profit rates. These positive payoffs support evidence that innovation fosters plant performance for the Chilean dataset in line with the conclusions of the existing literature.<sup>14</sup> Importantly, these positive payoffs provide validation to our novel product innovation measures, as their relationship with plant performance is consistent with that identified based on more traditionally used R&D and perceptionbased innovation indicators.

# **3. Model Specification**

In order to correctly identify the effects of innovation (and other plant characteristics) on plant survival, it is necessary to consider a hazard or duration model whose dependent variable is the time/spell between plant entry and exit (the survival spell).<sup>15</sup> The use of a hazard model is adequate for plant survival analysis due to the incomplete nature of the duration information. The hazard function represents the conditional probability of a plant ending a survival spell after _t_ periods, given that it survived until _t-1_ , (the elapsed duration of the survival spell) and given plant characteristics.

By contrast, when conventional estimation methods such as probit or OLS - the latter also called linear probability - are applied to the estimation of a plant exit model, they are in effect studying the unconditional probability of the event (e.g., the probability that a plant exits after 5 years in operation) rather than its conditional probability (e.g., the probability that a plant exits after 5 years in operation conditional on having survived until year 4). Kiefer (1988) introduces a useful sports analogy to illustrate the substantial difference between concepts and why the conditional probability approach is conceptually appropriate to address our research questions. In sports team competitions in which elimination happens when the team loses, the probability of surviving in the second round is the probability of winning conditional on making it to the second round, whereas the unconditional probability is defined in terms of a single event, i.e., the probability of winning the second round match. Similarly, hazard models account for the fact that the data contains not only information on

> 14 Such evidence has often been shown using the Crépon et al. (1998) or CDM model, which is the most popular method to estimate the innovation-performance link. The method has been applied to Chile using perception-based innovation measures for a cross-section of plants in the Chilean Innovation Survey by Crespi and Zuniga (2012). This method suffers however from problems of weak identification in the estimation of a causal relationship between innovation and firm performance. For example, as acknowledged by Crespi and Zuniga (2012), in order to be identified, the model needs to assume that certain firm characteristics such as firm size affect only the decision to invest in innovation activities but not the amount to be invested, nor the knowledge generated from such investments. 15 See Kiefer (1988), Klein and Moeschberger (1997), and Hosmer and Lemeshow (2008) on hazard models. The use of hazard models follows the empirical literature on firm survival reviewed by Manjon-Antolin and Arauzo-Carod (2008). In these models, the key concept is the hazard rate which is the probability that a plant will experience an event (exit) at time _t_ , given that the plant is at risk for having an event (the plant survived until _t-1_ ). The hazard rate is the unobserved rate at which events occur.

7