Product Offerings and Product Line Length Dynamics

Transcription

1 Product Offerings and Product Line Length Dynamics Xing Li Department of Economics, Stanford University, 579 Serra Mall, Stanford, CA This paper provides a model that uses preference heterogeneity to rationalize the cross-sectional and intertemporal variation in a firm s horizontal product differentiation strategies. Product-line dynamics arise from shocks to preference heterogeneity. For example, in the potato chip category I study, consumer concerns over fat levels in foods created two desirable alternatives (low fat and zero fat) for each flavor. On the supply side, firms learn about these changing tastes and adapt product lines accordingly. For tractability, the heterogeneity in preference is captured by the nesting parameter in an aggregate nested logit demand model. I find greater preference heterogeneity for chips in smaller packages and for markets with more demographic diversity. The dominant firm in the market bases its decisions primarily on its past experience in the market, with the latest preference shocks representing only 30% of the influence in product-line decisions. Gross margins are increased by 5% if firms have perfect information about preference heterogeneity. Costs for product line maintenance constitute about 2% of total revenue. Sunk costs incurred when expanding the product line are estimated to be four times the per-product fixed cost, thereby limiting the flexibility of product-line adjustment. The probability of line length adjustment grows from 70% to 90% under a smooth cost structure. 1. Introduction One of the central decisions firms make is the level of their product differentiation. Product differentiation can be exercised in two dimensions: vertically or horizontally. Vertical differentiation means providing an upgraded or downgraded model and charging a different price, for example, Apple iphone5s and iphone5c. Within the same model, firms can further differentiate horizontally by providing different features of colors, flavors, or designs. Apple 1

2 2 Li: Product Offerings and Product Line Length Dynamics offers iphone5s with three choices of colors; Dannon produces 6oz yogurt in different flavors. Both companies are doing horizontal product differentiation within the same model. There are at least two difference between these two types of product differentiation strategies. First, vertical differentiation is mainly driven by leaps in R&D success (e.g., Goettler and Gordon 2011), whereas horizontal differentiation is largely initiated by consumer tastes (e.g., Draganska and Jain 2005) that vary across different markets and over time. Furthermore, vertical differentiation usually involves higher fixed costs of adapting production processes, whereas horizontal differentiation typically utilizes the same process as existing products. For both reasons, horizontal differentiation is more flexible and therefore creates more variation in a firm s decisions. This variation in horizontal differentiation is what motivates my investigation into firms extensions and contractions of their product lines. Acknowledging the fact that consumers preference heterogeneity on the demand side is the primary driver of horizontal product-line, I propose the following framework to rationalize both cross-sectional and intertemporal variation in product-line decisions. The extent of preference heterogeneity varies across markets for reasons such as the concentration of different demographic groups. 1 Firms will provide a richer set of (horizontally differentiated) products in markets with a more heterogeneous preference to serve a larger proportion of consumers and make more profits. Within each market, firms can also adjust their product lines over time in response to changes in preference heterogeneity. 2 Firms are more likely to expand (contract) their product lines when preference heterogeneity increases (decreases). The main mechanism to support the above argument is as follows. Preference heterogeneity affects the tradeoff between cannibalization and new sales creation when expanding 1 In this paper, preference heterogeneity is an aggregate statistic for both variety seeking within individuals and preference heterogeneity among individuals. 2 For example, manufacturers of potato chip will consider the immigration of Asian and Hispanic population. They will also be aware of the consumers growing concern for their own health.

3 Li: Product Offerings and Product Line Length Dynamics 3 the product line. For multi-product firms, the newly launched product brings in new consumers and cannibalizes market shares from existing products. When consumer s preference is quite homogenous, it is difficult to initiate extra sales to new consumers by new product launching, and cannibalization effect dominates new sales creation effect. As a result, firms may not maintain a long product line. On the other hand, when consumer s preference is quite heterogeneous, new sales creation effect dominates and expanding product line is more profitable. To formalize and quantify the above argument, I model the demand side using Nested Logit. Different products (features) from the same brand are clustered in one nest (line) in the choice structure. The nesting parameter has the same behavioral interpretation as the heterogeneity of preference, which is an aggregate measure of both variety seeking within an individual and preference heterogeneity across individuals. 3 When products are more nested within the line, they are closer substitutes; consumers agree on the preference ranking among these products and the preference is more homogenous. 4 On the other hand, when products are less nested within the line, they are less substitutes; consumers have more varied views on their favorite products, and preference is more heterogenous. On the supply side, the multi-product firm chases time-varying preference heterogeneity by adjusting product line length, 5 which is described by an in-market learning model based 3 This modeling idea is rooted in the early motivation of nested logit model, that is specifying distributions of unobserved heterogeneity to capture substitution pattern. 4 Intuitively, consider two products that are equally favorable, and split the market. Suppose the price of one product rises. When these two products are closer substitutes, the market share of the second product will increase more, which means more people agree on the which product is their favorite. 5 In reality, the firm decides on the number and the contents of all products in line simultaneously. However, I only model the line length decision in this paper for the following three reasons. First, taste for potato chips depends on numerous flavors, so that it is difficult to write down a characteristic-based demand model to predict the demand

4 4 Li: Product Offerings and Product Line Length Dynamics on Hitsch (2006). Firms decide on product differentiation based on their belief of preference heterogeneities, and realized market outcomes help them to update their belief. On top of the standard in-market learning model, I allow the preference heterogeneity to evolve over time, which explains the frequent adjusting behavior for an experienced firm operating in a matured market for years. 6 The elegant representation of nested logit model that is linear in the nesting parameter makes modeling supply-side learning framework tractable. I apply the model to the potato chip market, where there is a leading firm (I call it Company A hereafter) with a market share of 60%. I find a more heterogeneous preference for potato chips in smaller packages, which implies consumers are more willing to try new flavors when buying small-packaged potato chips. I also find that a more diverse population in the local market will tend to exhibit more preference heterogeneity, which is confirmed by the estimation with a series of measures for population diversity in that market, including the dispersion of income and age distribution, and the diversity of ethnic groups. On the supply side, Company A applies in-market learning on preference heterogeneity to adjust his product line length. I find that Company A bases its decisions primarily on past experience in the market, with the latest preference shocks representing 30% of the influence. The marginal cost of offering one additional product is estimated to be $3,560 per million households by quarter; the total maintenance cost is estimated to be 2% of total revenue for an average line with a length of 22. I also estimate the sunk cost incurred when expanding the product differentiation to be three times the usual maintenance cost, which may limit the flexibility of product-line adjustments. for new products. Second, the action space will become extremely large if I model the content of products as well, i.e., for an average product line in my sample with a length of 20, the action space is {Offer,NotOffer} 20.Third,the dynamics of product line that I am focused in this paper requires more tractability. 6 Technically speaking, by allowing time-evolving preference heterogeneity, the precision of belief does not explode to infinity so that the belief will still change in response to market outcome, and so is product line strategies.

5 Li: Product Offerings and Product Line Length Dynamics 5 Based on the estimates, two counterfactual exercises evaluate the firm s optimal line length decisions under different product-line specific policy experiments. In the first exercise, I simulate the optimal line length decisions without the existence of extra cost for line length expansion. This removes the restrictions on Company A s flexibility in adjusting line length, and the probability of line length changes grows from 70% to 90%. In the second exercise, I consider the situation where Company A knows the precise value of preference heterogeneity at the time of product line length decisions. She can make a better decision based on the true value instead of some guess, and the gross margin is increased by 5%. A byproduct of the second counterfactual is to test the hypothesis of learning or knowing preference heterogeneity when making line length decisions. I construct a test based on gross margin, and the test result supports the assumption of learning rather than knowing about heterogeneity. Both simulations shed lights on firm s potential gain from product-line related improvement. The first one relates to a more efficient cost for product line maintenance, say, a more flexible contract on shelf-space and a better distribution system, and the second one relates to a better knowledge about consumers from sources other than market realizations. This paper is related to several strands of literature. First, there is a growing literature on firm s product differentiation and product-line design, both theoretically and empirically. Theoretical works have discovered varies factors to determine product differentiation, including communication cost to consumers (Villas-Boas 2004), vertical structure of distribution (Liu and Cui 2010), consumer s deliberation on their preference (Guo and Zhang 2012), variety preference and purchase cost (Bronnenberg 2014) and other rational interpretations as well as behavioral explanations such as cognitive overload (Iyengar and Lepper 2000), articulated preference (Chernev 2003a,b), and contextual effects (Orhun 2009). However, there are relatively few empirical papers in this field. Among those, most works take the product line as given and evaluate its implications in consumers demand (Hui 2004, Draganska

6 6 Li: Product Offerings and Product Line Length Dynamics and Jain 2006). The only work I know that explains the product line design is Draganska et al. (2009) that offer a supply-side model of product provisions for horizontally differentiated products. However, they restrict to a small subset of products and mainly attribute the cross-sectional variation in product line to various supply-side competition environment. This paper complements their work by offering a supply-side model for both cross-sectional and inter-temporal variation in the length of the whole product line where the driving force is preference heterogeneity on the demand side. Second, this paper contributes to the in-market learning literature by proposing a new learning object: preference heterogeneity. Numerous papers study demand-side learning about the quality of new products (Roberts and Urban 1988, Erdem and Keane 1996, Ching et al. 2013, Lin et al. 2014). On the supply side, Urban and Katz (1983) and Urban and Hauser (1993) address firms market experimentation in designing new products. Hitsch (2006) studies firms learning the quality of new products when making exit decisions. Another series of papers(crawford and Shum 2005, Narayanan and Manchanda 2009) considers physicians and patients learning about the effectiveness of drugs when making prescription decisions. This paper differs from those empirical learning papers in two perspectives. First, the learning object is preference heterogeneity rather than mean preference in most existing literature. Second, the learning object is evolving over time whereas in standard learning framework, the learning object is constant. 7 Third, this paper is also related to researches on variety seeking. Models for variety seeking find negative state dependence on past choice (Chintagunta 1998, 1999, Seetharaman et al. 2005, Dubé et al. 2009, 2010). This paper uses a different, but related metrics for the variety seeking in the aggregate level. Finally, the supply side is modeled similarly as researches 7 Lovett et al. (2009) also model time-evolving learning parameters.

7 Li: Product Offerings and Product Line Length Dynamics 7 on empirical entry and product positioning. 8 Early research on empirical entry infer firms profitability from their entry decisions (Reiss and Spiller 1989, Bresnahan and Reiss 1990, 1991, Berry 1992). Later research treats as endogenous variables the marketing mix other than price (Berry and Waldfogel 2001, Mazzeo 2002, Berry et al. 2004, Seim 2006, Crawford et al. 2011, Ryan and Tucker 2012). This paper contributes to this strand of literature by proposing a tractable model of product line length dynamics for multi-product firms. The rest of the paper is organized as follows. Section 2 introduces the data and some reduced-form evidences on line length dynamics. Section 3 provides an empirical model to quantify firm s optimal line length decisions driven by preference heterogeneity. Section 4 describes the full specification and identification. Section 5 shows the results, and section 6 concludes. 2. Product Offerings in US Potato Chip Market In this section, I will provide an overview of potato chip industry and description on the IRI Academic Dataset (Bronnenberg et al. 2008) that I use. 9 The last part of the section shows some reduced-form evidence on product line length dynamics The Potato Chip Market Potato chips can be found in most American households. An average US household will spend $80 a year in salty snacks. Potato chips have a dollar share of 30% in the industry of salty snacks, which means an average household will spend around $24 each year on potato chips (First-Research 2011). Chip manufacturers anticipate and respond to changes in consumer preferences. First of all, in the potato chip industry, the ability to be innovative and differentiate a product is the 8 Dubé et al. (2005) provide an excellent summary of these papers. 9 All estimates and analyses in this paper based on Information Resources Inc. data are by the author and not by Information Resources Inc.

8 8 Li: Product Offerings and Product Line Length Dynamics key to competition. As a result, manufacturers offer different choices of potato chips with different flavors, fat contents, and cut types. Furthermore, consumer s tastes vary by region and over time. For example, Joon (2013) states that consumers in the Midwestern region prefer thick cuts and consumers in the southwestern states prefer bold and spicy flavors. At the same time, many exogenous factors drive the evolution of tastes over time. Population migration is one such factor (Bronnenberg et al. 2012). Manufacturers are creating new spicy flavors catering to a growing Hispanic and Asian population (First-Research 2011). Consumers awareness of the health cost of eating potato chips high in trans fat and salt is another factor. To capitalize on this shift, leading manufacturers have introduced a number of new products with reduced fat and low salt content (Joon 2013). A third factor is the change in taste for (new) flavors. Firms can elicit this change by inviting consumers to submit their newly designed flavors. 10 With the existence of diehard fans of classically flavored potato chips, the regional and temporal variations of tastes imply changes in preference heterogeneity and have corresponding implications on product differentiation decisions. A second feature of potato chip industry is that it is highly concentrated, with a leading player (Company A) having a market share of 60%. The second largest player has a market share of only 5.2% (Joon 2013). Company A does not worry too much about potential entrants. First, consumers have strong brand preference in picking potato chips. They are willing to pay extra for branded chips. In addition, operating firms in this industry need to have good relations with upstream suppliers and downstream retailers. They use long-term contracts to hedge against the volatile prices for potatoes, sugars, oils, and fats from their suppliers, and they are competing for the best shelf spaces in grocery stores. 10 For example, Frito Lay holds the contest called Do us a flavor in each year to invite consumers to submit their newly designed flavors and launches the winners. The winning flavor will be awarded 1 million dollars.

9 Li: Product Offerings and Product Line Length Dynamics Data IusetheIRIAcademicDatasetfrom2001to2007toestimatethemodel. 11 The IRI academic dataset provides scanned sales data from a sample of grocery stores at the level of UPC-storeweek across 50 IRI markets. I restrict the analysis in this paper to the Salty Snack - Potato Chip industry. I restrict to 8-13 serving size packages in my analysis. For potato chips offered by firms other than the leading firm (Company A), I aggregate into the level of marketquarter. For potato chips by Company A, I aggregate to the level of feature-market-quarter, where one feature is defined as the triplet of flavor-cut-fat. 12 Company A has wide variation in the length of its product line, defined as the count of features sold in one market-quarter. Table 1 and Figure 1 present the distribution of line length. The average line length is with a standard deviation of The shortest line is in Raleigh/Durham q1, with a length of 8, whereas the longest line is in Chicago q2, that supplied 30 different features. Variation in line length derives from two sources: cross-sectional and inter-temporal. Chip lines vary widely in line length in both sources. Cross-sectionally, Pittsfield has the shortest line, with an average length of 16.89, whereas Houston has the longest line, with an average length of Line length also changes over time, as is shown in Table 1 and right panel of Figure 1. Line length is quite sticky, with about 30% cases there is zero changes, and in 85% the changes are within 2 features, but there are still cases where Company A is quite aggressive in line length adjustment. 11 Although the IRI Academic Dataset is available from 2001 to 2011, I only make use of seven years for the following reasons. First, the 2008 financial crisis heavily drove up prices of potato chips, which makes pricing decisions nontrivial and complicate the model. Second, Company A did a national launch of zero-trans fat in The reasons for the timing and scale of such a big event are beyond the scope of this project. Moreover, the concurrence of the two events further complicates the analysis. 12 Please refer online appendix for justification of data aggregation process.

10 10 Li: Product Offerings and Product Line Length Dynamics I supplement the IRI dataset by merging with the IPUM CPS data to get the demographics. Among 302 MSAs (Metropolitan Statistical Area) in CPS, I have identified 98 that can be merged with IRI markets. In terms of population, those matched MSAs constitute half of the total population nation-wide. I proxy the total market size by number of households in 2007, whereas other demographics that may correlate with preference heterogeneity are calculated in a quarter by city level Reduced-form Evidence on Dynamic Product Offering Before going into the structural estimation, I will show some reduced-form evidence on firms changing differentiation decisions based on market outcomes over time. When preference is homogenous, consumers tend to agree on the preference ranking of all features within a line, and in-line market shares for features are concentrated. In the extreme case, consumers fully agree on the preference ranking, and the in-line market share is 1 for the most preferred feature and 0 for others. In these cases, the model predicts that firms will contract the product line. On the contrary, when preference heterogeneity becomes high, consumers have various opinions about the most favorable feature, and in-line market shares become less concentrated. In this case, the model predicts that firms will expand the product line. To illustrate the argument above, I run the following regression: LineLength mt = HHI m,t LineLength m,t 1 + c m + d t + " mt where m indexes market, t denotes quarter, LineLength mt is the length of the product line, HHI mt is the Herfindahl Index for in-line market share (i.e., HHI mt = P f s2 f l,mt, where s f l,mt is the in-line market share for feature f in market-time mt). c m and d t are market and time fixed effects to control for geographic unobservables and seasoning effects. Baseline regression confirms the model prediction (Table 2, Column 1). The higher the market

11 Li: Product Offerings and Product Line Length Dynamics 11 concentration, the shorter the product line in response. A one standard-deviation change in HHI (0.03) will lead to a change in line length of One of the challenge for the interpretation of the estimate is that the measure of HHI is mechanically decreasing in line length, and the estimated correlation is artifactual. 13 The worry is partly true as shown in Online Appendix, and I use another measure of market concentration: the standard deviation of log in-line market share defined as StdLnShareInLine mt = Std ln s f l,mt which is not mechanically correlated with line length (Online Appendix). When in-line market shares are more concentrated, the standard deviation is high. Regression results still support our conjecture. A one standard-deviation increase in this concentration measure will lead to a 0.36 increase in line length (Table 2, Column 2). One alternative interpretation of the above findings is that firms will automatically withdraw losing features that are unpopular. To deal with this challenge, I change the dependent variable to be the indicator of line expansion. Regression results also confirm the initial theory proposed above (Table 2, Column 3,4). The higher the market concentration, the less likely the line gets expanded. A one standard-deviation decrease in HHI will lead to a higher chance of line expansion by 4.74% (Table 2, Column 3) and 4.60% (Table 2, Column 4). Compared to an average chance of line expansion of 34%, this increase is economically large. A final caveat is that all these reduced-form evidences are correlational, not causal. The complete model allows firms to adjust their line length based on all past market realizations rather than just the last one. To quantify the above mechanism, we will estimate a structural model with a richer set of specifications. 13 I regress line length on one-period lagged HHI. The mechanics in calculating HHI will contaminate the inference only when firms have some inertia to adjust line length.

12 12 Li: Product Offerings and Product Line Length Dynamics 3. A Model of Product Line Length Dynamics In this section, I propose a model that is structural in both demand and supply to capture the effect of preference heterogeneity on the tradeoff between cannibalization and new sales creation when firms are making product line length decisions. For simplicity, I assume that in each market m, thereisaseparatemonopolist.withineachmarket,themonopolistprovides alineofn t products indexed by j 2{1, 2,...,n t } to compete with one single outside good j =0 in each period t Demand Side For each market m and period t (suppressed temporarily), the utility for consumer i from consuming Company A chip j 2{1, 2,...,n} and outside goods j =0 is u ij =(a + " i )+( c j + " ij ) p j = j +(" i + " ij ) u i0 = " i0 where (a + " i ) is consumer s brand preference for company A, which includes average level a and consumer heterogeneity " i ; ( c j + " ij ) is consumer i s utility for product j, which also includes the mean value c j and consumer s heterogeneity " ij ; p j is the price for product j. After some rearrangement, the utility for consumer i consuming product j equals the mean utility level j = a + c j p j and consumer s heterogeneity (" i + " ij ). Following Berry (1994) and Cardell (1997), both " ij and (" i + " ij ) follows i.i.d. type I extreme value distribution. From the representation of c ij = c j + " ij,thevalueof measures consumer s preference heterogeneity over product j. 14 When is high, c ij varies a lot across different individual i, and the preference is heterogenous. On the other hand, lower implies more homogenous preference. 14 Here I am measuring the average level of preference heterogeneity across all products. Ideally we can assign j for each product j, but the data lack statistical power to identify all js

13 Li: Product Offerings and Product Line Length Dynamics 13 The nesting parameter is an aggregate statistics of both individual level variety seeking and cross-individual preference heterogeneity. If we think about the repeated purchases of one individual as different purchase occasions, the variety seeking behavior can be rationalized as the low correlation for individual-specific demand shocks among different products, which is captured as high in current model. With market level data, I cannot identify between variety seeking within individual or preference heterogeneity among individuals. But these two channels should have similar implication for product assortment decisions, which is presented later. The Nested Logit model proposed here can be easily estimated in linear GMM. Within each market m, ln s 1t ln s 0t = jt + t ln s j l,t = a + c j p jt + t ln s j l,t + jt (1) where s 1t is the market share for all Company A products, s 0t is the market share for all non-company-a products, s j l,t is the in-line market share, which equals s jt 1 s 0t. Following the standard model, I allow the taste for product j to vary by time, with c jt = c j + jt, where c j is the product fixed effects, and jt is the unobserved demand shock, which is distributed as N 0, Static Profit when is Known I assume that at the time of product line length decision, Company A does not know the precise value of mean utility jt so that she is taking expectation on over some distribution F ( ). There are three reasons behind. First, product line length decisions are made prior to the realization of demand, so Company A is ignorant about the demand shock jt.second, retailers can observe the demand shock and adjust the retail price p jt,sop jt is also unknown

14 14 Li: Product Offerings and Product Line Length Dynamics before market realization. Third, when Company A launches some new product, the value of c j is also unknown to her. 15 By making this assumptions, I abstract away the identity of each products in line and focus mainly on the length of product line. The total market share for Company from offering a product line with length n follows the nested logit representation with s (n, )=E exp (I) 1+exp(I) where I = ln nx j=1 j exp The total market share s (n, ) is increasing in n, increasingin, andsuper-modularinn and for most of the distributions F. 16 Super-modularity implies when expanding the line length, the marginal gain in total share is larger when the preference is more heterogenous. 17 Formally, let C (n, l) denote the cost of launching a line with length n while the line length in the last period is l. A myopic firm will choose n to maximize w M s (n, ) C (n, l) 15 This also assumes out the product launching in the vertical sense or mass market strategy. (Johnson and Myatt 2006). When a company decides to launch a new product, she can either play mass market strategy so that the new product is attractive to all consumers (i.e., with a high value of ) or niche market strategy that the feature is attractive to a set of consumers (i.e., similar ). In the potato chip industry, it is quite difficult to launch a potato chip that is favorable to all consumers and play mass market strategy. 16 Super-modular means s (n +1, ) s (n, ) is increasing in. ProofofthesepropertiesareprovidedinOnline Appendix. 17 This is consistent with the standard interpretation of price elasticity in the nested logit model. When products are more nested within line, the price elasticity is higher within nests than between nests. Lowering price for one feature will have larger cannibalization effect that will consume the market share of other products within the line than new sales creation effect that will increase the total share of all products in line. The same logic applies to the strategy of line expansion. The cannibalization effect of expanding the line dominates the business stealing effect when features are more nested, and in this case firms are less likely to expand the line.

15 Li: Product Offerings and Product Line Length Dynamics 15 where w is the manufacture margin, M is the market size. Let n (,m) be the optimal line length choice made, and super-modularity means n is increasing in t Dynamic Learning on Time-evolving As mentioned earlier, preference heterogeneity evolves over time due to many exogenous factors including population migration, health concerns, as well as evolving tastes for new flavors. I further assume that firms do not know the true value of preference heterogeneity when making line length decisions. Instead, they have some beliefs on this value and update their beliefs based on market realizations Learning from Market Realizations Suppose at the beginning of period t, Company A has a prior belief on t, which is modeled as a truncated normal with mean µ t and precision t,truncatedatunitinterval(0, 1), which is denoted as TN µ t, 1 t.aftermarket gets realized, the market shares on all products are observed, and Company A can observe one signal from each product j as derived from (1): ' jt =lns 1t ln s 0t a c j p j = t ln s j l,t + jt Aggregate signals from all products about the same t will get an aggregate signal 19 P P j ln s j l,t ' jt j ln s j l,t jt apple t = = t + P Pj ln2 s j l,t j ln2 s j l,t with precision h t = X j ln 2 s j l,t! Anicepropertyfortruncatednormalbeliefisthatitisalsoaconjugatepriorfornormal data generation process, which is shown in the next theorem 18 There is no direct test about the informational assumption that firms do not know the exact value of preference heterogeneity because the stationary learning model (as described below in this paper) and complete information model are not nested with each other. However, I will show some indirect test result based on simulation in later section. 19 For convenience, the notation ln 2 s j l,t means ln s 2 j l,t.

16 16 Li: Product Offerings and Product Line Length Dynamics Theorem 1. Suppose the prior is truncated normal t TN µ t, 2 t = t 1 and an unbounded signal is observed with value apple t and precision h t,thentheposteriorbelief is also truncated normal t apple t,h t TN µ 0t, ( 0t) 2 =( 0t) 1 with µ 0 t = t t + h t µ t + h t t + h t apple t (2) 0 t = t + h t (3) Proof is shown in Appendix?? Evolution of t The next step is to model the time-evolution of preference heterogeneity t. The reason for allowing t to evolve over time is two-folds. First, in the potato chip industry, we do observe preference heterogeneity changes over time and chip manufactures responds by adjusting their product line strategies. Second, for modeling perspective, if the preference heterogeneity is constant over time, as an experienced firm operating in a mature market, Company A is sophisticated enough to know the true value of preference preference heterogeneity and no intertemporal variation in product line should be observed. The large intertemporal variation in product line length motivates the assumption of time-evolving preference heterogeneity. If t is not truncated, a natural candidate model is random walk, with t+1 = t + t

17 Li: Product Offerings and Product Line Length Dynamics 17 where t N (0, 1) is the evolution error, or equivalently, t+1 t N t, 2 In the truncated case, I propose the following quasi random walk t+1 t f ( t ; ) which is similar to the random walk process as for unbounded case with acceptance-rejection at unit interval. Convoluted with the truncated normality on t,wecanapproximatethe prior belief of t+1 as TN µ t+1, 2 t+1 = 1 t+1 with µ t+1 = µ 0 t (4) 2 t+1 =( 0 t) (5) Details are included in Appendix?? Line Length Dynamics Chasing Time-evolving Preference Heterogeneity When we combine the above two pieces of dynamic learning and evolution, we can have the full description of firm s dynamic problem. The action-specific flow profit n (µ t, t,l t )=w M E (s (n, t ) µ t, t) C (n, l t ) and the value value function is V n (µ t, t,l t )= n (µ t, t,l t )+ E (V (µ t+1, t+1,l t+1 ) µ t, t,l t,n) V (µ,, l) =E max n (V n (µ,, l)+ n ) where the state variables are the belief mean, belief precision, as well as last period line length, and the transition probability is defined as (2) (3) (4) (5), with an additional one for l t+1 = n.

18 18 Li: Product Offerings and Product Line Length Dynamics 4. Empirical Specification and Identification In this section, I will present the full empirical specification and identification of the model. Similar to Hitsch (2006), I apply two-step estimation, where the demand side is estimated in linear GMM, and its parameters are plugged in to the supply side. I estimate the dynamic supply model by maximizing likelihood. This section ends with a discussion on the identification of the model Demand Side The demand side is modeled as a nested logit of with two nests where all Company A chips of different features are nested in one line, and all non-company A chips are treated as homogenous outside products. Based on (1), for each market m, ln s 1mt ln s 0mt = a m + c j p jmt + mt ln s j l,mt + jmt (6) Both p jmt and ln s j l,mt are endogenous, because they are correlated with the unobserved demand shock jmt. I employ the following sets of instruments for the two endogenous variables: The summation of characteristics (flavors, fat content and cut type) of other Company Achipssoldinthesamemarket-time X j 0 6=j x j 0 mt Average price of the same feature sold in other geographical markets in the same time 1 # X m 0 6=m p jm 0 t Other cost for raw materials, including potatoes, sugar, soy bean oil, edible butter, and edible tallow

19 Li: Product Offerings and Product Line Length Dynamics 19 Number of competitor brands and number of competitor UPCs other than Company A chips within the same market-time The first set of instruments are widely known as BLP instruments, which Berry et al. (1995) started to use. The underlying assumption is that the characteristics are exogenous to demand shocks. In the current model, the upstream wholesalers make product assortment decisions whereas downstream retailers make pricing decisions. In reality, grocery stores and manufacturers jointly decide what to display in advance. If some of the features do not sell well, grocery stores will lower prices to sell out the storage. In this case, it is natural to assume the assortment decision is made prior to the realization of local demand shock. The second set of instruments are known as Hausman instruments which Nevo (2001) started to use in demand estimation. The underlying assumption is that demand shocks are independent over different markets, but there are factors that may affect the pricing for all markets. These factors include, but are not restricted to, common cost shifters that affect the pricing decisions across markets. The last set of instruments consider the competition environment that was used in Bresnahan et al. (1997). The argument is that competition environments affect firms pricing decisions, which is orthogonal to demand shocks. In this project, I can also exploit the huge variation in the competition environment across different markets measured by the number of competitor brands and UPCs Supply Side - Flow Profit In each market m, the action-specific flow payoff of Company A is n,m (µ,, l) =w m M m E (s m (n, ) µ, ) H m c (n, l) exp (I) s m (n, ) =E Fm 1+exp(I) nx I = ln exp j=1 j

20 20 Li: Product Offerings and Product Line Length Dynamics In other words, I allow a market-specific value profit function and calibrate the parameters as follows: w m :manufacturer smargin,calibratedfromaveragepriceinthatmarket,adjustedby retailer s markup (15%), distributor s markup (25%) and manufacturer s gross margin (30%), i.e., w m = p m M m :marketsize,calibratedfromtotalnumberofhouseholdh m, with assumption that an average household spend X dollars per quarter in buying potato chips, where X is calculated from $24 spent by an average household in a year in potato chip consumption, adjusted, by quarters and market shares of large package sized chips, i.e., M m = H m 6 ShareLarge m / p m Cost of line length maintenance: assume a per-capita cost, i.e., C m (n, l)=h m c (n, l). In the estimation, I tried two specifications of the per-capita cost: linear and kink. In the linear specification, c (n, l)=c n. Inthekinkspecification,c (n, l)=(c 1 + c 2 1(n>l)) n F m :distributionofmeanutility, assume normality, with mean and variance calibrated by the empirical distribution of { jmt } j,t The only parameters to estimate in the flow profit is the cost parameter {c 1,c 2 } Supply Side - Dynamics Firm s dynamic problem is described as V n,m (µ t, t,l t )= n,m (µ t, t,l t )+ E m (V m (µ t+1, t+1,l t+1 ) µ t, t,l t,n) V m (µ,, l) =E max n (V n,m (µ,, l)+ n ) The unspecified parameters are initial belief (µ 1,m, 1,m), theevolutionrate,m as well as the scale of random fixed cost. All parameters are identified as shown from below, but I still impose the following cross-market restrictions to simplify the calculation.

21 Li: Product Offerings and Product Line Length Dynamics 21 1m: initialpriorprecisionisassumedtobeproportionaltotheprecisionofsignal. This is justified by stationary assumptions in the learning process. For markets with a more precise signal, the learning speed is expected to be fast. However, this is only valid if the belief precision is the same. I equalize the learning speed across all markets by assuming that the prior belief is proportional to signal precision, i.e., 1m = k h m, where h m = 1 # be the average precision. P t h mt,m: evolutionrateofpreferenceheterogeneity.fromstationaryassumption,,m = k (k + 1) h m after combining stationarity and (5) 1 1m = 1 1m + h m +,m µ 1m : initial prior mean, integrated from calibrated normal distribution, with mean and 20 variance estimated from {apple mt } t So the dynamic parameters to identify is {k, } 4.4. Identification This section briefly shows the identification of of supply side parameters without imposing any cross-market restriction, i.e., market-specific parameters are separately identified. In the current version, we assume that initial prior mean µ 1 is known (and integrated out in the estimation). However, the identification does not rely on this assumption. A stronger identification result without knowing prior mean is described in Appendix??. In our data, we can observe actual line length decisions, signal values and precisions, as well as prior mean {n t,apple t,h t,µ 1 } 20 Note that initial prior mean is also identifiable as is shown in Appendix??. However,Ifollowtheconventionof learning literature to integrate out this value.

22 22 Li: Product Offerings and Product Line Length Dynamics Based on these information, I will show the non-parametric identification of preference evolution rate, initial belief precision, and line length maintenance cost, and scale of fixed cost for launching 21 {, 1,c} Preference evolution rate and prior precision 1 Signal evolution rate measures how fast evolves over time. Intuitively, t can be estimated from demand, and this rate is identified by the demand side estimation ˆ t. Equivalently, the signal value apple t is calculated based on demand estimation, and is identified from Var (apple t+1 apple t ),becauseapple t+1 deviates from apple t by three reasons: signal error in period t, signalerrorinperiodt +1,and the deviation of t+1 from 1. The precision of the first two errors are known, so the rate of evolution is identified. Initial precision is identified by stationary assumptions that the precision belief does not explode. From the following equation 1 1 = h + we can pin down 1. The intuition is that when making line length decisions, Company A cannot rely too much on market signal, because signal is noisy, measured by h. Shecan neither rely too much on her prior belief, because evolves over time, as is measured by. The optimal balancing between these two sources pin down the belief precision in the stationary level. 21 Afinalsupplysideparameter is a nuisance parameter which is not non-parametrically identified. But since we have impose functional form assumption on the value function, including the estimation of this parameter will improve the model fit a lot.

23 Li: Product Offerings and Product Line Length Dynamics Cost of line length maintenance c From the last part, I have shown identification of 1 and. With the knowledge of µ 1, I can calculate the whole process of belief process {µ t, t}, and the state variable is known. The cost parameter is identified by the standard argument of Conditional Choice Probability E (n t µ t, t,l t ) proposed by Magnac and Thesmar (2002). Intuitively, fixing the belief precision, when the cost is low, optimal line length is more responsive to changes in belief mean, as is shown in Figure 2. The cost is identified by regressing actual line length n t on the belief mean µ t,controllingfor t. 5. Results This section shows the model estimates and various simulation results based on estimates obtained Demand Estimation In the demand side, I estimate a Nested Logit model specified in (6). I report the average estimates of preference heterogeneity by imposing mt = in this part, but in the supply side, I allow preference heterogeneity to vary by market and time. Table 3 reports the estimation result from the demand side. Column (1) disregards the existence of endogeneity problem and directly estimate the equation by OLS. Column (2) overcome this problem by applying three sets of instruments as described before. By comparing column (1) and column (2), I find that instrumental variables work well as expected. Both preference heterogeneity and price elasticity will be under-estimated without controlling for endogeneity, and the characteristic vectors only become significant in 2SLS specification. Note that the first two columns in Table 3 use characteristic vectors (flavor fixed effects, cut types, fat contents) to describe one product. In column (3), I replace with a more precise control, that is product fixed effects. The estimates for price elasticity does not change too much (-2.38 in Column 3 compared to in Column 2), but the estimates for preference

24 24 Li: Product Offerings and Product Line Length Dynamics heterogeneity almost doubled. As mentioned, the characteristics vectors cannot capture consumer s preference completely, so I take the product fixed effects estimates as benchmark case, where the preference heterogeneity is estimated to be 0.41 (with a standard error of 0.02, Column 3, Table 3). In Column (4), I allow price elasticity to vary by demographics. I find that price is less elastic in markets with a richer population measured by median income, or older population measured by median age, which coincides with most previous findings. The main parameter of interest is the preference heterogeneity in this paper, so in Table 4, I explore the source of preference heterogeneity by interacting with different observables. Column (1) copies the Column (3) from Table 3 to serve as a benchmark case. In Column (2), I estimate the same model but in the data for small-package-sized potato chips. I find that preference is more heterogenous (0.67 in Column 2 compared to 0.41 in Column 1) and price is more elastic (2.74 in Column 2 compared to 2.38 in Column 1). This extra heterogeneity in preference may come from the fact that consumers are more willingness to try new flavors when buying small sized potato chips. There are two sources of preference heterogeneity estimated in this paper: one is the preference heterogeneity between consumers, and the other is the preference heterogeneity within consumer but in different purchase occasions. I cannot separately identify these two sources with only market level data, but I believe that the second source is more significant in markets for small packaged potato chips. The difference in heterogeneity estimation supports the existence of heterogeneity within consumers in different purchase occasions, and this is related to variety seeking behavior. Another source of preference heterogeneity comes from population diversity. In Column (3)-(7) of Table 4, I explore to what extent population diversity can explain preference heterogeneity. The results are robust to a series of diversity measures. In Column (3), I uses interquartile of income distribution to measure the population diversity. I find that in markets

25 Li: Product Offerings and Product Line Length Dynamics 25 with a more disperse income distribution, the preference heterogeneity is significantly higher. To quantify this estimates, I take out two markets with minimum (0.04) and maximum (0.10) diversity measure, and the implied difference in heterogeneity is 0.09, 22 or 20% of the baseline heterogeneity of In column (4), the diversity measure is the dispersion of age distribution, and the implied difference in heterogeneity is 0.07, or 17% of baseline value. Other than the above two dispersions, the preference heterogeneity is also explained by diversity of ethnic groups. In Column (5), I use Asian population ratio in that market and find that in markets with a 10% higher Asian population ratio, the preference is more heterogenous by a measure of out of baseline value of In Column (6), I use Hispanic population ratio, and the interaction term is not significant. This is because there is a wide range of Hispanic population measure from 0 to 53%. If the true functional form is non-linear, using linear function form to approximate may not get significant result. Instead, Idiscretizethemeasureusingadummyforabovemedian,andtheestimatesisreportedin Column (7). In markets with above-median Hispanic population ratio, the preference is more heterogenous by a measure of 0.12 out of baseline value of Supply Estimation Ipluginthecoefficientsandestimatethesupplysidebymaximumlikelihood.Solvingthe original problem with brute force is difficult, because calculating the line share s m (n, ), the flow payoff n,m (µ,, l) and the state transition f (µ t+1, t+1 µ t, t,n) all requires simulation. However, I can employ numerical methods to further simplify the calculations. For s m (n, ), Iusepowerpolynomialstoapproximate.Becauseitdoesnotcontainany parameters to estimate, the approximation needs to be calculated only once. The reason for using polynomials is the ease for preserving monotonicity and super-modularity in the 22 This is calculated by ( ) 1.48

26 26 Li: Product Offerings and Product Line Length Dynamics approximated function, which is the key for identification. 23 To calculate n,m (µ,, l), I use quadrature to calculate the expectation with respect to although is distributed in truncated normal instead of normal. When the precision is quite high, and the mean is far from the boundary, the truncated normal can be approximated by standard normal because the probability of lying outside the boundary is low. In terms of state transition probability, because the line length stays at a high level (for the large package size, the line length ranges from 8 to 30, with an average of 22), and the precision does not explode because of the time-varying, Isimplyassumethestatetransitionprobabilitydoesnotdependonactionn, which relieves the computation burden. Finally, I use Chebyshev polynomials to approximate the value function and estimate the single-agent dynamic game with unobservable and timevarying state variables. 24 Table 5 reports the estimation results. I estimate the model in two specifications. In the first specification, I assume the maintenance cost per capita (1M household) is linear in the line length, whereas in the second specification, the marginal cost is higher when manufactures are expanding their lines. In the first specification, the marginal cost of expanding a line by length one is $3,560 per million of household. For an average line length of 22, the total (variable) cost of maintaining a line length in an average-size city with 2.63 million household is approximately $0.2 million. 25 As a comparison, the industrial in an averaged-sized city with average line length selling at average price is $8.96 million, 26 the product line related cost constitutes about 2% of total revenue. 23 IuseCVXtogettheapproximation,whichisaregularizedoptimizationpackage(Grantetal.2008).SeeAppendix?? for details. 24 The recent development of MPEC (Dubé et al. 2013) is also applicable to this model. 25 $3, = $0.2M, all numbers are taken from Table $ M = $8.96M, all numbers are taken from Table 1.