Sungho Park

Handling Endogenous Regressors by Joint Estimation Using Copulas

We propose a new statistical instrument-free method to tackle the endogeneity problem. The proposed method models the joint distribution of the endogenous regressor and the error term in the structural equation of interest (the structural error) using a copula method, and it makes inferences on the model parameters by maximizing the likelihood derived from the joint distribution. Similar to the “exclusion restriction” in instrumental variable methods, extant instrument-free methods require the assumption that the unobserved instruments are exogenous, a requirement that is difficult to meet. The proposed method does not require such an assumption. Other benefits of the proposed method are that it allows the modeling of discrete endogenous regressors and offers a new solution to the slope endogeneity problem. In addition to linear models, the method is applicable to the popular random coefficient logit model with either aggregate-level or individual-level data. We demonstrate the performance of the proposed method via a series of simulation studies and an empirical example.

Simulated Maximum Likelihood Estimator for the Random Coefficient Logit Model Using Aggregate Data

The authors propose a simulated maximum likelihood estimation method for the random coefficient logit model using aggregate data, accounting for heterogeneity and endogeneity. The method allows for two sources of randomness in observed market shares: unobserved product characteristics and sampling error. Because of the latter, the method is suitable when sample sizes underlying the shares are finite. In contrast, Berry, Levinsohn and Pakess commonly used approach assumes that observed shares have no sampling error. The method can be viewed as a generalization of Villas-Boas and Winers approach and is closely related to Petrin and Trains “control function” approach. The authors show that the proposed method provides unbiased and efficient estimates of demand parameters. They also obtain endogeneity test statistics as a by-product, including the direction of endogeneity bias. The model can be extended to incorporate Markov regime-switching dynamics in parameters and is open to other extensions based on maximum likelihood. The benefits of the proposed approach are achieved by assuming normality of the unobserved demand attributes, an assumption that imposes constraints on the types of pricing behaviors that are accommodated. However, the authors find in simulations that demand estimates are fairly robust to violations of these assumptions.

A Regime-Switching Model of Cyclical Category Buying

In many categories consumers display cyclical buying: they repeatedly purchase in the category for several periods, followed by several periods of not buying. We believe that the cyclicality is a manifestation of cross-category substitution by the consumer, caused by “variety-seeking” tendencies as well as by the firms marketing activities in all relevant categories. We propose a Markov regime-switching random coefficient logit model to represent these behaviors as stochastic switching between high and low category purchase tendencies. The main feature of the proposed model is that it divides the stream of purchase decisions of a consumer into distinct regimes with different parameter values that characterize high versus low purchase tendencies. In an empirical application of the model to purchases of yogurt-buying households, we find that as many as 38.3% households display cyclicality between high and low yogurt-purchasing tendencies. Predictions from our proposed model track observed yogurt purchases of households over time closely, and the model also fits better than two benchmark models. Alternating between high and low purchase tendencies may correspond with changing levels of consumer inventory in a substitute category. If one ignores this phenomenon, a correlation between yogurt inventory and the error term in utility arises, leading to biased estimates. Also, we show that cyclicality in buying has a key implication for a firms price promotion strategies: a price reduction that is offered to a household during its high purchasing tendency period will result in greater increases in sales than one that is offered during its low purchasing period. This opens up a new dimension for enhancing the effectiveness of promotions---customized timing of price reductions.

Mobile App Analytics: A Multiple Discrete-Continuous Choice Framework

The number of mobile apps launched in the market has exponentially grown to more than 2 million, but little is known about how users choose and consume apps of numerous categories. This study develops a utility theory-based structural model for mobile app analytics. We use the theoretical concepts of utility and satiation along with the factor analytic approach, as bases in simultaneously modeling the complex relationships among choice, consumption, and utility maximization for consumers of various mobile apps. Using a unique panel dataset detailing individual user-level mobile app time consumption, we quantify the baseline utility and satiation levels of diverse mobile apps and delineate how app preferences and consumption patterns vary across demographic groups and affected by persistent use and time trends. The findings suggest that users’ baseline utility substantially diverges across app categories and that their demographic characteristics and habit formation explain the appreciable heterogeneity in baseline utility and satiation. These parameters also exhibit positive and negative correlations in mobile websites and app categories. Our modeling approaches and computational methods can unlock new perspectives and opportunities for handling large-scale, micro-level data, while serving as important resources for big data analytics and mobile app analytics.

Temporal Disaggregation: Methods, Information Loss, and Diagnostics

This research provides a generalized framework to disaggregate lower-frequency time series and evaluate the disaggregation performance. The proposed framework combines two models in separate stages: a linear regression model to exploit related independent variables in the first stage and a state–space model to disaggregate the residual from the regression in the second stage. For the purpose of providing a set of practical criteria for assessing the disaggregation performance, we measure the information loss that occurs during temporal aggregation while examining what effects take place when aggregating data. To validate the proposed framework, we implement Monte Carlo simulations and provide two empirical studies. Supplementary materials for this article are available online.