Extensive Margin Adjustment of Multi-product Firms and Risk Diversification

Transcription

1 Extensive Margin Adjustment of Multi-product Firms and Risk Diversification Carlos Carvalho, Gee Hee Hong, Jing Zhou February 15, 2017 PRELIMINARY, PLEASE DO NOT QUOTE Abstract Product scope adjustment is a key feature of multi-product firms. In this paper, we take a novel perspective to study product scope adjustment through the lens of asset pricing. Using a unique panel scanner data set containing detailed information on products, matched with the financial information of their manufacturers, we find that firms with higher product turnover have lower financial risks and lower risk premia. We propose a stylized model with time-dependent, Calvo-type, product turnover rate to highlight the risk absorption channel of product scope adjustment: in response to an economy-wide shock, a firm s flexibility in product scope adjustment helps to dampen the shock, thereby, eliminating volatility in firm s asset price and lowering excess returns. JEL Codes: G12, L11, L21, L25, L60 Key Words: Product scope, multi-product firms, risk diversification, firm dynamics We are grateful to Ricardo Reis, Michael Weber, Yang Jiao and seminar participants at Columbia and the IMF for most helpful comments. We would also like to thank Ms. Sue Hutchinson and GS1 for providing the concordance table between UPC and manufacturers and Sung Ryong Kim, Dingding Xu for the early stage of data construction. All results are calculated based on data from The Nielsen Company (US), LLC and provided by the Marketing Data Center at The University of Chicago Booth School of Business. The views expressed in the paper are those of the author(s) and do not necessarily represent the views of the IMF, its Executive Board, or IMF management. Carvalho: PUC-Rio, cvianac@econ.puc-rio.br Hong: International Monetary Fund, ghong@imf.org Zhou: Columbia University, j.zhou@columbia.edu. 1

2 1 Introduction Recent studies document that U.S. manufacturing firms are predominantly multiproduct firms ( Broda and Weinstein (2010) and Bernard, Redding and Schott (2010)). These studies commonly highlight the importance of extensive margin adjustment via product creation and destruction as an important resource reallocation mechanism of multi-product firms. As such, multi-product firms are shown to improve their efficiency and enhance their productivity by shifting resources to a more productive use via introducing new products into the market while destroying some of the existing products. These studies also emphasize that among multi-product firms, there exists a substantial heterogeneity in firm s product turnover rate. That is, some firms adjust their product scopes more flexibly than others. Guided by these empirical findings, in this paper, we study multi-product firm s product scope adjustment from a novel perspective by linking the extent to which a firm flexibly adjusts its product scope in response to a shock with market-based financial risk from an asset pricing point of view. Do multi-product firms with higher product turnover exhibit lower financial risk? If so, why? Based on a rich scanner data set that covers products sold in many geographic locations in the U.S., we measure firm-specific extensive margin adjustment by tracing the number of products that are newly introduced to the market and also disappeared from the market at each period. Following the literature, such as, Broda and Weinstein (2010), we calculate product turnover rate as a measure of firm-specific extensive margin adjustment which is the sum of the values created by newly introduced items (creation rate) and the values destroyed by disappearing items (destruction rate). With the availability of manufacturer information in the scanner data set, we link these firm-level measures of the extensive margin adjustment to the corresponding firmlevel financial variables available from the CRSP database. In particular, we construct market-based risk measures defined as each firm s excess asset returns and volatility of firm s asset returns as our key variables to assess each firm s financial riskiness. We find that a higher product turnover rate eliminates risk. That is, firms that exhibit higher flexibility in product switching, reflected by the higher product turnover rate, show lower excess asset returns and lower volatility of asset returns. The result is robust when controlling for the standard financial indicators of firms, other important characteristics associated with product scope, such as R&D expenditure, and also industry-specific characteristics. Specifically, we find that one standard deviation increase (about 20 %) in a firm s product turnover rate leads to a decline of a 2 percentage point excess returns. 2

3 To provide a theoretical underpinning of the relationship between the extensive margin adjustment and asset pricing, we propose a model which incorporates timedependent, Calvo-type, firm-specific product turn over rate. To clarify, the main difference between the conventional Calvo-pricing model and ours is that in our model, Calvo parameter governs an exogenous probability of changing product scope instead of price in each period. We allow the optimal product scope to be determined endogenously, while firms are able to adjust the product scope only at an exogenously determined frequency. One important feature in determining the optimal product scope is the cannlibalization effects introduced in (Hottman, Redding and Weinstein (forthcoming)). The cannibalization effects confirm that there is an upper bound to the optimal size of a firm s product scope, as an increase in the number of goods after a certain point begins to erode the market share of the firm. Our model is able to generate a positive correlation between the degree of product scope adjustment and the excess return and volatility of asset returns in response to aggregate shocks, which are consistent with our empirical findings. That is, the excess return rate is higher when the firm is more rigid in product scope adjustment, represented by a higher value of the parameter. It is worth nothing that the angle that we take in this study is novel compared to previous studies on multi-product firm behavior which mainly studies the price-setting behaviors. These studies assume the number of products per firm to be static over time and focus instead on the economies of scope in menu costs for price adjustment patterns (for instance, Midrigan (2011), Bhattarai and Schoenle (2014)). In contrast, we are interested in the dynamic adjustment of firm s product scope over time, while assuming that the flexibility of product scope adjustment is a firm-specific feature. A firm-specific product scope adjustment (or turn over rate) is analogous to a sector-specific frequency of price adjustment in Carvalho (2006) or a firm-specific frequency of price adjustment as in Gorodnichenko and Weber (2016). There are empirical evidence that supports firm-specific extensive margin adjustment. For instance, Bernard, Redding and Schott (2010) documents that there exists a substantial cross-sectional variation in the flexibility of product scope adjustment in the U.S. manufacturing firms. Our paper contributes to several important strands of literature. First, it contributes to the studies on the firm s ability to diversify risk and the determinants of firm s survival and performance. From the classic theory of economics and finance to the recent development, the ability of firms to diversify risk has always been the essence of firm s performance and survival (Markowitz (1952), Sharpe (1964), for instance). Facing risk, firm adjusts leverage, engages or withdraws investment to achieve the optimal level of return and risk. However, as a firm constructs the optimal portfolio 3

4 by choosing assets with different riskiness and sensitivity to the market (i.e, capital asset-pricing model), it can also choose the optimal portfolio of its products, given its exposure of the economic-wide and product-specific shocks. This ability to exercise the extensive margin adjustment is a potential channel through which firm can manage risk and improve its performance in financial market. Second, our study is related to the growing work on multi-product firms. In conventional workhorse macroeconomic models, a firm is often assumed to be a single-product producer. As a result, an extensive margin adjustment of a firm is equivalent to as a firm s entry and exit. Existing theories of industry dynamics in other fields have also shared the view in that they model endogenous selection of products as entry and exit of a single-product producer (for instance, Jovanovic (1982), Hopenhayn (1992), Ericson and Pakes (1995), Melitz (2003), Bernard et al. (2007) and Bilbiie, Ghironi and Melitz (2012)). While still scant, there exists a growing literature that attempts to understand the price adjustment behaviors of multi-product firms as in Midrigan (2011), Bhattarai and Schoenle (2014), Pasten and Schoenle (2016). These work highlight the importance of the multi-product firm s pricing and the potential difference in the mechanism of pricing from that of a single-product firm. Here, studies have resorted to the role of rational inattention and economy of scale in price adjustments to explain the nature of multi-product firms. Empirically, some important studies have studied the product scope adjustment of multi-product firms (Bernard, Redding and Schott (2010) and Broda and Weinstein (2010)) and show that the relative sales and term length of a product compared to its peers plays a role in its turnover. Third, the idea of connecting the variety of goods with risk diversification is closely related to the rich literature which connects endogenous growth theory with variety of goods via technological progress. In the seminal work by Romer (1990) and Grossman and Helpman (1991), technological progress determines the firm s choice of the variety of inputs used for its production. The firm s incentive to use more variety of inputs, in turn, increases the average level of productivity. In a more recent work by Koren and Tenreyro (2013), the input-variety is further associated with diversification of varietyspecific risks in the mechanism referred to as the technological diversification. In this work, the level of economic development or technological progress endogenously determines the input variety of productions (both at a firm level and a country level), which in turn determines (decreases) the volatility (at the firm level and at the aggregate level). Finally, this paper contributes to the recently burgeoning literature that connect findings from micro-level price data set with asset pricing. For instance, Gorodnichenko and Weber (2016) and Weber (2014, memo) show that the price rigidity, that is the ability 4

5 of firm s to adjust to shocks through prices is closely related to the firm s risk-taking behavior and other financial characteristics that determine the asset prices of the firm. Relatedly, Herskovic (2015) shows that the changes in production network transmit risk and such transmission of risk is reflected in asset valuations. The remainder of the paper is structured as follows. Section 2 provides the intuition for the relationship between extensive margin adjustment and asset pricing using a simple CCAPM framework. Section 3 outlines the data description and the variables used for the ensuing sections. Section 4 reports the main empirical findings. Section 5 lays out the model to rationalie the empirical findings. Section 6 concludes. 2 The Relationship between Extensive Margin Adjustment and Asset Price Under C-CAPM Before diving into the empirical examination of how an extensive margin adjustment of a multi-product firm explains its asset valuations and market-based riskiness, we provide an intuition of the risk-absorption mechanism benefiting from classic consumption- CAPM framework. In the consumption-capm, an asset is priced using a subjective discount factor from a household s utility maximization problem. For instance, a household maximizes its expected life-time utility subject to an inter-temporal budget constraint defined by production income, consumption expenditure and return on investment on a group of assets 1,..., J as follows: [ max E C t,b β t ln C t t+1 i t=1 s.t.p t C t = P t Y t + J j=1 B j J t (Qj t + Dj t ) B j t+1 Qj t j=1 By definition, the return rate of each asset j can be written as R j t+1 = Qj t+1 + Dj t+1 Q j t and the pricing kernel is the that the expected return of any asset j is one. ) 1 = E t (R j t+1 M t+1, j where M t+1 = βu (C t+1 )/u (C t ) is the subjective discount factor. Therefore, excess return of each asset is negatively correlated with the covariance between the return rate 5

6 of asset j and the subjective discount factor which is the inverse of the growth rate of consumption expenditure under logarithm utility function. E t R j t+1 RF t+1 = RF t+1 (R Cov j t+1, M t+1 ( ) = Rt+1 F βcov R j t+1, C tp t /C t+1 P t+1 To see the role of extensive margin adjustment in asset pricing, assume a negative shock hits the economy. This shifts firm s profit curve to the left. As a result, firm should drop the varieties N to the new optimal number Ñ. However, not every firm can readjust its new optimal product scope. First, consider a firm with no extensive margin adjustment rigidity (probability of not able to change product scope: λ = 0 type). This firm will execute product turnover and will be able to maintain a high profit. On the contrary, the rigid firm (λ = 1 type) can not adjust its product scope at all. As a result, this firm with higher rigidity of extensive margin adjustment will suffer a loss in its profit. First, consider how such a shock leads to a change in a firm s return rate, the first term of the covariance. For a flexible firm (λ = 0 type), the return rate is unaffected by the external shock, as the product turnover which is reset to be at the optimal level absorbs and offsets the negative impact of the shock. As a result, the covariance term of λ = 0 type firms is zero, resulting in the excess return to be zero. On the contrary, consider a rigid firm (λ = 1 type), unable to reset its product scope to the optimal level. As a result, the firm experiences a large drop in its return rate. Combined with the inverse consumption growth due to the negative shock in the covariance term, a negative shock to this firm leads to an increase in excess return. Intuitively, excess return essentially compensates investors for risk, therefore, the higher the risk, the higher the excess return. With respect to extensive margin adjustment, more rigid firms find themselves more difficult in timely changing the product scope to cope with economy fluctuation, which results in higher risk. For the investors to still be willing to take the asset, its return has to be high enough to offset the excess risk bearing. In the following sections, we will directly test this negative relationship between excess return and extensive margin adjustment flexibility indicated by the risk compensation channel. Based on CCAMP, our prior will be: with other characteristics well controlled, the firm changes its product scope more often (indicating more flexibility at extensive margin) is associated with lower excess return on stock market; also, its risk, measured by the covariance between return rate and aggregate consumption growth is less negative. ) 6

7 π postshock π λ = 0 preshock Ñ N N π λ = 1 3 Data Description This section explains the data set and the key variables used to conduct our main empirical analysis. We pool together three different data sets from different sources - AC Nielsen Homescan Data, Bloomberg and Center for Research in Security Prices (CRSP). The three data sets are merged by the manufacturer identifier. First, the AC Nielsen Homescan data, also used in numerous studies in the literature including Broda and Weinstein (2010), provides a detailed information about the products consumed at retail grocery stores, as well as the household characteristics of those who consume these products. In particular, the Nielsen Homescan data comprises a representative panel of households that continually provides information about their purchases from these retail grocery stores at daily frequency. For each shopping trip, information on household s consumptions from these retailer stores are recorded and are then reported to AC Nielsen who identifies each household consumption basket by the Universal Product Code (UPC). The purchasing records by each household reported to AC Nielsen contain information about the transaction prices of products, the volumes of purchases and the retailer from which each household purchases. Collected annually from 2004 to 2014, Nielsen samples about 40,000 to 60,000 households over 20,000 zipcodes in the United States. To construct a nationally representative sample from these households, AC Nielsen further compares age, income and other demographic information of the households to the census data before applying projec- 7

8 tion factors to each household. Product coverage-wise, the Homescan data set covers around 700,000 UPCs every quarter and 3.2 million UPCs in total, and the expenditure logged in Homescan constitutes about one third of the total consumer expenditure. For our purposes, matching the products with manufacturer information is crucial. We identify manufacturers of each UPC using the GS1 Data Hub. 1. After collecting the manufacturer information for each product, we construct our key variables aggregated up to a firm-level. That is, we group product-level observations by manufacturers. For instance, all the products belonging to the same manufacturer, for instance, Johnson and Johnson, are grouped together. In turn, we construct the measures of product creation and destruction, following closely to the definition used in Broda and Weinstein (2010). Specifically, we count the number of varieties of each firm at annual level 2 and calculate extensive margin adjustment using the introduction and destruction rates defined as follows. ( ) # introduced UPC t creation rate t = # UPC t turnover rate t = ( # destroyed UPCt destruction rate t = # UPC t 1 ( weighted by sale ) weighted by sale # destroyed UPC t + # introduced UPC t # destroyed UPC t + # introduced UPC t + # maintained UPC weighted by sale In addition to the AC Nielsen Homescan data, we obtain firm-level financial variables from Bloomberg and CRISP. This is to match firm-level extensive margin adjustment measures constructed from the Homescan data with firm-level financial variables. In particular, we extract stock return information from CRSP and firm-specific financial variables from Bloomberg. Two key measures of market-based financial variables, as mentioned before, are excess stock returns and volatility of asset returns. These measures are mean to capture the level of risk that exceeds the risk of a benchmark asset or portfolio. Excess asset returns, return rate it are calculated at annual frequency, with r it representing the monthly excess return for asset i, month t = 1, 2,..., 12, by return rate it = (1 + r 1 )(1 + r 2 )...(1 + r 12 ) 1 Financial variables that we look at are the standards used in the literature and are from the CRSP data. These include leverage ratio, market value of the firm, bookto-market ratio, market beta, cash flow to name a few. After carefully matching the 1 GS1 US is the provider of UPC for firms. It serves more than 2 million businesses in 25 industries in the United States. It provides a company with up to 10 barcodes for a $250 initial membership fee and a $50 annual fee. 2 We use annual level to avoid the possible seasonal pattern in product turnover. ) 8

9 producers available in the scanner data with the firms in the CRSP, we have a sample of 203 firms. The summary statistics of main variables used are shown in Table 4. Since listed firm is a portion of the whole sample of Nielsen data, the representativeness of the sample is needed to demonstrate the applicability of our empirical analysis. To this end, we compare the extensive margin adjustment of the listed firm subsample versus the whole sample. As shown in Figure 1, listed firms adjust its product scope in a quite similar way to the whole sample in both introduction and destruction during the sample period. Also, from eyeballing the patterns, the finding that creation rates being cyclical and destruction rates to be stable over the years is consistent with Broda and Weinstein (2010). Listed Firm Figure 1: Extensive Margin Adjustment Whole Sample CreationRate DestructionRate CreationRate DestructionRate panel_year panel_year 4 Empirical Findings In this section, we assess to what degree a firm s extensive margin adjustment can explain its risk diversification, measured by its excess return, defined as the difference between its return and risk-free return, and volatility of asset returns. In the first two subsections, we present some stylized facts about extensive margin adjustment behaviors by the firms observed in our dataset. The rest of the section will focus on the empirical investigations on the relationship between extensive margin adjustment and firm s stock excess return and volatility of asset returns. 4.1 Extensive Margin Adjustment Rate is Sticky Here, we explore the cross-sectional aspect of product turn over observed in the data set. In particular, we check if a firm s extensive margin adjustment is sticky in the sense that a product turn over rate can be a firm-specific feature. Also, we check if there 9

10 is a significant cross-sectional variation across firms in terms of flexibility (or stickiness) of firm s extensive margin adjustment. In the existing literature, studies focused on the time-series aspect of firm s product turnover. For instance, Broda and Weinstein (2010) finds the strong pro-cyclicality of product turnover rate. In general, shocks hitting the firms in each period are either aggregate shocks or idiosyncratic shocks. The validity of sticky product turn over rate implies that the aggregate shock plays a key role in the evolution of firm s product turnover, and that the difference in the change in product turnover mainly comes from the interaction between the firm s stable characteristics and the aggregate shock. That said, the idiosyncratic shocks are well present in the reality, however, it might not the be the driving force in firm s extensive margin adjustment. On the contrary, if the data shows absence of stickiness in relative product turnover rate, one may expect that the firm s time-vary idiosyncratic shock might shuffling the ranks of the firms product turnover ability and offset the effect of aggregate shocks. To formally test the stickiness in our data, we divide the firms into two groups in each year based on product turnover rates including introduction rate, destruction rate and overall turnover. To control for the differences of product turnover rates in different industries, we constrain the grouping within industry. Based on this grouping, we calculate the transition matrix as the probability of firms staying or switching. Table 1 presents the results. The diagonal terms represent the probability of staying in the same state over time, while the off-diagonal terms represent the switching probability. Evident from the pictures, we find that the stayers dominate the transition, as about 70% low product turnover firms stay in low bin and over 90% of higher product turnover firms persistently conduct more product turnover than the rest. Overall, it supports the importance of a stable distribution of the firm ranking based on extensive margin and the leading role of aggregate shock in driving firm s product turnover. 4.2 Comparison between High vs Low Product Turnover Group The previous subsection provides evidence that an individual firm s turn over rate is indeed sticky, indicating the relative importance of aggregate shocks to idiosyncratic shocks in product scope adjustment. However, there exists a potential concern for endogeneity as firms with higher (or lower) turn over rates may exhibit certain firm characteristics or serve households with certain features that enable them to deal with aggregate shocks better. In this subsection, we check the potential endogeneity issue by comparing firm and consumer characteristics depending on product turnover rates. The concerns for endogeneity issue could arise for several reasons. For instance, one 10

11 could be concerned that firms with higher product turn over have healthier balance sheet comparing to their low turnover counterparts which enables them to cope better with aggregate shocks using extensive margin. Alternatively, it could also come from that firms from a high turnover bin serve wealthier household whose demand is less sensitive to aggregate shock and that the robust sales prevent firms from disruption in product introduction and destruction. A third hypothesis would be that the reason that firms could be consistently active on extensive margin is the retailer that the firms channel their products through. For instance, some high-end retailers might have superior stock management and promotion strategies that offset the negative demand shocks for their associated goods providers, which eventually benefit the firms performance on introducing and destroying products. In order to distinguish the hypothesis, we compare the characteristics of the top and bottom groups based the last section in all the three aspects, i.e. firm, purchaser and retailer. The unique data from Nielsen Homescan on purchaser s demographics is of great help for this analysis. In each year, Nielsen asks the panelist detailed information such as income, household composition, race, family member s age, education, occupation and the availability of facilities in their residence etc. to provide background knowledge on the demand side. On the retailer side, it is less easier to collect time-varying information as the available ones concentrating on the ones that are not easily quantifiable such as location, store type. However, based on the panelist s each shopping trip data, we track the retailer to which she went and calculate the an approximate of the retailer s total sales based on the total expenditure of the panelist. The sales information would be exceptionally useful to gauge the scale and quality of retailers. On the firm side, we make use of the balance sheet information from Bloomberg which is conventional in the literature. Table 2 presents the two-group comparison. In the first panel, we list the results for firm characteristics comparison including size, book-to-market ratio, beta, leverage, cash flow, stock turnover and spread. The results consistently show that the high product turnover group is not significantly different from the low counter party in all the key financial aspects. In the second panel, we move to the purchaser characteristics, and we present the household income, size, presence of child, and detailed information on household head. As Nielsen provide multiple choice question for several variables to the panelists, we summarize to dummy variables to facilitate the comparison. For instance, household income is divided into 10 ranges from which panelists can choose from while we take the median (which is also consistent with the national median household income level) to construct the income lower than median variable; in a similar vein, we summarize the education of household head to higher than high 11

12 school based on education achievement categories from grade school to post-grad school. The p-values show that the two groups of firms are remarkable similar in their demand side. For instance, the income level is very close and the household size is as close as to 0.01 standard deviation. In the last, we compare the sales of the retailers based on household shopping data, and it also shows there is no significant difference between the top and bottom groups. Overall, the analysis provide strong evidences that the high product turnover firms are not intrinsically different from the low firms, in all the financial health, demand and retailer sides. 4.3 Portfolio Analysis In the last two subsections, we provide empirical evidence that a firm s product turnover rate is quite persistent over time and that product turnover rate is not driven by certain balance sheet health, demand or retailer characteristics. In this section, we switch to the core of our analysis which is to assess the empirical relationship between extensive margin adjustment and market-based risk. Using the asset return constructed by CAPM, Fama-French 3-factor and 5-factor models, we compare if there is a significant difference in asset returns depending on firm s product turnover rates. To conduct this exercise, we first rank the firms according to their turnover rates, separately for introduction and destruction rate. Then, based on the ranking, we group firms into three portfolios from the least flexible on extensive margin to the most flexible. After determining the portfolio composition, we construct the market price for each portfolio as the weighted average of its underlying stocks prices, weighted by individual stock s market value.table 5 reports the results. It shows average return rates calculated by each of the three models for the bottom (firms with bottom third turnover rates) and the top (firms with top third turnover rates) bins. The last two columns report the differences in return rates between the bottom and the top bins and the statistical significances (p-values) of the differences. First, we find that there is a significant difference in return rates between firms with high introduction rates and low introduction rates. Firms with higher introduction rates has a statistically significantly lower returns, therefore, lower excess returns, compared to those with lower introduction rates. This holds true regardless of how the return rate for each portfolio is calculated. Second, we find that the difference disappears when firms are categorized based on destruction rates. There does not exist a significant difference in return rates across bins with different destruction rates. The different results for two dimensions of product turnover rates are consistent with the lack of 12

13 dynamics observed for destruction rates in Figure 1. Also, it is also consistent with Broda and Weinstein (2010) who finds that product turn over rate is largely driven by product creation (introduction) rate, not by product destruction rate. 4.4 Extensive Margin Adjustment and Risk Now, we turn to a firm-level analysis to explore a richer connection between firm s ability to adjust its product scope and its market-based financial riskiness. Specially, we set the baseline regressions as (1). In a panel setting, the key variables of interest here are the variables related to the extensive margin adjustment, such as the introduction rate, destruction rate and turnover rate. In addition to our key variables, we also control for a set of standard financial indicators of firms provided by Bloomberg. These variables include leverage, book-to-market ratio, price-to-cost margin, cash flow, market beta, spread, gross margin and industry portfolio rate of return and book-to-market ratio. return rate it = β 1 introduction rate it + β 2 destruction rate it + X it + ɛ it (1) Table 6 presents our first set of results. Consistent with the findings in the previous subsection, even in the firm-level analysis, we find that using introduction rates and destruction rates have different empirical relationships with stock return rates. Specifically, we find that a higher introduction rate is significantly negatively correlated with asset excess returns, while the effect is insignificant for destruction rate. Column (1) presents the benchmark regression with year fixed effect which is meant to control for some aggregate component of the shocks. When controlling for financial variables that are believed to affect the excess returns, the coefficient on the creation rate is negative and significant. This implies that those firms with higher extensive margin adjustment show less excess risks compared to the risk taken by a benchmark portfolio. It shows that one standard deviation decrease in product introduction rate (about 16%) leads to about a 1.6 percentage point increase in excess return. On the other hand, we do not find any meaningful correlation between excess return and firm s destruction rate. This finding is consistent with the empirical finding documented by Broda and Weinstein (2010), who shows the lack of cyclical pattern of destruction rate. The ensuing columns report the results with additional controls that have been implemented. These robustness checks include controlling for industry-specific characteristics (column (2)), R&D expenditure (column (3)) and total number of UPCs (column (4)). Throughout, negative and significant relationship between the excess asset return and the creation rate can be found in all of these alternative specifications. It is worth noting that in Column (4), the coefficient on the total number of UPCs also show negative and significant, which could imply that not only the change of product 13

14 scope but also the magnitude of product scope play a role in the risk diversification mechanism. In column (5), instead of creation rate, we use the turnover rate as the main independent variable to capture a firm s ability of extensive margin adjustment. In this specification, we also find that the firms with high turn over ratios exhibit lower excess asset returns. In Table 7, we use the second measure of market-based financial riskiness of firms, which is the volatility of asset returns. Controlling for a set of firm-specific financial variables, we also find that firms with higher creation and turnover rate show a significantly lower volatility of asset returns. In particular, a decline of creation rate by one standard deviation leads to 0.16 percentage point decline in volatility of firm s asset returns. Compared with the results in Table 6, we find qualitatively similar result. Here again, we also find that firm s destruction rate is not meaningfully related to firm s volatility of asset returns. Controlling for various financial variables that could affect asset volatility, the coefficient on the creation rate is consistently negative and significant. The robustness check carried out are analogous to the previous exercise, as industry portfolio and R&D expenditure in Column (2) and (3), respectively. Column (4) shows that again the importance of the total number of products that a firm produces on top of the product creation rate. Finally, column (5) shows that higher products turnover rate, which uses the total number of UPCs over time, is related to lower asset volatility and that the correlation is similar to introduction rate in magnitude. Another route to investigate the relationship between extensive margin adjustment and asset return can be drawn directly from the C-CAPM framework. Since in the previous section we established that the more rigid firms have lower correlation with inverse consumption expenditure growth due to the fact that the flexibility in product scope adjustment helps firms to absorb external balance, it would be natural to test whether this relationship is supported by the data. If yes, it would provide strong evidence to the risk channel via which product turnover affects the asset pricing side of the firm. Unlike the case of return rate which can be observed at any time point, the covariance requires sufficient long period of time to calculate, therefore we adopt the cross-sectional specification to see whether the firm with higher turnover rate on average shows a higher covariance with inverse consumption expenditure than its lower counterpart. Particularly, we employ the specification as (2), where the covariance is calculated using monthly return of the firm and the monthly private consumption from FRED. cov(r i, C C ) = β 1introduction rate i + β 2 destruction rate i + X i + ɛ i (2) Table 8 shows the on extensive margin adjustment and covariance. The benchmark 14

15 regression results are reported in the first column. Here, one standard deviation increase in the product introduction rate leads to an increase of asset volatility by about one standard deviation increase in covariance. Controlling for various financial variables that could affect asset volatility, the coefficient on the creation rate is consistently positive and significant. The robustness check carried out are analogous to the previous exercise, as R&D expenditure in Column (2). Column (3) shows that again the importance of the total number of products that a firm produces on top of the product creation rate. Finally, column (4) and (5) show that higher products turnover rate, which uses the total number of UPCs over time, is related to higher covariance and the magnitude is similar to introduction rate. 4.5 Robustness Check As mentioned before, pricing and the extensive margin adjustment observed in the scanner data are results of a complicated, multi-layered and joint decision-making process by the retailers and the manufacturers. Goldberg and Hellerstein (2012) and Hong and Li (forthcoming) highlight the importance of retailers in setting the prices in understanding pass-through of underlying shocks to retail prices. It is important to take into account the role of retailers in the decision-making of the extensive margin at the retail stores, as some of these decisions can be due to factors that are unrelated to the manufacturer s risk-diversification. For instance, loss-leading strategy and management of inventory are strategies often used in retail marketing to maximize the profit of the retailer. Similar concern applies to household as well. Bems and Di Giovanni (2014), Coibion, Gorodnichenko and Hong (2015) and Handbury (2013) show that evidences of non-homothetic preferences and the income-dependent product switching behavior of household. Therefore, the observed product turnover could be resulted from household s preference change, which is not directly related with manufacturer s ability of adjusting product scope. Although we have shown in the twogroup comparison that the high product turnover firms are not significantly different from those in the low groups in the aspect of demand and retailer, we would conduct additional checks using the granular firm data This robustness exercise is exclusively dedicated to control for the role of retailers and demand in explaining the product turnover behaviors. To isolate manufacturer s role in product turnover, we construct two sets of control variables. The first set of variables is the household-specific product creation and destruction rate, and the second set is the retailer-specific product creation and destruction rate. Household-specific creation and destruction ratios are constructed using 15

16 the household identifier available in the data set. To the extent that we can follow a household s consumption basket over the years at the UPC level, we can link the manufacturer of the UPC with the creation and destruction ratio. In other words, suppose a household i consumes goods Ci 1, C2 i, C3 i,...cn i, where 1, 2,...,N are UPCs. Manufacturers of UPCs can be identified and have their specific time-varying creation and destruction rate. Household, in turn, has time-varying construction and destruction rate based on the consumption basket. Retailer-specific creation and destruction ratios are constructed in the similar manner. Based on the portfolio of goods the retailer carries at time t, the goods can be matched to the manufacturer, which will have its own specific creation and destruction ratio. The following Table 10 reports the results using these sets of controls using asset return as the dependent variable. Column (1) introduces the set of retail-specific extensive margin measures as controls, Column (2) adds the set of household-specific extensive margin measures, and Column (3) contains both. Risk-diversification channel still survive with controlling for the potential effect from retailer and household, as both asset returns and volatility measures show significant negative signs, implying that the extensive margin adjustment reduces the firm s risk measures. Table 11 represents the similar robustness checks for the covariance between return rate and inverse consumption expenditure growth, and the possible turnover from retailer or household does not affect the pattern regarding the covariance, either. Another concern is that retailer or household might treat different firms differentially and that the retailer- or household-specific turnover rates can not serve as the proxy of retailer or household s role in the equilibrium turnover rates. To check to what extent retailers and households selectively treat firms, we construct annual turnover rates for each retailer-firm pair and zip code-firm pair 3 to conduct co-integration -type test. The idea is that, if retailers (households) differ significantly in add or drop products of the same firm, then retailer-(household-)firm specific turnover rates will be remarkably different from each other. Turnover Rate itj = α + Turnover Rate it, j + ɛ itj (3) To test whether the difference is significant, we construct the leave-one-out mean of the retailer-(household-)firm specific turnover rates using (3) for each firm and year to see its correlation with the very retailer (household). The test resembles the idea of cointegration of time series analysis - if there is no significant variation within 3 Ideally, we could construct household-firm pair turnover rates, but the sample will be too large to handle. Therefore, we assume that households within the same zip code share similar preference based on their location choice, e.g. income, occupation, etc. 16

17 the panel then each identity should cointegrate the panel average well. The results are listed in Table 9. We can observe that the coefficients for the leave-one-out mean is almost one, which strongly supports that different retailers (households) treat the products of a firm in a similar way and that the major contributor of variation shown in the turnover rates should be firm instead of retailer or household. 5 A Dynamic Model of Extensive Margin Adjustment In this section, we propose a model that explains the relationship between product scope adjustment and financial risk diversification measured as excess stock return and volatility. Before specifying in detail, we begin by specifying two main ingredients of the model. First, we introduce a time-dependent, Calvo-type, product turnover rate. That is, as a firm is able to adjust its price to the optimal level at an exogenous frequency in time-depdent pricing models, firms in our model are able to adjust their product scope to their optimal levels with an exogenous probability. The second ingredient of our model is the cannibalization effect introduced by Feenstra and Ma (2008), Eckel and Neery (2010) and more recently by Hottman, Redding and Weinstein (forthcoming). Conceptually, the cannibalization effect, measured as the partial elasticity of the sales of existing products with respect to the introduction of new products. If the partial elasticity is negative, the new product erodes the sales of existing products. What the cannibalization effect does in the model is that it enables the optimal product scope to be finite and to have an upper bound. With these key ingredients, our model shows that the channel through which a firm s product scope adjustment affects financial risk is the risk absorption associated with a firm s ability to adjust its scope of varieties to its optimal level. Specifically, if a firm is inhibited from maximizing its profits and from setting the product scope to its optimal level due to a high Calvo-parameter, the cost from this friction will be reflected in the return rate of the share on the firm. For the remaining part of the section, we will evaluate this channel by illustrating the model and the simulation results. 5.1 Household The economy is populated with households of GHH preference with consumption and labor. In each period, they work, consume and trade on the nominal bond market (B) and collect profit from all the firms ({D f kt }). The set-up of the optimal product scope in our model follows closely the spirit of Hottman, Redding and Weinstein (2016). The total consumption is constituted by 17

18 three layers of CES aggregator. The first layer is on a continuum of groups (k [0, 1) represented by the unit interval, the second layer (inter-firm) is on a unit interval of firms ( f [0, 1) 4, and the third layer (intra-firm) is on the current product scope u [0, N f kt of the firm. σ f, σ f, σ u represents the elascities across groups, firms and products, respectively. We assume that products the inter-firm elasticity σ f is smaller than intra-firm elasticity σ u ; that is, σ f σ u. While products introduced by the same firm are not perfect substitutes, we assume that products introduced by the same firm will be more substitutable than those introduced by different firms. In this way, product differentiation is intimately related to the cannibalization effects. As will be clearer in the ensuing section, such multi-layer consumption aggregator helps with product dynamics of a multi-product firm. In addition, this set-up enables us to introduce firm-specific flexibility in later section, which will be tied to asset returns which are defined at a firm level. Household s optimization problem can be specified as follows: they allocate consumption (to the level of product) and work subject to income from labor, bond holding and profit rebate of the firms. max t=0 β t[ ln C t χ L1+1/φ t 1 + φ 1 s.t. P t C t + B t+1 = W t L t + (1 + i t )B t + [ 1 C t = 0 σ k 1 σ C k kt [ 1 C kt = C C f kt = 5.2 Price of the Product σ f 1 σ f f kt 0 [ Nf kt 0 σ k σ dk k 1 σ f σ d f f 1 σu 1 σu σu Cu f kt du σu D f kt d f dk To concentrate on the friction on extensive margin, we adopt the fully flexible pricing framework. In each period, firms have linear production function using only labor with productivity Z t, and they are free to set price to the desired level. The optimal level of price is a constant markup over cost (Proposition 1). technology :Y u f kt = Z t L u f kt 4 Since the focus of the model is the product turnover, it abstracts away from firm entry and exit at this moment. 18

19 s.t. demand :C u f kt = C t P σ k t Proposition 1. The optimal price is P u f kt = σ f W t σ f 1 Z t P σ f σ k kt P σ u σ f f kt P σ u u f kt The optimal price looks familiar as with the absence of price rigidity firms always set price to a constant markup. However, since firms take the cannibalization effect, i.e. substitution within firm across products, into consideration, the markup is based on firm elasticity σ f instead of product elasticity σ u (P u f kt = σ u W t σ u 1 firm takes the effect of setting product s price on firm s price, P σ u σ f f kt choice variable rather than P σ u u f kt. Z t ). In other words, when P σ u u f kt becomes the 5.3 Firm s Decision on Optimal Product Scope: Without Friction In a similar logic as optimal price setting by equalizing margin cost to margin revenue, the optimal product scope setting is also resulted from equating margin cost and revenue of changing variety. On the marginal cost side, we follow Bergin and Corsetti (2008), assume fixed cost of maintaining the variety in each period: F units of effective labor. The period-by-period fixed cost can be viewed as fully depreciation of the capital associated with the product of the variety. On the margin revenue side, it involves more elements comparing to the cost due to the cannibalization effect. The total marginal revenue of changing product scope N is constituted by two parts: one is the productlevel consumption change due to the substitution effect between the products that stay and the introduced/destroyed product, and the other is the consumption specifically to the marginal product. The magnitudes the two effects are illustrated by Proposition 2. Proposition 2. Cannibalization effect product level: dc u f kt dn f kt N f kt C u f kt firm level: dc f kt dn f kt N f kt C f kt = σ f σ u 1 = σ u σ f σ u 1 Proposition 2 summarizes the two levels of cannibalization effect. On the product level, the substitution effect depends on the relative magnitude between the betweenproduct elasticity and between-firm elasticity. Two special cases are worth mentioning on the product-level cannibalization: firstly, when the consumers view the products within the firm in the same as the firms within groups, i.e. σ u = σ f, the product-level cannibalization effect is zero, which means that new product s consumption completely comes from the other firms sale. Secondly, if the products of the same firm are perfect substitutes, i.e. σ u, then cannibalization effect is 100% which means that the consumption change associated with the marginal product is completed offset by 19

20 the other products of the same firm. On the firm-level, cannibalization, under the assumption that substitution effect between products within firm is larger than that across firm (σ u > σ f ), the product-level cannibalization effect is negative while the firm-level one is positive ( love of variety ). Equating the marginal cost and revenue of product scope adjustment yields the optimal number of products under free adjustment. The optimal product scope is positively correlated with firm-level consumption, because higher demand leads to higher profit. However, it is negatively correlated with fixed cost of variety maintaining and between-product substitution effect, as these two increases the maginal cost and decreases the marginal revenue, respectively. N f kt = [ C σu 1 f kt σu F(σ u 1) 5.4 Firm s Decision on Optimal Product Scope: A Calvo-type Model As mentioned before, to specify the heterogeneous flexibility in product scope adjustment, we assume Calvo type of adjustment friction: firm in group k can adjust product scope with probability = 1 λ k in each period. Therefore, in each period, if firm can reset varieties, it will set Ñ f kt to maximize the expected profit (Λ is the Lagrange multiplier for household s budget constraint.) max Ñ f kt j=0 λ j k E t { Λt+j [ Ñf kt Λ t s.t.c u f kt+j = C t+j P σ k 0 (P u f kt+j MC t+j )C u f kt+j du FÑ f kt MC t+j } t+j Pσ f σ k kt+j P σ u σ f f kt+j P σ u u f kt+j Proposition 3. Optimal product scope with friction: [ σu σ f σu 1 (σ u 1)Ñf kt = j=0 λj k E t Λ t+j MC t+j C t+j P σ k kt+j [ j=0 λj k E t Λ t+j MC t+j F t+j Pσ f σ k MC σ f t+j Inheriting the Calvo-type model properties, the optimal product scope has a similar presentation to the optimal price level in canonical Calvo-pricing model: it is positively correlated with the discounted present value of the revenue if the product scope is not going to be allowed to changed forever, and it is negatively correlated with the discounted present value of the marginal cost if the product scope is permanently set. 5.5 Model Summary Combining the pieces, the competitive equilibrium of the model can be defined as 15 variables { P kt P t, P kt P t, Ñ kt, S kt, PVR kt, PVC kt, π t ( P t P t 1 ), C t, S t, L t, i t, W t P t, Λ t+1 Λ t } plus 2 exogenous processws {Z t, ν t } satisfying the following conditions. Although the aggregate 20