the multiplicative approach can be linked to an address model, where new products differentiate into dimensions that consumers are less willing to pay for. This is an economically more intuitive mechanism to generate product space congestion, than in the additive approach. 4 Testing for Product Space Congestion A priori, it is not necessarily obvious when a particular market is best modeled in a congestion framework or if alternatively a standard logit-type model yields accurate results. Naturally, markets with a large number of varieties and substantial changes in the number of products over time are more likely to exhibit congestion effects than stable markets with few varieties. 5 This would be different when including only J g,t, the number of varieties in nest g, for example. As long as there is more than one inside nest, there would be within-market variation of the number of products. 6 My findings are qualitatively unaffected when I drop the trend and seasonal dummies. Including market fixed effects, however, makes it difficult to identify the multiplicative congestion effects. This is in line with the argument that market fixed effects absorb any additive congestion effect. This makes it hard to jointly identify both additive and multiplicative congestion effects. 8

9 For all logit models, a necessary condition for the presence of product space congestion is that the variance of the idiosyncratic taste shocks, σɛ,t, 2 varies over time. σɛ,t 2 controls the distance of different varieties in product space. The higher this variance, the more room there is for differentiation. In markets with higher logit variance, therefore, consumers love-for-variety is stronger. Allowing for product space congestion in a nested logit model can be implemented easily by noting how it relates to the variances of the taste and nest shocks. Ben-Akiva and Lerman (1985) show that the following identity holds. ρ t = σ 2 ζ,t σ 2 ζ,t + σ2 ɛ,t (6) Both σ 2 ζ,t and σ2 ɛ,t cannot be identified jointly; only their ratio can. To illustrate, hold σ 2 ζ,t fixed. A fall in the variance of the logit errors causes a rise in the within-nest correlation coefficient. ρ t in turn controls the elasticity of demand for each variety j with respect to its own price, η jj and the price of any competing product, k, η jk. η jj,t = αp j 1 ρ t (1 ρ t s j g (1 ρ t )s j ) η jk,t = αp k 1 ρ t (ρ t s k g + (1 ρ t )s k ) j, k g η jk,t = αp k s k j g, k h (7) Both own-price elasticities and cross-price elasticities within each nest rise with the nesting coefficient. Only the cross-price elasticities across different nests are unaffected by a change in ρ t. 7 An increase in ρ t, therefore, directly affects competition. What we are looking for in industries with product space congestion is that markets with relatively many products are consistently estimated to have relatively low logit error variances. Using the above relation, increases in ρ t should go hand-in-hand with hikes in the number of varieties, J t. 4.1 Identifying Structural Breaks in ρ To formalize this notion, I use tests of parameter instability, developed in the literature on structural change (see Hansen (2001) for a survey). In order to assess how the estimated structural breaks in the nesting coefficient correlate with changes in the number of products, I want to allow for multiple structural changes. Moreover, I am only interested in the existence of breaks in ρ t and not all remaining coefficients (partial structural change). 8 Bai and Perron (1998) have developed a sequential test procedure that identifies multiple breaks of unknown timing. Starting from the nested logit model, the first stage allows for one break. For each possible split of the sample, the sum of squared residuals is computed. If the improvement in the sum of squared residuals over the nested logit model with constant ρ is sufficiently big, 7 This is due to the functional form of the nested logit model. Typically, these cross-elasticities play a minor role in demand systems estimated with a nested logit model, because their magnitudes are small. 8 In the nested logit model, ρ t affects all own-price and within-nest cross-price elasticities. The same applies to the other non-price characteristics. Only cross-price elasticities between different nests are not directly affected by ρ t. Thus, allowing for breaks in ρ t also affects the model implications of the remaining estimated preference parameters to a large extent. 9

10 Table 2: Identified Breaks in ρ t Break ρ {t} F-Statistic Asymptotic Crit. Value J {t} 8 ρ 1:7 = J 1:7 = (.0090) 30 ρ 22:29 = J 22:29 = (.0064) 30 ρ 30:38 = J 30:38 = (.0077) 22 ρ 8:21 = J 8:21 = (.0061) Corr {ρt},{j {t} }.9635 Period 8 December, 1996 Period 22 May, 1999 Period 30 September, 2000 Note: Based on the sequential test procedure for mutliple structural breaks of unknown timing outlined in Bai and Perron (1998). Breaks are listed in the sequence that they are identified. Asymptotic critical values are valid at the 2.5 percent significance level; see Table II, α =.975, q = 1. J {t} is the average number of varieties for the subsample {t}. the candidate break date is accepted. If there is more than one break satisfying this criterion, the break with the greatest improvement is chosen. The sum of squared residuals of this model with one break becomes the point of comparison for the next stage of the test procedure. The critical test values have to be obtained by simulation and can be found for a wide variety of cases in Bai and Perron (1998). This procedure is iterated until a stage fails to produce a break date that is accepted. The procedure of Bai and Perron (1998) relies on OLS estimates. As I detail further in the following section, least squares estimation of the demand system yields biased estimates of the price coefficient. Perron and Yamamoto (2013), however, show that it is generally preferable to estimate the structural breaks by using OLS, even when endogenous regressors are present. Table (2) summarizes the results of the sequential test procedure for the Swedish beer data. I identify three significant breaks in the nesting coefficient. The nesting coefficient is lowest for the first subsample, which covers the period from March to October The average number of varieties is also lowest for this period. In the following subsample, which stretches from December 1996 to March 1999, the nesting coefficient reaches its maximum. The same holds for the average number of varieties over this period. This patterns is repeated in the last two subsamples. As the average number of products falls from almost 291 to more than 275 and then to less than 269, so does the nesting coefficient. The correlation between the two series is almost perfect. Table (2) also lists the fourth candidate break date to illustrate that the failure to accept this break is quite clear. In summary, the identified breaks in the nesting coefficient provide strong evidence that ρ changes 10

11 over time. Moreover, the subsamples with higher numbers of varieties are consistently estimated to have higher values of ρ. Taken together, these findings suggest that there is product space congestion in the Swedish beer market data. 5 Estimation Using the Berry (1994) inversion with (1) and the functional form assumptions in (4), the two specifications I estimate, are given as follows. ln(s j,t ) ln(s o,t ) = x j,t β I α I p j,t + ρ ln(s j g,t ) + ξj,t I ln(s j,t ) ln(s o,t ) = x j,t β II α II p j,t + µ γ/jt ln(s j g,t ) + ξj,t II (8) Here, I use the superscripts I and II to differentiate between the estimated taste paramters and unobservables of the benchmark and congestion models, respectively. Before discussing identification, I turn to the endogeneity of prices. 5.1 Instruments The unobservable product characteristic, ξ, has a vertical interpretation in both demand models. All else equal, a higher realization of ξ j raises product j s market share, because consumers are willing to pay for the characteristic ξ. Firms optimally incorporate this into their price setting decisions and raise prices with higher realizations of ξ. This induces a positive correlation between prices and the structural error term and thereby prices are endogenous. Without instruments, the price coefficient, α, is biased towards zero. I follow the instrumenting strategy of Berry et al. (1995). All non-price characteristics are assumed to be exogenous. Each product s optimal price depends on its own attributes and the attributes of all other products; both products that are owned by the same firm and all other rival products. Given exogeneity, any function of the observed non-price characteristics qualifies as a potential instrument for price. Specifically, I use three functions: the mean of the characteristics of all products, the sum of characteristics of all products owned by the same firm, and the sum of characteristics over all rival firms. To raise the variation of the instruments, I follow the practices in Bresnahan et al. (1997) and Verboven (1996) and compute the instruments within product categories. As can be seen in Table (1), for the Swedish beer data there are several variables that can segment the beers into categories: the foreign dummy, the beer type dummies and the packaging dummies. Moreover, I also restrict the characteristics that I use for the computation of the instruments to those that have sufficient variation, namely the three taste characterics, the alcohol content and advertising expenditure. The remaining characteristics are dummy variables. The instruments that are computed within package categories perform well. Regressing these excluded instruments alone on price explains more than 25 percent of the variation price. Moreover, all the estimated coefficients are significant. When adding the included instruments, too, the fraction of the explained variance of prices rises to more than 60 percent. Using these instruments, the benchmark model passes the orthogonality restrictions at a significance level 11

12 of 2.5 percent. The congestion model attains a lower J-statistic and passes the orthogonality restrictions quite comfortably. 5.2 Identification I estimate both models with instrumental variables GMM. The identifying assumption is that the excluded instruments and the structural error terms are orthogonal to each other. E[z j,t ξ j,t ] = 0, j, t The objective function of the GMM estimators can be written as Q(ξ(θ)) = ξ(θ) T ZW Z T ξ(θ), where θ is the vector of coefficients to be estimated. For the congestion model, the GMM objective function value can be written to depend only on γ, the congestion parameter. The intuition is the same as in Nevo (2000). γ is the only non-linearly entering parameter. Given a specific value for γ, the log-nest-share term can be pulled over to the left side of the estimating equation. The remaining parameters can then be determined by regressing (2SLS) the linearly entering regressors on the altered dependent variable. The minimzer of Q(ξ(γ)), therefore, only has to search over the parameter space of γ and not θ. For both models, I adjust the weighting matrix for clustering of the unobservables at the firm level. Hoxby and Paserman (1998) show that tests of instrument orthogonality assuming homoscedasticity tend to over-reject the null of orthogonality if the data is characterized by strong intra-cluster correlation and little within-group variation of the instruments. Given the large number of products owned by several firms and the market overall, the instruments yield limited variation at the firm level. Computing the instruments at the package level raises the variation, but I found that adjusting the weighting matrix for clustering still aids in reducing the GMM estimator s objective function value Results Table (3) presents the estimated parameters for both models. The congestion parameter, γ, is statistically significant. maximum is.55. The implied minimum for the nesting coefficient is.46, while the This change raises the average own-price elasticity by roughly 20 percent. Therefore, the estimated congestion effects have a substantial impact on competition as the number of varieties in the market changes. In terms of all non-price characteristics, the two specifications yield broadly similar estimates. It is apparent that for the congestion model all coefficients are shifted to the right of their counterparts in the standard model. This has the effect of raising the magnitudes of the mean utilities in the congestion model, relative to the standard model. 10 This finding is in line with 9 The change in the parameters from the first to the second stage is limited and does not affect the results qualitatively. 10 In terms of the 2-norm, the magnitude of mean utilties in the congestion model are about 2 percent higher than in the benchmark model. 12

13 Table 3: Estimation Results Model Model Regressor (I) (II) Regressor (I) (II) Price Per Liter (SEK) Alcohol (% of Vol.) (.0070) (.009) (.025) (.036) ρ Advertising (mln SEK) (.006) (.017) (.012) γ Foreign (4.499) (.060) (.091) Richness Bottle (.33 Liter) (.010) (.017) (.050) (.037) Sweetness Bottle (.5 Liter) (.010) (.030) (.045) (.046) Bitterness Can (.33 Liter) (.006) (.021) (.112) (.130) Constant R (.097) (.107) J-statistic, (df) 26.93, (15) 22.87, (14) Note: Based on 10,506 observations and efficient instrumental variable GMM. Standard errors are clustered at the firm level and reported in parantheses. A linear trend and seasonal dummies are included as well but are not reported. The base of the power function is set to µ =.1. the results of Bajari and Benkard (2003). Not allowing for congestion effects in markets with many products diminishes the role of mean utilities (characteristics space) for explaining market shares. In the following Section, I assess how the two models differ in out-of-sample exercises in terms of their predictions for welfare and competition. 6 The Economic Implications of Product Space Congestion To trace out the economic implications of the two models, I simulate counterfactual market outcomes for markets having between 50 and 350 beers. The data covers a range from 230 to 300 varieties. I make the following assumptions for the counterfactuals. Non-price characteristics and marginal costs are exogenous. I simply match their empirical distribution, where I collapse the non-price characteristics into a single random variable, δ j, p = x j β + ξj. I have obtained the empirical distribution of marginal costs, by backing them out for each model given the estimated parameters, presented in Table (3). Moreover, to abstract from the issue of ownership concentration, I only allow for single-product firms. 11 Prices are the equilibrium outcome of Nash-Bertrand competition between varieties. For each number of products, I compute 100 sets of draws for δ p and marginal costs, ĉ. Given 11 Matching the actually observed level of concentration in the data does not qualitatively affect the results. 13

14 the draws, I obtain the equilibrium prices by solving ( θ)) 1 p = ĉ I Ω( δ; s( δ; θ), (9) where δ = δ p α p, I is the identity matrix and denotes point-wise multiplication. For each number of products, I compute the average of all outcome variables and 90 percent symmetric confidence intervals for these averages. 6.1 Consumer Welfare As I match the empirical distribution of non-price mean utilities, the average for this component of mean utilities is identical across all markets. Changes in welfare, therefore, can only stem from two sources: changes in consumers willingness to pay for more choice (love-for-variety) and changes in prices. For each of the models, the mean and standard deviation of marginal costs is also equal across markets. Following the notation in Berry (1994), let D g,t = j g eδ j/(1 ρ t). Then, consumer welfare in market t is given by CW t = 1 G α ln g=0 D 1 ρt g,t + K, (10) where K is an arbitrary constant, g indexes nests, and the market indexing for the nesting coefficient, ρ t, accommodates both the standard nested logit and aggregate congestion nested logit model. Let V g,t = Jg,t 1 j g eδ jt/(1 ρ t). I refer to this term as the average quality of varieties in nest g. Using this definition, consumer welfare can be re-written to illustrate the two principal components of welfare more clearly. CW t = 1 G α ln 1 + g=1 J 1 ρt g,t V 1 ρt g,t + K (11) Consumer welfare is monotonically increasing in both the number of varieties and the average quality of the beers in each nest. The former effect is the built-in love-for-variety in logit-type models. In the standard nested logit model, the willingness of consumers to pay for having the choice among more varieties is always present, irrespective of how many varieties are already in the market. This is because the within nest correlation, ρ t, is constant across all markets. In the congestion model, however, ρ t tends to one as the number of products grows large. This limits welfare gains from raising J g,t. Moreover, as product space becomes more and more congested with the entry of additional varieties, the average-quality term, V 1 ρt g,t, falls. 12 It is therefore possible that consumer welfare decreases with the entry of new products, provided that ρ t rises sufficiently fast with the number of varieties. Figure (2) plots the counterfactual change in welfare as the number of available varieties increases from 50 to 350. In the left panel the benchmark model predicts a substantial rise in welfare. Consumers gain roughly 10 SEK per liter in surplus, which corresponds to about 30 percent of 12 This is because j g δjt < 0, which guarantees that Dg,t/ ρt < 0. If this were not the case, consumer welfare would explode as ρ t 1. 14

15 Figure 2: Consumer Welfare Standard Nested Logit Aggregate Congestion CW( J ) CW(50) CW( J ) CW(50) J J Note: Based on 100 simulated market outcomes for each model and number of varieties. The increase in consumer welfare is measured in SEK per liter. The plotted thin lines are 90 percent bootstrapped confidence intervals for the average series. the average price across all markets. The results for the congestion model in the right panel look quite different. Up until about 135 varieties, consumers are predicted to gain less than 3.4 SEK per liter, which is about a third of the total gains in welfare in the benchmark model. From that point onwards, consumer welfare is roughly constant. Moreover, the estimates do not imply falling welfare over the range of products. Instead, the changes in the two components of consumer welfare seem to balance. As I detail in the following section, this result is driven by changes in prices. 6.2 Prices and Profitability Figure (3) plots the level of average prices for the two models across the range of products. Both models predict a fall in average price. For the benchmark model, the decrease is negligible: a sevenfold increase in the number of beers lowers the average price by less than 1.5 percent. In stark contrast, the congestion model predicts a fall in average price of almost 20 percent. Recall that average marginal costs are held constant across the markets. Thus, in the standard model, the entry of rival products has almost no effect on prices and thereby no effect on the 15

16 Figure 3: Average Market Prices 35.5 Standard Nested Logit 41 Aggregate Congestion Average Price Average Price Number of Varieties Number of Varieties Note: Based on 100 simulated market outcomes for each model and number of varieties. The plotted thin lines are 90 percent bootstrapped confidence intervals for the average series. profitability of the products in terms of relative markups over price. Table (4) shows the evolution of the Lerner indices and average own-price and cross-price elasticities for the two models. The evolution of relative markups over price reflect the changes in price as the number of varieties rises. The standard model predicts a fall in the average Lerner index of less than 5 percent, while the congestion model implies a reduction of almost 50 percent. Even though the difference between the two models is substantial in terms of magnitudes, so far, both models point in the same direction. Consumer welfare is (weakly) increasing and prices and markups over price are decreasing in the number of varieties. This is no longer the case, when turning to the effect of entry on market power. The implications for the congestion model are economically intuitive. Both, average own-price elasticities and the substitutability of beers sharing the same nest increase with the number of available varieties. Average own-price elasticities double from 3.6 to 7.2, while the average cross-price elasticities increase almost five-fold. This pattern is reversed for the benchmark model. As the number of varieties increases from 50 to 350, the average own-price elasticity decreases by 15 percent, and the average within-nest cross-price elasticity falls by more than 83 percent. Thus, in the standard model substantial entry of rival products reduces competitive pressure. This result is consistent with the benchmark model s muted response of prices to entry. Given the 16

17 Table 4: The Intensity of Competition and the Number of Varieties Average Lerner Index η jj η jk g J Standard Congestion Standard Congestion Standard Congestion [.256,.273] [.286,.305] [4.62,5.06] [3.43,3.75] [.001,.058] [0,.005] [.246,.270] [.241,.259] [4.41,4.84] [4.06,4.44] [0,.047] [0,.018] [.246,.266] [.198,.214] [4.21,4.59] [4.94,5.38] [0,.037] [0,.030] [.245,.265] [.167,.180] [4.07,4.45] [5.88,6.43] [0,.032] [0,.042] [.243,.264] [.144,.157] [3.96,4.37] [6.83,7.53] [0,.028] [0,.051] Note: Based on 100 simulated market outcomes for each model and number of varieties. The numbers in square brackets represent 90 percent symmetric confidence intervals around the reported averages. The average Lerner index is J 1 J j=1 (pj cj)/pj. massive rise in rival products, nearly constant prices can only be sutstained, if the substitutability between varieties diminishes with entry. This in turn is driven by consumers willingness to pay for an ever-increasing menu of choices. In summary, the lack of flexibility in ρ imposes too much competition when there are few varieties in the market and implies too little competition when a lot of beers are available. Moreover, not allowing ρ to adjust with the number of products yields a substantial overestimation of the welfare gains from the introduction of new varieties. 7 Conclusion Building on the work of Ackerberg and Rysman (2005), I find strong evidence for product space congestion in the Swedish beer market. While the average number of varieties over the sample period is close to 277, the congestion model predicts that there are no additional welfare beenefits from introducing more than 135 varieties. This points to substantial excess variety in the market. Even though consumer welfare is not decreasing beyond 135 beers on offer, it seems likely that the state-owned retailer could eliminate costs by substantially reducing the variety in its stores. The congestion model also delivers economically very intuitive predictions with regard to the effect of entry on competition. In a counterfactual that raises the number of beers from 50 to 350, average markups over marginal cost are reduced by half. In contrast, the standard nested logit model predicts that consumer welfare can be raised further by introducing more than 350 varieties in the stores of the Swedish retail monopoly. Moreover, the model delivers the prediction that entry attenuates competition in the market. For the same counterfactual, the average own-price elasticity drops by 15 percent, while the average withinnest cross-price elasticity falls by 83 percent. 17

18 My findings stress that the standard nested logit model can yield substantially biased predictions in counterfactual exercises, when dealing with markets with a large number of varieties and/or substantial changes in the number of products across markets. When bounding the distribution of fixed costs, for example, the standard nested logit model could deliver an estimate that is biased to the right. If substantial entry raises competition and thereby reduces operating profits, exit should become more likely. In the standard model, however, the opposite is the case. Substantial entry attenuates competition and thereby predicts too high operating profits. To explain actually occurring exit, fixed costs have to be sufficiently high. Similarly, the congestion model leaves room for a firm-driven proliferation of varieties, because an increase in products tends to raise substitutability. Firms with many products in their holdings can therefore shield themselves from competition. This market-power-generating effect for multiproduct firms should become more pronounced as there are more and more products in the market. In the standard model, however, product substitutability decreases substantially with entry. This points exactly in the opposite direction. Multi-product firms are relatively profitable when there are relatively few varieties. I leave a test of these conjectures for future research. Methodologically, I show how to use the sequential test procedure of Bai and Perron (1998) to test for the presence of product space congestion in a given data set. This reduces the ambiguity of when a market is best described in a congestion or standard logit framework. 8 References Ackerberg, Daniel A. and Marc Rysman, (2005), Unobserved Product Differentiation in Discrete- Choice Models: Estimating Price Elasticities and Welfare Effects, RAND Journal of Economics, 36(4), pp Bai, Jushan and Pierre Perron, (1998), Estimating and Testing Linear Models with Multiple Structural Changes, Econometrica, 66(1), pp Bajari, P. and C. Lanier Benkard, (2003), Discrete Choice Models as Structural Models of Demand: Some Economic Implications of Common Approaches, Manuscript, Yale University. Bajari, P. and C. Lanier Benkard, (2005), Demand Estimation with Heterogeneous Consumers and Unobserved Product Characteristics, Journal of Political Economy, 113(6), pp Ben-Akiva, Moshe and Steven R. Lerman, (1985), Discrete Choice Analysis: Theory and Application to Travel Demand, MIT Press. Berry, Steven T., (1994), Estimating Discrete-Choice Models of Product Differentiation, RAND Journal of Economics, 25(2), pp

19 Berry, Steven T. and Ariel Pakes, (2007), The Pure Characteristics Demand Model, International Economic Review, 48(4), pp Berry, Steven T., James Levinsohn and Ariel Pakes, (1995), Automobile Prices in Market Equilibrium, Econometrica, 63(4), pp Berry, Steven T. and Joel Waldfogel, (1999), Free Entry and Social Inefficiency in Radio Broadcasting, RAND Journal of Economics, 30(3), pp Bresnahan, Timothy F., Scott Stern and Manuel Trajtenberg, (1997), Market Segmentation and the Sources of Rents from Innovation: Personal Computers in the Late 1980s, RAND Journal of Economics, 28(0), pp Cardell, N.S., (1997), Variance Components Structures for the Extreme Value and Logistic Distributions with Applications to Models of Heterogeneity, Econometric Theory, 13(1997), pp Goolsbee, A. and Amil Petrin, (2004), The Consumer Gains from Direct Broadcast Satellites and the Competition with Cable TV, Econometrics, 72(2), pp Hansen, Bruce E., (2001), The New Econometrics of Structural Change: Dating Breaks in U.S. Labor Productivity, Journal of Economic Perspectives, 15(4), pp Mariuzzo, F., Patrick P. Walsh, and Ciara Whelan, (2010), Coverage of Retail Stores and Discrete Choice Models of Demand: Estimating Price Elasticities and Welfare Effects, International Journal of Industrial Organization, 28(5), pp Nevo, Aviv, (2000), A Practitioners Guide to Estimation of Random Coefficients Logit Models of Demand, Journal of Economics & Management Strategy, 9(4), pp Perron, Pierre and Yohei Yamamoto, (2013), Using OLS to Estimate and Test for Structural Changes in Models with Endogenous Regressors, forthcoming in the Journal of Applied Econometrics. Petrin, A., (2000), Quantifying the Benefits of New Products: The Case of the Minivan, Journal of Political Economy, 100(4), pp