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Growth Theory with Mathematica: Some Examples

Thomas M. Steger, ETH Zurich, July 2006

This page provides a collection Mathematica notebooks demonstrating how Mathematica can be used to investigate (continuous-time) growth models. The analysis typically comprises three steps: (1) determination of the steady state; (2) local stability analysis; (3) and simulation of the transition process.

The procedure which is employed throughout is backward integration as suggested by Brunner and Strulik (JEDC, 2002). This method is fairly simple and well suited for a large number of growth models. For more complicated models (especially higher-dimensional models), the relaxation procedure is recommended (Trimborn, Koch, Steger, 2006).

Why should growth economists care about (global) transitional dynamics? Here are two good reasons:

(1) The positive implications of growth models might differ drastically depending on whether an economy converges towards its BGP or grows along the BGP. This perspective is nicely summarized by the following statement due to Jonathan Temple (J. Econ. Surveys, 2003, p. 509): Ultimately, all that a long-run equilibrium of a model denotes is its final resting point, perhaps very distant in the future. We know very little about this destination, and should be paying more attention to the journey.

(2) Dynamic macroeconomic models are often employed to conduct comparative welfare investigations of different policy regimes or instruments. In this context, the transition process needs to be taken into account. Moreover, linearizing the dynamic system might be appropriate in many cases but can be potentially misleading especially when the analysis aims at a Pareto-ranking of different policy instruments.

1. The Ramsey model (nb; pdf)
1. Preliminaries: model, first-order conditions, and dynamic system
2. Simulation of adjustment process
3. Some empirical implications

2. The Ramsey model with subsistence consumption (nb; pdf)
1. Preliminaries: model, first-order conditions, and dynamic system
2. Simulation of adjustment process
3. Economic intuition for hump-shaped growth pattern

3. Redistribution in a dynamic perspective (nb; pdf)
1. Preliminaries: model, first-order conditions, and dynamic system
2. Simulation of the transition process
3. Complete time paths
4. Are workers really better off?
5. Appendix: The time path of the saving rate

4. The Grossman-Helpman (1991) model (nb; pdf)
1. Preliminaries: informal discussion and dynamic system
2. Stationary solution and stability
3. Simulation of adjustment process

5. A human-capital-based growth model (nb; pdf)
1. Preliminaries: model, first-order conditions, and dynamic system
2. The dynamic system in stationary variables
3. Simulation of transitional dynamics
4. Summary: growth cycles and indeterminacy

6. The Krugman (1991) model: Multiple Equilibria - History versus Expectations (nb; pdf)
1. Preliminaries: introduction and simple static model with multiple equilibria
2. A simple dynamic model with multiple equilibria
3. Cyclical adjustments
4. Monotonic adjustments
5. Summary: economic intuition

Some useful links

Economic Growth Resources (by J. Temple)

Penn World Data

World Development Reports (World Bank)

 

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