Dear Johannes,
My current model uses total factor productivity instead of labour-augmenting technology, I specify total factor productivity A follows an autogregressive form instead of technology growth rate ln(A/A(-1)) follows an autoregressive form. I set prior mean of autoregressive parameter rho to 0.75, I find posterior estimate of autoregressive parameter rho of total factor productivity is about 0.98, very close to 1 (unit root), is this an indication that I should specify technology growth rate ln(A/A(-1)) follow an autoregressive process instead of total factor productivity A follows an autoregressive process?
Assume A is total factor productivity in my model or labour-augmenting technology in alternative model. epsA is technology innovation. rho is autoregressive parameter. Y is production, K is capital, L is labour. alpha is capital share parameter.
My current model: production function: Y=A*(K^alpha)*(L^(1-alpha))
assume Abar is steady state of A.
Technology shock process: A=(1-rho)Abar+rhoA(-1)+epsA
Alternative model: Y=(K^alpha)((AL)^(1-alpha))
assume technology growth rate ga=ln(A/A(-1))
assume gabar is steady state of ga.
technology growth rate ga process: ga=(1-rho)gabar+rhoga+epsA
Which specification do you think is more appropriate? or does it depends on whether i can get an autoregressive parameter of technology that is Less close to 1(unit root)?
Thank you for looking at the long post.