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. 2024 Jun 11;19(6):e0304560. doi: 10.1371/journal.pone.0304560

Table 2. Main analysis of the effect of academic freedom (AF) on innovation quantity (patent applications).

Model (1) (2) (3) (4) (5)
Dependent variable Patent applicationst+2 (ln) Patent applicationst+2 (ln) Patent applicationst+2 (ln) Patent applicationst+2 (ln) Patent applicationst+2 (ln)
Statistic Coeff. (SE) Coeff. (SE). Coeff. (SE) Coeff. (SE) Coeff. (SE)
Indepdent variables
    AF (z) 0.345 (0.032)***
    AF (IV: Democracyt-5, z) 0.477 (0.060)***
    AF (IV: Democracy stockt-10, z) 0.442 (0.057)***
    AF (IV: AFt-5, z) 0.330 (0.043)***
    AF (IV: AF stockt-10, z) 0.315 (0.042)***
Controls
    Year/country dummies Yes Yes Yes Yes Yes
Countries (observations) 157 (12,392) 157 (11,809) 157 (11,257) 157 (11,569) 156 (10,753)
R2 (R2 adjusted) 0.811 (0.807) 0.815 (0.811) 0.818 (0.814) 0.817 (0.812) 0.820 (0.816)
MOP weak instrument test (F) - 2,395.13 (τ < 0.05) 4,114.46 (τ < 0.05) 5,946.18 (τ < 0.05) 11,895.90 (τ < 0.05)

Notes: The estimates in Model (1) are obtained from a pooled OLS regression. The estimates in Models (2)–(5) come from 2SLS regressions. All variables are described in Table 1. Robust standard errors in parentheses. The MOP weak instrument is based on Montiel Olea and Pflueger (2013), as implemented in STATA’s weakivtest command. High F-values indicate a strong instrument.

* p < 0.10

** p < 0.05

*** p < 0.01.