Table 9 Estimation results between patents and short-run economic growth

Real GDP growth rate per capita (t − 1)

0.307*** (0.035)

0.288*** (0.034)

0.312*** (0.032)

0.260*** (0.047)

0.259*** (0.061)

0.207*** (0.057)

0.228*** (0.017)

0.232*** (0.055)

Log of real GDP per capita (t − 1)

− 0.830*** (0.185)

− 3.442*** (0.842)

− 2.909 (2.022)

− 3.954*** (1.235)

− 0.498*** (0.125)

− 3.762*** (0.794)

− 2.991** (1.376)

0.460 (0.805)

Log of AI patents per million people

0.181*** (0.069)

0.360*** (0.113)

0.359 (0.490)

0.426* (0.253)

–

–

–

–

Log of total patents per million people

–

–

–

–

0.076 (0.057)

0.195* (0.106)

0.194 (0.267)

0.123 (0.132)

Population growth rate

− 0.440*** (0.078)

− 0.386*** (0.114)

− 0.384* (0.227)

− 0.338 (0.216)

− 0.310*** (0.084)

0.000 (0.166)

− 0.003 (0.403)

− 0.27 (0.293)

Gross capital formation growth rate (per capita)

0.117*** (0.030)

0.107*** (0.033)

0.106*** (0.024)

0.061 (0.062)

0.095*** (0.009)

0.090*** (0.009)

0.089*** (0.014)

0.082*** (0.027)

Government expenditure growth rate (per capita)

0.081*** (0.030)

0.083** (0.032)

0.082 (0.053)

0.125* (0.071)

0.097*** (0.024)

0.091*** (0.023)

0.090*** (0.034)

0.094 (0.057)

Trade openness

0.007*** (0.002)

0.010** (0.004)

0.010 (0.019)

0.020 (0.015)

0.006*** (0.001)

0.009** (0.004)

0.009 (0.012)

− 0.014 (0.009)

Human capital index growth rate

− 0.143 (0.107)

− 0.196 (0.136)

− 0.198 (0.555)

− 0.416 (0.371)

0.128 (0.127)

− 0.004 (0.135)

− 0.014 (0.580)

0.215 (0.268)

Inflation

0.002 (0.010)

0.013 (0.010)

0.013 (0.023)

0.092 (0.070)

− 0.001 (0.012)

0.004 (0.011)

0.004 (0.024)

0.043 (0.047)

Advanced economy (dummy)

0.931** (0.374)

1.596*** (0.477)

1.537 (2.178)

2.197*** (0.762)

0.107 (0.543)

2.486** (0.963)

2.375 (2.499)

0.615 (0.997)

Advanced x Log of AI patents per million people

− 0.165* (0.091)

− 0.370** (0.149)

− 0.368 (0.558)

− 0.681** (0.275)

–

–

–

–

Advanced × Log of total patents per million people

–

–

–

–

0.029 (0.078)

− 0.227 (0.151)

− 0.212 (0.390)

− 0.114 (0.162)

Constant

7.706*** (1.560)

32.653*** (7.960)

–

37.607*** (11.363)

4.314*** (0.956)

32.655*** (7.035)

–

− 2.888 (6.704)

Time dummies

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Yes

Number of instruments

–

–

–

121

–

–

–

110

Sargan-Hansen test (p-value)

–

–

–

0.143

–

–

–

0.375

AR(1) (p-value)

–

–

–

0.001

–

–

–

0.000

AR(2) (p-value)

–

–

–

0.236

–

–

–

0.727

N

2261

2261

2261

2261

4905

4905

4905

4905

n

120

120

120

120

141

141

141

141