Estimating Causal Installed-Base Effects: A Bias-Correction Approach

Abstract

New empirical models of consumer demand that incorporate social preferences, observational learning, word-of-mouth or network effects have the feature that the adoption of others in the reference group -the "installed-base" -has a causal effect on current adoption behavior. Estimation of such causal installed-base effects is challenging due to the potential for spurious correlation between the adoption of agents, arising from endogenous assortive matching into social groups (or homophily) and from the existence of unobservables across agents that are correlated. In the absence of experimental variation, the preferred solution is to control for these using a rich specification of fixed-effects, which is feasible with panel data. We show that fixedeffects estimators of this sort are inconsistent in the presence of installed-base effects; in our simulations, random-effects specifications perform even worse. Our analysis reveals the tension faced by the applied empiricist in this area: a rich control for unobservables increases the credibility of the reported causal effects, but the incorporation of these controls introduces biases of a new kind in this class of models. We present two solutions: an instrumental variable approach, and a new bias-correction approach, both of which deliver consistent estimates of causal installed-base effects. The bias-correction approach is tractable in this context because we are able to exploit the structure of the problem to solve analytically for the asymptotic bias of the installed-base estimator, and to incorporate it into the estimation routine. Our approach has implications for the measurement of social effects using non-experimental data, and for measuring marketing-mix effects in the presence of state-dependence in demand, more generally. Our empirical application to the adoption of the Toyota Prius Hybrid in California reveals evidence for social influence in diffusion, and demonstrates the importance of incorporating proper controls for the biases we identify.

Price Advertising by Manufacturers and Dealers

“…The release of new model-year units increases mean monthly demand. Recent truck sales in a zip code have a short-lived 22 positive effect on truck demand, consistent with the positive installed-base effects found by Narayanan and Nair (2013). 21 This finding is smaller than the -4.1 found by Albuquerque and Bronnenberg (2012) and the −7 6 reported by Chen et al (2008), but neither paper focused on pickup trucks.…”

“…16 The error term zjt captures unobserved zip-week departures from mean monthly truck demand. To allow individual demand to be influenced by past purchases within the zip code (Narayanan and Nair 2013), zjt is modeled as zjt =˜ zjt + YC zjt YC z , where YC zjt is a stock measure of recent sales of truck j in zip code z prior to time period t, 17 and YC z is attributable to word-of-mouth. Therefore, past sales in the zip code are used to control for possible autocorrelation in zip-and week-specific departures from mean monthly truck demand (Dasgupta et al 2007).…”

Visual Influence and Social Groups

“…Zip code-level data are frequently used when studying automobile decisions (Shriver 2010), particularly at the monthly level (Narayanan and Nair 2011). Such data not only are more commonly available but also facilitate the detection of visual influence effects beyond the noise likely to exist in individual-level transactions.…”

The value of environmental status signaling

“…5 For instance, Heutel and Muehlegger (2012) provide a model of hybrid technology diffusion under uncertainty regarding the quality of hybrid technology, and Narayanan and Nair (2013) provide evidence that Prius demand is, in part, driven by social influence. Sexton and Sexton (2014) provide an empirical model that is most closely related to our work.…”

“…Clearly, aggressive marketing campaigns are effective at increasing consumer awareness of the Prius, which in turn increases demand. Narayanan and Nair (2013) provide empirical evidence of social contagion effects increasing the demand for the Prius. Toyota marketing efforts can have two effects.…”