ARDL long-run coefficient

Dear all,

I have a question regarding the calculation of long-run coefficient from an ARDL model.

I would like to estimated the following ARDL model and then test whether y_t and x_1t are cointegrated by means of bounds testing approach :

Δy_t = β₀ + Σ β_iΔy_t-i + Σγ_jΔx_1t-j + θ₀y_t-1 + θ₁x_1t-1 + e_t


From this equation, I know that the long-run coefficient for x₁ is -(θ₁/ θ₀).
(the bounds test say that the two variables of interest are cointegrated)


I would like to know whether this long-run coefficient is equivalent to the long-run coefficient in the corresponding long-run relationship between y_t and x_1t (the levels model):

y_t = β₀ + a₁x_1t + v_t (levels model)



When I perfomed the estimates, the two different calculations of the long-run coefficient do not give the same results. I am confused and wonder where I could have made a mistake. Or must a₁ not necessarily be equal to -(θ₁/ θ₀)?

Thank you so much for your help

Here are the Stata results:




We can see that -(-.0168967/-.9508915 ) is not equal to -.029125