184may inﬂuence the probability of being selected by the programs. Second, to choose the matching variables X for the number of employees with high skills, we rely on models of ﬁrms’ relative demand for skills, which similarly can be derived from cost minimization under given factor prices and output (Hansson, 2000).

We present descriptive statistics for our outcome variables and the variables included in X in Table 2. The results show that the treated ﬁrms on average have approximately 20 employees and that about 55% of their employees had completed higher education during the pretreatment period. The corresponding average values for the post-treatment period suggest that the treated ﬁrms increased their number of employees by approximately 3% and that their share of workers with post-tertiary education increases by approximately 2 percentage points. Note also that the treated ﬁrms on average increase sales and value added by about 10% after receiving an R&D grant. To decide upon the coarseness of the respective variable, we use the generic algorithm proposed by the CEM-program cem in Stata. This means that the matching process gives a relatively high weight to the best-matched control ﬁrms (Blackwell et al., 2009). Table 3 presents the univariate L1 distance before and after the cem matching for our treatment and control group of ﬁrms, respectively. As can be seen in Table 3 below, matching reduces the differences unilaterally, except for proﬁts.

4.2 A Difference-in-Difference Analysis

After we constructed a control group using CEM, we turned our attention to estimating the average treatment effect of the treated ﬁrms. More formally, we want to investigate: Xn 1 d Pn ATT ¼ i¼1TiYi Ti ¼ 1 ½ ð Þ Yi Ti ¼ 0 ð ÞjX : ð1Þ

i¼1Ti

185Do Targeted R&D Grants toward SMEs Increase Employment and Demand for High. . .

Table 3 Imbalance test Treated vs. all ﬁrms Treated vs. control group L1 distance L1 distance Labor demand Value added (log) 0.45 0.24 Wage (log) 0.38 0.24 Skill 0.48 0.10 R&D skill 0.22 0.11 Proﬁts 0.08 0.13 No. of matched treated 481 Relative demand for skills Sales (log) 0.39 0.28 Capital (log) 0.30 0.19 Proﬁts 0.11 0.15 R&D intensity 0.35 0.37 No. of matched treated 484

The reason why we cannot simply compare the average performance between the control group and the treatment group is that we want to check for any differences between XC and XT that remain after matching. We therefore rely on a difference-indifference model to investigate the effect of the government support programs on our outcome variables number of employees and share of employees that have completed a higher education. The estimated model can in our ﬁxed-effect set-up be speciﬁed as follows:

Yit ¼ α þ δt þ β1Treatit þ β2Post treati: þ X0

itβX þ γt þ μi þ Eit, ð2Þ

where Treat is a dummy variable for the treatment (i.e., receiving a grant) or alternatively, the amount of money paid out to the ﬁrm. If the responses from the targeted ﬁrms are immediate, the effects of the grant should be captured ﬁrst and foremost by this variable. Post_treat is a post-treatment indicator taking the value one in the years following a treatment and zero otherwise. Given that the impact of the grant comes with a delay, the impact of the grant is captured by this variable. The set of control variables are included in the vector X, μi captures time-invariant ﬁrm effects, γt captures period-speciﬁc effect, and ε is white noise.

In the labor cost equation, it is standard to account for the cost of adjusting the number of employees. Adjustment costs introduce state dependence in the labor demand equation, which from a modeling perspective means that we ﬁt a dynamic lag to the labor demand model in Eq. (2). The dynamic panel data model is estimated using a system GMM estimator (Blundell & Bond, 1998), while relative demand for skills is estimated using a ﬁxed-effect model.

One critique of matching is that it can only account for selection to the extent it occurs through observed variables. In the basic model, we therefore include a parameter αi that captures unobserved variation speciﬁc to the ﬁrms and the period S.-O. Daunfeldt et al.

186under study. This eliminates selection bias on unobserved variables that do not vary within ﬁrms over the period under study. However, bias might still arise from ﬁrmspeciﬁc time-variant characteristics that we are not able to control for in the empirical analysis. We consider two extensions of the basic model. First, we investigate if the treatment effect of the grants is moderated by the size of the targeted ﬁrms. Second, to investigate dynamic aspects of grant programs, we estimate the effect of the targeted R&D grant up to 5 years after the support period ended.

5 Results

We present results for three different groups: (i) Treated ﬁrms only; (ii) Treated ﬁrms against a matched control group (which is our preferred estimator); and (iii) Treated ﬁrms against an unmatched control group of all non-treated ﬁrms. Differences between (ii) and (iii) can be seen as a signal of selection into the support programs and of how the treated ﬁrms deviate from the average ﬁrm. We also include an interaction effect to investigate how the effects of the targeted R&D grants vary with ﬁrm size.