2
$\begingroup$

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?

$\endgroup$
1
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.