In particular we check if there is a balance between

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we provide some details about the matching properties. In particular, we check if there is a balance between the treated and comparison firms, because after matching the treated and controls should be “statistically equivalent”. Propensity score matching aims to find a proper a comparison group that is statistically equivalent to the internationalized firm, except for the treatment (here: internationalization). Finding such firms is difficult because of non-random assignment to the treatment; that is, firms that choose to internationalize are different and tend to self-select into international activities. Hence, on average, firms that are not international are unlikely to be a good comparison for the treated group because of selection bias . For example, larger firms have a higher probability to internationalize, and thus comparison between the treated and non-treated is biased, because it is easier for larger firms to engage in innovation related activities (the outcome). Simple OLS regression techniques cannot be applied. So, when evaluating the impact of internationalization on differences in innovation between the treated and untreated, it is difficult to isolate the effect of internationalization because of self-selection into internationalization. The key benefit of propensity score matching is that it accounts and adjusts for these innate dissimilarities across international and non-international firms ( Dehejia and Wahba, 2002 ). Internationalized firms are matched with individual firms that are not internationalized based on an estimated probability that the firm would internationalize (the propensity score), hence it requires selection on observables and the existence of an untreated firm that can be compared to a treated firm. In absence of randomization, the groups must differ not only in terms of international activities, but also on their values of the observed characteristics in order to extract propensity scores. A first requirement of matching is to account for these differences in observables by controlling for a set of covariates ( conditional independence ). More formally, there must be a set of observable covariates such that when accounting for this set, the potential outcomes are independent of the treatment status. Hence, after controlling for several observables, the selection into the internationalization of the firm “looks” random; this is essential of the ‘construction’ of a counterfactual. A second requirement is that firms can be sufficiently matched to counterparts such that there is overlapping between the observable characteristics of the treated and the untreated firms ( common support ). Formally, common support means that for each value (or range)
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24 of the covariates, there is a positive probability of being both treated and untreated to ensure substantial overlap in the characteristics of international and not-international firms.
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