Does the 'Golden Rule of Public Finance' imply a lower long-run growth rate? A clarification

In a recent paper Minea and Villieu (2009) assert that the 'golden rule of public finance' implies a lower long-run growth rate than the balanced-budget rule. Their contribution is misleading because it is not the 'golden rule of public finance' that generates their result but rather the fact that public debt grows at the same rate as capital and GDP in the long-run in their paper. In this note we demonstrate that the 'golden rule of public finance' yields the same long-run growth rate as the balanced-budget rule provided that public debt asymptotically grows at a smaller rate than capital and GDP.