Appendix C

Technical Appendix

The committee performed a series of regressions to investigate the extent to which the differences in outcomes between funded and unfunded firms observed in Table 5-3 in Chapter 5 may in fact be due to the causal effect of Small Business Innovation Research (SBIR) or Small Business Technology Transfer (STTR) funding, as opposed to a tendency for the program to attract and fund firms that are inherently more likely to have successful outcomes regardless of whether they receive funding. This approach is based on a cross-sectional “long difference” model of firms’ outcomes after their first application to the program.

The empirical specifications of the post-first-application outcomes Y^post for each firm i are all of the form:

where Funded_i is an indicator variable that equals 1 if the firm’s first application is funded, β is the parameter of interest that is intended to capture the causal effect of first-application funding, X_i is a vector of control variables that enter the model via some function f, and ε_i is an idiosyncratic error term.

At a minimum, all of the specifications will include in X_i an indicator for whether a firm’s first application was at least discussed (as motivated by the differences shown in Figures 5-4 through 5-8), as well as a vector of time-fixed effects for the year of the firm’s first application. As an alternative to the first control (the “discussed” indicator), Table C-1 also reports a series of regressions restricted to firms whose first application was at least discussed.

Table C-1 reports the results of these regressions. Panel (a) includes the full sample, and panel (b) is the sample restricted to those whose first applications were discussed. In general, shifting from column (1) to column (5) corresponds to specifications with increasingly stringent control variables. Column (2) introduces institute/center (IC)-year specific fixed effects, effectively comparing two firms that both submitted their first applications to the same IC in the same year. Column (3) includes a preperiod outcome control (Y_i^pre) to account for the

TABLE C-1 Long Difference Firm-Level Regression Results, Aggregated Outcome Index

NOTE: Firm-level regressions based on Eq. (1). All regressions in panel (a) also include an indicator for whether the firm’s first application was discussed; panel (b) conditions the sample on this indicator equaling zero. Observations are firm-level. Robust standard errors in parentheses. IC = institute/center. F.E.= fixed effects.

^a p <0.1

^b p <0.05,

^c p <0.01.

“pretrends” apparent in Figures 5-4 through 5-8. Column (4) restricts the sample to those firms that the committee was able to match to their Guzman-Stern quality index, with column (5) then including the index as a control variable to account for the differences apparent in Figure 5-3.

Overall, Table C-1 illustrates the difficulty of establishing a suitable “control group” for the purposes of obtaining an unbiased estimate of β, the causal effect of receiving funding for a firm’s first SBIR application. With each successive specification, smaller β coefficients are estimated, declining from roughly 0.35 (i.e., funded firms have 0.35 standard deviation [s.d.] more outcomes) to 0.18. And since the standard errors on these point estimates remain relatively stable, ultimately the regressions estimate a statistically insignificant (p >0.1) coefficient in the most saturated models.

Since there is no clear source of exogenous variation in funding, the results shown in Table C-1 are inconclusive in terms of determining how much of the results documented in Table 5-3 are due to selection by the National Institutes of Health SBIR/STTR program (i.e., funding higher-quality firms) versus causal

effects of the program (i.e., providing funds that lead to outcomes that would not have occurred in the absence of those funds).

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