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This paper examines the effect of finance on long-term economic growth using Bayesian model averaging to address model uncertainty in cross-country growth regressions. The literature largely focuses on financial indicators that assess the financial depth of banks and stock markets. These indicators are examined jointly with newly developed indicators that assess the stability and efficiency of financial markets. Once the finance-growth regressions are subjected to model uncertainty, the results suggest that commonly used indicators of financial development are not robustly related to long-term growth. However, the findings from the global sample indicate that one newly developed indicator-the efficiency of financial intermediaries-is robustly related to long-term growth.

Bayesian Model Averaging --- Finance --- Growth

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Farm income --- Income averaging --- Income tax --- Taxation

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Averaging method (Differential equations) --- Differential equations --- Adiabatic invariants --- Asymptotic theory --- Differential equations - Asymptotic theory --- ADIABATIC INVARIANTS --- AVERAGING METHOD (DIFFERENTIAL EQUATIONS) --- DIFFERENTIAL EQUATIONS --- ASYMPTOTIC THEORY

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Numerical solutions of differential equations --- Mathematical physics --- Differential geometry. Global analysis --- Differential equations, Nonlinear --- Differentiable dynamical systems --- Averaging method (Differential equations) --- Equations différentielles non linéaires --- Dynamique différentiable --- Méthode des moyennes (Equations différentielles) --- Numerical solutions --- Solutions numériques --- Differentiable dynamical systems. --- Numerical solutions. --- Averaging method (Differential equations). --- Equations différentielles non linéaires --- Dynamique différentiable --- Méthode des moyennes (Equations différentielles) --- Solutions numériques --- Numerical analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Method of averaging (Differential equations) --- Differential equations, Nonlinear - Numerical solutions

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Perturbation theory and in particular normal form theory has shown strong growth during the last decades. So it is not surprising that the authors have presented an extensive revision of the first edition of the Averaging Methods in Nonlinear Dynamical Systems book. There are many changes, corrections and updates in chapters on Basic Material and Asymptotics, Averaging, and Attraction. Chapters on Periodic Averaging and Hyperbolicity, Classical (first level) Normal Form Theory, Nilpotent (classical) Normal Form, and Higher Level Normal Form Theory are entirely new and represent new insights in averaging, in particular its relation with dynamical systems and the theory of normal forms. Also new are surveys on invariant manifolds in Appendix C and averaging for PDEs in Appendix E. Since the first edition, the book has expanded in length and the third author, James Murdock has been added. Review of First Edition "One of the most striking features of the book is the nice collection of examples, which range from the very simple to some that are elaborate, realistic, and of considerable practical importance. Most of them are presented in careful detail and are illustrated with profuse, illuminating diagrams." - Mathematical Reviews.

Differential equations, Nonlinear --- Differentiable dynamical systems. --- Averaging method (Differential equations) --- Numerical solutions. --- Method of averaging (Differential equations) --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Numerical analysis --- Numerical solutions --- Differential equations, partial. --- Global analysis (Mathematics). --- Dynamical Systems and Ergodic Theory. --- Partial Differential Equations. --- Theoretical, Mathematical and Computational Physics. --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Partial differential equations --- Dynamics. --- Ergodic theory. --- Partial differential equations. --- Mathematical physics. --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Mathematical analysis --- Physical mathematics --- Physics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics