Harvard University economics professor Robert Barro, in his book

- Robert J. Barro: Determinants of Economic Growth: A Cross-Country Empirical Study, MIT Press, Cambridge MA 1997, ISBN=0-262-02421-7.

Details of Barro's latest fits are below. The two coefficients that determine the parabolic curve shown, are C(21) and C(22) where DEMOCDC1 is on an 0-1 scale (in the picture this has been redefined to be a 0-10 scale). Note their error bars are fairly small so these effects apparently are genuine. The curve has a peak and then curves back down, provided C(21)+2×C(22)<0. The statistical confidence that this is true (if we regard the two errors as uncorrelated), is about 97-98%.

System: GROWTHCH | ||||

Estimation Method: Iterative Three-Stage Least Squares | ||||

Date: 06/19/06 Time: 16:04 | ||||

Sample: 3 182 | ||||

Included observations: 85 | ||||

Total system (unbalanced) observations 235 | ||||

Simultaneous weighting matrix & coefficient iteration | ||||

Convergence achieved after: 6 weight matrices, 7 total coef iterations | ||||

Coefficient | Std. Error | t-Statistic | Prob. | |

C(1) | 0.267699 | 0.030522 | 8.770672 | 0.0000 |

C(2) | -0.023433 | 0.002806 | -8.350675 | 0.0000 |

C(4) | 0.003285 | 0.001579 | 2.080098 | 0.0387 |

C(7) | 0.005626 | 0.004455 | 1.262774 | 0.2080 |

C(9) | -0.069270 | 0.027732 | -2.497830 | 0.0132 |

C(10) | -3.294103 | 0.556276 | -5.921708 | 0.0000 |

C(12) | 0.305493 | 0.053068 | 5.756623 | 0.0000 |

C(15) | 0.017065 | 0.005872 | 2.906110 | 0.0040 |

C(16) | -0.015226 | 0.005260 | -2.894837 | 0.0042 |

C(19) | -0.017748 | 0.009878 | -1.796769 | 0.0737 |

C(20) | 0.058623 | 0.023416 | 2.503550 | 0.0130 |

C(21) | 0.093966 | 0.029231 | 3.214647 | 0.0015 |

C(22) | -0.083979 | 0.024726 | -3.396414 | 0.0008 |

C(31) | -0.008037 | 0.002807 | -2.862892 | 0.0046 |

C(32) | -0.012793 | 0.003316 | -3.857506 | 0.0002 |

Determinant residual covariance | 1.52E-11 | |||

Equation:
LINGRDEC1=C(1)+C(2)*LINGDP65L | ||||

*OPRESDEC1+C(9) | ||||

*TOTOPDEC1+C(15) | ||||

*DPDEC1+C(20)*INVLINDEC | ||||

*DEMOCDC1S | ||||

Instruments: C LINGDP60L UYRM65 OPRESDEC1 TOTOPDEC1 | ||||

RULELAW FERTL65 SPANPOR OTHCOL INVLIN6064 | ||||

GVLIN6064 LIFE60INV DEMOC65R DEMOC65RS | ||||

Observations: 70 | ||||

R-squared | 0.634778 | Mean dependent var | 0.025466 | |

Adjusted R-squared | 0.557890 | S.D. dependent var | 0.020532 | |

S.E. of regression | 0.013652 | Sum squared resid | 0.010624 | |

Durbin-Watson stat | 1.449268 | |||

Equation:
LINGRDEC2=C(1)+C(31)+C(2) | ||||

+C(7)*OPRESDEC2+C(9) | ||||

*TOTOPDEC2+C(15) | ||||

*DPDEC2+C(20)*INVLINDEC | ||||

*DEMOCDC2S | ||||

Instruments: C LINGDP70L UYRM75 OPRESDEC2 TOTOPDEC2 | ||||

RULELAW FERTL75 SPANPOR OTHCOL INVLIN7074 | ||||

GVLIN7074 LIFE70INV DEMOC75 DEMOC75S | ||||

Observations: 84 | ||||

R-squared | 0.497837 | Mean dependent var | 0.015558 | |

Adjusted R-squared | 0.404578 | S.D. dependent var | 0.024569 | |

S.E. of regression | 0.018958 | Sum squared resid | 0.025159 | |

Durbin-Watson stat | 2.540857 | |||

Equation:
LINGRDEC3=C(1)+C(32)+C(2) | ||||

+C(7)*OPRESDEC3+C(9) | ||||

*TOTOPDEC3+C(15) | ||||

*DPDEC3+C(20)*INVLINDEC | ||||

*DEMOCDC3S | ||||

Instruments: C LINGDP80L UYRM85 OPRESDEC3 TOTOPDEC3 | ||||

RULE85 FERTL85 SPANPOR OTHCOL INVLIN8084 GVLIN8084 | ||||

LIFE80INV DEMOC85 DEMOC85S | ||||

Observations: 81 | ||||

R-squared | 0.482747 | Mean dependent var | 0.014303 | |

Adjusted R-squared | 0.382385 | S.D. dependent var | 0.025853 | |

S.E. of regression | 0.020317 | Sum squared resid | 0.027658 | |

Durbin-Watson stat | 2.279647 | |||