we want to see if there is income convergence when trade liberalization takes place. we use two measures. . The fi rst is the standard deviation of the natural logarithm of real per worker income y.If for a group of countries this standard deviation decreases, it means that their per worker incomes converge. so we get one equation:

σ=βο+β1 *Dr+β2*t+ β3*t*Dr+u where Dr is a dummy equal to 1 for all t after trade liberalization and t is year.

the second measure we use is Δz. specifically, let y/ be the average log per worker income. then country's i distance to the average is z(i)=y(i)-y/. so let Δz=z(i,t+1)-z(i,t). so we estimate

Δz=βο+β1*z(i,t)+β2*z(i,t)*Dr+u

however the exercise says that Equations 1 and 2 will not be sucient to identify whether or not trade liberalisation has led to income convergence or income divergence.
You will construct control groups: countries which have not been party to a trade liberalisation. so Dj is a dummy equal to 1 if the country is a liberalizer. and we estimate the correct models which are:


σ(t)=β0+β1*Dr+β2*DJ+β3*Dr*DJ+β4*t+β5*t*Dr+β6*τ*DJ+β7*t*Dr*DJ+υ

and

Δz=βο+β1*z(i,t)+β2*z(i,t)*Dr+β3*z(i,t)*Dj+β4*z(i,t)*Dr*Dj+u

so finally my question is why the two initial equations 2 will not be sucient to identify whether or not trade liberalisation has led to income convergence or income divergence.

thank you in advance