<p>yes, the term that you showed for the ALDR non-stochastic steady state:</p>
<p><span class="math-container">$$\frac{ \beta_1  +  \beta_2 }{1- \rho_1 -\rho_2}$$</span></p>
<p>is long-run multiplier or sometimes also called long run equilibrium coefficient (see Verbeek 2008 Guide to Modern Econometrics 4th ed.  pp 340). As  far as I can understand there is not much difference between the two concepts in the context of ARDL model and they are used interchangeably.</p>
<p>The term non-stochastic steady state has wider application especially in macroeconomics (e.g. in growth theory), but often steady state results are just called long-run equilibrium because in most models steady state is attained only in long-run equilibrium.</p>

CC BY-SA 4.0
2020-10-20T21:16:06.653Z
2020-10-20T21:28:39.350Z
2020-10-20T21:28:39.350Z
1muflon1
<p>I am a little bit confused on the definition of long run equilibrium coefficient. Suppose I have an ARDL model as:</p>
<p><span class="math-container">$y_t = \rho_1 y_{t-1} + \rho_2 y_{t-2} + \beta_1x_{t-1} + \beta_2x_{t-2} $</span></p>
<p>The steady state non stochastic solution is:</p>
<p><span class="math-container">$y=\frac{ \beta_1  +  \beta_2 }{1- \rho_1 -\rho_2}x$</span></p>
<p>What is the definition of long run equilibrium coefficient for <span class="math-container">$x$</span> here? Is it defined as the coefficient of the steady state non stochastic solution <span class="math-container">$\frac{ \beta_1  +  \beta_2 }{1- \rho_1 -\rho_2}$</span>? What is the difference between the two concepts?</p>

<econometrics><time-series><steady-state><long-run>
Difference between long run coefficient and non stochastic steady state coefficient ARDL model
Giorgetto
# Difference between long run coefficient and non stochastic steady state coefficient ARDL model

(Asked by: username_0 on 2020-10-20)

I am a little bit confused on the definition of long run equilibrium coefficient. Suppose I have an ARDL model as:

$y\_t = \rho\_1 y\_{t-1} + \rho\_2 y\_{t-2} + \beta\_1x\_{t-1} + \beta\_2x\_{t-2} $

The steady state non stochastic solution is:

$y=\frac{ \beta\_1 + \beta\_2 }{1- \rho\_1 -\rho\_2}x$

What is the definition of long run equilibrium coefficient for $x$ here? Is it defined as the coefficient of the steady state non stochastic solution $\frac{ \beta\_1 + \beta\_2 }{1- \rho\_1 -\rho\_2}$? What is the difference between the two concepts?

**Tags:** econometrics, time-series, steady-state, long-run

---

## 1 answers

### Answer by username_1 on 2020-10-20. Score: 1 | Accepted answer

yes, the term that you showed for the ALDR non-stochastic steady state:

$$\frac{ \beta\_1 + \beta\_2 }{1- \rho\_1 -\rho\_2}$$

is long-run multiplier or sometimes also called long run equilibrium coefficient (see Verbeek 2008 Guide to Modern Econometrics 4th ed. pp 340). As far as I can understand there is not much difference between the two concepts in the context of ARDL model and they are used interchangeably.

The term non-stochastic steady state has wider application especially in macroeconomics (e.g. in growth theory), but often steady state results are just called long-run equilibrium because in most models steady state is attained only in long-run equilibrium.


---

