182question.3 Since firms are not randomly selected by the programs, it is central to identify a non-treated control group of firms that is as similar to the treated firms as possible across all relevant dimensions. Systematic differences between the control and treatment groups may otherwise bias the results. There are different ways to tackle this kind of selection issue, such as regression discontinuity design, instrumental variables, natural experiments, difference-in-difference, and various matching methods. Each alternative is associated with both advantages and disadvantages. For a firm i, let Ti ¼ 1 if it is treated, and Ti ¼ 0 if it is not, the effect on some outcome variable Yi can then be described as a function of Ti such that:

3Henceforth, we refer to firms that receive a grant from either Vinn Nu or Forska & Väx during the period as treated firms, and firms that do not receive support as non-treated firms. All results presented are for both programs. Results are qualitatively similar if we conduct separate estimations for each program. These results are not reported here, but are available from the authors upon request.

183Do Targeted R&D Grants toward SMEs Increase Employment and Demand for High. . .

ð Þ ¼ TiYi 1 ð Þ  1  Ti ð ÞYi 0 ð Þ Yi Ti

For treated firms, the counterfactual is given by Yi(0). The most effective method (if there is one) often depends on the nature of the problem and the data available. We have detailed information about both the treated and non-treated firms, as well about the grants, which have led us to opt for a matching method to approximate Yi(0). We let X be a vector of characteristics for N non-treated firms that explain Yi along with the probability of receiving a grant. To approximate Yi(0), matching methods strive to limit the number of non-treated firms in the dataset to M  N such that the characteristics between the limited set of matched firms (XM) become as similar as possible to the characteristics of the treated firms (XT). Given the distance function d(, ) we would like to have d(XM, XT) ffi0 (Iacus et al., 2011). Ideally, we would want to have d(XM, XT) ¼ 0, which corresponds to an exact matching between the treated and control firms with the same level in their covariates. Such ideal conditions, however, are rarely met in practice, especially for continuous covariates such as performance and profitability. To identify the control group of firms whose covariates are as similar as possible to the treated firms, we rely on the matching methods of Coarsened Exact Matching (CEM) developed by Iacus et al. (2011, 2012). Since small differences between the covariates for treated and control firms do not necessarily reflect economically meaningful differences, CEM allows for a coarsening of the variables upon which an exact matching can be performed. Any imbalance between the covariates of the treated and control firms is thus decided upon beforehand. This implies that the maximum imbalance that may result after the matching is bounded by the width of the coarsening bins. This type of matching has some advantages (Blackwell et al., 2009; Iacus et al., 2011, 2012), especially compared to the more commonly used Propensity Score Matching (PSM) (see King & Nielsen, 2015 for example). Most importantly, the CEM estimator satisfies the property of being monotonically imbalance bounding (MIB), which means that total balance can be improved by adjusting the balance of a single covariate. This property, for example, is not shared with PSM, where there is no way of knowing if the total balance in the matching has been improved by ameliorating the balance of a single covariate or by adding or removing covariates. The MIB property of CEM greatly facilitates our aim to, via matching, find a more appropriate control group consisting of untreated firms, contrary to PSM, which merely “works when it works, and when it does not work, it does not work (and when it does not work, keep working at it)” (Ho et al., 2007, p. 219).

We include different variables in X to accompany our two outcome variables. First, the number of employees corresponds to the firm’s demand for labor. The basic model of labor demand can be derived from the firm’s cost function as a function of the return to factors and value added (Hijzen & Swaim, 2008). In this case, we include wages and value added, measures of firm skill intensity and the profitability of the company. The latter can be seen as a beauty contest indicator that S.-O. Daunfeldt et al.

184Table 2 Treated firms, before and after grants Variable Treated before Treated after Ratiobefore/after Employment 19.83 20.34 1.03 Value added 9363 10,447 1.11 Wage 5880 6580 1.12 Share higher education 0.55 0.57 1.04 Profit ratio 12.1 1.37 0.11 Wage share higher ed. 0.59 0.60 1.02 Sales 27,512 31,054 1.13 Ln(capital stock) 6.21 6.19 1.00 Wage premium 2.32 2.66 1.15