Page 12 - IDEA Study 8 2017 Direct subsidies and R&D output in firms
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 techniques that enable us to estimate the subsidies’ causal impact on the firms’ private IP applications. Historically, researchers have focused on testing the effects of subsidies using difference- in-difference estimators, sample selection models, instrumental variables, and various matching estimators (ZúnΜƒiga-Vicente et al., 2014). In this paper, build on the growing body of research that employs matching techniques to deal with selection bias. Non- parametric propensity score matching attempts to reproduce the results of experiments or randomized controlled trials based on observational data. This technique combines a group of firms that received subsidies with a group of firms that did not but whose observable characteristics are the same as for the first group with the help of estimated treatment probabilities (propensity scores). There are several conditions we need to assume in order to estimate the effect of treatment using propensity score matching. Assumption 1: Conditional independence assumption states that conditional on a scalar function of observable firm characteristics, which affect probability of treatment 𝑝(𝑋𝑖) or the propensity score, selection bias disappears. This assumption implies that unobservable firm characteristics do not affect the treatment assignment and outcome of interest. \{π‘Œ0𝑖, π‘Œ1𝑖\} βŠ₯ 𝑇𝑖| 𝑝(𝑋𝑖) Assumption 2: Common support assumption states that the support of the conditional distribution of 𝑋𝑖 given 𝑇𝑖 = 0 overlaps with the support of the conditional distribution of 𝑋𝑖 given 𝑇𝑖 = 1. In other words, it states that for every 𝑋𝑖 we have both treated and untreated observations. Formally, if we define 𝑑̅ as the treatment level \{0,1\}, then the assumption 2 can be stated as follows: 0<π‘ƒπ‘Ÿπ‘œπ‘(𝑇𝑖 =𝑑̅|𝑋𝑖 =π‘₯)<1 Assumption 3: Stable unit treatment value assumption implies that treatment itself does not influence untreated firms, or, in other words, there are no β€œgeneral equilibrium effects”. In principle, this assumption could be a serious concern if there are sizeable spillover effects from interaction between treated and untreated firms, for example those in the same technological fields, regional clusters, via direct partnerships or common partners. 10 

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