Are High Advertising to Sales Ratios Justified by Advertising Elasticities? Evidence from Household Panel Data

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1 Are High Advertising to Sales Ratios Justified by Advertising Elasticities? Evidence from Household Panel Data Jeremy T. Fox University of Michigan and NBER Yuya Sasaki Johns Hopkins University Stefan Hoderlein Boston College January 2015 Advertising to sales ratios in consumer packaged goods categories can be around 10%. Dorfman and Steiner (1954) derive the optimal advertising to sales ratios as a function of the elasticities of advertising and price. In this paper, we use German household panel data on television advertising exposure and purchases for the laundry detergent category to estimate advertising elasticities. We estimate a panel data, semiparametric discrete choice model. We find that a special case of our model that does not adequately control for endogeneity can rationalize 10% advertising to sales ratios. However, the estimate of the advertising elasticity in our full model can explain advertising to sales ratios of only 0.5%, suggesting that most advertising practitioner beliefs in the effectiveness of advertising may come from endogeneity bias. Thanks to Christoph Nagel for advice on the data and to Arthur Lewbel for helpful comments. Our address are 1

2 1 Introduction Advertising expenditures are seemingly large in branded consumer packaged good industries. In the laundry detergent category in the United States, the advertising to sales ratio is around 10%. This means that 10% of the sales of manufacturers is spent on advertising by the advertisers. This large expenditure indicates that advertising plays a central role in the business strategies of firms. Dorfman and Steiner (1954) derive the optimal advertising to sales ratio for a static, profit maximizing firm that owns a single brand and chooses both price and advertising. Their first order conditions imply advertising $ revenue $ = advertising elasticity. price elasticity or that the advertising to sales ratio equals the ratio of the advertising and price elasticities. For a benchmark own price elasticity of -2 for a branded consumer packaged good such as laundry detergent, the advertising to sales ratio should be around 0.2 to justify the 10% advertising to sales ratio observed in the data. 1 We estimate the advertising elasticity using German household panel data that matches television advertisement exposure and household purchases in the laundry detergent category. This type of matched panel data on ad exposure and purchases is rare in the non-internet academic literature on advertising effectiveness. The household panel data cover 3782 households over a 24 month period and focus on nine leading detergent brands in Germany. We choose the brand with the highest sales as our focal brand and estimate a binary choice model of the household s decision to purchase this focal brand given the ads seen for the focal brand and the total ads seen for the rival detergent brands. The main outputs we consider are various advertising elasticities. We investigate whether the advertising elasticity for the focal brand is around 0.2, the level that explains the 10% advertising to sales ratio in the detergent category. A naive investigation using household panel data of this sort to estimate advertising elasticities suffers from at least four sources of endogeneity. 1) First, brand-level advertising may be correlated with brand-specific, aggregate demand shocks. Think about a brand choosing advertising campaigns to coincide with upswings (or downswings) in the fortunes of the brand. 2) Second, household ad exposures may be correlated with household persistent tastes for a brand or the laundry detergent category. Think about a detergent firm targeting ads to housewives by showing ads during daytime soap operas. 3) Third, time-specific household demand shocks may be correlated with a time-specific ad exposures. Think of a household that unobservedly goes on a beach vacation and does not watch television and does not buy laundry detergent. Such pairs of zero ad exposure and zero purchase will increase the correlation between ad exposure and purchase in the data and bias the estimated of the 1 Sutton (1992) argues that the effectiveness of advertising is also key to understanding market structure. If advertising shifts the price elasticity, then advertising-intensive industries will have a higher lower bound on market concentration. We do not estimate price elasticities so we will not investigate the effect of advertising on market structure. 2

3 advertising elasticity upwards. 4) Fourth, the past purchase history of a household should interact with ads in the purchase decision. For example, informative ads will primarily effect those that have not purchase the brand recently (Ackerberg, 2001). Likewise, laundry detergent is a storable good and those with stockpiled detergent may not respond to ads because they have no need for more detergent (Erdem, Imai and Keane, 2003; Hendel and Nevo, 2006). Past purchases is a lagged dependent variable that is likely correlated with time-invariant preferences and time-specific shocks, if such shocks are autocorrelated, as is plausible. Our model and data combine to form an identification strategy that addresses the four listed endogeneity problems. 1) To address the correlation of brand-level advertising with brand or category aggregate demand shocks, we exploit the data feature that ad exposure varies across households each month. Our model incorporates month-specific marginal distributions for time-specific shocks, which nest homogeneous (across households) month fixed effects, which can be correlated with advertising exposure. 2) To address household ad exposure being correlated with household persistent tastes for a brand or the detergent category, we exploit the data feature that ad exposure varies across time for a household. We estimate time-invariant household preference parameters that enter both the binary choice purchase equation and two auxiliary equations governing advertising exposure, one for the ads of the focal brand and the other for the ads of the rival brands. The time invariant household parameters in the binary choice equation are allowed to be correlated with the household parameters in the two ad exposure auxiliary equations. 3) To address time-specific household shocks being correlated with time-specific ad exposures, we allow the time-specific shocks in the ad exposure auxiliary equations to be correlated with the time-specific shocks in the purchase binary choice equation. 4) To incorporate the interaction of past purchase histories with advertising exposure, we properly model past purchases as analogous to lagged dependent variables in a binary choice equation. To properly distinguish the effect of state dependence (past purchases) from heterogeneity (in part autocorrelation in unobserved shocks), we allow for a flexible time-series dependence structure for the 24 month-specific shocks in the binary purchase equation (and in the ad exposure equations). We estimate a semi-structural model of choice. As mentioned above, there is a binary equation for purchasing the focal brand and two auxiliary equations governing advertising exposure, one for the ads of the focal brand and the other for the ads of the rival brands. All the parameters in this model are heterogeneous across households and, for shocks, across time periods for the same household. We say that the model is semi-structural because several features are abstracted away. First, the effect of price on purchase is not modeled because of a lack of data on the prices of brands not purchased. Second, the model of television ad exposure is effectively a vector autoregression rather than a structural demand model of households choosing between competing television programs and seeing ads as an incidental consequence of such entertainment decisions. Both of these semi-structural modeling decisions are made because of data limitations: a lack of price data and a lack of data on the television program the household is watching and competing television programs that are not viewed. 3

4 As mentioned, all parameters in our model are heterogeneous across households and across householdmonth pairs. We flexibly estimate the joint distribution of the vector of all time invariant and time specific household parameters. To make our model s likelihood easy to maximize, we fix a grid of realizations of the vector of all heterogeneous parameters. We then estimate only probability weights on this fixed grid of household type vectors. This adapts recent procedures advocating fixed grids of heterogeneous types to simplify optimization (Bajari et al., 2007; Train, 2008; Ackerberg, 2009; Fox et al., 2011, 2013). We are motivated by results on the nonparametric point identification of panel data models with lagged dependent variables (Sasaki, 2012; Kasahara and Shimotsu, 2008; Hu and Shiu, 2013). A key assumption maintained in this literature is that the time shocks in the outcome equation are independent over time. We significantly weaken this assumption by estimating a flexible time-series dependence structure for the 24 month-specific shocks. This means that we estimate a semi-structural, semiparametric model that is not a special case of a nonparametric model that is known to be point identified. We more credibly distinguish state dependence (effect of past purchases of detergent) and unobserved heterogeneity (time invariant preferences and time specific demand shocks) at the risk of losing point identification. Our current empirical results treat the model as point identified, which we can relax in future work. We present three main estimates of the advertising equation. For a model specification that addresses at most one of the four endogeneity issues mentioned previously, we find that the advertising elasticity is around 0.023, which almost exactly matches the elasticity of 0.02 needed to explain the 10% advertising to sales ratio in the detergent industry, using the Dorfman and Steiner condition and a benchmark own price elasticity of -2. We then estimate a slightly richer model that deals with some household-level forms of endogeneity but that does not address the correlation of advertising campaigns with aggregate brand or category demand shocks. For this slightly richer model, we find that the advertising elasticity drops from the earlier to Finally, our full model addresses all four sources of endogeneity bias. Using our full model, the advertising elasticity is estimated to be only This small advertising elasticity justifies an advertising to sales ratio of only 0.5% using the Dorfman and Steiner condition. The comparison of the seemingly large advertising elasticity of without adjusting for endogeneity and the preferred estimate of with such adjustment suggests that the beliefs of advertising practitioners about the effectiveness of advertising may be driven by making inappropriate conclusions from observational data with endogeneity bias. 1.1 Literature Review on Advertising Effectiveness Bagwell (2007) provides an excellent survey of theoretical and empirical work on advertising. Section 3 of Bagwell s survey describes a host of studies relating firm-level and industry-level advertising to sales. Typically advertising and sales are measured at the annual level. These studies suffer from an 4

5 endogeneity problem that makes a causal interpretation of their estimates questionable. In particular, advertising is determined by firms, and firms likely choose advertising levels as a function of factors not measured by the researcher. It is not clear whether sales are high due to high advertising levels or whether firms that would have higher sales anyway do more advertising. Section 8.1 of Bagwell s survey describes a handful of empirical studies looking at the effects of individual advertising exposure on individual purchase behavior. For example, Tellis (1988) uses individual data on sales and television advertising exposure for toilet tissue to estimate a model of sales as a function of past advertising exposure. More recently, Ackerberg (2001) uses similar panel data on yogurt to regress sales on television advertising interacted with an individual s purchase history. He finds that advertising only substantially increases sales for consumers who had never previously purchased a newly introduced brand. 2 In our opinion, these studies lack rich models of unobserved heterogeneity and do not deal with the endogeneity issues we address with our econometric method, although we use similar data. Compared to previous studies relating television advertising to purchase decisions, these data have more panelists, cover a longer time period and, because of their more recent collection, use more effective technologies for measuring advertising exposure and purchases. Thus, we expect the data quality to be higher than the data used in this small literature. There is a recent literature on internet ad exposure using experimental variation and before/after within-household comparisons (Lewis and Reiley, 2014; Golden, 2014; Thomas Blake, Forthcoming). This literature tends to find modest effects of internet advertising on sales, although the expenditure levels in the experiments are far below the levels spent by, say, detergent firms on television advertising. Another literature has used several empirical strategies to isolate plausibly independent variation in aggregate advertising using television media markets. Dubé and Manchanda (2005) and Gordon and Hartmann (2013) exploit ad price variation across media markets. Shapiro (2014) exploits a discontinuity in ads seen on the borders of media markets. Hartmann and Klapper (2014) and Smith, Stephens-Davidowitz and Varian (2013) exploit variation in the identity of the football teams playing in the Super Bowl, which affects viewership depending on the distribution of fans for those teams across markets. 2 Data Our study is motivated by access to data matching from Nielsen Germany matching information on television ad exposure with information on laundry detergent purchases. We focus on the 3782 households in the matched data who buy detergent at least once. The data cover July 2004 through June 2006, a period of time where internet ads and internet purchases played less of a role in Germany than they do today. 2 Shum (2004) is a similar empirical paper with aggregate advertising data. 5

6 A monitoring device is installed on the television in the household. Nielsen can see what channel the television is tuned to and hence match that to records on the ads shown. Except for the internet studies mentioned previously, this is one of the view datasets using for academic research with individual or household ad exposure linked to purchase data. As researchers, we have access to only the information on detergent ads, not the original television program being viewed or on ads for other product categories. As mentioned previously, these data prevent us from estimating a structural model of television program choice and hence incidental ad exposure. Also, the television monitoring device cannot detect whether a household member is in the room viewing the television (instead of using the bathroom, etc) and does not record the identity of the household member viewing the ad. This might be an issue if one household member makes detergent purchase decisions and another household member views an ad. Our econometric method does not adjust for such measurement issues and so our estimates must be interpreted to include the effects mentioned above. The purchase information is an example of homescan data. After visiting a grocery or similar store, each household member uses a device to scan the product bar codes of the purchased goods. We observe many things about detergent purchases, including brand pack size and the total spending on each product. Many of the television ads for laundry detergent ads focus on the brand and not pack size. Therefore, our dependent variable of interest in this advertising study is the binary decision to purchase our chosen focal brand. Ads in the detergent category do sometimes distinguish between liquid and powder detergents, although we prefer to focus on brand and not the finer distinction between powder and liquids. The same brand often sells both liquid and powder detergents. The data contain no information on price except as computed as the total spending on a product on a purchase occasion divided by the data s measure of the quantity purchased. Importantly, we cannot observe the prices in the store visited for detergent products not purchased. The data cover households geographically dispersed throughout Germany, so we rarely observe multiple households shopping at the same store. Because we lack information on price for goods that are not purchased, we do not include price in our semi-structural model of choice. We do include heterogeneous household and month specific demand shocks that have month-specific marginal distributions. These monthspecific marginal distributions nest homogeneous month fixed effects and proxy for aggregate time patterns in unmeasured prices. Similar arguments apply to other forms of promotions other than television ads themselves. The data break purchases down into twelve named brands as well as private label purchases and (separately) a collective category for minor brands that are not private labels. Not all brands advertise on television. We end up focusing our ads measures on seven large brands that routinely advertise on television. In our model, the key outcome is the decision to purchase a focal brand based on the ads seen for the focal brands and the total ads seen for the six other major advertised brands. We do not explicitly name the focal brand for confidentiality purposes, but it is the largest brand in terms of 6

7 Figure 1: Bin Count Monthly Ads Seen for Focal Brand Fraction of Month/Household Observations Number of Ads Seen for Focal Brand detergent sales in Germany. The seven major brands are owned by two global conglomerates, Henkel and Proctor and Gamble. This duopoly among the firms owning the major brands advertised on television plays no particular role in our study, which focuses on estimating the advertising elasticity. In our data, 47% of detergent purchase occasions result in the purchase of private label detergent. While private labels plays little role in our study except in our measurement of past laundry purchases, the large share of private labels is suggestive evidence that household heterogeneity is important to model. Because private labels are rarely advertised on television, a segment of the population may be relatively insensitive to television ads. Household heterogeneity is a key part of our model. The data in an approximate sense come in continuous time: the day of purchase is recorded and the exact time the ad is viewed is recorded. However, laundry is an infrequently purchased good; only 31% of households purchase detergent in a given month. For this reason, we aggregate our data to the month level. Our measures of ads are the total ads viewed for the month for the focal brand and the total ads viewed for the month for the six major rival brands. A monthly measure has the feature that the current month s ad exposure value will include ads not actually seen yet at the time of a purchase. For partly this reason, we expect lagged ads viewed to also be highly predictive of current purchases. Another reason that lagged ads predict current purchases is that detergent is a storable good; a household may not repurchase if they have detergent stockpiled at home. The individual brands have distinct seasonal patterns about when they choose to advertise on television. For our focal brand, it did not advertise in June for both of the years in our data. Other brands have different patterns. Figure 1 shows a bin count of ads seen for the focal brand in months other than June, across months and households. The figure shows that 27% of households view zero ads for the focal brand in a given month. Including households who view zero ads, the mean number of ads seen is 8, with a 7

8 standard deviation of 12. Indeed, Figure 1 shows a long right tail of households viewing 100 or even more ads for the focal brand. While not covered in the figure, the total ad count for the rival brands displays a similar shape, although the mean of 18 total rival ads per month is unsurprisingly higher than the mean of 8 ads for the focal brand. 3 Model Consider panel data on households i = 1,..., N with records of detergent purchase matched with records of ad viewing. There are T = 24 months of data. Y i,j,t denotes the binary indicator that household i purchases a product of the focal brand j during month t. Recall from above that the focal brand is the brand with the largest market share in Germany. Y i, j,t denotes the binary indicator that household i purchases a detergent product of any rival brand j during month t. X i,j,t denotes the number of ads viewed by household i from the focal brand j during month t. X i, j,t denotes the total number of ads viewed by household i for all detergent brands other than the focal brand during month t. U i denotes the unobserved heterogeneous type of household i, which indexes both time invariant heterogeneous parameters and time varying heterogeneous parameters. Using this notation, we study the dynamic choice model Y i,j,t = g t (Y i,j,t 1, X i,j,t,, X i,j,t+1 H, Y i, j,t 1, X i, j,t,, X i, j,t+1 H, U i ), (1) where H is the number of monthly lags of ad exposure we include to explain purchase. For our baseline specification, we choose H to be two months. Current and lagged ads proxy for a household s stock of goodwill towards the focal brand. Goodwill is not directly measured in most data. The ad exposure measures X i,j,t and X i, j,t are endogenous in the sense that they can be statistically dependent with the time invariant and time specific terms indexed by U i. Hence, we also model the dynamics of X i,j,t and X i, j,t. Let η i,j,t denote the proportion of seasonally varying leisure time L t that household i spends on watching television programs showing advertisements of the focal brand j during month t. Letting B j,t denote the unobserved frequency of broadcast advertisement at time t, we obtain the following relation. X i,j,t = η i,j,t L t B j,t. (2) We model the random process η i,j,t of television share of leisure time by the dynamic panel structure η i,j,t = h j (η i,j,t 1, η i, j,t 1, U i ), (3) where U i again indexes the time invariant and time specific heterogeneous unobservables other than 8

9 η i,j,t. Combining (2) and (3), we can write the dynamic process of focal brand ad exposure X i,j,t as X i,j,t = h j,t (X i,j,t 1, X i, j,t 1, U i ) := L t B j,t h j ( Xi,j,t 1 L t 1 B j,t 1, ) X i, j,t 1, U i. L t 1 B j,t 1 We can similarly write the dynamic process of total rival brand ad exposure X i, j,t as X i, j,t = h j,t (X i,j,t 1, X i, j,t 1, U i ). With the notation Z i,t = (Y i,j,t, X i,j,t+1, Y i, j,t, X i, j,t+1 ), the dynamic choice model and the ad exposure dynamics can be jointly written as Z i,t = G t (Z i,t 1,..., Z i,t H, U i ) := g (Y i,j,t 1, X i,j,t,, X i,j,t+1 H, Y i, j,t 1, X i, j,t,, X i, j,t+1 H, U i ) h j,t (X i,j,t 1, X i, j,t 1, U i ) h j,t (X i,j,t 1, X i, j,t 1, U i ). A literature has explored the nonparametric identification of G t = ( g, h j,t, h ) j,t (Sasaki, 2012; Kasahara and Shimotsu, 2008; Hu and Shiu, 2013). That literature emphasizes assumptions about the independence of time specific household shocks from both time invariant household preferences and lagged values of Z i,t. This rules out autocorrelation in time specific shocks, for example. Restricting the time series properties of time specific shocks in U i lowers the ability of the model to distinguish between state dependence, for example the role of Y i,j,t 1 and Y i, j,t 1 in g, from unobserved heterogeneity, for example the autocorrelation of the time-specific shocks. We do not make restrict the time series properties of time specific household shocks at the risk of losing the nonparametric identification established in the cited literature. We construct a likelihood criterion by modeling the joint distribution of observed data. To this end, we consider three separate components: 1) the initial conditions, 2) the heterogeneous dynamics of ad exposures (X i,j,t, X i, j,t ), and 3) the heterogeneous dynamic choice of Y i,j,t. The first component, the initial conditions of the joint distribution of the observed variables (Y i,j,1, X i,j,1, X i, j,1 ) and the unobserved variables in U i, is an important component of the data generating process. Unfortunately, initial conditions are not straightforward to model (Heckman, 1981). The correct specification of initial conditions would be essential if we had very short panel data, but the effect of its misspecification diminishes as the number of time periods increases. With our rich panel data set with 24 months of observations, we exclude the initial conditions term from our likelihood. The exposures (X i,j,t, X i, j,t ) do not have a stationary process because the underlying leisure time L t varies across seasons and advertisers may change their advertisement frequencies (B j,t, B j,t ) from time to time. However, we assume that the baseline proportions (η i,j,t, η i, j,t ) of leisure that 9

10 household i spends on watching television programs follows a stationary random process for each type of household. For each type U, η i,j,t follows the first-order autoregressive process η i,j,t = h (η i,j,t 1, η i, j,t 1, U) = α 0 (U) + α 1 (U) η i,j,t 1 + α 2 (U) η i, j,t 1 + λ 1,t (U), where the α(u) s are heterogeneous, time invariant parameters and λ 1,t (U) is a heterogeneous, time varying parameter. exposure X i,j,t : Using the relation (2), we obtain the implied dynamic law of focal brand ad X i,j,t E[X i,j,t ] = ᾱ 0(U) + α 1 (U) X i,j,t 1 E[X i,j,t 1 ] + α 2(U) X i, j,t 1 E[X i, j,t 1 ] + λ 1,t (U), where ᾱ 0 (U) = α 0 (U)/ E[η i,j,t ] and λ 1,t (U) = λ 1,t (U) / E[η i,j,t ]. Likewise, we have X i, j,t E[X i, j,t ] = γ 0(U) + γ 1 (U) X i,j,t 1 E[X i,j,t 1 ] + γ 2(U) X i, j,t 1 E[X i, j,t 1 ] + λ 2,t (U), where γ 0,t (U) = γ 0,t (U)/ E[η i, j,t ] and λ 2,t (U) = λ 2,t (U) / E[η i, j,t ]. Lastly, we use the following threshold crossing model for the dynamic discrete choice (1), g (Y i,j,t 1, X i,j,t,, X i,j,t+1 H, Y i, j,t 1, X i, j,t,, X i, j,t+1 H, U i ) = { H H 1 β 0 (U) + β 1 (U) β 1 (U) h X i,j,t h + β 2 (U) β 2 (U) h X i,j,t h Y i,j,t 1 h=0 +β 3 (U) Y i,j,t 1 + β 4 (U) (Y i,j,t 1 + Y i, j,t 1 ) + h=0 } H β 5 (U) β 5 (U) h X i, j,t h + λ 3,t (U) 0. h=0 This functional form includes the effects of current and lagged focal brand advertising, current and lagged rival brand advertising, lagged own brand purchases, lagged purchases of any brand of detergent, and interactions of lagged purchases with advertising. To reduce the number of heterogeneous parameters, each lagged advertising measure enters as a power law. We collect the heterogeneous time invariant and time specific household shocks in into a household parameter vector θ(u) = (ᾱ 0 (U), ᾱ 1 (U), ᾱ 2 (U), γ 0 (U), γ 1 (U), γ 2 (U), { β 0 (U), β 1 (U), β 2 (U), β 3 (U), β 4 (U), β 5 (U), ( λ1,t (U), λ 2,t (U), λ 3,t (U) ) ) T. t=h+2 The immediate goal of our empirical work is to identify the joint distribution of heterogeneous types U or, in other notation, the joint distribution F of the time specific and time invariant heterogeneous 10

11 parameters in the long vector θ (U). Below we use the estimated distribution ˆF to compute aggregate advertising elasticities. Our model addresses the four endogeneity issues mentioned in the introduction. 1. Brand-level advertising is allowed to be correlated with the demand shocks in the focal brand s purchase equation. We do not restrict the month-specific marginal distributions of λ 1,t (U), λ 2,t (U) and λ 3,t (U), which nests the incorporation of month fixed effects into our model s three equations. 2. The ad exposure of households is allowed to be correlated with the household persistent preferences in the purchase equation. In particular, the heterogeneous parameters β (U) in the purchase equation have an arbitrary joint distribution with the advertising exposure parameters ᾱ (U) and γ (U). 3. The time-specific household shocks in the purchase equation are allowed to be correlated with the time-specific ad exposure shocks. We do not restrict the joint distribution λ 1,t (U), λ 2,t (U) and λ 3,t (U) for time t. 4. Finally, we credibly distinguish the role of past purchase histories (Y i,j,t 1, Y i, j,t 1 ) from unobserved time invariant purchase parameters β (U) and time-specific household purchase shocks λ 3,t (U) by not restricting the time series process of λ 3,t (U). Fixing T = 24, we allow an arbitrary joint distribution of (λ 3,t (U)) T t=1. We allow flexible correlation in time-specific unobserved heterogeneity as an alternative to state dependence for explaining the observed patterns of purchase over time in the data. 4 Estimation Our immediate estimation goal is to estimate F, the joint distribution of θ (U). We use recent techniques from the literature to reduce the computational burden of this task. Following Bajari, Fox and Ryan (2007), Fox, Kim, Ryan and Bajari (2011), Fox, Kim and Yang (2013) and Train (2008), we pick a finite, fixed grid of ū parameter vectors θ(u) indexed by u. In practice, we generate a grid of size 2,000 using a Halton sequence. We then estimate the weights ρ = (ρ (u),..., ρ (ū)) by maximizing the likelihood. Using the model specification presented in the previous section, we can write the logarithm of the conditional density of the observed variables Z i = (Y i,j,t,..., Y i,j,1, X i,j,t,,..., X i,j,1, X i, j,t,,..., X i, j,1 ) 11

12 Table 1: Parameters for Monte Carlo ᾱ 0 Normal(0.5, ) α 1 Normal(0.5, ) α 2 Normal( 0.5, ) γ 0 Normal(0.5, ) γ 1 Normal( 0.5, ) γ 2 Normal(0.5, ) β 0 Normal( 0.5, ) β 1 Normal(0.0, ) β 2 Normal(0.5, ) β 3 Normal(0.0, ) β 4 Normal( 0.5, ) β 5 Normal( 0.5, ) given U i = u in terms of θ(u) as log p (Z i U i = u) = log f (Y i,j,h,, Y i,j,1, X i,j,h,, X i,j,1, X i, j,h,, X i, j,1 U i = u) T + log Φ i,j,t (θ(u)) t=h+1 where f denotes the density of the initial distribution of (Y i,j,h,, Y i,j,1, X i,j,h,, X i,j,1, X i, j,h,, X i, j,1 U i = u), and Φ i,j,t (θ(u)) is defined by a smoothed version of the outcomes Z i,t = (Y i,j,t, X i,j,t+1, Y i, j,t, X i, j,t+1 ) occurring. As stated earlier, we lack a model of the initial conditions and we drop this term. Because of our panel of 24 months, we hope the bias from dropping the initial conditions is minimal. We maximize the resulting likelihood over the weights ρ only. In practice, we employ the version of the EM algorithm in Train (2008) to find the maximum of the likelihood without employing a numerical optimization routine. 5 Monte Carlo We perform a Monte Carlo study of the performance of our estimator. We generate the heterogeneous parameters independently according to the rule in Table 1. In addition, we generate α 3 = 1 α 2 1 α2 2 1/2 and γ 3 = 1 γ 2 1 γ2 2 1/2. Figure 2 shows Monte Carlo simulation results based on 1,000 iterations with the sample size of (N, T ) = (100, 24) and the lag order H = 2 for the model. The solid curves indicate the true marginal CDFs of the heterogeneous parameters, while the dashed curves indicate the medians, the 95% intervals, and the 99% intervals of the Monte Carlo estimates of the marginal CDFs. Some true marginal CDFs fall well within the estimation bands while other true marginal CDFs do not lie within the Monte Carlo bands. 12

13 ᾱ 0 α 1 α 2 γ 0 γ 1 γ 2 β 0 β 1 β 2 β 3 β 4 β 5 Figure 2: Monte Carlo simulation results based on 1,000 iterations. The sample size is (N, T ) = (100, 24), and the lag order is H = 2. The grid of size 2,000 was generated using a Halton sequence. The solid curves indicate the true CDFs while the dashed curves indicate the medians, the 95% intervals, and the 99% intervals of the MC estimates of the CDFs. 13

14 α 1 α 2 γ 1 γ 2 β 1 β 2 β 3 β 4 β 5 α α γ γ β β β β β Table 2: Estimated correlations among the heterogeneous coefficients for the model III with the lag order H = 2 and the grid of size 2,000 generated using a Halton sequence. 6 Estimated Joint CDF and Advertising Elasticities 6.1 Estimated Joint CDF of the Heterogeneous Parameters We estimate the distribution F of the long random vector θ (U) using a subset of the full data. Figure 3 shows the estimated marginal CDFs of some key heterogeneous parameters in the three equations: focal brand advertising exposure, rival brand total advertising exposure, and the binary choice model for the focal brand. Our estimates of the joint distribution of the long vector θ (U) imply a correlation matrix for the heterogeneous parameters. The estimated correlation matrix for some of the key parameters is in Table Advertising Elasticities Our preferred notion of an advertising elasticity considers an increase in advertising by percent for the focal brand j only. This increase effects all the lags of advertising exposure for the focal brand j in that the new ad exposure is (1 + ) X i,j,t for all households i and months t. Lagged purchases are kept the same for simplicity; without modeling purchases of rival brands explicitly we cannot recompute the complete history of past purchases. With the perturbation of the focal brand ad exposure by, the advertising elasticity facing the focal brand j in month t averaged over household types and households is N ū i=1 u=1 Pr t (Y i,j,t = 1;, θ (u)) p (U = u; data i ) 1 Pr t (Y i,j,t = 1;, θ (u)), where the first term is the partial derivative of the probability of purchase with respect to for type u, the second term is the probability of household i being type u given its purchase history, and 14

15 α 1 α 2 γ 1 γ 2 β 1 β 2 β 3 β 4 β 5 Figure 3: Estimated CDFs of the heterogeneous parameters with the lag order H = 2 and the grid of size 2,000 generated using a Halton sequence. 15

16 the third term is the purchase probability itself. The estimated elasticity varies by months because existing ad exposures for the focal brand vary by month and because the distribution of the shocks λ 1,t (U), λ 2,t (U) and λ 3,t (U) varies by month. We computed advertising elasticities for three different models that differ in their treatment of the time shocks λ 1,t (U), λ 2,t (U) and λ 3,t (U). Model I is a simplified version of our model where λ 1,t (U), λ 2,t (U) and λ 3,t (U) are all normals that are independent over time for the same household and not correlated across equations. Also, the distribution of the λ 1,t (U), λ 2,t (U) and λ 3,t (U) s cannot vary across months, so that this specification does not nest homogeneous fixed effects. Model I does not address three of the four sources of endogeneity mentioned in the introduction; Model I does allow correlation between the heterogeneous time invariant parameters in the three equations. Model II allows λ 1,t (U), λ 2,t (U) and λ 3,t (U) to follow a multivariate normal distribution within a month, but still imposes independence across months and independence of the time shocks from the time invariant heterogeneous parameters. Model II hence generalizes Model I and somewhat addresses endogeneity concerns with household correlations in ad exposures and time shocks, within a month. Model III is the full model described previously. Table 3 reports data statistics, advertising elasticities for the focal brand, and average time effects. All specifications using advertising lags of up to H = 2 months. The estimated advertising elasticity does very considerably across months. We can see a burn in period perhaps caused by omitting the initial conditions for models I and II. After, the elasticities are typically higher for model I than model II and both models I and II typically have higher elasticities than the elasticities for model III. The most important result in the paper are the advertising elasticities that are averaged across months in addition to households and heterogeneous types, at the bottom of Table 3. For model I, the average advertising elasticity is The elasticity corresponds well to the advertising elasticity of 0.02 needed to explain the 10% advertising to sales ratio in the introduction. Model I deals with only one of the four sources of endogeneity bias mentioned in the introduction, so one conclusion is that the raw patterns in observational household data can lead an observer to conclude that advertising is effective enough to justify a 10% advertising to sales ratio. For model II, Table 3 shows that the mean advertising elasticity is By allowing multivariate normal time specific shocks with nonzero correlations across equations, model II deals with some forms of household level endogeneity but does not address the correlation of aggregate brand or category demand shocks with advertising campaigns. The survey by Bagwell (2007) emphasizes that the potential from bias in estimated advertising elasticities from such correlation is an important drawback of much of the prior empirical literature on advertising. Table 3 shows that the mean advertising elasticity for the full model, model III, is This small advertising elasticity confirms the importance of allowing for all the features of the full model, including allowing λ 1,t (U), λ 2,t (U) and λ 3,t (U) to have month specific marginal distributions, which nest homogeneous month fixed effects in order to address the correlation of aggregate brand or cat- 16

17 Data Statistics Averages Estimated Elasticities Average Time Effects X i,j,t X i, j,t Y i,j,t Y i, j,t (I) (II) (III) ᾱ 0,t γ 0,t β 0,t Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Average Table 3: Data statistics, estimated advertisement elasticities, and average time effects. The displayed values of X i,j,t and X i, j,t are divided by 100 compared to the actual values. Model I is the model with i.i.d. normal time shocks, model II is the model with multivariate normal time shocks, and model III is the full model. All results are based on the lag order H = 2. The last three columns show average time effects under model III. 17

18 (I) i.i.d. Normal Shocks (II) Multivariate Normal Shocks (III) Full Model H = 1 H = 2 H = 3 H = 1 H = 2 H = 3 H = 1 H = 2 H = 3 Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Average Table 4: Estimated advertisement elasticities. Model I is the model with i.i.d. normal time shocks, model II is the model with multivariate normal time shocks, and model III is the full model. egory demand shocks with advertising campaigns. The elasticity of is quite small. Using the benchmark own price elasticity of -2 from the introduction, an advertising elasticity justifies only a 0.5% advertising to sales ratio, using the Dorfman and Steiner condition. The low advertising elasticity from the full model is consistent with the advertising effectiveness elasticities perceived by advertising practitioners being driven by endogeneity bias from using observational data without correction for the sources of endogeneity bias we outlined in the introduction. Table 4 reports more advertising elasticities for models I III. The elasticities are first broken out by month; we can see, as before, that model I tends to have higher elasticities than model II and model II tends to have higher elasticities than model III. The table also shows how varying the number H of lags of advertising exposure alters the estimated advertising elasticities. There is no real pattern of how changing the lag length H effects the elasticities. Importantly, the low elasticities for the full model III are found regardless of the number of lags of advertising exposure included in the model. 18

19 7 Conclusion Our conclusion is that most of the advertising elasticity that a researcher not correcting for endogeneity bias might estimate is actually due to endogeneity bias. Therefore, practitioner beliefs about the effectiveness of advertising may arise not from the causal effects of advertising but from false conclusions from observational data without corrections for endogeneity. 19

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