Question

1. Explain DSGE Model with equation:

Answer 1

Dynamic Stochastic General Equilibrium (DSGE) model

The main characteristics of the model are:

(1) A DSGE model can help us to find a unique and complete equilibrium for a particular economy support by its structure and parameter foundation.

(2) It can help us to distinguish intra-temporal and inter-temporal effect, e.g. decision between work hours and consumption, the path of consumption.

(3) Mostly and ideally they should be micro founded.

(4) Make structural forecasting.

(5) Assessing ex-ante and ex-post policy and compare with empirical data.

(6) Understand economic process and causality between fundamentals.

Linear differential equations are useful to compute the DSGE models. Since most of the relationships are representations of rational expectation equations. This technique help us to compute them. It helps us to determine relations and correlations between variables. The computed solutions also allow observing the transmission mechanism of different shocks in the economy.

As R. Fermer (1999) describes, let us suppose a model structure generated by the following equations

where represent the so called belief of agents on and is an auto-regressive process with called random shocks following an iid process with .

Given and its steady state is , obtain the dynamics of the variable (should be an Euler equation).

One solution is taking a Taylor expansion from the differential equation (1), so we can represent it around a steady state:

Let it be ,

where

so that

Remember that a Taylor expansion(T.A.) is :

T.A. implies work with cycle component of the variables. Computing the equation (1) around a T.A.. we have:

--- Simple differential equation

The result show that the path of is explained by a rate "b" and future values of