<p>The term &quot;<strong>steady state</strong>&quot; is often somewhat ambiguous but always refers to a situation of no change over time. Specifically, it refers to a situation where a dynamic system does not change anymore, i.e., a fixed point. As such it is rather broad and has applications outside of economics. As Mark Leeds pointed out in his comment to Victor Ajevsky, that definition also applies to time series econometrics where, e.g., the Kalman filter will settle to a fixed point where the associated matrices do not change anymore.</p>
<p>In dynamic macroeconomics, people often distinguish two different types of steady states (often without explicitly stating which one they use):</p>
<ol>
<li>A <strong>non-stochastic or determininistic steady state</strong> is the fixed point where the model will settle asymptotically in the total absence of shocks. That is the concept used for models solved with perturbation techniques where a Taylor approximation about the steady state is conducted.</li>
<li>A <strong>stochastic steady state</strong> is the fixed point where the model will settle asymptotically if no shocks happen but agents still take into account that shocks may arise. It is also called the <a href="https://doi.org/10.1257/aer.104.12.4231" rel="noreferrer">risky steady state</a> or the <a href="https://doi.org/10.1257/aer.104.12.4231" rel="noreferrer">ergodic mean in the absence of shocks (EMAS)</a></li>
</ol>
<p>The term &quot;<strong>equilibrium</strong>&quot; instead refers to a situation where equilibrium conditions are satisified, regardless of whether there are still changes over time in dynamic systems. In an economic context, equilibrium usually requires some kind of market clearing, optimal behavior of economic agents (<span class="math-container">$\approx$</span> consumers maximize utility and firms maximize profits), and consistency of expectations (e.g. a rational expectations equilibrium). There are various equilibrium concepts, but they always impose more (economic) restrictions than a steady state.</p>
<p>To add to the confusion, there are also <strong>steady-state equilibria</strong>, and people sometimes simply refer to them as either steady states or equilibria. What is meant is an equilibrium of the economic model where dynamic variables do not change. Such steady-state equilibria most often arise in the context of heterogenous agent models without aggregate shocks. In those models, the markets will clear, and the relevant distributions, like the wealth distribution governing factor prices, will be a time-invariant distribution. This fixed point is, therefore, both a steady state and an equilibrium.</p>

CC BY-SA 4.0
2024-12-17T14:50:52.750Z
2024-12-17T14:50:52.750Z
jpfeifer
<ol>
<li>The &quot;steady state&quot; is a state of an economy where everything (any economic variable) does not change over time, i.e. a fixed point.</li>
<li>The  &quot;equilibrium&quot; is a state where demand is equal to supply, so that it may change over time, as such being dynamical; for example, in the case of the budget constraint with lag variables such as the interest rates, capital, assets etc. Thus, we have additional equations called clearing conditions.</li>
</ol>

CC BY-SA 4.0
2024-12-17T12:34:41.673Z
I'm not really well versed in economics but, in statistics, a kalman filter update can also reach what is called a "steady state" in its update. For example, the KF updating scheme should reach the point where the posterior variance of the update reaches a steady state. This means that the value of the posterior variance has reached a limiting value. But this concept of "steady state" does not just apply to the KF. It could also happen in an EM update where the likelihood doesn't change after a certain amount of iterations. The terminology can be relevant in any iterative updating scheme.
mark leeds
CC BY-SA 4.0
2024-12-17T12:46:04.123Z
So, my only point is, although Victor's answer was quite nice, the term "steady state" probably has a lot of meanings depending on the context.
mark leeds
CC BY-SA 4.0
2024-12-15T23:33:01.913Z
2024-12-19T19:02:19.390Z
2024-12-19T19:02:19.390Z
Victor Ajevsky
<p>I had a hard time distinguish the term &quot;equilibrium&quot; and &quot;steady state&quot;. Is there a specific rigourous <strong>mathematical</strong> definition of these 2 in economics?</p>
<p>Thank you very much for any comments/answers.</p>

CC BY-SA 4.0
2024-12-17T19:50:08.643Z
in economics jargon an equilibrium is a solution to a model (system of equations, or game etc). Perhaps, one of many. Steady state is an equilibrium in a dynamic model.
garej
<macroeconomics>
Equilibrium vs steady state
HumbleHongbo
# Equilibrium vs steady state

(Asked by: username_0 on 2024-12-15)

I had a hard time distinguish the term "equilibrium" and "steady state". Is there a specific rigourous **mathematical** definition of these 2 in economics?

Thank you very much for any comments/answers.

**Tags:** macroeconomics

> **Comments:**
> **username_1**: in economics jargon an equilibrium is a solution to a model (system of equations, or game etc). Perhaps, one of many. Steady state is an equilibrium in a dynamic model.  

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## 2 answers

### Answer by username_2 on 2024-12-17. Score: 5

The term "**steady state**" is often somewhat ambiguous but always refers to a situation of no change over time. Specifically, it refers to a situation where a dynamic system does not change anymore, i.e., a fixed point. As such it is rather broad and has applications outside of economics. As Mark Leeds pointed out in his comment to username_3, that definition also applies to time series econometrics where, e.g., the Kalman filter will settle to a fixed point where the associated matrices do not change anymore.

In dynamic macroeconomics, people often distinguish two different types of steady states (often without explicitly stating which one they use):

1. A **non-stochastic or determininistic steady state** is the fixed point where the model will settle asymptotically in the total absence of shocks. That is the concept used for models solved with perturbation techniques where a Taylor approximation about the steady state is conducted.
2. A **stochastic steady state** is the fixed point where the model will settle asymptotically if no shocks happen but agents still take into account that shocks may arise. It is also called the [risky steady state](https://doi.org/10.1257/aer.104.12.4231) or the [ergodic mean in the absence of shocks (EMAS)](https://doi.org/10.1257/aer.104.12.4231)

The term "**equilibrium**" instead refers to a situation where equilibrium conditions are satisified, regardless of whether there are still changes over time in dynamic systems. In an economic context, equilibrium usually requires some kind of market clearing, optimal behavior of economic agents ($\approx$ consumers maximize utility and firms maximize profits), and consistency of expectations (e.g. a rational expectations equilibrium). There are various equilibrium concepts, but they always impose more (economic) restrictions than a steady state.

To add to the confusion, there are also **steady-state equilibria**, and people sometimes simply refer to them as either steady states or equilibria. What is meant is an equilibrium of the economic model where dynamic variables do not change. Such steady-state equilibria most often arise in the context of heterogenous agent models without aggregate shocks. In those models, the markets will clear, and the relevant distributions, like the wealth distribution governing factor prices, will be a time-invariant distribution. This fixed point is, therefore, both a steady state and an equilibrium.


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### Answer by username_3 on 2024-12-15. Score: 0

1. The "steady state" is a state of an economy where everything (any economic variable) does not change over time, i.e. a fixed point.
2. The "equilibrium" is a state where demand is equal to supply, so that it may change over time, as such being dynamical; for example, in the case of the budget constraint with lag variables such as the interest rates, capital, assets etc. Thus, we have additional equations called clearing conditions.

> **Comments:**
> **username_4**: I'm not really well versed in economics but, in statistics, a kalman filter update can also reach what is called a "steady state" in its update. For example, the KF updating scheme should reach the point where the posterior variance of the update reaches a steady state. This means that the value of the posterior variance has reached a limiting value. But this concept of "steady state" does not just apply to the KF. It could also happen in an EM update where the likelihood doesn't change after a certain amount of iterations. The terminology can be relevant in any iterative updating scheme.  
> **username_4**: So, my only point is, although Victor's answer was quite nice, the term "steady state" probably has a lot of meanings depending on the context.  

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