Endogeneity and Simultaneity in Competitive Pricing and Advertising: A Logit Demand Analysis*
In this article, we use four data sets to provide a benchmark study of the effects of accounting for endogeneity and simultaneity in estimating marketing‐mix effects in a logit demand framework. We compare the results obtained from accounting for endogeneity only to those from accounting for both endogeneity and simultaneity, and in the latter case we allow for more general models of firm behavior to examine the consequences of imposing assumptions about the behavior of firms. We find that accounting for both endogeneity and simultaneity not only affects the parameter estimates but also results in efficiency gains that affect the statistical significance of the estimates.
I. Introduction
The logit model is widely used by marketing researchers. At the household level, starting with the study by Guadagni and Little (1983), it has been used extensively to study the affect of marketing variables on household brand‐choice behavior. The logit specification has also been used to model the relationship between the aggregate market shares and the marketing activities of the various brands in the given product market (Allenby 1989). Some recent studies have shown that, under certain conditions, the substantive implications for the effects of marketing variables are similar whether one uses the model at either the aggregate (e.g., store/chain) or the disaggregate (i.e., household) level (Allenby and Rossi 1991; Gupta et al. 1996).
A methodological issue in estimating the effects of marketing activities on brand market shares using the logit model is that of endogeneity of firm choices (see Besanko, Gupta, and Jain [1998] and Sudhir [2001a] using aggregate data and Villas‐Boas and Winer [1999] using household data). The general issue of endogeneity of firm choices has been recognized in marketing (Chintagunta and Vilcassim 1992; Erickson 1992; Kadiyali, Vilcassim, and Chintagunta 1996; Shanker 1997; Cotterill, Putsis, and Dhar 2000). However, researchers using the logit model have only recently recognized that estimating the response parameters while ignoring the decision rules that govern firms’ actions could lead to biased and inconsistent estimates of these parameters.
The importance of the endogeneity issue is based on the following argument. Firms in the marketplace make decisions on their marketing‐mix variables every time period. An important input into these decisions is the nature of the response of the firm’s market share to these marketing activities, that is, the marketing response function. For that, the logit model has been empirically found to provide a good representation. From the perspective of researchers trying to uncover the “true” effects of the marketing variables, however, it creates the following econometric problem. The researcher observes only a subset of variables, such as price and advertising, that drive firms’ market shares. Other variables, such as distribution and market coverage, which are not observed (but are known to firms), are treated as being part of the “error” term in the model. If firms’ choices of price and advertising levels depend on those (unobserved) variables, for example, price depends on product attributes, the explanatory variables in the model are correlated with the error term, which results in the endogeneity problem.
In the context of the logit model, the above econometric problem has been addressed in one of two ways. The first approach is to focus only on the demand side and use instruments for price and advertising. These instruments, while being correlated with the marketing‐mix variables, are treated as being uncorrelated with the error term. For example, in his study of the ready‐to‐eat cereal market across several geographic regions, Nevo (2001) uses the levels of marketing activities in geographic region Y (for example) as instruments for these variables in region X.
The alternative approach to address the endogeneity issue is to explicitly postulate the behavioral mechanism by which firms set their prices and advertising levels and use this information in estimating the demand parameters. This method, therefore, not only accounts for the endogeneity of the price and advertising variables but also accounts for the simultaneity of the quantity, price, and advertising decisions (see, e.g., Berry 1994; Berry, Levinsohn, and Pakes 1995; Besanko et al. 1998). Hence, the main difference between the two methods is that the former focuses only on the demand function to obtain consistent estimates for the effects of marketing‐mix variables, whereas the latter uses additional information regarding the “supply side.” The latter approach is, thus, an equilibrium demand‐and‐“supply” model.
In using the latter approach mentioned above, the question that arises is, How do firms make price and advertising choices that compose the “supply side”? Typically, a firm is assumed to maximize some objective function, for example, its profit level. If it is further assumed that all firms behave in a similar fashion, then the observed market behavior vis‐à‐vis price and advertising (for example) are the “equilibrium” outcomes for these firms. This gives us two sets of equations: (1) the logit response functions that link the firms’ market shares to their marketing activities via a set of response parameters and (2) a set of decision rules, based on optimizing behavior of firms that link the marketing activities of the firm to its market shares via the same set of model parameters. Together, they compose a simultaneous demand and supply‐side system. Econometrically, therefore, the approach of using only the demand function with instrumental variables accounts for the endogeneity of firms’ actions, whereas the latter approach accounts for endogeneity as well as for simultaneity in the response function and firms’ decision rules (for an early study on the importance of accounting for simultaneity, see Bass [1969]).
Clearly, including the equilibrium conditions involves a trade‐off. On the one hand, it can provide insights into the supply side (and the firms’ cost functions). On the other hand, it imposes more demands on the data, and an incorrect specification of the firms’ marketing‐mix decisions could lead to biased parameter estimates. Researchers have not hitherto addressed this issue and compared the estimates for price and advertising effects obtained from the two approaches.
An especially interesting aspect of misspecification of firms’ marketing‐mix decisions is the role of competition in these decisions. Most previous articles that have accounted for the supply side in pricing decisions, for example, Berry (1994), Berry et al. (1995), and Besanko et al. (1998), have imposed a very specific form of competition among firms. They assume that firms in the market interact with one another in a Bertrand‐Nash fashion. The actual form of competition in the market may be different from this assumption. This implies that the associated pricing‐decision rule can be very different from that associated with Bertrand‐Nash. Imposing a Bertrand‐Nash supply formulation, therefore, amounts to misspecification of the supply side, which can lead to inconsistent demand parameter estimates as well.
When advertising decisions are considered, we face an additional complexity in accounting for this source of misspecification on the supply side. It is likely that advertising decisions have multiperiod effects on the demand side. This results in a dynamic, as opposed to a static or single‐period, analysis of firm behavior. While one can continue to assume that firms make decisions every period, these decisions will now have to account for the effects of current advertising on future firm profits. In addition, a supply‐side model of advertising must also accommodate competitive interactions in a flexible manner so as to obtain unbiased estimates of the demand parameters, as well as the cost or supply‐side parameters.
When obtaining price and advertising levels for dynamic problems, two kinds of equilibrium have typically been studied—open loop and closed loop (see Erickson 1992). Deriving open‐loop equilibrium for our model formulation is relatively straightforward. In a recent study, Vilcassim, Kadiyali, and Chintagunta (1999) also examined price and advertising competition in a dynamic context. In that study, while the authors did incorporate flexible forms of market interaction, the analysis was not done using a logit demand model, and the advertising dynamics were incorporated using a limited 2‐period model formulation. A more complete analysis requires that the firm’s decision problem be formulated as one of infinite horizon. Deriving closed‐loop equilibrium advertising strategies while accommodating flexible forms of market conduct has remained elusive, despite advances in the theoretical literature on dynamic games (Maskin and Tirole 1988).
Consequently, we propose an intermediate solution that we refer to as an “adaptive policy.” Adaptive decisions, like closed‐loop decisions, take into consideration rivals’ future‐period reactions to the firm’s actions in the current period. The key difference between adaptive and closed‐loop policies is that the latter can be parameterized entirely by the firms’ demand and cost parameters. In our proposed adaptive policy, by contrast, firms’ reactions need to be explicitly parameterized via additional dynamic conduct parameters (DCPs) that capture rivals’ future actions. When the DCPs are zero, the adaptive policy reverts to the open‐loop solution. By allowing these DCPs to take any value, we allow for a general competitive model. This helps get around the potential misspecification problem with using the open‐loop solution. Because open‐loop price and advertising levels are obtained without accounting for such intertemporal reactions, we refer to them as “nonadaptive policies.”
Therefore, for product markets where firms make price and advertising decisions, we estimate two versions of the supply‐side equilibrium—the dynamic nonadaptive policy and the dynamic adaptive policy. Further, the nonadaptive decisions are nested within the adaptive behavior, and this allows us to empirically determine which model of firm behavior is most consistent with the data.
Summarizing, in this article we pursue the issue of endogeneity in the logit demand model. We compare three approaches used to account for endogeneity—the first accounts for demand‐side endogeneity, the second accounts for supply side as well but with restricted competitive assumptions, and the third accounts for a more general competitive model. The empirical analysis is done for a variety of market conditions. These are
| 1. | for three product categories (yogurt, a hair‐care product, and coffee); | ||||
| 2. | at different levels of market aggregation—national for the hair‐care product, national and regional for coffee, and a local market for yogurt; | ||||
| 3. | with weekly (yogurt and hair‐care product) as well as monthly (coffee) data; and | ||||
| 4. | for two different marketing‐mix decisions (price for yogurt; price and advertising for the other two). | ||||
The main contributions of this research are as follows. On the theoretical side, we extend the current literature on accounting for price endogeneity and simultaneity to the advertising domain. In particular, we obtain approximate closed‐form optimization rules for advertising when the carryover effects of this marketing instrument are accounted for. The more important contribution, however, is in showing empirically that ignoring the problem of endogeneity and simultaneity leads to biases in the estimated effects of price (and advertising) on demand. Interestingly, with a general formulation of interactions among firms, the Hausman test fails to reject the hypothesis that the set of parameters obtained when only accounting for endogeneity is significantly different from the specification that accounts for both endogeneity and simultaneity. Further, we show that imposing a restricted competitive assumption on the supply side produces inaccurate estimates on the demand side (and supply side). This finding is robust across four data sets and, hence, provides a benchmark for comparative purposes.
The remainder of this article is organized as follows. In Section II, we provide the model formulation. This is followed by a description of the empirical specification in Section III. In Sections IV and V, we discuss the data and empirical results. The final section concludes.
II. Model Formulation
Our objective in this section is to derive the dynamic equilibrium pricing and advertising rules that compose the supply side, given that an aggregate logit model can specify demand. These rules will be used in the analysis to account for the simultaneity of competitive price and advertising. We derive first the equilibrium advertising and pricing for the nonadaptive case, which is then followed by the adaptive case.
The market share of brand i, 
in period t is given by the logit model1 
where αi is the intrinsic preference for brand i, pit is the price of brand i in period t, β is price sensitivity, γ is advertising sensitivity, rit is the nonprice promotional intensity of brand i in period t, δ is promotional sensitivity, N is the number of competing brands in the market, and CAit denotes the cumulative advertising effect from all previous periods and the current period for brand i. In other words, if Ait represents the current period advertising for brand i (measured in gross rating points [GRPs]), then 
where σ is the carryover of advertising GRPs from one period to the next. Note that the existence of the carryover creates an intertemporal linkage in demand for the N firms (brands).
The advertising investments are measured in GRPs. Consequently, we need to translate these into monetary terms for use in the profit function. We define the advertising cost function (ACF), which relates GRPs to dollars, at time t by the following expression: 
where θ1i and θ2i are parameters that translate GRPs into dollars. Depending upon the magnitudes and signs of the parameters, θ1i and θ2i, advertising costs can be linear, concave, or convex in GRPs. Rather than impose a specific functional relationship between GRPs and dollar costs, we propose to estimate these parameters from market data.
We assume that firms choose their price and advertising levels in each time period. Given advertising carryover, in each period t the firm chooses its price and advertising level that maximizes profits from that period on. Hence, the firm’s profit‐maximization problem becomes one of infinite horizon and is equal to 
where M is the (fixed) market size, ρτ is the discount factor associated with profits τ periods hence, and 
. The assumption of a fixed market size is not an issue if the share formulation for Sit in equation (1) includes an outside good (see n. 1). However, in the absence of the outside good, one needs to check whether M depends on the prices and advertising levels of the N brands. Note from equation (4) that the firm’s control variables are the price and advertising levels in each period. As noted previously, there are two solution concepts (nonadaptive and adaptive) that can be used to obtain the equilibrium price and advertising levels. We discuss these in turn.
Open‐Loop (Nonadaptive) Solution The necessary conditions for a nonadaptive equilibrium are obtained by setting 
Assuming that there are no price dynamics and that pit affects profits only in period t, deriving the price first‐order condition is straightforward and yields 
where the parameters 
are introduced to capture deviations from Bertrand‐Nash (which we refer to simply as “Nash”) equilibrium pricing.2 We refer to them as “conduct parameters” (CPs), and they allow for flexible forms of interaction among firms. If all the CPs are zero, then the interaction among firms is Nash. Otherwise, competition among firms will be “softer” or “stronger” than Nash pricing, depending on the sign of the CPs. Hence, these CPs reflect the contemporaneous interactions among firms that can result in deviations from Nash behavior.
The nonadaptive (i.e., open loop) advertising level is obtained by differentiating the right‐hand side of equation (4) with respect to Ait. Note that because Ait appears in each of the terms in the objective function, one has to explicitly take this into account in the differentiation. Doing so, we obtain the nonadaptive‐advertising policy as follows: 
In the above expression, 
, and 
. There are several aspects about equation (7) worth noting. First, the right‐hand side of the equation is a function only of observable prices and shares and the model parameters. It is not a function of cumulative advertising levels. Further, if 
, then the equation reduces to that from a static optimization problem. Note, however, that the above expression entails an infinite sum. In empirical situations, one will not have access to the entire future time paths for the firms. The actual number of terms to be included in the above expression will depend on the discount factors for the firms. If firms do not weigh profits beyond a certain number of time periods, then the weight for the subsequent profits can be set to zero. Consequently, these terms would drop out of the equation. Second, the 
parameters are the advertising CPs and, as in the case of price, capture deviations from Nash behavior. Whether advertising competition is “stronger” or “softer” than Nash will depend on the signs and magnitudes of the CPs (if they are all zero, we will have Nash competition).
As described previously, the nonadaptive nature of the equilibrium derives from firm i not explicitly incorporating rivals’ responses in period 
to its pricing and advertising levels in period t. The adaptive equilibrium we discuss next explicitly accounts for such behavior.
Adaptive Solution (or General Form of Competition) A firm’s profit‐maximization problem, as set up above, cannot be solved for closed‐loop policies. We explored Markov‐perfect equilibria as in Maskin and Tirole (1988). This again revealed no solutions for the problem at hand. The economics literature has seen recent advances using numerical methods to characterize Markov‐perfect equilibria (Pakes 1998). However, these methods do not apply to our problem because the dynamic element in those models (investing in the improving “quality”—the brand‐specific intercepts) is such that it does not create an intertemporal link in the demand or cost functions over time. Consequently, the profits for the firms’ at any given point in time are functionally independent of the firms’ actions in the previous time periods. This is not the case with our model formulated because of the advertising carryover effects. Hence, we cannot use the methods based on Markov‐perfect equilibria to address the problem at hand.3
The key difference between the nonadaptive and adaptive solution is that the latter explicitly takes into account a rival’s reactions to the firm’s actions. The most general case occurs when
| i) | a firm can react to a rival’s action at time t in time period t and in any future time period, and | ||||
| ii) | a firm can react with the same instrument or a different instrument than that used by the rival firm. | ||||
In the above equations, the terms 
, 
, 
, and 
capture the reactions for the different firms at different time periods and different instruments. These intertemporal reactions are referred to as the DCPs. Because reactions in price could differ from reactions in advertising, firms have separate price and advertising DCPs. In principle, one can obtain a closed‐form solution to the above equations. However, empirical implementation is infeasible because there are infinitely many DCPs in the above equation. Hence, we focus on a very specific form of reaction.
We assume that the intertemporal reactions are Markovian in nature. In other words, firm j reacts to firm i’s decisions in period t, but it does so in period 
. Similarly, a reaction in period 
is a consequence of actions in period 
, and so forth. Just as is the case with Markov‐perfect equilibria, it is important to note that this is only one among several possible strategies that firms can follow. Nevertheless, it is an appealing strategy because of its “payoff relevant” property. We also assume that reactions take place in the initiating marketing instrument only. Hence, reactions to price changes with changes in advertising (and vice versa) are not considered. There is some empirical support for this assumption. For example, Leeflang and Wittink (1992) find that although cross‐instrument reactions do occur, simple reactions are far more common. The assumption also helps us conserve degrees of freedom in data. Operationally, as we show below, DCPs measure the deviations of a firm’s price and advertising levels from the nonadaptive case. Hence, when these 
, the firm behaves according to the nonadaptive equilibrium described previously.
We note that in a recent study, Erickson (1997) also examined dynamic advertising decisions using a conjectural variations framework. There are, however, some important differences between Erickson’s and our approach. The most important difference is that we estimate some of the dynamic conduct, or dynamic conjectural variation, parameters directly from the data, whereas Erickson sets them to some chosen values. As stated previously, the adaptive policy we develop has as a special case the open‐loop equilibrium, and it might well be that in a given empirical situation, the open‐loop solution may be the one most consistent with the data. Clearly, it is preferable to “let the data speak,” rather than impose nonzero values for the dynamic conjectural variation parameters. This also helps reduce the possibility of incorrect demand parameter estimates arising from misspecification of the supply function. Additionally, Erickson uses a Lanchester model for the evolution of market shares, whereas our objective is to examine the endogeneity within the context of a logit demand model where more than a single marketing‐mix variable has to be analyzed.
The necessary conditions for an adaptive equilibrium, are therefore given by 
The key difference between the necessary conditions in equations (6)–(8) is the presence of the DCP terms. These terms denote the response by firm j in period 
to firm i’s actions in time period t that are accounted for by firm i while making its price and advertising decisions. In the following, we denote the DCPs as follows: 
The D in the above DCPs refers to “dynamic.” As before, deriving the price first‐order condition for the adaptive equilibrium is straightforward and is given by 
In the above equation, 
is as defined in equation (9), while 
parameters are the contemporaneous CPs. An interesting feature of the pricing equation above is that the presence of DCPs creates pricing dynamics in addition to advertising dynamics. In other words, although there are no explicit price dynamics built into the model, firms’ accounting for rivals’ reactions induce an intertemporal linkage in their pricing decisions. If 
, we are back to the nonadaptive case.
The adaptive solution for advertising yields the following: 
In the above equation, 
is the advertising DCP, whereas 
is the contemporaneous CP. Again, with zero DCPs, we are back to the nonadaptive case. To interpret the DCPs, we rewrite the equilibrium price and advertising levels for the adaptive case (eqq. [10] and [11]) as follows: 
and 
where 
and 
are the nonadaptive equilibrium price and advertising given by equations (6) and (7), respectively.
The above equations (10′) and (11′) provide the justification for our adaptive equilibrium. Specifically, they indicate that when the DCPs are all zero, the adaptive equilibrium simplifies to the nonadaptive one—which we know is the open‐loop, or precommitment, equilibrium. Hence, the DCPs capture deviations from the open‐loop equilibrium in a manner that accounts for firms’ intertemporal reactions to one other.
Consider now the price DCPs. If 
is positive, then 
. That is, positive DCPs imply that firms are interacting in a manner that results in equilibrium prices that are higher than those under nonadaptive behavior. Consequently, the firms’ price/cost margins are also higher. What is it that could result in positive DCPs? We note that when firms repeatedly interact in the market, they could adopt a competitive stance that “softens” price competition. Evidence of this type of tacit collusion has been provided in several empirical studies (e.g., Kadiyali 1996). If, however, the DCPs are all negative, then 
, implying aggressive pricing behavior on the part of the market rivals. If the DCP is positive for one firm but negative for the other, then one firm is being accommodating, while the other is being aggressive. Of course, which of these conditions prevail in the market is an empirical question.
Turning our attention now to the advertising DCPs, we note that if they are all positive, then 
. That is, when the advertising DCPs are positive, the equilibrium advertising level under the adaptive decision rule is less than that under the nonadaptive case.4 Hence, firms can “soften” advertising competition by appropriate conduct. As with price competition, this softer stance can be brought about by repeated interaction in the marketplace. If the DCPs are all negative, then the level of advertising competition is higher, relative to the nonadaptive case. Mixed forms of interaction result when one DCP is positive and the other is negative. The empirical results show which condition prevails in the market.
III. Estimating Equations
In this section, we discuss how we go from the market‐share and firm‐optimization rules discussed above to the estimating equations, as well as the process used to document the effects of accounting for endogeneity. In the empirical estimation, to determine the effects of endogeneity and simultaneity of price and advertising decisions of firms, we use the following procedure:
| 1. | Estimate the system of demand equation (1) alone, treating price and advertising as exogenous variables. | ||||
| 2. | Estimate the system of demand equation (1) alone, using three‐stage least squares (3SLS) and treating price and advertising as endogenous variables. | ||||
| 3. | Estimate demand equation (1), pricing equation (6), and advertising equation (7) simultaneously, using 3SLS, where price, advertising, and shares are treated as endogenous variables. Advertising has dynamic effects, but competition is nonadaptive. | ||||
| 4. | Estimate demand equation (1), pricing equation (10), and advertising equation (11) simultaneously, where prices, advertising, and shares are treated as endogenous variables. Thus, we account for endogeneity and simultaneity, while allowing for general forms of competition as described in the adaptive equilibrium. | ||||
In the estimation, we convert the share equation to a logistic regression. We do not have data on the outside good for two of the three product categories (hair care and coffee), and, therefore, brand intercepts are all relative to the Nth brand. Further, because we observe advertising GRP levels only and not the cumulative advertising variable, we need to eliminate the CAit variable in favor of the advertising levels Ait. This is accomplished by taking the 1‐period lagged equation 
, multiplying it by σ, and subtracting it from 
(much like the Koyck transformation). This yields the following equation. 
where 
, and 
is the associated error term. We estimate 
. For the adaptive equilibrium case, price and advertising equations for 
are estimated as follows: 
The associated error terms are 
and 
. The terms 
are intended to account for econometric error.5 When demand, price, and advertising equations are estimated simultaneously, we assume that 
, 
, and 
are joint‐normally distributed and may be contemporaneously, although not temporally, correlated. We note the following features of the model specification:
| 1. | The nonadaptive price and advertising levels are nested within the adaptive price and advertising levels, that is, when all the | ||||
| 2. | The static price and advertising levels are nested within the nonadaptive price and advertising levels, that is, when | ||||
The above system of equations consists of 
demand equations, N pricing equations, and N advertising equations, for a total of 
equations. The variable T denotes the empirically determined upper bound for the number of terms retained in the pricing and advertising equations. This would depend upon the firms’ discount rates. Note from the above system of equations that the ACF parameters, 
and 
, and the market size parameter, M, are not all uniquely identified. What can be estimated are 
and 
.
Another issue we face is regarding the number of time periods T to be included in the analysis. Operationally, we did the following in determining T:
| 1. | We started with | ||||
| 2. | Using a likelihood ratio test, we stopped at the value of τ from which an increase did not result in a significant improvement in model fit. | ||||
| 3. | Given the finite time horizon, we set the discount factor, | ||||
One of the issues that we need to address in the dynamic case is the number of parameters to be estimated. For one of the product categories we consider, yogurt, we focus only on price competition because we do not have access to data on advertising. For this category, we estimate only the contemporaneous CPs. For the other three cases, we analyze both price and advertising competition. Given the paucity of data, that is, the number of observations available for estimation, we set all the contemporaneous 
in the estimation for these three data sets. Given that our focus is on the dynamic aspects of firm behavior in the presence of advertising, it is important to demonstrate the effect of adaptive versus nonadaptive behavior. We recognize that our estimates would be affected to the extent that we do not include the effects of the CPs in this case. Additionally, for two of the four data sets, we do not have enough data to estimate all of the DCPs. Therefore, for these data, we estimate the system with various combinations of DCPs to see which ones are insignificant, and we set those to zero to save degrees of freedom. Other estimation restrictions imposed because of the paucity of data are the equality of marginal costs and advertising costs across firms.
IV. Data
We use three different data sets in this study. Below, we describe details about each of them. There are several differences across these product categories that make these data sets interesting for our purpose. The categories vary from food to nonfood, perishables to nonperishables, and those with only price to those with price and advertising competition. Also, the data frequency is of two types—weekly and monthly—and there are data from local as well as national markets. This diversity of data will be useful in generating some insights into the effects of endogeneity and simultaneity on the estimated price and advertising effects. Table 1 shows the descriptive statistics for these data.
A. Yogurt
We study weekly price competition in the yogurt category. Hence, there are no DCPs in this case, and we estimate only the contemporaneous CPs. The (scanner) data on prices, sales, and feature/display activities are for Springfield, MO, for 102 weeks in 1986–88. These data are pooled over stores. There are four brands in this data set—Dannon, Yoplait, Weight Watchers, and Hiland. Using data from the household file for the same market, we obtain no‐purchase information, which we use as a measure of an outside good for the estimation of brand intercepts. An issue with examining competition among national brands from data of a local market is the role of the retailer in setting prices (Sudhir 2001b). Following Besanko et al. (1998), we assume that the retailer charges a fixed markup over manufacturer prices while determining the prices to the consumer.6 A critical issue in the estimation is the choice of instruments for price. Consistent with the Besanko et al. study, we chose cost‐side variables. These variables are the costs of fluid milk, container prices (plastic), and labor‐costs data taken from the Bureau of Labor Statistics (BLS).
B. A Hair‐Care Product
The data available are weekly data over a 2‐year period for three brands of a hair‐care product with the highest market shares in that subcategory. For reasons of data confidentiality, we cannot reveal either the brand names or the specific product category. The variables included are unit market shares, retail prices, advertising GRPs, and a couponing variable. The last variable is the total value of coupon drops in each week. Further, the variable is lagged by 1 week to capture the delayed effect of manufacturer coupons and is scaled by a factor of 10−4. For purposes of this analysis, we assume that the couponing variable is exogenous. This assumption may be reasonable because coupon drops are often planned well in advance and then executed according to a predetermined schedule. Given these data, we study price and advertising competition in the category.
The data are aggregated across stores and chains to the national level, so individual retailer behavior and interactions among retailers are not easily addressed. Because prices are at retail, and we have nationally aggregated data, we assume as before that retail prices reflect fixed markups over manufacturer wholesale prices. This facilitates the use of our proposed model formulation. The weekly nature of the data also drives our choice of time interval (i.e., week) for the analysis.
As instrumental variables for price, we used the costs of packaging (plastics) and inorganic chemicals (major ingredients of the product). These data are also from the BLS. For advertising, the ideal choice of instruments would have been weekly advertising costs. Unfortunately, we did not have access to those data. Therefore, we use lagged couponing as an instrument for advertising.
As mentioned previously, we had to impose the restriction of equality of marginal costs and advertising costs across brands. In the absence of these restrictions, we were unable to estimate the parameters of interest, possibly because of insufficient degrees of freedom. (With these restrictions, this category has one less parameter to estimate relative to the yogurt category, while the number of data points for yogurt is 701 compared to 114 for this category.) Clearly, if more data observations were available, such restrictions may not be needed.7
C. Coffee
The third data set we use is monthly data on a subcategory in coffee. Again, for data confidentiality reasons, we cannot reveal the subcategory or the brands in it. An interesting feature about coffee data is that it is available to us at two levels of aggregation—at the national level and at a regional level. We also have data on average price and advertising GRPs for all markets other than the single regional market for which we have data. Therefore, following Nevo (2001), we can use marketing variables from the average of all other markets as instruments for those in the regional market. Other instruments used in the regional market and in the national market include price of (Robusta) coffee beans and lagged promotions.
For this category, too, we had to impose estimation restrictions. We have only 35 (monthly) data points for this category, compared to 114 for the hair‐care category and 701 in the yogurt category. Therefore, more restrictions were required for parameter estimation. First, as we did with the hair‐care product, we impose the restrictions of equality of marginal costs and advertising costs. Second, by repeated estimation, we determined which CPs were insignificant and then set them to zero in the final estimation. Clearly, if more data points were available, there would not be a need for such restrictions.
An important issue that arises in the context of the hair‐care and coffee data sets is that we do not have measures of the outside good and focus on brand shares conditional on category purchase. This has several consequences. First, the elasticities obtained from the analysis will not be true demand elasticities because category expansion is not accounted for. Second, recall our assumption that the total market size, M, remains constant over time in our model development. For this assumption to be tenable, it must be the case that the total sales in the (sub‐) categories of interest are not sensitive to the prices and advertising levels of the brands included in the analysis. Accordingly, to verify this, we regressed total (sub‐) category sales in each case on the average price and total advertising level across brands. For both the hair‐care and coffee categories, we did not obtain statistically significant effects. Hence, our assumption on the market size appears reasonable, at least for the data at hand.
In summary, we have different kinds of products with different numbers of observations in the categories. In all cases, we used input costs as instruments for prices. Additionally, where multimarket data are available (as in the regional coffee market), we use outside market advertising levels as instruments for in‐market advertising. In the absence of such data, we used lagged values of the promotional variables.
Prior to discussing the results for the estimation, we note that they are conditioned on our assumption regarding the role of the retailer in setting prices. We assumed that the retailer plays only a passive role and sets prices using fixed markup rules. The importance of the role of the retailer and the consequences of ignoring it are likely to be dependent on the level of market aggregation in the data. That is, one would expect that where the data pertain to a local market, the role of the retailer in price setting is likely to be significant. However, with national U.S.‐level data, the role of the retailer in price setting is likely to be less important. Hence, by having different data sets that cover different levels of market aggregation, we can determine whether our results regarding endogeneity and simultaneity are robust to the assumption we have regarding the role of the retailer in price setting.
V. Results
A. Preliminary
The results of the estimation are presented in table 2 for yogurt, table 3 for the hair‐care product, table 4 for coffee with national data, and table 5 for coffee with regional data. Rather than describe results for each product category, we describe results across categories.
Regarding the time‐period length chosen, as described in the previous section, we carried out the three‐step procedure described previously to determine T. We note that a higher value of T does not increase the number of parameters to be estimated. Hence, it might seem reasonable that a higher T would fit the data better. However, this is not necessarily the case because increasing T with no additional parameters would also place greater restrictions on the same set of parameters. Indeed, we found that 
captures the dynamics for both the hair‐care product and coffee.
B. Accounting for Endogeneity and Simultaneity
We first discuss the results obtained from the demand‐function‐only analysis. The objective here is to compare the estimated price and advertising effects under the exogenous and endogenous formulations (cols. 1 and 2 in tables 2–5). We note that the estimated price effects are larger in each case when price is treated as being endogenous. This finding is consistent with the Besanko et al. (1998) finding. There is no obvious trend in the other parameters.
Next, consider the results when we account for both endogeneity and simultaneity. These estimates are in columns 3–5. Here, there are two cases for yogurt—when Nash behavior is imposed versus when the more general CP model is estimated. For the hair‐care product and coffee, with nonadaptive formulation, we will test both the static and dynamic advertising‐effects models.
Before introducing the results for accounting for the Nash behavior of competitors, we would like to simplify further discussion by considering first whether advertising has static or dynamic effects. For the hair‐care product, the difference in their objective function values is 12.27. The critical χ2 value with 1 degree of freedom (difference in number of parameters estimated) at 95% confidence is 3.84. For national coffee, the difference in objective functions is 13.21, and for regional coffee data, it is 4.66. Therefore, for all data sets with advertising data, the dynamic nonadaptive behavior formulation is a better description of firm behavior than the static advertising‐effects model of firm behavior.
Next, we would like to compare the adaptive versus nonadaptive response results, given that dynamic advertising effects capture the data better than static effects. If players behave in a nonadaptive manner, then all 
. A model with these restrictions imposed is nested within the adaptive model. For the hair‐care product, the objective function value for this nonadaptive model is 265.9, while that for the adaptive specification is 175.3. The critical χ2 value with 10 degrees of freedom (difference in number of parameters estimated) at the 95% level of significance is 18.31. The computed test‐statistic value of 90.6 is thus larger than the critical value. Hence, the nonadaptive equilibrium can be rejected in favor of the adaptive equilibrium. For national coffee data, the computed test‐statistic value is 20.08, and the critical χ2 value with 5 degrees of freedom is 11.07 for the 95% level of significance. We thus reject the nonadaptive formulation for that data too. For the regional coffee data, the computed value is 10.71. The critical value with 6 degrees of freedom at 90% confidence is 10.64, at 95%, 12.59. Therefore, adaptive behavior cannot be rejected at the 90% level of significance.
We now discuss the implications of accounting for endogeneity and simultaneity. Comparing the results in columns 1 and 2 against those in column 3 for yogurt and column 4 for the hair‐care product and coffee, we see that accounting for the simultaneity of price increases the estimated price parameter by a large amount. This is especially interesting because, in each of these cases, we used aggregate data rather than individual household‐level data. Researchers in marketing have documented how aggregate data lead to lower price elasticities than when household data are used (Christen et al. 1997). However, these researchers accounted for neither endogeneity nor simultaneity of price outcomes. Using four different data sets, we find that while accounting for endogeneity increases the price parameter somewhat, accounting for simultaneity increases price effects to magnitudes much closer to those estimated using household data. This is the case even when a strong behavioral assumption of Nash behavior is imposed on the data.
To examine the effects of a general model of firm competition, we compare for the yogurt category the results of column 4 in table 2 with those in columns 1–3. For the hair‐care product and coffee categories (tables 3–5), we compare the results in column 5 to those in the other columns of each table. In other words, the last column in each table is the general model accounting for endogeneity and simultaneity with flexible competitive conduct. Once again we see that price effects are much larger in this case than in column 1, where neither endogeneity nor simultaneity have been accounted for. In three of four cases, however (i.e., except regional coffee data), the effect is smaller than if Nash behavior was imposed. Therefore, estimates of price responses with Nash behavior are likely to be biased upward. The advertising effects are stronger in this case than in column 1 with no endogeneity and simultaneity, except for regional coffee data where it is equal to the column 1 estimates. We also find that price effects are considerably understated if advertising dynamics are not accounted for in the estimation. These results extend the Besanko et al. (1998) findings. Those authors concluded that ignoring endogeneity would affect such inferences. Our results indicate that ignoring dynamics when present could also lead to misleading inferences.
Hausman (1978) Specification Test As mentioned previously, a critical issue in estimating a demand‐and‐supply model is that in such models, a misspecification of the supply‐side equations can bias estimates of demand‐side parameters as well. To ensure that this is not the case, we performed a Hausman (1978) specification test. That is, we compared the two‐stage least squares (2SLS) estimates of demand to the 3SLS estimates of demand obtained from estimating demand and supply simultaneously. Under the null hypothesis of no misspecification of supply‐side equations, both the 2SLS and 3SLS estimates are consistent and unbiased. Under the alternative hypothesis of misspecification, the 2SLS estimates are unbiased, but the 3SLS estimates are biased because the misspecification in the first‐order conditions corrupts the demand‐function estimates. The empirical results of the Hausman specification tests were as follows. For yogurt, the critical χ2 value with 6 degrees of freedom (equal to the dimensionality of the variance‐covariance matrix) at 95% confidence is 12.59. The computed value is 12.4, which implies that we cannot reject the null of no misspecification at 95% confidence. For the hair‐care product, the computed χ2 value is 7.53. For the national coffee data, the estimated χ2 test‐statistic value is 8.23, and for the regional coffee data it is 8.07. The critical value is (with 6 degrees of freedom) again 12.59 at 95% confidence. Therefore, we cannot reject the null of no misspecification at 95% confidence in each case. We conclude, based on the Hausman specification test, that in all four data sets, the supply‐function specifications are not causing the demand‐side parameters to be biased.
Another way of determining whether accounting for endogeneity and simultaneity along with a flexible form of competitive conduct among firms makes sense is to examine whether the parameters under this estimation are more intuitive than in the other scenarios. Consider table 2. We see that for yogurt, the brand‐specific utility intercepts in column 1 are all negative (relative to the outside good), whereas in column 4 they are all positive, and three out of the four are significant. In table 3 for the hair‐care product, column 4 contains the implausible result of insignificant advertising effects but a positive and significant advertising carryover effect. However, the estimates given in column 5 show both a significant advertising effect as well as a significant carryover effect. Additionally, the carryover parameter seems unreasonably high at 0.90 in column 4 when Nash interaction is imposed but seems more reasonable at 0.55 in column 5 (see Leone 1995). In table 4, for the national coffee data, we see that the marginal‐cost estimate is negative with static advertising effects (col. 3) but is positive in column 5. Similarly, in table 5, for the regional coffee data, the marginal‐cost estimate is negative for both columns 3 and 4 and is positive only for column 5. Hence, from the standpoint of the face validity of the parameter estimates, the formulation with a flexible form of competitive interaction is more appealing than imposing Nash behavior.
Summarizing the results of both the specification tests and the reasonableness of the parameter estimates, the formulation with both endogeneity and simultaneity, as well as a flexible‐form firm interaction, seems to econometrically produce “the best” set of parameter estimates. This result underscores the need for accounting for all those issues, even when the primary focus of the empirical analysis is on obtaining accurate estimates of the demand effects of the marketing‐mix variables.
C. The Supply Side: Competitive Conduct and Cost Parameters
Although an analysis of the cost and competitive structure is not the primary focus of this study, we will, nevertheless, make some brief remarks about both of them. For the yogurt data, all the estimated cost parameters are less than prices, as expected. We also see “cooperative” pricing among the firms because all of the 
parameters are positive, which results in margins greater than those under Nash pricing behavior. Margins are large, ranging from 61.7% for the brand with the largest intrinsic preference (brand 2) to 27% for the one with lowest intrinsic brand preference (brand 3).
In the hair‐care product, the estimated marginal cost is less than the prices of all three brands. Most DCPs are not significantly different from zero.8 The exceptions are that firm 1 prices cooperatively with respect to firm 3, whereas firm 2 prices competitively with respect to firm 3. The only significant advertising DCP is of firm 3 advertising aggressively with respect to firm 2. Given that we are unable to estimate firm‐specific marginal costs, we cannot determine the relationship between these DCPs and marginal costs. However, firm 1’s cooperative pricing is consistent with its lowest intrinsic brand preference and its lowest market share. This cooperative pricing translates to the highest prices charged. Firm 3’s aggressive advertising is consistent with its highest intrinsic brand preference, its lowest prices, and its highest advertising GRPs.
For the national coffee data, the only significant interaction is that firm 2 prices competitively with respect to firm 3. Its aggressive stance is consistent with firm 2’s larger intrinsic brand preference and its larger market share. In advertising, firms 1 and 2 advertise competitively with respect to one another. Given firm 1’s much larger market share and larger intrinsic brand preference, as well as its larger GRPs, it is not clear why firm 2 should advertise aggressively relative to firm 1. The marginal‐cost estimate is below prices for all three firms.
For regional coffee data, we see a different competitive pattern than for national data. This is not surprising, given that the demand and cost conditions vary across markets. Firm 2 prices cooperatively to firm 1’s prices, and firm 1 to firm 2’s. In this market, firm 2 has more market share than firm 1 and also has higher intrinsic brand preference and higher GRPs than brand 1. However, firms 1 and 2 have the same market price. Firm 3 prices cooperatively to firm 1’s prices. Firm 3 is the smallest, with the lowest price and the lowest advertising GRPs, and, therefore, cooperative pricing is profitable for firm 3. Advertising competition is more intense than price competition, with all three significant DCPs being negative.
We also find that for the coffee data, more of the advertising DCPs are significant with the regional data relative to the national data (three vs. one). Further, we find that there is no pattern of significant advertising DCPs with respect to the choice of data intervals (weekly or monthly when we look across all four data sets). These results seem to suggest that the estimated interaction among firms seems to be more a function of the level of market aggregation than the data interval.
The results from the coffee category also reveal that some of our marginal‐cost estimates are negative and statistically different from zero. Clearly, this is unreasonable, so what might be an explanation for this finding? Note from tables 4 and 5 that the negative marginal‐cost effects are always accompanied by price coefficients that are closer in magnitude to zero, as compared to those from the dynamic adaptive‐advertising case. What this means is that when endogeneity is not fully accounted for, price effects are biased toward zero, and consequently, markups predicted by the corresponding models are “too large.” The only way the model can reconcile large markups with observed price levels is by implying negative marginal costs. Hence, these estimates are a consequence of the endogeneity issue not being fully addressed in the model and estimation.
Summarizing, the supply‐side estimation is not only critical to estimating econometrically accurate demand‐side parameters; it also enables a better understanding of the equilibrium competitive‐market structure. We find that there are significant departures from Nash competitive interaction in all cases, implying that such an assumption may be unreasonable, irrespective of the product category, level of market aggregation, or length of the data interval used in the analysis.
VI. Discussion and Conclusion
Marketers have used the logit to model household choice behavior, treating manufacturer choices of price and advertising as exogenous. Recently, researchers have demonstrated that it is important to account for endogeneity. Using four different data sets with different products, market‐level aggregations, and periodicity characteristics, we find in our analysis that accounting for endogeneity avoids biased estimates for marketing activities. However, to obtain efficient estimates, we also need to account for the optimization rules for price and advertising decisions. We also find that, compared to all other scenarios, estimating flexible competitive behavior produces the most intuitive parameters on both the demand and cost sides. These results are robust for data that differ in several ways—national versus regional versus local markets, weekly versus monthly data, perishables versus nonperishables, food versus nonfood items, and those with and those without advertising data.
These results are interesting for at least two reasons. First, modelers who do not model either endogeneity or simultaneity need to be aware of the biases in the estimates of their parameters. Our results show that even if the principal objective of the study is not one of understanding how decisions regarding the marketing‐mix variables are made, we must account for endogeneity in order to obtain unbiased estimates of managerially important measures such as price and advertising elasticities. Second, the insights gained on the competitive side complete the picture of why market equilibria are the way they are—a product of demand and supply‐side forces.
Going beyond the issue of incorporating endogeneity, our results indicate that incorporating the simultaneity in price and advertising leads to more efficient parameter estimates. Intuitively, this result comes about because incorporating simultaneity is akin to increasing the number of data points for estimation because in addition to the demand equations, there are also the price and advertising equations that can be exploited in the estimation. Cross‐equation restrictions reduce the number of independent parameters that need to be estimated and provide extra information that can be used in efficient estimation.
There are a number of possible avenues for future research. First, an important issue in using an aggregate logit model is that of heterogeneity in the response parameters (see Berry 1994; Berry et al. 1995; Nevo 2001; Sudhir 2001a). We do not address that issue due to the additional complexities created and the consequent inability to study equilibrium advertising behavior. Nevertheless, some recent research is attempting to address this issue (e.g., Dube, Hitsch, and Manchanda 2003). Future research should relax the assumption of a passive retailer. This may not be an appropriate assumption for pricing decisions where retailers use any type of category‐management system. Under such a system, a constant markup rule is not likely to prevail, and the observed retail prices will have to reflect the retailer’s decision‐making process. In order to accomplish that task, the data used in the empirical analysis will have to contain information on manufacturer transfer or wholesale prices (or alternatively, the retailer margins on each brand). However, obtaining such data for research is not an easy task.
Second, the analysis needs to be extended to other instruments of firm competition and incorporate richer demand specifications. We have chosen very simple demand specifications here for reasons of tractability. For example, one might want to use a more complex demand specification that incorporates a measure of brand loyalty, which is a function of past purchases, weighted exponentially. That greatly complicates obtaining estimable first‐order conditions. Nevertheless, future research needs to find ways to handle such formulations.
In summary, in this article we have attempted to provide a benchmark study of important effects and issues that must be considered when analyzing aggregate logit models of demand. Ignoring such effects can lead to biased parameter estimates of the effects of price and advertising on demand. We hope that future research will pursue these issues further and provide additional empirical generalizations that could assist marketing managers in choosing how to implement their marketing‐mix decisions.
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* We thank Sanjay Dhar and Sachin Gupta for their generosity with their time and data and Inseong Song for data‐extraction help. We also thank the editor and an anonymous reviewer for their comments on the article. Contact the corresponding author, Pradeep K. Chintagunta, at pradeep.chintagunta@chicagogsb.edu.
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1. By including a 1 in the denominator of the logit expression, we can also allow for the brands in the market to influence overall category sales. The 1 reflects the “outside good.”
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2. The conduct parameter
for marketing instrument m, brands j and i. -
3. The general dynamic programming problem is given by Bellman’s equation as follows:
. It is easy to verify that there is no closed‐form solution to the above problem. -
4. We reiterate that under both the adaptive and nonadaptive cases, the equilibrium advertising level is higher than the static case because of the advertising carryover effect.
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5. Some studies have interpreted the error term in the demand equation as stemming from brand‐specific temporal shocks (see, e.g., Besanko et al. 1998). Likewise, the error terms in the price and advertising equations could be a result of either demand shocks or cost shocks or both.
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6. We treat feature/display activities as exogenous to manufacturers. We recognize that future research needs to address this issue.
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7. We note that the contemporaneous CPs have already been set to zero for all categories except yogurt.
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8. Note that some of the DCP parameters in table 3 that are not statistically different from zero have large magnitudes; e.g., A1 with respect to A3 is −18.75. We redid the estimation by fixing all the nonsignificant DCP parameters to zero to see whether they had an affect on our other reported results. We find that while the magnitudes of some of the other parameters change somewhat, the nature of our results remains the same.