Question regarding Carlstrom and Feurst (1997)

Question

I am reading through Carlstrom and Feurst's 1997 paper Agency Costs, Net Worth, and Business Fluctuations: A Computable General Equilibrium Analysis and had a question, although it could apply to other papers as well. In the paper the authors derive 9 equations that uniquely derive an equilibrium in their model. Then in the next section they run empirical tests by starting at a steady state and then hitting the system with productivity and wage shocks to see the dynamics.

What I am confused about:

The equations that uniquely describe the solution already have shocks in them, so I am a little confused about what the steady state in the empirics section is. Here is the best answers I could come up with: They taking out the shocks, deriving the steady state, and then seeing how the shocks will move the system away from the steady state and then back over time. If anyone could confirm or deny this answer that would be great. This is a problem I have come across before when reading these papers with general equilibrium models with shocks.

Answer 1

What you address (and what is done in your referred paper) is called

Model Calibration

Many economic models use this method to determine one or more parameters:

Calibration is a strategy for finding numerical values for the parameters of artificial economic worlds.

As the widespread use of this technique, let me explain it with a universal example and order your statements to the correct steps here:

The Model

In the paper the authors derive 9 equations that uniquely derive an equilibrium in their model.

Let us construct a simple model to explain some dependent variable $y$. The only independent variable to explain $y$ is $x$. The only restriction in our model is, that $\frac{dy}{dx}=1$ must hold for any observation.

The steady state

Without any further requirements, it is simple to derive the whole model: $$y=x + \mathbf{t}$$ What can be seen, is the appearance of an unknown variable t. As our model contained a differential equation, such additional variables occur. How to deal with them?

Calibration

Then in the next section they run empirical tests by starting at a steady state and then hitting the system with productivity and wage shocks to see the dynamics.

Make use of your economic model and calibrate t to your data. Thats exactly what the authors do in order to see the dynamics. Lets assume you have the following three observations:

|    y    |    x    |
---------------------
|    3    |    1    |
|    4    |    2    |
|    5    |    3    |

Calibration finds an optimized solution for our yet unknown parameter t. For the three observations above, t would have a value of $2$. Now, you have your full model given with the formula: $$y=x+2$$

Further information

I recommend to read this paper, which discusses the use of calibration techniques in economic models. The authors discuss concrete various macroeconomic models on their critical use of calibration and offer more details and best practices on this technique.