Girma et al., 2007).<sup>18</sup> The popularity of the Cox model is due to its convenient estimation of the effects of plant characteristics on survival using a partial likelihood approach and making no assumptions on the shape of the baseline hazard function.<sup>19</sup> The effect of plant characteristics on survival is specified as a proportional shifter of the baseline hazard function. However, a major caveat of the Cox proportional hazard model is that it requires survival time to be a continuous variable and plants to be ordered exactly regarding their failure time.<sup>20</sup> This does not apply to our data which groups plant survival times into discrete intervals of one year, as is the case for most survival studies that use annual plant-level census data. While we know which plants and how many plants exit from year to year, we are unable to order plants‟ failure times within a year, so there are „ties‟ among plants. In the presence of a sizeable fraction of tied survival times the coefficient estimates and standard errors of the Cox model can be biased (Cox and Oakes, 1984).<sup>21</sup> This caveat applies also to continuous-time hazard models with a parametric baseline hazard function. Thus, discrete-time hazard models are more appropriate for our analysis.

Another major caveat is that the Cox model does not allow controlling for unobserved plant heterogeneity, namely the fact that plants may have differing duration distributions even after controlling for a rich set of plant characteristics, due to computational difficulties.<sup>22</sup> A failure to account for unobserved heterogeneity will lead to biases in the estimated effects of plant characteristics on survival (Van den Berg, 2001) and to spurious negative duration dependence of the estimated Cox hazard function (Heckman and Singer, 1984).<sup>23</sup> Unobserved plant heterogeneity can however be controlled for in the discrete-time hazard models discussed below, as well as in continuous-time models with parametric baseline hazard rates that we will consider in robustness checks. Despite its caveats, we will obtain robustness estimates based on the Cox model for

> 18 The Cox model is also widely used in studies examining the survival of trade flows at the product level (e.g., Besedes and Prusa, 2006; Brenton et al., 2010; Hess and Persson, 2011, 2012).

> 19 The baseline hazard function summarizes the pattern of duration dependence and is estimated non-parametrically. 20 Since the Cox model partial likelihood estimation requires duration times to be ordered chronologically, that assumes in effect that plant survival duration can take on any positive observable value (Hess and Persson, 2012). 21 These biases are present even when correcting the Cox partial likelihood function for the existence of „ties‟ using the method of Breslow (1974), as we do in Section 4.2.

> 22 A further caveat arises from the Cox model‟s proportional hazards assumption that the effect of plant characteristics on the hazard rate does not depend on time duration (i.e., on plant age). This assumption may fail due to unobserved heterogeneity but also because the effect of some plant characteristics on the hazard is inherently nonproportional (e.g., initial plant size is likely to affect differently the hazard rate of a very young versus a relatively older plant). This caveat can however be addressed within the model estimation by interacting variables with nonproportional effects with plant age, as we will do in Section 4.2.

> 23 The degree of negative duration dependence may be over-estimated when unobserved heterogeneity is not accounted for, because as time proceeds a selection process implies that only plants better suited to survive remain.

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