146 The Impact of the Act for the Development of Biotech and New Pharmaceuticals Industry on Firm Innovation in Taiwan for binary treatment (Rosenbaum and Rubin, 1983; Caliendo and Kopeinig, 2008). The propensity score is the predicted probability of a firm, P = Pr(D|X), given a vector of observed predictors X, where D equals one if the firm is an approved biopharmaceutical firm and zero otherwise. After the estimation of the propensity score of each firm, we adopt the nearest neighbor matching method to find the control firms for the treated firms. Dehejia and Wahba (2002) allow control firms to be matched more than one because of the substantial difference in sample size between treated firms and untreated firms.23 We select firms which have the nearest propensity score to the treated firm in each year to be control firms. In addition, to consider the sample size effect, we also choose firms which have the second, third, and fourth-nearest propensity scores to the treated firms to be control firms. For the intra-industry analysis, we use the data of the year before the approval year to find control firms because the approval year (i.e. the event year) of each approved biopharmaceutical firm is different. We use the logistic regression to estimate the propensity score and then use the pre-event total assets, ROA, Tobin’s Q, and R&D intensity as the explanatory variables in the logistic regression. In addition, for the interindustry comparison, we use a similar concept to identify control group firms from the high-tech industry. 3.3.3 Difference-in-differences (DID) Estimator We apply the DID approach to examine the effect of Biopharmaceutical Act on innovation because previous studies argue that DID is a useful instrument for evaluating the impact of certain policies which may only influence one part of the population (Blundell and Costa-Dias, 2009; Buckley and Shang, 2002; Lechner, 2011; Heckman, Ichimura, and Todd, 1997). The DID approach helps to eliminate the endogeneity problem because it assumes that unmeasured factors, such as the changes in economic conditions or other unobservable effects, affect both treated and control groups in similar ways. The DID approach can thus reduce the influence of other factors that may contaminate our treatment of the effect of the Biopharmaceutical Act on innovation. Following past literature on the basic DID approach, we first calculate the DID estimator. In our paper, the DID estimator calculates the effect of the Biopharmaceutical Act by estimating the difference in average innovation measures before and after the 23 Lane, Looney, and Wansley (1986) use three matched firms for one treated firm to avoid possible estimation bias.
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