Multipart Pricing of Information Goods

ion of the estimation procedure should yield similar evidence for our hypothesis. Empirically, alternative estimators providing similar support for our hypotheses lends validity to the results presented. To estimate this alternative estimator, we express the log-likelihood function of the process that determines the bundle size to be the following: N ln Oln 1 ln 0 P (9) Mullahy (1986) showed that the log-likelihood function for this two-phase process can be estimated by incorporating a logit model to estimate the first phase, when the effective bundle size remains zero since no purchase has been made, followed by a zero-truncated negative binomial model to estimate the second phase, when the bundle size becomes a positive integer and the value hurdle has been crossed. The log-likelihood function (9) thus can be translated into a negative binomial hurdle model with a two-part log-likelihood function. Estimates for the empirical relationship are obtained by simultaneously estimating the maximum likelihood estimators for the two-part log-likelihood function. In Table 4, we present the estimation results. To assess model goodness-of-fit, we computed the deviance for both models. We observed that for both models, likelihood ratio χ –tests for the deviance scores are significant, suggesting good model fit (Poisson: χ = 4217.69, p-value<0.01; Hurdle/NB: χ = 772.13, p-value<0.01). We also checked the extent to which the pricing scheme 8 For conciseness, we omit details of the log-likelihood function. A generic two-part log-likelihood function can be found in Hilbe (2007) pp.234. For specific representation, a technical appendix is also available at request from the authors. 28 contributed to the observed variance in the final bundle size over and above the effects of the control variables. We computed the change in deviance score in the same manner we did for the ordered logit model. For both the selection-corrected Poisson and hurdle models, we observed that pricing scheme contributed significantly to the observed variance in bundle size beyond the effects of the control variables (Poisson: χ = 300.84, p-value<0.01; Hurdle/NB: χ = 74.6, pvalue<0.01). From the regression results, we observed that all estimators provided strong support for H2. After controlling for browsing duration, browsing behavior, time and location, we observed that the impact of pricing scheme on bundle size is positive and significant (coeff. = 0.246, pvalue<0.001). The coefficients suggest that a change from pricing scheme #2 to #1 will result in an increase of 0.246 in the difference in the logs of expected bundle size. This means that after controlling for other exogenous factors, bundles purchased under pricing scheme #1 have on average 27.9% more items than those purchased under pricing scheme #2. Notably, in the process of testing H2, we also found further empirical support for H1. In the first stage of estimation for both the selection-corrected Poisson model and the hurdle model, the binary choice estimation suggests that pricing scheme #1 is negatively correlated with the outcome of a sale (Probit coefficient = -0.383, p-value< 0.01; Logit coefficient = -0.635, pvalue< 0.01). This supports our earlier finding from the ordered logit model that higher initial transaction costs lead to higher sales probability. 9 We will discuss the results provided by the selection corrected Poisson model; the reader can draw similar conclusions with other estimators presented 29 Table 4: Impact of Pricing Scheme on Bundle Size Variables Selection-Corrected Poisson regression Hurdle Model: LogitNegative Binomial Bundle Size D.V. Coeff. (S.D.) Coeff. (S.D.) Pricing Scheme 1 0.246 *** (0.0143) 0.234 *** (0.027) Time Control -0.0514*** (0.00771) -0.0589*** (0.0148) Session duration (in seconds) 6.29E-06 *** (1.60E-06) 2.75E-05*** (7.12e-06) Sample Count 1.05E-03 *** (3.80E-05) 1.13 E-03 *** (1.38E-04) Constant & Location dummies^ Results suppressed for conciseness Selection Function (Purchased) D.V. Coeff. (S.D.) Coeff. (S.D.) Pricing Scheme 1 -0.383*** (0.0243) -0.635 *** (0.0498) Time Control -0.0185 (0.0129) 0.0274 (0.0270) Session duration (in seconds) -4.09E-05 *** (6.93E-06) -9.27e-06 (1.09E-05) Sample Count 0.0112*** (1.94E-04) 0.0114*** (2.52E-04) Session duration (squared) 1.55E-11 *** (2.96E-12) Sample Count (squared) -1.08E-05*** (2.49E-07) Constant & Location dummies^ Results suppressed for conciseness Note: The selection function (bottom panel) measures the extent of which each independent variable affects the probability of sale by considering all browsing sessions (both sold and unsold). The coefficients in the top panel are the estimates of, ; , parameters of the independent variables that impact bundle size. These estimates consider the bundles created after taking into account the presence of sessions that did not result in a sale. 5. Discussion Applying Thaler’s Transaction Utility Theory and using data from a natural experiment, we found strong evidence that consumers react to the framing effects of a multipart pricing scheme. Departing from the usual application of normative models to explain consumer behavior in bundle purchases, we showed that consumers are susceptible to biases in their decision making process when faced with multipart pricing schemes. By increasing the unattractiveness of the initial bundle prices, consumers become less likely to purchase a bundle. All else equal, if consumers do purchase under low initial transaction utility conditions, they are likely to create 30 larger customizable bundles. Although the eventual prices and contents of two bundles may be the same, the process of which their prices are framed impacts their purchasing behavior, likely because of the the total transaction utility perceived by the consumers. This finding is in line with Thaler’s argument that given the non-linear utility function, the addition of gains and losses that result in the same net gain (or loss) position might correspond to different net utility positions. For example, an individual winning a $50 lottery twice in a week (addition of two gains), is likely to experience higher utility than another winning a single $100 lottery. 5.1 Implications For Theory and Research There are several important theoretical and managerial implications of this research. In terms of extensions to theory and research, this paper highlights the need for additional examination of behavioral models of economic decision making and their application in the pricing of information goods. Most theoretical pricing models of information goods are normative in nature and behavioral aspects of the consumption of information goods are largely unexplored to date. The importance of normative economic theories on bundling is unquestionable. However, with the support of empirical evidence, we have demonstrated how consumer’s bundling and purchasing behavior can be significantly impacted by differences in the framing of pricing schemes. This should encourage and inform future studies to consider decision anomalies and framing effects in the consumption of information goods. Through this research, we highlight the significance of using a natural experiment to answer important research questions. Though opportunities for natural experiments are few and far between, the applications of such instances are suited in establishing robust conclusions through pseudo-controlled environments. Further, the natural setting in which the data is being collected