Page 11 - IDEA Study 8 2017 Direct subsidies and R&D output in firms
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 Estimation strategy: matching estimator Non-random assignment of R&D subsidies makes it problematic to draw conclusions about subsidy effects by simply comparing data on firms that received and did not receive subsidies. The firms that received subsidies are different from those that did not, therefore evaluators would need to separate the effects of subsidy selection (selection bias) from the actual effect of the subsidies themselves (average treatment effect on the treated). The selection bias comes from two sources: applicants’ self-selection and actual project selection by the subsidy administrators based on formal criteria. It is likely that firms receiving R&D subsidies have also accepted government funds in the past (Zúñiga-Vicente et al., 2014), these firms are more innovative and their R&D projects in general have a higher probability of success (Cantner & Kösters, 2011). In addition, they may differ in other observable and unobservable characteristics. Let us define the problem and possible solutions formally. We are interested in whether R&D subsidies complement (“crowd-in”) or substitute ("crowd-out") private IP applications. Let treatment, i.e. whether a firm i receives a subsidy or not, be a binary random variable 𝑇𝑖 = \{0,1\}. Variable 𝑌𝑖 would be an outcome of interest, i.e. whether that firm applied for IP protection or not, and 𝑌1𝑖,𝑌0𝑖 are the potential outcomes for a firm i in case it receives 𝑇𝑖 = 1 or does not receive 𝑇𝑖 = 0 treatment. 𝑌𝑖 = \{𝑌1𝑖 𝑖𝑓 𝑇𝑖 = 1, 𝑓𝑖𝑟𝑚 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑 𝑠𝑢𝑏𝑠𝑖𝑑𝑦 𝑌0𝑖 𝑖𝑓 𝑇𝑖 = 0, 𝑓𝑖𝑟𝑚 𝑑𝑖𝑑 𝑛𝑜𝑡 𝑟𝑒𝑐𝑒𝑖𝑣𝑒 𝑠𝑢𝑏𝑠𝑖𝑑𝑦 The population value of the average treatment effect on the treated (ATT) is essential when we want to find the participants’ average gain from participation in the treatment. ATT is defined in terms of the observed difference in average outcome (i.e. private IP applications) and selection bias: 𝐴𝑇𝑇 = 𝐸\[𝑌1𝑖 − 𝑌0𝑖|𝑇𝑖 = 1\] = =(𝐸\[𝑌|𝑇 =1\]−𝐸\[𝑌|𝑇 =0\])−(𝐸\[𝑌 |𝑇 =1\]−𝐸\[𝑌 |𝑇 =0\]) ⏟ 𝑖 𝑖 𝑖 𝑖 ⏟ 0𝑖 𝑖 0𝑖 𝑖 𝑂𝑏𝑠𝑒𝑟𝑣𝑒𝑑 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 𝑖𝑛 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑌𝑖 𝑆𝑒𝑙𝑒𝑐𝑡𝑖𝑜𝑛 𝑏𝑖𝑎𝑠 In our case, firms that did not apply for R&D subsidies or did not receive subsidies 𝐸\[𝑌0𝑖|𝑇𝑖 = 0\] are likely to be less R&D intensive and innovative, or have less promising R&D projects. This means that the firms which received subsidies have better values of 𝑌0𝑖, making selection bias positive. Angrist & Pischke (2009) point out that random assignment could remove the selection bias, as it makes 𝑇𝑖 independent of potential outcomes. As we only have non-experimental data, we need to use econometric 9 

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