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Measuring the Effects of Marketing Solicitations


This research examines the effectiveness of marketing solicitations to customers by a commercial bank. For financial products, a customer might respond to marketing solicitations by either adopting the products directly or contacting the bank for additional information before deciding whether or not to adopt the products. Consequently, whether a customer adopts a product depends not only on the marketing solicitations themselves (the direct effect) but also on the amount of information (the indirect effect) obtained from contacts initiated by customers before potential product adoption. Decomposing the two effects is important in designing effective marketing campaigns. For this purpose, we develop a model of customers’ contact and product adoption decisions in response to marketing solicitations. We further evaluate the statistical significance associated with indirect effects using Bayesian mediation analysis. Our model estimates suggest significant direct and indirect effects of marketing solicitations. The indirect effects, though smaller in magnitude, lead to sizable economic value, in terms of targeting. This result underscores the importance of understanding the indirect effects of marketing solicitations. In addition, we discuss the insights derived from our model for marketing resource allocation among direct solicitations and experiences associated with customer-initiated contacts.

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Fig. 1


  1. 1.

  2. 2.

    For brevity, we refer to customer-initiated contacts as customer contact or simply contact for the remaining of the manuscript.

  3. 3.

    We also tried other specifications, particularly by including the average of the number of products held and contacts within the previous two and three periods. The results obtained from these specifications are qualitatively consistent


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Correspondence to Jialie Chen.



Computational Details for Mediation Analysis

Given the non-linear specification in our proposed Poison model, we are unable to infer the statistical significance of the proposed effects (shown in Fig. 1), from the posterior draws of the parameters alone. Instead, we follow the procedure Cheng et al. [7] proposed to infer the direct and indirect effects:

  1. 1.

    We first make 1000 draws of each parameter from its Markov chain Monte Carlo posterior draws. In our setting, the set of parameters includes not only those associated with the marketing solicitation itself ( \({S}_{it}^{\{O,F\}}\)) but also the interaction terms, or \(\{{S}_{it}^{\{O,F\}}\}\bullet {P}_{i,t-1}\) and\(\{{S}_{it}^{\{O,F\}}\}\bullet {N}_{i,t-1}\), which appear in both Eqs. (1) and (2). By doing so, we consider the effects of marketing solicitations through both the linear and interaction terms.

  2. 2.

    With each set of parameters drawn, we make the following predictions:

    1. a.

      We first predict the average number of prepurchase, postpurchase, and cancellation contacts made by all customers when there is (1) no solicitations or \({S}_{it}^{\{O,F\}}=0\), (2) one unit of additional offline solicitation only or \({S}_{it}^{F}=1\), and (3) one unit of additional online solicitation only or \({S}_{it}^{O}=1\). We define the number of contacts predicted under each of the three scenarios as \(\{{N}_{it,1}\}\), \(\left\{{N}_{it,2}\right\},\) and \(\{{N}_{it,3}\}\), respectively.

    2. b.

      Given the predictions of contact decisions, we can further predict the monthly average number of product adoptions of all customers under the following scenarios:

      1. i.

        No additional solicitations (base), where neither a direct nor an indirect effect occurs. Under that scenario, we assume that \({S}_{it}^{\{O,F\}}=0\) and use \({N}_{it,1}\) to predict product adoption.

      2. ii.

        No direct effect from offline (online) solicitation, but with an indirect effect occurring. Under this scenario, we assume that \({S}_{it}^{F}=0\) (\({S}_{it}^{O}=0)\) but use \({N}_{it,3}\) (\({N}_{it,2}\)) to predict product adoption.

        In that regard, offline (online) solicitation could change customer-initiated contacts and hence indirectly influences product adoptions. However, the solicitation could not directly shift product adoption decision as \({S}_{it}^{F}\) (\({S}_{it}^{O})\) is set to \(0\).

      3. iii.

        No indirect effect, but with a direct effect from offline (online) solicitation. Under this scenario, we assume that \({S}_{it}^{F}=1\) (\({S}_{it}^{O}=1)\) but use \({N}_{it,1}\) to predict product adoption.

        Contrary to scenario ii, offline (online) solicitation could directly shift product adoption through \({S}_{it}^{F}\) (\({S}_{it}^{O})\). However, the solicitation will place no impacts on contacts and hence no indirect effects on product adoptions.

  3. 3.

    We repeat the procedure for all 1000 draws of parameters and obtain 1000 sets of predictions for product adoption under the three scenarios. Using these predictions, we further compute the difference between predictions obtained under scenarios ii and i and the difference between scenarios iii and ii. The first difference represents the indirect effects and the second represents the direct effects of marketing solicitations. Using the 1000 sets of indirect and direct effects, we further compute the mean and credible interval of effects.

Our approach is therefore analogous to a bootstrap approach, with the modification of incorporating two predicted values.

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Chen, J., Rao, V.R. Measuring the Effects of Marketing Solicitations. Cust. Need. and Solut. (2021).

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  • Marketing solicitations
  • Attributions
  • Financial products
  • Direct effects
  • Indirect effects
  • Bayesian mediation analysis