Estimating installed-base effects in product adoption: Borrowing IVs from the dynamic panel data literature☆
Introduction
How an individual’s product adoption is influenced by the behavior among the individual’s reference group is an important topic. A specification with installed base is widely used to empirically answer such a question, where peer influence is measured as the impact of the size of past adopters (i.e., installed base) in the reference group on the individual’s choice (Iyengar et al., 2011, Bollinger and Gillingham, 2012, Narayanan and Nair, 2013). A key challenge in estimation of causal installed-base effects is homophily, a phenomenon that group members share similar preferences and thus tend to behave similarly.
Narayanan and Nair (2013) make an insightful observation that including group fixed effects to account for homophily leads to inconsistent estimates in models with installed base, and propose an IV approach and a bias correction approach as possible solutions. While they examine both, their main focus is on the bias correction approach, as they view the IV approach as infeasible in many contexts due to “the difficulty of finding exogenous variation that shifts the installed base over time but holds current adoption fixed”, a perception that seems fairly widespread in the literature (e.g., Bollinger and Gillingham (2012)).
This research note argues that borrowing insights from the dynamic panel data literature provides us with instruments that would be available in many settings. In dynamic panel data models, including the lagged dependent variable as a regressor leads to inconsistency of fixed effects estimator, and researchers have proposed to use lags and lagged differences of the lagged dependent variable as instruments after first-differencing (Anderson and Hsiao, 1981, Arellano and Bond, 1991). I argue that similar types of instruments can be used in the considered model. First-differencing is used to remove homophily, and the ensuing endogeneity is addressed by using lags and lagged differences of the installed base as IV. This approach has the key advantage of relying on only internal variables to generate instruments.
Narayanan and Nair (2013) note the close similarity between the considered model and dynamic panel data models, but suggest that finding IVs would be in general difficult in the considered setting. The contribution of this paper is to highlight an IV approach borrowed from the dynamic panel data literature as a readily available and feasible solution, thereby offering a nice complement to the bias correction approach.
Section snippets
Empirical model
An individual makes a binary choice of whether to adopt a product or not, if she has not yet adopted.1 The latent utility from adoption for individual , a member of group , in period is given by represents the installed base of adopters in ’s group in period
Monte Carlo simulations
In this section, I present a series of Monte Carlo results to examine the performance of the proposed IV approach. I simulate adoption behavior of individuals and aggregate it up to group-level data. I repeat the procedure to generate 500 datasets. Each dataset tracks 1000 groups with 10,000 members each, over 10 time periods. In each period, individual adopts the product if the utility from adoption is greater than the utility from no adoption, in case she has not yet adopted. The utility
Conclusion
In this research note, I discuss consistent estimation of causal installed-base effects in models that include both installed base and unobserved group-level heterogeneity. Contrary to the seemingly common perception that instruments are hard to find for such a model, I, borrowing insights from the dynamic panel data literature, propose an approach which does not require external instruments and rather uses internal variables to construct instruments. Monte Carlo simulations show that lags and
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Park gratefully acknowledges the support provided by the National Research Foundation of Korea (NRF) Grant 2018S1A5A2A01029529. The work was partly conducted when the author was an assistant professor at the Haas School of Business, University of California, Berkeley. I greatly thank three anonymous reviewers and the associate editor for their insightful comments and highly constructive suggestions. The usual disclaimer applies.