# Decentralized RBC Model

#### Background

This tool simulates the basic centralized RBC model.: \begin{align} C^{-\sigma}_t & = \beta E_t \left[ C_{t+1}^{-\sigma}\left(\alpha A_{t+1} K_{t+1}^{\alpha - 1}L_{t+1}^{1 - \alpha} + 1 - \delta\right)\right], \label{euler}\tag{1}\\ \phi (1 - L_t )^{-\eta} & = (1-\alpha)C_t^{-\sigma}A_t K_t^{\alpha}L_t^{-\alpha}, \label{labor}\tag{2}\\ Y_t & = A_t K^{\alpha}_t L^{1-\alpha}_t, \label{production}\tag{3}\\ Y_t & = C_t + I_t, \label{clearing}\tag{4}\\ I_t & = K_{t+1} - (1-\delta)K_t, \label{capital}\tag{5}\\ \log A_{t+1} & = \rho \log A_{t} + \epsilon_{t+1}, \label{tfp}\tag{6}\\ \end{align} where $$\epsilon_{t+1}\sim\mathcal{N}(0,\sigma_{\epsilon}^2)$$

#### Instructions

Choose the values the parameters. Then choose the number of periods for the simulation and select which type of simulation that you wish to perform:

1. Stochastic simulation: a new random value for the white noise process $$\epsilon_t$$ will be drawn for each period.
2. Impulse response: $$\epsilon_t$$ will be set to $$\sigma_{\epsilon}$$ in period 1 and to 0 in all subsequent periods.
Use the dropdown menu in the upper-right corner of each plot to download the simulated data in csv format.

Simulation Settings

Parameters