The Stochastic Growth Model

von Koen Vermeylen
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34 pages
This textbook provides a detailed summary of the key elements of The Stochastic Growth Model.
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The stochastic growth model, which is a version of the neoclassical growth model with microfoundations, provides the basis for many macroeconomic models which are used in contemporary macroeconomic research. This article, available for free download, is intended for readers with advanced knowledge of macroeconomics and related equations.

In his discussion, the author outlines a popular method of solving the stochastic growth model, in which it is linearized around a steady state and solved using undetermined coefficients. This analytical approach and solution was originally presented by John Y. Campbell in 1994.

The article provides detailed explanations throughout, subdividing the proof into several sections, including the steady state, linearization around the balanced growth path, and impulse response functions. Detailed figures and appendices are included.

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  1. Introduction
  2. The stochastic growth model
  3. The steady state
  4. Linearization around the balanced growth path
  5. Solution of the linearized model
  6. Impulse response functions
  7. Conclusions
  8. Appendix A
    1. A1. The maximization problem of the representative fi rm
    2. A2. The maximization problem of the representative household
  9. Appendix B
  10. Appendix C
    1. C1. The linearized production function
    2. C2. The linearized law of motion of the capital stock
    3. C3. The linearized fi rst-order condotion for the fi rm’s labor demand
    4. C4. The linearized fi rst-order condotion for the fi rm’s capital demand
    5. C5. The linearized Euler equation of the representative household
    6. C6. The linearized equillibrium condition in the goods market
  11. References