## Barro's latest GDP growth rate prediction fit

Harvard University economics professor Robert Barro, in his book

attempted to predict the annual GDP growth rate in a country from various facts about that country, based on least squares fitting to data. I emailed Barro to ask him for his scatterplot of country GDP-growth data, plus his fit of it to "democracy index" that is pictured on page 60 of his book. Barro replied in June 2006 that that data was 10 years old and here was his latest fit. The fit shows (see picture) that a country becomes better off economically (as measured by annual GDP growth rate, which increases additively by 2.6%) as its "democracy index of political rights" increases from 0 to 5.6 on an 0-10 scale. However, Barro finds that the GDP growth rate then decreases by 1.6% if the country is made still more democratic up to a maximum democratic rights level of 10. It appears that being "too democratic" is economically bad!

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+C(4)*UYRM65+C(7) *OPRESDEC1+C(9)*GVLINDEC1+C(10)*LIFE60INV+C(12) *TOTOPDEC1+C(15)*RULELAW+C(16)*FERTL65+C(19) *DPDEC1+C(20)*INVLINDEC1+C(21)*DEMOCDC1+C(22) *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)*LINGDP75L+C(4)*UYRM75 +C(7)*OPRESDEC2+C(9)*GVLINDEC2+C(10)*LIFE70INV+C(12) *TOTOPDEC2+C(15)*RULELAW+C(16)*FERTL75+C(19) *DPDEC2+C(20)*INVLINDEC2+C(21)*DEMOCDC2+C(22) *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)*LINGDP85L+C(4)*UYRM85 +C(7)*OPRESDEC3+C(9)*GVLINDEC3+C(10)*LIFE80INV+C(12) *TOTOPDEC3+C(15)*RULEDEC3+C(16)*FERTL85+C(19) *DPDEC3+C(20)*INVLINDEC3+C(21)*DEMOCDC3+C(22) *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