About the De-trending of Two-Sector Model

[Butree]

Hi,
I'm building up a model in which there are two types of intermediate firms with different productivity growth trends. If the average growth rate of type A firm is higher than that of type-B firm (with other features reserved in, say, a standard RBC model), and the the final good is a CES composite of the two goods produced by each type of firm, is it possible to define a balanced-growth path and de-trend the model economy in this case?
Thanks in advance for your help!

[jpfeifer]

I guess that depends on the exact model setup. What would happen in your model if productivity in sector A stays constant and the other one goes to infinity? Would you still get an interior solution? My guess is that your model will not imply a BGP. Maybe there is a generalized BGP, but you will definitely need special assumptions.

[Butree]

I guess that depends on the exact model setup. What would happen in your model if productivity in sector A stays constant and the other one goes to infinity? Would you still get an interior solution? My guess is that your model will not imply a BGP. Maybe there is a generalized BGP, but you will definitely need special assumptions.

Hi, Johannes,
thanks for your answer. Seems like I need to modify my model, and another question: what's the difference between my question and the two-sector model setup (say, a model with both consumption goods and investment goods, in each different types of goods is produced using different technologies, like the Basu, Fernald, and Liu paper)? In some of these models the average technology rates of different types of goods can be different.
Thanks again for you generous help!

[jpfeifer]

In those papers, the production structure is special. Investment goods are used to produce the consumption goods, which rely on capital in a Cobb-Douglas production function. Due to using Cobb-Douglas, you can write the composite technology growth as being labor-augmenting. This still results in a balanced growth path. Things typically work very differently if there is a non-unit elasticity of substitution (CES instead of CD)