# Total factor productivity instead or labour-augmenting technology

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.

Both specifications are fine. Note that due to the multiplicativity of Cobb-Douglas functions, there is no real difference between TFP and labor-augmenting technology. The true difference you are considering is imposing a unit root vs. having a stationary process.
Having an autocorrelation of 0.98 is no reason to worry and is quite common in the literature. Near unit root behavior would be upward of 0.99.