Exploring the Relationship Between Online Search and Offline Sales for Better "Nowcasting"

Online Appendix A

(Alternate Models)

In this appendix we present justification for four alternate models of advertising. These models differ in terms of the presumed impact of advertising (dashed line from advertising in figure 1). This is accomplished by allowing advertising to enter the system as a covariate in one or more of the three equations in the dynamic system.

A model of purchase acceleration (M2)

We consider a model where advertising has only a direct impact on sales. The direct effect of advertising spend on sales is the most basic and prominent approach employed by researchers in marketing [12, 18, 24]. We model the direct effect of advertising on sales by including advertising stock, gt, as a covariate in the sales equation of the system in (2):

(A.1)

where θ captures the direct impact of advertising stock on sales and is given in equation (3). As illustrated by the IRF in Figure (2), Model 2 (M2) is a model of purchase acceleration. That is, an

increase in advertising will generate a corresponding increase in contemporaneous sales at the expense of future sales. As a result, the IRF for this model is characterized by a classic, post-promotional dip [21, 27] and a decline in post- promotional search activity.

The purchase acceleration in sales results in a corresponding decline in latent interest (dt) through interest carryover . This decline in latent interest propagates itself and results in a corresponding dip in online search as expected. This process (dip in the post-promotional search activity) is demonstrated and captured in the IRF in Figure 2 for Model 2.

A model of online search escalation (M4)

Traditional media (television, newspaper, and radio) is still one of the most significant sources of information valued by tech-savvy younger consumers [13]. There is a rich body of literature that explores the impact of traditional advertising on consumer search behavior [3, 28]. The common theme is that advertising can increase consumers’ ability to recall prior product information or increase their evoked set, thus aiding in search. More recently, Mayzlin and Shin [25] discuss how uninformative advertising in mass media entices consumers to search.

Therefore, in Model 4 (M4) we allow advertising to exert an exclusive influence on online search. As shown in the IRF for Model 4 in Figure 2, this specification gives rise to an immediate increase in q but does not have a corresponding influence on either latent interest or sales. As shown in equation (A.2), M4 corresponds to a model where advertising results in online search escalation.

(A.2)

where δ captures the direct impact of advertising stock on online search. For completeness, we also investigate two other possible models that correspond to various combinations of the effects of advertising. In Model 5 (M5) we allow advertising to impact both sales and search, while

advertising is presumed to drive both search and latent interest in Model 6 (M6).

Advertising drives both sales and search (M5)

The IRF for Model 5 in Figure 2 clearly demonstrates the impact of advertising on both sales and search. It is interesting to note that this model differs from M3 where advertising impacts latent interest only. As can be seen, in M5, the impact of advertising results in both purchase acceleration and search escalation (at the expense of future sales and search) and therefore leads to an observable corresponding dip in post-promotional sales and search. M5 also differs from M2 (where advertising only impacts sales leading to an increase in only sales and a post-promotion dip in both sales and search). Thus, M5 is a model of concomitant purchase acceleration and search escalation.

(A.3)

Advertising drives both search and latent interest (M6)

Model 6 (M6) investigates the impact of advertising on both online search and latent interest. The IRF in Figure 2 captures the impact of advertising on both sales and search. The impact on sales is indirect (through latent interest) while the impact on search is both direct and indirect (through latent interest). The IRF for M6 looks very similar to M3, the main difference being the scale (y-axis) of the impact on search. In M3 the impact of advertising is only through latent interest (indirect) whereas in M6 advertising has a cumulative effect (both direct and indirect) and hence a higher peak for search. Thus, M6 captures the concurrent effect of advertising on search and latent interest and reduces to M3 if the impact of advertising on search is not significant.

(A.4

Online Appendix B

In this appendix, we show the step-by-step MCMC algorithm for the estimation of Model M3:

Define and

Equations in Model M3 can then be re-expressed in the following form

The following are the steps of the MCMC algorithm:

1)  Draw d1, d2, …, dt sequentially as follows:

Ø  For t=1, , that is, normal draws with

variance =and

mean= where d0 and v0 are the prior mean and variance for d1.

Ø  For t>1, , that is, normal draws with

variance=and

mean=.

2)  Draw β from , normal draws with variance= and mean= where β0 and V0 are the prior mean and variance for β.

3)  Draw l from , that is,

normal draws with variance= and mean= where l0 and vl are the prior mean and variance for l.

4)  Draw α from , that is, normal draws with variance= and mean= where α0 and vα are the prior mean and variance for α.

5)  Draw η from , that is,

normal draws with variance= and mean= where η0 and Vη are the prior mean and variance for η.

6)  Draw f using random-walk Metropolis-Hastings: First, let (i.e., a cdf function, an alternative function is the logistic function). With this transformation, f is restricted to be between 0 and 1. Next, let where step is assigned to be a small number such as 0.01, and is a random number generated from the standard normal distribution. Accept the new draw with probability

.

With the newly drawn f, calculate for t>1.

7)  Draw from , that is, Inverted chi-square draws with d.f.=t+n0 and scale =+s0 where n0 and s0 are the d.f. and scale parameter assumed in the prior distribution of .

8)  Draw from , that is, Inverted chi-square draws with d.f.=t-1+n0 and scale =+s0 where n0 and s0 are the d.f. and scale parameter assumed in the prior distribution of .

9)  Draw κ from , that is, normal draws with variance= and mean= where uκ and Vκ are the prior mean and variance for κ.

10)  Draw g from , that is, normal draws with variance= and mean= where uγ and Vγ are the prior mean and variance for g.

11)  Draw from , that is, Inverted chi-square draws with d.f.=t+n0 and scale =+s0 where n0 and s0 are the d.f. and scale parameter assumed in the prior distribution of .

Online Appendix C

In this appendix, we provide the results of the simulation study for our proposed model (M3) and demonstrate that we can recover the true parameter values. The sample size used for our simulation study is similar to our real data i.e. 52 weeks. The details of the estimation algorithm are provided in appendix B. Table C.1 provides the true values of the parameters used to generate the data and the corresponding posterior mean and standard deviation (in parenthesis). The MCMC chain was run for 10,000 iterations and the last 5000 draws were used to construct the 95% credible interval (in square brackets).

-- Insert Table C.1 about here --

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Table C.1

Parameter Estimates based on simulated data for Model 3 (M3)

β: 98.31 (1.2)
[94.25, 102.75]
True value: 100 / η: 4.94 (0.19)
[4.39, 5.62]
True value: 5 / κ: 99.40 (5.81)
[87.81, 109.69]
True value: 100 / γ: 1.99 (0.03)
[1.95, 2.05]
True value: 2
α: 0.77 (0.02)
[0.70, 0.84]
True value: 0.80 / λ: 199.00 (2.84)
[188.09, 207.69]
True value: 200 / ϕ: 0.21 (0.03)
[0.17, 0.28]
True value: 0.2 / σs2: 7.45 (2.41)
[3.82, 13.31]
True value: 10
σd2: 22.85 (5.86)
[14.68, 37.43]
True value: 20 / σq2: 16.76 (8.21)
[5.89, 37.07]
True value: 10


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Figure C.1

Trace plots of the simulation study for Model 3 (M3)

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