The Stochastic Growth Model

This textbook provides a detailed summary of the key elements of The Stochastic Growth Model.

This article presents the stochastic growth model. The stochastic growth model is a stochastic version of the neoclassical growth model with microfoundations,1 and provides the backbone of a lot of macroeconomic models that are used in modern macroeconomic research. The most popular way to solve the stochastic growth model, is to linearize the model around a steady state,2 and to solve the linearized model with the method of undetermined coefficients. This solution method is due to Campbell (1994).

The set-up of the stochastic growth model is given in the next section. Section 3 solves for the steady state, around which the model is linearized in section 4. The linearized model is then solved in section 5. Section 6 shows how the economy responds to stochastic shocks. Some concluding remarks are given in section 7.

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

Appendix A
A1. The maximization problem of the representative fi rm
A2. The maximization problem of the representative household

Appendix B

Appendix C
C1. The linearized production function
C2. The linearized law of motion of the capital stock
C3. The linearized fi rst-order condotion for the fi rm’s labor demand
C4. The linearized fi rst-order condotion for the fi rm’s capital demand
C5. The linearized Euler equation of the representative household
C6. The linearized equillibrium condition in the goods market

References